************** MAGMA ***************** Host 000-232-076.area1.spcsdns.net. (68.27.135.6) Time: Wed Dec 24 01:01:43 2003 Input: 2+2; Output: Magma V2.10-6 Wed Dec 24 2003 01:01:40 on modular [Seed = 2775822622] ------------------------------------- 4 Total time: 2.939 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.32.42.proxycache.rima-tde.net. (80.58.32.42) Time: Wed Dec 24 05:24:04 2003 Input: a:=5; a+3; Output: Magma V2.10-6 Wed Dec 24 2003 05:24:00 on modular [Seed = 2504246258] ------------------------------------- 8 Total time: 3.379 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.32.42.proxycache.rima-tde.net. (80.58.32.42) Time: Wed Dec 24 05:24:19 2003 Input: a:=5; a+3; a+2; Output: Magma V2.10-6 Wed Dec 24 2003 05:24:15 on modular [Seed = 4214074771] ------------------------------------- 8 7 Total time: 3.239 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.32.42.proxycache.rima-tde.net. (80.58.32.42) Time: Wed Dec 24 05:24:33 2003 Input: a:=5; #a+3; a+2; Output: Magma V2.10-6 Wed Dec 24 2003 05:24:30 on modular [Seed = 553023064] ------------------------------------- >> #a+3; ^ Runtime error in '#': Bad argument types Argument types given: RngIntElt 7 Total time: 2.869 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.32.42.proxycache.rima-tde.net. (80.58.32.42) Time: Wed Dec 24 05:24:48 2003 Input: a:=5; /#a+3;#/ a+2; Output: Magma V2.10-6 Wed Dec 24 2003 05:24:45 on modular [Seed = 199056704] ------------------------------------- >> /#a+3;#/ ^ User error: bad syntax 7 Total time: 3.029 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.32.42.proxycache.rima-tde.net. (80.58.32.42) Time: Wed Dec 24 05:25:01 2003 Input: a:=5; /*a+3;*/ a+2; Output: Magma V2.10-6 Wed Dec 24 2003 05:24:58 on modular [Seed = 1790721078] ------------------------------------- 7 Total time: 3.039 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.32.42.proxycache.rima-tde.net. (80.58.32.42) Time: Wed Dec 24 05:25:20 2003 Input: *a:=5; *a+3; *a+2; Output: Magma V2.10-6 Wed Dec 24 2003 05:25:17 on modular [Seed = 1552550647] ------------------------------------- >> *a:=5; ^ User error: bad syntax >> *a+3; ^ User error: bad syntax >> *a+2;; ^ User error: bad syntax Total time: 3.209 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.32.42.proxycache.rima-tde.net. (80.58.32.42) Time: Wed Dec 24 05:25:32 2003 Input: (*a):=5; *a+3; *a+2; Output: Magma V2.10-6 Wed Dec 24 2003 05:25:29 on modular [Seed = 2170017598] ------------------------------------- >> (*a):=5; ^ User error: bad syntax >> *a+3; ^ User error: bad syntax >> *a+2;; ^ User error: bad syntax Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.32.42.proxycache.rima-tde.net. (80.58.32.42) Time: Wed Dec 24 05:25:50 2003 Input: (~a):=5; ~a+3; ~a+2; Output: Magma V2.10-6 Wed Dec 24 2003 05:25:47 on modular [Seed = 4146176378] ------------------------------------- >> (~a):=5; ^ User error: Illegal left hand side of an assignment statement >> ~a+3; ^ Runtime error in '+': Bad argument types Argument types given: *nothing ~, RngIntElt >> ~a+2;; ^ Runtime error in '+': Bad argument types Argument types given: *nothing ~, RngIntElt Total time: 3.159 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.32.42.proxycache.rima-tde.net. (80.58.32.42) Time: Wed Dec 24 05:30:14 2003 Input: a:=5; //a+3; a+2; Output: Magma V2.10-6 Wed Dec 24 2003 05:30:11 on modular [Seed = 516443022] ------------------------------------- 7 Total time: 3.299 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.32.42.proxycache.rima-tde.net. (80.58.32.42) Time: Wed Dec 24 05:58:34 2003 Input: /* Klein quartic */ MAX:=6; c:=5; g:=3; semi:=[0,3]; /* basic del semigrup */ i_cond:=c-g; pertany:=func; gaps:=[i:i in [1..c-1]|not pertany(i)]; lambda:=func; lambdainv:=func; /* oplus, leq, nu */ oplus:=func; inferior:=func; ominus:=func; N:=func; nu:=func; /* order bound */ dORD:=func; Lconjunts:=[[0]]; Lmcinf:=[[0]]; Linterseccioinf:=[1]; Lunioinf:=[1]; index:=function(llista) i:=0; for j in llista do i:=i+2^j; end for; return(i); end function; /* mcinf:=function(Lconjunts,Lmcinf,llista) p:=Position(Lconjunts,llista); if p eq 0 then return -1; else return Lmcinf[p]; end if; end function; interseccioinf:=function(Lconjunts,Linterseccioinf,llista) p:=Position(Lconjunts,llista); if p eq 0 then return -1; else return Linterseccioinf[p]; end if; end function; unioinf:=function(Lconjunts,Lunioinf,llista) p:=Position(Lconjunts,llista); if p eq 0 then return -1; else return Lunioinf[p]; end if; end function; */ actualitzaconjunts:=function (Lconjunts,llista) return(Append(Lconjunts,llista)); end function; actualitzamcinf:=function(Lmcinf,llista) maxc:=llista[1]; if (maxc eq 0) then return (Append(Lmcinf,[0])); end if; trobat:=false; while not trobat do while not inferior(maxc,llista[1]) do maxc:=maxc-1; end while; j:=2; while j le #llista and inferior(maxc,llista[j]) do j:=j+1; end while; if j eq #llista+1 then trobat:=true; end if; maxc:=maxc-1; end while; maxc:=maxc+1; mcinfllista:=[maxc]; for h in gaps do candidat:=lambdainv(lambda(maxc)-h); if candidat gt 0 then j:=1; while j le #llista and inferior(candidat,llista[j]) do j:=j+1; end while; if j eq #llista+1 then mcinfllista:=Append(mcinfllista,candidat); end if; end if; end for; return(Append(Lmcinf,mcinfllista)); end function; actualitzainterseccioinf:=function(Lconjunts,Lmcinf,Linterseccioinf,Lunioinf,llista) if #llista eq 1 then return Append(Linterseccioinf,nu(llista[1])); else return Append(Linterseccioinf,unioinf(Lconjunts,Lunioinf,mcinf(Lconjunts,Lmcinf,llista))); end if; end function; actualitzaunioinf:=function(Lconjunts,Linterseccioinf,Lunioinf,llista) if #llista eq 1 then return Append(Lunioinf,nu(llista[1])); else return Append(Lunioinf,unioinf(Lconjunts,Lunioinf,[llista[i]:i in [1..(#llista-1)]])+nu(llista[#llista])-interseccioinf(Lconjunts,Linterseccioinf,llista)); end if; end function; for i in [1..MAX] do conjuntsaux:=Lconjunts; llista:=[i]; Lconjunts:=actualitzaconjunts(Lconjunts,llista); Lmcinf:=actualitzamcinf(Lmcinf,llista); Linterseccioinf:=actualitzainterseccioinf(Lconjunts,Lmcinf,Linterseccioinf,Lunioinf,llista); Lunioinf:=actualitzaunioinf(Lconjunts,Linterseccioinf,Lunioinf,llista); for conj in conjuntsaux do llista:=Append(conj,i); Lconjunts:=actualitzaconjunts(Lconjunts,llista); Lmcinf:=actualitzamcinf(Lmcinf,llista); Linterseccioinf:=actualitzainterseccioinf(Lconjunts,Lmcinf,Linterseccioinf,Lunioinf,llista); Lunioinf:=actualitzaunioinf(Lconjunts,Linterseccioinf,Lunioinf,llista); end for; end for; joinsets:=function(llista) unio:={}; for conj in llista do unio:=unio join conj; end for; return unio; end function; l:=#Lconjunts; print "CONJUNTS="; ; print "MCINF="; ; print "INTERSECCIOINF="; Linterseccioinf; print "UNIOINF="; Lunioinf; unioasac:=[#joinsets({N(i):i in llista}):llista in Lconjunts]; errors:=[Lunioinf[i]-unioasac[i]:i in [1..#unioasac]]; printf "VEREDICTE:="; [Lconjunts[i]:i in [1..#errors]|errors[i] ne 0]; Output: Magma V2.10-6 Wed Dec 24 2003 05:58:30 on modular [Seed = 2058105909] ------------------------------------- >> Append(Linterseccioinf,unioinf(Lconjunts,Lunioinf,mcinf(Lconjunts,Lmcinf, ^ User error: Identifier 'mcinf' has not been declared or assigned >> return Append(Lunioinf,unioinf(Lconjunts,Lunioinf,[llista[i]:i in [1..( ^ User error: Identifier 'unioinf' has not been declared or assigned >> Linterseccioinf:=actualitzainterseccioinf(Lconjunts,Lmcinf,Linterseccioinf, ^ User error: Identifier 'actualitzainterseccioinf' has not been declared or assigned CONJUNTS= <[ 0 ]> MCINF= <[ 0 ]> INTERSECCIOINF= [ 1 ] UNIOINF= [ 1 ] VEREDICTE:=[] Total time: 3.859 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.32.42.proxycache.rima-tde.net. (80.58.32.42) Time: Wed Dec 24 06:10:48 2003 Input: /* Klein quartic */ MAX:=6; c:=5; g:=3; semi:=[0,3]; /* basic del semigrup */ i_cond:=c-g; pertany:=func; gaps:=[i:i in [1..c-1]|not pertany(i)]; lambda:=func; lambdainv:=func; /* oplus, leq, nu */ oplus:=func; inferior:=func; ominus:=func; N:=func; nu:=func; /* order bound */ dORD:=func; Lconjunts:=[[0]]; Lmcinf:=[[0]]; Linterseccioinf:=[1]; Lunioinf:=[1]; index:=function(llista) i:=0; for j in llista do i:=i+2^j; end for; return(i); end function; /* mcinf:=function(Lconjunts,Lmcinf,llista) p:=Position(Lconjunts,llista); if p eq 0 then return -1; else return Lmcinf[p]; end if; end function; interseccioinf:=function(Lconjunts,Linterseccioinf,llista) p:=Position(Lconjunts,llista); if p eq 0 then return -1; else return Linterseccioinf[p]; end if; end function; unioinf:=function(Lconjunts,Lunioinf,llista) p:=Position(Lconjunts,llista); if p eq 0 then return -1; else return Lunioinf[p]; end if; end function; */ actualitzaconjunts:=function (Lconjunts,llista) return(Append(Lconjunts,llista)); end function; actualitzamcinf:=function(Lmcinf,llista) maxc:=llista[1]; if (maxc eq 0) then return (Append(Lmcinf,[0])); end if; trobat:=false; while not trobat do while not inferior(maxc,llista[1]) do maxc:=maxc-1; end while; j:=2; while j le #llista and inferior(maxc,llista[j]) do j:=j+1; end while; if j eq #llista+1 then trobat:=true; end if; maxc:=maxc-1; end while; maxc:=maxc+1; mcinfllista:=[maxc]; for h in gaps do candidat:=lambdainv(lambda(maxc)-h); if candidat gt 0 then j:=1; while j le #llista and inferior(candidat,llista[j]) do j:=j+1; end while; if j eq #llista+1 then mcinfllista:=Append(mcinfllista,candidat); end if; end if; end for; return(Append(Lmcinf,mcinfllista)); end function; actualitzainterseccioinf:=function(Lconjunts,Lmcinf,Linterseccioinf,Lunioinf,llista) if #llista eq 1 then return Append(Linterseccioinf,nu(llista[1])); else return Append(Linterseccioinf,unioinf(Lconjunts,Lunioinf,mcinf(Lconjunts,Lmcinf,llista))); end if; end function; actualitzaunioinf:=function(Lconjunts,Linterseccioinf,Lunioinf,llista) if #llista eq 1 then return Append(Lunioinf,nu(llista[1])); else return Append(Lunioinf,unioinf(Lconjunts,Lunioinf,[llista[i]:i in [1..(#llista-1)]])+nu(llista[#llista])-interseccioinf(Lconjunts,Linterseccioinf,llista)); end if; end function; for i in [1..MAX] do conjuntsaux:=Lconjunts; llista:=[i]; Lconjunts:=actualitzaconjunts(Lconjunts,llista); Lmcinf:=actualitzamcinf(Lmcinf,llista); Linterseccioinf:=actualitzainterseccioinf(Lconjunts,Lmcinf,Linterseccioinf,Lunioinf,llista); Lunioinf:=actualitzaunioinf(Lconjunts,Linterseccioinf,Lunioinf,llista); for conj in conjuntsaux do llista:=Append(conj,i); Lconjunts:=actualitzaconjunts(Lconjunts,llista); Lmcinf:=actualitzamcinf(Lmcinf,llista); Linterseccioinf:=actualitzainterseccioinf(Lconjunts,Lmcinf,Linterseccioinf,Lunioinf,llista); Lunioinf:=actualitzaunioinf(Lconjunts,Linterseccioinf,Lunioinf,llista); end for; end for; joinsets:=function(llista) unio:={}; for conj in llista do unio:=unio join conj; end for; return unio; end function; l:=#Lconjunts; print "CONJUNTS="; ; print "MCINF="; ; print "INTERSECCIOINF="; Linterseccioinf; print "UNIOINF="; Lunioinf; unioasac:=[#joinsets({N(i):i in llista}):llista in Lconjunts]; errors:=[Lunioinf[i]-unioasac[i]:i in [1..#unioasac]]; printf "VEREDICTE:="; [Lconjunts[i]:i in [1..#errors]|errors[i] ne 0]; Output: Magma V2.10-6 Wed Dec 24 2003 06:10:45 on modular [Seed = 3177969308] ------------------------------------- >> Append(Linterseccioinf,unioinf(Lconjunts,Lunioinf,mcinf(Lconjunts,Lmcinf, ^ User error: Identifier 'mcinf' has not been declared or assigned >> return Append(Lunioinf,unioinf(Lconjunts,Lunioinf,[llista[i]:i in [1..( ^ User error: Identifier 'unioinf' has not been declared or assigned >> Linterseccioinf:=actualitzainterseccioinf(Lconjunts,Lmcinf,Linterseccioinf, ^ User error: Identifier 'actualitzainterseccioinf' has not been declared or assigned CONJUNTS= <[ 0 ]> MCINF= <[ 0 ]> INTERSECCIOINF= [ 1 ] UNIOINF= [ 1 ] VEREDICTE:=[] Total time: 3.119 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.32.42.proxycache.rima-tde.net. (80.58.32.42) Time: Wed Dec 24 06:11:07 2003 Input: /* Klein quartic */ MAX:=6; c:=5; g:=3; semi:=[0,3]; /* basic del semigrup */ i_cond:=c-g; pertany:=func; gaps:=[i:i in [1..c-1]|not pertany(i)]; lambda:=func; lambdainv:=func; /* oplus, leq, nu */ oplus:=func; inferior:=func; ominus:=func; N:=func; nu:=func; /* order bound */ dORD:=func; Lconjunts:=[[0]]; Lmcinf:=[[0]]; Linterseccioinf:=[1]; Lunioinf:=[1]; index:=function(llista) i:=0; for j in llista do i:=i+2^j; end for; return(i); end function; /* mcinf:=function(Lconjunts,Lmcinf,llista) p:=Position(Lconjunts,llista); if p eq 0 then return -1; else return Lmcinf[p]; end if; end function; interseccioinf:=function(Lconjunts,Linterseccioinf,llista) p:=Position(Lconjunts,llista); if p eq 0 then return -1; else return Linterseccioinf[p]; end if; end function; unioinf:=function(Lconjunts,Lunioinf,llista) p:=Position(Lconjunts,llista); if p eq 0 then return -1; else return Lunioinf[p]; end if; end function; */ actualitzaconjunts:=function (Lconjunts,llista) return(Append(Lconjunts,llista)); end function; actualitzamcinf:=function(Lmcinf,llista) maxc:=llista[1]; if (maxc eq 0) then return (Append(Lmcinf,[0])); end if; trobat:=false; while not trobat do while not inferior(maxc,llista[1]) do maxc:=maxc-1; end while; j:=2; while j le #llista and inferior(maxc,llista[j]) do j:=j+1; end while; if j eq #llista+1 then trobat:=true; end if; maxc:=maxc-1; end while; maxc:=maxc+1; mcinfllista:=[maxc]; for h in gaps do candidat:=lambdainv(lambda(maxc)-h); if candidat gt 0 then j:=1; while j le #llista and inferior(candidat,llista[j]) do j:=j+1; end while; if j eq #llista+1 then mcinfllista:=Append(mcinfllista,candidat); end if; end if; end for; return(Append(Lmcinf,mcinfllista)); end function; actualitzainterseccioinf:=function(Lconjunts,Lmcinf,Linterseccioinf,Lunioinf,llista) if #llista eq 1 then return Append(Linterseccioinf,nu(llista[1])); else return Append(Linterseccioinf,Lunioinf[index(Lmcinf[index(llista)])); end if; end function; actualitzaunioinf:=function(Lconjunts,Linterseccioinf,Lunioinf,llista) if #llista eq 1 then return Append(Lunioinf,nu(llista[1])); else return Append(Lunioinf, Lunioinf[index([llista[i]:i in [1..(#llista-1)]])]+nu(llista[#llista])-Linterseccioinf[index(llista)]); end if; end function; for i in [1..MAX] do conjuntsaux:=Lconjunts; llista:=[i]; Lconjunts:=actualitzaconjunts(Lconjunts,llista); Lmcinf:=actualitzamcinf(Lmcinf,llista); Linterseccioinf:=actualitzainterseccioinf(Lconjunts,Lmcinf,Linterseccioinf,Lunioinf,llista); Lunioinf:=actualitzaunioinf(Lconjunts,Linterseccioinf,Lunioinf,llista); for conj in conjuntsaux do llista:=Append(conj,i); Lconjunts:=actualitzaconjunts(Lconjunts,llista); Lmcinf:=actualitzamcinf(Lmcinf,llista); Linterseccioinf:=actualitzainterseccioinf(Lconjunts,Lmcinf,Linterseccioinf,Lunioinf,llista); Lunioinf:=actualitzaunioinf(Lconjunts,Linterseccioinf,Lunioinf,llista); end for; end for; joinsets:=function(llista) unio:={}; for conj in llista do unio:=unio join conj; end for; return unio; end function; l:=#Lconjunts; print "CONJUNTS="; ; print "MCINF="; ; print "INTERSECCIOINF="; Linterseccioinf; print "UNIOINF="; Lunioinf; unioasac:=[#joinsets({N(i):i in llista}):llista in Lconjunts]; errors:=[Lunioinf[i]-unioasac[i]:i in [1..#unioasac]]; printf "VEREDICTE:="; [Lconjunts[i]:i in [1..#errors]|errors[i] ne 0]; /*r:=2; Subsets({0..MAX},r);*/ Output: Magma V2.10-6 Wed Dec 24 2003 06:11:04 on modular [Seed = 4062493102] ------------------------------------- >> Append(Linterseccioinf,Lunioinf[index(Lmcinf[index(llista)])); ^ User error: bad syntax >> end if; ^ User error: bad syntax >> end function; ^ User error: bad syntax >> Linterseccioinf:=actualitzainterseccioinf(Lconjunts,Lmcinf,Linterseccioinf, ^ User error: Identifier 'actualitzainterseccioinf' has not been declared or assigned CONJUNTS= <[ 0 ]> MCINF= <[ 0 ]> INTERSECCIOINF= [ 1 ] UNIOINF= [ 1 ] VEREDICTE:=[] Total time: 3.089 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.32.42.proxycache.rima-tde.net. (80.58.32.42) Time: Wed Dec 24 06:12:32 2003 Input: /* Klein quartic */ MAX:=6; c:=5; g:=3; semi:=[0,3]; /* basic del semigrup */ i_cond:=c-g; pertany:=func; gaps:=[i:i in [1..c-1]|not pertany(i)]; lambda:=func; lambdainv:=func; /* oplus, leq, nu */ oplus:=func; inferior:=func; ominus:=func; N:=func; nu:=func; /* order bound */ dORD:=func; Lconjunts:=[[0]]; Lmcinf:=[[0]]; Linterseccioinf:=[1]; Lunioinf:=[1]; index:=function(llista) i:=0; for j in llista do i:=i+2^j; end for; return(i); end function; /* mcinf:=function(Lconjunts,Lmcinf,llista) p:=Position(Lconjunts,llista); if p eq 0 then return -1; else return Lmcinf[p]; end if; end function; interseccioinf:=function(Lconjunts,Linterseccioinf,llista) p:=Position(Lconjunts,llista); if p eq 0 then return -1; else return Linterseccioinf[p]; end if; end function; unioinf:=function(Lconjunts,Lunioinf,llista) p:=Position(Lconjunts,llista); if p eq 0 then return -1; else return Lunioinf[p]; end if; end function; */ actualitzaconjunts:=function (Lconjunts,llista) return(Append(Lconjunts,llista)); end function; actualitzamcinf:=function(Lmcinf,llista) maxc:=llista[1]; if (maxc eq 0) then return (Append(Lmcinf,[0])); end if; trobat:=false; while not trobat do while not inferior(maxc,llista[1]) do maxc:=maxc-1; end while; j:=2; while j le #llista and inferior(maxc,llista[j]) do j:=j+1; end while; if j eq #llista+1 then trobat:=true; end if; maxc:=maxc-1; end while; maxc:=maxc+1; mcinfllista:=[maxc]; for h in gaps do candidat:=lambdainv(lambda(maxc)-h); if candidat gt 0 then j:=1; while j le #llista and inferior(candidat,llista[j]) do j:=j+1; end while; if j eq #llista+1 then mcinfllista:=Append(mcinfllista,candidat); end if; end if; end for; return(Append(Lmcinf,mcinfllista)); end function; actualitzainterseccioinf:=function(Lconjunts,Lmcinf,Linterseccioinf,Lunioinf,llista) if #llista eq 1 then return Append(Linterseccioinf,nu(llista[1])); else return Append(Linterseccioinf,Lunioinf[index(Lmcinf[index(llista)])]); end if; end function; actualitzaunioinf:=function(Lconjunts,Linterseccioinf,Lunioinf,llista) if #llista eq 1 then return Append(Lunioinf,nu(llista[1])); else return Append(Lunioinf, Lunioinf[index([llista[i]:i in [1..(#llista-1)]])]+nu(llista[#llista])-Linterseccioinf[index(llista)]); end if; end function; for i in [1..MAX] do conjuntsaux:=Lconjunts; llista:=[i]; Lconjunts:=actualitzaconjunts(Lconjunts,llista); Lmcinf:=actualitzamcinf(Lmcinf,llista); Linterseccioinf:=actualitzainterseccioinf(Lconjunts,Lmcinf,Linterseccioinf,Lunioinf,llista); Lunioinf:=actualitzaunioinf(Lconjunts,Linterseccioinf,Lunioinf,llista); for conj in conjuntsaux do llista:=Append(conj,i); Lconjunts:=actualitzaconjunts(Lconjunts,llista); Lmcinf:=actualitzamcinf(Lmcinf,llista); Linterseccioinf:=actualitzainterseccioinf(Lconjunts,Lmcinf,Linterseccioinf,Lunioinf,llista); Lunioinf:=actualitzaunioinf(Lconjunts,Linterseccioinf,Lunioinf,llista); end for; end for; joinsets:=function(llista) unio:={}; for conj in llista do unio:=unio join conj; end for; return unio; end function; l:=#Lconjunts; print "CONJUNTS="; ; print "MCINF="; ; print "INTERSECCIOINF="; Linterseccioinf; print "UNIOINF="; Lunioinf; unioasac:=[#joinsets({N(i):i in llista}):llista in Lconjunts]; errors:=[Lunioinf[i]-unioasac[i]:i in [1..#unioasac]]; printf "VEREDICTE:="; [Lconjunts[i]:i in [1..#errors]|errors[i] ne 0]; /*r:=2; Subsets({0..MAX},r);*/ Output: Magma V2.10-6 Wed Dec 24 2003 06:12:29 on modular [Seed = 3556941658] ------------------------------------- CONJUNTS= <[ 0 ], [ 1 ], [ 0, 1 ], [ 2 ], [ 0, 2 ], [ 1, 2 ], [ 0, 1, 2 ], [ 3 ], [ 0, 3 ], [ 1, 3 ], [ 0, 1, 3 ], [ 2, 3 ], [ 0, 2, 3 ], [ 1, 2, 3 ], [ 0, 1, 2, 3 ], [ 4 ], [ 0, 4 ], [ 1, 4 ], [ 0, 1, 4 ], [ 2, 4 ], [ 0, 2, 4 ], [ 1, 2, 4 ], [ 0, 1, 2, 4 ], [ 3, 4 ], [ 0, 3, 4 ], [ 1, 3, 4 ], [ 0, 1, 3, 4 ], [ 2, 3, 4 ], [ 0, 2, 3, 4 ], [ 1, 2, 3, 4 ], [ 0, 1, 2, 3, 4 ], [ 5 ], [ 0, 5 ], [ 1, 5 ], [ 0, 1, 5 ], [ 2, 5 ], [ 0, 2, 5 ], [ 1, 2, 5 ], [ 0, 1, 2, 5 ], [ 3, 5 ], [ 0, 3, 5 ], [ 1, 3, 5 ], [ 0, 1, 3, 5 ], [ 2, 3, 5 ], [ 0, 2, 3, 5 ], [ 1, 2, 3, 5 ], [ 0, 1, 2, 3, 5 ], [ 4, 5 ], [ 0, 4, 5 ], [ 1, 4, 5 ], [ 0, 1, 4, 5 ], [ 2, 4, 5 ], [ 0, 2, 4, 5 ], [ 1, 2, 4, 5 ], [ 0, 1, 2, 4, 5 ], [ 3, 4, 5 ], [ 0, 3, 4, 5 ], [ 1, 3, 4, 5 ], [ 0, 1, 3, 4, 5 ], [ 2, 3, 4, 5 ], [ 0, 2, 3, 4, 5 ], [ 1, 2, 3, 4, 5 ], [ 0, 1, 2, 3, 4, 5 ], [ 6 ], [ 0, 6 ], [ 1, 6 ], [ 0, 1, 6 ], [ 2, 6 ], [ 0, 2, 6 ], [ 1, 2, 6 ], [ 0, 1, 2, 6 ], [ 3, 6 ], [ 0, 3, 6 ], [ 1, 3, 6 ], [ 0, 1, 3, 6 ], [ 2, 3, 6 ], [ 0, 2, 3, 6 ], [ 1, 2, 3, 6 ], [ 0, 1, 2, 3, 6 ], [ 4, 6 ], [ 0, 4, 6 ], [ 1, 4, 6 ], [ 0, 1, 4, 6 ], [ 2, 4, 6 ], [ 0, 2, 4, 6 ], [ 1, 2, 4, 6 ], [ 0, 1, 2, 4, 6 ], [ 3, 4, 6 ], [ 0, 3, 4, 6 ], [ 1, 3, 4, 6 ], [ 0, 1, 3, 4, 6 ], [ 2, 3, 4, 6 ], [ 0, 2, 3, 4, 6 ], [ 1, 2, 3, 4, 6 ], [ 0, 1, 2, 3, 4, 6 ], [ 5, 6 ], [ 0, 5, 6 ], [ 1, 5, 6 ], [ 0, 1, 5, 6 ], [ 2, 5, 6 ], [ 0, 2, 5, 6 ], [ 1, 2, 5, 6 ], [ 0, 1, 2, 5, 6 ], [ 3, 5, 6 ], [ 0, 3, 5, 6 ], [ 1, 3, 5, 6 ], [ 0, 1, 3, 5, 6 ], [ 2, 3, 5, 6 ], [ 0, 2, 3, 5, 6 ], [ 1, 2, 3, 5, 6 ], [ 0, 1, 2, 3, 5, 6 ], [ 4, 5, 6 ], [ 0, 4, 5, 6 ], [ 1, 4, 5, 6 ], [ 0, 1, 4, 5, 6 ], [ 2, 4, 5, 6 ], [ 0, 2, 4, 5, 6 ], [ 1, 2, 4, 5, 6 ], [ 0, 1, 2, 4, 5, 6 ], [ 3, 4, 5, 6 ], [ 0, 3, 4, 5, 6 ], [ 1, 3, 4, 5, 6 ], [ 0, 1, 3, 4, 5, 6 ], [ 2, 3, 4, 5, 6 ], [ 0, 2, 3, 4, 5, 6 ], [ 1, 2, 3, 4, 5, 6 ], [ 0, 1, 2, 3, 4, 5, 6 ]> MCINF= <[ 0 ], [ 1 ], [ 0 ], [ 2 ], [ 0 ], [ 0 ], [ 0 ], [ 3 ], [ 0 ], [ 1 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 4 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 5 ], [ 0 ], [ 1 ], [ 0 ], [ 2 ], [ 0 ], [ 0 ], [ 0 ], [ 1 ], [ 0 ], [ 1 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 6 ], [ 0 ], [ 1 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 3 ], [ 0 ], [ 1 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 1 ], [ 0 ], [ 1 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 1 ], [ 0 ], [ 1 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ]> INTERSECCIOINF= [ 1, 2, 1, 2, 1, 1, 1, 3, 1, 2, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 4, 1, 2, 1, 2, 1, 1, 1, 2, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 4, 1, 2, 1, 1, 1, 1, 1, 3, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 2, 1, 1, 1, 1, 1, 2, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 ] UNIOINF= [ 1, 2, 2, 2, 2, 3, 3, 3, 3, 3, 4, 4, 4, 5, 5, 2, 2, 3, 3, 3, 3, 4, 4, 4, 4, 4, 5, 5, 5, 6, 6, 4, 4, 4, 5, 4, 5, 6, 6, 5, 6, 5, 7, 7, 7, 8, 8, 5, 5, 6, 6, 6, 6, 7, 7, 7, 7, 7, 8, 8, 8, 9, 9, 4, 4, 4, 5, 5, 5, 6, 6, 4, 6, 5, 7, 7, 7, 8, 8, 5, 5, 6, 6, 6, 6, 7, 7, 7, 7, 7, 8, 8, 8, 9, 9, 6, 7, 6, 8, 7, 8, 9, 9, 7, 9, 7, 10, 10, 10, 11, 11, 8, 8, 9, 9, 9, 9, 10, 10, 10, 10, 10, 11, 11, 11, 12, 12 ] VEREDICTE:=[ [ 0, 1, 3 ], [ 1, 2, 3 ], [ 0, 1, 2, 3 ], [ 0, 1, 3, 4 ], [ 1, 2, 3, 4 ], [ 0, 1, 2, 3, 4 ], [ 0, 1, 5 ], [ 0, 2, 5 ], [ 1, 2, 5 ], [ 0, 1, 2, 5 ], [ 0, 3, 5 ], [ 0, 1, 3, 5 ], [ 2, 3, 5 ], [ 0, 2, 3, 5 ], [ 1, 2, 3, 5 ], [ 0, 1, 2, 3, 5 ], [ 1, 4, 5 ], [ 0, 1, 4, 5 ], [ 2, 4, 5 ], [ 0, 2, 4, 5 ], [ 1, 2, 4, 5 ], [ 0, 1, 2, 4, 5 ], [ 3, 4, 5 ], [ 0, 3, 4, 5 ], [ 1, 3, 4, 5 ], [ 0, 1, 3, 4, 5 ], [ 2, 3, 4, 5 ], [ 0, 2, 3, 4, 5 ], [ 1, 2, 3, 4, 5 ], [ 0, 1, 2, 3, 4, 5 ], [ 0, 1, 6 ], [ 1, 2, 6 ], [ 0, 1, 2, 6 ], [ 0, 3, 6 ], [ 1, 3, 6 ], [ 0, 1, 3, 6 ], [ 2, 3, 6 ], [ 0, 2, 3, 6 ], [ 1, 2, 3, 6 ], [ 0, 1, 2, 3, 6 ], [ 1, 4, 6 ], [ 0, 1, 4, 6 ], [ 1, 2, 4, 6 ], [ 0, 1, 2, 4, 6 ], [ 3, 4, 6 ], [ 0, 3, 4, 6 ], [ 1, 3, 4, 6 ], [ 0, 1, 3, 4, 6 ], [ 2, 3, 4, 6 ], [ 0, 2, 3, 4, 6 ], [ 1, 2, 3, 4, 6 ], [ 0, 1, 2, 3, 4, 6 ], [ 0, 5, 6 ], [ 0, 1, 5, 6 ], [ 2, 5, 6 ], [ 0, 2, 5, 6 ], [ 1, 2, 5, 6 ], [ 0, 1, 2, 5, 6 ], [ 3, 5, 6 ], [ 0, 3, 5, 6 ], [ 1, 3, 5, 6 ], [ 0, 1, 3, 5, 6 ], [ 2, 3, 5, 6 ], [ 0, 2, 3, 5, 6 ], [ 1, 2, 3, 5, 6 ], [ 0, 1, 2, 3, 5, 6 ], [ 4, 5, 6 ], [ 0, 4, 5, 6 ], [ 1, 4, 5, 6 ], [ 0, 1, 4, 5, 6 ], [ 2, 4, 5, 6 ], [ 0, 2, 4, 5, 6 ], [ 1, 2, 4, 5, 6 ], [ 0, 1, 2, 4, 5, 6 ], [ 3, 4, 5, 6 ], [ 0, 3, 4, 5, 6 ], [ 1, 3, 4, 5, 6 ], [ 0, 1, 3, 4, 5, 6 ], [ 2, 3, 4, 5, 6 ], [ 0, 2, 3, 4, 5, 6 ], [ 1, 2, 3, 4, 5, 6 ], [ 0, 1, 2, 3, 4, 5, 6 ] ] Total time: 3.299 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.32.42.proxycache.rima-tde.net. (80.58.32.42) Time: Wed Dec 24 06:13:30 2003 Input: /* Klein quartic */ MAX:=6; c:=5; g:=3; semi:=[0,3]; /* basic del semigrup */ i_cond:=c-g; pertany:=func; gaps:=[i:i in [1..c-1]|not pertany(i)]; lambda:=func; lambdainv:=func; /* oplus, leq, nu */ oplus:=func; inferior:=func; ominus:=func; N:=func; nu:=func; /* order bound */ dORD:=func; Lconjunts:=[[0]]; Lmcinf:=[[0]]; Linterseccioinf:=[1]; Lunioinf:=[1]; index:=function(llista) i:=0; for j in llista do i:=i+2^j; end for; return(i); end function; /* mcinf:=function(Lconjunts,Lmcinf,llista) p:=Position(Lconjunts,llista); if p eq 0 then return -1; else return Lmcinf[p]; end if; end function; interseccioinf:=function(Lconjunts,Linterseccioinf,llista) p:=Position(Lconjunts,llista); if p eq 0 then return -1; else return Linterseccioinf[p]; end if; end function; unioinf:=function(Lconjunts,Lunioinf,llista) p:=Position(Lconjunts,llista); if p eq 0 then return -1; else return Lunioinf[p]; end if; end function; */ actualitzaconjunts:=function (Lconjunts,llista) return(Append(Lconjunts,llista)); end function; actualitzamcinf:=function(Lmcinf,llista) maxc:=llista[1]; if (maxc eq 0) then return (Append(Lmcinf,[0])); end if; trobat:=false; while not trobat do while not inferior(maxc,llista[1]) do maxc:=maxc-1; end while; j:=2; while j le #llista and inferior(maxc,llista[j]) do j:=j+1; end while; if j eq #llista+1 then trobat:=true; end if; maxc:=maxc-1; end while; maxc:=maxc+1; mcinfllista:=[maxc]; for h in gaps do candidat:=lambdainv(lambda(maxc)-h); if candidat gt 0 then j:=1; while j le #llista and inferior(candidat,llista[j]) do j:=j+1; end while; if j eq #llista+1 then mcinfllista:=Append(mcinfllista,candidat); end if; end if; end for; return(Append(Lmcinf,mcinfllista)); end function; actualitzainterseccioinf:=function(Lconjunts,Lmcinf,Linterseccioinf,Lunioinf,llista) if #llista eq 1 then return Append(Linterseccioinf,nu(llista[1])); else return Append(Linterseccioinf,Lunioinf[index(Lmcinf[index(llista)])]); end if; end function; actualitzaunioinf:=function(Lconjunts,Linterseccioinf,Lunioinf,llista) if #llista eq 1 then return Append(Lunioinf,nu(llista[1])); else return Append(Lunioinf, Lunioinf[index([llista[i]:i in [1..(#llista-1)]])]+nu(llista[#llista])-Linterseccioinf[index(llista)]); end if; end function; for i in [1..MAX] do conjuntsaux:=Lconjunts; llista:=[i]; Lconjunts:=actualitzaconjunts(Lconjunts,llista); Lmcinf:=actualitzamcinf(Lmcinf,llista); Linterseccioinf:=actualitzainterseccioinf(Lconjunts,Lmcinf,Linterseccioinf,Lunioinf,llista); Lunioinf:=actualitzaunioinf(Lconjunts,Linterseccioinf,Lunioinf,llista); for conj in conjuntsaux do llista:=Append(conj,i); Lconjunts:=actualitzaconjunts(Lconjunts,llista); Lmcinf:=actualitzamcinf(Lmcinf,llista); Linterseccioinf:=actualitzainterseccioinf(Lconjunts,Lmcinf,Linterseccioinf,Lunioinf,llista); Lunioinf:=actualitzaunioinf(Lconjunts,Linterseccioinf,Lunioinf,llista); end for; end for; joinsets:=function(llista) unio:={}; for conj in llista do unio:=unio join conj; end for; return unio; end function; l:=#Lconjunts; print "CONJUNTS="; ; print "MCINF="; ; print "INTERSECCIOINF="; Linterseccioinf; print "UNIOINF="; Lunioinf; unioasac:=[#joinsets({N(i):i in llista}):llista in Lconjunts]; errors:=[Lunioinf[i]-unioasac[i]:i in [1..#unioasac]]; printf "VEREDICTE:="; [Lconjunts[i]:i in [1..#errors]|errors[i] ne 0]; /*r:=2; Subsets({0..MAX},r);*/ [index[llista]:llista in Lconjunts]; Output: Magma V2.10-6 Wed Dec 24 2003 06:13:26 on modular [Seed = 2124953018] ------------------------------------- CONJUNTS= <[ 0 ], [ 1 ], [ 0, 1 ], [ 2 ], [ 0, 2 ], [ 1, 2 ], [ 0, 1, 2 ], [ 3 ], [ 0, 3 ], [ 1, 3 ], [ 0, 1, 3 ], [ 2, 3 ], [ 0, 2, 3 ], [ 1, 2, 3 ], [ 0, 1, 2, 3 ], [ 4 ], [ 0, 4 ], [ 1, 4 ], [ 0, 1, 4 ], [ 2, 4 ], [ 0, 2, 4 ], [ 1, 2, 4 ], [ 0, 1, 2, 4 ], [ 3, 4 ], [ 0, 3, 4 ], [ 1, 3, 4 ], [ 0, 1, 3, 4 ], [ 2, 3, 4 ], [ 0, 2, 3, 4 ], [ 1, 2, 3, 4 ], [ 0, 1, 2, 3, 4 ], [ 5 ], [ 0, 5 ], [ 1, 5 ], [ 0, 1, 5 ], [ 2, 5 ], [ 0, 2, 5 ], [ 1, 2, 5 ], [ 0, 1, 2, 5 ], [ 3, 5 ], [ 0, 3, 5 ], [ 1, 3, 5 ], [ 0, 1, 3, 5 ], [ 2, 3, 5 ], [ 0, 2, 3, 5 ], [ 1, 2, 3, 5 ], [ 0, 1, 2, 3, 5 ], [ 4, 5 ], [ 0, 4, 5 ], [ 1, 4, 5 ], [ 0, 1, 4, 5 ], [ 2, 4, 5 ], [ 0, 2, 4, 5 ], [ 1, 2, 4, 5 ], [ 0, 1, 2, 4, 5 ], [ 3, 4, 5 ], [ 0, 3, 4, 5 ], [ 1, 3, 4, 5 ], [ 0, 1, 3, 4, 5 ], [ 2, 3, 4, 5 ], [ 0, 2, 3, 4, 5 ], [ 1, 2, 3, 4, 5 ], [ 0, 1, 2, 3, 4, 5 ], [ 6 ], [ 0, 6 ], [ 1, 6 ], [ 0, 1, 6 ], [ 2, 6 ], [ 0, 2, 6 ], [ 1, 2, 6 ], [ 0, 1, 2, 6 ], [ 3, 6 ], [ 0, 3, 6 ], [ 1, 3, 6 ], [ 0, 1, 3, 6 ], [ 2, 3, 6 ], [ 0, 2, 3, 6 ], [ 1, 2, 3, 6 ], [ 0, 1, 2, 3, 6 ], [ 4, 6 ], [ 0, 4, 6 ], [ 1, 4, 6 ], [ 0, 1, 4, 6 ], [ 2, 4, 6 ], [ 0, 2, 4, 6 ], [ 1, 2, 4, 6 ], [ 0, 1, 2, 4, 6 ], [ 3, 4, 6 ], [ 0, 3, 4, 6 ], [ 1, 3, 4, 6 ], [ 0, 1, 3, 4, 6 ], [ 2, 3, 4, 6 ], [ 0, 2, 3, 4, 6 ], [ 1, 2, 3, 4, 6 ], [ 0, 1, 2, 3, 4, 6 ], [ 5, 6 ], [ 0, 5, 6 ], [ 1, 5, 6 ], [ 0, 1, 5, 6 ], [ 2, 5, 6 ], [ 0, 2, 5, 6 ], [ 1, 2, 5, 6 ], [ 0, 1, 2, 5, 6 ], [ 3, 5, 6 ], [ 0, 3, 5, 6 ], [ 1, 3, 5, 6 ], [ 0, 1, 3, 5, 6 ], [ 2, 3, 5, 6 ], [ 0, 2, 3, 5, 6 ], [ 1, 2, 3, 5, 6 ], [ 0, 1, 2, 3, 5, 6 ], [ 4, 5, 6 ], [ 0, 4, 5, 6 ], [ 1, 4, 5, 6 ], [ 0, 1, 4, 5, 6 ], [ 2, 4, 5, 6 ], [ 0, 2, 4, 5, 6 ], [ 1, 2, 4, 5, 6 ], [ 0, 1, 2, 4, 5, 6 ], [ 3, 4, 5, 6 ], [ 0, 3, 4, 5, 6 ], [ 1, 3, 4, 5, 6 ], [ 0, 1, 3, 4, 5, 6 ], [ 2, 3, 4, 5, 6 ], [ 0, 2, 3, 4, 5, 6 ], [ 1, 2, 3, 4, 5, 6 ], [ 0, 1, 2, 3, 4, 5, 6 ]> MCINF= <[ 0 ], [ 1 ], [ 0 ], [ 2 ], [ 0 ], [ 0 ], [ 0 ], [ 3 ], [ 0 ], [ 1 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 4 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 5 ], [ 0 ], [ 1 ], [ 0 ], [ 2 ], [ 0 ], [ 0 ], [ 0 ], [ 1 ], [ 0 ], [ 1 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 6 ], [ 0 ], [ 1 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 3 ], [ 0 ], [ 1 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 1 ], [ 0 ], [ 1 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 1 ], [ 0 ], [ 1 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ]> INTERSECCIOINF= [ 1, 2, 1, 2, 1, 1, 1, 3, 1, 2, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 4, 1, 2, 1, 2, 1, 1, 1, 2, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 4, 1, 2, 1, 1, 1, 1, 1, 3, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 2, 1, 1, 1, 1, 1, 2, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 ] UNIOINF= [ 1, 2, 2, 2, 2, 3, 3, 3, 3, 3, 4, 4, 4, 5, 5, 2, 2, 3, 3, 3, 3, 4, 4, 4, 4, 4, 5, 5, 5, 6, 6, 4, 4, 4, 5, 4, 5, 6, 6, 5, 6, 5, 7, 7, 7, 8, 8, 5, 5, 6, 6, 6, 6, 7, 7, 7, 7, 7, 8, 8, 8, 9, 9, 4, 4, 4, 5, 5, 5, 6, 6, 4, 6, 5, 7, 7, 7, 8, 8, 5, 5, 6, 6, 6, 6, 7, 7, 7, 7, 7, 8, 8, 8, 9, 9, 6, 7, 6, 8, 7, 8, 9, 9, 7, 9, 7, 10, 10, 10, 11, 11, 8, 8, 9, 9, 9, 9, 10, 10, 10, 10, 10, 11, 11, 11, 12, 12 ] VEREDICTE:=[ [ 0, 1, 3 ], [ 1, 2, 3 ], [ 0, 1, 2, 3 ], [ 0, 1, 3, 4 ], [ 1, 2, 3, 4 ], [ 0, 1, 2, 3, 4 ], [ 0, 1, 5 ], [ 0, 2, 5 ], [ 1, 2, 5 ], [ 0, 1, 2, 5 ], [ 0, 3, 5 ], [ 0, 1, 3, 5 ], [ 2, 3, 5 ], [ 0, 2, 3, 5 ], [ 1, 2, 3, 5 ], [ 0, 1, 2, 3, 5 ], [ 1, 4, 5 ], [ 0, 1, 4, 5 ], [ 2, 4, 5 ], [ 0, 2, 4, 5 ], [ 1, 2, 4, 5 ], [ 0, 1, 2, 4, 5 ], [ 3, 4, 5 ], [ 0, 3, 4, 5 ], [ 1, 3, 4, 5 ], [ 0, 1, 3, 4, 5 ], [ 2, 3, 4, 5 ], [ 0, 2, 3, 4, 5 ], [ 1, 2, 3, 4, 5 ], [ 0, 1, 2, 3, 4, 5 ], [ 0, 1, 6 ], [ 1, 2, 6 ], [ 0, 1, 2, 6 ], [ 0, 3, 6 ], [ 1, 3, 6 ], [ 0, 1, 3, 6 ], [ 2, 3, 6 ], [ 0, 2, 3, 6 ], [ 1, 2, 3, 6 ], [ 0, 1, 2, 3, 6 ], [ 1, 4, 6 ], [ 0, 1, 4, 6 ], [ 1, 2, 4, 6 ], [ 0, 1, 2, 4, 6 ], [ 3, 4, 6 ], [ 0, 3, 4, 6 ], [ 1, 3, 4, 6 ], [ 0, 1, 3, 4, 6 ], [ 2, 3, 4, 6 ], [ 0, 2, 3, 4, 6 ], [ 1, 2, 3, 4, 6 ], [ 0, 1, 2, 3, 4, 6 ], [ 0, 5, 6 ], [ 0, 1, 5, 6 ], [ 2, 5, 6 ], [ 0, 2, 5, 6 ], [ 1, 2, 5, 6 ], [ 0, 1, 2, 5, 6 ], [ 3, 5, 6 ], [ 0, 3, 5, 6 ], [ 1, 3, 5, 6 ], [ 0, 1, 3, 5, 6 ], [ 2, 3, 5, 6 ], [ 0, 2, 3, 5, 6 ], [ 1, 2, 3, 5, 6 ], [ 0, 1, 2, 3, 5, 6 ], [ 4, 5, 6 ], [ 0, 4, 5, 6 ], [ 1, 4, 5, 6 ], [ 0, 1, 4, 5, 6 ], [ 2, 4, 5, 6 ], [ 0, 2, 4, 5, 6 ], [ 1, 2, 4, 5, 6 ], [ 0, 1, 2, 4, 5, 6 ], [ 3, 4, 5, 6 ], [ 0, 3, 4, 5, 6 ], [ 1, 3, 4, 5, 6 ], [ 0, 1, 3, 4, 5, 6 ], [ 2, 3, 4, 5, 6 ], [ 0, 2, 3, 4, 5, 6 ], [ 1, 2, 3, 4, 5, 6 ], [ 0, 1, 2, 3, 4, 5, 6 ] ] >> [index[llista]:llista in Lconjunts]; ^ Runtime error in '[]': Bad argument types Total time: 3.079 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.32.42.proxycache.rima-tde.net. (80.58.32.42) Time: Wed Dec 24 06:13:57 2003 Input: /* Klein quartic */ MAX:=6; c:=5; g:=3; semi:=[0,3]; /* basic del semigrup */ i_cond:=c-g; pertany:=func; gaps:=[i:i in [1..c-1]|not pertany(i)]; lambda:=func; lambdainv:=func; /* oplus, leq, nu */ oplus:=func; inferior:=func; ominus:=func; N:=func; nu:=func; /* order bound */ dORD:=func; Lconjunts:=[[0]]; Lmcinf:=[[0]]; Linterseccioinf:=[1]; Lunioinf:=[1]; index:=function(llista) i:=0; for j in llista do i:=i+2^j; end for; return(i); end function; /* mcinf:=function(Lconjunts,Lmcinf,llista) p:=Position(Lconjunts,llista); if p eq 0 then return -1; else return Lmcinf[p]; end if; end function; interseccioinf:=function(Lconjunts,Linterseccioinf,llista) p:=Position(Lconjunts,llista); if p eq 0 then return -1; else return Linterseccioinf[p]; end if; end function; unioinf:=function(Lconjunts,Lunioinf,llista) p:=Position(Lconjunts,llista); if p eq 0 then return -1; else return Lunioinf[p]; end if; end function; */ actualitzaconjunts:=function (Lconjunts,llista) return(Append(Lconjunts,llista)); end function; actualitzamcinf:=function(Lmcinf,llista) maxc:=llista[1]; if (maxc eq 0) then return (Append(Lmcinf,[0])); end if; trobat:=false; while not trobat do while not inferior(maxc,llista[1]) do maxc:=maxc-1; end while; j:=2; while j le #llista and inferior(maxc,llista[j]) do j:=j+1; end while; if j eq #llista+1 then trobat:=true; end if; maxc:=maxc-1; end while; maxc:=maxc+1; mcinfllista:=[maxc]; for h in gaps do candidat:=lambdainv(lambda(maxc)-h); if candidat gt 0 then j:=1; while j le #llista and inferior(candidat,llista[j]) do j:=j+1; end while; if j eq #llista+1 then mcinfllista:=Append(mcinfllista,candidat); end if; end if; end for; return(Append(Lmcinf,mcinfllista)); end function; actualitzainterseccioinf:=function(Lconjunts,Lmcinf,Linterseccioinf,Lunioinf,llista) if #llista eq 1 then return Append(Linterseccioinf,nu(llista[1])); else return Append(Linterseccioinf,Lunioinf[index(Lmcinf[index(llista)])]); end if; end function; actualitzaunioinf:=function(Lconjunts,Linterseccioinf,Lunioinf,llista) if #llista eq 1 then return Append(Lunioinf,nu(llista[1])); else return Append(Lunioinf, Lunioinf[index([llista[i]:i in [1..(#llista-1)]])]+nu(llista[#llista])-Linterseccioinf[index(llista)]); end if; end function; for i in [1..MAX] do conjuntsaux:=Lconjunts; llista:=[i]; Lconjunts:=actualitzaconjunts(Lconjunts,llista); Lmcinf:=actualitzamcinf(Lmcinf,llista); Linterseccioinf:=actualitzainterseccioinf(Lconjunts,Lmcinf,Linterseccioinf,Lunioinf,llista); Lunioinf:=actualitzaunioinf(Lconjunts,Linterseccioinf,Lunioinf,llista); for conj in conjuntsaux do llista:=Append(conj,i); Lconjunts:=actualitzaconjunts(Lconjunts,llista); Lmcinf:=actualitzamcinf(Lmcinf,llista); Linterseccioinf:=actualitzainterseccioinf(Lconjunts,Lmcinf,Linterseccioinf,Lunioinf,llista); Lunioinf:=actualitzaunioinf(Lconjunts,Linterseccioinf,Lunioinf,llista); end for; end for; joinsets:=function(llista) unio:={}; for conj in llista do unio:=unio join conj; end for; return unio; end function; l:=#Lconjunts; print "CONJUNTS="; ; print "MCINF="; ; print "INTERSECCIOINF="; Linterseccioinf; print "UNIOINF="; Lunioinf; unioasac:=[#joinsets({N(i):i in llista}):llista in Lconjunts]; errors:=[Lunioinf[i]-unioasac[i]:i in [1..#unioasac]]; printf "VEREDICTE:="; [Lconjunts[i]:i in [1..#errors]|errors[i] ne 0]; /*r:=2; Subsets({0..MAX},r);*/ [index(llista):llista in Lconjunts]; Output: Magma V2.10-6 Wed Dec 24 2003 06:13:53 on modular [Seed = 3127701849] ------------------------------------- CONJUNTS= <[ 0 ], [ 1 ], [ 0, 1 ], [ 2 ], [ 0, 2 ], [ 1, 2 ], [ 0, 1, 2 ], [ 3 ], [ 0, 3 ], [ 1, 3 ], [ 0, 1, 3 ], [ 2, 3 ], [ 0, 2, 3 ], [ 1, 2, 3 ], [ 0, 1, 2, 3 ], [ 4 ], [ 0, 4 ], [ 1, 4 ], [ 0, 1, 4 ], [ 2, 4 ], [ 0, 2, 4 ], [ 1, 2, 4 ], [ 0, 1, 2, 4 ], [ 3, 4 ], [ 0, 3, 4 ], [ 1, 3, 4 ], [ 0, 1, 3, 4 ], [ 2, 3, 4 ], [ 0, 2, 3, 4 ], [ 1, 2, 3, 4 ], [ 0, 1, 2, 3, 4 ], [ 5 ], [ 0, 5 ], [ 1, 5 ], [ 0, 1, 5 ], [ 2, 5 ], [ 0, 2, 5 ], [ 1, 2, 5 ], [ 0, 1, 2, 5 ], [ 3, 5 ], [ 0, 3, 5 ], [ 1, 3, 5 ], [ 0, 1, 3, 5 ], [ 2, 3, 5 ], [ 0, 2, 3, 5 ], [ 1, 2, 3, 5 ], [ 0, 1, 2, 3, 5 ], [ 4, 5 ], [ 0, 4, 5 ], [ 1, 4, 5 ], [ 0, 1, 4, 5 ], [ 2, 4, 5 ], [ 0, 2, 4, 5 ], [ 1, 2, 4, 5 ], [ 0, 1, 2, 4, 5 ], [ 3, 4, 5 ], [ 0, 3, 4, 5 ], [ 1, 3, 4, 5 ], [ 0, 1, 3, 4, 5 ], [ 2, 3, 4, 5 ], [ 0, 2, 3, 4, 5 ], [ 1, 2, 3, 4, 5 ], [ 0, 1, 2, 3, 4, 5 ], [ 6 ], [ 0, 6 ], [ 1, 6 ], [ 0, 1, 6 ], [ 2, 6 ], [ 0, 2, 6 ], [ 1, 2, 6 ], [ 0, 1, 2, 6 ], [ 3, 6 ], [ 0, 3, 6 ], [ 1, 3, 6 ], [ 0, 1, 3, 6 ], [ 2, 3, 6 ], [ 0, 2, 3, 6 ], [ 1, 2, 3, 6 ], [ 0, 1, 2, 3, 6 ], [ 4, 6 ], [ 0, 4, 6 ], [ 1, 4, 6 ], [ 0, 1, 4, 6 ], [ 2, 4, 6 ], [ 0, 2, 4, 6 ], [ 1, 2, 4, 6 ], [ 0, 1, 2, 4, 6 ], [ 3, 4, 6 ], [ 0, 3, 4, 6 ], [ 1, 3, 4, 6 ], [ 0, 1, 3, 4, 6 ], [ 2, 3, 4, 6 ], [ 0, 2, 3, 4, 6 ], [ 1, 2, 3, 4, 6 ], [ 0, 1, 2, 3, 4, 6 ], [ 5, 6 ], [ 0, 5, 6 ], [ 1, 5, 6 ], [ 0, 1, 5, 6 ], [ 2, 5, 6 ], [ 0, 2, 5, 6 ], [ 1, 2, 5, 6 ], [ 0, 1, 2, 5, 6 ], [ 3, 5, 6 ], [ 0, 3, 5, 6 ], [ 1, 3, 5, 6 ], [ 0, 1, 3, 5, 6 ], [ 2, 3, 5, 6 ], [ 0, 2, 3, 5, 6 ], [ 1, 2, 3, 5, 6 ], [ 0, 1, 2, 3, 5, 6 ], [ 4, 5, 6 ], [ 0, 4, 5, 6 ], [ 1, 4, 5, 6 ], [ 0, 1, 4, 5, 6 ], [ 2, 4, 5, 6 ], [ 0, 2, 4, 5, 6 ], [ 1, 2, 4, 5, 6 ], [ 0, 1, 2, 4, 5, 6 ], [ 3, 4, 5, 6 ], [ 0, 3, 4, 5, 6 ], [ 1, 3, 4, 5, 6 ], [ 0, 1, 3, 4, 5, 6 ], [ 2, 3, 4, 5, 6 ], [ 0, 2, 3, 4, 5, 6 ], [ 1, 2, 3, 4, 5, 6 ], [ 0, 1, 2, 3, 4, 5, 6 ]> MCINF= <[ 0 ], [ 1 ], [ 0 ], [ 2 ], [ 0 ], [ 0 ], [ 0 ], [ 3 ], [ 0 ], [ 1 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 4 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 5 ], [ 0 ], [ 1 ], [ 0 ], [ 2 ], [ 0 ], [ 0 ], [ 0 ], [ 1 ], [ 0 ], [ 1 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 6 ], [ 0 ], [ 1 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 3 ], [ 0 ], [ 1 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 1 ], [ 0 ], [ 1 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 1 ], [ 0 ], [ 1 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ]> INTERSECCIOINF= [ 1, 2, 1, 2, 1, 1, 1, 3, 1, 2, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 4, 1, 2, 1, 2, 1, 1, 1, 2, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 4, 1, 2, 1, 1, 1, 1, 1, 3, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 2, 1, 1, 1, 1, 1, 2, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 ] UNIOINF= [ 1, 2, 2, 2, 2, 3, 3, 3, 3, 3, 4, 4, 4, 5, 5, 2, 2, 3, 3, 3, 3, 4, 4, 4, 4, 4, 5, 5, 5, 6, 6, 4, 4, 4, 5, 4, 5, 6, 6, 5, 6, 5, 7, 7, 7, 8, 8, 5, 5, 6, 6, 6, 6, 7, 7, 7, 7, 7, 8, 8, 8, 9, 9, 4, 4, 4, 5, 5, 5, 6, 6, 4, 6, 5, 7, 7, 7, 8, 8, 5, 5, 6, 6, 6, 6, 7, 7, 7, 7, 7, 8, 8, 8, 9, 9, 6, 7, 6, 8, 7, 8, 9, 9, 7, 9, 7, 10, 10, 10, 11, 11, 8, 8, 9, 9, 9, 9, 10, 10, 10, 10, 10, 11, 11, 11, 12, 12 ] VEREDICTE:=[ [ 0, 1, 3 ], [ 1, 2, 3 ], [ 0, 1, 2, 3 ], [ 0, 1, 3, 4 ], [ 1, 2, 3, 4 ], [ 0, 1, 2, 3, 4 ], [ 0, 1, 5 ], [ 0, 2, 5 ], [ 1, 2, 5 ], [ 0, 1, 2, 5 ], [ 0, 3, 5 ], [ 0, 1, 3, 5 ], [ 2, 3, 5 ], [ 0, 2, 3, 5 ], [ 1, 2, 3, 5 ], [ 0, 1, 2, 3, 5 ], [ 1, 4, 5 ], [ 0, 1, 4, 5 ], [ 2, 4, 5 ], [ 0, 2, 4, 5 ], [ 1, 2, 4, 5 ], [ 0, 1, 2, 4, 5 ], [ 3, 4, 5 ], [ 0, 3, 4, 5 ], [ 1, 3, 4, 5 ], [ 0, 1, 3, 4, 5 ], [ 2, 3, 4, 5 ], [ 0, 2, 3, 4, 5 ], [ 1, 2, 3, 4, 5 ], [ 0, 1, 2, 3, 4, 5 ], [ 0, 1, 6 ], [ 1, 2, 6 ], [ 0, 1, 2, 6 ], [ 0, 3, 6 ], [ 1, 3, 6 ], [ 0, 1, 3, 6 ], [ 2, 3, 6 ], [ 0, 2, 3, 6 ], [ 1, 2, 3, 6 ], [ 0, 1, 2, 3, 6 ], [ 1, 4, 6 ], [ 0, 1, 4, 6 ], [ 1, 2, 4, 6 ], [ 0, 1, 2, 4, 6 ], [ 3, 4, 6 ], [ 0, 3, 4, 6 ], [ 1, 3, 4, 6 ], [ 0, 1, 3, 4, 6 ], [ 2, 3, 4, 6 ], [ 0, 2, 3, 4, 6 ], [ 1, 2, 3, 4, 6 ], [ 0, 1, 2, 3, 4, 6 ], [ 0, 5, 6 ], [ 0, 1, 5, 6 ], [ 2, 5, 6 ], [ 0, 2, 5, 6 ], [ 1, 2, 5, 6 ], [ 0, 1, 2, 5, 6 ], [ 3, 5, 6 ], [ 0, 3, 5, 6 ], [ 1, 3, 5, 6 ], [ 0, 1, 3, 5, 6 ], [ 2, 3, 5, 6 ], [ 0, 2, 3, 5, 6 ], [ 1, 2, 3, 5, 6 ], [ 0, 1, 2, 3, 5, 6 ], [ 4, 5, 6 ], [ 0, 4, 5, 6 ], [ 1, 4, 5, 6 ], [ 0, 1, 4, 5, 6 ], [ 2, 4, 5, 6 ], [ 0, 2, 4, 5, 6 ], [ 1, 2, 4, 5, 6 ], [ 0, 1, 2, 4, 5, 6 ], [ 3, 4, 5, 6 ], [ 0, 3, 4, 5, 6 ], [ 1, 3, 4, 5, 6 ], [ 0, 1, 3, 4, 5, 6 ], [ 2, 3, 4, 5, 6 ], [ 0, 2, 3, 4, 5, 6 ], [ 1, 2, 3, 4, 5, 6 ], [ 0, 1, 2, 3, 4, 5, 6 ] ] [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127 ] Total time: 3.269 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.32.42.proxycache.rima-tde.net. (80.58.32.42) Time: Wed Dec 24 06:14:45 2003 Input: /* Klein quartic */ MAX:=6; c:=5; g:=3; semi:=[0,3]; /* basic del semigrup */ i_cond:=c-g; pertany:=func; gaps:=[i:i in [1..c-1]|not pertany(i)]; lambda:=func; lambdainv:=func; /* oplus, leq, nu */ oplus:=func; inferior:=func; ominus:=func; N:=func; nu:=func; /* order bound */ dORD:=func; Lconjunts:=[[0]]; Lmcinf:=[[0]]; Linterseccioinf:=[1]; Lunioinf:=[1]; index:=function(llista) i:=0; for j in llista do i:=i+2^j; end for; return(i); end function; /* mcinf:=function(Lconjunts,Lmcinf,llista) p:=Position(Lconjunts,llista); if p eq 0 then return -1; else return Lmcinf[p]; end if; end function; interseccioinf:=function(Lconjunts,Linterseccioinf,llista) p:=Position(Lconjunts,llista); if p eq 0 then return -1; else return Linterseccioinf[p]; end if; end function; unioinf:=function(Lconjunts,Lunioinf,llista) p:=Position(Lconjunts,llista); if p eq 0 then return -1; else return Lunioinf[p]; end if; end function; */ actualitzaconjunts:=function (Lconjunts,llista) return(Append(Lconjunts,llista)); end function; actualitzamcinf:=function(Lmcinf,llista) maxc:=llista[1]; if (maxc eq 0) then return (Append(Lmcinf,[0])); end if; trobat:=false; while not trobat do while not inferior(maxc,llista[1]) do maxc:=maxc-1; end while; j:=2; while j le #llista and inferior(maxc,llista[j]) do j:=j+1; end while; if j eq #llista+1 then trobat:=true; end if; maxc:=maxc-1; end while; maxc:=maxc+1; mcinfllista:=[maxc]; for h in gaps do candidat:=lambdainv(lambda(maxc)-h); if candidat gt 0 then j:=1; while j le #llista and inferior(candidat,llista[j]) do j:=j+1; end while; if j eq #llista+1 then mcinfllista:=Append(mcinfllista,candidat); end if; end if; end for; return(Append(Lmcinf,mcinfllista)); end function; actualitzainterseccioinf:=function(Lconjunts,Lmcinf,Linterseccioinf,Lunioinf,llista) if #llista eq 1 then return Append(Linterseccioinf,nu(llista[1])); else return Append(Linterseccioinf,Lunioinf[index(Lmcinf[index(llista)])]); end if; end function; actualitzaunioinf:=function(Lconjunts,Linterseccioinf,Lunioinf,llista) if #llista eq 1 then return Append(Lunioinf,nu(llista[1])); else return Append(Lunioinf, Lunioinf[index([llista[i]:i in [1..(#llista-1)]])]+nu(llista[#llista])-Linterseccioinf[index(llista)]); end if; end function; for i in [1..MAX] do conjuntsaux:=Lconjunts; llista:=[i]; Lconjunts:=actualitzaconjunts(Lconjunts,llista); Lmcinf:=actualitzamcinf(Lmcinf,llista); Linterseccioinf:=actualitzainterseccioinf(Lconjunts,Lmcinf,Linterseccioinf,Lunioinf,llista); Lunioinf:=actualitzaunioinf(Lconjunts,Linterseccioinf,Lunioinf,llista); for conj in conjuntsaux do llista:=Append(conj,i); Lconjunts:=actualitzaconjunts(Lconjunts,llista); Lmcinf:=actualitzamcinf(Lmcinf,llista); Linterseccioinf:=actualitzainterseccioinf(Lconjunts,Lmcinf,Linterseccioinf,Lunioinf,llista); Lunioinf:=actualitzaunioinf(Lconjunts,Linterseccioinf,Lunioinf,llista); end for; end for; joinsets:=function(llista) unio:={}; for conj in llista do unio:=unio join conj; end for; return unio; end function; l:=#Lconjunts; print "CONJUNTS="; ; print "MCINF="; ; print "INTERSECCIOINF="; Linterseccioinf; print "UNIOINF="; Lunioinf; unioasac:=[#joinsets({N(i):i in llista}):llista in Lconjunts]; errors:=[Lunioinf[i]-unioasac[i]:i in [1..#unioasac]]; printf "VEREDICTE:="; [Lconjunts[i]:i in [1..#errors]|errors[i] ne 0]; /*r:=2; Subsets({0..MAX},r);*/ [[llista,index(llista)]:llista in Lconjunts]; Output: Magma V2.10-6 Wed Dec 24 2003 06:14:40 on modular [Seed = 533288238] ------------------------------------- CONJUNTS= <[ 0 ], [ 1 ], [ 0, 1 ], [ 2 ], [ 0, 2 ], [ 1, 2 ], [ 0, 1, 2 ], [ 3 ], [ 0, 3 ], [ 1, 3 ], [ 0, 1, 3 ], [ 2, 3 ], [ 0, 2, 3 ], [ 1, 2, 3 ], [ 0, 1, 2, 3 ], [ 4 ], [ 0, 4 ], [ 1, 4 ], [ 0, 1, 4 ], [ 2, 4 ], [ 0, 2, 4 ], [ 1, 2, 4 ], [ 0, 1, 2, 4 ], [ 3, 4 ], [ 0, 3, 4 ], [ 1, 3, 4 ], [ 0, 1, 3, 4 ], [ 2, 3, 4 ], [ 0, 2, 3, 4 ], [ 1, 2, 3, 4 ], [ 0, 1, 2, 3, 4 ], [ 5 ], [ 0, 5 ], [ 1, 5 ], [ 0, 1, 5 ], [ 2, 5 ], [ 0, 2, 5 ], [ 1, 2, 5 ], [ 0, 1, 2, 5 ], [ 3, 5 ], [ 0, 3, 5 ], [ 1, 3, 5 ], [ 0, 1, 3, 5 ], [ 2, 3, 5 ], [ 0, 2, 3, 5 ], [ 1, 2, 3, 5 ], [ 0, 1, 2, 3, 5 ], [ 4, 5 ], [ 0, 4, 5 ], [ 1, 4, 5 ], [ 0, 1, 4, 5 ], [ 2, 4, 5 ], [ 0, 2, 4, 5 ], [ 1, 2, 4, 5 ], [ 0, 1, 2, 4, 5 ], [ 3, 4, 5 ], [ 0, 3, 4, 5 ], [ 1, 3, 4, 5 ], [ 0, 1, 3, 4, 5 ], [ 2, 3, 4, 5 ], [ 0, 2, 3, 4, 5 ], [ 1, 2, 3, 4, 5 ], [ 0, 1, 2, 3, 4, 5 ], [ 6 ], [ 0, 6 ], [ 1, 6 ], [ 0, 1, 6 ], [ 2, 6 ], [ 0, 2, 6 ], [ 1, 2, 6 ], [ 0, 1, 2, 6 ], [ 3, 6 ], [ 0, 3, 6 ], [ 1, 3, 6 ], [ 0, 1, 3, 6 ], [ 2, 3, 6 ], [ 0, 2, 3, 6 ], [ 1, 2, 3, 6 ], [ 0, 1, 2, 3, 6 ], [ 4, 6 ], [ 0, 4, 6 ], [ 1, 4, 6 ], [ 0, 1, 4, 6 ], [ 2, 4, 6 ], [ 0, 2, 4, 6 ], [ 1, 2, 4, 6 ], [ 0, 1, 2, 4, 6 ], [ 3, 4, 6 ], [ 0, 3, 4, 6 ], [ 1, 3, 4, 6 ], [ 0, 1, 3, 4, 6 ], [ 2, 3, 4, 6 ], [ 0, 2, 3, 4, 6 ], [ 1, 2, 3, 4, 6 ], [ 0, 1, 2, 3, 4, 6 ], [ 5, 6 ], [ 0, 5, 6 ], [ 1, 5, 6 ], [ 0, 1, 5, 6 ], [ 2, 5, 6 ], [ 0, 2, 5, 6 ], [ 1, 2, 5, 6 ], [ 0, 1, 2, 5, 6 ], [ 3, 5, 6 ], [ 0, 3, 5, 6 ], [ 1, 3, 5, 6 ], [ 0, 1, 3, 5, 6 ], [ 2, 3, 5, 6 ], [ 0, 2, 3, 5, 6 ], [ 1, 2, 3, 5, 6 ], [ 0, 1, 2, 3, 5, 6 ], [ 4, 5, 6 ], [ 0, 4, 5, 6 ], [ 1, 4, 5, 6 ], [ 0, 1, 4, 5, 6 ], [ 2, 4, 5, 6 ], [ 0, 2, 4, 5, 6 ], [ 1, 2, 4, 5, 6 ], [ 0, 1, 2, 4, 5, 6 ], [ 3, 4, 5, 6 ], [ 0, 3, 4, 5, 6 ], [ 1, 3, 4, 5, 6 ], [ 0, 1, 3, 4, 5, 6 ], [ 2, 3, 4, 5, 6 ], [ 0, 2, 3, 4, 5, 6 ], [ 1, 2, 3, 4, 5, 6 ], [ 0, 1, 2, 3, 4, 5, 6 ]> MCINF= <[ 0 ], [ 1 ], [ 0 ], [ 2 ], [ 0 ], [ 0 ], [ 0 ], [ 3 ], [ 0 ], [ 1 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 4 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 5 ], [ 0 ], [ 1 ], [ 0 ], [ 2 ], [ 0 ], [ 0 ], [ 0 ], [ 1 ], [ 0 ], [ 1 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 6 ], [ 0 ], [ 1 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 3 ], [ 0 ], [ 1 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 1 ], [ 0 ], [ 1 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 1 ], [ 0 ], [ 1 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ]> INTERSECCIOINF= [ 1, 2, 1, 2, 1, 1, 1, 3, 1, 2, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 4, 1, 2, 1, 2, 1, 1, 1, 2, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 4, 1, 2, 1, 1, 1, 1, 1, 3, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 2, 1, 1, 1, 1, 1, 2, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 ] UNIOINF= [ 1, 2, 2, 2, 2, 3, 3, 3, 3, 3, 4, 4, 4, 5, 5, 2, 2, 3, 3, 3, 3, 4, 4, 4, 4, 4, 5, 5, 5, 6, 6, 4, 4, 4, 5, 4, 5, 6, 6, 5, 6, 5, 7, 7, 7, 8, 8, 5, 5, 6, 6, 6, 6, 7, 7, 7, 7, 7, 8, 8, 8, 9, 9, 4, 4, 4, 5, 5, 5, 6, 6, 4, 6, 5, 7, 7, 7, 8, 8, 5, 5, 6, 6, 6, 6, 7, 7, 7, 7, 7, 8, 8, 8, 9, 9, 6, 7, 6, 8, 7, 8, 9, 9, 7, 9, 7, 10, 10, 10, 11, 11, 8, 8, 9, 9, 9, 9, 10, 10, 10, 10, 10, 11, 11, 11, 12, 12 ] VEREDICTE:=[ [ 0, 1, 3 ], [ 1, 2, 3 ], [ 0, 1, 2, 3 ], [ 0, 1, 3, 4 ], [ 1, 2, 3, 4 ], [ 0, 1, 2, 3, 4 ], [ 0, 1, 5 ], [ 0, 2, 5 ], [ 1, 2, 5 ], [ 0, 1, 2, 5 ], [ 0, 3, 5 ], [ 0, 1, 3, 5 ], [ 2, 3, 5 ], [ 0, 2, 3, 5 ], [ 1, 2, 3, 5 ], [ 0, 1, 2, 3, 5 ], [ 1, 4, 5 ], [ 0, 1, 4, 5 ], [ 2, 4, 5 ], [ 0, 2, 4, 5 ], [ 1, 2, 4, 5 ], [ 0, 1, 2, 4, 5 ], [ 3, 4, 5 ], [ 0, 3, 4, 5 ], [ 1, 3, 4, 5 ], [ 0, 1, 3, 4, 5 ], [ 2, 3, 4, 5 ], [ 0, 2, 3, 4, 5 ], [ 1, 2, 3, 4, 5 ], [ 0, 1, 2, 3, 4, 5 ], [ 0, 1, 6 ], [ 1, 2, 6 ], [ 0, 1, 2, 6 ], [ 0, 3, 6 ], [ 1, 3, 6 ], [ 0, 1, 3, 6 ], [ 2, 3, 6 ], [ 0, 2, 3, 6 ], [ 1, 2, 3, 6 ], [ 0, 1, 2, 3, 6 ], [ 1, 4, 6 ], [ 0, 1, 4, 6 ], [ 1, 2, 4, 6 ], [ 0, 1, 2, 4, 6 ], [ 3, 4, 6 ], [ 0, 3, 4, 6 ], [ 1, 3, 4, 6 ], [ 0, 1, 3, 4, 6 ], [ 2, 3, 4, 6 ], [ 0, 2, 3, 4, 6 ], [ 1, 2, 3, 4, 6 ], [ 0, 1, 2, 3, 4, 6 ], [ 0, 5, 6 ], [ 0, 1, 5, 6 ], [ 2, 5, 6 ], [ 0, 2, 5, 6 ], [ 1, 2, 5, 6 ], [ 0, 1, 2, 5, 6 ], [ 3, 5, 6 ], [ 0, 3, 5, 6 ], [ 1, 3, 5, 6 ], [ 0, 1, 3, 5, 6 ], [ 2, 3, 5, 6 ], [ 0, 2, 3, 5, 6 ], [ 1, 2, 3, 5, 6 ], [ 0, 1, 2, 3, 5, 6 ], [ 4, 5, 6 ], [ 0, 4, 5, 6 ], [ 1, 4, 5, 6 ], [ 0, 1, 4, 5, 6 ], [ 2, 4, 5, 6 ], [ 0, 2, 4, 5, 6 ], [ 1, 2, 4, 5, 6 ], [ 0, 1, 2, 4, 5, 6 ], [ 3, 4, 5, 6 ], [ 0, 3, 4, 5, 6 ], [ 1, 3, 4, 5, 6 ], [ 0, 1, 3, 4, 5, 6 ], [ 2, 3, 4, 5, 6 ], [ 0, 2, 3, 4, 5, 6 ], [ 1, 2, 3, 4, 5, 6 ], [ 0, 1, 2, 3, 4, 5, 6 ] ] >> [[llista,index(llista)]:llista in Lconjunts]; ^ Runtime error in [ ... ]: Could not find a valid universe Total time: 3.489 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.32.42.proxycache.rima-tde.net. (80.58.32.42) Time: Wed Dec 24 06:15:38 2003 Input: /* Klein quartic */ MAX:=6; c:=5; g:=3; semi:=[0,3]; /* basic del semigrup */ i_cond:=c-g; pertany:=func; gaps:=[i:i in [1..c-1]|not pertany(i)]; lambda:=func; lambdainv:=func; /* oplus, leq, nu */ oplus:=func; inferior:=func; ominus:=func; N:=func; nu:=func; /* order bound */ dORD:=func; Lconjunts:=[[0]]; Lmcinf:=[[0]]; Linterseccioinf:=[1]; Lunioinf:=[1]; index:=function(llista) i:=0; for j in llista do i:=i+2^j; end for; return(i); end function; /* mcinf:=function(Lconjunts,Lmcinf,llista) p:=Position(Lconjunts,llista); if p eq 0 then return -1; else return Lmcinf[p]; end if; end function; interseccioinf:=function(Lconjunts,Linterseccioinf,llista) p:=Position(Lconjunts,llista); if p eq 0 then return -1; else return Linterseccioinf[p]; end if; end function; unioinf:=function(Lconjunts,Lunioinf,llista) p:=Position(Lconjunts,llista); if p eq 0 then return -1; else return Lunioinf[p]; end if; end function; */ actualitzaconjunts:=function (Lconjunts,llista) return(Append(Lconjunts,llista)); end function; actualitzamcinf:=function(Lmcinf,llista) maxc:=llista[1]; if (maxc eq 0) then return (Append(Lmcinf,[0])); end if; trobat:=false; while not trobat do while not inferior(maxc,llista[1]) do maxc:=maxc-1; end while; j:=2; while j le #llista and inferior(maxc,llista[j]) do j:=j+1; end while; if j eq #llista+1 then trobat:=true; end if; maxc:=maxc-1; end while; maxc:=maxc+1; mcinfllista:=[maxc]; for h in gaps do candidat:=lambdainv(lambda(maxc)-h); if candidat gt 0 then j:=1; while j le #llista and inferior(candidat,llista[j]) do j:=j+1; end while; if j eq #llista+1 then mcinfllista:=Append(mcinfllista,candidat); end if; end if; end for; return(Append(Lmcinf,mcinfllista)); end function; actualitzainterseccioinf:=function(Lconjunts,Lmcinf,Linterseccioinf,Lunioinf,llista) if #llista eq 1 then return Append(Linterseccioinf,nu(llista[1])); else return Append(Linterseccioinf,Lunioinf[index(Lmcinf[index(llista)])]); end if; end function; actualitzaunioinf:=function(Lconjunts,Linterseccioinf,Lunioinf,llista) if #llista eq 1 then return Append(Lunioinf,nu(llista[1])); else return Append(Lunioinf, Lunioinf[index([llista[i]:i in [1..(#llista-1)]])]+nu(llista[#llista])-Linterseccioinf[index(llista)]); end if; end function; for i in [1..MAX] do conjuntsaux:=Lconjunts; llista:=[i]; Lconjunts:=actualitzaconjunts(Lconjunts,llista); Lmcinf:=actualitzamcinf(Lmcinf,llista); Linterseccioinf:=actualitzainterseccioinf(Lconjunts,Lmcinf,Linterseccioinf,Lunioinf,llista); Lunioinf:=actualitzaunioinf(Lconjunts,Linterseccioinf,Lunioinf,llista); for conj in conjuntsaux do llista:=Append(conj,i); Lconjunts:=actualitzaconjunts(Lconjunts,llista); Lmcinf:=actualitzamcinf(Lmcinf,llista); Linterseccioinf:=actualitzainterseccioinf(Lconjunts,Lmcinf,Linterseccioinf,Lunioinf,llista); Lunioinf:=actualitzaunioinf(Lconjunts,Linterseccioinf,Lunioinf,llista); end for; end for; joinsets:=function(llista) unio:={}; for conj in llista do unio:=unio join conj; end for; return unio; end function; l:=#Lconjunts; print "CONJUNTS="; ; print "MCINF="; ; print "INTERSECCIOINF="; Linterseccioinf; print "UNIOINF="; Lunioinf; unioasac:=[#joinsets({N(i):i in llista}):llista in Lconjunts]; errors:=[Lunioinf[i]-unioasac[i]:i in [1..#unioasac]]; printf "VEREDICTE:="; [Lconjunts[i]:i in [1..#errors]|errors[i] ne 0]; /*r:=2; Subsets({0..MAX},r);*/ [:llista in Lconjunts]; Output: Magma V2.10-6 Wed Dec 24 2003 06:15:34 on modular [Seed = 1672816932] ------------------------------------- CONJUNTS= <[ 0 ], [ 1 ], [ 0, 1 ], [ 2 ], [ 0, 2 ], [ 1, 2 ], [ 0, 1, 2 ], [ 3 ], [ 0, 3 ], [ 1, 3 ], [ 0, 1, 3 ], [ 2, 3 ], [ 0, 2, 3 ], [ 1, 2, 3 ], [ 0, 1, 2, 3 ], [ 4 ], [ 0, 4 ], [ 1, 4 ], [ 0, 1, 4 ], [ 2, 4 ], [ 0, 2, 4 ], [ 1, 2, 4 ], [ 0, 1, 2, 4 ], [ 3, 4 ], [ 0, 3, 4 ], [ 1, 3, 4 ], [ 0, 1, 3, 4 ], [ 2, 3, 4 ], [ 0, 2, 3, 4 ], [ 1, 2, 3, 4 ], [ 0, 1, 2, 3, 4 ], [ 5 ], [ 0, 5 ], [ 1, 5 ], [ 0, 1, 5 ], [ 2, 5 ], [ 0, 2, 5 ], [ 1, 2, 5 ], [ 0, 1, 2, 5 ], [ 3, 5 ], [ 0, 3, 5 ], [ 1, 3, 5 ], [ 0, 1, 3, 5 ], [ 2, 3, 5 ], [ 0, 2, 3, 5 ], [ 1, 2, 3, 5 ], [ 0, 1, 2, 3, 5 ], [ 4, 5 ], [ 0, 4, 5 ], [ 1, 4, 5 ], [ 0, 1, 4, 5 ], [ 2, 4, 5 ], [ 0, 2, 4, 5 ], [ 1, 2, 4, 5 ], [ 0, 1, 2, 4, 5 ], [ 3, 4, 5 ], [ 0, 3, 4, 5 ], [ 1, 3, 4, 5 ], [ 0, 1, 3, 4, 5 ], [ 2, 3, 4, 5 ], [ 0, 2, 3, 4, 5 ], [ 1, 2, 3, 4, 5 ], [ 0, 1, 2, 3, 4, 5 ], [ 6 ], [ 0, 6 ], [ 1, 6 ], [ 0, 1, 6 ], [ 2, 6 ], [ 0, 2, 6 ], [ 1, 2, 6 ], [ 0, 1, 2, 6 ], [ 3, 6 ], [ 0, 3, 6 ], [ 1, 3, 6 ], [ 0, 1, 3, 6 ], [ 2, 3, 6 ], [ 0, 2, 3, 6 ], [ 1, 2, 3, 6 ], [ 0, 1, 2, 3, 6 ], [ 4, 6 ], [ 0, 4, 6 ], [ 1, 4, 6 ], [ 0, 1, 4, 6 ], [ 2, 4, 6 ], [ 0, 2, 4, 6 ], [ 1, 2, 4, 6 ], [ 0, 1, 2, 4, 6 ], [ 3, 4, 6 ], [ 0, 3, 4, 6 ], [ 1, 3, 4, 6 ], [ 0, 1, 3, 4, 6 ], [ 2, 3, 4, 6 ], [ 0, 2, 3, 4, 6 ], [ 1, 2, 3, 4, 6 ], [ 0, 1, 2, 3, 4, 6 ], [ 5, 6 ], [ 0, 5, 6 ], [ 1, 5, 6 ], [ 0, 1, 5, 6 ], [ 2, 5, 6 ], [ 0, 2, 5, 6 ], [ 1, 2, 5, 6 ], [ 0, 1, 2, 5, 6 ], [ 3, 5, 6 ], [ 0, 3, 5, 6 ], [ 1, 3, 5, 6 ], [ 0, 1, 3, 5, 6 ], [ 2, 3, 5, 6 ], [ 0, 2, 3, 5, 6 ], [ 1, 2, 3, 5, 6 ], [ 0, 1, 2, 3, 5, 6 ], [ 4, 5, 6 ], [ 0, 4, 5, 6 ], [ 1, 4, 5, 6 ], [ 0, 1, 4, 5, 6 ], [ 2, 4, 5, 6 ], [ 0, 2, 4, 5, 6 ], [ 1, 2, 4, 5, 6 ], [ 0, 1, 2, 4, 5, 6 ], [ 3, 4, 5, 6 ], [ 0, 3, 4, 5, 6 ], [ 1, 3, 4, 5, 6 ], [ 0, 1, 3, 4, 5, 6 ], [ 2, 3, 4, 5, 6 ], [ 0, 2, 3, 4, 5, 6 ], [ 1, 2, 3, 4, 5, 6 ], [ 0, 1, 2, 3, 4, 5, 6 ]> MCINF= <[ 0 ], [ 1 ], [ 0 ], [ 2 ], [ 0 ], [ 0 ], [ 0 ], [ 3 ], [ 0 ], [ 1 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 4 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 5 ], [ 0 ], [ 1 ], [ 0 ], [ 2 ], [ 0 ], [ 0 ], [ 0 ], [ 1 ], [ 0 ], [ 1 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 6 ], [ 0 ], [ 1 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 3 ], [ 0 ], [ 1 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 1 ], [ 0 ], [ 1 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 1 ], [ 0 ], [ 1 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ]> INTERSECCIOINF= [ 1, 2, 1, 2, 1, 1, 1, 3, 1, 2, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 4, 1, 2, 1, 2, 1, 1, 1, 2, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 4, 1, 2, 1, 1, 1, 1, 1, 3, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 2, 1, 1, 1, 1, 1, 2, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 ] UNIOINF= [ 1, 2, 2, 2, 2, 3, 3, 3, 3, 3, 4, 4, 4, 5, 5, 2, 2, 3, 3, 3, 3, 4, 4, 4, 4, 4, 5, 5, 5, 6, 6, 4, 4, 4, 5, 4, 5, 6, 6, 5, 6, 5, 7, 7, 7, 8, 8, 5, 5, 6, 6, 6, 6, 7, 7, 7, 7, 7, 8, 8, 8, 9, 9, 4, 4, 4, 5, 5, 5, 6, 6, 4, 6, 5, 7, 7, 7, 8, 8, 5, 5, 6, 6, 6, 6, 7, 7, 7, 7, 7, 8, 8, 8, 9, 9, 6, 7, 6, 8, 7, 8, 9, 9, 7, 9, 7, 10, 10, 10, 11, 11, 8, 8, 9, 9, 9, 9, 10, 10, 10, 10, 10, 11, 11, 11, 12, 12 ] VEREDICTE:=[ [ 0, 1, 3 ], [ 1, 2, 3 ], [ 0, 1, 2, 3 ], [ 0, 1, 3, 4 ], [ 1, 2, 3, 4 ], [ 0, 1, 2, 3, 4 ], [ 0, 1, 5 ], [ 0, 2, 5 ], [ 1, 2, 5 ], [ 0, 1, 2, 5 ], [ 0, 3, 5 ], [ 0, 1, 3, 5 ], [ 2, 3, 5 ], [ 0, 2, 3, 5 ], [ 1, 2, 3, 5 ], [ 0, 1, 2, 3, 5 ], [ 1, 4, 5 ], [ 0, 1, 4, 5 ], [ 2, 4, 5 ], [ 0, 2, 4, 5 ], [ 1, 2, 4, 5 ], [ 0, 1, 2, 4, 5 ], [ 3, 4, 5 ], [ 0, 3, 4, 5 ], [ 1, 3, 4, 5 ], [ 0, 1, 3, 4, 5 ], [ 2, 3, 4, 5 ], [ 0, 2, 3, 4, 5 ], [ 1, 2, 3, 4, 5 ], [ 0, 1, 2, 3, 4, 5 ], [ 0, 1, 6 ], [ 1, 2, 6 ], [ 0, 1, 2, 6 ], [ 0, 3, 6 ], [ 1, 3, 6 ], [ 0, 1, 3, 6 ], [ 2, 3, 6 ], [ 0, 2, 3, 6 ], [ 1, 2, 3, 6 ], [ 0, 1, 2, 3, 6 ], [ 1, 4, 6 ], [ 0, 1, 4, 6 ], [ 1, 2, 4, 6 ], [ 0, 1, 2, 4, 6 ], [ 3, 4, 6 ], [ 0, 3, 4, 6 ], [ 1, 3, 4, 6 ], [ 0, 1, 3, 4, 6 ], [ 2, 3, 4, 6 ], [ 0, 2, 3, 4, 6 ], [ 1, 2, 3, 4, 6 ], [ 0, 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4, 5, 6 ], 121>, <[ 1, 3, 4, 5, 6 ], 122>, <[ 0, 1, 3, 4, 5, 6 ], 123>, <[ 2, 3, 4, 5, 6 ], 124>, <[ 0, 2, 3, 4, 5, 6 ], 125>, <[ 1, 2, 3, 4, 5, 6 ], 126>, <[ 0, 1, 2, 3, 4, 5, 6 ], 127> ] Total time: 3.759 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.32.42.proxycache.rima-tde.net. (80.58.32.42) Time: Wed Dec 24 06:29:27 2003 Input: /* Klein quartic */ MAX:=6; c:=5; g:=3; semi:=[0,3]; /* basic del semigrup */ i_cond:=c-g; pertany:=func; gaps:=[i:i in [1..c-1]|not pertany(i)]; lambda:=func; lambdainv:=func; /* oplus, leq, nu */ oplus:=func; inferior:=func; ominus:=func; N:=func; nu:=func; /* order bound */ dORD:=func; Lconjunts:=[[0]]; Lmcinf:=[[0]]; Linterseccioinf:=[1]; Lunioinf:=[1]; index:=function(llista) i:=0; for j in llista do i:=i+2^j; end for; return(i); end function; /* mcinf:=function(Lconjunts,Lmcinf,llista) p:=Position(Lconjunts,llista); if p eq 0 then return -1; else return Lmcinf[p]; end if; end function; interseccioinf:=function(Lconjunts,Linterseccioinf,llista) p:=Position(Lconjunts,llista); if p eq 0 then return -1; else return Linterseccioinf[p]; end if; end function; unioinf:=function(Lconjunts,Lunioinf,llista) p:=Position(Lconjunts,llista); if p eq 0 then return -1; else return Lunioinf[p]; end if; end function; */ actualitzaconjunts:=function (Lconjunts,llista) return(Append(Lconjunts,llista)); end function; actualitzamcinf:=function(Lmcinf,llista) maxc:=llista[1]; if (maxc eq 0) then return (Append(Lmcinf,[0])); end if; trobat:=false; while not trobat do while not inferior(maxc,llista[1]) do maxc:=maxc-1; end while; j:=2; while j le #llista and inferior(maxc,llista[j]) do j:=j+1; end while; if j eq #llista+1 then trobat:=true; end if; maxc:=maxc-1; end while; maxc:=maxc+1; mcinfllista:=[maxc]; for h in gaps do candidat:=lambdainv(lambda(maxc)-h); if candidat gt 0 then j:=1; while j le #llista and inferior(candidat,llista[j]) do j:=j+1; end while; if j eq #llista+1 then mcinfllista:=Append(mcinfllista,candidat); end if; end if; end for; return(Append(Lmcinf,mcinfllista)); end function; actualitzainterseccioinf:=function(Lconjunts,Lmcinf,Linterseccioinf,Lunioinf,llista) if #llista eq 1 then return Append(Linterseccioinf,nu(llista[1])); else return Append(Linterseccioinf,Lunioinf[index(Lmcinf[index(llista)])]); end if; end function; actualitzaunioinf:=function(Lconjunts,Linterseccioinf,Lunioinf,llista) if #llista eq 1 then return Append(Lunioinf,nu(llista[1])); else return Append(Lunioinf, Lunioinf[index([llista[i]:i in [1..(#llista-1)]])]+nu(llista[#llista])-Linterseccioinf[index(llista)]); end if; end function; for i in [1..MAX] do conjuntsaux:=Lconjunts; llista:=[i]; Lconjunts:=actualitzaconjunts(Lconjunts,llista); Lmcinf:=actualitzamcinf(Lmcinf,llista); Linterseccioinf:=actualitzainterseccioinf(Lconjunts,Lmcinf,Linterseccioinf,Lunioinf,llista); Lunioinf:=actualitzaunioinf(Lconjunts,Linterseccioinf,Lunioinf,llista); for conj in conjuntsaux do llista:=Append(conj,i); Lconjunts:=actualitzaconjunts(Lconjunts,llista); Lmcinf:=actualitzamcinf(Lmcinf,llista); Linterseccioinf:=actualitzainterseccioinf(Lconjunts,Lmcinf,Linterseccioinf,Lunioinf,llista); Lunioinf:=actualitzaunioinf(Lconjunts,Linterseccioinf,Lunioinf,llista); end for; end for; joinsets:=function(llista) unio:={}; for conj in llista do unio:=unio join conj; end for; return unio; end function; /* l:=#Lconjunts; print "CONJUNTS="; ; print "MCINF="; ; print "INTERSECCIOINF="; Linterseccioinf; print "UNIOINF="; Lunioinf;*/ unioasac:=[#joinsets({N(i):i in llista}):llista in Lconjunts]; errors:=[Lunioinf[i]-unioasac[i]:i in [1..#unioasac]]; printf "VEREDICTE:="; [Lconjunts[i]:i in [1..#errors]|errors[i] ne 0]; /*r:=2; Subsets({0..MAX},r);*/ Output: Magma V2.10-6 Wed Dec 24 2003 06:29:20 on modular [Seed = 2792415546] ------------------------------------- VEREDICTE:=[ [ 0, 1, 3 ], [ 1, 2, 3 ], [ 0, 1, 2, 3 ], [ 0, 1, 3, 4 ], [ 1, 2, 3, 4 ], [ 0, 1, 2, 3, 4 ], [ 0, 1, 5 ], [ 0, 2, 5 ], [ 1, 2, 5 ], [ 0, 1, 2, 5 ], [ 0, 3, 5 ], [ 0, 1, 3, 5 ], [ 2, 3, 5 ], [ 0, 2, 3, 5 ], [ 1, 2, 3, 5 ], [ 0, 1, 2, 3, 5 ], [ 1, 4, 5 ], [ 0, 1, 4, 5 ], [ 2, 4, 5 ], [ 0, 2, 4, 5 ], [ 1, 2, 4, 5 ], [ 0, 1, 2, 4, 5 ], [ 3, 4, 5 ], [ 0, 3, 4, 5 ], [ 1, 3, 4, 5 ], [ 0, 1, 3, 4, 5 ], [ 2, 3, 4, 5 ], [ 0, 2, 3, 4, 5 ], [ 1, 2, 3, 4, 5 ], [ 0, 1, 2, 3, 4, 5 ], [ 0, 1, 6 ], [ 1, 2, 6 ], [ 0, 1, 2, 6 ], [ 0, 3, 6 ], [ 1, 3, 6 ], [ 0, 1, 3, 6 ], [ 2, 3, 6 ], [ 0, 2, 3, 6 ], [ 1, 2, 3, 6 ], [ 0, 1, 2, 3, 6 ], [ 1, 4, 6 ], [ 0, 1, 4, 6 ], [ 1, 2, 4, 6 ], [ 0, 1, 2, 4, 6 ], [ 3, 4, 6 ], [ 0, 3, 4, 6 ], [ 1, 3, 4, 6 ], [ 0, 1, 3, 4, 6 ], [ 2, 3, 4, 6 ], [ 0, 2, 3, 4, 6 ], [ 1, 2, 3, 4, 6 ], [ 0, 1, 2, 3, 4, 6 ], [ 0, 5, 6 ], [ 0, 1, 5, 6 ], [ 2, 5, 6 ], [ 0, 2, 5, 6 ], [ 1, 2, 5, 6 ], [ 0, 1, 2, 5, 6 ], [ 3, 5, 6 ], [ 0, 3, 5, 6 ], [ 1, 3, 5, 6 ], [ 0, 1, 3, 5, 6 ], [ 2, 3, 5, 6 ], [ 0, 2, 3, 5, 6 ], [ 1, 2, 3, 5, 6 ], [ 0, 1, 2, 3, 5, 6 ], [ 4, 5, 6 ], [ 0, 4, 5, 6 ], [ 1, 4, 5, 6 ], [ 0, 1, 4, 5, 6 ], [ 2, 4, 5, 6 ], [ 0, 2, 4, 5, 6 ], [ 1, 2, 4, 5, 6 ], [ 0, 1, 2, 4, 5, 6 ], [ 3, 4, 5, 6 ], [ 0, 3, 4, 5, 6 ], [ 1, 3, 4, 5, 6 ], [ 0, 1, 3, 4, 5, 6 ], [ 2, 3, 4, 5, 6 ], [ 0, 2, 3, 4, 5, 6 ], [ 1, 2, 3, 4, 5, 6 ], [ 0, 1, 2, 3, 4, 5, 6 ] ] Total time: 3.339 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.32.42.proxycache.rima-tde.net. (80.58.32.42) Time: Wed Dec 24 06:31:20 2003 Input: /* Klein quartic */ /* MAX:=6; c:=5; g:=3; semi:=[0,3]; */ /* Hermitian curve */ MAX:=6; c:=12; g:=6; semi:=[0,4,5,8,9,10]; /* basic del semigrup */ i_cond:=c-g; pertany:=func; gaps:=[i:i in [1..c-1]|not pertany(i)]; lambda:=func; lambdainv:=func; /* oplus, leq, nu */ oplus:=func; inferior:=func; ominus:=func; N:=func; nu:=func; /* order bound */ dORD:=func; Lconjunts:=[[0]]; Lmcinf:=[[0]]; Linterseccioinf:=[1]; Lunioinf:=[1]; index:=function(llista) i:=0; for j in llista do i:=i+2^j; end for; return(i); end function; /* mcinf:=function(Lconjunts,Lmcinf,llista) p:=Position(Lconjunts,llista); if p eq 0 then return -1; else return Lmcinf[p]; end if; end function; interseccioinf:=function(Lconjunts,Linterseccioinf,llista) p:=Position(Lconjunts,llista); if p eq 0 then return -1; else return Linterseccioinf[p]; end if; end function; unioinf:=function(Lconjunts,Lunioinf,llista) p:=Position(Lconjunts,llista); if p eq 0 then return -1; else return Lunioinf[p]; end if; end function; */ actualitzaconjunts:=function (Lconjunts,llista) return(Append(Lconjunts,llista)); end function; actualitzamcinf:=function(Lmcinf,llista) maxc:=llista[1]; if (maxc eq 0) then return (Append(Lmcinf,[0])); end if; trobat:=false; while not trobat do while not inferior(maxc,llista[1]) do maxc:=maxc-1; end while; j:=2; while j le #llista and inferior(maxc,llista[j]) do j:=j+1; end while; if j eq #llista+1 then trobat:=true; end if; maxc:=maxc-1; end while; maxc:=maxc+1; mcinfllista:=[maxc]; for h in gaps do candidat:=lambdainv(lambda(maxc)-h); if candidat gt 0 then j:=1; while j le #llista and inferior(candidat,llista[j]) do j:=j+1; end while; if j eq #llista+1 then mcinfllista:=Append(mcinfllista,candidat); end if; end if; end for; return(Append(Lmcinf,mcinfllista)); end function; actualitzainterseccioinf:=function(Lconjunts,Lmcinf,Linterseccioinf,Lunioinf,llista) if #llista eq 1 then return Append(Linterseccioinf,nu(llista[1])); else return Append(Linterseccioinf,Lunioinf[index(Lmcinf[index(llista)])]); end if; end function; actualitzaunioinf:=function(Lconjunts,Linterseccioinf,Lunioinf,llista) if #llista eq 1 then return Append(Lunioinf,nu(llista[1])); else return Append(Lunioinf, Lunioinf[index([llista[i]:i in [1..(#llista-1)]])]+nu(llista[#llista])-Linterseccioinf[index(llista)]); end if; end function; for i in [1..MAX] do conjuntsaux:=Lconjunts; llista:=[i]; Lconjunts:=actualitzaconjunts(Lconjunts,llista); Lmcinf:=actualitzamcinf(Lmcinf,llista); Linterseccioinf:=actualitzainterseccioinf(Lconjunts,Lmcinf,Linterseccioinf,Lunioinf,llista); Lunioinf:=actualitzaunioinf(Lconjunts,Linterseccioinf,Lunioinf,llista); for conj in conjuntsaux do llista:=Append(conj,i); Lconjunts:=actualitzaconjunts(Lconjunts,llista); Lmcinf:=actualitzamcinf(Lmcinf,llista); Linterseccioinf:=actualitzainterseccioinf(Lconjunts,Lmcinf,Linterseccioinf,Lunioinf,llista); Lunioinf:=actualitzaunioinf(Lconjunts,Linterseccioinf,Lunioinf,llista); end for; end for; joinsets:=function(llista) unio:={}; for conj in llista do unio:=unio join conj; end for; return unio; end function; /* l:=#Lconjunts; print "CONJUNTS="; ; print "MCINF="; ; print "INTERSECCIOINF="; Linterseccioinf; print "UNIOINF="; Lunioinf;*/ unioasac:=[#joinsets({N(i):i in llista}):llista in Lconjunts]; errors:=[Lunioinf[i]-unioasac[i]:i in [1..#unioasac]]; printf "VEREDICTE:="; [Lconjunts[i]:i in [1..#errors]|errors[i] ne 0]; /*r:=2; Subsets({0..MAX},r);*/ Output: Magma V2.10-6 Wed Dec 24 2003 06:31:13 on modular [Seed = 3076649402] ------------------------------------- VEREDICTE:=[ [ 0, 1, 3 ], [ 1, 2, 3 ], [ 0, 1, 2, 3 ], [ 0, 1, 4 ], [ 0, 2, 4 ], [ 1, 2, 4 ], [ 0, 1, 2, 4 ], [ 0, 3, 4 ], [ 0, 1, 3, 4 ], [ 2, 3, 4 ], [ 0, 2, 3, 4 ], [ 1, 2, 3, 4 ], [ 0, 1, 2, 3, 4 ], [ 0, 2, 5 ], [ 1, 2, 5 ], [ 0, 1, 2, 5 ], [ 0, 1, 3, 5 ], [ 2, 3, 5 ], [ 0, 2, 3, 5 ], [ 1, 2, 3, 5 ], [ 0, 1, 2, 3, 5 ], [ 0, 4, 5 ], [ 1, 4, 5 ], [ 0, 1, 4, 5 ], [ 0, 2, 4, 5 ], [ 1, 2, 4, 5 ], [ 0, 1, 2, 4, 5 ], [ 3, 4, 5 ], [ 0, 3, 4, 5 ], [ 1, 3, 4, 5 ], [ 0, 1, 3, 4, 5 ], [ 2, 3, 4, 5 ], [ 0, 2, 3, 4, 5 ], [ 1, 2, 3, 4, 5 ], [ 0, 1, 2, 3, 4, 5 ], [ 0, 1, 6 ], [ 1, 2, 6 ], [ 0, 1, 2, 6 ], [ 0, 3, 6 ], [ 1, 3, 6 ], [ 0, 1, 3, 6 ], [ 2, 3, 6 ], [ 0, 2, 3, 6 ], [ 1, 2, 3, 6 ], [ 0, 1, 2, 3, 6 ], [ 0, 4, 6 ], [ 0, 1, 4, 6 ], [ 2, 4, 6 ], [ 0, 2, 4, 6 ], [ 1, 2, 4, 6 ], [ 0, 1, 2, 4, 6 ], [ 3, 4, 6 ], [ 0, 3, 4, 6 ], [ 1, 3, 4, 6 ], [ 0, 1, 3, 4, 6 ], [ 2, 3, 4, 6 ], [ 0, 2, 3, 4, 6 ], [ 1, 2, 3, 4, 6 ], [ 0, 1, 2, 3, 4, 6 ], [ 1, 5, 6 ], [ 0, 1, 5, 6 ], [ 0, 2, 5, 6 ], [ 1, 2, 5, 6 ], [ 0, 1, 2, 5, 6 ], [ 3, 5, 6 ], [ 0, 3, 5, 6 ], [ 1, 3, 5, 6 ], [ 0, 1, 3, 5, 6 ], [ 2, 3, 5, 6 ], [ 0, 2, 3, 5, 6 ], [ 1, 2, 3, 5, 6 ], [ 0, 1, 2, 3, 5, 6 ], [ 4, 5, 6 ], [ 0, 4, 5, 6 ], [ 1, 4, 5, 6 ], [ 0, 1, 4, 5, 6 ], [ 2, 4, 5, 6 ], [ 0, 2, 4, 5, 6 ], [ 1, 2, 4, 5, 6 ], [ 0, 1, 2, 4, 5, 6 ], [ 3, 4, 5, 6 ], [ 0, 3, 4, 5, 6 ], [ 1, 3, 4, 5, 6 ], [ 0, 1, 3, 4, 5, 6 ], [ 2, 3, 4, 5, 6 ], [ 0, 2, 3, 4, 5, 6 ], [ 1, 2, 3, 4, 5, 6 ], [ 0, 1, 2, 3, 4, 5, 6 ] ] Total time: 3.519 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.32.42.proxycache.rima-tde.net. (80.58.32.42) Time: Wed Dec 24 06:40:32 2003 Input: a:=0; a_b:=6; Output: Magma V2.10-6 Wed Dec 24 2003 06:40:29 on modular [Seed = 4013534158] ------------------------------------- Total time: 3.059 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.32.42.proxycache.rima-tde.net. (80.58.32.42) Time: Wed Dec 24 06:40:51 2003 Input: a:=4; a_b:=6; a+a_b; Output: Magma V2.10-6 Wed Dec 24 2003 06:40:48 on modular [Seed = 3811944367] ------------------------------------- 10 Total time: 3.069 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.32.42.proxycache.rima-tde.net. (80.58.32.42) Time: Wed Dec 24 06:46:22 2003 Input: a:=4; a_b:=6; a+a_b; a eq a_b; Output: Magma V2.10-6 Wed Dec 24 2003 06:46:19 on modular [Seed = 433019545] ------------------------------------- 10 false Total time: 3.069 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.32.42.proxycache.rima-tde.net. (80.58.32.42) Time: Wed Dec 24 06:46:36 2003 Input: a:=4; a_b:=6; a+a_b; not(a eq a_b); Output: Magma V2.10-6 Wed Dec 24 2003 06:46:32 on modular [Seed = 365123206] ------------------------------------- 10 true Total time: 3.549 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.32.42.proxycache.rima-tde.net. (80.58.32.42) Time: Wed Dec 24 07:01:51 2003 Input: /* Klein quartic */ MAX:=6; c:=5; g:=3; semi:=[0,3]; /* Hermitian curve */ /* MAX:=6; c:=12; g:=6; semi:=[0,4,5,8,9,10]; */ /* basic del semigrup */ i_cond:=c-g; pertany:=func; gaps:=[i:i in [1..c-1]|not pertany(i)]; lambda:=func; lambdainv:=func; /* oplus, leq, nu */ oplus:=func; inferior:=func; ominus:=func; N:=func; nu:=func; /* order bound */ dORD:=func; Lconjunts:=[[0]]; Lmcinf:=[[0]]; Linterseccioinf:=[1]; Lunioinf:=[1]; index:=function(llista) i:=0; for j in llista do i:=i+2^j; end for; return(i); end function; /* mcinf:=function(Lconjunts,Lmcinf,llista) p:=Position(Lconjunts,llista); if p eq 0 then return -1; else return Lmcinf[p]; end if; end function; interseccioinf:=function(Lconjunts,Linterseccioinf,llista) p:=Position(Lconjunts,llista); if p eq 0 then return -1; else return Linterseccioinf[p]; end if; end function; unioinf:=function(Lconjunts,Lunioinf,llista) p:=Position(Lconjunts,llista); if p eq 0 then return -1; else return Lunioinf[p]; end if; end function; */ actualitzaconjunts:=function (Lconjunts,llista) return(Append(Lconjunts,llista)); end function; actualitzamcinf:=function(Lmcinf,llista) maxc:=llista[1]; if (maxc eq 0) then return (Append(Lmcinf,[0])); end if; trobat:=false; while not trobat do while not inferior(maxc,llista[1]) do maxc:=maxc-1; end while; j:=2; while j le #llista and inferior(maxc,llista[j]) do j:=j+1; end while; if j eq #llista+1 then trobat:=true; end if; maxc:=maxc-1; end while; maxc:=maxc+1; mcinfllista:=[maxc]; for h in gaps do candidat:=lambdainv(lambda(maxc)-h); if candidat gt 0 then j:=1; while j le #llista and inferior(candidat,llista[j]) do j:=j+1; end while; if j eq #llista+1 then mcinfllista:=Append(mcinfllista,candidat); end if; end if; end for; return(Append(Lmcinf,mcinfllista)); end function; interseccio_ultim_unio_dels_altres:=function(llista) ultim:=llista[#llista]; if (maxc eq 0) then return ([0]); end if; maxc:=ultim-2; trobat:=false; while not trobat do while not inferior(maxc,ultim) do maxc:=maxc-1; end while; j:=1; while j le #llista-1 and not(inferior(maxc,llista[j])) do j:=j+1; end while; if j le #llista-1 then trobat:=true; end if; maxc:=maxc-1; end while; maxc:=maxc+1; ret:=[maxc]; for h in gaps do candidat:=lambdainv(lambda(maxc)-h); if candidat gt 0 and inferior(candidat,ultim) then j:=1; while j le #llista-1 and not(inferior(candidat,llista[j])) do j:=j+1; end while; if j le #llista-1 then ret:=Append(ret,candidat); end if; end if; end for; return(ret); end function; actualitzainterseccioinf:=function(Lconjunts,Lmcinf,Linterseccioinf,Lunioinf,llista) if #llista eq 1 then return Append(Linterseccioinf,nu(llista[1])); else return Append(Linterseccioinf,Lunioinf[index(Lmcinf[index(llista)])]); end if; end function; actualitzaunioinf:=function(Lconjunts,Linterseccioinf,Lunioinf,llista) if #llista eq 1 then return Append(Lunioinf,nu(llista[1])); else return Append(Lunioinf, Lunioinf[index([llista[i]:i in [1..(#llista-1)]])]+nu(llista[#llista])-Linterseccioinf[index(interseccio_ultim_unio_dels_altres(llista))]); end if; end function; for i in [1..MAX] do conjuntsaux:=Lconjunts; llista:=[i]; Lconjunts:=actualitzaconjunts(Lconjunts,llista); Lmcinf:=actualitzamcinf(Lmcinf,llista); Linterseccioinf:=actualitzainterseccioinf(Lconjunts,Lmcinf,Linterseccioinf,Lunioinf,llista); Lunioinf:=actualitzaunioinf(Lconjunts,Linterseccioinf,Lunioinf,llista); for conj in conjuntsaux do llista:=Append(conj,i); Lconjunts:=actualitzaconjunts(Lconjunts,llista); Lmcinf:=actualitzamcinf(Lmcinf,llista); Linterseccioinf:=actualitzainterseccioinf(Lconjunts,Lmcinf,Linterseccioinf,Lunioinf,llista); Lunioinf:=actualitzaunioinf(Lconjunts,Linterseccioinf,Lunioinf,llista); end for; end for; joinsets:=function(llista) unio:={}; for conj in llista do unio:=unio join conj; end for; return unio; end function; /* l:=#Lconjunts; print "CONJUNTS="; ; print "MCINF="; ; print "INTERSECCIOINF="; Linterseccioinf; print "UNIOINF="; Lunioinf;*/ unioasac:=[#joinsets({N(i):i in llista}):llista in Lconjunts]; errors:=[Lunioinf[i]-unioasac[i]:i in [1..#unioasac]]; printf "VEREDICTE:="; [Lconjunts[i]:i in [1..#errors]|errors[i] ne 0]; /*r:=2; Subsets({0..MAX},r);*/ Output: Magma V2.10-6 Wed Dec 24 2003 07:01:44 on modular [Seed = 2655527357] ------------------------------------- >> if (maxc eq 0) then ^ User error: Identifier 'maxc' has not been declared or assigned >> lista[#llista])-Linterseccioinf[index(interseccio_ultim_unio_dels_altres(ll ^ User error: Identifier 'interseccio_ultim_unio_dels_altres' has not been declared or assigned >> Lunioinf:=actualitzaunioinf(Lconjunts,Linterseccioinf,Lunioinf,llista); ^ User error: Identifier 'actualitzaunioinf' has not been declared or assigned VEREDICTE:=[] Total time: 3.399 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.32.42.proxycache.rima-tde.net. (80.58.32.42) Time: Wed Dec 24 07:03:52 2003 Input: /* Klein quartic */ MAX:=6; c:=5; g:=3; semi:=[0,3]; /* Hermitian curve */ /* MAX:=6; c:=12; g:=6; semi:=[0,4,5,8,9,10]; */ /* basic del semigrup */ i_cond:=c-g; pertany:=func; gaps:=[i:i in [1..c-1]|not pertany(i)]; lambda:=func; lambdainv:=func; /* oplus, leq, nu */ oplus:=func; inferior:=func; ominus:=func; N:=func; nu:=func; /* order bound */ dORD:=func; Lconjunts:=[[0]]; Lmcinf:=[[0]]; Linterseccioinf:=[1]; Lunioinf:=[1]; index:=function(llista) i:=0; for j in llista do i:=i+2^j; end for; return(i); end function; /* mcinf:=function(Lconjunts,Lmcinf,llista) p:=Position(Lconjunts,llista); if p eq 0 then return -1; else return Lmcinf[p]; end if; end function; interseccioinf:=function(Lconjunts,Linterseccioinf,llista) p:=Position(Lconjunts,llista); if p eq 0 then return -1; else return Linterseccioinf[p]; end if; end function; unioinf:=function(Lconjunts,Lunioinf,llista) p:=Position(Lconjunts,llista); if p eq 0 then return -1; else return Lunioinf[p]; end if; end function; */ actualitzaconjunts:=function (Lconjunts,llista) return(Append(Lconjunts,llista)); end function; actualitzamcinf:=function(Lmcinf,llista) maxc:=llista[1]; if (maxc eq 0) then return (Append(Lmcinf,[0])); end if; trobat:=false; while not trobat do while not inferior(maxc,llista[1]) do maxc:=maxc-1; end while; j:=2; while j le #llista and inferior(maxc,llista[j]) do j:=j+1; end while; if j eq #llista+1 then trobat:=true; end if; maxc:=maxc-1; end while; maxc:=maxc+1; mcinfllista:=[maxc]; for h in gaps do candidat:=lambdainv(lambda(maxc)-h); if candidat gt 0 then j:=1; while j le #llista and inferior(candidat,llista[j]) do j:=j+1; end while; if j eq #llista+1 then mcinfllista:=Append(mcinfllista,candidat); end if; end if; end for; return(Append(Lmcinf,mcinfllista)); end function; interseccio_ultim_unio_dels_altres:=function(llista) ultim:=llista[#llista]; maxc:=ultim-1; trobat:=false; while not trobat do while not inferior(maxc,ultim) do maxc:=maxc-1; end while; j:=1; while j le #llista-1 and not(inferior(maxc,llista[j])) do j:=j+1; end while; if j le #llista-1 then trobat:=true; end if; maxc:=maxc-1; end while; maxc:=maxc+1; ret:=[maxc]; for h in gaps do candidat:=lambdainv(lambda(maxc)-h); if candidat gt 0 and inferior(candidat,ultim) then j:=1; while j le #llista-1 and not(inferior(candidat,llista[j])) do j:=j+1; end while; if j le #llista-1 then ret:=Append(ret,candidat); end if; end if; end for; return(ret); end function; actualitzainterseccioinf:=function(Lconjunts,Lmcinf,Linterseccioinf,Lunioinf,llista) if #llista eq 1 then return Append(Linterseccioinf,nu(llista[1])); else return Append(Linterseccioinf,Lunioinf[index(Lmcinf[index(llista)])]); end if; end function; actualitzaunioinf:=function(Lconjunts,Linterseccioinf,Lunioinf,llista) if #llista eq 1 then return Append(Lunioinf,nu(llista[1])); else return Append(Lunioinf, Lunioinf[index([llista[i]:i in [1..(#llista-1)]])]+nu(llista[#llista])-Linterseccioinf[index(interseccio_ultim_unio_dels_altres(llista))]); end if; end function; for i in [1..MAX] do conjuntsaux:=Lconjunts; llista:=[i]; Lconjunts:=actualitzaconjunts(Lconjunts,llista); Lmcinf:=actualitzamcinf(Lmcinf,llista); Linterseccioinf:=actualitzainterseccioinf(Lconjunts,Lmcinf,Linterseccioinf,Lunioinf,llista); Lunioinf:=actualitzaunioinf(Lconjunts,Linterseccioinf,Lunioinf,llista); for conj in conjuntsaux do llista:=Append(conj,i); Lconjunts:=actualitzaconjunts(Lconjunts,llista); Lmcinf:=actualitzamcinf(Lmcinf,llista); Linterseccioinf:=actualitzainterseccioinf(Lconjunts,Lmcinf,Linterseccioinf,Lunioinf,llista); Lunioinf:=actualitzaunioinf(Lconjunts,Linterseccioinf,Lunioinf,llista); end for; end for; joinsets:=function(llista) unio:={}; for conj in llista do unio:=unio join conj; end for; return unio; end function; /* l:=#Lconjunts; print "CONJUNTS="; ; print "MCINF="; ; print "INTERSECCIOINF="; Linterseccioinf; print "UNIOINF="; Lunioinf;*/ unioasac:=[#joinsets({N(i):i in llista}):llista in Lconjunts]; errors:=[Lunioinf[i]-unioasac[i]:i in [1..#unioasac]]; printf "VEREDICTE:="; [Lconjunts[i]:i in [1..#errors]|errors[i] ne 0]; /*r:=2; Subsets({0..MAX},r);*/ Output: Magma V2.10-6 Wed Dec 24 2003 07:03:45 on modular [Seed = 2487364414] ------------------------------------- VEREDICTE:=[ [ 1, 2, 5 ], [ 0, 1, 2, 5 ], [ 2, 3, 5 ], [ 0, 2, 3, 5 ], [ 1, 2, 3, 5 ], [ 0, 1, 2, 3, 5 ], [ 1, 2, 4, 5 ], [ 0, 1, 2, 4, 5 ], [ 2, 3, 4, 5 ], [ 0, 2, 3, 4, 5 ], [ 1, 2, 3, 4, 5 ], [ 0, 1, 2, 3, 4, 5 ], [ 1, 2, 5, 6 ], [ 0, 1, 2, 5, 6 ], [ 2, 3, 5, 6 ], [ 0, 2, 3, 5, 6 ], [ 1, 2, 3, 5, 6 ], [ 0, 1, 2, 3, 5, 6 ], [ 1, 2, 4, 5, 6 ], [ 0, 1, 2, 4, 5, 6 ], [ 2, 3, 4, 5, 6 ], [ 0, 2, 3, 4, 5, 6 ], [ 1, 2, 3, 4, 5, 6 ], [ 0, 1, 2, 3, 4, 5, 6 ] ] Total time: 3.299 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.32.42.proxycache.rima-tde.net. (80.58.32.42) Time: Wed Dec 24 07:05:30 2003 Input: /* Klein quartic */ MAX:=6; c:=5; g:=3; semi:=[0,3]; /* Hermitian curve */ /* MAX:=6; c:=12; g:=6; semi:=[0,4,5,8,9,10]; */ /* basic del semigrup */ i_cond:=c-g; pertany:=func; gaps:=[i:i in [1..c-1]|not pertany(i)]; lambda:=func; lambdainv:=func; /* oplus, leq, nu */ oplus:=func; inferior:=func; ominus:=func; N:=func; nu:=func; /* order bound */ dORD:=func; Lconjunts:=[[0]]; Lmcinf:=[[0]]; Linterseccioinf:=[1]; Lunioinf:=[1]; index:=function(llista) i:=0; for j in llista do i:=i+2^j; end for; return(i); end function; /* mcinf:=function(Lconjunts,Lmcinf,llista) p:=Position(Lconjunts,llista); if p eq 0 then return -1; else return Lmcinf[p]; end if; end function; interseccioinf:=function(Lconjunts,Linterseccioinf,llista) p:=Position(Lconjunts,llista); if p eq 0 then return -1; else return Linterseccioinf[p]; end if; end function; unioinf:=function(Lconjunts,Lunioinf,llista) p:=Position(Lconjunts,llista); if p eq 0 then return -1; else return Lunioinf[p]; end if; end function; */ actualitzaconjunts:=function (Lconjunts,llista) return(Append(Lconjunts,llista)); end function; actualitzamcinf:=function(Lmcinf,llista) maxc:=llista[1]; if (maxc eq 0) then return (Append(Lmcinf,[0])); end if; trobat:=false; while not trobat do while not inferior(maxc,llista[1]) do maxc:=maxc-1; end while; j:=2; while j le #llista and inferior(maxc,llista[j]) do j:=j+1; end while; if j eq #llista+1 then trobat:=true; end if; maxc:=maxc-1; end while; maxc:=maxc+1; mcinfllista:=[maxc]; for h in gaps do candidat:=lambdainv(lambda(maxc)-h); if candidat gt 0 then j:=1; while j le #llista and inferior(candidat,llista[j]) do j:=j+1; end while; if j eq #llista+1 then mcinfllista:=Append(mcinfllista,candidat); end if; end if; end for; return(Append(Lmcinf,mcinfllista)); end function; interseccio_ultim_unio_dels_altres:=function(llista) ultim:=llista[#llista]; maxc:=ultim-1; trobat:=false; while not trobat do while not inferior(maxc,ultim) do maxc:=maxc-1; end while; j:=1; while j le #llista-1 and not(inferior(maxc,llista[j])) do j:=j+1; end while; if j le #llista-1 then trobat:=true; end if; maxc:=maxc-1; end while; maxc:=maxc+1; ret:=[maxc]; for h in gaps do candidat:=lambdainv(lambda(maxc)-h); if candidat gt 0 and inferior(candidat,ultim) then j:=1; while j le #llista-1 and not(inferior(candidat,llista[j])) do j:=j+1; end while; if j le #llista-1 then ret:=Append(ret,candidat); end if; end if; end for; return(ret); end function; actualitzainterseccioinf:=function(Lconjunts,Lmcinf,Linterseccioinf,Lunioinf,llista) if #llista eq 1 then return Append(Linterseccioinf,nu(llista[1])); else return Append(Linterseccioinf,Lunioinf[index(Lmcinf[index(llista)])]); end if; end function; actualitzaunioinf:=function(Lconjunts,Linterseccioinf,Lunioinf,llista) if #llista eq 1 then return Append(Lunioinf,nu(llista[1])); else return Append(Lunioinf, Lunioinf[index([llista[i]:i in [1..(#llista-1)]])]+nu(llista[#llista])-Linterseccioinf[index(interseccio_ultim_unio_dels_altres(llista))]); end if; end function; for i in [1..MAX] do conjuntsaux:=Lconjunts; llista:=[i]; Lconjunts:=actualitzaconjunts(Lconjunts,llista); Lmcinf:=actualitzamcinf(Lmcinf,llista); Linterseccioinf:=actualitzainterseccioinf(Lconjunts,Lmcinf,Linterseccioinf,Lunioinf,llista); Lunioinf:=actualitzaunioinf(Lconjunts,Linterseccioinf,Lunioinf,llista); for conj in conjuntsaux do llista:=Append(conj,i); Lconjunts:=actualitzaconjunts(Lconjunts,llista); Lmcinf:=actualitzamcinf(Lmcinf,llista); Linterseccioinf:=actualitzainterseccioinf(Lconjunts,Lmcinf,Linterseccioinf,Lunioinf,llista); Lunioinf:=actualitzaunioinf(Lconjunts,Linterseccioinf,Lunioinf,llista); end for; end for; joinsets:=function(llista) unio:={}; for conj in llista do unio:=unio join conj; end for; return unio; end function; /* l:=#Lconjunts; print "CONJUNTS="; ; print "MCINF="; ; print "INTERSECCIOINF="; Linterseccioinf; print "UNIOINF="; Lunioinf;*/ unioasac:=[#joinsets({N(i):i in llista}):llista in Lconjunts]; errors:=[Lunioinf[i]-unioasac[i]:i in [1..#unioasac]]; printf "VEREDICTE:="; [Lconjunts[i]:i in [1..#errors]|errors[i] ne 0]; /*r:=2; Subsets({0..MAX},r);*/ interseccio_ultim_unio_dels_altres([1,2,5]); [lambda(i):i in [1,2,5]]; Output: Magma V2.10-6 Wed Dec 24 2003 07:05:26 on modular [Seed = 3127641270] ------------------------------------- VEREDICTE:=[ [ 1, 2, 5 ], [ 0, 1, 2, 5 ], [ 2, 3, 5 ], [ 0, 2, 3, 5 ], [ 1, 2, 3, 5 ], [ 0, 1, 2, 3, 5 ], [ 1, 2, 4, 5 ], [ 0, 1, 2, 4, 5 ], [ 2, 3, 4, 5 ], [ 0, 2, 3, 4, 5 ], [ 1, 2, 3, 4, 5 ], [ 0, 1, 2, 3, 4, 5 ], [ 1, 2, 5, 6 ], [ 0, 1, 2, 5, 6 ], [ 2, 3, 5, 6 ], [ 0, 2, 3, 5, 6 ], [ 1, 2, 3, 5, 6 ], [ 0, 1, 2, 3, 5, 6 ], [ 1, 2, 4, 5, 6 ], [ 0, 1, 2, 4, 5, 6 ], [ 2, 3, 4, 5, 6 ], [ 0, 2, 3, 4, 5, 6 ], [ 1, 2, 3, 4, 5, 6 ], [ 0, 1, 2, 3, 4, 5, 6 ] ] [ 2, 1 ] [ 3, 5, 8 ] Total time: 3.299 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.32.42.proxycache.rima-tde.net. (80.58.32.42) Time: Wed Dec 24 07:13:52 2003 Input: /* Klein quartic */ MAX:=6; c:=5; g:=3; semi:=[0,3]; /* Hermitian curve */ /* MAX:=6; c:=12; g:=6; semi:=[0,4,5,8,9,10]; */ /* basic del semigrup */ i_cond:=c-g; pertany:=func; gaps:=[i:i in [1..c-1]|not pertany(i)]; lambda:=func; lambdainv:=func; /* oplus, leq, nu */ oplus:=func; inferior:=func; ominus:=func; N:=func; nu:=func; /* order bound */ dORD:=func; Lconjunts:=[[0]]; Lmcinf:=[[0]]; Linterseccioinf:=[1]; Lunioinf:=[1]; index:=function(llista) i:=0; for j in llista do i:=i+2^j; end for; return(i); end function; /* mcinf:=function(Lconjunts,Lmcinf,llista) p:=Position(Lconjunts,llista); if p eq 0 then return -1; else return Lmcinf[p]; end if; end function; interseccioinf:=function(Lconjunts,Linterseccioinf,llista) p:=Position(Lconjunts,llista); if p eq 0 then return -1; else return Linterseccioinf[p]; end if; end function; unioinf:=function(Lconjunts,Lunioinf,llista) p:=Position(Lconjunts,llista); if p eq 0 then return -1; else return Lunioinf[p]; end if; end function; */ actualitzaconjunts:=function (Lconjunts,llista) return(Append(Lconjunts,llista)); end function; actualitzamcinf:=function(Lmcinf,llista) maxc:=llista[1]; if (maxc eq 0) then return (Append(Lmcinf,[0])); end if; trobat:=false; while not trobat do while not inferior(maxc,llista[1]) do maxc:=maxc-1; end while; j:=2; while j le #llista and inferior(maxc,llista[j]) do j:=j+1; end while; if j eq #llista+1 then trobat:=true; end if; maxc:=maxc-1; end while; maxc:=maxc+1; mcinfllista:=[maxc]; for h in gaps do candidat:=lambdainv(lambda(maxc)-h); if candidat gt 0 then j:=1; while j le #llista and inferior(candidat,llista[j]) do j:=j+1; end while; if j eq #llista+1 then mcinfllista:=Append(mcinfllista,candidat); end if; end if; end for; return(Append(Lmcinf,mcinfllista)); end function; interseccio_ultim_unio_dels_altres:=function(llista) ultim:=llista[#llista]; maxc:=ultim-1; trobat:=false; while not trobat do while not inferior(maxc,ultim) do maxc:=maxc-1; end while; j:=1; while j le #llista-1 and not(inferior(maxc,llista[j])) do j:=j+1; end while; if j le #llista-1 then trobat:=true; end if; maxc:=maxc-1; end while; maxc:=maxc+1; ret:=[maxc]; for h in gaps do candidat:=lambdainv(lambda(maxc)-h); if candidat gt 0 and inferior(candidat,ultim) then j:=1; while j le #llista-1 and not(inferior(candidat,llista[j])) do j:=j+1; end while; if j le #llista-1 then ret:=Append(ret,candidat); end if; end if; end for; return(ret); end function; actualitzainterseccioinf:=function(Lconjunts,Lmcinf,Linterseccioinf,Lunioinf,llista) if #llista eq 1 then return Append(Linterseccioinf,nu(llista[1])); else return Append(Linterseccioinf,Lunioinf[index(Lmcinf[index(llista)])]); end if; end function; actualitzaunioinf:=function(Lconjunts,Linterseccioinf,Lunioinf,llista) if #llista eq 1 then return Append(Lunioinf,nu(llista[1])); else return Append(Lunioinf, Lunioinf[index([llista[i]:i in [1..(#llista-1)]])]+nu(llista[#llista])-Linterseccioinf[index(interseccio_ultim_unio_dels_altres(llista))]); end if; end function; for i in [1..MAX] do conjuntsaux:=Lconjunts; llista:=[i]; Lconjunts:=actualitzaconjunts(Lconjunts,llista); Lmcinf:=actualitzamcinf(Lmcinf,llista); Linterseccioinf:=actualitzainterseccioinf(Lconjunts,Lmcinf,Linterseccioinf,Lunioinf,llista); Lunioinf:=actualitzaunioinf(Lconjunts,Linterseccioinf,Lunioinf,llista); for conj in conjuntsaux do llista:=Append(conj,i); Lconjunts:=actualitzaconjunts(Lconjunts,llista); Lmcinf:=actualitzamcinf(Lmcinf,llista); Linterseccioinf:=actualitzainterseccioinf(Lconjunts,Lmcinf,Linterseccioinf,Lunioinf,llista); Lunioinf:=actualitzaunioinf(Lconjunts,Linterseccioinf,Lunioinf,llista); end for; end for; joinsets:=function(llista) unio:={}; for conj in llista do unio:=unio join conj; end for; return unio; end function; /* l:=#Lconjunts; print "CONJUNTS="; ; print "MCINF="; ; print "INTERSECCIOINF="; Linterseccioinf; print "UNIOINF="; Lunioinf;*/ unioasac:=[#joinsets({N(i):i in llista}):llista in Lconjunts]; errors:=[Lunioinf[i]-unioasac[i]:i in [1..#unioasac]]; printf "VEREDICTE:="; [Lconjunts[i]:i in [1..#errors]|errors[i] ne 0]; /*r:=2; Subsets({0..MAX},r);*/ interseccio_ultim_unio_dels_altres([1,2,5]); [lambda(i):i in [1,2,5]]; i:=index([1,2,5]); Lconjunts[i]; Lunioinf[i]; unioasac[i]; Output: Magma V2.10-6 Wed Dec 24 2003 07:13:44 on modular [Seed = 3913241626] ------------------------------------- VEREDICTE:=[ [ 1, 2, 5 ], [ 0, 1, 2, 5 ], [ 2, 3, 5 ], [ 0, 2, 3, 5 ], [ 1, 2, 3, 5 ], [ 0, 1, 2, 3, 5 ], [ 1, 2, 4, 5 ], [ 0, 1, 2, 4, 5 ], [ 2, 3, 4, 5 ], [ 0, 2, 3, 4, 5 ], [ 1, 2, 3, 4, 5 ], [ 0, 1, 2, 3, 4, 5 ], [ 1, 2, 5, 6 ], [ 0, 1, 2, 5, 6 ], [ 2, 3, 5, 6 ], [ 0, 2, 3, 5, 6 ], [ 1, 2, 3, 5, 6 ], [ 0, 1, 2, 3, 5, 6 ], [ 1, 2, 4, 5, 6 ], [ 0, 1, 2, 4, 5, 6 ], [ 2, 3, 4, 5, 6 ], [ 0, 2, 3, 4, 5, 6 ], [ 1, 2, 3, 4, 5, 6 ], [ 0, 1, 2, 3, 4, 5, 6 ] ] [ 2, 1 ] [ 3, 5, 8 ] [ 1, 2, 5 ] 6 4 Total time: 3.339 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.32.42.proxycache.rima-tde.net. (80.58.32.42) Time: Wed Dec 24 07:20:54 2003 Input: /* Klein quartic */ MAX:=6; c:=5; g:=3; semi:=[0,3]; /* Hermitian curve */ /* MAX:=6; c:=12; g:=6; semi:=[0,4,5,8,9,10]; */ /* basic del semigrup */ i_cond:=c-g; pertany:=func; gaps:=[i:i in [1..c-1]|not pertany(i)]; lambda:=func; lambdainv:=func; /* oplus, leq, nu */ oplus:=func; inferior:=func; ominus:=func; N:=func; nu:=func; /* order bound */ dORD:=func; Lconjunts:=[[0]]; Lmcinf:=[[0]]; Linterseccioinf:=[1]; Lunioinf:=[1]; index:=function(llista) i:=0; for j in llista do i:=i+2^j; end for; return(i); end function; /* mcinf:=function(Lconjunts,Lmcinf,llista) p:=Position(Lconjunts,llista); if p eq 0 then return -1; else return Lmcinf[p]; end if; end function; interseccioinf:=function(Lconjunts,Linterseccioinf,llista) p:=Position(Lconjunts,llista); if p eq 0 then return -1; else return Linterseccioinf[p]; end if; end function; unioinf:=function(Lconjunts,Lunioinf,llista) p:=Position(Lconjunts,llista); if p eq 0 then return -1; else return Lunioinf[p]; end if; end function; */ actualitzaconjunts:=function (Lconjunts,llista) return(Append(Lconjunts,llista)); end function; actualitzamcinf:=function(Lmcinf,llista) maxc:=llista[1]; if (maxc eq 0) then return (Append(Lmcinf,[0])); end if; trobat:=false; while not trobat do while not inferior(maxc,llista[1]) do maxc:=maxc-1; end while; j:=2; while j le #llista and inferior(maxc,llista[j]) do j:=j+1; end while; if j eq #llista+1 then trobat:=true; end if; maxc:=maxc-1; end while; maxc:=maxc+1; mcinfllista:=[maxc]; for h in gaps do candidat:=lambdainv(lambda(maxc)-h); if candidat gt 0 then j:=1; while j le #llista and inferior(candidat,llista[j]) do j:=j+1; end while; if j eq #llista+1 then mcinfllista:=Append(mcinfllista,candidat); end if; end if; end for; return(Append(Lmcinf,mcinfllista)); end function; interseccio_ultim_unio_dels_altres:=function(llista) ultim:=llista[#llista]; maxc:=ultim-1; trobat:=false; while not trobat do while not inferior(maxc,ultim) do maxc:=maxc-1; end while; j:=1; while j le #llista-1 and not(inferior(maxc,llista[j])) do j:=j+1; end while; if j le #llista-1 then trobat:=true; end if; maxc:=maxc-1; end while; maxc:=maxc+1; ret:=[maxc]; for h in gaps do candidat:=lambdainv(lambda(maxc)-h); if candidat gt 0 and inferior(candidat,ultim) then j:=1; while j le #llista-1 and not(inferior(candidat,llista[j])) do j:=j+1; end while; if j le #llista-1 then ret:=Append(ret,candidat); end if; end if; end for; return(index(ret)); end function; actualitzainterseccioinf:=function(Lconjunts,Lmcinf,Linterseccioinf,Lunioinf,llista) if #llista eq 1 then return Append(Linterseccioinf,nu(llista[1])); else return Append(Linterseccioinf,Lunioinf[index(Lmcinf[index(llista)])]); end if; end function; actualitzaunioinf:=function(Lconjunts,Linterseccioinf,Lunioinf,llista) if #llista eq 1 then return Append(Lunioinf,nu(llista[1])); else return Append(Lunioinf, Lunioinf[index([llista[i]:i in [1..(#llista-1)]])] +nu(llista[#llista])-Linterseccioinf[interseccio_ultim_unio_dels_altres(llista)]); end if; end function; for i in [1..MAX] do conjuntsaux:=Lconjunts; llista:=[i]; Lconjunts:=actualitzaconjunts(Lconjunts,llista); Lmcinf:=actualitzamcinf(Lmcinf,llista); Linterseccioinf:=actualitzainterseccioinf(Lconjunts,Lmcinf,Linterseccioinf,Lunioinf,llista); Lunioinf:=actualitzaunioinf(Lconjunts,Linterseccioinf,Lunioinf,llista); for conj in conjuntsaux do llista:=Append(conj,i); Lconjunts:=actualitzaconjunts(Lconjunts,llista); Lmcinf:=actualitzamcinf(Lmcinf,llista); Linterseccioinf:=actualitzainterseccioinf(Lconjunts,Lmcinf,Linterseccioinf,Lunioinf,llista); Lunioinf:=actualitzaunioinf(Lconjunts,Linterseccioinf,Lunioinf,llista); end for; end for; joinsets:=function(llista) unio:={}; for conj in llista do unio:=unio join conj; end for; return unio; end function; /* l:=#Lconjunts; print "CONJUNTS="; ; print "MCINF="; ; print "INTERSECCIOINF="; Linterseccioinf; print "UNIOINF="; Lunioinf;*/ unioasac:=[#joinsets({N(i):i in llista}):llista in Lconjunts]; errors:=[Lunioinf[i]-unioasac[i]:i in [1..#unioasac]]; printf "VEREDICTE:="; [Lconjunts[i]:i in [1..#errors]|errors[i] ne 0]; /*r:=2; Subsets({0..MAX},r);*/ llista:=[1,2,5]; [lambda(i):i in llista]; l:=interseccio_ultim_unio_dels_altres(llista); Lconjunts(l); Linterseccioinf[interseccio_ultim_unio_dels_altres(llista)]); Output: Magma V2.10-6 Wed Dec 24 2003 07:20:51 on modular [Seed = 988578195] ------------------------------------- VEREDICTE:=[ [ 1, 2, 5 ], [ 0, 1, 2, 5 ], [ 2, 3, 5 ], [ 0, 2, 3, 5 ], [ 1, 2, 3, 5 ], [ 0, 1, 2, 3, 5 ], [ 1, 2, 4, 5 ], [ 0, 1, 2, 4, 5 ], [ 2, 3, 4, 5 ], [ 0, 2, 3, 4, 5 ], [ 1, 2, 3, 4, 5 ], [ 0, 1, 2, 3, 4, 5 ], [ 1, 2, 5, 6 ], [ 0, 1, 2, 5, 6 ], [ 2, 3, 5, 6 ], [ 0, 2, 3, 5, 6 ], [ 1, 2, 3, 5, 6 ], [ 0, 1, 2, 3, 5, 6 ], [ 1, 2, 4, 5, 6 ], [ 0, 1, 2, 4, 5, 6 ], [ 2, 3, 4, 5, 6 ], [ 0, 2, 3, 4, 5, 6 ], [ 1, 2, 3, 4, 5, 6 ], [ 0, 1, 2, 3, 4, 5, 6 ] ] [ 3, 5, 8 ] >> Lconjunts(l); ^ Runtime error: Bad argument types Argument types given: RngIntElt, SeqEnum[SeqEnum] >> Linterseccioinf[interseccio_ultim_unio_dels_altres(llista)]); ^ User error: bad syntax Total time: 3.029 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.32.42.proxycache.rima-tde.net. (80.58.32.42) Time: Wed Dec 24 07:21:19 2003 Input: /* Klein quartic */ MAX:=6; c:=5; g:=3; semi:=[0,3]; /* Hermitian curve */ /* MAX:=6; c:=12; g:=6; semi:=[0,4,5,8,9,10]; */ /* basic del semigrup */ i_cond:=c-g; pertany:=func; gaps:=[i:i in [1..c-1]|not pertany(i)]; lambda:=func; lambdainv:=func; /* oplus, leq, nu */ oplus:=func; inferior:=func; ominus:=func; N:=func; nu:=func; /* order bound */ dORD:=func; Lconjunts:=[[0]]; Lmcinf:=[[0]]; Linterseccioinf:=[1]; Lunioinf:=[1]; index:=function(llista) i:=0; for j in llista do i:=i+2^j; end for; return(i); end function; /* mcinf:=function(Lconjunts,Lmcinf,llista) p:=Position(Lconjunts,llista); if p eq 0 then return -1; else return Lmcinf[p]; end if; end function; interseccioinf:=function(Lconjunts,Linterseccioinf,llista) p:=Position(Lconjunts,llista); if p eq 0 then return -1; else return Linterseccioinf[p]; end if; end function; unioinf:=function(Lconjunts,Lunioinf,llista) p:=Position(Lconjunts,llista); if p eq 0 then return -1; else return Lunioinf[p]; end if; end function; */ actualitzaconjunts:=function (Lconjunts,llista) return(Append(Lconjunts,llista)); end function; actualitzamcinf:=function(Lmcinf,llista) maxc:=llista[1]; if (maxc eq 0) then return (Append(Lmcinf,[0])); end if; trobat:=false; while not trobat do while not inferior(maxc,llista[1]) do maxc:=maxc-1; end while; j:=2; while j le #llista and inferior(maxc,llista[j]) do j:=j+1; end while; if j eq #llista+1 then trobat:=true; end if; maxc:=maxc-1; end while; maxc:=maxc+1; mcinfllista:=[maxc]; for h in gaps do candidat:=lambdainv(lambda(maxc)-h); if candidat gt 0 then j:=1; while j le #llista and inferior(candidat,llista[j]) do j:=j+1; end while; if j eq #llista+1 then mcinfllista:=Append(mcinfllista,candidat); end if; end if; end for; return(Append(Lmcinf,mcinfllista)); end function; interseccio_ultim_unio_dels_altres:=function(llista) ultim:=llista[#llista]; maxc:=ultim-1; trobat:=false; while not trobat do while not inferior(maxc,ultim) do maxc:=maxc-1; end while; j:=1; while j le #llista-1 and not(inferior(maxc,llista[j])) do j:=j+1; end while; if j le #llista-1 then trobat:=true; end if; maxc:=maxc-1; end while; maxc:=maxc+1; ret:=[maxc]; for h in gaps do candidat:=lambdainv(lambda(maxc)-h); if candidat gt 0 and inferior(candidat,ultim) then j:=1; while j le #llista-1 and not(inferior(candidat,llista[j])) do j:=j+1; end while; if j le #llista-1 then ret:=Append(ret,candidat); end if; end if; end for; return(index(ret)); end function; actualitzainterseccioinf:=function(Lconjunts,Lmcinf,Linterseccioinf,Lunioinf,llista) if #llista eq 1 then return Append(Linterseccioinf,nu(llista[1])); else return Append(Linterseccioinf,Lunioinf[index(Lmcinf[index(llista)])]); end if; end function; actualitzaunioinf:=function(Lconjunts,Linterseccioinf,Lunioinf,llista) if #llista eq 1 then return Append(Lunioinf,nu(llista[1])); else return Append(Lunioinf, Lunioinf[index([llista[i]:i in [1..(#llista-1)]])] +nu(llista[#llista])-Linterseccioinf[interseccio_ultim_unio_dels_altres(llista)]); end if; end function; for i in [1..MAX] do conjuntsaux:=Lconjunts; llista:=[i]; Lconjunts:=actualitzaconjunts(Lconjunts,llista); Lmcinf:=actualitzamcinf(Lmcinf,llista); Linterseccioinf:=actualitzainterseccioinf(Lconjunts,Lmcinf,Linterseccioinf,Lunioinf,llista); Lunioinf:=actualitzaunioinf(Lconjunts,Linterseccioinf,Lunioinf,llista); for conj in conjuntsaux do llista:=Append(conj,i); Lconjunts:=actualitzaconjunts(Lconjunts,llista); Lmcinf:=actualitzamcinf(Lmcinf,llista); Linterseccioinf:=actualitzainterseccioinf(Lconjunts,Lmcinf,Linterseccioinf,Lunioinf,llista); Lunioinf:=actualitzaunioinf(Lconjunts,Linterseccioinf,Lunioinf,llista); end for; end for; joinsets:=function(llista) unio:={}; for conj in llista do unio:=unio join conj; end for; return unio; end function; /* l:=#Lconjunts; print "CONJUNTS="; ; print "MCINF="; ; print "INTERSECCIOINF="; Linterseccioinf; print "UNIOINF="; Lunioinf;*/ unioasac:=[#joinsets({N(i):i in llista}):llista in Lconjunts]; errors:=[Lunioinf[i]-unioasac[i]:i in [1..#unioasac]]; printf "VEREDICTE:="; [Lconjunts[i]:i in [1..#errors]|errors[i] ne 0]; /*r:=2; Subsets({0..MAX},r);*/ llista:=[1,2,5]; [lambda(i):i in llista]; l:=interseccio_ultim_unio_dels_altres(llista); Lconjunts[l]; Linterseccioinf[interseccio_ultim_unio_dels_altres(llista)]); Output: Magma V2.10-6 Wed Dec 24 2003 07:21:16 on modular [Seed = 870680709] ------------------------------------- VEREDICTE:=[ [ 1, 2, 5 ], [ 0, 1, 2, 5 ], [ 2, 3, 5 ], [ 0, 2, 3, 5 ], [ 1, 2, 3, 5 ], [ 0, 1, 2, 3, 5 ], [ 1, 2, 4, 5 ], [ 0, 1, 2, 4, 5 ], [ 2, 3, 4, 5 ], [ 0, 2, 3, 4, 5 ], [ 1, 2, 3, 4, 5 ], [ 0, 1, 2, 3, 4, 5 ], [ 1, 2, 5, 6 ], [ 0, 1, 2, 5, 6 ], [ 2, 3, 5, 6 ], [ 0, 2, 3, 5, 6 ], [ 1, 2, 3, 5, 6 ], [ 0, 1, 2, 3, 5, 6 ], [ 1, 2, 4, 5, 6 ], [ 0, 1, 2, 4, 5, 6 ], [ 2, 3, 4, 5, 6 ], [ 0, 2, 3, 4, 5, 6 ], [ 1, 2, 3, 4, 5, 6 ], [ 0, 1, 2, 3, 4, 5, 6 ] ] [ 3, 5, 8 ] [ 1, 2 ] >> Linterseccioinf[interseccio_ultim_unio_dels_altres(llista)]); ^ User error: bad syntax Total time: 3.149 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.32.42.proxycache.rima-tde.net. (80.58.32.42) Time: Wed Dec 24 07:21:53 2003 Input: /* Klein quartic */ MAX:=6; c:=5; g:=3; semi:=[0,3]; /* Hermitian curve */ /* MAX:=6; c:=12; g:=6; semi:=[0,4,5,8,9,10]; */ /* basic del semigrup */ i_cond:=c-g; pertany:=func; gaps:=[i:i in [1..c-1]|not pertany(i)]; lambda:=func; lambdainv:=func; /* oplus, leq, nu */ oplus:=func; inferior:=func; ominus:=func; N:=func; nu:=func; /* order bound */ dORD:=func; Lconjunts:=[[0]]; Lmcinf:=[[0]]; Linterseccioinf:=[1]; Lunioinf:=[1]; index:=function(llista) i:=0; for j in llista do i:=i+2^j; end for; return(i); end function; /* mcinf:=function(Lconjunts,Lmcinf,llista) p:=Position(Lconjunts,llista); if p eq 0 then return -1; else return Lmcinf[p]; end if; end function; interseccioinf:=function(Lconjunts,Linterseccioinf,llista) p:=Position(Lconjunts,llista); if p eq 0 then return -1; else return Linterseccioinf[p]; end if; end function; unioinf:=function(Lconjunts,Lunioinf,llista) p:=Position(Lconjunts,llista); if p eq 0 then return -1; else return Lunioinf[p]; end if; end function; */ actualitzaconjunts:=function (Lconjunts,llista) return(Append(Lconjunts,llista)); end function; actualitzamcinf:=function(Lmcinf,llista) maxc:=llista[1]; if (maxc eq 0) then return (Append(Lmcinf,[0])); end if; trobat:=false; while not trobat do while not inferior(maxc,llista[1]) do maxc:=maxc-1; end while; j:=2; while j le #llista and inferior(maxc,llista[j]) do j:=j+1; end while; if j eq #llista+1 then trobat:=true; end if; maxc:=maxc-1; end while; maxc:=maxc+1; mcinfllista:=[maxc]; for h in gaps do candidat:=lambdainv(lambda(maxc)-h); if candidat gt 0 then j:=1; while j le #llista and inferior(candidat,llista[j]) do j:=j+1; end while; if j eq #llista+1 then mcinfllista:=Append(mcinfllista,candidat); end if; end if; end for; return(Append(Lmcinf,mcinfllista)); end function; interseccio_ultim_unio_dels_altres:=function(llista) ultim:=llista[#llista]; maxc:=ultim-1; trobat:=false; while not trobat do while not inferior(maxc,ultim) do maxc:=maxc-1; end while; j:=1; while j le #llista-1 and not(inferior(maxc,llista[j])) do j:=j+1; end while; if j le #llista-1 then trobat:=true; end if; maxc:=maxc-1; end while; maxc:=maxc+1; ret:=[maxc]; for h in gaps do candidat:=lambdainv(lambda(maxc)-h); if candidat gt 0 and inferior(candidat,ultim) then j:=1; while j le #llista-1 and not(inferior(candidat,llista[j])) do j:=j+1; end while; if j le #llista-1 then ret:=Append(ret,candidat); end if; end if; end for; return(index(ret)); end function; actualitzainterseccioinf:=function(Lconjunts,Lmcinf,Linterseccioinf,Lunioinf,llista) if #llista eq 1 then return Append(Linterseccioinf,nu(llista[1])); else return Append(Linterseccioinf,Lunioinf[index(Lmcinf[index(llista)])]); end if; end function; actualitzaunioinf:=function(Lconjunts,Linterseccioinf,Lunioinf,llista) if #llista eq 1 then return Append(Lunioinf,nu(llista[1])); else return Append(Lunioinf, Lunioinf[index([llista[i]:i in [1..(#llista-1)]])] +nu(llista[#llista])-Linterseccioinf[interseccio_ultim_unio_dels_altres(llista)]); end if; end function; for i in [1..MAX] do conjuntsaux:=Lconjunts; llista:=[i]; Lconjunts:=actualitzaconjunts(Lconjunts,llista); Lmcinf:=actualitzamcinf(Lmcinf,llista); Linterseccioinf:=actualitzainterseccioinf(Lconjunts,Lmcinf,Linterseccioinf,Lunioinf,llista); Lunioinf:=actualitzaunioinf(Lconjunts,Linterseccioinf,Lunioinf,llista); for conj in conjuntsaux do llista:=Append(conj,i); Lconjunts:=actualitzaconjunts(Lconjunts,llista); Lmcinf:=actualitzamcinf(Lmcinf,llista); Linterseccioinf:=actualitzainterseccioinf(Lconjunts,Lmcinf,Linterseccioinf,Lunioinf,llista); Lunioinf:=actualitzaunioinf(Lconjunts,Linterseccioinf,Lunioinf,llista); end for; end for; joinsets:=function(llista) unio:={}; for conj in llista do unio:=unio join conj; end for; return unio; end function; /* l:=#Lconjunts; print "CONJUNTS="; ; print "MCINF="; ; print "INTERSECCIOINF="; Linterseccioinf; print "UNIOINF="; Lunioinf;*/ unioasac:=[#joinsets({N(i):i in llista}):llista in Lconjunts]; errors:=[Lunioinf[i]-unioasac[i]:i in [1..#unioasac]]; printf "VEREDICTE:="; [Lconjunts[i]:i in [1..#errors]|errors[i] ne 0]; /*r:=2; Subsets({0..MAX},r);*/ llista:=[1,2,5]; [lambda(i):i in llista]; l:=interseccio_ultim_unio_dels_altres(llista); Lconjunts[l]; Linterseccioinf[interseccio_ultim_unio_dels_altres(llista)]; Output: Magma V2.10-6 Wed Dec 24 2003 07:21:50 on modular [Seed = 1218376604] ------------------------------------- VEREDICTE:=[ [ 1, 2, 5 ], [ 0, 1, 2, 5 ], [ 2, 3, 5 ], [ 0, 2, 3, 5 ], [ 1, 2, 3, 5 ], [ 0, 1, 2, 3, 5 ], [ 1, 2, 4, 5 ], [ 0, 1, 2, 4, 5 ], [ 2, 3, 4, 5 ], [ 0, 2, 3, 4, 5 ], [ 1, 2, 3, 4, 5 ], [ 0, 1, 2, 3, 4, 5 ], [ 1, 2, 5, 6 ], [ 0, 1, 2, 5, 6 ], [ 2, 3, 5, 6 ], [ 0, 2, 3, 5, 6 ], [ 1, 2, 3, 5, 6 ], [ 0, 1, 2, 3, 5, 6 ], [ 1, 2, 4, 5, 6 ], [ 0, 1, 2, 4, 5, 6 ], [ 2, 3, 4, 5, 6 ], [ 0, 2, 3, 4, 5, 6 ], [ 1, 2, 3, 4, 5, 6 ], [ 0, 1, 2, 3, 4, 5, 6 ] ] [ 3, 5, 8 ] [ 1, 2 ] 1 Total time: 3.189 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.32.42.proxycache.rima-tde.net. (80.58.32.42) Time: Wed Dec 24 07:23:08 2003 Input: /* Klein quartic */ MAX:=6; c:=5; g:=3; semi:=[0,3]; /* Hermitian curve */ /* MAX:=6; c:=12; g:=6; semi:=[0,4,5,8,9,10]; */ /* basic del semigrup */ i_cond:=c-g; pertany:=func; gaps:=[i:i in [1..c-1]|not pertany(i)]; lambda:=func; lambdainv:=func; /* oplus, leq, nu */ oplus:=func; inferior:=func; ominus:=func; N:=func; nu:=func; /* order bound */ dORD:=func; Lconjunts:=[[0]]; Lmcinf:=[[0]]; Linterseccioinf:=[1]; Lunioinf:=[1]; index:=function(llista) i:=0; for j in llista do i:=i+2^j; end for; return(i); end function; /* mcinf:=function(Lconjunts,Lmcinf,llista) p:=Position(Lconjunts,llista); if p eq 0 then return -1; else return Lmcinf[p]; end if; end function; interseccioinf:=function(Lconjunts,Linterseccioinf,llista) p:=Position(Lconjunts,llista); if p eq 0 then return -1; else return Linterseccioinf[p]; end if; end function; unioinf:=function(Lconjunts,Lunioinf,llista) p:=Position(Lconjunts,llista); if p eq 0 then return -1; else return Lunioinf[p]; end if; end function; */ actualitzaconjunts:=function (Lconjunts,llista) return(Append(Lconjunts,llista)); end function; actualitzamcinf:=function(Lmcinf,llista) maxc:=llista[1]; if (maxc eq 0) then return (Append(Lmcinf,[0])); end if; trobat:=false; while not trobat do while not inferior(maxc,llista[1]) do maxc:=maxc-1; end while; j:=2; while j le #llista and inferior(maxc,llista[j]) do j:=j+1; end while; if j eq #llista+1 then trobat:=true; end if; maxc:=maxc-1; end while; maxc:=maxc+1; mcinfllista:=[maxc]; for h in gaps do candidat:=lambdainv(lambda(maxc)-h); if candidat gt 0 then j:=1; while j le #llista and inferior(candidat,llista[j]) do j:=j+1; end while; if j eq #llista+1 then mcinfllista:=Append(mcinfllista,candidat); end if; end if; end for; return(Append(Lmcinf,mcinfllista)); end function; interseccio_ultim_unio_dels_altres:=function(llista) ultim:=llista[#llista]; maxc:=ultim-1; trobat:=false; while not trobat do while not inferior(maxc,ultim) do maxc:=maxc-1; end while; j:=1; while j le #llista-1 and not(inferior(maxc,llista[j])) do j:=j+1; end while; if j le #llista-1 then trobat:=true; end if; maxc:=maxc-1; end while; maxc:=maxc+1; ret:=[maxc]; for h in gaps do candidat:=lambdainv(lambda(maxc)-h); if candidat gt 0 and inferior(candidat,ultim) then j:=1; while j le #llista-1 and not(inferior(candidat,llista[j])) do j:=j+1; end while; if j le #llista-1 then ret:=Append(ret,candidat); end if; end if; end for; return(index(ret)); end function; actualitzainterseccioinf:=function(Lconjunts,Lmcinf,Linterseccioinf,Lunioinf,llista) if #llista eq 1 then return Append(Linterseccioinf,nu(llista[1])); else return Append(Linterseccioinf,Lunioinf[index(Lmcinf[index(llista)])]); end if; end function; actualitzaunioinf:=function(Lconjunts,Linterseccioinf,Lunioinf,llista) if #llista eq 1 then return Append(Lunioinf,nu(llista[1])); else return Append(Lunioinf, Lunioinf[index([llista[i]:i in [1..(#llista-1)]])] +nu(llista[#llista])-Linterseccioinf[interseccio_ultim_unio_dels_altres(llista)]); end if; end function; for i in [1..MAX] do conjuntsaux:=Lconjunts; llista:=[i]; Lconjunts:=actualitzaconjunts(Lconjunts,llista); Lmcinf:=actualitzamcinf(Lmcinf,llista); Linterseccioinf:=actualitzainterseccioinf(Lconjunts,Lmcinf,Linterseccioinf,Lunioinf,llista); Lunioinf:=actualitzaunioinf(Lconjunts,Linterseccioinf,Lunioinf,llista); for conj in conjuntsaux do llista:=Append(conj,i); Lconjunts:=actualitzaconjunts(Lconjunts,llista); Lmcinf:=actualitzamcinf(Lmcinf,llista); Linterseccioinf:=actualitzainterseccioinf(Lconjunts,Lmcinf,Linterseccioinf,Lunioinf,llista); Lunioinf:=actualitzaunioinf(Lconjunts,Linterseccioinf,Lunioinf,llista); end for; end for; joinsets:=function(llista) unio:={}; for conj in llista do unio:=unio join conj; end for; return unio; end function; /* l:=#Lconjunts; print "CONJUNTS="; ; print "MCINF="; ; print "INTERSECCIOINF="; Linterseccioinf; print "UNIOINF="; Lunioinf;*/ unioasac:=[#joinsets({N(i):i in llista}):llista in Lconjunts]; errors:=[Lunioinf[i]-unioasac[i]:i in [1..#unioasac]]; printf "VEREDICTE:="; [Lconjunts[i]:i in [1..#errors]|errors[i] ne 0]; /*r:=2; Subsets({0..MAX},r);*/ llista:=[1,2,5]; [lambda(i):i in llista]; l:=interseccio_ultim_unio_dels_altres(llista); Lconjunts[l]; Lunioinf[interseccio_ultim_unio_dels_altres(llista)]; Output: Magma V2.10-6 Wed Dec 24 2003 07:23:05 on modular [Seed = 1100479330] ------------------------------------- VEREDICTE:=[ [ 1, 2, 5 ], [ 0, 1, 2, 5 ], [ 2, 3, 5 ], [ 0, 2, 3, 5 ], [ 1, 2, 3, 5 ], [ 0, 1, 2, 3, 5 ], [ 1, 2, 4, 5 ], [ 0, 1, 2, 4, 5 ], [ 2, 3, 4, 5 ], [ 0, 2, 3, 4, 5 ], [ 1, 2, 3, 4, 5 ], [ 0, 1, 2, 3, 4, 5 ], [ 1, 2, 5, 6 ], [ 0, 1, 2, 5, 6 ], [ 2, 3, 5, 6 ], [ 0, 2, 3, 5, 6 ], [ 1, 2, 3, 5, 6 ], [ 0, 1, 2, 3, 5, 6 ], [ 1, 2, 4, 5, 6 ], [ 0, 1, 2, 4, 5, 6 ], [ 2, 3, 4, 5, 6 ], [ 0, 2, 3, 4, 5, 6 ], [ 1, 2, 3, 4, 5, 6 ], [ 0, 1, 2, 3, 4, 5, 6 ] ] [ 3, 5, 8 ] [ 1, 2 ] 3 Total time: 3.159 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.32.42.proxycache.rima-tde.net. (80.58.32.42) Time: Wed Dec 24 07:23:58 2003 Input: /* Klein quartic */ MAX:=6; c:=5; g:=3; semi:=[0,3]; /* Hermitian curve */ /* MAX:=6; c:=12; g:=6; semi:=[0,4,5,8,9,10]; */ /* basic del semigrup */ i_cond:=c-g; pertany:=func; gaps:=[i:i in [1..c-1]|not pertany(i)]; lambda:=func; lambdainv:=func; /* oplus, leq, nu */ oplus:=func; inferior:=func; ominus:=func; N:=func; nu:=func; /* order bound */ dORD:=func; Lconjunts:=[[0]]; Lmcinf:=[[0]]; Linterseccioinf:=[1]; Lunioinf:=[1]; index:=function(llista) i:=0; for j in llista do i:=i+2^j; end for; return(i); end function; /* mcinf:=function(Lconjunts,Lmcinf,llista) p:=Position(Lconjunts,llista); if p eq 0 then return -1; else return Lmcinf[p]; end if; end function; interseccioinf:=function(Lconjunts,Linterseccioinf,llista) p:=Position(Lconjunts,llista); if p eq 0 then return -1; else return Linterseccioinf[p]; end if; end function; unioinf:=function(Lconjunts,Lunioinf,llista) p:=Position(Lconjunts,llista); if p eq 0 then return -1; else return Lunioinf[p]; end if; end function; */ actualitzaconjunts:=function (Lconjunts,llista) return(Append(Lconjunts,llista)); end function; actualitzamcinf:=function(Lmcinf,llista) maxc:=llista[1]; if (maxc eq 0) then return (Append(Lmcinf,[0])); end if; trobat:=false; while not trobat do while not inferior(maxc,llista[1]) do maxc:=maxc-1; end while; j:=2; while j le #llista and inferior(maxc,llista[j]) do j:=j+1; end while; if j eq #llista+1 then trobat:=true; end if; maxc:=maxc-1; end while; maxc:=maxc+1; mcinfllista:=[maxc]; for h in gaps do candidat:=lambdainv(lambda(maxc)-h); if candidat gt 0 then j:=1; while j le #llista and inferior(candidat,llista[j]) do j:=j+1; end while; if j eq #llista+1 then mcinfllista:=Append(mcinfllista,candidat); end if; end if; end for; return(Append(Lmcinf,mcinfllista)); end function; interseccio_ultim_unio_dels_altres:=function(llista) ultim:=llista[#llista]; maxc:=ultim-1; trobat:=false; while not trobat do while not inferior(maxc,ultim) do maxc:=maxc-1; end while; j:=1; while j le #llista-1 and not(inferior(maxc,llista[j])) do j:=j+1; end while; if j le #llista-1 then trobat:=true; end if; maxc:=maxc-1; end while; maxc:=maxc+1; ret:=[maxc]; for h in gaps do candidat:=lambdainv(lambda(maxc)-h); if candidat gt 0 and inferior(candidat,ultim) then j:=1; while j le #llista-1 and not(inferior(candidat,llista[j])) do j:=j+1; end while; if j le #llista-1 then ret:=Append(ret,candidat); end if; end if; end for; return(index(ret)); end function; actualitzainterseccioinf:=function(Lconjunts,Lmcinf,Linterseccioinf,Lunioinf,llista) if #llista eq 1 then return Append(Linterseccioinf,nu(llista[1])); else return Append(Linterseccioinf,Lunioinf[index(Lmcinf[index(llista)])]); end if; end function; actualitzaunioinf:=function(Lconjunts,Linterseccioinf,Lunioinf,llista) if #llista eq 1 then return Append(Lunioinf,nu(llista[1])); else return Append(Lunioinf, Lunioinf[index([llista[i]:i in [1..(#llista-1)]])] +nu(llista[#llista])-Lunioinf[interseccio_ultim_unio_dels_altres(llista)]); end if; end function; for i in [1..MAX] do conjuntsaux:=Lconjunts; llista:=[i]; Lconjunts:=actualitzaconjunts(Lconjunts,llista); Lmcinf:=actualitzamcinf(Lmcinf,llista); Linterseccioinf:=actualitzainterseccioinf(Lconjunts,Lmcinf,Linterseccioinf,Lunioinf,llista); Lunioinf:=actualitzaunioinf(Lconjunts,Linterseccioinf,Lunioinf,llista); for conj in conjuntsaux do llista:=Append(conj,i); Lconjunts:=actualitzaconjunts(Lconjunts,llista); Lmcinf:=actualitzamcinf(Lmcinf,llista); Linterseccioinf:=actualitzainterseccioinf(Lconjunts,Lmcinf,Linterseccioinf,Lunioinf,llista); Lunioinf:=actualitzaunioinf(Lconjunts,Linterseccioinf,Lunioinf,llista); end for; end for; joinsets:=function(llista) unio:={}; for conj in llista do unio:=unio join conj; end for; return unio; end function; /* l:=#Lconjunts; print "CONJUNTS="; ; print "MCINF="; ; print "INTERSECCIOINF="; Linterseccioinf; print "UNIOINF="; Lunioinf;*/ unioasac:=[#joinsets({N(i):i in llista}):llista in Lconjunts]; errors:=[Lunioinf[i]-unioasac[i]:i in [1..#unioasac]]; printf "VEREDICTE:="; [Lconjunts[i]:i in [1..#errors]|errors[i] ne 0]; /*r:=2; Subsets({0..MAX},r);*/ llista:=[1,2,5]; [lambda(i):i in llista]; l:=interseccio_ultim_unio_dels_altres(llista); Lconjunts[l]; Linterseccioinf[interseccio_ultim_unio_dels_altres(llista)]; Output: Magma V2.10-6 Wed Dec 24 2003 07:23:55 on modular [Seed = 1451289607] ------------------------------------- VEREDICTE:=[] [ 3, 5, 8 ] [ 1, 2 ] 1 Total time: 3.079 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.32.42.proxycache.rima-tde.net. (80.58.32.42) Time: Wed Dec 24 07:34:46 2003 Input: /* Klein quartic */ MAX:=6; c:=5; g:=3; semi:=[0,3]; /* Hermitian curve */ /* MAX:=6; c:=12; g:=6; semi:=[0,4,5,8,9,10]; */ /* basic del semigrup */ i_cond:=c-g; pertany:=func; gaps:=[i:i in [1..c-1]|not pertany(i)]; lambda:=func; lambdainv:=func; /* oplus, leq, nu */ oplus:=func; inferior:=func; ominus:=func; N:=func; nu:=func; /* order bound */ dORD:=func; Lconjunts:=[[0]]; Lmcinf:=[[0]]; Linterseccioinf:=[1]; Lunioinf:=[1]; index:=function(llista) i:=0; for j in llista do i:=i+2^j; end for; return(i); end function; /* mcinf:=function(Lconjunts,Lmcinf,llista) p:=Position(Lconjunts,llista); if p eq 0 then return -1; else return Lmcinf[p]; end if; end function; interseccioinf:=function(Lconjunts,Linterseccioinf,llista) p:=Position(Lconjunts,llista); if p eq 0 then return -1; else return Linterseccioinf[p]; end if; end function; unioinf:=function(Lconjunts,Lunioinf,llista) p:=Position(Lconjunts,llista); if p eq 0 then return -1; else return Lunioinf[p]; end if; end function; */ actualitzaconjunts:=function (Lconjunts,llista) return(Append(Lconjunts,llista)); end function; actualitzamcinf:=function(Lmcinf,llista) maxc:=llista[1]; if (maxc eq 0) then return (Append(Lmcinf,[0])); end if; trobat:=false; while not trobat do while not inferior(maxc,llista[1]) do maxc:=maxc-1; end while; j:=2; while j le #llista and inferior(maxc,llista[j]) do j:=j+1; end while; if j eq #llista+1 then trobat:=true; end if; maxc:=maxc-1; end while; maxc:=maxc+1; mcinfllista:=[maxc]; for h in gaps do candidat:=lambdainv(lambda(maxc)-h); if candidat gt 0 then j:=1; while j le #llista and inferior(candidat,llista[j]) do j:=j+1; end while; if j eq #llista+1 then mcinfllista:=Append(mcinfllista,candidat); end if; end if; end for; return(Append(Lmcinf,mcinfllista)); end function; interseccio_ultim_unio_dels_altres:=function(llista) ultim:=llista[#llista]; maxc:=ultim-1; trobat:=false; while not trobat do while not inferior(maxc,ultim) do maxc:=maxc-1; end while; j:=1; while j le #llista-1 and not(inferior(maxc,llista[j])) do j:=j+1; end while; if j le #llista-1 then trobat:=true; end if; maxc:=maxc-1; end while; maxc:=maxc+1; ret:=[maxc]; for h in gaps do candidat:=lambdainv(lambda(maxc)-h); if candidat gt 0 and inferior(candidat,ultim) then j:=1; while j le #llista-1 and not(inferior(candidat,llista[j])) do j:=j+1; end while; if j le #llista-1 then ret:=Append(ret,candidat); end if; end if; end for; return(index(ret)); end function; actualitzainterseccioinf:=function(Lconjunts,Lmcinf,Linterseccioinf,Lunioinf,llista) if #llista eq 1 then return Append(Linterseccioinf,nu(llista[1])); else return Append(Linterseccioinf,Lunioinf[index(Lmcinf[index(llista)])]); end if; end function; actualitzaunioinf:=function(Lconjunts,Linterseccioinf,Lunioinf,llista) if #llista eq 1 then return Append(Lunioinf,nu(llista[1])); else return Append(Lunioinf, Lunioinf[index([llista[i]:i in [1..(#llista-1)]])] +nu(llista[#llista])-Lunioinf[interseccio_ultim_unio_dels_altres(llista)]); end if; end function; for i in [1..MAX] do conjuntsaux:=Lconjunts; llista:=[i]; Lconjunts:=actualitzaconjunts(Lconjunts,llista); Lmcinf:=actualitzamcinf(Lmcinf,llista); Linterseccioinf:=actualitzainterseccioinf(Lconjunts,Lmcinf,Linterseccioinf,Lunioinf,llista); Lunioinf:=actualitzaunioinf(Lconjunts,Linterseccioinf,Lunioinf,llista); for conj in conjuntsaux do llista:=Append(conj,i); Lconjunts:=actualitzaconjunts(Lconjunts,llista); Lmcinf:=actualitzamcinf(Lmcinf,llista); Linterseccioinf:=actualitzainterseccioinf(Lconjunts,Lmcinf,Linterseccioinf,Lunioinf,llista); Lunioinf:=actualitzaunioinf(Lconjunts,Linterseccioinf,Lunioinf,llista); end for; end for; joinsets:=function(llista) unio:={}; for conj in llista do unio:=unio join conj; end for; return unio; end function; /* l:=#Lconjunts; print "CONJUNTS="; ; print "MCINF="; ; print "INTERSECCIOINF="; Linterseccioinf; print "UNIOINF="; Lunioinf;*/ unioasac:=[#joinsets({N(i):i in llista}):llista in Lconjunts]; errors:=[Lunioinf[i]-unioasac[i]:i in [1..#unioasac]]; printf "VEREDICTE:="; [Lconjunts[i]:i in [1..#errors]|errors[i] ne 0]; /*r:=2; Subsets({0..MAX},r);*/ Output: Magma V2.10-6 Wed Dec 24 2003 07:34:42 on modular [Seed = 2404988775] ------------------------------------- VEREDICTE:=[] Total time: 3.389 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.32.42.proxycache.rima-tde.net. (80.58.32.42) Time: Wed Dec 24 07:35:14 2003 Input: /* Klein quartic */ MAX:=6; c:=5; g:=3; semi:=[0,3]; /* Hermitian curve */ MAX:=10; c:=12; g:=6; semi:=[0,4,5,8,9,10]; /* basic del semigrup */ i_cond:=c-g; pertany:=func; gaps:=[i:i in [1..c-1]|not pertany(i)]; lambda:=func; lambdainv:=func; /* oplus, leq, nu */ oplus:=func; inferior:=func; ominus:=func; N:=func; nu:=func; /* order bound */ dORD:=func; Lconjunts:=[[0]]; Lmcinf:=[[0]]; Linterseccioinf:=[1]; Lunioinf:=[1]; index:=function(llista) i:=0; for j in llista do i:=i+2^j; end for; return(i); end function; /* mcinf:=function(Lconjunts,Lmcinf,llista) p:=Position(Lconjunts,llista); if p eq 0 then return -1; else return Lmcinf[p]; end if; end function; interseccioinf:=function(Lconjunts,Linterseccioinf,llista) p:=Position(Lconjunts,llista); if p eq 0 then return -1; else return Linterseccioinf[p]; end if; end function; unioinf:=function(Lconjunts,Lunioinf,llista) p:=Position(Lconjunts,llista); if p eq 0 then return -1; else return Lunioinf[p]; end if; end function; */ actualitzaconjunts:=function (Lconjunts,llista) return(Append(Lconjunts,llista)); end function; actualitzamcinf:=function(Lmcinf,llista) maxc:=llista[1]; if (maxc eq 0) then return (Append(Lmcinf,[0])); end if; trobat:=false; while not trobat do while not inferior(maxc,llista[1]) do maxc:=maxc-1; end while; j:=2; while j le #llista and inferior(maxc,llista[j]) do j:=j+1; end while; if j eq #llista+1 then trobat:=true; end if; maxc:=maxc-1; end while; maxc:=maxc+1; mcinfllista:=[maxc]; for h in gaps do candidat:=lambdainv(lambda(maxc)-h); if candidat gt 0 then j:=1; while j le #llista and inferior(candidat,llista[j]) do j:=j+1; end while; if j eq #llista+1 then mcinfllista:=Append(mcinfllista,candidat); end if; end if; end for; return(Append(Lmcinf,mcinfllista)); end function; interseccio_ultim_unio_dels_altres:=function(llista) ultim:=llista[#llista]; maxc:=ultim-1; trobat:=false; while not trobat do while not inferior(maxc,ultim) do maxc:=maxc-1; end while; j:=1; while j le #llista-1 and not(inferior(maxc,llista[j])) do j:=j+1; end while; if j le #llista-1 then trobat:=true; end if; maxc:=maxc-1; end while; maxc:=maxc+1; ret:=[maxc]; for h in gaps do candidat:=lambdainv(lambda(maxc)-h); if candidat gt 0 and inferior(candidat,ultim) then j:=1; while j le #llista-1 and not(inferior(candidat,llista[j])) do j:=j+1; end while; if j le #llista-1 then ret:=Append(ret,candidat); end if; end if; end for; return(index(ret)); end function; actualitzainterseccioinf:=function(Lconjunts,Lmcinf,Linterseccioinf,Lunioinf,llista) if #llista eq 1 then return Append(Linterseccioinf,nu(llista[1])); else return Append(Linterseccioinf,Lunioinf[index(Lmcinf[index(llista)])]); end if; end function; actualitzaunioinf:=function(Lconjunts,Linterseccioinf,Lunioinf,llista) if #llista eq 1 then return Append(Lunioinf,nu(llista[1])); else return Append(Lunioinf, Lunioinf[index([llista[i]:i in [1..(#llista-1)]])] +nu(llista[#llista])-Lunioinf[interseccio_ultim_unio_dels_altres(llista)]); end if; end function; for i in [1..MAX] do conjuntsaux:=Lconjunts; llista:=[i]; Lconjunts:=actualitzaconjunts(Lconjunts,llista); Lmcinf:=actualitzamcinf(Lmcinf,llista); Linterseccioinf:=actualitzainterseccioinf(Lconjunts,Lmcinf,Linterseccioinf,Lunioinf,llista); Lunioinf:=actualitzaunioinf(Lconjunts,Linterseccioinf,Lunioinf,llista); for conj in conjuntsaux do llista:=Append(conj,i); Lconjunts:=actualitzaconjunts(Lconjunts,llista); Lmcinf:=actualitzamcinf(Lmcinf,llista); Linterseccioinf:=actualitzainterseccioinf(Lconjunts,Lmcinf,Linterseccioinf,Lunioinf,llista); Lunioinf:=actualitzaunioinf(Lconjunts,Linterseccioinf,Lunioinf,llista); end for; end for; joinsets:=function(llista) unio:={}; for conj in llista do unio:=unio join conj; end for; return unio; end function; /* l:=#Lconjunts; print "CONJUNTS="; ; print "MCINF="; ; print "INTERSECCIOINF="; Linterseccioinf; print "UNIOINF="; Lunioinf;*/ unioasac:=[#joinsets({N(i):i in llista}):llista in Lconjunts]; errors:=[Lunioinf[i]-unioasac[i]:i in [1..#unioasac]]; printf "VEREDICTE:="; [Lconjunts[i]:i in [1..#errors]|errors[i] ne 0]; /*r:=2; Subsets({0..MAX},r);*/ Output: Magma V2.10-6 Wed Dec 24 2003 07:35:07 on modular [Seed = 2555256937] ------------------------------------- VEREDICTE:=[] Total time: 6.500 seconds, Total memory usage: 2.42MB ************** MAGMA ***************** Host 80.58.32.42.proxycache.rima-tde.net. (80.58.32.42) Time: Wed Dec 24 07:36:55 2003 Input: /* Klein quartic */ printf "Klein quartic"; MAX:=6; c:=5; g:=3; semi:=[0,3]; /* Hermitian curve */ /* printf "hermitian curve"; MAX:=6; c:=12; g:=6; semi:=[0,4,5,8,9,10]; */ /* basic del semigrup */ i_cond:=c-g; pertany:=func; gaps:=[i:i in [1..c-1]|not pertany(i)]; lambda:=func; lambdainv:=func; /* oplus, leq, nu */ oplus:=func; inferior:=func; ominus:=func; N:=func; nu:=func; /* order bound */ dORD:=func; Lconjunts:=[[0]]; Lmcinf:=[[0]]; Linterseccioinf:=[1]; Lunioinf:=[1]; index:=function(llista) i:=0; for j in llista do i:=i+2^j; end for; return(i); end function; /* mcinf:=function(Lconjunts,Lmcinf,llista) p:=Position(Lconjunts,llista); if p eq 0 then return -1; else return Lmcinf[p]; end if; end function; interseccioinf:=function(Lconjunts,Linterseccioinf,llista) p:=Position(Lconjunts,llista); if p eq 0 then return -1; else return Linterseccioinf[p]; end if; end function; unioinf:=function(Lconjunts,Lunioinf,llista) p:=Position(Lconjunts,llista); if p eq 0 then return -1; else return Lunioinf[p]; end if; end function; */ actualitzaconjunts:=function (Lconjunts,llista) return(Append(Lconjunts,llista)); end function; actualitzamcinf:=function(Lmcinf,llista) maxc:=llista[1]; if (maxc eq 0) then return (Append(Lmcinf,[0])); end if; trobat:=false; while not trobat do while not inferior(maxc,llista[1]) do maxc:=maxc-1; end while; j:=2; while j le #llista and inferior(maxc,llista[j]) do j:=j+1; end while; if j eq #llista+1 then trobat:=true; end if; maxc:=maxc-1; end while; maxc:=maxc+1; mcinfllista:=[maxc]; for h in gaps do candidat:=lambdainv(lambda(maxc)-h); if candidat gt 0 then j:=1; while j le #llista and inferior(candidat,llista[j]) do j:=j+1; end while; if j eq #llista+1 then mcinfllista:=Append(mcinfllista,candidat); end if; end if; end for; return(Append(Lmcinf,mcinfllista)); end function; interseccio_ultim_unio_dels_altres:=function(llista) ultim:=llista[#llista]; maxc:=ultim-1; trobat:=false; while not trobat do while not inferior(maxc,ultim) do maxc:=maxc-1; end while; j:=1; while j le #llista-1 and not(inferior(maxc,llista[j])) do j:=j+1; end while; if j le #llista-1 then trobat:=true; end if; maxc:=maxc-1; end while; maxc:=maxc+1; ret:=[maxc]; for h in gaps do candidat:=lambdainv(lambda(maxc)-h); if candidat gt 0 and inferior(candidat,ultim) then j:=1; while j le #llista-1 and not(inferior(candidat,llista[j])) do j:=j+1; end while; if j le #llista-1 then ret:=Append(ret,candidat); end if; end if; end for; return(index(ret)); end function; actualitzainterseccioinf:=function(Lconjunts,Lmcinf,Linterseccioinf,Lunioinf,llista) if #llista eq 1 then return Append(Linterseccioinf,nu(llista[1])); else return Append(Linterseccioinf,Lunioinf[index(Lmcinf[index(llista)])]); end if; end function; actualitzaunioinf:=function(Lconjunts,Linterseccioinf,Lunioinf,llista) if #llista eq 1 then return Append(Lunioinf,nu(llista[1])); else return Append(Lunioinf, Lunioinf[index([llista[i]:i in [1..(#llista-1)]])] +nu(llista[#llista])-Lunioinf[interseccio_ultim_unio_dels_altres(llista)]); end if; end function; for i in [1..MAX] do conjuntsaux:=Lconjunts; llista:=[i]; Lconjunts:=actualitzaconjunts(Lconjunts,llista); Lmcinf:=actualitzamcinf(Lmcinf,llista); Linterseccioinf:=actualitzainterseccioinf(Lconjunts,Lmcinf,Linterseccioinf,Lunioinf,llista); Lunioinf:=actualitzaunioinf(Lconjunts,Linterseccioinf,Lunioinf,llista); for conj in conjuntsaux do llista:=Append(conj,i); Lconjunts:=actualitzaconjunts(Lconjunts,llista); Lmcinf:=actualitzamcinf(Lmcinf,llista); Linterseccioinf:=actualitzainterseccioinf(Lconjunts,Lmcinf,Linterseccioinf,Lunioinf,llista); Lunioinf:=actualitzaunioinf(Lconjunts,Linterseccioinf,Lunioinf,llista); end for; end for; joinsets:=function(llista) unio:={}; for conj in llista do unio:=unio join conj; end for; return unio; end function; /* l:=#Lconjunts; print "CONJUNTS="; ; print "MCINF="; ; print "INTERSECCIOINF="; Linterseccioinf; print "UNIOINF="; Lunioinf;*/ unioasac:=[#joinsets({N(i):i in llista}):llista in Lconjunts]; errors:=[Lunioinf[i]-unioasac[i]:i in [1..#unioasac]]; printf "VEREDICTE:="; [Lconjunts[i]:i in [1..#errors]|errors[i] ne 0]; /*r:=2; Subsets({0..MAX},r);*/ Output: Magma V2.10-6 Wed Dec 24 2003 07:36:52 on modular [Seed = 2943948993] ------------------------------------- Klein quarticVEREDICTE:=[] Total time: 3.029 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.32.42.proxycache.rima-tde.net. (80.58.32.42) Time: Wed Dec 24 07:37:29 2003 Input: /* Klein quartic */ /* printf "Klein quartic"; MAX:=6; c:=5; g:=3; semi:=[0,3]; */ /* Hermitian curve */ printf "hermitian curve"; MAX:=10; c:=12; g:=6; semi:=[0,4,5,8,9,10]; /* basic del semigrup */ i_cond:=c-g; pertany:=func; gaps:=[i:i in [1..c-1]|not pertany(i)]; lambda:=func; lambdainv:=func; /* oplus, leq, nu */ oplus:=func; inferior:=func; ominus:=func; N:=func; nu:=func; /* order bound */ dORD:=func; Lconjunts:=[[0]]; Lmcinf:=[[0]]; Linterseccioinf:=[1]; Lunioinf:=[1]; index:=function(llista) i:=0; for j in llista do i:=i+2^j; end for; return(i); end function; /* mcinf:=function(Lconjunts,Lmcinf,llista) p:=Position(Lconjunts,llista); if p eq 0 then return -1; else return Lmcinf[p]; end if; end function; interseccioinf:=function(Lconjunts,Linterseccioinf,llista) p:=Position(Lconjunts,llista); if p eq 0 then return -1; else return Linterseccioinf[p]; end if; end function; unioinf:=function(Lconjunts,Lunioinf,llista) p:=Position(Lconjunts,llista); if p eq 0 then return -1; else return Lunioinf[p]; end if; end function; */ actualitzaconjunts:=function (Lconjunts,llista) return(Append(Lconjunts,llista)); end function; actualitzamcinf:=function(Lmcinf,llista) maxc:=llista[1]; if (maxc eq 0) then return (Append(Lmcinf,[0])); end if; trobat:=false; while not trobat do while not inferior(maxc,llista[1]) do maxc:=maxc-1; end while; j:=2; while j le #llista and inferior(maxc,llista[j]) do j:=j+1; end while; if j eq #llista+1 then trobat:=true; end if; maxc:=maxc-1; end while; maxc:=maxc+1; mcinfllista:=[maxc]; for h in gaps do candidat:=lambdainv(lambda(maxc)-h); if candidat gt 0 then j:=1; while j le #llista and inferior(candidat,llista[j]) do j:=j+1; end while; if j eq #llista+1 then mcinfllista:=Append(mcinfllista,candidat); end if; end if; end for; return(Append(Lmcinf,mcinfllista)); end function; interseccio_ultim_unio_dels_altres:=function(llista) ultim:=llista[#llista]; maxc:=ultim-1; trobat:=false; while not trobat do while not inferior(maxc,ultim) do maxc:=maxc-1; end while; j:=1; while j le #llista-1 and not(inferior(maxc,llista[j])) do j:=j+1; end while; if j le #llista-1 then trobat:=true; end if; maxc:=maxc-1; end while; maxc:=maxc+1; ret:=[maxc]; for h in gaps do candidat:=lambdainv(lambda(maxc)-h); if candidat gt 0 and inferior(candidat,ultim) then j:=1; while j le #llista-1 and not(inferior(candidat,llista[j])) do j:=j+1; end while; if j le #llista-1 then ret:=Append(ret,candidat); end if; end if; end for; return(index(ret)); end function; actualitzainterseccioinf:=function(Lconjunts,Lmcinf,Linterseccioinf,Lunioinf,llista) if #llista eq 1 then return Append(Linterseccioinf,nu(llista[1])); else return Append(Linterseccioinf,Lunioinf[index(Lmcinf[index(llista)])]); end if; end function; actualitzaunioinf:=function(Lconjunts,Linterseccioinf,Lunioinf,llista) if #llista eq 1 then return Append(Lunioinf,nu(llista[1])); else return Append(Lunioinf, Lunioinf[index([llista[i]:i in [1..(#llista-1)]])] +nu(llista[#llista])-Lunioinf[interseccio_ultim_unio_dels_altres(llista)]); end if; end function; for i in [1..MAX] do conjuntsaux:=Lconjunts; llista:=[i]; Lconjunts:=actualitzaconjunts(Lconjunts,llista); Lmcinf:=actualitzamcinf(Lmcinf,llista); Linterseccioinf:=actualitzainterseccioinf(Lconjunts,Lmcinf,Linterseccioinf,Lunioinf,llista); Lunioinf:=actualitzaunioinf(Lconjunts,Linterseccioinf,Lunioinf,llista); for conj in conjuntsaux do llista:=Append(conj,i); Lconjunts:=actualitzaconjunts(Lconjunts,llista); Lmcinf:=actualitzamcinf(Lmcinf,llista); Linterseccioinf:=actualitzainterseccioinf(Lconjunts,Lmcinf,Linterseccioinf,Lunioinf,llista); Lunioinf:=actualitzaunioinf(Lconjunts,Linterseccioinf,Lunioinf,llista); end for; end for; joinsets:=function(llista) unio:={}; for conj in llista do unio:=unio join conj; end for; return unio; end function; /* l:=#Lconjunts; print "CONJUNTS="; ; print "MCINF="; ; print "INTERSECCIOINF="; Linterseccioinf; print "UNIOINF="; Lunioinf;*/ unioasac:=[#joinsets({N(i):i in llista}):llista in Lconjunts]; errors:=[Lunioinf[i]-unioasac[i]:i in [1..#unioasac]]; printf "VEREDICTE:="; [Lconjunts[i]:i in [1..#errors]|errors[i] ne 0]; /*r:=2; Subsets({0..MAX},r);*/ Output: Magma V2.10-6 Wed Dec 24 2003 07:37:23 on modular [Seed = 3161066293] ------------------------------------- hermitian curveVEREDICTE:=[] Total time: 5.969 seconds, Total memory usage: 2.42MB ************** MAGMA ***************** Host 80.58.32.42.proxycache.rima-tde.net. (80.58.32.42) Time: Wed Dec 24 07:38:43 2003 Input: /* Klein quartic */ /* printf "Klein quartic"; MAX:=6; c:=5; g:=3; semi:=[0,3]; */ /* Hermitian curve */ printf "hermitian curve"; MAX:=10; c:=12; g:=6; semi:=[0,4,5,8,9,10]; /* basic del semigrup */ i_cond:=c-g; pertany:=func; gaps:=[i:i in [1..c-1]|not pertany(i)]; lambda:=func; lambdainv:=func; /* oplus, leq, nu */ oplus:=func; inferior:=func; ominus:=func; N:=func; nu:=func; /* order bound */ dORD:=func; Lconjunts:=[[0]]; Lmcinf:=[[0]]; Linterseccioinf:=[1]; Lunioinf:=[1]; index:=function(llista) i:=0; for j in llista do i:=i+2^j; end for; return(i); end function; /* mcinf:=function(Lconjunts,Lmcinf,llista) p:=Position(Lconjunts,llista); if p eq 0 then return -1; else return Lmcinf[p]; end if; end function; interseccioinf:=function(Lconjunts,Linterseccioinf,llista) p:=Position(Lconjunts,llista); if p eq 0 then return -1; else return Linterseccioinf[p]; end if; end function; unioinf:=function(Lconjunts,Lunioinf,llista) p:=Position(Lconjunts,llista); if p eq 0 then return -1; else return Lunioinf[p]; end if; end function; */ actualitzaconjunts:=function (Lconjunts,llista) return(Append(Lconjunts,llista)); end function; actualitzamcinf:=function(Lmcinf,llista) maxc:=llista[1]; if (maxc eq 0) then return (Append(Lmcinf,[0])); end if; trobat:=false; while not trobat do while not inferior(maxc,llista[1]) do maxc:=maxc-1; end while; j:=2; while j le #llista and inferior(maxc,llista[j]) do j:=j+1; end while; if j eq #llista+1 then trobat:=true; end if; maxc:=maxc-1; end while; maxc:=maxc+1; mcinfllista:=[maxc]; for h in gaps do candidat:=lambdainv(lambda(maxc)-h); if candidat gt 0 then j:=1; while j le #llista and inferior(candidat,llista[j]) do j:=j+1; end while; if j eq #llista+1 then mcinfllista:=Append(mcinfllista,candidat); end if; end if; end for; return(Append(Lmcinf,mcinfllista)); end function; interseccio_ultim_unio_dels_altres:=function(llista) ultim:=llista[#llista]; maxc:=ultim-1; trobat:=false; while not trobat do while not inferior(maxc,ultim) do maxc:=maxc-1; end while; j:=1; while j le #llista-1 and not(inferior(maxc,llista[j])) do j:=j+1; end while; if j le #llista-1 then trobat:=true; end if; maxc:=maxc-1; end while; maxc:=maxc+1; ret:=[maxc]; for h in gaps do candidat:=lambdainv(lambda(maxc)-h); if candidat gt 0 and inferior(candidat,ultim) then j:=1; while j le #llista-1 and not(inferior(candidat,llista[j])) do j:=j+1; end while; if j le #llista-1 then ret:=Append(ret,candidat); end if; end if; end for; return(index(ret)); end function; actualitzainterseccioinf:=function(Lconjunts,Lmcinf,Linterseccioinf,Lunioinf,llista) if #llista eq 1 then return Append(Linterseccioinf,nu(llista[1])); else return Append(Linterseccioinf,Lunioinf[index(Lmcinf[index(llista)])]); end if; end function; actualitzaunioinf:=function(Lconjunts,Linterseccioinf,Lunioinf,llista) if #llista eq 1 then return Append(Lunioinf,nu(llista[1])); else return Append(Lunioinf, Lunioinf[index([llista[i]:i in [1..(#llista-1)]])] +nu(llista[#llista])-Lunioinf[interseccio_ultim_unio_dels_altres(llista)]); end if; end function; for i in [1..MAX] do conjuntsaux:=Lconjunts; llista:=[i]; Lconjunts:=actualitzaconjunts(Lconjunts,llista); Lmcinf:=actualitzamcinf(Lmcinf,llista); Linterseccioinf:=actualitzainterseccioinf(Lconjunts,Lmcinf,Linterseccioinf,Lunioinf,llista); Lunioinf:=actualitzaunioinf(Lconjunts,Linterseccioinf,Lunioinf,llista); for conj in conjuntsaux do llista:=Append(conj,i); Lconjunts:=actualitzaconjunts(Lconjunts,llista); Lmcinf:=actualitzamcinf(Lmcinf,llista); Linterseccioinf:=actualitzainterseccioinf(Lconjunts,Lmcinf,Linterseccioinf,Lunioinf,llista); Lunioinf:=actualitzaunioinf(Lconjunts,Linterseccioinf,Lunioinf,llista); end for; end for; joinsets:=function(llista) unio:={}; for conj in llista do unio:=unio join conj; end for; return unio; end function; /* l:=#Lconjunts; print "CONJUNTS="; ; print "MCINF="; ; print "INTERSECCIOINF="; Linterseccioinf; print "UNIOINF="; Lunioinf;*/ unioasac:=[#joinsets({N(i):i in llista}):llista in Lconjunts]; errors:=[Lunioinf[i]-unioasac[i]:i in [1..#unioasac]]; printf "VEREDICTE:="; [Lconjunts[i]:i in [1..#errors]|errors[i] ne 0]; r:=2; Subsets({0..MAX},r); Output: Magma V2.10-6 Wed Dec 24 2003 07:38:37 on modular [Seed = 3222697735] ------------------------------------- hermitian curveVEREDICTE:=[] { { 0, 5 }, { 4, 8 }, { 4, 9 }, { 7, 9 }, { 2, 10 }, { 8, 9 }, { 1, 10 }, { 1, 2 }, { 4, 10 }, { 5, 10 }, { 1, 6 }, { 7, 8 }, { 3, 5 }, { 2, 6 }, { 1, 4 }, { 6, 10 }, { 4, 7 }, { 3, 8 }, { 3, 9 }, { 6, 7 }, { 2, 4 }, { 0, 8 }, { 5, 8 }, { 0, 9 }, { 4, 6 }, { 5, 9 }, { 8, 10 }, { 5, 7 }, { 1, 7 }, { 3, 4 }, { 2, 7 }, { 7, 10 }, { 3, 7 }, { 9, 10 }, { 2, 3 }, { 5, 6 }, { 0, 2 }, { 2, 5 }, { 1, 3 }, { 4, 5 }, { 1, 5 }, { 0, 1 }, { 0, 10 }, { 3, 6 }, { 0, 6 }, { 1, 8 }, { 0, 4 }, { 2, 9 }, { 1, 9 }, { 2, 8 }, { 0, 7 }, { 0, 3 }, { 6, 8 }, { 3, 10 }, { 6, 9 } } Total time: 6.069 seconds, Total memory usage: 2.42MB ************** MAGMA ***************** Host 80.58.32.42.proxycache.rima-tde.net. (80.58.32.42) Time: Wed Dec 24 07:46:47 2003 Input: 2*[1,2,3,4]; Output: Magma V2.10-6 Wed Dec 24 2003 07:46:23 on modular [Seed = 1117059029] ------------------------------------- >> 2*[1,2,3,4];; ^ Runtime error in '*': Bad argument types Argument types given: RngIntElt, SeqEnum[RngIntElt] Total time: 3.810 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.32.42.proxycache.rima-tde.net. (80.58.32.42) Time: Wed Dec 24 07:46:54 2003 Input: 2*[1,2,3,4]; Output: Magma V2.10-6 Wed Dec 24 2003 07:46:43 on modular [Seed = 2708935706] ------------------------------------- >> 2*[1,2,3,4];; ^ Runtime error in '*': Bad argument types Argument types given: RngIntElt, SeqEnum[RngIntElt] Total time: 3.399 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.32.42.proxycache.rima-tde.net. (80.58.32.42) Time: Wed Dec 24 07:50:49 2003 Input: a:=func<{a,b}|a+b>; Output: Magma V2.10-6 Wed Dec 24 2003 07:50:34 on modular [Seed = 4163783709] ------------------------------------- >> a:=func<{a,b}|a+b>;; ^ User error: bad syntax Total time: 3.829 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.32.42.proxycache.rima-tde.net. (80.58.32.42) Time: Wed Dec 24 07:51:25 2003 Input: a:=func<[a,b]|a+b>; Output: Magma V2.10-6 Wed Dec 24 2003 07:51:02 on modular [Seed = 1790762658] ------------------------------------- >> a:=func<[a,b]|a+b>;; ^ User error: bad syntax Total time: 3.709 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.32.42.proxycache.rima-tde.net. (80.58.32.42) Time: Wed Dec 24 07:51:40 2003 Input: a:=func<|a+b>; Output: Magma V2.10-6 Wed Dec 24 2003 07:51:35 on modular [Seed = 1485761777] ------------------------------------- >> a:=func<|a+b>;; ^ User error: bad syntax Total time: 3.269 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.32.42.proxycache.rima-tde.net. (80.58.32.42) Time: Wed Dec 24 07:52:32 2003 Input: a:=func; a([2,3]); a(<2,3>); a({2,3}); Output: Magma V2.10-6 Wed Dec 24 2003 07:52:26 on modular [Seed = 1318649144] ------------------------------------- 5 5 [
:3]( l: { 2, 3 } ) >> a:=func; ^ Runtime error in '[]': Bad argument types Total time: 3.549 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.32.42.proxycache.rima-tde.net. (80.58.32.42) Time: Wed Dec 24 07:53:15 2003 Input: a:=func; a([2,3]); a(<2,3>); Output: Magma V2.10-6 Wed Dec 24 2003 07:52:51 on modular [Seed = 2775783165] ------------------------------------- 5 5 Total time: 3.779 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.32.42.proxycache.rima-tde.net. (80.58.32.42) Time: Wed Dec 24 08:02:21 2003 Input: /* Klein quartic */ printf "Klein quartic"; MAX:=6; c:=5; g:=3; semi:=[0,3]; /* Hermitian curve */ /* printf "hermitian curve"; MAX:=10; c:=12; g:=6; semi:=[0,4,5,8,9,10]; */ /* basic del semigrup */ i_cond:=c-g; pertany:=func; gaps:=[i:i in [1..c-1]|not pertany(i)]; lambda:=func; lambdainv:=func; /* oplus, leq, nu */ oplus:=func; inferior:=func; ominus:=func; N:=func; nu:=func; /* order bound */ dORD:=func; Lconjunts:=[[0]]; Lmcinf:=[[0]]; Linterseccioinf:=[1]; Lunioinf:=[1]; index:=function(llista) i:=0; for j in llista do i:=i+2^j; end for; return(i); end function; /* mcinf:=function(Lconjunts,Lmcinf,llista) p:=Position(Lconjunts,llista); if p eq 0 then return -1; else return Lmcinf[p]; end if; end function; interseccioinf:=function(Lconjunts,Linterseccioinf,llista) p:=Position(Lconjunts,llista); if p eq 0 then return -1; else return Linterseccioinf[p]; end if; end function; unioinf:=function(Lconjunts,Lunioinf,llista) p:=Position(Lconjunts,llista); if p eq 0 then return -1; else return Lunioinf[p]; end if; end function; */ actualitzaconjunts:=function (Lconjunts,llista) return(Append(Lconjunts,llista)); end function; actualitzamcinf:=function(Lmcinf,llista) maxc:=llista[1]; if (maxc eq 0) then return (Append(Lmcinf,[0])); end if; trobat:=false; while not trobat do while not inferior(maxc,llista[1]) do maxc:=maxc-1; end while; j:=2; while j le #llista and inferior(maxc,llista[j]) do j:=j+1; end while; if j eq #llista+1 then trobat:=true; end if; maxc:=maxc-1; end while; maxc:=maxc+1; mcinfllista:=[maxc]; for h in gaps do candidat:=lambdainv(lambda(maxc)-h); if candidat gt 0 then j:=1; while j le #llista and inferior(candidat,llista[j]) do j:=j+1; end while; if j eq #llista+1 then mcinfllista:=Append(mcinfllista,candidat); end if; end if; end for; return(Append(Lmcinf,mcinfllista)); end function; interseccio_ultim_unio_dels_altres:=function(llista) ultim:=llista[#llista]; maxc:=ultim-1; trobat:=false; while not trobat do while not inferior(maxc,ultim) do maxc:=maxc-1; end while; j:=1; while j le #llista-1 and not(inferior(maxc,llista[j])) do j:=j+1; end while; if j le #llista-1 then trobat:=true; end if; maxc:=maxc-1; end while; maxc:=maxc+1; ret:=[maxc]; for h in gaps do candidat:=lambdainv(lambda(maxc)-h); if candidat gt 0 and inferior(candidat,ultim) then j:=1; while j le #llista-1 and not(inferior(candidat,llista[j])) do j:=j+1; end while; if j le #llista-1 then ret:=Append(ret,candidat); end if; end if; end for; return(index(ret)); end function; actualitzainterseccioinf:=function(Lconjunts,Lmcinf,Linterseccioinf,Lunioinf,llista) if #llista eq 1 then return Append(Linterseccioinf,nu(llista[1])); else return Append(Linterseccioinf,Lunioinf[index(Lmcinf[index(llista)])]); end if; end function; actualitzaunioinf:=function(Lconjunts,Linterseccioinf,Lunioinf,llista) if #llista eq 1 then return Append(Lunioinf,nu(llista[1])); else return Append(Lunioinf, Lunioinf[index([llista[i]:i in [1..(#llista-1)]])] +nu(llista[#llista])-Lunioinf[interseccio_ultim_unio_dels_altres(llista)]); end if; end function; for i in [1..MAX] do conjuntsaux:=Lconjunts; llista:=[i]; Lconjunts:=actualitzaconjunts(Lconjunts,llista); Lmcinf:=actualitzamcinf(Lmcinf,llista); Linterseccioinf:=actualitzainterseccioinf(Lconjunts,Lmcinf,Linterseccioinf,Lunioinf,llista); Lunioinf:=actualitzaunioinf(Lconjunts,Linterseccioinf,Lunioinf,llista); for conj in conjuntsaux do llista:=Append(conj,i); Lconjunts:=actualitzaconjunts(Lconjunts,llista); Lmcinf:=actualitzamcinf(Lmcinf,llista); Linterseccioinf:=actualitzainterseccioinf(Lconjunts,Lmcinf,Linterseccioinf,Lunioinf,llista); Lunioinf:=actualitzaunioinf(Lconjunts,Linterseccioinf,Lunioinf,llista); end for; end for; joinsets:=function(llista) unio:={}; for conj in llista do unio:=unio join conj; end for; return unio; end function; /* l:=#Lconjunts; print "CONJUNTS="; ; print "MCINF="; ; print "INTERSECCIOINF="; Linterseccioinf; print "UNIOINF="; Lunioinf;*/ unioasac:=[#joinsets({N(i):i in llista}):llista in Lconjunts]; errors:=[Lunioinf[i]-unioasac[i]:i in [1..#unioasac]]; printf "VEREDICTE:="; [Lconjunts[i]:i in [1..#errors]|errors[i] ne 0]; r:=2; conj_r_elements:=func; max_index:=index([1..MAX]); conj_r_elements_ge_i:=func; conj_r_elements_ge_i(4,3); Output: Magma V2.10-6 Wed Dec 24 2003 08:02:04 on modular [Seed = 569872386] ------------------------------------- Klein quarticVEREDICTE:=[] >> conj_r_elements_ge_i(4,3); ^ Runtime error in procedure call: Number of arguments (2) does not equal expected number of arguments (1) Total time: 3.889 seconds, Total memory usage: 1.92MB ************** MAGMA ***************** Host 80.58.32.42.proxycache.rima-tde.net. (80.58.32.42) Time: Wed Dec 24 08:03:35 2003 Input: /* Klein quartic */ printf "Klein quartic"; MAX:=6; c:=5; g:=3; semi:=[0,3]; /* Hermitian curve */ /* printf "hermitian curve"; MAX:=10; c:=12; g:=6; semi:=[0,4,5,8,9,10]; */ /* basic del semigrup */ i_cond:=c-g; pertany:=func; gaps:=[i:i in [1..c-1]|not pertany(i)]; lambda:=func; lambdainv:=func; /* oplus, leq, nu */ oplus:=func; inferior:=func; ominus:=func; N:=func; nu:=func; /* order bound */ dORD:=func; Lconjunts:=[[0]]; Lmcinf:=[[0]]; Linterseccioinf:=[1]; Lunioinf:=[1]; index:=function(llista) i:=0; for j in llista do i:=i+2^j; end for; return(i); end function; /* mcinf:=function(Lconjunts,Lmcinf,llista) p:=Position(Lconjunts,llista); if p eq 0 then return -1; else return Lmcinf[p]; end if; end function; interseccioinf:=function(Lconjunts,Linterseccioinf,llista) p:=Position(Lconjunts,llista); if p eq 0 then return -1; else return Linterseccioinf[p]; end if; end function; unioinf:=function(Lconjunts,Lunioinf,llista) p:=Position(Lconjunts,llista); if p eq 0 then return -1; else return Lunioinf[p]; end if; end function; */ actualitzaconjunts:=function (Lconjunts,llista) return(Append(Lconjunts,llista)); end function; actualitzamcinf:=function(Lmcinf,llista) maxc:=llista[1]; if (maxc eq 0) then return (Append(Lmcinf,[0])); end if; trobat:=false; while not trobat do while not inferior(maxc,llista[1]) do maxc:=maxc-1; end while; j:=2; while j le #llista and inferior(maxc,llista[j]) do j:=j+1; end while; if j eq #llista+1 then trobat:=true; end if; maxc:=maxc-1; end while; maxc:=maxc+1; mcinfllista:=[maxc]; for h in gaps do candidat:=lambdainv(lambda(maxc)-h); if candidat gt 0 then j:=1; while j le #llista and inferior(candidat,llista[j]) do j:=j+1; end while; if j eq #llista+1 then mcinfllista:=Append(mcinfllista,candidat); end if; end if; end for; return(Append(Lmcinf,mcinfllista)); end function; interseccio_ultim_unio_dels_altres:=function(llista) ultim:=llista[#llista]; maxc:=ultim-1; trobat:=false; while not trobat do while not inferior(maxc,ultim) do maxc:=maxc-1; end while; j:=1; while j le #llista-1 and not(inferior(maxc,llista[j])) do j:=j+1; end while; if j le #llista-1 then trobat:=true; end if; maxc:=maxc-1; end while; maxc:=maxc+1; ret:=[maxc]; for h in gaps do candidat:=lambdainv(lambda(maxc)-h); if candidat gt 0 and inferior(candidat,ultim) then j:=1; while j le #llista-1 and not(inferior(candidat,llista[j])) do j:=j+1; end while; if j le #llista-1 then ret:=Append(ret,candidat); end if; end if; end for; return(index(ret)); end function; actualitzainterseccioinf:=function(Lconjunts,Lmcinf,Linterseccioinf,Lunioinf,llista) if #llista eq 1 then return Append(Linterseccioinf,nu(llista[1])); else return Append(Linterseccioinf,Lunioinf[index(Lmcinf[index(llista)])]); end if; end function; actualitzaunioinf:=function(Lconjunts,Linterseccioinf,Lunioinf,llista) if #llista eq 1 then return Append(Lunioinf,nu(llista[1])); else return Append(Lunioinf, Lunioinf[index([llista[i]:i in [1..(#llista-1)]])] +nu(llista[#llista])-Lunioinf[interseccio_ultim_unio_dels_altres(llista)]); end if; end function; for i in [1..MAX] do conjuntsaux:=Lconjunts; llista:=[i]; Lconjunts:=actualitzaconjunts(Lconjunts,llista); Lmcinf:=actualitzamcinf(Lmcinf,llista); Linterseccioinf:=actualitzainterseccioinf(Lconjunts,Lmcinf,Linterseccioinf,Lunioinf,llista); Lunioinf:=actualitzaunioinf(Lconjunts,Linterseccioinf,Lunioinf,llista); for conj in conjuntsaux do llista:=Append(conj,i); Lconjunts:=actualitzaconjunts(Lconjunts,llista); Lmcinf:=actualitzamcinf(Lmcinf,llista); Linterseccioinf:=actualitzainterseccioinf(Lconjunts,Lmcinf,Linterseccioinf,Lunioinf,llista); Lunioinf:=actualitzaunioinf(Lconjunts,Linterseccioinf,Lunioinf,llista); end for; end for; joinsets:=function(llista) unio:={}; for conj in llista do unio:=unio join conj; end for; return unio; end function; /* l:=#Lconjunts; print "CONJUNTS="; ; print "MCINF="; ; print "INTERSECCIOINF="; Linterseccioinf; print "UNIOINF="; Lunioinf;*/ unioasac:=[#joinsets({N(i):i in llista}):llista in Lconjunts]; errors:=[Lunioinf[i]-unioasac[i]:i in [1..#unioasac]]; printf "VEREDICTE:="; [Lconjunts[i]:i in [1..#errors]|errors[i] ne 0]; r:=2; conj_r_elements:=func; max_index:=index([1..MAX]); conj_r_elements_ge_i:=func; conj_r_elements_ge_i([4,3]); Output: Magma V2.10-6 Wed Dec 24 2003 08:03:28 on modular [Seed = 603296494] ------------------------------------- Klein quarticVEREDICTE:=[] [ 120 ] Total time: 4.099 seconds, Total memory usage: 1.92MB ************** MAGMA ***************** Host 80.58.32.42.proxycache.rima-tde.net. (80.58.32.42) Time: Wed Dec 24 08:05:38 2003 Input: /* Klein quartic */ printf "Klein quartic"; MAX:=6; c:=5; g:=3; semi:=[0,3]; /* Hermitian curve */ /* printf "hermitian curve"; MAX:=10; c:=12; g:=6; semi:=[0,4,5,8,9,10]; */ /* basic del semigrup */ i_cond:=c-g; pertany:=func; gaps:=[i:i in [1..c-1]|not pertany(i)]; lambda:=func; lambdainv:=func; /* oplus, leq, nu */ oplus:=func; inferior:=func; ominus:=func; N:=func; nu:=func; /* order bound */ dORD:=func; Lconjunts:=[[0]]; Lmcinf:=[[0]]; Linterseccioinf:=[1]; Lunioinf:=[1]; index:=function(llista) i:=0; for j in llista do i:=i+2^j; end for; return(i); end function; /* mcinf:=function(Lconjunts,Lmcinf,llista) p:=Position(Lconjunts,llista); if p eq 0 then return -1; else return Lmcinf[p]; end if; end function; interseccioinf:=function(Lconjunts,Linterseccioinf,llista) p:=Position(Lconjunts,llista); if p eq 0 then return -1; else return Linterseccioinf[p]; end if; end function; unioinf:=function(Lconjunts,Lunioinf,llista) p:=Position(Lconjunts,llista); if p eq 0 then return -1; else return Lunioinf[p]; end if; end function; */ actualitzaconjunts:=function (Lconjunts,llista) return(Append(Lconjunts,llista)); end function; actualitzamcinf:=function(Lmcinf,llista) maxc:=llista[1]; if (maxc eq 0) then return (Append(Lmcinf,[0])); end if; trobat:=false; while not trobat do while not inferior(maxc,llista[1]) do maxc:=maxc-1; end while; j:=2; while j le #llista and inferior(maxc,llista[j]) do j:=j+1; end while; if j eq #llista+1 then trobat:=true; end if; maxc:=maxc-1; end while; maxc:=maxc+1; mcinfllista:=[maxc]; for h in gaps do candidat:=lambdainv(lambda(maxc)-h); if candidat gt 0 then j:=1; while j le #llista and inferior(candidat,llista[j]) do j:=j+1; end while; if j eq #llista+1 then mcinfllista:=Append(mcinfllista,candidat); end if; end if; end for; return(Append(Lmcinf,mcinfllista)); end function; interseccio_ultim_unio_dels_altres:=function(llista) ultim:=llista[#llista]; maxc:=ultim-1; trobat:=false; while not trobat do while not inferior(maxc,ultim) do maxc:=maxc-1; end while; j:=1; while j le #llista-1 and not(inferior(maxc,llista[j])) do j:=j+1; end while; if j le #llista-1 then trobat:=true; end if; maxc:=maxc-1; end while; maxc:=maxc+1; ret:=[maxc]; for h in gaps do candidat:=lambdainv(lambda(maxc)-h); if candidat gt 0 and inferior(candidat,ultim) then j:=1; while j le #llista-1 and not(inferior(candidat,llista[j])) do j:=j+1; end while; if j le #llista-1 then ret:=Append(ret,candidat); end if; end if; end for; return(index(ret)); end function; actualitzainterseccioinf:=function(Lconjunts,Lmcinf,Linterseccioinf,Lunioinf,llista) if #llista eq 1 then return Append(Linterseccioinf,nu(llista[1])); else return Append(Linterseccioinf,Lunioinf[index(Lmcinf[index(llista)])]); end if; end function; actualitzaunioinf:=function(Lconjunts,Linterseccioinf,Lunioinf,llista) if #llista eq 1 then return Append(Lunioinf,nu(llista[1])); else return Append(Lunioinf, Lunioinf[index([llista[i]:i in [1..(#llista-1)]])] +nu(llista[#llista])-Lunioinf[interseccio_ultim_unio_dels_altres(llista)]); end if; end function; for i in [1..MAX] do conjuntsaux:=Lconjunts; llista:=[i]; Lconjunts:=actualitzaconjunts(Lconjunts,llista); Lmcinf:=actualitzamcinf(Lmcinf,llista); Linterseccioinf:=actualitzainterseccioinf(Lconjunts,Lmcinf,Linterseccioinf,Lunioinf,llista); Lunioinf:=actualitzaunioinf(Lconjunts,Linterseccioinf,Lunioinf,llista); for conj in conjuntsaux do llista:=Append(conj,i); Lconjunts:=actualitzaconjunts(Lconjunts,llista); Lmcinf:=actualitzamcinf(Lmcinf,llista); Linterseccioinf:=actualitzainterseccioinf(Lconjunts,Lmcinf,Linterseccioinf,Lunioinf,llista); Lunioinf:=actualitzaunioinf(Lconjunts,Linterseccioinf,Lunioinf,llista); end for; end for; joinsets:=function(llista) unio:={}; for conj in llista do unio:=unio join conj; end for; return unio; end function; /* l:=#Lconjunts; print "CONJUNTS="; ; print "MCINF="; ; print "INTERSECCIOINF="; Linterseccioinf; print "UNIOINF="; Lunioinf;*/ /* unioasac:=[#joinsets({N(i):i in llista}):llista in Lconjunts]; errors:=[Lunioinf[i]-unioasac[i]:i in [1..#unioasac]]; printf "VEREDICTE:="; [Lconjunts[i]:i in [1..#errors]|errors[i] ne 0]; */ conj_r_elements:=func; conj_r_elements(3); max_index:=index([1..MAX]); conj_r_elements_ge_i:=func; conj_r_elements_ge_i([4,3]); Output: Magma V2.10-6 Wed Dec 24 2003 08:05:34 on modular [Seed = 3725094571] ------------------------------------- Klein quartic[ 7, 11, 13, 14, 19, 21, 22, 25, 26, 28, 35, 37, 38, 41, 42, 44, 49, 50, 52, 56, 67, 69, 70, 73, 74, 76, 81, 82, 84, 88, 97, 98, 100, 104, 112 ] [ 120 ] Total time: 3.289 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.32.42.proxycache.rima-tde.net. (80.58.32.42) Time: Wed Dec 24 08:06:32 2003 Input: /* Klein quartic */ printf "Klein quartic"; MAX:=6; c:=5; g:=3; semi:=[0,3]; /* Hermitian curve */ /* printf "hermitian curve"; MAX:=10; c:=12; g:=6; semi:=[0,4,5,8,9,10]; */ /* basic del semigrup */ i_cond:=c-g; pertany:=func; gaps:=[i:i in [1..c-1]|not pertany(i)]; lambda:=func; lambdainv:=func; /* oplus, leq, nu */ oplus:=func; inferior:=func; ominus:=func; N:=func; nu:=func; /* order bound */ dORD:=func; Lconjunts:=[[0]]; Lmcinf:=[[0]]; Linterseccioinf:=[1]; Lunioinf:=[1]; index:=function(llista) i:=0; for j in llista do i:=i+2^j; end for; return(i); end function; /* mcinf:=function(Lconjunts,Lmcinf,llista) p:=Position(Lconjunts,llista); if p eq 0 then return -1; else return Lmcinf[p]; end if; end function; interseccioinf:=function(Lconjunts,Linterseccioinf,llista) p:=Position(Lconjunts,llista); if p eq 0 then return -1; else return Linterseccioinf[p]; end if; end function; unioinf:=function(Lconjunts,Lunioinf,llista) p:=Position(Lconjunts,llista); if p eq 0 then return -1; else return Lunioinf[p]; end if; end function; */ actualitzaconjunts:=function (Lconjunts,llista) return(Append(Lconjunts,llista)); end function; actualitzamcinf:=function(Lmcinf,llista) maxc:=llista[1]; if (maxc eq 0) then return (Append(Lmcinf,[0])); end if; trobat:=false; while not trobat do while not inferior(maxc,llista[1]) do maxc:=maxc-1; end while; j:=2; while j le #llista and inferior(maxc,llista[j]) do j:=j+1; end while; if j eq #llista+1 then trobat:=true; end if; maxc:=maxc-1; end while; maxc:=maxc+1; mcinfllista:=[maxc]; for h in gaps do candidat:=lambdainv(lambda(maxc)-h); if candidat gt 0 then j:=1; while j le #llista and inferior(candidat,llista[j]) do j:=j+1; end while; if j eq #llista+1 then mcinfllista:=Append(mcinfllista,candidat); end if; end if; end for; return(Append(Lmcinf,mcinfllista)); end function; interseccio_ultim_unio_dels_altres:=function(llista) ultim:=llista[#llista]; maxc:=ultim-1; trobat:=false; while not trobat do while not inferior(maxc,ultim) do maxc:=maxc-1; end while; j:=1; while j le #llista-1 and not(inferior(maxc,llista[j])) do j:=j+1; end while; if j le #llista-1 then trobat:=true; end if; maxc:=maxc-1; end while; maxc:=maxc+1; ret:=[maxc]; for h in gaps do candidat:=lambdainv(lambda(maxc)-h); if candidat gt 0 and inferior(candidat,ultim) then j:=1; while j le #llista-1 and not(inferior(candidat,llista[j])) do j:=j+1; end while; if j le #llista-1 then ret:=Append(ret,candidat); end if; end if; end for; return(index(ret)); end function; actualitzainterseccioinf:=function(Lconjunts,Lmcinf,Linterseccioinf,Lunioinf,llista) if #llista eq 1 then return Append(Linterseccioinf,nu(llista[1])); else return Append(Linterseccioinf,Lunioinf[index(Lmcinf[index(llista)])]); end if; end function; actualitzaunioinf:=function(Lconjunts,Linterseccioinf,Lunioinf,llista) if #llista eq 1 then return Append(Lunioinf,nu(llista[1])); else return Append(Lunioinf, Lunioinf[index([llista[i]:i in [1..(#llista-1)]])] +nu(llista[#llista])-Lunioinf[interseccio_ultim_unio_dels_altres(llista)]); end if; end function; for i in [1..MAX] do conjuntsaux:=Lconjunts; llista:=[i]; Lconjunts:=actualitzaconjunts(Lconjunts,llista); Lmcinf:=actualitzamcinf(Lmcinf,llista); Linterseccioinf:=actualitzainterseccioinf(Lconjunts,Lmcinf,Linterseccioinf,Lunioinf,llista); Lunioinf:=actualitzaunioinf(Lconjunts,Linterseccioinf,Lunioinf,llista); for conj in conjuntsaux do llista:=Append(conj,i); Lconjunts:=actualitzaconjunts(Lconjunts,llista); Lmcinf:=actualitzamcinf(Lmcinf,llista); Linterseccioinf:=actualitzainterseccioinf(Lconjunts,Lmcinf,Linterseccioinf,Lunioinf,llista); Lunioinf:=actualitzaunioinf(Lconjunts,Linterseccioinf,Lunioinf,llista); end for; end for; joinsets:=function(llista) unio:={}; for conj in llista do unio:=unio join conj; end for; return unio; end function; /* l:=#Lconjunts; print "CONJUNTS="; ; print "MCINF="; ; print "INTERSECCIOINF="; Linterseccioinf; print "UNIOINF="; Lunioinf;*/ /* unioasac:=[#joinsets({N(i):i in llista}):llista in Lconjunts]; errors:=[Lunioinf[i]-unioasac[i]:i in [1..#unioasac]]; printf "VEREDICTE:="; [Lconjunts[i]:i in [1..#errors]|errors[i] ne 0]; */ conj_r_elements:=func; [Lconjunts[i]: i in conj_r_elements(3)]; max_index:=index([1..MAX]); conj_r_elements_ge_i:=func; conj_r_elements_ge_i([3,3]); Output: Magma V2.10-6 Wed Dec 24 2003 08:06:28 on modular [Seed = 2893683859] ------------------------------------- Klein quartic[ [ 0, 1, 2 ], [ 0, 1, 3 ], [ 0, 2, 3 ], [ 1, 2, 3 ], [ 0, 1, 4 ], [ 0, 2, 4 ], [ 1, 2, 4 ], [ 0, 3, 4 ], [ 1, 3, 4 ], [ 2, 3, 4 ], [ 0, 1, 5 ], [ 0, 2, 5 ], [ 1, 2, 5 ], [ 0, 3, 5 ], [ 1, 3, 5 ], [ 2, 3, 5 ], [ 0, 4, 5 ], [ 1, 4, 5 ], [ 2, 4, 5 ], [ 3, 4, 5 ], [ 0, 1, 6 ], [ 0, 2, 6 ], [ 1, 2, 6 ], [ 0, 3, 6 ], [ 1, 3, 6 ], [ 2, 3, 6 ], [ 0, 4, 6 ], [ 1, 4, 6 ], [ 2, 4, 6 ], [ 3, 4, 6 ], [ 0, 5, 6 ], [ 1, 5, 6 ], [ 2, 5, 6 ], [ 3, 5, 6 ], [ 4, 5, 6 ] ] [ 56, 88, 104, 112 ] Total time: 3.299 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.32.42.proxycache.rima-tde.net. (80.58.32.42) Time: Wed Dec 24 08:07:50 2003 Input: /* Klein quartic */ printf "Klein quartic"; MAX:=6; c:=5; g:=3; semi:=[0,3]; /* Hermitian curve */ /* printf "hermitian curve"; MAX:=10; c:=12; g:=6; semi:=[0,4,5,8,9,10]; */ /* basic del semigrup */ i_cond:=c-g; pertany:=func; gaps:=[i:i in [1..c-1]|not pertany(i)]; lambda:=func; lambdainv:=func; /* oplus, leq, nu */ oplus:=func; inferior:=func; ominus:=func; N:=func; nu:=func; /* order bound */ dORD:=func; Lconjunts:=[[0]]; Lmcinf:=[[0]]; Linterseccioinf:=[1]; Lunioinf:=[1]; index:=function(llista) i:=0; for j in llista do i:=i+2^j; end for; return(i); end function; /* mcinf:=function(Lconjunts,Lmcinf,llista) p:=Position(Lconjunts,llista); if p eq 0 then return -1; else return Lmcinf[p]; end if; end function; interseccioinf:=function(Lconjunts,Linterseccioinf,llista) p:=Position(Lconjunts,llista); if p eq 0 then return -1; else return Linterseccioinf[p]; end if; end function; unioinf:=function(Lconjunts,Lunioinf,llista) p:=Position(Lconjunts,llista); if p eq 0 then return -1; else return Lunioinf[p]; end if; end function; */ actualitzaconjunts:=function (Lconjunts,llista) return(Append(Lconjunts,llista)); end function; actualitzamcinf:=function(Lmcinf,llista) maxc:=llista[1]; if (maxc eq 0) then return (Append(Lmcinf,[0])); end if; trobat:=false; while not trobat do while not inferior(maxc,llista[1]) do maxc:=maxc-1; end while; j:=2; while j le #llista and inferior(maxc,llista[j]) do j:=j+1; end while; if j eq #llista+1 then trobat:=true; end if; maxc:=maxc-1; end while; maxc:=maxc+1; mcinfllista:=[maxc]; for h in gaps do candidat:=lambdainv(lambda(maxc)-h); if candidat gt 0 then j:=1; while j le #llista and inferior(candidat,llista[j]) do j:=j+1; end while; if j eq #llista+1 then mcinfllista:=Append(mcinfllista,candidat); end if; end if; end for; return(Append(Lmcinf,mcinfllista)); end function; interseccio_ultim_unio_dels_altres:=function(llista) ultim:=llista[#llista]; maxc:=ultim-1; trobat:=false; while not trobat do while not inferior(maxc,ultim) do maxc:=maxc-1; end while; j:=1; while j le #llista-1 and not(inferior(maxc,llista[j])) do j:=j+1; end while; if j le #llista-1 then trobat:=true; end if; maxc:=maxc-1; end while; maxc:=maxc+1; ret:=[maxc]; for h in gaps do candidat:=lambdainv(lambda(maxc)-h); if candidat gt 0 and inferior(candidat,ultim) then j:=1; while j le #llista-1 and not(inferior(candidat,llista[j])) do j:=j+1; end while; if j le #llista-1 then ret:=Append(ret,candidat); end if; end if; end for; return(index(ret)); end function; actualitzainterseccioinf:=function(Lconjunts,Lmcinf,Linterseccioinf,Lunioinf,llista) if #llista eq 1 then return Append(Linterseccioinf,nu(llista[1])); else return Append(Linterseccioinf,Lunioinf[index(Lmcinf[index(llista)])]); end if; end function; actualitzaunioinf:=function(Lconjunts,Linterseccioinf,Lunioinf,llista) if #llista eq 1 then return Append(Lunioinf,nu(llista[1])); else return Append(Lunioinf, Lunioinf[index([llista[i]:i in [1..(#llista-1)]])] +nu(llista[#llista])-Lunioinf[interseccio_ultim_unio_dels_altres(llista)]); end if; end function; for i in [1..MAX] do conjuntsaux:=Lconjunts; llista:=[i]; Lconjunts:=actualitzaconjunts(Lconjunts,llista); Lmcinf:=actualitzamcinf(Lmcinf,llista); Linterseccioinf:=actualitzainterseccioinf(Lconjunts,Lmcinf,Linterseccioinf,Lunioinf,llista); Lunioinf:=actualitzaunioinf(Lconjunts,Linterseccioinf,Lunioinf,llista); for conj in conjuntsaux do llista:=Append(conj,i); Lconjunts:=actualitzaconjunts(Lconjunts,llista); Lmcinf:=actualitzamcinf(Lmcinf,llista); Linterseccioinf:=actualitzainterseccioinf(Lconjunts,Lmcinf,Linterseccioinf,Lunioinf,llista); Lunioinf:=actualitzaunioinf(Lconjunts,Linterseccioinf,Lunioinf,llista); end for; end for; joinsets:=function(llista) unio:={}; for conj in llista do unio:=unio join conj; end for; return unio; end function; /* l:=#Lconjunts; print "CONJUNTS="; ; print "MCINF="; ; print "INTERSECCIOINF="; Linterseccioinf; print "UNIOINF="; Lunioinf;*/ /* unioasac:=[#joinsets({N(i):i in llista}):llista in Lconjunts]; errors:=[Lunioinf[i]-unioasac[i]:i in [1..#unioasac]]; printf "VEREDICTE:="; [Lconjunts[i]:i in [1..#errors]|errors[i] ne 0]; */ conj_r_elements:=func; [Lconjunts[i]: i in conj_r_elements(3)]; max_index:=index([1..MAX]); conj_r_elements_ge_i:=func; conj_r_elements_ge_i([3,3]); [Lconjunts[i]: i in conj_r_elements_ge_i([3,3])]; Output: Magma V2.10-6 Wed Dec 24 2003 08:07:43 on modular [Seed = 2959474756] ------------------------------------- Klein quartic[ [ 0, 1, 2 ], [ 0, 1, 3 ], [ 0, 2, 3 ], [ 1, 2, 3 ], [ 0, 1, 4 ], [ 0, 2, 4 ], [ 1, 2, 4 ], [ 0, 3, 4 ], [ 1, 3, 4 ], [ 2, 3, 4 ], [ 0, 1, 5 ], [ 0, 2, 5 ], [ 1, 2, 5 ], [ 0, 3, 5 ], [ 1, 3, 5 ], [ 2, 3, 5 ], [ 0, 4, 5 ], [ 1, 4, 5 ], [ 2, 4, 5 ], [ 3, 4, 5 ], [ 0, 1, 6 ], [ 0, 2, 6 ], [ 1, 2, 6 ], [ 0, 3, 6 ], [ 1, 3, 6 ], [ 2, 3, 6 ], [ 0, 4, 6 ], [ 1, 4, 6 ], [ 2, 4, 6 ], [ 3, 4, 6 ], [ 0, 5, 6 ], [ 1, 5, 6 ], [ 2, 5, 6 ], [ 3, 5, 6 ], [ 4, 5, 6 ] ] [ 56, 88, 104, 112 ] [ [ 3, 4, 5 ], [ 3, 4, 6 ], [ 3, 5, 6 ], [ 4, 5, 6 ] ] Total time: 3.279 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.32.42.proxycache.rima-tde.net. (80.58.32.42) Time: Wed Dec 24 08:13:40 2003 Input: /* Klein quartic */ printf "Klein quartic"; MAX:=10; c:=5; g:=3; semi:=[0,3]; /* Hermitian curve */ /* printf "hermitian curve"; MAX:=10; c:=12; g:=6; semi:=[0,4,5,8,9,10]; */ /* basic del semigrup */ i_cond:=c-g; pertany:=func; gaps:=[i:i in [1..c-1]|not pertany(i)]; lambda:=func; lambdainv:=func; /* oplus, leq, nu */ oplus:=func; inferior:=func; ominus:=func; N:=func; nu:=func; /* order bound */ dORD:=func; Lconjunts:=[[0]]; Lmcinf:=[[0]]; Linterseccioinf:=[1]; Lunioinf:=[1]; index:=function(llista) i:=0; for j in llista do i:=i+2^j; end for; return(i); end function; /* mcinf:=function(Lconjunts,Lmcinf,llista) p:=Position(Lconjunts,llista); if p eq 0 then return -1; else return Lmcinf[p]; end if; end function; interseccioinf:=function(Lconjunts,Linterseccioinf,llista) p:=Position(Lconjunts,llista); if p eq 0 then return -1; else return Linterseccioinf[p]; end if; end function; unioinf:=function(Lconjunts,Lunioinf,llista) p:=Position(Lconjunts,llista); if p eq 0 then return -1; else return Lunioinf[p]; end if; end function; */ actualitzaconjunts:=function (Lconjunts,llista) return(Append(Lconjunts,llista)); end function; actualitzamcinf:=function(Lmcinf,llista) maxc:=llista[1]; if (maxc eq 0) then return (Append(Lmcinf,[0])); end if; trobat:=false; while not trobat do while not inferior(maxc,llista[1]) do maxc:=maxc-1; end while; j:=2; while j le #llista and inferior(maxc,llista[j]) do j:=j+1; end while; if j eq #llista+1 then trobat:=true; end if; maxc:=maxc-1; end while; maxc:=maxc+1; mcinfllista:=[maxc]; for h in gaps do candidat:=lambdainv(lambda(maxc)-h); if candidat gt 0 then j:=1; while j le #llista and inferior(candidat,llista[j]) do j:=j+1; end while; if j eq #llista+1 then mcinfllista:=Append(mcinfllista,candidat); end if; end if; end for; return(Append(Lmcinf,mcinfllista)); end function; interseccio_ultim_unio_dels_altres:=function(llista) ultim:=llista[#llista]; maxc:=ultim-1; trobat:=false; while not trobat do while not inferior(maxc,ultim) do maxc:=maxc-1; end while; j:=1; while j le #llista-1 and not(inferior(maxc,llista[j])) do j:=j+1; end while; if j le #llista-1 then trobat:=true; end if; maxc:=maxc-1; end while; maxc:=maxc+1; ret:=[maxc]; for h in gaps do candidat:=lambdainv(lambda(maxc)-h); if candidat gt 0 and inferior(candidat,ultim) then j:=1; while j le #llista-1 and not(inferior(candidat,llista[j])) do j:=j+1; end while; if j le #llista-1 then ret:=Append(ret,candidat); end if; end if; end for; return(index(ret)); end function; actualitzainterseccioinf:=function(Lconjunts,Lmcinf,Linterseccioinf,Lunioinf,llista) if #llista eq 1 then return Append(Linterseccioinf,nu(llista[1])); else return Append(Linterseccioinf,Lunioinf[index(Lmcinf[index(llista)])]); end if; end function; actualitzaunioinf:=function(Lconjunts,Linterseccioinf,Lunioinf,llista) if #llista eq 1 then return Append(Lunioinf,nu(llista[1])); else return Append(Lunioinf, Lunioinf[index([llista[i]:i in [1..(#llista-1)]])] +nu(llista[#llista])-Lunioinf[interseccio_ultim_unio_dels_altres(llista)]); end if; end function; for i in [1..MAX] do conjuntsaux:=Lconjunts; llista:=[i]; Lconjunts:=actualitzaconjunts(Lconjunts,llista); Lmcinf:=actualitzamcinf(Lmcinf,llista); Linterseccioinf:=actualitzainterseccioinf(Lconjunts,Lmcinf,Linterseccioinf,Lunioinf,llista); Lunioinf:=actualitzaunioinf(Lconjunts,Linterseccioinf,Lunioinf,llista); for conj in conjuntsaux do llista:=Append(conj,i); Lconjunts:=actualitzaconjunts(Lconjunts,llista); Lmcinf:=actualitzamcinf(Lmcinf,llista); Linterseccioinf:=actualitzainterseccioinf(Lconjunts,Lmcinf,Linterseccioinf,Lunioinf,llista); Lunioinf:=actualitzaunioinf(Lconjunts,Linterseccioinf,Lunioinf,llista); end for; end for; joinsets:=function(llista) unio:={}; for conj in llista do unio:=unio join conj; end for; return unio; end function; /* l:=#Lconjunts; print "CONJUNTS="; ; print "MCINF="; ; print "INTERSECCIOINF="; Linterseccioinf; print "UNIOINF="; Lunioinf; */ /* unioasac:=[#joinsets({N(i):i in llista}):llista in Lconjunts]; errors:=[Lunioinf[i]-unioasac[i]:i in [1..#unioasac]]; printf "VEREDICTE:="; [Lconjunts[i]:i in [1..#errors]|errors[i] ne 0]; */ conj_r_elements:=func; [Lconjunts[i]: i in conj_r_elements(3)]; max_index:=index([1..MAX]); conj_r_elements_ge_i:=func; [Lconjunts[i]: i in conj_r_elements_ge_i([3,3])]; gen_ham_weight:=func; [gen_ham_weight([r,i]): i in [1..5]]: r in [1..5]]; Output: Magma V2.10-6 Wed Dec 24 2003 08:13:34 on modular [Seed = 3127645477] ------------------------------------- Klein quartic[ [ 0, 1, 2 ], [ 0, 1, 3 ], [ 0, 2, 3 ], [ 1, 2, 3 ], [ 0, 1, 4 ], [ 0, 2, 4 ], [ 1, 2, 4 ], [ 0, 3, 4 ], [ 1, 3, 4 ], [ 2, 3, 4 ], [ 0, 1, 5 ], [ 0, 2, 5 ], [ 1, 2, 5 ], [ 0, 3, 5 ], [ 1, 3, 5 ], [ 2, 3, 5 ], [ 0, 4, 5 ], [ 1, 4, 5 ], [ 2, 4, 5 ], [ 3, 4, 5 ], [ 0, 1, 6 ], [ 0, 2, 6 ], [ 1, 2, 6 ], [ 0, 3, 6 ], [ 1, 3, 6 ], [ 2, 3, 6 ], [ 0, 4, 6 ], [ 1, 4, 6 ], [ 2, 4, 6 ], [ 3, 4, 6 ], [ 0, 5, 6 ], [ 1, 5, 6 ], [ 2, 5, 6 ], [ 3, 5, 6 ], [ 4, 5, 6 ], [ 0, 1, 7 ], [ 0, 2, 7 ], [ 1, 2, 7 ], [ 0, 3, 7 ], [ 1, 3, 7 ], [ 2, 3, 7 ], [ 0, 4, 7 ], [ 1, 4, 7 ], [ 2, 4, 7 ], [ 3, 4, 7 ], [ 0, 5, 7 ], [ 1, 5, 7 ], [ 2, 5, 7 ], [ 3, 5, 7 ], [ 4, 5, 7 ], [ 0, 6, 7 ], [ 1, 6, 7 ], [ 2, 6, 7 ], [ 3, 6, 7 ], [ 4, 6, 7 ], [ 5, 6, 7 ], [ 0, 1, 8 ], [ 0, 2, 8 ], [ 1, 2, 8 ], [ 0, 3, 8 ], [ 1, 3, 8 ], [ 2, 3, 8 ], [ 0, 4, 8 ], [ 1, 4, 8 ], [ 2, 4, 8 ], [ 3, 4, 8 ], [ 0, 5, 8 ], [ 1, 5, 8 ], [ 2, 5, 8 ], [ 3, 5, 8 ], [ 4, 5, 8 ], [ 0, 6, 8 ], [ 1, 6, 8 ], [ 2, 6, 8 ], [ 3, 6, 8 ], [ 4, 6, 8 ], [ 5, 6, 8 ], [ 0, 7, 8 ], [ 1, 7, 8 ], [ 2, 7, 8 ], [ 3, 7, 8 ], [ 4, 7, 8 ], [ 5, 7, 8 ], [ 6, 7, 8 ], [ 0, 1, 9 ], [ 0, 2, 9 ], [ 1, 2, 9 ], [ 0, 3, 9 ], [ 1, 3, 9 ], [ 2, 3, 9 ], [ 0, 4, 9 ], [ 1, 4, 9 ], [ 2, 4, 9 ], [ 3, 4, 9 ], [ 0, 5, 9 ], [ 1, 5, 9 ], [ 2, 5, 9 ], [ 3, 5, 9 ], [ 4, 5, 9 ], [ 0, 6, 9 ], [ 1, 6, 9 ], [ 2, 6, 9 ], [ 3, 6, 9 ], [ 4, 6, 9 ], [ 5, 6, 9 ], [ 0, 7, 9 ], [ 1, 7, 9 ], [ 2, 7, 9 ], [ 3, 7, 9 ], [ 4, 7, 9 ], [ 5, 7, 9 ], [ 6, 7, 9 ], [ 0, 8, 9 ], [ 1, 8, 9 ], [ 2, 8, 9 ], [ 3, 8, 9 ], [ 4, 8, 9 ], [ 5, 8, 9 ], [ 6, 8, 9 ], [ 7, 8, 9 ], [ 0, 1, 10 ], [ 0, 2, 10 ], [ 1, 2, 10 ], [ 0, 3, 10 ], [ 1, 3, 10 ], [ 2, 3, 10 ], [ 0, 4, 10 ], [ 1, 4, 10 ], [ 2, 4, 10 ], [ 3, 4, 10 ], [ 0, 5, 10 ], [ 1, 5, 10 ], [ 2, 5, 10 ], [ 3, 5, 10 ], [ 4, 5, 10 ], [ 0, 6, 10 ], [ 1, 6, 10 ], [ 2, 6, 10 ], [ 3, 6, 10 ], [ 4, 6, 10 ], [ 5, 6, 10 ], [ 0, 7, 10 ], [ 1, 7, 10 ], [ 2, 7, 10 ], [ 3, 7, 10 ], [ 4, 7, 10 ], [ 5, 7, 10 ], [ 6, 7, 10 ], [ 0, 8, 10 ], [ 1, 8, 10 ], [ 2, 8, 10 ], [ 3, 8, 10 ], [ 4, 8, 10 ], [ 5, 8, 10 ], [ 6, 8, 10 ], [ 7, 8, 10 ], [ 0, 9, 10 ], [ 1, 9, 10 ], [ 2, 9, 10 ], [ 3, 9, 10 ], [ 4, 9, 10 ], [ 5, 9, 10 ], [ 6, 9, 10 ], [ 7, 9, 10 ], [ 8, 9, 10 ] ] [ [ 3, 4, 5 ], [ 3, 4, 6 ], [ 3, 5, 6 ], [ 4, 5, 6 ], [ 3, 4, 7 ], [ 3, 5, 7 ], [ 4, 5, 7 ], [ 3, 6, 7 ], [ 4, 6, 7 ], [ 5, 6, 7 ], [ 3, 4, 8 ], [ 3, 5, 8 ], [ 4, 5, 8 ], [ 3, 6, 8 ], [ 4, 6, 8 ], [ 5, 6, 8 ], [ 3, 7, 8 ], [ 4, 7, 8 ], [ 5, 7, 8 ], [ 6, 7, 8 ], [ 3, 4, 9 ], [ 3, 5, 9 ], [ 4, 5, 9 ], [ 3, 6, 9 ], [ 4, 6, 9 ], [ 5, 6, 9 ], [ 3, 7, 9 ], [ 4, 7, 9 ], [ 5, 7, 9 ], [ 6, 7, 9 ], [ 3, 8, 9 ], [ 4, 8, 9 ], [ 5, 8, 9 ], [ 6, 8, 9 ], [ 7, 8, 9 ], [ 3, 4, 10 ], [ 3, 5, 10 ], [ 4, 5, 10 ], [ 3, 6, 10 ], [ 4, 6, 10 ], [ 5, 6, 10 ], [ 3, 7, 10 ], [ 4, 7, 10 ], [ 5, 7, 10 ], [ 6, 7, 10 ], [ 3, 8, 10 ], [ 4, 8, 10 ], [ 5, 8, 10 ], [ 6, 8, 10 ], [ 7, 8, 10 ], [ 3, 9, 10 ], [ 4, 9, 10 ], [ 5, 9, 10 ], [ 6, 9, 10 ], [ 7, 9, 10 ], [ 8, 9, 10 ] ] >> gen_ham_weight:=func ^ User error: bad syntax >> [gen_ham_weight([r,i]): i in [1..5]]: r in [1..5]]; ; ^ User error: bad syntax Total time: 5.379 seconds, Total memory usage: 2.42MB ************** MAGMA ***************** Host 80.58.32.42.proxycache.rima-tde.net. (80.58.32.42) Time: Wed Dec 24 08:15:37 2003 Input: /* Klein quartic */ printf "Klein quartic"; MAX:=10; c:=5; g:=3; semi:=[0,3]; /* Hermitian curve */ /* printf "hermitian curve"; MAX:=10; c:=12; g:=6; semi:=[0,4,5,8,9,10]; */ /* basic del semigrup */ i_cond:=c-g; pertany:=func; gaps:=[i:i in [1..c-1]|not pertany(i)]; lambda:=func; lambdainv:=func; /* oplus, leq, nu */ oplus:=func; inferior:=func; ominus:=func; N:=func; nu:=func; /* order bound */ dORD:=func; Lconjunts:=[[0]]; Lmcinf:=[[0]]; Linterseccioinf:=[1]; Lunioinf:=[1]; index:=function(llista) i:=0; for j in llista do i:=i+2^j; end for; return(i); end function; /* mcinf:=function(Lconjunts,Lmcinf,llista) p:=Position(Lconjunts,llista); if p eq 0 then return -1; else return Lmcinf[p]; end if; end function; interseccioinf:=function(Lconjunts,Linterseccioinf,llista) p:=Position(Lconjunts,llista); if p eq 0 then return -1; else return Linterseccioinf[p]; end if; end function; unioinf:=function(Lconjunts,Lunioinf,llista) p:=Position(Lconjunts,llista); if p eq 0 then return -1; else return Lunioinf[p]; end if; end function; */ actualitzaconjunts:=function (Lconjunts,llista) return(Append(Lconjunts,llista)); end function; actualitzamcinf:=function(Lmcinf,llista) maxc:=llista[1]; if (maxc eq 0) then return (Append(Lmcinf,[0])); end if; trobat:=false; while not trobat do while not inferior(maxc,llista[1]) do maxc:=maxc-1; end while; j:=2; while j le #llista and inferior(maxc,llista[j]) do j:=j+1; end while; if j eq #llista+1 then trobat:=true; end if; maxc:=maxc-1; end while; maxc:=maxc+1; mcinfllista:=[maxc]; for h in gaps do candidat:=lambdainv(lambda(maxc)-h); if candidat gt 0 then j:=1; while j le #llista and inferior(candidat,llista[j]) do j:=j+1; end while; if j eq #llista+1 then mcinfllista:=Append(mcinfllista,candidat); end if; end if; end for; return(Append(Lmcinf,mcinfllista)); end function; interseccio_ultim_unio_dels_altres:=function(llista) ultim:=llista[#llista]; maxc:=ultim-1; trobat:=false; while not trobat do while not inferior(maxc,ultim) do maxc:=maxc-1; end while; j:=1; while j le #llista-1 and not(inferior(maxc,llista[j])) do j:=j+1; end while; if j le #llista-1 then trobat:=true; end if; maxc:=maxc-1; end while; maxc:=maxc+1; ret:=[maxc]; for h in gaps do candidat:=lambdainv(lambda(maxc)-h); if candidat gt 0 and inferior(candidat,ultim) then j:=1; while j le #llista-1 and not(inferior(candidat,llista[j])) do j:=j+1; end while; if j le #llista-1 then ret:=Append(ret,candidat); end if; end if; end for; return(index(ret)); end function; actualitzainterseccioinf:=function(Lconjunts,Lmcinf,Linterseccioinf,Lunioinf,llista) if #llista eq 1 then return Append(Linterseccioinf,nu(llista[1])); else return Append(Linterseccioinf,Lunioinf[index(Lmcinf[index(llista)])]); end if; end function; actualitzaunioinf:=function(Lconjunts,Linterseccioinf,Lunioinf,llista) if #llista eq 1 then return Append(Lunioinf,nu(llista[1])); else return Append(Lunioinf, Lunioinf[index([llista[i]:i in [1..(#llista-1)]])] +nu(llista[#llista])-Lunioinf[interseccio_ultim_unio_dels_altres(llista)]); end if; end function; for i in [1..MAX] do conjuntsaux:=Lconjunts; llista:=[i]; Lconjunts:=actualitzaconjunts(Lconjunts,llista); Lmcinf:=actualitzamcinf(Lmcinf,llista); Linterseccioinf:=actualitzainterseccioinf(Lconjunts,Lmcinf,Linterseccioinf,Lunioinf,llista); Lunioinf:=actualitzaunioinf(Lconjunts,Linterseccioinf,Lunioinf,llista); for conj in conjuntsaux do llista:=Append(conj,i); Lconjunts:=actualitzaconjunts(Lconjunts,llista); Lmcinf:=actualitzamcinf(Lmcinf,llista); Linterseccioinf:=actualitzainterseccioinf(Lconjunts,Lmcinf,Linterseccioinf,Lunioinf,llista); Lunioinf:=actualitzaunioinf(Lconjunts,Linterseccioinf,Lunioinf,llista); end for; end for; joinsets:=function(llista) unio:={}; for conj in llista do unio:=unio join conj; end for; return unio; end function; /* l:=#Lconjunts; print "CONJUNTS="; ; print "MCINF="; ; print "INTERSECCIOINF="; Linterseccioinf; print "UNIOINF="; Lunioinf; */ /* unioasac:=[#joinsets({N(i):i in llista}):llista in Lconjunts]; errors:=[Lunioinf[i]-unioasac[i]:i in [1..#unioasac]]; printf "VEREDICTE:="; [Lconjunts[i]:i in [1..#errors]|errors[i] ne 0]; */ conj_r_elements:=func; // [Lconjunts[i]: i in conj_r_elements(3)]; max_index:=index([1..MAX]); conj_r_elements_ge_i:=func; // [Lconjunts[i]: i in conj_r_elements_ge_i([3,3])]; gen_ham_weight:=func; [gen_ham_weight([r,i]): i in [1..5]]: r in [1..5]]; Output: Magma V2.10-6 Wed Dec 24 2003 08:15:32 on modular [Seed = 2304714652] ------------------------------------- Klein quartic >> [gen_ham_weight([r,i]): i in [1..5]]: r in [1..5]]; ; ^ User error: bad syntax Total time: 5.059 seconds, Total memory usage: 2.42MB ************** MAGMA ***************** Host 80.58.32.42.proxycache.rima-tde.net. (80.58.32.42) Time: Wed Dec 24 08:16:14 2003 Input: /* Klein quartic */ printf "Klein quartic"; MAX:=10; c:=5; g:=3; semi:=[0,3]; /* Hermitian curve */ /* printf "hermitian curve"; MAX:=10; c:=12; g:=6; semi:=[0,4,5,8,9,10]; */ /* basic del semigrup */ i_cond:=c-g; pertany:=func; gaps:=[i:i in [1..c-1]|not pertany(i)]; lambda:=func; lambdainv:=func; /* oplus, leq, nu */ oplus:=func; inferior:=func; ominus:=func; N:=func; nu:=func; /* order bound */ dORD:=func; Lconjunts:=[[0]]; Lmcinf:=[[0]]; Linterseccioinf:=[1]; Lunioinf:=[1]; index:=function(llista) i:=0; for j in llista do i:=i+2^j; end for; return(i); end function; /* mcinf:=function(Lconjunts,Lmcinf,llista) p:=Position(Lconjunts,llista); if p eq 0 then return -1; else return Lmcinf[p]; end if; end function; interseccioinf:=function(Lconjunts,Linterseccioinf,llista) p:=Position(Lconjunts,llista); if p eq 0 then return -1; else return Linterseccioinf[p]; end if; end function; unioinf:=function(Lconjunts,Lunioinf,llista) p:=Position(Lconjunts,llista); if p eq 0 then return -1; else return Lunioinf[p]; end if; end function; */ actualitzaconjunts:=function (Lconjunts,llista) return(Append(Lconjunts,llista)); end function; actualitzamcinf:=function(Lmcinf,llista) maxc:=llista[1]; if (maxc eq 0) then return (Append(Lmcinf,[0])); end if; trobat:=false; while not trobat do while not inferior(maxc,llista[1]) do maxc:=maxc-1; end while; j:=2; while j le #llista and inferior(maxc,llista[j]) do j:=j+1; end while; if j eq #llista+1 then trobat:=true; end if; maxc:=maxc-1; end while; maxc:=maxc+1; mcinfllista:=[maxc]; for h in gaps do candidat:=lambdainv(lambda(maxc)-h); if candidat gt 0 then j:=1; while j le #llista and inferior(candidat,llista[j]) do j:=j+1; end while; if j eq #llista+1 then mcinfllista:=Append(mcinfllista,candidat); end if; end if; end for; return(Append(Lmcinf,mcinfllista)); end function; interseccio_ultim_unio_dels_altres:=function(llista) ultim:=llista[#llista]; maxc:=ultim-1; trobat:=false; while not trobat do while not inferior(maxc,ultim) do maxc:=maxc-1; end while; j:=1; while j le #llista-1 and not(inferior(maxc,llista[j])) do j:=j+1; end while; if j le #llista-1 then trobat:=true; end if; maxc:=maxc-1; end while; maxc:=maxc+1; ret:=[maxc]; for h in gaps do candidat:=lambdainv(lambda(maxc)-h); if candidat gt 0 and inferior(candidat,ultim) then j:=1; while j le #llista-1 and not(inferior(candidat,llista[j])) do j:=j+1; end while; if j le #llista-1 then ret:=Append(ret,candidat); end if; end if; end for; return(index(ret)); end function; actualitzainterseccioinf:=function(Lconjunts,Lmcinf,Linterseccioinf,Lunioinf,llista) if #llista eq 1 then return Append(Linterseccioinf,nu(llista[1])); else return Append(Linterseccioinf,Lunioinf[index(Lmcinf[index(llista)])]); end if; end function; actualitzaunioinf:=function(Lconjunts,Linterseccioinf,Lunioinf,llista) if #llista eq 1 then return Append(Lunioinf,nu(llista[1])); else return Append(Lunioinf, Lunioinf[index([llista[i]:i in [1..(#llista-1)]])] +nu(llista[#llista])-Lunioinf[interseccio_ultim_unio_dels_altres(llista)]); end if; end function; for i in [1..MAX] do conjuntsaux:=Lconjunts; llista:=[i]; Lconjunts:=actualitzaconjunts(Lconjunts,llista); Lmcinf:=actualitzamcinf(Lmcinf,llista); Linterseccioinf:=actualitzainterseccioinf(Lconjunts,Lmcinf,Linterseccioinf,Lunioinf,llista); Lunioinf:=actualitzaunioinf(Lconjunts,Linterseccioinf,Lunioinf,llista); for conj in conjuntsaux do llista:=Append(conj,i); Lconjunts:=actualitzaconjunts(Lconjunts,llista); Lmcinf:=actualitzamcinf(Lmcinf,llista); Linterseccioinf:=actualitzainterseccioinf(Lconjunts,Lmcinf,Linterseccioinf,Lunioinf,llista); Lunioinf:=actualitzaunioinf(Lconjunts,Linterseccioinf,Lunioinf,llista); end for; end for; joinsets:=function(llista) unio:={}; for conj in llista do unio:=unio join conj; end for; return unio; end function; /* l:=#Lconjunts; print "CONJUNTS="; ; print "MCINF="; ; print "INTERSECCIOINF="; Linterseccioinf; print "UNIOINF="; Lunioinf; */ /* unioasac:=[#joinsets({N(i):i in llista}):llista in Lconjunts]; errors:=[Lunioinf[i]-unioasac[i]:i in [1..#unioasac]]; printf "VEREDICTE:="; [Lconjunts[i]:i in [1..#errors]|errors[i] ne 0]; */ conj_r_elements:=func; // [Lconjunts[i]: i in conj_r_elements(3)]; max_index:=index([1..MAX]); conj_r_elements_ge_i:=func; // [Lconjunts[i]: i in conj_r_elements_ge_i([3,3])]; gen_ham_weight:=func; [[gen_ham_weight([r,i]): i in [1..5]]: r in [1..5]]; Output: Magma V2.10-6 Wed Dec 24 2003 08:16:09 on modular [Seed = 2420522600] ------------------------------------- Klein quartic[ [ 2, 2, 2, 2, 4 ], [ 3, 3, 4, 5, 6 ], [ 4, 5, 5, 6, 7 ], [ 5, 6, 7, 8, 9 ], [ 6, 7, 8, 9, 10 ] ] Total time: 5.269 seconds, Total memory usage: 2.42MB ************** MAGMA ***************** Host 80.58.32.42.proxycache.rima-tde.net. (80.58.32.42) Time: Wed Dec 24 08:20:06 2003 Input: /* Klein quartic */ printf "Klein quartic"; MAX:=10; c:=5; g:=3; semi:=[0,3]; /* Hermitian curve */ /* printf "hermitian curve"; MAX:=10; c:=12; g:=6; semi:=[0,4,5,8,9,10]; */ /* basic del semigrup */ i_cond:=c-g; pertany:=func; gaps:=[i:i in [1..c-1]|not pertany(i)]; lambda:=func; lambdainv:=func; /* oplus, leq, nu */ oplus:=func; inferior:=func; ominus:=func; N:=func; nu:=func; /* order bound */ dORD:=func; Lconjunts:=[[0]]; Lmcinf:=[[0]]; Linterseccioinf:=[1]; Lunioinf:=[1]; index:=function(llista) i:=0; for j in llista do i:=i+2^j; end for; return(i); end function; /* mcinf:=function(Lconjunts,Lmcinf,llista) p:=Position(Lconjunts,llista); if p eq 0 then return -1; else return Lmcinf[p]; end if; end function; interseccioinf:=function(Lconjunts,Linterseccioinf,llista) p:=Position(Lconjunts,llista); if p eq 0 then return -1; else return Linterseccioinf[p]; end if; end function; unioinf:=function(Lconjunts,Lunioinf,llista) p:=Position(Lconjunts,llista); if p eq 0 then return -1; else return Lunioinf[p]; end if; end function; */ actualitzaconjunts:=function (Lconjunts,llista) return(Append(Lconjunts,llista)); end function; actualitzamcinf:=function(Lmcinf,llista) maxc:=llista[1]; if (maxc eq 0) then return (Append(Lmcinf,[0])); end if; trobat:=false; while not trobat do while not inferior(maxc,llista[1]) do maxc:=maxc-1; end while; j:=2; while j le #llista and inferior(maxc,llista[j]) do j:=j+1; end while; if j eq #llista+1 then trobat:=true; end if; maxc:=maxc-1; end while; maxc:=maxc+1; mcinfllista:=[maxc]; for h in gaps do candidat:=lambdainv(lambda(maxc)-h); if candidat gt 0 then j:=1; while j le #llista and inferior(candidat,llista[j]) do j:=j+1; end while; if j eq #llista+1 then mcinfllista:=Append(mcinfllista,candidat); end if; end if; end for; return(Append(Lmcinf,mcinfllista)); end function; interseccio_ultim_unio_dels_altres:=function(llista) ultim:=llista[#llista]; maxc:=ultim-1; trobat:=false; while not trobat do while not inferior(maxc,ultim) do maxc:=maxc-1; end while; j:=1; while j le #llista-1 and not(inferior(maxc,llista[j])) do j:=j+1; end while; if j le #llista-1 then trobat:=true; end if; maxc:=maxc-1; end while; maxc:=maxc+1; ret:=[maxc]; for h in gaps do candidat:=lambdainv(lambda(maxc)-h); if candidat gt 0 and inferior(candidat,ultim) then j:=1; while j le #llista-1 and not(inferior(candidat,llista[j])) do j:=j+1; end while; if j le #llista-1 then ret:=Append(ret,candidat); end if; end if; end for; return(index(ret)); end function; actualitzainterseccioinf:=function(Lconjunts,Lmcinf,Linterseccioinf,Lunioinf,llista) if #llista eq 1 then return Append(Linterseccioinf,nu(llista[1])); else return Append(Linterseccioinf,Lunioinf[index(Lmcinf[index(llista)])]); end if; end function; actualitzaunioinf:=function(Lconjunts,Linterseccioinf,Lunioinf,llista) if #llista eq 1 then return Append(Lunioinf,nu(llista[1])); else return Append(Lunioinf, Lunioinf[index([llista[i]:i in [1..(#llista-1)]])] +nu(llista[#llista])-Lunioinf[interseccio_ultim_unio_dels_altres(llista)]); end if; end function; for i in [1..MAX] do conjuntsaux:=Lconjunts; llista:=[i]; Lconjunts:=actualitzaconjunts(Lconjunts,llista); Lmcinf:=actualitzamcinf(Lmcinf,llista); Linterseccioinf:=actualitzainterseccioinf(Lconjunts,Lmcinf,Linterseccioinf,Lunioinf,llista); Lunioinf:=actualitzaunioinf(Lconjunts,Linterseccioinf,Lunioinf,llista); for conj in conjuntsaux do llista:=Append(conj,i); Lconjunts:=actualitzaconjunts(Lconjunts,llista); Lmcinf:=actualitzamcinf(Lmcinf,llista); Linterseccioinf:=actualitzainterseccioinf(Lconjunts,Lmcinf,Linterseccioinf,Lunioinf,llista); Lunioinf:=actualitzaunioinf(Lconjunts,Linterseccioinf,Lunioinf,llista); end for; end for; joinsets:=function(llista) unio:={}; for conj in llista do unio:=unio join conj; end for; return unio; end function; /* l:=#Lconjunts; print "CONJUNTS="; ; print "MCINF="; ; print "INTERSECCIOINF="; Linterseccioinf; print "UNIOINF="; Lunioinf; */ /* unioasac:=[#joinsets({N(i):i in llista}):llista in Lconjunts]; errors:=[Lunioinf[i]-unioasac[i]:i in [1..#unioasac]]; printf "VEREDICTE:="; [Lconjunts[i]:i in [1..#errors]|errors[i] ne 0]; */ conj_r_elements:=func; [Lconjunts[i]: i in conj_r_elements(3)]; max_index:=index([1..MAX]); conj_r_elements_ge_i:=func; [Lconjunts[i]: i in conj_r_elements_ge_i([3,3])]; gen_ham_weight:=func; [gen_ham_weight([r,i]): i in [0..7]]: r in [0..7]]; Output: Magma V2.10-6 Wed Dec 24 2003 08:20:00 on modular [Seed = 1790756747] ------------------------------------- Klein quartic[ [ 0, 1, 2 ], [ 0, 1, 3 ], [ 0, 2, 3 ], [ 1, 2, 3 ], [ 0, 1, 4 ], [ 0, 2, 4 ], [ 1, 2, 4 ], [ 0, 3, 4 ], [ 1, 3, 4 ], [ 2, 3, 4 ], [ 0, 1, 5 ], [ 0, 2, 5 ], [ 1, 2, 5 ], [ 0, 3, 5 ], [ 1, 3, 5 ], [ 2, 3, 5 ], [ 0, 4, 5 ], [ 1, 4, 5 ], [ 2, 4, 5 ], [ 3, 4, 5 ], [ 0, 1, 6 ], [ 0, 2, 6 ], [ 1, 2, 6 ], [ 0, 3, 6 ], [ 1, 3, 6 ], [ 2, 3, 6 ], [ 0, 4, 6 ], [ 1, 4, 6 ], [ 2, 4, 6 ], [ 3, 4, 6 ], [ 0, 5, 6 ], [ 1, 5, 6 ], [ 2, 5, 6 ], [ 3, 5, 6 ], [ 4, 5, 6 ], [ 0, 1, 7 ], [ 0, 2, 7 ], [ 1, 2, 7 ], [ 0, 3, 7 ], [ 1, 3, 7 ], [ 2, 3, 7 ], [ 0, 4, 7 ], [ 1, 4, 7 ], [ 2, 4, 7 ], [ 3, 4, 7 ], [ 0, 5, 7 ], [ 1, 5, 7 ], [ 2, 5, 7 ], [ 3, 5, 7 ], [ 4, 5, 7 ], [ 0, 6, 7 ], [ 1, 6, 7 ], [ 2, 6, 7 ], [ 3, 6, 7 ], [ 4, 6, 7 ], [ 5, 6, 7 ], [ 0, 1, 8 ], [ 0, 2, 8 ], [ 1, 2, 8 ], [ 0, 3, 8 ], [ 1, 3, 8 ], [ 2, 3, 8 ], [ 0, 4, 8 ], [ 1, 4, 8 ], [ 2, 4, 8 ], [ 3, 4, 8 ], [ 0, 5, 8 ], [ 1, 5, 8 ], [ 2, 5, 8 ], [ 3, 5, 8 ], [ 4, 5, 8 ], [ 0, 6, 8 ], [ 1, 6, 8 ], [ 2, 6, 8 ], [ 3, 6, 8 ], [ 4, 6, 8 ], [ 5, 6, 8 ], [ 0, 7, 8 ], [ 1, 7, 8 ], [ 2, 7, 8 ], [ 3, 7, 8 ], [ 4, 7, 8 ], [ 5, 7, 8 ], [ 6, 7, 8 ], [ 0, 1, 9 ], [ 0, 2, 9 ], [ 1, 2, 9 ], [ 0, 3, 9 ], [ 1, 3, 9 ], [ 2, 3, 9 ], [ 0, 4, 9 ], [ 1, 4, 9 ], [ 2, 4, 9 ], [ 3, 4, 9 ], [ 0, 5, 9 ], [ 1, 5, 9 ], [ 2, 5, 9 ], [ 3, 5, 9 ], [ 4, 5, 9 ], [ 0, 6, 9 ], [ 1, 6, 9 ], [ 2, 6, 9 ], [ 3, 6, 9 ], [ 4, 6, 9 ], [ 5, 6, 9 ], [ 0, 7, 9 ], [ 1, 7, 9 ], [ 2, 7, 9 ], [ 3, 7, 9 ], [ 4, 7, 9 ], [ 5, 7, 9 ], [ 6, 7, 9 ], [ 0, 8, 9 ], [ 1, 8, 9 ], [ 2, 8, 9 ], [ 3, 8, 9 ], [ 4, 8, 9 ], [ 5, 8, 9 ], [ 6, 8, 9 ], [ 7, 8, 9 ], [ 0, 1, 10 ], [ 0, 2, 10 ], [ 1, 2, 10 ], [ 0, 3, 10 ], [ 1, 3, 10 ], [ 2, 3, 10 ], [ 0, 4, 10 ], [ 1, 4, 10 ], [ 2, 4, 10 ], [ 3, 4, 10 ], [ 0, 5, 10 ], [ 1, 5, 10 ], [ 2, 5, 10 ], [ 3, 5, 10 ], [ 4, 5, 10 ], [ 0, 6, 10 ], [ 1, 6, 10 ], [ 2, 6, 10 ], [ 3, 6, 10 ], [ 4, 6, 10 ], [ 5, 6, 10 ], [ 0, 7, 10 ], [ 1, 7, 10 ], [ 2, 7, 10 ], [ 3, 7, 10 ], [ 4, 7, 10 ], [ 5, 7, 10 ], [ 6, 7, 10 ], [ 0, 8, 10 ], [ 1, 8, 10 ], [ 2, 8, 10 ], [ 3, 8, 10 ], [ 4, 8, 10 ], [ 5, 8, 10 ], [ 6, 8, 10 ], [ 7, 8, 10 ], [ 0, 9, 10 ], [ 1, 9, 10 ], [ 2, 9, 10 ], [ 3, 9, 10 ], [ 4, 9, 10 ], [ 5, 9, 10 ], [ 6, 9, 10 ], [ 7, 9, 10 ], [ 8, 9, 10 ] ] [ [ 3, 4, 5 ], [ 3, 4, 6 ], [ 3, 5, 6 ], [ 4, 5, 6 ], [ 3, 4, 7 ], [ 3, 5, 7 ], [ 4, 5, 7 ], [ 3, 6, 7 ], [ 4, 6, 7 ], [ 5, 6, 7 ], [ 3, 4, 8 ], [ 3, 5, 8 ], [ 4, 5, 8 ], [ 3, 6, 8 ], [ 4, 6, 8 ], [ 5, 6, 8 ], [ 3, 7, 8 ], [ 4, 7, 8 ], [ 5, 7, 8 ], [ 6, 7, 8 ], [ 3, 4, 9 ], [ 3, 5, 9 ], [ 4, 5, 9 ], [ 3, 6, 9 ], [ 4, 6, 9 ], [ 5, 6, 9 ], [ 3, 7, 9 ], [ 4, 7, 9 ], [ 5, 7, 9 ], [ 6, 7, 9 ], [ 3, 8, 9 ], [ 4, 8, 9 ], [ 5, 8, 9 ], [ 6, 8, 9 ], [ 7, 8, 9 ], [ 3, 4, 10 ], [ 3, 5, 10 ], [ 4, 5, 10 ], [ 3, 6, 10 ], [ 4, 6, 10 ], [ 5, 6, 10 ], [ 3, 7, 10 ], [ 4, 7, 10 ], [ 5, 7, 10 ], [ 6, 7, 10 ], [ 3, 8, 10 ], [ 4, 8, 10 ], [ 5, 8, 10 ], [ 6, 8, 10 ], [ 7, 8, 10 ], [ 3, 9, 10 ], [ 4, 9, 10 ], [ 5, 9, 10 ], [ 6, 9, 10 ], [ 7, 9, 10 ], [ 8, 9, 10 ] ] >> gen_ham_weight:=func> [gen_ham_weight([r,i]): i in [0..7]]: r in [0..7]]; ; ^ User error: bad syntax Total time: 5.279 seconds, Total memory usage: 2.42MB ************** MAGMA ***************** Host 80.58.32.42.proxycache.rima-tde.net. (80.58.32.42) Time: Wed Dec 24 08:21:05 2003 Input: /* Klein quartic */ printf "Klein quartic"; MAX:=10; c:=5; g:=3; semi:=[0,3]; /* Hermitian curve */ /* printf "hermitian curve"; MAX:=10; c:=12; g:=6; semi:=[0,4,5,8,9,10]; */ /* basic del semigrup */ i_cond:=c-g; pertany:=func; gaps:=[i:i in [1..c-1]|not pertany(i)]; lambda:=func; lambdainv:=func; /* oplus, leq, nu */ oplus:=func; inferior:=func; ominus:=func; N:=func; nu:=func; /* order bound */ dORD:=func; Lconjunts:=[[0]]; Lmcinf:=[[0]]; Linterseccioinf:=[1]; Lunioinf:=[1]; index:=function(llista) i:=0; for j in llista do i:=i+2^j; end for; return(i); end function; /* mcinf:=function(Lconjunts,Lmcinf,llista) p:=Position(Lconjunts,llista); if p eq 0 then return -1; else return Lmcinf[p]; end if; end function; interseccioinf:=function(Lconjunts,Linterseccioinf,llista) p:=Position(Lconjunts,llista); if p eq 0 then return -1; else return Linterseccioinf[p]; end if; end function; unioinf:=function(Lconjunts,Lunioinf,llista) p:=Position(Lconjunts,llista); if p eq 0 then return -1; else return Lunioinf[p]; end if; end function; */ actualitzaconjunts:=function (Lconjunts,llista) return(Append(Lconjunts,llista)); end function; actualitzamcinf:=function(Lmcinf,llista) maxc:=llista[1]; if (maxc eq 0) then return (Append(Lmcinf,[0])); end if; trobat:=false; while not trobat do while not inferior(maxc,llista[1]) do maxc:=maxc-1; end while; j:=2; while j le #llista and inferior(maxc,llista[j]) do j:=j+1; end while; if j eq #llista+1 then trobat:=true; end if; maxc:=maxc-1; end while; maxc:=maxc+1; mcinfllista:=[maxc]; for h in gaps do candidat:=lambdainv(lambda(maxc)-h); if candidat gt 0 then j:=1; while j le #llista and inferior(candidat,llista[j]) do j:=j+1; end while; if j eq #llista+1 then mcinfllista:=Append(mcinfllista,candidat); end if; end if; end for; return(Append(Lmcinf,mcinfllista)); end function; interseccio_ultim_unio_dels_altres:=function(llista) ultim:=llista[#llista]; maxc:=ultim-1; trobat:=false; while not trobat do while not inferior(maxc,ultim) do maxc:=maxc-1; end while; j:=1; while j le #llista-1 and not(inferior(maxc,llista[j])) do j:=j+1; end while; if j le #llista-1 then trobat:=true; end if; maxc:=maxc-1; end while; maxc:=maxc+1; ret:=[maxc]; for h in gaps do candidat:=lambdainv(lambda(maxc)-h); if candidat gt 0 and inferior(candidat,ultim) then j:=1; while j le #llista-1 and not(inferior(candidat,llista[j])) do j:=j+1; end while; if j le #llista-1 then ret:=Append(ret,candidat); end if; end if; end for; return(index(ret)); end function; actualitzainterseccioinf:=function(Lconjunts,Lmcinf,Linterseccioinf,Lunioinf,llista) if #llista eq 1 then return Append(Linterseccioinf,nu(llista[1])); else return Append(Linterseccioinf,Lunioinf[index(Lmcinf[index(llista)])]); end if; end function; actualitzaunioinf:=function(Lconjunts,Linterseccioinf,Lunioinf,llista) if #llista eq 1 then return Append(Lunioinf,nu(llista[1])); else return Append(Lunioinf, Lunioinf[index([llista[i]:i in [1..(#llista-1)]])] +nu(llista[#llista])-Lunioinf[interseccio_ultim_unio_dels_altres(llista)]); end if; end function; for i in [1..MAX] do conjuntsaux:=Lconjunts; llista:=[i]; Lconjunts:=actualitzaconjunts(Lconjunts,llista); Lmcinf:=actualitzamcinf(Lmcinf,llista); Linterseccioinf:=actualitzainterseccioinf(Lconjunts,Lmcinf,Linterseccioinf,Lunioinf,llista); Lunioinf:=actualitzaunioinf(Lconjunts,Linterseccioinf,Lunioinf,llista); for conj in conjuntsaux do llista:=Append(conj,i); Lconjunts:=actualitzaconjunts(Lconjunts,llista); Lmcinf:=actualitzamcinf(Lmcinf,llista); Linterseccioinf:=actualitzainterseccioinf(Lconjunts,Lmcinf,Linterseccioinf,Lunioinf,llista); Lunioinf:=actualitzaunioinf(Lconjunts,Linterseccioinf,Lunioinf,llista); end for; end for; joinsets:=function(llista) unio:={}; for conj in llista do unio:=unio join conj; end for; return unio; end function; /* l:=#Lconjunts; print "CONJUNTS="; ; print "MCINF="; ; print "INTERSECCIOINF="; Linterseccioinf; print "UNIOINF="; Lunioinf; */ /* unioasac:=[#joinsets({N(i):i in llista}):llista in Lconjunts]; errors:=[Lunioinf[i]-unioasac[i]:i in [1..#unioasac]]; printf "VEREDICTE:="; [Lconjunts[i]:i in [1..#errors]|errors[i] ne 0]; */ conj_r_elements:=func; //[Lconjunts[i]: i in conj_r_elements(3)]; max_index:=index([1..MAX]); conj_r_elements_ge_i:=func; //[Lconjunts[i]: i in conj_r_elements_ge_i([3,3])]; gen_ham_weight:=func; [gen_ham_weight([r,i]): i in [0..7]]: r in [0..7]]; Output: Magma V2.10-6 Wed Dec 24 2003 08:20:59 on modular [Seed = 1940250280] ------------------------------------- Klein quartic >> gen_ham_weight:=func> [gen_ham_weight([r,i]): i in [0..7]]: r in [0..7]]; ; ^ User error: bad syntax Total time: 5.219 seconds, Total memory usage: 2.42MB ************** MAGMA ***************** Host 80.58.32.42.proxycache.rima-tde.net. (80.58.32.42) Time: Wed Dec 24 08:22:07 2003 Input: /* Klein quartic */ printf "Klein quartic"; MAX:=10; c:=5; g:=3; semi:=[0,3]; /* Hermitian curve */ /* printf "hermitian curve"; MAX:=10; c:=12; g:=6; semi:=[0,4,5,8,9,10]; */ /* basic del semigrup */ i_cond:=c-g; pertany:=func; gaps:=[i:i in [1..c-1]|not pertany(i)]; lambda:=func; lambdainv:=func; /* oplus, leq, nu */ oplus:=func; inferior:=func; ominus:=func; N:=func; nu:=func; /* order bound */ dORD:=func; Lconjunts:=[[0]]; Lmcinf:=[[0]]; Linterseccioinf:=[1]; Lunioinf:=[1]; index:=function(llista) i:=0; for j in llista do i:=i+2^j; end for; return(i); end function; /* mcinf:=function(Lconjunts,Lmcinf,llista) p:=Position(Lconjunts,llista); if p eq 0 then return -1; else return Lmcinf[p]; end if; end function; interseccioinf:=function(Lconjunts,Linterseccioinf,llista) p:=Position(Lconjunts,llista); if p eq 0 then return -1; else return Linterseccioinf[p]; end if; end function; unioinf:=function(Lconjunts,Lunioinf,llista) p:=Position(Lconjunts,llista); if p eq 0 then return -1; else return Lunioinf[p]; end if; end function; */ actualitzaconjunts:=function (Lconjunts,llista) return(Append(Lconjunts,llista)); end function; actualitzamcinf:=function(Lmcinf,llista) maxc:=llista[1]; if (maxc eq 0) then return (Append(Lmcinf,[0])); end if; trobat:=false; while not trobat do while not inferior(maxc,llista[1]) do maxc:=maxc-1; end while; j:=2; while j le #llista and inferior(maxc,llista[j]) do j:=j+1; end while; if j eq #llista+1 then trobat:=true; end if; maxc:=maxc-1; end while; maxc:=maxc+1; mcinfllista:=[maxc]; for h in gaps do candidat:=lambdainv(lambda(maxc)-h); if candidat gt 0 then j:=1; while j le #llista and inferior(candidat,llista[j]) do j:=j+1; end while; if j eq #llista+1 then mcinfllista:=Append(mcinfllista,candidat); end if; end if; end for; return(Append(Lmcinf,mcinfllista)); end function; interseccio_ultim_unio_dels_altres:=function(llista) ultim:=llista[#llista]; maxc:=ultim-1; trobat:=false; while not trobat do while not inferior(maxc,ultim) do maxc:=maxc-1; end while; j:=1; while j le #llista-1 and not(inferior(maxc,llista[j])) do j:=j+1; end while; if j le #llista-1 then trobat:=true; end if; maxc:=maxc-1; end while; maxc:=maxc+1; ret:=[maxc]; for h in gaps do candidat:=lambdainv(lambda(maxc)-h); if candidat gt 0 and inferior(candidat,ultim) then j:=1; while j le #llista-1 and not(inferior(candidat,llista[j])) do j:=j+1; end while; if j le #llista-1 then ret:=Append(ret,candidat); end if; end if; end for; return(index(ret)); end function; actualitzainterseccioinf:=function(Lconjunts,Lmcinf,Linterseccioinf,Lunioinf,llista) if #llista eq 1 then return Append(Linterseccioinf,nu(llista[1])); else return Append(Linterseccioinf,Lunioinf[index(Lmcinf[index(llista)])]); end if; end function; actualitzaunioinf:=function(Lconjunts,Linterseccioinf,Lunioinf,llista) if #llista eq 1 then return Append(Lunioinf,nu(llista[1])); else return Append(Lunioinf, Lunioinf[index([llista[i]:i in [1..(#llista-1)]])] +nu(llista[#llista])-Lunioinf[interseccio_ultim_unio_dels_altres(llista)]); end if; end function; for i in [1..MAX] do conjuntsaux:=Lconjunts; llista:=[i]; Lconjunts:=actualitzaconjunts(Lconjunts,llista); Lmcinf:=actualitzamcinf(Lmcinf,llista); Linterseccioinf:=actualitzainterseccioinf(Lconjunts,Lmcinf,Linterseccioinf,Lunioinf,llista); Lunioinf:=actualitzaunioinf(Lconjunts,Linterseccioinf,Lunioinf,llista); for conj in conjuntsaux do llista:=Append(conj,i); Lconjunts:=actualitzaconjunts(Lconjunts,llista); Lmcinf:=actualitzamcinf(Lmcinf,llista); Linterseccioinf:=actualitzainterseccioinf(Lconjunts,Lmcinf,Linterseccioinf,Lunioinf,llista); Lunioinf:=actualitzaunioinf(Lconjunts,Linterseccioinf,Lunioinf,llista); end for; end for; joinsets:=function(llista) unio:={}; for conj in llista do unio:=unio join conj; end for; return unio; end function; /* l:=#Lconjunts; print "CONJUNTS="; ; print "MCINF="; ; print "INTERSECCIOINF="; Linterseccioinf; print "UNIOINF="; Lunioinf; */ /* unioasac:=[#joinsets({N(i):i in llista}):llista in Lconjunts]; errors:=[Lunioinf[i]-unioasac[i]:i in [1..#unioasac]]; printf "VEREDICTE:="; [Lconjunts[i]:i in [1..#errors]|errors[i] ne 0]; */ conj_r_elements:=func; //[Lconjunts[i]: i in conj_r_elements(3)]; max_index:=index([1..MAX]); conj_r_elements_ge_i:=func; //[Lconjunts[i]: i in conj_r_elements_ge_i([3,3])]; gen_ham_weight:=func; [gen_ham_weight([r,i]): i in [0..7]]: r in [1..7]]; Output: Magma V2.10-6 Wed Dec 24 2003 08:22:02 on modular [Seed = 2108412135] ------------------------------------- Klein quartic >> [gen_ham_weight([r,i]): i in [0..7]]: r in [1..7]]; ; ^ User error: bad syntax Total time: 5.019 seconds, Total memory usage: 2.42MB ************** MAGMA ***************** Host 80.58.32.42.proxycache.rima-tde.net. (80.58.32.42) Time: Wed Dec 24 08:22:44 2003 Input: /* Klein quartic */ printf "Klein quartic"; MAX:=10; c:=5; g:=3; semi:=[0,3]; /* Hermitian curve */ /* printf "hermitian curve"; MAX:=10; c:=12; g:=6; semi:=[0,4,5,8,9,10]; */ /* basic del semigrup */ i_cond:=c-g; pertany:=func; gaps:=[i:i in [1..c-1]|not pertany(i)]; lambda:=func; lambdainv:=func; /* oplus, leq, nu */ oplus:=func; inferior:=func; ominus:=func; N:=func; nu:=func; /* order bound */ dORD:=func; Lconjunts:=[[0]]; Lmcinf:=[[0]]; Linterseccioinf:=[1]; Lunioinf:=[1]; index:=function(llista) i:=0; for j in llista do i:=i+2^j; end for; return(i); end function; /* mcinf:=function(Lconjunts,Lmcinf,llista) p:=Position(Lconjunts,llista); if p eq 0 then return -1; else return Lmcinf[p]; end if; end function; interseccioinf:=function(Lconjunts,Linterseccioinf,llista) p:=Position(Lconjunts,llista); if p eq 0 then return -1; else return Linterseccioinf[p]; end if; end function; unioinf:=function(Lconjunts,Lunioinf,llista) p:=Position(Lconjunts,llista); if p eq 0 then return -1; else return Lunioinf[p]; end if; end function; */ actualitzaconjunts:=function (Lconjunts,llista) return(Append(Lconjunts,llista)); end function; actualitzamcinf:=function(Lmcinf,llista) maxc:=llista[1]; if (maxc eq 0) then return (Append(Lmcinf,[0])); end if; trobat:=false; while not trobat do while not inferior(maxc,llista[1]) do maxc:=maxc-1; end while; j:=2; while j le #llista and inferior(maxc,llista[j]) do j:=j+1; end while; if j eq #llista+1 then trobat:=true; end if; maxc:=maxc-1; end while; maxc:=maxc+1; mcinfllista:=[maxc]; for h in gaps do candidat:=lambdainv(lambda(maxc)-h); if candidat gt 0 then j:=1; while j le #llista and inferior(candidat,llista[j]) do j:=j+1; end while; if j eq #llista+1 then mcinfllista:=Append(mcinfllista,candidat); end if; end if; end for; return(Append(Lmcinf,mcinfllista)); end function; interseccio_ultim_unio_dels_altres:=function(llista) ultim:=llista[#llista]; maxc:=ultim-1; trobat:=false; while not trobat do while not inferior(maxc,ultim) do maxc:=maxc-1; end while; j:=1; while j le #llista-1 and not(inferior(maxc,llista[j])) do j:=j+1; end while; if j le #llista-1 then trobat:=true; end if; maxc:=maxc-1; end while; maxc:=maxc+1; ret:=[maxc]; for h in gaps do candidat:=lambdainv(lambda(maxc)-h); if candidat gt 0 and inferior(candidat,ultim) then j:=1; while j le #llista-1 and not(inferior(candidat,llista[j])) do j:=j+1; end while; if j le #llista-1 then ret:=Append(ret,candidat); end if; end if; end for; return(index(ret)); end function; actualitzainterseccioinf:=function(Lconjunts,Lmcinf,Linterseccioinf,Lunioinf,llista) if #llista eq 1 then return Append(Linterseccioinf,nu(llista[1])); else return Append(Linterseccioinf,Lunioinf[index(Lmcinf[index(llista)])]); end if; end function; actualitzaunioinf:=function(Lconjunts,Linterseccioinf,Lunioinf,llista) if #llista eq 1 then return Append(Lunioinf,nu(llista[1])); else return Append(Lunioinf, Lunioinf[index([llista[i]:i in [1..(#llista-1)]])] +nu(llista[#llista])-Lunioinf[interseccio_ultim_unio_dels_altres(llista)]); end if; end function; for i in [1..MAX] do conjuntsaux:=Lconjunts; llista:=[i]; Lconjunts:=actualitzaconjunts(Lconjunts,llista); Lmcinf:=actualitzamcinf(Lmcinf,llista); Linterseccioinf:=actualitzainterseccioinf(Lconjunts,Lmcinf,Linterseccioinf,Lunioinf,llista); Lunioinf:=actualitzaunioinf(Lconjunts,Linterseccioinf,Lunioinf,llista); for conj in conjuntsaux do llista:=Append(conj,i); Lconjunts:=actualitzaconjunts(Lconjunts,llista); Lmcinf:=actualitzamcinf(Lmcinf,llista); Linterseccioinf:=actualitzainterseccioinf(Lconjunts,Lmcinf,Linterseccioinf,Lunioinf,llista); Lunioinf:=actualitzaunioinf(Lconjunts,Linterseccioinf,Lunioinf,llista); end for; end for; joinsets:=function(llista) unio:={}; for conj in llista do unio:=unio join conj; end for; return unio; end function; /* l:=#Lconjunts; print "CONJUNTS="; ; print "MCINF="; ; print "INTERSECCIOINF="; Linterseccioinf; print "UNIOINF="; Lunioinf; */ /* unioasac:=[#joinsets({N(i):i in llista}):llista in Lconjunts]; errors:=[Lunioinf[i]-unioasac[i]:i in [1..#unioasac]]; printf "VEREDICTE:="; [Lconjunts[i]:i in [1..#errors]|errors[i] ne 0]; */ conj_r_elements:=func; //[Lconjunts[i]: i in conj_r_elements(3)]; max_index:=index([1..MAX]); conj_r_elements_ge_i:=func; //[Lconjunts[i]: i in conj_r_elements_ge_i([3,3])]; gen_ham_weight:=func; [[gen_ham_weight([r,i]): i in [0..7]]: r in [1..7]]; Output: Magma V2.10-6 Wed Dec 24 2003 08:22:38 on modular [Seed = 1183902265] ------------------------------------- [
:172]( ri: [ 4, 7 ] ) >> gen_ham_weight:=func; gaps:=[i:i in [1..c-1]|not pertany(i)]; lambda:=func; lambdainv:=func; /* oplus, leq, nu */ oplus:=func; inferior:=func; ominus:=func; N:=func; nu:=func; /* order bound */ dORD:=func; Lconjunts:=[[0]]; Lmcinf:=[[0]]; Linterseccioinf:=[1]; Lunioinf:=[1]; index:=function(llista) i:=0; for j in llista do i:=i+2^j; end for; return(i); end function; /* mcinf:=function(Lconjunts,Lmcinf,llista) p:=Position(Lconjunts,llista); if p eq 0 then return -1; else return Lmcinf[p]; end if; end function; interseccioinf:=function(Lconjunts,Linterseccioinf,llista) p:=Position(Lconjunts,llista); if p eq 0 then return -1; else return Linterseccioinf[p]; end if; end function; unioinf:=function(Lconjunts,Lunioinf,llista) p:=Position(Lconjunts,llista); if p eq 0 then return -1; else return Lunioinf[p]; end if; end function; */ actualitzaconjunts:=function (Lconjunts,llista) return(Append(Lconjunts,llista)); end function; actualitzamcinf:=function(Lmcinf,llista) maxc:=llista[1]; if (maxc eq 0) then return (Append(Lmcinf,[0])); end if; trobat:=false; while not trobat do while not inferior(maxc,llista[1]) do maxc:=maxc-1; end while; j:=2; while j le #llista and inferior(maxc,llista[j]) do j:=j+1; end while; if j eq #llista+1 then trobat:=true; end if; maxc:=maxc-1; end while; maxc:=maxc+1; mcinfllista:=[maxc]; for h in gaps do candidat:=lambdainv(lambda(maxc)-h); if candidat gt 0 then j:=1; while j le #llista and inferior(candidat,llista[j]) do j:=j+1; end while; if j eq #llista+1 then mcinfllista:=Append(mcinfllista,candidat); end if; end if; end for; return(Append(Lmcinf,mcinfllista)); end function; interseccio_ultim_unio_dels_altres:=function(llista) ultim:=llista[#llista]; maxc:=ultim-1; trobat:=false; while not trobat do while not inferior(maxc,ultim) do maxc:=maxc-1; end while; j:=1; while j le #llista-1 and not(inferior(maxc,llista[j])) do j:=j+1; end while; if j le #llista-1 then trobat:=true; end if; maxc:=maxc-1; end while; maxc:=maxc+1; ret:=[maxc]; for h in gaps do candidat:=lambdainv(lambda(maxc)-h); if candidat gt 0 and inferior(candidat,ultim) then j:=1; while j le #llista-1 and not(inferior(candidat,llista[j])) do j:=j+1; end while; if j le #llista-1 then ret:=Append(ret,candidat); end if; end if; end for; return(index(ret)); end function; actualitzainterseccioinf:=function(Lconjunts,Lmcinf,Linterseccioinf,Lunioinf,llista) if #llista eq 1 then return Append(Linterseccioinf,nu(llista[1])); else return Append(Linterseccioinf,Lunioinf[index(Lmcinf[index(llista)])]); end if; end function; actualitzaunioinf:=function(Lconjunts,Linterseccioinf,Lunioinf,llista) if #llista eq 1 then return Append(Lunioinf,nu(llista[1])); else return Append(Lunioinf, Lunioinf[index([llista[i]:i in [1..(#llista-1)]])] +nu(llista[#llista])-Lunioinf[interseccio_ultim_unio_dels_altres(llista)]); end if; end function; for i in [1..MAX] do conjuntsaux:=Lconjunts; llista:=[i]; Lconjunts:=actualitzaconjunts(Lconjunts,llista); Lmcinf:=actualitzamcinf(Lmcinf,llista); Linterseccioinf:=actualitzainterseccioinf(Lconjunts,Lmcinf,Linterseccioinf,Lunioinf,llista); Lunioinf:=actualitzaunioinf(Lconjunts,Linterseccioinf,Lunioinf,llista); for conj in conjuntsaux do llista:=Append(conj,i); Lconjunts:=actualitzaconjunts(Lconjunts,llista); Lmcinf:=actualitzamcinf(Lmcinf,llista); Linterseccioinf:=actualitzainterseccioinf(Lconjunts,Lmcinf,Linterseccioinf,Lunioinf,llista); Lunioinf:=actualitzaunioinf(Lconjunts,Linterseccioinf,Lunioinf,llista); end for; end for; joinsets:=function(llista) unio:={}; for conj in llista do unio:=unio join conj; end for; return unio; end function; /* l:=#Lconjunts; print "CONJUNTS="; ; print "MCINF="; ; print "INTERSECCIOINF="; Linterseccioinf; print "UNIOINF="; Lunioinf; */ /* unioasac:=[#joinsets({N(i):i in llista}):llista in Lconjunts]; errors:=[Lunioinf[i]-unioasac[i]:i in [1..#unioasac]]; printf "VEREDICTE:="; [Lconjunts[i]:i in [1..#errors]|errors[i] ne 0]; */ conj_r_elements:=func; //[Lconjunts[i]: i in conj_r_elements(3)]; max_index:=index([1..MAX]); conj_r_elements_ge_i:=func; //[Lconjunts[i]: i in conj_r_elements_ge_i([3,3])]; unioinf_conj_r_elements_ge_i:=func; gen_ham_weight:=func; [[gen_ham_weight([r,i]): i in [0..7]]: r in [1..7]]; Output: Magma V2.10-6 Wed Dec 24 2003 08:28:37 on modular [Seed = 937532626] ------------------------------------- Klein quartic[ [ 2, 2, 2, 2, 4, 4, 5, 6 ], [ 3, 3, 4, 5, 6, 7, 8, 9 ], [ 4, 5, 5, 6, 7, 8, 9, 11 ], [ 5, 6, 7, 8, 9, 10, 11, -1 ], [ 6, 7, 8, 9, 10, 11, -1, -1 ], [ 7, 8, 9, 10, 11, -1, -1, -1 ], [ 8, 9, 10, 11, -1, -1, -1, -1 ] ] Total time: 5.949 seconds, Total memory usage: 2.42MB ************** MAGMA ***************** Host p14196-adsau12honb1-acca.tokyo.ocn.ne.jp. (219.161.161.196) Time: Wed Dec 24 09:11:27 2003 Input: g:=Group; comm:=CommutatorSubgroup(g); ReduceGenerators(comm); Output: Magma V2.10-6 Wed Dec 24 2003 09:11:24 on modular [Seed = 2024724907] ------------------------------------- Finitely presented group on 3 generators Generators as words in group g $.1 = g.2 * g.1^-1 $.2 = g.1^2 $.3 = g.1 * g.2 Relations $.3^3 = Id($) ($.1 * $.2)^3 = Id($) $.3^-1 * $.1 * $.3 * $.2 * $.3 * $.1^-1 * $.3^-1 * $.2^-1 = Id($) ($.1 * $.2 * $.3 * $.2)^2 = Id($) $.3 * $.1 * $.2 * $.3 * $.1 * $.3^-1 * $.1 * $.3 * $.1 * $.2 * $.1 = Id($) Total time: 2.999 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.32.42.proxycache.rima-tde.net. (80.58.32.42) Time: Wed Dec 24 11:27:38 2003 Input: /* Klein quartic */ printf "Klein quartic"; MAX:=10; c:=5; g:=3; semi:=[0,3]; /* Hermitian curve */ /* printf "hermitian curve"; MAX:=10; c:=12; g:=6; semi:=[0,4,5,8,9,10]; */ /* basic del semigrup */ i_cond:=c-g; pertany:=func; gaps:=[i:i in [1..c-1]|not pertany(i)]; lambda:=func; lambdainv:=func; /* oplus, leq, nu */ oplus:=func; inferior:=func; ominus:=func; N:=func; nu:=func; /* order bound */ dORD:=func; Lconjunts:=[[0]]; //Lmcinf:=[[0]]; //Linterseccioinf:=[1]; Lunioinf:=[1]; index:=function(llista) i:=0; for j in llista do i:=i+2^j; end for; return(i); end function; actualitzaconjunts:=function (Lconjunts,llista) return(Append(Lconjunts,llista)); end function; /* actualitzamcinf:=function(Lmcinf,llista) maxc:=llista[1]; if (maxc eq 0) then return (Append(Lmcinf,[0])); end if; trobat:=false; while not trobat do while not inferior(maxc,llista[1]) do maxc:=maxc-1; end while; j:=2; while j le #llista and inferior(maxc,llista[j]) do j:=j+1; end while; if j eq #llista+1 then trobat:=true; end if; maxc:=maxc-1; end while; maxc:=maxc+1; mcinfllista:=[maxc]; for h in gaps do candidat:=lambdainv(lambda(maxc)-h); if candidat gt 0 then j:=1; while j le #llista and inferior(candidat,llista[j]) do j:=j+1; end while; if j eq #llista+1 then mcinfllista:=Append(mcinfllista,candidat); end if; end if; end for; return(Append(Lmcinf,mcinfllista)); end function; */ interseccio_ultim_unio_dels_altres:=function(llista) ultim:=llista[#llista]; maxc:=ultim-1; trobat:=false; while not trobat do while not inferior(maxc,ultim) do maxc:=maxc-1; end while; j:=1; while j le #llista-1 and not(inferior(maxc,llista[j])) do j:=j+1; end while; if j le #llista-1 then trobat:=true; end if; maxc:=maxc-1; end while; maxc:=maxc+1; ret:=[maxc]; for h in gaps do candidat:=lambdainv(lambda(maxc)-h); if candidat gt 0 and inferior(candidat,ultim) then j:=1; while j le #llista-1 and not(inferior(candidat,llista[j])) do j:=j+1; end while; if j le #llista-1 then ret:=Append(ret,candidat); end if; end if; end for; return(index(ret)); end function; /* actualitzainterseccioinf:=function(Lconjunts,Lmcinf,Linterseccioinf,Lunioinf,llista) if #llista eq 1 then return Append(Linterseccioinf,nu(llista[1])); else return Append(Linterseccioinf,Lunioinf[index(Lmcinf[index(llista)])]); end if; end function; */ actualitzaunioinf:=function(Lconjunts,Lunioinf,llista) if #llista eq 1 then return Append(Lunioinf,nu(llista[1])); else return Append(Lunioinf, Lunioinf[index([llista[i]:i in [1..(#llista-1)]])]+nu(llista[#llista])-Lunioinf[interseccio_ultim_unio_dels_altres(llista)]); end if; end function; for i in [1..MAX] do conjuntsaux:=Lconjunts; llista:=[i]; Lconjunts:=actualitzaconjunts(Lconjunts,llista); // Lmcinf:=actualitzamcinf(Lmcinf,llista); // Linterseccioinf:=actualitzainterseccioinf(Lconjunts,Lmcinf,Linterseccioinf,Lunioinf,llista); Lunioinf:=actualitzaunioinf(Lconjunts,Linterseccioinf,Lunioinf,llista); for conj in conjuntsaux do llista:=Append(conj,i); Lconjunts:=actualitzaconjunts(Lconjunts,llista); // Lmcinf:=actualitzamcinf(Lmcinf,llista); // Linterseccioinf:=actualitzainterseccioinf(Lconjunts,Lmcinf,Linterseccioinf,Lunioinf,llista); Lunioinf:=actualitzaunioinf(Lconjunts,Linterseccioinf,Lunioinf,llista); end for; end for; /* l:=#Lconjunts; print "CONJUNTS="; ; print "MCINF="; ; print "INTERSECCIOINF="; Linterseccioinf; print "UNIOINF="; */ Lunioinf; /* joinsets:=function(llista) unio:={}; for conj in llista do unio:=unio join conj; end for; return unio; end function; unioasac:=[#joinsets({N(i):i in llista}):llista in Lconjunts]; errors:=[Lunioinf[i]-unioasac[i]:i in [1..#unioasac]]; printf "VEREDICTE:="; [Lconjunts[i]:i in [1..#errors]|errors[i] ne 0]; */ /* conj_r_elements:=func; //[Lconjunts[i]: i in conj_r_elements(3)]; max_index:=index([1..MAX]); conj_r_elements_ge_i:=func; //[Lconjunts[i]: i in conj_r_elements_ge_i([3,3])]; unioinf_conj_r_elements_ge_i:=func; gen_ham_weight:=func; [[gen_ham_weight([r,i]): i in [0..7]]: r in [1..7]]; */ Output: Magma V2.10-6 Wed Dec 24 2003 11:27:35 on modular [Seed = 4264067036] ------------------------------------- Klein quartic >> Lunioinf:=actualitzaunioinf(Lconjunts,Linterseccioinf,Lunioinf,llista); ^ User error: Identifier 'Linterseccioinf' has not been declared or assigned [ 1 ] Total time: 3.279 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.32.42.proxycache.rima-tde.net. (80.58.32.42) Time: Wed Dec 24 11:29:14 2003 Input: /* Klein quartic */ printf "Klein quartic"; MAX:=10; c:=5; g:=3; semi:=[0,3]; /* Hermitian curve */ /* printf "hermitian curve"; MAX:=10; c:=12; g:=6; semi:=[0,4,5,8,9,10]; */ /* basic del semigrup */ i_cond:=c-g; pertany:=func; gaps:=[i:i in [1..c-1]|not pertany(i)]; lambda:=func; lambdainv:=func; /* oplus, leq, nu */ oplus:=func; inferior:=func; ominus:=func; N:=func; nu:=func; /* order bound */ dORD:=func; Lconjunts:=[[0]]; //Lmcinf:=[[0]]; //Linterseccioinf:=[1]; Lunioinf:=[1]; index:=function(llista) i:=0; for j in llista do i:=i+2^j; end for; return(i); end function; actualitzaconjunts:=function (Lconjunts,llista) return(Append(Lconjunts,llista)); end function; /* actualitzamcinf:=function(Lmcinf,llista) maxc:=llista[1]; if (maxc eq 0) then return (Append(Lmcinf,[0])); end if; trobat:=false; while not trobat do while not inferior(maxc,llista[1]) do maxc:=maxc-1; end while; j:=2; while j le #llista and inferior(maxc,llista[j]) do j:=j+1; end while; if j eq #llista+1 then trobat:=true; end if; maxc:=maxc-1; end while; maxc:=maxc+1; mcinfllista:=[maxc]; for h in gaps do candidat:=lambdainv(lambda(maxc)-h); if candidat gt 0 then j:=1; while j le #llista and inferior(candidat,llista[j]) do j:=j+1; end while; if j eq #llista+1 then mcinfllista:=Append(mcinfllista,candidat); end if; end if; end for; return(Append(Lmcinf,mcinfllista)); end function; */ interseccio_ultim_unio_dels_altres:=function(llista) ultim:=llista[#llista]; maxc:=ultim-1; trobat:=false; while not trobat do while not inferior(maxc,ultim) do maxc:=maxc-1; end while; j:=1; while j le #llista-1 and not(inferior(maxc,llista[j])) do j:=j+1; end while; if j le #llista-1 then trobat:=true; end if; maxc:=maxc-1; end while; maxc:=maxc+1; ret:=[maxc]; for h in gaps do candidat:=lambdainv(lambda(maxc)-h); if candidat gt 0 and inferior(candidat,ultim) then j:=1; while j le #llista-1 and not(inferior(candidat,llista[j])) do j:=j+1; end while; if j le #llista-1 then ret:=Append(ret,candidat); end if; end if; end for; return(index(ret)); end function; /* actualitzainterseccioinf:=function(Lconjunts,Lmcinf,Linterseccioinf,Lunioinf,llista) if #llista eq 1 then return Append(Linterseccioinf,nu(llista[1])); else return Append(Linterseccioinf,Lunioinf[index(Lmcinf[index(llista)])]); end if; end function; */ actualitzaunioinf:=function(Lconjunts,Lunioinf,llista) if #llista eq 1 then return Append(Lunioinf,nu(llista[1])); else return Append(Lunioinf, Lunioinf[index([llista[i]:i in [1..(#llista-1)]])]+nu(llista[#llista])-Lunioinf[interseccio_ultim_unio_dels_altres(llista)]); end if; end function; for i in [1..MAX] do conjuntsaux:=Lconjunts; llista:=[i]; Lconjunts:=actualitzaconjunts(Lconjunts,llista); // Lmcinf:=actualitzamcinf(Lmcinf,llista); // Linterseccioinf:=actualitzainterseccioinf(Lconjunts,Lmcinf,Linterseccioinf,Lunioinf,llista); Lunioinf:=actualitzaunioinf(Lconjunts,Linterseccioinf,Lunioinf,llista); for conj in conjuntsaux do llista:=Append(conj,i); Lconjunts:=actualitzaconjunts(Lconjunts,llista); // Lmcinf:=actualitzamcinf(Lmcinf,llista); // Linterseccioinf:=actualitzainterseccioinf(Lconjunts,Lmcinf,Linterseccioinf,Lunioinf,llista); Lunioinf:=actualitzaunioinf(Lconjunts,Linterseccioinf,Lunioinf,llista); end for; end for; /* l:=#Lconjunts; print "CONJUNTS="; ; print "MCINF="; ; print "INTERSECCIOINF="; Linterseccioinf; print "UNIOINF="; */ Lunioinf; /* joinsets:=function(llista) unio:={}; for conj in llista do unio:=unio join conj; end for; return unio; end function; unioasac:=[#joinsets({N(i):i in llista}):llista in Lconjunts]; errors:=[Lunioinf[i]-unioasac[i]:i in [1..#unioasac]]; printf "VEREDICTE:="; [Lconjunts[i]:i in [1..#errors]|errors[i] ne 0]; */ /* conj_r_elements:=func; //[Lconjunts[i]: i in conj_r_elements(3)]; max_index:=index([1..MAX]); conj_r_elements_ge_i:=func; //[Lconjunts[i]: i in conj_r_elements_ge_i([3,3])]; unioinf_conj_r_elements_ge_i:=func; gen_ham_weight:=func; [[gen_ham_weight([r,i]): i in [0..7]]: r in [1..7]]; */ Output: Magma V2.10-6 Wed Dec 24 2003 11:29:11 on modular [Seed = 3239526466] ------------------------------------- Klein quartic >> Lunioinf:=actualitzaunioinf(Lconjunts,Linterseccioinf,Lunioinf,llista); ^ User error: Identifier 'Linterseccioinf' has not been declared or assigned [ 1 ] Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.32.42.proxycache.rima-tde.net. (80.58.32.42) Time: Wed Dec 24 11:29:17 2003 Input: /* Klein quartic */ printf "Klein quartic"; MAX:=10; c:=5; g:=3; semi:=[0,3]; /* Hermitian curve */ /* printf "hermitian curve"; MAX:=10; c:=12; g:=6; semi:=[0,4,5,8,9,10]; */ /* basic del semigrup */ i_cond:=c-g; pertany:=func; gaps:=[i:i in [1..c-1]|not pertany(i)]; lambda:=func; lambdainv:=func; /* oplus, leq, nu */ oplus:=func; inferior:=func; ominus:=func; N:=func; nu:=func; /* order bound */ dORD:=func; Lconjunts:=[[0]]; //Lmcinf:=[[0]]; //Linterseccioinf:=[1]; Lunioinf:=[1]; index:=function(llista) i:=0; for j in llista do i:=i+2^j; end for; return(i); end function; actualitzaconjunts:=function (Lconjunts,llista) return(Append(Lconjunts,llista)); end function; /* actualitzamcinf:=function(Lmcinf,llista) maxc:=llista[1]; if (maxc eq 0) then return (Append(Lmcinf,[0])); end if; trobat:=false; while not trobat do while not inferior(maxc,llista[1]) do maxc:=maxc-1; end while; j:=2; while j le #llista and inferior(maxc,llista[j]) do j:=j+1; end while; if j eq #llista+1 then trobat:=true; end if; maxc:=maxc-1; end while; maxc:=maxc+1; mcinfllista:=[maxc]; for h in gaps do candidat:=lambdainv(lambda(maxc)-h); if candidat gt 0 then j:=1; while j le #llista and inferior(candidat,llista[j]) do j:=j+1; end while; if j eq #llista+1 then mcinfllista:=Append(mcinfllista,candidat); end if; end if; end for; return(Append(Lmcinf,mcinfllista)); end function; */ interseccio_ultim_unio_dels_altres:=function(llista) ultim:=llista[#llista]; maxc:=ultim-1; trobat:=false; while not trobat do while not inferior(maxc,ultim) do maxc:=maxc-1; end while; j:=1; while j le #llista-1 and not(inferior(maxc,llista[j])) do j:=j+1; end while; if j le #llista-1 then trobat:=true; end if; maxc:=maxc-1; end while; maxc:=maxc+1; ret:=[maxc]; for h in gaps do candidat:=lambdainv(lambda(maxc)-h); if candidat gt 0 and inferior(candidat,ultim) then j:=1; while j le #llista-1 and not(inferior(candidat,llista[j])) do j:=j+1; end while; if j le #llista-1 then ret:=Append(ret,candidat); end if; end if; end for; return(index(ret)); end function; /* actualitzainterseccioinf:=function(Lconjunts,Lmcinf,Linterseccioinf,Lunioinf,llista) if #llista eq 1 then return Append(Linterseccioinf,nu(llista[1])); else return Append(Linterseccioinf,Lunioinf[index(Lmcinf[index(llista)])]); end if; end function; */ actualitzaunioinf:=function(Lconjunts,Lunioinf,llista) if #llista eq 1 then return Append(Lunioinf,nu(llista[1])); else return Append(Lunioinf, Lunioinf[index([llista[i]:i in [1..(#llista-1)]])]+nu(llista[#llista])-Lunioinf[interseccio_ultim_unio_dels_altres(llista)]); end if; end function; for i in [1..MAX] do conjuntsaux:=Lconjunts; llista:=[i]; Lconjunts:=actualitzaconjunts(Lconjunts,llista); // Lmcinf:=actualitzamcinf(Lmcinf,llista); // Linterseccioinf:=actualitzainterseccioinf(Lconjunts,Lmcinf,Linterseccioinf,Lunioinf,llista); Lunioinf:=actualitzaunioinf(Lconjunts,Linterseccioinf,Lunioinf,llista); for conj in conjuntsaux do llista:=Append(conj,i); Lconjunts:=actualitzaconjunts(Lconjunts,llista); // Lmcinf:=actualitzamcinf(Lmcinf,llista); // Linterseccioinf:=actualitzainterseccioinf(Lconjunts,Lmcinf,Linterseccioinf,Lunioinf,llista); Lunioinf:=actualitzaunioinf(Lconjunts,Linterseccioinf,Lunioinf,llista); end for; end for; /* l:=#Lconjunts; print "CONJUNTS="; ; print "MCINF="; ; print "INTERSECCIOINF="; Linterseccioinf; print "UNIOINF="; */ Lunioinf; /* joinsets:=function(llista) unio:={}; for conj in llista do unio:=unio join conj; end for; return unio; end function; unioasac:=[#joinsets({N(i):i in llista}):llista in Lconjunts]; errors:=[Lunioinf[i]-unioasac[i]:i in [1..#unioasac]]; printf "VEREDICTE:="; [Lconjunts[i]:i in [1..#errors]|errors[i] ne 0]; */ /* conj_r_elements:=func; //[Lconjunts[i]: i in conj_r_elements(3)]; max_index:=index([1..MAX]); conj_r_elements_ge_i:=func; //[Lconjunts[i]: i in conj_r_elements_ge_i([3,3])]; unioinf_conj_r_elements_ge_i:=func; gen_ham_weight:=func; [[gen_ham_weight([r,i]): i in [0..7]]: r in [1..7]]; */ Output: Magma V2.10-6 Wed Dec 24 2003 11:29:14 on modular [Seed = 3424275778] ------------------------------------- Klein quartic >> Lunioinf:=actualitzaunioinf(Lconjunts,Linterseccioinf,Lunioinf,llista); ^ User error: Identifier 'Linterseccioinf' has not been declared or assigned [ 1 ] Total time: 3.179 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.32.42.proxycache.rima-tde.net. (80.58.32.42) Time: Wed Dec 24 11:29:26 2003 Input: /* Klein quartic */ printf "Klein quartic"; MAX:=10; c:=5; g:=3; semi:=[0,3]; /* Hermitian curve */ /* printf "hermitian curve"; MAX:=10; c:=12; g:=6; semi:=[0,4,5,8,9,10]; */ /* basic del semigrup */ i_cond:=c-g; pertany:=func; gaps:=[i:i in [1..c-1]|not pertany(i)]; lambda:=func; lambdainv:=func; /* oplus, leq, nu */ oplus:=func; inferior:=func; ominus:=func; N:=func; nu:=func; /* order bound */ dORD:=func; Lconjunts:=[[0]]; //Lmcinf:=[[0]]; //Linterseccioinf:=[1]; Lunioinf:=[1]; index:=function(llista) i:=0; for j in llista do i:=i+2^j; end for; return(i); end function; actualitzaconjunts:=function (Lconjunts,llista) return(Append(Lconjunts,llista)); end function; /* actualitzamcinf:=function(Lmcinf,llista) maxc:=llista[1]; if (maxc eq 0) then return (Append(Lmcinf,[0])); end if; trobat:=false; while not trobat do while not inferior(maxc,llista[1]) do maxc:=maxc-1; end while; j:=2; while j le #llista and inferior(maxc,llista[j]) do j:=j+1; end while; if j eq #llista+1 then trobat:=true; end if; maxc:=maxc-1; end while; maxc:=maxc+1; mcinfllista:=[maxc]; for h in gaps do candidat:=lambdainv(lambda(maxc)-h); if candidat gt 0 then j:=1; while j le #llista and inferior(candidat,llista[j]) do j:=j+1; end while; if j eq #llista+1 then mcinfllista:=Append(mcinfllista,candidat); end if; end if; end for; return(Append(Lmcinf,mcinfllista)); end function; */ interseccio_ultim_unio_dels_altres:=function(llista) ultim:=llista[#llista]; maxc:=ultim-1; trobat:=false; while not trobat do while not inferior(maxc,ultim) do maxc:=maxc-1; end while; j:=1; while j le #llista-1 and not(inferior(maxc,llista[j])) do j:=j+1; end while; if j le #llista-1 then trobat:=true; end if; maxc:=maxc-1; end while; maxc:=maxc+1; ret:=[maxc]; for h in gaps do candidat:=lambdainv(lambda(maxc)-h); if candidat gt 0 and inferior(candidat,ultim) then j:=1; while j le #llista-1 and not(inferior(candidat,llista[j])) do j:=j+1; end while; if j le #llista-1 then ret:=Append(ret,candidat); end if; end if; end for; return(index(ret)); end function; /* actualitzainterseccioinf:=function(Lconjunts,Lmcinf,Linterseccioinf,Lunioinf,llista) if #llista eq 1 then return Append(Linterseccioinf,nu(llista[1])); else return Append(Linterseccioinf,Lunioinf[index(Lmcinf[index(llista)])]); end if; end function; */ actualitzaunioinf:=function(Lconjunts,Lunioinf,llista) if #llista eq 1 then return Append(Lunioinf,nu(llista[1])); else return Append(Lunioinf, Lunioinf[index([llista[i]:i in [1..(#llista-1)]])]+nu(llista[#llista])-Lunioinf[interseccio_ultim_unio_dels_altres(llista)]); end if; end function; for i in [1..MAX] do conjuntsaux:=Lconjunts; llista:=[i]; Lconjunts:=actualitzaconjunts(Lconjunts,llista); // Lmcinf:=actualitzamcinf(Lmcinf,llista); // Linterseccioinf:=actualitzainterseccioinf(Lconjunts,Lmcinf,Linterseccioinf,Lunioinf,llista); Lunioinf:=actualitzaunioinf(Lconjunts,Lunioinf,llista); for conj in conjuntsaux do llista:=Append(conj,i); Lconjunts:=actualitzaconjunts(Lconjunts,llista); // Lmcinf:=actualitzamcinf(Lmcinf,llista); // Linterseccioinf:=actualitzainterseccioinf(Lconjunts,Lmcinf,Linterseccioinf,Lunioinf,llista); Lunioinf:=actualitzaunioinf(Lconjunts,Lunioinf,llista); end for; end for; /* l:=#Lconjunts; print "CONJUNTS="; ; print "MCINF="; ; print "INTERSECCIOINF="; Linterseccioinf; print "UNIOINF="; Lunioinf; */ joinsets:=function(llista) unio:={}; for conj in llista do unio:=unio join conj; end for; return unio; end function; unioasac:=[#joinsets({N(i):i in llista}):llista in Lconjunts]; errors:=[Lunioinf[i]-unioasac[i]:i in [1..#unioasac]]; printf "VEREDICTE:="; [Lconjunts[i]:i in [1..#errors]|errors[i] ne 0]; /* conj_r_elements:=func; //[Lconjunts[i]: i in conj_r_elements(3)]; max_index:=index([1..MAX]); conj_r_elements_ge_i:=func; //[Lconjunts[i]: i in conj_r_elements_ge_i([3,3])]; unioinf_conj_r_elements_ge_i:=func; gen_ham_weight:=func; [[gen_ham_weight([r,i]): i in [0..7]]: r in [1..7]]; */ Output: Magma V2.10-6 Wed Dec 24 2003 11:29:21 on modular [Seed = 3996675931] ------------------------------------- Klein quarticVEREDICTE:=[] Total time: 4.889 seconds, Total memory usage: 2.22MB ************** MAGMA ***************** Host 80.58.32.42.proxycache.rima-tde.net. (80.58.32.42) Time: Wed Dec 24 11:35:17 2003 Input: /* Klein quartic */ printf "Klein quartic"; MAX:=10; c:=5; g:=3; semi:=[0,3]; /* Hermitian curve */ /* printf "hermitian curve"; MAX:=10; c:=12; g:=6; semi:=[0,4,5,8,9,10]; */ /* basic del semigrup */ i_cond:=c-g; pertany:=func; gaps:=[i:i in [1..c-1]|not pertany(i)]; lambda:=func; lambdainv:=func; /* oplus, leq, nu */ oplus:=func; inferior:=func; ominus:=func; N:=func; nu:=func; /* order bound */ dORD:=func; //PROVA NOU ALGORITME //----------------------- Lconjunts:=[[0]]; //Lmcinf:=[[0]]; //Linterseccioinf:=[1]; Lunioinf:=[1]; index:=function(llista) i:=0; for j in llista do i:=i+2^j; end for; return(i); end function; actualitzaconjunts:=function (Lconjunts,llista) return(Append(Lconjunts,llista)); end function; /* actualitzamcinf:=function(Lmcinf,llista) maxc:=llista[1]; if (maxc eq 0) then return (Append(Lmcinf,[0])); end if; trobat:=false; while not trobat do while not inferior(maxc,llista[1]) do maxc:=maxc-1; end while; j:=2; while j le #llista and inferior(maxc,llista[j]) do j:=j+1; end while; if j eq #llista+1 then trobat:=true; end if; maxc:=maxc-1; end while; maxc:=maxc+1; mcinfllista:=[maxc]; for h in gaps do candidat:=lambdainv(lambda(maxc)-h); if candidat gt 0 then j:=1; while j le #llista and inferior(candidat,llista[j]) do j:=j+1; end while; if j eq #llista+1 then mcinfllista:=Append(mcinfllista,candidat); end if; end if; end for; return(Append(Lmcinf,mcinfllista)); end function; */ interseccio_ultim_unio_dels_altres:=function(llista) ultim:=llista[#llista]; maxc:=ultim-1; trobat:=false; while not trobat do while not inferior(maxc,ultim) do maxc:=maxc-1; end while; j:=1; while j le #llista-1 and not(inferior(maxc,llista[j])) do j:=j+1; end while; if j le #llista-1 then trobat:=true; end if; maxc:=maxc-1; end while; maxc:=maxc+1; ret:=[maxc]; for h in gaps do candidat:=lambdainv(lambda(maxc)-h); if candidat gt 0 and inferior(candidat,ultim) then j:=1; while j le #llista-1 and not(inferior(candidat,llista[j])) do j:=j+1; end while; if j le #llista-1 then ret:=Append(ret,candidat); end if; end if; end for; return(index(ret)); end function; /* actualitzainterseccioinf:=function(Lconjunts,Lmcinf,Linterseccioinf,Lunioinf,llista) if #llista eq 1 then return Append(Linterseccioinf,nu(llista[1])); else return Append(Linterseccioinf,Lunioinf[index(Lmcinf[index(llista)])]); end if; end function; */ actualitzaunioinf:=function(Lconjunts,Lunioinf,llista) if #llista eq 1 then return Append(Lunioinf,nu(llista[1])); else return Append(Lunioinf, Lunioinf[index([llista[i]:i in [1..(#llista-1)]])]+nu(llista[#llista])-Lunioinf[interseccio_ultim_unio_dels_altres(llista)]); end if; end function; for i in [1..MAX] do conjuntsaux:=Lconjunts; llista:=[i]; Lconjunts:=actualitzaconjunts(Lconjunts,llista); // Lmcinf:=actualitzamcinf(Lmcinf,llista); // Linterseccioinf:=actualitzainterseccioinf(Lconjunts,Lmcinf,Linterseccioinf,Lunioinf,llista); Lunioinf:=actualitzaunioinf(Lconjunts,Lunioinf,llista); for conj in conjuntsaux do llista:=Append(conj,i); Lconjunts:=actualitzaconjunts(Lconjunts,llista); // Lmcinf:=actualitzamcinf(Lmcinf,llista); // Linterseccioinf:=actualitzainterseccioinf(Lconjunts,Lmcinf,Linterseccioinf,Lunioinf,llista); Lunioinf:=actualitzaunioinf(Lconjunts,Lunioinf,llista); end for; end for; /* l:=#Lconjunts; print "CONJUNTS="; ; print "MCINF="; ; print "INTERSECCIOINF="; Linterseccioinf; print "UNIOINF="; */ Lunioinf; //----------------------- //PROVA NOU ALGORITME /* //PROVA ALGORITME SIMPLE //----------------------- joinsets:=function(llista) unio:={}; for conj in llista do unio:=unio join conj; end for; return unio; end function; unioasac:=[#joinsets({N(i):i in llista}):llista in Lconjunts]; unioasac; //---------------------- //PROVA ALGORITME SIMPLE */ /* // COMPROVACIO errors:=[Lunioinf[i]-unioasac[i]:i in [1..#unioasac]]; printf "VEREDICTE:="; [Lconjunts[i]:i in [1..#errors]|errors[i] ne 0]; */ /* conj_r_elements:=func; //[Lconjunts[i]: i in conj_r_elements(3)]; max_index:=index([1..MAX]); conj_r_elements_ge_i:=func; //[Lconjunts[i]: i in conj_r_elements_ge_i([3,3])]; unioinf_conj_r_elements_ge_i:=func; gen_ham_weight:=func; [[gen_ham_weight([r,i]): i in [0..7]]: r in [1..7]]; */ Output: Magma V2.10-6 Wed Dec 24 2003 11:35:12 on modular [Seed = 2024703848] ------------------------------------- Klein quartic[ 1, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 2, 2, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 4, 4, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 6, 6, 4, 4, 4, 4, 5, 5, 5, 5, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 5, 5, 6, 6, 6, 6, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 5, 5, 5, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 6, 6, 5, 5, 5, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 7, 7, 6, 6, 6, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 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10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11 ] Total time: 4.379 seconds, Total memory usage: 2.22MB ************** MAGMA ***************** Host 80.58.32.42.proxycache.rima-tde.net. (80.58.32.42) Time: Wed Dec 24 11:36:24 2003 Input: /* Klein quartic */ printf "Klein quartic"; MAX:=10; c:=5; g:=3; semi:=[0,3]; /* Hermitian curve */ /* printf "hermitian curve"; MAX:=10; c:=12; g:=6; semi:=[0,4,5,8,9,10]; */ /* basic del semigrup */ i_cond:=c-g; pertany:=func; gaps:=[i:i in [1..c-1]|not pertany(i)]; lambda:=func; lambdainv:=func; /* oplus, leq, nu */ oplus:=func; inferior:=func; ominus:=func; N:=func; nu:=func; /* order bound */ dORD:=func; /* //PROVA NOU ALGORITME //----------------------- Lconjunts:=[[0]]; //Lmcinf:=[[0]]; //Linterseccioinf:=[1]; Lunioinf:=[1]; index:=function(llista) i:=0; for j in llista do i:=i+2^j; end for; return(i); end function; actualitzaconjunts:=function (Lconjunts,llista) return(Append(Lconjunts,llista)); end function; /* actualitzamcinf:=function(Lmcinf,llista) maxc:=llista[1]; if (maxc eq 0) then return (Append(Lmcinf,[0])); end if; trobat:=false; while not trobat do while not inferior(maxc,llista[1]) do maxc:=maxc-1; end while; j:=2; while j le #llista and inferior(maxc,llista[j]) do j:=j+1; end while; if j eq #llista+1 then trobat:=true; end if; maxc:=maxc-1; end while; maxc:=maxc+1; mcinfllista:=[maxc]; for h in gaps do candidat:=lambdainv(lambda(maxc)-h); if candidat gt 0 then j:=1; while j le #llista and inferior(candidat,llista[j]) do j:=j+1; end while; if j eq #llista+1 then mcinfllista:=Append(mcinfllista,candidat); end if; end if; end for; return(Append(Lmcinf,mcinfllista)); end function; */ interseccio_ultim_unio_dels_altres:=function(llista) ultim:=llista[#llista]; maxc:=ultim-1; trobat:=false; while not trobat do while not inferior(maxc,ultim) do maxc:=maxc-1; end while; j:=1; while j le #llista-1 and not(inferior(maxc,llista[j])) do j:=j+1; end while; if j le #llista-1 then trobat:=true; end if; maxc:=maxc-1; end while; maxc:=maxc+1; ret:=[maxc]; for h in gaps do candidat:=lambdainv(lambda(maxc)-h); if candidat gt 0 and inferior(candidat,ultim) then j:=1; while j le #llista-1 and not(inferior(candidat,llista[j])) do j:=j+1; end while; if j le #llista-1 then ret:=Append(ret,candidat); end if; end if; end for; return(index(ret)); end function; /* actualitzainterseccioinf:=function(Lconjunts,Lmcinf,Linterseccioinf,Lunioinf,llista) if #llista eq 1 then return Append(Linterseccioinf,nu(llista[1])); else return Append(Linterseccioinf,Lunioinf[index(Lmcinf[index(llista)])]); end if; end function; */ actualitzaunioinf:=function(Lconjunts,Lunioinf,llista) if #llista eq 1 then return Append(Lunioinf,nu(llista[1])); else return Append(Lunioinf, Lunioinf[index([llista[i]:i in [1..(#llista-1)]])]+nu(llista[#llista])-Lunioinf[interseccio_ultim_unio_dels_altres(llista)]); end if; end function; for i in [1..MAX] do conjuntsaux:=Lconjunts; llista:=[i]; Lconjunts:=actualitzaconjunts(Lconjunts,llista); // Lmcinf:=actualitzamcinf(Lmcinf,llista); // Linterseccioinf:=actualitzainterseccioinf(Lconjunts,Lmcinf,Linterseccioinf,Lunioinf,llista); Lunioinf:=actualitzaunioinf(Lconjunts,Lunioinf,llista); for conj in conjuntsaux do llista:=Append(conj,i); Lconjunts:=actualitzaconjunts(Lconjunts,llista); // Lmcinf:=actualitzamcinf(Lmcinf,llista); // Linterseccioinf:=actualitzainterseccioinf(Lconjunts,Lmcinf,Linterseccioinf,Lunioinf,llista); Lunioinf:=actualitzaunioinf(Lconjunts,Lunioinf,llista); end for; end for; /* l:=#Lconjunts; print "CONJUNTS="; ; print "MCINF="; ; print "INTERSECCIOINF="; Linterseccioinf; print "UNIOINF="; */ Lunioinf; //----------------------- //PROVA NOU ALGORITME */ //PROVA ALGORITME SIMPLE //----------------------- joinsets:=function(llista) unio:={}; for conj in llista do unio:=unio join conj; end for; return unio; end function; unioasac:=[#joinsets({N(i):i in llista}):llista in Lconjunts]; unioasac; //---------------------- //PROVA ALGORITME SIMPLE /* // COMPROVACIO errors:=[Lunioinf[i]-unioasac[i]:i in [1..#unioasac]]; printf "VEREDICTE:="; [Lconjunts[i]:i in [1..#errors]|errors[i] ne 0]; */ /* conj_r_elements:=func; //[Lconjunts[i]: i in conj_r_elements(3)]; max_index:=index([1..MAX]); conj_r_elements_ge_i:=func; //[Lconjunts[i]: i in conj_r_elements_ge_i([3,3])]; unioinf_conj_r_elements_ge_i:=func; gen_ham_weight:=func; [[gen_ham_weight([r,i]): i in [0..7]]: r in [1..7]]; */ Output: Magma V2.10-6 Wed Dec 24 2003 11:36:21 on modular [Seed = 2605540430] ------------------------------------- Klein quartic >> return(index(ret)); ^ User error: Identifier 'index' has not been declared or assigned >> Lunioinf[index([llista[i]:i in [1..(#llista-1)]])]+nu(llista[#llista])-Lun ^ User error: Identifier 'index' has not been declared or assigned >> conjuntsaux:=Lconjunts; ^ User error: Identifier 'Lconjunts' has not been declared or assigned >> Lunioinf; ^ User error: Identifier 'Lunioinf' has not been declared or assigned >> */ ^ User error: bad syntax >> unioasac:=[#joinsets({N(i):i in llista}):llista in Lconjunts]; ^ User error: Identifier 'Lconjunts' has not been declared or assigned >> unioasac; ^ User error: Identifier 'unioasac' has not been declared or assigned Total time: 3.029 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 80.58.32.42.proxycache.rima-tde.net. (80.58.32.42) Time: Wed Dec 24 11:40:24 2003 Input: /* Klein quartic */ printf "Klein quartic"; MAX:=10; c:=5; g:=3; semi:=[0,3]; /* Hermitian curve */ /* printf "hermitian curve"; MAX:=10; c:=12; g:=6; semi:=[0,4,5,8,9,10]; */ /* basic del semigrup */ i_cond:=c-g; pertany:=func; gaps:=[i:i in [1..c-1]|not pertany(i)]; lambda:=func; lambdainv:=func; /* oplus, leq, nu */ oplus:=func; inferior:=func; ominus:=func; N:=func; nu:=func; /* order bound */ dORD:=func; //PROVA NOU ALGORITME //----------------------- Lconjunts:=[[0]]; Lunioinf:=[1]; index:=function(llista) i:=0; for j in llista do i:=i+2^j; end for; return(i); end function; actualitzaconjunts:=function (Lconjunts,llista) return(Append(Lconjunts,llista)); end function; interseccio_ultim_unio_dels_altres:=function(llista) ultim:=llista[#llista]; maxc:=ultim-1; trobat:=false; while not trobat do while not inferior(maxc,ultim) do maxc:=maxc-1; end while; j:=1; while j le #llista-1 and not(inferior(maxc,llista[j])) do j:=j+1; end while; if j le #llista-1 then trobat:=true; end if; maxc:=maxc-1; end while; maxc:=maxc+1; ret:=[maxc]; for h in gaps do candidat:=lambdainv(lambda(maxc)-h); if candidat gt 0 and inferior(candidat,ultim) then j:=1; while j le #llista-1 and not(inferior(candidat,llista[j])) do j:=j+1; end while; if j le #llista-1 then ret:=Append(ret,candidat); end if; end if; end for; return(index(ret)); end function; actualitzaunioinf:=function(Lconjunts,Lunioinf,llista) if #llista eq 1 then return Append(Lunioinf,nu(llista[1])); else return Append(Lunioinf, Lunioinf[index([llista[i]:i in [1..(#llista-1)]])]+nu(llista[#llista])-Lunioinf[interseccio_ultim_unio_dels_altres(llista)]); end if; end function; for i in [1..MAX] do conjuntsaux:=Lconjunts; llista:=[i]; Lconjunts:=actualitzaconjunts(Lconjunts,llista); Lunioinf:=actualitzaunioinf(Lconjunts,Lunioinf,llista); for conj in conjuntsaux do llista:=Append(conj,i); Lconjunts:=actualitzaconjunts(Lconjunts,llista); Lunioinf:=actualitzaunioinf(Lconjunts,Lunioinf,llista); end for; end for; /* l:=#Lconjunts; print "CONJUNTS="; ; print "MCINF="; ; print "INTERSECCIOINF="; Linterseccioinf; print "UNIOINF="; */ Lunioinf; //----------------------- //PROVA NOU ALGORITME /* //PROVA ALGORITME SIMPLE //----------------------- joinsets:=function(llista) unio:={}; for conj in llista do unio:=unio join conj; end for; return unio; end function; unioasac:=[#joinsets({N(i):i in llista}):llista in Lconjunts]; unioasac; //---------------------- //PROVA ALGORITME SIMPLE */ /* // COMPROVACIO errors:=[Lunioinf[i]-unioasac[i]:i in [1..#unioasac]]; printf "VEREDICTE:="; [Lconjunts[i]:i in [1..#errors]|errors[i] ne 0]; */ /* conj_r_elements:=func; //[Lconjunts[i]: i in conj_r_elements(3)]; max_index:=index([1..MAX]); conj_r_elements_ge_i:=func; //[Lconjunts[i]: i in conj_r_elements_ge_i([3,3])]; unioinf_conj_r_elements_ge_i:=func; gen_ham_weight:=func; [[gen_ham_weight([r,i]): i in [0..7]]: r in [1..7]]; */ Output: Magma V2.10-6 Wed Dec 24 2003 11:40:20 on modular [Seed = 2058126403] ------------------------------------- Klein quartic[ 1, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 2, 2, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 4, 4, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 6, 6, 4, 4, 4, 4, 5, 5, 5, 5, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 5, 5, 6, 6, 6, 6, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 5, 5, 5, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 6, 6, 5, 5, 5, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 7, 7, 6, 6, 6, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 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9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11 ] Total time: 4.329 seconds, Total memory usage: 2.12MB ************** MAGMA ***************** Host 80.58.32.42.proxycache.rima-tde.net. (80.58.32.42) Time: Wed Dec 24 11:41:55 2003 Input: /* Klein quartic */ printf "Klein quartic"; MAX:=10; c:=5; g:=3; semi:=[0,3]; /* Hermitian curve */ /* printf "hermitian curve"; MAX:=10; c:=12; g:=6; semi:=[0,4,5,8,9,10]; */ /* basic del semigrup */ i_cond:=c-g; pertany:=func; gaps:=[i:i in [1..c-1]|not pertany(i)]; lambda:=func; lambdainv:=func; /* oplus, leq, nu */ oplus:=func; inferior:=func; ominus:=func; N:=func; nu:=func; /* order bound */ dORD:=func; //PROVA NOU ALGORITME //----------------------- Lconjunts:=[[0]]; Lunioinf:=[1]; index:=function(llista) i:=0; for j in llista do i:=i+2^j; end for; return(i); end function; actualitzaconjunts:=function (Lconjunts,llista) return(Append(Lconjunts,llista)); end function; interseccio_ultim_unio_dels_altres:=function(llista) ultim:=llista[#llista]; maxc:=ultim-1; trobat:=false; while not trobat do while not inferior(maxc,ultim) do maxc:=maxc-1; end while; j:=1; while j le #llista-1 and not(inferior(maxc,llista[j])) do j:=j+1; end while; if j le #llista-1 then trobat:=true; end if; maxc:=maxc-1; end while; maxc:=maxc+1; ret:=[maxc]; for h in gaps do candidat:=lambdainv(lambda(maxc)-h); if candidat gt 0 and inferior(candidat,ultim) then j:=1; while j le #llista-1 and not(inferior(candidat,llista[j])) do j:=j+1; end while; if j le #llista-1 then ret:=Append(ret,candidat); end if; end if; end for; return(index(ret)); end function; actualitzaunioinf:=function(Lconjunts,Lunioinf,llista) if #llista eq 1 then return Append(Lunioinf,nu(llista[1])); else return Append(Lunioinf, Lunioinf[index([llista[i]:i in [1..(#llista-1)]])]+nu(llista[#llista])-Lunioinf[interseccio_ultim_unio_dels_altres(llista)]); end if; end function; for i in [1..MAX] do conjuntsaux:=Lconjunts; llista:=[i]; Lconjunts:=actualitzaconjunts(Lconjunts,llista); // Lunioinf:=actualitzaunioinf(Lconjunts,Lunioinf,llista); for conj in conjuntsaux do llista:=Append(conj,i); Lconjunts:=actualitzaconjunts(Lconjunts,llista); // Lunioinf:=actualitzaunioinf(Lconjunts,Lunioinf,llista); end for; end for; /* l:=#Lconjunts; print "CONJUNTS="; ; print "MCINF="; ; print "INTERSECCIOINF="; Linterseccioinf; print "UNIOINF="; */ //Lunioinf; //----------------------- //PROVA NOU ALGORITME //PROVA ALGORITME SIMPLE //----------------------- joinsets:=function(llista) unio:={}; for conj in llista do unio:=unio join conj; end for; return unio; end function; unioasac:=[#joinsets({N(i):i in llista}):llista in Lconjunts]; unioasac; //---------------------- //PROVA ALGORITME SIMPLE /* // COMPROVACIO errors:=[Lunioinf[i]-unioasac[i]:i in [1..#unioasac]]; printf "VEREDICTE:="; [Lconjunts[i]:i in [1..#errors]|errors[i] ne 0]; */ /* conj_r_elements:=func; //[Lconjunts[i]: i in conj_r_elements(3)]; max_index:=index([1..MAX]); conj_r_elements_ge_i:=func; //[Lconjunts[i]: i in conj_r_elements_ge_i([3,3])]; unioinf_conj_r_elements_ge_i:=func; gen_ham_weight:=func; [[gen_ham_weight([r,i]): i in [0..7]]: r in [1..7]]; */ Output: Magma V2.10-6 Wed Dec 24 2003 11:41:51 on modular [Seed = 2992917552] ------------------------------------- Klein quartic[ 1, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 2, 2, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 4, 4, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 6, 6, 4, 4, 4, 4, 5, 5, 5, 5, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 5, 5, 6, 6, 6, 6, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 5, 5, 5, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 6, 6, 5, 5, 5, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 7, 7, 6, 6, 6, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 6, 6, 6, 6, 6, 6, 6, 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11, 11, 11, 11, 11, 11, 11 ] Total time: 4.119 seconds, Total memory usage: 2.12MB ************** MAGMA ***************** Host 80.58.32.42.proxycache.rima-tde.net. (80.58.32.42) Time: Wed Dec 24 11:43:18 2003 Input: /* Klein quartic */ printf "Klein quartic"; MAX:=20; c:=5; g:=3; semi:=[0,3]; /* Hermitian curve */ /* printf "hermitian curve"; MAX:=10; c:=12; g:=6; semi:=[0,4,5,8,9,10]; */ /* basic del semigrup */ i_cond:=c-g; pertany:=func; gaps:=[i:i in [1..c-1]|not pertany(i)]; lambda:=func; lambdainv:=func; /* oplus, leq, nu */ oplus:=func; inferior:=func; ominus:=func; N:=func; nu:=func; /* order bound */ dORD:=func; //PROVA NOU ALGORITME //----------------------- Lconjunts:=[[0]]; Lunioinf:=[1]; index:=function(llista) i:=0; for j in llista do i:=i+2^j; end for; return(i); end function; actualitzaconjunts:=function (Lconjunts,llista) return(Append(Lconjunts,llista)); end function; interseccio_ultim_unio_dels_altres:=function(llista) ultim:=llista[#llista]; maxc:=ultim-1; trobat:=false; while not trobat do while not inferior(maxc,ultim) do maxc:=maxc-1; end while; j:=1; while j le #llista-1 and not(inferior(maxc,llista[j])) do j:=j+1; end while; if j le #llista-1 then trobat:=true; end if; maxc:=maxc-1; end while; maxc:=maxc+1; ret:=[maxc]; for h in gaps do candidat:=lambdainv(lambda(maxc)-h); if candidat gt 0 and inferior(candidat,ultim) then j:=1; while j le #llista-1 and not(inferior(candidat,llista[j])) do j:=j+1; end while; if j le #llista-1 then ret:=Append(ret,candidat); end if; end if; end for; return(index(ret)); end function; actualitzaunioinf:=function(Lconjunts,Lunioinf,llista) if #llista eq 1 then return Append(Lunioinf,nu(llista[1])); else return Append(Lunioinf, Lunioinf[index([llista[i]:i in [1..(#llista-1)]])]+nu(llista[#llista])-Lunioinf[interseccio_ultim_unio_dels_altres(llista)]); end if; end function; for i in [1..MAX] do conjuntsaux:=Lconjunts; llista:=[i]; Lconjunts:=actualitzaconjunts(Lconjunts,llista); // Lunioinf:=actualitzaunioinf(Lconjunts,Lunioinf,llista); for conj in conjuntsaux do llista:=Append(conj,i); Lconjunts:=actualitzaconjunts(Lconjunts,llista); // Lunioinf:=actualitzaunioinf(Lconjunts,Lunioinf,llista); end for; end for; /* l:=#Lconjunts; print "CONJUNTS="; ; print "MCINF="; ; print "INTERSECCIOINF="; Linterseccioinf; print "UNIOINF="; */ //Lunioinf; //----------------------- //PROVA NOU ALGORITME //PROVA ALGORITME SIMPLE //----------------------- joinsets:=function(llista) unio:={}; for conj in llista do unio:=unio join conj; end for; return unio; end function; unioasac:=[#joinsets({N(i):i in llista}):llista in Lconjunts]; unioasac; //---------------------- //PROVA ALGORITME SIMPLE /* // COMPROVACIO errors:=[Lunioinf[i]-unioasac[i]:i in [1..#unioasac]]; printf "VEREDICTE:="; [Lconjunts[i]:i in [1..#errors]|errors[i] ne 0]; */ /* conj_r_elements:=func; //[Lconjunts[i]: i in conj_r_elements(3)]; max_index:=index([1..MAX]); conj_r_elements_ge_i:=func; //[Lconjunts[i]: i in conj_r_elements_ge_i([3,3])]; unioinf_conj_r_elements_ge_i:=func; gen_ham_weight:=func; [[gen_ham_weight([r,i]): i in [0..7]]: r in [1..7]]; */ Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Wed Dec 24 2003 11:42:55 on modular [Seed = 533324380] ------------------------------------- Errors: /home/mfd/gomagma: line 2: 29523 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host 80.58.32.42.proxycache.rima-tde.net. (80.58.32.42) Time: Wed Dec 24 11:43:55 2003 Input: /* Klein quartic */ printf "Klein quartic"; MAX:=15; c:=5; g:=3; semi:=[0,3]; /* Hermitian curve */ /* printf "hermitian curve"; MAX:=10; c:=12; g:=6; semi:=[0,4,5,8,9,10]; */ /* basic del semigrup */ i_cond:=c-g; pertany:=func; gaps:=[i:i in [1..c-1]|not pertany(i)]; lambda:=func; lambdainv:=func; /* oplus, leq, nu */ oplus:=func; inferior:=func; ominus:=func; N:=func; nu:=func; /* order bound */ dORD:=func; //PROVA NOU ALGORITME //----------------------- Lconjunts:=[[0]]; Lunioinf:=[1]; index:=function(llista) i:=0; for j in llista do i:=i+2^j; end for; return(i); end function; actualitzaconjunts:=function (Lconjunts,llista) return(Append(Lconjunts,llista)); end function; interseccio_ultim_unio_dels_altres:=function(llista) ultim:=llista[#llista]; maxc:=ultim-1; trobat:=false; while not trobat do while not inferior(maxc,ultim) do maxc:=maxc-1; end while; j:=1; while j le #llista-1 and not(inferior(maxc,llista[j])) do j:=j+1; end while; if j le #llista-1 then trobat:=true; end if; maxc:=maxc-1; end while; maxc:=maxc+1; ret:=[maxc]; for h in gaps do candidat:=lambdainv(lambda(maxc)-h); if candidat gt 0 and inferior(candidat,ultim) then j:=1; while j le #llista-1 and not(inferior(candidat,llista[j])) do j:=j+1; end while; if j le #llista-1 then ret:=Append(ret,candidat); end if; end if; end for; return(index(ret)); end function; actualitzaunioinf:=function(Lconjunts,Lunioinf,llista) if #llista eq 1 then return Append(Lunioinf,nu(llista[1])); else return Append(Lunioinf, Lunioinf[index([llista[i]:i in [1..(#llista-1)]])]+nu(llista[#llista])-Lunioinf[interseccio_ultim_unio_dels_altres(llista)]); end if; end function; for i in [1..MAX] do conjuntsaux:=Lconjunts; llista:=[i]; Lconjunts:=actualitzaconjunts(Lconjunts,llista); // Lunioinf:=actualitzaunioinf(Lconjunts,Lunioinf,llista); for conj in conjuntsaux do llista:=Append(conj,i); Lconjunts:=actualitzaconjunts(Lconjunts,llista); // Lunioinf:=actualitzaunioinf(Lconjunts,Lunioinf,llista); end for; end for; /* l:=#Lconjunts; print "CONJUNTS="; ; print "MCINF="; ; print "INTERSECCIOINF="; Linterseccioinf; print "UNIOINF="; */ //Lunioinf; //----------------------- //PROVA NOU ALGORITME //PROVA ALGORITME SIMPLE //----------------------- joinsets:=function(llista) unio:={}; for conj in llista do unio:=unio join conj; end for; return unio; end function; unioasac:=[#joinsets({N(i):i in llista}):llista in Lconjunts]; unioasac; //---------------------- //PROVA ALGORITME SIMPLE /* // COMPROVACIO errors:=[Lunioinf[i]-unioasac[i]:i in [1..#unioasac]]; printf "VEREDICTE:="; [Lconjunts[i]:i in [1..#errors]|errors[i] ne 0]; */ /* conj_r_elements:=func; //[Lconjunts[i]: i in conj_r_elements(3)]; max_index:=index([1..MAX]); conj_r_elements_ge_i:=func; //[Lconjunts[i]: i in conj_r_elements_ge_i([3,3])]; unioinf_conj_r_elements_ge_i:=func; gen_ham_weight:=func; [[gen_ham_weight([r,i]): i in [0..7]]: r in [1..7]]; */ Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Wed Dec 24 2003 11:43:32 on modular [Seed = 3778485401] ------------------------------------- Errors: /home/mfd/gomagma: line 2: 29613 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host 80.58.32.42.proxycache.rima-tde.net. (80.58.32.42) Time: Wed Dec 24 11:44:26 2003 Input: /* Klein quartic */ printf "Klein quartic"; MAX:=15; c:=5; g:=3; semi:=[0,3]; /* Hermitian curve */ /* printf "hermitian curve"; MAX:=10; c:=12; g:=6; semi:=[0,4,5,8,9,10]; */ /* basic del semigrup */ i_cond:=c-g; pertany:=func; gaps:=[i:i in [1..c-1]|not pertany(i)]; lambda:=func; lambdainv:=func; /* oplus, leq, nu */ oplus:=func; inferior:=func; ominus:=func; N:=func; nu:=func; /* order bound */ dORD:=func; //PROVA NOU ALGORITME //----------------------- Lconjunts:=[[0]]; Lunioinf:=[1]; index:=function(llista) i:=0; for j in llista do i:=i+2^j; end for; return(i); end function; actualitzaconjunts:=function (Lconjunts,llista) return(Append(Lconjunts,llista)); end function; interseccio_ultim_unio_dels_altres:=function(llista) ultim:=llista[#llista]; maxc:=ultim-1; trobat:=false; while not trobat do while not inferior(maxc,ultim) do maxc:=maxc-1; end while; j:=1; while j le #llista-1 and not(inferior(maxc,llista[j])) do j:=j+1; end while; if j le #llista-1 then trobat:=true; end if; maxc:=maxc-1; end while; maxc:=maxc+1; ret:=[maxc]; for h in gaps do candidat:=lambdainv(lambda(maxc)-h); if candidat gt 0 and inferior(candidat,ultim) then j:=1; while j le #llista-1 and not(inferior(candidat,llista[j])) do j:=j+1; end while; if j le #llista-1 then ret:=Append(ret,candidat); end if; end if; end for; return(index(ret)); end function; actualitzaunioinf:=function(Lconjunts,Lunioinf,llista) if #llista eq 1 then return Append(Lunioinf,nu(llista[1])); else return Append(Lunioinf, Lunioinf[index([llista[i]:i in [1..(#llista-1)]])]+nu(llista[#llista])-Lunioinf[interseccio_ultim_unio_dels_altres(llista)]); end if; end function; for i in [1..MAX] do conjuntsaux:=Lconjunts; llista:=[i]; Lconjunts:=actualitzaconjunts(Lconjunts,llista); // Lunioinf:=actualitzaunioinf(Lconjunts,Lunioinf,llista); for conj in conjuntsaux do llista:=Append(conj,i); Lconjunts:=actualitzaconjunts(Lconjunts,llista); // Lunioinf:=actualitzaunioinf(Lconjunts,Lunioinf,llista); end for; end for; /* l:=#Lconjunts; print "CONJUNTS="; ; print "MCINF="; ; print "INTERSECCIOINF="; Linterseccioinf; print "UNIOINF="; */ //Lunioinf; //----------------------- //PROVA NOU ALGORITME //PROVA ALGORITME SIMPLE //----------------------- joinsets:=function(llista) unio:={}; for conj in llista do unio:=unio join conj; end for; return unio; end function; unioasac:=[#joinsets({N(i):i in llista}):llista in Lconjunts]; unioasac; //---------------------- //PROVA ALGORITME SIMPLE /* // COMPROVACIO errors:=[Lunioinf[i]-unioasac[i]:i in [1..#unioasac]]; printf "VEREDICTE:="; [Lconjunts[i]:i in [1..#errors]|errors[i] ne 0]; */ /* conj_r_elements:=func; //[Lconjunts[i]: i in conj_r_elements(3)]; max_index:=index([1..MAX]); conj_r_elements_ge_i:=func; //[Lconjunts[i]: i in conj_r_elements_ge_i([3,3])]; unioinf_conj_r_elements_ge_i:=func; gen_ham_weight:=func; [[gen_ham_weight([r,i]): i in [0..7]]: r in [1..7]]; */ Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Wed Dec 24 2003 11:44:03 on modular [Seed = 3076606632] ------------------------------------- Errors: /home/mfd/gomagma: line 2: 29691 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host 80.58.32.42.proxycache.rima-tde.net. (80.58.32.42) Time: Wed Dec 24 11:44:58 2003 Input: /* Klein quartic */ printf "Klein quartic"; MAX:=12; c:=5; g:=3; semi:=[0,3]; /* Hermitian curve */ /* printf "hermitian curve"; MAX:=10; c:=12; g:=6; semi:=[0,4,5,8,9,10]; */ /* basic del semigrup */ i_cond:=c-g; pertany:=func; gaps:=[i:i in [1..c-1]|not pertany(i)]; lambda:=func; lambdainv:=func; /* oplus, leq, nu */ oplus:=func; inferior:=func; ominus:=func; N:=func; nu:=func; /* order bound */ dORD:=func; //PROVA NOU ALGORITME //----------------------- Lconjunts:=[[0]]; Lunioinf:=[1]; index:=function(llista) i:=0; for j in llista do i:=i+2^j; end for; return(i); end function; actualitzaconjunts:=function (Lconjunts,llista) return(Append(Lconjunts,llista)); end function; interseccio_ultim_unio_dels_altres:=function(llista) ultim:=llista[#llista]; maxc:=ultim-1; trobat:=false; while not trobat do while not inferior(maxc,ultim) do maxc:=maxc-1; end while; j:=1; while j le #llista-1 and not(inferior(maxc,llista[j])) do j:=j+1; end while; if j le #llista-1 then trobat:=true; end if; maxc:=maxc-1; end while; maxc:=maxc+1; ret:=[maxc]; for h in gaps do candidat:=lambdainv(lambda(maxc)-h); if candidat gt 0 and inferior(candidat,ultim) then j:=1; while j le #llista-1 and not(inferior(candidat,llista[j])) do j:=j+1; end while; if j le #llista-1 then ret:=Append(ret,candidat); end if; end if; end for; return(index(ret)); end function; actualitzaunioinf:=function(Lconjunts,Lunioinf,llista) if #llista eq 1 then return Append(Lunioinf,nu(llista[1])); else return Append(Lunioinf, Lunioinf[index([llista[i]:i in [1..(#llista-1)]])]+nu(llista[#llista])-Lunioinf[interseccio_ultim_unio_dels_altres(llista)]); end if; end function; for i in [1..MAX] do conjuntsaux:=Lconjunts; llista:=[i]; Lconjunts:=actualitzaconjunts(Lconjunts,llista); // Lunioinf:=actualitzaunioinf(Lconjunts,Lunioinf,llista); for conj in conjuntsaux do llista:=Append(conj,i); Lconjunts:=actualitzaconjunts(Lconjunts,llista); // Lunioinf:=actualitzaunioinf(Lconjunts,Lunioinf,llista); end for; end for; /* l:=#Lconjunts; print "CONJUNTS="; ; print "MCINF="; ; print "INTERSECCIOINF="; Linterseccioinf; print "UNIOINF="; */ //Lunioinf; //----------------------- //PROVA NOU ALGORITME //PROVA ALGORITME SIMPLE //----------------------- joinsets:=function(llista) unio:={}; for conj in llista do unio:=unio join conj; end for; return unio; end function; unioasac:=[#joinsets({N(i):i in llista}):llista in Lconjunts]; unioasac; //---------------------- //PROVA ALGORITME SIMPLE /* // COMPROVACIO errors:=[Lunioinf[i]-unioasac[i]:i in [1..#unioasac]]; printf "VEREDICTE:="; [Lconjunts[i]:i in [1..#errors]|errors[i] ne 0]; */ /* conj_r_elements:=func; //[Lconjunts[i]: i in conj_r_elements(3)]; max_index:=index([1..MAX]); conj_r_elements_ge_i:=func; //[Lconjunts[i]: i in conj_r_elements_ge_i([3,3])]; unioinf_conj_r_elements_ge_i:=func; gen_ham_weight:=func; [[gen_ham_weight([r,i]): i in [0..7]]: r in [1..7]]; */ Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Wed Dec 24 2003 11:44:35 on modular [Seed = 148829488] ------------------------------------- Errors: /home/mfd/gomagma: line 2: 29763 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host 80.58.32.42.proxycache.rima-tde.net. (80.58.32.42) Time: Wed Dec 24 11:46:20 2003 Input: /* Klein quartic */ printf "Klein quartic"; MAX:=12; c:=5; g:=3; semi:=[0,3]; /* Hermitian curve */ /* printf "hermitian curve"; MAX:=10; c:=12; g:=6; semi:=[0,4,5,8,9,10]; */ /* basic del semigrup */ i_cond:=c-g; pertany:=func; gaps:=[i:i in [1..c-1]|not pertany(i)]; lambda:=func; lambdainv:=func; /* oplus, leq, nu */ oplus:=func; inferior:=func; ominus:=func; N:=func; nu:=func; /* order bound */ dORD:=func; //PROVA NOU ALGORITME //----------------------- Lconjunts:=[[0]]; Lunioinf:=[1]; index:=function(llista) i:=0; for j in llista do i:=i+2^j; end for; return(i); end function; actualitzaconjunts:=function (Lconjunts,llista) return(Append(Lconjunts,llista)); end function; interseccio_ultim_unio_dels_altres:=function(llista) ultim:=llista[#llista]; maxc:=ultim-1; trobat:=false; while not trobat do while not inferior(maxc,ultim) do maxc:=maxc-1; end while; j:=1; while j le #llista-1 and not(inferior(maxc,llista[j])) do j:=j+1; end while; if j le #llista-1 then trobat:=true; end if; maxc:=maxc-1; end while; maxc:=maxc+1; ret:=[maxc]; for h in gaps do candidat:=lambdainv(lambda(maxc)-h); if candidat gt 0 and inferior(candidat,ultim) then j:=1; while j le #llista-1 and not(inferior(candidat,llista[j])) do j:=j+1; end while; if j le #llista-1 then ret:=Append(ret,candidat); end if; end if; end for; return(index(ret)); end function; actualitzaunioinf:=function(Lconjunts,Lunioinf,llista) if #llista eq 1 then return Append(Lunioinf,nu(llista[1])); else return Append(Lunioinf, Lunioinf[index([llista[i]:i in [1..(#llista-1)]])]+nu(llista[#llista])-Lunioinf[interseccio_ultim_unio_dels_altres(llista)]); end if; end function; for i in [1..MAX] do conjuntsaux:=Lconjunts; llista:=[i]; Lconjunts:=actualitzaconjunts(Lconjunts,llista); Lunioinf:=actualitzaunioinf(Lconjunts,Lunioinf,llista); for conj in conjuntsaux do llista:=Append(conj,i); Lconjunts:=actualitzaconjunts(Lconjunts,llista); Lunioinf:=actualitzaunioinf(Lconjunts,Lunioinf,llista); end for; end for; /* l:=#Lconjunts; print "CONJUNTS="; ; print "MCINF="; ; print "INTERSECCIOINF="; Linterseccioinf; print "UNIOINF="; */ Lunioinf; //----------------------- //PROVA NOU ALGORITME /* //PROVA ALGORITME SIMPLE //----------------------- joinsets:=function(llista) unio:={}; for conj in llista do unio:=unio join conj; end for; return unio; end function; unioasac:=[#joinsets({N(i):i in llista}):llista in Lconjunts]; unioasac; //---------------------- //PROVA ALGORITME SIMPLE */ /* // COMPROVACIO errors:=[Lunioinf[i]-unioasac[i]:i in [1..#unioasac]]; printf "VEREDICTE:="; [Lconjunts[i]:i in [1..#errors]|errors[i] ne 0]; */ /* conj_r_elements:=func; //[Lconjunts[i]: i in conj_r_elements(3)]; max_index:=index([1..MAX]); conj_r_elements_ge_i:=func; //[Lconjunts[i]: i in conj_r_elements_ge_i([3,3])]; unioinf_conj_r_elements_ge_i:=func; gen_ham_weight:=func; [[gen_ham_weight([r,i]): i in [0..7]]: r in [1..7]]; */ Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Wed Dec 24 2003 11:45:57 on modular [Seed = 1451273177] ------------------------------------- Errors: /home/mfd/gomagma: line 2: 29980 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host 80.58.32.42.proxycache.rima-tde.net. (80.58.32.42) Time: Wed Dec 24 11:46:36 2003 Input: /* Klein quartic */ printf "Klein quartic"; MAX:=10; c:=5; g:=3; semi:=[0,3]; /* Hermitian curve */ /* printf "hermitian curve"; MAX:=10; c:=12; g:=6; semi:=[0,4,5,8,9,10]; */ /* basic del semigrup */ i_cond:=c-g; pertany:=func; gaps:=[i:i in [1..c-1]|not pertany(i)]; lambda:=func; lambdainv:=func; /* oplus, leq, nu */ oplus:=func; inferior:=func; ominus:=func; N:=func; nu:=func; /* order bound */ dORD:=func; //PROVA NOU ALGORITME //----------------------- Lconjunts:=[[0]]; Lunioinf:=[1]; index:=function(llista) i:=0; for j in llista do i:=i+2^j; end for; return(i); end function; actualitzaconjunts:=function (Lconjunts,llista) return(Append(Lconjunts,llista)); end function; interseccio_ultim_unio_dels_altres:=function(llista) ultim:=llista[#llista]; maxc:=ultim-1; trobat:=false; while not trobat do while not inferior(maxc,ultim) do maxc:=maxc-1; end while; j:=1; while j le #llista-1 and not(inferior(maxc,llista[j])) do j:=j+1; end while; if j le #llista-1 then trobat:=true; end if; maxc:=maxc-1; end while; maxc:=maxc+1; ret:=[maxc]; for h in gaps do candidat:=lambdainv(lambda(maxc)-h); if candidat gt 0 and inferior(candidat,ultim) then j:=1; while j le #llista-1 and not(inferior(candidat,llista[j])) do j:=j+1; end while; if j le #llista-1 then ret:=Append(ret,candidat); end if; end if; end for; return(index(ret)); end function; actualitzaunioinf:=function(Lconjunts,Lunioinf,llista) if #llista eq 1 then return Append(Lunioinf,nu(llista[1])); else return Append(Lunioinf, Lunioinf[index([llista[i]:i in [1..(#llista-1)]])]+nu(llista[#llista])-Lunioinf[interseccio_ultim_unio_dels_altres(llista)]); end if; end function; for i in [1..MAX] do conjuntsaux:=Lconjunts; llista:=[i]; Lconjunts:=actualitzaconjunts(Lconjunts,llista); Lunioinf:=actualitzaunioinf(Lconjunts,Lunioinf,llista); for conj in conjuntsaux do llista:=Append(conj,i); Lconjunts:=actualitzaconjunts(Lconjunts,llista); Lunioinf:=actualitzaunioinf(Lconjunts,Lunioinf,llista); end for; end for; /* l:=#Lconjunts; print "CONJUNTS="; ; print "MCINF="; ; print "INTERSECCIOINF="; Linterseccioinf; print "UNIOINF="; */ Lunioinf; //----------------------- //PROVA NOU ALGORITME /* //PROVA ALGORITME SIMPLE //----------------------- joinsets:=function(llista) unio:={}; for conj in llista do unio:=unio join conj; end for; return unio; end function; unioasac:=[#joinsets({N(i):i in llista}):llista in Lconjunts]; unioasac; //---------------------- //PROVA ALGORITME SIMPLE */ /* // COMPROVACIO errors:=[Lunioinf[i]-unioasac[i]:i in [1..#unioasac]]; printf "VEREDICTE:="; [Lconjunts[i]:i in [1..#errors]|errors[i] ne 0]; */ /* conj_r_elements:=func; //[Lconjunts[i]: i in conj_r_elements(3)]; max_index:=index([1..MAX]); conj_r_elements_ge_i:=func; //[Lconjunts[i]: i in conj_r_elements_ge_i([3,3])]; unioinf_conj_r_elements_ge_i:=func; gen_ham_weight:=func; [[gen_ham_weight([r,i]): i in [0..7]]: r in [1..7]]; */ Output: Magma V2.10-6 Wed Dec 24 2003 11:46:32 on modular [Seed = 619895174] ------------------------------------- Klein quartic[ 1, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 2, 2, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 4, 4, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 6, 6, 4, 4, 4, 4, 5, 5, 5, 5, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 5, 5, 6, 6, 6, 6, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 5, 5, 5, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 6, 6, 5, 5, 5, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 7, 7, 6, 6, 6, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 6, 6, 6, 6, 6, 6, 6, 6, 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11, 11, 11, 11, 11, 11 ] Total time: 4.319 seconds, Total memory usage: 2.12MB ************** MAGMA ***************** Host 80.58.32.42.proxycache.rima-tde.net. (80.58.32.42) Time: Wed Dec 24 11:47:40 2003 Input: /* Klein quartic */ printf "Klein quartic"; MAX:=10; c:=5; g:=3; semi:=[0,3]; /* Hermitian curve */ /* printf "hermitian curve"; MAX:=10; c:=12; g:=6; semi:=[0,4,5,8,9,10]; */ /* basic del semigrup */ i_cond:=c-g; pertany:=func; gaps:=[i:i in [1..c-1]|not pertany(i)]; lambda:=func; lambdainv:=func; /* oplus, leq, nu */ oplus:=func; inferior:=func; ominus:=func; N:=func; nu:=func; /* order bound */ dORD:=func; //PROVA NOU ALGORITME //----------------------- Lconjunts:=[[0]]; Lunioinf:=[1]; index:=function(llista) i:=0; for j in llista do i:=i+2^j; end for; return(i); end function; actualitzaconjunts:=function (Lconjunts,llista) return(Append(Lconjunts,llista)); end function; interseccio_ultim_unio_dels_altres:=function(llista) ultim:=llista[#llista]; maxc:=ultim-1; trobat:=false; while not trobat do while not inferior(maxc,ultim) do maxc:=maxc-1; end while; j:=1; while j le #llista-1 and not(inferior(maxc,llista[j])) do j:=j+1; end while; if j le #llista-1 then trobat:=true; end if; maxc:=maxc-1; end while; maxc:=maxc+1; ret:=[maxc]; for h in gaps do candidat:=lambdainv(lambda(maxc)-h); if candidat gt 0 and inferior(candidat,ultim) then j:=1; while j le #llista-1 and not(inferior(candidat,llista[j])) do j:=j+1; end while; if j le #llista-1 then ret:=Append(ret,candidat); end if; end if; end for; return(index(ret)); end function; actualitzaunioinf:=function(Lconjunts,Lunioinf,llista) if #llista eq 1 then return Append(Lunioinf,nu(llista[1])); else return Append(Lunioinf, Lunioinf[index([llista[i]:i in [1..(#llista-1)]])]+nu(llista[#llista])-Lunioinf[interseccio_ultim_unio_dels_altres(llista)]); end if; end function; for i in [1..MAX] do conjuntsaux:=Lconjunts; llista:=[i]; Lconjunts:=actualitzaconjunts(Lconjunts,llista); // Lunioinf:=actualitzaunioinf(Lconjunts,Lunioinf,llista); for conj in conjuntsaux do llista:=Append(conj,i); Lconjunts:=actualitzaconjunts(Lconjunts,llista); // Lunioinf:=actualitzaunioinf(Lconjunts,Lunioinf,llista); end for; end for; /* l:=#Lconjunts; print "CONJUNTS="; ; print "MCINF="; ; print "INTERSECCIOINF="; Linterseccioinf; print "UNIOINF="; */ Lunioinf; //----------------------- //PROVA NOU ALGORITME //PROVA ALGORITME SIMPLE //----------------------- joinsets:=function(llista) unio:={}; for conj in llista do unio:=unio join conj; end for; return unio; end function; unioasac:=[#joinsets({N(i):i in llista}):llista in Lconjunts]; unioasac; //---------------------- //PROVA ALGORITME SIMPLE /* // COMPROVACIO errors:=[Lunioinf[i]-unioasac[i]:i in [1..#unioasac]]; printf "VEREDICTE:="; [Lconjunts[i]:i in [1..#errors]|errors[i] ne 0]; */ /* conj_r_elements:=func; //[Lconjunts[i]: i in conj_r_elements(3)]; max_index:=index([1..MAX]); conj_r_elements_ge_i:=func; //[Lconjunts[i]: i in conj_r_elements_ge_i([3,3])]; unioinf_conj_r_elements_ge_i:=func; gen_ham_weight:=func; [[gen_ham_weight([r,i]): i in [0..7]]: r in [1..7]]; */ Output: Magma V2.10-6 Wed Dec 24 2003 11:47:36 on modular [Seed = 1519167035] ------------------------------------- Klein quartic[ 1 ] [ 1, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 2, 2, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 4, 4, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 6, 6, 4, 4, 4, 4, 5, 5, 5, 5, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 5, 5, 6, 6, 6, 6, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 5, 5, 5, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 6, 6, 5, 5, 5, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 7, 7, 6, 6, 6, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 6, 6, 6, 6, 6, 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10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11 ] Total time: 4.159 seconds, Total memory usage: 2.12MB ************** MAGMA ***************** Host d66-183-120-209.bchsia.telus.net. (66.183.120.209) Time: Thu Dec 25 21:51:01 2003 Input: 1+1; Output: Magma V2.10-6 Thu Dec 25 2003 21:50:58 on modular [Seed = 182359833] ------------------------------------- 2 Total time: 2.879 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host d66-183-120-209.bchsia.telus.net. (66.183.120.209) Time: Thu Dec 25 21:51:40 2003 Input: 12*12; Output: Magma V2.10-6 Thu Dec 25 2003 21:51:37 on modular [Seed = 365004845] ------------------------------------- 144 Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host d66-183-120-209.bchsia.telus.net. (66.183.120.209) Time: Thu Dec 25 21:52:06 2003 Input: 13*13; Output: Magma V2.10-6 Thu Dec 25 2003 21:52:03 on modular [Seed = 482902350] ------------------------------------- 169 Total time: 2.879 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host d66-183-120-209.bchsia.telus.net. (66.183.120.209) Time: Thu Dec 25 23:44:33 2003 Input: 11*10; Output: Magma V2.10-6 Thu Dec 25 2003 23:44:30 on modular [Seed = 3812057164] ------------------------------------- 110 Total time: 2.889 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host node04.co.st-johns.fl.us. (205.138.150.5) Time: Sat Dec 27 13:02:40 2003 Input: expand((x^5-7)^50) Output: Magma V2.10-6 Sat Dec 27 2003 13:02:37 on modular [Seed = 1401005368] ------------------------------------- >> expand((x^5-7)^50); ^ User error: Identifier 'x' has not been declared or assigned Total time: 2.929 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host core-dr00.proxy.nacamar.net. (194.162.162.68) Time: Mon Dec 29 07:53:01 2003 Input: H:=HammingCode(GF(8),2); H; Output: Magma V2.10-6 Mon Dec 29 2003 07:52:56 on modular [Seed = 1072702418] ------------------------------------- [9, 7, 3] Hamming code (r = 2) over GF(2^3) Generator matrix: [ 1 0 0 0 0 0 0 1 $.1] [ 0 1 0 0 0 0 0 $.1 $.1^6] [ 0 0 1 0 0 0 0 $.1^6 $.1^3] [ 0 0 0 1 0 0 0 $.1^3 $.1^3] [ 0 0 0 0 1 0 0 $.1^3 $.1^6] [ 0 0 0 0 0 1 0 $.1^6 $.1] [ 0 0 0 0 0 0 1 $.1 1] Total time: 3.109 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host ctb-cache1-vif1.saix.net. (198.54.202.2) Time: Mon Dec 29 17:04:30 2003 Input: 234234324+238479234793; Output: Magma V2.10-6 Mon Dec 29 2003 17:04:27 on modular [Seed = 3828055869] ------------------------------------- 238713469117 Total time: 3.239 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host ctb-cache1-vif1.saix.net. (198.54.202.2) Time: Mon Dec 29 17:04:33 2003 Input: 234234324+238479234793; Output: Magma V2.10-6 Mon Dec 29 2003 17:04:29 on modular [Seed = 3945033780] ------------------------------------- 238713469117 Total time: 3.089 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (61.150.43.30) Time: Tue Dec 30 03:51:30 2003 Input: 1+2 Output: Magma V2.10-6 Tue Dec 30 2003 03:51:26 on modular [Seed = 3195059564] ------------------------------------- 3 Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host c207.134.75-245.clta.telus.com. (207.134.75.245) Time: Tue Dec 30 16:24:33 2003 Input: mc(t2-f)=(m+mc)(t-t1) Output: Magma V2.10-6 Tue Dec 30 2003 16:24:30 on modular [Seed = 366724936] ------------------------------------- >> mc(t2-f)=(m+mc)(t-t1); ^ User error: Identifier 't' has not been declared or assigned Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host c207.134.75-245.clta.telus.com. (207.134.75.245) Time: Tue Dec 30 16:26:26 2003 Input: mc(t2-f)=(m+mc)(m-t1) Output: Magma V2.10-6 Tue Dec 30 2003 16:26:23 on modular [Seed = 130667819] ------------------------------------- >> mc(t2-f)=(m+mc)(m-t1); ^ User error: Identifier 'm' has not been declared or assigned Total time: 2.909 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (194.165.15.161) Time: Wed Dec 31 15:41:02 2003 Input: PrintBinaryPrimitiveTrinomials(521,0); Output: Magma V2.10-6 Wed Dec 31 2003 15:40:59 on modular [Seed = 3742618817] ------------------------------------- >> PrintBinaryPrimitiveTrinomials(521,0);; ^ User error: Identifier 'PrintBinaryPrimitiveTrinomials' has not been declared or assigned Total time: 3.069 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (194.165.15.161) Time: Wed Dec 31 15:41:35 2003 Input: PrintBinaryPrimitivePentanomials(521,0); Output: Magma V2.10-6 Wed Dec 31 2003 15:41:32 on modular [Seed = 3777882840] ------------------------------------- >> PrintBinaryPrimitivePentanomials(521,0);; ^ User error: Identifier 'PrintBinaryPrimitivePentanomials' has not been declared or assigned Total time: 3.009 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (194.165.15.161) Time: Wed Dec 31 15:46:40 2003 Input: trinomial 31 Output: Magma V2.10-6 Wed Dec 31 2003 15:46:37 on modular [Seed = 2455672954] ------------------------------------- >> trinomial 31; ^ User error: bad syntax Total time: 2.919 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (194.165.15.161) Time: Wed Dec 31 15:47:07 2003 Input: trinomial 31 Output: Magma V2.10-6 Wed Dec 31 2003 15:47:04 on modular [Seed = 2808851754] ------------------------------------- >> trinomial 31; ^ User error: bad syntax Total time: 2.939 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (194.165.15.156) Time: Thu Jan 1 10:04:50 2004 Input: PrintBinaryPrimitivePentanomials(21,0); Output: Magma V2.10-6 Thu Jan 1 2004 10:04:47 on modular [Seed = 2269941682] ------------------------------------- >> PrintBinaryPrimitivePentanomials(21,0);; ^ User error: Identifier 'PrintBinaryPrimitivePentanomials' has not been declared or assigned Total time: 3.109 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (194.165.15.156) Time: Thu Jan 1 10:08:19 2004 Input: ? Output: Magma V2.10-6 Thu Jan 1 2004 10:08:16 on modular [Seed = 4047173931] ------------------------------------- =============================================================================== PATH: / KIND: Overview =============================================================================== You are reading about the Magma online help system. This system gives you information about Magma while you are at the computer. To see this help page at any time, all you have to do is to type ? ---------- The online help system comes in two modes: the single request mode and the Magma Help Browser. To enter the Browser, type ?? The Browser is useful if you intend to read several related help nodes, because you can exploit the tree structure of the online help. Once you are in the Browser, you can type help again to find out how to use the Browser, and for a more detailed explanation of the whole online help system. ---------- Single help requests begin with the ? character. Examples are: ?print ?magma ?ring ?example If your help request is ambiguous, Magma will return a numbered list of matches. To see the contents of one of them, type ? followed by its number. Some help pages suggest other pages that you might like to look at as well. They are prefixed by a code such as +3 or +5 . To read one of them, type ? followed by the code. You can also supply the full pathname of a help node, if you know it. For example: ?/system/quit ?/magma/module/homomorphism ---------- The online help system offers tab completion. If you type a few letters of your help request and then press the tab key, Magma will "complete" the request if there is a unique completion. Otherwise, it will complete the request as far as possible, and then emit a beep. Press the tab key again to see all the possibilities. ALWAYS PRESS TAB BEFORE THE END OF THE LINE, SO AS TO SEE EVERY RELEVANT HELP PAGE. (On a few operating systems, the tab completion feature cannot be made available.) ---------- The content of the online help system comes from two sources: the "Handbook of Magma Functions" (Bosma and Cannon) and specially-written overview nodes. You may also wish to consult the books "An Introduction to Algebraic Programming in Magma" (Cannon and Playoust) and "Solving Problems with Magma" (Bosma, Cannon, Playoust and Steel). ---------- The online help system is also available in an HTML form suitable for Internet browsers. To use this, move to a shell prompt (outside Magma) and type magmahelp ---------- To leave Magma, type quit; or -D. =============================================================================== Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (194.165.15.156) Time: Thu Jan 1 10:09:19 2004 Input: ?example Output: Magma V2.10-6 Thu Jan 1 2004 10:09:15 on modular [Seed = 3995462095] ------------------------------------- 1320 matches: 1 O /browser/example 2 O /browser/example/example-intrinsic 3 O /browser/example/example-intrinsic-restrict 4 O /browser/example/example-search 5 O /browser/example/example-walk 6 O /example 7 E /language/function-procedure-package/attribute/examples/\ Example-InteractiveUserAttributes 8 E /language/function-procedure-package/attribute/examples/\ Example-PackageUserAttributes 9 E /language/function-procedure-package/attribute/examples/\ Example-SystemAttributes 10 E /language/function-procedure-package/function-procedure/forward/\ Example-forward 11 E /language/function-procedure-package/function-procedure/function/\ Example-Parameters 12 E /language/function-procedure-package/function-procedure/function/\ Example-Recursion 13 E /language/function-procedure-package/function-procedure/function/\ Example-Underscore 14 E /language/function-procedure-package/function-procedure/\ procedure/Example-Procedures 15 E /language/function-procedure-package/package/import/Example-import 16 E /language/function-procedure-package/package/intrinsic/\ Example-intrinsic 17 E /language/function-procedure-package/package/require/\ Example-require 18 E /language/function-procedure-package/package/spec/Example-spec 19 E /language/function-procedure-package/package/startup-spec/\ Example-startup-spec 20 E /language/IO/file/operations/Example-GetTime 21 E /language/IO/file/operations/Example-LineCount 22 E /language/IO/file/reading-file/Example-Read 23 E /language/IO/print/auto-print/Example-auto-print 24 E /language/IO/print/printf/Example-printf 25 E /language/IO/print/printf/Example-printf 26 E /language/IO/print/printf/Example-printf2 27 E /language/IO/print/sprint/Example-Sprintf 28 E /language/IO/string/Boolean/Example-Strings 29 E /language/IO/string/parsing/Example-Regexp 30 E /language/IO/string/parsing/Example-Split 31 E /language/statement-expressions/assignment/generator-assignment/\ Example-GeneratorNaming 32 E /language/statement-expressions/assignment/generator-assignment/\ Example-GeneratorNamingSequence 33 E /language/statement-expressions/assignment/indexed-assignment/\ Example-Indexing 34 E /language/statement-expressions/assignment/mutation/\ Example-MutationAssignment 35 E /language/statement-expressions/assignment/simple-assignment/\ Example-Identifiers 36 E /language/statement-expressions/assignment/simple-assignment/\ Example-MultipleReturns 37 E /language/statement-expressions/boolean/equality-operators/\ Example-Equality 38 E /language/statement-expressions/boolean/iteration/Example-Booleans 39 E /language/statement-expressions/comment-continuation/\ Example-Various 40 E /language/statement-expressions/conditional/case-statement/\ Example-case 41 E /language/statement-expressions/conditional/\ conditional-expression/Example-InLineConditional 42 E /language/statement-expressions/conditional/\ conditional-statement/Example-if 43 E /language/statement-expressions/iteration/continue-break/\ Example-break 44 E /language/statement-expressions/iteration/repeat-statement/\ Example-repeat 45 E /language/statement-expressions/iteration/repeat-statement/\ Example-while 46 E /language/statement-expressions/misc/Example-IsIntrinsic 47 E /language/statement-expressions/random/Example-IsIntrinsic 48 E /language/statement-expressions/timing/Example-Time 49 E /language/statement-expressions/type/Example-TypeStructures 50 E /language/statement-expressions/where-is/Example-where 51 E /magma/aggregate/coproduct/retrieve/Example-cop 52 E /magma/aggregate/record-format/access-modification/\ Example-RecordAccess 53 E /magma/aggregate/record-format/creation-format/\ Example-RecordFormat 54 E /magma/aggregate/record-format/creation-record/Example-Record 55 E /magma/aggregate/sequence/detail/creation/arithmetic-progression/\ Example-Progression 56 E /magma/aggregate/sequence/detail/iteration/Example-NestedIteration 57 E /magma/aggregate/sequence/detail/operation/modification/\ Example-Farey 58 E /magma/aggregate/sequence/detail/operation/other/\ Example-EgyptianFractions 59 E /magma/aggregate/sequence/detail/power-sequence/\ Example-PowerSequence 60 E /magma/aggregate/sequence/detail/recursion-reduction-iteration/\ recursion/Example-Self 61 E /magma/aggregate/set/detail/access-modification/access/\ Example-Miscellaneous 62 E /magma/aggregate/set/detail/access-modification/element/\ Example-ExtractRep 63 E /magma/aggregate/set/detail/access-modification/element/\ Example-Random 64 E /magma/aggregate/set/detail/access-modification/modification/\ Example-Include 65 E /magma/aggregate/set/detail/creation/arithmetic-progression/\ Example-Progression 66 E /magma/aggregate/set/detail/creation/enumerated/\ Example-AlmostFermat 67 E /magma/aggregate/set/detail/creation/enumerated/Example-Universe 68 E /magma/aggregate/set/detail/creation/indexed/\ Example-AlmostFermatIndexed 69 E /magma/aggregate/set/detail/creation/multiset/Example-Multiset 70 E /magma/aggregate/set/detail/operation/binary/Example-Join 71 E /magma/aggregate/set/detail/power-set/Example-PowerSet 72 E /magma/aggregate/set/detail/quantifier/Example-Exists 73 E /magma/aggregate/set/detail/quantifier/Example-NestedExists 74 E /magma/aggregate/set/detail/reduction-iteration/Example-Reduction 75 E /magma/aggregate/tuple-cartesian-product/creation/\ Example-CartesianProduct 76 E /magma/aggregate/tuple-cartesian-product/tuple-access/\ Example-TupleAccess 77 E /magma/aggregate/tuple-cartesian-product/tuple/Example-Tuple 78 E /magma/combinatorial-geometrical-incidence/brandt-modules/\ ModBrdt:brandt-modules/Associated-Structures/\ Example-ModBrdt:Module-Creation 79 E /magma/combinatorial-geometrical-incidence/brandt-modules/\ ModBrdt:brandt-modules/Example-ModBrdt:Constructors 80 E /magma/combinatorial-geometrical-incidence/brandt-modules/\ ModBrdt:brandt-modules/Verbose-Output/\ Example-ModBrdt:Verbose-Output 81 E /magma/combinatorial-geometrical-incidence/brandt-modules/\ ModBrdt:dimension-formulas/Example-ModBrdt:Dimension 82 E /magma/combinatorial-geometrical-incidence/brandt-modules/\ ModBrdt:Subspaces/Example-ModBrdt:Decomposition 83 E /magma/combinatorial-geometrical-incidence/brandt-modules/\ ModBrdt:Subspaces/ModBrdt:Subspaces-Tests/\ Example-ModBrdt:EisensteinSubspace 84 E /magma/combinatorial-geometrical-incidence/elliptic-curve/\ creation/creation-change_ring/Example-BaseExtend 85 E /magma/combinatorial-geometrical-incidence/elliptic-curve/\ creation/creation-curve/Example-Creation 86 E /magma/combinatorial-geometrical-incidence/elliptic-curve/\ creation/creation-curve/Example-CreationFromCurve 87 E /magma/combinatorial-geometrical-incidence/elliptic-curve/\ creation/creation-curve/Example-CreationFromCurve2 88 E /magma/combinatorial-geometrical-incidence/elliptic-curve/\ creation/creation-model-predicates/Example-Models 89 E /magma/combinatorial-geometrical-incidence/elliptic-curve/\ creation/creation-predicates/Example-CreationTest 90 E /magma/combinatorial-geometrical-incidence/elliptic-curve/\ creation/twists/Example-NonquadraticTwists 91 E /magma/combinatorial-geometrical-incidence/elliptic-curve/\ creation/twists/Example-QuadraticTwists 92 E /magma/combinatorial-geometrical-incidence/elliptic-curve/\ database/Example-ecdb1 93 E /magma/combinatorial-geometrical-incidence/elliptic-curve/\ database/Example-ecdb2 94 E /magma/combinatorial-geometrical-incidence/elliptic-curve/\ ff_curves/abelian_group/Example-AbelianGroup 95 E /magma/combinatorial-geometrical-incidence/elliptic-curve/\ ff_curves/discrete_logs/Example-ECDL 96 E /magma/combinatorial-geometrical-incidence/elliptic-curve/\ ff_curves/ff_curves-point_counting/Example-Invariants to Read 97 E /magma/combinatorial-geometrical-incidence/elliptic-curve/\ ff_curves/ff_curves-point_counting/Example-Order 98 E /magma/combinatorial-geometrical-incidence/elliptic-curve/\ ff_curves/ff_curves-point_counting/Example-SEA 99 E /magma/combinatorial-geometrical-incidence/elliptic-curve/\ ff_curves/ff_curves-point_counting/Example-Twists 100 E /magma/combinatorial-geometrical-incidence/elliptic-curve/\ function_field/function_field-torsion_polynomials/\ Example-DivisionPolynomial 101 E /magma/combinatorial-geometrical-incidence/ellipt ** WARNING: Output too long, hence truncated. ************** MAGMA ***************** Host 3(NXDOMAIN) (194.165.15.156) Time: Thu Jan 1 10:10:19 2004 Input: x^31+x^3+1 Output: Magma V2.10-6 Thu Jan 1 2004 10:10:16 on modular [Seed = 3725973948] ------------------------------------- >> x^31+x^3+1; ^ User error: Identifier 'x' has not been declared or assigned Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (194.165.15.156) Time: Thu Jan 1 10:11:03 2004 Input: list (31,3); Output: Magma V2.10-6 Thu Jan 1 2004 10:11:00 on modular [Seed = 3608989801] ------------------------------------- >> list (31,3);; ^ User error: Identifier 'list' has not been declared or assigned Total time: 3.009 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (194.165.15.156) Time: Thu Jan 1 10:11:22 2004 Input: print Output: Magma V2.10-6 Thu Jan 1 2004 10:11:19 on modular [Seed = 3439774304] ------------------------------------- >> print; ^ User error: bad syntax Total time: 2.929 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (194.165.15.156) Time: Thu Jan 1 10:11:57 2004 Input: print Binary Primitive Pentanomials(16,0); Output: Magma V2.10-6 Thu Jan 1 2004 10:11:54 on modular [Seed = 972177082] ------------------------------------- >> print Binary Primitive Pentanomials(16,0);; ^ User error: bad syntax Total time: 2.989 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (194.165.15.156) Time: Thu Jan 1 10:12:16 2004 Input: print Binary Pentanomials(16,0); Output: Magma V2.10-6 Thu Jan 1 2004 10:12:13 on modular [Seed = 821770180] ------------------------------------- >> print Binary Pentanomials(16,0);; ^ User error: bad syntax Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (194.165.15.156) Time: Thu Jan 1 10:12:40 2004 Input: print Binary(16,0); Output: Magma V2.10-6 Thu Jan 1 2004 10:12:37 on modular [Seed = 736111863] ------------------------------------- >> print Binary(16,0);; ^ User error: Identifier 'Binary' has not been declared or assigned Total time: 3.089 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (194.165.15.156) Time: Thu Jan 1 10:12:57 2004 Input: print Binary (16,0); Output: Magma V2.10-6 Thu Jan 1 2004 10:12:53 on modular [Seed = 500570833] ------------------------------------- >> print Binary (16,0);; ^ User error: Identifier 'Binary' has not been declared or assigned Total time: 3.269 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (194.165.15.156) Time: Thu Jan 1 10:13:22 2004 Input: print PrimitivePentanomials(521,0); Output: Magma V2.10-6 Thu Jan 1 2004 10:13:19 on modular [Seed = 350163490] ------------------------------------- >> print PrimitivePentanomials(521,0);; ^ User error: Identifier 'PrimitivePentanomials' has not been declared or assigned Total time: 3.059 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (194.165.15.156) Time: Thu Jan 1 10:13:40 2004 Input: print Pentanomials(521,0); Output: Magma V2.10-6 Thu Jan 1 2004 10:13:37 on modular [Seed = 264505623] ------------------------------------- >> print Pentanomials(521,0);; ^ User error: Identifier 'Pentanomials' has not been declared or assigned Total time: 3.039 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (194.165.15.156) Time: Thu Jan 1 10:14:01 2004 Input: print(521,0); Output: Magma V2.10-6 Thu Jan 1 2004 10:13:57 on modular [Seed = 114098186] ------------------------------------- >> print(521,0);; ^ Runtime error in elt< ... >: No permutation group context in which to create cycle Total time: 3.059 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (194.165.15.156) Time: Thu Jan 1 10:14:18 2004 Input: print (21,0); Output: Magma V2.10-6 Thu Jan 1 2004 10:14:15 on modular [Seed = 1908045583] ------------------------------------- >> print (21,0);; ^ Runtime error in elt< ... >: No permutation group context in which to create cycle Total time: 3.039 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (194.165.15.156) Time: Thu Jan 1 10:14:37 2004 Input: print(21,0); Output: Magma V2.10-6 Thu Jan 1 2004 10:14:34 on modular [Seed = 1755541003] ------------------------------------- >> print(21,0);; ^ Runtime error in elt< ... >: No permutation group context in which to create cycle Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host ds10.internetdsl.tpnet.pl. (80.53.254.10) Time: Fri Jan 2 06:20:48 2004 Input: http://www.frenchfries.net/paul/factoring/theory/index.html Output: Magma V2.10-6 Fri Jan 2 2004 06:20:44 on modular [Seed = 619597574] ------------------------------------- >> ; ^ User error: bad syntax Total time: 3.119 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host h68-147-114-138.cg.shawcable.net. (68.147.114.138) Time: Fri Jan 2 20:40:52 2004 Input: isprime(2); Output: Magma V2.10-6 Fri Jan 2 2004 20:40:48 on modular [Seed = 3491361364] ------------------------------------- >> isprime(2);; ^ User error: Identifier 'isprime' has not been declared or assigned Total time: 3.279 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host h68-147-114-138.cg.shawcable.net. (68.147.114.138) Time: Fri Jan 2 20:41:23 2004 Input: 3^2; Output: Magma V2.10-6 Fri Jan 2 2004 20:41:20 on modular [Seed = 3641768765] ------------------------------------- 9 Total time: 3.269 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host h68-147-114-138.cg.shawcable.net. (68.147.114.138) Time: Fri Jan 2 20:48:26 2004 Input: 3^2; 2^7; Output: Magma V2.10-6 Fri Jan 2 2004 20:48:23 on modular [Seed = 922687090] ------------------------------------- 9 128 Total time: 3.269 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host h68-147-114-138.cg.shawcable.net. (68.147.114.138) Time: Fri Jan 2 20:55:42 2004 Input: ZetaFunction(R,4); Output: Magma V2.10-6 Fri Jan 2 2004 20:55:39 on modular [Seed = 214241844] ------------------------------------- >> ZetaFunction(R,4); ^ User error: Identifier 'R' has not been declared or assigned Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host h68-147-114-138.cg.shawcable.net. (68.147.114.138) Time: Fri Jan 2 20:58:03 2004 Input: print Factorization(20); Output: Magma V2.10-6 Fri Jan 2 2004 20:58:00 on modular [Seed = 450036881] ------------------------------------- [ <2, 2>, <5, 1> ] Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host h68-147-114-138.cg.shawcable.net. (68.147.114.138) Time: Fri Jan 2 21:01:11 2004 Input: isPrime(51); Output: Magma V2.10-6 Fri Jan 2 2004 21:01:08 on modular [Seed = 2024891711] ------------------------------------- >> isPrime(51); ^ User error: Identifier 'isPrime' has not been declared or assigned Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host h68-147-114-138.cg.shawcable.net. (68.147.114.138) Time: Fri Jan 2 21:02:27 2004 Input: NextPrime(12); Output: Magma V2.10-6 Fri Jan 2 2004 21:02:24 on modular [Seed = 1419594183] ------------------------------------- 13 Total time: 2.919 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host h68-147-114-138.cg.shawcable.net. (68.147.114.138) Time: Fri Jan 2 21:03:15 2004 Input: zetaFunction(2); Output: Magma V2.10-6 Fri Jan 2 2004 21:03:12 on modular [Seed = 2741681760] ------------------------------------- >> zetaFunction(2); ^ User error: Identifier 'zetaFunction' has not been declared or assigned Total time: 2.939 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host h68-147-114-138.cg.shawcable.net. (68.147.114.138) Time: Fri Jan 2 21:03:38 2004 Input: ZetaFunction(2); Output: Magma V2.10-6 Fri Jan 2 2004 21:03:35 on modular [Seed = 2858661758] ------------------------------------- 1.64493406684822643647241516657 Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host h68-147-114-138.cg.shawcable.net. (68.147.114.138) Time: Fri Jan 2 21:03:51 2004 Input: ZetaFunction(3); Output: Magma V2.10-6 Fri Jan 2 2004 21:03:48 on modular [Seed = 2977475990] ------------------------------------- 1.202056903159594285399738161386 Total time: 2.989 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host h68-147-114-138.cg.shawcable.net. (68.147.114.138) Time: Fri Jan 2 21:05:07 2004 Input: k :=3; zta := ZetaFunction(k); ztainv :=1.0/zta; Output: Magma V2.10-6 Fri Jan 2 2004 21:05:04 on modular [Seed = 3161825487] ------------------------------------- Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host h68-147-114-138.cg.shawcable.net. (68.147.114.138) Time: Fri Jan 2 21:05:18 2004 Input: k :=3; //zta := ZetaFunction(k); // ztainv :=1.0/zta; Output: Magma V2.10-6 Fri Jan 2 2004 21:05:15 on modular [Seed = 2336397299] ------------------------------------- Total time: 2.889 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host h68-147-114-138.cg.shawcable.net. (68.147.114.138) Time: Fri Jan 2 21:05:41 2004 Input: k :=3; zta := ZetaFunction(k); ztainv :=1.0/zta; print ztainv; Output: Magma V2.10-6 Fri Jan 2 2004 21:05:38 on modular [Seed = 2455473859] ------------------------------------- 0.83190737258070746868312627890 Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host ppp-62-10-141-79.dialup.tiscali.it. (62.10.141.79) Time: Fri Jan 2 21:07:41 2004 Input: 100+10 Output: Magma V2.10-6 Fri Jan 2 2004 21:07:38 on modular [Seed = 2555479121] ------------------------------------- 110 Total time: 2.989 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host ppp-62-10-141-79.dialup.tiscali.it. (62.10.141.79) Time: Fri Jan 2 21:08:10 2004 Input: (100+10)/10 Output: Magma V2.10-6 Fri Jan 2 2004 21:08:07 on modular [Seed = 3878616259] ------------------------------------- 11 Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host ppp-62-10-141-79.dialup.tiscali.it. (62.10.141.79) Time: Fri Jan 2 21:08:43 2004 Input: ((100+10)/10)*2 Output: Magma V2.10-6 Fri Jan 2 2004 21:08:40 on modular [Seed = 4114411262] ------------------------------------- 22 Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host px3so.cg.shawcable.net. (24.71.223.142) Time: Sat Jan 3 00:15:53 2004 Input: pp := func; procedure prime(s,n); ztainv :=1.0/ZetaFunction(s); q :=1-ztainv*pp(p,s,n); q := q^{1/s}; print "p, s, n and p_{n+1} are: ",p,s,n,q; end procedure; procedure pp(); k :=100; s := 100; prime(p,s,n); end procedure; Output: Magma V2.10-6 Sat Jan 3 2004 00:15:50 on modular [Seed = 2875376781] ------------------------------------- >> q :=1-ztainv*pp(p,s,n); ^ User error: Identifier 'p' has not been declared or assigned >> prime(p,s,n); ^ User error: Identifier 'p' has not been declared or assigned Total time: 2.929 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host px3so.cg.shawcable.net. (24.71.223.142) Time: Sat Jan 3 00:21:31 2004 Input: pr := func; procedure primecal(); s :=100; n := 100; prime(s,n); end procedure; procedure prime(s,n); q :=(1-1.0/ZetaFunction(s)*pr(p,s,n))^{1/s}; print "s, n and p_{n+1} are: ", s,n,q; end procedure; Output: Magma V2.10-6 Sat Jan 3 2004 00:21:28 on modular [Seed = 3161838277] ------------------------------------- >> prime(s,n); ^ User error: Identifier 'prime' has not been declared or assigned >> q :=(1-1.0/ZetaFunction(s)*pr(p,s,n))^{1/s}; ^ User error: Identifier 'p' has not been declared or assigned Total time: 2.859 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host px3so.cg.shawcable.net. (24.71.223.142) Time: Sat Jan 3 00:22:19 2004 Input: pr := func; procedure primecal(); s :=100; n := 100; primeca(s,n); end procedure; procedure primeca(s,n); q :=(1-1.0/ZetaFunction(s)*pr(p,s,n))^{1/s}; print "s, n and p_{n+1} are: ", s,n,q; end procedure; Output: Magma V2.10-6 Sat Jan 3 2004 00:22:16 on modular [Seed = 2253383727] ------------------------------------- >> primeca(s,n); ^ User error: Identifier 'primeca' has not been declared or assigned >> q :=(1-1.0/ZetaFunction(s)*pr(p,s,n))^{1/s}; ^ User error: Identifier 'p' has not been declared or assigned Total time: 2.909 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host px3so.cg.shawcable.net. (24.71.223.142) Time: Sat Jan 3 00:23:04 2004 Input: pr := func; procedure primeca(s,n); q :=(1-1.0/ZetaFunction(s)*pr(p,s,n))^{1/s}; print "s, n and p_{n+1} are: ", s,n,q; end procedure; procedure primecal(); s :=100; n := 100; primeca(s,n); end procedure; Output: Magma V2.10-6 Sat Jan 3 2004 00:23:01 on modular [Seed = 2438528773] ------------------------------------- >> q :=(1-1.0/ZetaFunction(s)*pr(p,s,n))^{1/s}; ^ User error: Identifier 'p' has not been declared or assigned >> primeca(s,n); ^ User error: Identifier 'primeca' has not been declared or assigned Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host R1.softjoys.com. (212.113.101.45) Time: Sat Jan 3 06:22:57 2004 Input: R := FunctionField(GF(5)); P := PolynomialRing(R); F := FunctionField(y^2 - 1/x); F; Output: Magma V2.10-6 Sat Jan 3 2004 06:22:53 on modular [Seed = 2125981545] ------------------------------------- Algebraic function field defined over Univariate rational function field over GF(5) by y^2 + 4/x Total time: 3.459 seconds, Total memory usage: 6.52MB ************** MAGMA ***************** Host R1.softjoys.com. (212.113.101.45) Time: Sat Jan 3 06:24:43 2004 Input: R := FunctionField(GF(5)); P := PolynomialRing(R); F := FunctionField(1/x); F; Output: Magma V2.10-6 Sat Jan 3 2004 06:24:40 on modular [Seed = 2009001493] ------------------------------------- >> F := FunctionField(1/x); ^ Runtime error in 'FunctionField': Bad argument types Argument types given: FldFunRatUElt >> F; ^ User error: Identifier 'F' has not been declared or assigned Total time: 3.049 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host R1.softjoys.com. (212.113.101.45) Time: Sat Jan 3 06:24:59 2004 Input: R := FunctionField(GF(5)); F := FunctionField(1/x); F; Output: Magma V2.10-6 Sat Jan 3 2004 06:24:56 on modular [Seed = 1822815742] ------------------------------------- >> F := FunctionField(1/x); ^ Runtime error in 'FunctionField': Bad argument types Argument types given: FldFunRatUElt >> F; ^ User error: Identifier 'F' has not been declared or assigned Total time: 2.929 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host R1.softjoys.com. (212.113.101.45) Time: Sat Jan 3 06:25:31 2004 Input: R := FunctionField(GF(5)); F; Output: Magma V2.10-6 Sat Jan 3 2004 06:25:28 on modular [Seed = 2572156971] ------------------------------------- >> F; ^ User error: Identifier 'F' has not been declared or assigned Total time: 2.989 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host R1.softjoys.com. (212.113.101.45) Time: Sat Jan 3 06:25:36 2004 Input: R := FunctionField(GF(5)); F; Output: Magma V2.10-6 Sat Jan 3 2004 06:25:33 on modular [Seed = 2522812193] ------------------------------------- >> F; ^ User error: Identifier 'F' has not been declared or assigned Total time: 2.999 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host R1.softjoys.com. (212.113.101.45) Time: Sat Jan 3 06:25:46 2004 Input: R := FunctionField(GF(5)); Output: Magma V2.10-6 Sat Jan 3 2004 06:25:43 on modular [Seed = 2403735074] ------------------------------------- Total time: 2.939 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host R1.softjoys.com. (212.113.101.45) Time: Sat Jan 3 07:00:58 2004 Input: K := GF(2, 4); X := FunctionField(K); Y := PolynomialRing(X); f := y^4+y+x^5; F := FunctionField(f); F; Output: Magma V2.10-6 Sat Jan 3 2004 07:00:55 on modular [Seed = 3339605546] ------------------------------------- Algebraic function field defined over Univariate rational function field over GF(2^4) by y^4 + y + x^5 Total time: 3.019 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host R1.softjoys.com. (212.113.101.45) Time: Sat Jan 3 07:01:39 2004 Input: K := GF(2, 4); X := FunctionField(K); Y := PolynomialRing(X); f := y^4+y+x^5; F := FunctionField(f); F; Genus(F); Output: Magma V2.10-6 Sat Jan 3 2004 07:01:36 on modular [Seed = 3794498264] ------------------------------------- Algebraic function field defined over Univariate rational function field over GF(2^4) by y^4 + y + x^5 6 Total time: 3.159 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host R1.softjoys.com. (212.113.101.45) Time: Sat Jan 3 07:03:24 2004 Input: K := GF(2, 4); X := FunctionField(K); Y := PolynomialRing(X); f := y^4+y+x^5; F := FunctionField(f); F; Genus(F); Decomposition(Oinf); Output: Magma V2.10-6 Sat Jan 3 2004 07:03:21 on modular [Seed = 466783115] ------------------------------------- Algebraic function field defined over Univariate rational function field over GF(2^4) by y^4 + y + x^5 6 >> Decomposition(Oinf); ^ User error: Identifier 'Oinf' has not been declared or assigned Total time: 3.159 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host R1.softjoys.com. (212.113.101.45) Time: Sat Jan 3 07:03:34 2004 Input: K := GF(2, 4); X := FunctionField(K); Y := PolynomialRing(X); f := y^4+y+x^5; F := FunctionField(f); F; Genus(F); Decomposition(0inf); Output: Magma V2.10-6 Sat Jan 3 2004 07:03:31 on modular [Seed = 316375704] ------------------------------------- Algebraic function field defined over Univariate rational function field over GF(2^4) by y^4 + y + x^5 6 >> Decomposition(0inf); ^ User error: bad syntax Total time: 3.099 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host R1.softjoys.com. (212.113.101.45) Time: Sat Jan 3 07:07:12 2004 Input: K := GF(2, 4); X := FunctionField(K); Y := PolynomialRing(X); f := y^4+y+x^5; F := FunctionField(f); F; Genus(F); Output: Magma V2.10-6 Sat Jan 3 2004 07:07:08 on modular [Seed = 13209461] ------------------------------------- Algebraic function field defined over Univariate rational function field over GF(2^4) by y^4 + y + x^5 6 Total time: 3.099 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host R1.softjoys.com. (212.113.101.45) Time: Sat Jan 3 07:07:51 2004 Input: K := GF(2, 4); X := FunctionField(K); Y := PolynomialRing(X); f := y; F := FunctionField(f); F; Genus(F); Output: Magma V2.10-6 Sat Jan 3 2004 07:07:47 on modular [Seed = 1005761713] ------------------------------------- Algebraic function field defined over Univariate rational function field over GF(2^4) by y 0 Total time: 3.039 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host R1.softjoys.com. (212.113.101.45) Time: Sat Jan 3 07:21:42 2004 Input: K := GF(2, 4); X := FunctionField(K); Y := PolynomialRing(X); f := y; F := FunctionField(f); F; Genus(F); print(F); Output: Magma V2.10-6 Sat Jan 3 2004 07:21:39 on modular [Seed = 1485952146] ------------------------------------- Algebraic function field defined over Univariate rational function field over GF(2^4) by y 0 Algebraic function field defined over Univariate rational function field over GF(2^4) by y Total time: 3.039 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host R1.softjoys.com. (212.113.101.45) Time: Sat Jan 3 07:23:04 2004 Input: K := GF(2, 4); X := FunctionField(K); Y := PolynomialRing(X); f := y; F := FunctionField(f); F; Genus(F); list(F); Output: Magma V2.10-6 Sat Jan 3 2004 07:23:00 on modular [Seed = 1385945455] ------------------------------------- Algebraic function field defined over Univariate rational function field over GF(2^4) by y 0 >> list(F); ^ User error: Identifier 'list' has not been declared or assigned Total time: 2.929 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host R1.softjoys.com. (212.113.101.45) Time: Sat Jan 3 07:26:37 2004 Input: K := GF(5); X := FunctionField(K); Y := PolynomialRing(X); f := y; F := FunctionField(f); F; Genus(F); Basis(F); Output: Magma V2.10-6 Sat Jan 3 2004 07:26:34 on modular [Seed = 1082772387] ------------------------------------- Algebraic function field defined over Univariate rational function field over GF(5) by y 0 [ 1 ] Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host R1.softjoys.com. (212.113.101.45) Time: Sat Jan 3 07:26:51 2004 Input: K := GF(5); X := FunctionField(K); Y := PolynomialRing(X); f := x; F := FunctionField(f); F; Genus(F); Basis(F); Output: Magma V2.10-6 Sat Jan 3 2004 07:26:48 on modular [Seed = 2058612843] ------------------------------------- >> F := FunctionField(f); ^ Runtime error in 'FunctionField': Bad argument types Argument types given: FldFunRatUElt >> F; ^ User error: Identifier 'F' has not been declared or assigned >> Genus(F); ^ User error: Identifier 'F' has not been declared or assigned >> Basis(F);; ^ User error: Identifier 'F' has not been declared or assigned Total time: 3.019 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host R1.softjoys.com. (212.113.101.45) Time: Sat Jan 3 07:27:01 2004 Input: K := GF(5); X := FunctionField(K); Y := PolynomialRing(X); f := y; F := FunctionField(f); F; Genus(F); Basis(F); Output: Magma V2.10-6 Sat Jan 3 2004 07:26:58 on modular [Seed = 1975320446] ------------------------------------- Algebraic function field defined over Univariate rational function field over GF(5) by y 0 [ 1 ] Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host R1.softjoys.com. (212.113.101.45) Time: Sat Jan 3 07:28:02 2004 Input: K := GF(5); X := FunctionField(K); Y := PolynomialRing(X); f := x*y^2 - 1; F := FunctionField(f); F; Genus(F); Basis(F); Output: Magma V2.10-6 Sat Jan 3 2004 07:27:58 on modular [Seed = 1822811707] ------------------------------------- Algebraic function field defined over Univariate rational function field over GF(5) by x*y^2 + 4 0 [ 1, y ] Total time: 3.309 seconds, Total memory usage: 6.52MB ************** MAGMA ***************** Host R1.softjoys.com. (212.113.101.45) Time: Sat Jan 3 07:30:18 2004 Input: > P := ProjectiveSpace(Rationals(),2); > C := Curve(P,x^4 + 2*x*y^2*z + 5*y*z^3); > F := FunctionField(C); > F; Output: Magma V2.10-6 Sat Jan 3 2004 07:30:15 on modular [Seed = 2622821970] ------------------------------------- Algebraic function field defined over Rational Field by $.1^4 + 2*$.1*$.2^2 + 5*$.2 Total time: 2.939 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host R1.softjoys.com. (212.113.101.45) Time: Sat Jan 3 07:30:35 2004 Input: > P := ProjectiveSpace(Rationals(),2); > C := Curve(P,x^4 + 2*x*y^2*z + 5*y*z^3); > F := FunctionField(C); > F; Basis(F); Output: Magma V2.10-6 Sat Jan 3 2004 07:30:32 on modular [Seed = 2539527526] ------------------------------------- Algebraic function field defined over Rational Field by $.1^4 + 2*$.1*$.2^2 + 5*$.2 >> Basis(F); ^ Runtime error in 'Basis': Function field is not a finite extension Total time: 2.939 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host R1.softjoys.com. (212.113.101.45) Time: Sat Jan 3 07:30:52 2004 Input: P := ProjectiveSpace(Rationals(),2); C := Curve(P,x^4 + 2*x*y^2*z + 5*y*z^3); F := FunctionField(C); F; Basis(F); Output: Magma V2.10-6 Sat Jan 3 2004 07:30:49 on modular [Seed = 2387018862] ------------------------------------- Algebraic function field defined over Rational Field by $.1^4 + 2*$.1*$.2^2 + 5*$.2 >> Basis(F); ^ Runtime error in 'Basis': Function field is not a finite extension Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host R1.softjoys.com. (212.113.101.45) Time: Sat Jan 3 07:31:29 2004 Input: P := ProjectiveSpace(Rationals(),2); C := Curve(P,x^4 + 2*x*y^2*z + 5*y*z^3); F := FunctionField(C); F; Genus(F); Output: Magma V2.10-6 Sat Jan 3 2004 07:31:26 on modular [Seed = 3111137470] ------------------------------------- Algebraic function field defined over Rational Field by $.1^4 + 2*$.1*$.2^2 + 5*$.2 2 Total time: 3.089 seconds, Total memory usage: 1.99MB ************** MAGMA ***************** Host R1.softjoys.com. (212.113.101.45) Time: Sat Jan 3 07:32:05 2004 Input: P := ProjectiveSpace(Rationals(),2); C := Curve(P,x^4 + 2*x*y^2*z + 5*y*z^3); F := FunctionField(C); F; Genus(F); Basis(C); Output: Magma V2.10-6 Sat Jan 3 2004 07:32:02 on modular [Seed = 3011132136] ------------------------------------- Algebraic function field defined over Rational Field by $.1^4 + 2*$.1*$.2^2 + 5*$.2 2 >> Basis(C); ^ Runtime error in 'Basis': Bad argument types Argument types given: Crv Total time: 2.969 seconds, Total memory usage: 1.99MB ************** MAGMA ***************** Host pcp486497pcs.howard01.md.comcast.net. (68.55.18.94) Time: Sat Jan 3 08:18:59 2004 Input: 2 + 3 Output: Magma V2.10-6 Sat Jan 3 2004 08:18:56 on modular [Seed = 80607836] ------------------------------------- 5 Total time: 2.999 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pcp486497pcs.howard01.md.comcast.net. (68.55.18.94) Time: Sat Jan 3 08:19:21 2004 Input: 2 + 3 Output: Magma V2.10-6 Sat Jan 3 2004 08:19:18 on modular [Seed = 922732664] ------------------------------------- 5 Total time: 2.980 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host px3so.cg.shawcable.net. (24.71.223.142) Time: Sat Jan 3 21:24:18 2004 Input: pi^3; Output: Magma V2.10-6 Sat Jan 3 2004 21:24:15 on modular [Seed = 1133184263] ------------------------------------- >> pi^3;; ^ User error: Identifier 'pi' has not been declared or assigned Total time: 2.979 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host px3so.cg.shawcable.net. (24.71.223.142) Time: Sat Jan 3 21:24:32 2004 Input: p^3; Output: Magma V2.10-6 Sat Jan 3 2004 21:24:29 on modular [Seed = 1519524876] ------------------------------------- >> p^3;; ^ User error: Identifier 'p' has not been declared or assigned Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 202-63-173-18.exatt.com. (202.63.173.18) Time: Sun Jan 4 02:02:56 2004 Input: 1234 Output: Magma V2.10-6 Sun Jan 4 2004 02:02:53 on modular [Seed = 1873275642] ------------------------------------- 1234 Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 202-63-173-18.exatt.com. (202.63.173.18) Time: Sun Jan 4 02:03:32 2004 Input: 1234+120 Output: Magma V2.10-6 Sun Jan 4 2004 02:03:29 on modular [Seed = 2024865201] ------------------------------------- 1354 Total time: 2.979 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host dialup-67.72.215.69.Dial1.Detroit1.Level3.net. (67.72.215.69) Time: Sun Jan 4 03:55:34 2004 Input: 10! Output: Magma V2.10-6 Sun Jan 4 2004 03:55:31 on modular [Seed = 3609148883] ------------------------------------- >> 10!; ^ User error: bad syntax Total time: 3.009 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host ar10-1i.dial-up.arnes.si. (194.249.4.65) Time: Sun Jan 4 07:50:38 2004 Input: N:=439; q:=2; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition (NewSubspace(CuspidalSubspace (ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; mde:=[]; Include(~cg,[N,i,1]); for j in [1..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); mde[j]:=cgo[j]/tam[j]; if Dimension(A[i]) eq 1 then cm:=GCD(tam[j], Order(TorsionSubgroup(EllipticCurve(A[i]))) ); mde[j]:= Numerator(cgo[j]/cm); end if; if Dimension(A[i]) ge 2 then s:=Factorization(Numerator(Evaluate (CharacteristicPolynomial( DualHeckeOperator(A[i],q)),q+1))); fs:=1; for j in [1..#s] do fs:=fs*s[j][1]; end for; cm:=GCD(tam[j],fs); mde[j]:= Numerator(cgo[j]/cm); end if; Include(~cg,[n[j][1],tam[j],mde[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: Magma V2.10-6 Sun Jan 4 2004 07:50:33 on modular [Seed = 1957906209] ------------------------------------- [ 439, 1, 1 ][] [ 439, 2, 1 ][ 439, 1, 1 ][] [ 439, 3, 1 ][ 439, 73, 1 ][] Total time: 4.409 seconds, Total memory usage: 5.56MB ************** MAGMA ***************** Host ar10-1i.dial-up.arnes.si. (194.249.4.65) Time: Sun Jan 4 07:51:44 2004 Input: N:=1001; q:=2; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition (NewSubspace(CuspidalSubspace (ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; mde:=[]; Include(~cg,[N,i,1]); for j in [1..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); mde[j]:=cgo[j]/tam[j]; if Dimension(A[i]) eq 1 then cm:=GCD(tam[j], Order(TorsionSubgroup(EllipticCurve(A[i]))) ); mde[j]:= Numerator(cgo[j]/cm); end if; if Dimension(A[i]) ge 2 then s:=Factorization(Numerator(Evaluate (CharacteristicPolynomial( DualHeckeOperator(A[i],q)),q+1))); fs:=1; for j in [1..#s] do fs:=fs*s[j][1]; end for; cm:=GCD(tam[j],fs); mde[j]:= Numerator(cgo[j]/cm); end if; Include(~cg,[n[j][1],tam[j],mde[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Sun Jan 4 2004 07:51:21 on modular [Seed = 231357960] ------------------------------------- Errors: /home/mfd/gomagma: line 2: 29505 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host ar10-1i.dial-up.arnes.si. (194.249.4.65) Time: Sun Jan 4 07:52:14 2004 Input: N:=823; q:=2; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition (NewSubspace(CuspidalSubspace (ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; mde:=[]; Include(~cg,[N,i,1]); for j in [1..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); mde[j]:=cgo[j]/tam[j]; if Dimension(A[i]) eq 1 then cm:=GCD(tam[j], Order(TorsionSubgroup(EllipticCurve(A[i]))) ); mde[j]:= Numerator(cgo[j]/cm); end if; if Dimension(A[i]) ge 2 then s:=Factorization(Numerator(Evaluate (CharacteristicPolynomial( DualHeckeOperator(A[i],q)),q+1))); fs:=1; for j in [1..#s] do fs:=fs*s[j][1]; end for; cm:=GCD(tam[j],fs); mde[j]:= Numerator(cgo[j]/cm); end if; Include(~cg,[n[j][1],tam[j],mde[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: Magma V2.10-6 Sun Jan 4 2004 07:52:06 on modular [Seed = 113325372] ------------------------------------- [ 823, 1, 1 ][] [ 823, 2, 1 ][ 823, 137, 1 ][] Total time: 7.729 seconds, Total memory usage: 12.31MB ************** MAGMA ***************** Host ar10-1i.dial-up.arnes.si. (194.249.4.65) Time: Sun Jan 4 07:52:56 2004 Input: N:=2000; q:=2; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition (NewSubspace(CuspidalSubspace (ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; mde:=[]; Include(~cg,[N,i,1]); for j in [1..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); mde[j]:=cgo[j]/tam[j]; if Dimension(A[i]) eq 1 then cm:=GCD(tam[j], Order(TorsionSubgroup(EllipticCurve(A[i]))) ); mde[j]:= Numerator(cgo[j]/cm); end if; if Dimension(A[i]) ge 2 then s:=Factorization(Numerator(Evaluate (CharacteristicPolynomial( DualHeckeOperator(A[i],q)),q+1))); fs:=1; for j in [1..#s] do fs:=fs*s[j][1]; end for; cm:=GCD(tam[j],fs); mde[j]:= Numerator(cgo[j]/cm); end if; Include(~cg,[n[j][1],tam[j],mde[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Sun Jan 4 2004 07:52:33 on modular [Seed = 417278917] ------------------------------------- Errors: /home/mfd/gomagma: line 2: 29524 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host ar10-1i.dial-up.arnes.si. (194.249.4.65) Time: Sun Jan 4 07:53:29 2004 Input: N:=456; q:=2; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition (NewSubspace(CuspidalSubspace (ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; mde:=[]; Include(~cg,[N,i,1]); for j in [1..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); mde[j]:=cgo[j]/tam[j]; if Dimension(A[i]) eq 1 then cm:=GCD(tam[j], Order(TorsionSubgroup(EllipticCurve(A[i]))) ); mde[j]:= Numerator(cgo[j]/cm); end if; if Dimension(A[i]) ge 2 then s:=Factorization(Numerator(Evaluate (CharacteristicPolynomial( DualHeckeOperator(A[i],q)),q+1))); fs:=1; for j in [1..#s] do fs:=fs*s[j][1]; end for; cm:=GCD(tam[j],fs); mde[j]:= Numerator(cgo[j]/cm); end if; Include(~cg,[n[j][1],tam[j],mde[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: Magma V2.10-6 Sun Jan 4 2004 07:53:19 on modular [Seed = 299246306] ------------------------------------- Do not know how to compute component group at 2 Total time: 9.979 seconds, Total memory usage: 4.86MB ************** MAGMA ***************** Host ar10-1i.dial-up.arnes.si. (194.249.4.65) Time: Sun Jan 4 08:03:42 2004 Input: N:=688; q:=2; n:=Factorization(N); A:=SortDecomposition(NewformDecomposition (NewSubspace(CuspidalSubspace (ModularSymbols(N,2,+1))))); for i in [1..#A] do cg:=[]; cgo:=[]; tam:=[]; mde:=[]; Include(~cg,[N,i,1]); for j in [1..#n] do cgo[j]:=ComponentGroupOrder(A[i],n[j][1]); tam[j]:=TamagawaNumber(A[i],n[j][1]); mde[j]:=cgo[j]/tam[j]; if Dimension(A[i]) eq 1 then cm:=GCD(tam[j], Order(TorsionSubgroup(EllipticCurve(A[i]))) ); mde[j]:= Numerator(cgo[j]/cm); end if; if Dimension(A[i]) ge 2 then s:=Factorization(Numerator(Evaluate (CharacteristicPolynomial( DualHeckeOperator(A[i],q)),q+1))); fs:=1; for j in [1..#s] do fs:=fs*s[j][1]; end for; cm:=GCD(tam[j],fs); mde[j]:= Numerator(cgo[j]/cm); end if; Include(~cg,[n[j][1],tam[j],mde[j]]); end for; for k in [1..#cg] do printf "%o",cg[k]; end for; print []; end for; Output: Magma V2.10-6 Sun Jan 4 2004 08:03:33 on modular [Seed = 3406625698] ------------------------------------- Do not know how to compute component group at 2 Total time: 8.789 seconds, Total memory usage: 4.85MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sun Jan 4 17:13:28 2004 Input: R:=PolynomialRing(IntegerRing()); CP:=CharacteristicPolynomial; DH:=DualHeckeOperator; for N in [11..11] do A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do C2:=CP(DH(A[i],2)); C3:=CP(DH(A[i],3)); C5:=CP(DH(A[i],5)); C7:=CP(DH(A[i],7)); C11:=CP(DH(A[i],11)); C13:=CP(DH(A[i],13)); B:=[N,i,2,C2,3,C3,5,C5,7,C7,11,C11,13,C13]; printf "%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o",B[1],B[2],B[3],B[4],B[5],B[6],B[7],B[8],B[9],B[10],B[11],B[12],B[13],B[14]; print []; end for; end for; for N in [560..560] do A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [7..#A] do C2:=CP(DH(A[i],2)); C3:=CP(DH(A[i],3)); C5:=CP(DH(A[i],5)); C7:=CP(DH(A[i],7)); C11:=CP(DH(A[i],11)); C13:=CP(DH(A[i],13)); B:=[N,i,2,C2,3,C3,5,C5,7,C7,11,C11,13,C13]; printf "%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o",B[1],B[2],B[3],B[4],B[5],B[6],B[7],B[8],B[9],B[10],B[11],B[12],B[13],B[14]; print []; end for; end for; Output: Magma V2.10-6 Sun Jan 4 2004 17:13:16 on modular [Seed = 3221713016] ------------------------------------- 11,1,2,$.1 + 2,3,$.1 + 1,5,$.1 - 1,7,$.1 + 2,11,$.1 - 1,13,$.1 - 4[] 560,7,2,x^2,3,x^2 - x - 8,5,x^2 + 2*x + 1,7,x^2 - 2*x + 1,11,x^2 + 7*x + 4,13,x^2 - 3*x - 6[] 560,8,2,x^2,3,x^2 + x - 4,5,x^2 - 2*x + 1,7,x^2 + 2*x + 1,11,x^2 - x - 4,13,x^2 - x - 38[] 560,9,2,x^2,3,x^2 - x - 4,5,x^2 - 2*x + 1,7,x^2 - 2*x + 1,11,x^2 + x - 4,13,x^2 - 5*x + 2[] Total time: 11.380 seconds, Total memory usage: 5.45MB ************** MAGMA ***************** Host R1.softjoys.com. (212.113.101.45) Time: Mon Jan 5 05:22:34 2004 Input: > D:=2*P1[2]+2*P1[3]; > D0:=Div!D; > D0; Divisor on Curve over GF(5) defined by x^3*y + x + y^3 > RiemannRochSpace(D0); KModule of dimension 2 over GF(5) Mapping from: KModule of dimension 2 over GF(5) to Algebraic function field defined over GF(5) by x^3*y + x + y^3 > B0:=Basis(D0); > B0; [ 1, 1/$.2 ] > D:=2*P1[4]+2*P1[5]; > D0:=Div!D; > D0; Divisor on Curve over GF(5) defined by x^3*y + x + y^3 > RiemannRochSpace(D0); KModule of dimension 2 over GF(5) Mapping from: KModule of dimension 2 over GF(5) to Algebraic function field defined over GF(5) by x^3*y + x + y^3 > B0:=Basis(D0); > B0; [ $.2/($.2 + 3), 1/($.2 + 3) ] Output: Magma V2.10-6 Mon Jan 5 2004 05:22:31 on modular [Seed = 2724505461] ------------------------------------- >> D:=2*P1[2]+2*P1[3]; ^ User error: Identifier 'P1' has not been declared or assigned >> D0:=Div!D; ^ User error: Identifier 'Div' has not been declared or assigned >> D0; ^ User error: Identifier 'D0' has not been declared or assigned >> Divisor on Curve over GF(5) defined by ^ User error: bad syntax >> RiemannRochSpace(D0); ^ User error: bad syntax >> KModule of dimension 2 over GF(5) ^ User error: bad syntax >> Mapping from: KModule of dimension 2 over GF(5) to Algebraic function field ^ User error: bad syntax >> defined over GF(5) by ^ User error: bad syntax >> B0:=Basis(D0); ^ User error: bad syntax >> B0; ^ User error: Identifier 'B0' has not been declared or assigned >> D:=2*P1[4]+2*P1[5]; ^ User error: bad syntax >> D0:=Div!D; ^ User error: Identifier 'Div' has not been declared or assigned >> D0; ^ User error: Identifier 'D0' has not been declared or assigned >> Divisor on Curve over GF(5) defined by ^ User error: bad syntax >> RiemannRochSpace(D0); ^ User error: bad syntax >> KModule of dimension 2 over GF(5) ^ User error: bad syntax >> Mapping from: KModule of dimension 2 over GF(5) to Algebraic function field ^ User error: bad syntax >> defined over GF(5) by ^ User error: bad syntax >> B0:=Basis(D0); ^ User error: bad syntax >> B0; ^ User error: Identifier 'B0' has not been declared or assigned >> [ $.2/($.2 + 3), 1/($.2 + 3) ] ^ Runtime error: Bad dollar structure Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host R1.softjoys.com. (212.113.101.45) Time: Mon Jan 5 05:58:32 2004 Input: > A := AffineSpace(FiniteField(5),2); > f:=x^3*y+y^3+x; > C:=Curve(A,f); > C; Curve over GF(5) defined by x^3*y + x + y^3 > D := ProjectiveClosure(C); > > D; Curve over GF(5) defined by X^3*Y + X*Z^3 + Y^3*Z Output: Magma V2.10-6 Mon Jan 5 2004 05:58:29 on modular [Seed = 3777469828] ------------------------------------- Curve over GF(5) defined by x^3*y + x + y^3 >> Curve over GF(5) defined by ^ User error: bad syntax >> D := ProjectiveClosure(C); ^ User error: bad syntax >> > ^ User error: bad syntax >> D; ^ User error: Identifier 'D' has not been declared or assigned >> Curve over GF(5) defined by ^ User error: bad syntax >> X^3*Y + X*Z^3 + Y^3*Z ^ User error: Identifier 'X' has not been declared or assigned Total time: 2.879 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host R1.softjoys.com. (212.113.101.45) Time: Mon Jan 5 05:58:51 2004 Input: A := AffineSpace(FiniteField(5),2); f:=x^3*y+y^3+x; C:=Curve(A,f); C; Curve over GF(5) defined by x^3*y + x + y^3 D := ProjectiveClosure(C); D; Curve over GF(5) defined by X^3*Y + X*Z^3 + Y^3*Z Output: Magma V2.10-6 Mon Jan 5 2004 05:58:48 on modular [Seed = 3945633715] ------------------------------------- Curve over GF(5) defined by x^3*y + x + y^3 >> Curve over GF(5) defined by ^ User error: bad syntax >> D := ProjectiveClosure(C); ^ User error: bad syntax >> D; ^ User error: Identifier 'D' has not been declared or assigned >> Curve over GF(5) defined by ^ User error: bad syntax >> X^3*Y + X*Z^3 + Y^3*Z ^ User error: Identifier 'X' has not been declared or assigned Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host R1.softjoys.com. (212.113.101.45) Time: Mon Jan 5 05:59:22 2004 Input: A := AffineSpace(FiniteField(5),2); f:=x^3*y+y^3+x; C:=Curve(A,f); C; x^3*y + x + y^3 D := ProjectiveClosure(C); D; Curve over GF(5) defined by X^3*Y + X*Z^3 + Y^3*Z Output: Magma V2.10-6 Mon Jan 5 2004 05:59:19 on modular [Seed = 3557992547] ------------------------------------- Curve over GF(5) defined by x^3*y + x + y^3 >> D := ProjectiveClosure(C); ^ User error: bad syntax >> D; ^ User error: Identifier 'D' has not been declared or assigned >> Curve over GF(5) defined by ^ User error: bad syntax >> X^3*Y + X*Z^3 + Y^3*Z ^ User error: Identifier 'X' has not been declared or assigned Total time: 2.889 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host R1.softjoys.com. (212.113.101.45) Time: Mon Jan 5 07:50:02 2004 Input: A := AffineSpace(FiniteField(5),2); f:=x^3*y+y^3+x; C:=Curve(A,f); C; Output: Magma V2.10-6 Mon Jan 5 2004 07:49:57 on modular [Seed = 2488465102] ------------------------------------- Curve over GF(5) defined by x^3*y + x + y^3 Total time: 3.059 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host reached (144.122.136.201) Time: Mon Jan 5 10:06:28 2004 Input: 2^32; Output: Magma V2.10-6 Mon Jan 5 2004 10:06:11 on modular [Seed = 282481246] ------------------------------------- 4294967296 Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host m201.math.metu.edu.tr. (144.122.136.201) Time: Mon Jan 5 10:07:03 2004 Input: 2^24; Output: Magma V2.10-6 Mon Jan 5 2004 10:06:59 on modular [Seed = 1806510549] ------------------------------------- 16777216 Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host m201.math.metu.edu.tr. (144.122.136.201) Time: Mon Jan 5 10:08:27 2004 Input: 2^32; Output: Magma V2.10-6 Mon Jan 5 2004 10:08:24 on modular [Seed = 2109423544] ------------------------------------- 4294967296 Total time: 2.929 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host m201.math.metu.edu.tr. (144.122.136.201) Time: Mon Jan 5 10:08:57 2004 Input: 2^32; Output: Magma V2.10-6 Mon Jan 5 2004 10:08:54 on modular [Seed = 2008102492] ------------------------------------- 4294967296 Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (199.111.119.60) Time: Mon Jan 5 12:04:52 2004 Input: EllipticCurve[1,2,3,1,1]; Output: Magma V2.10-6 Mon Jan 5 2004 12:04:48 on modular [Seed = 517519365] ------------------------------------- >> EllipticCurve[1,2,3,1,1];; ^ Runtime error in '[]': Bad argument types Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (199.111.119.60) Time: Mon Jan 5 12:06:26 2004 Input: EllipticCurve(1,2,3,1,1); Output: Magma V2.10-6 Mon Jan 5 2004 12:06:23 on modular [Seed = 1773129677] ------------------------------------- >> EllipticCurve(1,2,3,1,1);; ^ Runtime error in 'EllipticCurve': Bad argument types Argument types given: RngIntElt, RngIntElt, RngIntElt, RngIntElt, RngIntElt Total time: 2.929 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host ip-64-139-40-66.dsl.sjc.megapath.net. (64.139.40.66) Time: Mon Jan 5 13:39:15 2004 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: Magma V2.10-6 Mon Jan 5 2004 13:39:12 on modular [Seed = 1839987991] ------------------------------------- Replace this by some code, then click [PARI] or [MAGMA]! Total time: 2.919 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (213.40.3.65) Time: Mon Jan 5 14:12:09 2004 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: Magma V2.10-6 Mon Jan 5 2004 14:12:05 on modular [Seed = 3777456590] ------------------------------------- Replace this by some code, then click [PARI] or [MAGMA]! Total time: 3.019 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aybabtu.matrox.com. (138.11.254.204) Time: Tue Jan 6 10:24:15 2004 Input: f(x) = x^2 f(2) Output: Magma V2.10-6 Tue Jan 6 2004 10:24:12 on modular [Seed = 1839759735] ------------------------------------- >> f(2) ^ User error: bad syntax Total time: 2.919 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host ad14-m35.net.hinet.hr. (195.29.49.35) Time: Tue Jan 6 17:06:35 2004 Input: e=EllipticCurve([1,0,0,-3531474678706925407855636725500,2548317483638211729406118411284184511350250000]); Rank(e) Output: Magma V2.10-6 Tue Jan 6 2004 17:06:32 on modular [Seed = 1924562022] ------------------------------------- >> e=EllipticCurve([1,0,0,-3531474678706925407855636725500,2548317483638211729 ^ User error: Identifier 'e' has not been declared or assigned >> Rank(e) ^ User error: Identifier 'e' has not been declared or assigned Total time: 2.909 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host ad14-m35.net.hinet.hr. (195.29.49.35) Time: Tue Jan 6 17:07:06 2004 Input: Rank(EllipticCurve([1,0,0,-3531474678706925407855636725500,2548317483638211729406118411284184511350250000])) Output: Magma V2.10-6 Tue Jan 6 2004 17:07:02 on modular [Seed = 1806656913] ------------------------------------- Warning: rank computed (0) is only a lower bound (It may still be correct, though) Warning: rank computed (0) is only a lower bound (It may still be correct, though) 0 Total time: 3.489 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host ad14-m35.net.hinet.hr. (195.29.49.35) Time: Tue Jan 6 17:07:45 2004 Input: MordellWeilRank(EllipticCurve([1,0,0,-3531474678706925407855636725500,2548317483638211729406118411284184511350250000])) Output: Magma V2.10-6 Tue Jan 6 2004 17:07:41 on modular [Seed = 1553486477] ------------------------------------- Warning: rank computed (0) is only a lower bound (It may still be correct, though) Warning: rank computed (0) is only a lower bound (It may still be correct, though) 0 Total time: 3.529 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host ad14-m35.net.hinet.hr. (195.29.49.35) Time: Tue Jan 6 17:08:09 2004 Input: MordellWeilRankBounds(EllipticCurve([1,0,0,-3531474678706925407855636725500,2548317483638211729406118411284184511350250000])) Output: Magma V2.10-6 Tue Jan 6 2004 17:08:06 on modular [Seed = 1452431596] ------------------------------------- 0 3 Total time: 3.599 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host ad14-m35.net.hinet.hr. (195.29.49.35) Time: Tue Jan 6 17:08:54 2004 Input: MordellWeilRankBounds(EllipticCurve([0,0,0,-82,0])) Output: Magma V2.10-6 Tue Jan 6 2004 17:08:51 on modular [Seed = 1334526400] ------------------------------------- 3 3 Total time: 2.889 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host ad14-m35.net.hinet.hr. (195.29.49.35) Time: Tue Jan 6 17:09:38 2004 Input: MordellWeilRankBounds(EllipticCurve([0,-1,0,-24649,1355209])) Output: Magma V2.10-6 Tue Jan 6 2004 17:09:35 on modular [Seed = 1022898527] ------------------------------------- 4 4 Total time: 2.929 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host ad14-m35.net.hinet.hr. (195.29.49.35) Time: Tue Jan 6 17:10:40 2004 Input: MordellWeilRankBounds(EllipticCurve([0,0,1,-6349808647,193146346911036 ])) Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Tue Jan 6 2004 17:10:17 on modular [Seed = 753410329] ------------------------------------- Errors: /home/mfd/gomagma: line 2: 17232 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host ad14-m35.net.hinet.hr. (195.29.49.35) Time: Tue Jan 6 17:11:56 2004 Input: MordellWeilRankBounds(EllipticCurve([1,-1,1,-1608154463,25555312501831])) Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Tue Jan 6 2004 17:11:33 on modular [Seed = 635513036] ------------------------------------- Errors: /home/mfd/gomagma: line 2: 17241 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host ad14-m35.net.hinet.hr. (195.29.49.35) Time: Tue Jan 6 17:12:48 2004 Input: MordellWeilRankBounds(EllipticCurve([0,-1,0,-1485019900716,658252007072023716])) Output: Magma V2.10-6 Tue Jan 6 2004 17:12:35 on modular [Seed = 517608369] ------------------------------------- 7 9 Total time: 12.429 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host ad14-m35.net.hinet.hr. (195.29.49.35) Time: Tue Jan 6 17:13:48 2004 Input: MordellWeilRankBounds(EllipticCurve([1,0,0,-2060795223235870670,1037860392073475481628988676])) Output: Magma V2.10-6 Tue Jan 6 2004 17:13:43 on modular [Seed = 4265276053] ------------------------------------- 10 10 Total time: 4.189 seconds, Total memory usage: 3.00MB ************** MAGMA ***************** Host ad14-m35.net.hinet.hr. (195.29.49.35) Time: Tue Jan 6 17:14:48 2004 Input: MordellWeilRankBounds(EllipticCurve([1,0,1,34318214642441646362435632562579908747,3184376895814127197244886284686214848599453811643486936756])) Output: Magma V2.10-6 Tue Jan 6 2004 17:14:34 on modular [Seed = 4046847431] ------------------------------------- 12 15 Total time: 14.049 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host ad14-m35.net.hinet.hr. (195.29.49.35) Time: Tue Jan 6 17:16:01 2004 Input: MordellWeilGroup(EllipticCurve([0,0,1,-6349808647,193146346911036 ])) Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Tue Jan 6 2004 17:15:37 on modular [Seed = 3574716704] ------------------------------------- Errors: /home/mfd/gomagma: line 2: 17321 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host ad14-m35.net.hinet.hr. (195.29.49.35) Time: Tue Jan 6 17:16:29 2004 Input: MordellWeilRankBound(EllipticCurve([0,0,0,0,708291392738196762720225 ])) Output: Magma V2.10-6 Tue Jan 6 2004 17:16:25 on modular [Seed = 3322071555] ------------------------------------- >> MordellWeilRankBound(EllipticCurve([0,0,0,0,708291392738196762720225 ])) ^ User error: Identifier 'MordellWeilRankBound' has not been declared or assigned Total time: 3.009 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host ad14-m35.net.hinet.hr. (195.29.49.35) Time: Tue Jan 6 17:17:12 2004 Input: MordellWeilRankBounds(EllipticCurve([0,0,0,0,708291392738196762720225 ])) Output: ** WARNING: Computation used more memory than allowed. ** Magma V2.10-6 Tue Jan 6 2004 17:17:00 on modular [Seed = 3212555039] ------------------------------------- Current total memory usage: 95.4MB, failed memory request: 0.0MB System Error: User memory limit has been reached Current total memory usage: 95.4MB, failed memory request: 0.0MB System Error: User memory limit has been reached Current total memory usage: 95.4MB, failed memory request: 0.0MB System Error: User memory limit has been reached Current total memory usage: 95.4MB, failed memory request: 0.0MB System Error: User memory limit has been reached Current total memory usage: 95.4MB, failed memory request: 0.0MB Errors: Magma: Fatal Error: not enough memory to even recover ************** MAGMA ***************** Host ad14-m35.net.hinet.hr. (195.29.49.35) Time: Tue Jan 6 17:18:40 2004 Input: MordellWeilRankBounds(ElliticCurve([0,0,0,0,708291392738196762720225])) Output: Magma V2.10-6 Tue Jan 6 2004 17:18:37 on modular [Seed = 2977282800] ------------------------------------- >> MordellWeilRankBounds(ElliticCurve([0,0,0,0,708291392738196762720225])); ^ User error: Identifier 'ElliticCurve' has not been declared or assigned Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host ad14-m35.net.hinet.hr. (195.29.49.35) Time: Tue Jan 6 17:18:56 2004 Input: MordellWeilRankBounds(EllipticCurve([0,0,0,0,708291392738196762720225])) Output: ** WARNING: Computation used more memory than allowed. ** Magma V2.10-6 Tue Jan 6 2004 17:18:46 on modular [Seed = 2842534547] ------------------------------------- Current total memory usage: 95.4MB, failed memory request: 0.0MB System Error: User memory limit has been reached Current total memory usage: 95.4MB, failed memory request: 0.0MB System Error: User memory limit has been reached Current total memory usage: 95.4MB, failed memory request: 0.0MB System Error: User memory limit has been reached Total time: 10.299 seconds, Total memory usage: 100.00MB ************** MAGMA ***************** Host ad14-m35.net.hinet.hr. (195.29.49.35) Time: Tue Jan 6 17:20:43 2004 Input: MordellWeilRankBounds(EllipticCurve([0,0,0,0,7])) Output: Magma V2.10-6 Tue Jan 6 2004 17:20:39 on modular [Seed = 2286715715] ------------------------------------- 0 0 Total time: 2.969 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host ad14-m35.net.hinet.hr. (195.29.49.35) Time: Tue Jan 6 17:21:20 2004 Input: MordellWeilGroup(EllipticCurve([0,0,0,-36,0])) Output: Magma V2.10-6 Tue Jan 6 2004 17:21:16 on modular [Seed = 2126149081] ------------------------------------- Abelian Group isomorphic to Z/2 + Z/2 + Z Defined on 3 generators Relations: 2*$.1 = 0 2*$.2 = 0 Total time: 3.099 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host business.mysantanarow.com. (65.122.201.5) Time: Tue Jan 6 22:20:28 2004 Input: hello Output: Magma V2.10-6 Tue Jan 6 2004 22:20:25 on modular [Seed = 4063672189] ------------------------------------- >> hello; ^ User error: Identifier 'hello' has not been declared or assigned Total time: 2.999 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host mcmail.muzo.com. (194.228.69.30) Time: Wed Jan 7 04:28:09 2004 Input: 321654*54654 Output: Magma V2.10-6 Wed Jan 7 2004 04:28:05 on modular [Seed = 2218814157] ------------------------------------- 17579677716 Total time: 3.049 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host host194-236.pool80207.interbusiness.it. (80.207.236.194) Time: Wed Jan 7 06:12:13 2004 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: Magma V2.10-6 Wed Jan 7 2004 06:12:09 on modular [Seed = 3743091005] ------------------------------------- Replace this by some code, then click [PARI] or [MAGMA]! Total time: 2.979 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host host194-236.pool80207.interbusiness.it. (80.207.236.194) Time: Wed Jan 7 06:12:30 2004 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: Magma V2.10-6 Wed Jan 7 2004 06:12:27 on modular [Seed = 2909371229] ------------------------------------- Replace this by some code, then click [PARI] or [MAGMA]! Total time: 3.019 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (144.122.136.202) Time: Wed Jan 7 06:35:11 2004 Input: a:=4; a*5; Output: Magma V2.10-6 Wed Jan 7 2004 06:35:00 on modular [Seed = 1638248687] ------------------------------------- 20 Total time: 3.079 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (68.222.35.14) Time: Wed Jan 7 06:38:30 2004 Input: (x/y+y/x)^3*(x/y-y/x)^3 Output: Magma V2.10-6 Wed Jan 7 2004 06:38:27 on modular [Seed = 1587187335] ------------------------------------- >> (x/y+y/x)^3*(x/y-y/x)^3; ^ User error: Identifier 'x' has not been declared or assigned Total time: 3.179 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host lon-igate.mckinsey.com. (213.86.15.25) Time: Wed Jan 7 11:13:03 2004 Input: [ x^2 : x in [1..5] ]; Output: Magma V2.10-6 Wed Jan 7 2004 11:13:00 on modular [Seed = 3212619995] ------------------------------------- [ 1, 4, 9, 16, 25 ] Total time: 3.049 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host lon-igate.mckinsey.com. (213.86.15.25) Time: Wed Jan 7 11:13:22 2004 Input: Maximum ([ x^2 : x in [1..5] ]); Output: Magma V2.10-6 Wed Jan 7 2004 11:13:18 on modular [Seed = 2354021370] ------------------------------------- 25 5 Total time: 3.059 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host lon-igate.mckinsey.com. (213.86.15.25) Time: Wed Jan 7 11:18:10 2004 Input: F2 := FiniteField (2, 10); Output: Magma V2.10-6 Wed Jan 7 2004 11:18:07 on modular [Seed = 2656932041] ------------------------------------- Total time: 2.999 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host lon-igate.mckinsey.com. (213.86.15.25) Time: Wed Jan 7 11:19:19 2004 Input: F2[i] := FiniteField (2, 10); #F2; E := EllipticCurve(F, 1, 1, 1, 1); Output: Magma V2.10-6 Wed Jan 7 2004 11:19:16 on modular [Seed = 1638035330] ------------------------------------- >> F2[i] := FiniteField (2, 10); ^ User error: Identifier 'F2' has not been declared or assigned >> #F2; ^ User error: Identifier 'F2' has not been declared or assigned >> E := EllipticCurve(F, 1, 1, 1, 1); ^ User error: Identifier 'F' has not been declared or assigned Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host lon-igate.mckinsey.com. (213.86.15.25) Time: Wed Jan 7 11:19:45 2004 Input: F2 := FiniteField (2, 10); #F2; E := EllipticCurve(F, 1, 1, 1, 1); Output: Magma V2.10-6 Wed Jan 7 2004 11:19:42 on modular [Seed = 1958181517] ------------------------------------- 1024 >> E := EllipticCurve(F, 1, 1, 1, 1); ^ User error: Identifier 'F' has not been declared or assigned Total time: 2.939 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host lon-igate.mckinsey.com. (213.86.15.25) Time: Wed Jan 7 11:20:05 2004 Input: F2 := FiniteField (2, 10); #F2; EllipticCurve; E := EllipticCurve(F2, 1, 1, 1, 1); Output: Magma V2.10-6 Wed Jan 7 2004 11:20:02 on modular [Seed = 1317879963] ------------------------------------- 1024 Intrinsic 'EllipticCurve' Signatures: ( S) -> CrvEll The elliptic curve defined by the coefficients of S. S must be of length 2 or 5. ( D, N, I, J) -> CrvEll The J-th elliptic curve in the I-th isogeny class of conductor N found in the elliptic curve database D. ( D, S) -> SeqEnum An elliptic curve with label S (e.g. "101A" or "101A1") in the elliptic curve database D. ( D, N, S, J) -> SeqEnum The J-th elliptic curve of conductor N and label S (e.g. "A") in the elliptic curve database D. ( f, h) -> CrvEll Creates the elliptic curve defined by y^2 + h(x)*y = f(x), where h must be of degree at most 1 and f must be monic of degree 3. ( f) -> CrvEll Creates the elliptic curve defined by y^2 = f(x), where f must be monic of degree 3. ( j) -> CrvEll Creates an elliptic curve with j-invariant j. This version is deprecated and will be removed in a future release -- use EllipticCurveFromjInvariant() instead. ( C) -> CrvEll, Map Returns an elliptic curve from certain genus 1 curves with an easily recognised rational point. ( C, Point) -> CrvEll, MapSch Returns a Weierstrass model of a genus 1 curve with a point and also the map from C to that model. The point should be nonsingular. ( C, Place) -> CrvEll, MapSch Returns a Weierstrass model of a genus 1 curve with a degree 1 place and also the map from C to that model. ( f) -> CrvEll An elliptic curve with associated modular form f. ( M) -> SeqEnum [ StartPrec, Database ] An elliptic curve over the rational numbers that lies in the isogeny class of elliptic curves associated to M. >> E := EllipticCurve(F2, 1, 1, 1, 1); ^ Runtime error in 'EllipticCurve': Bad argument types Argument types given: FldFin, RngIntElt, RngIntElt, RngIntElt, RngIntElt Total time: 2.989 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host lon-igate.mckinsey.com. (213.86.15.25) Time: Wed Jan 7 11:22:27 2004 Input: F2 := FiniteField (2, 10); #F2; F2X := PolynomialRing(F2); (x+i)^3; EllipticCurve; // E := EllipticCurve(i, ); Output: Magma V2.10-6 Wed Jan 7 2004 11:22:24 on modular [Seed = 1368546422] ------------------------------------- 1024 x^3 + i*x^2 + i^2*x + i^3 Intrinsic 'EllipticCurve' Signatures: ( S) -> CrvEll The elliptic curve defined by the coefficients of S. S must be of length 2 or 5. ( D, N, I, J) -> CrvEll The J-th elliptic curve in the I-th isogeny class of conductor N found in the elliptic curve database D. ( D, S) -> SeqEnum An elliptic curve with label S (e.g. "101A" or "101A1") in the elliptic curve database D. ( D, N, S, J) -> SeqEnum The J-th elliptic curve of conductor N and label S (e.g. "A") in the elliptic curve database D. ( f, h) -> CrvEll Creates the elliptic curve defined by y^2 + h(x)*y = f(x), where h must be of degree at most 1 and f must be monic of degree 3. ( f) -> CrvEll Creates the elliptic curve defined by y^2 = f(x), where f must be monic of degree 3. ( j) -> CrvEll Creates an elliptic curve with j-invariant j. This version is deprecated and will be removed in a future release -- use EllipticCurveFromjInvariant() instead. ( C) -> CrvEll, Map Returns an elliptic curve from certain genus 1 curves with an easily recognised rational point. ( C, Point) -> CrvEll, MapSch Returns a Weierstrass model of a genus 1 curve with a point and also the map from C to that model. The point should be nonsingular. ( C, Place) -> CrvEll, MapSch Returns a Weierstrass model of a genus 1 curve with a degree 1 place and also the map from C to that model. ( f) -> CrvEll An elliptic curve with associated modular form f. ( M) -> SeqEnum [ StartPrec, Database ] An elliptic curve over the rational numbers that lies in the isogeny class of elliptic curves associated to M. Total time: 3.009 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host lon-igate.mckinsey.com. (213.86.15.25) Time: Wed Jan 7 11:23:01 2004 Input: F2 := FiniteField (2, 10); #F2; F2X := PolynomialRing(F2); (x+i)^3; EllipticCurve; E := EllipticCurve(i, x^3+x+1); Output: Magma V2.10-6 Wed Jan 7 2004 11:22:58 on modular [Seed = 619129121] ------------------------------------- 1024 x^3 + i*x^2 + i^2*x + i^3 Intrinsic 'EllipticCurve' Signatures: ( S) -> CrvEll The elliptic curve defined by the coefficients of S. S must be of length 2 or 5. ( D, N, I, J) -> CrvEll The J-th elliptic curve in the I-th isogeny class of conductor N found in the elliptic curve database D. ( D, S) -> SeqEnum An elliptic curve with label S (e.g. "101A" or "101A1") in the elliptic curve database D. ( D, N, S, J) -> SeqEnum The J-th elliptic curve of conductor N and label S (e.g. "A") in the elliptic curve database D. ( f, h) -> CrvEll Creates the elliptic curve defined by y^2 + h(x)*y = f(x), where h must be of degree at most 1 and f must be monic of degree 3. ( f) -> CrvEll Creates the elliptic curve defined by y^2 = f(x), where f must be monic of degree 3. ( j) -> CrvEll Creates an elliptic curve with j-invariant j. This version is deprecated and will be removed in a future release -- use EllipticCurveFromjInvariant() instead. ( C) -> CrvEll, Map Returns an elliptic curve from certain genus 1 curves with an easily recognised rational point. ( C, Point) -> CrvEll, MapSch Returns a Weierstrass model of a genus 1 curve with a point and also the map from C to that model. The point should be nonsingular. ( C, Place) -> CrvEll, MapSch Returns a Weierstrass model of a genus 1 curve with a degree 1 place and also the map from C to that model. ( f) -> CrvEll An elliptic curve with associated modular form f. ( M) -> SeqEnum [ StartPrec, Database ] An elliptic curve over the rational numbers that lies in the isogeny class of elliptic curves associated to M. >> E := EllipticCurve(i, x^3+x+1); ^ Runtime error in 'EllipticCurve': Bad argument types Argument types given: FldFinElt, RngUPolElt Total time: 2.949 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host lon-igate.mckinsey.com. (213.86.15.25) Time: Wed Jan 7 11:24:09 2004 Input: F2 := FiniteField (2, 10); #F2; F2X := PolynomialRing(F2); (x+i)^3; F2X; EllipticCurve; // E := EllipticCurve(i, x^3+x+1); Output: Magma V2.10-6 Wed Jan 7 2004 11:24:06 on modular [Seed = 922041335] ------------------------------------- 1024 x^3 + i*x^2 + i^2*x + i^3 Univariate Polynomial Ring in x over GF(2^10) Intrinsic 'EllipticCurve' Signatures: ( S) -> CrvEll The elliptic curve defined by the coefficients of S. S must be of length 2 or 5. ( D, N, I, J) -> CrvEll The J-th elliptic curve in the I-th isogeny class of conductor N found in the elliptic curve database D. ( D, S) -> SeqEnum An elliptic curve with label S (e.g. "101A" or "101A1") in the elliptic curve database D. ( D, N, S, J) -> SeqEnum The J-th elliptic curve of conductor N and label S (e.g. "A") in the elliptic curve database D. ( f, h) -> CrvEll Creates the elliptic curve defined by y^2 + h(x)*y = f(x), where h must be of degree at most 1 and f must be monic of degree 3. ( f) -> CrvEll Creates the elliptic curve defined by y^2 = f(x), where f must be monic of degree 3. ( j) -> CrvEll Creates an elliptic curve with j-invariant j. This version is deprecated and will be removed in a future release -- use EllipticCurveFromjInvariant() instead. ( C) -> CrvEll, Map Returns an elliptic curve from certain genus 1 curves with an easily recognised rational point. ( C, Point) -> CrvEll, MapSch Returns a Weierstrass model of a genus 1 curve with a point and also the map from C to that model. The point should be nonsingular. ( C, Place) -> CrvEll, MapSch Returns a Weierstrass model of a genus 1 curve with a degree 1 place and also the map from C to that model. ( f) -> CrvEll An elliptic curve with associated modular form f. ( M) -> SeqEnum [ StartPrec, Database ] An elliptic curve over the rational numbers that lies in the isogeny class of elliptic curves associated to M. Total time: 2.959 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host lon-igate.mckinsey.com. (213.86.15.25) Time: Wed Jan 7 11:25:31 2004 Input: F2 := FiniteField (2, 10); #F2; F2X := PolynomialRing(F2); (x+i)^3; // F2X; // EllipticCurve; E := EllipticCurve(x, x^3+x+1); Output: Magma V2.10-6 Wed Jan 7 2004 11:25:28 on modular [Seed = 96864410] ------------------------------------- 1024 x^3 + i*x^2 + i^2*x + i^3 >> E := EllipticCurve(x, x^3+x+1); ^ Runtime error in 'EllipticCurve': h polynomial must have degree at most 1 Total time: 2.979 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host lon-igate.mckinsey.com. (213.86.15.25) Time: Wed Jan 7 11:26:02 2004 Input: F2 := FiniteField (2, 10); #F2; F2X := PolynomialRing(F2); (x+i)^3; // F2X; // EllipticCurve; Degree (x+1); E := EllipticCurve(x+1, x^3+x+1); Output: Magma V2.10-6 Wed Jan 7 2004 11:25:59 on modular [Seed = 147522680] ------------------------------------- 1024 x^3 + i*x^2 + i^2*x + i^3 1 >> E := EllipticCurve(x+1, x^3+x+1); ^ Runtime error in 'EllipticCurve': h polynomial must have degree at most 1 Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host lon-igate.mckinsey.com. (213.86.15.25) Time: Wed Jan 7 11:26:26 2004 Input: F2 := FiniteField (2, 10); #F2; F2X := PolynomialRing(F2); (x+i)^3; // F2X; // EllipticCurve; Degree (x+1); E := EllipticCurve(x^2+1, x^3+x+1); Output: Magma V2.10-6 Wed Jan 7 2004 11:26:22 on modular [Seed = 467146578] ------------------------------------- 1024 x^3 + i*x^2 + i^2*x + i^3 1 >> E := EllipticCurve(x^2+1, x^3+x+1); ^ Runtime error in 'EllipticCurve': h polynomial must have degree at most 1 Total time: 3.079 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host lon-igate.mckinsey.com. (213.86.15.25) Time: Wed Jan 7 11:26:43 2004 Input: F2 := FiniteField (2, 10); #F2; F2X := PolynomialRing(F2); (x+i)^3; // F2X; EllipticCurve; Degree (x+1); E := EllipticCurve(x^2+1, x^3+x+1); Output: Magma V2.10-6 Wed Jan 7 2004 11:26:40 on modular [Seed = 3995984585] ------------------------------------- 1024 x^3 + i*x^2 + i^2*x + i^3 Intrinsic 'EllipticCurve' Signatures: ( S) -> CrvEll The elliptic curve defined by the coefficients of S. S must be of length 2 or 5. ( D, N, I, J) -> CrvEll The J-th elliptic curve in the I-th isogeny class of conductor N found in the elliptic curve database D. ( D, S) -> SeqEnum An elliptic curve with label S (e.g. "101A" or "101A1") in the elliptic curve database D. ( D, N, S, J) -> SeqEnum The J-th elliptic curve of conductor N and label S (e.g. "A") in the elliptic curve database D. ( f, h) -> CrvEll Creates the elliptic curve defined by y^2 + h(x)*y = f(x), where h must be of degree at most 1 and f must be monic of degree 3. ( f) -> CrvEll Creates the elliptic curve defined by y^2 = f(x), where f must be monic of degree 3. ( j) -> CrvEll Creates an elliptic curve with j-invariant j. This version is deprecated and will be removed in a future release -- use EllipticCurveFromjInvariant() instead. ( C) -> CrvEll, Map Returns an elliptic curve from certain genus 1 curves with an easily recognised rational point. ( C, Point) -> CrvEll, MapSch Returns a Weierstrass model of a genus 1 curve with a point and also the map from C to that model. The point should be nonsingular. ( C, Place) -> CrvEll, MapSch Returns a Weierstrass model of a genus 1 curve with a degree 1 place and also the map from C to that model. ( f) -> CrvEll An elliptic curve with associated modular form f. ( M) -> SeqEnum [ StartPrec, Database ] An elliptic curve over the rational numbers that lies in the isogeny class of elliptic curves associated to M. 1 >> E := EllipticCurve(x^2+1, x^3+x+1); ^ Runtime error in 'EllipticCurve': h polynomial must have degree at most 1 Total time: 2.999 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host lon-igate.mckinsey.com. (213.86.15.25) Time: Wed Jan 7 11:27:24 2004 Input: F2 := FiniteField (2, 10); #F2; F2X := PolynomialRing(F2); (x+i)^3; // F2X; EllipticCurve; Degree (x+1); E := EllipticCurve(x^3+x+1, x+1); Output: Magma V2.10-6 Wed Jan 7 2004 11:27:21 on modular [Seed = 4046650879] ------------------------------------- 1024 x^3 + i*x^2 + i^2*x + i^3 Intrinsic 'EllipticCurve' Signatures: ( S) -> CrvEll The elliptic curve defined by the coefficients of S. S must be of length 2 or 5. ( D, N, I, J) -> CrvEll The J-th elliptic curve in the I-th isogeny class of conductor N found in the elliptic curve database D. ( D, S) -> SeqEnum An elliptic curve with label S (e.g. "101A" or "101A1") in the elliptic curve database D. ( D, N, S, J) -> SeqEnum The J-th elliptic curve of conductor N and label S (e.g. "A") in the elliptic curve database D. ( f, h) -> CrvEll Creates the elliptic curve defined by y^2 + h(x)*y = f(x), where h must be of degree at most 1 and f must be monic of degree 3. ( f) -> CrvEll Creates the elliptic curve defined by y^2 = f(x), where f must be monic of degree 3. ( j) -> CrvEll Creates an elliptic curve with j-invariant j. This version is deprecated and will be removed in a future release -- use EllipticCurveFromjInvariant() instead. ( C) -> CrvEll, Map Returns an elliptic curve from certain genus 1 curves with an easily recognised rational point. ( C, Point) -> CrvEll, MapSch Returns a Weierstrass model of a genus 1 curve with a point and also the map from C to that model. The point should be nonsingular. ( C, Place) -> CrvEll, MapSch Returns a Weierstrass model of a genus 1 curve with a degree 1 place and also the map from C to that model. ( f) -> CrvEll An elliptic curve with associated modular form f. ( M) -> SeqEnum [ StartPrec, Database ] An elliptic curve over the rational numbers that lies in the isogeny class of elliptic curves associated to M. 1 Total time: 2.949 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host lon-igate.mckinsey.com. (213.86.15.25) Time: Wed Jan 7 11:27:57 2004 Input: F2 := FiniteField (2, 10); #F2; F2X := PolynomialRing(F2); (x+i)^3; // F2X; // EllipticCurve; E := EllipticCurve(x^3+x+1, x+1); time #E; Output: Magma V2.10-6 Wed Jan 7 2004 11:27:54 on modular [Seed = 3288844329] ------------------------------------- 1024 x^3 + i*x^2 + i^2*x + i^3 968 Time: 0.030 Total time: 2.989 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host lon-igate.mckinsey.com. (213.86.15.25) Time: Wed Jan 7 11:28:54 2004 Input: F2 := FiniteField (2, 10); #F2; F2X := PolynomialRing(F2); // F2X; // EllipticCurve; E := EllipticCurve(x^3+x+1, x+1); time #E; Isogeny; Output: Magma V2.10-6 Wed Jan 7 2004 11:28:51 on modular [Seed = 3591756402] ------------------------------------- 1024 968 Time: 0.020 Intrinsic 'Isogeny' Signatures: ( E, F, s, h, o) -> Map Returns the isogeny E -> F defined by the polynomials psi, phi, omega, taking (x, y) :-> (phi / psi^2, omega / psi^3). Psi and phi must be univariate (although elements of a multivariate polynomial ring) and the polynomials need not be coprime. ( E, P) -> Map Returns the isogeny E -> F corresponding to the point P on the modular curve X_0(N). Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host lon-igate.mckinsey.com. (213.86.15.25) Time: Wed Jan 7 11:30:15 2004 Input: F2 := FiniteField (2, 10); #F2; F2X := PolynomialRing(F2); // F2X; // EllipticCurve; E := EllipticCurve(x^3+x+1, x+1); time #E; // Isogeny; P := Random (E); P; Order(P); Output: Magma V2.10-6 Wed Jan 7 2004 11:30:12 on modular [Seed = 2724309457] ------------------------------------- 1024 968 Time: 0.020 (i^648 : i^1012 : 1) 11 Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host lon-igate.mckinsey.com. (213.86.15.25) Time: Wed Jan 7 11:30:40 2004 Input: F2 := FiniteField (2, 10); #F2; F2X := PolynomialRing(F2); // F2X; // EllipticCurve; E := EllipticCurve(x^3+x+1, x+1); time #E; Isogeny; P := Random (E); P; Order(P); Isogeny (E, P); Output: Magma V2.10-6 Wed Jan 7 2004 11:30:37 on modular [Seed = 3044458239] ------------------------------------- 1024 968 Time: 0.020 Intrinsic 'Isogeny' Signatures: ( E, F, s, h, o) -> Map Returns the isogeny E -> F defined by the polynomials psi, phi, omega, taking (x, y) :-> (phi / psi^2, omega / psi^3). Psi and phi must be univariate (although elements of a multivariate polynomial ring) and the polynomials need not be coprime. ( E, P) -> Map Returns the isogeny E -> F corresponding to the point P on the modular curve X_0(N). (i^185 : i^1003 : 1) 88 Isogeny( E: E, P: (i^185 : i^1003 : 1) ) In file "/usr/local/magma/package/Geometry/CrvMod/modular_isogenies.m", line 84, column 28: >> model_type := ModelType(X0); ^ Runtime error in 'ModelType': Bad argument types Argument types given: CrvEll Total time: 2.989 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host lon-igate.mckinsey.com. (213.86.15.25) Time: Wed Jan 7 11:31:28 2004 Input: F2 := FiniteField (2, 10); #F2; F2X := PolynomialRing(F2); // F2X; // EllipticCurve; E := EllipticCurve(x^3+x+1, x+1); time #E; // Isogeny; P := Random (E); P; Order(P); Output: Magma V2.10-6 Wed Jan 7 2004 11:31:25 on modular [Seed = 3095114626] ------------------------------------- 1024 968 Time: 0.020 (i^991 : i^969 : 1) 88 Total time: 2.989 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host user-vc8frgq.biz.mindspring.com. (216.135.238.26) Time: Wed Jan 7 18:30:19 2004 Input: P(n)=n(3n-1) P(P(n)) Output: Magma V2.10-6 Wed Jan 7 2004 18:30:16 on modular [Seed = 2471508602] ------------------------------------- >> P(n)=n(3n-1) ^ User error: bad syntax >> P(P(n)); ^ User error: Identifier 'n' has not been declared or assigned Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host user-vc8frgq.biz.mindspring.com. (216.135.238.26) Time: Wed Jan 7 18:30:36 2004 Input: P(n)=n*(3*n-1) P(P(n)) Output: Magma V2.10-6 Wed Jan 7 2004 18:30:33 on modular [Seed = 2589537122] ------------------------------------- >> P(P(n)); ^ User error: bad syntax Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host user-vc8frgq.biz.mindspring.com. (216.135.238.26) Time: Wed Jan 7 18:31:22 2004 Input: (n*(3*n-1))*(3*(n*(3*n-1))-1) Output: Magma V2.10-6 Wed Jan 7 2004 18:31:19 on modular [Seed = 1688718787] ------------------------------------- >> (n*(3*n-1))*(3*(n*(3*n-1))-1) ^ User error: Identifier 'n' has not been declared or assigned Total time: 2.939 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host user-vc8frgq.biz.mindspring.com. (216.135.238.26) Time: Wed Jan 7 18:31:55 2004 Input: P=n*(3*n-1) Output: Magma V2.10-6 Wed Jan 7 2004 18:31:52 on modular [Seed = 1840170213] ------------------------------------- >> P=n*(3*n-1); ^ User error: Identifier 'n' has not been declared or assigned Total time: 2.909 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host user-vc8frgq.biz.mindspring.com. (216.135.238.26) Time: Wed Jan 7 18:33:38 2004 Input: n=integer P=n*(3*n-1) Output: Magma V2.10-6 Wed Jan 7 2004 18:33:35 on modular [Seed = 1991630425] ------------------------------------- >> P=n*(3*n-1); ^ User error: bad syntax Total time: 2.929 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (156.143.48.248) Time: Wed Jan 7 19:31:45 2004 Input: ploth(n=1, 1000, pi(n)) Output: Magma V2.10-6 Wed Jan 7 2004 19:31:42 on modular [Seed = 399805606] ------------------------------------- >> ploth(n=1, 1000, pi(n)); ^ User error: Identifier 'n' has not been declared or assigned Total time: 2.919 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host durian.math.sci.kobe-u.ac.jp. (133.30.64.173) Time: Wed Jan 7 20:38:25 2004 Input: Q := RationalField(); > P := PolynomialRing(Q, 6);I := ideal

x*y + y*z + z*t + t*u + u*v + v*x, > x*y*z + y*z*t + z*t*u + t*u*v + u*v*x + v*x*y, > x*y*z*t + y*z*t*u + z*t*u*v + t*u*v*x + u*v*x*y + v*x*y*z, > x*y*z*t*u + y*z*t*u*v + z*t*u*v*x + t*u*v*x*y + u*v*x*y*z + v*x*y*z*t, > x*y*z*t*u*v - 1>; > time B := GroebnerBasis(I); Output: Magma V2.10-6 Wed Jan 7 2004 20:38:13 on modular [Seed = 3675803651] ------------------------------------- Time: 1.010 Total time: 3.979 seconds, Total memory usage: 2.84MB ************** MAGMA ***************** Host durian.math.sci.kobe-u.ac.jp. (133.30.64.173) Time: Wed Jan 7 20:39:08 2004 Input: B; Output: Magma V2.10-6 Wed Jan 7 2004 20:39:05 on modular [Seed = 3507640886] ------------------------------------- >> B;; ^ User error: Identifier 'B' has not been declared or assigned Total time: 2.929 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host durian.math.sci.kobe-u.ac.jp. (133.30.64.173) Time: Wed Jan 7 20:40:03 2004 Input: Q := RationalField(); > P := PolynomialRing(Q, 6); > I := ideal

x + y + z + t + u + v, > x*y + y*z + z*t + t*u + u*v + v*x, > x*y*z + y*z*t + z*t*u + t*u*v + u*v*x + v*x*y, > x*y*z*t + y*z*t*u + z*t*u*v + t*u*v*x + u*v*x*y + v*x*y*z, > x*y*z*t*u + y*z*t*u*v + z*t*u*v*x + t*u*v*x*y + u*v*x*y*z + v*x*y*z*t, > x*y*z*t*u*v - 1>; B:=GroebnerBasis(I); Output: Magma V2.10-6 Wed Jan 7 2004 20:39:59 on modular [Seed = 3221441393] ------------------------------------- Total time: 3.519 seconds, Total memory usage: 3.41MB ************** MAGMA ***************** Host banjo.cs.iitm.ernet.in. (202.141.24.2) Time: Thu Jan 8 03:09:30 2004 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: Magma V2.10-6 Thu Jan 8 2004 03:09:27 on modular [Seed = 3423527842] ------------------------------------- Replace this by some code, then click [PARI] or [MAGMA]! Total time: 2.919 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (80.90.160.162) Time: Thu Jan 8 04:52:46 2004 Input: /* * An implementation of the Number Field Sieve as described in * "Factoring Integers with the Number Field Sieve" by J.P. Buhler, * H.W. Lenstra, and Carl Pomerance. (Algorithm 11.1) * * This code is not at all optimized - it is demonstration of the * Magma computer algebra package, and to for people who want to * learn the Number Field Sieve algorithm or how to code it. Note * that the algebraic square root code is available only for the * most recent release of Magma. * * This code is best demonstrated for numbers around 20-digits. * Larger numbers will cause the program to take up too much memory, * and numbers that are too small do not work well with this algorithm. * * "print" statements that can be ommitted are left justified. * * by Contini - Fri March 3rd, 2000. */ function SelectPolynomial(n); /* select a degree according to the asymptotic formula */ d := Round( Root( 3 * Log(n)/Log(Log(n)) , 3 ) ); print "degree ", d; m := Iroot( n, d ); print "m := ", m, ";"; coeffs := []; for i := d to 0 by -1 do temp2 := m^i; coeff := n div temp2; /* Append (~coeffs, coeff); */ coeffs[i+1] := coeff; n -:= coeff*temp2; end for; P := PolynomialRing( IntegerRing() ); f := P!coeffs; return f, m, d; end function; procedure RationalSieve( ~sieve_array, y, FB, log_primes, ~prev_roots, m_mod_p, sieve_len); /* * RATIONAL SIEVE */ sieve_array := [0 : i in [1..sieve_len]]; for i in [1..#FB] do p := FB[i]; logp := log_primes[i]; /* * Compute loc - the first location in the sieve array * where p divides the corresponding residue */ loc := prev_roots[i] - m_mod_p[i]; if loc lt 0 then loc +:= p; end if; prev_roots[i] := loc; /* sieve begins at location 1, so skip location 0 */ if loc eq 0 then loc := p; end if; /* MAIN SIEVE LOOP */ while loc le sieve_len do sieve_array[loc] +:= logp; loc +:= p; end while; end for; end procedure; procedure AlgebraicSieve( ~nf_sieve_array, y, ~nf_prev_roots, log_primes, R_p_set, sieve_len ); /* * NUMBER FIELD SIEVE */ nf_sieve_array := [0 : i in [1..sieve_len]]; for i in [1..#R_p_set] do R_p := R_p_set[i]; p := R_p[1]; r := R_p[2]; logp := R_p[3]; loc := nf_prev_roots[i] - r; if loc lt 0 then loc +:= p; end if; nf_prev_roots[i] := loc; if loc eq 0 then loc := p; end if; /* MAIN SIEVE LOOP */ while loc le sieve_len do nf_sieve_array[loc] +:= logp; loc +:= p; end while; end for; end procedure; procedure ScanSieveArray( J, b, bm, y, d, sieve_array, nf_sieve_array, error_term, ~num_rels, sieve_len, ~M, FB, prev_roots, nf_prev_roots, R_p_set, enough_rels, ~smooth_alg_elts, char_cols, char_offset ); /* scan sieve array */ threshold := Round( Log( bm ) ) - error_term; zero := [0: i in [1..d]]; x := zero; x[1] := 1; x[2] := b; nf_threshold := Round( Log( Abs( Norm( J!x ) ) ) ) - error_term; for a in [1..sieve_len] do if sieve_array[a] ge threshold then /* rational side appears to be smooth */ if nf_sieve_array[a] ge nf_threshold then /* number field side appears to be smooth */ if Gcd(b, a) ne 1 then /* relation is redundant */ continue; end if; /* see if it really is smooth */ relation := []; rational_side := a + bm; for i in [1..#FB] do p := FB[i]; if a mod p eq prev_roots[i] then e := 0; quot, rem := Quotrem( rational_side, p ); repeat rational_side := quot; e +:= 1; quot, rem := Quotrem( rational_side, p ); until rem ne 0; Append( ~relation, [i, e] ); end if; end for; if Abs(rational_side) ne 1 then /* rational side is not smooth :-( */ continue; end if; /* try algebraic side */ x := zero; x[1] := a; x[2] := b; alg_elt := J!x; norm := IntegerRing()!Norm(alg_elt); for i in [1..#R_p_set] do R_p := R_p_set[i]; p := R_p[1]; if a mod p eq nf_prev_roots[i] then e := 0; quot, rem := Quotrem( norm, p ); repeat norm := quot; e +:= 1; quot, rem := Quotrem( norm, p ); until rem ne 0; Append( ~relation, [i+#FB, e] ); end if; end for; if Abs(norm) ne 1 then /* algebraic side is not smooth :-( */ continue; end if; /* The relation is a keeper! */ print "a := ", a, "; b:= ", b,";"; num_rels +:= 1; /* Compute the character columns corresponding to alg_elt */ for i in [1..#char_cols] do p := char_cols[i][1]; r := char_cols[i][2]; if LegendreSymbol( (a + b*r) mod p, p ) eq -1 then M[num_rels, i + char_offset] := 1; end if; end for; /* store the algebraic element */ Append( ~smooth_alg_elts, alg_elt ); /* store relation in matrix */ for j in [1..#relation] do M[num_rels, relation[j, 1]] := relation[j, 2]; end for; if num_rels eq enough_rels then break; end if; /* update the nf_threshold - since the norms grow somewhat quickly, we waste a lot of time on false reports if this update is not made */ x := zero; x[1] := a; x[2] := b; nf_threshold := Round( Log( Abs( Norm( J!x ) ) ) ); nf_threshold -:= error_term; end if; end if; end for; end procedure; function NFS( n ) f, m, d := SelectPolynomial(n); fprime := Derivative( f ); J := NumberField( f ); /* choose y - the bound for smoothness */ dlogd := d*Log(d); temp := 1.0/d * Log( n ); e := dlogd + Sqrt( dlogd^2 + 4*temp*Log(temp) ); y := Round( Exp( 0.5*e ) ); print "smoothness bound is ", y; /* prepare data for rational sieve */ FB := [p : p in [2..y] | IsPrime( p ) ]; log_primes := [Round(Log(p)) : p in FB]; prev_roots := [0: p in FB]; m_mod_p := [m mod p: p in FB]; /* prepare data for the algebraic sieve */ cols := #FB; R_p_set := []; nf_prev_roots := []; for p in FB do K := GF(p); roots_mod_p := Roots( f, K ); for i in [1..#roots_mod_p] do r := IntegerRing()!roots_mod_p[i][1]; /* also include the rounded logarithm of p in the storage */ Append( ~R_p_set, [p, r, Round(Log(p))] ); Append( ~nf_prev_roots, 0 ); cols +:= 1; end for; end for; smooth_alg_elts := []; /* create the character columns */ char_offset := cols; num_char_cols := 3 * Ilog2( n ); char_cols := []; p := NextPrime( y ); i := 0; repeat K := GF(p); roots_mod_p := Roots( f, K ); for j in [1..#roots_mod_p] do r := IntegerRing()!roots_mod_p[j][1]; Append( ~char_cols, [p, r] ); i +:= 1; if i eq num_char_cols then break; end if; end for; p := NextPrime( p ); until i eq num_char_cols; cols +:= num_char_cols; enough_rels := cols+50; print "will quit after", enough_rels," relations"; /* allow for an error in the sieve threshold */ error_term := 3; /* set up matrix */ M := RMatrixSpace (IntegerRing(), enough_rels, cols)!0; num_rels := 0; b := 1; /* bm = b*m */ bm := m; sieve_len := y * 25; while true do RationalSieve( ~sieve_array, y, FB, log_primes, ~prev_roots, m_mod_p, sieve_len ); AlgebraicSieve( ~nf_sieve_array, y, ~nf_prev_roots, log_primes, R_p_set, sieve_len ); ScanSieveArray( J, b, bm, y, d, sieve_array, nf_sieve_array, error_term, ~num_rels, sieve_len, ~M, FB, prev_roots, nf_prev_roots, R_p_set, enough_rels, ~smooth_alg_elts, char_cols, char_offset ); bm +:= m; b +:= 1; print "Number of relations: ", num_rels; if num_rels ge enough_rels then break; end if; end while; print "matrix size: ",num_rels," by ", cols; print "finding null space"; gf2 := GF(2); Mprime := RMatrixSpace (gf2, num_rels, cols)!M; time null_space := NullSpace( Mprime ); /* "free" Mprime */ Mprime := 0; for j in [1..Dimension(null_space)] do print "trying null space vector #",j; /* get the first element of the solution vector */ soln := ChangeUniverse (Eltseq (null_space.j), IntegerRing()); /* compute the exponents of a relation that involves an algebraic square and an integer square */ exps := RSpace(IntegerRing(), cols)!0; for i in [1..num_rels] do if soln[i] eq 1 then exps +:= M[i]; end if; end for; /* compute the square root x of the integer element of the relation */ x := 1; for i in [1..#FB] do e := exps[i]; if e gt 0 then x := (x * ( FB[i]^(e div 2) ) ) mod n; end if; end for; x := ( x * Evaluate( fprime, m ) ) mod n; print x,"^2 mod n = ", x^2 mod n; list := []; for i in [1..num_rels] do if soln[i] eq 1 then Append( ~list, smooth_alg_elts[i] ); end if; end for; Append( ~list, Evaluate( fprime, alpha )^2 ); /* Compute the square root beta of the algebraic element */ ok, l := Root(2, list, []); if ok eq false then print "Element is not a square... continuing!"; continue; end if; /* map the sqrt to an integer v modulo n */ v := 1; for i in [1..#l] do list := l[i]; prod_list := 1; for j in [1..#list] do seq := Eltseq( list[j] ); elt := 0; for k in [0..d-1] do num := Numerator( seq[k+1] ) mod n; den := Denominator( seq[k+1] ) mod n; elt +:= ( ( num * Modinv( den, n ) mod n) * Modexp( m, k, n ) ) mod n; end for; prod_list := (prod_list * elt) mod n; end for; v := v * Modexp( Modinv( prod_list, n ), 2^(i-1), n ) mod n; end for; print v,"^2 mod n = ", v^2 mod n; gcd := Gcd(x-v, n); print "Gcd of ",x-v," and ",v," is ", gcd; if gcd ne 1 and gcd ne n then print "FACTOR: ", gcd; return gcd; end if; end for; print "no factor found :-( "; return 0; end function; Output: WARNING: MAGMA command contains unsafe command 'memory', so it will not be executed. ************** MAGMA ***************** Host pD9530B26.dip.t-dialin.net. (217.83.11.38) Time: Thu Jan 8 17:24:37 2004 Input: p := NextPrime(10^9); p; K := GF(p); E := EllipticCurve([K | -1, 1]); time SEA(E : MaxSmooth := 1); Output: Magma V2.10-6 Thu Jan 8 2004 17:24:34 on modular [Seed = 3575067192] ------------------------------------- 1000000007 0 Time: 0.090 Total time: 3.059 seconds, Total memory usage: 2.75MB ************** MAGMA ***************** Host pD9530B26.dip.t-dialin.net. (217.83.11.38) Time: Thu Jan 8 17:27:40 2004 Input: p := 31648573662208007208411279340972174081655191771220726603117102285639562723584318781472781870749438532939445789762497; p; Output: Magma V2.10-6 Thu Jan 8 2004 17:27:37 on modular [Seed = 3895070462] ------------------------------------- 3164857366220800720841127934097217408165519177122072660311710228563956272358431\ 8781472781870749438532939445789762497 Total time: 3.089 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pD9530B26.dip.t-dialin.net. (217.83.11.38) Time: Thu Jan 8 17:29:04 2004 Input: p := 31648573662208007208411279340972174081655191771220726603117102285639562723584318781472781870749438532939445789762497; K := GF(p); E := EllipticCurve([K | 1, 0]); SEA(E : MaxSmooth := 1); Output: Magma V2.10-6 Thu Jan 8 2004 17:29:00 on modular [Seed = 4282194204] ------------------------------------- 3164857366220800720841127934097217408165519177122072660310671542798638878133954\ 6528939270299746635961126958582050640 Total time: 3.599 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pD9530B26.dip.t-dialin.net. (217.83.11.38) Time: Thu Jan 8 17:32:39 2004 Input: p := 31648573662208007208411279340972174081655191771220726603117102285639562723584318781472781870749438532939445789762497; K := GF(p); E := EllipticCurve([K | 1, 0]); SEA(E : MaxSmooth := 1); Factorization($1); Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Thu Jan 8 2004 17:32:16 on modular [Seed = 2387372977] ------------------------------------- 3164857366220800720841127934097217408165519177122072660310671542798638878133954\ 6528939270299746635961126958582050640 Errors: /home/mfd/gomagma: line 2: 28865 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host pD9530B26.dip.t-dialin.net. (217.83.11.38) Time: Thu Jan 8 17:33:38 2004 Input: p := 279731234232179; K := GF(p); E := EllipticCurve([K | 1, 0]); SEA(E : MaxSmooth := 1); Output: Magma V2.10-6 Thu Jan 8 2004 17:33:35 on modular [Seed = 2236047477] ------------------------------------- 279731234232180 Total time: 3.019 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pD9530B26.dip.t-dialin.net. (217.83.11.38) Time: Thu Jan 8 17:35:06 2004 Input: p := 279731234232179; K := GF(p); E := EllipticCurve([K | 1, 0]); SEA(E : MaxSmooth := 1); Factorization($1); Output: Magma V2.10-6 Thu Jan 8 2004 17:35:02 on modular [Seed = 2538959823] ------------------------------------- 279731234232180 [ <2, 2>, <3, 2>, <5, 1>, <823, 1>, <1123, 1>, <1681469, 1> ] Total time: 3.009 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pD9530B26.dip.t-dialin.net. (217.83.11.38) Time: Thu Jan 8 17:35:50 2004 Input: p := 1009; K := GF(p); E := EllipticCurve([K | 71, 602]); SEA(E : MaxSmooth := 1); Factorization($1); Output: Magma V2.10-6 Thu Jan 8 2004 17:35:46 on modular [Seed = 2926332579] ------------------------------------- 1060 [ <2, 2>, <5, 1>, <53, 1> ] Total time: 2.999 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pD9530B26.dip.t-dialin.net. (217.83.11.38) Time: Thu Jan 8 17:36:30 2004 Input: p := 279731234232179; K := GF(p); E := EllipticCurve([K | 1, 2]); SEA(E : MaxSmooth := 1); Factorization($1); Output: Magma V2.10-6 Thu Jan 8 2004 17:36:26 on modular [Seed = 2775007616] ------------------------------------- 0 >> Factorization($1); ^ Runtime error in 'Factorization': Argument 1 is not non-zero Total time: 3.169 seconds, Total memory usage: 2.75MB ************** MAGMA ***************** Host pD9530B26.dip.t-dialin.net. (217.83.11.38) Time: Thu Jan 8 17:36:57 2004 Input: p := 279731234232179; K := GF(p); E := EllipticCurve([K | 1, 2]); SEA(E : MaxSmooth := 1); Output: Magma V2.10-6 Thu Jan 8 2004 17:36:54 on modular [Seed = 3162396789] ------------------------------------- 0 Total time: 2.989 seconds, Total memory usage: 2.75MB ************** MAGMA ***************** Host pD9530B26.dip.t-dialin.net. (217.83.11.38) Time: Thu Jan 8 17:37:28 2004 Input: p := 2797312367; K := GF(p); E := EllipticCurve([K | 1, 2]); SEA(E : MaxSmooth := 1); Output: Magma V2.10-6 Thu Jan 8 2004 17:37:25 on modular [Seed = 3010549593] ------------------------------------- 0 Total time: 3.039 seconds, Total memory usage: 2.75MB ************** MAGMA ***************** Host pD9530B26.dip.t-dialin.net. (217.83.11.38) Time: Thu Jan 8 17:54:04 2004 Input: p := 22771656396649042914677651938348976006738044330885828909690000917475479649330897416453073715484777125675617411561753; K := GF(p); E := EllipticCurve([K | 1, 0]); SEA(E : MaxSmooth := 1); Output: Magma V2.10-6 Thu Jan 8 2004 17:54:00 on modular [Seed = 1351790742] ------------------------------------- 2277165639664904291467765193834897600673804433088582890968087619490985411965451\ 9076304824198934082753513693882127520 Total time: 3.589 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pD9530B26.dip.t-dialin.net. (217.83.11.38) Time: Thu Jan 8 17:59:28 2004 Input: p := 34434335923751399698518505516722285557281631663360135021571830978812886664047949565106992641249608613800031755822209; K := GF(p); E := EllipticCurve([K | 1, 0]); SEA(E : MaxSmooth := 1); Output: Magma V2.10-6 Thu Jan 8 2004 17:59:25 on modular [Seed = 1654701537] ------------------------------------- 3443433592375139969851850551672228555728163166336013502156054198056930829719069\ 4068389128882706321764053054021911760 Total time: 3.619 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pD9530B26.dip.t-dialin.net. (217.83.11.38) Time: Thu Jan 8 18:09:16 2004 Input: p := 21690482571471944131858536333908058782272452491831771308020961342630740764170913541267450561542337158596383516743897; K := GF(p); E := EllipticCurve([K | 1, 0]); SEA(E : MaxSmooth := 1); Output: Magma V2.10-6 Thu Jan 8 2004 18:09:13 on modular [Seed = 450414157] ------------------------------------- 2169048257147194413185853633390805878227245249183177130801288304892016253318338\ 1513845564003262104587338680209387280 Total time: 3.499 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pD9530B26.dip.t-dialin.net. (217.83.11.38) Time: Thu Jan 8 18:14:46 2004 Input: p := 27935674986520266205325579045503384555589668080548467527362175072470197761098090571694173551976792685114398933033353; K := GF(p); E := EllipticCurve([K | 1, 0]); SEA(E : MaxSmooth := 1); Output: Magma V2.10-6 Thu Jan 8 2004 18:14:43 on modular [Seed = 955966229] ------------------------------------- 2793567498652026620532557904550338455558966808054846752735212790270242752181874\ 3878157138687189351173894399046846240 Total time: 3.569 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pD9530E68.dip.t-dialin.net. (217.83.14.104) Time: Fri Jan 9 10:38:33 2004 Input: p := 2797312367; K := GF(p); E := EllipticCurve([K | 1, 2]); SEA(E : MaxSmooth := 1); Output: Magma V2.10-6 Fri Jan 9 2004 10:38:29 on modular [Seed = 96792757] ------------------------------------- 0 Total time: 3.209 seconds, Total memory usage: 2.75MB ************** MAGMA ***************** Host dirichlet.math.umass.edu. (128.119.47.126) Time: Fri Jan 9 14:19:20 2004 Input: IntegralQuarticPoints([6,24,34,24,9]) : [ RngIntElt ] -> [ SeqEnum ] Output: Magma V2.10-6 Fri Jan 9 2004 14:19:17 on modular [Seed = 1082229174] ------------------------------------- >> IntegralQuarticPoints([6,24,34,24,9]) : [ RngIntElt ] -> [ SeqEnum ]; ^ User error: bad syntax Total time: 3.189 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host dirichlet.math.umass.edu. (128.119.47.126) Time: Fri Jan 9 14:20:14 2004 Input: IntegralQuarticPoints([6,24,34,24,9]); Output: Magma V2.10-6 Fri Jan 9 2004 14:20:10 on modular [Seed = 1671602890] ------------------------------------- IntegralQuarticPoints( Q: Full Matrix Algebra of degree 2 over Integer Ring ) In file "/usr/local/magma/package/Geometry/CrvEll/sintpoints.m", line 2003, column 20: >> M:= Ceiling(M^(1/2)); ^ Runtime error in 'Ceiling': Argument 1 should be real Total time: 3.959 seconds, Total memory usage: 2.33MB ************** MAGMA ***************** Host dirichlet.math.umass.edu. (128.119.47.126) Time: Fri Jan 9 14:21:25 2004 Input: IntegralQuarticPoints([1, 0, -8, 8, 1]); Output: Magma V2.10-6 Fri Jan 9 2004 14:21:16 on modular [Seed = 1873719040] ------------------------------------- [ [ 2, -1 ], [ -6, -31 ], [ 0, 1 ] ] Total time: 9.069 seconds, Total memory usage: 2.33MB ************** MAGMA ***************** Host dirichlet.math.umass.edu. (128.119.47.126) Time: Fri Jan 9 14:22:22 2004 Input: IntegralQuarticPoints([27, 0, -180, 0, 324]); Output: Magma V2.10-6 Fri Jan 9 2004 14:22:18 on modular [Seed = 1991751263] ------------------------------------- [ [ 0, 18 ], [ 2, 6 ], [ -2, 6 ], [ 4, -66 ], [ -4, -66 ] ] Total time: 3.569 seconds, Total memory usage: 2.23MB ************** MAGMA ***************** Host dirichlet.math.umass.edu. (128.119.47.126) Time: Fri Jan 9 14:23:57 2004 Input: IntegralQuarticPoints([6, 24, 34, 24, 9]); Output: Magma V2.10-6 Fri Jan 9 2004 14:23:53 on modular [Seed = 130467725] ------------------------------------- IntegralQuarticPoints( Q: Full Matrix Algebra of degree 2 over Integer Ring ) In file "/usr/local/magma/package/Geometry/CrvEll/sintpoints.m", line 2003, column 20: >> M:= Ceiling(M^(1/2)); ^ Runtime error in 'Ceiling': Argument 1 should be real Total time: 3.919 seconds, Total memory usage: 2.33MB ************** MAGMA ***************** Host dirichlet.math.umass.edu. (128.119.47.126) Time: Fri Jan 9 14:25:27 2004 Input: IntegralQuarticPoints([6, 0, -2, 4, 1]); Output: Magma V2.10-6 Fri Jan 9 2004 14:25:23 on modular [Seed = 298921585] ------------------------------------- IntegralQuarticPoints( Q: Full Matrix Algebra of degree 2 over Integer Ring ) In file "/usr/local/magma/package/Geometry/CrvEll/sintpoints.m", line 2003, column 20: >> M:= Ceiling(M^(1/2)); ^ Runtime error in 'Ceiling': Argument 1 should be real Total time: 3.939 seconds, Total memory usage: 2.33MB ************** MAGMA ***************** Host dirichlet.math.umass.edu. (128.119.47.126) Time: Fri Jan 9 14:28:03 2004 Input: IntegralQuarticPoints([1,0,-12,144,216]); Output: Magma V2.10-6 Fri Jan 9 2004 14:28:00 on modular [Seed = 669456548] ------------------------------------- [] Total time: 3.329 seconds, Total memory usage: 2.33MB ************** MAGMA ***************** Host 24-205-67-29.pas-mres.charterpipeline.net. (24.205.67.29) Time: Fri Jan 9 16:17:40 2004 Input: ? Output: Magma V2.10-6 Fri Jan 9 2004 16:17:37 on modular [Seed = 2673851052] ------------------------------------- =============================================================================== PATH: / KIND: Overview =============================================================================== You are reading about the Magma online help system. This system gives you information about Magma while you are at the computer. To see this help page at any time, all you have to do is to type ? ---------- The online help system comes in two modes: the single request mode and the Magma Help Browser. To enter the Browser, type ?? The Browser is useful if you intend to read several related help nodes, because you can exploit the tree structure of the online help. Once you are in the Browser, you can type help again to find out how to use the Browser, and for a more detailed explanation of the whole online help system. ---------- Single help requests begin with the ? character. Examples are: ?print ?magma ?ring ?example If your help request is ambiguous, Magma will return a numbered list of matches. To see the contents of one of them, type ? followed by its number. Some help pages suggest other pages that you might like to look at as well. They are prefixed by a code such as +3 or +5 . To read one of them, type ? followed by the code. You can also supply the full pathname of a help node, if you know it. For example: ?/system/quit ?/magma/module/homomorphism ---------- The online help system offers tab completion. If you type a few letters of your help request and then press the tab key, Magma will "complete" the request if there is a unique completion. Otherwise, it will complete the request as far as possible, and then emit a beep. Press the tab key again to see all the possibilities. ALWAYS PRESS TAB BEFORE THE END OF THE LINE, SO AS TO SEE EVERY RELEVANT HELP PAGE. (On a few operating systems, the tab completion feature cannot be made available.) ---------- The content of the online help system comes from two sources: the "Handbook of Magma Functions" (Bosma and Cannon) and specially-written overview nodes. You may also wish to consult the books "An Introduction to Algebraic Programming in Magma" (Cannon and Playoust) and "Solving Problems with Magma" (Bosma, Cannon, Playoust and Steel). ---------- The online help system is also available in an HTML form suitable for Internet browsers. To use this, move to a shell prompt (outside Magma) and type magmahelp ---------- To leave Magma, type quit; or -D. =============================================================================== Total time: 2.929 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host dirichlet.math.umass.edu. (128.119.47.126) Time: Fri Jan 9 16:19:51 2004 Input: S6:=SymGrp(6); Output: Magma V2.10-6 Fri Jan 9 2004 16:19:48 on modular [Seed = 2825424158] ------------------------------------- >> S6:=SymGrp(6);; ^ User error: Identifier 'SymGrp' has not been declared or assigned Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host dirichlet.math.umass.edu. (128.119.47.126) Time: Fri Jan 9 16:20:19 2004 Input: S6:=SymmetricGroup(6); Output: Magma V2.10-6 Fri Jan 9 2004 16:20:16 on modular [Seed = 3111755243] ------------------------------------- Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host dirichlet.math.umass.edu. (128.119.47.126) Time: Fri Jan 9 16:20:58 2004 Input: S6:=SymmetricGroup(6);MaximalSubgroups(S6); Output: Magma V2.10-6 Fri Jan 9 2004 16:20:54 on modular [Seed = 1166369074] ------------------------------------- Conjugacy classes of subgroups ------------------------------ [1] Order 48 Length 15 Permutation group acting on a set of cardinality 6 Order = 48 = 2^4 * 3 (3, 6)(4, 5) (1, 6, 3)(2, 5, 4) (5, 6) (3, 4) (1, 2) [2] Order 48 Length 15 Permutation group acting on a set of cardinality 6 Order = 48 = 2^4 * 3 (2, 3) (2, 3, 4) (1, 2)(3, 4) (1, 4)(2, 3) (5, 6) [3] Order 72 Length 10 Permutation group acting on a set of cardinality 6 Order = 72 = 2^3 * 3^2 (1, 4) (1, 5)(2, 4)(3, 6) (1, 4)(2, 6) (1, 4, 3) (2, 5, 6) [4] Order 120 Length 6 Permutation group acting on a set of cardinality 6 Order = 120 = 2^3 * 3 * 5 (5, 6) (2, 6)(3, 4, 5) [5] Order 120 Length 6 Permutation group acting on a set of cardinality 6 Order = 120 = 2^3 * 3 * 5 (1, 2)(3, 4)(5, 6) (1, 3, 2, 4, 6, 5) [6] Order 360 Length 1 Permutation group acting on a set of cardinality 6 Order = 360 = 2^3 * 3^2 * 5 (3, 4)(5, 6) (1, 5)(2, 6, 3, 4) Total time: 2.969 seconds, Total memory usage: 1.94MB ************** MAGMA ***************** Host dirichlet.math.umass.edu. (128.119.47.126) Time: Fri Jan 9 16:21:56 2004 Input: S6:=SymmetricGroup(6);M6:=MaximalSubgroups(S6);m6[1] Output: Magma V2.10-6 Fri Jan 9 2004 16:21:53 on modular [Seed = 1284270204] ------------------------------------- >> S6:=SymmetricGroup(6);M6:=MaximalSubgroups(S6);m6[1] ^ User error: Identifier 'm6' has not been declared or assigned Total time: 3.009 seconds, Total memory usage: 1.94MB ************** MAGMA ***************** Host dirichlet.math.umass.edu. (128.119.47.126) Time: Fri Jan 9 16:22:16 2004 Input: S6:=SymmetricGroup(6);M6:=MaximalSubgroups(S6);M6[1] Output: Magma V2.10-6 Fri Jan 9 2004 16:22:13 on modular [Seed = 1469543315] ------------------------------------- rec | order := 48, length := 15, subgroup := Permutation group acting on a set of cardinality 6 Order = 48 = 2^4 * 3 (1, 2)(3, 6) (3, 6, 4) (1, 2)(3, 5)(4, 6) (1, 2)(3, 4)(5, 6) (1, 2)(3, 6)(4, 5) > Total time: 2.939 seconds, Total memory usage: 1.94MB ************** MAGMA ***************** Host dirichlet.math.umass.edu. (128.119.47.126) Time: Fri Jan 9 16:23:29 2004 Input: S6:=SymmetricGroup(6);M6:=MaximalSubgroups(S6);M61:=M6[1];ConjugacyClasses(M61); Output: Magma V2.10-6 Fri Jan 9 2004 16:23:26 on modular [Seed = 1587444433] ------------------------------------- >> S6:=SymmetricGroup(6);M6:=MaximalSubgroups(S6);M61:=M6[1];ConjugacyClasses( ^ Runtime error in 'ConjugacyClasses': Bad argument types Argument types given: Rec Total time: 2.979 seconds, Total memory usage: 1.94MB ************** MAGMA ***************** Host dirichlet.math.umass.edu. (128.119.47.126) Time: Fri Jan 9 16:23:37 2004 Input: S6:=SymmetricGroup(6);M6:=MaximalSubgroups(S6);M61:=M6[1];ConjugacyClasses(M61); Output: Magma V2.10-6 Fri Jan 9 2004 16:23:34 on modular [Seed = 1772703230] ------------------------------------- >> S6:=SymmetricGroup(6);M6:=MaximalSubgroups(S6);M61:=M6[1];ConjugacyClasses( ^ Runtime error in 'ConjugacyClasses': Bad argument types Argument types given: Rec Total time: 3.019 seconds, Total memory usage: 1.94MB ************** MAGMA ***************** Host dirichlet.math.umass.edu. (128.119.47.126) Time: Fri Jan 9 16:24:00 2004 Input: S6:=SymmetricGroup(6);M6:=MaximalSubgroups(S6);M61:=M6[1]; ConjugacyClasses(M61); Output: Magma V2.10-6 Fri Jan 9 2004 16:23:57 on modular [Seed = 1890604252] ------------------------------------- >> ConjugacyClasses(M61);; ^ Runtime error in 'ConjugacyClasses': Bad argument types Argument types given: Rec Total time: 2.959 seconds, Total memory usage: 1.94MB ************** MAGMA ***************** Host dirichlet.math.umass.edu. (128.119.47.126) Time: Fri Jan 9 16:24:34 2004 Input: S6:=SymmetricGroup(6);M6:=MaximalSubgroups(S6);M61:=M6[1]; Nclasses(M61); Output: Magma V2.10-6 Fri Jan 9 2004 16:24:31 on modular [Seed = 2075875381] ------------------------------------- >> Nclasses(M61);; ^ Runtime error in 'Nclasses': Bad argument types Argument types given: Rec Total time: 2.919 seconds, Total memory usage: 1.94MB ************** MAGMA ***************** Host dirichlet.math.umass.edu. (128.119.47.126) Time: Fri Jan 9 16:25:10 2004 Input: S6:=SymmetricGroup(6);M6:=MaximalSubgroups(S6); Nclasses(M6[1]); Output: Magma V2.10-6 Fri Jan 9 2004 16:25:07 on modular [Seed = 164178555] ------------------------------------- >> Nclasses(M6[1]);; ^ Runtime error in 'Nclasses': Bad argument types Argument types given: Rec Total time: 2.919 seconds, Total memory usage: 1.94MB ************** MAGMA ***************** Host dirichlet.math.umass.edu. (128.119.47.126) Time: Fri Jan 9 16:25:24 2004 Input: S6:=SymmetricGroup(6);M6:=MaximalSubgroups(S6);Nclasses(M6[1]); Output: Magma V2.10-6 Fri Jan 9 2004 16:25:21 on modular [Seed = 282080016] ------------------------------------- >> S6:=SymmetricGroup(6);M6:=MaximalSubgroups(S6);Nclasses(M6[1]);; ^ Runtime error in 'Nclasses': Bad argument types Argument types given: Rec Total time: 2.959 seconds, Total memory usage: 1.94MB ************** MAGMA ***************** Host dirichlet.math.umass.edu. (128.119.47.126) Time: Fri Jan 9 16:26:04 2004 Input: S6:=SymmetricGroup(6);M6:=MaximalSubgroups(S6);Classes(M6[1]); Output: Magma V2.10-6 Fri Jan 9 2004 16:26:01 on modular [Seed = 467351603] ------------------------------------- >> S6:=SymmetricGroup(6);M6:=MaximalSubgroups(S6);Classes(M6[1]);; ^ Runtime error in 'Classes': Bad argument types Argument types given: Rec Total time: 2.959 seconds, Total memory usage: 1.94MB ************** MAGMA ***************** Host dirichlet.math.umass.edu. (128.119.47.126) Time: Fri Jan 9 16:26:27 2004 Input: S6:=SymmetricGroup(6);M6:=MaximalSubgroups(S6); Output: Magma V2.10-6 Fri Jan 9 2004 16:26:24 on modular [Seed = 585236963] ------------------------------------- Total time: 2.939 seconds, Total memory usage: 1.94MB ************** MAGMA ***************** Host dirichlet.math.umass.edu. (128.119.47.126) Time: Fri Jan 9 16:27:02 2004 Input: S6:=SymmetricGroup(6);M6:=MaximalSubgroups(S6);G:=M6[1]; Output: Magma V2.10-6 Fri Jan 9 2004 16:26:58 on modular [Seed = 770510542] ------------------------------------- Total time: 2.979 seconds, Total memory usage: 1.94MB ************** MAGMA ***************** Host dirichlet.math.umass.edu. (128.119.47.126) Time: Fri Jan 9 16:27:13 2004 Input: S6:=SymmetricGroup(6);M6:=MaximalSubgroups(S6);M6[1]; Output: Magma V2.10-6 Fri Jan 9 2004 16:27:10 on modular [Seed = 888412122] ------------------------------------- rec | order := 48, length := 15, subgroup := Permutation group acting on a set of cardinality 6 Order = 48 = 2^4 * 3 (1, 6)(2, 3) (1, 4, 6)(2, 5, 3) (3, 6) (1, 2) (4, 5) > Total time: 2.919 seconds, Total memory usage: 1.94MB ************** MAGMA ***************** Host dirichlet.math.umass.edu. (128.119.47.126) Time: Fri Jan 9 16:28:04 2004 Input: S6:=SymmetricGroup(6);M6:=MaximalSubgroups(S6);M6[1]; G:=sub; Classes(G); Output: Magma V2.10-6 Fri Jan 9 2004 16:28:00 on modular [Seed = 1073683614] ------------------------------------- rec | order := 48, length := 15, subgroup := Permutation group acting on a set of cardinality 6 Order = 48 = 2^4 * 3 (1, 2)(5, 6) (1, 4, 2)(3, 6, 5) (2, 6) (1, 5) (3, 4) > Conjugacy Classes of group G ---------------------------- [1] Order 1 Length 1 Rep Id(G) [2] Order 2 Length 1 Rep (1, 2)(3, 6)(4, 5) [3] Order 2 Length 3 Rep (3, 6)(4, 5) [4] Order 2 Length 3 Rep (4, 5) [5] Order 2 Length 6 Rep (1, 6)(2, 3) [6] Order 2 Length 6 Rep (1, 6)(2, 3)(4, 5) [7] Order 3 Length 8 Rep (1, 4, 6)(2, 5, 3) [8] Order 4 Length 6 Rep (3, 5, 6, 4) [9] Order 4 Length 6 Rep (1, 3, 2, 6)(4, 5) [10] Order 6 Length 8 Rep (1, 4, 3, 2, 5, 6) Total time: 2.939 seconds, Total memory usage: 1.94MB ************** MAGMA ***************** Host 24-205-67-29.pas-mres.charterpipeline.net. (24.205.67.29) Time: Fri Jan 9 16:32:26 2004 Input: ?magma Output: Magma V2.10-6 Fri Jan 9 2004 16:32:22 on modular [Seed = 3524456565] ------------------------------------- 24 matches: 1 O /magma 2 O /system/Magma 3 O /system/Magma/update 4 S /magma/combinatorial-geometrical-incidence/plane/introduction/\ planes-in-magma 5 S /magma/group/automatic/creation/magma 6 S /magma/group/group-overview/creation-general/magma 7 S /magma/group/matrix/creation-general-linear-group/magma 8 S /magma/group/permutation/creation-symmetric/magma 9 S /magma/group/polycyclic/polycyclic-groups/magma 10 S /magma/group/rewrite-system/creation/magma 11 S /magma/module-lattice/vector-space-linear-transformation/\ creation-arithmetic/creation-magma 12 S /magma/ring-field-algebra/abelian-extension/introduction/magma 13 S /magma/ring-field-algebra/alg_grp/creation/complete-magma 14 S /magma/ring-field-algebra/algebraic-field/creation/magma 15 S /magma/ring-field-algebra/integer/nfs/nfs-data-files-formats/\ nfs-magma-native 16 S /magma/ring-field-algebra/matrix/creation/complete-magma 17 S /magma/ring-field-algebra/matrix/creation/general-magma 18 S /magma/ring-field-algebra/rational-function-field/operation/magma 19 S /magma/ring-field-algebra/rational/creation/magma 20 S /magma/ring-field-algebra/real-complex/creation/magma 21 S /magma/ring-field-algebra/univariate-polynomial/creation/magma 22 S /magma/semigroup/finitely-presented/presentation/general-magma 23 I /language/IO/print/printing-file/PrintFileMagma 24 I /magma/ring-field-algebra/detail/generic/predicate/\ IsMagmaEuclideanRing To view an entry, type ? followed by the number next to it Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 24-205-67-29.pas-mres.charterpipeline.net. (24.205.67.29) Time: Fri Jan 9 16:33:58 2004 Input: ? 2 Output: Magma V2.10-6 Fri Jan 9 2004 16:33:55 on modular [Seed = 3709730015] ------------------------------------- No numbers are defined Total time: 2.929 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 24-205-67-29.pas-mres.charterpipeline.net. (24.205.67.29) Time: Fri Jan 9 16:34:19 2004 Input: ?magma 1 Output: Magma V2.10-6 Fri Jan 9 2004 16:34:16 on modular [Seed = 3827615229] ------------------------------------- 24 matches: 1 O /magma 2 O /system/Magma 3 O /system/Magma/update 4 S /magma/combinatorial-geometrical-incidence/plane/introduction/\ planes-in-magma 5 S /magma/group/automatic/creation/magma 6 S /magma/group/group-overview/creation-general/magma 7 S /magma/group/matrix/creation-general-linear-group/magma 8 S /magma/group/permutation/creation-symmetric/magma 9 S /magma/group/polycyclic/polycyclic-groups/magma 10 S /magma/group/rewrite-system/creation/magma 11 S /magma/module-lattice/vector-space-linear-transformation/\ creation-arithmetic/creation-magma 12 S /magma/ring-field-algebra/abelian-extension/introduction/magma 13 S /magma/ring-field-algebra/alg_grp/creation/complete-magma 14 S /magma/ring-field-algebra/algebraic-field/creation/magma 15 S /magma/ring-field-algebra/integer/nfs/nfs-data-files-formats/\ nfs-magma-native 16 S /magma/ring-field-algebra/matrix/creation/complete-magma 17 S /magma/ring-field-algebra/matrix/creation/general-magma 18 S /magma/ring-field-algebra/rational-function-field/operation/magma 19 S /magma/ring-field-algebra/rational/creation/magma 20 S /magma/ring-field-algebra/real-complex/creation/magma 21 S /magma/ring-field-algebra/univariate-polynomial/creation/magma 22 S /magma/semigroup/finitely-presented/presentation/general-magma 23 I /language/IO/print/printing-file/PrintFileMagma 24 I /magma/ring-field-algebra/detail/generic/predicate/\ IsMagmaEuclideanRing To view an entry, type ? followed by the number next to it Total time: 2.929 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 24-205-67-29.pas-mres.charterpipeline.net. (24.205.67.29) Time: Fri Jan 9 16:35:00 2004 Input: 1+2 Output: Magma V2.10-6 Fri Jan 9 2004 16:34:57 on modular [Seed = 3996045102] ------------------------------------- 3 Total time: 2.939 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 24-205-67-29.pas-mres.charterpipeline.net. (24.205.67.29) Time: Fri Jan 9 16:35:24 2004 Input: ?prime Output: Magma V2.10-6 Fri Jan 9 2004 16:35:20 on modular [Seed = 4248689700] ------------------------------------- 45 matches: 1 S /magma/ring-field-algebra/function-field/ideals/boolean/\ pred-ideal-prime 2 S /magma/ring-field-algebra/function-field/ideals/\ ideal-ops-further/ideals-prime 3 S /magma/ring-field-algebra/integer/prime 4 I /magma/geometry/schemes/schemes-global/PrimeComponents 5 I /magma/geometry/supersingular-divisors-on-module-curves/\ properties/Prime 6 I /magma/group/finitely-presented-groups-advanced/\ soluble-quotients/tools-soluble-quotient-process/\ tools-specific-normal-series/KeepPrimePower 7 I /magma/module-lattice/lattice/genus/local_genus_invariants/Prime 8 I /magma/module-lattice/quadratic/creation/creation/PrimeForm 9 I /magma/ring-field-algebra/affine-algebra/operations/IsPrime 10 I /magma/ring-field-algebra/alg_quat/ideal-theory/creation-access/\ PrimeIdeal 11 I /magma/ring-field-algebra/algebraic-field/ideal-class-group/\ DegreeOnePrimeIdeals 12 I /magma/ring-field-algebra/algebraic-field/ideal/ideal-Boolean/\ IsPrime 13 I /magma/ring-field-algebra/detail/element/element-Boolean/IsPrime 14 I /magma/ring-field-algebra/detail/generic/related/PrimeField 15 I /magma/ring-field-algebra/detail/generic/related/PrimeRing 16 I /magma/ring-field-algebra/finite-Galois-field/creation/structure/\ PrimeField 17 I /magma/ring-field-algebra/function-field/elements/elt-other/\ DifferentiationSequence 18 I /magma/ring-field-algebra/function-field/ideals/boolean/IsPrime 19 I /magma/ring-field-algebra/function-field/structure-related/\ structure-related-other/PrimeRing 20 I /magma/ring-field-algebra/function-field/structure-related/\ structure-related-other/PrimeRing 21 I /magma/ring-field-algebra/function-field/structure-related/\ structure-related-other/PrimeRing 22 I /magma/ring-field-algebra/ideal-groebner/ideal-operation/\ predicate/IsPrime 23 I /magma/ring-field-algebra/integer/factor/factorization-related/\ PrimeBasis 24 I /magma/ring-field-algebra/integer/factor/factorization-related/\ PrimeBasis 25 I /magma/ring-field-algebra/integer/operation-element/\ element-Boolean/IsPrime 26 I /magma/ring-field-algebra/integer/prime/next-previous/NextPrime 27 I /magma/ring-field-algebra/integer/prime/next-previous/NextPrime 28 I /magma/ring-field-algebra/integer/prime/next-previous/\ PreviousPrime 29 I /magma/ring-field-algebra/integer/prime/next-previous/\ PreviousPrime 30 I /magma/ring-field-algebra/integer/prime/next-previous/PrimeBasis 31 I /magma/ring-field-algebra/integer/prime/next-previous/RandomPrime 32 I /magma/ring-field-algebra/integer/prime/next-previous/RandomPrime 33 I /magma/ring-field-algebra/integer/prime/primality/IsPrime 34 I /magma/ring-field-algebra/integer/prime/primality/IsPrimePower 35 I /magma/ring-field-algebra/integer/prime/primality/IsProbablePrime 36 I /magma/ring-field-algebra/integer/prime/primality/IsProbablePrime 37 I /magma/ring-field-algebra/integer/random/RandomPrime 38 I /magma/ring-field-algebra/integer/random/RandomPrime 39 I /magma/ring-field-algebra/local/invariants/Prime 40 I /magma/ring-field-algebra/local/invariants/PrimeRing 41 I /magma/ring-field-algebra/local/invariants/PrimeRing 42 I /magma/ring-field-algebra/local/invariants/PrimeRing 43 I /magma/ring-field-algebra/univariate-polynomial/finitefields/\ NumberOfPrimePolynomials 44 I /magma/ring-field-algebra/univariate-polynomial/finitefields/\ PrimePolynomials 45 I /magma/ring-field-algebra/univariate-polynomial/finitefields/\ RandomPrimePolynomial To view an entry, type ? followed by the number next to it Total time: 2.939 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 24-205-67-29.pas-mres.charterpipeline.net. (24.205.67.29) Time: Fri Jan 9 16:36:44 2004 Input: ?prime 23 Output: Magma V2.10-6 Fri Jan 9 2004 16:36:41 on modular [Seed = 2219091244] ------------------------------------- 45 matches: 1 S /magma/ring-field-algebra/function-field/ideals/boolean/\ pred-ideal-prime 2 S /magma/ring-field-algebra/function-field/ideals/\ ideal-ops-further/ideals-prime 3 S /magma/ring-field-algebra/integer/prime 4 I /magma/geometry/schemes/schemes-global/PrimeComponents 5 I /magma/geometry/supersingular-divisors-on-module-curves/\ properties/Prime 6 I /magma/group/finitely-presented-groups-advanced/\ soluble-quotients/tools-soluble-quotient-process/\ tools-specific-normal-series/KeepPrimePower 7 I /magma/module-lattice/lattice/genus/local_genus_invariants/Prime 8 I /magma/module-lattice/quadratic/creation/creation/PrimeForm 9 I /magma/ring-field-algebra/affine-algebra/operations/IsPrime 10 I /magma/ring-field-algebra/alg_quat/ideal-theory/creation-access/\ PrimeIdeal 11 I /magma/ring-field-algebra/algebraic-field/ideal-class-group/\ DegreeOnePrimeIdeals 12 I /magma/ring-field-algebra/algebraic-field/ideal/ideal-Boolean/\ IsPrime 13 I /magma/ring-field-algebra/detail/element/element-Boolean/IsPrime 14 I /magma/ring-field-algebra/detail/generic/related/PrimeField 15 I /magma/ring-field-algebra/detail/generic/related/PrimeRing 16 I /magma/ring-field-algebra/finite-Galois-field/creation/structure/\ PrimeField 17 I /magma/ring-field-algebra/function-field/elements/elt-other/\ DifferentiationSequence 18 I /magma/ring-field-algebra/function-field/ideals/boolean/IsPrime 19 I /magma/ring-field-algebra/function-field/structure-related/\ structure-related-other/PrimeRing 20 I /magma/ring-field-algebra/function-field/structure-related/\ structure-related-other/PrimeRing 21 I /magma/ring-field-algebra/function-field/structure-related/\ structure-related-other/PrimeRing 22 I /magma/ring-field-algebra/ideal-groebner/ideal-operation/\ predicate/IsPrime 23 I /magma/ring-field-algebra/integer/factor/factorization-related/\ PrimeBasis 24 I /magma/ring-field-algebra/integer/factor/factorization-related/\ PrimeBasis 25 I /magma/ring-field-algebra/integer/operation-element/\ element-Boolean/IsPrime 26 I /magma/ring-field-algebra/integer/prime/next-previous/NextPrime 27 I /magma/ring-field-algebra/integer/prime/next-previous/NextPrime 28 I /magma/ring-field-algebra/integer/prime/next-previous/\ PreviousPrime 29 I /magma/ring-field-algebra/integer/prime/next-previous/\ PreviousPrime 30 I /magma/ring-field-algebra/integer/prime/next-previous/PrimeBasis 31 I /magma/ring-field-algebra/integer/prime/next-previous/RandomPrime 32 I /magma/ring-field-algebra/integer/prime/next-previous/RandomPrime 33 I /magma/ring-field-algebra/integer/prime/primality/IsPrime 34 I /magma/ring-field-algebra/integer/prime/primality/IsPrimePower 35 I /magma/ring-field-algebra/integer/prime/primality/IsProbablePrime 36 I /magma/ring-field-algebra/integer/prime/primality/IsProbablePrime 37 I /magma/ring-field-algebra/integer/random/RandomPrime 38 I /magma/ring-field-algebra/integer/random/RandomPrime 39 I /magma/ring-field-algebra/local/invariants/Prime 40 I /magma/ring-field-algebra/local/invariants/PrimeRing 41 I /magma/ring-field-algebra/local/invariants/PrimeRing 42 I /magma/ring-field-algebra/local/invariants/PrimeRing 43 I /magma/ring-field-algebra/univariate-polynomial/finitefields/\ NumberOfPrimePolynomials 44 I /magma/ring-field-algebra/univariate-polynomial/finitefields/\ PrimePolynomials 45 I /magma/ring-field-algebra/univariate-polynomial/finitefields/\ RandomPrimePolynomial To view an entry, type ? followed by the number next to it Total time: 2.919 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 24-205-67-29.pas-mres.charterpipeline.net. (24.205.67.29) Time: Fri Jan 9 16:37:07 2004 Input: ? 23 Output: Magma V2.10-6 Fri Jan 9 2004 16:37:04 on modular [Seed = 2404364238] ------------------------------------- No numbers are defined Total time: 2.939 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 24-205-67-29.pas-mres.charterpipeline.net. (24.205.67.29) Time: Fri Jan 9 16:37:27 2004 Input: ? prime ? 23 Output: Magma V2.10-6 Fri Jan 9 2004 16:37:24 on modular [Seed = 2522265283] ------------------------------------- 45 matches: 1 S /magma/ring-field-algebra/function-field/ideals/boolean/\ pred-ideal-prime 2 S /magma/ring-field-algebra/function-field/ideals/\ ideal-ops-further/ideals-prime 3 S /magma/ring-field-algebra/integer/prime 4 I /magma/geometry/schemes/schemes-global/PrimeComponents 5 I /magma/geometry/supersingular-divisors-on-module-curves/\ properties/Prime 6 I /magma/group/finitely-presented-groups-advanced/\ soluble-quotients/tools-soluble-quotient-process/\ tools-specific-normal-series/KeepPrimePower 7 I /magma/module-lattice/lattice/genus/local_genus_invariants/Prime 8 I /magma/module-lattice/quadratic/creation/creation/PrimeForm 9 I /magma/ring-field-algebra/affine-algebra/operations/IsPrime 10 I /magma/ring-field-algebra/alg_quat/ideal-theory/creation-access/\ PrimeIdeal 11 I /magma/ring-field-algebra/algebraic-field/ideal-class-group/\ DegreeOnePrimeIdeals 12 I /magma/ring-field-algebra/algebraic-field/ideal/ideal-Boolean/\ IsPrime 13 I /magma/ring-field-algebra/detail/element/element-Boolean/IsPrime 14 I /magma/ring-field-algebra/detail/generic/related/PrimeField 15 I /magma/ring-field-algebra/detail/generic/related/PrimeRing 16 I /magma/ring-field-algebra/finite-Galois-field/creation/structure/\ PrimeField 17 I /magma/ring-field-algebra/function-field/elements/elt-other/\ DifferentiationSequence 18 I /magma/ring-field-algebra/function-field/ideals/boolean/IsPrime 19 I /magma/ring-field-algebra/function-field/structure-related/\ structure-related-other/PrimeRing 20 I /magma/ring-field-algebra/function-field/structure-related/\ structure-related-other/PrimeRing 21 I /magma/ring-field-algebra/function-field/structure-related/\ structure-related-other/PrimeRing 22 I /magma/ring-field-algebra/ideal-groebner/ideal-operation/\ predicate/IsPrime 23 I /magma/ring-field-algebra/integer/factor/factorization-related/\ PrimeBasis 24 I /magma/ring-field-algebra/integer/factor/factorization-related/\ PrimeBasis 25 I /magma/ring-field-algebra/integer/operation-element/\ element-Boolean/IsPrime 26 I /magma/ring-field-algebra/integer/prime/next-previous/NextPrime 27 I /magma/ring-field-algebra/integer/prime/next-previous/NextPrime 28 I /magma/ring-field-algebra/integer/prime/next-previous/\ PreviousPrime 29 I /magma/ring-field-algebra/integer/prime/next-previous/\ PreviousPrime 30 I /magma/ring-field-algebra/integer/prime/next-previous/PrimeBasis 31 I /magma/ring-field-algebra/integer/prime/next-previous/RandomPrime 32 I /magma/ring-field-algebra/integer/prime/next-previous/RandomPrime 33 I /magma/ring-field-algebra/integer/prime/primality/IsPrime 34 I /magma/ring-field-algebra/integer/prime/primality/IsPrimePower 35 I /magma/ring-field-algebra/integer/prime/primality/IsProbablePrime 36 I /magma/ring-field-algebra/integer/prime/primality/IsProbablePrime 37 I /magma/ring-field-algebra/integer/random/RandomPrime 38 I /magma/ring-field-algebra/integer/random/RandomPrime 39 I /magma/ring-field-algebra/local/invariants/Prime 40 I /magma/ring-field-algebra/local/invariants/PrimeRing 41 I /magma/ring-field-algebra/local/invariants/PrimeRing 42 I /magma/ring-field-algebra/local/invariants/PrimeRing 43 I /magma/ring-field-algebra/univariate-polynomial/finitefields/\ NumberOfPrimePolynomials 44 I /magma/ring-field-algebra/univariate-polynomial/finitefields/\ PrimePolynomials 45 I /magma/ring-field-algebra/univariate-polynomial/finitefields/\ RandomPrimePolynomial To view an entry, type ? followed by the number next to it Total time: 3.029 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 24-205-67-29.pas-mres.charterpipeline.net. (24.205.67.29) Time: Fri Jan 9 16:37:56 2004 Input: factor ? Output: Magma V2.10-6 Fri Jan 9 2004 16:37:53 on modular [Seed = 2707522001] ------------------------------------- >> factor ? ^ User error: bad syntax Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 24-205-67-29.pas-mres.charterpipeline.net. (24.205.67.29) Time: Fri Jan 9 16:38:16 2004 Input: ? factor Output: Magma V2.10-6 Fri Jan 9 2004 16:38:13 on modular [Seed = 2825423020] ------------------------------------- 11 matches: 1 S /magma/ring-field-algebra/integer/factor 2 I /magma/combinatorial-geometrical-incidence/hyperelliptic-curve/\ point_structures_jacobian/counting_jacobian/EulerFactor 3 I /magma/combinatorial-geometrical-incidence/hyperelliptic-curve/\ point_structures_jacobian/counting_jacobian/EulerFactor 4 I /magma/combinatorial-geometrical-incidence/hyperelliptic-curve/\ point_structures_jacobian/counting_jacobian/EulerFactorModChar 5 I /magma/group/braid/braid-groups-elements/\ braid-groups-elements-access/CanonicalFactorRepresentation 6 I /magma/group/permutation/\ characteristic-subgroup-normal-structure/socle/SocleFactor 7 I /magma/ring-field-algebra/algebraic-field/ideal-class-group/\ ClassGroupCyclicFactorGenerators 8 I /magma/ring-field-algebra/algebraic-field/ideal-class-group/\ FactorBasis 9 I /magma/ring-field-algebra/algebraic-field/ideal-class-group/\ FactorBasis 10 I /magma/ring-field-algebra/integer/nfs/nfs-process/\ nfs-factorization-stage/Factor 11 I /magma/ring-field-algebra/integer/nfs/nfs-process/\ nfs-factorization-stage/Factor To view an entry, type ? followed by the number next to it Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 24-205-67-29.pas-mres.charterpipeline.net. (24.205.67.29) Time: Fri Jan 9 16:38:53 2004 Input: ? factor ? 1 Output: Magma V2.10-6 Fri Jan 9 2004 16:38:50 on modular [Seed = 3010696088] ------------------------------------- 11 matches: 1 S /magma/ring-field-algebra/integer/factor 2 I /magma/combinatorial-geometrical-incidence/hyperelliptic-curve/\ point_structures_jacobian/counting_jacobian/EulerFactor 3 I /magma/combinatorial-geometrical-incidence/hyperelliptic-curve/\ point_structures_jacobian/counting_jacobian/EulerFactor 4 I /magma/combinatorial-geometrical-incidence/hyperelliptic-curve/\ point_structures_jacobian/counting_jacobian/EulerFactorModChar 5 I /magma/group/braid/braid-groups-elements/\ braid-groups-elements-access/CanonicalFactorRepresentation 6 I /magma/group/permutation/\ characteristic-subgroup-normal-structure/socle/SocleFactor 7 I /magma/ring-field-algebra/algebraic-field/ideal-class-group/\ ClassGroupCyclicFactorGenerators 8 I /magma/ring-field-algebra/algebraic-field/ideal-class-group/\ FactorBasis 9 I /magma/ring-field-algebra/algebraic-field/ideal-class-group/\ FactorBasis 10 I /magma/ring-field-algebra/integer/nfs/nfs-process/\ nfs-factorization-stage/Factor 11 I /magma/ring-field-algebra/integer/nfs/nfs-process/\ nfs-factorization-stage/Factor To view an entry, type ? followed by the number next to it =============================================================================== PATH: /magma/ring-field-algebra/integer/factor KIND: Section =============================================================================== Factorization. This section contains a description of most of the machinery provided in Magma for the factorization of integers. An account of the Number Field Sieve is deferred until later in the chapter. In the first subsection the general-purpose Factorization function is described. It employs a combination of methods in an attempt to find the complete prime factorization of a given integer. Some control is possible over each of the methods, but in general default choices for the parameters would give good results for a wide range of arguments. In the second subsection we decribe functions that enable access to each of the factorization methods available in Magma. The user has control over parameters for these methods. Factorization functions in Magma return a factorization sequence. This is a sequence of two-element tuples [ , ..., ], with p_1, <11, 1> ] 1 Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 24-205-67-29.pas-mres.charterpipeline.net. (24.205.67.29) Time: Fri Jan 9 16:40:40 2004 Input: prime(22) Output: Magma V2.10-6 Fri Jan 9 2004 16:40:37 on modular [Seed = 1284271321] ------------------------------------- >> prime(22) ^ User error: Identifier 'prime' has not been declared or assigned Total time: 3.009 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 24-205-67-29.pas-mres.charterpipeline.net. (24.205.67.29) Time: Fri Jan 9 16:41:03 2004 Input: prime ? Output: Magma V2.10-6 Fri Jan 9 2004 16:41:00 on modular [Seed = 1435858425] ------------------------------------- >> prime ? ^ User error: bad syntax Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 24-205-67-29.pas-mres.charterpipeline.net. (24.205.67.29) Time: Fri Jan 9 16:41:22 2004 Input: ? prime Output: Magma V2.10-6 Fri Jan 9 2004 16:41:19 on modular [Seed = 1587445473] ------------------------------------- 45 matches: 1 S /magma/ring-field-algebra/function-field/ideals/boolean/\ pred-ideal-prime 2 S /magma/ring-field-algebra/function-field/ideals/\ ideal-ops-further/ideals-prime 3 S /magma/ring-field-algebra/integer/prime 4 I /magma/geometry/schemes/schemes-global/PrimeComponents 5 I /magma/geometry/supersingular-divisors-on-module-curves/\ properties/Prime 6 I /magma/group/finitely-presented-groups-advanced/\ soluble-quotients/tools-soluble-quotient-process/\ tools-specific-normal-series/KeepPrimePower 7 I /magma/module-lattice/lattice/genus/local_genus_invariants/Prime 8 I /magma/module-lattice/quadratic/creation/creation/PrimeForm 9 I /magma/ring-field-algebra/affine-algebra/operations/IsPrime 10 I /magma/ring-field-algebra/alg_quat/ideal-theory/creation-access/\ PrimeIdeal 11 I /magma/ring-field-algebra/algebraic-field/ideal-class-group/\ DegreeOnePrimeIdeals 12 I /magma/ring-field-algebra/algebraic-field/ideal/ideal-Boolean/\ IsPrime 13 I /magma/ring-field-algebra/detail/element/element-Boolean/IsPrime 14 I /magma/ring-field-algebra/detail/generic/related/PrimeField 15 I /magma/ring-field-algebra/detail/generic/related/PrimeRing 16 I /magma/ring-field-algebra/finite-Galois-field/creation/structure/\ PrimeField 17 I /magma/ring-field-algebra/function-field/elements/elt-other/\ DifferentiationSequence 18 I /magma/ring-field-algebra/function-field/ideals/boolean/IsPrime 19 I /magma/ring-field-algebra/function-field/structure-related/\ structure-related-other/PrimeRing 20 I /magma/ring-field-algebra/function-field/structure-related/\ structure-related-other/PrimeRing 21 I /magma/ring-field-algebra/function-field/structure-related/\ structure-related-other/PrimeRing 22 I /magma/ring-field-algebra/ideal-groebner/ideal-operation/\ predicate/IsPrime 23 I /magma/ring-field-algebra/integer/factor/factorization-related/\ PrimeBasis 24 I /magma/ring-field-algebra/integer/factor/factorization-related/\ PrimeBasis 25 I /magma/ring-field-algebra/integer/operation-element/\ element-Boolean/IsPrime 26 I /magma/ring-field-algebra/integer/prime/next-previous/NextPrime 27 I /magma/ring-field-algebra/integer/prime/next-previous/NextPrime 28 I /magma/ring-field-algebra/integer/prime/next-previous/\ PreviousPrime 29 I /magma/ring-field-algebra/integer/prime/next-previous/\ PreviousPrime 30 I /magma/ring-field-algebra/integer/prime/next-previous/PrimeBasis 31 I /magma/ring-field-algebra/integer/prime/next-previous/RandomPrime 32 I /magma/ring-field-algebra/integer/prime/next-previous/RandomPrime 33 I /magma/ring-field-algebra/integer/prime/primality/IsPrime 34 I /magma/ring-field-algebra/integer/prime/primality/IsPrimePower 35 I /magma/ring-field-algebra/integer/prime/primality/IsProbablePrime 36 I /magma/ring-field-algebra/integer/prime/primality/IsProbablePrime 37 I /magma/ring-field-algebra/integer/random/RandomPrime 38 I /magma/ring-field-algebra/integer/random/RandomPrime 39 I /magma/ring-field-algebra/local/invariants/Prime 40 I /magma/ring-field-algebra/local/invariants/PrimeRing 41 I /magma/ring-field-algebra/local/invariants/PrimeRing 42 I /magma/ring-field-algebra/local/invariants/PrimeRing 43 I /magma/ring-field-algebra/univariate-polynomial/finitefields/\ NumberOfPrimePolynomials 44 I /magma/ring-field-algebra/univariate-polynomial/finitefields/\ PrimePolynomials 45 I /magma/ring-field-algebra/univariate-polynomial/finitefields/\ RandomPrimePolynomial To view an entry, type ? followed by the number next to it Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 24-205-67-29.pas-mres.charterpipeline.net. (24.205.67.29) Time: Fri Jan 9 16:42:32 2004 Input: ? ? Output: Magma V2.10-6 Fri Jan 9 2004 16:42:28 on modular [Seed = 1739028579] ------------------------------------- 2 matches: 1 O / 2 O /browser To view an entry, type ? followed by the number next to it Total time: 2.919 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 24-205-67-29.pas-mres.charterpipeline.net. (24.205.67.29) Time: Fri Jan 9 16:42:52 2004 Input: ? ? 2 Output: Magma V2.10-6 Fri Jan 9 2004 16:42:49 on modular [Seed = 1890611049] ------------------------------------- 2 matches: 1 O / 2 O /browser To view an entry, type ? followed by the number next to it Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 24-205-67-29.pas-mres.charterpipeline.net. (24.205.67.29) Time: Fri Jan 9 16:43:11 2004 Input: ? Output: Magma V2.10-6 Fri Jan 9 2004 16:43:07 on modular [Seed = 2042193493] ------------------------------------- =============================================================================== PATH: / KIND: Overview =============================================================================== You are reading about the Magma online help system. This system gives you information about Magma while you are at the computer. To see this help page at any time, all you have to do is to type ? ---------- The online help system comes in two modes: the single request mode and the Magma Help Browser. To enter the Browser, type ?? The Browser is useful if you intend to read several related help nodes, because you can exploit the tree structure of the online help. Once you are in the Browser, you can type help again to find out how to use the Browser, and for a more detailed explanation of the whole online help system. ---------- Single help requests begin with the ? character. Examples are: ?print ?magma ?ring ?example If your help request is ambiguous, Magma will return a numbered list of matches. To see the contents of one of them, type ? followed by its number. Some help pages suggest other pages that you might like to look at as well. They are prefixed by a code such as +3 or +5 . To read one of them, type ? followed by the code. You can also supply the full pathname of a help node, if you know it. For example: ?/system/quit ?/magma/module/homomorphism ---------- The online help system offers tab completion. If you type a few letters of your help request and then press the tab key, Magma will "complete" the request if there is a unique completion. Otherwise, it will complete the request as far as possible, and then emit a beep. Press the tab key again to see all the possibilities. ALWAYS PRESS TAB BEFORE THE END OF THE LINE, SO AS TO SEE EVERY RELEVANT HELP PAGE. (On a few operating systems, the tab completion feature cannot be made available.) ---------- The content of the online help system comes from two sources: the "Handbook of Magma Functions" (Bosma and Cannon) and specially-written overview nodes. You may also wish to consult the books "An Introduction to Algebraic Programming in Magma" (Cannon and Playoust) and "Solving Problems with Magma" (Bosma, Cannon, Playoust and Steel). ---------- The online help system is also available in an HTML form suitable for Internet browsers. To use this, move to a shell prompt (outside Magma) and type magmahelp ---------- To leave Magma, type quit; or -D. =============================================================================== Total time: 2.889 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 24-205-67-29.pas-mres.charterpipeline.net. (24.205.67.29) Time: Fri Jan 9 16:44:39 2004 Input: ?? Output: Magma V2.10-6 Fri Jan 9 2004 16:44:36 on modular [Seed = 46275974] ------------------------------------- Magma Help Browser Type help for more information Unknown command ";" Unknown command "quit;" Total time: 2.879 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 24-205-67-29.pas-mres.charterpipeline.net. (24.205.67.29) Time: Fri Jan 9 16:45:05 2004 Input: ?? Output: Magma V2.10-6 Fri Jan 9 2004 16:45:02 on modular [Seed = 282070926] ------------------------------------- Magma Help Browser Type help for more information Unknown command ";" Unknown command "quit;" Total time: 2.989 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host weil.math.umass.edu. (128.119.47.164) Time: Fri Jan 9 16:45:20 2004 Input: S6:=SymmetricGroup(6);M6:=MaximalSubgroups(S6); Output: Magma V2.10-6 Fri Jan 9 2004 16:45:17 on modular [Seed = 433653428] ------------------------------------- Total time: 2.989 seconds, Total memory usage: 1.94MB ************** MAGMA ***************** Host 24-205-67-29.pas-mres.charterpipeline.net. (24.205.67.29) Time: Fri Jan 9 16:45:23 2004 Input: ?? help Output: Magma V2.10-6 Fri Jan 9 2004 16:45:20 on modular [Seed = 568409745] ------------------------------------- 2 matches: 1 O / 2 O /browser To view an entry, type ? followed by the number next to it Total time: 2.919 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host weil.math.umass.edu. (128.119.47.164) Time: Fri Jan 9 16:45:35 2004 Input: S6:=SymmetricGroup(6);M6:=MaximalSubgroups(S6); M6; Output: Magma V2.10-6 Fri Jan 9 2004 16:45:31 on modular [Seed = 736834704] ------------------------------------- Conjugacy classes of subgroups ------------------------------ [1] Order 48 Length 15 Permutation group acting on a set of cardinality 6 Order = 48 = 2^4 * 3 (1, 6)(2, 3) (1, 4, 6)(2, 5, 3) (3, 6) (1, 2) (4, 5) [2] Order 48 Length 15 Permutation group acting on a set of cardinality 6 Order = 48 = 2^4 * 3 (1, 5) (1, 2, 5) (1, 2)(4, 5) (1, 5)(2, 4) (3, 6) [3] Order 72 Length 10 Permutation group acting on a set of cardinality 6 Order = 72 = 2^3 * 3^2 (2, 4) (1, 6)(2, 5)(3, 4) (2, 4)(5, 6) (1, 4, 2) (3, 6, 5) [4] Order 120 Length 6 Permutation group acting on a set of cardinality 6 Order = 120 = 2^3 * 3 * 5 (3, 6) (1, 2, 3)(5, 6) [5] Order 120 Length 6 Permutation group acting on a set of cardinality 6 Order = 120 = 2^3 * 3 * 5 (1, 2)(3, 6)(4, 5) (1, 5, 2, 6, 3, 4) [6] Order 360 Length 1 Permutation group acting on a set of cardinality 6 Order = 360 = 2^3 * 3^2 * 5 (1, 2)(3, 6) (1, 2, 5, 6)(3, 4) Total time: 2.989 seconds, Total memory usage: 1.94MB ************** MAGMA ***************** Host 24-205-67-29.pas-mres.charterpipeline.net. (24.205.67.29) Time: Fri Jan 9 16:45:42 2004 Input: ?? help ?2 Output: Magma V2.10-6 Fri Jan 9 2004 16:45:39 on modular [Seed = 888416887] ------------------------------------- 2 matches: 1 O / 2 O /browser To view an entry, type ? followed by the number next to it =============================================================================== PATH: /browser KIND: Overview =============================================================================== Introduction ------------ You are reading about the Magma Help Browser. To read this help page when you are in the Browser, type help The Browser is entered by typing ?? and it lets you browse through the Magma Help tree. When you are in the Browser, the prompt is ??> . To get from the Browser back to Magma, type quit or -D at the Browser prompt. Magma has a simpler help system, which you can access without entering the Browser. To find out about it, leave the Browser (as explained above) and then type ? While you are still in the Browser, you can type the single word "walk" (without the quotes) followed by to view the next help screen. Keep typing "walk" (or "w") to see further screens. [If you are in the Browser, type the single word "w" (without the quotes) followed by to view the next help screen.] =============================================================================== Total time: 3.029 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 24-205-67-29.pas-mres.charterpipeline.net. (24.205.67.29) Time: Fri Jan 9 16:46:28 2004 Input: ?? help ?2 walk Output: Magma V2.10-6 Fri Jan 9 2004 16:46:25 on modular [Seed = 1039999820] ------------------------------------- 2 matches: 1 O / 2 O /browser To view an entry, type ? followed by the number next to it =============================================================================== PATH: /browser KIND: Overview =============================================================================== Introduction ------------ You are reading about the Magma Help Browser. To read this help page when you are in the Browser, type help The Browser is entered by typing ?? and it lets you browse through the Magma Help tree. When you are in the Browser, the prompt is ??> . To get from the Browser back to Magma, type quit or -D at the Browser prompt. Magma has a simpler help system, which you can access without entering the Browser. To find out about it, leave the Browser (as explained above) and then type ? While you are still in the Browser, you can type the single word "walk" (without the quotes) followed by to view the next help screen. Keep typing "walk" (or "w") to see further screens. [If you are in the Browser, type the single word "w" (without the quotes) followed by to view the next help screen.] =============================================================================== Total time: 2.989 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 24-205-67-29.pas-mres.charterpipeline.net. (24.205.67.29) Time: Fri Jan 9 16:47:10 2004 Input: w Output: Magma V2.10-6 Fri Jan 9 2004 16:47:07 on modular [Seed = 3322337501] ------------------------------------- >> w ^ User error: Identifier 'w' has not been declared or assigned Total time: 2.879 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 24-205-67-29.pas-mres.charterpipeline.net. (24.205.67.29) Time: Fri Jan 9 16:47:26 2004 Input: ? Output: Magma V2.10-6 Fri Jan 9 2004 16:47:23 on modular [Seed = 3490762491] ------------------------------------- =============================================================================== PATH: / KIND: Overview =============================================================================== You are reading about the Magma online help system. This system gives you information about Magma while you are at the computer. To see this help page at any time, all you have to do is to type ? ---------- The online help system comes in two modes: the single request mode and the Magma Help Browser. To enter the Browser, type ?? The Browser is useful if you intend to read several related help nodes, because you can exploit the tree structure of the online help. Once you are in the Browser, you can type help again to find out how to use the Browser, and for a more detailed explanation of the whole online help system. ---------- Single help requests begin with the ? character. Examples are: ?print ?magma ?ring ?example If your help request is ambiguous, Magma will return a numbered list of matches. To see the contents of one of them, type ? followed by its number. Some help pages suggest other pages that you might like to look at as well. They are prefixed by a code such as +3 or +5 . To read one of them, type ? followed by the code. You can also supply the full pathname of a help node, if you know it. For example: ?/system/quit ?/magma/module/homomorphism ---------- The online help system offers tab completion. If you type a few letters of your help request and then press the tab key, Magma will "complete" the request if there is a unique completion. Otherwise, it will complete the request as far as possible, and then emit a beep. Press the tab key again to see all the possibilities. ALWAYS PRESS TAB BEFORE THE END OF THE LINE, SO AS TO SEE EVERY RELEVANT HELP PAGE. (On a few operating systems, the tab completion feature cannot be made available.) ---------- The content of the online help system comes from two sources: the "Handbook of Magma Functions" (Bosma and Cannon) and specially-written overview nodes. You may also wish to consult the books "An Introduction to Algebraic Programming in Magma" (Cannon and Playoust) and "Solving Problems with Magma" (Bosma, Cannon, Playoust and Steel). ---------- The online help system is also available in an HTML form suitable for Internet browsers. To use this, move to a shell prompt (outside Magma) and type magmahelp ---------- To leave Magma, type quit; or -D. =============================================================================== Total time: 2.999 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host weil.math.umass.edu. (128.119.47.164) Time: Fri Jan 9 16:47:48 2004 Input: S6:=SymmetricGroup(6);M6:=MaximalSubgroups(S6);M6[1]; Output: Magma V2.10-6 Fri Jan 9 2004 16:47:44 on modular [Seed = 3642345241] ------------------------------------- rec | order := 48, length := 15, subgroup := Permutation group acting on a set of cardinality 6 Order = 48 = 2^4 * 3 (1, 2)(3, 6) (3, 6, 4) (1, 2)(3, 5)(4, 6) (1, 2)(3, 4)(5, 6) (1, 2)(3, 6)(4, 5) > Total time: 2.919 seconds, Total memory usage: 1.94MB ************** MAGMA ***************** Host weil.math.umass.edu. (128.119.47.164) Time: Fri Jan 9 16:48:01 2004 Input: S6:=SymmetricGroup(6);M6:=MaximalSubgroups(S6);M6; Output: Magma V2.10-6 Fri Jan 9 2004 16:47:58 on modular [Seed = 3777101615] ------------------------------------- Conjugacy classes of subgroups ------------------------------ [1] Order 48 Length 15 Permutation group acting on a set of cardinality 6 Order = 48 = 2^4 * 3 (1, 5)(4, 6) (1, 5, 3)(2, 6, 4) (1, 6) (4, 5) (2, 3) [2] Order 48 Length 15 Permutation group acting on a set of cardinality 6 Order = 48 = 2^4 * 3 (3, 4) (3, 4, 5) (2, 3)(4, 5) (2, 5)(3, 4) (1, 6) [3] Order 72 Length 10 Permutation group acting on a set of cardinality 6 Order = 72 = 2^3 * 3^2 (2, 5) (1, 2)(3, 5)(4, 6) (2, 5)(3, 6) (2, 5, 4) (1, 6, 3) [4] Order 120 Length 6 Permutation group acting on a set of cardinality 6 Order = 120 = 2^3 * 3 * 5 (1, 6) (1, 4, 5)(3, 6) [5] Order 120 Length 6 Permutation group acting on a set of cardinality 6 Order = 120 = 2^3 * 3 * 5 (1, 6)(2, 3)(4, 5) (1, 2, 4, 3, 5, 6) [6] Order 360 Length 1 Permutation group acting on a set of cardinality 6 Order = 360 = 2^3 * 3^2 * 5 (1, 6)(4, 5) (1, 2)(3, 6, 4, 5) Total time: 2.929 seconds, Total memory usage: 1.94MB ************** MAGMA ***************** Host 24-205-67-29.pas-mres.charterpipeline.net. (24.205.67.29) Time: Fri Jan 9 16:48:11 2004 Input: ?prime Output: Magma V2.10-6 Fri Jan 9 2004 16:48:08 on modular [Seed = 3911841585] ------------------------------------- 45 matches: 1 S /magma/ring-field-algebra/function-field/ideals/boolean/\ pred-ideal-prime 2 S /magma/ring-field-algebra/function-field/ideals/\ ideal-ops-further/ideals-prime 3 S /magma/ring-field-algebra/integer/prime 4 I /magma/geometry/schemes/schemes-global/PrimeComponents 5 I /magma/geometry/supersingular-divisors-on-module-curves/\ properties/Prime 6 I /magma/group/finitely-presented-groups-advanced/\ soluble-quotients/tools-soluble-quotient-process/\ tools-specific-normal-series/KeepPrimePower 7 I /magma/module-lattice/lattice/genus/local_genus_invariants/Prime 8 I /magma/module-lattice/quadratic/creation/creation/PrimeForm 9 I /magma/ring-field-algebra/affine-algebra/operations/IsPrime 10 I /magma/ring-field-algebra/alg_quat/ideal-theory/creation-access/\ PrimeIdeal 11 I /magma/ring-field-algebra/algebraic-field/ideal-class-group/\ DegreeOnePrimeIdeals 12 I /magma/ring-field-algebra/algebraic-field/ideal/ideal-Boolean/\ IsPrime 13 I /magma/ring-field-algebra/detail/element/element-Boolean/IsPrime 14 I /magma/ring-field-algebra/detail/generic/related/PrimeField 15 I /magma/ring-field-algebra/detail/generic/related/PrimeRing 16 I /magma/ring-field-algebra/finite-Galois-field/creation/structure/\ PrimeField 17 I /magma/ring-field-algebra/function-field/elements/elt-other/\ DifferentiationSequence 18 I /magma/ring-field-algebra/function-field/ideals/boolean/IsPrime 19 I /magma/ring-field-algebra/function-field/structure-related/\ structure-related-other/PrimeRing 20 I /magma/ring-field-algebra/function-field/structure-related/\ structure-related-other/PrimeRing 21 I /magma/ring-field-algebra/function-field/structure-related/\ structure-related-other/PrimeRing 22 I /magma/ring-field-algebra/ideal-groebner/ideal-operation/\ predicate/IsPrime 23 I /magma/ring-field-algebra/integer/factor/factorization-related/\ PrimeBasis 24 I /magma/ring-field-algebra/integer/factor/factorization-related/\ PrimeBasis 25 I /magma/ring-field-algebra/integer/operation-element/\ element-Boolean/IsPrime 26 I /magma/ring-field-algebra/integer/prime/next-previous/NextPrime 27 I /magma/ring-field-algebra/integer/prime/next-previous/NextPrime 28 I /magma/ring-field-algebra/integer/prime/next-previous/\ PreviousPrime 29 I /magma/ring-field-algebra/integer/prime/next-previous/\ PreviousPrime 30 I /magma/ring-field-algebra/integer/prime/next-previous/PrimeBasis 31 I /magma/ring-field-algebra/integer/prime/next-previous/RandomPrime 32 I /magma/ring-field-algebra/integer/prime/next-previous/RandomPrime 33 I /magma/ring-field-algebra/integer/prime/primality/IsPrime 34 I /magma/ring-field-algebra/integer/prime/primality/IsPrimePower 35 I /magma/ring-field-algebra/integer/prime/primality/IsProbablePrime 36 I /magma/ring-field-algebra/integer/prime/primality/IsProbablePrime 37 I /magma/ring-field-algebra/integer/random/RandomPrime 38 I /magma/ring-field-algebra/integer/random/RandomPrime 39 I /magma/ring-field-algebra/local/invariants/Prime 40 I /magma/ring-field-algebra/local/invariants/PrimeRing 41 I /magma/ring-field-algebra/local/invariants/PrimeRing 42 I /magma/ring-field-algebra/local/invariants/PrimeRing 43 I /magma/ring-field-algebra/univariate-polynomial/finitefields/\ NumberOfPrimePolynomials 44 I /magma/ring-field-algebra/univariate-polynomial/finitefields/\ PrimePolynomials 45 I /magma/ring-field-algebra/univariate-polynomial/finitefields/\ RandomPrimePolynomial To view an entry, type ? followed by the number next to it Total time: 2.979 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host weil.math.umass.edu. (128.119.47.164) Time: Fri Jan 9 16:48:34 2004 Input: S6:=SymmetricGroup(6);M6:=MaximalSubgroups(S6); M6; Output: Magma V2.10-6 Fri Jan 9 2004 16:48:31 on modular [Seed = 4063423517] ------------------------------------- Conjugacy classes of subgroups ------------------------------ [1] Order 48 Length 15 Permutation group acting on a set of cardinality 6 Order = 48 = 2^4 * 3 (1, 2)(5, 6) (1, 4, 2)(3, 6, 5) (2, 6) (1, 5) (3, 4) [2] Order 48 Length 15 Permutation group acting on a set of cardinality 6 Order = 48 = 2^4 * 3 (4, 5) (1, 4, 5) (1, 5)(3, 4) (1, 3)(4, 5) (2, 6) [3] Order 72 Length 10 Permutation group acting on a set of cardinality 6 Order = 72 = 2^3 * 3^2 (1, 3) (1, 4)(2, 3)(5, 6) (1, 3)(4, 6) (1, 5, 3) (2, 6, 4) [4] Order 120 Length 6 Permutation group acting on a set of cardinality 6 Order = 120 = 2^3 * 3 * 5 (2, 6) (1, 2, 5)(4, 6) [5] Order 120 Length 6 Permutation group acting on a set of cardinality 6 Order = 120 = 2^3 * 3 * 5 (1, 5)(2, 6)(3, 4) (1, 6, 2, 3, 5, 4) [6] Order 360 Length 1 Permutation group acting on a set of cardinality 6 Order = 360 = 2^3 * 3^2 * 5 (1, 5)(2, 6) (1, 4, 6, 5)(2, 3) Total time: 2.899 seconds, Total memory usage: 1.94MB ************** MAGMA ***************** Host 24-205-67-29.pas-mres.charterpipeline.net. (24.205.67.29) Time: Fri Jan 9 16:48:41 2004 Input: ?prime ?3 Output: Magma V2.10-6 Fri Jan 9 2004 16:48:38 on modular [Seed = 4215006477] ------------------------------------- 45 matches: 1 S /magma/ring-field-algebra/function-field/ideals/boolean/\ pred-ideal-prime 2 S /magma/ring-field-algebra/function-field/ideals/\ ideal-ops-further/ideals-prime 3 S /magma/ring-field-algebra/integer/prime 4 I /magma/geometry/schemes/schemes-global/PrimeComponents 5 I /magma/geometry/supersingular-divisors-on-module-curves/\ properties/Prime 6 I /magma/group/finitely-presented-groups-advanced/\ soluble-quotients/tools-soluble-quotient-process/\ tools-specific-normal-series/KeepPrimePower 7 I /magma/module-lattice/lattice/genus/local_genus_invariants/Prime 8 I /magma/module-lattice/quadratic/creation/creation/PrimeForm 9 I /magma/ring-field-algebra/affine-algebra/operations/IsPrime 10 I /magma/ring-field-algebra/alg_quat/ideal-theory/creation-access/\ PrimeIdeal 11 I /magma/ring-field-algebra/algebraic-field/ideal-class-group/\ DegreeOnePrimeIdeals 12 I /magma/ring-field-algebra/algebraic-field/ideal/ideal-Boolean/\ IsPrime 13 I /magma/ring-field-algebra/detail/element/element-Boolean/IsPrime 14 I /magma/ring-field-algebra/detail/generic/related/PrimeField 15 I /magma/ring-field-algebra/detail/generic/related/PrimeRing 16 I /magma/ring-field-algebra/finite-Galois-field/creation/structure/\ PrimeField 17 I /magma/ring-field-algebra/function-field/elements/elt-other/\ DifferentiationSequence 18 I /magma/ring-field-algebra/function-field/ideals/boolean/IsPrime 19 I /magma/ring-field-algebra/function-field/structure-related/\ structure-related-other/PrimeRing 20 I /magma/ring-field-algebra/function-field/structure-related/\ structure-related-other/PrimeRing 21 I /magma/ring-field-algebra/function-field/structure-related/\ structure-related-other/PrimeRing 22 I /magma/ring-field-algebra/ideal-groebner/ideal-operation/\ predicate/IsPrime 23 I /magma/ring-field-algebra/integer/factor/factorization-related/\ PrimeBasis 24 I /magma/ring-field-algebra/integer/factor/factorization-related/\ PrimeBasis 25 I /magma/ring-field-algebra/integer/operation-element/\ element-Boolean/IsPrime 26 I /magma/ring-field-algebra/integer/prime/next-previous/NextPrime 27 I /magma/ring-field-algebra/integer/prime/next-previous/NextPrime 28 I /magma/ring-field-algebra/integer/prime/next-previous/\ PreviousPrime 29 I /magma/ring-field-algebra/integer/prime/next-previous/\ PreviousPrime 30 I /magma/ring-field-algebra/integer/prime/next-previous/PrimeBasis 31 I /magma/ring-field-algebra/integer/prime/next-previous/RandomPrime 32 I /magma/ring-field-algebra/integer/prime/next-previous/RandomPrime 33 I /magma/ring-field-algebra/integer/prime/primality/IsPrime 34 I /magma/ring-field-algebra/integer/prime/primality/IsPrimePower 35 I /magma/ring-field-algebra/integer/prime/primality/IsProbablePrime 36 I /magma/ring-field-algebra/integer/prime/primality/IsProbablePrime 37 I /magma/ring-field-algebra/integer/random/RandomPrime 38 I /magma/ring-field-algebra/integer/random/RandomPrime 39 I /magma/ring-field-algebra/local/invariants/Prime 40 I /magma/ring-field-algebra/local/invariants/PrimeRing 41 I /magma/ring-field-algebra/local/invariants/PrimeRing 42 I /magma/ring-field-algebra/local/invariants/PrimeRing 43 I /magma/ring-field-algebra/univariate-polynomial/finitefields/\ NumberOfPrimePolynomials 44 I /magma/ring-field-algebra/univariate-polynomial/finitefields/\ PrimePolynomials 45 I /magma/ring-field-algebra/univariate-polynomial/finitefields/\ RandomPrimePolynomial To view an entry, type ? followed by the number next to it =============================================================================== PATH: /magma/ring-field-algebra/integer/prime KIND: Section =============================================================================== Primes and Primality Testing. Primality testing algorithms enable the user to certify the primality of prime integers. Proving the primality of very big integers can be time consuming and therefore in some of the algorithms using primes and factorization of integers the user can speed up the algorithm by explicitly allowing Magma to use probable primes rather than certified primes. A probable prime is an integer that has failed some compositeness test; if an integer passes a compositeness test it will be composite, but there is a (small) probability that a composite number will fail the test and is hence called a probable prime. Each Miller-Rabin test for instance, has a probability of less than 1/4 of declaring a composite number probably prime; in practice that means that numbers that fail several such cheap independent Miller-Rabin compositeness tests will be prime. Unless specifically asked otherwise, Magma will use rigorous primality proofs. Subsections: [+1] primality [+2] next-previous =============================================================================== Total time: 2.989 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 24-205-67-29.pas-mres.charterpipeline.net. (24.205.67.29) Time: Fri Jan 9 16:49:39 2004 Input: ?PI Output: Magma V2.10-6 Fri Jan 9 2004 16:49:36 on modular [Seed = 2219088436] ------------------------------------- 2 matches: 1 S /magma/group/soluble/subgroups/Hall-pi-Sylow 2 I /magma/ring-field-algebra/real-complex/operation-element/\ constant/Pi To view an entry, type ? followed by the number next to it Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 24-205-67-29.pas-mres.charterpipeline.net. (24.205.67.29) Time: Fri Jan 9 16:50:03 2004 Input: ?pi Output: Magma V2.10-6 Fri Jan 9 2004 16:49:59 on modular [Seed = 2387514313] ------------------------------------- 2 matches: 1 S /magma/group/soluble/subgroups/Hall-pi-Sylow 2 I /magma/ring-field-algebra/real-complex/operation-element/\ constant/Pi To view an entry, type ? followed by the number next to it Total time: 3.169 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 24-205-67-29.pas-mres.charterpipeline.net. (24.205.67.29) Time: Fri Jan 9 16:50:28 2004 Input: ?PI Output: Magma V2.10-6 Fri Jan 9 2004 16:50:24 on modular [Seed = 2656994302] ------------------------------------- 2 matches: 1 S /magma/group/soluble/subgroups/Hall-pi-Sylow 2 I /magma/ring-field-algebra/real-complex/operation-element/\ constant/Pi To view an entry, type ? followed by the number next to it Total time: 2.999 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 24-205-67-29.pas-mres.charterpipeline.net. (24.205.67.29) Time: Fri Jan 9 16:50:47 2004 Input: ?PI ?2 Output: Magma V2.10-6 Fri Jan 9 2004 16:50:44 on modular [Seed = 2808593107] ------------------------------------- 2 matches: 1 S /magma/group/soluble/subgroups/Hall-pi-Sylow 2 I /magma/ring-field-algebra/real-complex/operation-element/\ constant/Pi To view an entry, type ? followed by the number next to it =============================================================================== PATH: /magma/ring-field-algebra/real-complex/operation-element/constant/Pi KIND: Intrinsic =============================================================================== Pi(R) : FldPr -> FldPrElt Pi(R) : FldRe -> FldReElt Pi(R) : FldCom -> FldComElt Pi(R, p) : FldPr, RngIntElt -> FldPrElt The value of pi computed to the accuracy associated with R if R is a field of fixed precision, and to the default precision if R is the free real field. To allow the calculation of the constant to a precision different from the default in the latter case, a version of this function with the precision as a second argument is available. =============================================================================== Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 24-205-67-29.pas-mres.charterpipeline.net. (24.205.67.29) Time: Fri Jan 9 17:43:11 2004 Input: ?list Output: Magma V2.10-6 Fri Jan 9 2004 17:43:08 on modular [Seed = 3179130111] ------------------------------------- 11 matches: 1 S /magma/aggregate/list 2 S /magma/ring-field-algebra/ideal-groebner/order/elim-list 3 I /language/function-procedure-package/attribute/access/\ ListAttributes 4 I /magma/aggregate/list/creation/SequenceToList 5 I /magma/aggregate/list/creation/TupleToList 6 I /magma/aggregate/tuple-cartesian-product/tuple-access/TupleToList 7 I /magma/geometry/grd-rng/gr-lists/gr-searching/K3ListCodimensions 8 I /system/environment-options/info/ListCategories 9 I /system/environment-options/info/ListCategories 10 I /system/environment-options/info/ListSignatures 11 I /system/environment-options/verbose/ListVerbose To view an entry, type ? followed by the number next to it Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host weil.math.umass.edu. (128.119.47.164) Time: Fri Jan 9 18:51:56 2004 Input: A6:=Alt(6);M6:=MaximalSubgroups(A6); M6; Output: Magma V2.10-6 Fri Jan 9 2004 18:51:53 on modular [Seed = 349443504] ------------------------------------- Conjugacy classes of subgroups ------------------------------ [1] Order 24 Length 15 Permutation group acting on a set of cardinality 6 Order = 24 = 2^3 * 3 (1, 3)(2, 4) (3, 6, 5) (1, 6)(3, 5) (1, 3)(5, 6) [2] Order 24 Length 15 Permutation group acting on a set of cardinality 6 Order = 24 = 2^3 * 3 (1, 3)(5, 6) (1, 4, 3)(2, 5, 6) (1, 6)(3, 5) (1, 6)(2, 4) [3] Order 36 Length 10 Permutation group acting on a set of cardinality 6 Order = 36 = 2^2 * 3^2 (1, 3)(2, 5, 4, 6) (2, 4)(5, 6) (1, 2, 4)(3, 6, 5) (1, 4, 2)(3, 6, 5) [4] Order 60 Length 6 Permutation group acting on a set of cardinality 6 Order = 60 = 2^2 * 3 * 5 (1, 5)(3, 4) (1, 6, 3) [5] Order 60 Length 6 Permutation group acting on a set of cardinality 6 Order = 60 = 2^2 * 3 * 5 (3, 5)(4, 6) (1, 4, 2)(3, 5, 6) Total time: 2.929 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host weil.math.umass.edu. (128.119.47.164) Time: Fri Jan 9 18:53:33 2004 Input: A6:=Alt(6);M6:=MaximalSubgroups(A6); M6; G:=sub; Classes(G); Output: Magma V2.10-6 Fri Jan 9 2004 18:53:30 on modular [Seed = 265227976] ------------------------------------- Conjugacy classes of subgroups ------------------------------ [1] Order 24 Length 15 Permutation group acting on a set of cardinality 6 Order = 24 = 2^3 * 3 (3, 4)(5, 6) (1, 4, 5)(2, 6, 3) (1, 2)(3, 5) (3, 5)(4, 6) [2] Order 24 Length 15 Permutation group acting on a set of cardinality 6 Order = 24 = 2^3 * 3 (3, 5)(4, 6) (1, 5, 3) (1, 2)(3, 5) (1, 3)(2, 5) [3] Order 36 Length 10 Permutation group acting on a set of cardinality 6 Order = 36 = 2^2 * 3^2 (1, 2)(3, 5, 6, 4) (3, 6)(4, 5) (1, 5, 4) (2, 3, 6) [4] Order 60 Length 6 Permutation group acting on a set of cardinality 6 Order = 60 = 2^2 * 3 * 5 (2, 5)(3, 6) (1, 4, 3)(2, 6, 5) [5] Order 60 Length 6 Permutation group acting on a set of cardinality 6 Order = 60 = 2^2 * 3 * 5 (2, 4)(5, 6) (1, 4, 5) Conjugacy Classes of group G ---------------------------- [1] Order 1 Length 1 Rep Id(G) [2] Order 2 Length 9 Rep (2, 4)(5, 6) [3] Order 3 Length 4 Rep (1, 2, 4)(3, 6, 5) [4] Order 3 Length 4 Rep (3, 6, 5) [5] Order 4 Length 9 Rep (1, 3)(2, 6, 4, 5) [6] Order 4 Length 9 Rep (1, 3)(2, 5, 4, 6) Total time: 2.979 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host weil.math.umass.edu. (128.119.47.164) Time: Fri Jan 9 19:03:51 2004 Input: A8:=Alt(8);M8:=MaximalSubgroups(A8); M8; G:=sub; Classes(G); Output: Magma V2.10-6 Fri Jan 9 2004 19:03:48 on modular [Seed = 1536894210] ------------------------------------- Conjugacy classes of subgroups ------------------------------ [1] Order 360 Length 56 Permutation group acting on a set of cardinality 8 Order = 360 = 2^3 * 3^2 * 5 (2, 6)(7, 8) (1, 7)(2, 3, 5)(4, 6) (1, 8, 7) [2] Order 720 Length 28 Permutation group acting on a set of cardinality 8 Order = 720 = 2^4 * 3^2 * 5 (1, 4, 3, 7, 5) (2, 6)(7, 8) [3] Order 2520 Length 8 Permutation group acting on a set of cardinality 8 Order = 2520 = 2^3 * 3^2 * 5 * 7 (1, 6, 7) (1, 4)(3, 7)(5, 8, 6) [4] Order 576 Length 35 Permutation group acting on a set of cardinality 8 Order = 576 = 2^6 * 3^2 (2, 8)(6, 7) (1, 4, 3, 5)(2, 6, 8, 7) (5, 6, 7) (1, 2, 8) (4, 6)(5, 7) (4, 5)(6, 7) (1, 8)(2, 3) (1, 2)(3, 8) [5] Order 1344 Length 15 Permutation group acting on a set of cardinality 8 Order = 1344 = 2^6 * 3 * 7 (1, 8, 4, 6)(2, 7, 5, 3) (1, 8, 3, 4)(2, 5, 7, 6) (1, 2)(3, 8)(4, 5)(6, 7) (1, 6)(2, 7)(3, 5)(4, 8) (1, 8)(2, 3)(4, 6)(5, 7) [6] Order 1344 Length 15 Permutation group acting on a set of cardinality 8 Order = 1344 = 2^6 * 3 * 7 (1, 6)(2, 3)(4, 7)(5, 8) (1, 6, 2, 8)(3, 7, 5, 4) (1, 6)(2, 4)(3, 7)(5, 8) (1, 3)(2, 5)(4, 8)(6, 7) (1, 2)(3, 5)(4, 6)(7, 8) Conjugacy Classes of group G ---------------------------- [1] Order 1 Length 1 Rep Id(G) [2] Order 2 Length 9 Rep (2, 4)(5, 6) [3] Order 3 Length 4 Rep (1, 2, 4)(3, 6, 5) [4] Order 3 Length 4 Rep (3, 6, 5) [5] Order 4 Length 9 Rep (1, 3)(2, 6, 4, 5) [6] Order 4 Length 9 Rep (1, 3)(2, 5, 4, 6) Total time: 3.009 seconds, Total memory usage: 2.24MB ************** MAGMA ***************** Host weil.math.umass.edu. (128.119.47.164) Time: Fri Jan 9 19:07:56 2004 Input: A8:=Alt(8);M8:=MaximalSubgroups(A8); M8; G:=sub; Classes(G); H:=sub; Classes(H); Output: Magma V2.10-6 Fri Jan 9 2004 19:07:53 on modular [Seed = 3078081235] ------------------------------------- Conjugacy classes of subgroups ------------------------------ [1] Order 360 Length 56 Permutation group acting on a set of cardinality 8 Order = 360 = 2^3 * 3^2 * 5 (2, 6)(3, 4) (1, 6, 7)(2, 8)(3, 5) (3, 5, 4) [2] Order 720 Length 28 Permutation group acting on a set of cardinality 8 Order = 720 = 2^4 * 3^2 * 5 (1, 5, 8, 7, 3) (2, 6)(3, 4) [3] Order 2520 Length 8 Permutation group acting on a set of cardinality 8 Order = 2520 = 2^3 * 3^2 * 5 * 7 (2, 3, 5) (1, 4, 2)(3, 7)(5, 8) [4] Order 576 Length 35 Permutation group acting on a set of cardinality 8 Order = 576 = 2^6 * 3^2 (2, 3)(4, 6) (1, 5, 8, 7)(2, 4, 3, 6) (1, 2, 3) (4, 5, 6) (1, 3)(2, 8) (1, 8)(2, 3) (4, 5)(6, 7) (4, 7)(5, 6) [5] Order 1344 Length 15 Permutation group acting on a set of cardinality 8 Order = 1344 = 2^6 * 3 * 7 (1, 7, 6, 3)(2, 5, 4, 8) (1, 3, 2, 6)(4, 7, 8, 5) (1, 8)(2, 3)(4, 7)(5, 6) (1, 7)(2, 5)(3, 6)(4, 8) (1, 3)(2, 8)(4, 5)(6, 7) [6] Order 1344 Length 15 Permutation group acting on a set of cardinality 8 Order = 1344 = 2^6 * 3 * 7 (1, 4)(2, 5)(3, 8)(6, 7) (1, 8, 7, 3)(2, 6, 4, 5) (1, 4)(2, 5)(3, 7)(6, 8) (1, 6)(2, 3)(4, 8)(5, 7) (1, 7)(2, 8)(3, 4)(5, 6) >> ; ^ User error: bad syntax >> Classes(G); ^ User error: Identifier 'G' has not been declared or assigned Conjugacy Classes of group H ---------------------------- [1] Order 1 Length 1 Rep Id(H) [2] Order 2 Length 7 Rep (1, 4)(2, 5)(3, 7)(6, 8) [3] Order 2 Length 42 Rep (1, 3)(2, 7)(4, 8)(5, 6) [4] Order 2 Length 42 Rep (2, 4)(7, 8) [5] Order 3 Length 224 Rep (1, 5, 8)(3, 4, 6) [6] Order 4 Length 84 Rep (1, 8, 4, 6)(2, 7, 5, 3) [7] Order 4 Length 168 Rep (1, 4, 3, 8)(2, 6, 7, 5) [8] Order 4 Length 168 Rep (1, 5)(2, 8, 4, 7) [9] Order 6 Length 224 Rep (1, 4)(2, 7, 8, 5, 3, 6) [10] Order 7 Length 192 Rep (1, 3, 5, 4, 2, 6, 8) [11] Order 7 Length 192 Rep (1, 4, 8, 5, 6, 3, 2) Total time: 3.009 seconds, Total memory usage: 2.24MB ************** MAGMA ***************** Host weil.math.umass.edu. (128.119.47.164) Time: Fri Jan 9 19:08:19 2004 Input: A8:=Alt(8);M8:=MaximalSubgroups(A8); M8; G:=sub; Classes(G); H:=sub; Classes(H); Output: Magma V2.10-6 Fri Jan 9 2004 19:08:15 on modular [Seed = 2842285284] ------------------------------------- Conjugacy classes of subgroups ------------------------------ [1] Order 360 Length 56 Permutation group acting on a set of cardinality 8 Order = 360 = 2^3 * 3^2 * 5 (1, 2)(3, 7) (2, 8)(3, 6)(4, 7, 5) (1, 2, 8) [2] Order 720 Length 28 Permutation group acting on a set of cardinality 8 Order = 720 = 2^4 * 3^2 * 5 (2, 4, 8, 6, 5) (1, 2)(3, 7) [3] Order 2520 Length 8 Permutation group acting on a set of cardinality 8 Order = 2520 = 2^3 * 3^2 * 5 * 7 (2, 8, 3) (1, 3, 4)(2, 5)(6, 8) [4] Order 576 Length 35 Permutation group acting on a set of cardinality 8 Order = 576 = 2^6 * 3^2 (1, 7)(2, 3) (1, 2, 7, 3)(4, 8, 6, 5) (2, 4, 3) (1, 8, 7) (2, 4)(3, 6) (2, 3)(4, 6) (1, 8)(5, 7) (1, 5)(7, 8) [5] Order 1344 Length 15 Permutation group acting on a set of cardinality 8 Order = 1344 = 2^6 * 3 * 7 (1, 6, 3, 8)(2, 4, 5, 7) (1, 5, 6, 8)(2, 3, 7, 4) (1, 5)(2, 3)(4, 6)(7, 8) (1, 6)(2, 7)(3, 8)(4, 5) (1, 8)(2, 4)(3, 6)(5, 7) [6] Order 1344 Length 15 Permutation group acting on a set of cardinality 8 Order = 1344 = 2^6 * 3 * 7 (1, 4)(2, 6)(3, 8)(5, 7) (1, 8, 3, 7)(2, 4, 6, 5) (1, 4)(2, 5)(3, 8)(6, 7) (1, 6)(2, 3)(4, 7)(5, 8) (1, 2)(3, 6)(4, 5)(7, 8) Conjugacy Classes of group G ---------------------------- [1] Order 1 Length 1 Rep Id(G) [2] Order 2 Length 6 Rep (4, 6)(5, 7) [3] Order 2 Length 9 Rep (1, 3)(2, 8)(4, 5)(6, 7) [4] Order 2 Length 12 Rep (1, 5)(2, 6)(3, 7)(4, 8) [5] Order 2 Length 12 Rep (1, 5)(2, 7)(3, 6)(4, 8) [6] Order 2 Length 36 Rep (2, 8)(4, 7) [7] Order 3 Length 16 Rep (5, 6, 7) [8] Order 3 Length 32 Rep (1, 3, 8)(4, 5, 7) [9] Order 3 Length 32 Rep (1, 3, 8)(4, 5, 6) [10] Order 4 Length 36 Rep (1, 2, 3, 8)(4, 7, 5, 6) [11] Order 4 Length 36 Rep (1, 4, 3, 5)(2, 6, 8, 7) [12] Order 4 Length 36 Rep (1, 4, 3, 5)(2, 7, 8, 6) [13] Order 4 Length 72 Rep (2, 8)(4, 7, 5, 6) [14] Order 6 Length 48 Rep (1, 3)(2, 8)(4, 5, 7) [15] Order 6 Length 96 Rep (1, 4, 3, 5, 8, 6)(2, 7) [16] Order 6 Length 96 Rep (1, 4, 3, 5, 8, 7)(2, 6) Conjugacy Classes of group H ---------------------------- [1] Order 1 Length 1 Rep Id(H) [2] Order 2 Length 7 Rep (1, 4)(2, 5)(3, 7)(6, 8) [3] Order 2 Length 42 Rep (1, 3)(2, 7)(4, 8)(5, 6) [4] Order 2 Length 42 Rep (2, 4)(7, 8) [5] Order 3 Length 224 Rep (1, 5, 8)(3, 4, 6) [6] Order 4 Length 84 Rep (1, 8, 4, 6)(2, 7, 5, 3) [7] Order 4 Length 168 Rep (1, 4, 3, 8)(2, 6, 7, 5) [8] Order 4 Length 168 Rep (1, 5)(2, 8, 4, 7) [9] Order 6 Length 224 Rep (1, 4)(2, 7, 8, 5, 3, 6) [10] Order 7 Length 192 Rep (1, 3, 5, 4, 2, 6, 8) [11] Order 7 Length 192 Rep (1, 4, 8, 5, 6, 3, 2) Total time: 3.029 seconds, Total memory usage: 2.24MB ************** MAGMA ***************** Host host-65-199-137-206.link.com.eg. (65.199.137.206) Time: Sat Jan 10 02:05:27 2004 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: Magma V2.10-6 Sat Jan 10 2004 02:05:24 on modular [Seed = 4097077241] ------------------------------------- Replace this by some code, then click [PARI] or [MAGMA]! Total time: 2.989 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host host-65-199-137-206.link.com.eg. (65.199.137.206) Time: Sat Jan 10 02:06:00 2004 Input: x^2 Output: Magma V2.10-6 Sat Jan 10 2004 02:05:57 on modular [Seed = 4012864643] ------------------------------------- >> x^2; ^ User error: Identifier 'x' has not been declared or assigned Total time: 3.009 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host f03v-10-160.d1.club-internet.fr. (212.194.45.160) Time: Sat Jan 10 08:31:40 2004 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: Magma V2.10-6 Sat Jan 10 2004 08:31:37 on modular [Seed = 1132692174] ------------------------------------- Replace this by some code, then click [PARI] or [MAGMA]! Total time: 3.029 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host modemcable030.42-200-24.mc.videotron.ca. (24.200.42.30) Time: Sat Jan 10 14:28:35 2004 Input: x³+2x²+7x+3 Output: Magma V2.10-6 Sat Jan 10 2004 14:28:32 on modular [Seed = 290521919] ------------------------------------- >> x^ó+2x^ò+7x+3; ^ User error: Unknown character (ascii value -77) Total time: 2.909 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host modemcable030.42-200-24.mc.videotron.ca. (24.200.42.30) Time: Sat Jan 10 14:29:42 2004 Input: 2*x^2=3 + 6*x^2 + 22*x + 12 Output: Magma V2.10-6 Sat Jan 10 2004 14:29:39 on modular [Seed = 1065299410] ------------------------------------- >> 2*x^2=3 + 6*x^2 + 22*x + 12; ^ User error: Identifier 'x' has not been declared or assigned Total time: 2.989 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host modemcable030.42-200-24.mc.videotron.ca. (24.200.42.30) Time: Sat Jan 10 14:44:46 2004 Input: solve 2*x^2=3 + 6*x^2 + 22*x + 12 Output: Magma V2.10-6 Sat Jan 10 2004 14:44:43 on modular [Seed = 4004444299] ------------------------------------- >> solve 2*x^2=3 + 6*x^2 + 22*x + 12; ^ User error: bad syntax Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host modemcable030.42-200-24.mc.videotron.ca. (24.200.42.30) Time: Sat Jan 10 14:49:06 2004 Input: solve( 2*x^2=3 + 6*x^2 + 22*x + 12=0) Output: Magma V2.10-6 Sat Jan 10 2004 14:49:03 on modular [Seed = 2395904495] ------------------------------------- >> solve( 2*x^2=3 + 6*x^2 + 22*x + 12=0); ^ User error: Identifier 'x' has not been declared or assigned Total time: 2.939 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host modemcable030.42-200-24.mc.videotron.ca. (24.200.42.30) Time: Sat Jan 10 14:50:16 2004 Input: polroots(2*x^3+ 6*x^2 + 22*x + 12 = 0) Output: Magma V2.10-6 Sat Jan 10 2004 14:50:12 on modular [Seed = 2732766616] ------------------------------------- >> polroots(2*x^3+ 6*x^2 + 22*x + 12 = 0); ^ User error: Identifier 'x' has not been declared or assigned Total time: 3.039 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host lns-vlq-1-82-65-162-47.adsl.proxad.net. (82.65.162.47) Time: Sat Jan 10 16:15:06 2004 Input: 6941372044925487738675387152189111745732039847701504273612536130666996402409750124783895966530170647511075085147439137214921516137540516588371707169957057 Output: Magma V2.10-6 Sat Jan 10 2004 16:15:03 on modular [Seed = 2918024885] ------------------------------------- 6941372044925487738675387152189111745732039847701504273612536130666996402409750\ 124783895966530170647511075085147439137214921516137540516588371707169957057 Total time: 2.979 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host p508F5134.dip0.t-ipconnect.de. (80.143.81.52) Time: Sun Jan 11 06:12:18 2004 Input: 123 Output: Magma V2.10-6 Sun Jan 11 2004 06:12:14 on modular [Seed = 526282880] ------------------------------------- 123 Total time: 3.149 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host p508F5134.dip0.t-ipconnect.de. (80.143.81.52) Time: Sun Jan 11 06:12:33 2004 Input: 123*4 Output: Magma V2.10-6 Sun Jan 11 2004 06:12:30 on modular [Seed = 105343369] ------------------------------------- 492 Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host cw178.neoplus.adsl.tpnet.pl. (80.54.219.178) Time: Sun Jan 11 08:06:15 2004 Input: 2+2 Output: Magma V2.10-6 Sun Jan 11 2004 08:06:12 on modular [Seed = 4071880871] ------------------------------------- 4 Total time: 3.039 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host cw178.neoplus.adsl.tpnet.pl. (80.54.219.178) Time: Sun Jan 11 08:06:34 2004 Input: 2+2+2 Output: Magma V2.10-6 Sun Jan 11 2004 08:06:31 on modular [Seed = 4257019835] ------------------------------------- 6 Total time: 2.989 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host cw178.neoplus.adsl.tpnet.pl. (80.54.219.178) Time: Sun Jan 11 08:07:05 2004 Input: G := [1 2 3]; IsPlanar(G); Output: Magma V2.10-6 Sun Jan 11 2004 08:07:02 on modular [Seed = 3836079747] ------------------------------------- >> G := [1 2 3]; ^ User error: bad syntax >> IsPlanar(G);; ^ User error: Identifier 'G' has not been declared or assigned Total time: 2.979 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host bln2-t2-2.mcbone.net. (62.104.208.83) Time: Sun Jan 11 11:59:57 2004 Input: g:=Sl(2,3); Output: Magma V2.10-6 Sun Jan 11 2004 11:59:53 on modular [Seed = 1865330293] ------------------------------------- >> g:=Sl(2,3);; ^ User error: Identifier 'Sl' has not been declared or assigned Total time: 3.210 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host wbar11.tampa1-4-4-132-114.tampa1.dsl-verizon.net. (4.4.132.114) Time: Sun Jan 11 16:09:55 2004 Input: 1+1 Output: Magma V2.10-6 Sun Jan 11 2004 16:09:52 on modular [Seed = 1646500311] ------------------------------------- 2 Total time: 2.909 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (212.128.18.14) Time: Mon Jan 12 11:33:43 2004 Input: P2 := ProjectiveSpace(RationalField(),2); a := 234; b := -33709; c := 127; C := Conic(P2,a*x^2 + b*y^2 + c*z^2); Output: Magma V2.10-6 Mon Jan 12 2004 11:33:39 on modular [Seed = 358062421] ------------------------------------- Total time: 3.029 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (212.128.18.14) Time: Mon Jan 12 11:33:56 2004 Input: P2 := ProjectiveSpace(RationalField(),2); a := 234; b := -33709; c := 127; C := Conic(P2,a*x^2 + b*y^2 + c*z^2); Output: Magma V2.10-6 Mon Jan 12 2004 11:33:52 on modular [Seed = 1629744434] ------------------------------------- Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (212.128.18.14) Time: Mon Jan 12 11:34:10 2004 Input: 2+2; Output: Magma V2.10-6 Mon Jan 12 2004 11:34:07 on modular [Seed = 1747641396] ------------------------------------- 4 Total time: 2.979 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (212.128.18.14) Time: Mon Jan 12 11:34:22 2004 Input: P2 := ProjectiveSpace(RationalField(),2); a := 234; b := -33709; c := 127; C := Conic(P2,a*x^2 + b*y^2 + c*z^2); Output: Magma V2.10-6 Mon Jan 12 2004 11:34:19 on modular [Seed = 2000026591] ------------------------------------- Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (212.128.18.14) Time: Mon Jan 12 11:34:34 2004 Input: P2 := ProjectiveSpace(RationalField(),2); a := 234; b := -33709; c := 127; C := Conic(P2,a*x^2 + b*y^2 + c*z^2); HasRationalPoint(C); Output: Magma V2.10-6 Mon Jan 12 2004 11:34:31 on modular [Seed = 2117923530] ------------------------------------- false Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (212.128.18.14) Time: Mon Jan 12 11:35:44 2004 Input: P2 := ProjectiveSpace(RationalField(),2); a := 234; b := -33709; c := 127; C := Conic(P2,a*x^2 + b*y^2 + c*z^2); HasRationalPoint(C); fac := Factorization(Integers()!Discriminant(C)); Output: Magma V2.10-6 Mon Jan 12 2004 11:35:41 on modular [Seed = 1208665270] ------------------------------------- false Total time: 2.929 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (212.128.18.14) Time: Mon Jan 12 11:35:54 2004 Input: P2 := ProjectiveSpace(RationalField(),2); a := 234; b := -33709; c := 127; C := Conic(P2,a*x^2 + b*y^2 + c*z^2); HasRationalPoint(C); fac := Factorization(Integers()!Discriminant(C)); fac; Output: Magma V2.10-6 Mon Jan 12 2004 11:35:51 on modular [Seed = 1461050259] ------------------------------------- false [ <2, 3>, <3, 2>, <13, 2>, <127, 1>, <2593, 1> ] Total time: 3.009 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (212.128.18.14) Time: Mon Jan 12 11:36:39 2004 Input: P2 := ProjectiveSpace(RationalField(),2); a := 234; b := -33709; c := 127; C := Conic(P2,a*x^2 + b*y^2 + c*z^2); HasRationalPoint(C); fac := Factorization(Integers()!Discriminant(C)); fac; NormResidueSymbol(-a/c,-b/c,p[1]) : p in fac ]; Output: Magma V2.10-6 Mon Jan 12 2004 11:36:36 on modular [Seed = 2816813712] ------------------------------------- false [ <2, 3>, <3, 2>, <13, 2>, <127, 1>, <2593, 1> ] >> NormResidueSymbol(-a/c,-b/c,p[1]) : p in fac ]; ^ User error: bad syntax Total time: 2.919 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (212.128.18.14) Time: Mon Jan 12 11:37:11 2004 Input: P2 := ProjectiveSpace(RationalField(),2); a := 234; b := -33709; c := 127; C := Conic(P2,a*x^2 + b*y^2 + c*z^2); HasRationalPoint(C); fac := Factorization(Integers()!Discriminant(C)); fac; [NormResidueSymbol(-a/c,-b/c,p[1]) : p in fac ]; Output: Magma V2.10-6 Mon Jan 12 2004 11:37:08 on modular [Seed = 2934711225] ------------------------------------- false [ <2, 3>, <3, 2>, <13, 2>, <127, 1>, <2593, 1> ] [ -1, 1, 1, -1, 1 ] Total time: 2.999 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (212.128.18.14) Time: Mon Jan 12 11:37:21 2004 Input: P2 := ProjectiveSpace(RationalField(),2); a := 234; b := -33709; c := 127; C := Conic(P2,a*x^2 + b*y^2 + c*z^2); HasRationalPoint(C); fac := Factorization(Integers()!Discriminant(C)); fac; &*[NormResidueSymbol(-a/c,-b/c,p[1]) : p in fac ]; Output: Magma V2.10-6 Mon Jan 12 2004 11:37:18 on modular [Seed = 3221041826] ------------------------------------- false [ <2, 3>, <3, 2>, <13, 2>, <127, 1>, <2593, 1> ] 1 Total time: 2.909 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (212.128.18.14) Time: Mon Jan 12 11:37:38 2004 Input: P2 := ProjectiveSpace(RationalField(),2); a := 234; b := -33709; c := 127; C := Conic(P2,a*x^2 + b*y^2 + c*z^2); HasRationalPoint(C); fac := Factorization(Integers()!Discriminant(C)); fac; &*[ : p in fac ]; Output: Magma V2.10-6 Mon Jan 12 2004 11:37:35 on modular [Seed = 2260995050] ------------------------------------- false [ <2, 3>, <3, 2>, <13, 2>, <127, 1>, <2593, 1> ] &*( S: [ <-1, <2, 3>>, <1, <3, 2>>, <1, <13, 2>>, <-1, <127, 1>>, <... ) reduct( S: [ <-1, <2, 3>>, <1, <3, 2>>, <1, <13, 2>>, <-1, <127, 1>>, <..., op: Intrinsic '*' , allow_empty: true, id: 1, ids: one ) In file "/usr/local/magma/package/Aggregate/SeqEnum/eseq_misc.m", line 45, column 20: >> s := op(s, x); ^ Runtime error in '*': Bad argument types Argument types given: Tup, Tup Total time: 2.989 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (212.128.18.14) Time: Mon Jan 12 11:37:46 2004 Input: P2 := ProjectiveSpace(RationalField(),2); a := 234; b := -33709; c := 127; C := Conic(P2,a*x^2 + b*y^2 + c*z^2); HasRationalPoint(C); fac := Factorization(Integers()!Discriminant(C)); fac; [ : p in fac ]; Output: Magma V2.10-6 Mon Jan 12 2004 11:37:43 on modular [Seed = 2379153657] ------------------------------------- false [ <2, 3>, <3, 2>, <13, 2>, <127, 1>, <2593, 1> ] [ <-1, <2, 3>>, <1, <3, 2>>, <1, <13, 2>>, <-1, <127, 1>>, <1, <2593, 1>> ] Total time: 3.009 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (212.128.18.14) Time: Mon Jan 12 11:37:58 2004 Input: P2 := ProjectiveSpace(RationalField(),2); a := 234; b := -33709; c := 127; C := Conic(P2,a*x^2 + b*y^2 + c*z^2); HasRationalPoint(C); fac := Factorization(Integers()!Discriminant(C)); [ : p in fac ]; Output: Magma V2.10-6 Mon Jan 12 2004 11:37:55 on modular [Seed = 2497059284] ------------------------------------- false [ <-1, <2, 3>>, <1, <3, 2>>, <1, <13, 2>>, <-1, <127, 1>>, <1, <2593, 1>> ] Total time: 2.939 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (212.128.18.14) Time: Mon Jan 12 11:38:10 2004 Input: P2 := ProjectiveSpace(RationalField(),2); a := 234; b := -33709; c := 127; C := Conic(P2,a*x^2 + b*y^2 + c*z^2); HasRationalPoint(C); fac := Factorization(Integers()!Discriminant(C)); [ : p in fac ]; BadPrimes(C); Output: Magma V2.10-6 Mon Jan 12 2004 11:38:07 on modular [Seed = 3819007663] ------------------------------------- false [ <-1, <2, 3>>, <1, <3, 2>>, <1, <13, 2>>, <-1, <127, 1>>, <1, <2593, 1>> ] [ 2, 127 ] Total time: 3.289 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (212.128.18.14) Time: Mon Jan 12 12:23:14 2004 Input: P2 := ProjectiveSpace(RationalField(),2); a := 234; b := -33709; c := 127; C := Conic(P2,a*x^2 + b*y^2 + c*z^2); HasRationalPoint(C); fac := Factorization(Integers()!Discriminant(C)); [ : p in fac ]; BadPrimes(C); HasSolubilityCertificate(C); Output: Magma V2.10-6 Mon Jan 12 2004 12:23:11 on modular [Seed = 4038223659] ------------------------------------- false [ <-1, <2, 3>>, <1, <3, 2>>, <1, <13, 2>>, <-1, <127, 1>>, <1, <2593, 1>> ] [ 2, 127 ] false Total time: 3.019 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (212.128.18.14) Time: Mon Jan 12 12:23:25 2004 Input: P2 := ProjectiveSpace(RationalField(),2); a := 23423423; b := -33709; c := 127; C := Conic(P2,a*x^2 + b*y^2 + c*z^2); HasRationalPoint(C); fac := Factorization(Integers()!Discriminant(C)); [ : p in fac ]; BadPrimes(C); HasSolubilityCertificate(C); Output: Magma V2.10-6 Mon Jan 12 2004 12:23:22 on modular [Seed = 4189807063] ------------------------------------- false [ <-1, <2, 2>>, <1, <13, 1>>, <-1, <41, 1>>, <1, <127, 1>>, <-1, <2593, 1>>, <-1, <571303, 1>> ] [ 2, 41, 2593, 571303 ] false Total time: 2.929 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (212.128.18.14) Time: Mon Jan 12 12:23:55 2004 Input: P2 := ProjectiveSpace(RationalField(),2); a := 23423423; b := -33709; c := 127; C := Conic(P2,a*x^2 + b*y^2 + c*z^2); HasRationalPoint(C); fac := Factorization(Integers()!Discriminant(C)); &*[NormResidueSymbol(-a/c,-b/c,p[1]) : p in fac ]; BadPrimes(C); HasSolubilityCertificate(C); Output: Magma V2.10-6 Mon Jan 12 2004 12:23:52 on modular [Seed = 3263191758] ------------------------------------- false 1 [ 2, 41, 2593, 571303 ] false Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (212.128.18.14) Time: Mon Jan 12 12:24:26 2004 Input: P2 := ProjectiveSpace(RationalField(),2); a := 23423423; b := -33709; c := 127; C := Conic(P2,a*x^2 + b*y^2 + c*z^2); HasRationalPoint(C); fac := Factorization(Integers()!Discriminant(C)); [NormResidueSymbol(-a/c,-b/c,p[1]) : p in fac ]; BadPrimes(C); HasSolubilityCertificate(C); Output: Magma V2.10-6 Mon Jan 12 2004 12:24:23 on modular [Seed = 3414774696] ------------------------------------- false [ -1, 1, -1, 1, -1, -1 ] [ 2, 41, 2593, 571303 ] false Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (212.128.18.14) Time: Mon Jan 12 12:24:43 2004 Input: P2 := ProjectiveSpace(RationalField(),2); a := 23423423; b := -337034234249; c := 127; C := Conic(P2,a*x^2 + b*y^2 + c*z^2); HasRationalPoint(C); fac := Factorization(Integers()!Discriminant(C)); [NormResidueSymbol(-a/c,-b/c,p[1]) : p in fac ]; BadPrimes(C); HasSolubilityCertificate(C); Output: Magma V2.10-6 Mon Jan 12 2004 12:24:40 on modular [Seed = 3701359776] ------------------------------------- false [ -1, 1, -1, 1, -1, -1 ] [ 2, 127, 571303, 849203 ] false Total time: 3.079 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (212.128.18.14) Time: Mon Jan 12 12:24:57 2004 Input: P2 := ProjectiveSpace(RationalField(),2); a := 23423423; b := -337034234249; c := 12452342347; C := Conic(P2,a*x^2 + b*y^2 + c*z^2); HasRationalPoint(C); fac := Factorization(Integers()!Discriminant(C)); [NormResidueSymbol(-a/c,-b/c,p[1]) : p in fac ]; BadPrimes(C); HasSolubilityCertificate(C); Output: Magma V2.10-6 Mon Jan 12 2004 12:24:53 on modular [Seed = 610712676] ------------------------------------- false [ -1, -1, 1, 1, -1, -1, 1 ] [ 2, 23, 571303, 849203 ] false Total time: 3.619 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (212.128.18.14) Time: Mon Jan 12 12:35:30 2004 Input: P2 := ProjectiveSpace(RationalField(),2); a := 23423423; b := -337034234249; c := 12452342347; C := Conic(P2,y^2-4*x*y-3*x^2+4*y+8*x-5); HasRationalPoint(C); fac := Factorization(Integers()!Discriminant(C)); [NormResidueSymbol(-a/c,-b/c,p[1]) : p in fac ]; BadPrimes(C); HasSolubilityCertificate(C); Output: Magma V2.10-6 Mon Jan 12 2004 12:35:26 on modular [Seed = 492799974] ------------------------------------- >> C := Conic(P2,y^2-4*x*y-3*x^2+4*y+8*x-5); ^ Runtime error in 'Conic': The polynomial is not homogeneous >> HasRationalPoint(C); ^ User error: Identifier 'C' has not been declared or assigned >> fac := Factorization(Integers()!Discriminant(C)); ^ User error: Identifier 'C' has not been declared or assigned >> [NormResidueSymbol(-a/c,-b/c,p[1]) : p in fac ]; ^ User error: Identifier 'fac' has not been declared or assigned >> BadPrimes(C); ^ User error: Identifier 'C' has not been declared or assigned >> HasSolubilityCertificate(C); ^ User error: Identifier 'C' has not been declared or assigned Total time: 2.939 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (212.128.18.14) Time: Mon Jan 12 12:36:01 2004 Input: P2 := ProjectiveSpace(RationalField(),2); a := 23423423; b := -337034234249; c := 12452342347; C := Conic(P2,y^2-4*x*y-3*x^2+4*y+8*x*z-5*z^2); HasRationalPoint(C); fac := Factorization(Integers()!Discriminant(C)); [NormResidueSymbol(-a/c,-b/c,p[1]) : p in fac ]; BadPrimes(C); HasSolubilityCertificate(C); Output: Magma V2.10-6 Mon Jan 12 2004 12:35:58 on modular [Seed = 1730543036] ------------------------------------- >> C := Conic(P2,y^2-4*x*y-3*x^2+4*y+8*x*z-5*z^2); ^ Runtime error in 'Conic': The polynomial is not homogeneous >> HasRationalPoint(C); ^ User error: Identifier 'C' has not been declared or assigned >> fac := Factorization(Integers()!Discriminant(C)); ^ User error: Identifier 'C' has not been declared or assigned >> [NormResidueSymbol(-a/c,-b/c,p[1]) : p in fac ]; ^ User error: Identifier 'fac' has not been declared or assigned >> BadPrimes(C); ^ User error: Identifier 'C' has not been declared or assigned >> HasSolubilityCertificate(C); ^ User error: Identifier 'C' has not been declared or assigned Total time: 2.939 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host PCjmedina.upct.es. (212.128.22.131) Time: Mon Jan 12 13:43:13 2004 Input: #g:=GL(2,3); Output: Magma V2.10-6 Mon Jan 12 2004 13:43:09 on modular [Seed = 3246615385] ------------------------------------- >> #g:=GL(2,3);; ^ User error: Illegal left hand side of an assignment statement Total time: 2.989 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host PCjmedina.upct.es. (212.128.22.131) Time: Mon Jan 12 13:43:27 2004 Input: #GL(2,3); Output: Magma V2.10-6 Mon Jan 12 2004 13:43:24 on modular [Seed = 3583475516] ------------------------------------- 48 Total time: 2.939 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host PCjmedina.upct.es. (212.128.22.131) Time: Mon Jan 12 13:44:02 2004 Input: g:=GL(2,3); for x in g do; print x; end for; Output: Magma V2.10-6 Mon Jan 12 2004 13:43:58 on modular [Seed = 3701372439] ------------------------------------- [1 0] [0 1] [2 1] [2 0] [1 1] [1 0] [0 2] [1 2] [2 0] [0 1] [1 2] [2 0] [2 2] [1 0] [0 1] [1 2] [1 0] [1 1] [2 1] [1 1] [1 1] [2 1] [0 2] [1 1] [2 0] [2 1] [1 2] [0 2] [2 2] [0 2] [0 1] [1 0] [1 0] [2 1] [2 1] [0 2] [1 1] [0 2] [0 2] [1 0] [2 0] [1 1] [1 2] [1 1] [2 2] [2 1] [0 1] [1 1] [1 0] [0 2] [2 1] [1 0] [1 1] [2 0] [0 2] [2 1] [2 0] [0 2] [1 2] [1 0] [2 2] [2 0] [0 1] [2 1] [1 0] [2 2] [2 1] [2 2] [1 1] [1 2] [0 2] [2 2] [2 0] [1 2] [1 2] [0 1] [2 2] [0 1] [0 1] [2 0] [1 0] [1 2] [2 1] [0 1] [1 1] [0 1] [0 2] [2 0] [2 0] [2 2] [1 2] [2 2] [2 2] [1 2] [0 1] [2 2] Total time: 2.929 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 2(SERVFAIL) (209.234.160.76) Time: Mon Jan 12 14:29:28 2004 Input: p := 1000000000000000000000000000057; F := POpen("sort -n", "w"); for i := 100 to 110 do fprintf F, "%30o (2^%o mod p)n", 2^i mod p, i; end for; delete F; Output: WARNING: MAGMA command contains unsafe command 'open', so it will not be executed. ************** MAGMA ***************** Host 3(NXDOMAIN) (212.205.76.74) Time: Tue Jan 13 01:35:49 2004 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: Magma V2.10-6 Tue Jan 13 2004 01:35:46 on modular [Seed = 1815068059] ------------------------------------- Replace this by some code, then click [PARI] or [MAGMA]! Total time: 2.939 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (212.205.76.74) Time: Tue Jan 13 01:36:35 2004 Input: print 2+4 ; Output: Magma V2.10-6 Tue Jan 13 2004 01:36:32 on modular [Seed = 1444251539] ------------------------------------- 6 Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (212.205.76.74) Time: Tue Jan 13 01:44:05 2004 Input: print 2+4 ; 2/3-4/5; Output: Magma V2.10-6 Tue Jan 13 2004 01:44:02 on modular [Seed = 3002163509] ------------------------------------- 6 -2/15 Total time: 2.889 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (212.205.76.74) Time: Tue Jan 13 01:46:28 2004 Input: 1/7 + 1/8; Output: Magma V2.10-6 Tue Jan 13 2004 01:46:25 on modular [Seed = 2479900647] ------------------------------------- 15/56 Total time: 2.869 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (212.205.76.74) Time: Tue Jan 13 01:47:20 2004 Input: 1/2+1/7 + 1/8; Output: Magma V2.10-6 Tue Jan 13 2004 01:47:17 on modular [Seed = 2244366789] ------------------------------------- 43/56 Total time: 3.059 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (212.205.76.74) Time: Tue Jan 13 01:48:12 2004 Input: 1/2+1/3; Output: Magma V2.10-6 Tue Jan 13 2004 01:48:08 on modular [Seed = 2362398737] ------------------------------------- 5/6 Total time: 3.019 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (212.205.76.74) Time: Tue Jan 13 01:49:03 2004 Input: 1.0/7.0; Output: Magma V2.10-6 Tue Jan 13 2004 01:49:00 on modular [Seed = 4155777822] ------------------------------------- 0.142857142857142857142857142855 Total time: 3.039 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (212.205.76.74) Time: Tue Jan 13 01:51:13 2004 Input: Factorial(19); Output: Magma V2.10-6 Tue Jan 13 2004 01:51:10 on modular [Seed = 3886297740] ------------------------------------- 121645100408832000 Total time: 2.999 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (212.205.76.74) Time: Tue Jan 13 01:51:33 2004 Input: Factorial(50); Output: Magma V2.10-6 Tue Jan 13 2004 01:51:30 on modular [Seed = 4004330409] ------------------------------------- 30414093201713378043612608166064768844377641568960512000000000000 Total time: 2.989 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (212.205.76.74) Time: Tue Jan 13 01:51:51 2004 Input: Factorial(150); Output: Magma V2.10-6 Tue Jan 13 2004 01:51:48 on modular [Seed = 3499296097] ------------------------------------- 5713383956445854590478932865261054003189553578601126418254837583317982912484539\ 8393126574488675311145377107878746854204162666250198684504466355949195922066574\ 9425920957357789293253572904449624724054167907221184454371222696755200000000000\ 00000000000000000000000000 Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (212.205.76.74) Time: Tue Jan 13 01:52:20 2004 Input: Factorial(1500); Output: Magma V2.10-6 Tue Jan 13 2004 01:52:17 on modular [Seed = 3684175439] ------------------------------------- 4811997796779774860166990093581379781834808040672613808130855941163057518900109\ 5591292230585206733851868464009619343585194052091124618166270271481881393331431\ 6279628102998441493337890446893955104871678797693253036994704678292343992633265\ 4565286074860507574636692832360664549227754112008343808672736937788767600021140\ 5318480244354207419604864176969950581435222198851194568984095705945549589054568\ 3217923389191494429859199577347929594024990968456430204018693811756039644243332\ 2211412597437481780424263330976980429395287003461935412501421004564766406324016\ 2007560108665290568646128342557147350985358724154623253371867470765120422073867\ 9639357752586921097530417620943435690504974703535317644815031747509118582309069\ 9836106608478775831611058573601336537743186073857226132573823365683527194735269\ 5180865573043834027955539012765489372645042504406597752357481931532872356635411\ 2245783340405222947464028295854584787087783463794318623688248190091770914440348\ 8594139431934391022316865586976179966907505952760850246559318139856621478680121\ 1651657222004123456498258513120359126022843038535083709796101565934859483203933\ 4433086014758131083630741185624044124201919471275854829191721730459611221227014\ 3429787069193215408298694595474825110578218158639727582034210147045730063359013\ 9512919549474113721711616912519714191760699935509810254849967087635936181176363\ 9542241860313466829288784928722494854566901388316101353779163279405037014002901\ 2550913214078261464049573351804867098336013409786036476263865889487317449987013\ 3559364805443430831459505987809215393353387232078177562975021460595422358573128\ 0854171623360302351386527354380530345319626208115660198968792752571639883520908\ 7493034611551833120292726370844672939438187988883954973187697868224932062859963\ 1628662375508826209854754631984276392670919216923002770077734756077549035942976\ 2091594162115814394614845095493703574867702768076875445801643146475950313689484\ 9028289717332801351843575870005642592263841188949652797584605271795804481373708\ 6806600171993703579485864029383208714528950303253881360812631162134750100307772\ 6343374670128204707156508107146899051214322595285054830539304022174006860616124\ 7165963019243486409453982808567746538302612835377107115230419754979887070613989\ 3609140045659756285435787771636258253666592102151236142132724425850991205720020\ 4936605808966008918885946596129277243578662659345176158412987891544622491696888\ 6009264028475638243174612035776793311958928046868734806178807298636278858222701\ 9465263474828590646048451070702923434422714349595857654843699542321849363652767\ 7719783146810135894429552198797020080689340966246506257697052333334628260138600\ 9869815518033114536565245348295549797991558643847468734567787445111770225044171\ 1504844638414485210092261397271970571029038581873069951161330495772310508760528\ 2497065142383842698086395070804182983183113613736285120417164151968683342541191\ 3713958914959721003215354594111466653049890652924079816480400739477592783604566\ 8573993316428972539932745757171947402454257142633700815922407278403640595355142\ 0755994460563379867172123162232577634121641808995327220393832444625114103466461\ 4886339723709627682265615756119466554575701742984240484030975892561865050792104\ 3007241637877939825811059339138925526124514467627126548126795078784022672860886\ 2519745813621417827864074028963096780089096632639870185381070508861934890124974\ 0500582072727123273372814177513272201386059116962069278929045679469840980855744\ 7756701311883266010859016027592252397754508251628808293537776536569608111330584\ 7971606948478989231967439702444518427022664033263173190921171511439716795000425\ 9026925509313021598441809741843547430046728194979822710252987373274902799207970\ 0287275900856241172902880909546551703263202853584498085358955307673717177961902\ 0810986187290463488490602496000000000000000000000000000000000000000000000000000\ 0000000000000000000000000000000000000000000000000000000000000000000000000000000\ 0000000000000000000000000000000000000000000000000000000000000000000000000000000\ 0000000000000000000000000000000000000000000000000000000000000000000000000000000\ 0000000000000000000000000000000000000000000000000000000000000000000000000000000\ 0000000 Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (212.205.76.74) Time: Tue Jan 13 01:54:06 2004 Input: GCD(512,68); Output: Magma V2.10-6 Tue Jan 13 2004 01:54:03 on modular [Seed = 3448642547] ------------------------------------- 4 Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (212.205.76.74) Time: Tue Jan 13 02:01:56 2004 Input: Sqrt(19); Output: Magma V2.10-6 Tue Jan 13 2004 02:01:53 on modular [Seed = 139190239] ------------------------------------- 4.358898943540673552236981983816 Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host proxy1.cc.biu.ac.il. (132.70.9.117) Time: Tue Jan 13 02:21:57 2004 Input: Z:= BraidGroup(6); Output: Magma V2.10-6 Tue Jan 13 2004 02:21:54 on modular [Seed = 1073978596] ------------------------------------- Total time: 3.029 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host proxy1.cc.biu.ac.il. (132.70.9.117) Time: Tue Jan 13 02:22:10 2004 Input: Z:= BraidGroup(6); Z Output: Magma V2.10-6 Tue Jan 13 2004 02:22:07 on modular [Seed = 1225430496] ------------------------------------- GrpBrd : Z on 6 strings Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host proxy1.cc.biu.ac.il. (132.70.9.117) Time: Tue Jan 13 02:23:14 2004 Input: Z:= BraidGroup(6); Z z=Z.1*Z.2*Z.1*Z.2*Z.1*Z.2 Output: Magma V2.10-6 Tue Jan 13 2004 02:23:11 on modular [Seed = 3204276823] ------------------------------------- >> z=Z.1*Z.2*Z.1*Z.2*Z.1*Z.2; ^ User error: bad syntax Total time: 2.919 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host proxy1.cc.biu.ac.il. (132.70.9.117) Time: Tue Jan 13 02:23:27 2004 Input: Z:= BraidGroup(6); Z z:=Z.1*Z.2*Z.1*Z.2*Z.1*Z.2 Output: Magma V2.10-6 Tue Jan 13 2004 02:23:24 on modular [Seed = 2816768893] ------------------------------------- >> z:=Z.1*Z.2*Z.1*Z.2*Z.1*Z.2; ^ User error: bad syntax Total time: 2.919 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host proxy1.cc.biu.ac.il. (132.70.9.117) Time: Tue Jan 13 02:23:47 2004 Input: Z:= BraidGroup(6); Z u:=Z.1*Z.2*Z.1*Z.2*Z.1*Z.2 Output: Magma V2.10-6 Tue Jan 13 2004 02:23:43 on modular [Seed = 2901373029] ------------------------------------- >> u:=Z.1*Z.2*Z.1*Z.2*Z.1*Z.2; ^ User error: bad syntax Total time: 2.999 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host proxy1.cc.biu.ac.il. (132.70.9.117) Time: Tue Jan 13 02:24:18 2004 Input: Z:= BraidGroup(6); Z Z.1*Z.2*Z.1*Z.2*Z.1*Z.2 Output: Magma V2.10-6 Tue Jan 13 2004 02:24:15 on modular [Seed = 2513848508] ------------------------------------- >> Z.1*Z.2*Z.1*Z.2*Z.1*Z.2; ^ User error: bad syntax Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host proxy1.cc.biu.ac.il. (132.70.9.117) Time: Tue Jan 13 02:27:23 2004 Input: Z:=BraidGroup(6); u:=Z.1; Output: Magma V2.10-6 Tue Jan 13 2004 02:27:20 on modular [Seed = 4054985759] ------------------------------------- Total time: 2.929 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host proxy1.cc.biu.ac.il. (132.70.9.117) Time: Tue Jan 13 02:27:42 2004 Input: Z:=BraidGroup(6); u:=Z.1; u; Output: Magma V2.10-6 Tue Jan 13 2004 02:27:39 on modular [Seed = 3869588283] ------------------------------------- Z.1 Total time: 2.889 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host proxy1.cc.biu.ac.il. (132.70.9.117) Time: Tue Jan 13 02:28:21 2004 Input: Z:=BraidGroup(6); u:=Z.1; u; v:=Z.1*Z.2; Output: Magma V2.10-6 Tue Jan 13 2004 02:28:18 on modular [Seed = 4021039563] ------------------------------------- Z.1 Total time: 3.019 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host proxy1.cc.biu.ac.il. (132.70.9.117) Time: Tue Jan 13 02:29:26 2004 Input: Z:=BraidGroup(6); u:=Z.1; u; v:=Z.1*Z.2; U:=Z.1*Z.2*Z.1; V=Z.2*Z.1*Z.2; Output: Magma V2.10-6 Tue Jan 13 2004 02:29:23 on modular [Seed = 3718120376] ------------------------------------- Z.1 >> V=Z.2*Z.1*Z.2;; ^ User error: Identifier 'V' has not been declared or assigned Total time: 2.909 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host proxy1.cc.biu.ac.il. (132.70.9.117) Time: Tue Jan 13 02:29:53 2004 Input: Z:=BraidGroup(6); u:=Z.1; u; u:=Z.1*Z.2; u:=Z.1*Z.2*Z.1; v:=Z.2*Z.1*Z.2; Output: Magma V2.10-6 Tue Jan 13 2004 02:29:50 on modular [Seed = 3246530457] ------------------------------------- Z.1 Total time: 2.919 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host proxy1.cc.biu.ac.il. (132.70.9.117) Time: Tue Jan 13 02:31:03 2004 Input: Z:=BraidGroup(6); u:=Z.1; u; u:=Z.1*Z.2; u:=Z.1*Z.2*Z.1; v:=Z.2*Z.1*Z.2; NormalForm(u*v); Output: Magma V2.10-6 Tue Jan 13 2004 02:31:00 on modular [Seed = 1031726014] ------------------------------------- Z.1 Z.2 * Z.1 * Z.2^2 * Z.1 * Z.2 Total time: 3.029 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host proxy1.cc.biu.ac.il. (132.70.9.117) Time: Tue Jan 13 02:31:33 2004 Input: Z:=BraidGroup(6); u:=Z.1; u; u:=Z.1*Z.2; u:=Z.1*Z.2*Z.1; v:=Z.2*Z.1*Z.2; y:=NormalForm(u*v); Output: Magma V2.10-6 Tue Jan 13 2004 02:31:30 on modular [Seed = 307350775] ------------------------------------- Z.1 Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host proxy1.cc.biu.ac.il. (132.70.9.117) Time: Tue Jan 13 02:31:56 2004 Input: Z:=BraidGroup(6); u:=Z.1; u; u:=Z.1*Z.2; u:=Z.1*Z.2*Z.1; v:=Z.2*Z.1*Z.2; y:=NormalForm(u*v^(-1)); Output: Magma V2.10-6 Tue Jan 13 2004 02:31:53 on modular [Seed = 256692689] ------------------------------------- Z.1 Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host proxy1.cc.biu.ac.il. (132.70.9.117) Time: Tue Jan 13 02:32:12 2004 Input: Z:=BraidGroup(6); u:=Z.1; u; u:=Z.1*Z.2; u:=Z.1*Z.2*Z.1; v:=Z.2*Z.1*Z.2; y:=NormalForm(u*v^(-1)); y; Output: Magma V2.10-6 Tue Jan 13 2004 02:32:09 on modular [Seed = 1932570045] ------------------------------------- Z.1 Id(Z) Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host proxy1.cc.biu.ac.il. (132.70.9.117) Time: Tue Jan 13 02:32:57 2004 Input: Z:=BraidGroup(6); u:=Z.1; u; u:=Z.1*Z.2; u:=Z.1*Z.2*Z.1; v:=Z.2*Z.1*Z.2; y:=NormalForm(u*v^(-1)); y; A:=Z.1; Output: Magma V2.10-6 Tue Jan 13 2004 02:32:54 on modular [Seed = 2050598251] ------------------------------------- Z.1 Id(Z) Total time: 3.039 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host proxy1.cc.biu.ac.il. (132.70.9.117) Time: Tue Jan 13 02:33:19 2004 Input: Z:=BraidGroup(6); u:=Z.1; u; u:=Z.1*Z.2; u:=Z.1*Z.2*Z.1; v:=Z.2*Z.1*Z.2; y:=NormalForm(u*v^(-1)); y; A:=Z.1; A; Output: Magma V2.10-6 Tue Jan 13 2004 02:33:16 on modular [Seed = 1747695459] ------------------------------------- Z.1 Id(Z) Z.1 Total time: 2.979 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (212.205.76.74) Time: Tue Jan 13 02:42:59 2004 Input: 1/0.; Output: Magma V2.10-6 Tue Jan 13 2004 02:42:56 on modular [Seed = 4122350658] ------------------------------------- >> 1/0.;; ^ User error: Real literal has no digits after decimal point Total time: 3.029 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (212.205.76.74) Time: Tue Jan 13 02:43:20 2004 Input: 1.0/0.0; Output: Magma V2.10-6 Tue Jan 13 2004 02:43:17 on modular [Seed = 4240383326] ------------------------------------- >> 1.0/0.0;; ^ Runtime error in '/': Division by zero Total time: 2.939 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (212.205.76.74) Time: Tue Jan 13 02:44:35 2004 Input: Sqrt(-1); Output: Magma V2.10-6 Tue Jan 13 2004 02:44:32 on modular [Seed = 3936947005] ------------------------------------- 1.0000000000000000000000000000*i Total time: 2.919 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (212.205.76.74) Time: Tue Jan 13 02:55:54 2004 Input: farey := func< n | Sort(Setseq({ a/b : a in {0..n}, b in {1..n} | a le b }))>; farey(100); Output: Magma V2.10-6 Tue Jan 13 2004 02:55:51 on modular [Seed = 3381276025] ------------------------------------- [ 0, 1/100, 1/99, 1/98, 1/97, 1/96, 1/95, 1/94, 1/93, 1/92, 1/91, 1/90, 1/89, 1/88, 1/87, 1/86, 1/85, 1/84, 1/83, 1/82, 1/81, 1/80, 1/79, 1/78, 1/77, 1/76, 1/75, 1/74, 1/73, 1/72, 1/71, 1/70, 1/69, 1/68, 1/67, 1/66, 1/65, 1/64, 1/63, 1/62, 1/61, 1/60, 1/59, 1/58, 1/57, 1/56, 1/55, 1/54, 1/53, 1/52, 1/51, 1/50, 2/99, 1/49, 2/97, 1/48, 2/95, 1/47, 2/93, 1/46, 2/91, 1/45, 2/89, 1/44, 2/87, 1/43, 2/85, 1/42, 2/83, 1/41, 2/81, 1/40, 2/79, 1/39, 2/77, 1/38, 2/75, 1/37, 2/73, 1/36, 2/71, 1/35, 2/69, 1/34, 2/67, 3/100, 1/33, 3/98, 2/65, 3/97, 1/32, 3/95, 2/63, 3/94, 1/31, 3/92, 2/61, 3/91, 1/30, 3/89, 2/59, 3/88, 1/29, 3/86, 2/57, 3/85, 1/28, 3/83, 2/55, 3/82, 1/27, 3/80, 2/53, 3/79, 1/26, 3/77, 2/51, 3/76, 1/25, 4/99, 3/74, 2/49, 3/73, 4/97, 1/24, 4/95, 3/71, 2/47, 3/70, 4/93, 1/23, 4/91, 3/68, 2/45, 3/67, 4/89, 1/22, 4/87, 3/65, 2/43, 3/64, 4/85, 1/21, 4/83, 3/62, 2/41, 3/61, 4/81, 1/20, 5/99, 4/79, 3/59, 5/98, 2/39, 5/97, 3/58, 4/77, 5/96, 1/19, 5/94, 4/75, 3/56, 5/93, 2/37, 5/92, 3/55, 4/73, 5/91, 1/18, 5/89, 4/71, 3/53, 5/88, 2/35, 5/87, 3/52, 4/69, 5/86, 1/17, 5/84, 4/67, 3/50, 5/83, 2/33, 5/82, 3/49, 4/65, 5/81, 6/97, 1/16, 6/95, 5/79, 4/63, 3/47, 5/78, 2/31, 5/77, 3/46, 4/61, 5/76, 6/91, 1/15, 6/89, 5/74, 4/59, 3/44, 5/73, 2/29, 5/72, 3/43, 7/100, 4/57, 5/71, 6/85, 7/99, 1/14, 7/97, 6/83, 5/69, 4/55, 7/96, 3/41, 5/68, 7/95, 2/27, 7/94, 5/67, 3/40, 7/93, 4/53, 5/66, 6/79, 7/92, 1/13, 7/90, 6/77, 5/64, 4/51, 7/89, 3/38, 5/63, 7/88, 2/25, 7/87, 5/62, 8/99, 3/37, 7/86, 4/49, 5/61, 6/73, 7/85, 8/97, 1/12, 8/95, 7/83, 6/71, 5/59, 4/47, 7/82, 3/35, 8/93, 5/58, 7/81, 2/23, 7/80, 5/57, 8/91, 3/34, 7/79, 4/45, 5/56, 6/67, 7/78, 8/89, 9/100, 1/11, 9/98, 8/87, 7/76, 6/65, 5/54, 9/97, 4/43, 7/75, 3/32, 8/85, 5/53, 7/74, 9/95, 2/21, 9/94, 7/73, 5/52, 8/83, 3/31, 7/72, 4/41, 9/92, 5/51, 6/61, 7/71, 8/81, 9/91, 1/10, 10/99, 9/89, 8/79, 7/69, 6/59, 5/49, 9/88, 4/39, 7/68, 10/97, 3/29, 8/77, 5/48, 7/67, 9/86, 2/19, 9/85, 7/66, 5/47, 8/75, 3/28, 10/93, 7/65, 4/37, 9/83, 5/46, 6/55, 7/64, 8/73, 9/82, 10/91, 11/100, 1/9, 11/98, 10/89, 9/80, 8/71, 7/62, 6/53, 11/97, 5/44, 9/79, 4/35, 11/96, 7/61, 10/87, 3/26, 11/95, 8/69, 5/43, 7/60, 9/77, 11/94, 2/17, 11/93, 9/76, 7/59, 5/42, 8/67, 11/92, 3/25, 10/83, 7/58, 11/91, 4/33, 9/74, 5/41, 11/90, 6/49, 7/57, 8/65, 9/73, 10/81, 11/89, 12/97, 1/8, 12/95, 11/87, 10/79, 9/71, 8/63, 7/55, 6/47, 11/86, 5/39, 9/70, 4/31, 11/85, 7/54, 10/77, 13/100, 3/23, 11/84, 8/61, 13/99, 5/38, 12/91, 7/53, 9/68, 11/83, 13/98, 2/15, 13/97, 11/82, 9/67, 7/52, 12/89, 5/37, 13/96, 8/59, 11/81, 3/22, 13/95, 10/73, 7/51, 11/80, 4/29, 13/94, 9/65, 5/36, 11/79, 6/43, 13/93, 7/50, 8/57, 9/64, 10/71, 11/78, 12/85, 13/92, 14/99, 1/7, 14/97, 13/90, 12/83, 11/76, 10/69, 9/62, 8/55, 7/48, 13/89, 6/41, 11/75, 5/34, 14/95, 9/61, 13/88, 4/27, 11/74, 7/47, 10/67, 13/87, 3/20, 14/93, 11/73, 8/53, 13/86, 5/33, 12/79, 7/46, 9/59, 11/72, 13/85, 15/98, 2/13, 15/97, 13/84, 11/71, 9/58, 7/45, 12/77, 5/32, 13/83, 8/51, 11/70, 14/89, 3/19, 13/82, 10/63, 7/44, 11/69, 15/94, 4/25, 13/81, 9/56, 14/87, 5/31, 16/99, 11/68, 6/37, 13/80, 7/43, 15/92, 8/49, 9/55, 10/61, 11/67, 12/73, 13/79, 14/85, 15/91, 16/97, 1/6, 16/95, 15/89, 14/83, 13/77, 12/71, 11/65, 10/59, 9/53, 17/100, 8/47, 15/88, 7/41, 13/76, 6/35, 17/99, 11/64, 16/93, 5/29, 14/81, 9/52, 13/75, 17/98, 4/23, 15/86, 11/63, 7/40, 17/97, 10/57, 13/74, 16/91, 3/17, 17/96, 14/79, 11/62, 8/45, 13/73, 5/28, 17/95, 12/67, 7/39, 16/89, 9/50, 11/61, 13/72, 15/83, 17/94, 2/11, 17/93, 15/82, 13/71, 11/60, 9/49, 16/87, 7/38, 12/65, 17/92, 5/27, 18/97, 13/70, 8/43, 11/59, 14/75, 17/91, 3/16, 16/85, 13/69, 10/53, 17/90, 7/37, 18/95, 11/58, 15/79, 19/100, 4/21, 17/89, 13/68, 9/47, 14/73, 19/99, 5/26, 16/83, 11/57, 17/88, 6/31, 19/98, 13/67, 7/36, 15/77, 8/41, 17/87, 9/46, 19/97, 10/51, 11/56, 12/61, 13/66, 14/71, 15/76, 16/81, 17/86, 18/91, 19/96, 1/5, 20/99, 19/94, 18/89, 17/84, 16/79, 15/74, 14/69, 13/64, 12/59, 11/54, 10/49, 19/93, 9/44, 17/83, 8/39, 15/73, 7/34, 20/97, 13/63, 19/92, 6/29, 17/82, 11/53, 16/77, 5/24, 19/91, 14/67, 9/43, 13/62, 17/81, 21/100, 4/19, 19/90, 15/71, 11/52, 18/85, 7/33, 17/80, 10/47, 13/61, 16/75, 19/89, 3/14, 20/93, 17/79, 14/65, 11/51, 19/88, 8/37, 21/97, 13/60, 18/83, 5/23, 17/78, 12/55, 19/87, 7/32, 16/73, 9/41, 20/91, 11/50, 13/59, 15/68, 17/77, 19/86, 21/95, 2/9, 21/94, 19/85, 17/76, 15/67, 13/58, 11/49, 20/89, 9/40, 16/71, 7/31, 19/84, 12/53, 17/75, 22/97, 5/22, 18/79, 13/57, 21/92, 8/35, 19/83, 11/48, 14/61, 17/74, 20/87, 23/100, 3/13, 22/95, 19/82, 16/69, 13/56, 23/99, 10/43, 17/73, 7/30, 18/77, 11/47, 15/64, 19/81, 23/98, 4/17, 21/89, 17/72, 13/55, 22/93, 9/38, 23/97, 14/59, 19/80, 5/21, 21/88, 16/67, 11/46, 17/71, 23/96, 6/25, 19/79, 13/54, 20/83, 7/29, 22/91, 15/62, 23/95, 8/33, 17/70, 9/37, 19/78, 10/41, 21/86, 11/45, 23/94, 12/49, 13/53, 14/57, 15/61, 16/65, 17/69, 18/73, 19/77, 20/81, 21/85, 22/89, 23/93, 24/97, 1/4, 25/99, 24/95, 23/91, 22/87, 21/83, 20/79, 19/75, 18/71, 17/67, 16/63, 15/59, 14/55, 13/51, 25/98, 12/47, 23/90, 11/43, 21/82, 10/39, 19/74, 9/35, 17/66, 25/97, 8/31, 23/89, 15/58, 22/85, 7/27, 20/77, 13/50, 19/73, 25/96, 6/23, 23/88, 17/65, 11/42, 16/61, 21/80, 26/99, 5/19, 24/91, 19/72, 14/53, 23/87, 9/34, 22/83, 13/49, 17/64, 21/79, 25/94, 4/15, 23/86, 19/71, 15/56, 26/97, 11/41, 18/67, 25/93, 7/26, 24/89, 17/63, 27/100, 10/37, 23/85, 13/48, 16/59, 19/70, 22/81, 25/92, 3/11, 26/95, 23/84, 20/73, 17/62, 14/51, 25/91, 11/40, 19/69, 27/98, 8/29, 21/76, 13/47, 18/65, 23/83, 5/18, 27/97, 22/79, 17/61, 12/43, 19/68, 26/93, 7/25, 23/82, 16/57, 25/89, 9/32, 20/71, 11/39, 24/85, 13/46, 28/99, 15/53, 17/60, 19/67, 21/74, 23/81, 25/88, 27/95, 2/7, 27/94, 25/87, 23/80, 21/73, 19/66, 17/59, 15/52, 28/97, 13/45, 24/83, 11/38, 20/69, 29/100, 9/31, 25/86, 16/55, 23/79, 7/24, 26/89, 19/65, 12/41, 29/99, 17/58, 22/75, 27/92, 5/17, 28/95, 23/78, 18/61, 13/44, 21/71, 29/98, 8/27, 27/91, 19/64, 11/37, 25/84, 14/47, 17/57, 20/67, 23/77, 26/87, 29/97, 3/10, 28/93, 25/83, 22/73, 19/63, 16/53, 29/96, 13/43, 23/76, 10/33, 27/89, 17/56, 24/79, 7/23, 25/82, 18/59, 29/95, 11/36, 26/85, 15/49, 19/62, 23/75, 27/88, 4/13, 29/94, 25/81, 21/68, 17/55, 30/97, 13/42, 22/71, 31/100, 9/29, 23/74, 14/45, 19/61, 24/77, 29/93, 5/16, 31/99, 26/83, 21/67, 16/51, 27/86, 11/35, 28/89, 17/54, 23/73, 29/92, 6/19, 31/98, 25/79, 19/60, 13/41, 20/63, 27/85, 7/22, 29/91, 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11/30, 29/79, 18/49, 25/68, 32/87, 7/19, 31/84, 24/65, 17/46, 27/73, 37/100, 10/27, 33/89, 23/62, 36/97, 13/35, 29/78, 16/43, 35/94, 19/51, 22/59, 25/67, 28/75, 31/83, 34/91, 37/99, 3/8, 35/93, 32/85, 29/77, 26/69, 23/61, 20/53, 37/98, 17/45, 31/82, 14/37, 25/66, 36/95, 11/29, 30/79, 19/50, 27/71, 35/92, 8/21, 37/97, 29/76, 21/55, 34/89, 13/34, 31/81, 18/47, 23/60, 28/73, 33/86, 38/99, 5/13, 37/96, 32/83, 27/70, 22/57, 17/44, 29/75, 12/31, 31/80, 19/49, 26/67, 33/85, 7/18, 37/95, 30/77, 23/59, 39/100, 16/41, 25/64, 34/87, 9/23, 38/97, 29/74, 20/51, 31/79, 11/28, 35/89, 24/61, 37/94, 13/33, 28/71, 15/38, 32/81, 17/43, 36/91, 19/48, 21/53, 23/58, 25/63, 27/68, 29/73, 31/78, 33/83, 35/88, 37/93, 39/98, 2/5, 39/97, 37/92, 35/87, 33/82, 31/77, 29/72, 27/67, 25/62, 23/57, 21/52, 40/99, 19/47, 36/89, 17/42, 32/79, 15/37, 28/69, 13/32, 37/91, 24/59, 35/86, 11/27, 31/76, 20/49, 29/71, 38/93, 9/22, 34/83, 25/61, 41/100, 16/39, 39/95, 23/56, 30/73, 37/90, 7/17, 40/97, 33/80, 26/63, 19/46, 31/75, 12/29, 41/99, 29/70, 17/41, 39/94, 22/53, 27/65, 32/77, 37/89, 5/12, 38/91, 33/79, 28/67, 23/55, 41/98, 18/43, 31/74, 13/31, 34/81, 21/50, 29/69, 37/88, 8/19, 35/83, 27/64, 19/45, 30/71, 41/97, 11/26, 36/85, 25/59, 39/92, 14/33, 31/73, 17/40, 37/87, 20/47, 23/54, 26/61, 29/68, 32/75, 35/82, 38/89, 41/96, 3/7, 43/100, 40/93, 37/86, 34/79, 31/72, 28/65, 25/58, 22/51, 41/95, 19/44, 35/81, 16/37, 29/67, 42/97, 13/30, 36/83, 23/53, 33/76, 43/99, 10/23, 37/85, 27/62, 17/39, 41/94, 24/55, 31/71, 38/87, 7/16, 39/89, 32/73, 25/57, 43/98, 18/41, 29/66, 40/91, 11/25, 37/84, 26/59, 41/93, 15/34, 34/77, 19/43, 42/95, 23/52, 27/61, 31/70, 35/79, 39/88, 43/97, 4/9, 41/92, 37/83, 33/74, 29/65, 25/56, 21/47, 38/85, 17/38, 30/67, 43/96, 13/29, 35/78, 22/49, 31/69, 40/89, 9/20, 41/91, 32/71, 23/51, 37/82, 14/31, 33/73, 19/42, 43/95, 24/53, 29/64, 34/75, 39/86, 44/97, 5/11, 41/90, 36/79, 31/68, 26/57, 21/46, 37/81, 16/35, 43/94, 27/59, 38/83, 11/24, 39/85, 28/61, 45/98, 17/37, 40/87, 23/50, 29/63, 35/76, 41/89, 6/13, 43/93, 37/80, 31/67, 25/54, 44/95, 19/41, 32/69, 45/97, 13/28, 46/99, 33/71, 20/43, 27/58, 34/73, 41/88, 7/15, 43/92, 36/77, 29/62, 22/47, 37/79, 15/32, 38/81, 23/49, 31/66, 39/83, 47/100, 8/17, 41/87, 33/70, 25/53, 42/89, 17/36, 43/91, 26/55, 35/74, 44/93, 9/19, 46/97, 37/78, 28/59, 47/99, 19/40, 29/61, 39/82, 10/21, 41/86, 31/65, 21/44, 32/67, 43/90, 11/23, 45/94, 34/71, 23/48, 35/73, 47/98, 12/25, 37/77, 25/52, 38/79, 13/27, 40/83, 27/56, ** WARNING: Output too long, hence truncated. ************** MAGMA ***************** Host 3(NXDOMAIN) (212.205.76.74) Time: Tue Jan 13 02:57:04 2004 Input: > farey(3); Output: Magma V2.10-6 Tue Jan 13 2004 02:57:01 on modular [Seed = 812897477] ------------------------------------- >> farey(3);; ^ User error: Identifier 'farey' has not been declared or assigned Total time: 2.999 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (212.205.76.74) Time: Tue Jan 13 02:57:59 2004 Input: farey := func< n | Sort(Setseq({ a/b : a in {0..n}, b in {1..n} | a le b }))farey(3); Output: Magma V2.10-6 Tue Jan 13 2004 02:57:56 on modular [Seed = 711577366] ------------------------------------- >> n {1..n} | a le b }))farey(3);; ^ User error: bad syntax Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (212.205.76.74) Time: Tue Jan 13 02:58:59 2004 Input: farey := func< n | Sort(Setseq({ a/b : a in {0..n}, b in {1..n} | a le b }))>; farey(3); Output: Magma V2.10-6 Tue Jan 13 2004 02:58:56 on modular [Seed = 610779484] ------------------------------------- [ 0, 1/3, 1/2, 2/3, 1 ] Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (212.205.76.74) Time: Tue Jan 13 02:59:16 2004 Input: farey := func< n | Sort(Setseq({ a/b : a in {0..n}, b in {1..n} | a le b }))>; farey(2); Output: Magma V2.10-6 Tue Jan 13 2004 02:59:13 on modular [Seed = 492763252] ------------------------------------- [ 0, 1/2, 1 ] Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (212.205.76.74) Time: Tue Jan 13 02:59:29 2004 Input: farey := func< n | Sort(Setseq({ a/b : a in {0..n}, b in {1..n} | a le b }))>; farey(1); Output: Magma V2.10-6 Tue Jan 13 2004 02:59:26 on modular [Seed = 374731632] ------------------------------------- [ 0, 1 ] Total time: 2.919 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (212.205.76.74) Time: Tue Jan 13 02:59:41 2004 Input: farey := func< n | Sort(Setseq({ a/b : a in {0..n}, b in {1..n} | a le b }))>; farey(0); Output: Magma V2.10-6 Tue Jan 13 2004 02:59:38 on modular [Seed = 256698973] ------------------------------------- [] Total time: 2.979 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (212.205.76.74) Time: Tue Jan 13 03:00:17 2004 Input: farey := func< n | Sort(Setseq({ a/b : a in {0..n}, b in {1..n} | a le b }))>; farey(-3); Output: Magma V2.10-6 Tue Jan 13 2004 03:00:14 on modular [Seed = 2134678217] ------------------------------------- [] Total time: 2.889 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (212.205.76.74) Time: Tue Jan 13 03:00:39 2004 Input: farey := func< n | Sort(Setseq({ a/b : a in {0..n}, b in {1..n} | a le b }))>; farey(4); Output: Magma V2.10-6 Tue Jan 13 2004 03:00:36 on modular [Seed = 1747684852] ------------------------------------- [ 0, 1/4, 1/3, 1/2, 2/3, 3/4, 1 ] Total time: 2.989 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (212.205.76.74) Time: Tue Jan 13 03:01:29 2004 Input: farey := func< n | Sort(Setseq({ a/b : a in {0..n}, b in {1..n} | a le b }))>; farey(5); Output: Magma V2.10-6 Tue Jan 13 2004 03:01:26 on modular [Seed = 1393604285] ------------------------------------- [ 0, 1/5, 1/4, 1/3, 2/5, 1/2, 3/5, 2/3, 3/4, 4/5, 1 ] Total time: 2.909 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (212.205.76.74) Time: Tue Jan 13 03:03:46 2004 Input: farey := func< n | Sort(Setseq({ a/b : a in {-n..n}, b in {-n..n} | a le b }))>; farey(5); Output: Magma V2.10-6 Tue Jan 13 2004 03:03:43 on modular [Seed = 1292806954] ------------------------------------- [

:3]( n: 5 ) >> farey := func< n | Sort(Setseq({ a/b : a in {-n..n}, b in {-n..n} | a le b ^ Runtime error in '/': Division by zero Total time: 2.979 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (212.205.76.74) Time: Tue Jan 13 03:05:35 2004 Input: farey := func< n | Sort(Setseq({ a/b : a in {-n..n}, b in {1..n} | a le b }))>; farey(5); Output: Magma V2.10-6 Tue Jan 13 2004 03:05:32 on modular [Seed = 3136904270] ------------------------------------- [ -5, -4, -3, -5/2, -2, -5/3, -3/2, -4/3, -5/4, -1, -4/5, -3/4, -2/3, -3/5, -1/2, -2/5, -1/3, -1/4, -1/5, 0, 1/5, 1/4, 1/3, 2/5, 1/2, 3/5, 2/3, 3/4, 4/5, 1 ] Total time: 3.019 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (212.205.76.74) Time: Tue Jan 13 03:29:36 2004 Input: Xgcd(12, 15); Output: Magma V2.10-6 Tue Jan 13 2004 03:29:33 on modular [Seed = 2463203015] ------------------------------------- 3 -1 1 Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (212.205.76.74) Time: Tue Jan 13 03:35:56 2004 Input: m,n:=12,5 d,x,m:=Xgcd(m, n); d;"=";x;"*";m;" + ";y;"*";n; Output: Magma V2.10-6 Tue Jan 13 2004 03:35:53 on modular [Seed = 4206434091] ------------------------------------- >> m,n:=12,5 ^ User error: bad syntax >> d,x,m:=Xgcd(m, n); ^ User error: Identifier 'm' has not been declared or assigned >> d;"=";x;"*";m;" + ";y;"*";n;; ^ User error: Identifier 'd' has not been declared or assigned = >> d;"=";x;"*";m;" + ";y;"*";n;; ^ User error: Identifier 'x' has not been declared or assigned * >> d;"=";x;"*";m;" + ";y;"*";n;; ^ User error: Identifier 'm' has not been declared or assigned + >> d;"=";x;"*";m;" + ";y;"*";n;; ^ User error: Identifier 'y' has not been declared or assigned * >> d;"=";x;"*";m;" + ";y;"*";n;; ^ User error: Identifier 'n' has not been declared or assigned Total time: 2.939 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (212.205.76.74) Time: Tue Jan 13 03:39:29 2004 Input: m := 12; n := 5; d, x, y := Xgcd(m, n); d;"=";x;"*";m;" + ";y;"*";n; Output: Magma V2.10-6 Tue Jan 13 2004 03:39:26 on modular [Seed = 4105640562] ------------------------------------- 1 = -2 * 12 + 5 * 5 Total time: 2.979 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (212.205.76.74) Time: Tue Jan 13 03:41:36 2004 Input: m := 12; n := 5; d, x, y := Xgcd(m, n); print d, "=", x, "*", m, " + ", y, "*", n; Output: Magma V2.10-6 Tue Jan 13 2004 03:41:33 on modular [Seed = 3836152801] ------------------------------------- 1 = -2 * 12 + 5 * 5 Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (212.205.76.74) Time: Tue Jan 13 03:42:25 2004 Input: m := 12; n := 4; d, x, y := Xgcd(m, n); print d, "=", x, "*", m, " + ", y, "*", n; Output: Magma V2.10-6 Tue Jan 13 2004 03:42:22 on modular [Seed = 3734843784] ------------------------------------- 4 = 0 * 12 + 1 * 4 Total time: 3.009 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (212.205.76.74) Time: Tue Jan 13 03:43:18 2004 Input: m := 120; n := 36; d, x, y := Xgcd(m, n); print d, "=", x, "*", m, " + ", y, "*", n; Output: Magma V2.10-6 Tue Jan 13 2004 03:43:15 on modular [Seed = 3616815180] ------------------------------------- 12 = 1 * 120 + -3 * 36 Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (212.205.76.74) Time: Tue Jan 13 03:44:01 2004 Input: m, n := 120, 36; d, x, y := Xgcd(m, n); print d, "=", x, "*", m, " + ", y, "*", n; Output: Magma V2.10-6 Tue Jan 13 2004 03:43:58 on modular [Seed = 3229822774] ------------------------------------- >> m, n := 120, 36; ^ User error: bad syntax >> d, x, y := Xgcd(m, n); ^ User error: Identifier 'm' has not been declared or assigned >> print d, "=", x, "*", m, " + ", y, "*", n;; ^ User error: Identifier 'd' has not been declared or assigned Total time: 2.979 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host proxy1.cc.biu.ac.il. (132.70.9.117) Time: Tue Jan 13 05:56:57 2004 Input: Br:=BraidGroup(6); Output: Magma V2.10-6 Tue Jan 13 2004 05:56:53 on modular [Seed = 3229830670] ------------------------------------- Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host proxy1.cc.biu.ac.il. (132.70.9.117) Time: Tue Jan 13 05:57:12 2004 Input: Br:=BraidGroup(6); Br; Output: Magma V2.10-6 Tue Jan 13 2004 05:57:08 on modular [Seed = 947631872] ------------------------------------- GrpBrd : Br on 6 strings Total time: 2.989 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host proxy1.cc.biu.ac.il. (132.70.9.117) Time: Tue Jan 13 05:58:01 2004 Input: Br:=BraidGroup(6); Br; Br:=BraidGroup(6); Output: Magma V2.10-6 Tue Jan 13 2004 05:57:58 on modular [Seed = 829603387] ------------------------------------- GrpBrd : Br on 6 strings Total time: 3.189 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host proxy1.cc.biu.ac.il. (132.70.9.117) Time: Tue Jan 13 05:58:17 2004 Input: Br:=BraidGroup(6); Br; Br:=BraidGroup(6); Br; Output: Magma V2.10-6 Tue Jan 13 2004 05:58:14 on modular [Seed = 593538137] ------------------------------------- GrpBrd : Br on 6 strings GrpBrd : Br on 6 strings Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host proxy1.cc.biu.ac.il. (132.70.9.117) Time: Tue Jan 13 05:59:08 2004 Input: Br:=BraidGroup(6); Br; Br:=BraidGroup(6); Br; v=a*b*a*(b*a*b)^-1; Output: Magma V2.10-6 Tue Jan 13 2004 05:59:05 on modular [Seed = 139167565] ------------------------------------- GrpBrd : Br on 6 strings GrpBrd : Br on 6 strings >> v=a*b*a*(b*a*b)^-1;; ^ User error: Identifier 'v' has not been declared or assigned Total time: 2.929 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (212.128.18.14) Time: Tue Jan 13 05:59:21 2004 Input: P2 := ProjectiveSpace(RationalField(),2); C := Conic(P2,y^2-4*x*y-3*x^2+4*y*z+8*x*z-5*z^2); HasRationalPoint(C); fac := Factorization(Integers()!Discriminant(C)); Output: Magma V2.10-6 Tue Jan 13 2004 05:59:17 on modular [Seed = 21139128] ------------------------------------- true (13/21 : 4/7 : 1) Total time: 3.489 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host proxy1.cc.biu.ac.il. (132.70.9.117) Time: Tue Jan 13 05:59:22 2004 Input: Br:=BraidGroup(6); Br; Br:=BraidGroup(6); Br; v:=a*b*a*(b*a*b)^-1; Output: Magma V2.10-6 Tue Jan 13 2004 05:59:18 on modular [Seed = 2084565958] ------------------------------------- GrpBrd : Br on 6 strings GrpBrd : Br on 6 strings Total time: 3.539 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host proxy1.cc.biu.ac.il. (132.70.9.117) Time: Tue Jan 13 05:59:53 2004 Input: Br:=BraidGroup(6); Br; Br:=BraidGroup(6); Br; v:=a*b*a*(b*a*b)^-1; v; Output: Magma V2.10-6 Tue Jan 13 2004 05:59:50 on modular [Seed = 1932590313] ------------------------------------- GrpBrd : Br on 6 strings GrpBrd : Br on 6 strings e^-1 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * e^2 * d * c * b * a * d * c * b * e * d * c * e * d * e^2 * d * c * b * a * e * d * c * b * e * d * c * e * d * e * d * c * b * a * d * c * b * e * d * c * e * d * e Total time: 2.909 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host proxy1.cc.biu.ac.il. (132.70.9.117) Time: Tue Jan 13 06:01:03 2004 Input: Br:=BraidGroup(6); Br; Br:=BraidGroup(6); Br; v:=a*b*a*(b*a*b)^-1; v; NormalForm(v); Output: Magma V2.10-6 Tue Jan 13 2004 06:00:57 on modular [Seed = 1595723914] ------------------------------------- GrpBrd : Br on 6 strings GrpBrd : Br on 6 strings e^-1 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * e^2 * d * c * b * a * d * c * b * e * d * c * e * d * e^2 * d * c * b * a * e * d * c * b * e * d * c * e * d * e * d * c * b * a * d * c * b * e * d * c * e * d * e Id(Br) Total time: 3.719 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (212.128.18.14) Time: Tue Jan 13 06:03:56 2004 Input: P2 := ProjectiveSpace(RationalField(),2); C := Conic(P2,y^2-4*x*y-3*x^2+4*y*z+8*x*z-5*z^2); HasRationalPoint(C); fac := Factorization(Integers()!Discriminant(C)); [ NormResidueSymbol(-a/c,-b/c,p[1]) : p in fac ]; Output: Magma V2.10-6 Tue Jan 13 2004 06:03:48 on modular [Seed = 2884123395] ------------------------------------- true (13/21 : 4/7 : 1) >> [ NormResidueSymbol(-a/c,-b/c,p[1]) : p in fac ]; ^ User error: Identifier 'a' has not been declared or assigned Total time: 4.779 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (212.128.18.14) Time: Tue Jan 13 06:04:42 2004 Input: P2 := ProjectiveSpace(RationalField(),2); C := Conic(P2,y^2-4*x*y-3*x^2+4*y*z+8*x*z-5*z^2); HasRationalPoint(C); fac := Factorization(Integers()!Discriminant(C)); NormResidueSymbol; Output: Magma V2.10-6 Tue Jan 13 2004 06:04:39 on modular [Seed = 2311723378] ------------------------------------- true (13/21 : 4/7 : 1) Intrinsic 'NormResidueSymbol' Signatures: ( a, b, p) -> RngIntElt ( a, b, p) -> RngIntElt Returns 1 if ax^2 + by^2 represents a p-adic nonzero square, and otherwise returns -1. Total time: 2.979 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host proxy1.cc.biu.ac.il. (132.70.9.117) Time: Tue Jan 13 06:05:51 2004 Input: Br:=BraidGroup(6); Output: Magma V2.10-6 Tue Jan 13 2004 06:05:47 on modular [Seed = 3667479530] ------------------------------------- Total time: 3.689 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host proxy1.cc.biu.ac.il. (132.70.9.117) Time: Tue Jan 13 06:05:57 2004 Input: Br:=BraidGroup(6); Output: Magma V2.10-6 Tue Jan 13 2004 06:05:54 on modular [Seed = 3549446909] ------------------------------------- Total time: 2.979 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host proxy1.cc.biu.ac.il. (132.70.9.117) Time: Tue Jan 13 06:06:08 2004 Input: Br:=BraidGroup(6); Br; Output: Magma V2.10-6 Tue Jan 13 2004 06:06:05 on modular [Seed = 3297203685] ------------------------------------- GrpBrd : Br on 6 strings Total time: 3.409 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (212.128.18.14) Time: Tue Jan 13 06:06:10 2004 Input: P2 := ProjectiveSpace(RationalField(),2); C := Conic(P2,y^2-4*x*y-3*x^2+4*y*z+8*x*z-5*z^2); HasRationalPoint(C); fac := Factorization(Integers()!Discriminant(C)); LegendreModel(C); Output: Magma V2.10-6 Tue Jan 13 2004 06:06:06 on modular [Seed = 3347338981] ------------------------------------- true (13/21 : 4/7 : 1) Conic over Rational Field defined by -3*x^2 + 21*y^2 + 7*z^2 Mapping from: CrvCon: C to Conic over Rational Field defined by -3*x^2 + 21*y^2 + 7*z^2 with equations : -7*x - 14/3*y + 28/3*z 7/3*y - 2/3*z z and inverse -1/7*x - 2/7*y + 8/7*z 3/7*y + 2/7*z z Total time: 3.489 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host proxy1.cc.biu.ac.il. (132.70.9.117) Time: Tue Jan 13 06:06:26 2004 Input: Br:=BraidGroup(6); Br; v:=ab; Output: Magma V2.10-6 Tue Jan 13 2004 06:06:23 on modular [Seed = 930391589] ------------------------------------- GrpBrd : Br on 6 strings >> v:=ab;; ^ User error: Identifier 'ab' has not been declared or assigned Total time: 2.919 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (212.128.18.14) Time: Tue Jan 13 06:06:53 2004 Input: P2 := ProjectiveSpace(RationalField(),2); C := Conic(P2,y^2-4*x*y-3*x^2+4*y*z+8*x*z-5*z^2); HasRationalPoint(C); fac := Factorization(Integers()!Discriminant(C)); c,m:=LegendreModel(C); c; Output: Magma V2.10-6 Tue Jan 13 2004 06:06:49 on modular [Seed = 560115797] ------------------------------------- true (13/21 : 4/7 : 1) Conic over Rational Field defined by -3*x^2 + 21*y^2 + 7*z^2 Total time: 2.979 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (212.128.18.14) Time: Tue Jan 13 06:07:15 2004 Input: P2 := ProjectiveSpace(RationalField(),2); C := Conic(P2,y^2-4*x*y-3*x^2+4*y*z+8*x*z-5*z^2); HasRationalPoint(C); fac := Factorization(Integers()!Discriminant(C)); c,m:=LegendreModel(C); c; Coeffcients(c); Output: Magma V2.10-6 Tue Jan 13 2004 06:07:11 on modular [Seed = 307331952] ------------------------------------- true (13/21 : 4/7 : 1) Conic over Rational Field defined by -3*x^2 + 21*y^2 + 7*z^2 >> Coeffcients(c);; ^ User error: Identifier 'Coeffcients' has not been declared or assigned Total time: 3.399 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (212.128.18.14) Time: Tue Jan 13 06:11:31 2004 Input: P2 := ProjectiveSpace(RationalField(),2); C := Conic(P2,y^2-4*x*y-3*x^2+4*y*z+8*x*z-5*z^2); HasRationalPoint(C); fac := Factorization(Integers()!Discriminant(C)); c,m:=LegendreModel(C); c; Coefficients(c); Output: Magma V2.10-6 Tue Jan 13 2004 06:11:27 on modular [Seed = 1410844214] ------------------------------------- true (13/21 : 4/7 : 1) Conic over Rational Field defined by -3*x^2 + 21*y^2 + 7*z^2 >> Coefficients(c);; ^ Runtime error in 'Coefficients': Bad argument types Argument types given: CrvCon Total time: 3.759 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host proxy1.cc.biu.ac.il. (132.70.9.117) Time: Tue Jan 13 06:16:20 2004 Input: Br:=BraidGroup(6); Output: Magma V2.10-6 Tue Jan 13 2004 06:16:16 on modular [Seed = 3364576117] ------------------------------------- >> Br:=BraidGroup(6); ^ Runtime error in 'AssignNames': Too many names given for this object Total time: 3.039 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host proxy1.cc.biu.ac.il. (132.70.9.117) Time: Tue Jan 13 06:16:40 2004 Input: Br:=BraidGroup(6); Output: Magma V2.10-6 Tue Jan 13 2004 06:16:37 on modular [Seed = 3279966315] ------------------------------------- >> Br:=BraidGroup(6); ^ Runtime error in 'AssignNames': Too many names given for this object Total time: 2.929 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host proxy1.cc.biu.ac.il. (132.70.9.117) Time: Tue Jan 13 06:16:56 2004 Input: Br:=BraidGroup(6); Output: Magma V2.10-6 Tue Jan 13 2004 06:16:53 on modular [Seed = 964340386] ------------------------------------- Total time: 2.979 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host proxy1.cc.biu.ac.il. (132.70.9.117) Time: Tue Jan 13 06:17:11 2004 Input: Br:=BraidGroup(6); u:=a*b*a; Output: Magma V2.10-6 Tue Jan 13 2004 06:17:08 on modular [Seed = 795655333] ------------------------------------- Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host proxy1.cc.biu.ac.il. (132.70.9.117) Time: Tue Jan 13 06:17:51 2004 Input: Br:=BraidGroup(6); u:=a*b*a; v:=b*a*b; f:=u*v^-1; Output: Magma V2.10-6 Tue Jan 13 2004 06:17:48 on modular [Seed = 610777030] ------------------------------------- Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host proxy1.cc.biu.ac.il. (132.70.9.117) Time: Tue Jan 13 06:18:05 2004 Input: Br:=BraidGroup(6); u:=a*b*a; v:=b*a*b; f:=u*v^-1; f; Output: Magma V2.10-6 Tue Jan 13 2004 06:18:02 on modular [Seed = 492736201] ------------------------------------- e^-1 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * e^2 * d * c * b * a * d * c * b * e * d * c * e * d * e^2 * d * c * b * a * e * d * c * b * e * d * c * e * d * e * d * c * b * a * d * c * b * e * d * c * e * d * e Total time: 2.989 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host proxy1.cc.biu.ac.il. (132.70.9.117) Time: Tue Jan 13 06:18:44 2004 Input: Br:=BraidGroup(6); u:=a*b*a; v:=b*a*b; f:=u*v^-1; f; NormalForm(f); Output: Magma V2.10-6 Tue Jan 13 2004 06:18:41 on modular [Seed = 88510762] ------------------------------------- e^-1 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * e^2 * d * c * b * a * d * c * b * e * d * c * e * d * e^2 * d * c * b * a * e * d * c * b * e * d * c * e * d * e * d * c * b * a * d * c * b * e * d * c * e * d * e Id(Br) Total time: 3.109 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host proxy1.cc.biu.ac.il. (132.70.9.117) Time: Tue Jan 13 06:24:37 2004 Input: S:="aba"; Output: Magma V2.10-6 Tue Jan 13 2004 06:24:34 on modular [Seed = 1815083296] ------------------------------------- Total time: 2.989 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host proxy1.cc.biu.ac.il. (132.70.9.117) Time: Tue Jan 13 06:24:51 2004 Input: S:="aba"; S[2] Output: Magma V2.10-6 Tue Jan 13 2004 06:24:48 on modular [Seed = 1697050843] ------------------------------------- b Total time: 2.929 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (212.128.18.14) Time: Tue Jan 13 06:55:01 2004 Input: P2 := ProjectiveSpace(RationalField(),2); C := Conic(P2,y^2-4*x*y-3*x^2+4*y*z+8*x*z-5*z^2); HasRationalPoint(C); fac := Factorization(Integers()!Discriminant(C)); c,m:=LegendreModel(C); c; ReducedLegendreModel(C); Output: Magma V2.10-6 Tue Jan 13 2004 06:54:57 on modular [Seed = 3018862364] ------------------------------------- true (13/21 : 4/7 : 1) Conic over Rational Field defined by -3*x^2 + 21*y^2 + 7*z^2 Conic over Rational Field defined by -7*x^2 + y^2 + 3*z^2 Mapping from: CrvCon: C to Conic over Rational Field defined by -7*x^2 + y^2 + 3*z^2 with equations : -3*x - 2*y + 4*z 7*y - 2*z z and inverse -1/3*x - 2/21*y + 8/7*z 1/7*y + 2/7*z z Total time: 3.079 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (212.128.18.14) Time: Tue Jan 13 06:55:16 2004 Input: P2 := ProjectiveSpace(RationalField(),2); C := Conic(P2,y^2-4*x*y-3*x^2+4*y*z+8*x*z-5*z^2); HasRationalPoint(C); fac := Factorization(Integers()!Discriminant(C)); c,m:=LegendreModel(C); c; cc,mm:=ReducedLegendreModel(C); Output: Magma V2.10-6 Tue Jan 13 2004 06:55:13 on modular [Seed = 2766616635] ------------------------------------- true (13/21 : 4/7 : 1) Conic over Rational Field defined by -3*x^2 + 21*y^2 + 7*z^2 Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (212.128.18.14) Time: Tue Jan 13 06:55:34 2004 Input: P2 := ProjectiveSpace(RationalField(),2); C := Conic(P2,y^2-4*x*y-3*x^2+4*y*z+8*x*z-5*z^2); HasRationalPoint(C); fac := Factorization(Integers()!Discriminant(C)); c,m:=LegendreModel(C); c; cc,mm:=ReducedLegendreModel(C); cc; Output: Magma V2.10-6 Tue Jan 13 2004 06:55:31 on modular [Seed = 2648572176] ------------------------------------- true (13/21 : 4/7 : 1) Conic over Rational Field defined by -3*x^2 + 21*y^2 + 7*z^2 Conic over Rational Field defined by -7*x^2 + y^2 + 3*z^2 Total time: 3.009 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (212.128.18.14) Time: Tue Jan 13 07:59:30 2004 Input: P2 := ProjectiveSpace(RationalField(),2); C := Conic(P2,y^2-4*x*y-3*x^2+4*y*z+8*x*z-5*z^2); HasRationalPoint(C); cc,mm:=ReducedLegendreModel(C); cc; RationalPoints(cc); Output: Magma V2.10-6 Tue Jan 13 2004 07:59:27 on modular [Seed = 678134712] ------------------------------------- true (13/21 : 4/7 : 1) Conic over Rational Field defined by -7*x^2 + y^2 + 3*z^2 >> RationalPoints(cc); ; ^ Runtime error in 'RationalPoints': A positive naive height bound must be given Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (212.128.18.14) Time: Tue Jan 13 07:59:46 2004 Input: P2 := ProjectiveSpace(RationalField(),2); C := Conic(P2,y^2-4*x*y-3*x^2+4*y*z+8*x*z-5*z^2); HasRationalPoint(C); cc,mm:=ReducedLegendreModel(C); cc; RationalPoints(cc,10); Output: Magma V2.10-6 Tue Jan 13 2004 07:59:43 on modular [Seed = 526169247] ------------------------------------- true (13/21 : 4/7 : 1) Conic over Rational Field defined by -7*x^2 + y^2 + 3*z^2 >> RationalPoints(cc,10); ; ^ Runtime error in 'RationalPoints': Bad argument types Argument types given: CrvCon, RngIntElt Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (212.128.18.14) Time: Tue Jan 13 08:00:19 2004 Input: P2 := ProjectiveSpace(RationalField(),2); C := Conic(P2,y^2-4*x*y-3*x^2+4*y*z+8*x*z-5*z^2); HasRationalPoint(C); cc,mm:=ReducedLegendreModel(C); cc; RationalPoints(cc : Bound := 32); Output: Magma V2.10-6 Tue Jan 13 2004 08:00:16 on modular [Seed = 223258322] ------------------------------------- true (13/21 : 4/7 : 1) Conic over Rational Field defined by -7*x^2 + y^2 + 3*z^2 {@ (-31 : 82 : 1), (-31 : -82 : 1), (-14 : 37 : 1), (-14 : -37 : 1), (-2 : 5 : 1), (-2 : -5 : 1), (-1 : 2 : 1), (-1 : -2 : 1), (1 : 2 : 1), (1 : -2 : 1), (2 : 5 : 1), (2 : -5 : 1), (14 : 37 : 1), (14 : -37 : 1), (31 : 82 : 1), (31 : -82 : 1), (-19/3 : 50/3 : 1), (-19/3 : -50/3 : 1), (-13/3 : 34/3 : 1), (-13/3 : -34/3 : 1), (-2/3 : 1/3 : 1), (-2/3 : -1/3 : 1), (2/3 : 1/3 : 1), (2/3 : -1/3 : 1), (13/3 : 34/3 : 1), (13/3 : -34/3 : 1), (19/3 : 50/3 : 1), (19/3 : -50/3 : 1), (-26/9 : 67/9 : 1), (-26/9 : -67/9 : 1), (-7/9 : 10/9 : 1), (-7/9 : -10/9 : 1), (7/9 : 10/9 : 1), (7/9 : -10/9 : 1), (26/9 : 67/9 : 1), (26/9 : -67/9 : 1), (-14/19 : 17/19 : 1), (-14/19 : -17/19 : 1), (-13/19 : 10/19 : 1), (-13/19 : -10/19 : 1), (13/19 : 10/19 : 1), (13/19 : -10/19 : 1), (14/19 : 17/19 : 1), (14/19 : -17/19 : 1), (-26/29 : 47/29 : 1), (-26/29 : -47/29 : 1), (-19/29 : 2/29 : 1), (-19/29 : -2/29 : 1), (19/29 : 2/29 : 1), (19/29 : -2/29 : 1), (26/29 : 47/29 : 1), (26/29 : -47/29 : 1), (-26/31 : 43/31 : 1), (-26/31 : -43/31 : 1), (26/31 : 43/31 : 1), (26/31 : -43/31 : 1) @} Total time: 2.969 seconds, Total memory usage: 29.50MB ************** MAGMA ***************** Host 3(NXDOMAIN) (212.128.18.14) Time: Tue Jan 13 08:01:21 2004 Input: P2 := ProjectiveSpace(RationalField(),2); C := Conic(P2,y^2-4*x*y-3*x^2+4*y*z+8*x*z-5*z^2); HasRationalPoint(C); cc,mm:=ReducedLegendreModel(C); cc; Parametrization(cc); Output: Magma V2.10-6 Tue Jan 13 2004 08:01:18 on modular [Seed = 1915870803] ------------------------------------- true (13/21 : 4/7 : 1) Conic over Rational Field defined by -7*x^2 + y^2 + 3*z^2 Mapping from: Projective Space of dimension 1 Variables : $.1, $.2 to CrvCon: cc with equations : -$.1^2 - 3*$.2^2 -2*$.1^2 - 6*$.1*$.2 + 6*$.2^2 $.1^2 - 4*$.1*$.2 - 3*$.2^2 and inverse 7*x + 2*y - 3*z y + 2*z and alternative inverse equations : 3/7*y + 6/7*z x - 2/7*y + 3/7*z Total time: 3.039 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (212.128.18.14) Time: Tue Jan 13 08:03:09 2004 Input: P2 := ProjectiveSpace(RationalField(),2); C := Conic(P2,y^2-4*x*y-3*x^2+4*y*z+8*x*z-5*z^2); HasRationalPoint(C); cc,mm:=ReducedLegendreModel(C); cc; ?Parametrization; Output: Magma V2.10-6 Tue Jan 13 2004 08:03:06 on modular [Seed = 1747698909] ------------------------------------- true (13/21 : 4/7 : 1) Conic over Rational Field defined by -7*x^2 + y^2 + 3*z^2 No references for word "Parametrization;" Total time: 3.009 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (212.128.18.14) Time: Tue Jan 13 08:03:28 2004 Input: P2 := ProjectiveSpace(RationalField(),2); C := Conic(P2,y^2-4*x*y-3*x^2+4*y*z+8*x*z-5*z^2); HasRationalPoint(C); cc,mm:=ReducedLegendreModel(C); cc; Parametrization; Output: Magma V2.10-6 Tue Jan 13 2004 08:03:24 on modular [Seed = 1595732989] ------------------------------------- true (13/21 : 4/7 : 1) Conic over Rational Field defined by -7*x^2 + y^2 + 3*z^2 Intrinsic 'Parametrization' Signatures: ( C, p) -> MapSch ( P, C, p) -> MapSch Parametrization of the rational curve C given a rational point p on C. The the affine or projective line P will be set as the domain of this map if included as an argument. ( C) -> MapSch ( P, C) -> MapSch Parametrization of the conic curve C; if provided, the projective line P will be used as the domain of this map. ( F, D) -> FldFunElt, SeqEnum Parametrization for the algebraic function field F defined by the divisor D of degree one. Total time: 2.999 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host slip-12-65-174-130.mis.prserv.net. (12.65.174.130) Time: Tue Jan 13 08:39:49 2004 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: Magma V2.10-6 Tue Jan 13 2004 08:39:46 on modular [Seed = 2665294723] ------------------------------------- Replace this by some code, then click [PARI] or [MAGMA]! Total time: 3.049 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host slip-12-65-174-130.mis.prserv.net. (12.65.174.130) Time: Tue Jan 13 08:40:40 2004 Input: 4a.b2-4.-b3 Output: Magma V2.10-6 Tue Jan 13 2004 08:40:37 on modular [Seed = 2395814884] ------------------------------------- >> 4a.b2-4.-b3; ^ User error: bad syntax Total time: 3.069 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (194.165.15.3) Time: Tue Jan 13 08:43:38 2004 Input: trinomial(8) Output: Magma V2.10-6 Tue Jan 13 2004 08:43:35 on modular [Seed = 4257106885] ------------------------------------- >> trinomial(8); ^ User error: Identifier 'trinomial' has not been declared or assigned Total time: 3.039 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (194.165.15.3) Time: Tue Jan 13 08:43:55 2004 Input: printtrinomial(8) Output: Magma V2.10-6 Tue Jan 13 2004 08:43:52 on modular [Seed = 4105650899] ------------------------------------- >> printtrinomial(8); ^ User error: Identifier 'printtrinomial' has not been declared or assigned Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (194.165.15.3) Time: Tue Jan 13 09:03:02 2004 Input: K :=GF(2); C := PrimitivePolynomial(K,2); C; Output: Magma V2.10-6 Tue Jan 13 2004 09:02:59 on modular [Seed = 896962535] ------------------------------------- D^2 + D + 1 Total time: 2.939 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (194.165.15.3) Time: Tue Jan 13 09:03:55 2004 Input: K :=GF(2); C := PrimitivePolynomial(K,8); C; Output: Magma V2.10-6 Tue Jan 13 2004 09:03:52 on modular [Seed = 1014990517] ------------------------------------- D^8 + D^4 + D^3 + D^2 + 1 Total time: 2.999 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (194.165.15.3) Time: Tue Jan 13 09:04:21 2004 Input: K :=GF(2); C := PrimitivePolynomial(K,521); C; Output: Magma V2.10-6 Tue Jan 13 2004 09:04:18 on modular [Seed = 3347348836] ------------------------------------- D^521 + D^32 + 1 Total time: 3.069 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (194.165.15.3) Time: Tue Jan 13 09:06:46 2004 Input: K :=GF(2); C := PrimitiveTrinomial(K,521); C; Output: Magma V2.10-6 Tue Jan 13 2004 09:06:43 on modular [Seed = 3583405799] ------------------------------------- >> C := PrimitiveTrinomial(K,521); ^ User error: Identifier 'PrimitiveTrinomial' has not been declared or assigned >> C; ^ User error: Identifier 'C' has not been declared or assigned Total time: 2.939 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (194.165.15.3) Time: Tue Jan 13 09:07:43 2004 Input: K :=GF(2); C := PrimitivePolynomial(K,521); C; Output: Magma V2.10-6 Tue Jan 13 2004 09:07:40 on modular [Seed = 3751568434] ------------------------------------- D^521 + D^32 + 1 Total time: 3.229 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (194.165.15.3) Time: Tue Jan 13 09:08:11 2004 Input: K :=GF(2); C := PrimitivePolynomial(521,0); C; Output: Magma V2.10-6 Tue Jan 13 2004 09:08:08 on modular [Seed = 3869597039] ------------------------------------- >> C := PrimitivePolynomial(521,0); ^ Runtime error in 'PrimitivePolynomial': Bad argument types Argument types given: RngIntElt, RngIntElt >> C; ^ User error: Identifier 'C' has not been declared or assigned Total time: 3.059 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (194.165.15.3) Time: Tue Jan 13 09:08:46 2004 Input: K :=GF(2); C := PrimitivePolynomial(K,521); C; Output: Magma V2.10-6 Tue Jan 13 2004 09:08:43 on modular [Seed = 4054993499] ------------------------------------- D^521 + D^32 + 1 Total time: 3.199 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (194.165.15.3) Time: Tue Jan 13 09:10:55 2004 Input: K :=GF(2); C := PrimitivePolynomialRing(K,521); C; Output: Magma V2.10-6 Tue Jan 13 2004 09:10:52 on modular [Seed = 2176990636] ------------------------------------- >> C := PrimitivePolynomialRing(K,521); ^ User error: Identifier 'PrimitivePolynomialRing' has not been declared or assigned >> C; ^ User error: Identifier 'C' has not been declared or assigned Total time: 3.129 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (194.165.15.3) Time: Tue Jan 13 09:11:22 2004 Input: K :=GF(2); C := PolynomialRing(521); C; Output: Magma V2.10-6 Tue Jan 13 2004 09:11:19 on modular [Seed = 2295018574] ------------------------------------- >> C := PolynomialRing(521); ^ Runtime error in 'PolynomialRing': Bad argument types Argument types given: RngIntElt >> C; ^ User error: Identifier 'C' has not been declared or assigned Total time: 2.999 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (194.165.15.3) Time: Tue Jan 13 09:13:42 2004 Input: K :=GF(2); for i in [1 .. 10] do C := PrimitivePolynomial(K,521); C; end for; Output: Magma V2.10-6 Tue Jan 13 2004 09:13:39 on modular [Seed = 2463182784] ------------------------------------- D^521 + D^32 + 1 D^521 + D^32 + 1 D^521 + D^32 + 1 D^521 + D^32 + 1 D^521 + D^32 + 1 D^521 + D^32 + 1 D^521 + D^32 + 1 D^521 + D^32 + 1 D^521 + D^32 + 1 D^521 + D^32 + 1 Total time: 3.169 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (194.165.15.3) Time: Tue Jan 13 09:16:06 2004 Input: K :=GF(2); for i in [1 .. 10] do C := MinimalPolynomial(521); C; end for; Output: Magma V2.10-6 Tue Jan 13 2004 09:16:03 on modular [Seed = 2783320135] ------------------------------------- D - 521 D - 521 D - 521 D - 521 D - 521 D - 521 D - 521 D - 521 D - 521 D - 521 Total time: 3.039 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (194.165.15.3) Time: Tue Jan 13 09:16:27 2004 Input: K :=GF(2); for i in [1 .. 10] do C := MaximalPolynomial(521); C; end for; Output: Magma V2.10-6 Tue Jan 13 2004 09:16:24 on modular [Seed = 2901348693] ------------------------------------- >> C := MaximalPolynomial(521); ^ User error: Identifier 'MaximalPolynomial' has not been declared or assigned Total time: 3.009 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (194.165.15.3) Time: Tue Jan 13 09:16:55 2004 Input: K :=GF(2); for i in [1 .. 10] do C := BinomialPolynomial(521); C; end for; Output: Magma V2.10-6 Tue Jan 13 2004 09:16:52 on modular [Seed = 3086223906] ------------------------------------- >> C := BinomialPolynomial(521); ^ Runtime error in 'BinomialPolynomial': Bad argument types Argument types given: RngIntElt Total time: 2.979 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (194.165.15.3) Time: Tue Jan 13 09:17:12 2004 Input: K :=GF(2); for i in [1 .. 10] do C := BinomialPolynomial(K,521); C; end for; Output: Magma V2.10-6 Tue Jan 13 2004 09:17:09 on modular [Seed = 1107427301] ------------------------------------- >> C := BinomialPolynomial(K,521); ^ Runtime error in 'BinomialPolynomial': Bad argument types Argument types given: FldFin, RngIntElt Total time: 3.059 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (194.165.15.3) Time: Tue Jan 13 09:17:50 2004 Input: K :=GF(2); for i in [1 .. 10] do C := PrimitivePolynomial(K,521); C; end for; Output: Magma V2.10-6 Tue Jan 13 2004 09:17:47 on modular [Seed = 1258878210] ------------------------------------- D^521 + D^32 + 1 D^521 + D^32 + 1 D^521 + D^32 + 1 D^521 + D^32 + 1 D^521 + D^32 + 1 D^521 + D^32 + 1 D^521 + D^32 + 1 D^521 + D^32 + 1 D^521 + D^32 + 1 D^521 + D^32 + 1 Total time: 3.149 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (194.165.15.3) Time: Tue Jan 13 09:18:11 2004 Input: K :=GF(2); for i in [1 .. 10] do C := PrintBinaryPrimitivePolynomial(K,521); C; end for; Output: Magma V2.10-6 Tue Jan 13 2004 09:18:08 on modular [Seed = 1343483442] ------------------------------------- >> C := PrintBinaryPrimitivePolynomial(K,521); ^ User error: Identifier 'PrintBinaryPrimitivePolynomial' has not been declared or assigned Total time: 3.049 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (194.165.15.3) Time: Tue Jan 13 09:18:26 2004 Input: K :=GF(2); for i in [1 .. 10] do C := BinaryPrimitivePolynomial(K,521); C; end for; Output: Magma V2.10-6 Tue Jan 13 2004 09:18:23 on modular [Seed = 1579016243] ------------------------------------- >> C := BinaryPrimitivePolynomial(K,521); ^ User error: Identifier 'BinaryPrimitivePolynomial' has not been declared or assigned Total time: 3.009 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (194.165.15.3) Time: Tue Jan 13 09:18:44 2004 Input: K :=GF(2); for i in [1 .. 10] do C := PrimitivePolynomial(2,521); C; end for; Output: Magma V2.10-6 Tue Jan 13 2004 09:18:41 on modular [Seed = 1730468196] ------------------------------------- >> C := PrimitivePolynomial(2,521); ^ Runtime error in 'PrimitivePolynomial': Bad argument types Argument types given: RngIntElt, RngIntElt Total time: 3.019 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (194.165.15.3) Time: Tue Jan 13 09:19:23 2004 Input: K :=GF(2); for i in [1 .. 10] do C := PrimitivePolynomial(K,521); C; K :=GF(2); end for; Output: Magma V2.10-6 Tue Jan 13 2004 09:19:20 on modular [Seed = 1815073350] ------------------------------------- D^521 + D^32 + 1 D^521 + D^32 + 1 D^521 + D^32 + 1 D^521 + D^32 + 1 D^521 + D^32 + 1 D^521 + D^32 + 1 D^521 + D^32 + 1 D^521 + D^32 + 1 D^521 + D^32 + 1 D^521 + D^32 + 1 Total time: 3.219 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (194.165.15.3) Time: Tue Jan 13 09:25:32 2004 Input: K :=GF(2); for i in [1 .. 10] do C := PrimitiveTrinomials(K,521); C; end for; Output: Magma V2.10-6 Tue Jan 13 2004 09:25:29 on modular [Seed = 155891346] ------------------------------------- >> C := PrimitiveTrinomials(K,521); ^ User error: Identifier 'PrimitiveTrinomials' has not been declared or assigned Total time: 3.009 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (194.165.15.3) Time: Tue Jan 13 09:25:53 2004 Input: K :=GF(2); for i in [1 .. 10] do C := PrimitivePolynomials(K,521); C; end for; Output: Magma V2.10-6 Tue Jan 13 2004 09:25:49 on modular [Seed = 374712762] ------------------------------------- >> C := PrimitivePolynomials(K,521); ^ User error: Identifier 'PrimitivePolynomials' has not been declared or assigned Total time: 3.009 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (194.165.15.3) Time: Tue Jan 13 09:26:21 2004 Input: K :=GF(2); for i in [1 .. 10] do C := PrimitivePolynomial(K,521); C; end for; Output: Magma V2.10-6 Tue Jan 13 2004 09:26:18 on modular [Seed = 475552852] ------------------------------------- D^521 + D^32 + 1 D^521 + D^32 + 1 D^521 + D^32 + 1 D^521 + D^32 + 1 D^521 + D^32 + 1 D^521 + D^32 + 1 D^521 + D^32 + 1 D^521 + D^32 + 1 D^521 + D^32 + 1 D^521 + D^32 + 1 Total time: 3.159 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (194.165.15.3) Time: Tue Jan 13 09:26:39 2004 Input: K :=GF(2); for i in [1 .. 10] do C := PrimitiveTrinomial(K,521); C; end for; Output: Magma V2.10-6 Tue Jan 13 2004 09:26:36 on modular [Seed = 627139963] ------------------------------------- >> C := PrimitiveTrinomial(K,521); ^ User error: Identifier 'PrimitiveTrinomial' has not been declared or assigned Total time: 2.939 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (194.165.15.3) Time: Tue Jan 13 09:26:59 2004 Input: K :=GF(2); for i in [1 .. 10] do C := PrimitivePolynomial(K,521); C; end for; Output: Magma V2.10-6 Tue Jan 13 2004 09:26:56 on modular [Seed = 846623296] ------------------------------------- D^521 + D^32 + 1 D^521 + D^32 + 1 D^521 + D^32 + 1 D^521 + D^32 + 1 D^521 + D^32 + 1 D^521 + D^32 + 1 D^521 + D^32 + 1 D^521 + D^32 + 1 D^521 + D^32 + 1 D^521 + D^32 + 1 Total time: 3.129 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (194.165.15.3) Time: Tue Jan 13 09:27:30 2004 Input: K :=GF(2); for i in [1 .. 10] do C := PrimitiveTrinomial(521); C; end for; Output: Magma V2.10-6 Tue Jan 13 2004 09:27:27 on modular [Seed = 947681333] ------------------------------------- >> C := PrimitiveTrinomial(521); ^ User error: Identifier 'PrimitiveTrinomial' has not been declared or assigned Total time: 2.989 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (194.165.15.3) Time: Tue Jan 13 09:28:02 2004 Input: K :=GF(2); for i in [1 .. 10] do C := PrimitivePolynomials(521); C; end for; Output: Magma V2.10-6 Tue Jan 13 2004 09:27:59 on modular [Seed = 3246752236] ------------------------------------- >> C := PrimitivePolynomials(521); ^ User error: Identifier 'PrimitivePolynomials' has not been declared or assigned Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (194.165.15.3) Time: Tue Jan 13 09:28:24 2004 Input: K :=GF(2); for i in [1 .. 10] do C := PrimitivePolynomial(K,521); C; end for; Output: Magma V2.10-6 Tue Jan 13 2004 09:28:21 on modular [Seed = 3431500811] ------------------------------------- D^521 + D^32 + 1 D^521 + D^32 + 1 D^521 + D^32 + 1 D^521 + D^32 + 1 D^521 + D^32 + 1 D^521 + D^32 + 1 D^521 + D^32 + 1 D^521 + D^32 + 1 D^521 + D^32 + 1 D^521 + D^32 + 1 Total time: 3.129 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (194.165.15.3) Time: Tue Jan 13 09:28:53 2004 Input: K :=GF(2); for i in [1 .. 10] do C := PrimitivePolynomial(K,521); C; end for; Output: Magma V2.10-6 Tue Jan 13 2004 09:28:50 on modular [Seed = 3819414275] ------------------------------------- D^521 + D^32 + 1 D^521 + D^32 + 1 D^521 + D^32 + 1 D^521 + D^32 + 1 D^521 + D^32 + 1 D^521 + D^32 + 1 D^521 + D^32 + 1 D^521 + D^32 + 1 D^521 + D^32 + 1 D^521 + D^32 + 1 Total time: 3.139 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (194.165.15.3) Time: Tue Jan 13 09:32:45 2004 Input: K :=GF(2); for i in [1 .. 10] do C := PolynomialRing(521); C; end for; Output: Magma V2.10-6 Tue Jan 13 2004 09:32:42 on modular [Seed = 4105221436] ------------------------------------- >> C := PolynomialRing(521); ^ Runtime error in 'PolynomialRing': Bad argument types Argument types given: RngIntElt Total time: 2.919 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (194.165.15.3) Time: Tue Jan 13 09:33:07 2004 Input: K :=GF(2); for i in [1 .. 10] do C := PolynomialRing(K,521); C; end for; Output: Magma V2.10-6 Tue Jan 13 2004 09:33:04 on modular [Seed = 4256807967] ------------------------------------- Polynomial ring of rank 521 over GF(2) Lexicographical Order Variables: D, $.2, $.3, $.4, $.5, $.6, $.7, $.8, $.9, $.10, $.11, $.12, $.13, $.14, $.15, $.16, $.17, $.18, $.19, $.20, $.21, $.22, $.23, $.24, $.25, $.26, $.27, $.28, $.29, $.30, $.31, $.32, $.33, $.34, $.35, $.36, $.37, $.38, $.39, $.40, $.41, $.42, $.43, $.44, $.45, $.46, $.47, $.48, $.49, $.50, $.51, $.52, $.53, $.54, $.55, $.56, $.57, $.58, $.59, $.60, $.61, $.62, $.63, $.64, $.65, $.66, $.67, $.68, $.69, $.70, $.71, $.72, $.73, $.74, $.75, $.76, $.77, $.78, $.79, $.80, $.81, $.82, $.83, $.84, $.85, $.86, $.87, $.88, $.89, $.90, $.91, $.92, $.93, $.94, $.95, $.96, $.97, $.98, $.99, $.100, $.101, $.102, $.103, $.104, $.105, $.106, $.107, $.108, $.109, $.110, $.111, $.112, $.113, $.114, $.115, $.116, $.117, $.118, $.119, $.120, $.121, $.122, $.123, $.124, $.125, $.126, $.127, $.128, $.129, $.130, $.131, $.132, $.133, $.134, $.135, $.136, $.137, $.138, $.139, $.140, $.141, $.142, $.143, $.144, $.145, $.146, $.147, $.148, $.149, $.150, $.151, $.152, $.153, $.154, $.155, $.156, $.157, $.158, $.159, $.160, $.161, $.162, $.163, $.164, $.165, $.166, $.167, $.168, $.169, $.170, $.171, $.172, $.173, $.174, $.175, $.176, $.177, $.178, $.179, $.180, $.181, $.182, $.183, $.184, $.185, $.186, $.187, $.188, $.189, $.190, $.191, $.192, $.193, $.194, $.195, $.196, $.197, $.198, $.199, $.200, $.201, $.202, $.203, $.204, $.205, $.206, $.207, $.208, $.209, $.210, $.211, $.212, $.213, $.214, $.215, $.216, $.217, $.218, $.219, $.220, $.221, $.222, $.223, $.224, $.225, $.226, $.227, $.228, $.229, $.230, $.231, $.232, $.233, $.234, $.235, $.236, $.237, $.238, $.239, $.240, $.241, $.242, $.243, $.244, $.245, $.246, $.247, $.248, $.249, $.250, $.251, $.252, $.253, $.254, $.255, $.256, $.257, $.258, $.259, $.260, $.261, $.262, $.263, $.264, $.265, $.266, $.267, $.268, $.269, $.270, $.271, $.272, $.273, $.274, $.275, $.276, $.277, $.278, $.279, $.280, $.281, $.282, $.283, $.284, $.285, $.286, $.287, $.288, $.289, $.290, $.291, $.292, $.293, $.294, $.295, $.296, $.297, $.298, $.299, $.300, $.301, $.302, $.303, $.304, $.305, $.306, $.307, $.308, $.309, $.310, $.311, $.312, $.313, $.314, $.315, $.316, $.317, $.318, $.319, $.320, $.321, $.322, $.323, $.324, $.325, $.326, $.327, $.328, $.329, $.330, $.331, $.332, $.333, $.334, $.335, $.336, $.337, $.338, $.339, $.340, $.341, $.342, $.343, $.344, $.345, $.346, $.347, $.348, $.349, $.350, $.351, $.352, $.353, $.354, $.355, $.356, $.357, $.358, $.359, $.360, $.361, $.362, $.363, $.364, $.365, $.366, $.367, $.368, $.369, $.370, $.371, $.372, $.373, $.374, $.375, $.376, $.377, $.378, $.379, $.380, $.381, $.382, $.383, $.384, $.385, $.386, $.387, $.388, $.389, $.390, $.391, $.392, $.393, $.394, $.395, $.396, $.397, $.398, $.399, $.400, $.401, $.402, $.403, $.404, $.405, $.406, $.407, $.408, $.409, $.410, $.411, $.412, $.413, $.414, $.415, $.416, $.417, $.418, $.419, $.420, $.421, $.422, $.423, $.424, $.425, $.426, $.427, $.428, $.429, $.430, $.431, $.432, $.433, $.434, $.435, $.436, $.437, $.438, $.439, $.440, $.441, $.442, $.443, $.444, $.445, $.446, $.447, $.448, $.449, $.450, $.451, $.452, $.453, $.454, $.455, $.456, $.457, $.458, $.459, $.460, $.461, $.462, $.463, $.464, $.465, $.466, $.467, $.468, $.469, $.470, $.471, $.472, $.473, $.474, $.475, $.476, $.477, $.478, $.479, $.480, $.481, $.482, $.483, $.484, $.485, $.486, $.487, $.488, $.489, $.490, $.491, $.492, $.493, $.494, $.495, $.496, $.497, $.498, $.499, $.500, $.501, $.502, $.503, $.504, $.505, $.506, $.507, $.508, $.509, $.510, $.511, $.512, $.513, $.514, $.515, $.516, $.517, $.518, $.519, $.520, $.521 Polynomial ring of rank 521 over GF(2) Lexicographical Order Variables: D, $.2, $.3, $.4, $.5, $.6, $.7, $.8, $.9, $.10, $.11, $.12, $.13, $.14, $.15, $.16, $.17, $.18, $.19, $.20, $.21, $.22, $.23, $.24, $.25, $.26, $.27, $.28, $.29, $.30, $.31, $.32, $.33, $.34, $.35, $.36, $.37, $.38, $.39, $.40, $.41, $.42, $.43, $.44, $.45, $.46, $.47, $.48, $.49, $.50, $.51, $.52, $.53, $.54, $.55, $.56, $.57, $.58, $.59, $.60, $.61, $.62, $.63, $.64, $.65, $.66, $.67, $.68, $.69, $.70, $.71, $.72, $.73, $.74, $.75, $.76, $.77, $.78, $.79, $.80, $.81, $.82, $.83, $.84, $.85, $.86, $.87, $.88, $.89, $.90, $.91, $.92, $.93, $.94, $.95, $.96, $.97, $.98, $.99, $.100, $.101, $.102, $.103, $.104, $.105, $.106, $.107, $.108, $.109, $.110, $.111, $.112, $.113, $.114, $.115, $.116, $.117, $.118, $.119, $.120, $.121, $.122, $.123, $.124, $.125, $.126, $.127, $.128, $.129, $.130, $.131, $.132, $.133, $.134, $.135, $.136, $.137, $.138, $.139, $.140, $.141, $.142, $.143, $.144, $.145, $.146, $.147, $.148, $.149, $.150, $.151, $.152, $.153, $.154, $.155, $.156, $.157, $.158, $.159, $.160, $.161, $.162, $.163, $.164, $.165, $.166, $.167, $.168, $.169, $.170, $.171, $.172, $.173, $.174, $.175, $.176, $.177, $.178, $.179, $.180, $.181, $.182, $.183, $.184, $.185, $.186, $.187, $.188, $.189, $.190, $.191, $.192, $.193, $.194, $.195, $.196, $.197, $.198, $.199, $.200, $.201, $.202, $.203, $.204, $.205, $.206, $.207, $.208, $.209, $.210, $.211, $.212, $.213, $.214, $.215, $.216, $.217, $.218, $.219, $.220, $.221, $.222, $.223, $.224, $.225, $.226, $.227, $.228, $.229, $.230, $.231, $.232, $.233, $.234, $.235, $.236, $.237, $.238, $.239, $.240, $.241, $.242, $.243, $.244, $.245, $.246, $.247, $.248, $.249, $.250, $.251, $.252, $.253, $.254, $.255, $.256, $.257, $.258, $.259, $.260, $.261, $.262, $.263, $.264, $.265, $.266, $.267, $.268, $.269, $.270, $.271, $.272, $.273, $.274, $.275, $.276, $.277, $.278, $.279, $.280, $.281, $.282, $.283, $.284, $.285, $.286, $.287, $.288, $.289, $.290, $.291, $.292, $.293, $.294, $.295, $.296, $.297, $.298, $.299, $.300, $.301, $.302, $.303, $.304, $.305, $.306, $.307, $.308, $.309, $.310, $.311, $.312, $.313, $.314, $.315, $.316, $.317, $.318, $.319, $.320, $.321, $.322, $.323, $.324, $.325, $.326, $.327, $.328, $.329, $.330, $.331, $.332, $.333, $.334, $.335, $.336, $.337, $.338, $.339, $.340, $.341, $.342, $.343, $.344, $.345, $.346, $.347, $.348, $.349, $.350, $.351, $.352, $.353, $.354, $.355, $.356, $.357, $.358, $.359, $.360, $.361, $.362, $.363, $.364, $.365, $.366, $.367, $.368, $.369, $.370, $.371, $.372, $.373, $.374, $.375, $.376, $.377, $.378, $.379, $.380, $.381, $.382, $.383, $.384, $.385, $.386, $.387, $.388, $.389, $.390, $.391, $.392, $.393, $.394, $.395, $.396, $.397, $.398, $.399, $.400, $.401, $.402, $.403, $.404, $.405, $.406, $.407, $.408, $.409, $.410, $.411, $.412, $.413, $.414, $.415, $.416, $.417, $.418, $.419, $.420, $.421, $.422, $.423, $.424, $.425, $.426, $.427, $.428, $.429, $.430, $.431, $.432, $.433, $.434, $.435, $.436, $.437, $.438, $.439, $.440, $.441, $.442, $.443, $.444, $.445, $.446, $.447, $.448, $.449, $.450, $.451, $.452, $.453, $.454, $.455, $.456, $.457, $.458, $.459, $.460, $.461, $.462, $.463, $.464, $.465, $.466, $.467, $.468, $.469, $.470, $.471, $.472, $.473, $.474, $.475, $.476, $.477, $.478, $.479, $.480, $.481, $.482, $.483, $.484, $.485, $.486, $.487, $.488, $.489, $.490, $.491, $.492, $.493, $.494, $.495, $.496, $.497, $.498, $.499, $.500, $.501, $.502, $.503, $.504, $.505, $.506, $.507, $.508, $.509, $.510, $.511, $.512, $.513, $.514, $.515, $.516, $.517, $.518, $.519, $.520, $.521 Polynomial ring of rank 521 over GF(2) Lexicographical Order Variables: D, $.2, $.3, $.4, $.5, $.6, $.7, $.8, $.9, $.10, $.11, $.12, $.13, $.14, $.15, $.16, $.17, $.18, $.19, $.20, $.21, $.22, $.23, $.24, $.25, $.26, $.27, $.28, $.29, $.30, $.31, $.32, $.33, $.34, $.35, $.36, $.37, $.38, $.39, $.40, $.41, $.42, $.43, $.44, $.45, $.46, $.47, $.48, $.49, $.50, $.51, $.52, $.53, $.54, $.55, $.56, $.57, $.58, $.59, $.60, $.61, $.62, $.63, $.64, $.65, $.66, $.67, $.68, $.69, $.70, $.71, $.72, $.73, $.74, $.75, $.76, $.77, $.78, $.79, $.80, $.81, $.82, $.83, $.84, $.85, $.86, $.87, $.88, $.89, $.90, $.91, $.92, $.93, $.94, $.95, $.96, $.97, $.98, $.99, $.100, $.101, $.102, $.103, $.104, $.105, $.106, $.107, $.108, $.109, $.110, $.111, $.112, $.113, $.114, $.115, $.116, $.117, $.118, $.119, $.120, $.121, $.122, $.123, $.124, $.125, $.126, $.127, $.128, $.129, $.130, $.131, $.132, $.133, $.134, $.135, $.136, $.137, $.138, $.139, $.140, $.141, $.142, $.143, $.144, $.145, $.146, $.147, $.148, $.149, $.150, $.151, $.152, $.153, $.154, $.155, $.156, $.157, $.158, $.159, $.160, $.161, $.162, $.163, $.164, $.165, $.166, $.167, $.168, $.169, $.170, $.171, $.172, $.173, $.174, $.175, $.176, $.177, $.178, $.179, $.180, $.181, $.182, $.183, $.184, $.185, $.186, $.187, $.188, $.189, $.190, $.191, $.192, $.193, $.194, $.195, $.196, $.197, $.198, $.199, $.200, $.201, $.202, $.203, $.204, $.205, $.206, $.207, $.208, $.209, $.210, $.211, $.212, $.213, $.214, $.215, $.216, $.217, $.218, $.219, $.220, $.221, $.222, $.223, $.224, $.225, $.226, $.227, $.228, $.229, $.230, $.231, $.232, $.233, $.234, $.235, $.236, $.237, $.238, $.239, $.240, $.241, $.242, $.243, $.244, $.245, $.246, $.247, $.248, $.249, $.250, $.251, $.252, $.253, $.254, $.255, $.256, $.257, $.258, $.259, $.260, $.261, $.262, $.263, $.264, $.265, $.266, $.267, $.268, $.269, $.270, $.271, $.272, $.273, $.274, $.275, $.276, $.277, $.278, $.279, $.280, $.281, $.282, $.283, $.284, $.285, $.286, $.287, $.288, $.289, $.290, $.291, $.292, $.293, $.294, $.295, $.296, $.297, $.298, $.299, $.300, $.301, $.302, $.303, $.304, $.305, $.306, $.307, $.308, $.309, $.310, $.311, $.312, $.313, $.314, $.315, $.316, $.317, $.318, $.319, $.320, $.321, $.322, $.323, $.324, $.325, $.326, $.327, $.328, $.329, $.330, $.331, $.332, $.333, $.334, $.335, $.336, $.337, $.338, $.339, $.340, $.341, $.342, $.343, $.344, $.345, $.346, $.347, $.348, $.349, $.350, $.351, $.352, $.353, $.354, $.355, $.356, $.357, $.358, $.359, $.360, $.361, $.362, $.363, $.364, $.365, $.366, $.367, $.368, $.369, ** WARNING: Output too long, hence truncated. ************** MAGMA ***************** Host 3(NXDOMAIN) (194.165.15.3) Time: Tue Jan 13 09:34:37 2004 Input: K :=GF(2); for i in [1 .. 10] do C := PrimitivePolynomial(K,521); C; end for; Output: Magma V2.10-6 Tue Jan 13 2004 09:34:34 on modular [Seed = 2295122224] ------------------------------------- D^521 + D^32 + 1 D^521 + D^32 + 1 D^521 + D^32 + 1 D^521 + D^32 + 1 D^521 + D^32 + 1 D^521 + D^32 + 1 D^521 + D^32 + 1 D^521 + D^32 + 1 D^521 + D^32 + 1 D^521 + D^32 + 1 Total time: 3.159 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (194.165.15.3) Time: Tue Jan 13 09:38:01 2004 Input: K :=GF(2); for i in [1 .. 10] do C := PrimitivePolynomialRing(521); C; end for; Output: Magma V2.10-6 Tue Jan 13 2004 09:37:58 on modular [Seed = 2615138591] ------------------------------------- >> C := PrimitivePolynomialRing(521); ^ User error: Identifier 'PrimitivePolynomialRing' has not been declared or assigned Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (194.165.15.3) Time: Tue Jan 13 09:38:18 2004 Input: K :=GF(2); for i in [1 .. 10] do C := PolynomialRing(521); C; end for; Output: Magma V2.10-6 Tue Jan 13 2004 09:38:15 on modular [Seed = 2699354677] ------------------------------------- >> C := PolynomialRing(521); ^ Runtime error in 'PolynomialRing': Bad argument types Argument types given: RngIntElt Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (194.165.15.3) Time: Tue Jan 13 09:38:35 2004 Input: K :=GF(2); for i in [1 .. 10] do C := PolynomialRing(K,521); C; end for; Output: Magma V2.10-6 Tue Jan 13 2004 09:38:31 on modular [Seed = 2850941708] ------------------------------------- Polynomial ring of rank 521 over GF(2) Lexicographical Order Variables: D, $.2, $.3, $.4, $.5, $.6, $.7, $.8, $.9, $.10, $.11, $.12, $.13, $.14, $.15, $.16, $.17, $.18, $.19, $.20, $.21, $.22, $.23, $.24, $.25, $.26, $.27, $.28, $.29, $.30, $.31, $.32, $.33, $.34, $.35, $.36, $.37, $.38, $.39, $.40, $.41, $.42, $.43, $.44, $.45, $.46, $.47, $.48, $.49, $.50, $.51, $.52, $.53, $.54, $.55, $.56, $.57, $.58, $.59, $.60, $.61, $.62, $.63, $.64, $.65, $.66, $.67, $.68, $.69, $.70, $.71, $.72, $.73, $.74, $.75, $.76, $.77, $.78, $.79, $.80, $.81, $.82, $.83, $.84, $.85, $.86, $.87, $.88, $.89, $.90, $.91, $.92, $.93, $.94, $.95, $.96, $.97, $.98, $.99, $.100, $.101, $.102, $.103, $.104, $.105, $.106, $.107, $.108, $.109, $.110, $.111, $.112, $.113, $.114, $.115, $.116, $.117, $.118, $.119, $.120, $.121, $.122, $.123, $.124, $.125, $.126, $.127, $.128, $.129, $.130, $.131, $.132, $.133, $.134, $.135, $.136, $.137, $.138, $.139, $.140, $.141, $.142, $.143, $.144, $.145, $.146, $.147, $.148, $.149, $.150, $.151, $.152, $.153, $.154, $.155, $.156, $.157, $.158, $.159, $.160, $.161, $.162, $.163, $.164, $.165, $.166, $.167, $.168, $.169, $.170, $.171, $.172, $.173, $.174, $.175, $.176, $.177, $.178, $.179, $.180, $.181, $.182, $.183, $.184, $.185, $.186, $.187, $.188, $.189, $.190, $.191, $.192, $.193, $.194, $.195, $.196, $.197, $.198, $.199, $.200, $.201, $.202, $.203, $.204, $.205, $.206, $.207, $.208, $.209, $.210, $.211, $.212, $.213, $.214, $.215, $.216, $.217, $.218, $.219, $.220, $.221, $.222, $.223, $.224, $.225, $.226, $.227, $.228, $.229, $.230, $.231, $.232, $.233, $.234, $.235, $.236, $.237, $.238, $.239, $.240, $.241, $.242, $.243, $.244, $.245, $.246, $.247, $.248, $.249, $.250, $.251, $.252, $.253, $.254, $.255, $.256, $.257, $.258, $.259, $.260, $.261, $.262, $.263, $.264, $.265, $.266, $.267, $.268, $.269, $.270, $.271, $.272, $.273, $.274, $.275, $.276, $.277, $.278, $.279, $.280, $.281, $.282, $.283, $.284, $.285, $.286, $.287, $.288, $.289, $.290, $.291, $.292, $.293, $.294, $.295, $.296, $.297, $.298, $.299, $.300, $.301, $.302, $.303, $.304, $.305, $.306, $.307, $.308, $.309, $.310, $.311, $.312, $.313, $.314, $.315, $.316, $.317, $.318, $.319, $.320, $.321, $.322, $.323, $.324, $.325, $.326, $.327, $.328, $.329, $.330, $.331, $.332, $.333, $.334, $.335, $.336, $.337, $.338, $.339, $.340, $.341, $.342, $.343, $.344, $.345, $.346, $.347, $.348, $.349, $.350, $.351, $.352, $.353, $.354, $.355, $.356, $.357, $.358, $.359, $.360, $.361, $.362, $.363, $.364, $.365, $.366, $.367, $.368, $.369, $.370, $.371, $.372, $.373, $.374, $.375, $.376, $.377, $.378, $.379, $.380, $.381, $.382, $.383, $.384, $.385, $.386, $.387, $.388, $.389, $.390, $.391, $.392, $.393, $.394, $.395, $.396, $.397, $.398, $.399, $.400, $.401, $.402, $.403, $.404, $.405, $.406, $.407, $.408, $.409, $.410, $.411, $.412, $.413, $.414, $.415, $.416, $.417, $.418, $.419, $.420, $.421, $.422, $.423, $.424, $.425, $.426, $.427, $.428, $.429, $.430, $.431, $.432, $.433, $.434, $.435, $.436, $.437, $.438, $.439, $.440, $.441, $.442, $.443, $.444, $.445, $.446, $.447, $.448, $.449, $.450, $.451, $.452, $.453, $.454, $.455, $.456, $.457, $.458, $.459, $.460, $.461, $.462, $.463, $.464, $.465, $.466, $.467, $.468, $.469, $.470, $.471, $.472, $.473, $.474, $.475, $.476, $.477, $.478, $.479, $.480, $.481, $.482, $.483, $.484, $.485, $.486, $.487, $.488, $.489, $.490, $.491, $.492, $.493, $.494, $.495, $.496, $.497, $.498, $.499, $.500, $.501, $.502, $.503, $.504, $.505, $.506, $.507, $.508, $.509, $.510, $.511, $.512, $.513, $.514, $.515, $.516, $.517, $.518, $.519, $.520, $.521 Polynomial ring of rank 521 over GF(2) Lexicographical Order Variables: D, $.2, $.3, $.4, $.5, $.6, $.7, $.8, $.9, $.10, $.11, $.12, $.13, $.14, $.15, $.16, $.17, $.18, $.19, $.20, $.21, $.22, $.23, $.24, $.25, $.26, $.27, $.28, $.29, $.30, $.31, $.32, $.33, $.34, $.35, $.36, $.37, $.38, $.39, $.40, $.41, $.42, $.43, $.44, $.45, $.46, $.47, $.48, $.49, $.50, $.51, $.52, $.53, $.54, $.55, $.56, $.57, $.58, $.59, $.60, $.61, $.62, $.63, $.64, $.65, $.66, $.67, $.68, $.69, $.70, $.71, $.72, $.73, $.74, $.75, $.76, $.77, $.78, $.79, $.80, $.81, $.82, $.83, $.84, $.85, $.86, $.87, $.88, $.89, $.90, $.91, $.92, $.93, $.94, $.95, $.96, $.97, $.98, $.99, $.100, $.101, $.102, $.103, $.104, $.105, $.106, $.107, $.108, $.109, $.110, $.111, $.112, $.113, $.114, $.115, $.116, $.117, $.118, $.119, $.120, $.121, $.122, $.123, $.124, $.125, $.126, $.127, $.128, $.129, $.130, $.131, $.132, $.133, $.134, $.135, $.136, $.137, $.138, $.139, $.140, $.141, $.142, $.143, $.144, $.145, $.146, $.147, $.148, $.149, $.150, $.151, $.152, $.153, $.154, $.155, $.156, $.157, $.158, $.159, $.160, $.161, $.162, $.163, $.164, $.165, $.166, $.167, $.168, $.169, $.170, $.171, $.172, $.173, $.174, $.175, $.176, $.177, $.178, $.179, $.180, $.181, $.182, $.183, $.184, $.185, $.186, $.187, $.188, $.189, $.190, $.191, $.192, $.193, $.194, $.195, $.196, $.197, $.198, $.199, $.200, $.201, $.202, $.203, $.204, $.205, $.206, $.207, $.208, $.209, $.210, $.211, $.212, $.213, $.214, $.215, $.216, $.217, $.218, $.219, $.220, $.221, $.222, $.223, $.224, $.225, $.226, $.227, $.228, $.229, $.230, $.231, $.232, $.233, $.234, $.235, $.236, $.237, $.238, $.239, $.240, $.241, $.242, $.243, $.244, $.245, $.246, $.247, $.248, $.249, $.250, $.251, $.252, $.253, $.254, $.255, $.256, $.257, $.258, $.259, $.260, $.261, $.262, $.263, $.264, $.265, $.266, $.267, $.268, $.269, $.270, $.271, $.272, $.273, $.274, $.275, $.276, $.277, $.278, $.279, $.280, $.281, $.282, $.283, $.284, $.285, $.286, $.287, $.288, $.289, $.290, $.291, $.292, $.293, $.294, $.295, $.296, $.297, $.298, $.299, $.300, $.301, $.302, $.303, $.304, $.305, $.306, $.307, $.308, $.309, $.310, $.311, $.312, $.313, $.314, $.315, $.316, $.317, $.318, $.319, $.320, $.321, $.322, $.323, $.324, $.325, $.326, $.327, $.328, $.329, $.330, $.331, $.332, $.333, $.334, $.335, $.336, $.337, $.338, $.339, $.340, $.341, $.342, $.343, $.344, $.345, $.346, $.347, $.348, $.349, $.350, $.351, $.352, $.353, $.354, $.355, $.356, $.357, $.358, $.359, $.360, $.361, $.362, $.363, $.364, $.365, $.366, $.367, $.368, $.369, $.370, $.371, $.372, $.373, $.374, $.375, $.376, $.377, $.378, $.379, $.380, $.381, $.382, $.383, $.384, $.385, $.386, $.387, $.388, $.389, $.390, $.391, $.392, $.393, $.394, $.395, $.396, $.397, $.398, $.399, $.400, $.401, $.402, $.403, $.404, $.405, $.406, $.407, $.408, $.409, $.410, $.411, $.412, $.413, $.414, $.415, $.416, $.417, $.418, $.419, $.420, $.421, $.422, $.423, $.424, $.425, $.426, $.427, $.428, $.429, $.430, $.431, $.432, $.433, $.434, $.435, $.436, $.437, $.438, $.439, $.440, $.441, $.442, $.443, $.444, $.445, $.446, $.447, $.448, $.449, $.450, $.451, $.452, $.453, $.454, $.455, $.456, $.457, $.458, $.459, $.460, $.461, $.462, $.463, $.464, $.465, $.466, $.467, $.468, $.469, $.470, $.471, $.472, $.473, $.474, $.475, $.476, $.477, $.478, $.479, $.480, $.481, $.482, $.483, $.484, $.485, $.486, $.487, $.488, $.489, $.490, $.491, $.492, $.493, $.494, $.495, $.496, $.497, $.498, $.499, $.500, $.501, $.502, $.503, $.504, $.505, $.506, $.507, $.508, $.509, $.510, $.511, $.512, $.513, $.514, $.515, $.516, $.517, $.518, $.519, $.520, $.521 Polynomial ring of rank 521 over GF(2) Lexicographical Order Variables: D, $.2, $.3, $.4, $.5, $.6, $.7, $.8, $.9, $.10, $.11, $.12, $.13, $.14, $.15, $.16, $.17, $.18, $.19, $.20, $.21, $.22, $.23, $.24, $.25, $.26, $.27, $.28, $.29, $.30, $.31, $.32, $.33, $.34, $.35, $.36, $.37, $.38, $.39, $.40, $.41, $.42, $.43, $.44, $.45, $.46, $.47, $.48, $.49, $.50, $.51, $.52, $.53, $.54, $.55, $.56, $.57, $.58, $.59, $.60, $.61, $.62, $.63, $.64, $.65, $.66, $.67, $.68, $.69, $.70, $.71, $.72, $.73, $.74, $.75, $.76, $.77, $.78, $.79, $.80, $.81, $.82, $.83, $.84, $.85, $.86, $.87, $.88, $.89, $.90, $.91, $.92, $.93, $.94, $.95, $.96, $.97, $.98, $.99, $.100, $.101, $.102, $.103, $.104, $.105, $.106, $.107, $.108, $.109, $.110, $.111, $.112, $.113, $.114, $.115, $.116, $.117, $.118, $.119, $.120, $.121, $.122, $.123, $.124, $.125, $.126, $.127, $.128, $.129, $.130, $.131, $.132, $.133, $.134, $.135, $.136, $.137, $.138, $.139, $.140, $.141, $.142, $.143, $.144, $.145, $.146, $.147, $.148, $.149, $.150, $.151, $.152, $.153, $.154, $.155, $.156, $.157, $.158, $.159, $.160, $.161, $.162, $.163, $.164, $.165, $.166, $.167, $.168, $.169, $.170, $.171, $.172, $.173, $.174, $.175, $.176, $.177, $.178, $.179, $.180, $.181, $.182, $.183, $.184, $.185, $.186, $.187, $.188, $.189, $.190, $.191, $.192, $.193, $.194, $.195, $.196, $.197, $.198, $.199, $.200, $.201, $.202, $.203, $.204, $.205, $.206, $.207, $.208, $.209, $.210, $.211, $.212, $.213, $.214, $.215, $.216, $.217, $.218, $.219, $.220, $.221, $.222, $.223, $.224, $.225, $.226, $.227, $.228, $.229, $.230, $.231, $.232, $.233, $.234, $.235, $.236, $.237, $.238, $.239, $.240, $.241, $.242, $.243, $.244, $.245, $.246, $.247, $.248, $.249, $.250, $.251, $.252, $.253, $.254, $.255, $.256, $.257, $.258, $.259, $.260, $.261, $.262, $.263, $.264, $.265, $.266, $.267, $.268, $.269, $.270, $.271, $.272, $.273, $.274, $.275, $.276, $.277, $.278, $.279, $.280, $.281, $.282, $.283, $.284, $.285, $.286, $.287, $.288, $.289, $.290, $.291, $.292, $.293, $.294, $.295, $.296, $.297, $.298, $.299, $.300, $.301, $.302, $.303, $.304, $.305, $.306, $.307, $.308, $.309, $.310, $.311, $.312, $.313, $.314, $.315, $.316, $.317, $.318, $.319, $.320, $.321, $.322, $.323, $.324, $.325, $.326, $.327, $.328, $.329, $.330, $.331, $.332, $.333, $.334, $.335, $.336, $.337, $.338, $.339, $.340, $.341, $.342, $.343, $.344, $.345, $.346, $.347, $.348, $.349, $.350, $.351, $.352, $.353, $.354, $.355, $.356, $.357, $.358, $.359, $.360, $.361, $.362, $.363, $.364, $.365, $.366, $.367, $.368, $.369, ** WARNING: Output too long, hence truncated. ************** MAGMA ***************** Host 3(NXDOMAIN) (194.165.15.3) Time: Tue Jan 13 09:39:00 2004 Input: K :=GF(2); for i in [1 .. 10] do C := PolynomialRing(K,8); C; end for; Output: Magma V2.10-6 Tue Jan 13 2004 09:38:57 on modular [Seed = 3069375989] ------------------------------------- Polynomial ring of rank 8 over GF(2) Lexicographical Order Variables: D, $.2, $.3, $.4, $.5, $.6, $.7, $.8 Polynomial ring of rank 8 over GF(2) Lexicographical Order Variables: D, $.2, $.3, $.4, $.5, $.6, $.7, $.8 Polynomial ring of rank 8 over GF(2) Lexicographical Order Variables: D, $.2, $.3, $.4, $.5, $.6, $.7, $.8 Polynomial ring of rank 8 over GF(2) Lexicographical Order Variables: D, $.2, $.3, $.4, $.5, $.6, $.7, $.8 Polynomial ring of rank 8 over GF(2) Lexicographical Order Variables: D, $.2, $.3, $.4, $.5, $.6, $.7, $.8 Polynomial ring of rank 8 over GF(2) Lexicographical Order Variables: D, $.2, $.3, $.4, $.5, $.6, $.7, $.8 Polynomial ring of rank 8 over GF(2) Lexicographical Order Variables: D, $.2, $.3, $.4, $.5, $.6, $.7, $.8 Polynomial ring of rank 8 over GF(2) Lexicographical Order Variables: D, $.2, $.3, $.4, $.5, $.6, $.7, $.8 Polynomial ring of rank 8 over GF(2) Lexicographical Order Variables: D, $.2, $.3, $.4, $.5, $.6, $.7, $.8 Polynomial ring of rank 8 over GF(2) Lexicographical Order Variables: D, $.2, $.3, $.4, $.5, $.6, $.7, $.8 Total time: 2.939 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (194.165.15.3) Time: Tue Jan 13 09:39:42 2004 Input: K :=GF(2); for i in [1 .. 10] do C := TrinomialRing(K,8); C; end for; Output: Magma V2.10-6 Tue Jan 13 2004 09:39:39 on modular [Seed = 3220962518] ------------------------------------- >> C := TrinomialRing(K,8); ^ User error: Identifier 'TrinomialRing' has not been declared or assigned Total time: 3.009 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (194.165.15.3) Time: Tue Jan 13 09:40:08 2004 Input: K :=GF(2); C := TrinomialRing(K,8); Output: Magma V2.10-6 Tue Jan 13 2004 09:40:05 on modular [Seed = 1309281608] ------------------------------------- >> C := TrinomialRing(K,8); ^ User error: Identifier 'TrinomialRing' has not been declared or assigned Total time: 2.989 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (194.165.15.3) Time: Tue Jan 13 09:40:32 2004 Input: K :=GF(2); C := PrimitivePolynomial(K,8); Output: Magma V2.10-6 Tue Jan 13 2004 09:40:29 on modular [Seed = 1427183179] ------------------------------------- Total time: 2.999 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (194.165.15.3) Time: Tue Jan 13 09:40:52 2004 Input: K :=GF(2); C := PrimitivePolynomial(K,8); C; Output: Magma V2.10-6 Tue Jan 13 2004 09:40:49 on modular [Seed = 1545084782] ------------------------------------- D^8 + D^4 + D^3 + D^2 + 1 Total time: 2.989 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (194.165.15.3) Time: Tue Jan 13 09:41:14 2004 Input: K :=GF(2); C := PrimitivePolynomial(K,8); C; C := PrimitivePolynomial(K,8); C; C := PrimitivePolynomial(K,8); C; Output: Magma V2.10-6 Tue Jan 13 2004 09:41:11 on modular [Seed = 1781410222] ------------------------------------- D^8 + D^4 + D^3 + D^2 + 1 D^8 + D^4 + D^3 + D^2 + 1 D^8 + D^4 + D^3 + D^2 + 1 Total time: 3.049 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (194.165.15.3) Time: Tue Jan 13 09:41:36 2004 Input: K :=GF(2); C := PrimitivePolynomial(K,8); C; C := PrimitivePolynomial(K,8); C; C := PrimitivePolynomial(K,8); C; Output: Magma V2.10-6 Tue Jan 13 2004 09:41:33 on modular [Seed = 1882469294] ------------------------------------- D^8 + D^4 + D^3 + D^2 + 1 E^8 + E^4 + E^3 + E^2 + 1 F^8 + F^4 + F^3 + F^2 + 1 Total time: 3.019 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (194.165.15.3) Time: Tue Jan 13 09:42:06 2004 Input: K :=GF(2); C := PrimitivePolynomial(K,8); C; Output: Magma V2.10-6 Tue Jan 13 2004 09:42:03 on modular [Seed = 2117746054] ------------------------------------- X^8 + X^4 + X^3 + X^2 + 1 Total time: 3.009 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (194.165.15.3) Time: Tue Jan 13 09:42:48 2004 Input: K :=GF(2); C := PrimitivePolynomial(K,10000); C; Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Tue Jan 13 2004 09:42:25 on modular [Seed = 71321494] ------------------------------------- Errors: /home/mfd/gomagma: line 2: 839 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host 3(NXDOMAIN) (194.165.15.3) Time: Tue Jan 13 09:43:07 2004 Input: K :=GF(2); C := PrimitivePolynomial(K,1000); C; Output: Magma V2.10-6 Tue Jan 13 2004 09:43:03 on modular [Seed = 324489383] ------------------------------------- X^1000 + X^992 + X^968 + X^960 + X^936 + X^928 + X^904 + X^896 + X^872 + X^864 + X^840 + X^832 + X^808 + X^800 + X^776 + X^768 + X^744 + X^736 + X^712 + X^704 + X^680 + X^672 + X^648 + X^640 + X^616 + X^608 + X^584 + X^576 + X^552 + X^544 + X^520 + X^512 + X^488 + X^480 + X^456 + X^448 + X^424 + X^416 + X^392 + X^384 + X^360 + X^352 + X^328 + X^320 + X^296 + X^288 + X^264 + X^256 + X^232 + X^224 + X^200 + X^192 + X^168 + X^160 + X^136 + X^128 + X^104 + X^96 + X^72 + X^64 + X^40 + X^32 + X^8 + X^5 + X^3 + X^2 + 1 Total time: 4.479 seconds, Total memory usage: 1.99MB ************** MAGMA ***************** Host 3(NXDOMAIN) (194.165.15.3) Time: Tue Jan 13 09:54:00 2004 Input: K :=GF(2); P := x^8 + x^2 +1; C := IsPrimitive(P); C; Output: Magma V2.10-6 Tue Jan 13 2004 09:53:56 on modular [Seed = 3347284224] ------------------------------------- >> P := x^8 + x^2 +1; ^ User error: Identifier 'x' has not been declared or assigned >> C := IsPrimitive(P); ^ User error: Identifier 'P' has not been declared or assigned >> C; ^ User error: Identifier 'C' has not been declared or assigned Total time: 2.999 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (194.165.15.3) Time: Tue Jan 13 09:57:15 2004 Input: K :=GF(2); P := x^8 + x^2 +1; C := IsPrimitive(101); C; Output: Magma V2.10-6 Tue Jan 13 2004 09:57:12 on modular [Seed = 3583087326] ------------------------------------- >> P := x^8 + x^2 +1; ^ User error: Identifier 'x' has not been declared or assigned >> C := IsPrimitive(101); ^ Runtime error in 'IsPrimitive': Bad argument types Argument types given: RngIntElt >> C; ^ User error: Identifier 'C' has not been declared or assigned Total time: 2.939 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (194.165.15.3) Time: Tue Jan 13 09:57:28 2004 Input: K :=GF(2); C := IsPrimitive(101); C; Output: Magma V2.10-6 Tue Jan 13 2004 09:57:24 on modular [Seed = 3700988875] ------------------------------------- >> C := IsPrimitive(101); ^ Runtime error in 'IsPrimitive': Bad argument types Argument types given: RngIntElt >> C; ^ User error: Identifier 'C' has not been declared or assigned Total time: 3.009 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (194.165.15.3) Time: Tue Jan 13 09:59:11 2004 Input: K :=GF(2); B := B * Coefficient(B, 2)^-1; B; C := IsPrimitive(B); C; Output: Magma V2.10-6 Tue Jan 13 2004 09:59:08 on modular [Seed = 3954158612] ------------------------------------- >> B := B * Coefficient(B, 2)^-1; ^ User error: Identifier 'B' has not been declared or assigned >> B; ^ User error: Identifier 'B' has not been declared or assigned >> C := IsPrimitive(B); ^ User error: Identifier 'B' has not been declared or assigned >> C; ^ User error: Identifier 'C' has not been declared or assigned Total time: 2.999 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (194.165.15.3) Time: Tue Jan 13 10:07:52 2004 Input: P := PolynomialAlgebra(GF(2)); for m in [2..1000] do for> print MinimalPolynomial(PrimitiveElement(GF(2^m))); for> end for; Output: Magma V2.10-6 Tue Jan 13 2004 10:07:48 on modular [Seed = 2816732704] ------------------------------------- >> for> print MinimalPolynomial(PrimitiveElement(GF(2^m))); ^ User error: bad syntax >> for> ^ User error: bad syntax >> end for; ^ User error: bad syntax Total time: 2.979 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (194.165.15.3) Time: Tue Jan 13 10:08:29 2004 Input: P := PolynomialAlgebra(GF(2)); for m in [2..100] do print MinimalPolynomial(PrimitiveElement(GF(2^m))); end for; Output: Magma V2.10-6 Tue Jan 13 2004 10:08:18 on modular [Seed = 2934630159] ------------------------------------- x^2 + x + 1 x^3 + x + 1 x^4 + x + 1 x^5 + x^2 + 1 x^6 + x^4 + x^3 + x + 1 x^7 + x + 1 x^8 + x^4 + x^3 + x^2 + 1 x^9 + x^4 + 1 x^10 + x^6 + x^5 + x^3 + x^2 + x + 1 x^11 + x^2 + 1 x^12 + x^7 + x^6 + x^5 + x^3 + x + 1 x^13 + x^4 + x^3 + x + 1 x^14 + x^7 + x^5 + x^3 + 1 x^15 + x^5 + x^4 + x^2 + 1 x^16 + x^5 + x^3 + x^2 + 1 x^17 + x^3 + 1 x^18 + x^12 + x^10 + x + 1 x^19 + x^5 + x^2 + x + 1 x^20 + x^10 + x^9 + x^7 + x^6 + x^5 + x^4 + x + 1 x^21 + x^6 + x^5 + x^2 + 1 x^22 + x^12 + x^11 + x^10 + x^9 + x^8 + x^6 + x^5 + 1 x^23 + x^5 + 1 x^24 + x^16 + x^15 + x^14 + x^13 + x^10 + x^9 + x^7 + x^5 + x^3 + 1 x^25 + x^8 + x^6 + x^2 + 1 x^26 + x^14 + x^10 + x^8 + x^7 + x^6 + x^4 + x + 1 x^27 + x^12 + x^10 + x^9 + x^7 + x^5 + x^3 + x^2 + 1 x^28 + x^13 + x^7 + x^6 + x^5 + x^2 + 1 x^29 + x^2 + 1 x^30 + x^17 + x^16 + x^13 + x^11 + x^7 + x^5 + x^3 + x^2 + x + 1 x^31 + x^3 + 1 x^32 + x^15 + x^9 + x^7 + x^4 + x^3 + 1 x^33 + x^13 + x^12 + x^11 + x^10 + x^8 + x^6 + x^3 + 1 x^34 + x^16 + x^15 + x^12 + x^11 + x^8 + x^7 + x^6 + x^5 + x^4 + x^2 + x + 1 x^35 + x^11 + x^10 + x^7 + x^5 + x^2 + 1 x^36 + x^23 + x^22 + x^20 + x^19 + x^17 + x^14 + x^13 + x^8 + x^6 + x^5 + x + 1 x^37 + x^5 + x^4 + x^3 + x^2 + x + 1 x^38 + x^14 + x^10 + x^9 + x^8 + x^5 + x^2 + x + 1 x^39 + x^15 + x^12 + x^11 + x^10 + x^9 + x^7 + x^6 + x^5 + x^2 + 1 x^40 + x^23 + x^21 + x^18 + x^16 + x^15 + x^13 + x^12 + x^8 + x^5 + x^3 + x + 1 x^41 + x^3 + 1 x^42 + x^30 + x^26 + x^25 + x^24 + x^20 + x^18 + x^12 + x^11 + x^9 + x^6 + x^5 + x^2 + x + 1 x^43 + x^6 + x^4 + x^3 + 1 x^44 + x^24 + x^19 + x^17 + x^16 + x^4 + x^3 + x + 1 x^45 + x^20 + x^17 + x^15 + x^14 + x^12 + x^11 + x^6 + 1 x^46 + x^44 + x^41 + x^40 + x^39 + x^38 + x^32 + x^31 + x^30 + x^27 + x^26 + x^24 + x^23 + x^21 + x^20 + x^17 + x^12 + x^5 + x^4 + x^3 + x^2 + x + 1 x^47 + x^5 + 1 x^48 + x^25 + x^23 + x^17 + x^12 + x^11 + x^10 + x^8 + x^7 + x^3 + 1 x^49 + x^10 + x^8 + x^6 + x^4 + x^3 + x^2 + x + 1 x^50 + x^4 + x^3 + x^2 + 1 x^51 + x^16 + x^15 + x^12 + x^9 + x^6 + 1 x^52 + x^3 + 1 x^53 + x^6 + x^2 + x + 1 x^54 + x^34 + x^32 + x^31 + x^30 + x^29 + x^27 + x^25 + x^21 + x^18 + x^17 + x^16 + x^15 + x^13 + x^7 + x^4 + x^2 + x + 1 x^55 + x^11 + x^10 + x^9 + x^7 + x^4 + 1 x^56 + x^7 + x^4 + x^2 + 1 x^57 + x^21 + x^19 + x^16 + x^13 + x^11 + x^10 + x^8 + x^6 + x^5 + x^4 + x^3 + x^2 + x + 1 x^58 + x^19 + 1 x^59 + x^6 + x^5 + x^4 + x^3 + x + 1 x^60 + x + 1 x^61 + x^5 + x^2 + x + 1 x^62 + x^61 + x^60 + x^57 + x^55 + x^54 + x^52 + x^51 + x^47 + x^44 + x^42 + x^38 + x^37 + x^34 + x^33 + x^32 + x^31 + x^27 + x^26 + x^25 + x^24 + x^22 + x^20 + x^16 + x^15 + x^14 + x^12 + x^11 + x^10 + x^9 + x^7 + x^6 + x^2 + x + 1 x^63 + x + 1 x^64 + x^4 + x^3 + x + 1 x^65 + x^15 + x^14 + x^13 + x^12 + x^10 + x^9 + x^7 + x^5 + x + 1 x^66 + x^63 + x^62 + x^59 + x^58 + x^57 + x^56 + x^53 + x^51 + x^49 + x^45 + x^44 + x^43 + x^40 + x^37 + x^35 + x^34 + x^33 + x^32 + x^27 + x^23 + x^22 + x^19 + x^16 + x^15 + x^11 + x^10 + x^8 + x^7 + x^6 + x^5 + x^4 + 1 x^67 + x^5 + x^2 + x + 1 x^68 + x^9 + 1 x^69 + x^6 + x^5 + x^2 + 1 x^70 + x^5 + x^3 + x + 1 x^71 + x^5 + x^3 + x + 1 x^72 + x^10 + x^9 + x^3 + 1 x^73 + x^4 + x^3 + x^2 + 1 x^74 + x^73 + x^71 + x^70 + x^64 + x^60 + x^59 + x^58 + x^55 + x^52 + x^48 + x^47 + x^46 + x^43 + x^40 + x^38 + x^37 + x^34 + x^32 + x^30 + x^29 + x^27 + x^25 + x^20 + x^18 + x^17 + x^15 + x^13 + x^8 + x^5 + x^2 + x + 1 x^75 + x^6 + x^3 + x + 1 x^76 + x^75 + x^73 + x^72 + x^69 + x^64 + x^58 + x^57 + x^56 + x^55 + x^54 + x^53 + x^52 + x^51 + x^50 + x^47 + x^44 + x^37 + x^35 + x^32 + x^30 + x^27 + x^26 + x^25 + x^23 + x^20 + x^19 + x^18 + x^17 + x^10 + x^9 + x^8 + x^7 + x^6 + x^3 + x + 1 x^77 + x^6 + x^5 + x^2 + 1 x^78 + x^76 + x^75 + x^71 + x^69 + x^67 + x^65 + x^64 + x^60 + x^58 + x^56 + x^55 + x^54 + x^53 + x^52 + x^48 + x^47 + x^46 + x^45 + x^42 + x^39 + x^35 + x^32 + x^30 + x^29 + x^27 + x^24 + x^23 + x^20 + x^18 + x^16 + x^15 + x^9 + x^8 + x^7 + x^5 + x^4 + x^3 + 1 x^79 + x^4 + x^3 + x^2 + 1 x^80 + x^9 + x^4 + x^2 + 1 x^81 + x^4 + 1 x^82 + x^81 + x^80 + x^76 + x^75 + x^73 + x^69 + x^68 + x^67 + x^66 + x^65 + x^63 + x^62 + x^61 + x^60 + x^58 + x^57 + x^56 + x^55 + x^54 + x^53 + x^51 + x^50 + x^48 + x^47 + x^45 + x^43 + x^39 + x^38 + x^36 + x^35 + x^32 + x^28 + x^27 + x^23 + x^20 + x^19 + x^16 + x^14 + x^13 + x^11 + x^10 + x^9 + x^4 + x^2 + x + 1 x^83 + x^7 + x^4 + x^2 + 1 x^84 + x^83 + x^82 + x^80 + x^79 + x^78 + x^76 + x^75 + x^74 + x^73 + x^72 + x^71 + x^69 + x^66 + x^61 + x^60 + x^57 + x^54 + x^52 + x^46 + x^45 + x^44 + x^42 + x^41 + x^39 + x^33 + x^31 + x^29 + x^25 + x^23 + x^22 + x^19 + x^17 + x^15 + x^13 + x^12 + x^11 + x^10 + x^9 + x^8 + x^7 + x^4 + x^3 + x + 1 x^85 + x^8 + x^2 + x + 1 x^86 + x^81 + x^79 + x^75 + x^74 + x^73 + x^71 + x^70 + x^69 + x^67 + x^65 + x^62 + x^61 + x^59 + x^56 + x^54 + x^51 + x^49 + x^48 + x^45 + x^44 + x^43 + x^42 + x^41 + x^38 + x^35 + x^34 + x^32 + x^29 + x^28 + x^26 + x^25 + x^20 + x^14 + x^13 + x^12 + x^10 + x^8 + x^7 + x^6 + x^5 + x^4 + x^3 + x + 1 x^87 + x^13 + 1 x^88 + x^86 + x^85 + x^84 + x^83 + x^78 + x^77 + x^76 + x^75 + x^74 + x^71 + x^67 + x^64 + x^60 + x^59 + x^58 + x^57 + x^55 + x^53 + x^50 + x^48 + x^47 + x^44 + x^42 + x^41 + x^40 + x^38 + x^37 + x^36 + x^34 + x^33 + x^31 + x^27 + x^26 + x^22 + x^20 + x^17 + x^15 + x^14 + x^11 + x^5 + x^4 + 1 x^89 + x^6 + x^5 + x^3 + 1 x^90 + x^88 + x^86 + x^85 + x^84 + x^82 + x^79 + x^78 + x^75 + x^74 + x^72 + x^71 + x^70 + x^63 + x^60 + x^59 + x^56 + x^55 + x^53 + x^51 + x^50 + x^48 + x^44 + x^41 + x^38 + x^34 + x^32 + x^31 + x^30 + x^22 + x^21 + x^18 + x^17 + x^14 + x^12 + x^9 + x^8 + x^5 + x^2 + x + 1 x^91 + x^8 + x^5 + x + 1 x^92 + x^90 + x^89 + x^87 + x^84 + x^82 + x^81 + x^79 + x^77 + x^76 + x^75 + x^72 + x^70 + x^69 + x^65 + x^64 + x^63 + x^62 + x^60 + x^59 + x^58 + x^57 + x^55 + x^49 + x^47 + x^43 + x^39 + x^36 + x^32 + x^30 + x^28 + x^21 + x^16 + x^15 + x^14 + x^12 + x^10 + x^9 + x^5 + x + 1 x^93 + x^2 + 1 x^94 + x^21 + 1 x^95 + x^11 + 1 x^96 + x^10 + x^9 + x^6 + 1 x^97 + x^6 + 1 x^98 + x^11 + 1 x^99 + x^95 + x^90 + x^88 + x^85 + x^82 + x^80 + x^77 + x^75 + x^74 + x^70 + x^69 + x^68 + x^67 + x^65 + x^64 + x^60 + x^59 + x^58 + x^55 + x^54 + x^50 + x^49 + x^41 + x^40 + x^39 + x^38 + x^35 + x^33 + x^31 + x^30 + x^28 + x^27 + x^26 + x^23 + x^21 + x^20 + x^19 + x^15 + x^14 + x^8 + x^7 + x^4 + x^3 + x^2 + x + 1 x^100 + x^96 + x^68 + x^64 + x^36 + x^32 + x^15 + x^14 + x^13 + x^12 + x^11 + x^10 + x^9 + x^8 + x^7 + x^6 + x^5 + x^3 + x^2 + x + 1 Total time: 11.000 seconds, Total memory usage: 14.37MB ************** MAGMA ***************** Host 3(NXDOMAIN) (194.165.15.3) Time: Tue Jan 13 10:09:39 2004 Input: P := PolynomialAlgebra(GF(2)); for m in [2..100] do print MinimalTrinomial(PrimitiveElement(GF(2^m))); end for; Output: Magma V2.10-6 Tue Jan 13 2004 10:09:36 on modular [Seed = 3052535750] ------------------------------------- >> print MinimalTrinomial(PrimitiveElement(GF(2^m))); ^ User error: Identifier 'MinimalTrinomial' has not been declared or assigned Total time: 2.989 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (194.165.15.3) Time: Tue Jan 13 10:10:03 2004 Input: P := PolynomialAlgebra(GF(2)); for m in [2..100] do print Trinomial(PrimitiveElement(GF(2^m))); end for; Output: Magma V2.10-6 Tue Jan 13 2004 10:10:00 on modular [Seed = 3170432695] ------------------------------------- >> print Trinomial(PrimitiveElement(GF(2^m))); ^ User error: Identifier 'Trinomial' has not been declared or assigned Total time: 3.149 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (194.165.15.3) Time: Tue Jan 13 10:10:28 2004 Input: P := PolynomialAlgebra(GF(2)); for m in [2..10] do print Polynomial(PrimitiveElement(GF(2^m))); end for; Output: Magma V2.10-6 Tue Jan 13 2004 10:10:25 on modular [Seed = 1259274606] ------------------------------------- >> print Polynomial(PrimitiveElement(GF(2^m))); ^ Runtime error in 'Polynomial': Bad argument types Argument types given: FldFinElt Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (194.165.15.3) Time: Tue Jan 13 10:11:05 2004 Input: P := PolynomialAlgebra(GF(2)); for m in [2..10] do print minimalPolynomial(PrimitiveElement(GF(2^m))); end for; Output: Magma V2.10-6 Tue Jan 13 2004 10:11:02 on modular [Seed = 1495077787] ------------------------------------- >> print minimalPolynomial(PrimitiveElement(GF(2^m))); ^ User error: Identifier 'minimalPolynomial' has not been declared or assigned Total time: 2.979 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (194.165.15.3) Time: Tue Jan 13 10:11:22 2004 Input: P := PolynomialAlgebra(GF(2)); for m in [2..10] do print MinimalPolynomial(PrimitiveElement(GF(2^m))); end for; Output: Magma V2.10-6 Tue Jan 13 2004 10:11:19 on modular [Seed = 1646667953] ------------------------------------- x^2 + x + 1 x^3 + x + 1 x^4 + x + 1 x^5 + x^2 + 1 x^6 + x^4 + x^3 + x + 1 x^7 + x + 1 x^8 + x^4 + x^3 + x^2 + 1 x^9 + x^4 + 1 x^10 + x^6 + x^5 + x^3 + x^2 + x + 1 Total time: 2.889 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (194.165.15.3) Time: Tue Jan 13 10:12:01 2004 Input: P := PolynomialAlgebra(GF(2)); for m in [520..525] do print MinimalPolynomial(PrimitiveElement(GF(2^m))); end for; Output: Magma V2.10-6 Tue Jan 13 2004 10:11:55 on modular [Seed = 1798250900] ------------------------------------- x^520 + x^512 + x^15 + x^14 + x^13 + x^12 + x^8 + x^7 + x^6 + x^5 + x^4 + x^2 + 1 x^521 + x^32 + 1 x^522 + x^361 + x^359 + x^348 + x^339 + x^336 + x^332 + x^331 + x^315 + x^307 + x^304 + x^300 + x^299 + x^297 + x^295 + x^284 + x^275 + x^272 + x^268 + x^267 + x^200 + x^187 + x^185 + x^179 + x^178 + x^174 + x^171 + x^168 + x^167 + x^163 + x^162 + x^159 + x^156 + x^153 + x^149 + x^147 + x^146 + x^145 + x^144 + x^142 + x^140 + x^139 + x^138 + x^137 + x^133 + x^130 + x^129 + x^114 + x^112 + x^108 + x^106 + x^105 + x^104 + x^103 + x^101 + x^99 + x^97 + x^95 + x^92 + x^89 + x^85 + x^83 + x^82 + x^81 + x^80 + x^78 + x^76 + x^75 + x^74 + x^73 + x^72 + x^69 + x^66 + x^65 + x^59 + x^57 + x^51 + x^50 + x^46 + x^43 + x^40 + x^35 + x^34 + x^31 + x^28 + x^26 + x^25 + x^24 + x^21 + x^18 + x^17 + x^16 + x^14 + x^13 + x^12 + x^8 + x^7 + x^5 + 1 x^523 + x^13 + x^6 + x^2 + 1 x^524 + x^167 + 1 x^525 + x^6 + x^4 + x + 1 Total time: 5.439 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 3(NXDOMAIN) (194.165.15.3) Time: Tue Jan 13 10:14:05 2004 Input: P := PolynomialAlgebra(GF(2)); for m in [520..525] do print MinimalPolynomial(PrimitiveElement(GF(2))); end for; Output: Magma V2.10-6 Tue Jan 13 2004 10:14:00 on modular [Seed = 2067738630] ------------------------------------- x + 1 x + 1 x + 1 x + 1 x + 1 x + 1 Total time: 3.059 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (194.165.15.3) Time: Tue Jan 13 10:14:34 2004 Input: P := PolynomialAlgebra(GF(2)); for m in [520..525] do print MinimalPolynomial(PrimitiveElement(GF(521))); end for; Output: Magma V2.10-6 Tue Jan 13 2004 10:14:31 on modular [Seed = 222905886] ------------------------------------- $.1 + 518 $.1 + 518 $.1 + 518 $.1 + 518 $.1 + 518 $.1 + 518 Total time: 3.009 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (194.165.15.3) Time: Tue Jan 13 10:17:09 2004 Input: P := PolynomialAlgebra(GF(2)); for m in [520..525] do print PrintBinaryPrimitiveTrinomials(329); end for; Output: Magma V2.10-6 Tue Jan 13 2004 10:17:06 on modular [Seed = 324491429] ------------------------------------- >> print PrintBinaryPrimitiveTrinomials(329); ^ User error: Identifier 'PrintBinaryPrimitiveTrinomials' has not been declared or assigned Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (194.165.15.3) Time: Tue Jan 13 10:17:30 2004 Input: P := PolynomialAlgebra(GF(2)); for m in [520..525] do print BinaryPrimitiveTrinomials(329); end for; Output: Magma V2.10-6 Tue Jan 13 2004 10:17:27 on modular [Seed = 610297959] ------------------------------------- >> print BinaryPrimitiveTrinomials(329); ^ User error: Identifier 'BinaryPrimitiveTrinomials' has not been declared or assigned Total time: 2.989 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (194.165.15.3) Time: Tue Jan 13 10:17:48 2004 Input: P := PolynomialAlgebra(GF(2)); for m in [520..525] do print PrimitiveTrinomials(329); end for; Output: Magma V2.10-6 Tue Jan 13 2004 10:17:45 on modular [Seed = 761880944] ------------------------------------- >> print PrimitiveTrinomials(329); ^ User error: Identifier 'PrimitiveTrinomials' has not been declared or assigned Total time: 3.029 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (194.165.15.3) Time: Tue Jan 13 10:18:11 2004 Input: P := PolynomialAlgebra(GF(2)); for m in [520..525] do print PrimitivePolynomials(329); end for; Output: Magma V2.10-6 Tue Jan 13 2004 10:18:07 on modular [Seed = 913472093] ------------------------------------- >> print PrimitivePolynomials(329); ^ User error: Identifier 'PrimitivePolynomials' has not been declared or assigned Total time: 3.039 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (194.165.15.3) Time: Tue Jan 13 10:18:44 2004 Input: P := PolynomialAlgebra(GF(2)); K := GF(2) for m in [520..525] do print PrimitivePolynomial(K,329); end for; Output: Magma V2.10-6 Tue Jan 13 2004 10:18:41 on modular [Seed = 1065055018] ------------------------------------- >> for m in [520..525] do ^ User error: bad syntax >> print PrimitivePolynomial(K,329); ^ User error: Identifier 'K' has not been declared or assigned >> end for; ^ User error: bad syntax Total time: 2.999 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (194.165.15.3) Time: Tue Jan 13 10:19:10 2004 Input: P := PolynomialAlgebra(GF(2)); K := GF(2) print PrimitivePolynomial(K,329); Output: Magma V2.10-6 Tue Jan 13 2004 10:19:07 on modular [Seed = 3229912303] ------------------------------------- >> print PrimitivePolynomial(K,329); ^ User error: bad syntax Total time: 2.989 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (194.165.15.3) Time: Tue Jan 13 10:20:24 2004 Input: P := PolynomialAlgebra(GF(2)); K := GF(2) for m in [1 .. 5] do print PrimitivePolynomial(K,329); end for; Output: Magma V2.10-6 Tue Jan 13 2004 10:20:20 on modular [Seed = 3499400225] ------------------------------------- >> for m in [1 .. 5] do ^ User error: bad syntax >> print PrimitivePolynomial(K,329); ^ User error: Identifier 'K' has not been declared or assigned >> end for; ^ User error: bad syntax Total time: 2.939 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host fenfak84063.fenfak.ege.edu.tr. (155.223.84.63) Time: Tue Jan 13 11:38:06 2004 Input: 2^10000 Output: Magma V2.10-6 Tue Jan 13 2004 11:38:03 on modular [Seed = 3296762474] ------------------------------------- 1995063116880758384883742162683585083823496831886192454852008949852943883022194\ 6631919961684036194597899331129423209124271556491349413781117593785932096323957\ 8557300467937945267652465512660598955205500869181933115425086084606181046855090\ 7486608962488809048989483800925394163325785062156830947390255691238806522509664\ 3874441046759871626985453222868538161694315775629640762836880760732228535091641\ 4761839563814589694638994108409605362678210646214273333940365255656495306031426\ 8023496940033593431665145929777327966577560617258203140799419817960737824568376\ 2280037302885487251900834464581454650557929601414833921615734588139257095379769\ 1192778008269577356744441230620187578363255027283237892707103738028663930314281\ 3324140162419567169057406141965434232463880124885614730520743199225961179625013\ 0992860241708340807605932320161268492288496255841312844061536738951487114256315\ 1110897455142033138202029316409575964647560104058458415660720449628670165150619\ 2063100418642227590867090057460641785695191145605506825125040600751984226189805\ 9237118054444788072906395242548339221982707404473162376760846613033778706039803\ 4131971334936546227005631699374555082417809728109832913144035718775247685098572\ 7693792643322159939987688666080836883783802764328277517227365757274478411229438\ 9733810861607423253291974813120197604178281965697475898164531258434135959862784\ 1301281854062834766490886905210475808826158239619857701224070443305830758690393\ 1960460340497315658320867210591330090375282341553974539439771525745529051021231\ 0947321610753474825740775273986348298498340756937955646638621874569499279016572\ 1037013644331358172143117913982229838458473344402709641828510050729277483645505\ 7863450110085298781238947392869954083434615880704395911898581514577917714361969\ 8728131459483783202081474982171858011389071228250905826817436220577475921417653\ 7156877256149045829049924610286300815355833081301019876758562343435389554091756\ 2340084488752616264356864883351946372037729324009445624692325435040067802727383\ 7755376406726898636241037491410966718557050759098100246789880178271925953381282\ 4219540283027594084489550146766683896979968862416363133763939033734558014076367\ 4187771105538422573949911018646821969658165148513049422236994771476306915546821\ 7682876200362777257723781365331611196811280792669481887201298643660768551639860\ 5346022978715575179473852463694469230878942659482170080511203223654962881690357\ 3912136833839359175641873385051097027161391543959099159815465441733631165693603\ 1122249937969999226781732358023111862644575299135758175008199839236284615249881\ 0889602322443621737716180863570154684840586223297928538756234865564405369626220\ 1896357102881236156751254333830327002909766865056855715750551672751889919412971\ 1337690149916181315171544007728650573189557450920330185304847113818315407324053\ 3190384620840364217637039115506397890007428536721962809034779745333204683687958\ 6858023795221862912008074281955131794815762444829851846150970488802727472157468\ 8131594750409732115080498190455803416826949787141316063210686391511681774304792\ 596709376 Total time: 2.939 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (128.164.140.228) Time: Tue Jan 13 12:07:49 2004 Input: 2^49988585 Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Tue Jan 13 2004 12:07:26 on modular [Seed = 2463561497] ------------------------------------- Errors: /home/mfd/gomagma: line 2: 1495 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host DSL217-132-218-227.bb.netvision.net.il. (217.132.218.227) Time: Tue Jan 13 13:08:18 2004 Input: S:="abc"; S; Output: Magma V2.10-6 Tue Jan 13 2004 13:08:15 on modular [Seed = 459239250] ------------------------------------- abc Total time: 2.909 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host DSL217-132-218-227.bb.netvision.net.il. (217.132.218.227) Time: Tue Jan 13 13:08:49 2004 Input: S:="abc"; S; S[1]; Output: Magma V2.10-6 Tue Jan 13 2004 13:08:46 on modular [Seed = 543446088] ------------------------------------- abc a Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host DSL217-132-218-227.bb.netvision.net.il. (217.132.218.227) Time: Tue Jan 13 13:09:40 2004 Input: S:="abc"; S; S[1]; Br:=BraidGroup; Output: Magma V2.10-6 Tue Jan 13 2004 13:09:37 on modular [Seed = 695033102] ------------------------------------- abc a >> Br:=BraidGroup;; ^ Runtime error in 'AssignNames': Bad argument types Argument types given: Intrinsic ~, SeqEnum[MonStgElt] Total time: 3.009 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host vhe-370047.sshn.net. (195.169.221.8) Time: Tue Jan 13 13:10:28 2004 Input: Q := PolynomialRing(Integers()); f := x^4 - 8*x^2 +8; K := NumberField(f); Output: Magma V2.10-6 Tue Jan 13 2004 13:10:24 on modular [Seed = 964513263] ------------------------------------- Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host DSL217-132-218-227.bb.netvision.net.il. (217.132.218.227) Time: Tue Jan 13 13:11:16 2004 Input: S:="abc"; S; S[1]; Br<>:=BraidGroup; T:="ab"; T[1]*T[1]^(-1); Output: Magma V2.10-6 Tue Jan 13 2004 13:11:13 on modular [Seed = 3465198153] ------------------------------------- abc a >> Br<>:=BraidGroup; ^ User error: bad syntax >> T[1]*T[1]^(-1); ^ Runtime error in '^': Argument 2 (-1) should be >= 0 Total time: 2.919 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host vhe-370047.sshn.net. (195.169.221.8) Time: Tue Jan 13 13:11:41 2004 Input: Q := PolynomialRing(Integers()); f := x^4 - 8*x^2 +8; K := NumberField(f); Discriminant(f); Output: Magma V2.10-6 Tue Jan 13 2004 13:11:38 on modular [Seed = 3616777035] ------------------------------------- 131072 Total time: 2.999 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host vhe-370047.sshn.net. (195.169.221.8) Time: Tue Jan 13 13:12:16 2004 Input: Q := PolynomialRing(Integers()); f := x^4 - 8*x^2 +8; K := NumberField(f); Discriminant(f); M := MaximumOrder(K); Discriminant(M); Output: Magma V2.10-6 Tue Jan 13 2004 13:12:13 on modular [Seed = 3700992103] ------------------------------------- 131072 >> M := MaximumOrder(K); ^ User error: Identifier 'MaximumOrder' has not been declared or assigned >> Discriminant(M); ^ User error: Identifier 'M' has not been declared or assigned Total time: 2.939 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host DSL217-132-218-227.bb.netvision.net.il. (217.132.218.227) Time: Tue Jan 13 13:12:25 2004 Input: S:="abc"; S; S[1]; Br:=BraidGroup(6); T:="ab"; T[1]*T[1]^(-1); Output: Magma V2.10-6 Tue Jan 13 2004 13:12:22 on modular [Seed = 3802568610] ------------------------------------- abc a >> T[1]*T[1]^(-1); ^ Runtime error in '^': Argument 2 (-1) should be >= 0 Total time: 2.929 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host DSL217-132-218-227.bb.netvision.net.il. (217.132.218.227) Time: Tue Jan 13 13:18:02 2004 Input: S:="abc"; S; S[1]; Br:=BraidGroup(6); T:="ab"; T[1]*T[1]^(-1); read T[1]; Output: WARNING: MAGMA command contains unsafe command 'read', so it will not be executed. ************** MAGMA ***************** Host DSL217-132-218-227.bb.netvision.net.il. (217.132.218.227) Time: Tue Jan 13 13:21:44 2004 Input: S:="abc"; S; S[1]; Br:=BraidGroup(6); T:="ab"; StringToCode(T) Output: Magma V2.10-6 Tue Jan 13 2004 13:21:41 on modular [Seed = 2260922869] ------------------------------------- abc a 97 Total time: 3.049 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host DSL217-132-218-227.bb.netvision.net.il. (217.132.218.227) Time: Tue Jan 13 13:57:57 2004 Input: length("abcd"); Output: Magma V2.10-6 Tue Jan 13 2004 13:57:54 on modular [Seed = 1031357128] ------------------------------------- >> length("abcd"); ^ User error: Identifier 'length' has not been declared or assigned Total time: 3.069 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host DSL217-132-218-227.bb.netvision.net.il. (217.132.218.227) Time: Tue Jan 13 13:58:19 2004 Input: Length("abcd"); Output: Magma V2.10-6 Tue Jan 13 2004 13:58:16 on modular [Seed = 3296770891] ------------------------------------- >> Length("abcd"); ^ Runtime error in 'Length': Bad argument types Argument types given: MonStgElt Total time: 3.149 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host DSL217-132-218-227.bb.netvision.net.il. (217.132.218.227) Time: Tue Jan 13 13:59:43 2004 Input: A:="abcd"; Output: Magma V2.10-6 Tue Jan 13 2004 13:59:40 on modular [Seed = 3415198608] ------------------------------------- Total time: 3.199 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host DSL217-132-218-227.bb.netvision.net.il. (217.132.218.227) Time: Tue Jan 13 13:59:58 2004 Input: A:="abcd"; #A; Output: Magma V2.10-6 Tue Jan 13 2004 13:59:54 on modular [Seed = 3533099711] ------------------------------------- 4 Total time: 3.079 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host DSL217-132-218-227.bb.netvision.net.il. (217.132.218.227) Time: Tue Jan 13 14:11:58 2004 Input: A:="abcd"; #A; A[1]; f:=function(s) n:= Output: Magma V2.10-6 Tue Jan 13 2004 14:11:55 on modular [Seed = 2361953840] ------------------------------------- 4 a >> ; ^ User error: bad syntax Total time: 3.059 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host DSL217-132-218-227.bb.netvision.net.il. (217.132.218.227) Time: Tue Jan 13 14:12:19 2004 Input: A:="abcd"; #A; A[1]; Output: Magma V2.10-6 Tue Jan 13 2004 14:12:16 on modular [Seed = 2480378052] ------------------------------------- 4 a Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (194.165.15.3) Time: Tue Jan 13 14:32:58 2004 Input: p := 2^331; p; Output: Magma V2.10-6 Tue Jan 13 2004 14:32:55 on modular [Seed = 1208766439] ------------------------------------- 4374501449566023848745004454235242730706338861786424872851541212819905998398751\ 846447026354046107648 Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (194.165.15.3) Time: Tue Jan 13 14:33:35 2004 Input: p := 2^331; Factorization(p); Output: Magma V2.10-6 Tue Jan 13 2004 14:33:32 on modular [Seed = 1124551431] ------------------------------------- [ <2, 331> ] Total time: 2.919 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (194.165.15.3) Time: Tue Jan 13 14:34:05 2004 Input: p := 2^273; Factorization(p); Output: Magma V2.10-6 Tue Jan 13 2004 14:34:02 on modular [Seed = 1545098302] ------------------------------------- [ <2, 273> ] Total time: 2.909 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (194.165.15.3) Time: Tue Jan 13 14:34:37 2004 Input: p := (2^273)-1; Factorization(p); Output: Magma V2.10-6 Tue Jan 13 2004 14:34:33 on modular [Seed = 1427201364] ------------------------------------- [ <7, 2>, <79, 1>, <127, 1>, <337, 1>, <911, 1>, <8191, 1>, <121369, 1>, <108749551, 1>, <112901153, 1>, <23140471537, 1>, <4093204977277417, 1>, <86977595801949844993, 1> ] Total time: 3.739 seconds, Total memory usage: 2.99MB ************** MAGMA ***************** Host 3(NXDOMAIN) (194.165.15.3) Time: Tue Jan 13 14:35:09 2004 Input: p := (2^8)-1; Factorization(p); Output: Magma V2.10-6 Tue Jan 13 2004 14:35:06 on modular [Seed = 1679846470] ------------------------------------- [ <3, 1>, <5, 1>, <17, 1> ] Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (194.165.15.3) Time: Tue Jan 13 14:35:28 2004 Input: p := (2^6)-1; Factorization(p); Output: Magma V2.10-6 Tue Jan 13 2004 14:35:25 on modular [Seed = 2100917576] ------------------------------------- [ <3, 2>, <7, 1> ] Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (194.165.15.3) Time: Tue Jan 13 14:35:50 2004 Input: p := (2^273)-1; Factorization(p); Output: Magma V2.10-6 Tue Jan 13 2004 14:35:46 on modular [Seed = 1983020716] ------------------------------------- [ <7, 2>, <79, 1>, <127, 1>, <337, 1>, <911, 1>, <8191, 1>, <121369, 1>, <108749551, 1>, <112901153, 1>, <23140471537, 1>, <4093204977277417, 1>, <86977595801949844993, 1> ] Total time: 3.449 seconds, Total memory usage: 2.99MB ************** MAGMA ***************** Host 3(NXDOMAIN) (194.165.15.3) Time: Tue Jan 13 14:37:16 2004 Input: p := (2^521)-1; Factorization(p); Output: Magma V2.10-6 Tue Jan 13 2004 14:37:12 on modular [Seed = 21301665] ------------------------------------- [ <6864797660130609714981900799081393217269435300143305409394463459185543183397\ 6560521225596406614545549772963113914808580371219879997166438125740282911150571\ 51, 1> ] Total time: 3.569 seconds, Total memory usage: 2.99MB ************** MAGMA ***************** Host 3(NXDOMAIN) (194.165.15.3) Time: Tue Jan 13 14:37:58 2004 Input: p := (2^493)-1; Factorization(p); Output: Magma V2.10-6 Tue Jan 13 2004 14:37:46 on modular [Seed = 459215449] ------------------------------------- [ <233, 1>, <1103, 1>, <2089, 1>, <131071, 1>, <3616649, 1>, <10353001, 1>, <970596583005459173652432922101781006420152100417834935620226828285267019891114\ 1357299732185324536769414538999508070197039, 1> ] Total time: 11.319 seconds, Total memory usage: 2.99MB ************** MAGMA ***************** Host 3(NXDOMAIN) (194.165.15.3) Time: Tue Jan 13 14:41:12 2004 Input: p := (2^471)-1; Factorization(p); Output: Magma V2.10-6 Tue Jan 13 2004 14:41:06 on modular [Seed = 745022902] ------------------------------------- [ <7, 1>, <852133201, 1>, <60726444167, 1>, <1654058017289, 1>, <2134387368610417, 1>, <4767828205180602862488887736985607398666751166000769605\ 012698283856806259916006281652253453751, 1> ] Total time: 4.699 seconds, Total memory usage: 2.99MB ************** MAGMA ***************** Host 3(NXDOMAIN) (194.165.15.3) Time: Tue Jan 13 14:41:40 2004 Input: p := (2^41)-1; Factorization(p); Output: Magma V2.10-6 Tue Jan 13 2004 14:41:37 on modular [Seed = 643968927] ------------------------------------- [ <13367, 1>, <164511353, 1> ] Total time: 2.919 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (194.165.15.3) Time: Tue Jan 13 14:41:56 2004 Input: p := (2^471)-1; Factorization(p); Output: Magma V2.10-6 Tue Jan 13 2004 14:41:51 on modular [Seed = 1065039496] ------------------------------------- [ <7, 1>, <852133201, 1>, <60726444167, 1>, <1654058017289, 1>, <2134387368610417, 1>, <4767828205180602862488887736985607398666751166000769605\ 012698283856806259916006281652253453751, 1> ] Total time: 4.789 seconds, Total memory usage: 2.99MB ************** MAGMA ***************** Host 3(NXDOMAIN) (194.165.15.3) Time: Tue Jan 13 14:43:04 2004 Input: p := (2^331)-1; Factorization(p); Output: Magma V2.10-6 Tue Jan 13 2004 14:43:00 on modular [Seed = 3415196103] ------------------------------------- [ <16937389168607, 1>, <865118802936559, 1>, <298542624980197463613767215333569428005686468835821253721796682625551919, 1> ] Total time: 3.529 seconds, Total memory usage: 2.99MB ************** MAGMA ***************** Host 3(NXDOMAIN) (194.165.15.3) Time: Tue Jan 13 14:43:38 2004 Input: p := (2^317)-1; Factorization(p); Output: Magma V2.10-6 Tue Jan 13 2004 14:43:35 on modular [Seed = 3296775915] ------------------------------------- [ <9511, 1>, <587492521482839879, 1>, <4868122671322098041565641, 1>, <9815639231755686605031317440031161584572466128599, 1> ] Total time: 3.089 seconds, Total memory usage: 2.99MB ************** MAGMA ***************** Host 3(NXDOMAIN) (194.165.15.3) Time: Tue Jan 13 14:43:56 2004 Input: p := (2^311)-1; Factorization(p); Output: Magma V2.10-6 Tue Jan 13 2004 14:43:52 on modular [Seed = 3734689006] ------------------------------------- [ <5344847, 1>, <2647649373910205158468946067671, 1>, <294803681348959296477194164064643062187559537539328375831, 1> ] Total time: 3.579 seconds, Total memory usage: 2.99MB ************** MAGMA ***************** Host 3(NXDOMAIN) (194.165.15.3) Time: Tue Jan 13 14:44:11 2004 Input: p := (2^293)-1; Factorization(p); Output: Magma V2.10-6 Tue Jan 13 2004 14:44:08 on modular [Seed = 3616791831] ------------------------------------- [ <40122362455616221971122353, 1>, <3966452270281388904156112207107579216439107\ 43103031701971222447, 1> ] Total time: 3.289 seconds, Total memory usage: 2.99MB ************** MAGMA ***************** Host 3(NXDOMAIN) (194.165.15.3) Time: Tue Jan 13 14:44:30 2004 Input: p := (2^417)-1; Factorization(p); Output: Magma V2.10-6 Tue Jan 13 2004 14:44:26 on modular [Seed = 3768904242] ------------------------------------- [ <7, 1>, <5625767248687, 1>, <7606017793609, 1>, <123876132205208335762278423601, 1>, <91218603148026315357293387146275367218703\ 08627534265066967795115502591, 1> ] Total time: 3.719 seconds, Total memory usage: 2.99MB ************** MAGMA ***************** Host 3(NXDOMAIN) (194.165.15.3) Time: Tue Jan 13 14:46:11 2004 Input: p := (2^457)-1; Factorization(p); Output: Magma V2.10-6 Tue Jan 13 2004 14:45:55 on modular [Seed = 4256823110] ------------------------------------- [ <150327409, 1>, <247553941968992978493531934444940989829116509732371457865094\ 3035813830300993611462717419801770460539016610145009605554380104535919, 1> ] Total time: 16.410 seconds, Total memory usage: 2.99MB ************** MAGMA ***************** Host 3(NXDOMAIN) (194.165.15.3) Time: Tue Jan 13 14:46:58 2004 Input: p := (2^419)-1; Factorization(p); Output: Magma V2.10-6 Tue Jan 13 2004 14:46:55 on modular [Seed = 4138925457] ------------------------------------- [ <839, 1>, <903780021613921, 1>, <5800422716722833271214743, 1>, <10287968884341772230096159036619433593, 1>, <29919490848598531825060153417921002916701815927, 1> ] Total time: 3.159 seconds, Total memory usage: 2.99MB ************** MAGMA ***************** Host 3(NXDOMAIN) (194.165.15.3) Time: Tue Jan 13 14:48:09 2004 Input: p := (2^317)-1; Factorization(p); Output: Magma V2.10-6 Tue Jan 13 2004 14:48:06 on modular [Seed = 2160364478] ------------------------------------- [ <9511, 1>, <587492521482839879, 1>, <4868122671322098041565641, 1>, <9815639231755686605031317440031161584572466128599, 1> ] Total time: 3.169 seconds, Total memory usage: 2.99MB ************** MAGMA ***************** Host 3(NXDOMAIN) (194.165.15.3) Time: Tue Jan 13 14:48:36 2004 Input: p := (2^311)-1; Factorization(p); Output: Magma V2.10-6 Tue Jan 13 2004 14:48:32 on modular [Seed = 2581434945] ------------------------------------- [ <5344847, 1>, <2647649373910205158468946067671, 1>, <294803681348959296477194164064643062187559537539328375831, 1> ] Total time: 3.529 seconds, Total memory usage: 2.99MB ************** MAGMA ***************** Host 3(NXDOMAIN) (194.165.15.3) Time: Tue Jan 13 14:49:11 2004 Input: p := (2^293)-1; Factorization(p); Output: Magma V2.10-6 Tue Jan 13 2004 14:49:07 on modular [Seed = 2463537513] ------------------------------------- [ <40122362455616221971122353, 1>, <3966452270281388904156112207107579216439107\ 43103031701971222447, 1> ] Total time: 3.279 seconds, Total memory usage: 2.99MB ************** MAGMA ***************** Host 3(NXDOMAIN) (194.165.15.3) Time: Tue Jan 13 14:49:47 2004 Input: p := (2^271)-1; Factorization(p); Output: Magma V2.10-6 Tue Jan 13 2004 14:49:43 on modular [Seed = 2900928307] ------------------------------------- [ <15242475217, 1>, <2489277578681318902773305415678200452563642739707732865421\ 88386932989391, 1> ] Total time: 3.819 seconds, Total memory usage: 2.99MB ************** MAGMA ***************** Host 3(NXDOMAIN) (194.165.15.3) Time: Tue Jan 13 14:50:10 2004 Input: p := (2^8)-1; Factorization(p); Output: Magma V2.10-6 Tue Jan 13 2004 14:50:07 on modular [Seed = 3170416411] ------------------------------------- [ <3, 1>, <5, 1>, <17, 1> ] Total time: 2.889 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (194.165.15.3) Time: Tue Jan 13 14:51:34 2004 Input: k := GF(2); C := PrimitivePolynomial(k,521); C; Output: Magma V2.10-6 Tue Jan 13 2004 14:51:31 on modular [Seed = 3052517822] ------------------------------------- X^521 + X^32 + 1 Total time: 3.029 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (194.165.15.3) Time: Tue Jan 13 14:52:29 2004 Input: k := GF(2); C := PrimitivePolynomial(k,521); C; C := C * Coefficient(C,0)^-1; C; Output: Magma V2.10-6 Tue Jan 13 2004 14:52:26 on modular [Seed = 1107709553] ------------------------------------- X^521 + X^32 + 1 X^521 + X^32 + 1 Total time: 3.129 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (194.165.15.3) Time: Tue Jan 13 14:54:05 2004 Input: k := GF(2); C := PrimitivePolynomial(k,521); C; C := C * Coefficient(C,0)^-1; C; S := LSFRSequence (C,[K|1,1],(2^521)-1); S; Output: Magma V2.10-6 Tue Jan 13 2004 14:54:02 on modular [Seed = 1561940430] ------------------------------------- X^521 + X^32 + 1 X^521 + X^32 + 1 >> S := LSFRSequence (C,[K|1,1],(2^521)-1); ^ User error: Identifier 'K' has not been declared or assigned >> S; ^ User error: Identifier 'S' has not been declared or assigned Total time: 3.069 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (194.165.15.3) Time: Tue Jan 13 14:55:11 2004 Input: k := GF(2); C := PrimitivePolynomial(k,521); C; C := C * Coefficient(C,0)^-1; C; S := LSFRSequence (C,[K| 1,1],(2^521)-1); S; Output: Magma V2.10-6 Tue Jan 13 2004 14:55:08 on modular [Seed = 1747739965] ------------------------------------- X^521 + X^32 + 1 X^521 + X^32 + 1 >> S := LSFRSequence (C,[K| 1,1],(2^521)-1); ^ User error: Identifier 'K' has not been declared or assigned >> S; ^ User error: Identifier 'S' has not been declared or assigned Total time: 3.069 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (194.165.15.3) Time: Tue Jan 13 14:55:55 2004 Input: k := GF(2); C := PrimitivePolynomial(k,521); C; C := C * Coefficient(C,0)^-1; C; S := LSFRSequence (C,[1,1],(2^521)-1); S; Output: Magma V2.10-6 Tue Jan 13 2004 14:55:52 on modular [Seed = 1663528546] ------------------------------------- X^521 + X^32 + 1 X^521 + X^32 + 1 >> S := LSFRSequence (C,[1,1],(2^521)-1); ^ User error: Identifier 'LSFRSequence' has not been declared or assigned >> S; ^ User error: Identifier 'S' has not been declared or assigned Total time: 3.109 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (194.165.15.3) Time: Tue Jan 13 14:56:36 2004 Input: k := GF(2); C := PrimitivePolynomial(k,7); C; C := C * Coefficient(C,0)^-1; C; S := LSFRSequence (C,[K,1,1],(2^521)-1); S; Output: Magma V2.10-6 Tue Jan 13 2004 14:56:33 on modular [Seed = 2050914114] ------------------------------------- X^7 + X + 1 X^7 + X + 1 >> S := LSFRSequence (C,[K,1,1],(2^521)-1); ^ User error: Identifier 'K' has not been declared or assigned >> S; ^ User error: Identifier 'S' has not been declared or assigned Total time: 2.979 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (194.165.15.3) Time: Tue Jan 13 14:57:43 2004 Input: k := GF(2); C := PrimitivePolynomial(k,7); C; C := C * Coefficient(C,0)^-1; C; S := LSFRSequence (C,[Kl 1,1],48); S; Output: Magma V2.10-6 Tue Jan 13 2004 14:57:40 on modular [Seed = 139199989] ------------------------------------- X^7 + X + 1 X^7 + X + 1 >> S := LSFRSequence (C,[Kl 1,1],48); ^ User error: bad syntax >> S; ^ User error: Identifier 'S' has not been declared or assigned Total time: 2.929 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (194.165.15.3) Time: Tue Jan 13 14:58:05 2004 Input: k := GF(2); C := PrimitivePolynomial(k,7); C; C := C * Coefficient(C,0)^-1; C; S := LSFRSequence (C,[K| 1,1],48); S; Output: Magma V2.10-6 Tue Jan 13 2004 14:58:02 on modular [Seed = 54988416] ------------------------------------- X^7 + X + 1 X^7 + X + 1 >> S := LSFRSequence (C,[K| 1,1],48); ^ User error: Identifier 'K' has not been declared or assigned >> S; ^ User error: Identifier 'S' has not been declared or assigned Total time: 2.999 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (194.165.15.3) Time: Tue Jan 13 14:59:19 2004 Input: k := GF(2); C := PrimitivePolynomial(k,7); C; IsPrimitive(C); Output: Magma V2.10-6 Tue Jan 13 2004 14:59:16 on modular [Seed = 442373191] ------------------------------------- X^7 + X + 1 true Total time: 2.919 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (194.165.15.3) Time: Tue Jan 13 15:00:21 2004 Input: k := GF(2); C := PrimitivePolynomial(k,7); C; C := 1 + X^3 + X^13 + X^521; IsPrimitive(C); Output: Magma V2.10-6 Tue Jan 13 2004 15:00:18 on modular [Seed = 711861297] ------------------------------------- X^7 + X + 1 false Total time: 2.989 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (194.165.15.3) Time: Tue Jan 13 15:00:45 2004 Input: k := GF(2); C := PrimitivePolynomial(k,7); C; C := 1 + X^32 + X^521; IsPrimitive(C); Output: Magma V2.10-6 Tue Jan 13 2004 15:00:42 on modular [Seed = 627124998] ------------------------------------- X^7 + X + 1 true Total time: 3.039 seconds, Total memory usage: 1.99MB ************** MAGMA ***************** Host 3(NXDOMAIN) (194.165.15.3) Time: Tue Jan 13 15:02:19 2004 Input: k := GF(2); C := PrimitivePolynomial(k,7); C; for m in [32..520] do C := 1 + X^m + X^521; IsPrimitive(C); for end; Output: Magma V2.10-6 Tue Jan 13 2004 15:02:16 on modular [Seed = 3229929025] ------------------------------------- X^7 + X + 1 >> for end; ^ User error: bad syntax Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (194.165.15.3) Time: Tue Jan 13 15:02:39 2004 Input: k := GF(2); C := PrimitivePolynomial(k,7); C; for m in [32..520] do C := 1 + X^m + X^521; IsPrimitive(C); end for; Output: Magma V2.10-6 Tue Jan 13 2004 15:02:36 on modular [Seed = 3667842127] ------------------------------------- X^7 + X + 1 true false false false false false false false false false false false false false false false true false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false true false false false false false false false false false true false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false true false false false false false false false false false true false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false true false false false false false false false false false false false false false false false true false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false false Total time: 3.429 seconds, Total memory usage: 2.09MB ************** MAGMA ***************** Host 3(NXDOMAIN) (194.165.15.3) Time: Tue Jan 13 15:05:23 2004 Input: k := GF(2); C := PrimitivePolynomial(k,7); C; for m in [32..520] do C := 1 + X^m + X^521; if IsPrimitive(C) then C; end if; end for; Output: Magma V2.10-6 Tue Jan 13 2004 15:05:20 on modular [Seed = 3920487968] ------------------------------------- X^7 + X + 1 X^521 + X^32 + 1 X^521 + X^48 + 1 X^521 + X^158 + 1 X^521 + X^168 + 1 X^521 + X^353 + 1 X^521 + X^363 + 1 X^521 + X^473 + 1 X^521 + X^489 + 1 Total time: 3.379 seconds, Total memory usage: 2.09MB ************** MAGMA ***************** Host 3(NXDOMAIN) (194.165.15.3) Time: Tue Jan 13 15:08:10 2004 Input: k := GF(2); C := PrimitivePolynomial(k,7); C; for n in [1..520]do for m in [32..520] do C := 1 + X^m + X^n + X^521; if IsPrimitive(C) then C; end if; end for; end for; Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Tue Jan 13 2004 15:07:47 on modular [Seed = 3819434937] ------------------------------------- X^7 + X + 1 Errors: /home/mfd/gomagma: line 2: 2474 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host 3(NXDOMAIN) (194.165.15.3) Time: Tue Jan 13 15:08:49 2004 Input: k := GF(2); C := PrimitivePolynomial(k,7); C; for n in [1..20]do for m in [32..520] do C := 1 + X^m + X^n + X^521; if IsPrimitive(C) then C; end if; end for; end for; Output: Magma V2.10-6 Tue Jan 13 2004 15:08:45 on modular [Seed = 4206815998] ------------------------------------- X^7 + X + 1 Total time: 3.779 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (194.165.15.3) Time: Tue Jan 13 15:09:15 2004 Input: k := GF(2); C := PrimitivePolynomial(k,7); C; for n in [20..50]do for m in [32..520] do C := 1 + X^m + X^n + X^521; if IsPrimitive(C) then C; end if; end for; end for; Output: Magma V2.10-6 Tue Jan 13 2004 15:09:10 on modular [Seed = 4122076634] ------------------------------------- X^7 + X + 1 Total time: 4.249 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (194.165.15.3) Time: Tue Jan 13 15:09:53 2004 Input: k := GF(2); C := PrimitivePolynomial(k,7); C; for n in [1..50]do for m in [1..520] do C := 1 + X^m + X^n + X^521; if IsPrimitive(C) then C; end if; end for; end for; Output: Magma V2.10-6 Tue Jan 13 2004 15:09:48 on modular [Seed = 2361957449] ------------------------------------- X^7 + X + 1 Total time: 5.079 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (194.165.15.3) Time: Tue Jan 13 15:10:22 2004 Input: k := GF(2); C := PrimitivePolynomial(k,7); C; for n in [50..100]do for m in [1..520] do C := 1 + X^m + X^n + X^521; if IsPrimitive(C) then C; end if; end for; end for; Output: Magma V2.10-6 Tue Jan 13 2004 15:10:17 on modular [Seed = 2631437436] ------------------------------------- X^7 + X + 1 Total time: 5.139 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (194.165.15.3) Time: Tue Jan 13 15:11:10 2004 Input: k := GF(2); C := PrimitivePolynomial(k,9); C; for n in [100..150]do for m in [1..520] do C := 1 + X^m + X^n + X^521; if IsPrimitive(C) then C; end if; end for; end for; Output: Magma V2.10-6 Tue Jan 13 2004 15:11:05 on modular [Seed = 2547222279] ------------------------------------- X^9 + X^4 + 1 Total time: 5.179 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (194.165.15.3) Time: Tue Jan 13 15:11:37 2004 Input: k := GF(2); C := PrimitivePolynomial(k,9); C; for n in [150..250]do for m in [1..520] do C := 1 + X^m + X^n + X^521; if IsPrimitive(C) then C; end if; end for; end for; Output: Magma V2.10-6 Tue Jan 13 2004 15:11:29 on modular [Seed = 2934619670] ------------------------------------- X^9 + X^4 + 1 Total time: 7.379 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (194.165.15.3) Time: Tue Jan 13 15:12:06 2004 Input: k := GF(2); C := PrimitivePolynomial(k,9); C; for n in [250..350]do for m in [1..520] do C := 1 + X^m + X^n + X^521; if IsPrimitive(C) then C; end if; end for; end for; Output: Magma V2.10-6 Tue Jan 13 2004 15:11:58 on modular [Seed = 3120408830] ------------------------------------- X^9 + X^4 + 1 Total time: 7.639 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (194.165.15.3) Time: Tue Jan 13 15:12:29 2004 Input: k := GF(2); C := PrimitivePolynomial(k,9); C; for n in [350..450]do for m in [1..520] do C := 1 + X^m + X^n + X^521; if IsPrimitive(C) then C; end if; end for; end for; Output: Magma V2.10-6 Tue Jan 13 2004 15:12:21 on modular [Seed = 3019350748] ------------------------------------- X^9 + X^4 + 1 Total time: 7.709 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (194.165.15.3) Time: Tue Jan 13 15:12:54 2004 Input: k := GF(2); C := PrimitivePolynomial(k,9); C; for n in [450..520]do for m in [1..520] do C := 1 + X^m + X^n + X^521; if IsPrimitive(C) then C; end if; end for; end for; Output: Magma V2.10-6 Tue Jan 13 2004 15:12:48 on modular [Seed = 1225611331] ------------------------------------- X^9 + X^4 + 1 Total time: 6.289 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (194.165.15.3) Time: Tue Jan 13 15:14:23 2004 Input: k := GF(2); C := PrimitivePolynomial(k,9); C; for n in [0..100]do for m in [1..520] do C := 1 + X^m + X^n + X^521; if IsPrimitive(C) then C; end if; end for; end for; Output: Magma V2.10-6 Tue Jan 13 2004 15:14:15 on modular [Seed = 1174558619] ------------------------------------- X^9 + X^4 + 1 Total time: 7.309 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (194.165.15.3) Time: Tue Jan 13 15:15:22 2004 Input: k := GF(2); C := PrimitivePolynomial(k,9); C; for n in [0..100]do for m in [1..520] do C := 1 + X^m + X^521; if IsPrimitive(C) then C; end if; end for; end for; Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Tue Jan 13 2004 15:14:59 on modular [Seed = 1595625174] ------------------------------------- X^9 + X^4 + 1 X^521 + X^32 + 1 X^521 + X^48 + 1 X^521 + X^158 + 1 X^521 + X^168 + 1 X^521 + X^353 + 1 X^521 + X^363 + 1 X^521 + X^473 + 1 X^521 + X^489 + 1 X^521 + X^32 + 1 X^521 + X^48 + 1 X^521 + X^158 + 1 X^521 + X^168 + 1 X^521 + X^353 + 1 X^521 + X^363 + 1 X^521 + X^473 + 1 X^521 + X^489 + 1 X^521 + X^32 + 1 X^521 + X^48 + 1 X^521 + X^158 + 1 X^521 + X^168 + 1 X^521 + X^353 + 1 X^521 + X^363 + 1 X^521 + X^473 + 1 X^521 + X^489 + 1 X^521 + X^32 + 1 X^521 + X^48 + 1 X^521 + X^158 + 1 X^521 + X^168 + 1 X^521 + X^353 + 1 X^521 + X^363 + 1 X^521 + X^473 + 1 X^521 + X^489 + 1 X^521 + X^32 + 1 X^521 + X^48 + 1 X^521 + X^158 + 1 X^521 + X^168 + 1 X^521 + X^353 + 1 X^521 + X^363 + 1 X^521 + X^473 + 1 X^521 + X^489 + 1 X^521 + X^32 + 1 X^521 + X^48 + 1 X^521 + X^158 + 1 X^521 + X^168 + 1 X^521 + X^353 + 1 X^521 + X^363 + 1 X^521 + X^473 + 1 X^521 + X^489 + 1 X^521 + X^32 + 1 X^521 + X^48 + 1 X^521 + X^158 + 1 X^521 + X^168 + 1 X^521 + 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Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host 3(NXDOMAIN) (194.165.15.3) Time: Tue Jan 13 15:17:25 2004 Input: k := GF(2); C := PrimitivePolynomial(k,9); C; for n in [0..100]do for m in [1..520] do C := 1 + X^m + X^n + X^17 + X^521; if IsPrimitive(C) then C; end if; end for; end for; Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Tue Jan 13 2004 15:17:02 on modular [Seed = 1747745308] ------------------------------------- X^9 + X^4 + 1 X^521 + X^111 + X^17 + X + 1 X^521 + X^319 + X^17 + X + 1 X^521 + X^412 + X^17 + X + 1 X^521 + X^420 + X^17 + X + 1 X^521 + X^426 + X^17 + X + 1 X^521 + X^386 + X^17 + X^2 + 1 X^521 + X^333 + X^17 + X^3 + 1 X^521 + X^377 + X^17 + X^3 + 1 X^521 + X^416 + X^17 + X^3 + 1 X^521 + X^189 + X^17 + X^4 + 1 X^521 + X^487 + X^17 + X^4 + 1 X^521 + X^505 + X^17 + X^4 + 1 X^521 + X^75 + X^17 + X^5 + 1 X^521 + X^83 + X^17 + X^5 + 1 X^521 + X^111 + X^17 + X^5 + 1 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(194.165.15.3) Time: Tue Jan 13 15:19:17 2004 Input: k := GF(2); C := PrimitivePolynomial(k,9); C; for n in [0..200]do for m in [1..520] do C := 1 + X^m + X^n + X^521; if IsPrimitive(C) then C; end if; end for; end for; Output: Magma V2.10-6 Tue Jan 13 2004 15:19:05 on modular [Seed = 2134601100] ------------------------------------- X^9 + X^4 + 1 Total time: 11.859 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (194.165.15.3) Time: Tue Jan 13 15:19:46 2004 Input: k := GF(2); C := PrimitivePolynomial(k,9); C; for n in [0..300]do for m in [1..520] do C := 1 + X^m + X^n + X^521; if IsPrimitive(C) then C; end if; end for; end for; Output: Magma V2.10-6 Tue Jan 13 2004 15:19:29 on modular [Seed = 1949329135] ------------------------------------- X^9 + X^4 + 1 Total time: 16.420 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (194.165.15.3) Time: Tue Jan 13 15:20:25 2004 Input: k := GF(2); C := PrimitivePolynomial(k,9); C; for n in [300..520]do for m in [1..520] do C := 1 + X^m + X^n + X^521; if IsPrimitive(C) then C; end if; end for; end for; Output: Magma V2.10-6 Tue Jan 13 2004 15:20:11 on modular [Seed = 408685230] ------------------------------------- X^9 + X^4 + 1 Total time: 13.649 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (194.165.15.3) Time: Tue Jan 13 15:22:43 2004 Input: k := GF(2); C := PrimitivePolynomial(k,9); C; for t in [1..10] do for n in [1..200]do for m in [1..520] do C := 1 + X^m + X^n + X^t + X^521; if IsPrimitive(C) then C; end if; end for; end for; end for; Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Tue Jan 13 2004 15:22:20 on modular [Seed = 374474016] ------------------------------------- X^9 + X^4 + 1 X^521 + X^32 + 1 X^521 + X^48 + 1 X^521 + X^158 + 1 X^521 + X^168 + 1 X^521 + X^353 + 1 X^521 + X^363 + 1 X^521 + X^473 + 1 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X^521 + X^349 + X^54 + X + 1 X^521 + X^517 + X^54 + X + 1 X^521 + X^55 + X^51 + X + 1 X^521 + X^101 + X^55 + X + 1 X^521 + X^191 + X^55 + X + 1 X^521 + X^441 + X^55 + X + 1 X^521 + X^513 + X^55 + X + 1 X^521 + X^148 + X^56 + X + 1 X^521 + X^309 + X^56 + X + 1 X^521 + X^405 + X^56 + X + 1 X^521 + X^442 + X^56 + X + 1 Errors: /home/mfd/gomagma: line 2: 2652 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host 3(NXDOMAIN) (194.165.15.3) Time: Tue Jan 13 15:24:36 2004 Input: k := GF(2); for t in [1..10] do for n in [1..200]do for m in [1..520] do C := 1 + X^m + X^n + X^t + X^521; if IsPrimitive(C) then C; end if; end for; end for; end for; Output: Magma V2.10-6 Tue Jan 13 2004 15:24:32 on modular [Seed = 795556709] ------------------------------------- >> C := 1 + X^m + X^n + X^t + X^521; ^ User error: Identifier 'X' has not been declared or assigned Total time: 2.989 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (194.165.15.3) Time: Tue Jan 13 15:25:24 2004 Input: k := GF(2); C := 1; for t in [1..10] do for n in [1..200]do for m in [1..520] do C := 1 + X^m + X^n + X^t + X^521; if IsPrimitive(C) then C; end if; end for; end for; end for; Output: Magma V2.10-6 Tue Jan 13 2004 15:25:21 on modular [Seed = 947661891] ------------------------------------- >> C := 1; ^ Runtime error in 'AssignNames': Bad argument types Argument types given: RngIntElt ~, SeqEnum[MonStgElt] >> C := 1 + X^m + X^n + X^t + X^521; ^ User error: Identifier 'X' has not been declared or assigned Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (194.165.15.3) Time: Tue Jan 13 15:26:21 2004 Input: k := GF(2); C := PrimitivePolynomial(k,2); for t in [1..10] do for n in [1..200]do for m in [1..520] do C := 1 + X^m + X^n + X^t + X^521; if IsPrimitive(C) then C; end if; end for; end for; end for; Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Tue Jan 13 2004 15:25:58 on modular [Seed = 829760813] ------------------------------------- X^521 + X^32 + 1 X^521 + X^48 + 1 X^521 + X^158 + 1 X^521 + X^168 + 1 X^521 + X^353 + 1 X^521 + X^363 + 1 X^521 + X^473 + 1 X^521 + X^489 + 1 X^521 + X^159 + X^2 + X + 1 X^521 + X^382 + X^2 + X + 1 X^521 + X^20 + X^3 + X + 1 X^521 + X^91 + X^3 + X + 1 X^521 + X^116 + X^3 + X + 1 X^521 + X^127 + X^3 + X + 1 X^521 + X^179 + X^3 + X + 1 X^521 + X^211 + X^3 + X + 1 X^521 + X^370 + X^3 + X + 1 X^521 + X^391 + X^3 + X + 1 X^521 + X^512 + X^3 + X + 1 X^521 + X^213 + X^4 + X + 1 X^521 + X^363 + X^4 + X + 1 X^521 + X^516 + X^4 + X + 1 X^521 + X^415 + X^5 + X + 1 X^521 + X^477 + X^5 + X + 1 X^521 + X^510 + X^5 + X + 1 X^521 + X^49 + X^6 + X + 1 X^521 + X^217 + X^6 + X + 1 X^521 + X^383 + X^6 + X + 1 X^521 + X^506 + X^6 + X + 1 X^521 + X^83 + X^7 + X + 1 X^521 + X^93 + X^7 + X + 1 X^521 + X^149 + X^7 + X + 1 X^521 + X^212 + X^7 + X + 1 X^521 + X^233 + X^7 + X 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X^521 + X^489 + X^52 + X + 1 X^521 + X^53 + X^9 + X + 1 X^521 + X^66 + X^53 + X + 1 X^521 + X^253 + X^53 + X + 1 X^521 + X^370 + X^53 + X + 1 X^521 + X^376 + X^53 + X + 1 X^521 + X^505 + X^53 + X + 1 X^521 + X^169 + X^54 + X + 1 X^521 + X^286 + X^54 + X + 1 X^521 + X^349 + X^54 + X + 1 X^521 + X^517 + X^54 + X + 1 X^521 + X^55 + X^51 + X + 1 X^521 + X^101 + X^55 + X + 1 X^521 + X^191 + X^55 + X + 1 X^521 + X^441 + X^55 + X + 1 X^521 + X^513 + X^55 + X + 1 X^521 + X^148 + X^56 + X + 1 X^521 + X^309 + X^56 + X + 1 Errors: /home/mfd/gomagma: line 2: 2683 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host 3(NXDOMAIN) (194.165.15.3) Time: Tue Jan 13 15:27:50 2004 Input: k := GF(2); C := PrimitivePolynomial(k,2); for t in [1..10] do for n in [1..100]do for m in [1..520] do C := 1 + X^m + X^n + X^t + X^521; if IsPrimitive(C) then C; end if; end for; end for; end for; Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Tue Jan 13 2004 15:27:27 on modular [Seed = 3482049322] ------------------------------------- X^521 + X^32 + 1 X^521 + X^48 + 1 X^521 + X^158 + 1 X^521 + X^168 + 1 X^521 + X^353 + 1 X^521 + X^363 + 1 X^521 + X^473 + 1 X^521 + X^489 + 1 X^521 + X^159 + X^2 + X + 1 X^521 + X^382 + X^2 + X + 1 X^521 + X^20 + X^3 + X + 1 X^521 + X^91 + X^3 + X + 1 X^521 + X^116 + X^3 + X + 1 X^521 + X^127 + X^3 + X + 1 X^521 + X^179 + X^3 + X + 1 X^521 + X^211 + X^3 + X + 1 X^521 + X^370 + X^3 + X + 1 X^521 + X^391 + X^3 + X + 1 X^521 + X^512 + X^3 + X + 1 X^521 + X^213 + X^4 + X + 1 X^521 + X^363 + X^4 + X + 1 X^521 + X^516 + X^4 + X + 1 X^521 + X^415 + X^5 + X + 1 X^521 + X^477 + X^5 + X + 1 X^521 + X^510 + X^5 + X + 1 X^521 + X^49 + X^6 + X + 1 X^521 + X^217 + X^6 + X + 1 X^521 + X^383 + X^6 + X + 1 X^521 + X^506 + X^6 + X + 1 X^521 + X^83 + X^7 + X + 1 X^521 + X^93 + X^7 + X + 1 X^521 + X^149 + X^7 + X + 1 X^521 + X^212 + X^7 + X + 1 X^521 + X^233 + X^7 + X + 1 X^521 + X^285 + 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+ X + 1 X^521 + X^53 + X^9 + X + 1 X^521 + X^66 + X^53 + X + 1 X^521 + X^253 + X^53 + X + 1 X^521 + X^370 + X^53 + X + 1 X^521 + X^376 + X^53 + X + 1 X^521 + X^505 + X^53 + X + 1 X^521 + X^169 + X^54 + X + 1 X^521 + X^286 + X^54 + X + 1 X^521 + X^349 + X^54 + X + 1 X^521 + X^517 + X^54 + X + 1 X^521 + X^55 + X^51 + X + 1 X^521 + X^101 + X^55 + X + 1 X^521 + X^191 + X^55 + X + 1 X^521 + X^441 + X^55 + X + 1 X^521 + X^513 + X^55 + X + 1 X^521 + X^148 + X^56 + X + 1 Errors: /home/mfd/gomagma: line 2: 2693 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host 3(NXDOMAIN) (194.165.15.3) Time: Tue Jan 13 15:28:38 2004 Input: k := GF(2); C := PrimitivePolynomial(k,2); for t in [1..5] do for n in [1..100]do for m in [1..520] do C := 1 + X^m + X^n + X^t + X^521; if IsPrimitive(C) then C; end if; end for; end for; end for; Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Tue Jan 13 2004 15:28:15 on 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X + 1 X^521 + X^253 + X^53 + X + 1 X^521 + X^370 + X^53 + X + 1 X^521 + X^376 + X^53 + X + 1 X^521 + X^505 + X^53 + X + 1 X^521 + X^169 + X^54 + X + 1 X^521 + X^286 + X^54 + X + 1 X^521 + X^349 + X^54 + X + 1 X^521 + X^517 + X^54 + X + 1 X^521 + X^55 + X^51 + X + 1 X^521 + X^101 + X^55 + X + 1 X^521 + X^191 + X^55 + X + 1 X^521 + X^441 + X^55 + X + 1 X^521 + X^513 + X^55 + X + 1 X^521 + X^148 + X^56 + X + 1 Errors: /home/mfd/gomagma: line 2: 2702 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host 3(NXDOMAIN) (194.165.15.3) Time: Tue Jan 13 15:29:30 2004 Input: k := GF(2); C := PrimitivePolynomial(k,2); for t in [1..2] do for n in [1..100]do for m in [1..520] do C := 1 + X^m + X^n + X^t + X^521; if IsPrimitive(C) then C; end if; end for; end for; end for; Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Tue Jan 13 2004 15:29:07 on modular [Seed = 3717843076] 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X + 1 X^521 + X^370 + X^53 + X + 1 X^521 + X^376 + X^53 + X + 1 X^521 + X^505 + X^53 + X + 1 X^521 + X^169 + X^54 + X + 1 X^521 + X^286 + X^54 + X + 1 X^521 + X^349 + X^54 + X + 1 X^521 + X^517 + X^54 + X + 1 X^521 + X^55 + X^51 + X + 1 X^521 + X^101 + X^55 + X + 1 Errors: /home/mfd/gomagma: line 2: 2711 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host 3(NXDOMAIN) (194.165.15.3) Time: Tue Jan 13 15:30:21 2004 Input: k := GF(2); C := PrimitivePolynomial(k,2); for t in [1..2] do for n in [1..100]do for m in [1..520] do C := 1 + X^m + X^n + X^1 + X^521; if IsPrimitive(C) then C; end if; end for; end for; end for; Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Tue Jan 13 2004 15:29:58 on modular [Seed = 3937337318] ------------------------------------- X^521 + X^32 + 1 X^521 + X^48 + 1 X^521 + X^158 + 1 X^521 + X^168 + 1 X^521 + X^353 + 1 X^521 + X^363 + 1 X^521 + X^473 + 1 X^521 + X^489 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+ X + 1 X^521 + X^517 + X^54 + X + 1 X^521 + X^55 + X^51 + X + 1 X^521 + X^101 + X^55 + X + 1 X^521 + X^191 + X^55 + X + 1 X^521 + X^441 + X^55 + X + 1 X^521 + X^513 + X^55 + X + 1 X^521 + X^148 + X^56 + X + 1 Errors: /home/mfd/gomagma: line 2: 2720 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host 3(NXDOMAIN) (194.165.15.3) Time: Tue Jan 13 15:31:27 2004 Input: k := GF(2); C := PrimitivePolynomial(k,2); for n in [1..100]do for m in [1..520] do C := 1 + X^m + X^n + X^1 + X^521; if IsPrimitive(C) then C; end if; end for; end for; Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Tue Jan 13 2004 15:31:04 on modular [Seed = 4206817080] ------------------------------------- X^521 + X^32 + 1 X^521 + X^48 + 1 X^521 + X^158 + 1 X^521 + X^168 + 1 X^521 + X^353 + 1 X^521 + X^363 + 1 X^521 + X^473 + 1 X^521 + X^489 + 1 X^521 + X^159 + X^2 + X + 1 X^521 + X^382 + X^2 + X + 1 X^521 + X^20 + X^3 + X 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X^521 + X^280 + X^48 + X + 1 X^521 + X^382 + X^48 + X + 1 X^521 + X^445 + X^48 + X + 1 X^521 + X^476 + X^48 + X + 1 X^521 + X^49 + X^6 + X + 1 X^521 + X^135 + X^49 + X + 1 X^521 + X^197 + X^49 + X + 1 X^521 + X^423 + X^49 + X + 1 X^521 + X^440 + X^49 + X + 1 X^521 + X^474 + X^49 + X + 1 X^521 + X^76 + X^50 + X + 1 X^521 + X^342 + X^50 + X + 1 X^521 + X^370 + X^50 + X + 1 X^521 + X^55 + X^51 + X + 1 X^521 + X^80 + X^51 + X + 1 X^521 + X^137 + X^51 + X + 1 X^521 + X^181 + X^51 + X + 1 X^521 + X^272 + X^51 + X + 1 X^521 + X^320 + X^51 + X + 1 X^521 + X^203 + X^52 + X + 1 X^521 + X^273 + X^52 + X + 1 X^521 + X^450 + X^52 + X + 1 X^521 + X^489 + X^52 + X + 1 X^521 + X^53 + X^9 + X + 1 X^521 + X^66 + X^53 + X + 1 X^521 + X^253 + X^53 + X + 1 X^521 + X^370 + X^53 + X + 1 X^521 + X^376 + X^53 + X + 1 X^521 + X^505 + X^53 + X + 1 X^521 + X^169 + X^54 + X + 1 X^521 + X^286 + X^54 + X + 1 X^521 + X^349 + X^54 + X + 1 X^521 + X^517 + X^54 + X + 1 X^521 + X^55 + X^51 + X + 1 X^521 + X^101 + X^55 + X + 1 X^521 + X^191 + X^55 + X + 1 X^521 + X^441 + X^55 + X + 1 Errors: /home/mfd/gomagma: line 2: 2736 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host 3(NXDOMAIN) (194.165.15.3) Time: Tue Jan 13 15:32:30 2004 Input: k := GF(2); C := PrimitivePolynomial(k,12); for n in [1..100]do for m in [1..520] do C := 1 + X^m + X^n + X^1 + X^521; if IsPrimitive(C) then C; end if; end for; end for; Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Tue Jan 13 2004 15:32:07 on modular [Seed = 4088915582] ------------------------------------- X^521 + X^32 + 1 X^521 + X^48 + 1 X^521 + X^158 + 1 X^521 + X^168 + 1 X^521 + X^353 + 1 X^521 + X^363 + 1 X^521 + X^473 + 1 X^521 + X^489 + 1 X^521 + X^159 + X^2 + X + 1 X^521 + X^382 + X^2 + X + 1 X^521 + X^20 + X^3 + X + 1 X^521 + X^91 + X^3 + X + 1 X^521 + X^116 + X^3 + X + 1 X^521 + X^127 + X^3 + X + 1 X^521 + X^179 + X^3 + X + 1 X^521 + X^211 + X^3 + X + 1 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+ X + 1 X^521 + X^405 + X^56 + X + 1 X^521 + X^442 + X^56 + X + 1 X^521 + X^109 + X^57 + X + 1 X^521 + X^262 + X^57 + X + 1 X^521 + X^284 + X^57 + X + 1 X^521 + X^412 + X^57 + X + 1 X^521 + X^433 + X^57 + X + 1 Errors: /home/mfd/gomagma: line 2: 2745 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host 3(NXDOMAIN) (194.165.15.3) Time: Tue Jan 13 15:33:10 2004 Input: k := GF(2); C := PrimitivePolynomial(k,12); for n in [1..100]do for m in [1..520] do C := 1 + X^m + X^n + X^10 + X^521; if IsPrimitive(C) then C; end if; end for; end for; Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Tue Jan 13 2004 15:32:47 on modular [Seed = 2311953452] ------------------------------------- X^521 + X^41 + X^10 + X + 1 X^521 + X^321 + X^10 + X + 1 X^521 + X^389 + X^10 + X + 1 X^521 + X^114 + X^10 + X^2 + 1 X^521 + X^46 + X^10 + X^3 + 1 X^521 + X^448 + X^10 + X^3 + 1 X^521 + X^476 + X^10 + X^3 + 1 X^521 + 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X^48 + 1 X^521 + X^48 + X^14 + X^10 + 1 X^521 + X^62 + X^48 + X^10 + 1 X^521 + X^136 + X^48 + X^10 + 1 X^521 + X^232 + X^48 + X^10 + 1 X^521 + X^283 + X^48 + X^10 + 1 X^521 + X^311 + X^48 + X^10 + 1 X^521 + X^374 + X^48 + X^10 + 1 X^521 + X^49 + X^38 + X^10 + 1 X^521 + X^206 + X^49 + X^10 + 1 X^521 + X^209 + X^49 + X^10 + 1 X^521 + X^275 + X^49 + X^10 + 1 X^521 + X^288 + X^49 + X^10 + 1 X^521 + X^294 + X^49 + X^10 + 1 X^521 + X^324 + X^49 + X^10 + 1 X^521 + X^341 + X^49 + X^10 + 1 X^521 + X^401 + X^49 + X^10 + 1 X^521 + X^428 + X^49 + X^10 + 1 X^521 + X^506 + X^49 + X^10 + 1 X^521 + X^512 + X^49 + X^10 + 1 X^521 + X^196 + X^50 + X^10 + 1 X^521 + X^396 + X^50 + X^10 + 1 X^521 + X^489 + X^50 + X^10 + 1 X^521 + X^110 + X^51 + X^10 + 1 X^521 + X^172 + X^51 + X^10 + 1 X^521 + X^260 + X^51 + X^10 + 1 X^521 + X^376 + X^51 + X^10 + 1 X^521 + X^434 + X^51 + X^10 + 1 X^521 + X^460 + X^51 + X^10 + 1 X^521 + X^194 + X^52 + X^10 + 1 X^521 + X^234 + X^52 + X^10 + 1 X^521 + X^299 + X^52 + X^10 + 1 X^521 + X^518 + X^52 + X^10 + 1 X^521 + X^70 + X^53 + X^10 + 1 X^521 + X^105 + X^53 + X^10 + 1 X^521 + X^175 + X^53 + X^10 + 1 X^521 + X^101 + X^54 + X^10 + 1 X^521 + X^167 + X^54 + X^10 + 1 X^521 + X^223 + X^54 + X^10 + 1 X^521 + X^245 + X^54 + X^10 + 1 X^521 + X^439 + X^54 + X^10 + 1 X^521 + X^467 + X^54 + X^10 + 1 X^521 + X^502 + X^54 + X^10 + 1 X^521 + X^161 + X^55 + X^10 + 1 Errors: /home/mfd/gomagma: line 2: 2755 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host 3(NXDOMAIN) (194.165.15.3) Time: Tue Jan 13 15:34:03 2004 Input: k := GF(2); C := PrimitivePolynomial(k,12); for n in [1..100]do for m in [1..520] do C := 1 + X^m + X^n + X^521; if IsPrimitive(C) then C; end if; end for; end for; Output: Magma V2.10-6 Tue Jan 13 2004 15:33:55 on modular [Seed = 2227213053] ------------------------------------- Total time: 7.249 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (194.165.15.3) Time: Tue Jan 13 15:34:37 2004 Input: k := GF(2); C := PrimitivePolynomial(k,12); C; for n in [1..300]do for m in [1..520] do C := 1 + X^m + X^n + X^521; if IsPrimitive(C) then C; end if; end for; end for; Output: Magma V2.10-6 Tue Jan 13 2004 15:34:21 on modular [Seed = 2648279962] ------------------------------------- X^12 + X^7 + X^6 + X^5 + X^3 + X + 1 Total time: 16.260 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (194.165.15.3) Time: Tue Jan 13 15:35:40 2004 Input: k := GF(2); C := PrimitivePolynomial(k,12); C; for m in [1..520] do C := 1 + X^m + X^521; if IsPrimitive(C) then C; end if; end for; Output: Magma V2.10-6 Tue Jan 13 2004 15:35:36 on modular [Seed = 2934618236] ------------------------------------- X^12 + X^7 + X^6 + X^5 + X^3 + X + 1 X^521 + X^32 + 1 X^521 + X^48 + 1 X^521 + X^158 + 1 X^521 + X^168 + 1 X^521 + X^353 + 1 X^521 + X^363 + 1 X^521 + X^473 + 1 X^521 + X^489 + 1 Total time: 3.479 seconds, Total memory usage: 2.09MB ************** MAGMA ***************** Host 3(NXDOMAIN) (194.165.15.3) Time: Tue Jan 13 15:36:35 2004 Input: k := GF(2); C := PrimitivePolynomial(k,12); C; for m in [1..331] do C := 1 + X^m + X^521; if IsPrimitive(C) then C; end if; end for; Output: Magma V2.10-6 Tue Jan 13 2004 15:36:32 on modular [Seed = 2816717117] ------------------------------------- X^12 + X^7 + X^6 + X^5 + X^3 + X + 1 X^521 + X^32 + 1 X^521 + X^48 + 1 X^521 + X^158 + 1 X^521 + X^168 + 1 Total time: 3.219 seconds, Total memory usage: 2.09MB ************** MAGMA ***************** Host 3(NXDOMAIN) (194.165.15.3) Time: Tue Jan 13 15:36:54 2004 Input: k := GF(2); C := PrimitivePolynomial(k,12); C; for m in [1..331] do C := 1 + X^m + X^331; if IsPrimitive(C) then C; end if; end for; Output: Magma V2.10-6 Tue Jan 13 2004 15:36:51 on modular [Seed = 3170413077] ------------------------------------- X^12 + X^7 + X^6 + X^5 + X^3 + X + 1 >> if IsPrimitive(C) then ^ Runtime error in 'IsPrimitive': Degree of argument 1 must be >= 1 Total time: 3.069 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (194.165.15.3) Time: Tue Jan 13 15:37:17 2004 Input: k := GF(2); C := PrimitivePolynomial(k,12); C; for m in [1..330] do C := 1 + X^m + X^331; if IsPrimitive(C) then C; end if; end for; Output: Magma V2.10-6 Tue Jan 13 2004 15:37:14 on modular [Seed = 3052512005] ------------------------------------- X^12 + X^7 + X^6 + X^5 + X^3 + X + 1 Total time: 3.039 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (194.165.15.3) Time: Tue Jan 13 15:37:43 2004 Input: k := GF(2); C := PrimitivePolynomial(k,331); C; for m in [1..330] do C := 1 + X^m + X^331; if IsPrimitive(C) then C; end if; end for; Output: Magma V2.10-6 Tue Jan 13 2004 15:37:39 on modular [Seed = 1107711258] ------------------------------------- X^331 + X^10 + X^6 + X^2 + 1 Total time: 3.029 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (210.77.19.20) Time: Tue Jan 13 20:47:39 2004 Input: F := EllipticCurve([0, 17]); F; Output: Magma V2.10-6 Tue Jan 13 2004 20:47:35 on modular [Seed = 3069339985] ------------------------------------- Elliptic Curve defined by y^2 = x^3 + 17 over Rational Field Total time: 3.069 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (210.77.19.20) Time: Tue Jan 13 20:48:52 2004 Input: F := EllipticCurve([0, 17]); F; Output: Magma V2.10-6 Tue Jan 13 2004 20:48:49 on modular [Seed = 2850900472] ------------------------------------- Elliptic Curve defined by y^2 = x^3 + 17 over Rational Field Total time: 3.089 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (210.77.19.20) Time: Tue Jan 13 20:49:42 2004 Input: F := EllipticCurve([0, 17]); F; MW, f := MordellWeilGroup(F); MW; a := f(MW.1); b := f(MW.2); a, b; intpts := [ pt : i, j in [-4..4] | IsIntegral(pt) where pt is i*a + j*b] ; intpts; #intpts; Output: Magma V2.10-6 Tue Jan 13 2004 20:49:38 on modular [Seed = 1394062128] ------------------------------------- Elliptic Curve defined by y^2 = x^3 + 17 over Rational Field Abelian Group isomorphic to Z + Z Defined on 2 generators (free) (-2 : 3 : 1) (4 : 9 : 1) [ (52 : -375 : 1), (8 : 23 : 1), (5234 : 378661 : 1), (-1 : 4 : 1), (-2 : -3 : 1), (2 : -5 : 1), (43 : -282 : 1), (4 : -9 : 1), (4 : 9 : 1), (43 : 282 : 1), (2 : 5 : 1), (-2 : 3 : 1), (-1 : -4 : 1), (5234 : -378661 : 1), (8 : -23 : 1), (52 : 375 : 1) ] 16 Total time: 3.739 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host nycmny1-ar5-4-35-085-151.nycmny1.elnk.dsl.genuity.net. (4.35.85.151) Time: Tue Jan 13 20:53:41 2004 Input: 8*64 Output: Magma V2.10-6 Tue Jan 13 2004 20:53:38 on modular [Seed = 1107731249] ------------------------------------- 512 Total time: 2.909 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (210.77.19.20) Time: Tue Jan 13 21:34:05 2004 Input: F := EllipticCurve([0, -4]); F; MW, f := MordellWeilGroup(F); MW; a := f(MW.1); b := f(MW.2); a, b; intpts := [ pt : i, j in [-4..4] | IsIntegral(pt) where pt is i*a + j*b] ; intpts; #intpts; Output: Magma V2.10-6 Tue Jan 13 2004 21:34:02 on modular [Seed = 1191423374] ------------------------------------- Elliptic Curve defined by y^2 = x^3 - 4 over Rational Field Abelian Group isomorphic to Z Defined on 1 generator (free) >> b := f(MW.2); ^ Runtime error in '.': Argument 2 (2) should be in the range [-1 .. 1] >> a, b; ^ User error: Identifier 'b' has not been declared or assigned >> IsIntegral(pt) where pt is i*a + j*b] ; ^ User error: Identifier 'b' has not been declared or assigned >> intpts; ^ User error: Identifier 'intpts' has not been declared or assigned >> #intpts;; ^ User error: Identifier 'intpts' has not been declared or assigned Total time: 3.139 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 3(NXDOMAIN) (210.77.19.20) Time: Tue Jan 13 21:34:41 2004 Input: F := EllipticCurve([-4, 0]); F; MW, f := MordellWeilGroup(F); MW; a := f(MW.1); b := f(MW.2); a, b; intpts := [ pt : i, j in [-4..4] | IsIntegral(pt) where pt is i*a + j*b] ; intpts; #intpts; Output: Magma V2.10-6 Tue Jan 13 2004 21:34:38 on modular [Seed = 1309320355] ------------------------------------- Elliptic Curve defined by y^2 = x^3 - 4*x over Rational Field Abelian Group isomorphic to Z/2 + Z/2 Defined on 2 generators Relations: 2*MW.1 = 0 2*MW.2 = 0 (-2 : 0 : 1) (0 : 0 : 1) [ (0 : 0 : 1), (0 : 0 : 1), (0 : 0 : 1), (0 : 0 : 1), (-2 : 0 : 1), (2 : 0 : 1), (-2 : 0 : 1), (2 : 0 : 1), (-2 : 0 : 1), (2 : 0 : 1), (-2 : 0 : 1), (2 : 0 : 1), (-2 : 0 : 1), (0 : 0 : 1), (0 : 0 : 1), (0 : 0 : 1), (0 : 0 : 1), (-2 : 0 : 1), (2 : 0 : 1), (-2 : 0 : 1), (2 : 0 : 1), (-2 : 0 : 1), (2 : 0 : 1), (-2 : 0 : 1), (2 : 0 : 1), (-2 : 0 : 1), (0 : 0 : 1), (0 : 0 : 1), (0 : 0 : 1), (0 : 0 : 1), (-2 : 0 : 1), (2 : 0 : 1), (-2 : 0 : 1), (2 : 0 : 1), (-2 : 0 : 1), (2 : 0 : 1), (-2 : 0 : 1), (2 : 0 : 1), (-2 : 0 : 1), (0 : 0 : 1), (0 : 0 : 1), (0 : 0 : 1), (0 : 0 : 1), (-2 : 0 : 1), (2 : 0 : 1), (-2 : 0 : 1), (2 : 0 : 1), (-2 : 0 : 1), (2 : 0 : 1), (-2 : 0 : 1), (2 : 0 : 1), (-2 : 0 : 1), (0 : 0 : 1), (0 : 0 : 1), (0 : 0 : 1), (0 : 0 : 1) ] 56 Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (210.77.19.20) Time: Tue Jan 13 21:41:02 2004 Input: E := EllipticCurve([-27, 55350]); E; M := MinimalModel(E); M; G, h := TorsionSubgroup(E); torsion_pts_E := [ h(g) : g in G ]; torsion_pts_E; G2, h2 := TorsionSubgroup(M); torsion_pts_M := [ h2(g) : g in G2 ]; torsion_pts_M; Output: Magma V2.10-6 Tue Jan 13 2004 21:40:59 on modular [Seed = 1629850889] ------------------------------------- Elliptic Curve defined by y^2 = x^3 - 27*x + 55350 over Rational Field Elliptic Curve defined by y^2 + x*y + y = x^3 + x^2 + 1 over Rational Field [ (0 : 1 : 0), (51 : 432 : 1), (-21 : 216 : 1), (-21 : -216 : 1), (51 : -432 : 1) ] [ (0 : 1 : 0), (1 : 1 : 1), (-1 : 1 : 1), (-1 : -1 : 1), (1 : -3 : 1) ] Total time: 2.999 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (210.77.19.20) Time: Tue Jan 13 21:41:37 2004 Input: E := EllipticCurve([-4, 0]); E; M := MinimalModel(E); M; G, h := TorsionSubgroup(E); torsion_pts_E := [ h(g) : g in G ]; torsion_pts_E; G2, h2 := TorsionSubgroup(M); torsion_pts_M := [ h2(g) : g in G2 ]; torsion_pts_M; Output: Magma V2.10-6 Tue Jan 13 2004 21:41:34 on modular [Seed = 1747747941] ------------------------------------- Elliptic Curve defined by y^2 = x^3 - 4*x over Rational Field Elliptic Curve defined by y^2 = x^3 - 4*x over Rational Field [ (0 : 1 : 0), (-2 : 0 : 1), (0 : 0 : 1), (2 : 0 : 1) ] [ (0 : 1 : 0), (-2 : 0 : 1), (0 : 0 : 1), (2 : 0 : 1) ] Total time: 3.039 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (210.77.19.20) Time: Tue Jan 13 21:42:52 2004 Input: E := EllipticCurve([-25, 0]); E; M := MinimalModel(E); M; G, h := TorsionSubgroup(E); torsion_pts_E := [ h(g) : g in G ]; torsion_pts_E; G2, h2 := TorsionSubgroup(M); torsion_pts_M := [ h2(g) : g in G2 ]; torsion_pts_M; Output: Magma V2.10-6 Tue Jan 13 2004 21:42:49 on modular [Seed = 492433895] ------------------------------------- Elliptic Curve defined by y^2 = x^3 - 25*x over Rational Field Elliptic Curve defined by y^2 = x^3 - 25*x over Rational Field [ (0 : 1 : 0), (5 : 0 : 1), (0 : 0 : 1), (-5 : 0 : 1) ] [ (0 : 1 : 0), (5 : 0 : 1), (0 : 0 : 1), (-5 : 0 : 1) ] Total time: 3.039 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (210.77.19.20) Time: Tue Jan 13 21:43:11 2004 Input: E := EllipticCurve([-25, 32]); E; M := MinimalModel(E); M; G, h := TorsionSubgroup(E); torsion_pts_E := [ h(g) : g in G ]; torsion_pts_E; G2, h2 := TorsionSubgroup(M); torsion_pts_M := [ h2(g) : g in G2 ]; torsion_pts_M; Output: Magma V2.10-6 Tue Jan 13 2004 21:43:08 on modular [Seed = 71362795] ------------------------------------- Elliptic Curve defined by y^2 = x^3 - 25*x + 32 over Rational Field Elliptic Curve defined by y^2 = x^3 - 25*x + 32 over Rational Field [ (0 : 1 : 0) ] [ (0 : 1 : 0) ] Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (210.77.19.20) Time: Tue Jan 13 21:43:27 2004 Input: E := EllipticCurve([-25, 128]); E; M := MinimalModel(E); M; G, h := TorsionSubgroup(E); torsion_pts_E := [ h(g) : g in G ]; torsion_pts_E; G2, h2 := TorsionSubgroup(M); torsion_pts_M := [ h2(g) : g in G2 ]; torsion_pts_M; Output: Magma V2.10-6 Tue Jan 13 2004 21:43:24 on modular [Seed = 863494060] ------------------------------------- Elliptic Curve defined by y^2 = x^3 - 25*x + 128 over Rational Field Elliptic Curve defined by y^2 = x^3 - 25*x + 128 over Rational Field [ (0 : 1 : 0) ] [ (0 : 1 : 0) ] Total time: 3.019 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (210.77.19.20) Time: Tue Jan 13 21:43:39 2004 Input: E := EllipticCurve([-23, 128]); E; M := MinimalModel(E); M; G, h := TorsionSubgroup(E); torsion_pts_E := [ h(g) : g in G ]; torsion_pts_E; G2, h2 := TorsionSubgroup(M); torsion_pts_M := [ h2(g) : g in G2 ]; torsion_pts_M; Output: Magma V2.10-6 Tue Jan 13 2004 21:43:36 on modular [Seed = 981391025] ------------------------------------- Elliptic Curve defined by y^2 = x^3 - 23*x + 128 over Rational Field Elliptic Curve defined by y^2 = x^3 - 23*x + 128 over Rational Field [ (0 : 1 : 0) ] [ (0 : 1 : 0) ] Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (210.77.19.20) Time: Tue Jan 13 21:43:55 2004 Input: E := EllipticCurve([-23, 12]); E; M := MinimalModel(E); M; G, h := TorsionSubgroup(E); torsion_pts_E := [ h(g) : g in G ]; torsion_pts_E; G2, h2 := TorsionSubgroup(M); torsion_pts_M := [ h2(g) : g in G2 ]; torsion_pts_M; Output: Magma V2.10-6 Tue Jan 13 2004 21:43:52 on modular [Seed = 560319898] ------------------------------------- Elliptic Curve defined by y^2 = x^3 - 23*x + 12 over Rational Field Elliptic Curve defined by y^2 = x^3 - 23*x + 12 over Rational Field [ (0 : 1 : 0) ] [ (0 : 1 : 0) ] Total time: 3.079 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (194.165.15.3) Time: Wed Jan 14 01:28:26 2004 Input: p := 2^521; p; Output: Magma V2.10-6 Wed Jan 14 2004 01:28:23 on modular [Seed = 4206779179] ------------------------------------- 6864797660130609714981900799081393217269435300143305409394463459185543183397656\ 052122559640661454554977296311391480858037121987999716643812574028291115057152 Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (194.165.15.3) Time: Wed Jan 14 01:29:03 2004 Input: p := (2^521)-1; p; Output: Magma V2.10-6 Wed Jan 14 2004 01:29:00 on modular [Seed = 3819389465] ------------------------------------- 6864797660130609714981900799081393217269435300143305409394463459185543183397656\ 052122559640661454554977296311391480858037121987999716643812574028291115057151 Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (194.165.15.3) Time: Wed Jan 14 02:40:58 2004 Input: p := (2^401)-1; Factorisation (p-1); p; Output: Magma V2.10-6 Wed Jan 14 2004 02:40:54 on modular [Seed = 1798298042] ------------------------------------- [ <2, 1>, <3, 1>, <5, 3>, <11, 1>, <17, 1>, <31, 1>, <41, 1>, <101, 1>, <251, 1>, <257, 1>, <401, 1>, <601, 1>, <1601, 1>, <1801, 1>, <4051, 1>, <8101, 1>, <25601, 1>, <61681, 1>, <268501, 1>, <340801, 1>, <2787601, 1>, <82471201, 1>, <3173389601, 1>, <4278255361, 1>, <432363203127002885506543172618401, 1> ] 5164499756173817179311838344006023748659411585658447025661318713081295244033682\ 389259290706560275662871806343945494986751 Total time: 4.019 seconds, Total memory usage: 2.99MB ************** MAGMA ***************** Host 3(NXDOMAIN) (194.165.15.3) Time: Wed Jan 14 02:41:30 2004 Input: p := (2^271)-1; Factorisation (p-1); p; Output: Magma V2.10-6 Wed Jan 14 2004 02:41:27 on modular [Seed = 307667170] ------------------------------------- [ <2, 1>, <3, 4>, <7, 1>, <11, 1>, <19, 1>, <31, 1>, <73, 1>, <151, 1>, <271, 1>, <331, 1>, <631, 1>, <811, 1>, <15121, 1>, <23311, 1>, <87211, 1>, <262657, 1>, <348031, 1>, <18837001, 1>, <49971617830801, 1>, <385838642647891, 1> ] 3794275180128377091639574036764685364535950857523710002444946112771297432041422\ 847 Total time: 3.259 seconds, Total memory usage: 2.99MB ************** MAGMA ***************** Host 3(NXDOMAIN) (194.165.15.3) Time: Wed Jan 14 02:41:52 2004 Input: p := (2^271)-1; Factorisation (p); p; Output: Magma V2.10-6 Wed Jan 14 2004 02:41:48 on modular [Seed = 425569266] ------------------------------------- [ <15242475217, 1>, <2489277578681318902773305415678200452563642739707732865421\ 88386932989391, 1> ] 3794275180128377091639574036764685364535950857523710002444946112771297432041422\ 847 Total time: 3.799 seconds, Total memory usage: 2.99MB ************** MAGMA ***************** Host 3(NXDOMAIN) (194.165.15.3) Time: Wed Jan 14 02:42:29 2004 Input: p := (2^293)-1; Factorisation (p); p; Output: Magma V2.10-6 Wed Jan 14 2004 02:42:25 on modular [Seed = 4502198] ------------------------------------- [ <40122362455616221971122353, 1>, <3966452270281388904156112207107579216439107\ 43103031701971222447, 1> ] 1591434356511317254897223194069826688321459682551512695809484726058110390440106\ 8017057791 Total time: 3.239 seconds, Total memory usage: 2.99MB ************** MAGMA ***************** Host 3(NXDOMAIN) (194.165.15.3) Time: Wed Jan 14 02:42:59 2004 Input: p := (2^311)-1; Factorisation (p); p; Output: Magma V2.10-6 Wed Jan 14 2004 02:42:55 on modular [Seed = 913474718] ------------------------------------- [ <5344847, 1>, <2647649373910205158468946067671, 1>, <294803681348959296477194164064643062187559537539328375831, 1> ] 4171849679533027504677776769862406473833407270227837441302815640277772901915313\ 574263597826047 Total time: 3.619 seconds, Total memory usage: 2.99MB ************** MAGMA ***************** Host 3(NXDOMAIN) (194.165.15.3) Time: Wed Jan 14 02:43:25 2004 Input: p := (2^317)-1; Factorisation (p); p; Output: Magma V2.10-6 Wed Jan 14 2004 02:43:21 on modular [Seed = 1031376499] ------------------------------------- [ <9511, 1>, <587492521482839879, 1>, <4868122671322098041565641, 1>, <9815639231755686605031317440031161584572466128599, 1> ] 2669983794901137602993777132711940143253380652945815962433802009777774657225800\ 68752870260867071 Total time: 3.249 seconds, Total memory usage: 2.99MB ************** MAGMA ***************** Host 3(NXDOMAIN) (194.165.15.3) Time: Wed Jan 14 02:43:51 2004 Input: p := (2^331)-1; Factorisation (p); p; Output: Magma V2.10-6 Wed Jan 14 2004 02:43:47 on modular [Seed = 610309952] ------------------------------------- [ <16937389168607, 1>, <865118802936559, 1>, <298542624980197463613767215333569428005686468835821253721796682625551919, 1> ] 4374501449566023848745004454235242730706338861786424872851541212819905998398751\ 846447026354046107647 Total time: 3.599 seconds, Total memory usage: 2.99MB ************** MAGMA ***************** Host 3(NXDOMAIN) (194.165.15.3) Time: Wed Jan 14 02:44:11 2004 Input: p := (2^347)-1; Factorisation (p); p; Output: Magma V2.10-6 Wed Jan 14 2004 02:44:07 on modular [Seed = 728733755] ------------------------------------- [ <14143189112952632419639, 1>, <2027034530254598711604006944281449672934166611\ 2096057885992643120463337596490211193, 1> ] 2866873269987589389513526119127608675995706236460351404671986049233653595110606\ 01008752319138765710819327 Total time: 4.219 seconds, Total memory usage: 2.99MB ************** MAGMA ***************** Host 3(NXDOMAIN) (194.165.15.3) Time: Wed Jan 14 02:44:35 2004 Input: p := (2^401)-1; Factorisation (p); p; Output: Magma V2.10-6 Wed Jan 14 2004 02:44:32 on modular [Seed = 3533070821] ------------------------------------- [ <856971565399, 1>, <2136958965524920285681, 1>, <594538100848945223169882301931953, 1>, <47433587754438046660400107045347804188\ 40545962266329593, 1> ] 5164499756173817179311838344006023748659411585658447025661318713081295244033682\ 389259290706560275662871806343945494986751 Total time: 3.209 seconds, Total memory usage: 2.99MB ************** MAGMA ***************** Host 3(NXDOMAIN) (194.165.15.3) Time: Wed Jan 14 02:44:51 2004 Input: p := (2^419)-1; Factorisation (p); p; Output: Magma V2.10-6 Wed Jan 14 2004 02:44:48 on modular [Seed = 3650972414] ------------------------------------- [ <839, 1>, <903780021613921, 1>, <5800422716722833271214743, 1>, <10287968884341772230096159036619433593, 1>, <29919490848598531825060153417921002916701815927, 1> ] 1353842624082429130653522550851115089568572790710847937094960732721983060451965\ 636249987502980536903367866802227247837807116287 Total time: 3.179 seconds, Total memory usage: 2.99MB ************** MAGMA ***************** Host 3(NXDOMAIN) (194.165.15.3) Time: Wed Jan 14 02:45:34 2004 Input: p := (2^457)-1; Factorisation (p); p; Output: Magma V2.10-6 Wed Jan 14 2004 02:45:14 on modular [Seed = 3431497489] ------------------------------------- [ <150327409, 1>, <247553941968992978493531934444940989829116509732371457865094\ 3035813830300993611462717419801770460539016610145009605554380104535919, 1> ] 3721414268393507279612537896386583215890643766719068468641229819804873155140597\ 36743009817965446945567110411062408283101969716033850703871 Total time: 19.569 seconds, Total memory usage: 2.99MB ************** MAGMA ***************** Host 3(NXDOMAIN) (194.165.15.3) Time: Wed Jan 14 02:45:54 2004 Input: p := (2^521)-1; Factorisation (p); p; Output: Magma V2.10-6 Wed Jan 14 2004 02:45:50 on modular [Seed = 4088872970] ------------------------------------- [ <6864797660130609714981900799081393217269435300143305409394463459185543183397\ 6560521225596406614545549772963113914808580371219879997166438125740282911150571\ 51, 1> ] 6864797660130609714981900799081393217269435300143305409394463459185543183397656\ 052122559640661454554977296311391480858037121987999716643812574028291115057151 Total time: 3.579 seconds, Total memory usage: 2.99MB ************** MAGMA ***************** Host 3(NXDOMAIN) (194.165.15.3) Time: Wed Jan 14 02:46:49 2004 Input: p := (2^331)-1; Factorisation (p); p; Output: Magma V2.10-6 Wed Jan 14 2004 02:46:46 on modular [Seed = 4206774603] ------------------------------------- [ <16937389168607, 1>, <865118802936559, 1>, <298542624980197463613767215333569428005686468835821253721796682625551919, 1> ] 4374501449566023848745004454235242730706338861786424872851541212819905998398751\ 846447026354046107647 Total time: 3.499 seconds, Total memory usage: 2.99MB ************** MAGMA ***************** Host DSL217-132-22-167.bb.netvision.net.il. (217.132.22.167) Time: Wed Jan 14 05:35:26 2004 Input: Br:=BraidGroup; Output: Magma V2.10-6 Wed Jan 14 2004 05:35:22 on modular [Seed = 2362038204] ------------------------------------- >> Br:=BraidGroup;; ^ Runtime error in 'AssignNames': Bad argument types Argument types given: Intrinsic ~, SeqEnum[MonStgElt] Total time: 2.979 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host DSL217-132-22-167.bb.netvision.net.il. (217.132.22.167) Time: Wed Jan 14 05:35:49 2004 Input: Br:=BraidGroup(6); Output: Magma V2.10-6 Wed Jan 14 2004 05:35:46 on modular [Seed = 2244009565] ------------------------------------- Total time: 2.989 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host DSL217-132-22-167.bb.netvision.net.il. (217.132.22.167) Time: Wed Jan 14 05:36:18 2004 Input: Br:=BraidGroup(6); FundamentalElement(Br); Output: Magma V2.10-6 Wed Jan 14 2004 05:36:15 on modular [Seed = 3002591607] ------------------------------------- e * d * c * b * a * e * d * c * b * e * d * c * e * d * e Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host DSL217-132-22-167.bb.netvision.net.il. (217.132.22.167) Time: Wed Jan 14 05:37:02 2004 Input: Br:=BraidGroup(6); l:=FundamentalElement(Br); Output: Magma V2.10-6 Wed Jan 14 2004 05:36:59 on modular [Seed = 2884563002] ------------------------------------- Total time: 3.009 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host DSL217-132-22-167.bb.netvision.net.il. (217.132.22.167) Time: Wed Jan 14 05:38:18 2004 Input: Br:=BraidGroup(6); l:=FundamentalElement(Br); E:=e^(-1); D:=d^(-1); C:=c^(-1); B:=b^(-1); A:=a^(-1); Output: Magma V2.10-6 Wed Jan 14 2004 05:38:15 on modular [Seed = 2716138988] ------------------------------------- Total time: 2.909 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host DSL217-132-22-167.bb.netvision.net.il. (217.132.22.167) Time: Wed Jan 14 05:42:30 2004 Input: Br:=BraidGroup(6); l:=FundamentalElement(Br); E:=e^(-1); D:=d^(-1); C:=c^(-1); B:=b^(-1); A:=a^(-1); s[1]:=d^3; s[2]:=(c^d)^2; s[3]:=c^3; s[4]:=c^3; s[5]:=(c^(D*c))^2; s[6]:=b^(c*d*d*c*c); s[7]:=(b^(c^3))^3; s[8]:=e^(d*c*b*b*c*d*d*c*b); s[9]:=(e^(d*c*b))^3; s[10]:=a^(b*c*d*e*e*d*c*b); s[11]:=a; s[12]:=(c^D)^2; s[13]:=s[12]; s[14]:=d^3; Output: Magma V2.10-6 Wed Jan 14 2004 05:42:27 on modular [Seed = 1427114013] ------------------------------------- >> s[1]:=d^3; ^ User error: Identifier 's' has not been declared or assigned >> s[2]:=(c^d)^2; ^ User error: Identifier 's' has not been declared or assigned >> s[3]:=c^3; ^ User error: Identifier 's' has not been declared or assigned >> s[4]:=c^3; ^ User error: Identifier 's' has not been declared or assigned >> s[5]:=(c^(D*c))^2; ^ User error: Identifier 's' has not been declared or assigned >> s[6]:=b^(c*d*d*c*c); ^ User error: Identifier 's' has not been declared or assigned >> s[7]:=(b^(c^3))^3; ^ User error: Identifier 's' has not been declared or assigned >> s[8]:=e^(d*c*b*b*c*d*d*c*b); ^ User error: Identifier 's' has not been declared or assigned >> s[9]:=(e^(d*c*b))^3; ^ User error: Identifier 's' has not been declared or assigned >> s[10]:=a^(b*c*d*e*e*d*c*b); ^ User error: Identifier 's' has not been declared or assigned >> s[11]:=a; ^ User error: Identifier 's' has not been declared or assigned >> s[12]:=(c^D)^2; ^ User error: Identifier 's' has not been declared or assigned >> s[13]:=s[12]; ^ User error: Identifier 's' has not been declared or assigned >> s[14]:=d^3;; ^ User error: Identifier 's' has not been declared or assigned Total time: 2.989 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host DSL217-132-22-167.bb.netvision.net.il. (217.132.22.167) Time: Wed Jan 14 05:52:06 2004 Input: Br:=BraidGroup(6); l:=FundamentalElement(Br); E:=e^(-1); D:=d^(-1); C:=c^(-1); B:=b^(-1); A:=a^(-1); s:=vector(14,Br); s[1]:=d^3; s[2]:=(c^d)^2; s[3]:=c^3; s[4]:=c^3; s[5]:=(c^(D*c))^2; s[6]:=b^(c*d*d*c*c); s[7]:=(b^(c^3))^3; s[8]:=e^(d*c*b*b*c*d*d*c*b); s[9]:=(e^(d*c*b))^3; s[10]:=a^(b*c*d*e*e*d*c*b); s[11]:=a; s[12]:=(c^D)^2; s[13]:=s[12]; s[14]:=d^3; Output: Magma V2.10-6 Wed Jan 14 2004 05:52:03 on modular [Seed = 2134515831] ------------------------------------- >> s:=vector(14,Br); ^ User error: Identifier 'vector' has not been declared or assigned >> s[1]:=d^3; ^ User error: Identifier 's' has not been declared or assigned >> s[2]:=(c^d)^2; ^ User error: Identifier 's' has not been declared or assigned >> s[3]:=c^3; ^ User error: Identifier 's' has not been declared or assigned >> s[4]:=c^3; ^ User error: Identifier 's' has not been declared or assigned >> s[5]:=(c^(D*c))^2; ^ User error: Identifier 's' has not been declared or assigned >> s[6]:=b^(c*d*d*c*c); ^ User error: Identifier 's' has not been declared or assigned >> s[7]:=(b^(c^3))^3; ^ User error: Identifier 's' has not been declared or assigned >> s[8]:=e^(d*c*b*b*c*d*d*c*b); ^ User error: Identifier 's' has not been declared or assigned >> s[9]:=(e^(d*c*b))^3; ^ User error: Identifier 's' has not been declared or assigned >> s[10]:=a^(b*c*d*e*e*d*c*b); ^ User error: Identifier 's' has not been declared or assigned >> s[11]:=a; ^ User error: Identifier 's' has not been declared or assigned >> s[12]:=(c^D)^2; ^ User error: Identifier 's' has not been declared or assigned >> s[13]:=s[12]; ^ User error: Identifier 's' has not been declared or assigned >> s[14]:=d^3;; ^ User error: Identifier 's' has not been declared or assigned Total time: 2.989 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host DSL217-132-22-167.bb.netvision.net.il. (217.132.22.167) Time: Wed Jan 14 05:52:25 2004 Input: Br:=BraidGroup(6); l:=FundamentalElement(Br); E:=e^(-1); D:=d^(-1); C:=c^(-1); B:=b^(-1); A:=a^(-1); s:=Vector(14,Br); s[1]:=d^3; s[2]:=(c^d)^2; s[3]:=c^3; s[4]:=c^3; s[5]:=(c^(D*c))^2; s[6]:=b^(c*d*d*c*c); s[7]:=(b^(c^3))^3; s[8]:=e^(d*c*b*b*c*d*d*c*b); s[9]:=(e^(d*c*b))^3; s[10]:=a^(b*c*d*e*e*d*c*b); s[11]:=a; s[12]:=(c^D)^2; s[13]:=s[12]; s[14]:=d^3; Output: Magma V2.10-6 Wed Jan 14 2004 05:52:22 on modular [Seed = 1983064395] ------------------------------------- >> s:=Vector(14,Br); ^ Runtime error in 'Vector': Bad argument types Argument types given: RngIntElt, GrpBrd >> s[1]:=d^3; ^ User error: Identifier 's' has not been declared or assigned >> s[2]:=(c^d)^2; ^ User error: Identifier 's' has not been declared or assigned >> s[3]:=c^3; ^ User error: Identifier 's' has not been declared or assigned >> s[4]:=c^3; ^ User error: Identifier 's' has not been declared or assigned >> s[5]:=(c^(D*c))^2; ^ User error: Identifier 's' has not been declared or assigned >> s[6]:=b^(c*d*d*c*c); ^ User error: Identifier 's' has not been declared or assigned >> s[7]:=(b^(c^3))^3; ^ User error: Identifier 's' has not been declared or assigned >> s[8]:=e^(d*c*b*b*c*d*d*c*b); ^ User error: Identifier 's' has not been declared or assigned >> s[9]:=(e^(d*c*b))^3; ^ User error: Identifier 's' has not been declared or assigned >> s[10]:=a^(b*c*d*e*e*d*c*b); ^ User error: Identifier 's' has not been declared or assigned >> s[11]:=a; ^ User error: Identifier 's' has not been declared or assigned >> s[12]:=(c^D)^2; ^ User error: Identifier 's' has not been declared or assigned >> s[13]:=s[12]; ^ User error: Identifier 's' has not been declared or assigned >> s[14]:=d^3;; ^ User error: Identifier 's' has not been declared or assigned Total time: 2.979 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host DSL217-132-22-167.bb.netvision.net.il. (217.132.22.167) Time: Wed Jan 14 06:08:25 2004 Input: Br:=BraidGroup(6); l:=FundamentalElement(Br); E:=e^(-1); D:=d^(-1); C:=c^(-1); B:=b^(-1); A:=a^(-1); s:=[**]; Append(s,d^3); Append(s,(c^d)^2); Append(s,c^3); Append(s,c^3); Append(s,(c^(D*c))^2); Append(s,b^(c*d*d*c*c)); Append(s,(b^(c^3))^3); Append(s,e^(d*c*b*b*c*d*d*c*b)); Append(s,(e^(d*c*b))^3); Append(s,a^(b*c*d*e*e*d*c*b)); Append(s,a); Append(s,(c^D)^2)); Append(s,(c^D)^2)); Append(s,d^3); Output: Magma V2.10-6 Wed Jan 14 2004 06:08:20 on modular [Seed = 947739463] ------------------------------------- [* d^3 *] [* e^-1 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * d * c * b * e * d * c * e * d * e * c * b * e * d * c * b * a * e * d * c * b * e * d * c * d * e * c * d *] [* c^3 *] [* c^3 *] [* e^-1 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * d * c * e * d * e * b * c * e * d * c * b * a * e * d * c * b * e * d * c * d * e * c * e * d * c * b * a * e * d * c * b * d * c * e * d * e * b * c * e * d * c * b * a * e * d * c * b * e * d * c * d * e * c *] [* e^-1 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * d * c * e * d * e^2 * d * c * b * a * e * d * c * b * d * c * e * d * e^2 * d * c * b * a * e * d * c * b * e * d * c * d * e^2 * d * c * b * a * d * c * b * e * d * c * e * d * e^2 * d * c * b * a * e * d * c * b * d * c * e * d * e * b * c * d^2 * c^2 *] [* e^-1 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * d * c * e * d * e^2 * d * c * b * a * e * d * c * b * d * c * e * d * e^2 * d * c * b * a * e * d * c * b * d * c * e * d * e * b * c^3 * e * d * c * b * a * e * d * c * b * d * c * e * d * e^2 * d * c * b * a * e * d * c * b * d * c * e * d * e^2 * d * c * b * a * e * d * c * b * d * c * e * d * e * d * c^3 * e * d * c * b * a * e * d * c * b * d * c * e * d * e^2 * d * c * b * a * e * d * c * b * d * c * e * d * e^2 * d * c * b * a * e * d * c * b * d * c * e * d * e * b * c^3 *] [* e^-1 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * d * c * b * e * d * c * e * d * e^2 * d * c * b * a * e * d * c * b * d * c * e * d * e^2 * d * c * b * a * e * d * c * b * e * d * c * d * e^2 * d * c * b * a * d * c * b * e * d * c * e * d * e^2 * d * c * b * a * e * d * c * b * d * c * e * d * e^2 * d * c * b * a * e * d * c * b * e * d * c * d * e^2 * d * c * b * a * d * c * b * e * d * c * e * d * e^2 * d * c * b * a * e * d * c * b * d * c * e * d * e^2 * d * c * b * a * e * d * c * b * e * d * c * d * e^2 * d * c * b^2 * c * d^2 * c * b *] [* e^-1 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * d * c * b * e * d * c * e * d * e^2 * d * c * b * a * e * d * c * b * d * c * e * d * e^2 * d * c * b * a * e * d * c * b * e * d * c * d * e^2 * d * c * b * e * d * c * b * a * e * d * c * b * e * d * c * d * e^2 * d * c * b * a * e * d * c * b * d * c * e * d * e^2 * d * c * b * a * d * c * b * e * d * c * e * d * e * a * b * c * d * e * d * c * b * a * d * c * b * e * d * c * e * d * e^2 * d * c * b * a * e * d * c * b * d * c * e * d * e^2 * d * c * b * a * e * d * c * b * e * d * c * d * e^2 * d * c * b *] [* e^-1 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * d * e^2 * d * c * b * a * e * d * c * b * d * c * e * d * e^2 * d * c * b * a * d * c * b * e * d * c * e * d * e^2 * d * c * b * a * e * d * c * b * e * d * c * e * d^2 * c * b * a * e * d * c * b * e * d * c * e * d * e^2 * d * c * b * a * e * d * c * b * e * d * c * d * e^2 * d * c * b * a * e * d * c * b * d * c * e * d * e^2 * d * c * b * a * d * c * b * e * d * c * e * d * e * a * b * c * d * e^2 * d * c * b *] [* a *] >> Append(s,(c^D)^2)); ^ User error: bad syntax >> Append(s,(c^D)^2)); ^ User error: bad syntax [* d^3 *] Total time: 3.239 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host DSL217-132-22-167.bb.netvision.net.il. (217.132.22.167) Time: Wed Jan 14 06:11:19 2004 Input: Br:=BraidGroup(6); l:=FundamentalElement(Br); E:=e^(-1); D:=d^(-1); C:=c^(-1); B:=b^(-1); A:=a^(-1); s:=[**]; Append(s,d^3); Append(s,(c^d)^2); n:=#s; W:=Id(Br) for i from 1 to n do W*=s[i]; end for ; normalform(W); Append(s,c^3); Append(s,c^3); Append(s,(c^(D*c))^2); Append(s,b^(c*d*d*c*c)); Append(s,(b^(c^3))^3); Append(s,e^(d*c*b*b*c*d*d*c*b)); Append(s,(e^(d*c*b))^3); Append(s,a^(b*c*d*e*e*d*c*b)); Append(s,a); Append(s,(c^D)^2)); Append(s,(c^D)^2)); Append(s,d^3); Output: Magma V2.10-6 Wed Jan 14 2004 06:11:16 on modular [Seed = 678251431] ------------------------------------- [* d^3 *] [* e^-1 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * d * c * b * e * d * c * e * d * e * c * b * e * d * c * b * a * e * d * c * b * e * d * c * d * e * c * d *] >> for i from 1 to n ^ User error: bad syntax >> do W*=s[i]; ^ User error: bad syntax >> end for ; ^ User error: bad syntax >> normalform(W); ^ User error: Identifier 'W' has not been declared or assigned [* c^3 *] [* c^3 *] [* e^-1 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * d * c * e * d * e * b * c * e * d * c * b * a * e * d * c * b * e * d * c * d * e * c * e * d * c * b * a * e * d * c * b * d * c * e * d * e * b * c * e * d * c * b * a * e * d * c * b * e * d * c * d * e * c *] [* e^-1 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * d * c * e * d * e^2 * d * c * b * a * e * d * c * b * d * c * e * d * e^2 * d * c * b * a * e * d * c * b * e * d * c * d * e^2 * d * c * b * a * d * c * b * e * d * c * e * d * e^2 * d * c * b * a * e * d * c * b * d * c * e * d * e * b * c * d^2 * c^2 *] [* e^-1 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * d * c * e * d * e^2 * d * c * b * a * e * d * c * b * d * c * e * d * e^2 * d * c * b * a * e * d * c * b * d * c * e * d * e * b * c^3 * e * d * c * b * a * e * d * c * b * d * c * e * d * e^2 * d * c * b * a * e * d * c * b * d * c * e * d * e^2 * d * c * b * a * e * d * c * b * d * c * e * d * e * d * c^3 * e * d * c * b * a * e * d * c * b * d * c * e * d * e^2 * d * c * b * a * e * d * c * b * d * c * e * d * e^2 * d * c * b * a * e * d * c * b * d * c * e * d * e * b * c^3 *] [* e^-1 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * d * c * b * e * d * c * e * d * e^2 * d * c * b * a * e * d * c * b * d * c * e * d * e^2 * d * c * b * a * e * d * c * b * e * d * c * d * e^2 * d * c * b * a * d * c * b * e * d * c * e * d * e^2 * d * c * b * a * e * d * c * b * d * c * e * d * e^2 * d * c * b * a * e * d * c * b * e * d * c * d * e^2 * d * c * b * a * d * c * b * e * d * c * e * d * e^2 * d * c * b * a * e * d * c * b * d * c * e * d * e^2 * d * c * b * a * e * d * c * b * e * d * c * d * e^2 * d * c * b^2 * c * d^2 * c * b *] [* e^-1 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * d * c * b * e * d * c * e * d * e^2 * d * c * b * a * e * d * c * b * d * c * e * d * e^2 * d * c * b * a * e * d * c * b * e * d * c * d * e^2 * d * c * b * e * d * c * b * a * e * d * c * b * e * d * c * d * e^2 * d * c * b * a * e * d * c * b * d * c * e * d * e^2 * d * c * b * a * d * c * b * e * d * c * e * d * e * a * b * c * d * e * d * c * b * a * d * c * b * e * d * c * e * d * e^2 * d * c * b * a * e * d * c * b * d * c * e * d * e^2 * d * c * b * a * e * d * c * b * e * d * c * d * e^2 * d * c * b *] [* e^-1 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * d * e^2 * d * c * b * a * e * d * c * b * d * c * e * d * e^2 * d * c * b * a * d * c * b * e * d * c * e * d * e^2 * d * c * b * a * e * d * c * b * e * d * c * e * d^2 * c * b * a * e * d * c * b * e * d * c * e * d * e^2 * d * c * b * a * e * d * c * b * e * d * c * d * e^2 * d * c * b * a * e * d * c * b * d * c * e * d * e^2 * d * c * b * a * d * c * b * e * d * c * e * d * e * a * b * c * d * e^2 * d * c * b *] [* a *] >> Append(s,(c^D)^2)); ^ User error: bad syntax >> Append(s,(c^D)^2)); ^ User error: bad syntax [* d^3 *] Total time: 3.089 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host DSL217-132-22-167.bb.netvision.net.il. (217.132.22.167) Time: Wed Jan 14 06:15:27 2004 Input: Br:=BraidGroup(6); l:=FundamentalElement(Br); E:=e^(-1); D:=d^(-1); C:=c^(-1); B:=b^(-1); A:=a^(-1); s:=[**]; Append(s,d^3); Append(s,(c^d)^2); n:=#s; W:=Id(Br) for i from 1 to n do W*=s[i]; end for ; normalform(W); Append(s,c^3); Append(s,c^3); Append(s,(c^(D*c))^2); Append(s,b^(c*d*d*c*c)); Append(s,(b^(c^3))^3); Append(s,e^(d*c*b*b*c*d*d*c*b)); Append(s,(e^(d*c*b))^3); Append(s,a^(b*c*d*e*e*d*c*b)); Append(s,a); Append(s,(c^D)^2)); Append(s,(c^D)^2)); Append(s,d^3); Output: Magma V2.10-6 Wed Jan 14 2004 06:15:24 on modular [Seed = 3734747721] ------------------------------------- [* d^3 *] [* e^-1 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * d * c * b * e * d * c * e * d * e * c * b * e * d * c * b * a * e * d * c * b * e * d * c * d * e * c * d *] >> for i from 1 to n ^ User error: bad syntax >> do W*=s[i]; ^ User error: bad syntax >> end for ; ^ User error: bad syntax >> normalform(W); ^ User error: Identifier 'W' has not been declared or assigned [* c^3 *] [* c^3 *] [* e^-1 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * d * c * e * d * e * b * c * e * d * c * b * a * e * d * c * b * e * d * c * d * e * c * e * d * c * b * a * e * d * c * b * d * c * e * d * e * b * c * e * d * c * b * a * e * d * c * b * e * d * c * d * e * c *] [* e^-1 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * d * c * e * d * e^2 * d * c * b * a * e * d * c * b * d * c * e * d * e^2 * d * c * b * a * e * d * c * b * e * d * c * d * e^2 * d * c * b * a * d * c * b * e * d * c * e * d * e^2 * d * c * b * a * e * d * c * b * d * c * e * d * e * b * c * d^2 * c^2 *] [* e^-1 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * d * c * e * d * e^2 * d * c * b * a * e * d * c * b * d * c * e * d * e^2 * d * c * b * a * e * d * c * b * d * c * e * d * e * b * c^3 * e * d * c * b * a * e * d * c * b * d * c * e * d * e^2 * d * c * b * a * e * d * c * b * d * c * e * d * e^2 * d * c * b * a * e * d * c * b * d * c * e * d * e * d * c^3 * e * d * c * b * a * e * d * c * b * d * c * e * d * e^2 * d * c * b * a * e * d * c * b * d * c * e * d * e^2 * d * c * b * a * e * d * c * b * d * c * e * d * e * b * c^3 *] [* e^-1 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * d * c * b * e * d * c * e * d * e^2 * d * c * b * a * e * d * c * b * d * c * e * d * e^2 * d * c * b * a * e * d * c * b * e * d * c * d * e^2 * d * c * b * a * d * c * b * e * d * c * e * d * e^2 * d * c * b * a * e * d * c * b * d * c * e * d * e^2 * d * c * b * a * e * d * c * b * e * d * c * d * e^2 * d * c * b * a * d * c * b * e * d * c * e * d * e^2 * d * c * b * a * e * d * c * b * d * c * e * d * e^2 * d * c * b * a * e * d * c * b * e * d * c * d * e^2 * d * c * b^2 * c * d^2 * c * b *] [* e^-1 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * d * c * b * e * d * c * e * d * e^2 * d * c * b * a * e * d * c * b * d * c * e * d * e^2 * d * c * b * a * e * d * c * b * e * d * c * d * e^2 * d * c * b * e * d * c * b * a * e * d * c * b * e * d * c * d * e^2 * d * c * b * a * e * d * c * b * d * c * e * d * e^2 * d * c * b * a * d * c * b * e * d * c * e * d * e * a * b * c * d * e * d * c * b * a * d * c * b * e * d * c * e * d * e^2 * d * c * b * a * e * d * c * b * d * c * e * d * e^2 * d * c * b * a * e * d * c * b * e * d * c * d * e^2 * d * c * b *] [* e^-1 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * d * e^2 * d * c * b * a * e * d * c * b * d * c * e * d * e^2 * d * c * b * a * d * c * b * e * d * c * e * d * e^2 * d * c * b * a * e * d * c * b * e * d * c * e * d^2 * c * b * a * e * d * c * b * e * d * c * e * d * e^2 * d * c * b * a * e * d * c * b * e * d * c * d * e^2 * d * c * b * a * e * d * c * b * d * c * e * d * e^2 * d * c * b * a * d * c * b * e * d * c * e * d * e * a * b * c * d * e^2 * d * c * b *] [* a *] >> Append(s,(c^D)^2)); ^ User error: bad syntax >> Append(s,(c^D)^2)); ^ User error: bad syntax [* d^3 *] Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host DSL217-132-22-167.bb.netvision.net.il. (217.132.22.167) Time: Wed Jan 14 06:19:24 2004 Input: Br:=BraidGroup(6); l:=FundamentalElement(Br); E:=e^(-1); D:=d^(-1); C:=c^(-1); B:=b^(-1); A:=a^(-1); s:=[**]; Append(s,d^3); Append(s,(c^d)^2); Append(s,c^3); Append(s,c^3); Append(s,(c^(D*c))^2); Append(s,b^(c*d*d*c*c)); Append(s,(b^(c^3))^3); Append(s,e^(d*c*b*b*c*d*d*c*b)); Append(s,(e^(d*c*b))^3); Append(s,a^(b*c*d*e*e*d*c*b)); Append(s,a); Append(s,(c^D)^2)); Append(s,(c^D)^2)); Append(s,d^3); n:=#s; W:=Id(Br) for i:=1 to n by do W*=s[i]; end for ; normalform(W); Output: Magma V2.10-6 Wed Jan 14 2004 06:19:21 on modular [Seed = 3566317878] ------------------------------------- [* d^3 *] [* e^-1 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * d * c * b * e * d * c * e * d * e * c * b * e * d * c * b * a * e * d * c * b * e * d * c * d * e * c * d *] [* c^3 *] [* c^3 *] [* e^-1 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * d * c * e * d * e * b * c * e * d * c * b * a * e * d * c * b * e * d * c * d * e * c * e * d * c * b * a * e * d * c * b * d * c * e * d * e * b * c * e * d * c * b * a * e * d * c * b * e * d * c * d * e * c *] [* e^-1 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * d * c * e * d * e^2 * d * c * b * a * e * d * c * b * d * c * e * d * e^2 * d * c * b * a * e * d * c * b * e * d * c * d * e^2 * d * c * b * a * d * c * b * e * d * c * e * d * e^2 * d * c * b * a * e * d * c * b * d * c * e * d * e * b * c * d^2 * c^2 *] [* e^-1 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * d * c * e * d * e^2 * d * c * b * a * e * d * c * b * d * c * e * d * e^2 * d * c * b * a * e * d * c * b * d * c * e * d * e * b * c^3 * e * d * c * b * a * e * d * c * b * d * c * e * d * e^2 * d * c * b * a * e * d * c * b * d * c * e * d * e^2 * d * c * b * a * e * d * c * b * d * c * e * d * e * d * c^3 * e * d * c * b * a * e * d * c * b * d * c * e * d * e^2 * d * c * b * a * e * d * c * b * d * c * e * d * e^2 * d * c * b * a * e * d * c * b * d * c * e * d * e * b * c^3 *] [* e^-1 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * d * c * b * e * d * c * e * d * e^2 * d * c * b * a * e * d * c * b * d * c * e * d * e^2 * d * c * b * a * e * d * c * b * e * d * c * d * e^2 * d * c * b * a * d * c * b * e * d * c * e * d * e^2 * d * c * b * a * e * d * c * b * d * c * e * d * e^2 * d * c * b * a * e * d * c * b * e * d * c * d * e^2 * d * c * b * a * d * c * b * e * d * c * e * d * e^2 * d * c * b * a * e * d * c * b * d * c * e * d * e^2 * d * c * b * a * e * d * c * b * e * d * c * d * e^2 * d * c * b^2 * c * d^2 * c * b *] [* e^-1 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * d * c * b * e * d * c * e * d * e^2 * d * c * b * a * e * d * c * b * d * c * e * d * e^2 * d * c * b * a * e * d * c * b * e * d * c * d * e^2 * d * c * b * e * d * c * b * a * e * d * c * b * e * d * c * d * e^2 * d * c * b * a * e * d * c * b * d * c * e * d * e^2 * d * c * b * a * d * c * b * e * d * c * e * d * e * a * b * c * d * e * d * c * b * a * d * c * b * e * d * c * e * d * e^2 * d * c * b * a * e * d * c * b * d * c * e * d * e^2 * d * c * b * a * e * d * c * b * e * d * c * d * e^2 * d * c * b *] [* e^-1 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * d * e^2 * d * c * b * a * e * d * c * b * d * c * e * d * e^2 * d * c * b * a * d * c * b * e * d * c * e * d * e^2 * d * c * b * a * e * d * c * b * e * d * c * e * d^2 * c * b * a * e * d * c * b * e * d * c * e * d * e^2 * d * c * b * a * e * d * c * b * e * d * c * d * e^2 * d * c * b * a * e * d * c * b * d * c * e * d * e^2 * d * c * b * a * d * c * b * e * d * c * e * d * e * a * b * c * d * e^2 * d * c * b *] [* a *] >> Append(s,(c^D)^2)); ^ User error: bad syntax >> Append(s,(c^D)^2)); ^ User error: bad syntax [* d^3 *] >> for i:=1 to n by ^ User error: bad syntax >> do W*=s[i]; ^ User error: bad syntax >> end for ; ^ User error: bad syntax >> normalform(W);; ^ User error: Identifier 'W' has not been declared or assigned Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host DSL217-132-22-167.bb.netvision.net.il. (217.132.22.167) Time: Wed Jan 14 06:19:54 2004 Input: Br:=BraidGroup(6); l:=FundamentalElement(Br); E:=e^(-1); D:=d^(-1); C:=c^(-1); B:=b^(-1); A:=a^(-1); s:=[**]; Append(s,d^3); Append(s,(c^d)^2); Append(s,c^3); Append(s,c^3); Append(s,(c^(D*c))^2); Append(s,b^(c*d*d*c*c)); Append(s,(b^(c^3))^3); Append(s,e^(d*c*b*b*c*d*d*c*b)); Append(s,(e^(d*c*b))^3); Append(s,a^(b*c*d*e*e*d*c*b)); Append(s,a); Append(s,(c^D)^2)); Append(s,(c^D)^2)); Append(s,d^3); n:=#s; W:=Id(Br) for i:=1 to n by 1 do W*=s[i]; end for ; normalform(W); Output: Magma V2.10-6 Wed Jan 14 2004 06:19:51 on modular [Seed = 3263670094] ------------------------------------- [* d^3 *] [* e^-1 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * d * c * b * e * d * c * e * d * e * c * b * e * d * c * b * a * e * d * c * b * e * d * c * d * e * c * d *] [* c^3 *] [* c^3 *] [* e^-1 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * d * c * e * d * e * b * c * e * d * c * b * a * e * d * c * b * e * d * c * d * e * c * e * d * c * b * a * e * d * c * b * d * c * e * d * e * b * c * e * d * c * b * a * e * d * c * b * e * d * c * d * e * c *] [* e^-1 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * d * c * e * d * e^2 * d * c * b * a * e * d * c * b * d * c * e * d * e^2 * d * c * b * a * e * d * c * b * e * d * c * d * e^2 * d * c * b * a * d * c * b * e * d * c * e * d * e^2 * d * c * b * a * e * d * c * b * d * c * e * d * e * b * c * d^2 * c^2 *] [* e^-1 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * d * c * e * d * e^2 * d * c * b * a * e * d * c * b * d * c * e * d * e^2 * d * c * b * a * e * d * c * b * d * c * e * d * e * b * c^3 * e * d * c * b * a * e * d * c * b * d * c * e * d * e^2 * d * c * b * a * e * d * c * b * d * c * e * d * e^2 * d * c * b * a * e * d * c * b * d * c * e * d * e * d * c^3 * e * d * c * b * a * e * d * c * b * d * c * e * d * e^2 * d * c * b * a * e * d * c * b * d * c * e * d * e^2 * d * c * b * a * e * d * c * b * d * c * e * d * e * b * c^3 *] [* e^-1 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * d * c * b * e * d * c * e * d * e^2 * d * c * b * a * e * d * c * b * d * c * e * d * e^2 * d * c * b * a * e * d * c * b * e * d * c * d * e^2 * d * c * b * a * d * c * b * e * d * c * e * d * e^2 * d * c * b * a * e * d * c * b * d * c * e * d * e^2 * d * c * b * a * e * d * c * b * e * d * c * d * e^2 * d * c * b * a * d * c * b * e * d * c * e * d * e^2 * d * c * b * a * e * d * c * b * d * c * e * d * e^2 * d * c * b * a * e * d * c * b * e * d * c * d * e^2 * d * c * b^2 * c * d^2 * c * b *] [* e^-1 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * d * c * b * e * d * c * e * d * e^2 * d * c * b * a * e * d * c * b * d * c * e * d * e^2 * d * c * b * a * e * d * c * b * e * d * c * d * e^2 * d * c * b * e * d * c * b * a * e * d * c * b * e * d * c * d * e^2 * d * c * b * a * e * d * c * b * d * c * e * d * e^2 * d * c * b * a * d * c * b * e * d * c * e * d * e * a * b * c * d * e * d * c * b * a * d * c * b * e * d * c * e * d * e^2 * d * c * b * a * e * d * c * b * d * c * e * d * e^2 * d * c * b * a * e * d * c * b * e * d * c * d * e^2 * d * c * b *] [* e^-1 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * d * e^2 * d * c * b * a * e * d * c * b * d * c * e * d * e^2 * d * c * b * a * d * c * b * e * d * c * e * d * e^2 * d * c * b * a * e * d * c * b * e * d * c * e * d^2 * c * b * a * e * d * c * b * e * d * c * e * d * e^2 * d * c * b * a * e * d * c * b * e * d * c * d * e^2 * d * c * b * a * e * d * c * b * d * c * e * d * e^2 * d * c * b * a * d * c * b * e * d * c * e * d * e * a * b * c * d * e^2 * d * c * b *] [* a *] >> Append(s,(c^D)^2)); ^ User error: bad syntax >> Append(s,(c^D)^2)); ^ User error: bad syntax [* d^3 *] >> for i:=1 to n by 1 ^ User error: bad syntax >> do W*=s[i]; ^ User error: bad syntax >> end for ; ^ User error: bad syntax >> normalform(W);; ^ User error: Identifier 'W' has not been declared or assigned Total time: 3.029 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host DSL217-132-22-167.bb.netvision.net.il. (217.132.22.167) Time: Wed Jan 14 06:21:08 2004 Input: Br:=BraidGroup(6); l:=FundamentalElement(Br); E:=e^(-1); D:=d^(-1); C:=c^(-1); B:=b^(-1); A:=a^(-1); s:=[**]; Append(s,d^3); Append(s,(c^d)^2); Append(s,c^3); Append(s,c^3); Append(s,(c^(D*c))^2); Append(s,b^(c*d*d*c*c)); Append(s,(b^(c^3))^3); Append(s,e^(d*c*b*b*c*d*d*c*b)); Append(s,(e^(d*c*b))^3); Append(s,a^(b*c*d*e*e*d*c*b)); Append(s,a); Append(s,(c^D)^2); Append(s,(c^D)^2); Append(s,d^3); n:=#s; W:=Id(Br) for i:=1 to n by 1 do W*=s[i]; end for ; normalform(W); Output: Magma V2.10-6 Wed Jan 14 2004 06:21:05 on modular [Seed = 4055144331] ------------------------------------- [* d^3 *] [* e^-1 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * d * c * b * e * d * c * e * d * e * c * b * e * d * c * b * a * e * d * c * b * e * d * c * d * e * c * d *] [* c^3 *] [* c^3 *] [* e^-1 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * d * c * e * d * e * b * c * e * d * c * b * a * e * d * c * b * e * d * c * d * e * c * e * d * c * b * a * e * d * c * b * d * c * e * d * e * b * c * e * d * c * b * a * e * d * c * b * e * d * c * d * e * c *] [* e^-1 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * d * c * e * d * e^2 * d * c * b * a * e * d * c * b * d * c * e * d * e^2 * d * c * b * a * e * d * c * b * e * d * c * d * e^2 * d * c * b * a * d * c * b * e * d * c * e * d * e^2 * d * c * b * a * e * d * c * b * d * c * e * d * e * b * c * d^2 * c^2 *] [* e^-1 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * d * c * e * d * e^2 * d * c * b * a * e * d * c * b * d * c * e * d * e^2 * d * c * b * a * e * d * c * b * d * c * e * d * e * b * c^3 * e * d * c * b * a * e * d * c * b * d * c * e * d * e^2 * d * c * b * a * e * d * c * b * d * c * e * d * e^2 * d * c * b * a * e * d * c * b * d * c * e * d * e * d * c^3 * e * d * c * b * a * e * d * c * b * d * c * e * d * e^2 * d * c * b * a * e * d * c * b * d * c * e * d * e^2 * d * c * b * a * e * d * c * b * d * c * e * d * e * b * c^3 *] [* e^-1 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * d * c * b * e * d * c * e * d * e^2 * d * c * b * a * e * d * c * b * d * c * e * d * e^2 * d * c * b * a * e * d * c * b * e * d * c * d * e^2 * d * c * b * a * d * c * b * e * d * c * e * d * e^2 * d * c * b * a * e * d * c * b * d * c * e * d * e^2 * d * c * b * a * e * d * c * b * e * d * c * d * e^2 * d * c * b * a * d * c * b * e * d * c * e * d * e^2 * d * c * b * a * e * d * c * b * d * c * e * d * e^2 * d * c * b * a * e * d * c * b * e * d * c * d * e^2 * d * c * b^2 * c * d^2 * c * b *] [* e^-1 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * d * c * b * e * d * c * e * d * e^2 * d * c * b * a * e * d * c * b * d * c * e * d * e^2 * d * c * b * a * e * d * c * b * e * d * c * d * e^2 * d * c * b * e * d * c * b * a * e * d * c * b * e * d * c * d * e^2 * d * c * b * a * e * d * c * b * d * c * e * d * e^2 * d * c * b * a * d * c * b * e * d * c * e * d * e * a * b * c * d * e * d * c * b * a * d * c * b * e * d * c * e * d * e^2 * d * c * b * a * e * d * c * b * d * c * e * d * e^2 * d * c * b * a * e * d * c * b * e * d * c * d * e^2 * d * c * b *] [* e^-1 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * d * e^2 * d * c * b * a * e * d * c * b * d * c * e * d * e^2 * d * c * b * a * d * c * b * e * d * c * e * d * e^2 * d * c * b * a * e * d * c * b * e * d * c * e * d^2 * c * b * a * e * d * c * b * e * d * c * e * d * e^2 * d * c * b * a * e * d * c * b * e * d * c * d * e^2 * d * c * b * a * e * d * c * b * d * c * e * d * e^2 * d * c * b * a * d * c * b * e * d * c * e * d * e * a * b * c * d * e^2 * d * c * b *] [* a *] [* e^-1 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-1 * d * c * e * d * c * b * a * d * c * b * e * d * c * e * d * e * b * c * e * d * c * b * a * e * d * c * b * e * d * c * d * e *] [* e^-1 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-1 * d * c * e * d * c * b * a * d * c * b * e * d * c * e * d * e * b * c * e * d * c * b * a * e * d * c * b * e * d * c * d * e *] [* d^3 *] >> for i:=1 to n by 1 ^ User error: bad syntax >> do W*=s[i]; ^ User error: b ** WARNING: Output too long, hence truncated. ************** MAGMA ***************** Host DSL217-132-22-167.bb.netvision.net.il. (217.132.22.167) Time: Wed Jan 14 06:23:57 2004 Input: Br:=BraidGroup(6); l:=FundamentalElement(Br); E:=e^(-1); D:=d^(-1); C:=c^(-1); B:=b^(-1); A:=a^(-1); s:=[**]; Append(s,d^3); Append(s,(c^d)^2); Append(s,c^3); Append(s,c^3); Append(s,(c^(D*c))^2); Append(s,b^(c*d*d*c*c)); Append(s,(b^(c^3))^3); Append(s,e^(d*c*b*b*c*d*d*c*b)); Append(s,(e^(d*c*b))^3); Append(s,a^(b*c*d*e*e*d*c*b)); Append(s,a); Append(s,(c^D)^2); Append(s,(c^D)^2); Append(s,d^3); n:=#s; W:=Id(Br) for i:=1 to n do W*=s[i]; end for ; normalform(W); Output: Magma V2.10-6 Wed Jan 14 2004 06:23:54 on modular [Seed = 3970534013] ------------------------------------- [* d^3 *] [* e^-1 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * d * c * b * e * d * c * e * d * e * c * b * e * d * c * b * a * e * d * c * b * e * d * c * d * e * c * d *] [* c^3 *] [* c^3 *] [* e^-1 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * d * c * e * d * e * b * c * e * d * c * b * a * e * d * c * b * e * d * c * d * e * c * e * d * c * b * a * e * d * c * b * d * c * e * d * e * b * c * e * d * c * b * a * e * d * c * b * e * d * c * d * e * c *] [* e^-1 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * d * c * e * d * e^2 * d * c * b * a * e * d * c * b * d * c * e * d * e^2 * d * c * b * a * e * d * c * b * e * d * c * d * e^2 * d * c * b * a * d * c * b * e * d * c * e * d * e^2 * d * c * b * a * e * d * c * b * d * c * e * d * e * b * c * d^2 * c^2 *] [* e^-1 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * d * c * e * d * e^2 * d * c * b * a * e * d * c * b * d * c * e * d * e^2 * d * c * b * a * e * d * c * b * d * c * e * d * e * b * c^3 * e * d * c * b * a * e * d * c * b * d * c * e * d * e^2 * d * c * b * a * e * d * c * b * d * c * e * d * e^2 * d * c * b * a * e * d * c * b * d * c * e * d * e * d * c^3 * e * d * c * b * a * e * d * c * b * d * c * e * d * e^2 * d * c * b * a * e * d * c * b * d * c * e * d * e^2 * d * c * b * a * e * d * c * b * d * c * e * d * e * b * c^3 *] [* e^-1 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * d * c * b * e * d * c * e * d * e^2 * d * c * b * a * e * d * c * b * d * c * e * d * e^2 * d * c * b * a * e * d * c * b * e * d * c * d * e^2 * d * c * b * a * d * c * b * e * d * c * e * d * e^2 * d * c * b * a * e * d * c * b * d * c * e * d * e^2 * d * c * b * a * e * d * c * b * e * d * c * d * e^2 * d * c * b * a * d * c * b * e * d * c * e * d * e^2 * d * c * b * a * e * d * c * b * d * c * e * d * e^2 * d * c * b * a * e * d * c * b * e * d * c * d * e^2 * d * c * b^2 * c * d^2 * c * b *] [* e^-1 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * d * c * b * e * d * c * e * d * e^2 * d * c * b * a * e * d * c * b * d * c * e * d * e^2 * d * c * b * a * e * d * c * b * e * d * c * d * e^2 * d * c * b * e * d * c * b * a * e * d * c * b * e * d * c * d * e^2 * d * c * b * a * e * d * c * b * d * c * e * d * e^2 * d * c * b * a * d * c * b * e * d * c * e * d * e * a * b * c * d * e * d * c * b * a * d * c * b * e * d * c * e * d * e^2 * d * c * b * a * e * d * c * b * d * c * e * d * e^2 * d * c * b * a * e * d * c * b * e * d * c * d * e^2 * d * c * b *] [* e^-1 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * d * e^2 * d * c * b * a * e * d * c * b * d * c * e * d * e^2 * d * c * b * a * d * c * b * e * d * c * e * d * e^2 * d * c * b * a * e * d * c * b * e * d * c * e * d^2 * c * b * a * e * d * c * b * e * d * c * e * d * e^2 * d * c * b * a * e * d * c * b * e * d * c * d * e^2 * d * c * b * a * e * d * c * b * d * c * e * d * e^2 * d * c * b * a * d * c * b * e * d * c * e * d * e * a * b * c * d * e^2 * d * c * b *] [* a *] [* e^-1 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-1 * d * c * e * d * c * b * a * d * c * b * e * d * c * e * d * e * b * c * e * d * c * b * a * e * d * c * b * e * d * c * d * e *] [* e^-1 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-1 * d * c * e * d * c * b * a * d * c * b * e * d * c * e * d * e * b * c * e * d * c * b * a * e * d * c * b * e * d * c * d * e *] [* d^3 *] >> for i:=1 to n do ^ User error: bad syntax >> W*=s[i]; ^ User error: bad ** WARNING: Output too long, hence truncated. ************** MAGMA ***************** Host DSL217-132-22-167.bb.netvision.net.il. (217.132.22.167) Time: Wed Jan 14 06:26:52 2004 Input: #s; Output: Magma V2.10-6 Wed Jan 14 2004 06:26:49 on modular [Seed = 2446653107] ------------------------------------- >> #s;; ^ User error: Identifier 's' has not been declared or assigned Total time: 3.119 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host DSL217-132-22-167.bb.netvision.net.il. (217.132.22.167) Time: Wed Jan 14 06:31:10 2004 Input: Br:=BraidGroup(6); C:=c^(-1); D:=d^(-1); w:=(d^3)*(c^d)^2)*(s,c^3)*c^3(c^(D*c))^2)*b^(c*d*d*c*c))*(b^(c^3))^3)*e^(d*c*b*b*c*d*d*c*b))*(e^(d*c*b))^3)*a^(b*c*d*e*e*d*c*b))*a*(c^D)^2)*(c^D)^2**d^3; normalform(w); Output: Magma V2.10-6 Wed Jan 14 2004 06:31:07 on modular [Seed = 2227301540] ------------------------------------- >> C:=c^(-1); ^ User error: Identifier 'c' has not been declared or assigned >> w:=(d^3)*(c^d)^2)*(s,c^3)*c^3(c^(D*c))^2)*b^(c*d*d*c*c))*(b^(c^3))^3)*e^(d* ^ User error: bad syntax >> normalform(w);; ^ User error: Identifier 'w' has not been declared or assigned Total time: 2.929 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host DSL217-132-22-167.bb.netvision.net.il. (217.132.22.167) Time: Wed Jan 14 06:31:29 2004 Input: Br:=BraidGroup(6); C:=c^(-1); D:=d^(-1); w:=(d^3)*(c^d)^2)*(s,c^3)*c^3(c^(D*c))^2)*b^(c*d*d*c*c))*(b^(c^3))^3)*e^(d*c*b*b*c*d*d*c*b))*(e^(d*c*b))^3)*a^(b*c*d*e*e*d*c*b))*a*(c^D)^2)*(c^D)^2**d^3; normalform(w); Output: Magma V2.10-6 Wed Jan 14 2004 06:31:26 on modular [Seed = 3019299686] ------------------------------------- >> w:=(d^3)*(c^d)^2)*(s,c^3)*c^3(c^(D*c))^2)*b^(c*d*d*c*c))*(b^(c^3))^3)*e^(d* ^ User error: bad syntax >> normalform(w);; ^ User error: Identifier 'w' has not been declared or assigned Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host DSL217-132-22-167.bb.netvision.net.il. (217.132.22.167) Time: Wed Jan 14 06:31:58 2004 Input: Br:=BraidGroup(6); C:=c^(-1); D:=d^(-1); w:=(d^3)*(c^d)^2*(s,c^3)*c^3(c^(D*c))^2)*b^(c*d*d*c*c))*(b^(c^3))^3)*e^(d*c*b*b*c*d*d*c*b))*(e^(d*c*b))^3)*a^(b*c*d*e*e*d*c*b))*a*(c^D)^2)*(c^D)^2**d^3; normalform(w); Output: Magma V2.10-6 Wed Jan 14 2004 06:31:55 on modular [Seed = 2867839578] ------------------------------------- >> w:=(d^3)*(c^d)^2*(s,c^3)*c^3(c^(D*c))^2)*b^(c*d*d*c*c))*(b^(c^3))^3)*e^(d*c ^ User error: bad syntax >> normalform(w);; ^ User error: Identifier 'w' has not been declared or assigned Total time: 2.919 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host DSL217-132-22-167.bb.netvision.net.il. (217.132.22.167) Time: Wed Jan 14 06:32:19 2004 Input: Br:=BraidGroup(6); C:=c^(-1); D:=d^(-1); w:=(d^3)*(c^d)^2*(c^3)*c^3*(c^(D*c))^2)*b^(c*d*d*c*c))*(b^(c^3))^3)*e^(d*c*b*b*c*d*d*c*b))*(e^(d*c*b))^3)*a^(b*c*d*e*e*d*c*b))*a*(c^D)^2)*(c^D)^2**d^3; normalform(w); Output: Magma V2.10-6 Wed Jan 14 2004 06:32:16 on modular [Seed = 2716125498] ------------------------------------- >> w:=(d^3)*(c^d)^2*(c^3)*c^3*(c^(D*c))^2)*b^(c*d*d*c*c))*(b^(c^3))^3)*e^(d*c* ^ User error: bad syntax >> normalform(w);; ^ User error: Identifier 'w' has not been declared or assigned Total time: 2.939 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host DSL217-132-22-167.bb.netvision.net.il. (217.132.22.167) Time: Wed Jan 14 06:32:28 2004 Input: Br:=BraidGroup(6); C:=c^(-1); D:=d^(-1); w:=(d^3)*(c^d)^2*(c^3)*c^3*(c^(D*c))^2)*b^(c*d*d*c*c))*(b^(c^3))^3)*e^(d*c*b*b*c*d*d*c*b))*(e^(d*c*b))^3)*a^(b*c*d*e*e*d*c*b))*a*(c^D)^2)*(c^D)^2*d^3; normalform(w); Output: Magma V2.10-6 Wed Jan 14 2004 06:32:25 on modular [Seed = 1595553738] ------------------------------------- >> w:=(d^3)*(c^d)^2*(c^3)*c^3*(c^(D*c))^2)*b^(c*d*d*c*c))*(b^(c^3))^3)*e^(d*c* ^ User error: bad syntax >> normalform(w);; ^ User error: Identifier 'w' has not been declared or assigned Total time: 2.939 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host DSL217-132-22-167.bb.netvision.net.il. (217.132.22.167) Time: Wed Jan 14 06:34:28 2004 Input: Br:=BraidGroup(6); C:=c^(-1); D:=d^(-1); w:=(d^3)*(c^d)^2*(c^3)*c^3*(c^(D*c))^2*b^(c*d*d*c*c))*(b^(c^3))^3)*e^(d*c*b*b*c*d*d*c*b))*(e^(d*c*b))^3)*a^(b*c*d*e*e*d*c*b))*a*(c^D)^2)*(c^D)^2*d^3; normalform(w); Output: Magma V2.10-6 Wed Jan 14 2004 06:34:25 on modular [Seed = 1393965646] ------------------------------------- >> w:=(d^3)*(c^d)^2*(c^3)*c^3*(c^(D*c))^2*b^(c*d*d*c*c))*(b^(c^3))^3)*e^(d*c*b ^ User error: bad syntax >> normalform(w);; ^ User error: Identifier 'w' has not been declared or assigned Total time: 3.039 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host DSL217-132-22-167.bb.netvision.net.il. (217.132.22.167) Time: Wed Jan 14 06:34:43 2004 Input: Br:=BraidGroup(6); C:=c^(-1); D:=d^(-1); w:=(d^3)*(c^d)^2*(c^3)*c^3*(c^(D*c))^2*b^(c*d*d*c*c)*(b^(c^3))^3)*e^(d*c*b*b*c*d*d*c*b))*(e^(d*c*b))^3)*a^(b*c*d*e*e*d*c*b))*a*(c^D)^2)*(c^D)^2*d^3; normalform(w); Output: Magma V2.10-6 Wed Jan 14 2004 06:34:40 on modular [Seed = 1140927816] ------------------------------------- >> w:=(d^3)*(c^d)^2*(c^3)*c^3*(c^(D*c))^2*b^(c*d*d*c*c)*(b^(c^3))^3)*e^(d*c*b* ^ User error: bad syntax >> normalform(w);; ^ User error: Identifier 'w' has not been declared or assigned Total time: 2.989 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host DSL217-132-22-167.bb.netvision.net.il. (217.132.22.167) Time: Wed Jan 14 06:35:40 2004 Input: Br:=BraidGroup(6); C:=c^(-1); D:=d^(-1); w:=(d^3)*(c^d)^2*(c^3)*c^3*(c^(D*c))^2*b^(c*d*d*c*c)*(b^(c^3))^3*e^(d*c*b*b*c*d*d*c*b))*(e^(d*c*b))^3)*a^(b*c*d*e*e*d*c*b))*a*(c^D)^2)*(c^D)^2*d^3; normalform(w); Output: Magma V2.10-6 Wed Jan 14 2004 06:35:36 on modular [Seed = 2033979565] ------------------------------------- >> ^(c^3))^3*e^(d*c*b*b*c*d*d*c*b))*(e^(d*c*b))^3)*a^(b*c*d*e*e*d*c*b))*a*(c^D ^ User error: bad syntax >> normalform(w);; ^ User error: Identifier 'w' has not been declared or assigned Total time: 2.999 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host DSL217-132-22-167.bb.netvision.net.il. (217.132.22.167) Time: Wed Jan 14 06:36:17 2004 Input: Br:=BraidGroup(6); C:=c^(-1); D:=d^(-1); w:=(d^3)*(c^d)^2*(c^3)*c^3*(c^(D*c))^2*b^(c*d*d*c*c)*(b^(c^3))^3*e^(d*c*b*b*c*d*d*c*b)*(e^(d*c*b))^3*a^(b*c*d*e*e*d*c*b)*a*(c^D)^2*(c^D)^2*d^3; normalform(w); Output: Magma V2.10-6 Wed Jan 14 2004 06:36:14 on modular [Seed = 1916214144] ------------------------------------- >> normalform(w);; ^ User error: Identifier 'normalform' has not been declared or assigned Total time: 3.029 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host DSL217-132-22-167.bb.netvision.net.il. (217.132.22.167) Time: Wed Jan 14 06:36:36 2004 Input: Br:=BraidGroup(6); C:=c^(-1); D:=d^(-1); w:=(d^3)*(c^d)^2*(c^3)*c^3*(c^(D*c))^2*b^(c*d*d*c*c)*(b^(c^3))^3*e^(d*c*b*b*c*d*d*c*b)*(e^(d*c*b))^3*a^(b*c*d*e*e*d*c*b)*a*(c^D)^2*(c^D)^2*d^3; NormalForm(w); Output: Magma V2.10-6 Wed Jan 14 2004 06:36:33 on modular [Seed = 1798177526] ------------------------------------- e^-1 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * b * e * d * c * e * d * e^2 * d * c * b * a * d * c * b * c * e * d * e^2 * d * c * b * a * e * d * c * b * d * c * e * d * e^2 * d * c * b * a * c * b * c * e * d * e^2 * d * c * b * a * c * b * c * e * d * e^2 * d * c * b * a * c * b * e * d * c * e * d * e * d * c * d^2 * c * d^2 * c^2 * d^3 * c^3 * d^2 Total time: 2.999 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host DSL217-132-22-167.bb.netvision.net.il. (217.132.22.167) Time: Wed Jan 14 06:39:26 2004 Input: Br:=BraidGroup(6); C:=c^(-1); D:=d^(-1); w:=(d^3)*(c^d)^2*(c^3)*c^3*(c^(D*c))^2*b^(c*d*d*c*c)*(b^(c^3))^3*e^(d*c*b*b*c*d*d*c*b)*(e^(d*c*b))^3*a^(b*c*d*e*e*d*c*b)*a*(c^D)^2*(c^D)^2*d^3; NormalForm(w); l:=FundamentalElement(Br); NormalForm(w*l^(-2)) Output: Magma V2.10-6 Wed Jan 14 2004 06:39:23 on modular [Seed = 492336938] ------------------------------------- e^-1 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * b * e * d * c * e * d * e^2 * d * c * b * a * d * c * b * c * e * d * e^2 * d * c * b * a * e * d * c * b * d * c * e * d * e^2 * d * c * b * a * c * b * c * e * d * e^2 * d * c * b * a * c * b * c * e * d * e^2 * d * c * b * a * c * b * e * d * c * e * d * e * d * c * d^2 * c * d^2 * c^2 * d^3 * c^3 * d^2 e^-1 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * b * e * d * c * e * d * e^2 * d * c * b * a * d * c * b * c * e * d * e^2 * d * c * b * a * e * d * c * b * d * c * e * d * e^2 * d * c * b * a * c * b * c * e * d * e^2 * d * c * b * a * c * b * c * e * d * e^2 * d * c * b * a * c * b * e * d * c * e * d * e * d * c * d^2 * c * d^2 * c^2 * d^3 * c^3 * d^2 Total time: 2.989 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host DSL217-132-22-167.bb.netvision.net.il. (217.132.22.167) Time: Wed Jan 14 06:40:03 2004 Input: Br:=BraidGroup(6); C:=c^(-1); D:=d^(-1); w:=(d^3)*(c^d)^2*(c^3)*c^3*(c^(D*c))^2*b^(c*d*d*c*c)*(b^(c^3))^3*e^(d*c*b*b*c*d*d*c*b)*(e^(d*c*b))^3*a^(b*c*d*e*e*d*c*b)*a*(c^D)^2*(c^D)^2*d^3; NormalForm(w); l:=FundamentalElement(Br); t:=NormalForm(w*l^(-2)); t; Output: Magma V2.10-6 Wed Jan 14 2004 06:39:59 on modular [Seed = 374570181] ------------------------------------- e^-1 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * b * e * d * c * e * d * e^2 * d * c * b * a * d * c * b * c * e * d * e^2 * d * c * b * a * e * d * c * b * d * c * e * d * e^2 * d * c * b * a * c * b * c * e * d * e^2 * d * c * b * a * c * b * c * e * d * e^2 * d * c * b * a * c * b * e * d * c * e * d * e * d * c * d^2 * c * d^2 * c^2 * d^3 * c^3 * d^2 e^-1 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * b * e * d * c * e * d * e^2 * d * c * b * a * d * c * b * c * e * d * e^2 * d * c * b * a * e * d * c * b * d * c * e * d * e^2 * d * c * b * a * c * b * c * e * d * e^2 * d * c * b * a * c * b * c * e * d * e^2 * d * c * b * a * c * b * e * d * c * e * d * e * d * c * d^2 * c * d^2 * c^2 * d^3 * c^3 * d^2 Total time: 3.149 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host DSL217-132-22-167.bb.netvision.net.il. (217.132.22.167) Time: Wed Jan 14 06:45:34 2004 Input: Br:=BraidGroup(6); C:=c^(-1); D:=d^(-1); w:=(d^3)*(c^d)^2*(c^3)*c^3*(c^(D*c))^2*b^(c*d*d*c*c)*(b^(c^3))^3*e^(d*c*b*b*c*d*d*c*b)*(e^(d*c*b))^3*a^(b*c*d*e*e*d*c*b)*a*(c^D)^2*(c^D)^2*d^3; NormalForm(w); l:=FundamentalElement(Br); w eq l^2; Output: Magma V2.10-6 Wed Jan 14 2004 06:45:30 on modular [Seed = 54945924] ------------------------------------- e^-1 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * b * e * d * c * e * d * e^2 * d * c * b * a * d * c * b * c * e * d * e^2 * d * c * b * a * e * d * c * b * d * c * e * d * e^2 * d * c * b * a * c * b * c * e * d * e^2 * d * c * b * a * c * b * c * e * d * e^2 * d * c * b * a * c * b * e * d * c * e * d * e * d * c * d^2 * c * d^2 * c^2 * d^3 * c^3 * d^2 false Total time: 2.929 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host DSL217-132-22-167.bb.netvision.net.il. (217.132.22.167) Time: Wed Jan 14 06:46:12 2004 Input: Br:=BraidGroup(6); C:=c^(-1); D:=d^(-1); w:=(d^3)*(c^d)^2*(c^3)*c^3*(c^(D*c))^2*b^(c*d*d*c*c)*(b^(c^3))^3*e^(d*c*b*b*c*d*d*c*b)*(e^(d*c*b))^3*a^(b*c*d*e*e*d*c*b)*a*(c^D)^2*(c^D)^2*d^3; NormalForm(w); l:=FundamentalElement(Br); w eq l^2; l Output: Magma V2.10-6 Wed Jan 14 2004 06:46:09 on modular [Seed = 879843433] ------------------------------------- e^-1 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * b * e * d * c * e * d * e^2 * d * c * b * a * d * c * b * c * e * d * e^2 * d * c * b * a * e * d * c * b * d * c * e * d * e^2 * d * c * b * a * c * b * c * e * d * e^2 * d * c * b * a * c * b * c * e * d * e^2 * d * c * b * a * c * b * e * d * c * e * d * e * d * c * d^2 * c * d^2 * c^2 * d^3 * c^3 * d^2 false e * d * c * b * a * e * d * c * b * e * d * c * e * d * e Total time: 2.979 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host DSL217-132-22-167.bb.netvision.net.il. (217.132.22.167) Time: Wed Jan 14 06:53:32 2004 Input: Br:=BraidGroup(6); C:=c^(-1); D:=d^(-1); w:=(d^3)*(c^d)^2*(c^3)*c^3*(c^(D*c))^2*b^(c*d*d*c*c)*(b^(c^3))^3*e^(d*c*b*b*c*d*d*c*b)*(e^(d*c*b))^3*a^(b*c*d*e*e*d*c*b)*a*(c^D)^2*(c^D)^2*d^3; NormalForm(w); l:=FundamentalElement(Br); w eq l^2; a^b; l Output: Magma V2.10-6 Wed Jan 14 2004 06:53:29 on modular [Seed = 660753090] ------------------------------------- e^-1 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * b * e * d * c * e * d * e^2 * d * c * b * a * d * c * b * c * e * d * e^2 * d * c * b * a * e * d * c * b * d * c * e * d * e^2 * d * c * b * a * c * b * c * e * d * e^2 * d * c * b * a * c * b * c * e * d * e^2 * d * c * b * a * c * b * e * d * c * e * d * e * d * c * d^2 * c * d^2 * c^2 * d^3 * c^3 * d^2 false e^-1 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * d * c * b * e * d * c * e * d * e * a * b e * d * c * b * a * e * d * c * b * e * d * c * e * d * e Total time: 2.939 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host DSL217-132-22-167.bb.netvision.net.il. (217.132.22.167) Time: Wed Jan 14 06:54:05 2004 Input: Br:=BraidGroup(6); C:=c^(-1); D:=d^(-1); w:=(d^3)*(c^d)^2*(c^3)*c^3*(c^(D*c))^2*b^(c*d*d*c*c)*(b^(c^3))^3*e^(d*c*b*b*c*d*d*c*b)*(e^(d*c*b))^3*a^(b*c*d*e*e*d*c*b)*a*(c^D)^2*(c^D)^2*d^3; NormalForm(w); l:=FundamentalElement(Br); w eq l^2; k:=a^b; l Output: Magma V2.10-6 Wed Jan 14 2004 06:54:02 on modular [Seed = 3634214238] ------------------------------------- e^-1 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * b * e * d * c * e * d * e^2 * d * c * b * a * d * c * b * c * e * d * e^2 * d * c * b * a * e * d * c * b * d * c * e * d * e^2 * d * c * b * a * c * b * c * e * d * e^2 * d * c * b * a * c * b * c * e * d * e^2 * d * c * b * a * c * b * e * d * c * e * d * e * d * c * d^2 * c * d^2 * c^2 * d^3 * c^3 * d^2 false e * d * c * b * a * e * d * c * b * e * d * c * e * d * e Total time: 3.009 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host DSL217-132-22-167.bb.netvision.net.il. (217.132.22.167) Time: Wed Jan 14 06:54:23 2004 Input: Br:=BraidGroup(6); C:=c^(-1); D:=d^(-1); w:=(d^3)*(c^d)^2*(c^3)*c^3*(c^(D*c))^2*b^(c*d*d*c*c)*(b^(c^3))^3*e^(d*c*b*b*c*d*d*c*b)*(e^(d*c*b))^3*a^(b*c*d*e*e*d*c*b)*a*(c^D)^2*(c^D)^2*d^3; NormalForm(w); l:=FundamentalElement(Br); w eq l^2; k:=a^b; k; l Output: Magma V2.10-6 Wed Jan 14 2004 06:54:20 on modular [Seed = 3516185697] ------------------------------------- e^-1 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * b * e * d * c * e * d * e^2 * d * c * b * a * d * c * b * c * e * d * e^2 * d * c * b * a * e * d * c * b * d * c * e * d * e^2 * d * c * b * a * c * b * c * e * d * e^2 * d * c * b * a * c * b * c * e * d * e^2 * d * c * b * a * c * b * e * d * c * e * d * e * d * c * d^2 * c * d^2 * c^2 * d^3 * c^3 * d^2 false e^-1 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * d * c * b * e * d * c * e * d * e * a * b e * d * c * b * a * e * d * c * b * e * d * c * e * d * e Total time: 2.979 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host DSL217-132-22-167.bb.netvision.net.il. (217.132.22.167) Time: Wed Jan 14 06:55:42 2004 Input: Br:=BraidGroup(6); k:=a^b; k; Output: Magma V2.10-6 Wed Jan 14 2004 06:55:39 on modular [Seed = 3330517153] ------------------------------------- e^-1 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * d * c * b * e * d * c * e * d * e * a * b Total time: 2.889 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host DSL217-132-22-167.bb.netvision.net.il. (217.132.22.167) Time: Wed Jan 14 06:56:16 2004 Input: Br:=BraidGroup(6); a^b; Output: Magma V2.10-6 Wed Jan 14 2004 06:56:13 on modular [Seed = 4290417150] ------------------------------------- e^-1 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * d * c * b * e * d * c * e * d * e * a * b Total time: 3.009 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host DSL217-132-22-167.bb.netvision.net.il. (217.132.22.167) Time: Wed Jan 14 09:53:12 2004 Input: Br:=BraidGroup(6); w:=d*d*d*D*c*d*D*c*d*D*c*d*c*c*c*c*c*c*C*d*c*D*c*C*d*c*D*c*C*C*D*D* *C*b*c*d*d*c*c*C*C*D*D*C*b*c*d*d*c*c*C*C*D*D*C*b*c*d*d*c*c*C*C*D* D*C*b*c*d*d*c*c*B*C*D*D*C*B*B*C*D*e*d*c*b*b*c*d*d*c*b*B*C*D*e*d *c*b*B*C*D*e*d*c*b*B*C*D*e*d*c*b*B*C*D*E*E*D*C*B*a*b*c*d*e*e*d*c *b*a*d*c*D*d*c*D*d*c*D*d*c*D*d*d*d ; l:=FundamentalElement(Br); w eq l^2; Output: Magma V2.10-6 Wed Jan 14 2004 09:53:09 on modular [Seed = 1865054425] ------------------------------------- >> *C*b*c*d*d*c*c*C*C*D*D*C*b*c*d*d*c*c*C*C*D*D*C*b*c*d*d*c*c*C*C*D* ^ User error: bad syntax >> D*C*b*c*d*d*c*c*B*C*D*D*C*B*B*C*D*e*d*c*b*b*c*d*d*c*b*B*C*D*e*d ^ User error: Identifier 'D' has not been declared or assigned >> w eq l^2; ^ User error: Identifier 'w' has not been declared or assigned Total time: 3.079 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host DSL217-132-22-167.bb.netvision.net.il. (217.132.22.167) Time: Wed Jan 14 09:54:32 2004 Input: Br:=BraidGroup(6); A:=a^(-1); B:=b^(-1); C:=c^(-1); D:=d^(-1); E:=e^(-1); w:=d*d*d*D*c*d*D*c*d*D*c*d*c*c*c*c*c*c*C*d*c*D*c*C*d*c*D*c*C*C*D*D *C*b*c*d*d*c*c*C*C*D*D*C*b*c*d*d*c*c*C*C*D*D*C*b*c*d*d*c*c*C*C*D* D*C*b*c*d*d*c*c*B*C*D*D*C*B*B*C*D*e*d*c*b*b*c*d*d*c*b*B*C*D*e*d *c*b*B*C*D*e*d*c*b*B*C*D*e*d*c*b*B*C*D*E*E*D*C*B*a*b*c*d*e*e*d*c *b*a*d*c*D*d*c*D*d*c*D*d*c*D*d*d*d ; l:=FundamentalElement(Br); w eq l^2; Output: Magma V2.10-6 Wed Jan 14 2004 09:54:29 on modular [Seed = 1983082032] ------------------------------------- false Total time: 3.069 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host DSL217-132-22-167.bb.netvision.net.il. (217.132.22.167) Time: Wed Jan 14 09:55:17 2004 Input: Br:=BraidGroup(6); A:=a^(-1); B:=b^(-1); C:=c^(-1); D:=d^(-1); E:=e^(-1); w:=d*d*d*D*c*d*D*c*d*D*c*d*c*c*c*c*c*c*C*d*c*D*c*C*d*c*D*c*C*C*D*D *C*b*c*d*d*c*c*C*C*D*D*C*b*c*d*d*c*c*C*C*D*D*C*b*c*d*d*c*c*C*C*D* D*C*b*c*d*d*c*c*B*C*D*D*C*B*B*C*D*e*d*c*b*b*c*d*d*c*b*B*C*D*e*d *c*b*B*C*D*e*d*c*b*B*C*D*e*d*c*b*B*C*D*E*E*D*C*B*a*b*c*d*e*e*d*c *b*a*d*c*D*d*c*D*d*c*D*d*c*D*d*d*d ; l:=FundamentalElement(Br); w eq l^2; k:=a *b k; Output: Magma V2.10-6 Wed Jan 14 2004 09:55:14 on modular [Seed = 1528709994] ------------------------------------- false >> k; ^ User error: bad syntax Total time: 2.989 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host DSL217-132-22-167.bb.netvision.net.il. (217.132.22.167) Time: Wed Jan 14 09:55:57 2004 Input: Br:=BraidGroup(6); A:=a^(-1); B:=b^(-1); C:=c^(-1); D:=d^(-1); E:=e^(-1); w:=d*d*d*D*c*d*D*c*d*D*c*d*c*c*c*c*c*c*C*d*c*D*c*C*d*c*D*c*C*C*D*D *C*b*c*d*d*c*c*C*C*D*D*C*b*c*d*d*c*c*C*C*D*D*C*b*c*d*d*c*c*C*C*D* D*C*b*c*d*d*c*c*B*C*D*D*C*B*B*C*D*e*d*c*b*b*c*d*d*c*b*B*C*D*e*d *c*b*B*C*D*e*d*c*b*B*C*D*e*d*c*b*B*C*D*E*E*D*C*B*a*b*c*d*e*e*d*c *b*a*d*c*D*d*c*D*d*c*D*d*c*D*d*d*d ; l:=FundamentalElement(Br); w eq l^2; k:=a *b; k; Output: Magma V2.10-6 Wed Jan 14 2004 09:55:54 on modular [Seed = 577190459] ------------------------------------- false a * b Total time: 3.179 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host DSL217-132-22-167.bb.netvision.net.il. (217.132.22.167) Time: Wed Jan 14 10:02:09 2004 Input: Br:=BraidGroup(6); A:=a^(-1); B:=b^(-1); C:=c^(-1); D:=d^(-1); E:=e^(-1); w:=d*d*d*D*c*d*D*c*d*D*c*d*c*c*c*c*c*c*C*d*c*D*c*C*d*c*D*c*C*C*D*D *C*b*c*d*d*c*c*C*C*D*D*C*b*c*d*d*c*c*C*C*D*D*C*b*c*d*d*c*c*C*C*D* D*C*b*c*d*d*c*c*B*C*D*D*C*B*B*C*D*e*d*c*b*b*c*d*d*c*b*B*C*D*e*d *c*b*B*C*D*e*d*c*b*B*C*D*e*d*c*b*B*C*D*E*E*D*C*B*a*b*c*d*e*e*d*c *b*a*d*c*D*d*c*D*d*c*D*d*c*D*d*d*d ; l:=FundamentalElement(Br); w eq l^2; f := BurauRepresentation(B); f(w); Output: Magma V2.10-6 Wed Jan 14 2004 10:02:05 on modular [Seed = 3263683404] ------------------------------------- false >> f := BurauRepresentation(B); ^ Runtime error in 'BurauRepresentation': Bad argument types Argument types given: GrpBrdElt >> f(w); ^ User error: Identifier 'f' has not been declared or assigned Total time: 2.939 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host DSL217-132-22-167.bb.netvision.net.il. (217.132.22.167) Time: Wed Jan 14 10:02:33 2004 Input: Br:=BraidGroup(6); A:=a^(-1); B:=b^(-1); C:=c^(-1); D:=d^(-1); E:=e^(-1); w:=d*d*d*D*c*d*D*c*d*D*c*d*c*c*c*c*c*c*C*d*c*D*c*C*d*c*D*c*C*C*D*D *C*b*c*d*d*c*c*C*C*D*D*C*b*c*d*d*c*c*C*C*D*D*C*b*c*d*d*c*c*C*C*D* D*C*b*c*d*d*c*c*B*C*D*D*C*B*B*C*D*e*d*c*b*b*c*d*d*c*b*B*C*D*e*d *c*b*B*C*D*e*d*c*b*B*C*D*e*d*c*b*B*C*D*E*E*D*C*B*a*b*c*d*e*e*d*c *b*a*d*c*D*d*c*D*d*c*D*d*c*D*d*d*d ; l:=FundamentalElement(Br); w eq l^2; f := BurauRepresentation(Br); f(w); Output: Magma V2.10-6 Wed Jan 14 2004 10:02:30 on modular [Seed = 2917709768] ------------------------------------- false [$.1^6 - $.1 + 1 -$.1^2 + $.1 -$.1^3 + $.1^2 -$.1^4 + $.1^3 -$.1^5 + $.1^4 -$.1^6 + $.1^5] [-$.1 + 1 ($.1^7 - 2*$.1^6 + $.1^5 + $.1^3 - $.1 + 1)/$.1^4 ($.1^12 - 2*$.1^11 + 2*$.1^10 - $.1^9 - $.1^5 + 3*$.1^4 - 2*$.1^3 - $.1^2 + 2*$.1 - 1)/$.1^4 ($.1^14 - 2*$.1^13 + 3*$.1^12 - 4*$.1^11 + 3*$.1^10 - $.1^9 - $.1^5 + 3*$.1^4 - 2*$.1^3 - $.1^2 + 2*$.1 - 1)/$.1^3 (-$.1^13 + 2*$.1^12 - 3*$.1^11 + 3*$.1^10 - $.1^9 - $.1^5 + 3*$.1^4 - 2*$.1^3 - $.1^2 + 2*$.1 - 1)/$.1^2 -$.1^6 + $.1^5] [-$.1 + 1 ($.1^8 - 3*$.1^7 + 4*$.1^6 - 4*$.1^5 + 5*$.1^4 - 3*$.1^3 - $.1^2 + 2*$.1 - 1)/$.1^5 (-$.1^17 + 4*$.1^16 - 8*$.1^15 + 8*$.1^14 - 2*$.1^13 - 7*$.1^12 + 11*$.1^11 - 6*$.1^10 - 3*$.1^9 + 8*$.1^8 - 5*$.1^7 - 4*$.1^6 + 12*$.1^5 - 11*$.1^4 + 3*$.1^3 + 3*$.1^2 - 3*$.1 + 1)/$.1^5 (-$.1^19 + 4*$.1^18 - 8*$.1^17 + 12*$.1^16 - 13*$.1^15 + 9*$.1^14 + $.1^13 - 11*$.1^12 + 14*$.1^11 - 7*$.1^10 - 3*$.1^9 + 8*$.1^8 - 5*$.1^7 - 4*$.1^6 + 12*$.1^5 - 11*$.1^4 + 3*$.1^3 + 3*$.1^2 - 3*$.1 + 1)/$.1^4 ($.1^18 - 4*$.1^17 + 8*$.1^16 - 11*$.1^15 + 9*$.1^14 - $.1^13 - 9*$.1^12 + 13*$.1^11 - 7*$.1^10 - 3*$.1^9 + 8*$.1^8 - 5*$.1^7 - 4*$.1^6 + 12*$.1^5 - 11*$.1^4 + 3*$.1^3 + 3*$.1^2 - 3*$.1 + 1)/$.1^3 -$.1^6 + $.1^5] [-$.1 + 1 (2*$.1^8 - 5*$.1^7 + 7*$.1^6 - 8*$.1^5 + 8*$.1^4 - 5*$.1^3 + 2*$.1 - 1)/$.1^5 ($.1^18 - 4*$.1^17 + 10*$.1^16 - 14*$.1^15 + 12*$.1^14 - 2*$.1^13 - 10*$.1^12 + 14*$.1^11 - 6*$.1^10 - 6*$.1^9 + 11*$.1^8 - 5*$.1^7 - 8*$.1^6 + 18*$.1^5 - 16*$.1^4 + 6*$.1^3 + 2*$.1^2 - 3*$.1 + 1)/$.1^5 ($.1^20 - 4*$.1^19 + 10*$.1^18 - 18*$.1^17 + 24*$.1^16 - 24*$.1^15 + 15*$.1^14 - 14*$.1^12 + 17*$.1^11 - 7*$.1^10 - 6*$.1^9 + 11*$.1^8 - 5*$.1^7 - 8*$.1^6 + 18*$.1^5 - 16*$.1^4 + 6*$.1^3 + 2*$.1^2 - 3*$.1 + 1)/$.1^4 (-$.1^19 + 4*$.1^18 - 10*$.1^17 + 17*$.1^16 - 20*$.1^15 + 14*$.1^14 - $.1^13 - 12*$.1^12 + 16*$.1^11 - 7*$.1^10 - 6*$.1^9 + 11*$.1^8 - 5*$.1^7 - 8*$.1^6 + 18*$.1^5 - 16*$.1^4 + 6*$.1^3 + 2*$.1^2 - 3*$.1 + 1)/$.1^3 -$.1^6 + $.1^5] [-$.1 + 1 ($.1^8 - 3*$.1^7 + 4*$.1^6 - 5*$.1^5 + 6*$.1^4 - 4*$.1^3 + 2*$.1 - 1)/$.1^5 (-$.1^17 + 4*$.1^16 - 9*$.1^15 + 10*$.1^14 - 4*$.1^13 - 6*$.1^12 + 12*$.1^11 - 8*$.1^10 - 2*$.1^9 + 9*$.1^8 - 7*$.1^7 - 3*$.1^6 + 13*$.1^5 - 13*$.1^4 + 5*$.1^3 + 2*$.1^2 - 3*$.1 + 1)/$.1^5 (-$.1^19 + 4*$.1^18 - 9*$.1^17 + 14*$.1^16 - 16*$.1^15 + 12*$.1^14 - 2*$.1^13 - 10*$.1^12 + 15*$.1^11 - 9*$.1^10 - 2*$.1^9 + 9*$.1^8 - 7*$.1^7 - 3*$.1^6 + 13*$.1^5 - 13*$.1^4 + 5*$.1^3 + 2*$.1^2 - 3*$.1 + 1)/$.1^4 ($.1^18 - 4*$.1^17 + 9*$.1^16 - 13*$.1^15 + 12*$.1^14 - 3*$.1^13 - 8*$.1^12 + 14*$.1^11 - 9*$.1^10 - 2*$.1^9 + 9*$.1^8 - 7*$.1^7 - 3*$.1^6 + 13*$.1^5 - 13*$.1^4 + 5*$.1^3 + 2*$.1^2 - 3*$.1 + 1)/$.1^3 -$.1^6 + $.1^5] [-$.1 + 1 -$.1^2 + $.1 -$.1^3 + $.1^2 -$.1^4 + $.1^3 -$.1^5 + $.1^4 $.1^5] Total time: 3.079 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host DSL217-132-22-167.bb.netvision.net.il. (217.132.22.167) Time: Wed Jan 14 10:23:01 2004 Input: s:="dddDcdDcdccccccCdcDcCdcDcCCDDCbcddccCCCbcccCCCbcccCCCbcccBCDDCBBCDedcbbcddcbBCDedcbBCDedcbBCDedcbBCDEEDCBabcdeedcbadcDdcDdcDdcDddd "; #s; Output: Magma V2.10-6 Wed Jan 14 2004 10:22:58 on modular [Seed = 2799941648] ------------------------------------- 131 Total time: 3.059 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host DSL217-132-22-167.bb.netvision.net.il. (217.132.22.167) Time: Wed Jan 14 10:31:03 2004 Input: s:="dddDcdDcdccccccCdcDcCdcDcCCDDCbcddccCCCbcccCCCbcccCCCbcccBCDDCBBCDedcbbcddcbBCDedcbBCDedcbBCDedcbBCDEEDCBabcdeedcbadcDdcDdcDdcDddd "; #s; Output: Magma V2.10-6 Wed Jan 14 2004 10:31:00 on modular [Seed = 3204161134] ------------------------------------- 131 Total time: 3.009 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host DSL217-132-22-167.bb.netvision.net.il. (217.132.22.167) Time: Wed Jan 14 10:31:41 2004 Input: s:="dddDcdDcdccccccCdcDcCdcDcCCDDCbcddccCCCbcccCCCbcccCCCbcccBCDDCBBCDedcbbcddcbBCDedcbBCDedcbBCDedcbBCDEEDCBabcdeedcbadcDdcDdcDdcDddd"; #s; Output: Magma V2.10-6 Wed Jan 14 2004 10:31:38 on modular [Seed = 2160435262] ------------------------------------- 130 Total time: 3.069 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host DSL217-132-22-167.bb.netvision.net.il. (217.132.22.167) Time: Wed Jan 14 10:32:50 2004 Input: s:="dddDcdDcdccccccCdcDcCdcDcCCDDCbcddccCCCbcccCCCbcccCCCbcccBCDDCBBCDedcbbcddcbBCDedcbBCDedcbBCDedcbBCDEEDCBabcdeedcbadcDdcDdcDdcDddd"; #s; Output: Magma V2.10-6 Wed Jan 14 2004 10:32:47 on modular [Seed = 2496771567] ------------------------------------- 130 Total time: 3.049 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host DSL217-132-22-167.bb.netvision.net.il. (217.132.22.167) Time: Wed Jan 14 10:37:29 2004 Input: Br:=BraidGroup(6); A:=a^(-1); B:=b^(-1); C:=c^(-1); D:=d^(-1); E:=e^(-1); w:=d*d*d*D*c*d*D*c*d*c*c*c*c*c*c*C*d*cD*c*C*d*c*D*c*C*C*D*D*C*b*c*d*d*c*c*C*C*C*b*c*c*c*C*C*C*b*c*c*c*C*C*C*b*c*c*c*B*C*D*D*C*B*B*C*D*e*d*c*b*b*c*d*d*c*b*B*C*D*e*d*c*b*B*C*D*e*d*c*b*B*C*D*e*d*c*b*B*C*D*E**E*D*C*B*a*b*c*d*e*e*d*c*b*a*d*c*D*d*c*D*d*c*D*d*c*D*d*d*d"; #s; Output: Magma V2.10-6 Wed Jan 14 2004 10:37:26 on modular [Seed = 1696614198] ------------------------------------- >> *b*B*C*D*e*d*c*b*B*C*D*e*d*c*b*B*C*D*E**E*D*C*B*a*b*c*d*e*e*d*c*b*a*d*c*D*d ^ User error: bad syntax >> #s;; ^ User error: Identifier 's' has not been declared or assigned Total time: 3.029 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host DSL217-132-22-167.bb.netvision.net.il. (217.132.22.167) Time: Wed Jan 14 10:38:51 2004 Input: Br:=BraidGroup(6); A:=a^(-1); B:=b^(-1); C:=c^(-1); D:=d^(-1); E:=e^(-1); w:=d*d*d*D*c*d*D*c*d*c*c*c*c*c*c*C*d*cD*c*C*d*c*D*c*C*C*D*D*C*b*c*d*d*c*c*C*C*C*b*c*c*c*C*C*C*b*c*c*c*C*C*C*b*c*c*c*B*C*D*D*C*B*B*C*D*e*d*c*b*b*c*d*d*c*b*B*C*D*e*d*c*b*B*C*D*e*d*c*b*B*C*D*e*d*c*b*B*C*D*E*E*D*C*B*a*b*c*d*e*e*d*c*b*a*d*c*D*d*c*D*d*c*D*d*c*D*d*d*d"; Output: Magma V2.10-6 Wed Jan 14 2004 10:38:47 on modular [Seed = 1865043341] ------------------------------------- >> quit; ^ User error: Unterminated string Total time: 2.919 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host DSL217-132-22-167.bb.netvision.net.il. (217.132.22.167) Time: Wed Jan 14 10:39:12 2004 Input: Br:=BraidGroup(6); A:=a^(-1); B:=b^(-1); C:=c^(-1); D:=d^(-1); E:=e^(-1); w:=d*d*d*D*c*d*D*c*d*c*c*c*c*c*c*C*d*cD*c*C*d*c*D*c*C*C*D*D*C*b*c*d*d*c*c*C*C*C*b*c*c*c*C*C*C*b*c*c*c*C*C*C*b*c*c*c*B*C*D*D*C*B*B*C*D*e*d*c*b*b*c*d*d*c*b*B*C*D*e*d*c*b*B*C*D*e*d*c*b*B*C*D*e*d*c*b*B*C*D*E*E*D*C*B*a*b*c*d*e*e*d*c*b*a*d*c*D*d*c*D*d*c*D*d*c*D*d*d*d"; Output: Magma V2.10-6 Wed Jan 14 2004 10:39:09 on modular [Seed = 1983075470] ------------------------------------- >> quit; ^ User error: Unterminated string Total time: 3.019 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host DSL217-132-22-167.bb.netvision.net.il. (217.132.22.167) Time: Wed Jan 14 10:39:28 2004 Input: Br:=BraidGroup(6); A:=a^(-1); B:=b^(-1); C:=c^(-1); D:=d^(-1); E:=e^(-1); w:=d*d*d*D*c*d*D*c*d*c*c*c*c*c*c*C*d*cD*c*C*d*c*D*c*C*C*D*D*C*b*c*d*d*c*c*C*C*C*b*c*c*c*C*C*C*b*c*c*c*C*C*C*b*c*c*c*B*C*D*D*C*B*B*C*D*e*d*c*b*b*c*d*d*c*b*B*C*D*e*d*c*b*B*C*D*e*d*c*b*B*C*D*e*d*c*b*B*C*D*E*E*D*C*B*a*b*c*d*e*e*d*c*b*a*d*c*D*d*c*D*d*c*D*d*c*D*d*d*d; Output: Magma V2.10-6 Wed Jan 14 2004 10:39:25 on modular [Seed = 2033998769] ------------------------------------- >> w:=d*d*d*D*c*d*D*c*d*c*c*c*c*c*c*C*d*cD*c*C*d*c*D*c*C*C*D*D*C*b*c*d*d*c*c*C ^ User error: Identifier 'cD' has not been declared or assigned Total time: 3.059 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host DSL217-132-22-167.bb.netvision.net.il. (217.132.22.167) Time: Wed Jan 14 10:39:47 2004 Input: Br:=BraidGroup(6); A:=a^(-1); B:=b^(-1); C:=c^(-1); D:=d^(-1); E:=e^(-1); w:=d*d*d*D*c*d*D*c*d*c*c*c*c*c*c*C*d*c*D*c*C*d*c*D*c*C*C*D*D*C*b*c*d*d*c*c*C*C*C*b*c*c*c*C*C*C*b*c*c*c*C*C*C*b*c*c*c*B*C*D*D*C*B*B*C*D*e*d*c*b*b*c*d*d*c*b*B*C*D*e*d*c*b*B*C*D*e*d*c*b*B*C*D*e*d*c*b*B*C*D*E*E*D*C*B*a*b*c*d*e*e*d*c*b*a*d*c*D*d*c*D*d*c*D*d*c*D*d*d*d; Output: Magma V2.10-6 Wed Jan 14 2004 10:39:44 on modular [Seed = 1074094821] ------------------------------------- Total time: 3.029 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host DSL217-132-22-167.bb.netvision.net.il. (217.132.22.167) Time: Wed Jan 14 10:41:00 2004 Input: Br:=BraidGroup(6); A:=a^(-1); B:=b^(-1); C:=c^(-1); D:=d^(-1); E:=e^(-1); w:=d*d*d*D*c*d*D*c*d*c*c*c*c*c*c*C*d*c*D*c*C*d*c*D*c*C*C*D*D*C*b*c*d*d*c*c*C*C*C*b*c*c*c*C*C*C*b*c*c*c*C*C*C*b*c*c*c*B*C*D*D*C*B*B*C*D*e*d*c*b*b*c*d*d*c*b*B*C*D*e*d*c*b*B*C*D*e*d*c*b*B*C*D*e*d*c*b*B*C*D*E*E*D*C*B*a*b*c*d*e*e*d*c*b*a*d*c*D*d*c*D*d*c*D*d*c*D*d*d*d; w; Output: Magma V2.10-6 Wed Jan 14 2004 10:40:57 on modular [Seed = 1343583036] ------------------------------------- e^-1 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-1 * d^3 * e * d * c * b * a * d * c * b * e * d * c * e * d * e * c * b * e * d * c * b * a * e * d * c * b * e * d * c * d * e * c * d * c^6 * e * d * c * b * a * e * d * c * b * d * c * e * d * e * b * c * e * d * c * b * a * e * d * c * b * e * d * c * d * e * c * e * d * c * b * a * e * d * c * b * d * c * e * d * e * b * c * e * d * c * b * a * e * d * c * b * e * d * c * d * e * c * e * d * c * b * a * e * d * c * b * d * c * e * d * e^2 * d * c * b * a * e * d * c * b * d * c * e * d * e^2 * d * c * b * a * d * c * b * e * d * c * e * d * e^2 * d * c * b * a * e * d * c * b * e * d * c * d * e^2 * d * c * b * a * e * d * c * b * d * c * e * d * e * d * c * b^2 * c^2 * e * d * c * b * a * e * d * c * b * d * c * e * d * e^2 * d * c * b * a * e * d * c * b * d * c * e * d * e^2 * d * c * b * a * e * d * c * b * d * c * e * d * e * b * c^3 * e * d * c * b * a * e * d * c * b * d * c * e * d * e^2 * d * c * b * a * e * d * c * b * d * c * e * d * e^2 * d * c * b * a * e * d * c * b * d * c * e * d * e * d * c^3 * e * d * c * b * a * e * d * c * b * d * c * e * d * e^2 * d * c * b * a * e * d * c * b * d * c * e * d * e^2 * d * c * b * a * e * d * c * b * d * c * e * d * e * b * c^3 * e * d * c * b * a * e * d * c * b * e * d * c * d * e^2 * d * c * b * a * e * d * c * b * d * c * e * d * e^2 * d * c * b * a * d * c * b * e * d * c * e * d * e^2 * d * c * b * a * e * d * c * b * e * d * c * d * e^2 * d * c * b * a * e * d * c * b * d * c * e * d * e^2 * d * c * b * a * d * c * b * e * d * c * e * d * e^2 * d * c * b * a * e * d * c * b * e * d * c * d * e^2 * d * c * b * a * e * d * c * b * d * c * e * d * e^2 * d * c * b * a * d * c * b * e * d * c * e * d * e * a * b * c * d^2 * c * b^2 * c * d * e * d * c * b * a * d * c * b * e * d * c * e * d * e^2 * d * c * b * a * e * d * c * b * d * c * e * d * e^2 * d * c * b * a * e * d * c * b * e * d * c * d * e^2 * d * c * b * e * d * c * b * a * e * d * c * b * e * d * c * d * e^2 * d * c * b * a * e * d * c * b * d * c * e * d * e^2 * d * c * b * a * d * c * b * e * d * c * e * d * e * a * b * c * d * e * d * c * b * a * d * c * b * e * d * c * e * d * e^2 * d * c * b * a * e * d * c * b * d * c * e * d * e^2 * d * c * b * a * e * d * c * b * e * d * c * d * e^2 * d * c * b * e * d * c * b * a * e * d * c * b * e * d * c * d * e^2 * d * c * b * a * e * d * c * b * d * c * e * d * e^2 * d * c * b * a * d * c * b * e * d * c * e * d * e^2 * d * c * b * a * e * d * c * b * e * d * c * e * d^2 * c * b * a * e * d * c * b * e * d * c * e * d * e^2 * d * c * b * a * e * d * c * b * e * d * c * d * e^2 * d * c * b * a * e * d * c * b * d * c * e * d * e^2 * d * c * b * a * d * c * b * e * d * c * e * d * e * a * b * c * d * e^2 * d * c * b * a * d * c * e * d * c * b * a * d * c * b * e * d * c * e * d * e * b * c * e * d * c * b * a * e * d * c * b * e * d * c * d * e * d * c * e * d * c * b * a * d * c * b * e * d * c * e * d * e * b * c * e * d * c * b * a * e * d * c * b * e * d * c * d * e * d^3 :=BraidGroup(6); A:=a^(-1); B:=b^(-1); C:=c^(-1); D:=d^(-1); E:=e^(-1); w:=d*d*d*D*c*d*D*c*d*c*c*c*c*c*c*C*d*c*D*c*C*d*c*D*c*C*C*D*D*C*b*c*d*d*c*c*C*C*C*b*c*c*c*C*C*C*b*c*c*c*C*C*C*b*c*c*c*B*C*D*D*C*B*B*C*D*e*d*c*b*b*c*d*d*c*b*B*C*D*e*d*c*b*B*C*D*e*d*c*b*B*C*D*e*d*c*b*B*C*D*E*E*D*C*B*a*b*c*d*e*e*d*c*b*a*d*c*D*d*c*D*d*c*D*d*c*D*d*d*d; w; NormalForm(w); Output: Magma V2.10-6 Wed Jan 14 2004 10:41:43 on modular [Seed = 1528723465] ------------------------------------- e^-1 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-1 * d^3 * e * d * c * b * a * d * c * b * e * d * c * e * d * e * c * b * e * d * c * b * a * e * d * c * b * e * d * c * d * e * c * d * c^6 * e * d * c * b * a * e * d * c * b * d * c * e * d * e * b * c * e * d * c * b * a * e * d * c * b * e * d * c * d * e * c * e * d * c * b * a * e * d * c * b * d * c * e * d * e * b * c * e * d * c * b * a * e * d * c * b * e * d * c * d * e * c * e * d * c * b * a * e * d * c * b * d * c * e * d * e^2 * d * c * b * a * e * d * c * b * d * c * e * d * e^2 * d * c * b * a * d * c * b * e * d * c * e * d * e^2 * d * c * b * a * e * d * c * b * e * d * c * d * e^2 * d * c * b * a * e * d * c * b * d * c * e * d * e * d * c * b^2 * c^2 * e * d * c * b * a * e * d * c * b * d * c * e * d * e^2 * d * c * b * a * e * d * c * b * d * c * e * d * e^2 * d * c * b * a * e * d * c * b * d * c * e * d * e * b * c^3 * e * d * c * b * a * e * d * c * b * d * c * e * d * e^2 * d * c * b * a * e * d * c * b * d * c * e * d * e^2 * d * c * b * a * e * d * c * b * d * c * e * d * e * d * c^3 * e * d * c * b * a * e * d * c * b * d * c * e * d * e^2 * d * c * b * a * e * d * c * b * d * c * e * d * e^2 * d * c * b * a * e * d * c * b * d * c * e * d * e * b * c^3 * e * d * c * b * a * e * d * c * b * e * d * c * d * e^2 * d * c * b * a * e * d * c * b * d * c * e * d * e^2 * d * c * b * a * d * c * b * e * d * c * e * d * e^2 * d * c * b * a * e * d * c * b * e * d * c * d * e^2 * d * c * b * a * e * d * c * b * d * c * e * d * e^2 * d * c * b * a * d * c * b * e * d * c * e * d * e^2 * d * c * b * a * e * d * c * b * e * d * c * d * e^2 * d * c * b * a * e * d * c * b * d * c * e * d * e^2 * d * c * b * a * d * c * b * e * d * c * e * d * e * a * b * c * d^2 * c * b^2 * c * d * e * d * c * b * a * d * c * b * e * d * c * e * d * e^2 * d * c * b * a * e * d * c * b * d * c * e * d * e^2 * d * c * b * a * e * d * c * b * e * d * c * d * e^2 * d * c * b * e * d * c * b * a * e * d * c * b * e * d * c * d * e^2 * d * c * b * a * e * d * c * b * d * c * e * d * e^2 * d * c * b * a * d * c * b * e * d * c * e * d * e * a * b * c * d * e * d * c * b * a * d * c * b * e * d * c * e * d * e^2 * d * c * b * a * e * d * c * b * d * c * e * d * e^2 * d * c * b * a * e * d * c * b * e * d * c * d * e^2 * d * c * b * e * d * c * b * a * e * d * c * b * e * d * c * d * e^2 * d * c * b * a * e * d * c * b * d * c * e * d * e^2 * d * c * b * a * d * c * b * e * d * c * e * d * e^2 * d * c * b * a * e * d * c * b * e * d * c * e * d^2 * c * b * a * e * d * c * b * e * d * c * e * d * e^2 * d * c * b * a * e * d * c * b * e * d * c * d * e^2 * d * c * b * a * e * d * c * b * d * c * e * d * e^2 * d * c * b * a * d * c * b * e * d * c * e * d * e * a * b * c * d * e^2 * d * c * b * a * d * c * e * d * c * b * a * d * c * b * e * d * c * e * d * e * b * c * e * d * c * b * a * e * d * c * b * e * d * c * d * e * d * c * e * d * c * b * a * d * c * b * e * d * c * e * d * e * b * c * e * d * c * b * a * e * d * c * b * e * d * c * d * e * d^3 :=BraidGroup(6); A:=a^(-1); B:=b^(-1); C:=c^(-1); D:=d^(-1); E:=e^(-1); w:=d*d*d*D*c*d*D*c*d*c*c*c*c*c*c*C*d*c*D*c*C*d*c*D*c*C*C*D*D*C*b*c*d*d*c*c*C*C*C*b*c*c*c*C*C*C*b*c*c*c*C*C*C*b*c*c*c*B*C*D*D*C*B*B*C*D*e*d*c*b*b*c*d*d*c*b*B*C*D*e*d*c*b*B*C*D*e*d*c*b*B*C*D*e*d*c*b*B*C*D*E*E*D*C*B*a*b*c*d*e*e*d*c*b*a*d*c*D*d*c*D*d*c*D*d*c*D*d*d*d; NormalForm(w); Output: Magma V2.10-6 Wed Jan 14 2004 10:42:07 on modular [Seed = 577175816] ------------------------------------- e^-1 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * a^-1 * b^-1 * c^-1 * d^-1 * e^-2 * d^-1 * e^-1 * c^-1 * d^-1 * e^-1 * b^-1 * c^-1 * d^-1 * e^-1 * b * e * d * c * e * d * e^2 * d * c * b * a * d * c * b * c * e * d * e^2 * d * c * b * a * e * d * c * b * d * c * e * d * e^2 * d * c * b * a * c * b * c * e * d * e^2 * d * c * b * a * c * b * c * e * d * e^2 * d * c * b * a * c * b * e * d * c * e * d * e * d * c * d^2 * c * d^2 * c^2 * d^3 * c^3 * d^2 Total time: 3.069 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 0x503fe304.odnxx1.adsl-dhcp.tele.dk. (80.63.227.4) Time: Wed Jan 14 14:49:15 2004 Input: Factorization(21152923813644279445637889283551800700802491206174149213598656176159750053385842115946365356305306542786771153583613865570045471663739101218972164851995066805188927363175826739); Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Wed Jan 14 2004 14:48:52 on modular [Seed = 2328844231] ------------------------------------- Errors: /home/mfd/gomagma: line 2: 10723 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host 0x503fe304.odnxx1.adsl-dhcp.tele.dk. (80.63.227.4) Time: Wed Jan 14 14:49:40 2004 Input: Factorization(211529238136); Output: Magma V2.10-6 Wed Jan 14 2004 14:49:37 on modular [Seed = 2243975357] ------------------------------------- [ <2, 3>, <47, 1>, <67, 1>, <661, 1>, <12703, 1> ] Total time: 3.009 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 0x503fe304.odnxx1.adsl-dhcp.tele.dk. (80.63.227.4) Time: Wed Jan 14 14:50:00 2004 Input: Factorization(311277); Output: Magma V2.10-6 Wed Jan 14 2004 14:49:57 on modular [Seed = 2631483792] ------------------------------------- [ <3, 1>, <19, 1>, <43, 1>, <127, 1> ] Total time: 3.019 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host ade-ce4.chariot.net.au. (203.87.94.182) Time: Thu Jan 15 00:21:52 2004 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: Magma V2.10-6 Thu Jan 15 2004 00:21:49 on modular [Seed = 829903404] ------------------------------------- Replace this by some code, then click [PARI] or [MAGMA]! Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host ade-ce4.chariot.net.au. (203.87.94.182) Time: Thu Jan 15 00:22:45 2004 Input: "integ(sin(x),x) Output: Magma V2.10-6 Thu Jan 15 2004 00:22:42 on modular [Seed = 981228008] ------------------------------------- >> quit; ^ User error: Unterminated string Total time: 2.909 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host ade-ce4.chariot.net.au. (203.87.94.182) Time: Thu Jan 15 00:23:23 2004 Input: " integ( x^2,x) " Output: Magma V2.10-6 Thu Jan 15 2004 00:23:20 on modular [Seed = 593838235] ------------------------------------- integ( x^2,x) Total time: 2.919 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host ade-ce4.chariot.net.au. (203.87.94.182) Time: Thu Jan 15 00:24:02 2004 Input: " 121! " Output: Magma V2.10-6 Thu Jan 15 2004 00:23:59 on modular [Seed = 762007218] ------------------------------------- 121! Total time: 2.909 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host web-cache-3.ocs.mq.edu.au. (137.111.13.34) Time: Thu Jan 15 00:54:28 2004 Input: x := CongruenceSubgroup[3]; y := Generators[x]; y; Output: Magma V2.10-6 Thu Jan 15 2004 00:54:25 on modular [Seed = 3903751049] ------------------------------------- >> x := CongruenceSubgroup[3]; ^ Runtime error in '[]': Bad argument types >> y := Generators[x]; ^ User error: Identifier 'x' has not been declared or assigned >> y;; ^ User error: Identifier 'y' has not been declared or assigned Total time: 2.989 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host web-cache-3.ocs.mq.edu.au. (137.111.13.34) Time: Thu Jan 15 00:54:42 2004 Input: x := CongruenceSubgroup[3]; y := Generators[x]; y; Output: Magma V2.10-6 Thu Jan 15 2004 00:54:39 on modular [Seed = 3516381825] ------------------------------------- >> x := CongruenceSubgroup[3]; ^ Runtime error in '[]': Bad argument types >> y := Generators[x]; ^ User error: Identifier 'x' has not been declared or assigned >> y;; ^ User error: Identifier 'y' has not been declared or assigned Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host web-cache-3.ocs.mq.edu.au. (137.111.13.34) Time: Thu Jan 15 00:55:03 2004 Input: x := 5; y :=6; x+y; Output: Magma V2.10-6 Thu Jan 15 2004 00:55:00 on modular [Seed = 3734549914] ------------------------------------- 11 Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host web-cache-3.ocs.mq.edu.au. (137.111.13.34) Time: Thu Jan 15 00:55:43 2004 Input: x := 4; x; Output: Magma V2.10-6 Thu Jan 15 2004 00:55:40 on modular [Seed = 2968968092] ------------------------------------- 4 Total time: 2.919 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host web-cache-3.ocs.mq.edu.au. (137.111.13.34) Time: Thu Jan 15 00:56:20 2004 Input: x := CongruenceSubgroup[3]; y := Generators[x]; y; Output: Magma V2.10-6 Thu Jan 15 2004 00:56:17 on modular [Seed = 3120550472] ------------------------------------- >> x := CongruenceSubgroup[3]; ^ Runtime error in '[]': Bad argument types >> y := Generators[x]; ^ User error: Identifier 'x' has not been declared or assigned >> y;; ^ User error: Identifier 'y' has not been declared or assigned Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host web-cache-3.ocs.mq.edu.au. (137.111.13.34) Time: Thu Jan 15 00:57:01 2004 Input: CongruenceSubgroup[3]; Output: Magma V2.10-6 Thu Jan 15 2004 00:56:58 on modular [Seed = 2732902776] ------------------------------------- >> CongruenceSubgroup[3]; ^ Runtime error in '[]': Bad argument types Total time: 2.919 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host web-cache-3.ocs.mq.edu.au. (137.111.13.34) Time: Thu Jan 15 00:57:25 2004 Input: CongruenceSubgroup(3); Output: Magma V2.10-6 Thu Jan 15 2004 00:57:22 on modular [Seed = 2884485145] ------------------------------------- Gamma(3) Total time: 2.959 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host web-cache-3.ocs.mq.edu.au. (137.111.13.34) Time: Thu Jan 15 00:57:48 2004 Input: Generators(CongruenceSubgroup(3)); Output: Magma V2.10-6 Thu Jan 15 2004 00:57:45 on modular [Seed = 2496855869] ------------------------------------- [ [-1 0] [ 3 -1], [ 7 -3] [12 -5], [ 4 -3] [ 3 -2] ] Total time: 2.989 seconds, Total memory usage: 1.99MB ************** MAGMA ***************** Host web-cache-3.ocs.mq.edu.au. (137.111.13.34) Time: Thu Jan 15 00:59:39 2004 Input: Generators(GammaUpper0(3)); Output: Magma V2.10-6 Thu Jan 15 2004 00:59:36 on modular [Seed = 2665018022] ------------------------------------- [ [-1 0] [ 1 -1], [ 1 -3] [ 1 -2] ] Total time: 2.999 seconds, Total memory usage: 1.99MB ************** MAGMA ***************** Host web-cache-3.ocs.mq.edu.au. (137.111.13.34) Time: Thu Jan 15 01:00:34 2004 Input: Generators(CongruenceSubgroup(1)); Output: Magma V2.10-6 Thu Jan 15 2004 01:00:31 on modular [Seed = 2412372864] ------------------------------------- [ [1 1] [0 1], [ 0 1] [-1 0] ] Total time: 3.019 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host web-cache-3.ocs.mq.edu.au. (137.111.13.34) Time: Thu Jan 15 02:44:22 2004 Input: Generators(GammaUpper0(3)); Output: Magma V2.10-6 Thu Jan 15 2004 02:44:18 on modular [Seed = 2513670455] ------------------------------------- [ [-1 0] [ 1 -1], [ 1 -3] [ 1 -2] ] Total time: 2.979 seconds, Total memory usage: 1.99MB ************** MAGMA ***************** Host web-cache-3.ocs.mq.edu.au. (137.111.13.34) Time: Thu Jan 15 02:48:54 2004 Input: Generators(Gamma(3)); Output: Magma V2.10-6 Thu Jan 15 2004 02:48:51 on modular [Seed = 1982886887] ------------------------------------- >> Generators(Gamma(3)); ^ Runtime error in 'Generators': Bad argument types Argument types given: FldPrElt Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host web-cache-3.ocs.mq.edu.au. (137.111.13.34) Time: Thu Jan 15 02:49:13 2004 Input: Generators(CongruenceSubgroup(3)); Output: Magma V2.10-6 Thu Jan 15 2004 02:49:10 on modular [Seed = 2134473467] ------------------------------------- [ [-1 0] [ 3 -1], [ 7 -3] [12 -5], [ 4 -3] [ 3 -2] ] Total time: 2.999 seconds, Total memory usage: 1.99MB ************** MAGMA ***************** Host web-cache-3.ocs.mq.edu.au. (137.111.13.34) Time: Thu Jan 15 02:53:19 2004 Input: K = CongruenceSubgroup(3); L = GammaUpper0(3); Generators(K intersection L); Output: Magma V2.10-6 Thu Jan 15 2004 02:53:16 on modular [Seed = 1360484302] ------------------------------------- >> K = CongruenceSubgroup(3); ^ User error: Identifier 'K' has not been declared or assigned >> L = GammaUpper0(3); ^ User error: Identifier 'L' has not been declared or assigned >> Generators(K intersection L); ^ User error: bad syntax Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host web-cache-3.ocs.mq.edu.au. (137.111.13.34) Time: Thu Jan 15 02:53:36 2004 Input: K := CongruenceSubgroup(3); L := GammaUpper0(3); Generators(K intersection L); Output: Magma V2.10-6 Thu Jan 15 2004 02:53:33 on modular [Seed = 1578653905] ------------------------------------- >> Generators(K intersection L); ^ User error: bad syntax Total time: 2.969 seconds, Total memory usage: 1.99MB ************** MAGMA ***************** Host web-cache-3.ocs.mq.edu.au. (137.111.13.34) Time: Thu Jan 15 02:54:37 2004 Input: K := CongruenceSubgroup(3); L := GammaUpper0(3); Generators(K meet L); Output: Magma V2.10-6 Thu Jan 15 2004 02:54:34 on modular [Seed = 1140998924] ------------------------------------- Generators( G: Gamma(3) ) FareySymbol( group: Gamma(3) ) FareySymbol( group: Gamma(3), restrictions: [] ) CanLink( group: Gamma(3), L: [ [ -1, 0, 0, 1, 0, -4 ], [ 0, 1, 1, 1, 0, 0 ], [ 1, 1, 1, 0..., e: [ 0, 1, 1, 1, 0, 0 ] ) HackobjCoerceGrpPSL2( G: Gamma(3), S: [1 0] [0 1] ) eq( G: PSL2(Integer Ring), H: Gamma(3) ) In file "/home/was/magma/packages/fundom/congruence_subgroups.m", line 663, column 25: >> return (G`Level eq H`Level) and ^ Runtime error in 'eq': Bad argument types Argument types given: RngIntElt, SeqEnum[RngIntElt] Total time: 3.069 seconds, Total memory usage: 1.99MB ************** MAGMA ***************** Host web-cache-3.ocs.mq.edu.au. (137.111.13.34) Time: Thu Jan 15 02:55:22 2004 Input: K := CongruenceSubgroup(3); L := GammaUpper0(3); M : = K meet L; Generators(M); Output: Magma V2.10-6 Thu Jan 15 2004 02:55:19 on modular [Seed = 829896228] ------------------------------------- >> M : = K meet L; ^ User error: bad syntax >> Generators(M); ^ User error: Identifier 'M' has not been declared or assigned Total time: 2.929 seconds, Total memory usage: 1.99MB ************** MAGMA ***************** Host web-cache-3.ocs.mq.edu.au. (137.111.13.34) Time: Thu Jan 15 02:56:30 2004 Input: K := CongruenceSubgroup(3); L := GammaUpper0(3); M : = Intersection(K,L); Generators(M); Output: Magma V2.10-6 Thu Jan 15 2004 02:56:27 on modular [Seed = 1048066535] ------------------------------------- >> M : = Intersection(K,L); ^ User error: bad syntax >> Generators(M); ^ User error: Identifier 'M' has not been declared or assigned Total time: 2.979 seconds, Total memory usage: 1.99MB ************** MAGMA ***************** Host web-cache-3.ocs.mq.edu.au. (137.111.13.34) Time: Thu Jan 15 02:56:53 2004 Input: K := CongruenceSubgroup(3); L := GammaUpper0(3); G : = Intersection(K,L); Generators(G); Output: Magma V2.10-6 Thu Jan 15 2004 02:56:49 on modular [Seed = 660676759] ------------------------------------- >> G : = Intersection(K,L); ^ User error: bad syntax >> Generators(G); ^ User error: Identifier 'G' has not been declared or assigned Total time: 2.969 seconds, Total memory usage: 1.99MB ************** MAGMA ***************** Host web-cache-3.ocs.mq.edu.au. (137.111.13.34) Time: Thu Jan 15 02:57:18 2004 Input: K := CongruenceSubgroup(3); L := GammaUpper0(3); Generators(Intersection(K,L)); Output: Magma V2.10-6 Thu Jan 15 2004 02:57:15 on modular [Seed = 745155461] ------------------------------------- Generators( G: Gamma(3) ) FareySymbol( group: Gamma(3) ) FareySymbol( group: Gamma(3), restrictions: [] ) CanLink( group: Gamma(3), L: [ [ -1, 0, 0, 1, 0, -4 ], [ 0, 1, 1, 1, 0, 0 ], [ 1, 1, 1, 0..., e: [ 0, 1, 1, 1, 0, 0 ] ) HackobjCoerceGrpPSL2( G: Gamma(3), S: [1 0] [0 1] ) eq( G: PSL2(Integer Ring), H: Gamma(3) ) In file "/home/was/magma/packages/fundom/congruence_subgroups.m", line 663, column 25: >> return (G`Level eq H`Level) and ^ Runtime error in 'eq': Bad argument types Argument types given: RngIntElt, SeqEnum[RngIntElt] Total time: 3.019 seconds, Total memory usage: 1.99MB ************** MAGMA ***************** Host r3u232.mistral.cz. (213.220.212.232) Time: Thu Jan 15 09:12:53 2004 Input: 2*2 Output: Magma V2.10-6 Thu Jan 15 2004 09:12:49 on modular [Seed = 4055314025] ------------------------------------- 4 Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 168ext7.cab.uniroma3.it. (193.204.163.2) Time: Thu Jan 15 09:25:47 2004 Input: 5+9 Output: Magma V2.10-6 Thu Jan 15 2004 09:25:33 on modular [Seed = 3120519965] ------------------------------------- 14 Total time: 3.089 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 203-195-199-244.now-india.net.in. (203.195.199.244) Time: Thu Jan 15 12:14:18 2004 Input: Factorization(x^8 - 1); Output: Magma V2.10-6 Thu Jan 15 2004 12:14:15 on modular [Seed = 2227310307] ------------------------------------- >> Factorization(x^8 - 1);; ^ User error: Identifier 'x' has not been declared or assigned Total time: 3.029 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 203-195-199-244.now-india.net.in. (203.195.199.244) Time: Thu Jan 15 12:16:38 2004 Input: Factorial(18); Output: Magma V2.10-6 Thu Jan 15 2004 12:16:35 on modular [Seed = 2901026399] ------------------------------------- 6402373705728000 Total time: 2.989 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host hilbert.lip6.fr. (132.227.66.218) Time: Thu Jan 15 12:27:53 2004 Input: Factorization(3*x+1); Output: Magma V2.10-6 Thu Jan 15 2004 12:27:49 on modular [Seed = 4122179680] ------------------------------------- >> Factorization(3*x+1);; ^ User error: Identifier 'x' has not been declared or assigned Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host p5086E8C2.dip0.t-ipconnect.de. (80.134.232.194) Time: Thu Jan 15 13:08:35 2004 Input: X:=Matrix(K, 6, 6, [1,1,0,-1,-1,0, 0,0,0,1,-1,0, 0,-1,0,2/3,3/5,0, 0,1/3,0,0,0,-1, 0,0,1,0,0,-1, 0,0,-4,1,1,0]); X; Output: Magma V2.10-6 Thu Jan 15 2004 13:08:32 on modular [Seed = 2193888675] ------------------------------------- >> X:=Matrix(K, 6, 6, [1,1,0,-1,-1,0, 0,0,0,1,-1,0, 0,-1,0,2/3,3/5,0, 0,1/ ^ User error: Identifier 'K' has not been declared or assigned >> X;; ^ User error: Identifier 'X' has not been declared or assigned Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host p5086E8C2.dip0.t-ipconnect.de. (80.134.232.194) Time: Thu Jan 15 13:09:23 2004 Input: X:=Matrix(R, 6, 6, [1,1,0,-1,-1,0, 0,0,0,1,-1,0, 0,-1,0,2/3,3/5,0, 0,1/3,0,0,0,-1, 0,0,1,0,0,-1, 0,0,-4,1,1,0]); X; Output: Magma V2.10-6 Thu Jan 15 2004 13:09:20 on modular [Seed = 2446788288] ------------------------------------- >> X:=Matrix(R, 6, 6, [1,1,0,-1,-1,0, 0,0,0,1,-1,0, 0,-1,0,2/3,3/5,0, 0,1/ ^ User error: Identifier 'R' has not been declared or assigned >> X;; ^ User error: Identifier 'X' has not been declared or assigned Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host p5086E8C2.dip0.t-ipconnect.de. (80.134.232.194) Time: Thu Jan 15 13:10:10 2004 Input: X:=Matrix(6, 6, [1,1,0,-1,-1,0, 0,0,0,1,-1,0, 0,-1,0,2/3,3/5,0, 0,1/3,0,0,0,-1, 0,0,1,0,0,-1, 0,0,-4,1,1,0]); X; Output: Magma V2.10-6 Thu Jan 15 2004 13:10:07 on modular [Seed = 2716284639] ------------------------------------- [ 1 1 0 -1 -1 0] [ 0 0 0 1 -1 0] [ 0 -1 0 2/3 3/5 0] [ 0 1/3 0 0 0 -1] [ 0 0 1 0 0 -1] [ 0 0 -4 1 1 0] Total time: 2.999 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host p5086E8C2.dip0.t-ipconnect.de. (80.134.232.194) Time: Thu Jan 15 13:11:43 2004 Input: X:=Matrix(6, 6, [1,1,0,-1,-1,0, 0,0,0,1,-1,0, 0,-1,0,2/3,3/5,0, 0,1/3,0,0,0,-1, 0,0,1,0,0,-1, 0,0,-4,1,1,0]); X; W:=Vector([0,2,0,0,2,0]) W; Output: Magma V2.10-6 Thu Jan 15 2004 13:11:40 on modular [Seed = 2917874288] ------------------------------------- [ 1 1 0 -1 -1 0] [ 0 0 0 1 -1 0] [ 0 -1 0 2/3 3/5 0] [ 0 1/3 0 0 0 -1] [ 0 0 1 0 0 -1] [ 0 0 -4 1 1 0] >> W;; ^ User error: bad syntax Total time: 2.939 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host p5086E8C2.dip0.t-ipconnect.de. (80.134.232.194) Time: Thu Jan 15 13:11:56 2004 Input: X:=Matrix(6, 6, [1,1,0,-1,-1,0, 0,0,0,1,-1,0, 0,-1,0,2/3,3/5,0, 0,1/3,0,0,0,-1, 0,0,1,0,0,-1, 0,0,-4,1,1,0]); X; W:=Vector([0,2,0,0,2,0]); W; Output: Magma V2.10-6 Thu Jan 15 2004 13:11:53 on modular [Seed = 3035767644] ------------------------------------- [ 1 1 0 -1 -1 0] [ 0 0 0 1 -1 0] [ 0 -1 0 2/3 3/5 0] [ 0 1/3 0 0 0 -1] [ 0 0 1 0 0 -1] [ 0 0 -4 1 1 0] (0 2 0 0 2 0) Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host p5086E8C2.dip0.t-ipconnect.de. (80.134.232.194) Time: Thu Jan 15 13:12:45 2004 Input: X:=Matrix(6, 6, [1,1,0,-1,-1,0, 0,0,0,1,-1,0, 0,-1,0,2/3,3/5,0, 0,1/3,0,0,0,-1, 0,0,1,0,0,-1, 0,0,-4,1,1,0]); X; W:=Vector([0,2,0,0,2,0]); W; N:=Solution(X,W); N; Output: Magma V2.10-6 Thu Jan 15 2004 13:12:42 on modular [Seed = 3220776868] ------------------------------------- [ 1 1 0 -1 -1 0] [ 0 0 0 1 -1 0] [ 0 -1 0 2/3 3/5 0] [ 0 1/3 0 0 0 -1] [ 0 0 1 0 0 -1] [ 0 0 -4 1 1 0] (0 2 0 0 2 0) >> N:=Solution(X,W); ^ Runtime error in 'Solution': Arguments 1 and 2 have incompatible coefficient rings >> N;; ^ User error: Identifier 'N' has not been declared or assigned Total time: 2.989 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host p5086E8C2.dip0.t-ipconnect.de. (80.134.232.194) Time: Thu Jan 15 13:13:35 2004 Input: X:=Matrix(6, 6, [1,1,0,-1,-1,0, 0,0,0,1,-1,0, 0,-1,0,2/3,3/5,0, 0,1/3,0,0,0,-1, 0,0,1,0,0,-1, 0,0,-4,1,1,0]); X; W:=Vector([0,2,0,0,2,0]); W; V,N:=Solution(X,W); V; N; Output: Magma V2.10-6 Thu Jan 15 2004 13:13:32 on modular [Seed = 3415036806] ------------------------------------- [ 1 1 0 -1 -1 0] [ 0 0 0 1 -1 0] [ 0 -1 0 2/3 3/5 0] [ 0 1/3 0 0 0 -1] [ 0 0 1 0 0 -1] [ 0 0 -4 1 1 0] (0 2 0 0 2 0) >> V,N:=Solution(X,W); ^ Runtime error in 'Solution': Arguments 1 and 2 have incompatible coefficient rings >> V; ^ User error: Identifier 'V' has not been declared or assigned >> N;; ^ User error: Identifier 'N' has not been declared or assigned Total time: 3.019 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host p5086E8C2.dip0.t-ipconnect.de. (80.134.232.194) Time: Thu Jan 15 13:14:51 2004 Input: R:=real(); X:=Matrix(R, 6, 6, [1,1,0,-1,-1,0, 0,0,0,1,-1,0, 0,-1,0,2/3,3/5,0, 0,1/3,0,0,0,-1, 0,0,1,0,0,-1, 0,0,-4,1,1,0]); X; W:=Vector(R, [0,2,0,0,2,0]); W; V,N:=Solution(X, W); V; N; Output: Magma V2.10-6 Thu Jan 15 2004 13:14:48 on modular [Seed = 3583200588] ------------------------------------- >> R:=real(); ^ User error: Identifier 'real' has not been declared or assigned >> X:=Matrix(R, 6, 6, [1,1,0,-1,-1,0, 0,0,0,1,-1,0, 0,-1,0,2/3,3/5,0, 0,1/ ^ User error: Identifier 'R' has not been declared or assigned >> X; ^ User error: Identifier 'X' has not been declared or assigned >> W:=Vector(R, [0,2,0,0,2,0]); ^ User error: Identifier 'R' has not been declared or assigned >> W; ^ User error: Identifier 'W' has not been declared or assigned >> V,N:=Solution(X, W); ^ User error: Identifier 'X' has not been declared or assigned >> V; ^ User error: Identifier 'V' has not been declared or assigned >> N;; ^ User error: Identifier 'N' has not been declared or assigned Total time: 3.019 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host p5086E8C2.dip0.t-ipconnect.de. (80.134.232.194) Time: Thu Jan 15 13:15:00 2004 Input: R:=real; X:=Matrix(R, 6, 6, [1,1,0,-1,-1,0, 0,0,0,1,-1,0, 0,-1,0,2/3,3/5,0, 0,1/3,0,0,0,-1, 0,0,1,0,0,-1, 0,0,-4,1,1,0]); X; W:=Vector(R, [0,2,0,0,2,0]); W; V,N:=Solution(X, W); V; N; Output: Magma V2.10-6 Thu Jan 15 2004 13:14:57 on modular [Seed = 3701097596] ------------------------------------- >> R:=real; ^ User error: Identifier 'real' has not been declared or assigned >> X:=Matrix(R, 6, 6, [1,1,0,-1,-1,0, 0,0,0,1,-1,0, 0,-1,0,2/3,3/5,0, 0,1/ ^ User error: Identifier 'R' has not been declared or assigned >> X; ^ User error: Identifier 'X' has not been declared or assigned >> W:=Vector(R, [0,2,0,0,2,0]); ^ User error: Identifier 'R' has not been declared or assigned >> W; ^ User error: Identifier 'W' has not been declared or assigned >> V,N:=Solution(X, W); ^ User error: Identifier 'X' has not been declared or assigned >> V; ^ User error: Identifier 'V' has not been declared or assigned >> N;; ^ User error: Identifier 'N' has not been declared or assigned Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host p5086E8C2.dip0.t-ipconnect.de. (80.134.232.194) Time: Thu Jan 15 13:16:00 2004 Input: R:=GF(3); X:=Matrix(R, 6, 6, [1,1,0,-1,-1,0, 0,0,0,1,-1,0, 0,-1,0,2/3,3/5,0, 0,1/3,0,0,0,-1, 0,0,1,0,0,-1, 0,0,-4,1,1,0]); X; W:=Vector(R, [0,2,0,0,2,0]); W; V,N:=Solution(X, W); V; N; Output: Magma V2.10-6 Thu Jan 15 2004 13:15:57 on modular [Seed = 3954012983] ------------------------------------- >> X:=Matrix(R, 6, 6, [1,1,0,-1,-1,0, 0,0,0,1,-1,0, 0,-1,0,2/3,3/5,0, 0,1/ ^ Runtime error in 'Matrix': Can't coerce sequence element 16 into the coefficient ring >> X; ^ User error: Identifier 'X' has not been declared or assigned (0 2 0 0 2 0) >> V,N:=Solution(X, W); ^ User error: Identifier 'X' has not been declared or assigned >> V; ^ User error: Identifier 'V' has not been declared or assigned >> N;; ^ User error: Identifier 'N' has not been declared or assigned Total time: 2.979 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host p5086E8C2.dip0.t-ipconnect.de. (80.134.232.194) Time: Thu Jan 15 13:17:59 2004 Input: R:=RealField(); X:=Matrix(R, 6, 6, [1,1,0,-1,-1,0, 0,0,0,1,-1,0, 0,-1,0,2/3,3/5,0, 0,1/3,0,0,0,-1, 0,0,1,0,0,-1, 0,0,-4,1,1,0]); X; W:=Vector(R, [0,2,0,0,2,0]); W; V,N:=Solution(X, W); V; N; Output: Magma V2.10-6 Thu Jan 15 2004 13:17:56 on modular [Seed = 4071910311] ------------------------------------- [ 1 1 0 -1 -1 0] [ 0 0 0 1 -1 0] [ 0 -1 0 2/3 3/5 0] [ 0 1/3 0 0 0 -1] [ 0 0 1 0 0 -1] [ 0 0 -4/1 1 1 0] (0 2 0 0 2 0) ( 0 -2/7 -150/7 -408/7 408/7 102/7) Vector space of degree 6, dimension 0 over Real Field Total time: 2.939 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host p5086E8C2.dip0.t-ipconnect.de. (80.134.232.194) Time: Thu Jan 15 13:23:47 2004 Input: R:=RealField(); X:=Matrix(R, 6, 6, [1,1,0,-1,-1,0, 0,0,0,1,-1,0, 0,-1,0,0.666,0.6,0, 0,0.333,0,0,0,-1, 0,0,1,0,0,-1, 0,0,-4,1,1,0]); X; W:=Vector(R, [0,2,0,0,2,0]); W; V,N:=Solution(X, W); V; N; Output: Magma V2.10-6 Thu Jan 15 2004 13:23:44 on modular [Seed = 324372897] ------------------------------------- [1 1 0 -1 -1 0] [0 0 0 1 -1 0] [0 -1 0 0.66599999999999999999999999999 0.59999999999999999999999999999 0] [0 0.332999999999999999999999999995 0 0 0 -1] [0 0 1 0 0 -1] [0 0 -4 1 1 0] (0 2 0 0 2 0) (0 -0.298946724133533957307898294110 -21.244038662620183111881869880651 -57.78990589375430363928489453840 57.78990589375430363928489453840 14.447476473438575909821223634601) Vector space of degree 6, dimension 0 over Real Field Total time: 3.069 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host RJ141219205.user.veloxzone.com.br. (200.141.219.205) Time: Thu Jan 15 17:21:42 2004 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: Magma V2.10-6 Thu Jan 15 2004 17:21:39 on modular [Seed = 1646604313] ------------------------------------- Replace this by some code, then click [PARI] or [MAGMA]! Total time: 2.999 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host dsl-203-33-162-116.NSW.netspace.net.au. (203.33.162.116) Time: Thu Jan 15 21:54:14 2004 Input: 1 Output: Magma V2.10-6 Thu Jan 15 2004 21:54:10 on modular [Seed = 3103763168] ------------------------------------- 1 Total time: 3.019 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host h00096bd05fc4.ne.client2.attbi.com. (65.96.162.217) Time: Thu Jan 15 22:02:06 2004 Input: ModularSymbols("389A"); Output: Magma V2.10-6 Thu Jan 15 2004 22:02:02 on modular [Seed = 104927783] ------------------------------------- Modular symbols space for Gamma_0(389) of weight 2 and dimension 2 over Rational Field Total time: 4.409 seconds, Total memory usage: 3.55MB ************** MAGMA ***************** Host septsix.celar.fr. (192.134.105.76) Time: Fri Jan 16 02:59:44 2004 Input: 34*89; Output: Magma V2.10-6 Fri Jan 16 2004 02:59:41 on modular [Seed = 3532983090] ------------------------------------- 3026 Total time: 3.119 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host ibm21.ilab.sztaki.hu. (195.111.1.97) Time: Fri Jan 16 07:34:06 2004 Input: MaximalSubgroups( Alt(51)); Output: Magma V2.10-6 Fri Jan 16 2004 07:33:58 on modular [Seed = 930131219] ------------------------------------- Conjugacy classes of subgroups ------------------------------ [ 1] Order 3010299982077507642851328000 Length 257635246075526315926272895552000000000 Permutation group acting on a set of cardinality 51 Order = 2^31 * 3^23 * 5^3 * 7^2 * 11 * 13 * 17 (1, 24, 20, 38, 14, 19, 13, 32, 16, 33, 4, 26, 31, 8, 36, 3, 37)(2, 9, 7, 43, 23, 51, 47, 45, 27, 35, 41, 42, 40, 39, 34, 46, 50)(5, 44, 18, 15, 6, 22, 10, 17, 48, 12, 30, 28, 29, 11, 25, 21, 49) (7, 43, 23)(20, 38, 24)(21, 49, 25) (7, 25, 24)(20, 21, 43) (7, 25)(21, 43) (1, 20, 19, 32, 33, 26, 8, 3)(2, 7, 23, 45, 35, 42, 39, 46)(4, 31, 36, 37, 24, 38, 13, 16)(6, 10, 48, 30, 29, 25, 49, 18)(9, 43, 47, 27, 41, 40, 34, 50)(11, 21, 44, 15, 22, 17, 12, 28) (7, 24, 25) (24, 25)(38, 49) (1, 37, 3, 36, 8, 31, 26, 4, 33, 16, 32, 13, 19, 20, 24)(2, 50, 46, 34, 39, 40, 42, 41, 35, 27, 45, 47, 43, 7, 9)(6, 15, 18, 44, 21, 25, 11, 29, 28, 30, 12, 48, 17, 10, 22) (1, 19, 13, 32, 16, 33, 4, 26, 31, 8, 36, 3, 37)(2, 9, 47, 45, 27, 35, 41, 42, 40, 39, 34, 46, 50)(6, 22, 10, 17, 48, 12, 30, 28, 29, 11, 44, 18, 15) (1, 9, 11)(7, 24, 25) (1, 11)(24, 25) (5, 14)(7, 24) (7, 47, 45)(13, 24, 19)(18, 25, 44) (7, 24, 25)(19, 47, 44) (19, 44)(24, 25) (1, 24, 19)(7, 47, 9)(11, 25, 44) (7, 47)(13, 32)(15, 18)(19, 24)(25, 44)(27, 45) (13, 18)(24, 25) (1, 24)(6, 15)(7, 9)(11, 25)(16, 32)(27, 35) (15, 32)(24, 25) (1, 24)(6, 22)(7, 9)(11, 25)(16, 33)(35, 41) (6, 16)(24, 25) (1, 24)(4, 33)(7, 9)(10, 22)(11, 25)(41, 42) (22, 33)(24, 25) (1, 24)(4, 26)(7, 9)(10, 17)(11, 25)(40, 42) (4, 10)(24, 25) (1, 24, 19, 13, 32, 16, 33, 4, 26, 8, 36, 3, 37)(2, 9, 7, 47, 45, 27, 35, 41, 42, 40, 34, 46, 50)(6, 22, 10, 17, 12, 30, 28, 29, 11, 25, 44, 18, 15) (17, 26)(24, 25) (1, 37, 3, 36, 8, 4, 33, 16, 32, 24, 19)(2, 50, 46, 34, 42, 41, 35, 27, 7, 47, 9)(6, 15, 25, 44, 11, 29, 28, 30, 12, 10, 22) (24, 25)(31, 48) (1, 37, 3, 36, 4, 33, 16)(2, 50, 46, 42, 41, 35, 9)(6, 11, 29, 28, 30, 10, 22) (8, 12)(24, 25) (1, 37, 3, 33, 24)(2, 50, 41, 7, 9)(11, 29, 28, 22, 25) (24, 25)(30, 36) (1, 24)(2, 50)(3, 37)(7, 9)(11, 25)(28, 29) (3, 28)(24, 25) (1, 37, 24)(2, 7, 9)(11, 29, 25) (24, 25)(29, 37) (1, 24)(7, 9, 25, 11) (1, 2, 7)(3, 36)(9, 29, 25)(11, 37, 24)(28, 30)(38, 49)(46, 50) (1, 25, 50, 27, 41, 42, 46)(3, 32, 33, 4, 36, 9, 24, 28, 15, 22, 10, 30, 11, 7)(38, 49) [ 2] Order 134997833927585283481170873006686208000000000 Length 5744976449471863238250 Permutation group acting on a set of cardinality 51 Order = 2^45 * 3^19 * 5^9 * 7^6 * 11^3 * 13^3 * 17^3 (1, 18, 39)(2, 14, 10)(3, 5, 42)(4, 29, 47)(6, 46, 20)(7, 13, 48)(8, 21, 35)(9, 19, 17)(11, 45, 26)(12, 43, 32)(15, 34, 24)(16, 30, 23)(22, 50, 38)(25, 27, 31)(28, 51, 33)(36, 49, 41)(37, 44, 40) (1, 13, 39)(2, 47, 10)(3, 14, 42)(4, 29, 44)(5, 33, 28)(6, 46, 23)(7, 27, 48)(8, 20, 35)(9, 45, 17)(11, 18, 26)(12, 21, 32)(15, 31, 25)(16, 30, 49)(19, 40, 37)(22, 50, 51)(24, 43, 34)(36, 38, 41) (1, 11, 9, 37, 29, 2, 3, 28, 50, 36, 30, 46, 8, 24, 25, 7)(5, 14, 47, 44, 19, 45, 18, 13, 27, 15, 43, 20, 23, 49, 38, 51) (4, 10, 42, 33, 22, 41, 16, 6, 35, 32, 34, 31, 48, 39, 26, 17, 40)(5, 14, 47, 44, 19, 45, 18, 13, 27, 15, 43, 21, 20, 23, 49, 38, 51) (1, 7, 25, 24, 8, 46, 30, 36, 50, 28, 3, 2, 29, 37, 9, 11)(5, 51, 38, 49, 23, 20, 21, 15, 27, 13, 18, 45, 19, 44, 47, 14) (1, 7, 25, 24, 8, 46, 30, 36, 50, 28, 3, 2, 29, 37, 9, 11)(4, 10, 42, 33, 22, 41, 16, 6, 35, 34, 31, 48, 39, 26, 17, 40) (1, 7, 25, 24, 8, 46, 30, 36, 50, 28, 3, 2, 29, 37, 9, 11)(4, 10, 42, 33, 22, 41, 16, 6, 35, 34, 31, 48, 39, 26, 17, 40)(15, 21, 43) (1, 11, 9, 37, 29, 2, 3, 28, 50, 36, 30, 46, 8, 24, 25, 7)(5, 14, 47, 44, 19, 45, 18, 13, 27, 21, 23, 49, 38, 51) (1, 11, 9, 37, 29, 2, 3, 28, 50, 36, 30, 46, 8, 24, 25, 7)(4, 40, 17, 26, 39, 48, 31, 34, 6, 16, 41, 22, 33, 42, 10)(15, 21) (4, 42, 22, 16, 34, 48, 26, 40, 10, 33, 41, 6, 31, 39, 17) (5, 51, 38, 49, 23, 15, 13, 18, 45, 19, 44, 47, 14) (15, 21)(31, 34) (15, 21, 23) (15, 23)(31, 34) (1, 7, 25, 24, 46, 30, 36, 50, 28, 3, 2, 29, 37, 9, 11) (15, 49)(31, 34) (6, 16)(31, 34) (24, 25)(31, 34) (16, 31, 34) (24, 25)(34, 41) (15, 38)(31, 34) (1, 11, 9, 37, 29, 2, 3, 28, 50, 36, 30, 24, 7) (24, 30, 25) (15, 23)(24, 36) (22, 34)(24, 25) (15, 51)(31, 34) (1, 30, 28, 29, 11, 24, 2, 9, 7, 36, 3, 37)(15, 23) (24, 25)(33, 34) (5, 15)(31, 34) (15, 23)(24, 28) (24, 25)(34, 42) (14, 15)(31, 34) (3, 24)(31, 34) (10, 34)(24, 25) (15, 47)(31, 34) (2, 24)(15, 23) (4, 34)(24, 25) (15, 44)(31, 34) (24, 29)(31, 34) (24, 25)(34, 40) (15, 19)(31, 34) (24, 37)(31, 34) (17, 34)(24, 25) (15, 45)(31, 34) (9, 24)(31, 34) (24, 25)(26, 34) (13, 45, 44, 14, 51, 49, 23)(15, 19)(31, 34) (11, 24)(31, 34) (17, 34, 39) (13, 15)(31, 34) (1, 24)(31, 34) (4, 47)(5, 42)(6, 20)(10, 14)(13, 48)(15, 34)(16, 23)(17, 19)(18, 39)(21, 32, 43, 35)(22, 38)(26, 45)(27, 31)(33, 51)(40, 44)(41, 49) (7, 24, 25) [ 3] Order 3127769281108316625135363142492857827328000000000000 Length 247959266474052 Permutation group acting on a set of cardinality 51 Order = 2^44 * 3^20 * 5^12 * 7^6 * 11^4 * 13^3 * 17^2 * 19^2 * 23^2 (5, 14, 47, 44, 19, 45, 18, 13, 27, 15, 32, 35, 6, 16, 41, 22, 33, 42, 43, 21, 20, 23, 49, 38, 51) (21, 42, 43) (5, 47, 19, 18, 27, 32, 6, 41, 33, 43, 23, 38)(13, 15, 35, 16, 22, 42, 21, 49, 51, 14, 44, 45) (5, 51, 38, 49, 23, 21, 42, 33, 22, 41, 16, 6, 35, 32, 15, 27, 13, 18, 45, 19, 44, 47, 14) (21, 42, 33) (23, 49)(33, 42) (22, 42, 33) (33, 42)(38, 49) (33, 42)(38, 51) (5, 51)(33, 42) (5, 14)(33, 42) (14, 47)(33, 42) (21, 42)(44, 47) (19, 44)(21, 42) (19, 45)(33, 42) (18, 45)(33, 42) (13, 18)(33, 42) (13, 27)(33, 42) (15, 27)(33, 42) (15, 32)(33, 42) (32, 35)(33, 42) (13, 15, 35, 16, 41, 22, 42, 38, 14, 47, 19, 45, 18) (13, 45, 47, 42, 19, 14, 41, 16, 35) (13, 15)(14, 47, 22, 33) (13, 35, 41, 16, 15, 18, 33, 14, 47)(22, 45, 42) (13, 15, 42, 45, 41, 14, 22, 18, 35) (13, 45, 14, 16, 22, 41, 18, 35, 42, 15, 33) (13, 18, 33, 45, 22, 16, 42)(15, 41, 35) (13, 22, 18, 16, 41, 35)(15, 42) (13, 33, 15)(16, 42, 22, 41, 35) (15, 35, 42, 16, 22) (16, 41, 35, 33)(22, 42) (16, 41, 22, 42, 33) (33, 42, 41) (1, 7, 25, 24, 10, 4, 40, 17, 26, 39, 48, 31, 34, 12, 8, 46, 30, 36, 50, 28, 3, 2, 29, 37, 9, 11)(21, 42) (4, 24, 10) (1, 25, 10, 17, 39, 31, 12, 46, 36, 28, 2, 37, 11, 7, 24, 4, 26, 48, 34, 8, 30, 50, 3, 29, 9) (1, 11, 9, 37, 29, 2, 3, 28, 50, 36, 30, 46, 8, 12, 34, 31, 48, 39, 26, 17, 4, 24, 25, 7)(33, 42) (4, 24, 25) (17, 26)(24, 25) (7, 24, 25) (24, 25)(26, 39) (24, 25)(39, 48) (24, 25)(31, 48) (24, 25)(31, 34) (12, 34)(24, 25) (8, 12)(24, 25) (4, 24)(8, 46) (4, 24)(30, 46) (24, 25)(30, 36) (24, 25)(36, 50) (24, 25)(28, 50) (3, 28)(24, 25) (2, 3)(24, 25) (2, 29)(24, 25) (24, 25)(29, 37) (1, 7, 24, 26, 48, 31, 34, 12, 8, 30, 36, 50, 28, 3, 2, 29, 37, 11)(33, 42) (1, 28, 34, 25, 2, 8)(3, 12, 11, 50, 31, 29, 30, 24, 37, 36, 48, 7) (1, 3, 8, 25, 29, 36, 7, 2, 30, 50, 34, 37, 28, 12, 31, 11)(33, 42) (1, 24, 11)(2, 36)(3, 30, 50, 34, 7, 29, 28, 8, 12, 25, 37)(33, 42) (1, 11, 24, 34, 8)(2, 36, 37, 50, 7, 28, 3) (1, 37, 36, 34, 2, 7, 11, 24, 28, 25)(3, 50, 29)(33, 42) (1, 3, 28, 37, 50, 29)(2, 7, 34)(33, 42) (1, 11, 24)(2, 37, 29)(3, 25, 28, 7)(33, 42) (1, 24, 3, 7)(2, 25) (1, 11, 37, 25, 2, 24)(33, 42) (1, 7, 11, 25)(33, 42) (1, 24, 7, 25)(33, 42) (24, 25)(33, 42) (1, 2)(11, 24)(22, 33, 42) [ 4] Order 394098929419647894 ** WARNING: Output too long, hence truncated. ************** MAGMA ***************** Host ibm21.ilab.sztaki.hu. (195.111.1.97) Time: Fri Jan 16 07:34:35 2004 Input: PrimitiveGroup(51,12); Output: Magma V2.10-6 Fri Jan 16 2004 07:34:32 on modular [Seed = 1014736502] ------------------------------------- >> PrimitiveGroup(51,12);; ^ Runtime error in 'PrimitiveGroup': The group number given (12) exceeds the number of primitive groups of degree 51 (2) Total time: 3.019 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host ibm21.ilab.sztaki.hu. (195.111.1.97) Time: Fri Jan 16 07:34:52 2004 Input: PrimitiveGroup(120,2); Output: Magma V2.10-6 Fri Jan 16 2004 07:34:49 on modular [Seed = 711831633] ------------------------------------- Permutation group acting on a set of cardinality 120 Order = 5040 = 2^4 * 3^2 * 5 * 7 Sym(7) AlmostSimple Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host ibm21.ilab.sztaki.hu. (195.111.1.97) Time: Fri Jan 16 07:36:38 2004 Input: MaximalSubgroups( Alt(120)); Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Fri Jan 16 2004 07:36:15 on modular [Seed = 1460719098] ------------------------------------- Errors: /home/mfd/gomagma: line 2: 21061 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host ibm21.ilab.sztaki.hu. (195.111.1.97) Time: Fri Jan 16 07:37:10 2004 Input: MaximalSubgroups( Alt(80)); Output: Magma V2.10-6 Fri Jan 16 2004 07:36:48 on modular [Seed = 1545324206] ------------------------------------- Conjugacy classes of subgroups ------------------------------ [ 1] Order 246480 Length 145183092028285869634070784086308284983740379\ 224208358846781574688061991349156420080065207861248000000000000000000 Permutation group acting on a set of cardinality 80 Order = 246480 = 2^4 * 3 * 5 * 13 * 79 (1, 54, 36, 69, 38, 59, 47, 51, 24, 43, 14, 39, 34, 79, 68, 46, 41, 12, 63, 27, 21, 23, 8, 76, 44, 35, 19, 60, 40, 10, 61, 29, 70, 9, 25, 7, 57, 78, 55)(2, 71, 66, 65, 16, 49, 75, 6, 45, 50, 56, 26, 32, 73, 67, 62, 18, 28, 37, 33, 13, 52, 80, 53, 72, 77, 48, 42, 30, 22, 20, 17, 64, 15, 5, 58, 4, 3, 31) (1, 50, 80)(2, 9, 3)(4, 49, 10)(5, 33, 12)(6, 42, 57)(7, 61, 41)(8, 55, 23)(11, 62, 74)(13, 25, 18)(14, 43, 76)(15, 34, 77)(16, 19, 71)(17, 66, 78)(20, 64, 24)(21, 69, 27)(22, 46, 48)(26, 58, 44)(28, 73, 54)(29, 63, 70)(30, 31, 38)(32, 75, 79)(35, 39, 47)(36, 45, 52)(37, 40, 72)(51, 56, 67)(53, 59, 65) [ 2] Order 19341472512297209890382807040000000000000000000 Length 1850155333332565691862604612438504840489598409403595463907676319416549376 Permutation group acting on a set of cardinality 80 Order = 2^62 * 3^22 * 5^19 * 7^2 * 11 * 13 (1, 69, 4, 68, 58, 66, 47, 6, 51, 22, 10, 20, 25, 54, 80)(2, 14, 3, 7, 44, 42, 53, 5, 35, 24, 63, 64, 67, 73, 13)(8, 38, 37, 30, 26, 36, 79, 43, 32, 71, 55, 48, 57, 41, 76)(9, 77, 16, 18, 59, 61, 31, 33, 60, 34, 49, 45, 52, 28, 56)(12, 78, 75, 17, 21, 70, 39, 65, 19, 27, 46, 40, 62, 72, 50) (2, 14, 3, 7, 44, 11, 53, 5, 35, 24, 63, 64, 67, 73, 13)(4, 68, 58, 66, 47, 6, 51, 22, 10, 20, 25, 54, 80, 15, 69)(8, 38, 37, 30, 26, 36, 74, 43, 32, 71, 55, 48, 57, 41, 76)(9, 77, 16, 18, 59, 61, 31, 33, 60, 23, 49, 45, 52, 28, 56)(12, 78, 75, 17, 21, 70, 39, 65, 19, 27, 46, 29, 62, 72, 50) (1, 15, 69, 4, 68, 58, 66, 47, 6, 51, 22, 10, 20, 25, 54)(2, 14, 3, 7, 42, 11, 53, 5, 35, 24, 63, 64, 67, 73, 13)(8, 38, 37, 30, 26, 79, 74, 43, 32, 71, 55, 48, 57, 41, 76)(9, 77, 16, 18, 59, 61, 31, 33, 34, 23, 49, 45, 52, 28, 56)(12, 78, 75, 17, 21, 70, 39, 65, 19, 27, 40, 29, 62, 72, 50) (2, 14, 3, 7, 44, 74, 53, 5, 35, 24, 63, 64, 67, 73, 13)(4, 68, 58, 66, 47, 6, 51, 22, 10, 20, 25, 54, 80, 29, 69)(8, 38, 37, 30, 26, 36, 23, 43, 32, 71, 55, 48, 57, 41, 76)(9, 77, 16, 18, 59, 61, 31, 33, 60, 15, 49, 45, 52, 28, 56)(11, 62, 72, 50, 12, 78, 75, 17, 21, 70, 39, 65, 19, 27, 46) (11, 23, 15, 29)(36, 46, 80, 60) (2, 13, 73, 67, 64, 63, 24, 35, 5, 53, 11, 7, 14)(4, 69, 15, 54, 20, 10, 22, 51, 6, 47, 66, 58, 68)(8, 76, 41, 57, 48, 55, 71, 32, 43, 74, 26, 37, 38)(9, 56, 28, 52, 45, 49, 23, 33, 61, 59, 18, 16, 77)(12, 50, 72, 62, 29, 27, 65, 39, 70, 21, 17, 75, 78) (2, 13, 73, 67, 64, 63, 24, 35, 5, 53, 11, 3, 14)(4, 69, 15, 25, 20, 10, 22, 51, 6, 47, 66, 58, 68)(8, 76, 41, 57, 48, 55, 71, 32, 43, 74, 30, 37, 38)(9, 56, 28, 52, 45, 49, 23, 31, 61, 59, 18, 16, 77)(12, 50, 72, 62, 29, 19, 65, 39, 70, 21, 17, 75, 78) (1, 29, 69, 4, 68, 58, 66, 47, 6, 51, 22, 10, 20, 25, 54)(2, 14, 3, 7, 42, 74, 53, 5, 35, 24, 63, 64, 67, 73, 13)(8, 38, 37, 30, 26, 79, 23, 43, 32, 71, 55, 48, 57, 41, 76)(9, 77, 16, 18, 59, 61, 31, 33, 34, 15, 49, 45, 52, 28, 56)(11, 62, 72, 50, 12, 78, 75, 17, 21, 70, 39, 65, 19, 27, 40) (1, 34, 79, 40)(36, 60, 80, 46) (7, 26, 33, 54, 27)(34, 79)(36, 46, 80, 60) (2, 3, 14)(7, 26, 33, 54, 27)(10, 25, 20)(19, 65, 39)(30, 37, 38)(31, 61, 59)(34, 79)(36, 46, 80, 60) (11, 29, 15, 74)(34, 79)(43, 49, 69, 62, 53) (1, 40, 79)(15, 74, 29) (26, 27, 54, 33)(36, 60, 80, 46) (1, 34, 40)(43, 69, 53, 49, 62) (1, 34)(29, 74) (2, 13, 73, 67, 64, 63, 24, 35, 5, 53, 27, 39, 70, 21, 17, 75, 78, 12, 50, 72, 62, 54, 10, 22, 51, 6, 47, 66, 58, 68, 4, 69, 33, 59, 18, 16, 77, 9, 56, 28, 52, 45, 49, 26, 38, 8, 76, 41, 57, 48, 55, 71, 32, 43, 7)(34, 79)(36, 60, 80, 46) (34, 40)(43, 62, 69, 49) (15, 29, 74) (1, 34)(15, 29) (1, 40, 34)(2, 3, 26, 59, 31, 54, 39, 19, 7, 38, 30, 33, 10, 25, 27)(4, 5, 45, 72, 32)(6, 67, 77, 17, 41)(8, 22, 13, 18, 70)(9, 75, 57, 47, 64)(12, 55, 58, 24, 28)(16, 21, 76, 51, 73)(35, 52, 50, 71, 68)(43, 69, 53, 49, 62) (1, 40)(15, 29) (3, 30, 31, 25, 19)(26, 27, 54, 33)(36, 60) (2, 13, 3, 38, 8, 30, 59, 18, 31, 10, 22, 25, 39, 70, 19)(26, 27, 54, 33)(34, 79)(36, 80, 46) (46, 80, 60) (1, 40)(43, 49, 69, 62) (3, 31, 25, 19)(36, 60) (1, 40)(46, 80) (1, 40, 79, 34)(2, 3, 22, 39, 19, 18, 10, 25, 8, 59, 31, 13, 38, 30, 70)(4, 45, 32, 5, 72)(6, 77, 41, 67, 17)(9, 57, 64, 75, 47)(12, 55, 58, 24, 28)(15, 29)(16, 76, 73, 21, 51)(35, 50, 68, 52, 71)(36, 60, 46, 80)(43, 62, 49, 53, 69)(48, 56) (1, 34)(3, 19, 31)(4, 32, 72, 45, 5)(6, 41, 17, 77, 67)(9, 64, 47, 57, 75)(15, 29)(16, 73, 51, 76, 21)(25, 30)(26, 54, 27)(35, 68, 71, 50, 52)(36, 46)(43, 53, 62, 69, 49)(48, 56)(60, 80) (1, 79)(2, 13, 51, 10, 22, 76, 38, 8, 21, 39, 70, 16, 59, 18, 73)(3, 25)(4, 32, 72, 45, 5)(6, 41, 17, 77, 67)(9, 64, 47, 57, 75)(15, 29)(19, 30, 31)(26, 54, 27)(34, 40)(35, 68, 71, 50, 52)(36, 46, 80, 60)(43, 53, 62, 69, 49)(48, 56) (27, 54, 33) (1, 34, 40)(15, 29)(19, 31, 25)(20, 61, 37, 65)(46, 80, 60) (1, 40)(27, 54) (2, 3, 16, 38, 30, 51, 59, 31, 21, 10, 25, 73, 39, 19, 76)(4, 5, 45, 72, 32)(6, 67, 77, 17, 41)(9, 75, 57, 47, 64)(15, 29)(26, 27)(28, 55)(34, 40)(36, 80, 60)(37, 61)(43, 69, 53, 49, 62)(48, 56) (1, 34, 40, 79)(3, 31)(4, 32, 72, 45, 5)(6, 41, 17, 77, 67)(9, 64, 47, 57, 75)(20, 61, 37, 65)(26, 54, 27)(28, 55)(36, 60, 80)(43, 69, 53, 49, 62) (1, 79)(3, 73, 6, 30, 51, 41, 25, 21, 77, 19, 76, 17)(4, 32, 72, 45, 5)(9, 64, 47, 57, 75)(16, 67, 31)(20, 37, 65)(26, 54, 33, 27)(28, 55)(43, 69, 53, 49, 62)(46, 60, 80) (19, 25, 31) (1, 40)(10, 59, 38, 39)(20, 65, 61)(27, 54, 33)(46, 80, 60) (1, 40)(19, 25) (1, 79, 34, 40)(2, 31, 77)(3, 67, 10, 25, 6, 38, 19, 41, 39)(4, 72, 5, 32, 45)(9, 64, 47, 57, 75)(17, 59, 30)(26, 27, 33)(28, 55)(35, 71, 68, 50)(36, 60)(43, 53, 62, 69, 49) (1, 34, 79)(3, 31)(9, 64, 47, 57, 75)(10, 59, 38, 39)(15, 29)(20, 37, 65, 61)(26, 27, 54)(43, 69, 53, 49, 62)(52, 71)(60, 80) (1, 34, 79)(2, 6, 75)(3, 19, 31)(9, 39, 41)(10, 17, 64, 38, 77, 47)(15, 29)(20, 65, 37)(28, 55)(36, 46)(43, 49, 69, 62, 53)(48, 56)(57, 59, 67)(60, 80) (20, 61, 65) (8, 70, 22, 18)(10, 39, 59)(19, 25, 31)(46, 80) (20, 65)(27, 54) (1, 40, 34)(2, 10, 39)(3, 19)(4, 72, 5, 32)(6, 17)(8, 18, 70, 22)(9, 75, 64)(15, 29)(20, 65)(25, 31)(26, 33, 27, 54)(28, 55)(35, 50, 68, 71, 52)(36, 60, 80)(37, 61)(41, 67)(43, 53, 62, 69, 49)(47, 57) (1, 40, 34, 79)(8, 70, 22, 18)(10, 38, 39, 59)(15, 29)(20, 37, 65, 61)(25, 31)(27, 54)(32, 45)(36, 80, 60)(43, 53, 62, 69, 49) (2, 47, 69, 13, 45, 59, 64, 53, 18, 72, 39, 75, 62, 70, 5)(3, 17, 71, 76, 55)(4, 10, 9, 49, 8, 32, 38, 57, 43, 22)(6, 35, 21, 24, 25, 41, 68, 16, 28, 30)(12, 19, 77, 50, 51, 58, 31, 67, 52, 73)(15, 74)(20, 37, 61)(26, 27)(33, 54)(34, 40, 79)(36, 60)(46, 80)(48, 56, 66) (10, 59, 39) (16, 76, 21, 51)(18, 22, 70)(20, 61, 65)(27, 54) (10, 39)(20, 65) (1, 79, 34, 40)(3, 25)(4, 32, 45, 5, 72)(8, 22)(9, 57, 75)(10, 59)(16, 21, 51, 76)(18, 70)(19, 31)(20, 65, 61)(38, 39)(43, 69, 62, 53)(46, 60, 80)(48, 56)(52, 71)(66, 78) (1, 34, 40)(18, 70)(19, 31)(20, 61)(27, 54)(43, 49)(46, 60) (1, 40)(2, 4, 52, 77, 69, 59, 72, 35, 17, 49)(5, 71, 41, 53, 38, 45, 68, 67, 62, 10, 32, 50, 6, 43, 39)(8, 22)(9, 57, 47, 64, 75)(12, 28, 58, 55)(15, 74, 29)(19, 25)(26, 27)(34, 79)(36, 60, 46)(48, 66)(51, 76)(61, 65) (1, 34, 79)(4, 72, 5, 45, 32)(8, 22)(9, 75, 57)(10, 38)(15, 74, 29)(16, 76, 51, 21)(18, 70)(19, 25, 31)(20, 65, 37, 61)(27, 54, 33)(36, 80)(43, 69, 53)(46, 60)(48, 56)(49, 62)(66, 78) (1, 40)(20, 65)(22, 70)(27, 54)(49, 62, 69) (4, 72, 5, 45)(10, 39, 59)(16, 51, 21)(19, 25, 31)(28, 55)(29, 74)(37, 61, 65)(41, 67)(46, 60, 80) (10, 39)(20, 65)(49, 69, 62) (5, 72, 45)(6, 17, 41, 67)(9, 75, 57)(10, 39)(12, 58)(16, 51, 21)(18, 22, 70)(19, 31, 25)(20, 61)(28, 55)(34, 40)(43, 69)(46, 80)(48, 66, 78) (20, 65)(62 ** WARNING: Output too long, hence truncated. ************** MAGMA ***************** Host ibm21.ilab.sztaki.hu. (195.111.1.97) Time: Fri Jan 16 07:38:17 2004 Input: MaximalSubgroups( Alt(100)); Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Fri Jan 16 2004 07:37:54 on modular [Seed = 1157815925] ------------------------------------- Errors: /home/mfd/gomagma: line 2: 21079 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host ibm21.ilab.sztaki.hu. (195.111.1.97) Time: Fri Jan 16 07:39:35 2004 Input: PrimitiveGroup(5,3); Output: Magma V2.10-6 Fri Jan 16 2004 07:39:32 on modular [Seed = 1916135908] ------------------------------------- Permutation group acting on a set of cardinality 5 Order = 20 = 2^2 * 5 (1, 2, 3, 4, 5) (1, 2, 4, 3) AGL(1, 5) Affine Total time: 2.909 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host ibm21.ilab.sztaki.hu. (195.111.1.97) Time: Fri Jan 16 08:13:55 2004 Input: #PrimitiveGroup(5,3)^12; Factorial(5); Output: Magma V2.10-6 Fri Jan 16 2004 08:13:52 on modular [Seed = 3187285567] ------------------------------------- 4096000000000000 120 Total time: 3.039 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host ibm21.ilab.sztaki.hu. (195.111.1.97) Time: Fri Jan 16 08:14:25 2004 Input: #PrimitiveGroup(5,2)^12; Factorial(5); Output: Magma V2.10-6 Fri Jan 16 2004 08:14:22 on modular [Seed = 2867661078] ------------------------------------- 1000000000000 120 Total time: 2.929 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host ibm21.ilab.sztaki.hu. (195.111.1.97) Time: Fri Jan 16 08:14:43 2004 Input: PrimitiveGroup(5,2)^12; Output: Magma V2.10-6 Fri Jan 16 2004 08:14:40 on modular [Seed = 3549720577] ------------------------------------- >> PrimitiveGroup(5,2)^12; ; ^ Runtime error in '^': Bad argument types Argument types given: GrpPerm, RngIntElt Total time: 2.929 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host ibm21.ilab.sztaki.hu. (195.111.1.97) Time: Fri Jan 16 08:15:26 2004 Input: PrimitiveGroup(5,2); PrimitiveGroup(5,3); Output: Magma V2.10-6 Fri Jan 16 2004 08:15:23 on modular [Seed = 3263521083] ------------------------------------- Permutation group acting on a set of cardinality 5 Order = 10 = 2 * 5 (1, 2, 3, 4, 5) (1, 4)(2, 3) D(2*5) Affine Permutation group acting on a set of cardinality 5 Order = 20 = 2^2 * 5 (1, 2, 3, 4, 5) (1, 2, 4, 3) AGL(1, 5) Affine Total time: 2.939 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host ibm21.ilab.sztaki.hu. (195.111.1.97) Time: Fri Jan 16 08:17:35 2004 Input: PrimitiveGroup(6,2); PrimitiveGroup(6,1); Output: Magma V2.10-6 Fri Jan 16 2004 08:17:32 on modular [Seed = 3414978485] ------------------------------------- Permutation group acting on a set of cardinality 6 Order = 120 = 2^3 * 3 * 5 (3, 5, 4, 6) (1, 6, 2)(3, 4, 5) PGL(2, 5) AlmostSimple Permutation group acting on a set of cardinality 6 Order = 60 = 2^2 * 3 * 5 (3, 4)(5, 6) (1, 6, 2)(3, 4, 5) PSL(2, 5) AlmostSimple Total time: 2.979 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host ibm21.ilab.sztaki.hu. (195.111.1.97) Time: Fri Jan 16 08:19:15 2004 Input: PrimitiveGroup(7,4); PrimitiveGroup(7,5); Output: Magma V2.10-6 Fri Jan 16 2004 08:19:12 on modular [Seed = 4038546482] ------------------------------------- Permutation group acting on a set of cardinality 7 Order = 42 = 2 * 3 * 7 (1, 2, 3, 4, 5, 6, 7) (1, 3, 2, 6, 4, 5) AGL(1, 7) Affine Permutation group acting on a set of cardinality 7 Order = 168 = 2^3 * 3 * 7 (1, 4)(6, 7) (1, 3, 2)(4, 7, 5) L(3, 2) AlmostSimple Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host ibm21.ilab.sztaki.hu. (195.111.1.97) Time: Fri Jan 16 08:19:28 2004 Input: Name(PrimitiveGroup(7,4)); PrimitiveGroup(7,5); Output: Magma V2.10-6 Fri Jan 16 2004 08:19:25 on modular [Seed = 4190002486] ------------------------------------- >> Name(PrimitiveGroup(7,4)); PrimitiveGroup(7,5);; ^ Runtime error in 'Name': Bad argument types Argument types given: GrpPerm Permutation group acting on a set of cardinality 7 Order = 168 = 2^3 * 3 * 7 (1, 4)(6, 7) (1, 3, 2)(4, 7, 5) L(3, 2) AlmostSimple Total time: 2.979 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host ibm21.ilab.sztaki.hu. (195.111.1.97) Time: Fri Jan 16 08:21:48 2004 Input: PrimitiveGroup(7,4); PrimitiveGroup(7,5); Output: Magma V2.10-6 Fri Jan 16 2004 08:21:45 on modular [Seed = 4004072341] ------------------------------------- Permutation group acting on a set of cardinality 7 Order = 42 = 2 * 3 * 7 (1, 2, 3, 4, 5, 6, 7) (1, 3, 2, 6, 4, 5) AGL(1, 7) Affine Permutation group acting on a set of cardinality 7 Order = 168 = 2^3 * 3 * 7 (1, 4)(6, 7) (1, 3, 2)(4, 7, 5) L(3, 2) AlmostSimple Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host ibm21.ilab.sztaki.hu. (195.111.1.97) Time: Fri Jan 16 08:22:55 2004 Input: PrimitiveGroup(8,5); PrimitiveGroup(8,3); Output: Magma V2.10-6 Fri Jan 16 2004 08:22:52 on modular [Seed = 374453161] ------------------------------------- Permutation group acting on a set of cardinality 8 Order = 336 = 2^4 * 3 * 7 (1, 2, 3, 4, 5, 6, 7) (2, 4, 3, 7, 5, 6) (1, 8)(2, 7)(3, 4)(5, 6) PGL(2, 7) AlmostSimple Permutation group acting on a set of cardinality 8 Order = 1344 = 2^6 * 3 * 7 (1, 2, 3, 4, 5, 6, 7) (2, 3)(4, 7) (1, 8)(2, 4)(3, 7)(5, 6) ASL(3, 2) Affine Total time: 3.019 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host ibm21.ilab.sztaki.hu. (195.111.1.97) Time: Fri Jan 16 08:23:06 2004 Input: PrimitiveGroup(8,5); PrimitiveGroup(8,3); Output: Magma V2.10-6 Fri Jan 16 2004 08:23:03 on modular [Seed = 475773368] ------------------------------------- Permutation group acting on a set of cardinality 8 Order = 336 = 2^4 * 3 * 7 (1, 2, 3, 4, 5, 6, 7) (2, 4, 3, 7, 5, 6) (1, 8)(2, 7)(3, 4)(5, 6) PGL(2, 7) AlmostSimple Permutation group acting on a set of cardinality 8 Order = 1344 = 2^6 * 3 * 7 (1, 2, 3, 4, 5, 6, 7) (2, 3)(4, 7) (1, 8)(2, 4)(3, 7)(5, 6) ASL(3, 2) Affine Total time: 3.069 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host ibm21.ilab.sztaki.hu. (195.111.1.97) Time: Fri Jan 16 08:24:23 2004 Input: PrimitiveGroup(9,7); PrimitiveGroup(9,6); Output: Magma V2.10-6 Fri Jan 16 2004 08:24:20 on modular [Seed = 189574428] ------------------------------------- Permutation group acting on a set of cardinality 9 Order = 432 = 2^4 * 3^3 (1, 2, 3)(4, 5, 6)(7, 8, 9) (2, 6, 4, 9, 3, 8, 7, 5) (2, 4, 9)(3, 7, 5) AGL(2, 3) Affine Permutation group acting on a set of cardinality 9 Order = 216 = 2^3 * 3^3 (1, 2, 3)(4, 5, 6)(7, 8, 9) (2, 4, 3, 7)(5, 6, 9, 8) (2, 4, 9)(3, 7, 5) 3^2:(2'A(4)) Affine Total time: 3.099 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host ibm21.ilab.sztaki.hu. (195.111.1.97) Time: Fri Jan 16 08:27:48 2004 Input: [[ PrimitiveGroupDescription( 9, x ) : x in [ z ] : z in [[7],[6,9]]; Output: Magma V2.10-6 Fri Jan 16 2004 08:27:45 on modular [Seed = 896701431] ------------------------------------- >> [[ PrimitiveGroupDescription( 9, x ) : x in [ z ] : z in [[7],[6,9]];; ^ User error: bad syntax Total time: 2.989 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host ibm21.ilab.sztaki.hu. (195.111.1.97) Time: Fri Jan 16 08:28:07 2004 Input: [[ PrimitiveGroupDescription( 9, x ) : x in [ z ]] : z in [[7],[6,9]]]; Output: Magma V2.10-6 Fri Jan 16 2004 08:28:04 on modular [Seed = 1014733515] ------------------------------------- >> [[ PrimitiveGroupDescription( 9, x ) : x in [ z ]] : z in [[7],[6,9]]];; ^ Runtime error in 'PrimitiveGroupDescription': Bad argument types Argument types given: RngIntElt, SeqEnum[RngIntElt] Total time: 2.979 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host ibm21.ilab.sztaki.hu. (195.111.1.97) Time: Fri Jan 16 08:28:54 2004 Input: [[ PrimitiveGroupDescription( 9, x ) : x in z ] : z in [[7],[6,9]]]; Output: Magma V2.10-6 Fri Jan 16 2004 08:28:51 on modular [Seed = 728534059] ------------------------------------- [ [ AGL(2, 3) ], [ 3^2:(2'A(4)), PGammaL(2, 8) ] ] Total time: 3.039 seconds, Total memory usage: 2.00MB ************** MAGMA ***************** Host ibm21.ilab.sztaki.hu. (195.111.1.97) Time: Fri Jan 16 08:30:52 2004 Input: [[ PrimitiveGroupDescription( 10, x ) : x in z ] : z in [[7],[6]]]; Output: Magma V2.10-6 Fri Jan 16 2004 08:30:49 on modular [Seed = 1511914944] ------------------------------------- [ [ PGammaL(2, 9) ], [ M(10) ] ] Total time: 2.939 seconds, Total memory usage: 2.00MB ************** MAGMA ***************** Host ibm21.ilab.sztaki.hu. (195.111.1.97) Time: Fri Jan 16 08:38:10 2004 Input: maxprim:=[ [[ ], [ ], [ ]], // 1 [[ ], [ ], [ ]], // 2 [[ ], [ ], [ ]], // 3 [[ ], [ ], [ ]], // 4 [[3], [2], [ ]], // 5 [[2], [1], [ ]], // 6 [[4], [5], [5]], // 7 [[5], [3], [3]], // 8 [[7], [6,9], [9]], // 9 [[7], [6], [ ]], // 10 [[4], [6], [6]], // 11 [[2], [4], [4]], // 12 [[6], [5,7], [7]], // 13 [[2], [1], [ ]], // 14 [[ ], [4], [4]], // 15 [[ ], [20], [20]], // 16 [[5], [4,8], [8]], // 17 [[2], [1], [ ]], // 18 [[6], [5], [ ]], // 19 [[2], [1], [ ]], // 20 [[1,3,7], [2,6], [ ]], // 21 [[2], [1], [ ]], // 22 [[4], [5], [5]], // 23 [[2], [3], [3]], // 24 [[22,26], [21,24], [ ]], // 25 [[5], [2], [ ]], // 26 [[11], [13,10], [13]], // 27 [[11], [9,12], [12]], // 28 [[ ], [ ], [ ]], // 29 [[ ], [ ], [ ]], // 30 [[ ], [9,10], [9,10]], // 31 [[ ], [3], [3]], // 32 [[ ], [2], [2]], // 33 [[ ], [ ], [ ]], // 34 [[ ], [4], [4]], // 35 [[19, 8], [18,20], [20]], // 36 [[ ], [ ], [ ]], // 37 [[ ], [ ], [ ]], // 38 [[ ], [ ], [ ]], // 39 [[4,6], [2,5], [ ]], // 40 [[ ], [ ], [ ]], // 41 [[ ], [ ], [ ]], // 42 [[ ], [ ], [ ]], // 43 [[ ], [ ], [ ]], // 44 [[5], [4,7], [7]], // 45 [[ ], [ ], [ ]], // 46 [[ ], [ ], [ ]], // 47 [[ ], [ ], [ ]], // 48 [[33,38], [32,36], [ ]], // 49 [[6], [2,7], [7]], // 50 [[ ], [ ], [ ]], // 51 [[ ], [1], [1]], // 52 [[ ], [ ], [ ]], // 53 [[ ], [ ], [ ]], // 54 [[6], [5], [ ]], // 55 [[6, 7], [2, 4], [ ]], // 56 [[ ], [1, 3], [1, 3]], // 57 [[ ], [ ], [ ]], // 58 [[ ], [ ], [ ]], // 59 [[5], [4], [ ]], // 60 [[ ], [ ], [ ]], // 61 [[ ], [ ], [ ]], // 62 [[4], [6, 3, 1], [6, 3]], // 63 [[ ], [64, 72], [64, 72]], // 64 [[2], [11, 1, 7, 5], [11, 7, 5]], // 65 [[ ], [5], [5]], // 66 [[ ], [ ], [ ]], // 67 [[3], [2], [ ]], // 68 [[ ], [ ], [ ]], // 69 [[ ], [ ], [ ]], // 70 [[ ], [ ], [ ]], // 71 [[ ], [ ], [ ]], // 72 [[ ], [14], [14]], // 73 [[ ], [ ], [ ]], // 74 [[ ], [ ], [ ]], // 75 [[ ], [ ], [ ]], // 76 [[ ], [2], [2]], // 77 [[2, 4], [1, 3], [ ]], // 78 [[ ], [ ], [ ]], // 79 [[ ], [ ], [ ]], // 80 [[145, 153], [144, 152], [ ]], // 81 [[ 8], [6], [ ]], // 82 [[ ], [ ], [ ]], // 83 [[3], [1], [ ]], // 84 [[4], [3], [ ]], // 85 [[ ], [ ], [ ]], // 86 [[ ], [ ], [ ]], // 87 [[ ], [ ], [ ]], // 88 [[ ], [ ], [ ]], // 89 [[ ], [ ], [ ]], // 90 [[6], [ 8, 5], [ 8]], // 91 [[ ], [ ], [ ]], // 92 [[ ], [ ], [ ]], // 93 [[ ], [ ], [ ]], // 94 [[ ], [ ], [ ]], // 95 [[ ], [ ], [ ]], // 96 [[ ], [ ], [ ]], // 97 [[ ], [ ], [ ]], // 98 [[ ], [ ], [ ]], // 99 [[36, 34, 32], [33, 35], [ ]], // 100 [[ ], [ ], [ ]], // 101 [[ ], [1], [1]], // 102 [[ ], [ ], [ ]], // 103 [[ ], [ ], [ ]], // 104 [[3, 9], [8, 7], [7]], // 105 [[ ], [ ], [ ]], // 106 [[ ], [ ], [ ]], // 107 [[ ], [ ], [ ]], // 108 [[ ], [ ], [ ]], // 109 [[ ], [ ], [ ]], // 110 [[ ], [ ], [ ]], // 111 [[ ], [8], [8]], // 112 [[ ], [ ], [ ]], // 113 [[ ], [ ], [ ]], // 114 [[ ], [ ], [ ]], // 115 [[ ], [ ], [ ]], // 116 [[ ], [1, 3], [1, 3]], // 117 [[ ], [ ], [ ]], // 118 [[ ], [2], [2]], // 119 [[10], [21, 4, 8, 13, 19, 18], [21, 4, 13, 19, 18]]]; // 120 [ [ PrimitiveGroupDescription( i, n ) : n in maxprim[i]] : in [1..120]]; Output: Magma V2.10-6 Fri Jan 16 2004 08:38:07 on modular [Seed = 1242424166] ------------------------------------- >> [ [ PrimitiveGroupDescription( i, n ) : n in maxprim[i]] : in [1..120]];; ^ User error: bad syntax Total time: 2.999 seconds, Total memory usage: 1.90MB ************** MAGMA ***************** Host ibm21.ilab.sztaki.hu. (195.111.1.97) Time: Fri Jan 16 08:38:28 2004 Input: maxprim:=[ [[ ], [ ], [ ]], // 1 [[ ], [ ], [ ]], // 2 [[ ], [ ], [ ]], // 3 [[ ], [ ], [ ]], // 4 [[3], [2], [ ]], // 5 [[2], [1], [ ]], // 6 [[4], [5], [5]], // 7 [[5], [3], [3]], // 8 [[7], [6,9], [9]], // 9 [[7], [6], [ ]], // 10 [[4], [6], [6]], // 11 [[2], [4], [4]], // 12 [[6], [5,7], [7]], // 13 [[2], [1], [ ]], // 14 [[ ], [4], [4]], // 15 [[ ], [20], [20]], // 16 [[5], [4,8], [8]], // 17 [[2], [1], [ ]], // 18 [[6], [5], [ ]], // 19 [[2], [1], [ ]], // 20 [[1,3,7], [2,6], [ ]], // 21 [[2], [1], [ ]], // 22 [[4], [5], [5]], // 23 [[2], [3], [3]], // 24 [[22,26], [21,24], [ ]], // 25 [[5], [2], [ ]], // 26 [[11], [13,10], [13]], // 27 [[11], [9,12], [12]], // 28 [[ ], [ ], [ ]], // 29 [[ ], [ ], [ ]], // 30 [[ ], [9,10], [9,10]], // 31 [[ ], [3], [3]], // 32 [[ ], [2], [2]], // 33 [[ ], [ ], [ ]], // 34 [[ ], [4], [4]], // 35 [[19, 8], [18,20], [20]], // 36 [[ ], [ ], [ ]], // 37 [[ ], [ ], [ ]], // 38 [[ ], [ ], [ ]], // 39 [[4,6], [2,5], [ ]], // 40 [[ ], [ ], [ ]], // 41 [[ ], [ ], [ ]], // 42 [[ ], [ ], [ ]], // 43 [[ ], [ ], [ ]], // 44 [[5], [4,7], [7]], // 45 [[ ], [ ], [ ]], // 46 [[ ], [ ], [ ]], // 47 [[ ], [ ], [ ]], // 48 [[33,38], [32,36], [ ]], // 49 [[6], [2,7], [7]], // 50 [[ ], [ ], [ ]], // 51 [[ ], [1], [1]], // 52 [[ ], [ ], [ ]], // 53 [[ ], [ ], [ ]], // 54 [[6], [5], [ ]], // 55 [[6, 7], [2, 4], [ ]], // 56 [[ ], [1, 3], [1, 3]], // 57 [[ ], [ ], [ ]], // 58 [[ ], [ ], [ ]], // 59 [[5], [4], [ ]], // 60 [[ ], [ ], [ ]], // 61 [[ ], [ ], [ ]], // 62 [[4], [6, 3, 1], [6, 3]], // 63 [[ ], [64, 72], [64, 72]], // 64 [[2], [11, 1, 7, 5], [11, 7, 5]], // 65 [[ ], [5], [5]], // 66 [[ ], [ ], [ ]], // 67 [[3], [2], [ ]], // 68 [[ ], [ ], [ ]], // 69 [[ ], [ ], [ ]], // 70 [[ ], [ ], [ ]], // 71 [[ ], [ ], [ ]], // 72 [[ ], [14], [14]], // 73 [[ ], [ ], [ ]], // 74 [[ ], [ ], [ ]], // 75 [[ ], [ ], [ ]], // 76 [[ ], [2], [2]], // 77 [[2, 4], [1, 3], [ ]], // 78 [[ ], [ ], [ ]], // 79 [[ ], [ ], [ ]], // 80 [[145, 153], [144, 152], [ ]], // 81 [[ 8], [6], [ ]], // 82 [[ ], [ ], [ ]], // 83 [[3], [1], [ ]], // 84 [[4], [3], [ ]], // 85 [[ ], [ ], [ ]], // 86 [[ ], [ ], [ ]], // 87 [[ ], [ ], [ ]], // 88 [[ ], [ ], [ ]], // 89 [[ ], [ ], [ ]], // 90 [[6], [ 8, 5], [ 8]], // 91 [[ ], [ ], [ ]], // 92 [[ ], [ ], [ ]], // 93 [[ ], [ ], [ ]], // 94 [[ ], [ ], [ ]], // 95 [[ ], [ ], [ ]], // 96 [[ ], [ ], [ ]], // 97 [[ ], [ ], [ ]], // 98 [[ ], [ ], [ ]], // 99 [[36, 34, 32], [33, 35], [ ]], // 100 [[ ], [ ], [ ]], // 101 [[ ], [1], [1]], // 102 [[ ], [ ], [ ]], // 103 [[ ], [ ], [ ]], // 104 [[3, 9], [8, 7], [7]], // 105 [[ ], [ ], [ ]], // 106 [[ ], [ ], [ ]], // 107 [[ ], [ ], [ ]], // 108 [[ ], [ ], [ ]], // 109 [[ ], [ ], [ ]], // 110 [[ ], [ ], [ ]], // 111 [[ ], [8], [8]], // 112 [[ ], [ ], [ ]], // 113 [[ ], [ ], [ ]], // 114 [[ ], [ ], [ ]], // 115 [[ ], [ ], [ ]], // 116 [[ ], [1, 3], [1, 3]], // 117 [[ ], [ ], [ ]], // 118 [[ ], [2], [2]], // 119 [[10], [21, 4, 8, 13, 19, 18], [21, 4, 13, 19, 18]]]; // 120 [ [ PrimitiveGroupDescription( i, n ) : n in maxprim[i]] : i in [1..120]]; Output: Magma V2.10-6 Fri Jan 16 2004 08:38:25 on modular [Seed = 1899419699] ------------------------------------- >> [ [ PrimitiveGroupDescription( i, n ) : n in maxprim[i]] : i in [1..120]];; ^ Runtime error in 'PrimitiveGroupDescription': Bad argument types Argument types given: RngIntElt, SeqEnum[RngIntElt] Total time: 2.939 seconds, Total memory usage: 1.90MB ************** MAGMA ***************** Host ibm21.ilab.sztaki.hu. (195.111.1.97) Time: Fri Jan 16 08:39:52 2004 Input: maxprim:=[ [[ ], [ ], [ ]], // 1 [[ ], [ ], [ ]], // 2 [[ ], [ ], [ ]], // 3 [[ ], [ ], [ ]], // 4 [[3], [2], [ ]], // 5 [[2], [1], [ ]], // 6 [[4], [5], [5]], // 7 [[5], [3], [3]], // 8 [[7], [6,9], [9]], // 9 [[7], [6], [ ]], // 10 [[4], [6], [6]], // 11 [[2], [4], [4]], // 12 [[6], [5,7], [7]], // 13 [[2], [1], [ ]], // 14 [[ ], [4], [4]], // 15 [[ ], [20], [20]], // 16 [[5], [4,8], [8]], // 17 [[2], [1], [ ]], // 18 [[6], [5], [ ]], // 19 [[2], [1], [ ]], // 20 [[1,3,7], [2,6], [ ]], // 21 [[2], [1], [ ]], // 22 [[4], [5], [5]], // 23 [[2], [3], [3]], // 24 [[22,26], [21,24], [ ]], // 25 [[5], [2], [ ]], // 26 [[11], [13,10], [13]], // 27 [[11], [9,12], [12]], // 28 [[ ], [ ], [ ]], // 29 [[ ], [ ], [ ]], // 30 [[ ], [9,10], [9,10]], // 31 [[ ], [3], [3]], // 32 [[ ], [2], [2]], // 33 [[ ], [ ], [ ]], // 34 [[ ], [4], [4]], // 35 [[19, 8], [18,20], [20]], // 36 [[ ], [ ], [ ]], // 37 [[ ], [ ], [ ]], // 38 [[ ], [ ], [ ]], // 39 [[4,6], [2,5], [ ]], // 40 [[ ], [ ], [ ]], // 41 [[ ], [ ], [ ]], // 42 [[ ], [ ], [ ]], // 43 [[ ], [ ], [ ]], // 44 [[5], [4,7], [7]], // 45 [[ ], [ ], [ ]], // 46 [[ ], [ ], [ ]], // 47 [[ ], [ ], [ ]], // 48 [[33,38], [32,36], [ ]], // 49 [[6], [2,7], [7]], // 50 [[ ], [ ], [ ]], // 51 [[ ], [1], [1]], // 52 [[ ], [ ], [ ]], // 53 [[ ], [ ], [ ]], // 54 [[6], [5], [ ]], // 55 [[6, 7], [2, 4], [ ]], // 56 [[ ], [1, 3], [1, 3]], // 57 [[ ], [ ], [ ]], // 58 [[ ], [ ], [ ]], // 59 [[5], [4], [ ]], // 60 [[ ], [ ], [ ]], // 61 [[ ], [ ], [ ]], // 62 [[4], [6, 3, 1], [6, 3]], // 63 [[ ], [64, 72], [64, 72]], // 64 [[2], [11, 1, 7, 5], [11, 7, 5]], // 65 [[ ], [5], [5]], // 66 [[ ], [ ], [ ]], // 67 [[3], [2], [ ]], // 68 [[ ], [ ], [ ]], // 69 [[ ], [ ], [ ]], // 70 [[ ], [ ], [ ]], // 71 [[ ], [ ], [ ]], // 72 [[ ], [14], [14]], // 73 [[ ], [ ], [ ]], // 74 [[ ], [ ], [ ]], // 75 [[ ], [ ], [ ]], // 76 [[ ], [2], [2]], // 77 [[2, 4], [1, 3], [ ]], // 78 [[ ], [ ], [ ]], // 79 [[ ], [ ], [ ]], // 80 [[145, 153], [144, 152], [ ]], // 81 [[ 8], [6], [ ]], // 82 [[ ], [ ], [ ]], // 83 [[3], [1], [ ]], // 84 [[4], [3], [ ]], // 85 [[ ], [ ], [ ]], // 86 [[ ], [ ], [ ]], // 87 [[ ], [ ], [ ]], // 88 [[ ], [ ], [ ]], // 89 [[ ], [ ], [ ]], // 90 [[6], [ 8, 5], [ 8]], // 91 [[ ], [ ], [ ]], // 92 [[ ], [ ], [ ]], // 93 [[ ], [ ], [ ]], // 94 [[ ], [ ], [ ]], // 95 [[ ], [ ], [ ]], // 96 [[ ], [ ], [ ]], // 97 [[ ], [ ], [ ]], // 98 [[ ], [ ], [ ]], // 99 [[36, 34, 32], [33, 35], [ ]], // 100 [[ ], [ ], [ ]], // 101 [[ ], [1], [1]], // 102 [[ ], [ ], [ ]], // 103 [[ ], [ ], [ ]], // 104 [[3, 9], [8, 7], [7]], // 105 [[ ], [ ], [ ]], // 106 [[ ], [ ], [ ]], // 107 [[ ], [ ], [ ]], // 108 [[ ], [ ], [ ]], // 109 [[ ], [ ], [ ]], // 110 [[ ], [ ], [ ]], // 111 [[ ], [8], [8]], // 112 [[ ], [ ], [ ]], // 113 [[ ], [ ], [ ]], // 114 [[ ], [ ], [ ]], // 115 [[ ], [ ], [ ]], // 116 [[ ], [1, 3], [1, 3]], // 117 [[ ], [ ], [ ]], // 118 [[ ], [2], [2]], // 119 [[10], [21, 4, 8, 13, 19, 18], [21, 4, 13, 19, 18]]]; // 120 [ [ PrimitiveGroupDescription( i, n ) : n in maxprim[i]] : i in [1..120]]; Output: Magma V2.10-6 Fri Jan 16 2004 08:39:49 on modular [Seed = 1663355605] ------------------------------------- >> [ [ PrimitiveGroupDescription( i, n ) : n in maxprim[i]] : i in [1..120]];; ^ Runtime error in 'PrimitiveGroupDescription': Bad argument types Argument types given: RngIntElt, SeqEnum[RngIntElt] Total time: 3.059 seconds, Total memory usage: 1.90MB ************** MAGMA ***************** Host ibm21.ilab.sztaki.hu. (195.111.1.97) Time: Fri Jan 16 08:40:49 2004 Input: maxprim:=[ [[ ], [ ], [ ]], // 1 [[ ], [ ], [ ]], // 2 [[ ], [ ], [ ]], // 3 [[ ], [ ], [ ]], // 4 [[3], [2], [ ]], // 5 [[2], [1], [ ]], // 6 [[4], [5], [5]], // 7 [[5], [3], [3]], // 8 [[7], [6,9], [9]], // 9 [[7], [6], [ ]], // 10 [[4], [6], [6]], // 11 [[2], [4], [4]], // 12 [[6], [5,7], [7]], // 13 [[2], [1], [ ]], // 14 [[ ], [4], [4]], // 15 [[ ], [20], [20]], // 16 [[5], [4,8], [8]], // 17 [[2], [1], [ ]], // 18 [[6], [5], [ ]], // 19 [[2], [1], [ ]], // 20 [[1,3,7], [2,6], [ ]], // 21 [[2], [1], [ ]], // 22 [[4], [5], [5]], // 23 [[2], [3], [3]], // 24 [[22,26], [21,24], [ ]], // 25 [[5], [2], [ ]], // 26 [[11], [13,10], [13]], // 27 [[11], [9,12], [12]], // 28 [[ ], [ ], [ ]], // 29 [[ ], [ ], [ ]], // 30 [[ ], [9,10], [9,10]], // 31 [[ ], [3], [3]], // 32 [[ ], [2], [2]], // 33 [[ ], [ ], [ ]], // 34 [[ ], [4], [4]], // 35 [[19, 8], [18,20], [20]], // 36 [[ ], [ ], [ ]], // 37 [[ ], [ ], [ ]], // 38 [[ ], [ ], [ ]], // 39 [[4,6], [2,5], [ ]], // 40 [[ ], [ ], [ ]], // 41 [[ ], [ ], [ ]], // 42 [[ ], [ ], [ ]], // 43 [[ ], [ ], [ ]], // 44 [[5], [4,7], [7]], // 45 [[ ], [ ], [ ]], // 46 [[ ], [ ], [ ]], // 47 [[ ], [ ], [ ]], // 48 [[33,38], [32,36], [ ]], // 49 [[6], [2,7], [7]], // 50 [[ ], [ ], [ ]], // 51 [[ ], [1], [1]], // 52 [[ ], [ ], [ ]], // 53 [[ ], [ ], [ ]], // 54 [[6], [5], [ ]], // 55 [[6, 7], [2, 4], [ ]], // 56 [[ ], [1, 3], [1, 3]], // 57 [[ ], [ ], [ ]], // 58 [[ ], [ ], [ ]], // 59 [[5], [4], [ ]], // 60 [[ ], [ ], [ ]], // 61 [[ ], [ ], [ ]], // 62 [[4], [6, 3, 1], [6, 3]], // 63 [[ ], [64, 72], [64, 72]], // 64 [[2], [11, 1, 7, 5], [11, 7, 5]], // 65 [[ ], [5], [5]], // 66 [[ ], [ ], [ ]], // 67 [[3], [2], [ ]], // 68 [[ ], [ ], [ ]], // 69 [[ ], [ ], [ ]], // 70 [[ ], [ ], [ ]], // 71 [[ ], [ ], [ ]], // 72 [[ ], [14], [14]], // 73 [[ ], [ ], [ ]], // 74 [[ ], [ ], [ ]], // 75 [[ ], [ ], [ ]], // 76 [[ ], [2], [2]], // 77 [[2, 4], [1, 3], [ ]], // 78 [[ ], [ ], [ ]], // 79 [[ ], [ ], [ ]], // 80 [[145, 153], [144, 152], [ ]], // 81 [[ 8], [6], [ ]], // 82 [[ ], [ ], [ ]], // 83 [[3], [1], [ ]], // 84 [[4], [3], [ ]], // 85 [[ ], [ ], [ ]], // 86 [[ ], [ ], [ ]], // 87 [[ ], [ ], [ ]], // 88 [[ ], [ ], [ ]], // 89 [[ ], [ ], [ ]], // 90 [[6], [ 8, 5], [ 8]], // 91 [[ ], [ ], [ ]], // 92 [[ ], [ ], [ ]], // 93 [[ ], [ ], [ ]], // 94 [[ ], [ ], [ ]], // 95 [[ ], [ ], [ ]], // 96 [[ ], [ ], [ ]], // 97 [[ ], [ ], [ ]], // 98 [[ ], [ ], [ ]], // 99 [[36, 34, 32], [33, 35], [ ]], // 100 [[ ], [ ], [ ]], // 101 [[ ], [1], [1]], // 102 [[ ], [ ], [ ]], // 103 [[ ], [ ], [ ]], // 104 [[3, 9], [8, 7], [7]], // 105 [[ ], [ ], [ ]], // 106 [[ ], [ ], [ ]], // 107 [[ ], [ ], [ ]], // 108 [[ ], [ ], [ ]], // 109 [[ ], [ ], [ ]], // 110 [[ ], [ ], [ ]], // 111 [[ ], [8], [8]], // 112 [[ ], [ ], [ ]], // 113 [[ ], [ ], [ ]], // 114 [[ ], [ ], [ ]], // 115 [[ ], [ ], [ ]], // 116 [[ ], [1, 3], [1, 3]], // 117 [[ ], [ ], [ ]], // 118 [[ ], [2], [2]], // 119 [[10], [21, 4, 8, 13, 19, 18], [21, 4, 13, 19, 18]]]; // 120 [ [[ PrimitiveGroupDescription( i, n ) : n in i] : i in maxprim[j]] : j in [1..120]]; Output: Magma V2.10-6 Fri Jan 16 2004 08:40:46 on modular [Seed = 2480159326] ------------------------------------- >> [ [[ PrimitiveGroupDescription( i, n ) : n in i] : i in maxprim[j]] : j in ^ Runtime error in 'PrimitiveGroupDescription': Bad argument types Argument types given: SeqEnum[RngIntElt], RngIntElt Total time: 2.909 seconds, Total memory usage: 1.90MB ************** MAGMA ***************** Host ibm21.ilab.sztaki.hu. (195.111.1.97) Time: Fri Jan 16 08:41:36 2004 Input: maxprim:=[ [[ ], [ ], [ ]], // 1 [[ ], [ ], [ ]], // 2 [[ ], [ ], [ ]], // 3 [[ ], [ ], [ ]], // 4 [[3], [2], [ ]], // 5 [[2], [1], [ ]], // 6 [[4], [5], [5]], // 7 [[5], [3], [3]], // 8 [[7], [6,9], [9]], // 9 [[7], [6], [ ]], // 10 [[4], [6], [6]], // 11 [[2], [4], [4]], // 12 [[6], [5,7], [7]], // 13 [[2], [1], [ ]], // 14 [[ ], [4], [4]], // 15 [[ ], [20], [20]], // 16 [[5], [4,8], [8]], // 17 [[2], [1], [ ]], // 18 [[6], [5], [ ]], // 19 [[2], [1], [ ]], // 20 [[1,3,7], [2,6], [ ]], // 21 [[2], [1], [ ]], // 22 [[4], [5], [5]], // 23 [[2], [3], [3]], // 24 [[22,26], [21,24], [ ]], // 25 [[5], [2], [ ]], // 26 [[11], [13,10], [13]], // 27 [[11], [9,12], [12]], // 28 [[ ], [ ], [ ]], // 29 [[ ], [ ], [ ]], // 30 [[ ], [9,10], [9,10]], // 31 [[ ], [3], [3]], // 32 [[ ], [2], [2]], // 33 [[ ], [ ], [ ]], // 34 [[ ], [4], [4]], // 35 [[19, 8], [18,20], [20]], // 36 [[ ], [ ], [ ]], // 37 [[ ], [ ], [ ]], // 38 [[ ], [ ], [ ]], // 39 [[4,6], [2,5], [ ]], // 40 [[ ], [ ], [ ]], // 41 [[ ], [ ], [ ]], // 42 [[ ], [ ], [ ]], // 43 [[ ], [ ], [ ]], // 44 [[5], [4,7], [7]], // 45 [[ ], [ ], [ ]], // 46 [[ ], [ ], [ ]], // 47 [[ ], [ ], [ ]], // 48 [[33,38], [32,36], [ ]], // 49 [[6], [2,7], [7]], // 50 [[ ], [ ], [ ]], // 51 [[ ], [1], [1]], // 52 [[ ], [ ], [ ]], // 53 [[ ], [ ], [ ]], // 54 [[6], [5], [ ]], // 55 [[6, 7], [2, 4], [ ]], // 56 [[ ], [1, 3], [1, 3]], // 57 [[ ], [ ], [ ]], // 58 [[ ], [ ], [ ]], // 59 [[5], [4], [ ]], // 60 [[ ], [ ], [ ]], // 61 [[ ], [ ], [ ]], // 62 [[4], [6, 3, 1], [6, 3]], // 63 [[ ], [64, 72], [64, 72]], // 64 [[2], [11, 1, 7, 5], [11, 7, 5]], // 65 [[ ], [5], [5]], // 66 [[ ], [ ], [ ]], // 67 [[3], [2], [ ]], // 68 [[ ], [ ], [ ]], // 69 [[ ], [ ], [ ]], // 70 [[ ], [ ], [ ]], // 71 [[ ], [ ], [ ]], // 72 [[ ], [14], [14]], // 73 [[ ], [ ], [ ]], // 74 [[ ], [ ], [ ]], // 75 [[ ], [ ], [ ]], // 76 [[ ], [2], [2]], // 77 [[2, 4], [1, 3], [ ]], // 78 [[ ], [ ], [ ]], // 79 [[ ], [ ], [ ]], // 80 [[145, 153], [144, 152], [ ]], // 81 [[ 8], [6], [ ]], // 82 [[ ], [ ], [ ]], // 83 [[3], [1], [ ]], // 84 [[4], [3], [ ]], // 85 [[ ], [ ], [ ]], // 86 [[ ], [ ], [ ]], // 87 [[ ], [ ], [ ]], // 88 [[ ], [ ], [ ]], // 89 [[ ], [ ], [ ]], // 90 [[6], [ 8, 5], [ 8]], // 91 [[ ], [ ], [ ]], // 92 [[ ], [ ], [ ]], // 93 [[ ], [ ], [ ]], // 94 [[ ], [ ], [ ]], // 95 [[ ], [ ], [ ]], // 96 [[ ], [ ], [ ]], // 97 [[ ], [ ], [ ]], // 98 [[ ], [ ], [ ]], // 99 [[36, 34, 32], [33, 35], [ ]], // 100 [[ ], [ ], [ ]], // 101 [[ ], [1], [1]], // 102 [[ ], [ ], [ ]], // 103 [[ ], [ ], [ ]], // 104 [[3, 9], [8, 7], [7]], // 105 [[ ], [ ], [ ]], // 106 [[ ], [ ], [ ]], // 107 [[ ], [ ], [ ]], // 108 [[ ], [ ], [ ]], // 109 [[ ], [ ], [ ]], // 110 [[ ], [ ], [ ]], // 111 [[ ], [8], [8]], // 112 [[ ], [ ], [ ]], // 113 [[ ], [ ], [ ]], // 114 [[ ], [ ], [ ]], // 115 [[ ], [ ], [ ]], // 116 [[ ], [1, 3], [1, 3]], // 117 [[ ], [ ], [ ]], // 118 [[ ], [2], [2]], // 119 [[10], [21, 4, 8, 13, 19, 18], [21, 4, 13, 19, 18]]]; // 120 [ [[ PrimitiveGroupDescription( i, n ) : n in k] : k in maxprim[i]] : i in [1..120]]; Output: Magma V2.10-6 Fri Jan 16 2004 08:41:32 on modular [Seed = 2598187141] ------------------------------------- [ [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [ AGL(1, 5) ], [ D(2*5) ], [] ], [ [ PGL(2, 5) ], [ PSL(2, 5) ], [] ], [ [ AGL(1, 7) ], [ L(3, 2) ], [ L(3, 2) ] ], [ [ PGL(2, 7) ], [ ASL(3, 2) ], [ ASL(3, 2) ] ], [ [ AGL(2, 3) ], [ 3^2:(2'A(4)), PGammaL(2, 8) ], [ PGammaL(2, 8) ] ], [ [ PGammaL(2, 9) ], [ M(10) ], [] ], [ [ AGL(1, 11) ], [ M(11) ], [ M(11) ] ], [ [ PGL(2, 11) ], [ M(12) ], [ M(12) ] ], [ [ AGL(1, 13) ], [ 13:6, L(3, 3) ], [ L(3, 3) ] ], [ [ PGL(2, 13) ], [ PSL(2, 13) ], [] ], [ [], [ PSL(4, 2) ], [ PSL(4, 2) ] ], [ [], [ 2^4.PSL(4, 2) ], [ 2^4.PSL(4, 2) ] ], [ [ AGL(1, 17) ], [ 17:8, L(2, 2^4):4 = PGammaL(2, 2^4) ], [ L(2, 2^4):4 = PGammaL(2, 2^4) ] ], [ [ PGL(2, 17) ], [ PSL(2, 17) ], [] ], [ [ AGL(1, 19) ], [ 19:9 ], [] ], [ [ PGL(2, 19) ], [ PSL(2, 19) ], [] ], [ [ PGL(2, 7), S(7), PGammaL(3, 4) ], [ A(7), PGL(3, 4) ], [] ], [ [ M(22):2 ], [ M(22) ], [] ], [ [ AGL(1, 23) ], [ M(23) ], [ M(23) ] ], [ [ PGL(2, 23) ], [ M(24) ], [ M(24) ] ], [ [ AGL(2, 5), (S(5) x S(5)):2 ], [ ASL(2, 5):2, (A(5) x A(5)):2^2 ], [] ], [ [ PGammaL(2, 25) ], [ PSigmaL(2, 25) ], [] ], [ [ AGL(3, 3) ], [ PSp(4, 3):2, ASL(3, 3) ], [ PSp(4, 3):2 ] ], [ [ PGammaL(2, 27) ], [ PSL(2, 27):3, PSp(6, 2) ], [ PSp(6, 2) ] ], [ [], [], [] ], [ [], [], [] ], [ [], [ L(3, 5), L(5, 2) ], [ L(3, 5), L(5, 2) ] ], [ [], [ ASL(5, 2) ], [ ASL(5, 2) ] ], [ [], [ PGammaL(2, 32) ], [ PGammaL(2, 32) ] ], [ [], [], [] ], [ [], [ S(8) ], [ S(8) ] ], [ [ S(9), (S(6) x S(6)):2 ], [ A(9), PSp(6, 2) ], [ PSp(6, 2) ] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [ PSp(4, 3):2, PGL(4, 3) ], [ PSp(4, 3), PSL(4, 3) ], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [ PSp(4, 3):2 ], [ PSp(4, 3), S(10) ], [ S(10) ] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [ AGL(2, 7), (S(7) x S(7)):2 ], [ ASL(2, 7):3, (A(7) x A(7)):2^2 ], [] ], [ [ PGammaL(2, 49) ], [ PGL(2, 49), PSU(3, 5):2 ], [ PSU(3, 5):2 ] ], [ [], [], [] ], [ [], [ PSL(3, 3).2 ], [ PSL(3, 3).2 ] ], [ [], [], [] ], [ [], [], [] ], [ [ Sym(11) ], [ Alt(11) ], [] ], [ [ Sym(8), PSL(3, 4).2^2 ], [ Alt(8), PSL(3, 4).2_2 ], [] ], [ [], [ PSL(2, 19), PSL(3, 7).3 ], [ PSL(2, 19), PSL(3, 7).3 ] ], [ [], [], [] ], [ [], [], [] ], [ [ Alt(5)^2.2^2 ], [ Alt(5) wreath Sym(2) ], [] ], [ [], [], [] ], [ [], [], [] ], [ [ PSU(3, 3).2 ], [ PSL(6, 2), PSU(3, 3).2, PSU(3, 3) ], [ PSL(6, 2), PSU(3, 3).2 ] ], [ [], [ AGL(6, 2), Sym(8) wreath Sym(2) ], [ AGL(6, 2), Sym(8) wreath Sym(2) ] ], [ [ PSigmaL(2, 5^2) ], [ PGammaL(2, 2^6), PSL(2, 5^2), PGammaU(3, 4), PSz(8).3 ], [ PGammaL(2, 2^6), PGammaU(3, 4), PSz(8).3 ] ], [ [], [ Sym(12) ], [ Sym(12) ] ], [ [], [], [] ], [ [ PSigmaL(2, 16) ], [ PSL(2, 16).2 ], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [ L(3, 2^3):3 = PGammaL(3, 2^3) ], [ L(3, 2^3):3 = PGammaL(3, 2^3) ] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [ M_22.2 ], [ M_22.2 ] ], [ [ PGL(2, 13), Sym(13) ], [ PSL(2, 13), Alt(13) ], [] ], [ [], [], [] ], [ [], [], [] ], [ [ AGL(4, 3), Sym(9) \wreath Sym(2) ], [ ASL(4, 3), Alt(9)^2.2^2 ], [] ], [ [ PGammaL(2, 3^4) ], [ PSL(2, 3^4).4 ], [] ], [ [], [], [] ], [ [ Sym(9) ], [ Alt(9) ], [] ], [ [ PSigmaL(4, 4) ], [ PSL(4, 4) ], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [ PGammaL(3, 9) ], [ Sym(14), PSL(3, 9) ], [ Sym(14) ] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [ HS:2, J_2.2, Sym(10) \wreath Sym(2) ], [ J_2, HS ], [] ], [ [], [], [] ], [ [], [ PSL(2, 17) ], [ PSL(2, 17) ] ], [ [], [], [] ], [ [], [], [] ], [ [ Sym(8), Sym(15) ], [ Alt(15), PSL(3, 4).D_12 ], [ PSL(3, 4).D_12 ] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [ PSU(4, 3).D_8 ], [ PSU(4, 3).D_8 ] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [ PSL(3, 3).2, PSL(4, 3).2 ], [ PSL(3, 3).2, PSL(4, 3).2 ] ], [ [], [], [] ], [ [], [ PSO-(8, 2) ], [ PSO-(8, 2) ] ], [ [ PSL(3, 4).2^2 ], [ Sym(16), PSigmaL(2, 16), PSL(3, 4).2, PSp(6, 2), PSp(8, 2), PSO+(8, 2) ], [ Sym(16), PSigmaL(2, 16), PSp(6, 2), PSp(8, 2), PSO+(8, 2) ] ] ] Total time: 3.189 seconds, Total memory usage: 2.20MB ************** MAGMA ***************** Host ibm21.ilab.sztaki.hu. (195.111.1.97) Time: Fri Jan 16 08:43:43 2004 Input: maxprim:=[ [[ ], [ ], [ ]], // 1 [[ ], [ ], [ ]], // 2 [[ ], [ ], [ ]], // 3 [[ ], [ ], [ ]], // 4 [[3], [2], [ ]], // 5 [[2], [1], [ ]], // 6 [[4], [5], [5]], // 7 [[5], [3], [3]], // 8 [[7], [6,9], [9]], // 9 [[7], [6], [ ]], // 10 [[4], [6], [6]], // 11 [[2], [4], [4]], // 12 [[6], [5,7], [7]], // 13 [[2], [1], [ ]], // 14 [[ ], [4], [4]], // 15 [[ ], [20], [20]], // 16 [[5], [4,8], [8]], // 17 [[2], [1], [ ]], // 18 [[6], [5], [ ]], // 19 [[2], [1], [ ]], // 20 [[1,3,7], [2,6], [ ]], // 21 [[2], [1], [ ]], // 22 [[4], [5], [5]], // 23 [[2], [3], [3]], // 24 [[22,26], [21,24], [ ]], // 25 [[5], [2], [ ]], // 26 [[11], [13,10], [13]], // 27 [[11], [9,12], [12]], // 28 [[ ], [ ], [ ]], // 29 [[ ], [ ], [ ]], // 30 [[ ], [9,10], [9,10]], // 31 [[ ], [3], [3]], // 32 [[ ], [2], [2]], // 33 [[ ], [ ], [ ]], // 34 [[ ], [4], [4]], // 35 [[19, 8], [18,20], [20]], // 36 [[ ], [ ], [ ]], // 37 [[ ], [ ], [ ]], // 38 [[ ], [ ], [ ]], // 39 [[4,6], [2,5], [ ]], // 40 [[ ], [ ], [ ]], // 41 [[ ], [ ], [ ]], // 42 [[ ], [ ], [ ]], // 43 [[ ], [ ], [ ]], // 44 [[5], [4,7], [7]], // 45 [[ ], [ ], [ ]], // 46 [[ ], [ ], [ ]], // 47 [[ ], [ ], [ ]], // 48 [[33,38], [32,36], [ ]], // 49 [[6], [2,7], [7]], // 50 [[ ], [ ], [ ]], // 51 [[ ], [1], [1]], // 52 [[ ], [ ], [ ]], // 53 [[ ], [ ], [ ]], // 54 [[6], [5], [ ]], // 55 [[6, 7], [2, 4], [ ]], // 56 [[ ], [1, 3], [1, 3]], // 57 [[ ], [ ], [ ]], // 58 [[ ], [ ], [ ]], // 59 [[5], [4], [ ]], // 60 [[ ], [ ], [ ]], // 61 [[ ], [ ], [ ]], // 62 [[4], [6, 3, 1], [6, 3]], // 63 [[ ], [64, 72], [64, 72]], // 64 [[2], [11, 1, 7, 5], [11, 7, 5]], // 65 [[ ], [5], [5]], // 66 [[ ], [ ], [ ]], // 67 [[3], [2], [ ]], // 68 [[ ], [ ], [ ]], // 69 [[ ], [ ], [ ]], // 70 [[ ], [ ], [ ]], // 71 [[ ], [ ], [ ]], // 72 [[ ], [14], [14]], // 73 [[ ], [ ], [ ]], // 74 [[ ], [ ], [ ]], // 75 [[ ], [ ], [ ]], // 76 [[ ], [2], [2]], // 77 [[2, 4], [1, 3], [ ]], // 78 [[ ], [ ], [ ]], // 79 [[ ], [ ], [ ]], // 80 [[145, 153], [144, 152], [ ]], // 81 [[ 8], [6], [ ]], // 82 [[ ], [ ], [ ]], // 83 [[3], [1], [ ]], // 84 [[4], [3], [ ]], // 85 [[ ], [ ], [ ]], // 86 [[ ], [ ], [ ]], // 87 [[ ], [ ], [ ]], // 88 [[ ], [ ], [ ]], // 89 [[ ], [ ], [ ]], // 90 [[6], [ 8, 5], [ 8]], // 91 [[ ], [ ], [ ]], // 92 [[ ], [ ], [ ]], // 93 [[ ], [ ], [ ]], // 94 [[ ], [ ], [ ]], // 95 [[ ], [ ], [ ]], // 96 [[ ], [ ], [ ]], // 97 [[ ], [ ], [ ]], // 98 [[ ], [ ], [ ]], // 99 [[36, 34, 32], [33, 35], [ ]], // 100 [[ ], [ ], [ ]], // 101 [[ ], [1], [1]], // 102 [[ ], [ ], [ ]], // 103 [[ ], [ ], [ ]], // 104 [[3, 9], [8, 7], [7]], // 105 [[ ], [ ], [ ]], // 106 [[ ], [ ], [ ]], // 107 [[ ], [ ], [ ]], // 108 [[ ], [ ], [ ]], // 109 [[ ], [ ], [ ]], // 110 [[ ], [ ], [ ]], // 111 [[ ], [8], [8]], // 112 [[ ], [ ], [ ]], // 113 [[ ], [ ], [ ]], // 114 [[ ], [ ], [ ]], // 115 [[ ], [ ], [ ]], // 116 [[ ], [1, 3], [1, 3]], // 117 [[ ], [ ], [ ]], // 118 [[ ], [2], [2]], // 119 [[10], [21, 4, 8, 13, 19, 18], [21, 4, 13, 19, 18]]]; // 120 [ [[ PrimitiveGroupDescription( i, n ) : n in k | #PrimitiveGroup(i,n)^12>=Factorial(i)] : k in maxprim[i]] : i in [1..120]]; Output: Magma V2.10-6 Fri Jan 16 2004 08:43:40 on modular [Seed = 2177248030] ------------------------------------- >> [ [[ PrimitiveGroupDescription( i, n ) : n in k | #PrimitiveGroup(i,n)^12>= ^ User error: bad syntax Total time: 2.939 seconds, Total memory usage: 1.90MB ************** MAGMA ***************** Host ibm21.ilab.sztaki.hu. (195.111.1.97) Time: Fri Jan 16 08:44:08 2004 Input: maxprim:=[ [[ ], [ ], [ ]], // 1 [[ ], [ ], [ ]], // 2 [[ ], [ ], [ ]], // 3 [[ ], [ ], [ ]], // 4 [[3], [2], [ ]], // 5 [[2], [1], [ ]], // 6 [[4], [5], [5]], // 7 [[5], [3], [3]], // 8 [[7], [6,9], [9]], // 9 [[7], [6], [ ]], // 10 [[4], [6], [6]], // 11 [[2], [4], [4]], // 12 [[6], [5,7], [7]], // 13 [[2], [1], [ ]], // 14 [[ ], [4], [4]], // 15 [[ ], [20], [20]], // 16 [[5], [4,8], [8]], // 17 [[2], [1], [ ]], // 18 [[6], [5], [ ]], // 19 [[2], [1], [ ]], // 20 [[1,3,7], [2,6], [ ]], // 21 [[2], [1], [ ]], // 22 [[4], [5], [5]], // 23 [[2], [3], [3]], // 24 [[22,26], [21,24], [ ]], // 25 [[5], [2], [ ]], // 26 [[11], [13,10], [13]], // 27 [[11], [9,12], [12]], // 28 [[ ], [ ], [ ]], // 29 [[ ], [ ], [ ]], // 30 [[ ], [9,10], [9,10]], // 31 [[ ], [3], [3]], // 32 [[ ], [2], [2]], // 33 [[ ], [ ], [ ]], // 34 [[ ], [4], [4]], // 35 [[19, 8], [18,20], [20]], // 36 [[ ], [ ], [ ]], // 37 [[ ], [ ], [ ]], // 38 [[ ], [ ], [ ]], // 39 [[4,6], [2,5], [ ]], // 40 [[ ], [ ], [ ]], // 41 [[ ], [ ], [ ]], // 42 [[ ], [ ], [ ]], // 43 [[ ], [ ], [ ]], // 44 [[5], [4,7], [7]], // 45 [[ ], [ ], [ ]], // 46 [[ ], [ ], [ ]], // 47 [[ ], [ ], [ ]], // 48 [[33,38], [32,36], [ ]], // 49 [[6], [2,7], [7]], // 50 [[ ], [ ], [ ]], // 51 [[ ], [1], [1]], // 52 [[ ], [ ], [ ]], // 53 [[ ], [ ], [ ]], // 54 [[6], [5], [ ]], // 55 [[6, 7], [2, 4], [ ]], // 56 [[ ], [1, 3], [1, 3]], // 57 [[ ], [ ], [ ]], // 58 [[ ], [ ], [ ]], // 59 [[5], [4], [ ]], // 60 [[ ], [ ], [ ]], // 61 [[ ], [ ], [ ]], // 62 [[4], [6, 3, 1], [6, 3]], // 63 [[ ], [64, 72], [64, 72]], // 64 [[2], [11, 1, 7, 5], [11, 7, 5]], // 65 [[ ], [5], [5]], // 66 [[ ], [ ], [ ]], // 67 [[3], [2], [ ]], // 68 [[ ], [ ], [ ]], // 69 [[ ], [ ], [ ]], // 70 [[ ], [ ], [ ]], // 71 [[ ], [ ], [ ]], // 72 [[ ], [14], [14]], // 73 [[ ], [ ], [ ]], // 74 [[ ], [ ], [ ]], // 75 [[ ], [ ], [ ]], // 76 [[ ], [2], [2]], // 77 [[2, 4], [1, 3], [ ]], // 78 [[ ], [ ], [ ]], // 79 [[ ], [ ], [ ]], // 80 [[145, 153], [144, 152], [ ]], // 81 [[ 8], [6], [ ]], // 82 [[ ], [ ], [ ]], // 83 [[3], [1], [ ]], // 84 [[4], [3], [ ]], // 85 [[ ], [ ], [ ]], // 86 [[ ], [ ], [ ]], // 87 [[ ], [ ], [ ]], // 88 [[ ], [ ], [ ]], // 89 [[ ], [ ], [ ]], // 90 [[6], [ 8, 5], [ 8]], // 91 [[ ], [ ], [ ]], // 92 [[ ], [ ], [ ]], // 93 [[ ], [ ], [ ]], // 94 [[ ], [ ], [ ]], // 95 [[ ], [ ], [ ]], // 96 [[ ], [ ], [ ]], // 97 [[ ], [ ], [ ]], // 98 [[ ], [ ], [ ]], // 99 [[36, 34, 32], [33, 35], [ ]], // 100 [[ ], [ ], [ ]], // 101 [[ ], [1], [1]], // 102 [[ ], [ ], [ ]], // 103 [[ ], [ ], [ ]], // 104 [[3, 9], [8, 7], [7]], // 105 [[ ], [ ], [ ]], // 106 [[ ], [ ], [ ]], // 107 [[ ], [ ], [ ]], // 108 [[ ], [ ], [ ]], // 109 [[ ], [ ], [ ]], // 110 [[ ], [ ], [ ]], // 111 [[ ], [8], [8]], // 112 [[ ], [ ], [ ]], // 113 [[ ], [ ], [ ]], // 114 [[ ], [ ], [ ]], // 115 [[ ], [ ], [ ]], // 116 [[ ], [1, 3], [1, 3]], // 117 [[ ], [ ], [ ]], // 118 [[ ], [2], [2]], // 119 [[10], [21, 4, 8, 13, 19, 18], [21, 4, 13, 19, 18]]]; // 120 [ [[ PrimitiveGroupDescription( i, n ) : n in k | #PrimitiveGroup(i,n)^12 ge Factorial(i)] : k in maxprim[i]] : i in [1..120]]; Output: Magma V2.10-6 Fri Jan 16 2004 08:44:05 on modular [Seed = 2412258617] ------------------------------------- [ [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [ AGL(1, 5) ], [ D(2*5) ], [] ], [ [ PGL(2, 5) ], [ PSL(2, 5) ], [] ], [ [ AGL(1, 7) ], [ L(3, 2) ], [ L(3, 2) ] ], [ [ PGL(2, 7) ], [ ASL(3, 2) ], [ ASL(3, 2) ] ], [ [ AGL(2, 3) ], [ 3^2:(2'A(4)), PGammaL(2, 8) ], [ PGammaL(2, 8) ] ], [ [ PGammaL(2, 9) ], [ M(10) ], [] ], [ [ AGL(1, 11) ], [ M(11) ], [ M(11) ] ], [ [ PGL(2, 11) ], [ M(12) ], [ M(12) ] ], [ [ AGL(1, 13) ], [ 13:6, L(3, 3) ], [ L(3, 3) ] ], [ [ PGL(2, 13) ], [ PSL(2, 13) ], [] ], [ [], [ PSL(4, 2) ], [ PSL(4, 2) ] ], [ [], [ 2^4.PSL(4, 2) ], [ 2^4.PSL(4, 2) ] ], [ [ AGL(1, 17) ], [ 17:8, L(2, 2^4):4 = PGammaL(2, 2^4) ], [ L(2, 2^4):4 = PGammaL(2, 2^4) ] ], [ [ PGL(2, 17) ], [ PSL(2, 17) ], [] ], [ [ AGL(1, 19) ], [ 19:9 ], [] ], [ [ PGL(2, 19) ], [ PSL(2, 19) ], [] ], [ [ PGL(2, 7), S(7), PGammaL(3, 4) ], [ A(7), PGL(3, 4) ], [] ], [ [ M(22):2 ], [ M(22) ], [] ], [ [ AGL(1, 23) ], [ M(23) ], [ M(23) ] ], [ [ PGL(2, 23) ], [ M(24) ], [ M(24) ] ], [ [ AGL(2, 5), (S(5) x S(5)):2 ], [ ASL(2, 5):2, (A(5) x A(5)):2^2 ], [] ], [ [ PGammaL(2, 25) ], [ PSigmaL(2, 25) ], [] ], [ [ AGL(3, 3) ], [ PSp(4, 3):2, ASL(3, 3) ], [ PSp(4, 3):2 ] ], [ [ PGammaL(2, 27) ], [ PSL(2, 27):3, PSp(6, 2) ], [ PSp(6, 2) ] ], [ [], [], [] ], [ [], [], [] ], [ [], [ L(3, 5), L(5, 2) ], [ L(3, 5), L(5, 2) ] ], [ [], [ ASL(5, 2) ], [ ASL(5, 2) ] ], [ [], [ PGammaL(2, 32) ], [ PGammaL(2, 32) ] ], [ [], [], [] ], [ [], [ S(8) ], [ S(8) ] ], [ [ S(9), (S(6) x S(6)):2 ], [ A(9), PSp(6, 2) ], [ PSp(6, 2) ] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [ PSp(4, 3):2, PGL(4, 3) ], [ PSp(4, 3), PSL(4, 3) ], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [ PSp(4, 3):2 ], [ S(10) ], [ S(10) ] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [ (S(7) x S(7)):2 ], [ (A(7) x A(7)):2^2 ], [] ], [ [], [ PSU(3, 5):2 ], [ PSU(3, 5):2 ] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [ Sym(11) ], [ Alt(11) ], [] ], [ [], [], [] ], [ [], [ PSL(3, 7).3 ], [ PSL(3, 7).3 ] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [ PSL(6, 2) ], [ PSL(6, 2) ] ], [ [], [ AGL(6, 2), Sym(8) wreath Sym(2) ], [ AGL(6, 2), Sym(8) wreath Sym(2) ] ], [ [], [], [] ], [ [], [ Sym(12) ], [ Sym(12) ] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [ Sym(13) ], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [ Sym(9) \wreath Sym(2) ], [ Alt(9)^2.2^2 ], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [ Sym(10) \wreath Sym(2) ], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ] ] Total time: 3.149 seconds, Total memory usage: 2.20MB ************** MAGMA ***************** Host ibm21.ilab.sztaki.hu. (195.111.1.97) Time: Fri Jan 16 08:48:10 2004 Input: maxprim:=[ [[ ], [ ], [ ]], // 1 [[ ], [ ], [ ]], // 2 [[ ], [ ], [ ]], // 3 [[ ], [ ], [ ]], // 4 [[3], [2], [ ]], // 5 [[2], [1], [ ]], // 6 [[4], [5], [5]], // 7 [[5], [3], [3]], // 8 [[7], [6,9], [9]], // 9 [[7], [6], [ ]], // 10 [[4], [6], [6]], // 11 [[2], [4], [4]], // 12 [[6], [5,7], [7]], // 13 [[2], [1], [ ]], // 14 [[ ], [4], [4]], // 15 [[ ], [20], [20]], // 16 [[5], [4,8], [8]], // 17 [[2], [1], [ ]], // 18 [[6], [5], [ ]], // 19 [[2], [1], [ ]], // 20 [[1,3,7], [2,6], [ ]], // 21 [[2], [1], [ ]], // 22 [[4], [5], [5]], // 23 [[2], [3], [3]], // 24 [[22,26], [21,24], [ ]], // 25 [[5], [2], [ ]], // 26 [[11], [13,10], [13]], // 27 [[11], [9,12], [12]], // 28 [[ ], [ ], [ ]], // 29 [[ ], [ ], [ ]], // 30 [[ ], [9,10], [9,10]], // 31 [[ ], [3], [3]], // 32 [[ ], [2], [2]], // 33 [[ ], [ ], [ ]], // 34 [[ ], [4], [4]], // 35 [[19, 8], [18,20], [20]], // 36 [[ ], [ ], [ ]], // 37 [[ ], [ ], [ ]], // 38 [[ ], [ ], [ ]], // 39 [[4,6], [2,5], [ ]], // 40 [[ ], [ ], [ ]], // 41 [[ ], [ ], [ ]], // 42 [[ ], [ ], [ ]], // 43 [[ ], [ ], [ ]], // 44 [[5], [4,7], [7]], // 45 [[ ], [ ], [ ]], // 46 [[ ], [ ], [ ]], // 47 [[ ], [ ], [ ]], // 48 [[33,38], [32,36], [ ]], // 49 [[6], [2,7], [7]], // 50 [[ ], [ ], [ ]], // 51 [[ ], [1], [1]], // 52 [[ ], [ ], [ ]], // 53 [[ ], [ ], [ ]], // 54 [[6], [5], [ ]], // 55 [[6, 7], [2, 4], [ ]], // 56 [[ ], [1, 3], [1, 3]], // 57 [[ ], [ ], [ ]], // 58 [[ ], [ ], [ ]], // 59 [[5], [4], [ ]], // 60 [[ ], [ ], [ ]], // 61 [[ ], [ ], [ ]], // 62 [[4], [6, 3, 1], [6, 3]], // 63 [[ ], [64, 72], [64, 72]], // 64 [[2], [11, 1, 7, 5], [11, 7, 5]], // 65 [[ ], [5], [5]], // 66 [[ ], [ ], [ ]], // 67 [[3], [2], [ ]], // 68 [[ ], [ ], [ ]], // 69 [[ ], [ ], [ ]], // 70 [[ ], [ ], [ ]], // 71 [[ ], [ ], [ ]], // 72 [[ ], [14], [14]], // 73 [[ ], [ ], [ ]], // 74 [[ ], [ ], [ ]], // 75 [[ ], [ ], [ ]], // 76 [[ ], [2], [2]], // 77 [[2, 4], [1, 3], [ ]], // 78 [[ ], [ ], [ ]], // 79 [[ ], [ ], [ ]], // 80 [[145, 153], [144, 152], [ ]], // 81 [[ 8], [6], [ ]], // 82 [[ ], [ ], [ ]], // 83 [[3], [1], [ ]], // 84 [[4], [3], [ ]], // 85 [[ ], [ ], [ ]], // 86 [[ ], [ ], [ ]], // 87 [[ ], [ ], [ ]], // 88 [[ ], [ ], [ ]], // 89 [[ ], [ ], [ ]], // 90 [[6], [ 8, 5], [ 8]], // 91 [[ ], [ ], [ ]], // 92 [[ ], [ ], [ ]], // 93 [[ ], [ ], [ ]], // 94 [[ ], [ ], [ ]], // 95 [[ ], [ ], [ ]], // 96 [[ ], [ ], [ ]], // 97 [[ ], [ ], [ ]], // 98 [[ ], [ ], [ ]], // 99 [[36, 34, 32], [33, 35], [ ]], // 100 [[ ], [ ], [ ]], // 101 [[ ], [1], [1]], // 102 [[ ], [ ], [ ]], // 103 [[ ], [ ], [ ]], // 104 [[3, 9], [8, 7], [7]], // 105 [[ ], [ ], [ ]], // 106 [[ ], [ ], [ ]], // 107 [[ ], [ ], [ ]], // 108 [[ ], [ ], [ ]], // 109 [[ ], [ ], [ ]], // 110 [[ ], [ ], [ ]], // 111 [[ ], [8], [8]], // 112 [[ ], [ ], [ ]], // 113 [[ ], [ ], [ ]], // 114 [[ ], [ ], [ ]], // 115 [[ ], [ ], [ ]], // 116 [[ ], [1, 3], [1, 3]], // 117 [[ ], [ ], [ ]], // 118 [[ ], [2], [2]], // 119 [[10], [21, 4, 8, 13, 19, 18], [21, 4, 13, 19, 18]]]; // 120 [ [[ PrimitiveGroupDescription( i, n ) : n in k | #PrimitiveGroup(i,n)^12 > Factorial(i)] : k in maxprim[i]] : i in [1..120]]; Output: Magma V2.10-6 Fri Jan 16 2004 08:48:06 on modular [Seed = 3120435772] ------------------------------------- >> [ [[ PrimitiveGroupDescription( i, n ) : n in k | #PrimitiveGroup(i,n)^12 > ^ User error: bad syntax Total time: 2.959 seconds, Total memory usage: 1.90MB ************** MAGMA ***************** Host ibm21.ilab.sztaki.hu. (195.111.1.97) Time: Fri Jan 16 08:49:16 2004 Input: maxprim:=[ [[ ], [ ], [ ]], // 1 [[ ], [ ], [ ]], // 2 [[ ], [ ], [ ]], // 3 [[ ], [ ], [ ]], // 4 [[3], [2], [ ]], // 5 [[2], [1], [ ]], // 6 [[4], [5], [5]], // 7 [[5], [3], [3]], // 8 [[7], [6,9], [9]], // 9 [[7], [6], [ ]], // 10 [[4], [6], [6]], // 11 [[2], [4], [4]], // 12 [[6], [5,7], [7]], // 13 [[2], [1], [ ]], // 14 [[ ], [4], [4]], // 15 [[ ], [20], [20]], // 16 [[5], [4,8], [8]], // 17 [[2], [1], [ ]], // 18 [[6], [5], [ ]], // 19 [[2], [1], [ ]], // 20 [[1,3,7], [2,6], [ ]], // 21 [[2], [1], [ ]], // 22 [[4], [5], [5]], // 23 [[2], [3], [3]], // 24 [[22,26], [21,24], [ ]], // 25 [[5], [2], [ ]], // 26 [[11], [13,10], [13]], // 27 [[11], [9,12], [12]], // 28 [[ ], [ ], [ ]], // 29 [[ ], [ ], [ ]], // 30 [[ ], [9,10], [9,10]], // 31 [[ ], [3], [3]], // 32 [[ ], [2], [2]], // 33 [[ ], [ ], [ ]], // 34 [[ ], [4], [4]], // 35 [[19, 8], [18,20], [20]], // 36 [[ ], [ ], [ ]], // 37 [[ ], [ ], [ ]], // 38 [[ ], [ ], [ ]], // 39 [[4,6], [2,5], [ ]], // 40 [[ ], [ ], [ ]], // 41 [[ ], [ ], [ ]], // 42 [[ ], [ ], [ ]], // 43 [[ ], [ ], [ ]], // 44 [[5], [4,7], [7]], // 45 [[ ], [ ], [ ]], // 46 [[ ], [ ], [ ]], // 47 [[ ], [ ], [ ]], // 48 [[33,38], [32,36], [ ]], // 49 [[6], [2,7], [7]], // 50 [[ ], [ ], [ ]], // 51 [[ ], [1], [1]], // 52 [[ ], [ ], [ ]], // 53 [[ ], [ ], [ ]], // 54 [[6], [5], [ ]], // 55 [[6, 7], [2, 4], [ ]], // 56 [[ ], [1, 3], [1, 3]], // 57 [[ ], [ ], [ ]], // 58 [[ ], [ ], [ ]], // 59 [[5], [4], [ ]], // 60 [[ ], [ ], [ ]], // 61 [[ ], [ ], [ ]], // 62 [[4], [6, 3, 1], [6, 3]], // 63 [[ ], [64, 72], [64, 72]], // 64 [[2], [11, 1, 7, 5], [11, 7, 5]], // 65 [[ ], [5], [5]], // 66 [[ ], [ ], [ ]], // 67 [[3], [2], [ ]], // 68 [[ ], [ ], [ ]], // 69 [[ ], [ ], [ ]], // 70 [[ ], [ ], [ ]], // 71 [[ ], [ ], [ ]], // 72 [[ ], [14], [14]], // 73 [[ ], [ ], [ ]], // 74 [[ ], [ ], [ ]], // 75 [[ ], [ ], [ ]], // 76 [[ ], [2], [2]], // 77 [[2, 4], [1, 3], [ ]], // 78 [[ ], [ ], [ ]], // 79 [[ ], [ ], [ ]], // 80 [[145, 153], [144, 152], [ ]], // 81 [[ 8], [6], [ ]], // 82 [[ ], [ ], [ ]], // 83 [[3], [1], [ ]], // 84 [[4], [3], [ ]], // 85 [[ ], [ ], [ ]], // 86 [[ ], [ ], [ ]], // 87 [[ ], [ ], [ ]], // 88 [[ ], [ ], [ ]], // 89 [[ ], [ ], [ ]], // 90 [[6], [ 8, 5], [ 8]], // 91 [[ ], [ ], [ ]], // 92 [[ ], [ ], [ ]], // 93 [[ ], [ ], [ ]], // 94 [[ ], [ ], [ ]], // 95 [[ ], [ ], [ ]], // 96 [[ ], [ ], [ ]], // 97 [[ ], [ ], [ ]], // 98 [[ ], [ ], [ ]], // 99 [[36, 34, 32], [33, 35], [ ]], // 100 [[ ], [ ], [ ]], // 101 [[ ], [1], [1]], // 102 [[ ], [ ], [ ]], // 103 [[ ], [ ], [ ]], // 104 [[3, 9], [8, 7], [7]], // 105 [[ ], [ ], [ ]], // 106 [[ ], [ ], [ ]], // 107 [[ ], [ ], [ ]], // 108 [[ ], [ ], [ ]], // 109 [[ ], [ ], [ ]], // 110 [[ ], [ ], [ ]], // 111 [[ ], [8], [8]], // 112 [[ ], [ ], [ ]], // 113 [[ ], [ ], [ ]], // 114 [[ ], [ ], [ ]], // 115 [[ ], [ ], [ ]], // 116 [[ ], [1, 3], [1, 3]], // 117 [[ ], [ ], [ ]], // 118 [[ ], [2], [2]], // 119 [[10], [21, 4, 8, 13, 19, 18], [21, 4, 13, 19, 18]]]; // 120 [ [[ PrimitiveGroupDescription( i, n ) : n in k | #PrimitiveGroup(i,n)^12 gt Factorial(i)] : k in maxprim[i]] : i in [1..120]]; Output: Magma V2.10-6 Fri Jan 16 2004 08:49:13 on modular [Seed = 2699496298] ------------------------------------- [ [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [ AGL(1, 5) ], [ D(2*5) ], [] ], [ [ PGL(2, 5) ], [ PSL(2, 5) ], [] ], [ [ AGL(1, 7) ], [ L(3, 2) ], [ L(3, 2) ] ], [ [ PGL(2, 7) ], [ ASL(3, 2) ], [ ASL(3, 2) ] ], [ [ AGL(2, 3) ], [ 3^2:(2'A(4)), PGammaL(2, 8) ], [ PGammaL(2, 8) ] ], [ [ PGammaL(2, 9) ], [ M(10) ], [] ], [ [ AGL(1, 11) ], [ M(11) ], [ M(11) ] ], [ [ PGL(2, 11) ], [ M(12) ], [ M(12) ] ], [ [ AGL(1, 13) ], [ 13:6, L(3, 3) ], [ L(3, 3) ] ], [ [ PGL(2, 13) ], [ PSL(2, 13) ], [] ], [ [], [ PSL(4, 2) ], [ PSL(4, 2) ] ], [ [], [ 2^4.PSL(4, 2) ], [ 2^4.PSL(4, 2) ] ], [ [ AGL(1, 17) ], [ 17:8, L(2, 2^4):4 = PGammaL(2, 2^4) ], [ L(2, 2^4):4 = PGammaL(2, 2^4) ] ], [ [ PGL(2, 17) ], [ PSL(2, 17) ], [] ], [ [ AGL(1, 19) ], [ 19:9 ], [] ], [ [ PGL(2, 19) ], [ PSL(2, 19) ], [] ], [ [ PGL(2, 7), S(7), PGammaL(3, 4) ], [ A(7), PGL(3, 4) ], [] ], [ [ M(22):2 ], [ M(22) ], [] ], [ [ AGL(1, 23) ], [ M(23) ], [ M(23) ] ], [ [ PGL(2, 23) ], [ M(24) ], [ M(24) ] ], [ [ AGL(2, 5), (S(5) x S(5)):2 ], [ ASL(2, 5):2, (A(5) x A(5)):2^2 ], [] ], [ [ PGammaL(2, 25) ], [ PSigmaL(2, 25) ], [] ], [ [ AGL(3, 3) ], [ PSp(4, 3):2, ASL(3, 3) ], [ PSp(4, 3):2 ] ], [ [ PGammaL(2, 27) ], [ PSL(2, 27):3, PSp(6, 2) ], [ PSp(6, 2) ] ], [ [], [], [] ], [ [], [], [] ], [ [], [ L(3, 5), L(5, 2) ], [ L(3, 5), L(5, 2) ] ], [ [], [ ASL(5, 2) ], [ ASL(5, 2) ] ], [ [], [ PGammaL(2, 32) ], [ PGammaL(2, 32) ] ], [ [], [], [] ], [ [], [ S(8) ], [ S(8) ] ], [ [ S(9), (S(6) x S(6)):2 ], [ A(9), PSp(6, 2) ], [ PSp(6, 2) ] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [ PSp(4, 3):2, PGL(4, 3) ], [ PSp(4, 3), PSL(4, 3) ], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [ PSp(4, 3):2 ], [ S(10) ], [ S(10) ] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [ (S(7) x S(7)):2 ], [ (A(7) x A(7)):2^2 ], [] ], [ [], [ PSU(3, 5):2 ], [ PSU(3, 5):2 ] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [ Sym(11) ], [ Alt(11) ], [] ], [ [], [], [] ], [ [], [ PSL(3, 7).3 ], [ PSL(3, 7).3 ] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [ PSL(6, 2) ], [ PSL(6, 2) ] ], [ [], [ AGL(6, 2), Sym(8) wreath Sym(2) ], [ AGL(6, 2), Sym(8) wreath Sym(2) ] ], [ [], [], [] ], [ [], [ Sym(12) ], [ Sym(12) ] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [ Sym(13) ], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [ Sym(9) \wreath Sym(2) ], [ Alt(9)^2.2^2 ], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [ Sym(10) \wreath Sym(2) ], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ] ] Total time: 3.259 seconds, Total memory usage: 2.20MB ************** MAGMA ***************** Host ibm21.ilab.sztaki.hu. (195.111.1.97) Time: Fri Jan 16 08:58:29 2004 Input: maxprim:=[ [[ ], [ ], [ ]], // 1 [[ ], [ ], [ ]], // 2 [[ ], [ ], [ ]], // 3 [[ ], [ ], [ ]], // 4 [[3], [2], [ ]], // 5 [[2], [1], [ ]], // 6 [[4], [5], [5]], // 7 [[5], [3], [3]], // 8 [[7], [6,9], [9]], // 9 [[7], [6], [ ]], // 10 [[4], [6], [6]], // 11 [[2], [4], [4]], // 12 [[6], [5,7], [7]], // 13 [[2], [1], [ ]], // 14 [[ ], [4], [4]], // 15 [[ ], [20], [20]], // 16 [[5], [4,8], [8]], // 17 [[2], [1], [ ]], // 18 [[6], [5], [ ]], // 19 [[2], [1], [ ]], // 20 [[1,3,7], [2,6], [ ]], // 21 [[2], [1], [ ]], // 22 [[4], [5], [5]], // 23 [[2], [3], [3]], // 24 [[22,26], [21,24], [ ]], // 25 [[5], [2], [ ]], // 26 [[11], [13,10], [13]], // 27 [[11], [9,12], [12]], // 28 [[ ], [ ], [ ]], // 29 [[ ], [ ], [ ]], // 30 [[ ], [9,10], [9,10]], // 31 [[ ], [3], [3]], // 32 [[ ], [2], [2]], // 33 [[ ], [ ], [ ]], // 34 [[ ], [4], [4]], // 35 [[19, 8], [18,20], [20]], // 36 [[ ], [ ], [ ]], // 37 [[ ], [ ], [ ]], // 38 [[ ], [ ], [ ]], // 39 [[4,6], [2,5], [ ]], // 40 [[ ], [ ], [ ]], // 41 [[ ], [ ], [ ]], // 42 [[ ], [ ], [ ]], // 43 [[ ], [ ], [ ]], // 44 [[5], [4,7], [7]], // 45 [[ ], [ ], [ ]], // 46 [[ ], [ ], [ ]], // 47 [[ ], [ ], [ ]], // 48 [[33,38], [32,36], [ ]], // 49 [[6], [2,7], [7]], // 50 [[ ], [ ], [ ]], // 51 [[ ], [1], [1]], // 52 [[ ], [ ], [ ]], // 53 [[ ], [ ], [ ]], // 54 [[6], [5], [ ]], // 55 [[6, 7], [2, 4], [ ]], // 56 [[ ], [1, 3], [1, 3]], // 57 [[ ], [ ], [ ]], // 58 [[ ], [ ], [ ]], // 59 [[5], [4], [ ]], // 60 [[ ], [ ], [ ]], // 61 [[ ], [ ], [ ]], // 62 [[4], [6, 3, 1], [6, 3]], // 63 [[ ], [64, 72], [64, 72]], // 64 [[2], [11, 1, 7, 5], [11, 7, 5]], // 65 [[ ], [5], [5]], // 66 [[ ], [ ], [ ]], // 67 [[3], [2], [ ]], // 68 [[ ], [ ], [ ]], // 69 [[ ], [ ], [ ]], // 70 [[ ], [ ], [ ]], // 71 [[ ], [ ], [ ]], // 72 [[ ], [14], [14]], // 73 [[ ], [ ], [ ]], // 74 [[ ], [ ], [ ]], // 75 [[ ], [ ], [ ]], // 76 [[ ], [2], [2]], // 77 [[2, 4], [1, 3], [ ]], // 78 [[ ], [ ], [ ]], // 79 [[ ], [ ], [ ]], // 80 [[145, 153], [144, 152], [ ]], // 81 [[ 8], [6], [ ]], // 82 [[ ], [ ], [ ]], // 83 [[3], [1], [ ]], // 84 [[4], [3], [ ]], // 85 [[ ], [ ], [ ]], // 86 [[ ], [ ], [ ]], // 87 [[ ], [ ], [ ]], // 88 [[ ], [ ], [ ]], // 89 [[ ], [ ], [ ]], // 90 [[6], [ 8, 5], [ 8]], // 91 [[ ], [ ], [ ]], // 92 [[ ], [ ], [ ]], // 93 [[ ], [ ], [ ]], // 94 [[ ], [ ], [ ]], // 95 [[ ], [ ], [ ]], // 96 [[ ], [ ], [ ]], // 97 [[ ], [ ], [ ]], // 98 [[ ], [ ], [ ]], // 99 [[36, 34, 32], [33, 35], [ ]], // 100 [[ ], [ ], [ ]], // 101 [[ ], [1], [1]], // 102 [[ ], [ ], [ ]], // 103 [[ ], [ ], [ ]], // 104 [[3, 9], [8, 7], [7]], // 105 [[ ], [ ], [ ]], // 106 [[ ], [ ], [ ]], // 107 [[ ], [ ], [ ]], // 108 [[ ], [ ], [ ]], // 109 [[ ], [ ], [ ]], // 110 [[ ], [ ], [ ]], // 111 [[ ], [8], [8]], // 112 [[ ], [ ], [ ]], // 113 [[ ], [ ], [ ]], // 114 [[ ], [ ], [ ]], // 115 [[ ], [ ], [ ]], // 116 [[ ], [1, 3], [1, 3]], // 117 [[ ], [ ], [ ]], // 118 [[ ], [2], [2]], // 119 [[10], [21, 4, 8, 13, 19, 18], [21, 4, 13, 19, 18]]]; // 120 [ [[ PrimitiveGroupDescription( i, n ) : n in k | #PrimitiveGroup(i,n)^12 ge Factorial(i)/2] : k in maxprim[i]] : i in [1..120]]; Output: Magma V2.10-6 Fri Jan 16 2004 08:58:26 on modular [Seed = 3651041224] ------------------------------------- [ [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [ AGL(1, 5) ], [ D(2*5) ], [] ], [ [ PGL(2, 5) ], [ PSL(2, 5) ], [] ], [ [ AGL(1, 7) ], [ L(3, 2) ], [ L(3, 2) ] ], [ [ PGL(2, 7) ], [ ASL(3, 2) ], [ ASL(3, 2) ] ], [ [ AGL(2, 3) ], [ 3^2:(2'A(4)), PGammaL(2, 8) ], [ PGammaL(2, 8) ] ], [ [ PGammaL(2, 9) ], [ M(10) ], [] ], [ [ AGL(1, 11) ], [ M(11) ], [ M(11) ] ], [ [ PGL(2, 11) ], [ M(12) ], [ M(12) ] ], [ [ AGL(1, 13) ], [ 13:6, L(3, 3) ], [ L(3, 3) ] ], [ [ PGL(2, 13) ], [ PSL(2, 13) ], [] ], [ [], [ PSL(4, 2) ], [ PSL(4, 2) ] ], [ [], [ 2^4.PSL(4, 2) ], [ 2^4.PSL(4, 2) ] ], [ [ AGL(1, 17) ], [ 17:8, L(2, 2^4):4 = PGammaL(2, 2^4) ], [ L(2, 2^4):4 = PGammaL(2, 2^4) ] ], [ [ PGL(2, 17) ], [ PSL(2, 17) ], [] ], [ [ AGL(1, 19) ], [ 19:9 ], [] ], [ [ PGL(2, 19) ], [ PSL(2, 19) ], [] ], [ [ PGL(2, 7), S(7), PGammaL(3, 4) ], [ A(7), PGL(3, 4) ], [] ], [ [ M(22):2 ], [ M(22) ], [] ], [ [ AGL(1, 23) ], [ M(23) ], [ M(23) ] ], [ [ PGL(2, 23) ], [ M(24) ], [ M(24) ] ], [ [ AGL(2, 5), (S(5) x S(5)):2 ], [ ASL(2, 5):2, (A(5) x A(5)):2^2 ], [] ], [ [ PGammaL(2, 25) ], [ PSigmaL(2, 25) ], [] ], [ [ AGL(3, 3) ], [ PSp(4, 3):2, ASL(3, 3) ], [ PSp(4, 3):2 ] ], [ [ PGammaL(2, 27) ], [ PSL(2, 27):3, PSp(6, 2) ], [ PSp(6, 2) ] ], [ [], [], [] ], [ [], [], [] ], [ [], [ L(3, 5), L(5, 2) ], [ L(3, 5), L(5, 2) ] ], [ [], [ ASL(5, 2) ], [ ASL(5, 2) ] ], [ [], [ PGammaL(2, 32) ], [ PGammaL(2, 32) ] ], [ [], [], [] ], [ [], [ S(8) ], [ S(8) ] ], [ [ S(9), (S(6) x S(6)):2 ], [ A(9), PSp(6, 2) ], [ PSp(6, 2) ] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [ PSp(4, 3):2, PGL(4, 3) ], [ PSp(4, 3), PSL(4, 3) ], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [ PSp(4, 3):2 ], [ S(10) ], [ S(10) ] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [ (S(7) x S(7)):2 ], [ (A(7) x A(7)):2^2 ], [] ], [ [ PGammaL(2, 49) ], [ PSU(3, 5):2 ], [ PSU(3, 5):2 ] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [ Sym(11) ], [ Alt(11) ], [] ], [ [], [], [] ], [ [], [ PSL(3, 7).3 ], [ PSL(3, 7).3 ] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [ PSL(6, 2) ], [ PSL(6, 2) ] ], [ [], [ AGL(6, 2), Sym(8) wreath Sym(2) ], [ AGL(6, 2), Sym(8) wreath Sym(2) ] ], [ [], [], [] ], [ [], [ Sym(12) ], [ Sym(12) ] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [ Sym(13) ], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [ Sym(9) \wreath Sym(2) ], [ Alt(9)^2.2^2 ], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [ Sym(10) \wreath Sym(2) ], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ] ] Total time: 3.249 seconds, Total memory usage: 2.20MB ************** MAGMA ***************** Host ibm21.ilab.sztaki.hu. (195.111.1.97) Time: Fri Jan 16 08:59:31 2004 Input: maxprim:=[ [[ ], [ ], [ ]], // 1 [[ ], [ ], [ ]], // 2 [[ ], [ ], [ ]], // 3 [[ ], [ ], [ ]], // 4 [[3], [2], [ ]], // 5 [[2], [1], [ ]], // 6 [[4], [5], [5]], // 7 [[5], [3], [3]], // 8 [[7], [6,9], [9]], // 9 [[7], [6], [ ]], // 10 [[4], [6], [6]], // 11 [[2], [4], [4]], // 12 [[6], [5,7], [7]], // 13 [[2], [1], [ ]], // 14 [[ ], [4], [4]], // 15 [[ ], [20], [20]], // 16 [[5], [4,8], [8]], // 17 [[2], [1], [ ]], // 18 [[6], [5], [ ]], // 19 [[2], [1], [ ]], // 20 [[1,3,7], [2,6], [ ]], // 21 [[2], [1], [ ]], // 22 [[4], [5], [5]], // 23 [[2], [3], [3]], // 24 [[22,26], [21,24], [ ]], // 25 [[5], [2], [ ]], // 26 [[11], [13,10], [13]], // 27 [[11], [9,12], [12]], // 28 [[ ], [ ], [ ]], // 29 [[ ], [ ], [ ]], // 30 [[ ], [9,10], [9,10]], // 31 [[ ], [3], [3]], // 32 [[ ], [2], [2]], // 33 [[ ], [ ], [ ]], // 34 [[ ], [4], [4]], // 35 [[19, 8], [18,20], [20]], // 36 [[ ], [ ], [ ]], // 37 [[ ], [ ], [ ]], // 38 [[ ], [ ], [ ]], // 39 [[4,6], [2,5], [ ]], // 40 [[ ], [ ], [ ]], // 41 [[ ], [ ], [ ]], // 42 [[ ], [ ], [ ]], // 43 [[ ], [ ], [ ]], // 44 [[5], [4,7], [7]], // 45 [[ ], [ ], [ ]], // 46 [[ ], [ ], [ ]], // 47 [[ ], [ ], [ ]], // 48 [[33,38], [32,36], [ ]], // 49 [[6], [2,7], [7]], // 50 [[ ], [ ], [ ]], // 51 [[ ], [1], [1]], // 52 [[ ], [ ], [ ]], // 53 [[ ], [ ], [ ]], // 54 [[6], [5], [ ]], // 55 [[6, 7], [2, 4], [ ]], // 56 [[ ], [1, 3], [1, 3]], // 57 [[ ], [ ], [ ]], // 58 [[ ], [ ], [ ]], // 59 [[5], [4], [ ]], // 60 [[ ], [ ], [ ]], // 61 [[ ], [ ], [ ]], // 62 [[4], [6, 3, 1], [6, 3]], // 63 [[ ], [64, 72], [64, 72]], // 64 [[2], [11, 1, 7, 5], [11, 7, 5]], // 65 [[ ], [5], [5]], // 66 [[ ], [ ], [ ]], // 67 [[3], [2], [ ]], // 68 [[ ], [ ], [ ]], // 69 [[ ], [ ], [ ]], // 70 [[ ], [ ], [ ]], // 71 [[ ], [ ], [ ]], // 72 [[ ], [14], [14]], // 73 [[ ], [ ], [ ]], // 74 [[ ], [ ], [ ]], // 75 [[ ], [ ], [ ]], // 76 [[ ], [2], [2]], // 77 [[2, 4], [1, 3], [ ]], // 78 [[ ], [ ], [ ]], // 79 [[ ], [ ], [ ]], // 80 [[145, 153], [144, 152], [ ]], // 81 [[ 8], [6], [ ]], // 82 [[ ], [ ], [ ]], // 83 [[3], [1], [ ]], // 84 [[4], [3], [ ]], // 85 [[ ], [ ], [ ]], // 86 [[ ], [ ], [ ]], // 87 [[ ], [ ], [ ]], // 88 [[ ], [ ], [ ]], // 89 [[ ], [ ], [ ]], // 90 [[6], [ 8, 5], [ 8]], // 91 [[ ], [ ], [ ]], // 92 [[ ], [ ], [ ]], // 93 [[ ], [ ], [ ]], // 94 [[ ], [ ], [ ]], // 95 [[ ], [ ], [ ]], // 96 [[ ], [ ], [ ]], // 97 [[ ], [ ], [ ]], // 98 [[ ], [ ], [ ]], // 99 [[36, 34, 32], [33, 35], [ ]], // 100 [[ ], [ ], [ ]], // 101 [[ ], [1], [1]], // 102 [[ ], [ ], [ ]], // 103 [[ ], [ ], [ ]], // 104 [[3, 9], [8, 7], [7]], // 105 [[ ], [ ], [ ]], // 106 [[ ], [ ], [ ]], // 107 [[ ], [ ], [ ]], // 108 [[ ], [ ], [ ]], // 109 [[ ], [ ], [ ]], // 110 [[ ], [ ], [ ]], // 111 [[ ], [8], [8]], // 112 [[ ], [ ], [ ]], // 113 [[ ], [ ], [ ]], // 114 [[ ], [ ], [ ]], // 115 [[ ], [ ], [ ]], // 116 [[ ], [1, 3], [1, 3]], // 117 [[ ], [ ], [ ]], // 118 [[ ], [2], [2]], // 119 [[10], [21, 4, 8, 13, 19, 18], [21, 4, 13, 19, 18]]]; // 120 l1 := [ [[ PrimitiveGroupDescription( i, n ) : n in k | #PrimitiveGroup(i,n)^12 gt Factorial(i)] : k in maxprim[i]] : i in [1..120]]; l2 := [ [[ PrimitiveGroupDescription( i, n ) : n in k | #PrimitiveGroup(i,n)^12 ge Factorial(i)/2] : k in maxprim[i]] : i in [1..120]]; l1 = l2; Output: Magma V2.10-6 Fri Jan 16 2004 08:59:27 on modular [Seed = 3230101139] ------------------------------------- [ [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [ AGL(1, 5) ], [ D(2*5) ], [] ], [ [ PGL(2, 5) ], [ PSL(2, 5) ], [] ], [ [ AGL(1, 7) ], [ L(3, 2) ], [ L(3, 2) ] ], [ [ PGL(2, 7) ], [ ASL(3, 2) ], [ ASL(3, 2) ] ], [ [ AGL(2, 3) ], [ 3^2:(2'A(4)), PGammaL(2, 8) ], [ PGammaL(2, 8) ] ], [ [ PGammaL(2, 9) ], [ M(10) ], [] ], [ [ AGL(1, 11) ], [ M(11) ], [ M(11) ] ], [ [ PGL(2, 11) ], [ M(12) ], [ M(12) ] ], [ [ AGL(1, 13) ], [ 13:6, L(3, 3) ], [ L(3, 3) ] ], [ [ PGL(2, 13) ], [ PSL(2, 13) ], [] ], [ [], [ PSL(4, 2) ], [ PSL(4, 2) ] ], [ [], [ 2^4.PSL(4, 2) ], [ 2^4.PSL(4, 2) ] ], [ [ AGL(1, 17) ], [ 17:8, L(2, 2^4):4 = PGammaL(2, 2^4) ], [ L(2, 2^4):4 = PGammaL(2, 2^4) ] ], [ [ PGL(2, 17) ], [ PSL(2, 17) ], [] ], [ [ AGL(1, 19) ], [ 19:9 ], [] ], [ [ PGL(2, 19) ], [ PSL(2, 19) ], [] ], [ [ PGL(2, 7), S(7), PGammaL(3, 4) ], [ A(7), PGL(3, 4) ], [] ], [ [ M(22):2 ], [ M(22) ], [] ], [ [ AGL(1, 23) ], [ M(23) ], [ M(23) ] ], [ [ PGL(2, 23) ], [ M(24) ], [ M(24) ] ], [ [ AGL(2, 5), (S(5) x S(5)):2 ], [ ASL(2, 5):2, (A(5) x A(5)):2^2 ], [] ], [ [ PGammaL(2, 25) ], [ PSigmaL(2, 25) ], [] ], [ [ AGL(3, 3) ], [ PSp(4, 3):2, ASL(3, 3) ], [ PSp(4, 3):2 ] ], [ [ PGammaL(2, 27) ], [ PSL(2, 27):3, PSp(6, 2) ], [ PSp(6, 2) ] ], [ [], [], [] ], [ [], [], [] ], [ [], [ L(3, 5), L(5, 2) ], [ L(3, 5), L(5, 2) ] ], [ [], [ ASL(5, 2) ], [ ASL(5, 2) ] ], [ [], [ PGammaL(2, 32) ], [ PGammaL(2, 32) ] ], [ [], [], [] ], [ [], [ S(8) ], [ S(8) ] ], [ [ S(9), (S(6) x S(6)):2 ], [ A(9), PSp(6, 2) ], [ PSp(6, 2) ] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [ PSp(4, 3):2, PGL(4, 3) ], [ PSp(4, 3), PSL(4, 3) ], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [ PSp(4, 3):2 ], [ S(10) ], [ S(10) ] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [ (S(7) x S(7)):2 ], [ (A(7) x A(7)):2^2 ], [] ], [ [], [ PSU(3, 5):2 ], [ PSU(3, 5):2 ] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [ Sym(11) ], [ Alt(11) ], [] ], [ [], [], [] ], [ [], [ PSL(3, 7).3 ], [ PSL(3, 7).3 ] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [ PSL(6, 2) ], [ PSL(6, 2) ] ], [ [], [ AGL(6, 2), Sym(8) wreath Sym(2) ], [ AGL(6, 2), Sym(8) wreath Sym(2) ] ], [ [], [], [] ], [ [], [ Sym(12) ], [ Sym(12) ] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [ Sym(13) ], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [ Sym(9) \wreath Sym(2) ], [ Alt(9)^2.2^2 ], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [ Sym(10) \wreath Sym(2) ], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ] ] = [ [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [ AGL(1, 5) ], [ D(2*5) ], [] ], [ [ PGL(2, 5) ], [ PSL(2, 5) ], [] ], [ [ AGL(1, 7) ], [ L(3, 2) ], [ L(3, 2) ] ], [ [ PGL(2, 7) ], [ ASL(3, 2) ], [ ASL(3, 2) ] ], [ [ AGL(2, 3) ], [ 3^2:(2'A(4)), PGammaL(2, 8) ], [ PGammaL(2, 8) ] ], [ [ PGammaL(2, 9) ], [ M(10) ], [] ], [ [ AGL(1, 11) ], [ M(11) ], [ M(11) ] ], [ [ PGL(2, 11) ], [ M(12) ], [ M(12) ] ], [ [ AGL(1, 13) ], [ 13:6, L(3, 3) ], [ L(3, 3) ] ], [ [ PGL(2, 13) ], [ PSL(2, 13) ], [] ], [ [], [ PSL(4, 2) ], [ PSL(4, 2) ] ], [ [], [ 2^4.PSL(4, 2) ], [ 2^4.PSL(4, 2) ] ], [ [ AGL(1, 17) ], [ 17:8, L(2, 2^4):4 = PGammaL(2, 2^4) ], [ L(2, 2^4):4 = PGammaL(2, 2^4) ] ], [ [ PGL(2, 17) ], [ PSL(2, 17) ], [] ], [ [ AGL(1, 19) ], [ 19:9 ], [] ], [ [ PGL(2, 19) ], [ PSL(2, 19) ], [] ], [ [ PGL(2, 7), S(7), PGammaL(3, 4) ], [ A(7), PGL(3, 4) ], [] ], [ [ M(22):2 ], [ M(22) ], [] ], [ [ AGL(1, 23) ], [ M(23) ], [ M(23) ] ], [ [ PGL(2, 23) ], [ M(24) ], [ M(24) ] ], [ [ AGL(2, 5), (S(5) x S(5)):2 ], [ ASL(2, 5):2, (A(5) x A(5)):2^2 ], [] ], [ [ PGammaL(2, 25) ], [ PSigmaL(2, 25) ], [] ], [ [ AGL(3, 3) ], [ PSp(4, 3):2, ASL(3, 3) ], [ PSp(4, 3):2 ] ], [ [ PGammaL(2, 27) ], [ PSL(2, 27):3, PSp(6, 2) ], [ PSp(6, 2) ] ], [ [], [], [] ], [ [], [], [] ], [ [], [ L(3, 5), L(5, 2) ], [ L(3, 5), L(5, 2) ] ], [ [], [ ASL(5, 2) ], [ ASL(5, 2) ] ], [ [], [ PGammaL(2, 32) ], [ PGammaL(2, 32) ] ], [ [], [], [] ], [ [], [ S(8) ], [ S(8) ] ], [ [ S(9), (S(6) x S(6)):2 ], [ A(9), PSp(6, 2) ], [ PSp(6, 2) ] ], [ [], [], [] ], [ [], [], [] ], [ [], [], ** WARNING: Output too long, hence truncated. ************** MAGMA ***************** Host ibm21.ilab.sztaki.hu. (195.111.1.97) Time: Fri Jan 16 08:59:53 2004 Input: maxprim:=[ [[ ], [ ], [ ]], // 1 [[ ], [ ], [ ]], // 2 [[ ], [ ], [ ]], // 3 [[ ], [ ], [ ]], // 4 [[3], [2], [ ]], // 5 [[2], [1], [ ]], // 6 [[4], [5], [5]], // 7 [[5], [3], [3]], // 8 [[7], [6,9], [9]], // 9 [[7], [6], [ ]], // 10 [[4], [6], [6]], // 11 [[2], [4], [4]], // 12 [[6], [5,7], [7]], // 13 [[2], [1], [ ]], // 14 [[ ], [4], [4]], // 15 [[ ], [20], [20]], // 16 [[5], [4,8], [8]], // 17 [[2], [1], [ ]], // 18 [[6], [5], [ ]], // 19 [[2], [1], [ ]], // 20 [[1,3,7], [2,6], [ ]], // 21 [[2], [1], [ ]], // 22 [[4], [5], [5]], // 23 [[2], [3], [3]], // 24 [[22,26], [21,24], [ ]], // 25 [[5], [2], [ ]], // 26 [[11], [13,10], [13]], // 27 [[11], [9,12], [12]], // 28 [[ ], [ ], [ ]], // 29 [[ ], [ ], [ ]], // 30 [[ ], [9,10], [9,10]], // 31 [[ ], [3], [3]], // 32 [[ ], [2], [2]], // 33 [[ ], [ ], [ ]], // 34 [[ ], [4], [4]], // 35 [[19, 8], [18,20], [20]], // 36 [[ ], [ ], [ ]], // 37 [[ ], [ ], [ ]], // 38 [[ ], [ ], [ ]], // 39 [[4,6], [2,5], [ ]], // 40 [[ ], [ ], [ ]], // 41 [[ ], [ ], [ ]], // 42 [[ ], [ ], [ ]], // 43 [[ ], [ ], [ ]], // 44 [[5], [4,7], [7]], // 45 [[ ], [ ], [ ]], // 46 [[ ], [ ], [ ]], // 47 [[ ], [ ], [ ]], // 48 [[33,38], [32,36], [ ]], // 49 [[6], [2,7], [7]], // 50 [[ ], [ ], [ ]], // 51 [[ ], [1], [1]], // 52 [[ ], [ ], [ ]], // 53 [[ ], [ ], [ ]], // 54 [[6], [5], [ ]], // 55 [[6, 7], [2, 4], [ ]], // 56 [[ ], [1, 3], [1, 3]], // 57 [[ ], [ ], [ ]], // 58 [[ ], [ ], [ ]], // 59 [[5], [4], [ ]], // 60 [[ ], [ ], [ ]], // 61 [[ ], [ ], [ ]], // 62 [[4], [6, 3, 1], [6, 3]], // 63 [[ ], [64, 72], [64, 72]], // 64 [[2], [11, 1, 7, 5], [11, 7, 5]], // 65 [[ ], [5], [5]], // 66 [[ ], [ ], [ ]], // 67 [[3], [2], [ ]], // 68 [[ ], [ ], [ ]], // 69 [[ ], [ ], [ ]], // 70 [[ ], [ ], [ ]], // 71 [[ ], [ ], [ ]], // 72 [[ ], [14], [14]], // 73 [[ ], [ ], [ ]], // 74 [[ ], [ ], [ ]], // 75 [[ ], [ ], [ ]], // 76 [[ ], [2], [2]], // 77 [[2, 4], [1, 3], [ ]], // 78 [[ ], [ ], [ ]], // 79 [[ ], [ ], [ ]], // 80 [[145, 153], [144, 152], [ ]], // 81 [[ 8], [6], [ ]], // 82 [[ ], [ ], [ ]], // 83 [[3], [1], [ ]], // 84 [[4], [3], [ ]], // 85 [[ ], [ ], [ ]], // 86 [[ ], [ ], [ ]], // 87 [[ ], [ ], [ ]], // 88 [[ ], [ ], [ ]], // 89 [[ ], [ ], [ ]], // 90 [[6], [ 8, 5], [ 8]], // 91 [[ ], [ ], [ ]], // 92 [[ ], [ ], [ ]], // 93 [[ ], [ ], [ ]], // 94 [[ ], [ ], [ ]], // 95 [[ ], [ ], [ ]], // 96 [[ ], [ ], [ ]], // 97 [[ ], [ ], [ ]], // 98 [[ ], [ ], [ ]], // 99 [[36, 34, 32], [33, 35], [ ]], // 100 [[ ], [ ], [ ]], // 101 [[ ], [1], [1]], // 102 [[ ], [ ], [ ]], // 103 [[ ], [ ], [ ]], // 104 [[3, 9], [8, 7], [7]], // 105 [[ ], [ ], [ ]], // 106 [[ ], [ ], [ ]], // 107 [[ ], [ ], [ ]], // 108 [[ ], [ ], [ ]], // 109 [[ ], [ ], [ ]], // 110 [[ ], [ ], [ ]], // 111 [[ ], [8], [8]], // 112 [[ ], [ ], [ ]], // 113 [[ ], [ ], [ ]], // 114 [[ ], [ ], [ ]], // 115 [[ ], [ ], [ ]], // 116 [[ ], [1, 3], [1, 3]], // 117 [[ ], [ ], [ ]], // 118 [[ ], [2], [2]], // 119 [[10], [21, 4, 8, 13, 19, 18], [21, 4, 13, 19, 18]]]; // 120 l1 := [ [[ PrimitiveGroupDescription( i, n ) : n in k | #PrimitiveGroup(i,n)^12 gt Factorial(i)] : k in maxprim[i]] : i in [1..120]]; l2 := [ [[ PrimitiveGroupDescription( i, n ) : n in k | #PrimitiveGroup(i,n)^12 ge Factorial(i)/2] : k in maxprim[i]] : i in [1..120]]; l1 eq l2; Output: Magma V2.10-6 Fri Jan 16 2004 08:59:50 on modular [Seed = 3465109643] ------------------------------------- false Total time: 3.349 seconds, Total memory usage: 2.27MB ************** MAGMA ***************** Host ibm21.ilab.sztaki.hu. (195.111.1.97) Time: Fri Jan 16 09:00:41 2004 Input: maxprim:=[ [[ ], [ ], [ ]], // 1 [[ ], [ ], [ ]], // 2 [[ ], [ ], [ ]], // 3 [[ ], [ ], [ ]], // 4 [[3], [2], [ ]], // 5 [[2], [1], [ ]], // 6 [[4], [5], [5]], // 7 [[5], [3], [3]], // 8 [[7], [6,9], [9]], // 9 [[7], [6], [ ]], // 10 [[4], [6], [6]], // 11 [[2], [4], [4]], // 12 [[6], [5,7], [7]], // 13 [[2], [1], [ ]], // 14 [[ ], [4], [4]], // 15 [[ ], [20], [20]], // 16 [[5], [4,8], [8]], // 17 [[2], [1], [ ]], // 18 [[6], [5], [ ]], // 19 [[2], [1], [ ]], // 20 [[1,3,7], [2,6], [ ]], // 21 [[2], [1], [ ]], // 22 [[4], [5], [5]], // 23 [[2], [3], [3]], // 24 [[22,26], [21,24], [ ]], // 25 [[5], [2], [ ]], // 26 [[11], [13,10], [13]], // 27 [[11], [9,12], [12]], // 28 [[ ], [ ], [ ]], // 29 [[ ], [ ], [ ]], // 30 [[ ], [9,10], [9,10]], // 31 [[ ], [3], [3]], // 32 [[ ], [2], [2]], // 33 [[ ], [ ], [ ]], // 34 [[ ], [4], [4]], // 35 [[19, 8], [18,20], [20]], // 36 [[ ], [ ], [ ]], // 37 [[ ], [ ], [ ]], // 38 [[ ], [ ], [ ]], // 39 [[4,6], [2,5], [ ]], // 40 [[ ], [ ], [ ]], // 41 [[ ], [ ], [ ]], // 42 [[ ], [ ], [ ]], // 43 [[ ], [ ], [ ]], // 44 [[5], [4,7], [7]], // 45 [[ ], [ ], [ ]], // 46 [[ ], [ ], [ ]], // 47 [[ ], [ ], [ ]], // 48 [[33,38], [32,36], [ ]], // 49 [[6], [2,7], [7]], // 50 [[ ], [ ], [ ]], // 51 [[ ], [1], [1]], // 52 [[ ], [ ], [ ]], // 53 [[ ], [ ], [ ]], // 54 [[6], [5], [ ]], // 55 [[6, 7], [2, 4], [ ]], // 56 [[ ], [1, 3], [1, 3]], // 57 [[ ], [ ], [ ]], // 58 [[ ], [ ], [ ]], // 59 [[5], [4], [ ]], // 60 [[ ], [ ], [ ]], // 61 [[ ], [ ], [ ]], // 62 [[4], [6, 3, 1], [6, 3]], // 63 [[ ], [64, 72], [64, 72]], // 64 [[2], [11, 1, 7, 5], [11, 7, 5]], // 65 [[ ], [5], [5]], // 66 [[ ], [ ], [ ]], // 67 [[3], [2], [ ]], // 68 [[ ], [ ], [ ]], // 69 [[ ], [ ], [ ]], // 70 [[ ], [ ], [ ]], // 71 [[ ], [ ], [ ]], // 72 [[ ], [14], [14]], // 73 [[ ], [ ], [ ]], // 74 [[ ], [ ], [ ]], // 75 [[ ], [ ], [ ]], // 76 [[ ], [2], [2]], // 77 [[2, 4], [1, 3], [ ]], // 78 [[ ], [ ], [ ]], // 79 [[ ], [ ], [ ]], // 80 [[145, 153], [144, 152], [ ]], // 81 [[ 8], [6], [ ]], // 82 [[ ], [ ], [ ]], // 83 [[3], [1], [ ]], // 84 [[4], [3], [ ]], // 85 [[ ], [ ], [ ]], // 86 [[ ], [ ], [ ]], // 87 [[ ], [ ], [ ]], // 88 [[ ], [ ], [ ]], // 89 [[ ], [ ], [ ]], // 90 [[6], [ 8, 5], [ 8]], // 91 [[ ], [ ], [ ]], // 92 [[ ], [ ], [ ]], // 93 [[ ], [ ], [ ]], // 94 [[ ], [ ], [ ]], // 95 [[ ], [ ], [ ]], // 96 [[ ], [ ], [ ]], // 97 [[ ], [ ], [ ]], // 98 [[ ], [ ], [ ]], // 99 [[36, 34, 32], [33, 35], [ ]], // 100 [[ ], [ ], [ ]], // 101 [[ ], [1], [1]], // 102 [[ ], [ ], [ ]], // 103 [[ ], [ ], [ ]], // 104 [[3, 9], [8, 7], [7]], // 105 [[ ], [ ], [ ]], // 106 [[ ], [ ], [ ]], // 107 [[ ], [ ], [ ]], // 108 [[ ], [ ], [ ]], // 109 [[ ], [ ], [ ]], // 110 [[ ], [ ], [ ]], // 111 [[ ], [8], [8]], // 112 [[ ], [ ], [ ]], // 113 [[ ], [ ], [ ]], // 114 [[ ], [ ], [ ]], // 115 [[ ], [ ], [ ]], // 116 [[ ], [1, 3], [1, 3]], // 117 [[ ], [ ], [ ]], // 118 [[ ], [2], [2]], // 119 [[10], [21, 4, 8, 13, 19, 18], [21, 4, 13, 19, 18]]]; // 120 l1 := [ [[ PrimitiveGroupDescription( i, n ) : n in k | #PrimitiveGroup(i,n)^12 gt Factorial(i)] : k in maxprim[i]] : i in [1..120]]; l2 := [ [[ PrimitiveGroupDescription( i, n ) : n in k | #PrimitiveGroup(i,n)^12 ge Factorial(i)/2] : k in maxprim[i]] : i in [1..120]]; [ i : i in [1.120] | l1[i] ne l2[i]]; Output: Magma V2.10-6 Fri Jan 16 2004 09:00:38 on modular [Seed = 4240134761] ------------------------------------- >> [ i : i in [1.120] | l1[i] ne l2[i]];; ^ Runtime error in '[]': Bad argument types Total time: 3.459 seconds, Total memory usage: 2.27MB ************** MAGMA ***************** Host ibm21.ilab.sztaki.hu. (195.111.1.97) Time: Fri Jan 16 09:01:37 2004 Input: maxprim:=[ [[ ], [ ], [ ]], // 1 [[ ], [ ], [ ]], // 2 [[ ], [ ], [ ]], // 3 [[ ], [ ], [ ]], // 4 [[3], [2], [ ]], // 5 [[2], [1], [ ]], // 6 [[4], [5], [5]], // 7 [[5], [3], [3]], // 8 [[7], [6,9], [9]], // 9 [[7], [6], [ ]], // 10 [[4], [6], [6]], // 11 [[2], [4], [4]], // 12 [[6], [5,7], [7]], // 13 [[2], [1], [ ]], // 14 [[ ], [4], [4]], // 15 [[ ], [20], [20]], // 16 [[5], [4,8], [8]], // 17 [[2], [1], [ ]], // 18 [[6], [5], [ ]], // 19 [[2], [1], [ ]], // 20 [[1,3,7], [2,6], [ ]], // 21 [[2], [1], [ ]], // 22 [[4], [5], [5]], // 23 [[2], [3], [3]], // 24 [[22,26], [21,24], [ ]], // 25 [[5], [2], [ ]], // 26 [[11], [13,10], [13]], // 27 [[11], [9,12], [12]], // 28 [[ ], [ ], [ ]], // 29 [[ ], [ ], [ ]], // 30 [[ ], [9,10], [9,10]], // 31 [[ ], [3], [3]], // 32 [[ ], [2], [2]], // 33 [[ ], [ ], [ ]], // 34 [[ ], [4], [4]], // 35 [[19, 8], [18,20], [20]], // 36 [[ ], [ ], [ ]], // 37 [[ ], [ ], [ ]], // 38 [[ ], [ ], [ ]], // 39 [[4,6], [2,5], [ ]], // 40 [[ ], [ ], [ ]], // 41 [[ ], [ ], [ ]], // 42 [[ ], [ ], [ ]], // 43 [[ ], [ ], [ ]], // 44 [[5], [4,7], [7]], // 45 [[ ], [ ], [ ]], // 46 [[ ], [ ], [ ]], // 47 [[ ], [ ], [ ]], // 48 [[33,38], [32,36], [ ]], // 49 [[6], [2,7], [7]], // 50 [[ ], [ ], [ ]], // 51 [[ ], [1], [1]], // 52 [[ ], [ ], [ ]], // 53 [[ ], [ ], [ ]], // 54 [[6], [5], [ ]], // 55 [[6, 7], [2, 4], [ ]], // 56 [[ ], [1, 3], [1, 3]], // 57 [[ ], [ ], [ ]], // 58 [[ ], [ ], [ ]], // 59 [[5], [4], [ ]], // 60 [[ ], [ ], [ ]], // 61 [[ ], [ ], [ ]], // 62 [[4], [6, 3, 1], [6, 3]], // 63 [[ ], [64, 72], [64, 72]], // 64 [[2], [11, 1, 7, 5], [11, 7, 5]], // 65 [[ ], [5], [5]], // 66 [[ ], [ ], [ ]], // 67 [[3], [2], [ ]], // 68 [[ ], [ ], [ ]], // 69 [[ ], [ ], [ ]], // 70 [[ ], [ ], [ ]], // 71 [[ ], [ ], [ ]], // 72 [[ ], [14], [14]], // 73 [[ ], [ ], [ ]], // 74 [[ ], [ ], [ ]], // 75 [[ ], [ ], [ ]], // 76 [[ ], [2], [2]], // 77 [[2, 4], [1, 3], [ ]], // 78 [[ ], [ ], [ ]], // 79 [[ ], [ ], [ ]], // 80 [[145, 153], [144, 152], [ ]], // 81 [[ 8], [6], [ ]], // 82 [[ ], [ ], [ ]], // 83 [[3], [1], [ ]], // 84 [[4], [3], [ ]], // 85 [[ ], [ ], [ ]], // 86 [[ ], [ ], [ ]], // 87 [[ ], [ ], [ ]], // 88 [[ ], [ ], [ ]], // 89 [[ ], [ ], [ ]], // 90 [[6], [ 8, 5], [ 8]], // 91 [[ ], [ ], [ ]], // 92 [[ ], [ ], [ ]], // 93 [[ ], [ ], [ ]], // 94 [[ ], [ ], [ ]], // 95 [[ ], [ ], [ ]], // 96 [[ ], [ ], [ ]], // 97 [[ ], [ ], [ ]], // 98 [[ ], [ ], [ ]], // 99 [[36, 34, 32], [33, 35], [ ]], // 100 [[ ], [ ], [ ]], // 101 [[ ], [1], [1]], // 102 [[ ], [ ], [ ]], // 103 [[ ], [ ], [ ]], // 104 [[3, 9], [8, 7], [7]], // 105 [[ ], [ ], [ ]], // 106 [[ ], [ ], [ ]], // 107 [[ ], [ ], [ ]], // 108 [[ ], [ ], [ ]], // 109 [[ ], [ ], [ ]], // 110 [[ ], [ ], [ ]], // 111 [[ ], [8], [8]], // 112 [[ ], [ ], [ ]], // 113 [[ ], [ ], [ ]], // 114 [[ ], [ ], [ ]], // 115 [[ ], [ ], [ ]], // 116 [[ ], [1, 3], [1, 3]], // 117 [[ ], [ ], [ ]], // 118 [[ ], [2], [2]], // 119 [[10], [21, 4, 8, 13, 19, 18], [21, 4, 13, 19, 18]]]; // 120 l1 := [ [[ PrimitiveGroupDescription( i, n ) : n in k | #PrimitiveGroup(i,n)^12 gt Factorial(i)] : k in maxprim[i]] : i in [1..120]]; l2 := [ [[ PrimitiveGroupDescription( i, n ) : n in k | #PrimitiveGroup(i,n)^12 ge Factorial(i)/2] : k in maxprim[i]] : i in [1..120]]; [ i : i in [1..120] | l1[i] ne l2[i]]; Output: Magma V2.10-6 Fri Jan 16 2004 09:01:33 on modular [Seed = 509194423] ------------------------------------- [ 50 ] Total time: 3.479 seconds, Total memory usage: 2.27MB ************** MAGMA ***************** Host ibm21.ilab.sztaki.hu. (195.111.1.97) Time: Fri Jan 16 09:02:07 2004 Input: maxprim:=[ [[ ], [ ], [ ]], // 1 [[ ], [ ], [ ]], // 2 [[ ], [ ], [ ]], // 3 [[ ], [ ], [ ]], // 4 [[3], [2], [ ]], // 5 [[2], [1], [ ]], // 6 [[4], [5], [5]], // 7 [[5], [3], [3]], // 8 [[7], [6,9], [9]], // 9 [[7], [6], [ ]], // 10 [[4], [6], [6]], // 11 [[2], [4], [4]], // 12 [[6], [5,7], [7]], // 13 [[2], [1], [ ]], // 14 [[ ], [4], [4]], // 15 [[ ], [20], [20]], // 16 [[5], [4,8], [8]], // 17 [[2], [1], [ ]], // 18 [[6], [5], [ ]], // 19 [[2], [1], [ ]], // 20 [[1,3,7], [2,6], [ ]], // 21 [[2], [1], [ ]], // 22 [[4], [5], [5]], // 23 [[2], [3], [3]], // 24 [[22,26], [21,24], [ ]], // 25 [[5], [2], [ ]], // 26 [[11], [13,10], [13]], // 27 [[11], [9,12], [12]], // 28 [[ ], [ ], [ ]], // 29 [[ ], [ ], [ ]], // 30 [[ ], [9,10], [9,10]], // 31 [[ ], [3], [3]], // 32 [[ ], [2], [2]], // 33 [[ ], [ ], [ ]], // 34 [[ ], [4], [4]], // 35 [[19, 8], [18,20], [20]], // 36 [[ ], [ ], [ ]], // 37 [[ ], [ ], [ ]], // 38 [[ ], [ ], [ ]], // 39 [[4,6], [2,5], [ ]], // 40 [[ ], [ ], [ ]], // 41 [[ ], [ ], [ ]], // 42 [[ ], [ ], [ ]], // 43 [[ ], [ ], [ ]], // 44 [[5], [4,7], [7]], // 45 [[ ], [ ], [ ]], // 46 [[ ], [ ], [ ]], // 47 [[ ], [ ], [ ]], // 48 [[33,38], [32,36], [ ]], // 49 [[6], [2,7], [7]], // 50 [[ ], [ ], [ ]], // 51 [[ ], [1], [1]], // 52 [[ ], [ ], [ ]], // 53 [[ ], [ ], [ ]], // 54 [[6], [5], [ ]], // 55 [[6, 7], [2, 4], [ ]], // 56 [[ ], [1, 3], [1, 3]], // 57 [[ ], [ ], [ ]], // 58 [[ ], [ ], [ ]], // 59 [[5], [4], [ ]], // 60 [[ ], [ ], [ ]], // 61 [[ ], [ ], [ ]], // 62 [[4], [6, 3, 1], [6, 3]], // 63 [[ ], [64, 72], [64, 72]], // 64 [[2], [11, 1, 7, 5], [11, 7, 5]], // 65 [[ ], [5], [5]], // 66 [[ ], [ ], [ ]], // 67 [[3], [2], [ ]], // 68 [[ ], [ ], [ ]], // 69 [[ ], [ ], [ ]], // 70 [[ ], [ ], [ ]], // 71 [[ ], [ ], [ ]], // 72 [[ ], [14], [14]], // 73 [[ ], [ ], [ ]], // 74 [[ ], [ ], [ ]], // 75 [[ ], [ ], [ ]], // 76 [[ ], [2], [2]], // 77 [[2, 4], [1, 3], [ ]], // 78 [[ ], [ ], [ ]], // 79 [[ ], [ ], [ ]], // 80 [[145, 153], [144, 152], [ ]], // 81 [[ 8], [6], [ ]], // 82 [[ ], [ ], [ ]], // 83 [[3], [1], [ ]], // 84 [[4], [3], [ ]], // 85 [[ ], [ ], [ ]], // 86 [[ ], [ ], [ ]], // 87 [[ ], [ ], [ ]], // 88 [[ ], [ ], [ ]], // 89 [[ ], [ ], [ ]], // 90 [[6], [ 8, 5], [ 8]], // 91 [[ ], [ ], [ ]], // 92 [[ ], [ ], [ ]], // 93 [[ ], [ ], [ ]], // 94 [[ ], [ ], [ ]], // 95 [[ ], [ ], [ ]], // 96 [[ ], [ ], [ ]], // 97 [[ ], [ ], [ ]], // 98 [[ ], [ ], [ ]], // 99 [[36, 34, 32], [33, 35], [ ]], // 100 [[ ], [ ], [ ]], // 101 [[ ], [1], [1]], // 102 [[ ], [ ], [ ]], // 103 [[ ], [ ], [ ]], // 104 [[3, 9], [8, 7], [7]], // 105 [[ ], [ ], [ ]], // 106 [[ ], [ ], [ ]], // 107 [[ ], [ ], [ ]], // 108 [[ ], [ ], [ ]], // 109 [[ ], [ ], [ ]], // 110 [[ ], [ ], [ ]], // 111 [[ ], [8], [8]], // 112 [[ ], [ ], [ ]], // 113 [[ ], [ ], [ ]], // 114 [[ ], [ ], [ ]], // 115 [[ ], [ ], [ ]], // 116 [[ ], [1, 3], [1, 3]], // 117 [[ ], [ ], [ ]], // 118 [[ ], [2], [2]], // 119 [[10], [21, 4, 8, 13, 19, 18], [21, 4, 13, 19, 18]]]; // 120 l1 := [ [[ PrimitiveGroupDescription( i, n ) : n in k | #PrimitiveGroup(i,n)^12 gt Factorial(i)] : k in maxprim[i]] : i in [1..120]]; l2 := [ [[ PrimitiveGroupDescription( i, n ) : n in k | #PrimitiveGroup(i,n)^12 ge Factorial(i)/2] : k in maxprim[i]] : i in [1..120]]; l2[50]; Output: Magma V2.10-6 Fri Jan 16 2004 09:02:03 on modular [Seed = 121678280] ------------------------------------- [ [ PGammaL(2, 49) ], [ PSU(3, 5):2 ], [ PSU(3, 5):2 ] ] Total time: 3.429 seconds, Total memory usage: 2.27MB ************** MAGMA ***************** Host ibm21.ilab.sztaki.hu. (195.111.1.97) Time: Fri Jan 16 10:33:40 2004 Input: maxprim := [[[ ], [ ], [ ]], // 101 [[ ], [1], [1]], // 102 [[ ], [ ], [ ]], // 103 [[ ], [ ], [ ]], // 104 [[3, 9], [8, 7], [7]], // 105 [[ ], [ ], [ ]], // 106 [[ ], [ ], [ ]], // 107 [[ ], [ ], [ ]], // 108 [[ ], [ ], [ ]], // 109 [[ ], [ ], [ ]], // 110 [[ ], [ ], [ ]], // 111 [[ ], [8], [8]], // 112 [[ ], [ ], [ ]], // 113 [[ ], [ ], [ ]], // 114 [[ ], [ ], [ ]], // 115 [[ ], [ ], [ ]], // 116 [[ ], [1, 3], [1, 3]], // 117 [[ ], [ ], [ ]], // 118 [[ ], [2], [2]], // 119 [[10], [21, 4, 8, 13, 19, 18], [21, 4, 13, 19, 18]], // 120 [[48, 54], [47, 53, 55], [55]], // 121 [[5], [3], [ ]], // 122 [[ ], [ ], [ ]], // 123 [[ ], [ ], [ ]], // 124 [[32, 42], [31, 39], [ ]], // 125 [[12, 13, 17], [8, 10, 6, 15], [6]], // 126 [[ ], [13], [13]], // 127 [[ ], [3], [3]], // 128 [[ ], [2], [2]], // 129 [[5], [2], [ ]], // 130 [[ ], [ ], [ ]], // 131 [[ ], [ ], [ ]], // 132 [[ ], [1], [1]], // 133 [[ ], [ ], [ ]], // 134 [[ ], [3], [3]], // 135 [[12], [11, 10], [10]], // 136 [[ ], [ ], [ ]], // 137 [[ ], [ ], [ ]], // 138 [[ ], [ ], [ ]], // 139 [[ ], [ ], [ ]], // 140 [[ ], [ ], [ ]], // 141 [[ ], [ ], [ ]], // 142 [[ ], [ ], [ ]], // 143 [[ ], [10, 12, 14, 15], [10, 12, 14, 15]], // 144 [[ ], [ ], [ ]], // 145 [[ ], [ ], [ ]], // 146 [[ ], [ ], [ ]], // 147 [[ ], [ ], [ ]], // 148 [[ ], [ ], [ ]], // 149 [[ ], [ ], [ ]], // 150 [[ ], [ ], [ ]], // 151 [[ ], [ ], [ ]], // 152 [[ ], [4], [4]], // 153 [[ ], [ ], [ ]], // 154 [[ ], [1], [1]], // 155 [[7], [6], [ ]], // 156 [[ ], [ ], [ ]], // 157 [[ ], [ ], [ ]], // 158 [[ ], [ ], [ ]], // 159 [[ ], [ ], [ ]], // 160 [[ ], [ ], [ ]], // 161 [[5], [3], [ ]], // 162 [[ ], [ ], [ ]], // 163 [[ ], [ ], [ ]], // 164 [[4], [5, 2], [5]], // 165 [[ ], [ ], [ ]], // 166 [[ ], [ ], [ ]], // 167 [[5], [4], [ ]], // 168 [[68, 73], [67, 72], [ ]], // 169 [[5], [3], [ ]], // 170 [[4, 2], [3, 1], [ ]], // 171 [[ ], [ ], [ ]], // 172 [[ ], [ ], [ ]], // 173 [[ ], [ ], [ ]], // 174 [[2], [1, 4], [4]], // 175 [[ ], [3, 4], [3, 4]], // 176 [[ ], [ ], [ ]], // 177 [[ ], [ ], [ ]], // 178 [[ ], [ ], [ ]], // 179 [[ ], [ ], [ ]], // 180 [[ ], [ ], [ ]], // 181 [[ ], [ ], [ ]], // 182 [[ ], [2], [2]], // 183 [[ ], [ ], [ ]], // 184 [[ ], [ ], [ ]], // 185 [[ ], [1], [1]], // 186 [[ ], [ ], [ ]], // 187 [[ ], [ ], [ ]], // 188 [[ ], [ ], [ ]], // 189 [[ ], [4], [4]], // 190 [[ ], [ ], [ ]], // 191 [[ ], [ ], [ ]], // 192 [[ ], [ ], [ ]], // 193 [[ ], [ ], [ ]], // 194 [[ ], [ ], [ ]], // 195 [[8], [ ], [ ]], // 196 [[ ], [ ], [ ]], // 197 [[ ], [ ], [ ]], // 198 [[ ], [ ], [ ]], // 199 [[ ], [ ], [ ]]]; // 200 [[ PrimitiveGroupDescription( i+100, n ) : n in k ] : k in z ] : z in maxprim[i]] : i in [1..100]]; Output: Magma V2.10-6 Fri Jan 16 2004 10:33:37 on modular [Seed = 2766987489] ------------------------------------- >> [[ PrimitiveGroupDescription( i+100, n ) : n in k ] : k in z ] : z in maxpr ^ User error: bad syntax Total time: 3.019 seconds, Total memory usage: 1.90MB ************** MAGMA ***************** Host ibm21.ilab.sztaki.hu. (195.111.1.97) Time: Fri Jan 16 10:34:13 2004 Input: maxprim := [[[ ], [ ], [ ]], // 101 [[ ], [1], [1]], // 102 [[ ], [ ], [ ]], // 103 [[ ], [ ], [ ]], // 104 [[3, 9], [8, 7], [7]], // 105 [[ ], [ ], [ ]], // 106 [[ ], [ ], [ ]], // 107 [[ ], [ ], [ ]], // 108 [[ ], [ ], [ ]], // 109 [[ ], [ ], [ ]], // 110 [[ ], [ ], [ ]], // 111 [[ ], [8], [8]], // 112 [[ ], [ ], [ ]], // 113 [[ ], [ ], [ ]], // 114 [[ ], [ ], [ ]], // 115 [[ ], [ ], [ ]], // 116 [[ ], [1, 3], [1, 3]], // 117 [[ ], [ ], [ ]], // 118 [[ ], [2], [2]], // 119 [[10], [21, 4, 8, 13, 19, 18], [21, 4, 13, 19, 18]], // 120 [[48, 54], [47, 53, 55], [55]], // 121 [[5], [3], [ ]], // 122 [[ ], [ ], [ ]], // 123 [[ ], [ ], [ ]], // 124 [[32, 42], [31, 39], [ ]], // 125 [[12, 13, 17], [8, 10, 6, 15], [6]], // 126 [[ ], [13], [13]], // 127 [[ ], [3], [3]], // 128 [[ ], [2], [2]], // 129 [[5], [2], [ ]], // 130 [[ ], [ ], [ ]], // 131 [[ ], [ ], [ ]], // 132 [[ ], [1], [1]], // 133 [[ ], [ ], [ ]], // 134 [[ ], [3], [3]], // 135 [[12], [11, 10], [10]], // 136 [[ ], [ ], [ ]], // 137 [[ ], [ ], [ ]], // 138 [[ ], [ ], [ ]], // 139 [[ ], [ ], [ ]], // 140 [[ ], [ ], [ ]], // 141 [[ ], [ ], [ ]], // 142 [[ ], [ ], [ ]], // 143 [[ ], [10, 12, 14, 15], [10, 12, 14, 15]], // 144 [[ ], [ ], [ ]], // 145 [[ ], [ ], [ ]], // 146 [[ ], [ ], [ ]], // 147 [[ ], [ ], [ ]], // 148 [[ ], [ ], [ ]], // 149 [[ ], [ ], [ ]], // 150 [[ ], [ ], [ ]], // 151 [[ ], [ ], [ ]], // 152 [[ ], [4], [4]], // 153 [[ ], [ ], [ ]], // 154 [[ ], [1], [1]], // 155 [[7], [6], [ ]], // 156 [[ ], [ ], [ ]], // 157 [[ ], [ ], [ ]], // 158 [[ ], [ ], [ ]], // 159 [[ ], [ ], [ ]], // 160 [[ ], [ ], [ ]], // 161 [[5], [3], [ ]], // 162 [[ ], [ ], [ ]], // 163 [[ ], [ ], [ ]], // 164 [[4], [5, 2], [5]], // 165 [[ ], [ ], [ ]], // 166 [[ ], [ ], [ ]], // 167 [[5], [4], [ ]], // 168 [[68, 73], [67, 72], [ ]], // 169 [[5], [3], [ ]], // 170 [[4, 2], [3, 1], [ ]], // 171 [[ ], [ ], [ ]], // 172 [[ ], [ ], [ ]], // 173 [[ ], [ ], [ ]], // 174 [[2], [1, 4], [4]], // 175 [[ ], [3, 4], [3, 4]], // 176 [[ ], [ ], [ ]], // 177 [[ ], [ ], [ ]], // 178 [[ ], [ ], [ ]], // 179 [[ ], [ ], [ ]], // 180 [[ ], [ ], [ ]], // 181 [[ ], [ ], [ ]], // 182 [[ ], [2], [2]], // 183 [[ ], [ ], [ ]], // 184 [[ ], [ ], [ ]], // 185 [[ ], [1], [1]], // 186 [[ ], [ ], [ ]], // 187 [[ ], [ ], [ ]], // 188 [[ ], [ ], [ ]], // 189 [[ ], [4], [4]], // 190 [[ ], [ ], [ ]], // 191 [[ ], [ ], [ ]], // 192 [[ ], [ ], [ ]], // 193 [[ ], [ ], [ ]], // 194 [[ ], [ ], [ ]], // 195 [[8], [ ], [ ]], // 196 [[ ], [ ], [ ]], // 197 [[ ], [ ], [ ]], // 198 [[ ], [ ], [ ]], // 199 [[ ], [ ], [ ]]]; // 200 [[ PrimitiveGroupDescription( i+100, n ) : n in k ] : k in maxprim[i]] : i in [1..100]]; Output: Magma V2.10-6 Fri Jan 16 2004 10:34:10 on modular [Seed = 2917525963] ------------------------------------- >> k in maxprim[i]] : i in [1..100]];; ^ User error: bad syntax Total time: 2.919 seconds, Total memory usage: 1.90MB ************** MAGMA ***************** Host ibm21.ilab.sztaki.hu. (195.111.1.97) Time: Fri Jan 16 10:34:30 2004 Input: maxprim := [[[ ], [ ], [ ]], // 101 [[ ], [1], [1]], // 102 [[ ], [ ], [ ]], // 103 [[ ], [ ], [ ]], // 104 [[3, 9], [8, 7], [7]], // 105 [[ ], [ ], [ ]], // 106 [[ ], [ ], [ ]], // 107 [[ ], [ ], [ ]], // 108 [[ ], [ ], [ ]], // 109 [[ ], [ ], [ ]], // 110 [[ ], [ ], [ ]], // 111 [[ ], [8], [8]], // 112 [[ ], [ ], [ ]], // 113 [[ ], [ ], [ ]], // 114 [[ ], [ ], [ ]], // 115 [[ ], [ ], [ ]], // 116 [[ ], [1, 3], [1, 3]], // 117 [[ ], [ ], [ ]], // 118 [[ ], [2], [2]], // 119 [[10], [21, 4, 8, 13, 19, 18], [21, 4, 13, 19, 18]], // 120 [[48, 54], [47, 53, 55], [55]], // 121 [[5], [3], [ ]], // 122 [[ ], [ ], [ ]], // 123 [[ ], [ ], [ ]], // 124 [[32, 42], [31, 39], [ ]], // 125 [[12, 13, 17], [8, 10, 6, 15], [6]], // 126 [[ ], [13], [13]], // 127 [[ ], [3], [3]], // 128 [[ ], [2], [2]], // 129 [[5], [2], [ ]], // 130 [[ ], [ ], [ ]], // 131 [[ ], [ ], [ ]], // 132 [[ ], [1], [1]], // 133 [[ ], [ ], [ ]], // 134 [[ ], [3], [3]], // 135 [[12], [11, 10], [10]], // 136 [[ ], [ ], [ ]], // 137 [[ ], [ ], [ ]], // 138 [[ ], [ ], [ ]], // 139 [[ ], [ ], [ ]], // 140 [[ ], [ ], [ ]], // 141 [[ ], [ ], [ ]], // 142 [[ ], [ ], [ ]], // 143 [[ ], [10, 12, 14, 15], [10, 12, 14, 15]], // 144 [[ ], [ ], [ ]], // 145 [[ ], [ ], [ ]], // 146 [[ ], [ ], [ ]], // 147 [[ ], [ ], [ ]], // 148 [[ ], [ ], [ ]], // 149 [[ ], [ ], [ ]], // 150 [[ ], [ ], [ ]], // 151 [[ ], [ ], [ ]], // 152 [[ ], [4], [4]], // 153 [[ ], [ ], [ ]], // 154 [[ ], [1], [1]], // 155 [[7], [6], [ ]], // 156 [[ ], [ ], [ ]], // 157 [[ ], [ ], [ ]], // 158 [[ ], [ ], [ ]], // 159 [[ ], [ ], [ ]], // 160 [[ ], [ ], [ ]], // 161 [[5], [3], [ ]], // 162 [[ ], [ ], [ ]], // 163 [[ ], [ ], [ ]], // 164 [[4], [5, 2], [5]], // 165 [[ ], [ ], [ ]], // 166 [[ ], [ ], [ ]], // 167 [[5], [4], [ ]], // 168 [[68, 73], [67, 72], [ ]], // 169 [[5], [3], [ ]], // 170 [[4, 2], [3, 1], [ ]], // 171 [[ ], [ ], [ ]], // 172 [[ ], [ ], [ ]], // 173 [[ ], [ ], [ ]], // 174 [[2], [1, 4], [4]], // 175 [[ ], [3, 4], [3, 4]], // 176 [[ ], [ ], [ ]], // 177 [[ ], [ ], [ ]], // 178 [[ ], [ ], [ ]], // 179 [[ ], [ ], [ ]], // 180 [[ ], [ ], [ ]], // 181 [[ ], [ ], [ ]], // 182 [[ ], [2], [2]], // 183 [[ ], [ ], [ ]], // 184 [[ ], [ ], [ ]], // 185 [[ ], [1], [1]], // 186 [[ ], [ ], [ ]], // 187 [[ ], [ ], [ ]], // 188 [[ ], [ ], [ ]], // 189 [[ ], [4], [4]], // 190 [[ ], [ ], [ ]], // 191 [[ ], [ ], [ ]], // 192 [[ ], [ ], [ ]], // 193 [[ ], [ ], [ ]], // 194 [[ ], [ ], [ ]], // 195 [[8], [ ], [ ]], // 196 [[ ], [ ], [ ]], // 197 [[ ], [ ], [ ]], // 198 [[ ], [ ], [ ]], // 199 [[ ], [ ], [ ]]]; // 200 [[[ PrimitiveGroupDescription( i+100, n ) : n in k ] : k in maxprim[i]] : i in [1..100]]; Output: Magma V2.10-6 Fri Jan 16 2004 10:34:27 on modular [Seed = 3600716353] ------------------------------------- [ [ [], [], [] ], [ [], [ PSL(2, 17) ], [ PSL(2, 17) ] ], [ [], [], [] ], [ [], [], [] ], [ [ Sym(8), Sym(15) ], [ Alt(15), PSL(3, 4).D_12 ], [ PSL(3, 4).D_12 ] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [ PSU(4, 3).D_8 ], [ PSU(4, 3).D_8 ] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [ PSL(3, 3).2, PSL(4, 3).2 ], [ PSL(3, 3).2, PSL(4, 3).2 ] ], [ [], [], [] ], [ [], [ PSO-(8, 2) ], [ PSO-(8, 2) ] ], [ [ PSL(3, 4).2^2 ], [ Sym(16), PSigmaL(2, 16), PSL(3, 4).2, PSp(6, 2), PSp(8, 2), PSO+(8, 2) ], [ Sym(16), PSigmaL(2, 16), PSp(6, 2), PSp(8, 2), PSO+(8, 2) ] ], [ [ AGL(2, 11), Sym(11) \wreath Sym(2) ], [ 11^2:(5 \times SL(2, 11)), Alt(11)^2.4, PSL(5, 3) ], [ PSL(5, 3) ] ], [ [ PGammaL(2, 11^2) ], [ PSL(2, 11^2).2 ], [] ], [ [], [], [] ], [ [], [], [] ], [ [ 5^3:(SL(3, 5):2), Alt(5)^3.Sym(4) ], [ ASL(3, 5), Alt(5)^3.D_12 ], [] ], [ [ Sym(10), PGammaL(2, 5^3), PSU(4, 3).2^2 ], [ Alt(10), PSigmaL(2, 5^3), PGammaU(3, 5), PSU(4, 3).2 ], [ PGammaU(3, 5) ] ], [ [], [ L(7, 2) ], [ L(7, 2) ] ], [ [], [ AGL(7, 2) ], [ AGL(7, 2) ] ], [ [], [ PGammaL(2, 2^7) ], [ PGammaL(2, 2^7) ] ], [ [ PSL(4, 3).2^2 ], [ PGL(4, 3) ], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [ PSL(3, 11) ], [ PSL(3, 11) ] ], [ [], [], [] ], [ [], [ PSO+(8, 2) ], [ PSO+(8, 2) ] ], [ [ Sym(17) ], [ Alt(17), PSp(8, 2) ], [ PSp(8, 2) ] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [ Sym(12) \wreath Sym(2), PSL(3, 3).2, M_12.2, M_12.2 ], [ Sym(12) \wreath Sym(2), PSL(3, 3).2, M_12.2, M_12.2 ] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [ Sym(18) ], [ Sym(18) ] ], [ [], [], [] ], [ [], [ PSL(5, 2) ], [ PSL(5, 2) ] ], [ [ PGL(4, 5) ], [ PSL(4, 5).2 ], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [ PSU(4, 3).2^2 ], [ PSU(4, 3).2 ], [] ], [ [], [], [] ], [ [], [], [] ], [ [ PGammaU(5, 2) ], [ Sym(11), PSU(5, 2) ], [ Sym(11) ] ], [ [], [], [] ], [ [], [], [] ], [ [ PSL(2, 7)^2.2^2 ], [ PSL(2, 7) wreath 2 ], [] ], [ [ AGL(2, 13), Sym(13) \wreath Sym(2) ], [ 13^2:(3 \times 4.PSL(2, 13)), Alt(13)^2.2^2 ], [] ], [ [ PGammaL(2, 13^2) ], [ PSigmaL(2, 13^2) ], [] ], [ [ Sym(19), PGL(2, 19) ], [ Alt(19), PSL(2, 19) ], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [ PSigmaL(2, 7^2) ], [ PSL(2, 7^2), PSigmaU(3, 5) ], [ PSigmaU(3, 5) ] ], [ [], [ PGammaU(5, 2), HS ], [ PGammaU(5, 2), HS ] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [ PGammaL(3, 13) ], [ PGammaL(3, 13) ] ], [ [], [], [] ], [ [], [], [] ], [ [], [ PSL(3, 5).2 ], [ PSL(3, 5).2 ] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [ Sym(20) ], [ Sym(20) ] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [ Sym(14) \wreath Sym(2) ], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ] ] Total time: 3.259 seconds, Total memory usage: 2.10MB ************** MAGMA ***************** Host ibm21.ilab.sztaki.hu. (195.111.1.97) Time: Fri Jan 16 10:35:31 2004 Input: maxprim := [[[ ], [ ], [ ]], // 101 [[ ], [1], [1]], // 102 [[ ], [ ], [ ]], // 103 [[ ], [ ], [ ]], // 104 [[3, 9], [8, 7], [7]], // 105 [[ ], [ ], [ ]], // 106 [[ ], [ ], [ ]], // 107 [[ ], [ ], [ ]], // 108 [[ ], [ ], [ ]], // 109 [[ ], [ ], [ ]], // 110 [[ ], [ ], [ ]], // 111 [[ ], [8], [8]], // 112 [[ ], [ ], [ ]], // 113 [[ ], [ ], [ ]], // 114 [[ ], [ ], [ ]], // 115 [[ ], [ ], [ ]], // 116 [[ ], [1, 3], [1, 3]], // 117 [[ ], [ ], [ ]], // 118 [[ ], [2], [2]], // 119 [[10], [21, 4, 8, 13, 19, 18], [21, 4, 13, 19, 18]], // 120 [[48, 54], [47, 53, 55], [55]], // 121 [[5], [3], [ ]], // 122 [[ ], [ ], [ ]], // 123 [[ ], [ ], [ ]], // 124 [[32, 42], [31, 39], [ ]], // 125 [[12, 13, 17], [8, 10, 6, 15], [6]], // 126 [[ ], [13], [13]], // 127 [[ ], [3], [3]], // 128 [[ ], [2], [2]], // 129 [[5], [2], [ ]], // 130 [[ ], [ ], [ ]], // 131 [[ ], [ ], [ ]], // 132 [[ ], [1], [1]], // 133 [[ ], [ ], [ ]], // 134 [[ ], [3], [3]], // 135 [[12], [11, 10], [10]], // 136 [[ ], [ ], [ ]], // 137 [[ ], [ ], [ ]], // 138 [[ ], [ ], [ ]], // 139 [[ ], [ ], [ ]], // 140 [[ ], [ ], [ ]], // 141 [[ ], [ ], [ ]], // 142 [[ ], [ ], [ ]], // 143 [[ ], [10, 12, 14, 15], [10, 12, 14, 15]], // 144 [[ ], [ ], [ ]], // 145 [[ ], [ ], [ ]], // 146 [[ ], [ ], [ ]], // 147 [[ ], [ ], [ ]], // 148 [[ ], [ ], [ ]], // 149 [[ ], [ ], [ ]], // 150 [[ ], [ ], [ ]], // 151 [[ ], [ ], [ ]], // 152 [[ ], [4], [4]], // 153 [[ ], [ ], [ ]], // 154 [[ ], [1], [1]], // 155 [[7], [6], [ ]], // 156 [[ ], [ ], [ ]], // 157 [[ ], [ ], [ ]], // 158 [[ ], [ ], [ ]], // 159 [[ ], [ ], [ ]], // 160 [[ ], [ ], [ ]], // 161 [[5], [3], [ ]], // 162 [[ ], [ ], [ ]], // 163 [[ ], [ ], [ ]], // 164 [[4], [5, 2], [5]], // 165 [[ ], [ ], [ ]], // 166 [[ ], [ ], [ ]], // 167 [[5], [4], [ ]], // 168 [[68, 73], [67, 72], [ ]], // 169 [[5], [3], [ ]], // 170 [[4, 2], [3, 1], [ ]], // 171 [[ ], [ ], [ ]], // 172 [[ ], [ ], [ ]], // 173 [[ ], [ ], [ ]], // 174 [[2], [1, 4], [4]], // 175 [[ ], [3, 4], [3, 4]], // 176 [[ ], [ ], [ ]], // 177 [[ ], [ ], [ ]], // 178 [[ ], [ ], [ ]], // 179 [[ ], [ ], [ ]], // 180 [[ ], [ ], [ ]], // 181 [[ ], [ ], [ ]], // 182 [[ ], [2], [2]], // 183 [[ ], [ ], [ ]], // 184 [[ ], [ ], [ ]], // 185 [[ ], [1], [1]], // 186 [[ ], [ ], [ ]], // 187 [[ ], [ ], [ ]], // 188 [[ ], [ ], [ ]], // 189 [[ ], [4], [4]], // 190 [[ ], [ ], [ ]], // 191 [[ ], [ ], [ ]], // 192 [[ ], [ ], [ ]], // 193 [[ ], [ ], [ ]], // 194 [[ ], [ ], [ ]], // 195 [[8], [ ], [ ]], // 196 [[ ], [ ], [ ]], // 197 [[ ], [ ], [ ]], // 198 [[ ], [ ], [ ]], // 199 [[ ], [ ], [ ]]]; // 200 [[[ PrimitiveGroupDescription( i+100, n ) : n in k | #PrimitiveGroup(i+100,n)^12 ge Factorial(i+100)/2 ] : k in maxprim[i]] : i in [1..100]]; Output: Magma V2.10-6 Fri Jan 16 2004 10:35:27 on modular [Seed = 3297542255] ------------------------------------- [ [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ] ] Total time: 3.259 seconds, Total memory usage: 1.90MB ************** MAGMA ***************** Host ibm21.ilab.sztaki.hu. (195.111.1.97) Time: Fri Jan 16 10:37:03 2004 Input: maxprim := [[[ ], [ ], [ ]], // 201 [[ ], [ ], [ ]], // 202 [[ ], [1], [1]], // 203 [[ ], [ ], [ ]], // 204 [[ ], [ ], [ ]], // 205 [[ ], [ ], [ ]], // 206 [[ ], [ ], [ ]], // 207 [[ ], [3], [3]], // 208 [[ ], [ ], [ ]], // 209 [[4], [2, 3], [2]], // 210 [[ ], [ ], [ ]], // 211 [[ ], [ ], [ ]], // 212 [[ ], [ ], [ ]], // 213 [[ ], [ ], [ ]], // 214 [[ ], [ ], [ ]], // 215 [[ ], [20], [20]], // 216 [[ ], [ ], [ ]], // 217 [[ ], [ ], [ ]], // 218 [[ ], [ ], [ ]], // 219 [[3], [2], [ ]], // 220 [[ ], [ ], [ ]], // 221 [[ ], [ ], [ ]], // 222 [[ ], [ ], [ ]], // 223 [[ ], [ ], [ ]], // 224 [[10], [8], [ ]], // 225 [[ ], [ ], [ ]], // 226 [[ ], [ ], [ ]], // 227 [[ ], [ ], [ ]], // 228 [[ ], [ ], [ ]], // 229 [[ ], [ ], [ ]], // 230 [[ ], [4], [4]], // 231 [[ ], [ ], [ ]], // 232 [[ ], [ ], [ ]], // 233 [[ ], [2], [2]], // 234 [[ ], [ ], [ ]], // 235 [[ ], [ ], [ ]], // 236 [[ ], [ ], [ ]], // 237 [[ ], [ ], [ ]], // 238 [[ ], [ ], [ ]], // 239 [[ ], [ ], [ ]], // 240 [[ ], [ ], [ ]], // 241 [[ ], [ ], [ ]], // 242 [[34], [33], [ ]], // 243 [[4], [3], [ ]], // 244 [[ ], [ ], [ ]], // 245 [[ ], [ ], [ ]], // 246 [[ ], [ ], [ ]], // 247 [[ ], [1], [1]], // 248 [[ ], [ ], [ ]], // 249 [[ ], [ ], [ ]], // 250 [[ ], [ ], [ ]], // 251 [[ ], [ ], [ ]], // 252 [[7, 3], [6, 1, 2], [1]], // 253 [[ ], [ ], [ ]], // 254 [[ ], [2], [2]], // 255 [[ ], [238, 242], [238, 242]], // 256 [[ ], [13], [13]], // 257 [[ ], [ ], [ ]], // 258 [[ ], [ ], [ ]], // 259 [[ ], [ ], [ ]], // 260 [[ ], [ ], [ ]], // 261 [[ ], [ ], [ ]], // 262 [[ ], [ ], [ ]], // 263 [[ ], [ ], [ ]], // 264 [[ ], [ ], [ ]], // 265 [[ ], [1], [1]], // 266 [[ ], [ ], [ ]], // 267 [[ ], [ ], [ ]], // 268 [[ ], [ ], [ ]], // 269 [[ ], [ ], [ ]], // 270 [[ ], [ ], [ ]], // 271 [[ ], [ ], [ ]], // 272 [[ ], [6], [6]], // 273 [[ ], [ ], [ ]], // 274 [[ ], [2], [2]], // 275 [[ ], [6, 4], [6, 4]], // 276 [[ ], [ ], [ ]], // 277 [[ ], [ ], [ ]], // 278 [[ ], [ ], [ ]], // 279 [[12, 22, 14], [10, 19, 13], [ ]], // 280 [[ ], [ ], [ ]], // 281 [[ ], [ ], [ ]], // 282 [[ ], [ ], [ ]], // 283 [[ ], [ ], [ ]], // 284 [[ ], [1], [1]], // 285 [[2], [1], [ ]], // 286 [[ ], [ ], [ ]], // 287 [[ ], [ ], [ ]], // 288 [[80, 95], [79, 93], [ ]], // 289 [[5], [3], [ ]], // 290 [[ ], [ ], [ ]], // 291 [[ ], [ ], [ ]], // 292 [[ ], [ ], [ ]], // 293 [[ ], [ ], [ ]], // 294 [[ ], [ ], [ ]], // 295 [[ ], [ ], [ ]], // 296 [[2], [1], [ ]], // 297 [[ ], [ ], [ ]], // 298 [[ ], [ ], [ ]], // 299 [[9, 5, 7], [8, 2, 6], [ ]], // 300 [[ ], [ ], [ ]], // 301 [[ ], [ ], [ ]], // 302 [[ ], [ ], [ ]], // 303 [[ ], [ ], [ ]], // 304 [[ ], [ ], [ ]], // 305 [[ ], [ ], [ ]], // 306 [[ ], [13], [13]], // 307 [[ ], [ ], [ ]], // 308 [[ ], [ ], [ ]], // 309 [[ ], [ ], [ ]], // 310 [[ ], [ ], [ ]], // 311 [[ ], [ ], [ ]], // 312 [[ ], [ ], [ ]], // 313 [[ ], [ ], [ ]], // 314 [[2], [3, 1], [3]], // 315 [[ ], [ ], [ ]], // 316 [[ ], [ ], [ ]], // 317 [[ ], [ ], [ ]], // 318 [[ ], [ ], [ ]], // 319 [[ ], [ ], [ ]], // 320 [[ ], [ ], [ ]], // 321 [[ ], [ ], [ ]], // 322 [[ ], [ ], [ ]], // 323 [[8], [ ], [ ]], // 324 [[10], [12, 9, 7], [12, 7]], // 325 [[ ], [ ], [ ]], // 326 [[ ], [ ], [ ]], // 327 [[ ], [ ], [ ]], // 328 [[ ], [ ], [ ]], // 329 [[ ], [4, 2], [4, 2]], // 330 [[ ], [ ], [ ]], // 331 [[ ], [ ], [ ]], // 332 [[ ], [ ], [ ]], // 333 [[ ], [ ], [ ]], // 334 [[ ], [ ], [ ]], // 335 [[ ], [6, 7], [6, 7]], // 336 [[ ], [ ], [ ]], // 337 [[ ], [ ], [ ]], // 338 [[ ], [ ], [ ]], // 339 [[ ], [ ], [ ]], // 340 [[2], [1], [ ]], // 341 [[ ], [ ], [ ]], // 342 [[76, 88], [75, 85], [ ]], // 343 [[6], [5, 2], [2]], // 344 [[ ], [ ], [ ]], // 345 [[ ], [ ], [ ]], // 346 [[ ], [ ], [ ]], // 347 [[ ], [ ], [ ]], // 348 [[ ], [ ], [ ]], // 349 [[ ], [ ], [ ]], // 350 [[9, 4, 7], [8, 3, 6], [ ]], // 351 [[ ], [ ], [ ]], // 352 [[ ], [ ], [ ]], // 353 [[ ], [ ], [ ]], // 354 [[ ], [ ], [ ]], // 355 [[ ], [ ], [ ]], // 356 [[5], [2], [ ]], // 357 [[ ], [ ], [ ]], // 358 [[ ], [ ], [ ]], // 359 [[16], [11], [ ]], // 360 [[86, 90], [85, 88], [ ]], // 361 [[5], [4], [ ]], // 362 [[ ], [ ], [ ]], // 363 [[9, 5], [7, 8, 3], [7]], // 364 [[ ], [ ], [ ]], // 365 [[ ], [ ], [ ]], // 366 [[ ], [ ], [ ]], // 367 [[ ], [ ], [ ]], // 368 [[3], [2], [ ]], // 369 [[ ], [ ], [ ]], // 370 [[ ], [ ], [ ]], // 371 [[ ], [ ], [ ]], // 372 [[ ], [ ], [ ]], // 373 [[ ], [ ], [ ]], // 374 [[ ], [ ], [ ]], // 375 [[ ], [ ], [ ]], // 376 [[ ], [ ], [ ]], // 377 [[ ], [9, 7], [9, 7]], // 378 [[ ], [ ], [ ]], // 379 [[ ], [ ], [ ]], // 380 [[ ], [2], [2]], // 381 [[ ], [ ], [ ]], // 382 [[ ], [ ], [ ]], // 383 [[ ], [ ], [ ]], // 384 [[ ], [ ], [ ]], // 385 [[ ], [ ], [ ]], // 386 [[ ], [ ], [ ]], // 387 [[ ], [ ], [ ]], // 388 [[ ], [ ], [ ]], // 389 [[ ], [ ], [ ]], // 390 [[ ], [ ], [ ]], // 391 [[ ], [ ], [ ]], // 392 [[ ], [ ], [ ]], // 393 [[ ], [ ], [ ]], // 394 [[ ], [ ], [ ]], // 395 [[ ], [2], [2]], // 396 [[ ], [ ], [ ]], // 397 [[ ], [ ], [ ]], // 398 [[ ], [ ], [ ]], // 399 [[14], [8, 13], [8]]]; // 400 // 200 [[[ PrimitiveGroupDescription( i+200, n ) : n in k | #PrimitiveGroup(i+200,n)^12 ge Factorial(i+100)/2 ] : k in maxprim[i]] : i in [1..200]]; Output: Magma V2.10-6 Fri Jan 16 2004 10:36:59 on modular [Seed = 3448080578] ------------------------------------- [ [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [ Sym(21) ], [ Alt(21) ], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [ Sym(15) \wreath Sym(2) ], [ Alt(15)^2.4 ], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [ Sym(22) ], [ Sym(22) ] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [ Sym(16) \wreath Sym(2) ], [ Sym(16) \wreath Sym(2) ] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [ Sym(17) \wreath Sym(2) ], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ] ] Total time: 3.649 seconds, Total memory usage: 2.20MB ************** MAGMA ***************** Host ibm21.ilab.sztaki.hu. (195.111.1.97) Time: Fri Jan 16 10:38:43 2004 Input: maxprim := [[[ ], [ ], [ ]], // 201 [[ ], [ ], [ ]], // 202 [[ ], [1], [1]], // 203 [[ ], [ ], [ ]], // 204 [[ ], [ ], [ ]], // 205 [[ ], [ ], [ ]], // 206 [[ ], [ ], [ ]], // 207 [[ ], [3], [3]], // 208 [[ ], [ ], [ ]], // 209 [[4], [2, 3], [2]], // 210 [[ ], [ ], [ ]], // 211 [[ ], [ ], [ ]], // 212 [[ ], [ ], [ ]], // 213 [[ ], [ ], [ ]], // 214 [[ ], [ ], [ ]], // 215 [[ ], [20], [20]], // 216 [[ ], [ ], [ ]], // 217 [[ ], [ ], [ ]], // 218 [[ ], [ ], [ ]], // 219 [[3], [2], [ ]], // 220 [[ ], [ ], [ ]], // 221 [[ ], [ ], [ ]], // 222 [[ ], [ ], [ ]], // 223 [[ ], [ ], [ ]], // 224 [[10], [8], [ ]], // 225 [[ ], [ ], [ ]], // 226 [[ ], [ ], [ ]], // 227 [[ ], [ ], [ ]], // 228 [[ ], [ ], [ ]], // 229 [[ ], [ ], [ ]], // 230 [[ ], [4], [4]], // 231 [[ ], [ ], [ ]], // 232 [[ ], [ ], [ ]], // 233 [[ ], [2], [2]], // 234 [[ ], [ ], [ ]], // 235 [[ ], [ ], [ ]], // 236 [[ ], [ ], [ ]], // 237 [[ ], [ ], [ ]], // 238 [[ ], [ ], [ ]], // 239 [[ ], [ ], [ ]], // 240 [[ ], [ ], [ ]], // 241 [[ ], [ ], [ ]], // 242 [[34], [33], [ ]], // 243 [[4], [3], [ ]], // 244 [[ ], [ ], [ ]], // 245 [[ ], [ ], [ ]], // 246 [[ ], [ ], [ ]], // 247 [[ ], [1], [1]], // 248 [[ ], [ ], [ ]], // 249 [[ ], [ ], [ ]], // 250 [[ ], [ ], [ ]], // 251 [[ ], [ ], [ ]], // 252 [[7, 3], [6, 1, 2], [1]], // 253 [[ ], [ ], [ ]], // 254 [[ ], [2], [2]], // 255 [[ ], [238, 242], [238, 242]], // 256 [[ ], [13], [13]], // 257 [[ ], [ ], [ ]], // 258 [[ ], [ ], [ ]], // 259 [[ ], [ ], [ ]], // 260 [[ ], [ ], [ ]], // 261 [[ ], [ ], [ ]], // 262 [[ ], [ ], [ ]], // 263 [[ ], [ ], [ ]], // 264 [[ ], [ ], [ ]], // 265 [[ ], [1], [1]], // 266 [[ ], [ ], [ ]], // 267 [[ ], [ ], [ ]], // 268 [[ ], [ ], [ ]], // 269 [[ ], [ ], [ ]], // 270 [[ ], [ ], [ ]], // 271 [[ ], [ ], [ ]], // 272 [[ ], [6], [6]], // 273 [[ ], [ ], [ ]], // 274 [[ ], [2], [2]], // 275 [[ ], [6, 4], [6, 4]], // 276 [[ ], [ ], [ ]], // 277 [[ ], [ ], [ ]], // 278 [[ ], [ ], [ ]], // 279 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[ ]], // 359 [[16], [11], [ ]], // 360 [[86, 90], [85, 88], [ ]], // 361 [[5], [4], [ ]], // 362 [[ ], [ ], [ ]], // 363 [[9, 5], [7, 8, 3], [7]], // 364 [[ ], [ ], [ ]], // 365 [[ ], [ ], [ ]], // 366 [[ ], [ ], [ ]], // 367 [[ ], [ ], [ ]], // 368 [[3], [2], [ ]], // 369 [[ ], [ ], [ ]], // 370 [[ ], [ ], [ ]], // 371 [[ ], [ ], [ ]], // 372 [[ ], [ ], [ ]], // 373 [[ ], [ ], [ ]], // 374 [[ ], [ ], [ ]], // 375 [[ ], [ ], [ ]], // 376 [[ ], [ ], [ ]], // 377 [[ ], [9, 7], [9, 7]], // 378 [[ ], [ ], [ ]], // 379 [[ ], [ ], [ ]], // 380 [[ ], [2], [2]], // 381 [[ ], [ ], [ ]], // 382 [[ ], [ ], [ ]], // 383 [[ ], [ ], [ ]], // 384 [[ ], [ ], [ ]], // 385 [[ ], [ ], [ ]], // 386 [[ ], [ ], [ ]], // 387 [[ ], [ ], [ ]], // 388 [[ ], [ ], [ ]], // 389 [[ ], [ ], [ ]], // 390 [[ ], [ ], [ ]], // 391 [[ ], [ ], [ ]], // 392 [[ ], [ ], [ ]], // 393 [[ ], [ ], [ ]], // 394 [[ ], [ ], [ ]], // 395 [[ ], [2], [2]], // 396 [[ ], [ ], [ ]], // 397 [[ ], [ ], [ ]], // 398 [[ ], [ ], [ ]], // 399 [[14], [8, 13], [8]]]; // 400 // 200 [[[ PrimitiveGroupDescription( i+200, n ) : n in k | #PrimitiveGroup(i+200,n)^12 ge Factorial(i+200)/2 ] : k in maxprim[i]] : i in [1..200]]; Output: Magma V2.10-6 Fri Jan 16 2004 10:38:40 on modular [Seed = 4139692898] ------------------------------------- [ [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ], [ [], [], [] ] ] Total time: 3.629 seconds, Total memory usage: 2.00MB ************** MAGMA ***************** Host ibm21.ilab.sztaki.hu. (195.111.1.97) Time: Fri Jan 16 10:40:38 2004 Input: maxprim := [[[ ], [ ], [ ]], // 401 [[ ], [ ], [ ]], // 402 [[ ], [ ], [ ]], // 403 [[ ], [ ], [ ]], // 404 [[ ], [ ], [ ]], // 405 [[4, 2], [3, 1], [ ]], // 406 [[ ], [ ], [ ]], // 407 [[ ], [ ], [ ]], // 408 [[ ], [ ], [ ]], // 409 [[ ], [ ], [ ]], // 410 [[ ], [ ], [ ]], // 411 [[ ], [ ], [ ]], // 412 [[ ], [ ], [ ]], // 413 [[ ], [ ], [ ]], // 414 [[ ], [ ], [ ]], // 415 [[ ], [5], [5]], // 416 [[ ], [ ], [ ]], // 417 [[ ], [ ], [ ]], // 418 [[ ], [ ], [ ]], // 419 [[ ], [ ], [ ]], // 420 [[ ], [ ], [ ]], // 421 [[ ], [ ], [ ]], // 422 [[ ], [ ], [ ]], // 423 [[ ], [ ], [ ]], // 424 [[1], [ ], [ ]], // 425 [[ ], [ ], [ ]], // 426 [[ ], [ ], [ ]], // 427 [[ ], [ ], [ ]], // 428 [[ ], [ ], [ ]], // 429 [[ ], [ ], [ ]], // 430 [[ ], [ ], [ ]], // 431 [[ ], [ ], [ ]], // 432 [[ ], [ ], [ ]], // 433 [[ ], [ ], [ ]], // 434 [[ ], [4], [4]], // 435 [[ ], [ ], [ ]], // 436 [[ ], [ ], [ ]], // 437 [[ ], [ ], [ ]], // 438 [[ ], [ ], [ ]], 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***************** Host ibm21.ilab.sztaki.hu. (195.111.1.97) Time: Fri Jan 16 10:42:27 2004 Input: maxprim := [[[ ], [ ], [ ]], // 401 [[ ], [ ], [ ]], // 402 [[ ], [ ], [ ]], // 403 [[ ], [ ], [ ]], // 404 [[ ], [ ], [ ]], // 405 [[4, 2], [3, 1], [ ]], // 406 [[ ], [ ], [ ]], // 407 [[ ], [ ], [ ]], // 408 [[ ], [ ], [ ]], // 409 [[ ], [ ], [ ]], // 410 [[ ], [ ], [ ]], // 411 [[ ], [ ], [ ]], // 412 [[ ], [ ], [ ]], // 413 [[ ], [ ], [ ]], // 414 [[ ], [ ], [ ]], // 415 [[ ], [5], [5]], // 416 [[ ], [ ], [ ]], // 417 [[ ], [ ], [ ]], // 418 [[ ], [ ], [ ]], // 419 [[ ], [ ], [ ]], // 420 [[ ], [ ], [ ]], // 421 [[ ], [ ], [ ]], // 422 [[ ], [ ], [ ]], // 423 [[ ], [ ], [ ]], // 424 [[1], [ ], [ ]], // 425 [[ ], [ ], [ ]], // 426 [[ ], [ ], [ ]], // 427 [[ ], [ ], [ ]], // 428 [[ ], [ ], [ ]], // 429 [[ ], [ ], [ ]], // 430 [[ ], [ ], [ ]], // 431 [[ ], [ ], [ ]], // 432 [[ ], [ ], [ ]], // 433 [[ ], [ ], [ ]], // 434 [[ ], [4], [4]], // 435 [[ ], [ ], [ ]], // 436 [[ ], [ ], [ ]], // 437 [[ ], [ ], [ ]], // 438 [[ ], [ ], [ ]], 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972 [[ ], [ ], [ ]], // 973 [[ ], [ ], [ ]], // 974 [[ ], [ ], [ ]], // 975 [[ ], [ ], [ ]], // 976 [[ ], [ ], [ ]], // 977 [[ ], [ ], [ ]], // 978 [[ ], [ ], [ ]], // 979 [[ ], [2], [2]], // 980 [[ ], [ ], [ ]], // 981 [[ ], [ ], [ ]], // 982 [[ ], [ ], [ ]], // 983 [[ ], [ ], [ ]], // 984 [[ ], [ ], [ ]], // 985 [[ ], [ ], [ ]], // 986 [[ ], [ ], [ ]], // 987 [[ ], [ ], [ ]], // 988 [[ ], [ ], [ ]], // 989 [[2], [1], [ ]], // 990 [[ ], [ ], [ ]], // 991 [[ ], [ ], [ ]], // 992 [[ ], [2], [2]], // 993 [[ ], [ ], [ ]], // 994 [[ ], [ ], [ ]], // 995 [[ ], [ ], [ ]], // 996 [[ ], [ ], [ ]], // 997 [[ ], [ ], [ ]], // 998 [[ ], [ ], [ ]] // 999 ]; l := [[[ PrimitiveGroupDescription( i+400, n ) : n in k | #PrimitiveGroup(i+400,n)^12 ge Factorial(i+400)/2 ] : k in maxprim[i]] : i in [1..599]]; [i : i in [1..599] | l[i] eq [[],[],[]]]; Output: Magma V2.10-6 Fri Jan 16 2004 10:42:22 on modular [Seed = 274224731] ------------------------------------- [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 150, 151, 152, 153, 154, 155, 156, 157, 158, 159, 160, 161, 162, 163, 164, 165, 166, 167, 168, 169, 170, 171, 172, 173, 174, 175, 176, 177, 178, 179, 180, 181, 182, 183, 184, 185, 186, 187, 188, 189, 190, 191, 192, 193, 194, 195, 196, 197, 198, 199, 200, 201, 202, 203, 204, 205, 206, 207, 208, 209, 210, 211, 212, 213, 214, 215, 216, 217, 218, 219, 220, 221, 222, 223, 224, 225, 226, 227, 228, 229, 230, 231, 232, 233, 234, 235, 236, 237, 238, 239, 240, 241, 242, 243, 244, 245, 246, 247, 248, 249, 250, 251, 252, 253, 254, 255, 256, 257, 258, 259, 260, 261, 262, 263, 264, 265, 266, 267, 268, 269, 270, 271, 272, 273, 274, 275, 276, 277, 278, 279, 280, 281, 282, 283, 284, 285, 286, 287, 288, 289, 290, 291, 292, 293, 294, 295, 296, 297, 298, 299, 300, 301, 302, 303, 304, 305, 306, 307, 308, 309, 310, 311, 312, 313, 314, 315, 316, 317, 318, 319, 320, 321, 322, 323, 324, 325, 326, 327, 328, 329, 330, 331, 332, 333, 334, 335, 336, 337, 338, 339, 340, 341, 342, 343, 344, 345, 346, 347, 348, 349, 350, 351, 352, 353, 354, 355, 356, 357, 358, 359, 360, 361, 362, 363, 364, 365, 366, 367, 368, 369, 370, 371, 372, 373, 374, 375, 376, 377, 378, 379, 380, 381, 382, 383, 384, 385, 386, 387, 388, 389, 390, 391, 392, 393, 394, 395, 396, 397, 398, 399, 400, 401, 402, 403, 404, 405, 406, 407, 408, 409, 410, 411, 412, 413, 414, 415, 416, 417, 418, 419, 420, 421, 422, 423, 424, 425, 426, 427, 428, 429, 430, 431, 432, 433, 434, 435, 436, 437, 438, 439, 440, 441, 442, 443, 444, 445, 446, 447, 448, 449, 450, 451, 452, 453, 454, 455, 456, 457, 458, 459, 460, 461, 462, 463, 464, 465, 466, 467, 468, 469, 470, 471, 472, 473, 474, 475, 476, 477, 478, 479, 480, 481, 482, 483, 484, 485, 486, 487, 488, 489, 490, 491, 492, 493, 494, 495, 496, 497, 498, 499, 500, 501, 502, 503, 504, 505, 506, 507, 508, 509, 510, 511, 512, 513, 514, 515, 516, 517, 518, 519, 520, 521, 522, 523, 524, 525, 526, 527, 528, 529, 530, 531, 532, 533, 534, 535, 536, 537, 538, 539, 540, 541, 542, 543, 544, 545, 546, 547, 548, 549, 550, 551, 552, 553, 554, 555, 556, 557, 558, 559, 560, 561, 562, 563, 564, 565, 566, 567, 568, 569, 570, 571, 572, 573, 574, 575, 576, 577, 578, 579, 580, 581, 582, 583, 584, 585, 586, 587, 588, 589, 590, 591, 592, 593, 594, 595, 596, 597, 598, 599 ] Total time: 5.329 seconds, Total memory usage: 2.20MB ************** MAGMA ***************** Host ibm21.ilab.sztaki.hu. (195.111.1.97) Time: Fri Jan 16 10:42:46 2004 Input: maxprim := [[[ ], [ ], [ ]], // 401 [[ ], [ ], [ ]], // 402 [[ ], [ ], [ ]], // 403 [[ ], [ ], [ ]], // 404 [[ ], [ ], [ ]], // 405 [[4, 2], [3, 1], [ ]], // 406 [[ ], [ ], [ ]], // 407 [[ ], [ ], [ ]], // 408 [[ ], [ ], [ ]], // 409 [[ ], [ ], [ ]], // 410 [[ ], [ ], [ ]], // 411 [[ ], [ ], [ ]], // 412 [[ ], [ ], [ ]], // 413 [[ ], [ ], [ ]], // 414 [[ ], [ ], [ ]], // 415 [[ ], [5], [5]], // 416 [[ ], [ ], [ ]], // 417 [[ ], [ ], [ ]], // 418 [[ ], [ ], [ ]], // 419 [[ ], [ ], [ ]], // 420 [[ ], [ ], [ ]], // 421 [[ ], [ ], [ ]], // 422 [[ ], [ ], [ ]], // 423 [[ ], [ ], [ ]], // 424 [[1], [ ], [ ]], // 425 [[ ], [ ], [ ]], // 426 [[ ], [ ], [ ]], // 427 [[ ], [ ], [ ]], // 428 [[ ], [ ], [ ]], // 429 [[ ], [ ], [ ]], // 430 [[ ], [ ], [ ]], // 431 [[ ], [ ], [ ]], // 432 [[ ], [ ], [ ]], // 433 [[ ], [ ], [ ]], // 434 [[ ], [4], [4]], // 435 [[ ], [ ], [ ]], // 436 [[ ], [ ], [ ]], // 437 [[ ], [ ], [ ]], // 438 [[ ], [ ], [ ]], 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972 [[ ], [ ], [ ]], // 973 [[ ], [ ], [ ]], // 974 [[ ], [ ], [ ]], // 975 [[ ], [ ], [ ]], // 976 [[ ], [ ], [ ]], // 977 [[ ], [ ], [ ]], // 978 [[ ], [ ], [ ]], // 979 [[ ], [2], [2]], // 980 [[ ], [ ], [ ]], // 981 [[ ], [ ], [ ]], // 982 [[ ], [ ], [ ]], // 983 [[ ], [ ], [ ]], // 984 [[ ], [ ], [ ]], // 985 [[ ], [ ], [ ]], // 986 [[ ], [ ], [ ]], // 987 [[ ], [ ], [ ]], // 988 [[ ], [ ], [ ]], // 989 [[2], [1], [ ]], // 990 [[ ], [ ], [ ]], // 991 [[ ], [ ], [ ]], // 992 [[ ], [2], [2]], // 993 [[ ], [ ], [ ]], // 994 [[ ], [ ], [ ]], // 995 [[ ], [ ], [ ]], // 996 [[ ], [ ], [ ]], // 997 [[ ], [ ], [ ]], // 998 [[ ], [ ], [ ]] // 999 ]; l := [[[ PrimitiveGroupDescription( i+400, n ) : n in k | #PrimitiveGroup(i+400,n)^12 ge Factorial(i+400)/2 ] : k in maxprim[i]] : i in [1..599]]; [i : i in [1..599] | l[i] ne [[],[],[]]]; Output: Magma V2.10-6 Fri Jan 16 2004 10:42:41 on modular [Seed = 458448255] ------------------------------------- [] Total time: 5.169 seconds, Total memory usage: 2.20MB ************** MAGMA ***************** Host 3(NXDOMAIN) (194.165.15.3) Time: Fri Jan 16 13:26:08 2004 Input: k := GF(2); C := PrimitivePolynomial(k,9); C; for n in [5..20] do for m in [5..20] do C := (1 + X^(m*(i-1)))*(1 + X^m)*(1 + X^(n*(i-1)))*(1 + X^n) + X^521; if IsPrimitive(C) then C; end if; end for; end for; Output: Magma V2.10-6 Fri Jan 16 2004 13:26:05 on modular [Seed = 3600726653] ------------------------------------- X^9 + X^4 + 1 >> C := (1 + X^(m*(i-1)))*(1 + X^m)*(1 + X^(n*(i-1)))*(1 + X^n) + X^52 ^ User error: Identifier 'i' has not been declared or assigned Total time: 2.999 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (194.165.15.3) Time: Fri Jan 16 13:26:38 2004 Input: k := GF(2); C := PrimitivePolynomial(k,9); C; i=13 for n in [5..20] do for m in [5..20] do C := (1 + X^(m*(i-1)))*(1 + X^m)*(1 + X^(n*(i-1)))*(1 + X^n) + X^521; if IsPrimitive(C) then C; end if; end for; end for; Output: Magma V2.10-6 Fri Jan 16 2004 13:26:35 on modular [Seed = 3751260946] ------------------------------------- X^9 + X^4 + 1 >> for n in [5..20] do ^ User error: bad syntax >> C := (1 + X^(m*(i-1)))*(1 + X^m)*(1 + X^(n*(i-1)))*(1 + X^n) + X^52 ^ User error: Identifier 'i' has not been declared or assigned >> end for; ^ User error: bad syntax Total time: 3.019 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (194.165.15.3) Time: Fri Jan 16 13:26:59 2004 Input: k := GF(2); C := PrimitivePolynomial(k,9); C; i :=13; for n in [5..20] do for m in [5..20] do C := (1 + X^(m*(i-1)))*(1 + X^m)*(1 + X^(n*(i-1)))*(1 + X^n) + X^521; if IsPrimitive(C) then C; end if; end for; end for; Output: Magma V2.10-6 Fri Jan 16 2004 13:26:55 on modular [Seed = 3297552445] ------------------------------------- X^9 + X^4 + 1 X^521 + X^169 + X^163 + X^162 + X^156 + X^97 + X^91 + X^90 + X^85 + X^84 + X^79 + X^78 + X^72 + X^13 + X^7 + X^6 + 1 X^521 + X^169 + X^163 + X^162 + X^156 + X^97 + X^91 + X^90 + X^85 + X^84 + X^79 + X^78 + X^72 + X^13 + X^7 + X^6 + 1 X^521 + X^377 + X^363 + X^362 + X^348 + X^209 + X^197 + X^195 + X^194 + X^183 + X^182 + X^180 + X^168 + X^29 + X^15 + X^14 + 1 X^521 + X^377 + X^363 + X^362 + X^348 + X^209 + X^197 + X^195 + X^194 + X^183 + X^182 + X^180 + X^168 + X^29 + X^15 + X^14 + 1 X^521 + X^455 + X^439 + X^436 + X^420 + X^263 + X^247 + X^244 + X^228 + X^227 + X^211 + X^208 + X^192 + X^35 + X^19 + X^16 + 1 X^521 + X^455 + X^439 + X^436 + X^420 + X^263 + X^247 + X^244 + X^228 + X^227 + X^211 + X^208 + X^192 + X^35 + X^19 + X^16 + 1 Total time: 3.699 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 3(NXDOMAIN) (194.165.15.3) Time: Fri Jan 16 13:27:29 2004 Input: k := GF(2); C := PrimitivePolynomial(k,9); C; i :=16; for n in [5..20] do for m in [5..20] do C := (1 + X^(m*(i-1)))*(1 + X^m)*(1 + X^(n*(i-1)))*(1 + X^n) + X^521; if IsPrimitive(C) then C; end if; end for; end for; Output: Magma V2.10-6 Fri Jan 16 2004 13:27:24 on modular [Seed = 3448086743] ------------------------------------- X^9 + X^4 + 1 X^521 + X^368 + X^357 + X^356 + X^345 + X^203 + X^192 + X^191 + X^188 + X^180 + X^177 + X^176 + X^165 + X^23 + X^12 + X^11 + 1 X^521 + X^368 + X^357 + X^356 + X^345 + X^203 + X^192 + X^191 + X^188 + X^180 + X^177 + X^176 + X^165 + X^23 + X^12 + X^11 + 1 Total time: 4.319 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 3(NXDOMAIN) (194.165.15.3) Time: Fri Jan 16 13:28:31 2004 Input: k := GF(2); C := PrimitivePolynomial(k,9); C; i :=16; for n in [1..50] do for m in [1..50] do C := (1 + X^(m*(i-1)))*(1 + X^m)*(1 + X^(n*(i-1)))*(1 + X^n) + X^521; if IsPrimitive(C) then C; end if; end for; end for; Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Fri Jan 16 2004 13:28:08 on modular [Seed = 4072316892] ------------------------------------- X^9 + X^4 + 1 X^640 + X^639 + X^625 + X^624 + X^601 + X^600 + X^586 + X^585 + X^521 + X^55 + X^54 + X^40 + X^39 + X^16 + X^15 + X + 1 X^521 + X^464 + X^462 + X^437 + X^435 + X^434 + X^432 + X^407 + X^405 + X^59 + X^57 + X^32 + X^30 + X^29 + X^27 + X^2 + 1 X^521 + X^320 + X^317 + X^303 + X^300 + X^275 + X^272 + X^258 + X^255 + X^65 + X^62 + X^48 + X^45 + X^20 + X^17 + X^3 + 1 X^521 + X^368 + X^357 + X^356 + X^345 + X^203 + X^192 + X^191 + X^188 + X^180 + X^177 + X^176 + X^165 + X^23 + X^12 + X^11 + 1 X^521 + X^368 + X^357 + X^356 + X^345 + X^203 + X^192 + X^191 + X^188 + X^180 + X^177 + X^176 + X^165 + X^23 + X^12 + X^11 + 1 X^608 + X^593 + X^585 + X^570 + X^521 + X^383 + X^368 + X^360 + X^345 + X^263 + X^248 + X^240 + X^225 + X^38 + X^23 + X^15 + 1 X^521 + X^320 + X^317 + X^303 + X^300 + X^275 + X^272 + X^258 + X^255 + X^65 + X^62 + X^48 + X^45 + X^20 + X^17 + X^3 + 1 X^608 + X^593 + X^585 + X^570 + X^521 + X^383 + X^368 + X^360 + X^345 + X^263 + X^248 + X^240 + X^225 + X^38 + X^23 + X^15 + 1 X^521 + X^464 + X^462 + X^437 + X^435 + X^434 + X^432 + X^407 + X^405 + X^59 + X^57 + X^32 + X^30 + X^29 + X^27 + X^2 + 1 X^640 + X^639 + X^625 + X^624 + X^601 + X^600 + X^586 + X^585 + X^521 + X^55 + X^54 + X^40 + X^39 + X^16 + X^15 + X + 1 X^1376 + X^1337 + X^1329 + X^1290 + X^791 + X^752 + X^744 + X^705 + X^671 + X^632 + X^624 + X^585 + X^521 + X^86 + X^47 + X^39 + 1 Errors: /home/mfd/gomagma: line 2: 22244 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host 3(NXDOMAIN) (194.165.15.3) Time: Fri Jan 16 13:29:21 2004 Input: k := GF(2); C := PrimitivePolynomial(k,9); C; i :=16; for n in [1..40] do for m in [1..40] do C := (1 + X^(m*(i-1)))*(1 + X^m)*(1 + X^(n*(i-1)))*(1 + X^n) + X^521; if IsPrimitive(C) then C; end if; end for; end for; Output: Magma V2.10-6 Fri Jan 16 2004 13:29:09 on modular [Seed = 4222850712] ------------------------------------- X^9 + X^4 + 1 X^640 + X^639 + X^625 + X^624 + X^601 + X^600 + X^586 + X^585 + X^521 + X^55 + X^54 + X^40 + X^39 + X^16 + X^15 + X + 1 X^521 + X^464 + X^462 + X^437 + X^435 + X^434 + X^432 + X^407 + X^405 + X^59 + X^57 + X^32 + X^30 + X^29 + X^27 + X^2 + 1 X^521 + X^320 + X^317 + X^303 + X^300 + X^275 + X^272 + X^258 + X^255 + X^65 + X^62 + X^48 + X^45 + X^20 + X^17 + X^3 + 1 X^521 + X^368 + X^357 + X^356 + X^345 + X^203 + X^192 + X^191 + X^188 + X^180 + X^177 + X^176 + X^165 + X^23 + X^12 + X^11 + 1 X^521 + X^368 + X^357 + X^356 + X^345 + X^203 + X^192 + X^191 + X^188 + X^180 + X^177 + X^176 + X^165 + X^23 + X^12 + X^11 + 1 X^608 + X^593 + X^585 + X^570 + X^521 + X^383 + X^368 + X^360 + X^345 + X^263 + X^248 + X^240 + X^225 + X^38 + X^23 + X^15 + 1 X^521 + X^320 + X^317 + X^303 + X^300 + X^275 + X^272 + X^258 + X^255 + X^65 + X^62 + X^48 + X^45 + X^20 + X^17 + X^3 + 1 X^608 + X^593 + X^585 + X^570 + X^521 + X^383 + X^368 + X^360 + X^345 + X^263 + X^248 + X^240 + X^225 + X^38 + X^23 + X^15 + 1 X^521 + X^464 + X^462 + X^437 + X^435 + X^434 + X^432 + X^407 + X^405 + X^59 + X^57 + X^32 + X^30 + X^29 + X^27 + X^2 + 1 X^640 + X^639 + X^625 + X^624 + X^601 + X^600 + X^586 + X^585 + X^521 + X^55 + X^54 + X^40 + X^39 + X^16 + X^15 + X + 1 Total time: 12.339 seconds, Total memory usage: 1.99MB ************** MAGMA ***************** Host 3(NXDOMAIN) (194.165.15.3) Time: Fri Jan 16 13:30:01 2004 Input: k := GF(2); C := PrimitivePolynomial(k,9); C; i :=16; for n in [1..40] do for m in [1..50] do C := (1 + X^(m*(i-1)))*(1 + X^m)*(1 + X^(n*(i-1)))*(1 + X^n) + X^521; if IsPrimitive(C) then C; end if; end for; end for; Output: Magma V2.10-6 Fri Jan 16 2004 13:29:42 on modular [Seed = 3785985121] ------------------------------------- X^9 + X^4 + 1 X^640 + X^639 + X^625 + X^624 + X^601 + X^600 + X^586 + X^585 + X^521 + X^55 + X^54 + X^40 + X^39 + X^16 + X^15 + X + 1 X^521 + X^464 + X^462 + X^437 + X^435 + X^434 + X^432 + X^407 + X^405 + X^59 + X^57 + X^32 + X^30 + X^29 + X^27 + X^2 + 1 X^521 + X^320 + X^317 + X^303 + X^300 + X^275 + X^272 + X^258 + X^255 + X^65 + X^62 + X^48 + X^45 + X^20 + X^17 + X^3 + 1 X^521 + X^368 + X^357 + X^356 + X^345 + X^203 + X^192 + X^191 + X^188 + X^180 + X^177 + X^176 + X^165 + X^23 + X^12 + X^11 + 1 X^521 + X^368 + X^357 + X^356 + X^345 + X^203 + X^192 + X^191 + X^188 + X^180 + X^177 + X^176 + X^165 + X^23 + X^12 + X^11 + 1 X^608 + X^593 + X^585 + X^570 + X^521 + X^383 + X^368 + X^360 + X^345 + X^263 + X^248 + X^240 + X^225 + X^38 + X^23 + X^15 + 1 X^521 + X^320 + X^317 + X^303 + X^300 + X^275 + X^272 + X^258 + X^255 + X^65 + X^62 + X^48 + X^45 + X^20 + X^17 + X^3 + 1 X^608 + X^593 + X^585 + X^570 + X^521 + X^383 + X^368 + X^360 + X^345 + X^263 + X^248 + X^240 + X^225 + X^38 + X^23 + X^15 + 1 X^521 + X^464 + X^462 + X^437 + X^435 + X^434 + X^432 + X^407 + X^405 + X^59 + X^57 + X^32 + X^30 + X^29 + X^27 + X^2 + 1 X^640 + X^639 + X^625 + X^624 + X^601 + X^600 + X^586 + X^585 + X^521 + X^55 + X^54 + X^40 + X^39 + X^16 + X^15 + X + 1 X^1376 + X^1337 + X^1329 + X^1290 + X^791 + X^752 + X^744 + X^705 + X^671 + X^632 + X^624 + X^585 + X^521 + X^86 + X^47 + X^39 + 1 Total time: 18.229 seconds, Total memory usage: 2.37MB ************** MAGMA ***************** Host 3(NXDOMAIN) (194.165.15.3) Time: Fri Jan 16 13:30:38 2004 Input: k := GF(2); C := PrimitivePolynomial(k,9); C; i :=16; for n in [1..35] do for m in [1..35] do C := (1 + X^(m*(i-1)))*(1 + X^m)*(1 + X^(n*(i-1)))*(1 + X^n) + X^521; if IsPrimitive(C) then C; end if; end for; end for; Output: Magma V2.10-6 Fri Jan 16 2004 13:30:30 on modular [Seed = 525824718] ------------------------------------- X^9 + X^4 + 1 X^521 + X^464 + X^462 + X^437 + X^435 + X^434 + X^432 + X^407 + X^405 + X^59 + X^57 + X^32 + X^30 + X^29 + X^27 + X^2 + 1 X^521 + X^320 + X^317 + X^303 + X^300 + X^275 + X^272 + X^258 + X^255 + X^65 + X^62 + X^48 + X^45 + X^20 + X^17 + X^3 + 1 X^521 + X^368 + X^357 + X^356 + X^345 + X^203 + X^192 + X^191 + X^188 + X^180 + X^177 + X^176 + X^165 + X^23 + X^12 + X^11 + 1 X^521 + X^368 + X^357 + X^356 + X^345 + X^203 + X^192 + X^191 + X^188 + X^180 + X^177 + X^176 + X^165 + X^23 + X^12 + X^11 + 1 X^608 + X^593 + X^585 + X^570 + X^521 + X^383 + X^368 + X^360 + X^345 + X^263 + X^248 + X^240 + X^225 + X^38 + X^23 + X^15 + 1 X^521 + X^320 + X^317 + X^303 + X^300 + X^275 + X^272 + X^258 + X^255 + X^65 + X^62 + X^48 + X^45 + X^20 + X^17 + X^3 + 1 X^608 + X^593 + X^585 + X^570 + X^521 + X^383 + X^368 + X^360 + X^345 + X^263 + X^248 + X^240 + X^225 + X^38 + X^23 + X^15 + 1 X^521 + X^464 + X^462 + X^437 + X^435 + X^434 + X^432 + X^407 + X^405 + X^59 + X^57 + X^32 + X^30 + X^29 + X^27 + X^2 + 1 Total time: 8.460 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 3(NXDOMAIN) (194.165.15.3) Time: Fri Jan 16 13:31:11 2004 Input: k := GF(2); C := PrimitivePolynomial(k,9); C; i :=8; for n in [1..35] do for m in [1..35] do C := (1 + X^(m*(i-1)))*(1 + X^m)*(1 + X^(n*(i-1)))*(1 + X^n) + X^521; if IsPrimitive(C) then C; end if; end for; end for; Output: Magma V2.10-6 Fri Jan 16 2004 13:31:04 on modular [Seed = 105802745] ------------------------------------- X^9 + X^4 + 1 X^521 + X^264 + X^260 + X^236 + X^235 + X^232 + X^231 + X^207 + X^203 + X^61 + X^57 + X^33 + X^32 + X^29 + X^28 + X^4 + 1 X^521 + X^272 + X^268 + X^244 + X^242 + X^240 + X^238 + X^214 + X^210 + X^62 + X^58 + X^34 + X^32 + X^30 + X^28 + X^4 + 1 X^521 + X^288 + X^283 + X^257 + X^253 + X^252 + X^248 + X^222 + X^217 + X^71 + X^66 + X^40 + X^36 + X^35 + X^31 + X^5 + 1 X^521 + X^208 + X^202 + X^188 + X^182 + X^166 + X^160 + X^146 + X^140 + X^68 + X^62 + X^48 + X^42 + X^26 + X^20 + X^6 + 1 X^521 + X^224 + X^217 + X^203 + X^196 + X^175 + X^168 + X^154 + X^147 + X^77 + X^70 + X^56 + X^49 + X^28 + X^21 + X^7 + 1 X^521 + X^288 + X^278 + X^262 + X^252 + X^218 + X^208 + X^192 + X^182 + X^106 + X^96 + X^80 + X^70 + X^36 + X^26 + X^10 + 1 X^521 + X^288 + X^277 + X^263 + X^252 + X^211 + X^200 + X^186 + X^175 + X^113 + X^102 + X^88 + X^77 + X^36 + X^25 + X^11 + 1 X^521 + X^368 + X^354 + X^336 + X^322 + X^270 + X^256 + X^238 + X^224 + X^144 + X^130 + X^112 + X^98 + X^46 + X^32 + X^14 + 1 X^521 + X^392 + X^378 + X^357 + X^343 + X^294 + X^280 + X^259 + X^245 + X^147 + X^133 + X^112 + X^98 + X^49 + X^35 + X^14 + 1 X^521 + X^336 + X^321 + X^309 + X^294 + X^231 + X^216 + X^204 + X^189 + X^147 + X^132 + X^120 + X^105 + X^42 + X^27 + X^15 + 1 X^521 + X^368 + X^352 + X^338 + X^322 + X^256 + X^240 + X^226 + X^210 + X^158 + X^142 + X^128 + X^112 + X^46 + X^30 + X^16 + 1 X^521 + X^400 + X^382 + X^368 + X^350 + X^274 + X^256 + X^242 + X^224 + X^176 + X^158 + X^144 + X^126 + X^50 + X^32 + X^18 + 1 X^521 + X^416 + X^397 + X^383 + X^364 + X^283 + X^264 + X^250 + X^231 + X^185 + X^166 + X^152 + X^133 + X^52 + X^33 + X^19 + 1 X^521 + X^208 + X^202 + X^188 + X^182 + X^166 + X^160 + X^146 + X^140 + X^68 + X^62 + X^48 + X^42 + X^26 + X^20 + X^6 + 1 X^521 + X^336 + X^316 + X^314 + X^294 + X^196 + X^182 + X^176 + X^174 + X^162 + X^160 + X^154 + X^140 + X^42 + X^22 + X^20 + 1 X^521 + X^224 + X^217 + X^203 + X^196 + X^175 + X^168 + X^154 + X^147 + X^77 + X^70 + X^56 + X^49 + X^28 + X^21 + X^7 + 1 X^521 + X^336 + X^316 + X^314 + X^294 + X^196 + X^182 + X^176 + X^174 + X^162 + X^160 + X^154 + X^140 + X^42 + X^22 + X^20 + 1 X^521 + X^288 + X^277 + X^263 + X^252 + X^211 + X^200 + X^186 + X^175 + X^113 + X^102 + X^88 + X^77 + X^36 + X^25 + X^11 + 1 X^521 + X^288 + X^278 + X^262 + X^252 + X^218 + X^208 + X^192 + X^182 + X^106 + X^96 + X^80 + X^70 + X^36 + X^26 + X^10 + 1 X^521 + X^336 + X^321 + X^309 + X^294 + X^231 + X^216 + X^204 + X^189 + X^147 + X^132 + X^120 + X^105 + X^42 + X^27 + X^15 + 1 X^521 + X^264 + X^260 + X^236 + X^235 + X^232 + X^231 + X^207 + X^203 + X^61 + X^57 + X^33 + X^32 + X^29 + X^28 + X^4 + 1 X^521 + X^272 + X^268 + X^244 + X^242 + X^240 + X^238 + X^214 + X^210 + X^62 + X^58 + X^34 + X^32 + X^30 + X^28 + X^4 + 1 X^521 + X^368 + X^352 + X^338 + X^322 + X^256 + X^240 + X^226 + X^210 + X^158 + X^142 + X^128 + X^112 + X^46 + X^30 + X^16 + 1 X^521 + X^288 + X^283 + X^257 + X^253 + X^252 + X^248 + X^222 + X^217 + X^71 + X^66 + X^40 + X^36 + X^35 + X^31 + X^5 + 1 X^521 + X^368 + X^354 + X^336 + X^322 + X^270 + X^256 + X^238 + X^224 + X^144 + X^130 + X^112 + X^98 + X^46 + X^32 + X^14 + 1 X^521 + X^400 + X^382 + X^368 + X^350 + X^274 + X^256 + X^242 + X^224 + X^176 + X^158 + X^144 + X^126 + X^50 + X^32 + X^18 + 1 X^521 + X^416 + X^397 + X^383 + X^364 + X^283 + X^264 + X^250 + X^231 + X^185 + X^166 + X^152 + X^133 + X^52 + X^33 + X^19 + 1 X^521 + X^392 + X^378 + X^357 + X^343 + X^294 + X^280 + X^259 + X^245 + X^147 + X^133 + X^112 + X^98 + X^49 + X^35 + X^14 + 1 Total time: 6.629 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 3(NXDOMAIN) (194.165.15.3) Time: Fri Jan 16 13:32:12 2004 Input: k := GF(2); C := PrimitivePolynomial(k,9); C; i :=9; for n in [1..35] do for m in [1..35] do C := (1 + X^(m*(i-1)))*(1 + X^m)*(1 + X^(n*(i-1)))*(1 + X^n) + X^521; if IsPrimitive(C) then C; end if; end for; end for; Output: Magma V2.10-6 Fri Jan 16 2004 13:32:02 on modular [Seed = 222651192] ------------------------------------- X^9 + X^4 + 1 X^521 + X^270 + X^268 + X^254 + X^252 + X^242 + X^240 + X^226 + X^224 + X^46 + X^44 + X^30 + X^28 + X^18 + X^16 + X^2 + 1 X^521 + X^243 + X^237 + X^222 + X^216 + X^195 + X^189 + X^174 + X^168 + X^75 + X^69 + X^54 + X^48 + X^27 + X^21 + X^6 + 1 X^521 + X^306 + X^298 + X^280 + X^272 + X^242 + X^234 + X^216 + X^208 + X^98 + X^90 + X^72 + X^64 + X^34 + X^26 + X^8 + 1 X^521 + X^306 + X^297 + X^281 + X^272 + X^234 + X^225 + X^209 + X^200 + X^106 + X^97 + X^81 + X^72 + X^34 + X^25 + X^9 + 1 X^521 + X^216 + X^206 + X^202 + X^192 + X^136 + X^126 + X^122 + X^112 + X^104 + X^94 + X^90 + X^80 + X^24 + X^14 + X^10 + 1 X^521 + X^216 + X^206 + X^202 + X^192 + X^136 + X^126 + X^122 + X^112 + X^104 + X^94 + X^90 + X^80 + X^24 + X^14 + X^10 + 1 X^521 + X^414 + X^400 + X^382 + X^368 + X^302 + X^288 + X^270 + X^256 + X^158 + X^144 + X^126 + X^112 + X^46 + X^32 + X^14 + 1 X^521 + X^333 + X^318 + X^311 + X^296 + X^213 + X^198 + X^191 + X^176 + X^157 + X^142 + X^135 + X^120 + X^37 + X^22 + X^15 + 1 X^521 + X^450 + X^434 + X^416 + X^400 + X^322 + X^306 + X^288 + X^272 + X^178 + X^162 + X^144 + X^128 + X^50 + X^34 + X^16 + 1 X^521 + X^369 + X^351 + X^346 + X^328 + X^225 + X^207 + X^202 + X^185 + X^184 + X^167 + X^162 + X^144 + X^41 + X^23 + X^18 + 1 X^521 + X^396 + X^378 + X^370 + X^352 + X^252 + X^234 + X^226 + X^208 + X^188 + X^170 + X^162 + X^144 + X^44 + X^26 + X^18 + 1 X^521 + X^243 + X^237 + X^222 + X^216 + X^195 + X^189 + X^174 + X^168 + X^75 + X^69 + X^54 + X^48 + X^27 + X^21 + X^6 + 1 X^521 + X^450 + X^429 + X^421 + X^400 + X^282 + X^261 + X^253 + X^232 + X^218 + X^197 + X^189 + X^168 + X^50 + X^29 + X^21 + 1 X^521 + X^333 + X^318 + X^311 + X^296 + X^213 + X^198 + X^191 + X^176 + X^157 + X^142 + X^135 + X^120 + X^37 + X^22 + X^15 + 1 X^521 + X^369 + X^351 + X^346 + X^328 + X^225 + X^207 + X^202 + X^185 + X^184 + X^167 + X^162 + X^144 + X^41 + X^23 + X^18 + 1 X^521 + X^306 + X^297 + X^281 + X^272 + X^234 + X^225 + X^209 + X^200 + X^106 + X^97 + X^81 + X^72 + X^34 + X^25 + X^9 + 1 X^521 + X^306 + X^298 + X^280 + X^272 + X^242 + X^234 + X^216 + X^208 + X^98 + X^90 + X^72 + X^64 + X^34 + X^26 + X^8 + 1 X^521 + X^396 + X^378 + X^370 + X^352 + X^252 + X^234 + X^226 + X^208 + X^188 + X^170 + X^162 + X^144 + X^44 + X^26 + X^18 + 1 X^521 + X^270 + X^268 + X^254 + X^252 + X^242 + X^240 + X^226 + X^224 + X^46 + X^44 + X^30 + X^28 + X^18 + X^16 + X^2 + 1 X^521 + X^450 + X^429 + X^421 + X^400 + X^282 + X^261 + X^253 + X^232 + X^218 + X^197 + X^189 + X^168 + X^50 + X^29 + X^21 + 1 X^521 + X^414 + X^400 + X^382 + X^368 + X^302 + X^288 + X^270 + X^256 + X^158 + X^144 + X^126 + X^112 + X^46 + X^32 + X^14 + 1 X^521 + X^450 + X^434 + X^416 + X^400 + X^322 + X^306 + X^288 + X^272 + X^178 + X^162 + X^144 + X^128 + X^50 + X^34 + X^16 + 1 Total time: 6.769 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 3(NXDOMAIN) (194.165.15.3) Time: Fri Jan 16 13:34:13 2004 Input: k := GF(2); C := PrimitivePolynomial(k,9); C; for n in [1..35] do for m in [1..35] do C := (1 + X^m)*(1 + X^n) + X^521; if IsPrimitive(C) then C; end if; end for; end for; Output: Magma V2.10-6 Fri Jan 16 2004 13:34:09 on modular [Seed = 846879876] ------------------------------------- X^9 + X^4 + 1 X^521 + X^9 + X^7 + X^2 + 1 X^521 + X^24 + X^22 + X^2 + 1 X^521 + X^23 + X^18 + X^5 + 1 X^521 + X^9 + X^7 + X^2 + 1 X^521 + X^44 + X^35 + X^9 + 1 X^521 + X^32 + 1 X^521 + X^48 + X^32 + X^16 + 1 X^521 + X^23 + X^18 + X^5 + 1 X^521 + X^43 + X^22 + X^21 + 1 X^521 + X^24 + X^22 + X^2 + 1 X^521 + X^43 + X^22 + X^21 + 1 X^521 + X^48 + 1 X^521 + X^60 + X^35 + X^25 + 1 X^521 + X^59 + X^30 + X^29 + 1 X^521 + X^59 + X^30 + X^29 + 1 X^521 + X^48 + X^32 + X^16 + 1 X^521 + X^44 + X^35 + X^9 + 1 X^521 + X^60 + X^35 + X^25 + 1 Total time: 3.899 seconds, Total memory usage: 2.09MB ************** MAGMA ***************** Host 3(NXDOMAIN) (194.165.15.3) Time: Fri Jan 16 13:34:52 2004 Input: k := GF(2); C := PrimitivePolynomial(k,9); C; for n in [1..60] do for m in [1..60] do C := (1 + X^m)*(1 + X^n) + X^521; if IsPrimitive(C) then C; end if; end for; end for; Output: Magma V2.10-6 Fri Jan 16 2004 13:34:46 on modular [Seed = 963729384] ------------------------------------- X^9 + X^4 + 1 X^521 + X^9 + X^7 + X^2 + 1 X^521 + X^24 + X^22 + X^2 + 1 X^521 + X^47 + X^45 + X^2 + 1 X^521 + X^48 + X^46 + X^2 + 1 X^521 + X^44 + X^40 + X^4 + 1 X^521 + X^51 + X^47 + X^4 + 1 X^521 + X^61 + X^57 + X^4 + 1 X^521 + X^23 + X^18 + X^5 + 1 X^521 + X^9 + X^7 + X^2 + 1 X^521 + X^65 + X^58 + X^7 + 1 X^521 + X^54 + X^46 + X^8 + 1 X^521 + X^44 + X^35 + X^9 + 1 X^521 + X^52 + X^40 + X^12 + 1 X^521 + X^67 + X^52 + X^15 + 1 X^521 + X^32 + 1 X^521 + X^48 + X^32 + X^16 + 1 X^521 + X^66 + X^49 + X^17 + 1 X^521 + X^23 + X^18 + X^5 + 1 X^521 + X^59 + X^40 + X^19 + 1 X^521 + X^43 + X^22 + X^21 + 1 X^521 + X^24 + X^22 + X^2 + 1 X^521 + X^43 + X^22 + X^21 + 1 X^521 + X^48 + 1 X^521 + X^63 + X^39 + X^24 + 1 X^521 + X^68 + X^44 + X^24 + 1 X^521 + X^60 + X^35 + X^25 + 1 X^521 + X^70 + X^45 + X^25 + 1 X^521 + X^80 + X^54 + X^26 + 1 X^521 + X^59 + X^30 + X^29 + 1 X^521 + X^59 + X^30 + X^29 + 1 X^521 + X^48 + X^32 + X^16 + 1 X^521 + X^93 + X^60 + X^33 + 1 X^521 + X^44 + X^35 + X^9 + 1 X^521 + X^60 + X^35 + X^25 + 1 X^521 + X^95 + X^58 + X^37 + 1 X^521 + X^63 + X^39 + X^24 + 1 X^521 + X^44 + X^40 + X^4 + 1 X^521 + X^52 + X^40 + X^12 + 1 X^521 + X^59 + X^40 + X^19 + 1 X^521 + X^68 + X^44 + X^24 + 1 X^521 + X^101 + X^57 + X^44 + 1 X^521 + X^47 + X^45 + X^2 + 1 X^521 + X^70 + X^45 + X^25 + 1 X^521 + X^48 + X^46 + X^2 + 1 X^521 + X^54 + X^46 + X^8 + 1 X^521 + X^51 + X^47 + X^4 + 1 X^521 + X^66 + X^49 + X^17 + 1 X^521 + X^104 + X^54 + X^50 + 1 X^521 + X^67 + X^52 + X^15 + 1 X^521 + X^80 + X^54 + X^26 + 1 X^521 + X^104 + X^54 + X^50 + 1 X^521 + X^61 + X^57 + X^4 + 1 X^521 + X^101 + X^57 + X^44 + 1 X^521 + X^65 + X^58 + X^7 + 1 X^521 + X^95 + X^58 + X^37 + 1 X^521 + X^119 + X^60 + X^59 + 1 X^521 + X^93 + X^60 + X^33 + 1 X^521 + X^119 + X^60 + X^59 + 1 Total time: 5.849 seconds, Total memory usage: 1.99MB ************** MAGMA ***************** Host 3(NXDOMAIN) (194.165.15.3) Time: Fri Jan 16 13:36:13 2004 Input: k := GF(2); C := PrimitivePolynomial(k,9); C; i := 16; for n in [1..60] do for m in [1..60] do C := (1 + X^(m*i))*(1 + X^(n*i)) + X^521; if IsPrimitive(C) then C; end if; end for; end for; Output: Magma V2.10-6 Fri Jan 16 2004 13:36:00 on modular [Seed = 727925804] ------------------------------------- X^9 + X^4 + 1 X^521 + X^32 + 1 X^521 + X^48 + X^32 + X^16 + 1 X^521 + X^48 + X^32 + X^16 + 1 X^521 + X^144 + X^112 + X^32 + 1 X^521 + X^144 + X^112 + X^32 + 1 X^521 + X^336 + X^176 + X^160 + 1 X^521 + X^336 + X^176 + X^160 + 1 Total time: 11.609 seconds, Total memory usage: 2.34MB ************** MAGMA ***************** Host 3(NXDOMAIN) (194.165.15.3) Time: Fri Jan 16 13:37:17 2004 Input: k := GF(2); C := PrimitivePolynomial(k,9); C; i := 18; for n in [1..60] do for m in [1..60] do C := (1 + X^(m*i))*(1 + X^(n*i)) + X^521; if IsPrimitive(C) then C; end if; end for; end for; Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Fri Jan 16 2004 13:36:54 on modular [Seed = 1377451267] ------------------------------------- X^9 + X^4 + 1 X^521 + X^270 + X^252 + X^18 + 1 X^756 + X^720 + X^521 + X^36 + 1 X^846 + X^792 + X^521 + X^54 + 1 X^521 + X^306 + X^234 + X^72 + 1 X^521 + X^216 + X^126 + X^90 + 1 X^972 + X^882 + X^521 + X^90 + 1 X^521 + X^216 + X^126 + X^90 + 1 X^521 + X^414 + X^288 + X^126 + 1 X^521 + X^486 + X^360 + X^126 + 1 X^521 + X^450 + X^306 + X^144 + 1 X^521 + X^396 + X^234 + X^162 + 1 X^774 + X^558 + X^521 + X^216 + 1 X^521 + X^306 + X^234 + X^72 + 1 X^521 + X^396 + X^234 + X^162 + 1 X^521 + X^270 + X^252 + X^18 + 1 X^630 + X^521 + X^360 + X^270 + 1 X^521 + X^414 + X^288 + X^126 + 1 X^521 + X^450 + X^306 + X^144 + 1 X^1350 + X^1008 + X^521 + X^342 + 1 X^521 + X^486 + X^360 + X^126 + 1 X^630 + X^521 + X^360 + X^270 + 1 X^1116 + X^666 + X^521 + X^450 + 1 X^774 + X^558 + X^521 + X^216 + 1 X^1278 + X^702 + X^576 + X^521 + 1 X^1116 + X^666 + X^521 + X^450 + 1 X^1278 + X^702 + X^576 + X^521 + 1 X^756 + X^720 + X^521 + X^36 + 1 X^846 + X^792 + X^521 + X^54 + 1 Errors: /home/mfd/gomagma: line 2: 22341 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host 3(NXDOMAIN) (194.165.15.3) Time: Fri Jan 16 13:39:12 2004 Input: k := GF(2); C := PrimitivePolynomial(k,9); C; i := 16; for n in [1..60] do for m in [1..60] do C := (1 + X^(m*i))*(1 + X^(n*i)) + X^521; if IsPrimitive(C) then C; end if; end for; end for; Output: Magma V2.10-6 Fri Jan 16 2004 13:39:00 on modular [Seed = 1158490774] ------------------------------------- X^9 + X^4 + 1 X^521 + X^32 + 1 X^521 + X^48 + X^32 + X^16 + 1 X^521 + X^48 + X^32 + X^16 + 1 X^521 + X^144 + X^112 + X^32 + 1 X^521 + X^144 + X^112 + X^32 + 1 X^521 + X^336 + X^176 + X^160 + 1 X^521 + X^336 + X^176 + X^160 + 1 Total time: 11.599 seconds, Total memory usage: 2.34MB ************** MAGMA ***************** Host 3(NXDOMAIN) (194.165.15.3) Time: Fri Jan 16 13:40:25 2004 Input: k := GF(2); C := PrimitivePolynomial(k,9); C; i := 15; for n in [1..60] do for m in [1..60] do C := (1 + X^(m*i))*(1 + X^(n*i)) + X^521; if IsPrimitive(C) then C; end if; end for; end for; Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Fri Jan 16 2004 13:40:02 on modular [Seed = 1950090337] ------------------------------------- X^9 + X^4 + 1 X^521 + X^165 + X^135 + X^30 + 1 X^750 + X^720 + X^521 + X^30 + 1 X^521 + X^510 + X^465 + X^45 + 1 X^825 + X^720 + X^521 + X^105 + 1 X^521 + X^330 + X^210 + X^120 + 1 X^521 + X^165 + X^135 + X^30 + 1 X^521 + X^330 + X^210 + X^120 + 1 X^525 + X^521 + X^315 + X^210 + 1 X^930 + X^705 + X^521 + X^225 + 1 X^630 + X^521 + X^360 + X^270 + 1 X^825 + X^540 + X^521 + X^285 + 1 X^615 + X^521 + X^315 + X^300 + 1 X^525 + X^521 + X^315 + X^210 + 1 X^615 + X^521 + X^315 + X^300 + 1 X^915 + X^570 + X^521 + X^345 + 1 X^630 + X^521 + X^360 + X^270 + 1 X^1305 + X^855 + X^521 + X^450 + 1 X^521 + X^510 + X^465 + X^45 + 1 X^825 + X^540 + X^521 + X^285 + 1 X^915 + X^570 + X^521 + X^345 + 1 X^930 + X^705 + X^521 + X^225 + 1 X^750 + X^720 + X^521 + X^30 + 1 X^825 + X^720 + X^521 + X^105 + 1 X^1305 + X^855 + X^521 + X^450 + 1 Errors: /home/mfd/gomagma: line 2: 22371 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host 3(NXDOMAIN) (194.165.15.3) Time: Fri Jan 16 13:41:47 2004 Input: k := GF(2); C := PrimitivePolynomial(k,9); C; i := 13; for n in [1..60] do for m in [1..60] do C := (1 + X^(m*i))*(1 + X^(n*i)) + X^521; if IsPrimitive(C) then C; end if; end for; end for; Output: Magma V2.10-6 Fri Jan 16 2004 13:41:33 on modular [Seed = 2066942769] ------------------------------------- X^9 + X^4 + 1 X^521 + X^468 + X^455 + X^13 + 1 X^521 + X^494 + X^481 + X^13 + 1 X^521 + X^403 + X^364 + X^39 + 1 X^598 + X^521 + X^520 + X^78 + 1 X^806 + X^728 + X^521 + X^78 + 1 X^521 + X^468 + X^377 + X^91 + 1 X^521 + X^455 + X^351 + X^104 + 1 X^521 + X^494 + X^390 + X^104 + 1 X^521 + X^494 + X^351 + X^143 + 1 X^521 + X^351 + X^195 + X^156 + 1 X^533 + X^521 + X^351 + X^182 + 1 X^521 + X^351 + X^195 + X^156 + 1 X^521 + X^481 + X^286 + X^195 + 1 X^521 + X^494 + X^286 + X^208 + 1 X^521 + X^481 + X^247 + X^234 + 1 X^521 + X^481 + X^247 + X^234 + 1 X^521 + X^481 + X^286 + X^195 + 1 X^521 + X^494 + X^286 + X^208 + 1 X^521 + X^455 + X^351 + X^104 + 1 X^521 + X^494 + X^351 + X^143 + 1 X^533 + X^521 + X^351 + X^182 + 1 X^521 + X^403 + X^364 + X^39 + 1 X^521 + X^468 + X^377 + X^91 + 1 X^1118 + X^741 + X^521 + X^377 + 1 X^521 + X^494 + X^390 + X^104 + 1 X^521 + X^468 + X^455 + X^13 + 1 X^521 + X^494 + X^481 + X^13 + 1 X^1196 + X^715 + X^521 + X^481 + 1 X^598 + X^521 + X^520 + X^78 + 1 X^1196 + X^715 + X^521 + X^481 + 1 X^806 + X^728 + X^521 + X^78 + 1 X^1118 + X^741 + X^521 + X^377 + 1 Total time: 14.099 seconds, Total memory usage: 3.13MB ************** MAGMA ***************** Host 3(NXDOMAIN) (194.165.15.3) Time: Fri Jan 16 13:43:54 2004 Input: k := GF(2); C := PrimitivePolynomial(k,9); C; for n in [1..60] do for m in [1..60] do C := (1 + X^(m*17))*(1 + X^(n*13)) + X^521; if IsPrimitive(C) then C; end if; end for; end for; Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Fri Jan 16 2004 13:43:31 on modular [Seed = 1646924454] ------------------------------------- X^9 + X^4 + 1 X^521 + X^193 + X^102 + X^91 + 1 X^975 + X^884 + X^521 + X^91 + 1 X^1138 + X^969 + X^521 + X^169 + 1 X^521 + X^267 + X^182 + X^85 + 1 X^633 + X^521 + X^425 + X^208 + 1 X^521 + X^272 + X^221 + X^51 + 1 X^521 + X^353 + X^234 + X^119 + 1 X^521 + X^349 + X^247 + X^102 + 1 X^521 + X^400 + X^247 + X^153 + 1 X^706 + X^521 + X^459 + X^247 + 1 X^521 + X^413 + X^260 + X^153 + 1 X^753 + X^521 + X^493 + X^260 + 1 X^699 + X^521 + X^374 + X^325 + 1 Errors: /home/mfd/gomagma: line 2: 22389 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host 3(NXDOMAIN) (194.165.15.3) Time: Fri Jan 16 13:45:46 2004 Input: k := GF(2); C := PrimitivePolynomial(k,9); C; for n in [1..50] do for m in [1..50] do C := (1 + X^(m*19))*(1 + X^(n*13)) + X^521; if IsPrimitive(C) then C; end if; end for; end for; Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Fri Jan 16 2004 13:45:23 on modular [Seed = 2497504704] ------------------------------------- X^9 + X^4 + 1 X^686 + X^608 + X^521 + X^78 + 1 X^521 + X^360 + X^208 + X^152 + 1 X^521 + X^481 + X^247 + X^234 + 1 Errors: /home/mfd/gomagma: line 2: 22403 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host 3(NXDOMAIN) (194.165.15.3) Time: Fri Jan 16 13:46:46 2004 Input: k := GF(2); C := PrimitivePolynomial(k,9); C; for n in [1..50] do for m in [1..50] do C := (1 + X^(m*19))*(1 + X^(n*17)) + X^521; if IsPrimitive(C) then C; end if; end for; end for; Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Fri Jan 16 2004 13:46:23 on modular [Seed = 2614356723] ------------------------------------- X^9 + X^4 + 1 X^521 + X^207 + X^190 + X^17 + 1 X^521 + X^376 + X^342 + X^34 + 1 X^521 + X^431 + X^380 + X^51 + 1 X^521 + X^349 + X^247 + X^102 + 1 X^521 + X^400 + X^247 + X^153 + 1 X^531 + X^521 + X^361 + X^170 + 1 X^521 + X^508 + X^304 + X^204 + 1 X^521 + X^350 + X^255 + X^95 + 1 X^958 + X^703 + X^521 + X^255 + 1 Errors: /home/mfd/gomagma: line 2: 22412 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host 3(NXDOMAIN) (194.165.15.3) Time: Fri Jan 16 13:47:52 2004 Input: k := GF(2); C := PrimitivePolynomial(k,9); C; for n in [1..50] do for m in [1..50] do C := (1 + X^(m*19))*(1 + X^(n*23)) + X^521; if IsPrimitive(C) then C; end if; end for; end for; Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Fri Jan 16 2004 13:47:29 on modular [Seed = 2194338644] ------------------------------------- X^9 + X^4 + 1 X^521 + X^464 + X^418 + X^46 + 1 X^521 + X^411 + X^342 + X^69 + 1 X^625 + X^521 + X^418 + X^207 + 1 X^521 + X^344 + X^230 + X^114 + 1 X^521 + X^329 + X^253 + X^76 + 1 X^915 + X^570 + X^521 + X^345 + 1 X^1166 + X^798 + X^521 + X^368 + 1 Errors: /home/mfd/gomagma: line 2: 22421 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host 3(NXDOMAIN) (194.165.15.3) Time: Fri Jan 16 13:49:00 2004 Input: k := GF(2); C := PrimitivePolynomial(k,9); C; for n in [1..50] do for m in [1..50] do C := (1 + X^(m*17))*(1 + X^(n*23)) + X^521; if IsPrimitive(C) then C; end if; end for; end for; Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Fri Jan 16 2004 13:48:37 on modular [Seed = 2311191451] ------------------------------------- X^9 + X^4 + 1 X^521 + X^291 + X^153 + X^138 + 1 X^521 + X^325 + X^187 + X^138 + 1 X^521 + X^224 + X^207 + X^17 + 1 X^697 + X^521 + X^391 + X^306 + 1 X^986 + X^595 + X^521 + X^391 + 1 X^795 + X^521 + X^506 + X^289 + 1 Errors: /home/mfd/gomagma: line 2: 22430 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host 3(NXDOMAIN) (194.165.15.3) Time: Fri Jan 16 13:50:06 2004 Input: k := GF(2); C := PrimitivePolynomial(k,9); C; for n in [1..50] do for m in [1..50] do C := (1 + X^(m*17))*(1 + X^(n*31)) + X^521; if IsPrimitive(C) then C; end if; end for; end for; Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Fri Jan 16 2004 13:49:43 on modular [Seed = 2969092832] ------------------------------------- X^9 + X^4 + 1 X^521 + X^322 + X^186 + X^136 + 1 X^721 + X^521 + X^442 + X^279 + 1 Errors: /home/mfd/gomagma: line 2: 22439 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host 3(NXDOMAIN) (194.165.15.3) Time: Fri Jan 16 13:51:00 2004 Input: k := GF(2); C := PrimitivePolynomial(k,9); C; for n in [1..50] do for m in [1..50] do C := (1 + X^(m*13))*(1 + X^(n*31)) + X^521; if IsPrimitive(C) then C; end if; end for; end for; Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Fri Jan 16 2004 13:50:37 on modular [Seed = 2951208389] ------------------------------------- X^9 + X^4 + 1 X^521 + X^223 + X^130 + X^93 + 1 X^521 + X^431 + X^338 + X^93 + 1 X^521 + X^251 + X^186 + X^65 + 1 X^721 + X^521 + X^442 + X^279 + 1 X^915 + X^521 + X^481 + X^434 + 1 X^803 + X^521 + X^465 + X^338 + 1 X^801 + X^775 + X^521 + X^26 + 1 Errors: /home/mfd/gomagma: line 2: 22456 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host 3(NXDOMAIN) (194.165.15.3) Time: Fri Jan 16 13:53:03 2004 Input: k := GF(2); C := PrimitivePolynomial(k,9); C; for i in [1..30] do for n in [1..40] do for m in [1..40] do C := (1 + X^(m*13))*(1 + X^(n*31))*(1 + X^(i*17)) + X^521; if IsPrimitive(C) then C; end if; end for; end for; end for; Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Fri Jan 16 2004 13:52:40 on modular [Seed = 3600720953] ------------------------------------- X^9 + X^4 + 1 X^521 + X^318 + X^301 + X^225 + X^208 + X^110 + X^93 + X^17 + 1 X^561 + X^544 + X^521 + X^327 + X^310 + X^251 + X^234 + X^17 + 1 X^521 + X^498 + X^481 + X^420 + X^403 + X^95 + X^78 + X^17 + 1 X^802 + X^785 + X^521 + X^451 + X^434 + X^368 + X^351 + X^17 + 1 X^803 + X^786 + X^699 + X^682 + X^521 + X^121 + X^104 + X^17 + 1 Errors: /home/mfd/gomagma: line 2: 22465 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host 3(NXDOMAIN) (194.165.15.3) Time: Fri Jan 16 13:54:29 2004 Input: k := GF(2); C := PrimitivePolynomial(k,9); C; for i in [1..30] do for n in [1..40] do for m in [1..40] do C := (1 + X^(m*13))*(1 + X^(n*23))*(1 + X^(i*17)) + X^521; if IsPrimitive(C) then C; end if; end for; end for; end for; Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Fri Jan 16 2004 13:54:06 on modular [Seed = 3700731781] ------------------------------------- X^9 + X^4 + 1 X^521 + X^430 + X^413 + X^407 + X^390 + X^40 + X^23 + X^17 + 1 X^504 + X^498 + X^481 + X^40 + X^23 + X^17 + 1 X^584 + X^567 + X^521 + X^446 + X^429 + X^155 + X^138 + X^17 + 1 X^521 + X^445 + X^428 + X^238 + X^224 + X^221 + X^207 + X^17 + 1 X^693 + X^676 + X^521 + X^394 + X^377 + X^316 + X^299 + X^17 + 1 X^521 + X^495 + X^478 + X^339 + X^322 + X^173 + X^156 + X^17 + 1 X^705 + X^688 + X^523 + X^521 + X^506 + X^199 + X^182 + X^17 + 1 X^806 + X^789 + X^546 + X^529 + X^521 + X^277 + X^260 + X^17 + 1 X^921 + X^904 + X^661 + X^644 + X^521 + X^277 + X^260 + X^17 + 1 Errors: /home/mfd/gomagma: line 2: 22475 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host 3(NXDOMAIN) (194.165.15.3) Time: Fri Jan 16 13:56:02 2004 Input: k := GF(2); C := PrimitivePolynomial(k,9); C; for i in [1..30] do for n in [1..40] do for m in [1..40] do C := (1 + X^(m*13))*(1 + X^(n*19))*(1 + X^(i*17)) + X^521; if IsPrimitive(C) then C; end if; end for; end for; end for; Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Fri Jan 16 2004 13:55:37 on modular [Seed = 4189162055] ------------------------------------- X^9 + X^4 + 1 X^521 + X^218 + X^201 + X^199 + X^182 + X^36 + X^19 + X^17 + 1 X^521 + X^360 + X^343 + X^303 + X^286 + X^74 + X^57 + X^17 + 1 X^521 + X^401 + X^384 + X^245 + X^228 + X^173 + X^156 + X^17 + 1 X^521 + X^366 + X^349 + X^340 + X^323 + X^43 + X^26 + X^17 + 1 X^521 + X^470 + X^453 + X^340 + X^323 + X^147 + X^130 + X^17 + 1 X^572 + X^555 + X^521 + X^416 + X^399 + X^173 + X^156 + X^17 + 1 X^707 + X^690 + X^521 + X^473 + X^456 + X^251 + X^234 + X^17 + 1 X^620 + X^603 + X^568 + X^551 + X^521 + X^69 + X^52 + X^17 + 1 X^875 + X^858 + X^758 + X^741 + X^521 + X^134 + X^117 + X^17 + 1 X^901 + X^884 + X^758 + X^741 + X^521 + X^160 + X^143 + X^17 + 1 X^533 + X^521 + X^499 + X^476 + X^442 + X^91 + X^57 + X^34 + 1 X^521 + X^387 + X^353 + X^216 + X^205 + X^182 + X^171 + X^34 + 1 X^521 + X^497 + X^463 + X^307 + X^273 + X^224 + X^190 + X^34 + 1 X^633 + X^599 + X^521 + X^424 + X^390 + X^243 + X^209 + X^34 + 1 X^521 + X^314 + X^280 + X^262 + X^228 + X^86 + X^52 + X^34 + 1 X^521 + X^496 + X^462 + X^268 + X^262 + X^234 + X^228 + X^34 + 1 X^748 + X^714 + X^521 + X^463 + X^429 + X^319 + X^285 + X^34 + 1 X^521 + X^480 + X^446 + X^376 + X^342 + X^138 + X^104 + X^34 + 1 X^740 + X^706 + X^521 + X^398 + X^376 + X^364 + X^342 + X^34 + 1 X^725 + X^691 + X^521 + X^452 + X^418 + X^307 + X^273 + X^34 + 1 Errors: /home/mfd/gomagma: line 2: 22510 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host 3(NXDOMAIN) (194.165.15.3) Time: Fri Jan 16 13:58:25 2004 Input: k := GF(2); C := PrimitivePolynomial(k,9); C; for i in [1..30] do for n in [1..40] do for m in [1..40] do C := (1 + X^(m*41))*(1 + X^(n*19))*(1 + X^(i*17)) + X^521; if IsPrimitive(C) then C; end if; end for; end for; end for; Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Fri Jan 16 2004 13:58:01 on modular [Seed = 274228273] ------------------------------------- X^9 + X^4 + 1 X^938 + X^921 + X^919 + X^902 + X^521 + X^36 + X^19 + X^17 + 1 X^1531 + X^1514 + X^1493 + X^1476 + X^521 + X^55 + X^38 + X^17 + 1 X^521 + X^317 + X^300 + X^222 + X^205 + X^112 + X^95 + X^17 + 1 X^521 + X^513 + X^496 + X^304 + X^287 + X^226 + X^209 + X^17 + 1 X^561 + X^544 + X^521 + X^397 + X^380 + X^181 + X^164 + X^17 + 1 Errors: /home/mfd/gomagma: line 2: 22536 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host 3(NXDOMAIN) (194.165.15.3) Time: Fri Jan 16 13:59:41 2004 Input: k := GF(2); C := PrimitivePolynomial(k,9); C; for i in [1..30] do for n in [1..40] do for m in [1..40] do C := (1 + X^(m*41))*(1 + X^(n*23))*(1 + X^(i*17)) + X^521; if IsPrimitive(C) then C; end if; end for; end for; end for; Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Fri Jan 16 2004 13:59:18 on modular [Seed = 205813906] ------------------------------------- X^9 + X^4 + 1 Errors: /home/mfd/gomagma: line 2: 22548 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host 3(NXDOMAIN) (194.165.15.3) Time: Fri Jan 16 14:00:22 2004 Input: k := GF(2); C := PrimitivePolynomial(k,9); C; for i in [1..30] do for n in [1..40] do for m in [1..40] do C := (1 + X^(m*41))*(1 + X^(n*23))*(1 + X^(i*19)) + X^521; if IsPrimitive(C) then C; end if; end for; end for; end for; Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Fri Jan 16 2004 13:59:58 on modular [Seed = 946883726] ------------------------------------- X^9 + X^4 + 1 X^690 + X^671 + X^552 + X^533 + X^521 + X^157 + X^138 + X^19 + 1 Errors: /home/mfd/gomagma: line 2: 22560 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host 3(NXDOMAIN) (194.165.15.3) Time: Fri Jan 16 14:01:04 2004 Input: k := GF(2); C := PrimitivePolynomial(k,9); C; for i in [1..30] do for n in [1..40] do for m in [1..40] do C := (1 + X^(m*37))*(1 + X^(n*23))*(1 + X^(i*19)) + X^521; if IsPrimitive(C) then C; end if; end for; end for; end for; Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Fri Jan 16 2004 14:00:41 on modular [Seed = 677403881] ------------------------------------- X^9 + X^4 + 1 X^865 + X^846 + X^796 + X^777 + X^521 + X^88 + X^69 + X^19 + 1 X^563 + X^544 + X^521 + X^341 + X^322 + X^241 + X^222 + X^19 + 1 Errors: /home/mfd/gomagma: line 2: 22576 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host 3(NXDOMAIN) (194.165.15.3) Time: Fri Jan 16 14:01:50 2004 Input: k := GF(2); C := PrimitivePolynomial(k,9); C; for i in [1..30] do for n in [1..40] do for m in [1..40] do C := (1 + X^(m*31))*(1 + X^(n*23))*(1 + X^(i*19)) + X^521; if IsPrimitive(C) then C; end if; end for; end for; end for; Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Fri Jan 16 2004 14:01:27 on modular [Seed = 1394288204] ------------------------------------- X^9 + X^4 + 1 X^521 + X^305 + X^286 + X^236 + X^217 + X^88 + X^69 + X^19 + 1 X^901 + X^882 + X^763 + X^744 + X^521 + X^157 + X^138 + X^19 + 1 Errors: /home/mfd/gomagma: line 2: 22603 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host 3(NXDOMAIN) (194.165.15.3) Time: Fri Jan 16 14:06:18 2004 Input: k := GF(2); C := PrimitivePolynomial(k,9); C; for k in [1..13] do for i in [1..25] do for n in [1..30] do for m in [1..35] do C := (1 + X^(m*29))*(1 + X^(n*23))*(1 + X^(i*19))*(1 + X^(k*19)) + X^521; if IsPrimitive(C) then C; end if; end for; end for; end for; end for; Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Fri Jan 16 2004 14:05:55 on modular [Seed = 1091123018] ------------------------------------- X^9 + X^4 + 1 X^727 + X^689 + X^589 + X^551 + X^521 + X^176 + X^138 + X^38 + 1 X^521 + X^326 + X^288 + X^268 + X^230 + X^96 + X^58 + X^38 + 1 Errors: /home/mfd/gomagma: line 2: 22617 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host 3(NXDOMAIN) (194.165.15.3) Time: Fri Jan 16 14:07:17 2004 Input: k := GF(2); C := PrimitivePolynomial(k,9); C; for k in [1..13] do for i in [1..25] do for n in [1..30] do for m in [1..35] do C := (1 + X^(m*29))*(1 + X^(n*23))*(1 + X^(i*19))*(1 + X^(k*17)) + X^521; if IsPrimitive(C) then C; end if; end for; end for; end for; end for; Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Fri Jan 16 2004 14:06:54 on modular [Seed = 2050100268] ------------------------------------- X^9 + X^4 + 1 X^521 + X^209 + X^192 + X^190 + X^173 + X^151 + X^134 + X^132 + X^115 + X^94 + X^77 + X^75 + X^58 + X^36 + X^19 + X^17 + 1 X^521 + X^232 + X^215 + X^213 + X^196 + X^174 + X^157 + X^155 + X^138 + X^94 + X^77 + X^75 + X^58 + X^36 + X^19 + X^17 + 1 X^1273 + X^1256 + X^1254 + X^1237 + X^790 + X^773 + X^771 + X^754 + X^521 + X^519 + X^502 + X^500 + X^483 + X^36 + X^19 + X^17 + 1 Errors: /home/mfd/gomagma: line 2: 22626 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host 3(NXDOMAIN) (194.165.15.3) Time: Fri Jan 16 14:09:10 2004 Input: k := GF(2); C := PrimitivePolynomial(k,9); C; for k in [1..13] do for i in [1..25] do for n in [1..30] do for m in [1..35] do C := (1 + X^(m*17))*(1 + X^(n*23))*(1 + X^(i*19))*(1 + X^(k*13)) + X^521; if IsPrimitive(C) then C; end if; end for; end for; end for; end for; Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Fri Jan 16 2004 14:08:47 on modular [Seed = 1933247956] ------------------------------------- X^9 + X^4 + 1 X^521 + X^89 + X^76 + X^70 + X^66 + X^57 + X^55 + X^53 + X^47 + X^42 + X^36 + X^34 + X^32 + X^23 + X^19 + X^13 + 1 X^521 + X^209 + X^196 + X^190 + X^177 + X^124 + X^117 + X^111 + X^105 + X^104 + X^98 + X^92 + X^85 + X^32 + X^19 + X^13 + 1 X^521 + X^391 + X^378 + X^372 + X^359 + X^253 + X^240 + X^234 + X^221 + X^170 + X^157 + X^151 + X^138 + X^32 + X^19 + X^13 + 1 X^521 + X^346 + X^333 + X^327 + X^314 + X^193 + X^185 + X^180 + X^174 + X^172 + X^166 + X^161 + X^153 + X^32 + X^19 + X^13 + 1 X^637 + X^624 + X^618 + X^605 + X^521 + X^338 + X^331 + X^325 + X^319 + X^318 + X^312 + X^306 + X^299 + X^32 + X^19 + X^13 + 1 X^907 + X^894 + X^888 + X^875 + X^584 + X^571 + X^565 + X^552 + X^521 + X^355 + X^342 + X^336 + X^323 + X^32 + X^19 + X^13 + 1 X^603 + X^590 + X^580 + X^567 + X^546 + X^533 + X^523 + X^521 + X^510 + X^93 + X^80 + X^70 + X^57 + X^36 + X^23 + X^13 + 1 X^643 + X^630 + X^597 + X^586 + X^584 + X^573 + X^540 + X^527 + X^521 + X^116 + X^103 + X^70 + X^59 + X^57 + X^46 + X^13 + 1 X^593 + X^580 + X^536 + X^523 + X^521 + X^478 + X^465 + X^421 + X^408 + X^185 + X^172 + X^128 + X^115 + X^70 + X^57 + X^13 + 1 X^521 + X^340 + X^327 + X^323 + X^310 + X^283 + X^270 + X^266 + X^253 + X^87 + X^74 + X^70 + X^57 + X^30 + X^17 + X^13 + 1 X^521 + X^459 + X^446 + X^402 + X^389 + X^323 + X^310 + X^266 + X^253 + X^206 + X^193 + X^149 + X^136 + X^70 + X^57 + X^13 + 1 X^587 + X^574 + X^553 + X^540 + X^530 + X^521 + X^517 + X^496 + X^483 + X^104 + X^91 + X^70 + X^57 + X^47 + X^34 + X^13 + 1 Errors: /home/mfd/gomagma: line 2: 22635 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host linux141.ma.utexas.edu. (146.6.139.116) Time: Fri Jan 16 16:06:36 2004 Input: ellinit([1,0,1,0,0]) Output: Magma V2.10-6 Fri Jan 16 2004 16:06:33 on modular [Seed = 4273401022] ------------------------------------- >> ellinit([1,0,1,0,0]) ^ User error: Identifier 'ellinit' has not been declared or assigned Total time: 2.989 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host ppp-111-169.26-151.libero.it. (151.26.169.111) Time: Fri Jan 16 19:31:46 2004 Input: 1+1 Output: Magma V2.10-6 Fri Jan 16 2004 19:31:43 on modular [Seed = 172148857] ------------------------------------- 2 Total time: 2.919 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host ppp-111-169.26-151.libero.it. (151.26.169.111) Time: Fri Jan 16 19:32:37 2004 Input: 121! Output: Magma V2.10-6 Fri Jan 16 2004 19:32:34 on modular [Seed = 880604810] ------------------------------------- >> 121!; ^ User error: bad syntax Total time: 2.939 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host ppp-111-169.26-151.libero.it. (151.26.169.111) Time: Fri Jan 16 19:33:09 2004 Input: 121!; Output: Magma V2.10-6 Fri Jan 16 2004 19:33:06 on modular [Seed = 761655283] ------------------------------------- >> 121!;; ^ User error: bad syntax Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host ppp-111-169.26-151.libero.it. (151.26.169.111) Time: Fri Jan 16 19:33:23 2004 Input: 121! Output: Magma V2.10-6 Fri Jan 16 2004 19:33:20 on modular [Seed = 543744748] ------------------------------------- >> 121!; ^ User error: bad syntax Total time: 2.939 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (193.219.169.234) Time: Mon Jan 19 06:51:12 2004 Input: (a-b)*(a+b)+b^2 Output: Magma V2.10-6 Mon Jan 19 2004 06:51:08 on modular [Seed = 2749900658] ------------------------------------- >> (a-b)*(a+b)+b^2; ^ User error: Identifier 'a' has not been declared or assigned Total time: 3.179 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (194.165.15.3) Time: Mon Jan 19 14:01:04 2004 Input: for k in [1..13] do for i in [1..25] do for n in [1..30] do for m in [1..35] do C := (1 + X^(m*29))*(1 + X^(n*23))*(1 + X^(i*19))*(1 + X^(k*17)) + X^521; if IsPrimitive(C) then C; end if; end for; end for; end for; end for; Output: Magma V2.10-6 Mon Jan 19 2004 14:01:01 on modular [Seed = 1595094579] ------------------------------------- >> C := (1 + X^(m*29))*(1 + X^(n*23))*(1 + X^(i*19))*(1 + X^(k*17)) + ^ User error: Identifier 'X' has not been declared or assigned Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (194.165.15.3) Time: Mon Jan 19 14:02:11 2004 Input: k := GF(2); C := PrimitivePolynomial(k,9); C; for k in [1..13] do for i in [1..25] do for n in [1..30] do for m in [1..35] do C := (1 + X^(m*29))*(1 + X^(n*23))*(1 + X^(i*19))*(1 + X^(k*17)) + X^521; if IsPrimitive(C) then C; end if; end for; end for; end for; end for; Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Mon Jan 19 2004 14:01:48 on modular [Seed = 1797718774] ------------------------------------- X^9 + X^4 + 1 X^521 + X^209 + X^192 + X^190 + X^173 + X^151 + X^134 + X^132 + X^115 + X^94 + X^77 + X^75 + X^58 + X^36 + X^19 + X^17 + 1 X^521 + X^232 + X^215 + X^213 + X^196 + X^174 + X^157 + X^155 + X^138 + X^94 + X^77 + X^75 + X^58 + X^36 + X^19 + X^17 + 1 X^1273 + X^1256 + X^1254 + X^1237 + X^790 + X^773 + X^771 + X^754 + X^521 + X^519 + X^502 + X^500 + X^483 + X^36 + X^19 + X^17 + 1 Errors: /home/mfd/gomagma: line 2: 16746 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host 3(NXDOMAIN) (194.165.15.3) Time: Mon Jan 19 14:03:37 2004 Input: k := GF(2); C := PrimitivePolynomial(k,9); C; for k in [1..13] do for i in [1..25] do for n in [1..30] do for m in [1..35] do C := (1 + X^(m*17))*(1 + X^(n*23))*(1 + X^(i*19))*(1 + X^(k*13)) + X^521; if IsPrimitive(C) then C; n; i; k; m; end if; end for; end for; end for; end for; Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Mon Jan 19 2004 14:03:14 on modular [Seed = 1916672897] ------------------------------------- X^9 + X^4 + 1 X^521 + X^89 + X^76 + X^70 + X^66 + X^57 + X^55 + X^53 + X^47 + X^42 + X^36 + X^34 + X^32 + X^23 + X^19 + X^13 + 1 1 1 1 2 X^521 + X^209 + X^196 + X^190 + X^177 + X^124 + X^117 + X^111 + X^105 + X^104 + X^98 + X^92 + X^85 + X^32 + X^19 + X^13 + 1 4 1 1 5 X^521 + X^391 + X^378 + X^372 + X^359 + X^253 + X^240 + X^234 + X^221 + X^170 + X^157 + X^151 + X^138 + X^32 + X^19 + X^13 + 1 6 1 1 13 X^521 + X^346 + X^333 + X^327 + X^314 + X^193 + X^185 + X^180 + X^174 + X^172 + X^166 + X^161 + X^153 + X^32 + X^19 + X^13 + 1 7 1 1 9 X^637 + X^624 + X^618 + X^605 + X^521 + X^338 + X^331 + X^325 + X^319 + X^318 + X^312 + X^306 + X^299 + X^32 + X^19 + X^13 + 1 13 1 1 18 X^907 + X^894 + X^888 + X^875 + X^584 + X^571 + X^565 + X^552 + X^521 + X^355 + X^342 + X^336 + X^323 + X^32 + X^19 + X^13 + 1 24 1 1 19 X^603 + X^590 + X^580 + X^567 + X^546 + X^533 + X^523 + X^521 + X^510 + X^93 + X^80 + X^70 + X^57 + X^36 + X^23 + X^13 + 1 1 3 1 30 X^643 + X^630 + X^597 + X^586 + X^584 + X^573 + X^540 + X^527 + X^521 + X^116 + X^103 + X^70 + X^59 + X^57 + X^46 + X^13 + 1 2 3 1 31 X^593 + X^580 + X^536 + X^523 + X^521 + X^478 + X^465 + X^421 + X^408 + X^185 + X^172 + X^128 + X^115 + X^70 + X^57 + X^13 + 1 5 3 1 24 X^521 + X^340 + X^327 + X^323 + X^310 + X^283 + X^270 + X^266 + X^253 + X^87 + X^74 + X^70 + X^57 + X^30 + X^17 + X^13 + 1 11 3 1 1 X^521 + X^459 + X^446 + X^402 + X^389 + X^323 + X^310 + X^266 + X^253 + X^206 + X^193 + X^149 + X^136 + X^70 + X^57 + X^13 + 1 11 3 1 8 X^587 + X^574 + X^553 + X^540 + X^530 + X^521 + X^517 + X^496 + X^483 + X^104 + X^91 + X^70 + X^57 + X^47 + X^34 + X^13 + 1 21 3 1 2 X^918 + X^905 + X^861 + X^848 + X^714 + X^701 + X^657 + X^644 + X^521 + X^274 + X^261 + X^217 + X^204 + X^70 + X^57 + X^13 + 1 28 3 1 12 Errors: /home/mfd/gomagma: line 2: 16755 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host L0123P15.dipool.highway.telekom.at. (62.46.79.79) Time: Mon Jan 19 14:33:22 2004 Input: znstar(60) Output: Magma V2.10-6 Mon Jan 19 2004 14:33:19 on modular [Seed = 3247288639] ------------------------------------- >> znstar(60); ^ User error: Identifier 'znstar' has not been declared or assigned Total time: 2.989 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host carroll.math.ubc.ca. (142.103.161.252) Time: Mon Jan 19 14:36:55 2004 Input: E:=EllipticCurve([0,1]); Output: Magma V2.10-6 Mon Jan 19 2004 14:36:52 on modular [Seed = 3430989081] ------------------------------------- Total time: 2.919 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host carroll.math.ubc.ca. (142.103.161.252) Time: Mon Jan 19 14:37:42 2004 Input: E:=EllipticCurve([0,1]); TorsionSubgroup(E); Output: Magma V2.10-6 Mon Jan 19 2004 14:37:38 on modular [Seed = 3617301972] ------------------------------------- Abelian Group isomorphic to Z/6 Defined on 1 generator Relations: 6*$.1 = 0 Total time: 2.909 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (194.165.15.3) Time: Mon Jan 19 14:38:55 2004 Input: k := GF(2); C := PrimitivePolynomial(k,9); C; for j in [2..16] do for k in [1..13] do for i in [1..25] do for n in [1..30] do for m in [1..35] do C := ((1 + X^(m*17))^j)*((1 + X^(n*23))^j)*((1 + X^(i*19))^j)*((1 + X^(k*13))^j) + X^521; if IsPrimitive(C) then C; n; i; k; m; end if; end for; end for; end for; end for; end for; Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Mon Jan 19 2004 14:38:31 on modular [Seed = 3786249175] ------------------------------------- X^9 + X^4 + 1 X^938 + X^912 + X^900 + X^874 + X^846 + X^820 + X^808 + X^782 + X^521 + X^156 + X^130 + X^118 + X^92 + X^64 + X^38 + X^26 + 1 2 1 1 23 X^1428 + X^1402 + X^1390 + X^1364 + X^1152 + X^1126 + X^1114 + X^1088 + X^521 + X^340 + X^314 + X^302 + X^276 + X^64 + X^38 + X^26 + 1 6 1 1 32 X^1010 + X^984 + X^934 + X^918 + X^908 + X^892 + X^842 + X^816 + X^521 + X^194 + X^168 + X^118 + X^102 + X^92 + X^76 + X^26 + 1 2 2 1 24 Errors: /home/mfd/gomagma: line 2: 16864 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host 3(NXDOMAIN) (194.165.15.3) Time: Mon Jan 19 14:40:07 2004 Input: k := GF(2); C := PrimitivePolynomial(k,9); C; for j in [2..16] do for k in [1..13] do for i in [1..25] do for n in [1..30] do for m in [1..35] do C := ((1 + X^(m*17))^j)*((1 + X^(n*29))^j)*((1 + X^(i*19))^j)*((1 + X^(k*13))^j) + X^521; if IsPrimitive(C) then C; n; i; k; m; end if; end for; end for; end for; end for; end for; Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Mon Jan 19 2004 14:39:44 on modular [Seed = 3903101545] ------------------------------------- X^9 + X^4 + 1 X^998 + X^972 + X^960 + X^934 + X^760 + X^734 + X^722 + X^696 + X^521 + X^302 + X^276 + X^264 + X^238 + X^64 + X^38 + X^26 + 1 12 1 1 7 X^1614 + X^1588 + X^1576 + X^1550 + X^934 + X^908 + X^896 + X^870 + X^744 + X^718 + X^706 + X^680 + X^521 + X^64 + X^38 + X^26 + 1 15 1 1 20 Errors: /home/mfd/gomagma: line 2: 16873 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host carroll.math.ubc.ca. (142.103.161.252) Time: Mon Jan 19 14:40:53 2004 Input: E:=EllipticCurve([0,2]); TorsionSubgroup(E); Output: Magma V2.10-6 Mon Jan 19 2004 14:40:50 on modular [Seed = 4239429183] ------------------------------------- Abelian Group of order 1 Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (194.165.15.3) Time: Mon Jan 19 14:41:02 2004 Input: k := GF(2); C := PrimitivePolynomial(k,9); C; for j in [2..16] do for k in [1..13] do for i in [1..25] do for n in [1..30] do for m in [1..35] do C := ((1 + X^(m*17))^j)*((1 + X^(n*31))^j)*((1 + X^(i*19))^j)*((1 + X^(k*13))^j) + X^521; if IsPrimitive(C) then C; n; i; k; m; end if; end for; end for; end for; end for; end for; Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Mon Jan 19 2004 14:40:39 on modular [Seed = 4223109453] ------------------------------------- X^9 + X^4 + 1 Errors: /home/mfd/gomagma: line 2: 16890 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host carroll.math.ubc.ca. (142.103.161.252) Time: Mon Jan 19 14:41:09 2004 Input: E:=EllipticCurve([0,17]); IntegerPoints(E); Output: Magma V2.10-6 Mon Jan 19 2004 14:41:06 on modular [Seed = 239238366] ------------------------------------- >> IntegerPoints(E);; ^ User error: Identifier 'IntegerPoints' has not been declared or assigned Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (194.165.15.3) Time: Mon Jan 19 14:41:44 2004 Input: k := GF(2); C := PrimitivePolynomial(k,9); C; for j in [2..16] do for k in [1..13] do for i in [1..25] do for n in [1..30] do for m in [1..35] do C := ((1 + X^(m*17))^j)*((1 + X^(n*11))^j)*((1 + X^(i*19))^j)*((1 + X^(k*13))^j) + X^521; if IsPrimitive(C) then C; n; i; k; m; end if; end for; end for; end for; end for; end for; Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Mon Jan 19 2004 14:41:21 on modular [Seed = 391865844] ------------------------------------- X^9 + X^4 + 1 X^521 + X^210 + X^184 + X^172 + X^166 + X^146 + X^140 + X^128 + X^108 + X^102 + X^82 + X^70 + X^64 + X^44 + X^38 + X^26 + 1 2 1 1 3 X^844 + X^818 + X^806 + X^780 + X^778 + X^752 + X^740 + X^714 + X^521 + X^130 + X^104 + X^92 + X^66 + X^64 + X^38 + X^26 + 1 3 1 1 21 X^521 + X^468 + X^442 + X^430 + X^404 + X^336 + X^310 + X^298 + X^272 + X^196 + X^170 + X^158 + X^132 + X^64 + X^38 + X^26 + 1 6 1 1 8 X^1604 + X^1578 + X^1566 + X^1540 + X^1186 + X^1160 + X^1148 + X^1122 + X^521 + X^482 + X^456 + X^444 + X^418 + X^64 + X^38 + X^26 + 1 19 1 1 33 X^534 + X^521 + X^508 + X^458 + X^406 + X^356 + X^330 + X^204 + X^178 + X^128 + X^76 + X^26 + 1 15 2 1 3 Errors: /home/mfd/gomagma: line 2: 16917 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host carroll.math.ubc.ca. (142.103.161.252) Time: Mon Jan 19 14:42:07 2004 Input: E:=EllipticCurve([0,17]); IntegralPoints(E); Output: Magma V2.10-6 Mon Jan 19 2004 14:41:56 on modular [Seed = 475033370] ------------------------------------- [ (4 : -9 : 1), (8 : -23 : 1), (-2 : 3 : 1), (2 : 5 : 1), (43 : 282 : 1), (-1 : 4 : 1), (5234 : 378661 : 1), (52 : -375 : 1) ] [ [ <(4 : -9 : 1), 1> ], [ <(-2 : -3 : 1), -2> ], [ <(-2 : -3 : 1), -1> ], [ <(4 : -9 : 1), 1>, <(-2 : -3 : 1), -1> ], [ <(4 : -9 : 1), 2>, <(-2 : -3 : 1), -1> ], [ <(4 : -9 : 1), 1>, <(-2 : -3 : 1), 1> ], [ <(4 : -9 : 1), 3>, <(-2 : -3 : 1), 1> ], [ <(4 : -9 : 1), 1>, <(-2 : -3 : 1), 2> ] ] Total time: 10.079 seconds, Total memory usage: 2.42MB ************** MAGMA ***************** Host carroll.math.ubc.ca. (142.103.161.252) Time: Mon Jan 19 14:44:07 2004 Input: M:=ModularCurve(X, "Classical", 5); Output: Magma V2.10-6 Mon Jan 19 2004 14:44:04 on modular [Seed = 677665710] ------------------------------------- >> M:=ModularCurve(X, "Classical", 5);; ^ User error: Identifier 'X' has not been declared or assigned Total time: 3.159 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (194.165.15.3) Time: Mon Jan 19 14:44:16 2004 Input: k := GF(2); C := PrimitivePolynomial(k,9); C; for j in [2..16] do for k in [1..13] do for i in [1..25] do for n in [1..30] do for m in [1..35] do C := ((1 + X^m)^j)*((1 + X^n)^j)*((1 + X^i)^j)*((1 + X^k)^j) + X^521; if IsPrimitive(C) then C; n; i; k; m; end if; end for; end for; end for; end for; end for; Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Mon Jan 19 2004 14:43:53 on modular [Seed = 627660382] ------------------------------------- X^9 + X^4 + 1 X^521 + X^56 + X^54 + X^52 + X^50 + X^6 + X^4 + X^2 + 1 1 1 1 25 X^521 + X^54 + X^46 + X^8 + 1 2 1 1 23 X^521 + X^24 + X^20 + X^16 + X^8 + X^4 + 1 4 1 1 6 X^521 + X^24 + X^20 + X^16 + X^8 + X^4 + 1 6 1 1 4 X^521 + X^42 + X^38 + X^30 + X^26 + X^16 + X^12 + X^4 + 1 6 1 1 13 X^521 + X^36 + X^32 + X^22 + X^14 + X^4 + 1 7 1 1 9 X^521 + X^36 + X^32 + X^22 + X^14 + X^4 + 1 9 1 1 7 X^521 + X^44 + X^40 + X^4 + 1 10 1 1 10 X^521 + X^68 + X^64 + X^48 + X^44 + X^24 + X^20 + X^4 + 1 10 1 1 22 X^521 + X^42 + X^38 + X^30 + X^26 + X^16 + X^12 + X^4 + 1 13 1 1 6 X^521 + X^96 + X^92 + X^64 + X^60 + X^36 + X^32 + X^4 + 1 16 1 1 30 X^521 + X^104 + X^100 + X^64 + X^60 + X^44 + X^40 + X^4 + 1 20 1 1 30 X^521 + X^68 + X^64 + X^48 + X^44 + X^24 + X^20 + X^4 + 1 22 1 1 10 X^521 + X^54 + X^46 + X^8 + 1 23 1 1 2 X^521 + X^56 + X^54 + X^52 + X^50 + X^6 + X^4 + X^2 + 1 25 1 1 1 X^521 + X^96 + X^92 + X^64 + X^60 + X^36 + X^32 + X^4 + 1 30 1 1 16 X^521 + X^104 + X^100 + X^64 + X^60 + X^44 + X^40 + X^4 + 1 30 1 1 20 X^521 + X^54 + X^46 + X^8 + 1 1 2 1 23 X^521 + X^78 + X^76 + X^70 + X^68 + X^10 + X^8 + X^2 + 1 2 2 1 34 X^521 + X^40 + X^38 + X^36 + X^32 + X^30 + X^28 + X^12 + X^10 + X^8 + X^4 + X^2 + 1 3 2 1 14 X^521 + X^42 + X^40 + X^38 + X^36 + X^34 + X^32 + X^30 + X^28 + X^14 + X^12 + X^10 + X^8 + X^6 + X^4 + X^2 + 1 4 2 1 14 X^521 + X^32 + X^30 + X^28 + X^26 + X^22 + X^20 + X^18 + X^14 + X^12 + X^10 + X^6 + X^4 + X^2 + 1 5 2 1 8 X^521 + X^36 + X^34 + X^32 + X^30 + X^22 + X^14 + X^6 + X^4 + X^2 + 1 7 2 1 8 X^521 + X^32 + X^30 + X^28 + X^26 + X^22 + X^20 + X^18 + X^14 + X^12 + X^10 + X^6 + X^4 + X^2 + 1 8 2 1 5 X^521 + X^36 + X^34 + X^32 + X^30 + X^22 + X^14 + X^6 + X^4 + X^2 + 1 8 2 1 7 X^521 + X^56 + X^54 + X^52 + X^50 + X^38 + X^36 + X^34 + X^32 + X^24 + X^22 + X^20 + X^18 + X^6 + X^4 + X^2 + 1 9 2 1 16 X^521 + X^40 + X^38 + X^36 + X^32 + X^30 + X^28 + X^12 + X^10 + X^8 + X^4 + X^2 + 1 14 2 1 3 X^521 + X^42 + X^40 + X^38 + X^36 + X^34 + X^32 + X^30 + X^28 + X^14 + X^12 + X^10 + X^8 + X^6 + X^4 + X^2 + 1 14 2 1 4 X^521 + X^80 + X^78 + X^76 + X^74 + X^52 + X^50 + X^48 + X^46 + X^34 + X^32 + X^30 + X^28 + X^6 + X^4 + X^2 + 1 14 2 1 23 X^521 + X^56 + X^54 + X^52 + X^50 + X^38 + X^36 + X^34 + X^32 + X^24 + X^22 + X^20 + X^18 + X^6 + X^4 + X^2 + 1 16 2 1 9 X^521 + X^106 + X^104 + X^102 + X^100 + X^72 + X^70 + X^68 + X^66 + X^40 + X^38 + X^36 + X^34 + X^6 + X^4 + X^2 + 1 17 2 1 33 X^521 + X^54 + X^46 + X^8 + 1 23 2 1 1 X^521 + X^80 + X^78 + X^76 + X^74 + X^52 + X^50 + X^48 + X^46 + X^34 + X^32 + X^30 + X^28 + X^6 + X^4 + X^2 + 1 23 2 1 14 X^521 + X^40 + X^38 + X^36 + X^32 + X^30 + X^28 + X^12 + X^10 + X^8 + X^4 + X^2 + 1 2 3 1 14 X^521 + X^76 + X^74 + X^70 + X^66 + X^62 + X^60 + X^16 + X^14 + X^10 + X^6 + X^2 + 1 4 3 1 30 X^521 + X^80 + X^78 + X^74 + X^72 + X^70 + X^68 + X^64 + X^62 + X^18 + X^16 + X^12 + X^10 + X^8 + X^6 + X^2 + 1 5 3 1 31 X^521 + X^68 + X^66 + X^62 + X^60 + X^56 + X^54 + X^50 + X^48 + X^20 + X^18 + X^14 + X^12 + X^8 + X^6 + X^2 + 1 6 3 1 24 X^521 + X^90 + X^88 + X^84 + X^82 + X^74 + X^72 + X^68 + X^66 + X^24 + X^22 + X^18 + X^16 + X^8 + X^6 + X^2 + 1 8 3 1 33 X^521 + X^94 + X^92 + X^88 + X^86 + X^78 + X^76 + X^72 + X^70 + X^24 + X^22 + X^18 + X^16 + X^8 + X^6 + X^2 + 1 8 3 1 35 X^521 + X^68 + X^66 + X^62 + X^60 + X^50 + X^48 + X^44 + X^42 + X^26 + X^24 + X^20 + X^18 + X^8 + X^6 + X^2 + 1 9 3 1 21 X^521 + X^40 + X^38 + X^36 + X^32 + X^30 + X^28 + X^12 + X^10 + X^8 + X^4 + X^2 + 1 14 3 1 2 X^521 + X^68 + X^66 + X^62 + X^60 + X^50 + X^48 + X^44 + X^42 + X^26 + X^24 + X^20 + X^18 + X^8 + X^6 + X^2 + 1 21 3 1 9 X^521 + X^68 + X^66 + X^62 + X^60 + X^56 + X^54 + X^50 + X^48 + X^20 + X^18 + X^14 + X^12 + X^8 + X^6 + X^2 + 1 24 3 1 6 X^521 + X^118 + X^116 + X^112 + X^110 + X^68 + X^66 + X^62 + X^60 + X^58 + X^56 + X^52 + X^50 + X^8 + X^6 + X^2 + 1 25 3 1 30 X^521 + X^76 + X^74 + X^70 + X^66 + X^62 + X^60 + X^16 + X^14 + X^10 + X^6 + X^2 + 1 30 3 1 4 X^521 + X^118 + X^116 + X^112 + X^110 + X^68 + X^66 + X^62 + X^60 + X^58 + X^56 + X^52 + X^50 + X^8 + X^6 + X^2 + 1 30 3 1 25 X^521 + X^24 + X^20 + X^16 + X^8 + X^4 + 1 1 4 1 6 X^521 + X^42 + X^40 + X^38 + X^36 + X^34 + X^32 + X^30 + X^28 + X^14 + X^12 + X^10 + X^8 + X^6 + X^4 + X^2 + 1 2 4 1 14 X^521 + X^76 + X^74 + X^70 + X^66 + X^62 + X^60 + X^16 + X^14 + X^10 + X^6 + X^2 + 1 3 4 1 30 X^521 + X^24 + X^20 + X^16 + X^8 + X^4 + 1 6 4 1 1 X^521 + X^54 + X^52 + X^46 + X^44 + X^42 + X^40 + X^34 + X^32 + X^22 + X^20 + X^14 + X^12 + X^10 + X^8 + X^2 + 1 6 4 1 16 X^521 + X^48 + X^46 + X^40 + X^38 + X^34 + X^32 + X^26 + X^22 + X^16 + X^14 + X^10 + X^8 + X^2 + 1 7 4 1 12 X^521 + X^62 + X^60 + X^54 + X^52 + X^40 + X^38 + X^24 + X^22 + X^10 + X^8 + X^2 + 1 11 4 1 15 X^521 + X^48 + X^46 + X^40 + X^38 + X^34 + X^32 + X^26 + X^22 + X^16 + X^14 + X^10 + X^8 + X^2 + 1 12 4 1 7 X^521 + X^84 + X^82 + X^76 + X^74 + X^60 + X^58 + X^52 + X^50 + X^34 + X^32 + X^26 + X^24 + X^10 + X^8 + X^2 + 1 12 4 1 25 X^521 + X^42 + X^40 + X^38 + X^36 + X^34 + X^32 + X^30 + X^28 + X^14 + X^12 + X^10 + X^8 + X^6 + X^4 + X^2 + 1 14 4 1 2 X^521 + X^62 + X^60 + X^54 + X^52 + X^40 + X^38 + X^24 + X^22 + X^10 + X^8 + X^2 + 1 15 4 1 11 X^521 + X^54 + X^52 + X^46 + X^44 + X^42 + X^40 + X^34 + X^32 + X^22 + X^20 + X^14 + X^12 + X^10 + X^8 + X^2 + 1 16 4 1 6 X^521 + X^98 + X^96 + X^90 + X^88 + X^66 + X^64 + X^58 + X^56 + X^42 + X^40 + X^34 + X^32 + X^10 + X^8 + X^2 + 1 16 4 1 28 X^521 + X^78 + X^76 + X^70 + X^68 + X^10 + X^8 + X^2 + 1 17 4 1 17 X^521 + X^110 + X^108 + X^102 + X^100 + X^68 + X^66 + X^60 + X^58 + X^52 + X^50 + X^44 + X^42 + X^10 + X^8 + X^2 + 1 21 4 1 29 X^521 + X^84 + X^82 + X^76 + X^74 + X^60 + X^58 + X^52 + X^50 + X^34 + X^32 + X^26 + X^24 + X^10 + X^8 + X^2 + 1 25 4 1 12 X^521 + X^122 + X^120 + X^114 + X^112 + X^70 + X^68 + X^54 + X^52 + X^10 + X^8 + X^2 + 1 26 4 1 30 X^521 + X^98 + X^96 + X^90 + X^88 + X^66 + X^64 + X^58 + X^56 + X^42 + X^40 + X^34 + X^32 + X^10 + X^8 + X^2 + 1 28 4 1 16 X^521 + X^110 + X^108 + X^102 + X^100 + X^68 + X^66 + X^60 + X^58 + X^52 + X^50 + X^44 + X^42 + X^10 + X^8 + X^2 + 1 29 4 1 21 X^521 + X^76 + X^74 + X^70 + X^66 + X^62 + X^60 + X^16 + X^14 + X^10 + X^6 + X^2 + 1 30 4 1 3 X^521 + X^122 + X^120 + X^114 + X^112 + X^70 + X^68 + X^54 + X^52 + X^10 + X^8 + X^2 + 1 30 4 1 26 X^521 + X^140 + X^138 + X^132 + X^130 + X^80 + X^78 + X^72 + X^68 + X^62 + X^60 + X^10 + X^8 + X^2 + 1 30 4 1 35 X^521 + X^32 + X^30 + X^28 + X^26 + X^22 + X^20 + X^18 + X^14 + X^12 + X^10 + X^6 + X^4 + X^2 + 1 2 5 1 8 X^521 + X^80 + X^78 + X^74 + X^72 + X^70 + X^68 + X^64 + X^62 + X^18 + X^16 + X^12 + X^10 + X^8 + X^6 + X^2 + 1 3 5 1 31 X^521 + X^32 + X^30 + X^28 + X^26 + X^22 + X^20 + X^18 + X^14 + X^12 + X^10 + X^6 + X^4 + X^2 + 1 8 5 1 2 X^521 + X^88 + X^86 + X^78 + X^76 + X^72 + X^70 + X^62 + X^60 + X^28 + X^26 + X^18 + X^16 + X^12 + X^10 + X^2 + 1 8 5 1 30 X^521 + X^68 + X^66 + X^58 + X^56 + X^46 + X^44 + X^36 + X^32 + X^24 + X^22 + X^12 + X^10 + X^2 + 1 11 5 1 17 X^521 + X^92 + X^90 + X^82 + X^80 + X^68 + X^66 + X^58 + X^56 + X^36 + X^34 + X^26 + X^24 + X^12 + X^10 + X^2 + 1 12 5 1 28 X^521 + X^68 + X^66 + X^58 + X^56 + X^46 + X^44 + X^36 + X^32 + X^24 + X^22 + X^12 + X^10 + X^2 + 1 17 5 1 11 X^521 + X^128 + X^126 + X^118 + X^116 + X^82 + X^80 + X^72 + X^70 + X^58 + X^56 + X^48 + X^46 + X^12 + X^10 + X^2 + 1 23 5 1 35 X^521 + X^92 + X^90 + X^82 + X^80 + X^68 + X^66 + X^58 + X^56 + X^36 + X^34 + X^26 + X^24 + X^12 + X^10 + X^2 + 1 28 5 1 12 X^521 + X^88 + X^86 + X^78 + X^76 + X^72 + X^70 + X^62 + X^60 + X^28 + X^26 + X^18 + X^16 + X^12 + X^10 + X^2 + 1 30 5 1 8 X^521 + X^24 + X^20 + X^16 + X^8 + X^4 + 1 1 6 1 4 X^521 + X^42 + X^38 + X^30 + X^26 + X^16 + X^12 + X^4 + 1 1 6 1 13 X^521 + X^68 + X^66 + X^62 + X^60 + X^56 + X^54 + X^50 + X^48 + X^20 + X^18 + X^14 + X^12 + X^8 + X^6 + X^2 + 1 3 6 1 24 X^521 + X^24 + X^20 + X^16 + X^8 + X^4 + 1 4 6 1 1 X^521 + X^54 + X^52 + X^46 + X^44 + X^42 + X^40 + X^34 + X^32 + X^22 + X^20 + X^14 + X^12 + X^10 + X^8 + X^2 + 1 4 6 1 16 X^521 + X^56 + X^54 + X^44 + X^40 + X^30 + X^26 + X^16 + X^12 + X^2 + 1 7 6 1 14 X^521 + X^50 + X^48 + X^38 + X^36 + X^34 + X^32 + X^30 + X^28 + X^22 + X^20 + X^18 + X^16 + X^14 + X^12 + X^2 + 1 8 6 1 10 X^521 + X^60 + X^58 + X^48 + X^46 + X^42 + X^40 + X^32 + X^28 + X^20 + X^18 + X^14 + X^12 + X^2 + 1 9 6 1 14 X^521 + X^50 + X^48 + X^38 + X^36 + X^34 + X^32 + X^30 + X^28 + X^22 + X^20 + X^18 + X^16 + X^14 + X^12 + X^2 + 1 10 6 1 8 X^521 + X^68 + X^66 + X^56 + X^54 + X^48 + X^46 + X^36 + X^32 + X^22 + X^20 + X^14 + X^12 + X^2 + 1 10 6 1 17 X^521 + X^42 + X^38 + X^30 + X^26 + X^16 + X^12 + X^4 + 1 13 6 1 1 X^521 + X^92 + X^90 + X^80 + X^78 + X^66 + X^64 + X^54 + X^52 + X^40 + X^38 + X^28 + X^26 + X^14 + X^12 + X^2 + 1 13 6 1 26 X^521 + X^56 + X^54 + X^44 + X^40 + X^30 + X^26 + X^16 + X^12 + X^2 + 1 14 6 1 7 X^521 + X^60 + X^58 + X^48 + X^46 + X^42 + X^40 + X^32 + X^28 + X^20 + X^18 + X^14 + X^12 + X^2 + 1 14 6 1 9 X^521 + X^54 + X^52 + X^46 + X^44 + X^42 + X^40 + X^34 + X^32 + X^22 + X^20 + X^14 + X^12 + X^10 + X^8 + X^2 + 1 16 6 1 4 X^521 + X^86 + X^84 + X^74 + X^72 + X^54 + X^52 + X^46 + X^44 + X^42 + X^40 + X^34 + X^32 + X^14 + X^12 + X^2 + 1 16 6 1 20 X^521 + X^92 + X^90 + X^80 + X^78 + X^60 + X^58 + X^48 + X^44 + X^34 + X^32 + X^14 + X^12 + X^2 + 1 16 6 1 23 X^521 + X^68 + X^66 + X^56 + X^54 + X^48 + X^46 + X^36 + X^32 + X^22 + X^20 + X^14 + X^12 + X^2 + 1 17 6 1 10 X^521 + X^120 + X^118 + X^108 + X^106 + X^82 + X^80 + X^70 + X^68 + X^52 + X^50 + X^40 + X^38 + X^14 + X^12 + X^2 + 1 19 6 1 34 X^521 + X^86 + X^84 + X^74 + X^72 + X^54 + X^52 + X^46 + X^44 + X^42 + X^40 + X^34 + X^32 + X^14 + X^12 + X^ ** WARNING: Output too long, hence truncated. Errors: /home/mfd/gomagma: line 2: 16935 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host carroll.math.ubc.ca. (142.103.161.252) Time: Mon Jan 19 14:44:28 2004 Input: M:=ModularCurve(0, "Classical", 5); Output: Magma V2.10-6 Mon Jan 19 2004 14:44:25 on modular [Seed = 997673120] ------------------------------------- >> M:=ModularCurve(0, "Classical", 5);; ^ Runtime error in 'ModularCurve': Bad argument types Argument types given: RngIntElt, MonStgElt, RngIntElt Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (194.165.15.3) Time: Mon Jan 19 14:45:49 2004 Input: k := GF(2); C := PrimitivePolynomial(k,9); C; for j in [2..32] do for k in [1..13] do for i in [1..25] do for n in [1..30] do for m in [1..35] do C := ((1 + X^m)^j)*((1 + X^n)^j)*((1 + X^i)^j)*((1 + X^k)^j) + X^521; if IsPrimitive(C) then C; n; i; k; m; j end if; end for; end for; end for; end for; end for; Output: Magma V2.10-6 Mon Jan 19 2004 14:45:46 on modular [Seed = 1258764451] ------------------------------------- X^9 + X^4 + 1 >> end if; ^ User error: bad syntax >> end for; ^ User error: bad syntax >> end for; ^ User error: bad syntax >> end for; ^ User error: bad syntax >> end for; ^ User error: bad syntax >> end for; ^ User error: bad syntax Total time: 2.939 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (194.165.15.3) Time: Mon Jan 19 14:46:48 2004 Input: k := GF(2); C := PrimitivePolynomial(k,9); C; for j in [2..32] do for k in [1..13] do for i in [1..25] do for n in [1..30] do for m in [1..35] do C := ((1 + X^m)^j)*((1 + X^n)^j)*((1 + X^i)^j)*((1 + X^k)^j) + X^521; if IsPrimitive(C) then C; n; i; k; m; j; end if; end for; end for; end for; end for; end for; Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Mon Jan 19 2004 14:46:25 on modular [Seed = 1344021571] ------------------------------------- X^9 + X^4 + 1 X^521 + X^56 + X^54 + X^52 + X^50 + X^6 + X^4 + X^2 + 1 1 1 1 25 2 X^521 + X^54 + X^46 + X^8 + 1 2 1 1 23 2 X^521 + X^24 + X^20 + X^16 + X^8 + X^4 + 1 4 1 1 6 2 X^521 + X^24 + X^20 + X^16 + X^8 + X^4 + 1 6 1 1 4 2 X^521 + X^42 + X^38 + X^30 + X^26 + X^16 + X^12 + X^4 + 1 6 1 1 13 2 X^521 + X^36 + X^32 + X^22 + X^14 + X^4 + 1 7 1 1 9 2 X^521 + X^36 + X^32 + X^22 + X^14 + X^4 + 1 9 1 1 7 2 X^521 + X^44 + X^40 + X^4 + 1 10 1 1 10 2 X^521 + X^68 + X^64 + X^48 + X^44 + X^24 + X^20 + X^4 + 1 10 1 1 22 2 X^521 + X^42 + X^38 + X^30 + X^26 + X^16 + X^12 + X^4 + 1 13 1 1 6 2 X^521 + X^96 + X^92 + X^64 + X^60 + X^36 + X^32 + X^4 + 1 16 1 1 30 2 X^521 + X^104 + X^100 + X^64 + X^60 + X^44 + X^40 + X^4 + 1 20 1 1 30 2 X^521 + X^68 + X^64 + X^48 + X^44 + X^24 + X^20 + X^4 + 1 22 1 1 10 2 X^521 + X^54 + X^46 + X^8 + 1 23 1 1 2 2 X^521 + X^56 + X^54 + X^52 + X^50 + X^6 + X^4 + X^2 + 1 25 1 1 1 2 X^521 + X^96 + X^92 + X^64 + X^60 + X^36 + X^32 + X^4 + 1 30 1 1 16 2 X^521 + X^104 + X^100 + X^64 + X^60 + X^44 + X^40 + X^4 + 1 30 1 1 20 2 X^521 + X^54 + X^46 + X^8 + 1 1 2 1 23 2 X^521 + X^78 + X^76 + X^70 + X^68 + X^10 + X^8 + X^2 + 1 2 2 1 34 2 X^521 + X^40 + X^38 + X^36 + X^32 + X^30 + X^28 + X^12 + X^10 + X^8 + X^4 + X^2 + 1 3 2 1 14 2 X^521 + X^42 + X^40 + X^38 + X^36 + X^34 + X^32 + X^30 + X^28 + X^14 + X^12 + X^10 + X^8 + X^6 + X^4 + X^2 + 1 4 2 1 14 2 X^521 + X^32 + X^30 + X^28 + X^26 + X^22 + X^20 + X^18 + X^14 + X^12 + X^10 + X^6 + X^4 + X^2 + 1 5 2 1 8 2 X^521 + X^36 + X^34 + X^32 + X^30 + X^22 + X^14 + X^6 + X^4 + X^2 + 1 7 2 1 8 2 X^521 + X^32 + X^30 + X^28 + X^26 + X^22 + X^20 + X^18 + X^14 + X^12 + X^10 + X^6 + X^4 + X^2 + 1 8 2 1 5 2 X^521 + X^36 + X^34 + X^32 + X^30 + X^22 + X^14 + X^6 + X^4 + X^2 + 1 8 2 1 7 2 X^521 + X^56 + X^54 + X^52 + X^50 + X^38 + X^36 + X^34 + X^32 + X^24 + X^22 + X^20 + X^18 + X^6 + X^4 + X^2 + 1 9 2 1 16 2 X^521 + X^40 + X^38 + X^36 + X^32 + X^30 + X^28 + X^12 + X^10 + X^8 + X^4 + X^2 + 1 14 2 1 3 2 X^521 + X^42 + X^40 + X^38 + X^36 + X^34 + X^32 + X^30 + X^28 + X^14 + X^12 + X^10 + X^8 + X^6 + X^4 + X^2 + 1 14 2 1 4 2 X^521 + X^80 + X^78 + X^76 + X^74 + X^52 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+ X^10 + X^8 + X^2 + 1 29 4 1 21 2 X^521 + X^76 + X^74 + X^70 + X^66 + X^62 + X^60 + X^16 + X^14 + X^10 + X^6 + X^2 + 1 30 4 1 3 2 X^521 + X^122 + X^120 + X^114 + X^112 + X^70 + X^68 + X^54 + X^52 + X^10 + X^8 + X^2 + 1 30 4 1 26 2 X^521 + X^140 + X^138 + X^132 + X^130 + X^80 + X^78 + X^72 + X^68 + X^62 + X^60 + X^10 + X^8 + X^2 + 1 30 4 1 35 2 X^521 + X^32 + X^30 + X^28 + X^26 + X^22 + X^20 + X^18 + X^14 + X^12 + X^10 + X^6 + X^4 + X^2 + 1 2 5 1 8 2 X^521 + X^80 + X^78 + X^74 + X^72 + X^70 + X^68 + X^64 + X^62 + X^18 + X^16 + X^12 + X^10 + X^8 + X^6 + X^2 + 1 3 5 1 31 2 X^521 + X^32 + X^30 + X^28 + X^26 + X^22 + X^20 + X^18 + X^14 + X^12 + X^10 + X^6 + X^4 + X^2 + 1 8 5 1 2 2 X^521 + X^88 + X^86 + X^78 + X^76 + X^72 + X^70 + X^62 + X^60 + X^28 + X^26 + X^18 + X^16 + X^12 + X^10 + X^2 + 1 8 5 1 30 2 X^521 + X^68 + X^66 + X^58 + X^56 + X^46 + X^44 + X^36 + X^32 + X^24 + X^22 + X^12 + X^10 + X^2 + 1 11 5 1 17 2 X^521 + X^92 + X^90 + X^82 + X^80 + X^68 + X^66 + X^58 + X^56 + X^36 + X^34 + X^26 + X^24 + X^12 + X^10 + X^2 + 1 12 5 1 28 2 X^521 + X^68 + X^66 + X^58 + X^56 + X^46 + X^44 + X^36 + X^32 + X^24 + X^22 + X^12 + X^10 + X^2 + 1 17 5 1 11 2 X^521 + X^128 + X^126 + X^118 + X^116 + X^82 + X^80 + X^72 + X^70 + X^58 + X^56 + X^48 + X^46 + X^12 + X^10 + X^2 + 1 23 5 1 35 2 X^521 + X^92 + X^90 + X^82 + X^80 + X^68 + X^66 + X^58 + X^56 + X^36 + X^34 + X^26 + X^24 + X^12 + X^10 + X^2 + 1 28 5 1 12 2 X^521 + X^88 + X^86 + X^78 + X^76 + X^72 + X^70 + X^62 + X^60 + X^28 + X^26 + X^18 + X^16 + X^12 + X^10 + X^2 + 1 30 5 1 8 2 X^521 + X^24 + X^20 + X^16 + X^8 + X^4 + 1 1 6 1 4 2 X^521 + X^42 + X^38 + X^30 + X^26 + X^16 + X^12 + X^4 + 1 1 6 1 13 2 X^521 + X^68 + X^66 + X^62 + X^60 + X^56 + X^54 + X^50 + X^48 + X^20 + X^18 + X^14 + X^12 + X^8 + X^6 + X^2 + 1 3 6 1 24 2 X^521 + X^24 + X^20 + X^16 + X^8 + X^4 + 1 4 6 1 1 2 X^521 + X^54 + X^52 + X^46 + X^44 + X^42 + X^40 + X^34 + X^32 + X^22 + X^20 + X^14 + X^12 + X^10 + X^8 + X^2 + 1 4 6 1 16 2 X^521 + X^56 + X^54 + X^44 + X^40 + X^30 + X^26 + X^16 + X^12 + X^2 + 1 7 6 1 14 2 X^521 + X^50 + X^48 + X^38 + X^36 + X^34 + X^32 + X^30 + X^28 + X^22 + X^20 + X^18 + X^16 + X^14 + X^12 + X^2 + 1 8 6 1 10 2 X^521 + X^60 + X^58 + X^48 + X^46 + X^42 + X^40 + X^32 + X^28 + X^20 + X^18 + X^14 + X^12 + X^2 + 1 9 6 1 14 2 X^521 + X^50 + X^48 + X^38 + X^36 + X^34 + X^32 + X^30 + X^28 + X^22 + X^20 + X^18 + X^16 + X^14 + X^12 + X^2 + 1 10 6 1 8 2 X^521 + X^68 + X^66 + X^56 + X^54 + X^48 + X^46 + X^36 + X^32 + X^22 + X^20 + X^14 + X^12 + X^2 + 1 10 6 1 17 2 X^521 + X^42 + X^38 + X^30 + X^26 + X^16 + X^12 + X^4 + 1 13 6 1 1 2 X^521 + X^92 + X^90 + X^80 + X^78 + X^66 + X^64 + X^54 + X^52 + X^40 + X^38 + X^28 + X^26 + X^14 + X^12 + X^2 + 1 13 6 1 26 2 X^521 + X^56 + X^54 + X^44 + X^40 + X^30 + X^26 + X^16 + X^12 + X^2 + 1 14 6 1 7 2 X^521 + X^60 + X^58 + X^48 + X^46 + X^42 + X^40 + X^32 + X^28 + X^20 + X^18 + X^14 + X^12 + X^2 + 1 14 6 1 9 2 X^521 + X^54 + X^52 + X^46 + X^44 + X^42 + X^40 + X^34 + X^32 + X^22 + X^20 + X^14 + X^12 + X^10 + X^8 + X^2 + 1 16 6 1 4 2 X^521 + X^86 + X^84 + X^74 + X^72 + X^54 + X^52 + X^46 + X^44 + X^42 + X^40 + X^34 + X^32 + X^14 + X^12 + X^2 + 1 16 6 1 20 2 X^521 + X^92 + X^90 + X^80 + X^78 + X^60 + X^58 + X^48 + X^44 + X^34 + X^32 + X^14 + X^12 + X^2 + 1 16 6 1 23 2 X^521 + X^68 + X^66 + X^56 + X^54 + X^48 + X^46 + X^36 + X^32 + X^22 + X^20 + X^14 + X^12 + X^2 + 1 17 6 1 10 2 X^521 + X^120 + X^118 + X^108 + X^106 + X^82 + X^80 + ** WARNING: Output too long, hence truncated. Errors: /home/mfd/gomagma: line 2: 16978 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host 3(NXDOMAIN) (194.165.15.3) Time: Mon Jan 19 14:47:53 2004 Input: k := GF(2); C := PrimitivePolynomial(k,9); C; for j in [16..32] do for k in [1..13] do for i in [1..25] do for n in [1..30] do for m in [1..35] do C := ((1 + X^m)^j)*((1 + X^n)^j)*((1 + X^i)^j)*((1 + X^k)^j) + X^521; if IsPrimitive(C) then C; n; i; k; m; j; end if; end for; end for; end for; end for; end for; Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Mon Jan 19 2004 14:47:29 on modular [Seed = 1494560010] ------------------------------------- X^9 + X^4 + 1 X^521 + X^192 + X^160 + X^128 + X^64 + X^32 + 1 4 1 1 6 16 X^521 + X^192 + X^160 + X^128 + X^64 + X^32 + 1 6 1 1 4 16 X^521 + X^336 + X^304 + X^192 + X^176 + X^160 + X^144 + X^32 + 1 9 1 1 10 16 X^521 + X^336 + X^304 + X^192 + X^176 + X^160 + X^144 + X^32 + 1 10 1 1 9 16 X^521 + X^480 + X^464 + X^416 + X^400 + X^80 + X^64 + X^16 + 1 2 2 1 25 16 X^521 + X^448 + X^432 + X^416 + X^400 + X^304 + X^288 + X^272 + X^256 + X^192 + X^176 + X^160 + X^144 + X^48 + X^32 + X^16 + 1 9 2 1 16 16 X^521 + X^512 + X^496 + X^480 + X^464 + X^320 + X^304 + X^288 + X^272 + X^240 + X^224 + X^208 + X^192 + X^48 + X^32 + X^16 + 1 12 2 1 17 16 X^521 + X^448 + X^432 + X^416 + X^400 + X^304 + X^288 + X^272 + X^256 + X^192 + X^176 + X^160 + X^144 + X^48 + X^32 + X^16 + 1 16 2 1 9 16 X^521 + X^512 + X^496 + X^480 + X^464 + X^320 + X^304 + X^288 + X^272 + X^240 + X^224 + X^208 + X^192 + X^48 + X^32 + X^16 + 1 17 2 1 12 16 X^521 + X^480 + X^464 + X^416 + X^400 + X^80 + X^64 + X^16 + 1 25 2 1 2 16 X^521 + X^160 + X^144 + X^112 + X^96 + X^64 + X^48 + X^16 + 1 3 3 1 3 16 X^521 + X^448 + X^432 + X^352 + X^336 + X^112 + X^96 + X^16 + 1 3 3 1 21 16 X^521 + X^384 + X^368 + X^336 + X^320 + X^288 + X^272 + X^240 + X^224 + X^160 + X^144 + X^112 + X^96 + X^64 + X^48 + X^16 + 1 6 3 1 14 16 X^521 + X^288 + X^272 + X^240 + X^224 + X^64 + X^48 + X^16 + 1 7 3 1 7 16 X^521 + X^384 + X^368 + X^336 + X^320 + X^288 + X^272 + X^240 + X^224 + X^160 + X^144 + X^112 + X^96 + X^64 + X^48 + X^16 + 1 14 3 1 6 16 X^521 + X^448 + X^432 + X^352 + X^336 + X^112 + X^96 + X^16 + 1 21 3 1 3 16 X^521 + X^192 + X^160 + X^128 + X^64 + X^32 + 1 1 4 1 6 16 X^521 + X^192 + X^160 + X^128 + X^64 + X^32 + 1 6 4 1 1 16 X^521 + X^192 + X^160 + X^128 + X^64 + X^32 + 1 1 6 1 4 16 X^521 + X^384 + X^368 + X^336 + X^320 + X^288 + X^272 + X^240 + X^224 + X^160 + X^144 + X^112 + X^96 + X^64 + X^48 + X^16 + 1 3 6 1 14 16 X^521 + X^192 + X^160 + X^128 + X^64 + X^32 + 1 4 6 1 1 16 X^521 + X^448 + X^432 + X^256 + X^240 + X^208 + X^192 + X^16 + 1 6 6 1 15 16 X^521 + X^400 + X^384 + X^304 + X^272 + X^224 + X^208 + X^192 + X^176 + X^128 + X^96 + X^16 + 1 7 6 1 11 16 X^521 + X^480 + X^464 + X^384 + X^368 + X^336 + X^320 + X^256 + X^224 + X^160 + X^144 + X^112 + X^96 + X^16 + 1 9 6 1 14 16 X^521 + X^400 + X^384 + X^304 + X^272 + X^224 + X^208 + X^192 + X^176 + X^128 + X^96 + X^16 + 1 11 6 1 7 16 X^521 + X^384 + X^368 + X^336 + X^320 + X^288 + X^272 + X^240 + X^224 + X^160 + X^144 + X^112 + X^96 + X^64 + X^48 + X^16 + 1 14 6 1 3 16 X^521 + X^480 + X^464 + X^384 + X^368 + X^336 + X^320 + X^256 + X^224 + X^160 + X^144 + X^112 + X^96 + X^16 + 1 14 6 1 9 16 X^521 + X^448 + X^432 + X^256 + X^240 + X^208 + X^192 + X^16 + 1 15 6 1 6 16 X^521 + X^288 + X^272 + X^240 + X^224 + X^64 + X^48 + X^16 + 1 3 7 1 7 16 Errors: /home/mfd/gomagma: line 2: 16987 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host 3(NXDOMAIN) (194.165.15.3) Time: Mon Jan 19 14:49:49 2004 Input: k := GF(2); C := PrimitivePolynomial(k,9); C; for j in [8..16] do for k in [1..13] do for i in [1..25] do for n in [1..30] do for m in [1..35] do C := ((1 + X^m)^j)*((1 + X^n)^j)*((1 + X^i)^j)*((1 + X^k)^j) + X^521; if IsPrimitive(C) then C; n; i; k; m; j; end if; end for; end for; end for; end for; end for; Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Mon Jan 19 2004 14:49:26 on modular [Seed = 1714033314] ------------------------------------- X^9 + X^4 + 1 X^521 + X^32 + 1 1 1 1 1 8 X^521 + X^168 + X^160 + X^152 + X^144 + X^24 + X^16 + X^8 + 1 1 1 1 18 8 X^521 + X^48 + X^32 + X^16 + 1 2 1 1 2 8 X^521 + X^144 + X^112 + X^32 + 1 2 1 1 14 8 X^521 + X^72 + X^56 + X^48 + X^40 + X^32 + X^24 + X^16 + 1 3 1 1 4 8 X^521 + X^208 + X^192 + X^184 + X^168 + X^40 + X^24 + X^16 + 1 3 1 1 21 8 X^521 + X^72 + X^56 + X^48 + X^40 + X^32 + X^24 + X^16 + 1 4 1 1 3 8 X^521 + X^176 + X^160 + X^136 + X^120 + X^56 + X^40 + X^16 + 1 5 1 1 15 8 X^521 + X^160 + X^144 + X^112 + X^96 + X^64 + X^48 + X^16 + 1 6 1 1 12 8 X^521 + X^288 + X^272 + X^240 + X^224 + X^64 + X^48 + X^16 + 1 6 1 1 28 8 X^521 + X^224 + X^208 + X^152 + X^136 + X^88 + X^72 + X^16 + 1 9 1 1 17 8 X^521 + X^256 + X^240 + X^184 + X^168 + X^88 + X^72 + X^16 + 1 9 1 1 21 8 X^521 + X^160 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+ X^8 + 1 26 2 1 17 8 X^521 + X^480 + X^472 + X^464 + X^456 + X^272 + X^264 + X^256 + X^248 + X^232 + X^224 + X^216 + X^208 + X^24 + X^16 + X^8 + 1 26 2 1 31 8 X^521 + X^72 + X^56 + X^48 + X^40 + X^32 + X^24 + X^16 + 1 1 3 1 4 8 X^521 + X^208 + X^192 + X^184 + X^168 + X^40 + X^24 + X^16 + 1 1 3 1 21 8 X^521 + X^96 + X^88 + X^80 + X^64 + X^56 + X^40 + X^32 + X^16 + X^8 + 1 2 3 1 6 8 X^521 + X^216 + X^208 + X^200 + X^184 + X^176 + X^168 + X^48 + X^40 + X^32 + X^16 + X^8 + 1 2 3 1 21 8 X^521 + X^160 + X^152 + X^112 + X^104 + X^56 + X^48 + X^8 + 1 3 3 1 13 8 X^521 + X^72 + X^56 + X^48 + X^40 + X^32 + X^24 + X^16 + 1 4 3 1 1 8 X^521 + X^96 + X^88 + X^80 + X^64 + X^56 + X^40 + X^32 + X^16 + X^8 + 1 6 3 1 2 8 X^521 + X^200 + X^192 + X^176 + X^168 + X^144 + X^136 + X^120 + X^112 + X^88 + X^80 + X^64 + X^56 + X^32 + X^24 + X^8 + 1 7 3 1 14 8 X^521 + X^168 + X^160 + X^144 + X^136 + X^104 + X^88 + X^80 + X^64 + X^32 + X^24 + X^8 + 1 8 3 1 9 8 X^521 + X^344 + X^336 + X^320 + X^312 + X^280 + X^272 + X^256 + X^248 + X^96 + X^88 + X^72 + X^64 + X^32 + X^24 + X^8 + 1 8 3 1 31 8 X^521 + X^168 + X^160 + X^144 + X^136 + X^104 + X^88 + X^80 + X^64 + X^32 + X^24 + X^8 + 1 9 3 1 8 8 X^521 + X^176 + X^168 + X^152 + X^144 + X^32 + X^24 + X^8 + 1 9 3 1 9 8 X^521 + X^248 + X^240 + X^224 + X^216 + X^168 + X^160 + X^144 + X^136 + X^112 + X^104 + X^88 + X^80 + X^32 + X^24 + X^8 + 1 10 3 1 17 8 X^521 + X^272 + X^264 + X^248 + X^240 + X^192 + X^184 + X^168 + X^160 + X^112 + X^104 + X^88 + X^80 + X^32 + X^24 + X^8 + 1 10 3 1 20 8 X^521 + X^392 + X^384 + X^368 + X^360 + X^296 + X^288 + X^272 + X^264 + X^128 + X^120 + X^104 + X^96 + X^32 + X^24 + X^8 + 1 12 3 1 33 8 X^521 + X^160 + X^152 + X^112 + X^104 + X^56 + X^48 + X^8 + 1 13 3 1 3 8 X^521 + X^200 + X^192 + X^176 + X^168 + X^144 + X^136 + X^120 + X^112 + X^88 + X^80 + X^64 + X^56 + X^32 + X^24 + X^8 + 1 14 3 1 7 8 X^521 + X^248 + X^240 + X^224 + X^216 + X^168 + X^160 + X^144 + X^136 + X^112 + X^104 + X^88 + X^80 + X^32 + X^24 + X^8 + 1 17 3 1 10 8 X^521 + X^272 + X^264 + X^248 + X^240 + X^192 + X^184 + X^168 + X^160 + X^112 + X^104 + X^88 + X^80 + X^32 + X^24 + X^8 + 1 20 3 1 10 8 X^521 + X^408 + X^400 + X^384 + X^376 + X^248 + X^240 + X^224 + X^216 + X^192 + X^184 + X^168 + X^160 + X^32 + X^24 + X^8 + 1 20 3 1 27 8 X^521 + X^208 + X^192 + X^184 + X^168 + X^40 + X^24 + X^16 + 1 21 3 1 1 8 X^521 + X^216 + X^208 + X^200 + X^184 + X^176 + X^168 + X^48 + X^40 + X^32 + X^16 + X^8 + 1 21 3 1 2 8 X^521 + X^432 + X^424 + X^408 + X^400 + X^256 + X^248 + X^232 + X^224 + X^208 + X^200 + X^184 + X^176 + X^32 + X^24 + X^8 + 1 22 3 1 28 8 X^521 + X^456 + X^448 + X^432 + X^424 + X^272 + X^264 + X^248 + X^240 + X^216 + X^208 + X^192 + X^184 + X^32 + X^24 + X^8 + 1 23 3 1 30 8 X^521 + X^448 + X^440 + X^424 + X^416 + X^256 + X^248 + X^232 + X^216 + X^200 + X^192 + X^32 + X^24 + X^8 + 1 24 3 1 28 8 X^521 + X^456 + X^448 + X^432 + X^424 + X^256 + X^248 + X^208 + X^200 + X^32 + X^24 + X^8 + 1 25 3 1 28 8 X^521 + X^408 + X^400 + X^384 + X^376 + 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Errors: /home/mfd/gomagma: line 2: 16996 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host carroll.math.ubc.ca. (142.103.161.252) Time: Mon Jan 19 14:51:38 2004 Input: E:=EllipticCurve([0,17]); TorsionGroup(E); Output: Magma V2.10-6 Mon Jan 19 2004 14:51:35 on modular [Seed = 2067205694] ------------------------------------- >> TorsionGroup(E);; ^ User error: Identifier 'TorsionGroup' has not been declared or assigned Total time: 3.109 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host carroll.math.ubc.ca. (142.103.161.252) Time: Mon Jan 19 14:51:52 2004 Input: E:=EllipticCurve([0,2]); TorsionSubgroup(E); Output: Magma V2.10-6 Mon Jan 19 2004 14:51:49 on modular [Seed = 2244604114] ------------------------------------- Abelian Group of order 1 Total time: 3.039 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host carroll.math.ubc.ca. (142.103.161.252) Time: Mon Jan 19 14:52:16 2004 Input: F:=QuadraticField(2); E:=EllipticCurve([0,2]); TorsionSubgroup(E); Output: Magma V2.10-6 Mon Jan 19 2004 14:52:12 on modular [Seed = 2447238399] ------------------------------------- Abelian Group of order 1 Total time: 3.059 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (194.165.15.3) Time: Mon Jan 19 14:52:24 2004 Input: k := GF(2); C := PrimitivePolynomial(k,9); C; for j in [8..16] do for k in [1..13] do for i in [4..25] do for n in [18..30] do for m in [1..35] do C := ((1 + X^m)^j)*((1 + X^n)^j)*((1 + X^i)^j)*((1 + X^k)^j) + X^521; if IsPrimitive(C) then C; n; i; k; m; j; end if; end for; end for; end for; end for; end for; Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Mon Jan 19 2004 14:52:01 on modular [Seed = 2464081905] ------------------------------------- X^9 + X^4 + 1 X^521 + X^400 + X^392 + X^368 + 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Errors: /home/mfd/gomagma: line 2: 17040 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host carroll.math.ubc.ca. (142.103.161.252) Time: Mon Jan 19 14:52:28 2004 Input: F:=QuadraticField(2); E:=EllipticCurve([0,2]); TorsionSubgroup(E); Output: Magma V2.10-6 Mon Jan 19 2004 14:52:25 on modular [Seed = 2750404312] ------------------------------------- Abelian Group of order 1 Total time: 2.919 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (194.165.15.3) Time: Mon Jan 19 14:54:08 2004 Input: k := GF(2); C := PrimitivePolynomial(k,9); C; for j in [8..16] do for k in [1..13] do for i in [12..25] do for n in [25..30] do for m in [1..35] do C := ((1 + X^m)^j)*((1 + X^n)^j)*((1 + X^i)^j)*((1 + X^k)^j) + X^521; if IsPrimitive(C) then C; n; i; k; m; j; end if; end for; end for; end for; end for; end for; Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Mon Jan 19 2004 14:53:45 on modular [Seed = 2850413666] ------------------------------------- X^9 + X^4 + 1 X^521 + X^384 + X^376 + X^304 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X^96 + X^24 + 1 26 13 3 12 8 X^521 + X^496 + X^472 + X^392 + X^368 + X^360 + X^336 + X^264 + X^256 + X^240 + X^232 + X^160 + X^136 + X^128 + X^104 + X^24 + 1 29 13 3 17 8 X^521 + X^376 + X^352 + X^344 + X^320 + X^264 + X^240 + X^232 + X^208 + X^168 + X^144 + X^136 + X^112 + X^56 + X^32 + X^24 + 1 26 14 3 4 8 X^521 + X^512 + X^488 + X^400 + X^376 + X^352 + X^328 + X^296 + X^272 + X^240 + X^216 + X^184 + X^160 + X^136 + X^112 + X^24 + 1 27 14 3 20 8 X^521 + X^440 + X^416 + X^344 + X^296 + X^240 + X^224 + X^216 + X^200 ** WARNING: Output too long, hence truncated. Errors: /home/mfd/gomagma: line 2: 17067 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host carroll.math.ubc.ca. (142.103.161.252) Time: Mon Jan 19 14:54:10 2004 Input: F:=QuadraticField(2); x:=FundamentalUnit(F); E:=EllipticCurve([0,2]); TorsionSubgroup(E); Output: Magma V2.10-6 Mon Jan 19 2004 14:54:07 on modular [Seed = 2900416881] ------------------------------------- Abelian Group of order 1 Total time: 2.979 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host carroll.math.ubc.ca. (142.103.161.252) Time: Mon Jan 19 14:54:27 2004 Input: F:=QuadraticField(2); x:=FundamentalUnit(F); E:=EllipticCurve([0,x^2]); TorsionSubgroup(E); Output: Magma V2.10-6 Mon Jan 19 2004 14:54:23 on modular [Seed = 3220425298] ------------------------------------- Abelian Group isomorphic to Z/3 Defined on 1 generator Relations: 3*$.1 = 0 Mapping from: Abelian Group isomorphic to Z/3 Defined on 1 generator Relations: 3*$.1 = 0 to CrvEll: E given by a rule [no inverse] Total time: 3.159 seconds, Total memory usage: 2.35MB ************** MAGMA ***************** Host carroll.math.ubc.ca. (142.103.161.252) Time: Mon Jan 19 14:56:21 2004 Input: F:=QuadraticField(2); x:=FundamentalUnit(F); y:=2+sqrt(2); E:=EllipticCurve([0,x^2]); TorsionSubgroup(E); Output: Magma V2.10-6 Mon Jan 19 2004 14:56:17 on modular [Seed = 3430988463] ------------------------------------- >> y:=2+sqrt(2); ^ User error: Identifier 'sqrt' has not been declared or assigned Abelian Group isomorphic to Z/3 Defined on 1 generator Relations: 3*$.1 = 0 Mapping from: Abelian Group isomorphic to Z/3 Defined on 1 generator Relations: 3*$.1 = 0 to CrvEll: E given by a rule [no inverse] Total time: 3.299 seconds, Total memory usage: 2.35MB ************** MAGMA ***************** Host 3(NXDOMAIN) (194.165.15.3) Time: Mon Jan 19 14:56:49 2004 Input: k := GF(2); C := PrimitivePolynomial(k,9); C; for j in [8..16] do for k in [8..13] do for i in [14..25] do for n in [27..30] do for m in [1..35] do C := ((1 + X^m)^j)*((1 + X^n)^j)*((1 + X^i)^j)*((1 + X^k)^j) + X^521; if IsPrimitive(C) then C; n; i; k; m; j; end if; end for; end for; end for; end for; end for; Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Mon Jan 19 2004 14:56:26 on modular [Seed = 3667307698] ------------------------------------- X^9 + X^4 + 1 X^521 + X^488 + X^424 + X^416 + X^376 + X^352 + X^312 + X^304 + X^248 + X^240 + X^184 + X^176 + X^136 + X^112 + X^72 + X^64 + 1 30 14 8 9 8 X^521 + X^472 + X^352 + X^344 + X^248 + X^224 + X^128 + X^120 + 1 28 15 8 8 8 X^521 + X^512 + X^448 + X^432 + X^384 + X^368 + X^320 + X^304 + X^272 + X^240 + X^208 + X^192 + X^144 + X^128 + X^80 + X^64 + 1 30 16 8 10 8 X^521 + X^496 + X^432 + X^424 + X^360 + X^352 + X^288 + X^208 + X^144 + X^136 + X^72 + X^64 + 1 27 18 8 9 8 X^521 + X^464 + X^432 + X^400 + X^368 + X^320 + X^288 + X^256 + X^240 + X^224 + X^208 + X^176 + X^144 + X^96 + X^64 + X^32 + 1 28 18 8 4 8 X^521 + X^472 + X^448 + X^408 + X^384 + X^304 + X^280 + X^256 + X^240 + X^232 + X^216 + X^192 + X^168 + X^88 + X^64 + X^24 + 1 27 21 8 3 8 X^521 + X^504 + X^480 + X^440 + X^416 + X^312 + X^288 + X^280 + X^256 + X^248 + X^224 + X^216 + X^192 + X^88 + X^64 + X^24 + 1 28 24 8 3 8 X^521 + X^488 + X^424 + X^416 + X^376 + X^352 + X^312 + X^304 + X^248 + X^240 + X^184 + X^176 + X^136 + X^112 + X^72 + X^64 + 1 30 14 9 8 8 X^521 + X^456 + X^416 + X^384 + X^344 + X^336 + X^296 + X^264 + X^232 + X^224 + X^192 + X^160 + X^120 + X^112 + X^72 + X^40 + 1 28 15 9 5 8 X^521 + X^496 + X^376 + X^352 + X^264 + X^232 + X^144 + X^120 + 1 29 15 9 9 8 X^521 + X^472 + X^424 + X^400 + X^352 + X^344 + X^296 + X^272 + X^248 + X^224 + X^200 + X^176 + X^128 + X^120 + X^72 + X^48 + 1 28 16 9 6 8 X^521 + X^448 + X^432 + X^376 + X^360 + X^304 + X^288 + X^160 + X^144 + X^88 + X^72 + X^16 + 1 27 18 9 2 8 X^521 + X^496 + X^432 + X^424 + X^360 + X^352 + X^288 + X^208 + X^144 + X^136 + X^72 + X^64 + 1 27 18 9 8 8 X^521 + X^472 + X^464 + X^400 + X^392 + X^304 + X^296 + X^248 + X^240 + X^232 + X^224 + X^176 + X^168 + X^80 + X^72 + X^8 + 1 28 21 9 1 8 X^521 + X^504 + X^472 + X^432 + X^400 + X^336 + X^304 + X^272 + X^264 + X^240 + X^232 + X^200 + X^168 + X^104 + X^72 + X^32 + 1 29 21 9 4 8 X^521 + X^512 + X^472 + X^440 + X^400 + X^328 + X^296 + X^288 + X^224 + X^216 + X^184 + X^112 + X^72 + X^40 + 1 27 23 9 5 8 X^521 + X^512 + X^448 + X^432 + X^384 + X^368 + X^320 + X^304 + X^272 + X^240 + X^208 + X^192 + X^144 + X^128 + X^80 + X^64 + 1 30 16 10 8 8 X^521 + X^464 + X^440 + X^384 + X^360 + X^328 + X^304 + X^248 + X^240 + X^224 + X^216 + X^160 + X^136 + X^104 + X^80 + X^24 + 1 28 17 10 3 8 X^521 + X^504 + X^448 + X^424 + X^368 + X^360 + X^304 + X^200 + X^144 + X^136 + X^80 + X^56 + 1 28 18 10 7 8 X^521 + X^496 + X^472 + X^416 + X^392 + X^344 + X^320 + X^264 + X^256 + X^240 + X^232 + X^176 + X^152 + X^104 + X^80 + X^24 + 1 30 19 10 3 8 X^521 + X^512 + X^488 + X^432 + X^408 + X^344 + X^320 + X^272 + X^264 + X^248 + X^240 + X^192 + X^168 + X^104 + X^80 + X^24 + 1 30 21 10 3 8 X^521 + X^512 + X^480 + X^432 + X^400 + X^336 + X^304 + X^288 + X^224 + X^208 + X^176 + X^112 + X^80 + X^32 + 1 28 22 10 4 8 X^521 + X^520 + X^496 + X^440 + X^416 + X^328 + X^304 + X^296 + X^272 + X^248 + X^224 + X^216 + X^192 + X^104 + X^80 + X^24 + 1 28 24 10 3 8 X^521 + X^472 + X^424 + X^384 + X^352 + X^336 + X^304 + X^264 + X^256 + X^216 + X^208 + X^168 + X^136 + X^120 + X^88 + X^48 + 1 27 15 11 6 8 X^521 + X^464 + X^440 + X^376 + X^352 + X^328 + X^304 + X^248 + X^240 + X^224 + X^216 + X^160 + X^136 + X^112 + X^88 + X^24 + 1 27 17 11 3 8 X^521 + X^480 + X^448 + X^392 + X^360 + X^344 + X^312 + X^168 + X^136 + X^120 + X^88 + X^32 + 1 28 17 11 4 8 Errors: /home/mfd/gomagma: line 2: 17112 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host carroll.math.ubc.ca. (142.103.161.252) Time: Mon Jan 19 14:57:23 2004 Input: F:=QuadraticField(2); x:=FundamentalUnit(F); y:=2+s; E:=EllipticCurve([0,x^2]); TorsionSubgroup(E); Output: Magma V2.10-6 Mon Jan 19 2004 14:57:19 on modular [Seed = 3819935102] ------------------------------------- Abelian Group isomorphic to Z/3 Defined on 1 generator Relations: 3*$.1 = 0 Mapping from: Abelian Group isomorphic to Z/3 Defined on 1 generator Relations: 3*$.1 = 0 to CrvEll: E given by a rule [no inverse] Total time: 3.169 seconds, Total memory usage: 2.35MB ************** MAGMA ***************** Host carroll.math.ubc.ca. (142.103.161.252) Time: Mon Jan 19 14:57:53 2004 Input: F:=QuadraticField(2); x:=FundamentalUnit(F); E:=EllipticCurve([0,s^2]); TorsionSubgroup(E); Output: Magma V2.10-6 Mon Jan 19 2004 14:57:50 on modular [Seed = 3903102548] ------------------------------------- Abelian Group isomorphic to Z/3 Defined on 1 generator Relations: 3*$.1 = 0 Mapping from: Abelian Group isomorphic to Z/3 Defined on 1 generator Relations: 3*$.1 = 0 to CrvEll: E given by a rule [no inverse] Total time: 3.219 seconds, Total memory usage: 2.25MB ************** MAGMA ***************** Host carroll.math.ubc.ca. (142.103.161.252) Time: Mon Jan 19 14:58:10 2004 Input: F:=QuadraticField(2); x:=FundamentalUnit(F); E:=EllipticCurve([0,s^2]); print(s^2); TorsionSubgroup(E); Output: Magma V2.10-6 Mon Jan 19 2004 14:58:07 on modular [Seed = 4105732665] ------------------------------------- 2 Abelian Group isomorphic to Z/3 Defined on 1 generator Relations: 3*$.1 = 0 Mapping from: Abelian Group isomorphic to Z/3 Defined on 1 generator Relations: 3*$.1 = 0 to CrvEll: E given by a rule [no inverse] Total time: 3.479 seconds, Total memory usage: 2.25MB ************** MAGMA ***************** Host 3(NXDOMAIN) (194.165.15.3) Time: Mon Jan 19 14:58:28 2004 Input: k := GF(2); C := PrimitivePolynomial(k,9); C; for j in [8..16] do for k in [8..13] do for i in [23..25] do for n in [27..30] do for m in [1..35] do C := ((1 + X^m)^j)*((1 + X^n)^j)*((1 + X^i)^j)*((1 + X^k)^j) + X^521; if IsPrimitive(C) then C; n; i; k; m; j; end if; end for; end for; end for; end for; end for; Output: ** WARNING: Computation time 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Errors: /home/mfd/gomagma: line 2: 17139 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host 3(NXDOMAIN) (194.165.15.3) Time: Mon Jan 19 15:01:56 2004 Input: k := GF(2); C := PrimitivePolynomial(k,9); C; for k in [1..16] do for i in [1..16] do for n in [1..16] do for m in [1..16] do C := ((1 + X^11)^m)*((1 + X^13)^n)*((1 + X^17)^i)*((1 + X^19)^k) + X^521; if IsPrimitive(C) then C; n; i; k; m; j; end if; end for; end for; end for; end for; Output: Magma V2.10-6 Mon Jan 19 2004 15:01:53 on modular [Seed = 577656208] ------------------------------------- X^9 + X^4 + 1 >> j; ^ User error: Identifier 'j' has not been declared or assigned Total time: 2.939 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (194.165.15.3) Time: Mon Jan 19 15:02:46 2004 Input: k := GF(2); C := PrimitivePolynomial(k,9); C; for k in [1..16] do for i in [1..16] do for n in [1..16] do for m in [1..16] do C := ((1 + X^11)^m)*((1 + X^13)^n)*((1 + X^17)^i)*((1 + X^19)^k) + X^521; if IsPrimitive(C) then C; n; i; k; m; end if; end for; end for; end for; end for; Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Mon Jan 19 2004 15:02:23 on modular [Seed = 694509285] ------------------------------------- X^9 + X^4 + 1 X^521 + X^381 + X^368 + X^364 + X^362 + X^351 + X^349 + X^345 + X^332 + X^329 + X^316 + X^312 + X^310 + X^299 + X^297 + X^293 + X^280 + X^277 + X^264 + X^260 + X^258 + X^247 + X^245 + X^241 + X^228 + X^225 + X^212 + X^208 + X^206 + X^205 + X^195 + X^193 + X^192 + X^189 + X^188 + X^186 + X^176 + X^175 + X^173 + X^169 + X^156 + X^153 + X^140 + X^136 + X^134 + X^123 + X^121 + X^117 + X^104 + X^101 + X^88 + X^84 + X^82 + X^71 + X^69 + X^65 + X^52 + X^49 + X^36 + X^32 + X^30 + X^19 + X^17 + X^13 + 1 13 1 1 16 X^521 + X^309 + X^298 + X^296 + X^290 + X^287 + X^285 + X^283 + X^279 + X^277 + X^276 + X^275 + X^274 + X^272 + X^270 + X^268 + X^266 + X^265 + 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Errors: /home/mfd/gomagma: line 2: 17194 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host 3(NXDOMAIN) (194.165.15.3) Time: Mon Jan 19 15:05:02 2004 Input: k := GF(2); C := PrimitivePolynomial(k,9); C; for k in [1..8] do for i in [1..8] do for n in [1..8] do for m in [1..8] do C := ((1 + X^11)^m)*((1 + X^13)^n)*((1 + X^17)^i)*((1 + X^19)^k) + X^521; if IsPrimitive(C) then C; n; i; k; m; end if; end for; end for; end for; end for; Output: Magma V2.10-6 Mon Jan 19 2004 15:04:52 on modular [Seed = 813451351] ------------------------------------- X^9 + X^4 + 1 X^521 + X^164 + X^142 + X^138 + X^130 + X^126 + X^120 + X^116 + X^108 + X^100 + X^98 + X^94 + X^92 + X^86 + X^78 + X^72 + X^70 + X^66 + X^64 + X^56 + X^48 + X^44 + X^38 + X^34 + X^26 + X^22 + 1 2 2 2 6 X^521 + X^246 + X^233 + X^229 + X^224 + X^220 + X^216 + X^212 + X^211 + X^208 + X^203 + X^202 + X^199 + X^198 + X^191 + X^189 + X^180 + X^178 + X^176 + X^174 + X^173 + X^169 + X^168 + X^167 + X^165 + X^164 + 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X^78 + X^76 + X^52 + X^26 + 1 6 8 4 8 X^521 + X^204 + X^187 + X^185 + X^182 + X^178 + X^168 + X^165 + X^163 + X^161 + X^160 + X^159 + X^156 + X^146 + X^143 + X^142 + X^141 + X^139 + X^138 + X^137 + X^134 + X^128 + X^124 + X^121 + X^120 + X^119 + X^117 + X^115 + X^112 + X^111 + X^109 + X^106 + X^98 + X^95 + X^93 + X^92 + X^89 + X^87 + X^85 + X^84 + X^83 + X^80 + X^76 + X^70 + X^67 + X^66 + X^65 + X^63 + X^62 + X^61 + X^58 + X^48 + X^45 + X^44 + X^43 + X^41 + X^39 + X^36 + X^26 + X^22 + X^19 + X^17 + 1 2 1 5 6 X^521 + X^294 + X^283 + X^281 + X^270 + X^268 + X^260 + X^257 + X^256 + X^255 + X^250 + X^249 + X^247 + X^245 + X^244 + X^243 + X^242 + X^239 + X^237 + X^236 + X^234 + X^232 + X^231 + X^230 + X^229 + X^226 + X^224 + X^223 + X^222 + X^221 + X^219 + X^217 + X^213 + X^212 + X^210 + X^209 + X^208 + X^207 + X^206 + X^205 + X^204 + X^201 + X^200 + X^199 + X^197 + X^196 + X^195 + X^194 + X^193 + X^192 + X^191 ** WARNING: Output too long, hence truncated. ************** MAGMA ***************** Host 3(NXDOMAIN) (194.165.15.3) Time: Mon Jan 19 15:06:32 2004 Input: k := GF(2); C := PrimitivePolynomial(k,9); C; for k in [6..8] do for i in [1..8] do for n in [1..8] do for m in [1..8] do C := ((1 + X^11)^m)*((1 + X^13)^n)*((1 + X^17)^i)*((1 + X^19)^k) + X^521; if IsPrimitive(C) then C; n; i; k; m; end if; end for; end for; end for; end for; Output: Magma V2.10-6 Mon Jan 19 2004 15:06:26 on modular [Seed = 1108228739] ------------------------------------- X^9 + X^4 + 1 X^521 + X^294 + X^283 + X^281 + X^270 + X^268 + X^260 + X^257 + X^256 + X^255 + X^250 + X^249 + X^247 + X^245 + X^244 + X^243 + X^242 + X^239 + X^237 + X^236 + X^234 + X^232 + X^231 + X^230 + X^229 + X^226 + X^224 + X^223 + X^222 + X^221 + X^219 + X^217 + X^213 + X^212 + X^210 + X^209 + X^208 + X^207 + X^206 + X^205 + X^204 + X^201 + X^200 + X^199 + X^197 + X^196 + X^195 + X^194 + X^193 + X^192 + X^191 + X^190 + X^188 + X^187 + X^186 + X^183 + X^182 + X^181 + X^177 + X^175 + X^170 + X^168 + X^167 + X^164 + X^163 + X^162 + X^157 + X^156 + X^155 + X^154 + X^152 + X^151 + X^150 + X^149 + X^145 + X^144 + X^143 + X^142 + X^140 + X^139 + X^138 + X^137 + X^132 + X^131 + X^130 + X^127 + X^126 + X^124 + X^119 + X^117 + X^113 + X^112 + X^111 + X^108 + X^107 + X^106 + X^104 + X^103 + X^102 + X^101 + X^100 + X^99 + X^98 + X^97 + X^95 + X^94 + X^93 + X^90 + X^89 + X^88 + X^87 + X^86 + X^85 + X^84 + X^82 + X^81 + X^77 + X^75 + X^73 + X^72 + X^71 + X^70 + X^68 + X^65 + X^64 + X^63 + X^62 + X^60 + X^58 + X^57 + X^55 + X^52 + X^51 + X^50 + X^49 + X^47 + X^45 + X^44 + X^39 + X^38 + X^37 + X^34 + X^26 + X^24 + X^13 + X^11 + 1 7 2 6 5 X^521 + X^296 + X^285 + X^279 + X^268 + X^262 + X^258 + X^251 + X^247 + X^245 + X^244 + X^241 + X^234 + X^233 + X^230 + X^228 + X^227 + X^224 + X^220 + X^217 + X^216 + X^213 + X^211 + X^210 + X^209 + X^207 + X^206 + X^203 + X^200 + X^199 + X^196 + X^195 + X^194 + X^193 + X^192 + X^190 + X^189 + X^186 + X^183 + X^179 + X^178 + X^177 + X^176 + X^175 + X^173 + X^172 + 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X^52 + X^49 + X^44 + X^38 + X^11 + 1 4 8 6 5 X^521 + X^368 + X^346 + X^330 + X^324 + X^316 + X^308 + X^302 + X^294 + X^292 + X^286 + X^278 + X^272 + X^270 + X^264 + X^256 + X^254 + X^250 + X^248 + X^240 + X^234 + X^226 + X^218 + X^212 + X^202 + X^196 + X^194 + X^174 + X^172 + X^166 + X^156 + X^150 + X^142 + X^134 + X^128 + X^120 + X^118 + X^114 + X^112 + X^104 + X^98 + X^96 + X^90 + X^82 + X^76 + X^74 + X^66 + X^60 + X^52 + X^44 + X^38 + X^22 + 1 4 8 6 6 X^521 + X^288 + X^271 + X^269 + X^262 + X^252 + X^250 + X^245 + X^244 + X^243 + X^233 + X^231 + X^227 + X^226 + X^225 + X^224 + X^220 + X^218 + X^214 + X^212 + X^208 + X^207 + X^206 + X^205 + X^203 + X^199 + X^195 + X^194 + X^193 + X^189 + X^188 + X^187 + X^186 + X^184 + X^180 + X^177 + X^175 + X^174 + X^170 + X^169 + X^168 + X^167 + X^165 + X^161 + X^159 + X^158 + X^156 + X^155 + X^151 + X^149 + X^148 + X^146 + X^142 + X^140 + X^139 + X^137 + X^133 + X^132 + X^130 + X^129 + X^127 + X^123 + X^121 + X^120 + X^119 + X^118 + X^114 + X^113 + X^111 + X^108 + X^104 + X^102 + X^101 + X^100 + X^99 + X^95 + X^94 + X^93 + X^89 + X^85 + X^83 + X^82 + X^81 + X^80 + X^76 + X^74 + X^70 + X^68 + X^64 + X^63 + X^62 + X^61 + X^57 + X^55 + X^45 + X^44 + X^43 + X^38 + X^36 + X^26 + X^19 + X^17 + 1 2 5 7 4 X^521 + X^338 + X^327 + X^325 + X^321 + X^319 + X^314 + X^310 + X^306 + X^302 + X^300 + X^297 + X^295 + X^294 + X^291 + X^287 + X^286 + X^278 + X^277 + X^276 + X^273 + X^272 + X^269 + X^268 + X^267 + X^266 + X^264 + X^262 + X^256 + X^254 + X^253 + X^250 + X^249 + X^248 + X^247 + X^246 + X^243 + X^240 + X^237 + X^235 + X^234 + X^230 + X^229 + X^228 + X^227 + X^226 + X^225 + X^224 + X^221 + X^218 + X^216 + X^214 + X^213 + X^212 + X^211 + X^210 + X^208 + X^206 + X^199 + X^198 + X^197 + X^196 + X^195 + X^193 + X^192 + X^191 + X^190 + X^189 + X^188 + X^187 + X^186 + X^185 + X^180 + X^179 + X^178 + X^176 + X^175 + X^172 + X^171 + X^170 + X^168 + X^167 + X^166 + X^163 + X^162 + X^160 + X^159 + X^158 + X^153 + X^152 + X^151 + X^150 + X^149 + X^148 + X^147 + X^146 + X^145 + X^143 + X^142 + X^141 + X^140 + X^139 + X^132 + X^130 + X^128 + X^127 + X^126 + X^125 + X^124 + X^122 + X^120 + X^117 + X^114 + X^113 + X^112 + X^111 + X^110 + X^109 + X^108 + X^104 + X^103 + X^101 + X^98 + X^95 + X^92 + X^91 + X^90 + X^89 + X^88 + X^85 + X^84 + X^82 + X^76 + X^74 + X^72 + X^71 + X^70 + X^69 + X^66 + X^65 + X^62 + X^61 + X^60 + X^52 + X^51 + X^47 + X^44 + X^43 + X^41 + X^38 + X^36 + X^32 + X^28 + X^24 + X^19 + X^17 + X^13 + X^11 + 1 5 5 7 5 X^521 + X^339 + X^322 + X^317 + X^300 + X^295 + X^278 + X^273 + X^256 + X^235 + X^218 + X^213 + X^196 + X^191 + X^187 + X^174 + X^170 + X^169 + X^165 + X^152 + X^148 + X^143 + X^126 + X^121 + X^104 + X^83 + X^66 + X^61 + X^44 + X^39 + X^22 + X^17 + 1 8 1 8 6 X^521 + X^378 + X^344 + X^290 + X^274 + X^256 + X^240 + X^226 + X^192 + X^186 + X^152 + X^138 + X^122 + X^104 + X^88 + X^34 + 1 8 2 8 8 X^521 + X^299 + X^282 + X^265 + X^255 + X^248 + X^247 + X^238 + X^230 + X^221 + X^213 + X^204 + X^203 + X^196 + X^186 + X^169 + X^152 + X^147 + X^130 + X^113 + X^103 + X^96 + X^95 + X^86 + X^78 + X^69 + X^61 + X^52 + X^51 + X^44 + X^34 + X^17 + 1 4 3 8 4 X^521 + X^312 + X^290 + X^286 + X^268 + X^264 + X^246 + X^244 + X^242 + X^222 + X^220 + X^218 + X^200 + X^196 + X^178 + X^174 + X^160 + X^152 + X^138 + X^134 + X^116 + X^112 + X^94 + X^92 + X^90 + X^70 + X^68 + X^66 + X^48 + X^44 + X^26 + X^22 + 1 2 4 8 6 X^521 + X^348 + X^337 + X^331 + X^326 + X^322 + X^320 + X^315 + X^311 + X^309 + X^305 + X^300 + X^298 + X^296 + X^294 + X^289 + X^285 + X^283 + X^280 + X^279 + X^274 + X^272 + X^270 + X^269 + X^268 + X^259 + X^258 + X^257 + X^254 + X^253 + X^252 + X^248 + X^247 + X^246 + X^243 + X^242 + X^241 + X^232 + X^231 + X^230 + X^228 + X^226 + X^221 + X^220 + X^217 + X^215 + X^211 + X^206 + X^204 + X^202 + X^200 + X^196 + X^195 + X^191 + X^189 + X^180 + X^179 + X^178 + X^170 + X^169 + X^168 + X^159 + X^157 + X^153 + X^152 + X^148 + X^146 + X^144 + X^142 + X^137 + X^133 + X^131 + X^128 + X^127 + X^122 + X^120 + X^118 + X^117 + X^116 + X^107 + X^106 + X^105 + X^102 + X^101 + X^100 + X^96 + X^95 + X^94 + X^91 + X^90 + X^89 + X^80 + X^79 + X^78 + X^76 + X^74 + X^69 + X^68 + X^65 + X^63 + X^59 + X^54 + X^52 + X^50 + X^48 + X^43 + X^39 + X^37 + X^33 + X^28 + X^26 + X^22 + X^17 + X^11 + 1 6 5 8 3 X^521 + X^363 + X^346 + X^341 + X^324 + X^295 + X^278 + X^273 + X^259 + X^256 + X^242 + X^237 + X^220 + X^211 + X^194 + X^191 + X^189 + X^174 + X^172 + X^169 + X^152 + X^143 + X^126 + X^121 + X^107 + X^104 + X^90 + X^85 + X^68 + X^39 + X^22 + X^17 + 1 8 5 8 2 X^521 + X^354 + X^341 + X^337 + X^328 + X^324 + X^320 + X^315 + X^311 + X^310 + X^307 + X^303 + X^298 + X^297 + X^294 + X^293 + X^290 + X^286 + X^284 + X^281 + X^280 + X^277 + X^276 + X^273 + X^271 + X^269 + X^267 + X^264 + X^263 + X^260 + X^259 + X^256 + X^254 + X^252 + X^250 + X^247 + X^246 + X^243 + X^242 + X^239 + X^237 + X^235 + X^233 + X^230 + X^229 + X^226 + X^225 + X^222 + X^220 + X^216 + X^213 + X^212 + X^209 + X^208 + X^203 + X^202 + X^199 + X^196 + X^195 + X^191 + X^189 + X^186 + X^185 + X^182 + X^178 + X^176 + X^172 + X^169 + X^168 + X^165 + X^163 + X^159 + X^158 + X^155 + X^152 + X^151 + X^146 + X^145 + X^142 + X^141 + X^138 + X^134 + X^132 + X^129 + X^128 + X^125 + X^124 + X^121 + X^119 + X^117 + X^115 + X^112 + X^111 + X^108 + X^107 + X^104 + X^102 + X^100 + X^98 + X^95 + X^94 + X^91 + X^90 + X^87 + X^85 + X^83 + X^81 + X^78 + X^77 + X^74 + X^73 + X^70 + X^68 + X^64 + X^61 + X^60 + X^57 + X^56 + X^51 + X^47 + X^44 + X^43 + X^39 + X^34 + X^30 + X^26 + X^17 + X^13 + 1 3 7 8 4 X^521 + X^393 + X^380 + X^371 + X^367 + X^358 + X^354 + X^349 + X^345 + X^336 + X^332 + X^327 + X^323 + X^314 + X^310 + X^301 + X^288 + X^257 + X^244 + X^241 + X^235 + X^231 + X^228 + X^222 + X^219 + X^218 + X^215 + X^213 + X^209 + X^206 ** WARNING: Output too long, hence truncated. ************** MAGMA ***************** Host 3(NXDOMAIN) (194.165.15.3) Time: Mon Jan 19 15:08:17 2004 Input: k := GF(2); C := PrimitivePolynomial(k,9); C; for i in [1..8] do for n in [1..8] do for m in [1..8] do C := ((1 + X^11)^m)*((1 + X^13)^n)*((1 + X^17)^i)*((1 + X^19)^8) + X^521; if IsPrimitive(C) then C; n; i; m; end if; end for; end for; end for; Output: Magma V2.10-6 Mon Jan 19 2004 15:08:13 on modular [Seed = 1225076839] ------------------------------------- X^9 + X^4 + 1 X^521 + X^339 + X^322 + X^317 + X^300 + X^295 + X^278 + X^273 + X^256 + X^235 + X^218 + X^213 + X^196 + X^191 + X^187 + X^174 + X^170 + X^169 + X^165 + X^152 + X^148 + X^143 + X^126 + X^121 + X^104 + X^83 + X^66 + X^61 + X^44 + X^39 + X^22 + X^17 + 1 8 1 6 X^521 + X^378 + X^344 + X^290 + X^274 + X^256 + X^240 + X^226 + X^192 + X^186 + X^152 + X^138 + X^122 + X^104 + X^88 + X^34 + 1 8 2 8 X^521 + X^299 + X^282 + X^265 + X^255 + X^248 + X^247 + X^238 + X^230 + X^221 + X^213 + X^204 + X^203 + X^196 + X^186 + X^169 + X^152 + X^147 + X^130 + X^113 + X^103 + X^96 + X^95 + X^86 + X^78 + X^69 + X^61 + X^52 + X^51 + X^44 + X^34 + X^17 + 1 4 3 4 X^521 + X^312 + X^290 + X^286 + X^268 + X^264 + X^246 + X^244 + X^242 + X^222 + X^220 + X^218 + X^200 + X^196 + X^178 + X^174 + X^160 + X^152 + X^138 + X^134 + X^116 + X^112 + X^94 + X^92 + X^90 + X^70 + X^68 + X^66 + X^48 + X^44 + X^26 + X^22 + 1 2 4 6 X^521 + X^348 + X^337 + X^331 + X^326 + X^322 + X^320 + X^315 + X^311 + X^309 + X^305 + X^300 + X^298 + X^296 + X^294 + X^289 + X^285 + X^283 + X^280 + X^279 + X^274 + X^272 + X^270 + X^269 + X^268 + X^259 + X^258 + X^257 + X^254 + X^253 + X^252 + X^248 + X^247 + X^246 + X^243 + X^242 + X^241 + X^232 + X^231 + X^230 + X^228 + X^226 + X^221 + X^220 + X^217 + X^215 + X^211 + X^206 + X^204 + X^202 + X^200 + X^196 + X^195 + X^191 + X^189 + X^180 + X^179 + X^178 + X^170 + X^169 + X^168 + X^159 + X^157 + X^153 + X^152 + X^148 + X^146 + X^144 + X^142 + X^137 + X^133 + X^131 + X^128 + X^127 + X^122 + X^120 + X^118 + X^117 + X^116 + X^107 + X^106 + X^105 + X^102 + X^101 + X^100 + X^96 + X^95 + X^94 + X^91 + X^90 + X^89 + X^80 + X^79 + X^78 + X^76 + X^74 + X^69 + X^68 + X^65 + X^63 + X^59 + X^54 + X^52 + X^50 + X^48 + X^43 + X^39 + X^37 + X^33 + X^28 + X^26 + X^22 + X^17 + X^11 + 1 6 5 3 X^521 + X^363 + X^346 + X^341 + X^324 + X^295 + X^278 + X^273 + X^259 + X^256 + X^242 + X^237 + X^220 + X^211 + X^194 + X^191 + X^189 + X^174 + X^172 + X^169 + X^152 + X^143 + X^126 + X^121 + X^107 + X^104 + X^90 + X^85 + X^68 + X^39 + X^22 + X^17 + 1 8 5 2 X^521 + X^354 + X^341 + X^337 + X^328 + X^324 + X^320 + X^315 + X^311 + X^310 + X^307 + X^303 + X^298 + X^297 + X^294 + X^293 + X^290 + X^286 + X^284 + X^281 + X^280 + X^277 + X^276 + X^273 + X^271 + X^269 + X^267 + X^264 + X^263 + X^260 + X^259 + X^256 + X^254 + X^252 + X^250 + X^247 + X^246 + X^243 + X^242 + X^239 + X^237 + X^235 + X^233 + X^230 + X^229 + X^226 + X^225 + X^222 + X^220 + X^216 + X^213 + X^212 + X^209 + X^208 + X^203 + X^202 + X^199 + X^196 + X^195 + X^191 + X^189 + X^186 + X^185 + X^182 + X^178 + X^176 + X^172 + X^169 + X^168 + X^165 + X^163 + X^159 + X^158 + X^155 + X^152 + X^151 + X^146 + X^145 + X^142 + X^141 + X^138 + X^134 + X^132 + X^129 + X^128 + X^125 + X^124 + X^121 + X^119 + X^117 + X^115 + X^112 + X^111 + X^108 + X^107 + X^104 + X^102 + X^100 + X^98 + X^95 + X^94 + X^91 + X^90 + X^87 + X^85 + X^83 + X^81 + X^78 + X^77 + X^74 + X^73 + X^70 + X^68 + X^64 + X^61 + X^60 + X^57 + X^56 + X^51 + X^47 + X^44 + X^43 + X^39 + X^34 + X^30 + X^26 + X^17 + X^13 + 1 3 7 4 X^521 + X^393 + X^380 + X^371 + X^367 + X^358 + X^354 + X^349 + X^345 + X^336 + X^332 + X^327 + X^323 + X^314 + X^310 + X^301 + X^288 + X^257 + X^244 + X^241 + X^235 + X^231 + X^228 + X^222 + X^219 + X^218 + X^215 + X^213 + X^209 + X^206 + X^202 + X^200 + X^197 + X^196 + X^193 + X^191 + X^187 + X^184 + X^180 + X^178 + X^175 + X^174 + X^171 + X^165 + X^162 + X^158 + X^152 + X^149 + X^136 + X^105 + X^92 + X^83 + X^79 + X^70 + X^66 + X^61 + X^57 + X^48 + X^44 + X^39 + X^35 + X^26 + X^22 + X^13 + 1 3 8 6 Total time: 3.929 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (194.165.15.3) Time: Mon Jan 19 15:10:13 2004 Input: k := GF(2); C := PrimitivePolynomial(k,9); C; for i in [1..8] do for n in [1..8] do C := ((1 + X^11)^8)*((1 + X^13)^n)*((1 + X^17)^i)*((1 + X^19)^8) + X^521; if IsPrimitive(C) then C; n; i; end if; end for; end for; Output: Magma V2.10-6 Mon Jan 19 2004 15:10:10 on modular [Seed = 1494556920] ------------------------------------- X^9 + X^4 + 1 X^521 + X^378 + X^344 + X^290 + X^274 + X^256 + X^240 + X^226 + X^192 + X^186 + X^152 + X^138 + X^122 + X^104 + X^88 + X^34 + 1 8 2 Total time: 3.139 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (194.165.15.3) Time: Mon Jan 19 15:12:32 2004 Input: k := GF(2); C := PrimitivePolynomial(k,9); C; for i in [8..16]do for n in [8..16]do C := ((1 + X^11)^8)*((1 + X^13)^n)*((1 + X^17)^i)*((1 + X^19)^8) + X^521; if IsPrimitive(C) then C; n; i; end if; end for; end for; Output: Magma V2.10-6 Mon Jan 19 2004 15:12:29 on modular [Seed = 1730878793] ------------------------------------- X^9 + X^4 + 1 Total time: 3.099 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (194.165.15.3) Time: Mon Jan 19 15:12:55 2004 Input: k := GF(2); C := PrimitivePolynomial(k,9); C; for i in [1..16]do for n in [1..16]do C := ((1 + X^11)^8)*((1 + X^13)^n)*((1 + X^17)^i)*((1 + X^19)^8) + X^521; if IsPrimitive(C) then C; n; i; end if; end for; end for; Output: Magma V2.10-6 Mon Jan 19 2004 15:12:51 on modular [Seed = 1847727150] ------------------------------------- X^9 + X^4 + 1 X^521 + X^378 + X^344 + X^290 + X^274 + X^256 + X^240 + X^226 + X^192 + X^186 + X^152 + X^138 + X^122 + X^104 + X^88 + X^34 + 1 8 2 X^521 + X^464 + X^412 + X^396 + X^376 + X^360 + X^344 + X^324 + X^312 + X^292 + X^272 + X^260 + X^256 + X^244 + X^240 + X^224 + X^220 + X^208 + X^204 + X^192 + X^172 + X^152 + X^140 + X^120 + X^104 + X^88 + X^68 + X^52 + 1 12 4 Total time: 3.699 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 3(NXDOMAIN) (194.165.15.3) Time: Mon Jan 19 15:14:33 2004 Input: k := GF(2); C := PrimitivePolynomial(k,9); C; for n in [1..32]do C := ((1 + X^11)^8)*((1 + X^13)^n)*((1 + X^17)^8)*((1 + X^19)^8) + X^521; if IsPrimitive(C) then C; n; end if; end for; Output: Magma V2.10-6 Mon Jan 19 2004 15:14:30 on modular [Seed = 1966673872] ------------------------------------- X^9 + X^4 + 1 Total time: 3.039 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (194.165.15.3) Time: Mon Jan 19 15:15:02 2004 Input: k := GF(2); C := PrimitivePolynomial(k,9); C; for n in [32..128]do C := ((1 + X^11)^8)*((1 + X^13)^n)*((1 + X^17)^8)*((1 + X^19)^8) + X^521; if IsPrimitive(C) then C; n; end if; end for; Output: Magma V2.10-6 Mon Jan 19 2004 15:14:58 on modular [Seed = 2083522237] ------------------------------------- X^9 + X^4 + 1 X^870 + X^844 + X^818 + X^792 + X^782 + X^756 + X^734 + X^730 + X^718 + X^708 + X^704 + X^692 + X^682 + X^666 + X^656 + X^646 + X^640 + X^630 + X^620 + X^604 + X^594 + X^582 + X^578 + X^568 + X^556 + X^552 + X^530 + X^521 + X^504 + X^494 + X^468 + X^454 + X^442 + X^428 + X^416 + X^402 + X^376 + X^366 + X^340 + X^318 + X^314 + X^302 + X^292 + X^288 + X^276 + X^266 + X^250 + X^240 + X^230 + X^224 + X^214 + X^204 + X^188 + X^178 + X^166 + X^162 + X^152 + X^140 + X^136 + X^114 + X^88 + X^78 + X^52 + X^26 + 1 38 Total time: 4.929 seconds, Total memory usage: 1.99MB ************** MAGMA ***************** Host 3(NXDOMAIN) (194.165.15.3) Time: Mon Jan 19 15:16:25 2004 Input: k := GF(2); C := PrimitivePolynomial(k,9); C; for n in [1..16] do C := ((1 + X^11)^16)*((1 + X^13)^n)*((1 + X^17)^16)*((1 + X^19)^16) + X^521; if IsPrimitive(C) then C; n; end if; end for; Output: Magma V2.10-6 Mon Jan 19 2004 15:16:22 on modular [Seed = 2395141531] ------------------------------------- X^9 + X^4 + 1 Total time: 2.979 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (194.165.15.3) Time: Mon Jan 19 15:17:26 2004 Input: k := GF(2); C := PrimitivePolynomial(k,9); C; for n in [1..16] do C := ((1 + X^11)^16)*((1 + X^13)^n)*((1 + X^17)^16) + X^521; if IsPrimitive(C) then C; n; end if; end for; Output: Magma V2.10-6 Mon Jan 19 2004 15:17:23 on modular [Seed = 2514087621] ------------------------------------- X^9 + X^4 + 1 Total time: 2.989 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (194.165.15.3) Time: Mon Jan 19 15:18:01 2004 Input: k := GF(2); C := PrimitivePolynomial(k,9); C; for n in [1..16] do C := ((1 + X^11)^8)*((1 + X^13)^n)*((1 + X^11)^8) + X^521; if IsPrimitive(C) then C; n; end if; end for; Output: Magma V2.10-6 Mon Jan 19 2004 15:17:58 on modular [Seed = 2630936553] ------------------------------------- X^9 + X^4 + 1 Total time: 2.909 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (194.165.15.3) Time: Mon Jan 19 15:19:10 2004 Input: k := GF(2); C := PrimitivePolynomial(k,9); C; for m in [1..16] do for n in [1..16] do C := ((1 + X^11)^m)*((1 + X^17)^n) + X^329; if IsPrimitive(C) then C; n; end if; end for; end for; Output: Magma V2.10-6 Mon Jan 19 2004 15:19:05 on modular [Seed = 2884096018] ------------------------------------- X^9 + X^4 + 1 X^329 + X^101 + X^90 + X^79 + X^68 + X^33 + X^22 + X^11 + 1 4 X^329 + X^83 + X^66 + X^61 + X^44 + X^39 + X^22 + X^17 + 1 1 X^329 + X^207 + X^190 + X^173 + X^156 + X^139 + X^122 + X^119 + X^105 + X^102 + X^88 + X^85 + X^68 + X^51 + X^34 + X^17 + 1 7 X^329 + X^224 + X^136 + X^88 + 1 8 X^329 + X^309 + X^292 + X^241 + X^224 + X^221 + X^204 + X^173 + X^156 + X^153 + X^136 + X^105 + X^88 + X^85 + X^68 + X^17 + 1 13 X^329 + X^171 + X^154 + X^149 + X^132 + X^127 + X^110 + X^105 + X^88 + X^83 + X^66 + X^61 + X^44 + X^39 + X^22 + X^17 + 1 1 Total time: 4.739 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (194.165.15.3) Time: Mon Jan 19 15:19:33 2004 Input: k := GF(2); C := PrimitivePolynomial(k,9); C; for m in [1..16] do for n in [1..16] do C := ((1 + X^11)^m)*((1 + X^17)^n) + X^329; if IsPrimitive(C) then C; n; m; end if; end for; end for; Output: Magma V2.10-6 Mon Jan 19 2004 15:19:30 on modular [Seed = 2986199648] ------------------------------------- X^9 + X^4 + 1 X^329 + X^101 + X^90 + X^79 + X^68 + X^33 + X^22 + X^11 + 1 4 3 X^329 + X^83 + X^66 + X^61 + X^44 + X^39 + X^22 + X^17 + 1 1 6 X^329 + X^207 + X^190 + X^173 + X^156 + X^139 + X^122 + X^119 + X^105 + X^102 + X^88 + X^85 + X^68 + X^51 + X^34 + X^17 + 1 7 8 X^329 + X^224 + X^136 + X^88 + 1 8 8 X^329 + X^309 + X^292 + X^241 + X^224 + X^221 + X^204 + X^173 + X^156 + X^153 + X^136 + X^105 + X^88 + X^85 + X^68 + X^17 + 1 13 8 X^329 + X^171 + X^154 + X^149 + X^132 + X^127 + X^110 + X^105 + X^88 + X^83 + X^66 + X^61 + X^44 + X^39 + X^22 + X^17 + 1 1 14 Total time: 3.759 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (194.165.15.3) Time: Mon Jan 19 15:20:37 2004 Input: k := GF(2); C := PrimitivePolynomial(k,9); C; for m in [1..16] do for n in [1..16] do C := ((1 + X^n)^8)*((1 + X^m)^8) + X^329; if IsPrimitive(C) then C; n; m; end if; end for; end for; Output: Magma V2.10-6 Mon Jan 19 2004 15:20:33 on modular [Seed = 3247291859] ------------------------------------- X^9 + X^4 + 1 X^329 + X^128 + X^104 + X^24 + 1 13 3 X^329 + X^128 + X^104 + X^24 + 1 3 13 X^329 + X^232 + X^120 + X^112 + 1 15 14 X^329 + X^232 + X^120 + X^112 + 1 14 15 Total time: 4.759 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (194.165.15.3) Time: Mon Jan 19 15:22:01 2004 Input: k := GF(2); C := PrimitivePolynomial(k,9); C; for m in [1..18] do for n in [1..18] do C := ((1 + X^n)^8)*((1 + X^m)^8) + X^329; if IsPrimitive(C) then C; n; m; end if; end for; end for; Output: Magma V2.10-6 Mon Jan 19 2004 15:21:56 on modular [Seed = 3481514920] ------------------------------------- X^9 + X^4 + 1 X^329 + X^128 + X^104 + X^24 + 1 13 3 X^329 + X^224 + X^136 + X^88 + 1 17 11 X^329 + X^128 + X^104 + X^24 + 1 3 13 X^329 + X^232 + X^120 + X^112 + 1 15 14 X^329 + X^232 + X^120 + X^112 + 1 14 15 X^329 + X^224 + X^136 + X^88 + 1 11 17 Total time: 4.549 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (194.165.15.3) Time: Mon Jan 19 15:22:52 2004 Input: k := GF(2); C := PrimitivePolynomial(k,9); C; for m in [1..18] do for n in [1..18] do C := ((1 + X^n)^8)*((1 + X^m)^8) + X^521; if IsPrimitive(C) then C; n; m; end if; end for; end for; Output: Magma V2.10-6 Mon Jan 19 2004 15:22:48 on modular [Seed = 3600460364] ------------------------------------- X^9 + X^4 + 1 X^521 + X^32 + 1 2 2 X^521 + X^48 + X^32 + X^16 + 1 4 2 X^521 + X^48 + 1 3 3 X^521 + X^96 + X^72 + X^24 + 1 9 3 X^521 + X^144 + X^120 + X^24 + 1 15 3 X^521 + X^48 + X^32 + X^16 + 1 2 4 X^521 + X^144 + X^112 + X^32 + 1 14 4 X^521 + X^168 + X^112 + X^56 + 1 14 7 X^521 + X^96 + X^72 + X^24 + 1 3 9 X^521 + X^144 + X^112 + X^32 + 1 4 14 X^521 + X^168 + X^112 + X^56 + 1 7 14 X^521 + X^144 + X^120 + X^24 + 1 3 15 Total time: 3.399 seconds, Total memory usage: 1.99MB ************** MAGMA ***************** Host 3(NXDOMAIN) (194.165.15.3) Time: Mon Jan 19 15:24:17 2004 Input: k := GF(2); C := PrimitivePolynomial(k,9); C; for k in [1..18] do for m in [1..18] do for n in [1..18] do C := ((1 + X^n)^8)*((1 + X^m)^8)*((1 + X^k)^8) + X^521; if IsPrimitive(C) then C; n; m; k; end if; end for; end for; end for; Output: Magma V2.10-6 Mon Jan 19 2004 15:24:06 on modular [Seed = 3717308728] ------------------------------------- X^9 + X^4 + 1 X^521 + X^32 + 1 2 1 1 X^521 + X^48 + X^32 + X^16 + 1 4 1 1 X^521 + X^32 + 1 1 2 1 X^521 + X^168 + X^160 + X^152 + X^144 + X^24 + X^16 + X^8 + 1 18 2 1 X^521 + X^176 + X^168 + X^152 + X^144 + X^32 + X^24 + X^8 + 1 18 3 1 X^521 + X^48 + X^32 + X^16 + 1 1 4 1 X^521 + X^168 + X^160 + X^136 + X^128 + X^40 + X^32 + X^8 + 1 16 4 1 X^521 + X^160 + X^152 + X^112 + X^104 + X^56 + X^48 + X^8 + 1 13 6 1 X^521 + X^160 + X^152 + X^104 + X^96 + X^64 + X^56 + X^8 + 1 12 7 1 X^521 + X^176 + X^168 + X^120 + X^112 + X^64 + X^56 + X^8 + 1 14 7 1 X^521 + X^208 + X^200 + X^152 + X^144 + X^64 + X^56 + X^8 + 1 18 7 1 X^521 + X^160 + X^152 + X^104 + X^96 + X^64 + X^56 + X^8 + 1 7 12 1 X^521 + X^160 + X^152 + X^112 + X^104 + X^56 + X^48 + X^8 + 1 6 13 1 X^521 + X^176 + X^168 + X^120 + X^112 + X^64 + X^56 + X^8 + 1 7 14 1 X^521 + X^168 + X^160 + X^136 + X^128 + X^40 + X^32 + X^8 + 1 4 16 1 X^521 + X^168 + X^160 + X^152 + X^144 + X^24 + X^16 + X^8 + 1 2 18 1 X^521 + X^176 + X^168 + X^152 + X^144 + X^32 + X^24 + X^8 + 1 3 18 1 X^521 + X^208 + X^200 + X^152 + X^144 + X^64 + X^56 + X^8 + 1 7 18 1 X^521 + X^32 + 1 1 1 2 X^521 + X^168 + X^160 + X^152 + X^144 + X^24 + X^16 + X^8 + 1 18 1 2 X^521 + X^48 + X^32 + X^16 + 1 2 2 2 X^521 + X^144 + X^112 + X^32 + 1 14 2 2 X^521 + X^72 + X^56 + X^48 + X^40 + X^32 + X^24 + X^16 + 1 4 3 2 X^521 + X^72 + X^56 + X^48 + X^40 + X^32 + X^24 + X^16 + 1 3 4 2 X^521 + X^176 + X^160 + X^136 + X^120 + X^56 + X^40 + X^16 + 1 15 5 2 X^521 + X^160 + X^144 + X^112 + X^96 + X^64 + X^48 + X^16 + 1 12 6 2 X^521 + X^224 + X^208 + X^152 + X^136 + X^88 + X^72 + X^16 + 1 17 9 2 X^521 + X^160 + X^144 + X^112 + X^96 + X^64 + X^48 + X^16 + 1 6 12 2 X^521 + X^264 + X^248 + X^160 + X^144 + X^120 + X^104 + X^16 + 1 18 13 2 X^521 + X^144 + X^112 + X^32 + 1 2 14 2 X^521 + X^264 + X^248 + X^152 + X^136 + X^128 + X^112 + X^16 + 1 17 14 2 X^521 + X^176 + X^160 + X^136 + X^120 + X^56 + X^40 + X^16 + 1 5 15 2 X^521 + X^224 + X^208 + X^152 + X^136 + X^88 + X^72 + X^16 + 1 9 17 2 X^521 + X^264 + X^248 + X^152 + X^136 + X^128 + X^112 + X^16 + 1 14 17 2 X^521 + X^168 + X^160 + X^152 + X^144 + X^24 + X^16 + X^8 + 1 1 18 2 X^521 + X^264 + X^248 + X^160 + X^144 + X^120 + X^104 + X^16 + 1 13 18 2 X^521 + X^176 + X^168 + X^152 + X^144 + X^32 + X^24 + X^8 + 1 18 1 3 X^521 + X^72 + X^56 + X^48 + X^40 + X^32 + X^24 + X^16 + 1 4 2 3 X^521 + X^72 + X^56 + X^48 + X^40 + X^32 + X^24 + X^16 + 1 2 4 3 X^521 + X^120 + X^96 + X^80 + X^64 + X^56 + X^40 + X^24 + 1 7 5 3 X^521 + X^168 + X^144 + X^120 + X^96 + X^72 + X^48 + X^24 + 1 12 6 3 X^521 + X^120 + X^96 + X^80 + X^64 + X^56 + X^40 + X^24 + 1 5 7 3 X^521 + X^224 + X^200 + X^144 + X^120 + X^104 + X^80 + X^24 + 1 15 10 3 X^521 + X^240 + X^216 + X^152 + X^128 + X^112 + X^88 + X^24 + 1 16 11 3 X^521 + X^168 + X^144 + X^120 + X^96 + X^72 + X^48 + X^24 + 1 6 12 3 X^521 + X^224 + X^200 + X^144 + X^120 + X^104 + X^80 + X^24 + 1 10 15 3 X^521 + X^240 + X^216 + X^152 + X^128 + X^112 + X^88 + X^24 + 1 11 16 3 X^521 + X^176 + X^168 + X^152 + X^144 + X^32 + X^24 + X^8 + 1 1 18 3 X^521 + X^48 + X^32 + X^16 + 1 1 1 4 X^521 + X^168 + X^160 + X^136 + X^128 + X^40 + X^32 + X^8 + 1 16 1 4 X^521 + X^72 + X^56 + X^48 + X^40 + X^32 + X^24 + X^16 + 1 3 2 4 X^521 + X^72 + X^56 + X^48 + X^40 + X^32 + X^24 + X^16 + 1 2 3 4 X^521 + X^144 + X^112 + X^32 + 1 7 7 4 X^521 + X^192 + X^160 + X^128 + X^64 + X^32 + 1 12 8 4 X^521 + X^192 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X^136 + X^104 + X^80 + 1 10 17 13 X^521 + X^264 + X^248 + X^160 + X^144 + X^120 + X^104 + X^16 + 1 2 18 13 X^521 + X^176 + X^168 + X^120 + X^112 + X^64 + X^56 + X^8 + 1 7 1 14 X^521 + X^144 + X^112 + X^32 + 1 2 2 14 X^521 + X^264 + X^248 + X^152 + X^136 + X^128 + X^112 + X^16 + 1 17 2 14 X^521 + X^176 + X^168 + X^120 + X^112 + X^64 + X^56 + X^8 + 1 1 7 14 X^521 + X^304 + X^232 + X^192 + X^184 + X^120 + X^112 + X^72 + 1 15 9 14 X^521 + X^344 + X^256 + X^232 + X^200 + X^144 + X^112 + X^88 + 1 18 11 14 X^521 + X^336 + X^240 + X^224 + X^208 + X^128 + X^112 + X^96 + 1 16 12 14 X^521 + X^304 + X^232 + X^192 + X^184 + X^120 + X^112 + X^72 + 1 9 15 14 X^521 + X^336 + X^240 + X^224 + X^208 + X^128 + X^112 + X^96 + 1 12 16 14 X^521 + X^264 + X^248 + X^152 + X^136 + X^128 + X^112 + X^16 + 1 2 17 14 X^521 + X^392 + X^280 + X^256 + X^248 + X^144 + X^136 + X^112 + 1 18 17 14 X^521 + X^344 + X^256 + X^232 + X^200 + X^144 + X^112 + X^88 + 1 11 18 14 X^521 + X^392 + X^280 + X^256 + X^248 + X^144 + X^136 + X^112 + 1 17 18 14 X^521 + X^176 + X^160 + X^136 + X^120 + X^56 + X^40 + X^16 + 1 5 2 15 X^521 + X^224 + X^200 + X^144 + X^120 + X^104 + X^80 + X^24 + 1 10 3 15 X^521 + X^176 + X^160 + X^136 + X^120 + X^56 + X^40 + X^16 + 1 2 5 15 X^521 + X^288 + X^248 + X^168 + X^160 + X^128 + X^120 + X^40 + 1 16 5 15 X^521 + X^240 + X^184 + X^176 + X^64 + X^56 + 1 8 7 15 X^521 + X^240 + X^184 + X^176 + X^64 + X^56 + 1 7 8 15 X^521 + X^272 + X^208 + X^184 + X^152 + X^120 + X^88 + X^64 + 1 11 8 15 X^521 + X^3 ** WARNING: Output too long, hence truncated. ************** MAGMA ***************** Host 3(NXDOMAIN) (194.165.15.3) Time: Mon Jan 19 15:26:05 2004 Input: k := GF(2); C := PrimitivePolynomial(k,9); C; for j in [1..17] do for k in [1..17] do for m in [1..17] do for n in [1..17] do C := ((1 + X^n)^8)*((1 + X^m)^8)*((1 + X^k)^8)*((1 + X^j)^8) + X^521; if IsPrimitive(C) then C; n; m; k; j; end if; end for; end for; end for; end for; Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Mon Jan 19 2004 15:25:42 on modular [Seed = 4020474538] ------------------------------------- X^9 + X^4 + 1 X^521 + X^32 + 1 1 1 1 1 X^521 + X^48 + X^32 + X^16 + 1 2 2 1 1 X^521 + X^144 + X^112 + X^32 + 1 14 2 1 1 X^521 + X^72 + X^56 + X^48 + X^40 + X^32 + X^24 + X^16 + 1 4 3 1 1 X^521 + X^72 + X^56 + X^48 + X^40 + X^32 + X^24 + X^16 + 1 3 4 1 1 X^521 + X^176 + X^160 + X^136 + X^120 + X^56 + X^40 + X^16 + 1 15 5 1 1 X^521 + X^160 + X^144 + X^112 + X^96 + X^64 + X^48 + X^16 + 1 12 6 1 1 X^521 + X^224 + X^208 + X^152 + X^136 + X^88 + X^72 + X^16 + 1 17 9 1 1 X^521 + X^160 + X^144 + X^112 + X^96 + X^64 + X^48 + X^16 + 1 6 12 1 1 X^521 + X^144 + X^112 + X^32 + 1 2 14 1 1 X^521 + X^264 + X^248 + X^152 + X^136 + X^128 + X^112 + X^16 + 1 17 14 1 1 X^521 + X^176 + X^160 + X^136 + X^120 + X^56 + X^40 + X^16 + 1 5 15 1 1 X^521 + X^224 + X^208 + X^152 + X^136 + X^88 + X^72 + X^16 + 1 9 17 1 1 X^521 + X^264 + X^248 + X^152 + X^136 + 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X^104 + X^88 + X^80 + X^64 + X^32 + X^24 + X^8 + 1 8 3 9 1 X^521 + X^176 + X^168 + X^152 + X^144 + X^32 + X^24 + X^8 + 1 9 3 9 1 X^521 + X^208 + X^200 + X^152 + X^144 + X^64 + X^56 + X^8 + 1 9 7 9 1 X^521 + X^168 + X^160 + X^144 + X^136 + X^104 + X^88 + X^80 + X^64 + X^32 + X^24 + X^8 + 1 3 8 9 1 X^521 + X^168 + X^160 + X^152 + X^144 + X^24 + X^16 + X^8 + 1 2 9 9 1 X^521 + X^176 + X^168 + X^152 + X^144 + X^32 + X^24 + X^8 + 1 3 9 9 1 X^521 + X^208 + X^200 + X^152 + X^144 + X^64 + X^56 + X^8 + 1 7 9 9 1 X^521 + X^176 + X^168 + X^160 + X^152 + X^104 + X^72 + X^24 + X^16 + X^8 + 1 2 10 9 1 X^521 + X^224 + X^216 + X^208 + X^200 + X^152 + X^144 + X^136 + X^128 + X^96 + X^88 + X^80 + X^72 + X^24 + X^16 + X^8 + 1 2 16 9 1 X^521 + X^224 + X^208 + X^152 + X^136 + X^88 + X^72 + X^16 + 1 1 17 9 1 X^521 + X^144 + X^136 + X^128 + X^120 + X^104 + ** WARNING: Output too long, hence truncated. Errors: /home/mfd/gomagma: line 2: 17388 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host 3(NXDOMAIN) (194.165.15.3) Time: Mon Jan 19 15:27:15 2004 Input: k := GF(2); C := PrimitivePolynomial(k,9); C; for j in [11..17] do for k in [11..17] do for m in [11..17] do for n in [11..17] do C := ((1 + X^n)^8)*((1 + X^m)^8)*((1 + X^k)^8)*((1 + X^j)^8) + X^521; if IsPrimitive(C) then C; n; m; k; j; end if; end for; end for; end for; end for; Output: Magma V2.10-6 Mon Jan 19 2004 15:27:06 on modular [Seed = 4139420527] ------------------------------------- X^9 + X^4 + 1 X^521 + X^408 + X^320 + X^312 + X^304 + X^288 + X^224 + X^216 + X^208 + X^200 + X^192 + X^184 + X^120 + X^104 + X^96 + X^88 + 1 15 13 12 11 X^521 + X^408 + X^320 + X^312 + X^304 + X^288 + X^224 + X^216 + X^208 + X^200 + X^192 + X^184 + X^120 + X^104 + X^96 + X^88 + 1 13 15 12 11 X^521 + X^408 + X^320 + X^312 + X^304 + X^288 + X^224 + X^216 + X^208 + X^200 + X^192 + X^184 + X^120 + X^104 + X^96 + X^88 + 1 15 12 13 11 X^521 + X^408 + X^320 + X^312 + X^304 + X^288 + X^224 + X^216 + X^208 + X^200 + X^192 + X^184 + X^120 + X^104 + X^96 + X^88 + 1 12 15 13 11 X^521 + X^408 + X^320 + X^312 + X^304 + X^288 + X^224 + X^216 + X^208 + X^200 + X^192 + X^184 + X^120 + X^104 + X^96 + X^88 + 1 13 12 15 11 X^521 + X^408 + X^320 + X^312 + X^304 + X^288 + X^224 + X^216 + X^208 + X^200 + X^192 + X^184 + X^120 + X^104 + X^96 + X^88 + 1 12 13 15 11 X^521 + X^408 + X^320 + X^312 + X^304 + X^288 + X^224 + X^216 + X^208 + X^200 + X^192 + X^184 + X^120 + X^104 + X^96 + X^88 + 1 15 13 11 12 X^521 + X^408 + X^320 + X^312 + X^304 + X^288 + X^224 + X^216 + X^208 + X^200 + X^192 + X^184 + X^120 + X^104 + X^96 + X^88 + 1 13 15 11 12 X^521 + X^408 + X^320 + X^312 + X^304 + X^288 + X^224 + X^216 + X^208 + X^200 + X^192 + X^184 + X^120 + X^104 + X^96 + X^88 + 1 15 11 13 12 X^521 + X^408 + X^320 + X^312 + X^304 + X^288 + X^224 + X^216 + X^208 + X^200 + X^192 + X^184 + X^120 + X^104 + X^96 + X^88 + 1 11 15 13 12 X^521 + X^408 + X^320 + X^312 + X^304 + X^288 + X^224 + X^216 + X^208 + X^200 + X^192 + X^184 + X^120 + X^104 + X^96 + X^88 + 1 13 11 15 12 X^521 + X^408 + X^320 + X^312 + X^304 + X^288 + X^224 + X^216 + X^208 + X^200 + X^192 + X^184 + X^120 + X^104 + X^96 + X^88 + 1 11 13 15 12 X^521 + X^408 + X^320 + X^312 + X^304 + X^288 + X^224 + X^216 + X^208 + X^200 + X^192 + X^184 + X^120 + X^104 + X^96 + X^88 + 1 15 12 11 13 X^521 + X^408 + X^320 + X^312 + X^304 + X^288 + X^224 + X^216 + X^208 + X^200 + X^192 + X^184 + X^120 + X^104 + X^96 + X^88 + 1 12 15 11 13 X^521 + X^408 + X^320 + X^312 + X^304 + X^288 + X^224 + X^216 + X^208 + X^200 + X^192 + X^184 + X^120 + X^104 + X^96 + X^88 + 1 15 11 12 13 X^521 + X^408 + X^320 + X^312 + X^304 + X^288 + X^224 + X^216 + X^208 + X^200 + X^192 + X^184 + X^120 + X^104 + X^96 + X^88 + 1 11 15 12 13 X^521 + X^456 + X^344 + X^320 + X^248 + X^208 + X^136 + X^112 + 1 17 14 13 13 X^521 + X^456 + X^344 + X^320 + X^248 + X^208 + X^136 + X^112 + 1 14 17 13 13 X^521 + X^456 + X^344 + X^320 + X^248 + X^208 + X^136 + X^112 + 1 17 13 14 13 X^521 + X^456 + X^344 + X^320 + X^248 + X^208 + X^136 + X^112 + 1 13 17 14 13 X^521 + X^408 + X^320 + X^312 + X^304 + X^288 + X^224 + X^216 + X^208 + X^200 + X^192 + X^184 + X^120 + X^104 + X^96 + X^88 + 1 12 11 15 13 X^521 + X^408 + X^320 + X^312 + X^304 + X^288 + X^224 + X^216 + X^208 + X^200 + X^192 + X^184 + X^120 + X^104 + X^96 + X^88 + 1 11 12 15 13 X^521 + X^456 + X^344 + X^320 + X^248 + X^208 + X^136 + X^112 + 1 14 13 17 13 X^521 + X^456 + X^344 + X^320 + X^248 + X^208 + X^136 + X^112 + 1 13 14 17 13 X^521 + X^456 + X^344 + X^320 + X^248 + X^208 + X^136 + X^112 + 1 17 13 13 14 X^521 + X^456 + X^344 + X^320 + X^248 + X^208 + X^136 + X^112 + 1 13 17 13 14 X^521 + X^472 + X^352 + X^344 + X^248 + X^224 + X^128 + X^120 + 1 16 15 14 14 X^521 + X^472 + X^352 + X^344 + X^248 + X^224 + X^128 + X^120 + 1 15 16 14 14 X^521 + X^472 + X^352 + X^344 + X^248 + X^224 + X^128 + X^120 + 1 16 14 15 14 X^521 + X^472 + X^352 + X^344 + X^248 + X^224 + X^128 + X^120 + 1 14 16 15 14 X^521 + X^472 + X^352 + X^344 + X^248 + X^224 + X^128 + X^120 + 1 15 14 16 14 X^521 + X^472 + X^352 + X^344 + X^248 + X^224 + X^128 + X^120 + 1 14 15 16 14 X^521 + X^504 + X^392 + X^368 + X^256 + X^248 + X^136 + X^112 + 1 17 16 16 14 X^521 + X^504 + X^392 + X^368 + X^256 + X^248 + X^136 + X^112 + 1 16 17 16 14 X^521 + X^456 + X^344 + X^320 + X^248 + X^208 + X^136 + X^112 + 1 13 13 17 14 X^521 + X^504 + X^392 + X^368 + X^256 + X^248 + X^136 + X^112 + 1 16 16 17 14 X^521 + X^408 + X^320 + X^312 + X^304 + X^288 + X^224 + X^216 + X^208 + X^200 + X^192 + X^184 + X^120 + X^104 + X^96 + X^88 + 1 13 12 11 15 X^521 + X^408 + X^320 + X^312 + X^304 + X^288 + X^224 + X^216 + X^208 + X^200 + X^192 + X^184 + X^120 + X^104 + X^96 + X^88 + 1 12 13 11 15 X^521 + X^408 + X^320 + X^312 + X^304 + X^288 + X^224 + X^216 + X^208 + X^200 + X^192 + X^184 + X^120 + X^104 + X^96 + X^88 + 1 13 11 12 15 X^521 + X^408 + X^320 + X^312 + X^304 + X^288 + X^224 + X^216 + X^208 + X^200 + X^192 + X^184 + X^120 + X^104 + X^96 + X^88 + 1 11 13 12 15 X^521 + X^408 + X^320 + X^312 + X^304 + X^288 + X^224 + X^216 + X^208 + X^200 + X^192 + X^184 + X^120 + X^104 + X^96 + X^88 + 1 12 11 13 15 X^521 + X^408 + X^320 + X^312 + X^304 + X^288 + X^224 + X^216 + X^208 + X^200 + X^192 + X^184 + X^120 + X^104 + X^96 + X^88 + 1 11 12 13 15 X^521 + X^472 + X^352 + X^344 + X^248 + X^224 + X^128 + X^120 + 1 16 14 14 15 X^521 + X^472 + X^352 + X^344 + X^248 + X^224 + X^128 + X^120 + 1 14 16 14 15 X^521 + X^472 + X^352 + X^344 + X^248 + X^224 + X^128 + X^120 + 1 14 14 16 15 X^521 + X^472 + X^352 + X^344 + X^248 + X^224 + X^128 + X^120 + 1 15 14 14 16 X^521 + X^472 + X^352 + X^344 + X^248 + X^224 + X^128 + X^120 + 1 14 15 14 16 X^521 + X^504 + X^392 + X^368 + X^256 + X^248 + X^136 + X^112 + 1 17 16 14 16 X^521 + X^504 + X^392 + X^368 + X^256 + X^248 + X^136 + X^112 + 1 16 17 14 16 X^521 + X^472 + X^352 + X^344 + X^248 + X^224 + X^128 + X^120 + 1 14 14 15 16 X^521 + X^504 + X^392 + X^368 + X^256 + X^248 + X^136 + X^112 + 1 17 14 16 16 X^521 + X^504 + X^392 + X^368 + X^256 + X^248 + X^136 + X^112 + 1 14 17 16 16 X^521 + X^504 + X^392 + X^368 + X^256 + X^248 + X^136 + X^112 + 1 16 14 17 16 X^521 + X^504 + X^392 + X^368 + X^256 + X^248 + X^136 + X^112 + 1 14 16 17 16 X^521 + X^456 + X^344 + X^320 + X^248 + X^208 + X^136 + X^112 + 1 14 13 13 17 X^521 + X^456 + X^344 + X^320 + X^248 + X^208 + X^136 + X^112 + 1 13 14 13 17 X^521 + X^456 + X^344 + X^320 + X^248 + X^208 + X^136 + X^112 + 1 13 13 14 17 X^521 + X^504 + X^392 + X^368 + X^256 + X^248 + X^136 + X^112 + 1 16 16 14 17 X^521 + X^504 + X^392 + X^368 + X^256 + X^248 + X^136 + X^112 + 1 16 14 16 17 X^521 + X^504 + X^392 + X^368 + X^256 + X^248 + X^136 + X^112 + 1 14 16 16 17 Total time: 8.500 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (194.165.15.3) Time: Mon Jan 19 15:29:53 2004 Input: k := GF(2); C := PrimitivePolynomial(k,9); C; for j in [11..18] do for k in [11..18] do for m in [11..18] do for n in [11..18] do C := ((1 + X^n)^8)*((1 + X^m)^8)*((1 + X^k)^8)*((1 + X^j)^8) + X^521; if IsPrimitive(C) then C; n; m; k; j; end if; end for; end for; end for; end for; Output: Magma V2.10-6 Mon Jan 19 2004 15:29:40 on modular [Seed = 4256269258] ------------------------------------- X^9 + X^4 + 1 X^521 + X^408 + X^320 + X^312 + X^304 + X^288 + X^224 + X^216 + X^208 + X^200 + X^192 + X^184 + X^120 + X^104 + X^96 + X^88 + 1 15 13 12 11 X^521 + X^408 + X^320 + X^312 + X^304 + X^288 + X^224 + X^216 + X^208 + X^200 + X^192 + X^184 + X^120 + X^104 + X^96 + X^88 + 1 13 15 12 11 X^521 + X^408 + X^320 + X^312 + X^304 + X^288 + X^224 + X^216 + X^208 + X^200 + X^192 + X^184 + X^120 + X^104 + X^96 + X^88 + 1 15 12 13 11 X^521 + X^408 + X^320 + X^312 + X^304 + X^288 + X^224 + X^216 + X^208 + X^200 + X^192 + X^184 + X^120 + X^104 + X^96 + X^88 + 1 12 15 13 11 X^521 + X^408 + X^320 + X^312 + X^304 + X^288 + X^224 + X^216 + X^208 + X^200 + X^192 + X^184 + X^120 + X^104 + X^96 + X^88 + 1 13 12 15 11 X^521 + X^408 + X^320 + X^312 + X^304 + X^288 + X^224 + X^216 + X^208 + X^200 + X^192 + X^184 + X^120 + X^104 + X^96 + X^88 + 1 12 13 15 11 X^521 + X^408 + X^320 + X^312 + X^304 + X^288 + X^224 + X^216 + X^208 + X^200 + X^192 + X^184 + X^120 + X^104 + X^96 + X^88 + 1 15 13 11 12 X^521 + X^408 + X^320 + X^312 + X^304 + X^288 + X^224 + X^216 + X^208 + X^200 + X^192 + X^184 + X^120 + X^104 + X^96 + X^88 + 1 13 15 11 12 X^521 + X^408 + X^320 + X^312 + X^304 + X^288 + X^224 + X^216 + X^208 + X^200 + X^192 + X^184 + X^120 + X^104 + X^96 + X^88 + 1 15 11 13 12 X^521 + X^408 + X^320 + X^312 + X^304 + X^288 + X^224 + X^216 + X^208 + X^200 + X^192 + X^184 + X^120 + X^104 + X^96 + X^88 + 1 11 15 13 12 X^521 + X^408 + X^320 + X^312 + X^304 + X^288 + X^224 + X^216 + X^208 + X^200 + X^192 + X^184 + X^120 + X^104 + X^96 + X^88 + 1 13 11 15 12 X^521 + X^408 + X^320 + X^312 + X^304 + X^288 + X^224 + X^216 + X^208 + X^200 + X^192 + X^184 + X^120 + 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X^184 + X^120 + X^104 + X^96 + X^88 + 1 12 11 15 13 X^521 + X^408 + X^320 + X^312 + X^304 + X^288 + X^224 + X^216 + X^208 + X^200 + X^192 + X^184 + X^120 + X^104 + X^96 + X^88 + 1 11 12 15 13 X^521 + X^456 + X^344 + X^320 + X^248 + X^208 + X^136 + X^112 + 1 14 13 17 13 X^521 + X^456 + X^344 + X^320 + X^248 + X^208 + X^136 + X^112 + 1 13 14 17 13 X^521 + X^456 + X^344 + X^320 + X^248 + X^208 + X^136 + X^112 + 1 17 13 13 14 X^521 + X^456 + X^344 + X^320 + X^248 + X^208 + X^136 + X^112 + 1 13 17 13 14 X^521 + X^472 + X^352 + X^344 + X^248 + X^224 + X^128 + X^120 + 1 16 15 14 14 X^521 + X^472 + X^352 + X^344 + X^248 + X^224 + X^128 + X^120 + 1 15 16 14 14 X^521 + X^472 + X^352 + X^344 + X^248 + X^224 + X^128 + X^120 + 1 16 14 15 14 X^521 + X^472 + X^352 + X^344 + X^248 + X^224 + X^128 + X^120 + 1 14 16 15 14 X^521 + X^472 + X^352 + X^344 + X^248 + X^224 + X^128 + X^120 + 1 15 14 16 14 X^521 + X^472 + X^352 + X^344 + X^248 + X^224 + X^128 + X^120 + 1 14 15 16 14 X^521 + X^504 + X^392 + X^368 + X^256 + X^248 + X^136 + X^112 + 1 17 16 16 14 X^521 + X^504 + X^392 + X^368 + X^256 + X^248 + X^136 + X^112 + 1 16 17 16 14 X^521 + X^456 + X^344 + X^320 + X^248 + X^208 + X^136 + X^112 + 1 13 13 17 14 X^521 + X^504 + X^392 + X^368 + X^256 + X^248 + X^136 + X^112 + 1 16 16 17 14 X^521 + X^408 + X^320 + X^312 + X^304 + X^288 + X^224 + X^216 + X^208 + X^200 + X^192 + X^184 + X^120 + X^104 + X^96 + X^88 + 1 13 12 11 15 X^521 + X^408 + X^320 + X^312 + X^304 + X^288 + X^224 + X^216 + X^208 + X^200 + X^192 + X^184 + X^120 + X^104 + X^96 + X^88 + 1 12 13 11 15 X^521 + X^408 + X^320 + X^312 + X^304 + X^288 + X^224 + X^216 + X^208 + X^200 + X^192 + X^184 + X^120 + X^104 + X^96 + X^88 + 1 13 11 12 15 X^521 + X^408 + X^320 + X^312 + X^304 + X^288 + X^224 + X^216 + X^208 + X^200 + X^192 + X^184 + X^120 + X^104 + X^96 + X^88 + 1 11 13 12 15 X^521 + X^408 + X^320 + X^312 + X^304 + X^288 + X^224 + X^216 + X^208 + X^200 + X^192 + X^184 + X^120 + X^104 + X^96 + X^88 + 1 12 11 13 15 X^521 + X^408 + X^320 + X^312 + X^304 + X^288 + X^224 + X^216 + X^208 + X^200 + X^192 + X^184 + X^120 + X^104 + X^96 + X^88 + 1 11 12 13 15 X^521 + X^472 + X^352 + X^344 + X^248 + X^224 + X^128 + X^120 + 1 16 14 14 15 X^521 + X^472 + X^352 + X^344 + X^248 + X^224 + X^128 + X^120 + 1 14 16 14 15 X^521 + X^472 + X^352 + X^344 + X^248 + X^224 + X^128 + X^120 + 1 14 14 16 15 X^521 + X^472 + X^352 + X^344 + X^248 + X^224 + X^128 + X^120 + 1 15 14 14 16 X^521 + X^472 + X^352 + X^344 + X^248 + X^224 + X^128 + X^120 + 1 14 15 14 16 X^521 + X^504 + X^392 + X^368 + X^256 + X^248 + X^136 + X^112 + 1 17 16 14 16 X^521 + X^504 + X^392 + X^368 + X^256 + X^248 + X^136 + X^112 + 1 16 17 14 16 X^521 + X^472 + X^352 + X^344 + X^248 + X^224 + X^128 + X^120 + 1 14 14 15 16 X^521 + X^504 + X^392 + X^368 + X^256 + X^248 + X^136 + X^112 + 1 17 14 16 16 X^521 + X^504 + X^392 + X^368 + X^256 + X^248 + X^136 + X^112 + 1 14 17 16 16 X^521 + X^504 + X^392 + X^368 + X^256 + X^248 + X^136 + X^112 + 1 16 14 17 16 X^521 + X^504 + X^392 + X^368 + X^256 + X^248 + X^136 + X^112 + 1 14 16 17 16 X^521 + X^456 + X^344 + X^320 + X^248 + X^208 + X^136 + X^112 + 1 14 13 13 17 X^521 + X^456 + X^344 + X^320 + X^248 + X^208 + X^136 + X^112 + 1 13 14 13 17 X^521 + X^456 + X^344 + X^320 + X^248 + X^208 + X^136 + X^112 + 1 13 13 14 17 X^521 + X^504 + X^392 + X^368 + X^256 + X^248 + X^136 + X^112 + 1 16 16 14 17 X^521 + X^504 + X^392 + X^368 + X^256 + X^248 + X^136 + X^112 + 1 16 14 16 17 X^521 + X^504 + X^392 + X^368 + X^256 + X^248 + X^136 + X^112 + 1 14 16 16 17 Total time: 12.689 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (194.165.15.3) Time: Mon Jan 19 15:31:53 2004 Input: k := GF(2); C := PrimitivePolynomial(k,9); C; for i in [11..17] do for j in [11..17] do for k in [11..17] do for m in [11..17] do for n in [11..17] do C := ((1 + X^n)^8)*((1 + X^m)^8)*((1 + X^k)^8)*((1 + X^j)^8)*((1 + X^i)^8) + X^521; if IsPrimitive(C) then C; n; m; k; j; i; end if; end for; end for; end for; end for; end for; Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Mon Jan 19 2004 15:31:30 on modular [Seed = 189232557] ------------------------------------- X^9 + X^4 + 1 X^521 + X^488 + X^400 + X^392 + X^376 + X^304 + X^296 + X^288 + X^280 + X^208 + X^200 + X^192 + X^184 + X^112 + X^96 + X^88 + 1 14 12 12 12 11 X^521 + X^488 + X^400 + X^392 + X^376 + X^304 + X^296 + X^288 + X^280 + X^208 + X^200 + X^192 + X^184 + X^112 + X^96 + X^88 + 1 12 14 12 12 11 X^521 + X^488 + X^400 + X^392 + X^376 + X^304 + X^296 + X^288 + X^280 + X^208 + X^200 + X^192 + X^184 + X^112 + X^96 + X^88 + 1 12 12 14 12 11 X^521 + X^488 + X^400 + X^392 + X^376 + X^304 + X^296 + X^288 + X^280 + X^208 + X^200 + X^192 + X^184 + X^112 + X^96 + X^88 + 1 12 12 12 14 11 X^521 + X^488 + X^400 + X^392 + X^376 + X^304 + X^296 + X^288 + X^280 + X^208 + X^200 + X^192 + X^184 + X^112 + X^96 + X^88 + 1 14 12 12 11 12 X^521 + X^488 + X^400 + X^392 + X^376 + X^304 + X^296 + X^288 + X^280 + X^208 + X^200 + X^192 + X^184 + X^112 + X^96 + X^88 + 1 12 14 12 11 12 X^521 + X^488 + X^400 + X^392 + X^376 + X^304 + X^296 + X^288 + X^280 + X^208 + X^200 + X^192 + X^184 + X^112 + X^96 + X^88 + 1 12 12 14 11 12 X^521 + X^488 + X^400 + X^392 + X^376 + X^304 + X^296 + X^288 + X^280 + X^208 + X^200 + X^192 + X^184 + X^112 + X^96 + X^88 + 1 14 12 11 12 12 X^521 + X^488 + X^400 + X^392 + X^376 + X^304 + X^296 + X^288 + X^280 + X^208 + X^200 + X^192 + X^184 + X^112 + X^96 + X^88 + 1 12 14 11 12 12 X^521 + X^488 + X^400 + X^392 + X^376 + X^304 + X^296 + X^288 + X^280 + X^208 + X^200 + X^192 + X^184 + X^112 + X^96 + X^88 + 1 14 11 12 12 12 X^521 + X^488 + X^400 + X^392 + X^376 + X^304 + X^296 + X^288 + X^280 + X^208 + X^200 + X^192 + X^184 + X^112 + X^96 + X^88 + 1 11 14 12 12 12 X^521 + X^488 + X^400 + X^392 + X^376 + X^304 + X^296 + X^288 + X^280 + X^208 + X^200 + X^192 + X^184 + X^112 + X^96 + X^88 + 1 12 11 14 12 12 X^521 + X^488 + X^400 + X^392 + X^376 + X^304 + X^296 + X^288 + X^280 + X^208 + X^200 + X^192 + X^184 + X^112 + X^96 + X^88 + 1 11 12 14 12 12 X^521 + X^488 + X^400 + X^392 + X^376 + X^304 + X^296 + X^288 + X^280 + X^208 + X^200 + X^192 + X^184 + X^112 + X^96 + X^88 + 1 12 12 11 14 12 X^521 + X^488 + X^400 + X^392 + X^376 + X^304 + X^296 + X^288 + X^280 + X^208 + X^200 + X^192 + X^184 + X^112 + X^96 + X^88 + 1 12 11 12 14 12 X^521 + X^488 + X^400 + X^392 + X^376 + X^304 + X^296 + X^288 + X^280 + X^208 + X^200 + X^192 + X^184 + X^112 + X^96 + X^88 + 1 11 12 12 14 12 Errors: /home/mfd/gomagma: line 2: 17423 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host 3(NXDOMAIN) (194.165.15.3) Time: Mon Jan 19 15:33:56 2004 Input: k := GF(2); C := PrimitivePolynomial(k,9); C; for i in [1..11] do for j in [1..11] do for k in [1..11] do for m in [1..11] do for n in [1..11] do C := ((1 + X^n)^8)*((1 + X^m)^8)*((1 + X^k)^8)*((1 + X^j)^8)*((1 + X^i)^8) + X^521; if IsPrimitive(C) then C; n; m; k; j; i; end if; end for; end for; end for; end for; end for; Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Mon Jan 19 2004 15:33:33 on modular [Seed = 508715271] ------------------------------------- X^9 + X^4 + 1 X^521 + X^48 + X^32 + X^16 + 1 2 1 1 1 1 X^521 + X^48 + X^32 + X^16 + 1 1 2 1 1 1 X^521 + X^96 + X^88 + X^80 + X^64 + X^56 + X^40 + X^32 + X^16 + X^8 + 1 6 3 1 1 1 X^521 + X^144 + X^136 + X^128 + X^120 + X^104 + X^96 + X^88 + X^80 + X^64 + X^56 + X^48 + X^40 + X^24 + X^16 + X^8 + 1 10 5 1 1 1 X^521 + X^96 + X^88 + X^80 + X^64 + X^56 + X^40 + X^32 + X^16 + X^8 + 1 3 6 1 1 1 X^521 + X^168 + X^160 + X^152 + X^144 + X^24 + X^16 + X^8 + 1 9 9 1 1 1 X^521 + X^176 + X^168 + X^160 + X^152 + X^104 + X^72 + X^24 + X^16 + X^8 + 1 10 9 1 1 1 X^521 + X^144 + X^136 + X^128 + X^120 + X^104 + X^96 + X^88 + X^80 + X^64 + X^56 + X^48 + X^40 + X^24 + X^16 + X^8 + 1 5 10 1 1 1 X^521 + X^176 + X^168 + X^160 + X^152 + X^104 + X^72 + X^24 + X^16 + X^8 + 1 9 10 1 1 1 X^521 + X^48 + X^32 + X^16 + 1 1 1 2 1 1 X^521 + X^72 + X^56 + X^48 + X^40 + X^32 + X^24 + X^16 + 1 3 2 2 1 1 X^521 + X^72 + X^56 + X^48 + X^40 + X^32 + X^24 + X^16 + 1 2 3 2 1 1 X^521 + X^144 + X^112 + X^32 + 1 7 7 2 1 1 X^521 + X^96 + X^88 + X^80 + X^64 + X^56 + X^40 + X^32 + X^16 + X^8 + 1 6 1 3 1 1 X^521 + X^72 + X^56 + X^48 + X^40 + X^32 + X^24 + X^16 + 1 2 2 3 1 1 X^521 + X^96 + X^88 + X^80 + X^64 + X^56 + X^40 + X^32 + X^16 + X^8 + 1 1 6 3 1 1 X^521 + X^200 + X^184 + X^168 + X^152 + X^128 + X^120 + X^112 + X^104 + X^96 + X^88 + X^80 + X^72 + X^48 + X^32 + X^16 + 1 10 9 4 1 1 X^521 + X^200 + X^184 + X^168 + X^152 + X^128 + X^120 + X^112 + X^104 + X^96 + X^88 + X^80 + X^72 + X^48 + X^32 + X^16 + 1 9 10 4 1 1 X^521 + X^144 + X^136 + X^128 + X^120 + X^104 + X^96 + X^88 + X^80 + X^64 + X^56 + X^48 + X^40 + X^24 + X^16 + X^8 + 1 10 1 5 1 1 X^521 + X^144 + X^136 + X^128 + X^120 + X^104 + X^96 + X^88 + X^80 + X^64 + X^56 + X^48 + X^40 + X^24 + 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X^160 + X^144 + X^136 + X^128 + X^120 + X^112 + X^96 + X^80 + X^64 + X^56 + X^48 + X^40 + X^32 + X^16 + X^8 + 1 3 7 9 2 1 X^521 + X^224 + X^216 + X^208 + X^200 + X^152 + X^144 + X^136 + X^128 + X^96 + X^88 + X^80 + X^72 + X^24 + X^16 + X^8 + 1 8 8 9 2 1 X^521 + X^216 + X^208 + X^200 + X^192 + X^168 + X^160 + X^120 + X^112 + X^104 + X^96 + X^56 + X^48 + X^24 + X^16 + X^8 + 1 8 6 10 2 1 X^521 + X^216 + X^208 + X^200 + X^192 + X^168 + X^160 + X^120 + X^112 + X^104 + X^96 + X^56 + X^48 + X^24 + X^16 + X^8 + 1 6 8 10 2 1 X^521 + X^216 + X^208 + X^200 + X^192 + X^176 + X^168 + X^160 + X^144 + X^136 + X^120 + X^96 + X^80 + X^72 + X^56 + X^48 + X^40 + X^24 + X^16 + X^8 + 1 8 5 11 2 1 X^521 + X^216 + X^208 + X^200 + X^192 + X^176 + X^168 + X^160 + X^144 + X^136 + X^120 + X^96 + X^80 + X^72 + X^56 + X^48 + X^40 + X^24 + X^16 + X^8 + 1 5 8 11 2 1 X^521 + X^96 + X^88 + X^80 + X^64 + X^56 + X^40 + X^32 + X^16 + X^8 + 1 6 1 1 3 1 X^521 + ** WARNING: Output too long, hence truncated. Errors: /home/mfd/gomagma: line 2: 17434 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host 3(NXDOMAIN) (194.165.15.3) Time: Mon Jan 19 15:35:33 2004 Input: k := GF(2); C := PrimitivePolynomial(k,9); C; for i in [4..11] do for j in [4..11] do for k in [4..11] do for m in [4..11] do for n in [4..11] do C := ((1 + X^n)^8)*((1 + X^m)^8)*((1 + X^k)^8)*((1 + X^j)^8)*((1 + X^i)^8) + X^521; if IsPrimitive(C) then C; n; m; k; j; i; end if; end for; end for; end for; end for; end for; Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Mon Jan 19 2004 15:35:10 on modular [Seed = 594500697] ------------------------------------- X^9 + X^4 + 1 X^521 + X^192 + X^160 + X^128 + X^64 + X^32 + 1 6 6 4 4 4 X^521 + X^192 + X^160 + X^128 + X^64 + X^32 + 1 6 4 6 4 4 X^521 + X^192 + X^160 + X^128 + X^64 + X^32 + 1 4 6 6 4 4 X^521 + X^264 + X^216 + X^200 + X^192 + X^184 + X^152 + X^144 + X^136 + X^128 + X^120 + 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X^288 + X^248 + X^224 + X^200 + X^192 + X^184 + X^160 + X^152 + X^136 + X^128 + X^104 + X^96 + X^88 + X^64 + X^40 + 1 8 6 11 6 5 X^521 + X^288 + X^248 + X^224 + X^200 + X^192 + X^184 + X^160 + X^152 + X^136 + X^128 + X^104 + X^96 + X^88 + X^64 + X^40 + 1 6 8 11 6 5 X^521 + X^296 + X^248 + X^208 + X^160 + X^136 + X^88 + ** WARNING: Output too long, hence truncated. Errors: /home/mfd/gomagma: line 2: 17447 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host 3(NXDOMAIN) (194.165.15.3) Time: Mon Jan 19 15:37:45 2004 Input: k := GF(2); C := PrimitivePolynomial(k,9); C; for i in [4..11] do for j in [4..11] do for k in [4..11] do for m in [4..11] do for n in [4..11] do C := ((1 + X^n)^8)*((1 + X^m)^8)*((1 + X^k)^8)*((1 + X^j)^8)*((1 + X^i)^8) + X^521; if IsPrimitive(C) then if n<>m and k<>j and i<>k and j<>n then C; n; m; k; j; i; end if; end if; end for; end for; end for; end for; end for; Output: Magma V2.10-6 Mon Jan 19 2004 15:37:42 on modular [Seed = 913978917] ------------------------------------- X^9 + X^4 + 1 >> if n<>m and k<>j and i<>k and j<>n then ^ User error: bad syntax X^9 + X^4 + 1 >> n; ^ User error: Identifier 'n' has not been declared or assigned >> m; ^ User error: Identifier 'm' has not been declared or assigned Finite field of size 2 >> j; ^ User error: Identifier 'j' has not been declared or assigned >> i; ^ User error: Identifier 'i' has not been declared or assigned >> end if; ^ User error: bad syntax >> end if; ^ User error: bad syntax >> end for; ^ User error: bad syntax >> end for; ^ User error: bad syntax >> end for; ^ User error: bad syntax >> end for; ^ User error: bad syntax >> end for;; ^ User error: bad syntax Total time: 2.939 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (194.165.15.3) Time: Mon Jan 19 15:39:01 2004 Input: k := GF(2); C := PrimitivePolynomial(k,9); C; for i in [4..11] do for j in [4..11] do for k in [4..11] do for m in [4..11] do for n in [4..11] do C := ((1 + X^n)^8)*((1 + X^m)^8)*((1 + X^k)^8)*((1 + X^j)^8)*((1 + X^i)^8) + X^521; if IsPrimitive(C) then if (n!=m) and k<>j and i<>k and j<>n then C; n; m; k; j; i; end if; end if; end for; end for; end for; end for; end for; Output: Magma V2.10-6 Mon Jan 19 2004 15:38:58 on modular [Seed = 1064517465] ------------------------------------- X^9 + X^4 + 1 >> if (n!=m) and k<>j and i<>k and j<>n then ^ User error: bad syntax X^9 + X^4 + 1 >> n; ^ User error: Identifier 'n' has not been declared or assigned >> m; ^ User error: Identifier 'm' has not been declared or assigned Finite field of size 2 >> j; ^ User error: Identifier 'j' has not been declared or assigned >> i; ^ User error: Identifier 'i' has not been declared or assigned >> end if; ^ User error: bad syntax >> end if; ^ User error: bad syntax >> end for; ^ User error: bad syntax >> end for; ^ User error: bad syntax >> end for; ^ User error: bad syntax >> end for; ^ User error: bad syntax >> end for;; ^ User error: bad syntax Total time: 2.939 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (194.165.15.3) Time: Mon Jan 19 15:39:25 2004 Input: k := GF(2); C := PrimitivePolynomial(k,9); C; for i in [4..11] do for j in [4..11] do for k in [4..11] do for m in [4..11] do for n in [4..11] do C := ((1 + X^n)^8)*((1 + X^m)^8)*((1 + X^k)^8)*((1 + X^j)^8)*((1 + X^i)^8) + X^521; if IsPrimitive(C) then if (n<>m) and k<>j and i<>k and j<>n then C; n; m; k; j; i; end if; end if; end for; end for; end for; end for; end for; Output: Magma V2.10-6 Mon Jan 19 2004 15:39:22 on modular [Seed = 1074544702] ------------------------------------- X^9 + X^4 + 1 >> if (n<>m) and k<>j and i<>k and j<>n then ^ User error: bad syntax X^9 + X^4 + 1 >> n; ^ User error: Identifier 'n' has not been declared or assigned >> m; ^ User error: Identifier 'm' has not been declared or assigned Finite field of size 2 >> j; ^ User error: Identifier 'j' has not been declared or assigned >> i; ^ User error: Identifier 'i' has not been declared or assigned >> end if; ^ User error: bad syntax >> end if; ^ User error: bad syntax >> end for; ^ User error: bad syntax >> end for; ^ User error: bad syntax >> end for; ^ User error: bad syntax >> end for; ^ User error: bad syntax >> end for;; ^ User error: bad syntax Total time: 3.049 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (194.165.15.3) Time: Mon Jan 19 15:59:52 2004 Input: k := GF(2); C := PrimitivePolynomial(k,9); C; for i in [4..11] do for j in [4..11] do for k in [4..11] do for m in [4..11] do for n in [4..11] do C := ((1 + X^n)^8)*((1 + X^m)^8)*((1 + X^k)^8)*((1 + X^j)^8)*((1 + X^i)^8) + X^521; if IsPrimitive(C) then if (n eq m) or (k eq j) or (i eq k) or (j eq n) then else C; n; m; k; j; i; end if; end if; end for; end for; end for; end for; end for; Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Mon Jan 19 2004 15:59:29 on modular [Seed = 2800395155] ------------------------------------- X^9 + X^4 + 1 X^521 + X^192 + X^160 + X^128 + X^64 + X^32 + 1 6 4 6 4 4 X^521 + X^264 + X^216 + X^200 + X^192 + X^184 + X^152 + X^144 + X^136 + X^128 + X^120 + X^112 + X^80 + X^72 + X^64 + X^48 + 1 10 9 6 4 4 X^521 + X^264 + X^216 + X^200 + X^192 + X^184 + X^152 + X^144 + X^136 + 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Errors: /home/mfd/gomagma: line 2: 17570 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host 3(NXDOMAIN) (194.165.15.3) Time: Mon Jan 19 16:01:09 2004 Input: k := GF(2); C := PrimitivePolynomial(k,9); C; for i in [4..11] do for j in [4..11] do for k in [4..11] do for m in [4..11] do for n in [4..11] do C := ((1 + X^n)^8)*((1 + X^m)^8)*((1 + X^k)^8)*((1 + X^j)^8)*((1 + X^i)^8) + X^521; if IsPrimitive(C) then if (n eq m) or (k eq j) or (i eq k) or (j eq n) or (i eq j) then else C; n; m; k; j; i; end if; end if; end for; end for; end for; end for; end for; Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Mon Jan 19 2004 16:00:46 on modular [Seed = 3086725837] ------------------------------------- X^9 + X^4 + 1 X^521 + X^264 + X^216 + X^200 + X^192 + X^184 + X^152 + X^144 + X^136 + X^128 + X^120 + X^112 + X^80 + X^72 + X^64 + X^48 + 1 10 4 9 6 4 X^521 + X^264 + X^216 + X^200 + X^192 + X^184 + 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+ X^248 + X^208 + X^160 + X^136 + X^88 + X^48 + 1 10 5 6 11 5 X^521 + X^288 + X^248 + X^224 + X^200 + X^192 + X^184 + X^160 + X^152 + X^136 + X^128 + X^104 + X^96 + X^88 + X^64 + X^40 + 1 8 6 6 11 5 X^521 + X^288 + X^248 + X^224 + X^200 + X^192 + X^184 + X^160 + X^152 + X^136 + X^128 + X^104 + X^96 + X^88 + X^64 + X^40 + 1 6 8 6 11 5 X^521 + X^296 + X^248 + X^208 + X^160 + X^136 + X^88 + X^48 + 1 5 10 6 11 5 X^521 + X^296 + X^248 + X^208 + X^160 + X^136 + X^88 + X^48 + 1 6 5 10 11 5 X^521 + X^296 + X^248 + X^208 + X^160 + X^136 + X^88 + X^48 + 1 5 6 10 11 5 X^521 + X^336 + X^176 + X^160 + 1 5 11 10 11 5 X^521 + X^264 + X^216 + X^200 + X^192 + X^184 + X^152 + X^144 + X^136 + X^128 + X^120 + X^112 + X^80 + X^72 + X^64 + X^48 + 1 10 4 9 4 6 X^521 + X^264 + X^216 + X^200 + X^192 + X^184 + X^152 + X^144 + X^136 + X^128 + X^120 + X^112 + X^80 + X^72 + X^64 + X^48 + 1 9 4 10 4 6 X^521 + X^264 + X^216 + X^200 + X^192 + X^184 + X^152 + X^144 + X^136 + X^128 + X^120 + X^112 + X^80 + X^72 + X^64 + X^48 + 1 9 5 8 5 6 X^521 + X^288 + X^248 + X^224 + X^200 + X^192 + X^184 + X^160 + X^152 + X^136 + X^128 + X^104 + X^96 + X^88 + X^64 + X^40 + 1 11 6 8 5 6 X^521 + X^288 + X^248 + X^224 + X^200 + X^192 + X^184 + X^160 + X^152 + X^136 + X^128 + X^104 + X^96 + X^88 + X^64 + X^40 + 1 6 11 8 5 6 X^521 + X^264 + X^216 + X^200 + X^192 + X^184 + X^152 + X^144 + X^136 + X^128 + X^120 + X^112 + X^80 + X^72 + X^64 + X^48 + 1 8 5 9 5 6 X^521 + X^296 + X^248 + X^208 + X^160 + X^136 + X^88 + X^48 + 1 11 5 10 5 6 X^521 + X^296 + X^248 + X^208 + X^160 + X^136 + X^88 + X^48 + 1 10 5 11 5 6 X^521 + X^288 + X^248 + X^224 + X^200 + X^192 + X^184 + X^160 + X^152 + X^136 + X^128 + X^104 + X^96 + X^88 + X^64 + X^40 + 1 8 6 11 5 6 X^521 + X^288 + X^248 + X^224 + X^200 + X^192 + X^184 + X^160 + X^152 + X^136 + X^128 + X^104 + X^96 + X^88 + X^64 + X^40 + 1 6 8 11 5 6 Errors: /home/mfd/gomagma: line 2: 17587 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host 3(NXDOMAIN) (194.165.15.3) Time: Mon Jan 19 16:02:21 2004 Input: k := GF(2); C := PrimitivePolynomial(k,9); C; for i in [4..11] do for j in [4..11] do for k in [4..11] do for m in [4..11] do for n in [4..11] do C := ((1 + X^n)^8)*((1 + X^m)^8)*((1 + X^k)^8)*((1 + X^j)^8)*((1 + X^i)^8) + X^521; if IsPrimitive(C) then if (n eq m) or (k eq j) or (i eq k) or (j eq n) or (i eq j) or (m eq i) then else C; n; m; k; j; i; end if; end if; end for; end for; end for; end for; end for; Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Mon Jan 19 2004 16:01:58 on modular [Seed = 3566784790] ------------------------------------- X^9 + X^4 + 1 X^521 + X^264 + X^216 + X^200 + X^192 + X^184 + X^152 + X^144 + X^136 + X^128 + X^120 + X^112 + X^80 + X^72 + X^64 + X^48 + 1 4 10 9 6 4 X^521 + X^264 + X^216 + X^200 + X^192 + X^184 + X^152 + X^144 + X^136 + X^128 + X^120 + X^112 + X^80 + X^72 + X^64 + X^48 + 1 4 9 10 6 4 X^521 + X^264 + X^216 + X^200 + X^192 + X^184 + X^152 + X^144 + X^136 + X^128 + X^120 + X^112 + X^80 + X^72 + X^64 + X^48 + 1 4 10 6 9 4 X^521 + X^264 + X^216 + X^200 + X^192 + X^184 + X^152 + X^144 + X^136 + X^128 + X^120 + X^112 + X^80 + X^72 + X^64 + X^48 + 1 4 6 10 9 4 X^521 + X^336 + X^304 + X^192 + X^176 + X^160 + X^144 + X^32 + 1 10 9 10 9 4 X^521 + X^352 + X^320 + X^280 + X^264 + X^248 + X^232 + X^120 + X^104 + X^88 + X^72 + X^32 + 1 11 10 10 9 4 X^521 + X^352 + X^320 + X^280 + X^264 + X^248 + X^232 + X^120 + X^104 + X^88 + X^72 + X^32 + 1 10 11 10 9 4 X^521 + X^264 + X^216 + X^200 + X^192 + X^184 + X^152 + X^144 + X^136 + X^128 + X^120 + X^112 + X^80 + X^72 + X^64 + X^48 + 1 4 9 6 10 4 X^521 + X^264 + X^216 + X^200 + X^192 + X^184 + X^152 + X^144 + X^136 + X^128 + X^120 + X^112 + X^80 + X^72 + X^64 + X^48 + 1 4 6 9 10 4 X^521 + X^336 + X^304 + X^192 + X^176 + X^160 + X^144 + X^32 + 1 9 10 9 10 4 X^521 + X^352 + X^320 + X^280 + X^264 + X^248 + X^232 + X^120 + X^104 + X^88 + X^72 + X^32 + 1 11 10 9 10 4 X^521 + X^352 + X^320 + X^280 + X^264 + X^248 + X^232 + X^120 + X^104 + X^88 + X^72 + X^32 + 1 9 10 11 10 4 X^521 + X^352 + X^320 + X^280 + X^264 + X^248 + X^232 + X^120 + X^104 + X^88 + X^72 + X^32 + 1 10 9 10 11 4 X^521 + X^352 + X^320 + X^280 + X^264 + X^248 + X^232 + X^120 + X^104 + X^88 + X^72 + X^32 + 1 9 10 10 11 4 X^521 + X^288 + X^248 + X^224 + X^200 + X^192 + X^184 + X^160 + X^152 + X^136 + X^128 + X^104 + X^96 + X^88 + X^64 + X^40 + 1 11 6 8 6 5 X^521 + X^264 + X^216 + X^200 + X^192 + X^184 + X^152 + X^144 + X^136 + X^128 + X^120 + X^112 + X^80 + X^72 + X^64 + X^48 + 1 5 9 8 6 5 X^521 + X^264 + X^216 + X^200 + X^192 + X^184 + X^152 + X^144 + X^136 + X^128 + X^120 + X^112 + X^80 + X^72 + X^64 + X^48 + 1 5 8 9 6 5 X^521 + X^296 + X^248 + X^208 + X^160 + X^136 + X^88 + X^48 + 1 5 11 10 6 5 X^521 + X^288 + X^248 + X^224 + X^200 + X^192 + X^184 + X^160 + X^152 + X^136 + X^128 + X^104 + X^96 + X^88 + X^64 + X^40 + 1 8 6 11 6 5 X^521 + X^296 + X^248 + X^208 + X^160 + X^136 + X^88 + X^48 + 1 5 10 11 6 5 X^521 + X^296 + X^256 + X^232 + X^216 + X^192 + X^184 + X^176 + X^152 + X^144 + X^120 + X^112 + X^104 + X^80 + X^64 + X^40 + 1 10 7 8 7 5 X^521 + X^296 + X^256 + X^232 + X^216 + X^192 + X^184 + X^176 + X^152 + X^144 + X^120 + X^112 + X^104 + X^80 + X^64 + X^40 + 1 8 7 10 7 5 X^521 + X^288 + X^248 + X^224 + X^200 + X^192 + X^184 + X^160 + X^152 + X^136 + X^128 + X^104 + X^96 + X^88 + X^64 + X^40 + 1 11 6 6 8 5 X^521 + X^264 + X^216 + X^200 + X^192 + X^184 + X^152 + X^144 + X^136 + X^128 + X^120 + X^112 + X^80 + X^72 + X^64 + X^48 + 1 5 9 6 8 5 X^521 + X^288 + X^248 + X^224 + X^200 + X^192 + X^184 + X^160 + X^152 + X^136 + X^128 + X^104 + X^96 + X^88 + X^64 + X^40 + 1 6 11 6 8 5 X^521 + X^296 + X^256 + X^232 + X^216 + X^192 + X^184 + X^176 + X^152 + X^144 + X^120 + X^112 + X^104 + X^80 + X^64 + X^40 + 1 10 7 7 8 5 X^521 + X^296 + X^256 + X^232 + X^216 + X^192 + X^184 + X^176 + X^152 + X^144 + X^120 + X^112 + X^104 + X^80 + X^64 + X^40 + 1 7 10 7 8 5 X^521 + X^264 + X^216 + X^200 + X^192 + X^184 + X^152 + X^144 + X^136 + X^128 + X^120 + X^112 + X^80 + X^72 + X^64 + X^48 + 1 5 6 9 8 5 X^521 + X^264 + X^216 + X^200 + X^192 + X^184 + X^152 + X^144 + X^136 + X^128 + X^120 + X^112 + X^80 + X^72 + X^64 + X^48 + 1 5 8 6 9 5 X^521 + X^264 + X^216 + X^200 + X^192 + X^184 + X^152 + X^144 + X^136 + X^128 + X^120 + X^112 + X^80 + X^72 + X^64 + X^48 + 1 5 6 8 9 5 X^521 + X^296 + X^248 + X^208 + X^160 + X^136 + X^88 + X^48 + 1 5 11 6 10 5 X^521 + X^296 + X^256 + X^232 + X^216 + X^192 + X^184 + X^176 + X^152 + X^144 + X^120 + X^112 + X^104 + X^80 + X^64 + X^40 + 1 8 7 7 10 5 X^521 + X^296 + X^256 + X^232 + X^216 + X^192 + X^184 + X^176 + X^152 + X^144 + X^120 + X^112 + X^104 + X^80 + X^64 + X^40 + 1 7 8 7 10 5 X^521 + X^296 + X^248 + X^208 + X^160 + X^136 + X^88 + X^48 + 1 5 6 11 10 5 X^521 + X^336 + X^176 + X^160 + 1 5 11 11 10 5 X^521 + X^288 + X^248 + X^224 + X^200 + X^192 + X^184 + X^160 + X^152 + X^136 + X^128 + X^104 + X^96 + X^88 + X^64 + X^40 + 1 8 6 6 11 5 X^521 + X^288 + X^248 + X^224 + X^200 + X^192 + X^184 + X^160 + X^152 + X^136 + X^128 + X^104 + X^96 + X^88 + X^64 + X^40 + 1 6 8 6 11 5 X^521 + X^296 + X^248 + X^208 + X^160 + X^136 + X^88 + X^48 + 1 5 10 6 11 5 X^521 + X^296 + X^248 + X^208 + X^160 + X^136 + X^88 + X^48 + 1 5 6 10 11 5 X^521 + X^336 + X^176 + X^160 + 1 5 11 10 11 5 X^521 + X^264 + X^216 + X^200 + X^192 + X^184 + X^152 + X^144 + X^136 + X^128 + X^120 + X^112 + X^80 + X^72 + X^64 + X^48 + 1 10 4 9 4 6 X^521 + X^264 + X^216 + X^200 + X^192 + X^184 + X^152 + X^144 + X^136 + X^128 + X^120 + X^112 + X^80 + X^72 + X^64 + X^48 + 1 9 4 10 4 6 X^521 + X^264 + X^216 + X^200 + X^192 + X^184 + X^152 + X^144 + X^136 + X^128 + X^120 + X^112 + X^80 + X^72 + X^64 + X^48 + 1 9 5 8 5 6 X^521 + X^288 + X^248 + X^224 + X^200 + X^192 + X^184 + X^160 + X^152 + X^136 + X^128 + X^104 + X^96 + X^88 + X^64 + X^40 + 1 6 11 8 5 6 X^521 + X^264 + X^216 + X^200 + X^192 + X^184 + X^152 + X^144 + X^136 + X^128 + X^120 + X^112 + X^80 + X^72 + X^64 + X^48 + 1 8 5 9 5 6 Errors: /home/mfd/gomagma: line 2: 17616 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host 3(NXDOMAIN) (194.165.15.3) Time: Mon Jan 19 16:03:22 2004 Input: k := GF(2); C := PrimitivePolynomial(k,9); C; for i in [4..11] do for j in [4..11] do for k in [4..11] do for m in [4..11] do for n in [4..11] do C := ((1 + X^n)^8)*((1 + X^m)^8)*((1 + X^k)^8)*((1 + X^j)^8)*((1 + X^i)^8) + X^521; if IsPrimitive(C) then if (n eq m) or (k eq j) or (i eq k) or (j eq n) or (i eq j) or (m eq i) or (n eq i) then else C; n; m; k; j; i; end if; end if; end for; end for; end for; end for; end for; Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Mon Jan 19 2004 16:02:59 on modular [Seed = 3717323738] ------------------------------------- X^9 + X^4 + 1 X^521 + X^336 + X^304 + X^192 + X^176 + X^160 + X^144 + X^32 + 1 10 9 10 9 4 X^521 + X^352 + X^320 + X^280 + X^264 + X^248 + X^232 + X^120 + X^104 + X^88 + X^72 + X^32 + 1 11 10 10 9 4 X^521 + X^352 + X^320 + X^280 + X^264 + X^248 + X^232 + X^120 + X^104 + X^88 + X^72 + X^32 + 1 10 11 10 9 4 X^521 + X^336 + X^304 + X^192 + X^176 + X^160 + X^144 + X^32 + 1 9 10 9 10 4 X^521 + X^352 + X^320 + X^280 + X^264 + X^248 + X^232 + X^120 + X^104 + X^88 + X^72 + X^32 + 1 11 10 9 10 4 X^521 + X^352 + X^320 + X^280 + X^264 + X^248 + X^232 + X^120 + X^104 + X^88 + X^72 + X^32 + 1 9 10 11 10 4 X^521 + X^352 + X^320 + X^280 + X^264 + X^248 + X^232 + X^120 + X^104 + X^88 + X^72 + X^32 + 1 10 9 10 11 4 X^521 + X^352 + X^320 + X^280 + X^264 + X^248 + X^232 + X^120 + X^104 + X^88 + X^72 + X^32 + 1 9 10 10 11 4 X^521 + X^288 + X^248 + X^224 + X^200 + X^192 + X^184 + X^160 + X^152 + X^136 + X^128 + X^104 + X^96 + X^88 + X^64 + X^40 + 1 11 6 8 6 5 X^521 + X^288 + X^248 + X^224 + X^200 + X^192 + X^184 + X^160 + X^152 + X^136 + X^128 + X^104 + X^96 + X^88 + X^64 + X^40 + 1 8 6 11 6 5 X^521 + X^296 + X^256 + X^232 + X^216 + X^192 + X^184 + X^176 + X^152 + X^144 + X^120 + X^112 + X^104 + X^80 + X^64 + X^40 + 1 10 7 8 7 5 X^521 + X^296 + X^256 + X^232 + X^216 + X^192 + X^184 + X^176 + X^152 + X^144 + X^120 + X^112 + X^104 + X^80 + X^64 + X^40 + 1 8 7 10 7 5 X^521 + X^288 + X^248 + X^224 + X^200 + X^192 + X^184 + X^160 + X^152 + X^136 + X^128 + X^104 + X^96 + X^88 + X^64 + X^40 + 1 11 6 6 8 5 X^521 + X^288 + X^248 + X^224 + X^200 + X^192 + X^184 + X^160 + X^152 + X^136 + X^128 + X^104 + X^96 + X^88 + X^64 + X^40 + 1 6 11 6 8 5 X^521 + X^296 + X^256 + X^232 + X^216 + X^192 + X^184 + X^176 + X^152 + X^144 + X^120 + X^112 + X^104 + X^80 + X^64 + X^40 + 1 10 7 7 8 5 X^521 + X^296 + X^256 + X^232 + X^216 + X^192 + X^184 + X^176 + X^152 + X^144 + X^120 + X^112 + X^104 + X^80 + X^64 + X^40 + 1 7 10 7 8 5 X^521 + X^296 + X^256 + X^232 + X^216 + X^192 + X^184 + X^176 + X^152 + X^144 + X^120 + X^112 + X^104 + X^80 + X^64 + X^40 + 1 8 7 7 10 5 X^521 + X^296 + X^256 + X^232 + X^216 + X^192 + X^184 + X^176 + X^152 + X^144 + X^120 + X^112 + X^104 + X^80 + X^64 + X^40 + 1 7 8 7 10 5 X^521 + X^288 + X^248 + X^224 + X^200 + X^192 + X^184 + X^160 + X^152 + X^136 + X^128 + X^104 + X^96 + X^88 + X^64 + X^40 + 1 8 6 6 11 5 X^521 + X^288 + X^248 + X^224 + X^200 + X^192 + X^184 + X^160 + X^152 + X^136 + X^128 + X^104 + X^96 + X^88 + X^64 + X^40 + 1 6 8 6 11 5 X^521 + X^264 + X^216 + X^200 + X^192 + X^184 + X^152 + X^144 + X^136 + X^128 + X^120 + X^112 + X^80 + X^72 + X^64 + X^48 + 1 10 4 9 4 6 X^521 + X^264 + X^216 + X^200 + X^192 + X^184 + X^152 + X^144 + X^136 + X^128 + X^120 + X^112 + X^80 + X^72 + X^64 + X^48 + 1 9 4 10 4 6 X^521 + X^264 + X^216 + X^200 + X^192 + X^184 + X^152 + X^144 + X^136 + X^128 + X^120 + X^112 + X^80 + X^72 + X^64 + X^48 + 1 9 5 8 5 6 X^521 + X^264 + X^216 + X^200 + X^192 + X^184 + X^152 + X^144 + X^136 + X^128 + X^120 + X^112 + X^80 + X^72 + X^64 + X^48 + 1 8 5 9 5 6 X^521 + X^296 + X^248 + X^208 + X^160 + X^136 + X^88 + X^48 + 1 11 5 10 5 6 X^521 + X^296 + X^248 + X^208 + X^160 + X^136 + X^88 + X^48 + 1 10 5 11 5 6 Errors: /home/mfd/gomagma: line 2: 17625 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host 3(NXDOMAIN) (194.165.15.3) Time: Mon Jan 19 16:04:46 2004 Input: k := GF(2); C := PrimitivePolynomial(k,9); C; for i in [4..11] do for j in [4..11] do for k in [4..11] do for m in [4..11] do for n in [4..11] do C := ((1 + X^n)^8)*((1 + X^m)^8)*((1 + X^k)^8)*((1 + X^j)^8)*((1 + X^i)^8) + X^521; if IsPrimitive(C) then if (n eq m) or (k eq j) or (i eq k) or (j eq n) or (i eq j) or (m eq i) or (n eq i) or (n eq k) or (m eq k) then else C; n; m; k; j; i; end if; end if; end for; end for; end for; end for; end for; Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Mon Jan 19 2004 16:04:23 on modular [Seed = 3869958325] ------------------------------------- X^9 + X^4 + 1 X^521 + X^352 + X^320 + X^280 + X^264 + X^248 + X^232 + X^120 + X^104 + X^88 + X^72 + X^32 + 1 11 10 9 10 4 X^521 + X^352 + X^320 + X^280 + X^264 + X^248 + X^232 + X^120 + X^104 + X^88 + X^72 + X^32 + 1 9 10 11 10 4 X^521 + X^288 + X^248 + X^224 + X^200 + X^192 + X^184 + X^160 + X^152 + X^136 + X^128 + X^104 + X^96 + X^88 + X^64 + X^40 + 1 11 6 8 6 5 X^521 + X^288 + X^248 + X^224 + X^200 + X^192 + X^184 + X^160 + X^152 + X^136 + X^128 + X^104 + X^96 + X^88 + X^64 + X^40 + 1 8 6 11 6 5 X^521 + X^296 + X^256 + X^232 + X^216 + X^192 + X^184 + X^176 + X^152 + X^144 + X^120 + X^112 + X^104 + X^80 + X^64 + X^40 + 1 10 7 8 7 5 X^521 + X^296 + X^256 + X^232 + X^216 + X^192 + X^184 + X^176 + X^152 + X^144 + X^120 + X^112 + X^104 + X^80 + X^64 + X^40 + 1 8 7 10 7 5 X^521 + X^264 + X^216 + X^200 + X^192 + X^184 + X^152 + X^144 + X^136 + X^128 + X^120 + X^112 + X^80 + X^72 + X^64 + X^48 + 1 10 4 9 4 6 X^521 + X^264 + X^216 + X^200 + X^192 + X^184 + X^152 + X^144 + X^136 + X^128 + X^120 + X^112 + X^80 + X^72 + X^64 + X^48 + 1 9 4 10 4 6 X^521 + X^264 + X^216 + X^200 + X^192 + X^184 + X^152 + X^144 + X^136 + X^128 + X^120 + X^112 + X^80 + X^72 + X^64 + X^48 + 1 9 5 8 5 6 X^521 + X^264 + X^216 + X^200 + X^192 + X^184 + X^152 + X^144 + X^136 + X^128 + X^120 + X^112 + X^80 + X^72 + X^64 + X^48 + 1 8 5 9 5 6 X^521 + X^296 + X^248 + X^208 + X^160 + X^136 + X^88 + X^48 + 1 11 5 10 5 6 X^521 + X^296 + X^248 + X^208 + X^160 + X^136 + X^88 + X^48 + 1 10 5 11 5 6 Errors: /home/mfd/gomagma: line 2: 17634 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host 3(NXDOMAIN) (194.165.15.3) Time: Mon Jan 19 16:05:44 2004 Input: k := GF(2); C := PrimitivePolynomial(k,9); C; for i in [4..11] do for j in [4..11] do for k in [4..11] do for m in [4..11] do for n in [4..11] do C := ((1 + X^n)^8)*((1 + X^m)^8)*((1 + X^k)^8)*((1 + X^j)^8)*((1 + X^i)^8) + X^521; if IsPrimitive(C) then if (n eq m) or (k eq j) or (i eq k) or (j eq n) or (i eq j) or (m eq i) or (n eq i) or (n eq k) or (m eq k) or (m eq j) then else C; n; m; k; j; i; end if; end if; end for; end for; end for; end for; end for; Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Mon Jan 19 2004 16:05:21 on modular [Seed = 3953651070] ------------------------------------- X^9 + X^4 + 1 Errors: /home/mfd/gomagma: line 2: 17647 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host 3(NXDOMAIN) (194.165.15.3) Time: Mon Jan 19 16:07:22 2004 Input: k := GF(2); C := PrimitivePolynomial(k,9); C; for j in [4..11] do for k in [4..11] do for m in [4..11] do for n in [4..11] do C := ((1 + X^n)^8)*((1 + X^m)^8)*((1 + X^k)^8)*((1 + X^j)^8) + X^521; if IsPrimitive(C) then if (n eq m) or (k eq j) or (j eq n) or (n eq k) or (m eq k) or (m eq j) then else C; n; m; k; j; end if; end if; end for; end for; end for; end for; Output: Magma V2.10-6 Mon Jan 19 2004 16:07:11 on modular [Seed = 4273141765] ------------------------------------- X^9 + X^4 + 1 X^521 + X^232 + X^200 + X^192 + X^144 + X^128 + X^120 + X^112 + X^104 + X^88 + X^40 + X^32 + 1 11 9 5 4 X^521 + X^232 + X^200 + X^192 + X^144 + X^128 + X^120 + X^112 + X^104 + X^88 + X^40 + X^32 + 1 9 11 5 4 X^521 + X^232 + X^200 + X^192 + X^144 + X^128 + X^120 + X^112 + X^104 + X^88 + X^40 + X^32 + 1 11 5 9 4 X^521 + X^232 + X^200 + X^192 + X^144 + X^128 + X^120 + X^112 + X^104 + X^88 + X^40 + X^32 + 1 5 11 9 4 X^521 + X^232 + X^200 + X^192 + X^144 + X^128 + X^120 + X^112 + X^104 + X^88 + X^40 + X^32 + 1 9 5 11 4 X^521 + X^232 + X^200 + X^192 + X^144 + X^128 + X^120 + X^112 + X^104 + X^88 + X^40 + X^32 + 1 5 9 11 4 X^521 + X^232 + X^200 + X^192 + X^144 + X^128 + X^120 + X^112 + X^104 + X^88 + X^40 + X^32 + 1 11 9 4 5 X^521 + X^232 + X^200 + X^192 + X^144 + X^128 + X^120 + X^112 + X^104 + X^88 + X^40 + X^32 + 1 9 11 4 5 X^521 + X^232 + X^200 + X^192 + X^144 + X^128 + X^120 + X^112 + X^104 + X^88 + X^40 + X^32 + 1 11 4 9 5 X^521 + X^232 + X^200 + X^192 + X^144 + X^128 + X^120 + X^112 + X^104 + X^88 + X^40 + X^32 + 1 4 11 9 5 X^521 + X^232 + X^200 + X^192 + X^144 + X^128 + X^120 + X^112 + X^104 + X^88 + X^40 + X^32 + 1 9 4 11 5 X^521 + X^232 + X^200 + X^192 + X^144 + X^128 + X^120 + X^112 + X^104 + X^88 + X^40 + X^32 + 1 4 9 11 5 X^521 + X^264 + X^216 + X^200 + X^192 + X^184 + X^152 + X^144 + X^136 + X^128 + X^120 + X^112 + X^80 + X^72 + X^64 + X^48 + 1 10 9 8 6 X^521 + X^264 + X^216 + X^200 + X^192 + X^184 + X^152 + X^144 + X^136 + X^128 + X^120 + X^112 + X^80 + X^72 + X^64 + X^48 + 1 9 10 8 6 X^521 + X^264 + X^216 + X^200 + X^192 + X^184 + X^152 + X^144 + X^136 + X^128 + X^120 + X^112 + X^80 + X^72 + X^64 + X^48 + 1 10 8 9 6 X^521 + X^264 + X^216 + X^200 + X^192 + X^184 + X^152 + X^144 + X^136 + X^128 + X^120 + X^112 + X^80 + X^72 + X^64 + X^48 + 1 8 10 9 6 X^521 + X^264 + X^216 + X^200 + X^192 + X^184 + X^152 + X^144 + X^136 + X^128 + X^120 + X^112 + X^80 + X^72 + X^64 + X^48 + 1 9 8 10 6 X^521 + X^264 + X^216 + X^200 + X^192 + X^184 + X^152 + X^144 + X^136 + X^128 + X^120 + X^112 + X^80 + X^72 + X^64 + X^48 + 1 8 9 10 6 X^521 + X^264 + X^216 + X^200 + X^192 + X^184 + X^152 + X^144 + X^136 + X^128 + X^120 + X^112 + X^80 + X^72 + X^64 + X^48 + 1 10 9 6 8 X^521 + X^264 + X^216 + X^200 + X^192 + X^184 + X^152 + X^144 + X^136 + X^128 + X^120 + X^112 + X^80 + X^72 + X^64 + X^48 + 1 9 10 6 8 X^521 + X^264 + X^216 + X^200 + X^192 + X^184 + X^152 + X^144 + X^136 + X^128 + X^120 + X^112 + X^80 + X^72 + X^64 + X^48 + 1 10 6 9 8 X^521 + X^264 + X^216 + X^200 + X^192 + X^184 + X^152 + X^144 + X^136 + X^128 + X^120 + X^112 + X^80 + X^72 + X^64 + X^48 + 1 6 10 9 8 X^521 + X^264 + X^216 + X^200 + X^192 + X^184 + X^152 + X^144 + X^136 + X^128 + X^120 + X^112 + X^80 + X^72 + X^64 + X^48 + 1 9 6 10 8 X^521 + X^264 + X^216 + X^200 + X^192 + X^184 + X^152 + X^144 + X^136 + X^128 + X^120 + X^112 + X^80 + X^72 + X^64 + X^48 + 1 6 9 10 8 X^521 + X^232 + X^200 + X^192 + X^144 + X^128 + X^120 + X^112 + X^104 + X^88 + X^40 + X^32 + 1 11 5 4 9 X^521 + X^232 + X^200 + X^192 + X^144 + X^128 + X^120 + X^112 + X^104 + X^88 + X^40 + X^32 + 1 5 11 4 9 X^521 + X^232 + X^200 + X^192 + X^144 + X^128 + X^120 + X^112 + X^104 + X^88 + X^40 + X^32 + 1 11 4 5 9 X^521 + X^232 + X^200 + X^192 + X^144 + X^128 + X^120 + X^112 + X^104 + X^88 + X^40 + X^32 + 1 4 11 5 9 X^521 + X^264 + X^216 + X^200 + X^192 + X^184 + X^152 + X^144 + X^136 + X^128 + X^120 + X^112 + X^80 + X^72 + X^64 + X^48 + 1 10 8 6 9 X^521 + X^264 + X^216 + X^200 + X^192 + X^184 + X^152 + X^144 + X^136 + X^128 + X^120 + X^112 + X^80 + X^72 + X^64 + X^48 + 1 8 10 6 9 X^521 + X^264 + X^216 + X^200 + X^192 + X^184 + X^152 + X^144 + X^136 + X^128 + X^120 + X^112 + X^80 + X^72 + X^64 + X^48 + 1 10 6 8 9 X^521 + X^264 + X^216 + X^200 + X^192 + X^184 + X^152 + X^144 + X^136 + X^128 + X^120 + X^112 + X^80 + X^72 + X^64 + X^48 + 1 6 10 8 9 X^521 + X^264 + X^216 + X^200 + X^192 + X^184 + X^152 + X^144 + X^136 + X^128 + X^120 + X^112 + X^80 + X^72 + X^64 + X^48 + 1 8 6 10 9 X^521 + X^264 + X^216 + X^200 + X^192 + X^184 + X^152 + X^144 + X^136 + X^128 + X^120 + X^112 + X^80 + X^72 + X^64 + X^48 + 1 6 8 10 9 X^521 + X^232 + X^200 + X^192 + X^144 + X^128 + X^120 + X^112 + X^104 + X^88 + X^40 + X^32 + 1 5 4 11 9 X^521 + X^232 + X^200 + X^192 + X^144 + X^128 + X^120 + X^112 + X^104 + X^88 + X^40 + X^32 + 1 4 5 11 9 X^521 + X^264 + X^216 + X^200 + X^192 + X^184 + X^152 + X^144 + X^136 + X^128 + X^120 + X^112 + X^80 + X^72 + X^64 + X^48 + 1 9 8 6 10 X^521 + X^264 + X^216 + X^200 + X^192 + X^184 + X^152 + X^144 + X^136 + X^128 + X^120 + X^112 + X^80 + X^72 + X^64 + X^48 + 1 8 9 6 10 X^521 + X^264 + X^216 + X^200 + X^192 + X^184 + X^152 + X^144 + X^136 + X^128 + X^120 + X^112 + X^80 + X^72 + X^64 + X^48 + 1 9 6 8 10 X^521 + X^264 + X^216 + X^200 + X^192 + X^184 + X^152 + X^144 + X^136 + X^128 + X^120 + X^112 + X^80 + X^72 + X^64 + X^48 + 1 6 9 8 10 X^521 + X^264 + X^216 + X^200 + X^192 + X^184 + X^152 + X^144 + X^136 + X^128 + X^120 + X^112 + X^80 + X^72 + X^64 + X^48 + 1 8 6 9 10 X^521 + X^264 + X^216 + X^200 + X^192 + X^184 + X^152 + X^144 + X^136 + X^128 + X^120 + X^112 + X^80 + X^72 + X^64 + X^48 + 1 6 8 9 10 X^521 + X^232 + X^200 + X^192 + X^144 + X^128 + X^120 + X^112 + X^104 + X^88 + X^40 + X^32 + 1 9 5 4 11 X^521 + X^232 + X^200 + X^192 + X^144 + X^128 + X^120 + X^112 + X^104 + X^88 + X^40 + X^32 + 1 5 9 4 11 X^521 + X^232 + X^200 + X^192 + X^144 + X^128 + X^120 + X^112 + X^104 + X^88 + X^40 + X^32 + 1 9 4 5 11 X^521 + X^232 + X^200 + X^192 + X^144 + X^128 + X^120 + X^112 + X^104 + X^88 + X^40 + X^32 + 1 4 9 5 11 X^521 + X^232 + X^200 + X^192 + X^144 + X^128 + X^120 + X^112 + X^104 + X^88 + X^40 + X^32 + 1 5 4 9 11 X^521 + X^232 + X^200 + X^192 + X^144 + X^128 + X^120 + X^112 + X^104 + X^88 + X^40 + X^32 + 1 4 5 9 11 Total time: 10.649 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host h53.85.213.151.ip.alltel.net. (151.213.85.53) Time: Mon Jan 19 19:16:22 2004 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: Magma V2.10-6 Mon Jan 19 2004 19:16:19 on modular [Seed = 1394565126] ------------------------------------- Replace this by some code, then click [PARI] or [MAGMA]! Total time: 2.989 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (194.165.15.3) Time: Tue Jan 20 00:17:03 2004 Input: k := GF(2); C := PrimitivePolynomial(k,9); C; for j in [11..17] do for k in [11..17] do for m in [11..17] do for n in [11..17] do C := ((1 + X^n)^8)*((1 + X^m)^8)*((1 + X^k)^8)*((1 + X^j)^8) + X^521; if IsPrimitive(C) then if (n ne m) and (n ne k) and (n ne j) and (m ne k) and (m ne j) and (k ne j) then C; n; m; k; j; end if; end if; end for; end for; end for; end for; Output: Magma V2.10-6 Tue Jan 20 2004 00:16:54 on modular [Seed = 1578280852] ------------------------------------- X^9 + X^4 + 1 X^521 + X^408 + X^320 + X^312 + X^304 + X^288 + X^224 + X^216 + X^208 + X^200 + X^192 + X^184 + X^120 + X^104 + X^96 + X^88 + 1 15 13 12 11 X^521 + X^408 + X^320 + X^312 + X^304 + X^288 + X^224 + X^216 + X^208 + X^200 + X^192 + X^184 + X^120 + X^104 + X^96 + X^88 + 1 13 15 12 11 X^521 + X^408 + X^320 + X^312 + X^304 + X^288 + X^224 + X^216 + X^208 + X^200 + X^192 + X^184 + X^120 + X^104 + X^96 + X^88 + 1 15 12 13 11 X^521 + X^408 + X^320 + X^312 + X^304 + X^288 + X^224 + X^216 + X^208 + X^200 + X^192 + X^184 + X^120 + X^104 + X^96 + X^88 + 1 12 15 13 11 X^521 + X^408 + X^320 + X^312 + X^304 + X^288 + X^224 + X^216 + X^208 + X^200 + X^192 + X^184 + X^120 + X^104 + X^96 + X^88 + 1 13 12 15 11 X^521 + X^408 + X^320 + X^312 + X^304 + X^288 + X^224 + X^216 + X^208 + X^200 + X^192 + X^184 + X^120 + X^104 + X^96 + X^88 + 1 12 13 15 11 X^521 + X^408 + X^320 + X^312 + X^304 + X^288 + X^224 + X^216 + X^208 + X^200 + X^192 + X^184 + X^120 + X^104 + X^96 + X^88 + 1 15 13 11 12 X^521 + X^408 + X^320 + X^312 + X^304 + X^288 + X^224 + X^216 + X^208 + X^200 + X^192 + X^184 + X^120 + X^104 + X^96 + X^88 + 1 13 15 11 12 X^521 + X^408 + X^320 + X^312 + X^304 + X^288 + X^224 + X^216 + X^208 + X^200 + X^192 + X^184 + X^120 + X^104 + X^96 + X^88 + 1 15 11 13 12 X^521 + X^408 + X^320 + X^312 + X^304 + X^288 + X^224 + X^216 + X^208 + X^200 + X^192 + X^184 + X^120 + X^104 + X^96 + X^88 + 1 11 15 13 12 X^521 + X^408 + X^320 + X^312 + X^304 + X^288 + X^224 + X^216 + X^208 + X^200 + X^192 + X^184 + X^120 + X^104 + X^96 + X^88 + 1 13 11 15 12 X^521 + X^408 + X^320 + X^312 + X^304 + X^288 + X^224 + X^216 + X^208 + X^200 + X^192 + X^184 + X^120 + X^104 + X^96 + X^88 + 1 11 13 15 12 X^521 + X^408 + X^320 + X^312 + X^304 + X^288 + X^224 + X^216 + X^208 + X^200 + X^192 + X^184 + X^120 + X^104 + X^96 + X^88 + 1 15 12 11 13 X^521 + X^408 + X^320 + X^312 + X^304 + X^288 + X^224 + X^216 + X^208 + X^200 + X^192 + X^184 + X^120 + X^104 + X^96 + X^88 + 1 12 15 11 13 X^521 + X^408 + X^320 + X^312 + X^304 + X^288 + X^224 + X^216 + X^208 + X^200 + X^192 + X^184 + X^120 + X^104 + X^96 + X^88 + 1 15 11 12 13 X^521 + X^408 + X^320 + X^312 + X^304 + X^288 + X^224 + X^216 + X^208 + X^200 + X^192 + X^184 + X^120 + X^104 + X^96 + X^88 + 1 11 15 12 13 X^521 + X^408 + X^320 + X^312 + X^304 + X^288 + X^224 + X^216 + X^208 + X^200 + X^192 + X^184 + X^120 + X^104 + X^96 + X^88 + 1 12 11 15 13 X^521 + X^408 + X^320 + X^312 + X^304 + X^288 + X^224 + X^216 + X^208 + X^200 + X^192 + X^184 + X^120 + X^104 + X^96 + X^88 + 1 11 12 15 13 X^521 + X^408 + X^320 + X^312 + X^304 + X^288 + X^224 + X^216 + X^208 + X^200 + X^192 + X^184 + X^120 + X^104 + X^96 + X^88 + 1 13 12 11 15 X^521 + X^408 + X^320 + X^312 + X^304 + X^288 + X^224 + X^216 + X^208 + X^200 + X^192 + X^184 + X^120 + X^104 + X^96 + X^88 + 1 12 13 11 15 X^521 + X^408 + X^320 + X^312 + X^304 + X^288 + X^224 + X^216 + X^208 + X^200 + X^192 + X^184 + X^120 + X^104 + X^96 + X^88 + 1 13 11 12 15 X^521 + X^408 + X^320 + X^312 + X^304 + X^288 + X^224 + X^216 + X^208 + X^200 + X^192 + X^184 + X^120 + X^104 + X^96 + X^88 + 1 11 13 12 15 X^521 + X^408 + X^320 + X^312 + X^304 + X^288 + X^224 + X^216 + X^208 + X^200 + X^192 + X^184 + X^120 + X^104 + X^96 + X^88 + 1 12 11 13 15 X^521 + X^408 + X^320 + X^312 + X^304 + X^288 + X^224 + X^216 + X^208 + X^200 + X^192 + X^184 + X^120 + X^104 + X^96 + X^88 + 1 11 12 13 15 Total time: 8.569 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (194.165.15.3) Time: Tue Jan 20 00:26:04 2004 Input: k := GF(2); C := PrimitivePolynomial(k,9); C; for j in [11..23] do for k in [11..17] do for m in [11..17] do for n in [11..17] do C := ((1 + X^n)^8)*((1 + X^m)^8)*((1 + X^k)^8)*((1 + X^j)^8) + X^521; if IsPrimitive(C) then if (n ne m) and (n ne k) and (n ne j) and (m ne k) and (m ne j) and (k ne j) then C; n; m; k; j; end if; end if; end for; end for; end for; end for; Output: Magma V2.10-6 Tue Jan 20 2004 00:25:49 on modular [Seed = 2614583371] ------------------------------------- X^9 + X^4 + 1 X^521 + X^408 + X^320 + X^312 + X^304 + X^288 + X^224 + X^216 + X^208 + X^200 + X^192 + X^184 + X^120 + X^104 + X^96 + X^88 + 1 15 13 12 11 X^521 + X^408 + X^320 + X^312 + X^304 + X^288 + X^224 + X^216 + X^208 + X^200 + X^192 + X^184 + X^120 + X^104 + X^96 + X^88 + 1 13 15 12 11 X^521 + X^408 + 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X^96 + X^88 + 1 12 11 16 21 X^521 + X^480 + X^392 + X^384 + X^352 + X^312 + X^296 + X^264 + X^256 + X^224 + X^216 + X^184 + X^168 + X^128 + X^96 + X^88 + 1 11 12 16 21 X^521 + X^512 + X^416 + X^392 + X^384 + X^344 + X^296 + X^288 + X^264 + X^248 + X^224 + X^216 + X^168 + X^128 + X^120 + X^96 + 1 15 12 16 21 X^521 + X^512 + X^416 + X^392 + X^384 + X^344 + X^296 + X^288 + X^264 + X^248 + X^224 + X^216 + X^168 + X^128 + X^120 + X^96 + 1 12 15 16 21 X^521 + X^488 + X^400 + X^384 + X^376 + X^304 + X^296 + X^288 + X^272 + X^216 + X^200 + X^192 + X^184 + X^112 + X^104 + X^88 + 1 14 13 11 23 X^521 + X^488 + X^400 + X^384 + X^376 + X^304 + X^296 + X^288 + X^272 + X^216 + X^200 + X^192 + X^184 + X^112 + X^104 + X^88 + 1 13 14 11 23 X^521 + X^488 + X^400 + X^384 + X^376 + X^304 + X^296 + X^288 + X^272 + X^216 + X^200 + X^192 + X^184 + X^112 + X^104 + X^88 + 1 14 11 13 23 X^521 + X^488 + X^400 + X^384 + X^376 + X^304 + X^296 + X^288 + X^272 + X^216 + X^200 + X^192 + X^184 + X^112 + X^104 + X^88 + 1 11 14 13 23 X^521 + X^488 + X^400 + X^384 + X^376 + X^304 + X^296 + X^288 + X^272 + X^216 + X^200 + X^192 + X^184 + X^112 + X^104 + X^88 + 1 13 11 14 23 X^521 + X^488 + X^400 + X^384 + X^376 + X^304 + X^296 + X^288 + X^272 + X^216 + X^200 + X^192 + X^184 + X^112 + X^104 + X^88 + 1 11 13 14 23 Total time: 14.559 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (194.165.15.3) Time: Tue Jan 20 00:40:07 2004 Input: k := GF(2); C := PrimitivePolynomial(k,9); C; for j in [11..23] do for k in [11..17] do for m in [11..17] do for n in [11..17] do C := ((1 + X^n)^8)*((1 + X^m)^8)*((1 + X^k)^8)*((1 + X^j)^8) + X^521; if IsPrimitive(C) then if (n ne m) and (n ne k) and (n ne j) and (m ne k) and (m ne j) and (k ne j) then C; n; m; k; j; end if; end if; end for; end for; end for; end for; C := X^521 + X^408 + X^320 + X^312 + X^304 + X^288 + X^224 + X^216 + X^208 + X^200 + X^192 + X^184 + X^120 + X^104 + X^96 + X^88 + 1 IsPrimitive(C); Output: Magma V2.10-6 Tue Jan 20 2004 00:39:52 on modular [Seed = 2497211314] ------------------------------------- X^9 + X^4 + 1 X^521 + X^408 + X^320 + X^312 + X^304 + X^288 + X^224 + X^216 + X^208 + X^200 + X^192 + X^184 + X^120 + X^104 + X^96 + X^88 + 1 15 13 12 11 X^521 + X^408 + X^320 + X^312 + X^304 + X^288 + X^224 + X^216 + X^208 + X^200 + X^192 + X^184 + X^120 + X^104 + X^96 + X^88 + 1 13 15 12 11 X^521 + X^408 + X^320 + X^312 + X^304 + X^288 + X^224 + X^216 + X^208 + X^200 + X^192 + X^184 + X^120 + X^104 + X^96 + X^88 + 1 15 12 13 11 X^521 + X^408 + X^320 + X^312 + X^304 + X^288 + X^224 + X^216 + X^208 + X^200 + X^192 + X^184 + X^120 + X^104 + X^96 + X^88 + 1 12 15 13 11 X^521 + X^408 + X^320 + X^312 + X^304 + X^288 + X^224 + X^216 + X^208 + X^200 + X^192 + X^184 + X^120 + X^104 + X^96 + X^88 + 1 13 12 15 11 X^521 + X^408 + X^320 + X^312 + X^304 + X^288 + X^224 + X^216 + X^208 + X^200 + X^192 + X^184 + X^120 + X^104 + X^96 + X^88 + 1 12 13 15 11 X^521 + X^408 + X^320 + X^312 + X^304 + 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X^96 + 1 15 16 12 21 X^521 + X^512 + X^416 + X^392 + X^384 + X^344 + X^296 + X^288 + X^264 + X^248 + X^224 + X^216 + X^168 + X^128 + X^120 + X^96 + 1 16 12 15 21 X^521 + X^512 + X^416 + X^392 + X^384 + X^344 + X^296 + X^288 + X^264 + X^248 + X^224 + X^216 + X^168 + X^128 + X^120 + X^96 + 1 12 16 15 21 X^521 + X^480 + X^392 + X^384 + X^352 + X^312 + X^296 + X^264 + X^256 + X^224 + X^216 + X^184 + X^168 + X^128 + X^96 + X^88 + 1 12 11 16 21 X^521 + X^480 + X^392 + X^384 + X^352 + X^312 + X^296 + X^264 + X^256 + X^224 + X^216 + X^184 + X^168 + X^128 + X^96 + X^88 + 1 11 12 16 21 X^521 + X^512 + X^416 + X^392 + X^384 + X^344 + X^296 + X^288 + X^264 + X^248 + X^224 + X^216 + X^168 + X^128 + X^120 + X^96 + 1 15 12 16 21 X^521 + X^512 + X^416 + X^392 + X^384 + X^344 + X^296 + X^288 + X^264 + X^248 + X^224 + X^216 + X^168 + X^128 + X^120 + X^96 + 1 12 15 16 21 X^521 + X^488 + X^400 + X^384 + X^376 + X^304 + X^296 + X^288 + X^272 + X^216 + X^200 + X^192 + X^184 + X^112 + X^104 + X^88 + 1 14 13 11 23 X^521 + X^488 + X^400 + X^384 + X^376 + X^304 + X^296 + X^288 + X^272 + X^216 + X^200 + X^192 + X^184 + X^112 + X^104 + X^88 + 1 13 14 11 23 X^521 + X^488 + X^400 + X^384 + X^376 + X^304 + X^296 + X^288 + X^272 + X^216 + X^200 + X^192 + X^184 + X^112 + X^104 + X^88 + 1 14 11 13 23 X^521 + X^488 + X^400 + X^384 + X^376 + X^304 + X^296 + X^288 + X^272 + X^216 + X^200 + X^192 + X^184 + X^112 + X^104 + X^88 + 1 11 14 13 23 X^521 + X^488 + X^400 + X^384 + X^376 + X^304 + X^296 + X^288 + X^272 + X^216 + X^200 + X^192 + X^184 + X^112 + X^104 + X^88 + 1 13 11 14 23 X^521 + X^488 + X^400 + X^384 + X^376 + X^304 + X^296 + X^288 + X^272 + X^216 + X^200 + X^192 + X^184 + X^112 + X^104 + X^88 + 1 11 13 14 23 >> IsPrimitive(C); ^ User error: bad syntax Total time: 14.630 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (194.165.15.3) Time: Tue Jan 20 00:41:17 2004 Input: k := GF(2); C := PrimitivePolynomial(k,9); C; for j in [11..23] do for k in [11..17] do for m in [11..17] do for n in [11..17] do C := ((1 + X^n)^8)*((1 + X^m)^8)*((1 + X^k)^8)*((1 + X^j)^8) + X^521; if IsPrimitive(C) then if (n ne m) and (n ne k) and (n ne j) and (m ne k) and (m ne j) and (k ne j) then C; n; m; k; j; end if; end if; end for; end for; end for; end for; C := X^521 + X^408 + X^320 + X^312 + X^304 + X^288 + X^224 + X^216 + X^208 + X^200 + X^192 + X^184 + X^120 + X^104 + X^96 + X^88 + 1 if IsPrimitive(C)then C := 111; C; end if; Output: Magma V2.10-6 Tue Jan 20 2004 00:41:01 on modular [Seed = 3086698708] ------------------------------------- X^9 + X^4 + 1 X^521 + X^408 + X^320 + X^312 + X^304 + X^288 + X^224 + X^216 + X^208 + X^200 + X^192 + X^184 + X^120 + X^104 + X^96 + X^88 + 1 15 13 12 11 X^521 + X^408 + X^320 + X^312 + X^304 + X^288 + X^224 + X^216 + X^208 + X^200 + X^192 + X^184 + X^120 + X^104 + X^96 + X^88 + 1 13 15 12 11 X^521 + X^408 + X^320 + X^312 + X^304 + X^288 + X^224 + X^216 + X^208 + X^200 + X^192 + X^184 + X^120 + X^104 + X^96 + X^88 + 1 15 12 13 11 X^521 + X^408 + X^320 + X^312 + X^304 + X^288 + X^224 + X^216 + X^208 + X^200 + X^192 + X^184 + X^120 + X^104 + X^96 + X^88 + 1 12 15 13 11 X^521 + X^408 + X^320 + X^312 + X^304 + X^288 + X^224 + X^216 + X^208 + X^200 + X^192 + X^184 + X^120 + X^104 + X^96 + X^88 + 1 13 12 15 11 X^521 + X^408 + X^320 + X^312 + X^304 + X^288 + X^224 + X^216 + X^208 + X^200 + X^192 + X^184 + X^120 + X^104 + X^96 + X^88 + 1 12 13 15 11 X^521 + X^408 + X^320 + X^312 + X^304 + X^288 + X^224 + X^216 + X^208 + X^200 + X^192 + X^184 + X^120 + X^104 + X^96 + X^88 + 1 15 13 11 12 X^521 + X^408 + X^320 + X^312 + X^304 + X^288 + X^224 + X^216 + X^208 + X^200 + X^192 + X^184 + X^120 + X^104 + X^96 + X^88 + 1 13 15 11 12 X^521 + X^408 + X^320 + X^312 + X^304 + X^288 + X^224 + X^216 + X^208 + X^200 + X^192 + X^184 + X^120 + X^104 + X^96 + X^88 + 1 15 11 13 12 X^521 + X^408 + X^320 + X^312 + X^304 + X^288 + X^224 + X^216 + X^208 + X^200 + X^192 + X^184 + X^120 + X^104 + X^96 + X^88 + 1 11 15 13 12 X^521 + X^408 + X^320 + X^312 + X^304 + X^288 + X^224 + X^216 + X^208 + X^200 + X^192 + X^184 + X^120 + X^104 + X^96 + X^88 + 1 13 11 15 12 X^521 + X^408 + X^320 + X^312 + X^304 + X^288 + X^224 + X^216 + X^208 + X^200 + X^192 + X^184 + X^120 + X^104 + X^96 + X^88 + 1 11 13 15 12 X^521 + X^408 + X^320 + X^312 + X^304 + X^288 + X^224 + X^216 + X^208 + X^200 + X^192 + X^184 + X^120 + X^104 + X^96 + X^88 + 1 15 12 11 13 X^521 + X^408 + X^320 + X^312 + X^304 + X^288 + X^224 + X^216 + X^208 + X^200 + X^192 + X^184 + X^120 + X^104 + X^96 + X^88 + 1 12 15 11 13 X^521 + X^408 + X^320 + X^312 + X^304 + X^288 + X^224 + X^216 + X^208 + X^200 + X^192 + X^184 + X^120 + X^104 + X^96 + X^88 + 1 15 11 12 13 X^521 + X^408 + X^320 + X^312 + X^304 + X^288 + X^224 + X^216 + X^208 + X^200 + X^192 + X^184 + X^120 + X^104 + X^96 + X^88 + 1 11 15 12 13 X^521 + X^408 + X^320 + X^312 + X^304 + X^288 + X^224 + X^216 + X^208 + X^200 + X^192 + X^184 + X^120 + X^104 + X^96 + X^88 + 1 12 11 15 13 X^521 + X^408 + X^320 + X^312 + X^304 + X^288 + X^224 + X^216 + X^208 + X^200 + X^192 + X^184 + X^120 + X^104 + X^96 + X^88 + 1 11 12 15 13 X^521 + X^408 + X^320 + X^312 + X^304 + X^288 + X^224 + X^216 + X^208 + X^200 + X^192 + X^184 + X^120 + X^104 + X^96 + X^88 + 1 13 12 11 15 X^521 + X^408 + X^320 + X^312 + X^304 + X^288 + X^224 + X^216 + X^208 + X^200 + X^192 + X^184 + X^120 + X^104 + X^96 + X^88 + 1 12 13 11 15 X^521 + X^408 + X^320 + X^312 + X^304 + X^288 + X^224 + X^216 + X^208 + X^200 + X^192 + X^184 + X^120 + X^104 + X^96 + X^88 + 1 13 11 12 15 X^521 + X^408 + X^320 + X^312 + X^304 + X^288 + X^224 + X^216 + X^208 + X^200 + X^192 + X^184 + X^120 + X^104 + X^96 + X^88 + 1 11 13 12 15 X^521 + X^408 + X^320 + X^312 + X^304 + X^288 + X^224 + X^216 + X^208 + X^200 + X^192 + X^184 + X^120 + X^104 + X^96 + X^88 + 1 12 11 13 15 X^521 + X^408 + X^320 + X^312 + X^304 + X^288 + X^224 + X^216 + X^208 + X^200 + X^192 + X^184 + X^120 + X^104 + X^96 + X^88 + 1 11 12 13 15 X^521 + X^480 + X^392 + X^384 + X^344 + X^320 + X^296 + X^256 + X^248 + X^232 + X^224 + X^184 + X^160 + X^136 + X^96 + X^88 + 1 17 12 11 20 X^521 + X^472 + X^384 + X^368 + X^352 + X^312 + X^280 + X^264 + X^248 + X^224 + X^208 + X^192 + X^160 + X^120 + X^104 + X^88 + 1 15 13 11 20 X^521 + X^472 + X^384 + X^368 + X^352 + X^312 + X^280 + X^264 + X^248 + X^224 + X^208 + X^192 + X^160 + X^120 + X^104 + X^88 + 1 13 15 11 20 X^521 + X^480 + X^392 + X^384 + X^344 + X^320 + X^296 + X^256 + X^248 + X^232 + X^224 + X^184 + X^160 + X^136 + X^96 + X^88 + 1 12 17 11 20 X^521 + X^480 + X^392 + X^384 + X^344 + X^320 + X^296 + X^256 + X^248 + X^232 + X^224 + X^184 + X^160 + X^136 + X^96 + X^88 + 1 17 11 12 20 X^521 + X^480 + X^392 + X^384 + X^344 + X^320 + X^296 + X^256 + X^248 + X^232 + X^224 + X^184 + X^160 + X^136 + X^96 + X^88 + 1 11 17 12 20 X^521 + X^472 + X^384 + X^368 + X^352 + X^312 + X^280 + X^264 + X^248 + X^224 + X^208 + X^192 + X^160 + X^120 + X^104 + X^88 + 1 15 11 13 20 X^521 + X^472 + X^384 + X^368 + X^352 + X^312 + X^280 + X^264 + X^248 + X^224 + X^208 + X^192 + X^160 + X^120 + X^104 + X^88 + 1 11 15 13 20 X^521 + X^472 + X^384 + X^368 + X^352 + X^312 + X^280 + X^264 + X^248 + X^224 + X^208 + X^192 + X^160 + X^120 + X^104 + X^88 + 1 13 11 15 20 X^521 + X^472 + X^384 + X^368 + X^352 + X^312 + X^280 + X^264 + X^248 + X^224 + X^208 + X^192 + X^160 + X^120 + X^104 + X^88 + 1 11 13 15 20 X^521 + X^480 + X^392 + X^384 + X^344 + X^320 + X^296 + X^256 + X^248 + X^232 + X^224 + X^184 + X^160 + X^136 + X^96 + X^88 + 1 12 11 17 20 X^521 + X^480 + X^392 + X^384 + X^344 + X^320 + X^296 + X^256 + X^248 + X^232 + X^224 + X^184 + X^160 + X^136 + X^96 + X^88 + 1 11 12 17 20 X^521 + X^480 + X^392 + X^384 + X^352 + X^312 + X^296 + X^264 + X^256 + X^224 + X^216 + X^184 + X^168 + X^128 + X^96 + X^88 + 1 16 12 11 21 X^521 + X^480 + X^392 + X^384 + X^352 + X^312 + X^296 + X^264 + X^256 + X^224 + X^216 + X^184 + X^168 + X^128 + X^96 + X^88 + 1 12 16 11 21 X^521 + X^480 + X^392 + X^384 + X^352 + X^312 + X^296 + X^264 + X^256 + X^224 + X^216 + X^184 + X^168 + X^128 + X^96 + X^88 + 1 16 11 12 21 X^521 + X^512 + X^416 + X^392 + X^384 + X^344 + X^296 + X^288 + X^264 + X^248 + X^224 + X^216 + X^168 + X^128 + X^120 + X^96 + 1 16 15 12 21 X^521 + X^480 + X^392 + X^384 + X^352 + X^312 + X^296 + X^264 + X^256 + X^224 + X^216 + X^184 + X^168 + X^128 + X^96 + X^88 + 1 11 16 12 21 X^521 + X^512 + X^416 + X^392 + X^384 + X^344 + X^296 + X^288 + X^264 + X^248 + X^224 + X^216 + X^168 + X^128 + X^120 + X^96 + 1 15 16 12 21 X^521 + X^512 + X^416 + X^392 + X^384 + X^344 + X^296 + X^288 + X^264 + X^248 + X^224 + X^216 + X^168 + X^128 + X^120 + X^96 + 1 16 12 15 21 X^521 + X^512 + X^416 + X^392 + X^384 + X^344 + X^296 + X^288 + X^264 + X^248 + X^224 + X^216 + X^168 + X^128 + X^120 + X^96 + 1 12 16 15 21 X^521 + X^480 + X^392 + X^384 + X^352 + X^312 + X^296 + X^264 + X^256 + X^224 + X^216 + X^184 + X^168 + X^128 + X^96 + X^88 + 1 12 11 16 21 X^521 + X^480 + X^392 + X^384 + X^352 + X^312 + X^296 + X^264 + X^256 + X^224 + X^216 + X^184 + X^168 + X^128 + X^96 + X^88 + 1 11 12 16 21 X^521 + X^512 + X^416 + X^392 + X^384 + X^344 + X^296 + X^288 + X^264 + X^248 + X^224 + X^216 + X^168 + X^128 + X^120 + X^96 + 1 15 12 16 21 X^521 + X^512 + X^416 + X^392 + X^384 + X^344 + X^296 + X^288 + X^264 + X^248 + X^224 + X^216 + X^168 + X^128 + X^120 + X^96 + 1 12 15 16 21 X^521 + X^488 + X^400 + X^384 + X^376 + X^304 + X^296 + X^288 + X^272 + X^216 + X^200 + X^192 + X^184 + X^112 + X^104 + X^88 + 1 14 13 11 23 X^521 + X^488 + X^400 + X^384 + X^376 + X^304 + X^296 + X^288 + X^272 + X^216 + X^200 + X^192 + X^184 + X^112 + X^104 + X^88 + 1 13 14 11 23 X^521 + X^488 + X^400 + X^384 + X^376 + X^304 + X^296 + X^288 + X^272 + X^216 + X^200 + X^192 + X^184 + X^112 + X^104 + X^88 + 1 14 11 13 23 X^521 + X^488 + X^400 + X^384 + X^376 + X^304 + X^296 + X^288 + X^272 + X^216 + X^200 + X^192 + X^184 + X^112 + X^104 + X^88 + 1 11 14 13 23 X^521 + X^488 + X^400 + X^384 + X^376 + X^304 + X^296 + X^288 + X^272 + X^216 + X^200 + X^192 + X^184 + X^112 + X^104 + X^88 + 1 13 11 14 23 X^521 + X^488 + X^400 + X^384 + X^376 + X^304 + X^296 + X^288 + X^272 + X^216 + X^200 + X^192 + X^184 + X^112 + X^104 + X^88 + 1 11 13 14 23 >> if IsPrimitive(C)then ^ User error: bad syntax 111 >> end if; ^ User error: bad syntax Total time: 14.849 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (194.165.15.3) Time: Tue Jan 20 00:42:14 2004 Input: k := GF(2); C := PrimitivePolynomial(k,9); C; for j in [11..23] do for k in [11..17] do for m in [11..17] do for n in [11..17] do C := ((1 + X^n)^8)*((1 + X^m)^8)*((1 + X^k)^8)*((1 + X^j)^8) + X^521; if IsPrimitive(C) then if (n ne m) and (n ne k) and (n ne j) and (m ne k) and (m ne j) and (k ne j) then C; n; m; k; j; end if; end if; end for; end for; end for; end for; C := X^521 + X^408 + X^320 + X^312 + X^304 + X^288 + X^224 + X^216 + X^208 + X^200 + X^192 + X^184 + X^120 + X^104 + X^96 + X^88 + 1 if IsPrimitive(C)then C := 111; C; end if; Output: Magma V2.10-6 Tue Jan 20 2004 00:41:59 on modular [Seed = 3247259240] ------------------------------------- X^9 + X^4 + 1 X^521 + X^408 + X^320 + X^312 + X^304 + X^288 + X^224 + X^216 + X^208 + X^200 + X^192 + X^184 + X^120 + X^104 + X^96 + X^88 + 1 15 13 12 11 X^521 + X^408 + X^320 + X^312 + X^304 + X^288 + X^224 + X^216 + X^208 + X^200 + X^192 + X^184 + X^120 + X^104 + X^96 + X^88 + 1 13 15 12 11 X^521 + X^408 + X^320 + X^312 + X^304 + X^288 + X^224 + X^216 + X^208 + X^200 + X^192 + X^184 + X^120 + X^104 + X^96 + X^88 + 1 15 12 13 11 X^521 + X^408 + X^320 + X^312 + X^304 + X^288 + X^224 + X^216 + X^208 + X^200 + X^192 + X^184 + X^120 + X^104 + X^96 + X^88 + 1 12 15 13 11 X^521 + X^408 + X^320 + X^312 + X^304 + X^288 + X^224 + X^216 + X^208 + X^200 + X^192 + X^184 + X^120 + X^104 + X^96 + X^88 + 1 13 12 15 11 X^521 + X^408 + X^320 + X^312 + X^304 + X^288 + X^224 + X^216 + X^208 + X^200 + X^192 + X^184 + X^120 + X^104 + X^96 + X^88 + 1 12 13 15 11 X^521 + X^408 + X^320 + X^312 + X^304 + X^288 + X^224 + X^216 + X^208 + X^200 + X^192 + X^184 + X^120 + X^104 + X^96 + X^88 + 1 15 13 11 12 X^521 + X^408 + X^320 + X^312 + X^304 + X^288 + X^224 + X^216 + X^208 + X^200 + X^192 + X^184 + X^120 + X^104 + X^96 + X^88 + 1 13 15 11 12 X^521 + X^408 + X^320 + X^312 + X^304 + X^288 + X^224 + X^216 + X^208 + X^200 + X^192 + X^184 + X^120 + X^104 + X^96 + X^88 + 1 15 11 13 12 X^521 + X^408 + X^320 + X^312 + X^304 + X^288 + X^224 + X^216 + X^208 + X^200 + X^192 + X^184 + X^120 + X^104 + X^96 + X^88 + 1 11 15 13 12 X^521 + X^408 + X^320 + X^312 + X^304 + X^288 + X^224 + X^216 + X^208 + X^200 + X^192 + X^184 + X^120 + X^104 + X^96 + X^88 + 1 13 11 15 12 X^521 + X^408 + X^320 + X^312 + X^304 + X^288 + X^224 + X^216 + X^208 + X^200 + X^192 + X^184 + X^120 + X^104 + X^96 + X^88 + 1 11 13 15 12 X^521 + X^408 + X^320 + X^312 + X^304 + X^288 + X^224 + X^216 + X^208 + X^200 + X^192 + X^184 + X^120 + X^104 + X^96 + X^88 + 1 15 12 11 13 X^521 + X^408 + X^320 + X^312 + X^304 + X^288 + X^224 + X^216 + X^208 + X^200 + X^192 + X^184 + X^120 + X^104 + X^96 + X^88 + 1 12 15 11 13 X^521 + X^408 + X^320 + X^312 + X^304 + X^288 + X^224 + X^216 + X^208 + X^200 + X^192 + X^184 + X^120 + X^104 + X^96 + X^88 + 1 15 11 12 13 X^521 + X^408 + X^320 + X^312 + X^304 + X^288 + X^224 + X^216 + X^208 + X^200 + X^192 + X^184 + X^120 + X^104 + X^96 + X^88 + 1 11 15 12 13 X^521 + X^408 + X^320 + X^312 + X^304 + X^288 + X^224 + X^216 + X^208 + X^200 + X^192 + X^184 + X^120 + X^104 + X^96 + X^88 + 1 12 11 15 13 X^521 + X^408 + X^320 + X^312 + X^304 + X^288 + X^224 + X^216 + X^208 + X^200 + X^192 + X^184 + X^120 + X^104 + X^96 + X^88 + 1 11 12 15 13 X^521 + X^408 + X^320 + X^312 + X^304 + X^288 + X^224 + X^216 + X^208 + X^200 + X^192 + X^184 + X^120 + X^104 + X^96 + X^88 + 1 13 12 11 15 X^521 + X^408 + X^320 + X^312 + X^304 + X^288 + X^224 + X^216 + X^208 + X^200 + X^192 + X^184 + X^120 + X^104 + X^96 + X^88 + 1 12 13 11 15 X^521 + X^408 + X^320 + X^312 + X^304 + X^288 + X^224 + X^216 + X^208 + X^200 + X^192 + X^184 + X^120 + X^104 + X^96 + X^88 + 1 13 11 12 15 X^521 + X^408 + X^320 + X^312 + X^304 + X^288 + X^224 + X^216 + X^208 + X^200 + X^192 + X^184 + X^120 + X^104 + X^96 + X^88 + 1 11 13 12 15 X^521 + X^408 + X^320 + X^312 + X^304 + X^288 + X^224 + X^216 + X^208 + X^200 + X^192 + X^184 + X^120 + X^104 + X^96 + X^88 + 1 12 11 13 15 X^521 + X^408 + X^320 + X^312 + X^304 + X^288 + X^224 + X^216 + X^208 + X^200 + X^192 + X^184 + X^120 + X^104 + X^96 + X^88 + 1 11 12 13 15 X^521 + X^480 + X^392 + X^384 + X^344 + X^320 + X^296 + X^256 + X^248 + X^232 + X^224 + X^184 + X^160 + X^136 + X^96 + X^88 + 1 17 12 11 20 X^521 + X^472 + X^384 + X^368 + X^352 + X^312 + X^280 + X^264 + X^248 + X^224 + X^208 + X^192 + X^160 + X^120 + X^104 + X^88 + 1 15 13 11 20 X^521 + X^472 + X^384 + X^368 + X^352 + X^312 + X^280 + X^264 + X^248 + X^224 + X^208 + X^192 + X^160 + X^120 + X^104 + X^88 + 1 13 15 11 20 X^521 + X^480 + X^392 + X^384 + X^344 + X^320 + X^296 + X^256 + X^248 + X^232 + X^224 + X^184 + X^160 + X^136 + X^96 + X^88 + 1 12 17 11 20 X^521 + X^480 + X^392 + X^384 + X^344 + X^320 + X^296 + X^256 + X^248 + X^232 + X^224 + X^184 + X^160 + X^136 + X^96 + X^88 + 1 17 11 12 20 X^521 + X^480 + X^392 + X^384 + X^344 + X^320 + X^296 + X^256 + X^248 + X^232 + X^224 + X^184 + X^160 + X^136 + X^96 + X^88 + 1 11 17 12 20 X^521 + X^472 + X^384 + X^368 + X^352 + X^312 + X^280 + X^264 + X^248 + X^224 + X^208 + X^192 + X^160 + X^120 + X^104 + X^88 + 1 15 11 13 20 X^521 + X^472 + X^384 + X^368 + X^352 + X^312 + X^280 + X^264 + X^248 + X^224 + X^208 + X^192 + X^160 + X^120 + X^104 + X^88 + 1 11 15 13 20 X^521 + X^472 + X^384 + X^368 + X^352 + X^312 + X^280 + X^264 + X^248 + X^224 + X^208 + X^192 + X^160 + X^120 + X^104 + X^88 + 1 13 11 15 20 X^521 + X^472 + X^384 + X^368 + X^352 + X^312 + X^280 + X^264 + X^248 + X^224 + X^208 + X^192 + X^160 + X^120 + X^104 + X^88 + 1 11 13 15 20 X^521 + X^480 + X^392 + X^384 + X^344 + X^320 + X^296 + X^256 + X^248 + X^232 + X^224 + X^184 + X^160 + X^136 + X^96 + X^88 + 1 12 11 17 20 X^521 + X^480 + X^392 + X^384 + X^344 + X^320 + X^296 + X^256 + X^248 + X^232 + X^224 + X^184 + X^160 + X^136 + X^96 + X^88 + 1 11 12 17 20 X^521 + X^480 + X^392 + X^384 + X^352 + X^312 + X^296 + X^264 + X^256 + X^224 + X^216 + X^184 + X^168 + X^128 + X^96 + X^88 + 1 16 12 11 21 X^521 + X^480 + X^392 + X^384 + X^352 + X^312 + X^296 + X^264 + X^256 + X^224 + X^216 + X^184 + X^168 + X^128 + X^96 + X^88 + 1 12 16 11 21 X^521 + X^480 + X^392 + X^384 + X^352 + X^312 + X^296 + X^264 + X^256 + X^224 + X^216 + X^184 + X^168 + X^128 + X^96 + X^88 + 1 16 11 12 21 X^521 + X^512 + X^416 + X^392 + X^384 + X^344 + X^296 + X^288 + X^264 + X^248 + X^224 + X^216 + X^168 + X^128 + X^120 + X^96 + 1 16 15 12 21 X^521 + X^480 + X^392 + X^384 + X^352 + X^312 + X^296 + X^264 + X^256 + X^224 + X^216 + X^184 + X^168 + X^128 + X^96 + X^88 + 1 11 16 12 21 X^521 + X^512 + X^416 + X^392 + X^384 + X^344 + X^296 + X^288 + X^264 + X^248 + X^224 + X^216 + X^168 + X^128 + X^120 + X^96 + 1 15 16 12 21 X^521 + X^512 + X^416 + X^392 + X^384 + X^344 + X^296 + X^288 + X^264 + X^248 + X^224 + X^216 + X^168 + X^128 + X^120 + X^96 + 1 16 12 15 21 X^521 + X^512 + X^416 + X^392 + X^384 + X^344 + X^296 + X^288 + X^264 + X^248 + X^224 + X^216 + X^168 + X^128 + X^120 + X^96 + 1 12 16 15 21 X^521 + X^480 + X^392 + X^384 + X^352 + X^312 + X^296 + X^264 + X^256 + X^224 + X^216 + X^184 + X^168 + X^128 + X^96 + X^88 + 1 12 11 16 21 X^521 + X^480 + X^392 + X^384 + X^352 + X^312 + X^296 + X^264 + X^256 + X^224 + X^216 + X^184 + X^168 + X^128 + X^96 + X^88 + 1 11 12 16 21 X^521 + X^512 + X^416 + X^392 + X^384 + X^344 + X^296 + X^288 + X^264 + X^248 + X^224 + X^216 + X^168 + X^128 + X^120 + X^96 + 1 15 12 16 21 X^521 + X^512 + X^416 + X^392 + X^384 + X^344 + X^296 + X^288 + X^264 + X^248 + X^224 + X^216 + X^168 + X^128 + X^120 + X^96 + 1 12 15 16 21 X^521 + X^488 + X^400 + X^384 + X^376 + X^304 + X^296 + X^288 + X^272 + X^216 + X^200 + X^192 + X^184 + X^112 + X^104 + X^88 + 1 14 13 11 23 X^521 + X^488 + X^400 + X^384 + X^376 + X^304 + X^296 + X^288 + X^272 + X^216 + X^200 + X^192 + X^184 + X^112 + X^104 + X^88 + 1 13 14 11 23 X^521 + X^488 + X^400 + X^384 + X^376 + X^304 + X^296 + X^288 + X^272 + X^216 + X^200 + X^192 + X^184 + X^112 + X^104 + X^88 + 1 14 11 13 23 X^521 + X^488 + X^400 + X^384 + X^376 + X^304 + X^296 + X^288 + X^272 + X^216 + X^200 + X^192 + X^184 + X^112 + X^104 + X^88 + 1 11 14 13 23 X^521 + X^488 + X^400 + X^384 + X^376 + X^304 + X^296 + X^288 + X^272 + X^216 + X^200 + X^192 + X^184 + X^112 + X^104 + X^88 + 1 13 11 14 23 X^521 + X^488 + X^400 + X^384 + X^376 + X^304 + X^296 + X^288 + X^272 + X^216 + X^200 + X^192 + X^184 + X^112 + X^104 + X^88 + 1 11 13 14 23 >> if IsPrimitive(C)then ^ User error: bad syntax 111 >> end if; ^ User error: bad syntax Total time: 14.679 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (194.165.15.3) Time: Tue Jan 20 00:49:55 2004 Input: k := GF(2); C := PrimitivePolynomial(k,9); C; for j in [11..23] do for k in [11..13] do for m in [11..13] do for n in [11..13] do C := ((1 + X^n)^8)*((1 + X^m)^8)*((1 + X^k)^8)*((1 + X^j)^8) + X^521; if IsPrimitive(C) then if (n ne m) and (n ne k) and (n ne j) and (m ne k) and (m ne j) and (k ne j) then C; n; m; k; j; end if; end if; end for; end for; end for; end for; Output: Magma V2.10-6 Tue Jan 20 2004 00:49:51 on modular [Seed = 847164226] ------------------------------------- X^9 + X^4 + 1 X^521 + X^408 + X^320 + X^312 + X^304 + X^288 + X^224 + X^216 + X^208 + X^200 + X^192 + X^184 + X^120 + X^104 + X^96 + X^88 + 1 13 12 11 15 X^521 + X^408 + X^320 + X^312 + X^304 + X^288 + X^224 + X^216 + X^208 + X^200 + X^192 + X^184 + X^120 + X^104 + X^96 + X^88 + 1 12 13 11 15 X^521 + X^408 + X^320 + X^312 + X^304 + X^288 + X^224 + X^216 + X^208 + X^200 + X^192 + X^184 + X^120 + X^104 + X^96 + X^88 + 1 13 11 12 15 X^521 + X^408 + X^320 + X^312 + X^304 + X^288 + X^224 + X^216 + X^208 + X^200 + X^192 + X^184 + X^120 + X^104 + X^96 + X^88 + 1 11 13 12 15 X^521 + X^408 + X^320 + X^312 + X^304 + X^288 + X^224 + X^216 + X^208 + X^200 + X^192 + X^184 + X^120 + X^104 + X^96 + X^88 + 1 12 11 13 15 X^521 + X^408 + X^320 + X^312 + X^304 + X^288 + X^224 + X^216 + X^208 + X^200 + X^192 + X^184 + X^120 + X^104 + X^96 + X^88 + 1 11 12 13 15 Total time: 3.639 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (194.165.15.3) Time: Tue Jan 20 03:52:28 2004 Input: k := GF(2); C := PrimitivePolynomial(k,9); C; C := ((1 + X^12)^8)*((1 + X^15)^8)*((1 + X^16)^8)*((1 + X^21)^8) + X^521; if IsPrimitive(C) then C; end if; Output: Magma V2.10-6 Tue Jan 20 2004 03:52:25 on modular [Seed = 761364850] ------------------------------------- X^9 + X^4 + 1 X^521 + X^512 + X^416 + X^392 + X^384 + X^344 + X^296 + X^288 + X^264 + X^248 + X^224 + X^216 + X^168 + X^128 + X^120 + X^96 + 1 Total time: 3.079 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (194.165.15.3) Time: Tue Jan 20 04:04:18 2004 Input: k := GF(2); C := PrimitivePolynomial(k,9); C; C := ((1 + X^11)^8)*((1 + X^13)^8)*((1 + X^14)^8)*((1 + X^23)^8) + X^521; if IsPrimitive(C) then C; end if; Output: Magma V2.10-6 Tue Jan 20 2004 04:04:15 on modular [Seed = 1014010667] ------------------------------------- X^9 + X^4 + 1 X^521 + X^488 + X^400 + X^384 + X^376 + X^304 + X^296 + X^288 + X^272 + X^216 + X^200 + X^192 + X^184 + X^112 + X^104 + X^88 + 1 Total time: 3.319 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (194.165.15.3) Time: Tue Jan 20 04:05:33 2004 Input: k := GF(2); C := PrimitivePolynomial(k,9); C; C := ((1 + X^11)^8)*((1 + X^12)^8)*((1 + X^16)^8)*((1 + X^21)^8) + X^521; if IsPrimitive(C) then C; end if; Output: Magma V2.10-6 Tue Jan 20 2004 04:05:29 on modular [Seed = 694519400] ------------------------------------- X^9 + X^4 + 1 X^521 + X^480 + X^392 + X^384 + X^352 + X^312 + X^296 + X^264 + X^256 + X^224 + X^216 + X^184 + X^168 + X^128 + X^96 + X^88 + 1 Total time: 3.629 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (194.165.15.3) Time: Tue Jan 20 04:06:33 2004 Input: k := GF(2); C := PrimitivePolynomial(k,9); C; C := ((1 + X^11)^8)*((1 + X^12)^8)*((1 + X^17)^8)*((1 + X^20)^8) + X^521; if IsPrimitive(C) then C; end if; Output: Magma V2.10-6 Tue Jan 20 2004 04:06:29 on modular [Seed = 594513070] ------------------------------------- X^9 + X^4 + 1 X^521 + X^480 + X^392 + X^384 + X^344 + X^320 + X^296 + X^256 + X^248 + X^232 + X^224 + X^184 + X^160 + X^136 + X^96 + X^88 + 1 Total time: 3.269 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (194.165.15.3) Time: Tue Jan 20 04:07:34 2004 Input: k := GF(2); C := PrimitivePolynomial(k,9); C; C := ((1 + X^11)^8)*((1 + X^13)^8)*((1 + X^15)^8)*((1 + X^20)^8) + X^521; if IsPrimitive(C) then C; end if; Output: Magma V2.10-6 Tue Jan 20 2004 04:07:30 on modular [Seed = 1544614806] ------------------------------------- X^9 + X^4 + 1 X^521 + X^472 + X^384 + X^368 + X^352 + X^312 + X^280 + X^264 + X^248 + X^224 + X^208 + X^192 + X^160 + X^120 + X^104 + X^88 + 1 Total time: 3.269 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (194.165.15.3) Time: Tue Jan 20 04:08:51 2004 Input: k := GF(2); C := PrimitivePolynomial(k,9); C; C := ((1 + X^11)^8)*((1 + X^12)^8)*((1 + X^13)^8)*((1 + X^15)^8) + X^521; if IsPrimitive(C) then C; end if; Output: Magma V2.10-6 Tue Jan 20 2004 04:08:48 on modular [Seed = 1427760493] ------------------------------------- X^9 + X^4 + 1 X^521 + X^408 + X^320 + X^312 + X^304 + X^288 + X^224 + X^216 + X^208 + X^200 + X^192 + X^184 + X^120 + X^104 + X^96 + X^88 + 1 Total time: 3.319 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (143.235.219.2) Time: Tue Jan 20 06:45:06 2004 Input: (x+y)^3 Output: Magma V2.10-6 Tue Jan 20 2004 06:45:03 on modular [Seed = 2211370789] ------------------------------------- >> (x+y)^3 ^ User error: Identifier 'x' has not been declared or assigned Total time: 2.999 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 1-1-5-46b.orby.sth.bostream.se. (82.182.86.197) Time: Tue Jan 20 06:55:53 2004 Input: factorint((10^43-1)/9) Output: Magma V2.10-6 Tue Jan 20 2004 06:55:50 on modular [Seed = 2699950079] ------------------------------------- >> factorint((10^43-1)/9); ^ User error: Identifier 'factorint' has not been declared or assigned Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (194.165.15.100) Time: Tue Jan 20 10:00:44 2004 Input: ? Output: Magma V2.10-6 Tue Jan 20 2004 10:00:40 on modular [Seed = 594420132] ------------------------------------- =============================================================================== PATH: /language/statement KIND: Overview =============================================================================== A statement is a complete command to Magma. Every statement must end with a semicolon ( ; ). If you press the key before typing ; then Magma may give you a special prompt symbol such as print> or if> to remind you that the statement is not yet finished. EXAMPLE: > print 5+8; > DivBy3 := func< n | IsZero(n mod 3) >; =============================================================================== Total time: 2.939 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host dialup-67.75.105.117.Dial1.Stamford1.Level3.net. (67.75.105.117) Time: Tue Jan 20 20:58:11 2004 Input: > X := Matrix(IntegerRing(), 2, 2, [1,2, 3,4]); > X; Output: Magma V2.10-6 Tue Jan 20 2004 20:58:08 on modular [Seed = 4003689077] ------------------------------------- [1 2] [3 4] Total time: 2.909 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host dialup-67.75.105.117.Dial1.Stamford1.Level3.net. (67.75.105.117) Time: Tue Jan 20 20:58:25 2004 Input: > X := Matrix(IntegerRing(), 2, 2, [1,2, 3,4]); > X; Output: Magma V2.10-6 Tue Jan 20 2004 20:58:22 on modular [Seed = 3853023600] ------------------------------------- [1 2] [3 4] Total time: 2.989 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host Donnelly.iuhb02.iu-bremen.de. (212.201.48.249) Time: Wed Jan 21 04:38:46 2004 Input: E:=EllipticCurve(([0,-1,0,-4,4]) Output: Magma V2.10-6 Wed Jan 21 2004 04:38:43 on modular [Seed = 4256429420] ------------------------------------- >> E:=EllipticCurve(([0,-1,0,-4,4]); ^ User error: bad syntax Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host Donnelly.iuhb02.iu-bremen.de. (212.201.48.249) Time: Wed Jan 21 04:38:55 2004 Input: E:=EllipticCurve(([0,-1,0,-4,4]) Output: Magma V2.10-6 Wed Jan 21 2004 04:38:52 on modular [Seed = 3936674420] ------------------------------------- >> E:=EllipticCurve(([0,-1,0,-4,4]); ^ User error: bad syntax Total time: 2.919 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host Donnelly.iuhb02.iu-bremen.de. (212.201.48.249) Time: Wed Jan 21 04:39:51 2004 Input: E:=EllipticCurve(([0,-1,0,-4,4]) Output: Magma V2.10-6 Wed Jan 21 2004 04:39:48 on modular [Seed = 3297430546] ------------------------------------- >> E:=EllipticCurve(([0,-1,0,-4,4]); ^ User error: bad syntax Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host Donnelly.iuhb02.iu-bremen.de. (212.201.48.249) Time: Wed Jan 21 04:39:59 2004 Input: E:=EllipticCurve(([0,-1,0,-4,4]); Output: Magma V2.10-6 Wed Jan 21 2004 04:39:56 on modular [Seed = 3447964947] ------------------------------------- >> E:=EllipticCurve(([0,-1,0,-4,4]);; ^ User error: bad syntax Total time: 2.889 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host Donnelly.iuhb02.iu-bremen.de. (212.201.48.249) Time: Wed Jan 21 04:40:24 2004 Input: E:=EllipticCurve([0,-1,0,-4,4]) Output: Magma V2.10-6 Wed Jan 21 2004 04:40:21 on modular [Seed = 1014117642] ------------------------------------- Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host Donnelly.iuhb02.iu-bremen.de. (212.201.48.249) Time: Wed Jan 21 04:40:40 2004 Input: E:=EllipticCurve([0,-1,0,-4,4]) E Output: Magma V2.10-6 Wed Jan 21 2004 04:40:37 on modular [Seed = 728048141] ------------------------------------- >> E; ^ User error: bad syntax Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host Donnelly.iuhb02.iu-bremen.de. (212.201.48.249) Time: Wed Jan 21 04:40:52 2004 Input: E:=EllipticCurve([0,-1,0,-4,4]) E; Output: Magma V2.10-6 Wed Jan 21 2004 04:40:49 on modular [Seed = 308026112] ------------------------------------- >> E;; ^ User error: bad syntax Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host Donnelly.iuhb02.iu-bremen.de. (212.201.48.249) Time: Wed Jan 21 04:41:05 2004 Input: E=EllipticCurve([0,-1,0,-4,4]) E Output: Magma V2.10-6 Wed Jan 21 2004 04:41:02 on modular [Seed = 491983872] ------------------------------------- >> E; ^ User error: bad syntax Total time: 3.169 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host igel2.math.uni-duesseldorf.de. (134.99.156.101) Time: Wed Jan 21 04:41:10 2004 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: Magma V2.10-6 Wed Jan 21 2004 04:40:59 on modular [Seed = 408293632] ------------------------------------- Replace this by some code, then click [PARI] or [MAGMA]! Total time: 3.059 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host Donnelly.iuhb02.iu-bremen.de. (212.201.48.249) Time: Wed Jan 21 04:41:40 2004 Input: E:=EllipticCurve([0,-1,0,-4,4]) Q:=Rationals Q Output: Magma V2.10-6 Wed Jan 21 2004 04:41:37 on modular [Seed = 239077228] ------------------------------------- >> Q:=Rationals ^ User error: bad syntax >> Q; ^ User error: Identifier 'Q' has not been declared or assigned Total time: 2.889 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host Donnelly.iuhb02.iu-bremen.de. (212.201.48.249) Time: Wed Jan 21 04:41:53 2004 Input: E:=EllipticCurve([0,-1,0,-4,4]) Q:=RationalField Q Output: Magma V2.10-6 Wed Jan 21 2004 04:41:49 on modular [Seed = 1966832667] ------------------------------------- >> Q:=RationalField ^ User error: bad syntax >> Q; ^ User error: Identifier 'Q' has not been declared or assigned Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host Donnelly.iuhb02.iu-bremen.de. (212.201.48.249) Time: Wed Jan 21 04:42:07 2004 Input: E:=EllipticCurve([0,-1,0,-4,4]) Q=RationalField Q Output: Magma V2.10-6 Wed Jan 21 2004 04:42:04 on modular [Seed = 2083681571] ------------------------------------- >> Q=RationalField ^ User error: bad syntax >> Q; ^ User error: Identifier 'Q' has not been declared or assigned Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host Donnelly.iuhb02.iu-bremen.de. (212.201.48.249) Time: Wed Jan 21 04:45:22 2004 Input: E:=EllipticCurve([0,-1,0,-4,4]) jInvariant(E) Output: Magma V2.10-6 Wed Jan 21 2004 04:45:19 on modular [Seed = 1427857225] ------------------------------------- >> jInvariant(E); ^ User error: bad syntax Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host Donnelly.iuhb02.iu-bremen.de. (212.201.48.249) Time: Wed Jan 21 04:45:57 2004 Input: E:=EllipticCurve([0,-1,0,-4,4]): jInvariant(E) Output: Magma V2.10-6 Wed Jan 21 2004 04:45:54 on modular [Seed = 1544705596] ------------------------------------- >> E:=EllipticCurve([0,-1,0,-4,4]): ^ User error: bad syntax >> jInvariant(E); ^ User error: Identifier 'E' has not been declared or assigned Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host Donnelly.iuhb02.iu-bremen.de. (212.201.48.249) Time: Wed Jan 21 04:46:20 2004 Input: E:=EllipticCurve([0,-1,0,-4,4]) jInvariant(E) Output: Magma V2.10-6 Wed Jan 21 2004 04:46:17 on modular [Seed = 1258635537] ------------------------------------- >> jInvariant(E); ^ User error: bad syntax Total time: 2.879 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host Donnelly.iuhb02.iu-bremen.de. (212.201.48.249) Time: Wed Jan 21 04:46:43 2004 Input: E:=EllipticCurve([0,-1,0,-4,4]) Discriminant(E) Output: Magma V2.10-6 Wed Jan 21 2004 04:46:40 on modular [Seed = 3002906625] ------------------------------------- >> Discriminant(E); ^ User error: bad syntax Total time: 2.939 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host Donnelly.iuhb02.iu-bremen.de. (212.201.48.249) Time: Wed Jan 21 04:47:42 2004 Input: E Output: Magma V2.10-6 Wed Jan 21 2004 04:47:39 on modular [Seed = 3120018225] ------------------------------------- >> E ^ User error: Identifier 'E' has not been declared or assigned Total time: 2.919 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host Donnelly.iuhb02.iu-bremen.de. (212.201.48.249) Time: Wed Jan 21 04:47:58 2004 Input: E:=EllipticCurve([0,-1,0,-4,4]),E Output: Magma V2.10-6 Wed Jan 21 2004 04:47:55 on modular [Seed = 2817109343] ------------------------------------- >> E:=EllipticCurve([0,-1,0,-4,4]),E ^ User error: bad syntax Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host Donnelly.iuhb02.iu-bremen.de. (212.201.48.249) Time: Wed Jan 21 04:48:17 2004 Input: E:=EllipticCurve([0,-1,0,-4,4]); E Output: Magma V2.10-6 Wed Jan 21 2004 04:48:14 on modular [Seed = 2933957699] ------------------------------------- Elliptic Curve defined by y^2 = x^3 - x^2 - 4*x + 4 over Rational Field Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host Donnelly.iuhb02.iu-bremen.de. (212.201.48.249) Time: Wed Jan 21 04:48:38 2004 Input: E:=EllipticCurve([0,-1,0,-4,4]); jInvariant(E) Output: Magma V2.10-6 Wed Jan 21 2004 04:48:35 on modular [Seed = 2514198357] ------------------------------------- 35152/9 Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host Donnelly.iuhb02.iu-bremen.de. (212.201.48.249) Time: Wed Jan 21 04:50:41 2004 Input: E:=EllipticCurve[0,0,0,4,0]); jInvariant(E) Output: Magma V2.10-6 Wed Jan 21 2004 04:50:38 on modular [Seed = 2244710104] ------------------------------------- >> E:=EllipticCurve[0,0,0,4,0]); ^ User error: bad syntax >> jInvariant(E) ^ User error: Identifier 'E' has not been declared or assigned Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host Donnelly.iuhb02.iu-bremen.de. (212.201.48.249) Time: Wed Jan 21 04:50:54 2004 Input: E:=EllipticCurve([0,0,0,4,0]); jInvariant(E) Output: Magma V2.10-6 Wed Jan 21 2004 04:50:51 on modular [Seed = 2361558980] ------------------------------------- 1728 Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host Donnelly.iuhb02.iu-bremen.de. (212.201.48.249) Time: Wed Jan 21 04:51:57 2004 Input: E:=EllipticCurve([0,0,0,4,0]); jInvariant(E); Discriminant(E) Output: Magma V2.10-6 Wed Jan 21 2004 04:51:54 on modular [Seed = 4223004786] ------------------------------------- 1728 -4096 Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host Donnelly.iuhb02.iu-bremen.de. (212.201.48.249) Time: Wed Jan 21 04:55:01 2004 Input: E:=EllipticCurve([0,-1,0,-33,62]); jInvariant(E); Discriminant(E) Output: Magma V2.10-6 Wed Jan 21 2004 04:54:58 on modular [Seed = 3786403232] ------------------------------------- 16384/5 1250000 Total time: 3.009 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host Donnelly.iuhb02.iu-bremen.de. (212.201.48.249) Time: Wed Jan 21 04:55:53 2004 Input: E:=EllipticCurve([1,1,1,-30,-76]); jInvariant(E); Discriminant(E) Output: Magma V2.10-6 Wed Jan 21 2004 04:55:50 on modular [Seed = 3970097273] ------------------------------------- -24729001 -121 Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host Donnelly.iuhb02.iu-bremen.de. (212.201.48.249) Time: Wed Jan 21 04:58:11 2004 Input: E:=EllipticCurve([1,1,1,-30,-76]); jInvariant(E); Factor(Discriminant(E)) Output: Magma V2.10-6 Wed Jan 21 2004 04:58:08 on modular [Seed = 3667187673] ------------------------------------- -24729001 >> Factor(Discriminant(E)) ^ Runtime error in 'Factor': Bad argument types Argument types given: FldRatElt Total time: 2.909 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host Donnelly.iuhb02.iu-bremen.de. (212.201.48.249) Time: Wed Jan 21 05:00:11 2004 Input: E:=EllipticCurve([1,1,1,-30,-76]); jInvariant(E); Discriminant(E); -24729001/121 Output: Magma V2.10-6 Wed Jan 21 2004 05:00:08 on modular [Seed = 3397699409] ------------------------------------- -24729001 -121 -2248091/11 Total time: 2.919 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host n032234.cs.kun.nl. (131.174.32.234) Time: Wed Jan 21 05:49:52 2004 Input: 1+1 Output: Magma V2.10-6 Wed Jan 21 2004 05:49:49 on modular [Seed = 1630500888] ------------------------------------- 2 Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host n032234.cs.kun.nl. (131.174.32.234) Time: Wed Jan 21 05:50:48 2004 Input: x+x Output: Magma V2.10-6 Wed Jan 21 2004 05:50:45 on modular [Seed = 1361004768] ------------------------------------- >> x+x; ^ User error: Identifier 'x' has not been declared or assigned Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host n032234.cs.kun.nl. (131.174.32.234) Time: Wed Jan 21 05:51:17 2004 Input: 100! Output: Magma V2.10-6 Wed Jan 21 2004 05:51:14 on modular [Seed = 1511277516] ------------------------------------- >> 100!; ^ User error: bad syntax Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host n032234.cs.kun.nl. (131.174.32.234) Time: Wed Jan 21 05:51:36 2004 Input: 2^10 Output: Magma V2.10-6 Wed Jan 21 2004 05:51:33 on modular [Seed = 1124948674] ------------------------------------- 1024 Total time: 2.919 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host n032234.cs.kun.nl. (131.174.32.234) Time: Wed Jan 21 05:51:46 2004 Input: 2^100 Output: Magma V2.10-6 Wed Jan 21 2004 05:51:43 on modular [Seed = 3036327231] ------------------------------------- 1267650600228229401496703205376 Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host n032234.cs.kun.nl. (131.174.32.234) Time: Wed Jan 21 05:51:55 2004 Input: 2^1000 Output: Magma V2.10-6 Wed Jan 21 2004 05:51:52 on modular [Seed = 3186861121] ------------------------------------- 1071508607186267320948425049060001810561404811705533607443750388370351051124936\ 1224931983788156958581275946729175531468251871452856923140435984577574698574803\ 9345677748242309854210746050623711418779541821530464749835819412673987675591655\ 43946077062914571196477686542167660429831652624386837205668069376 Total time: 2.939 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host n032234.cs.kun.nl. (131.174.32.234) Time: Wed Jan 21 05:52:06 2004 Input: 2^10000 Output: Magma V2.10-6 Wed Jan 21 2004 05:52:03 on modular [Seed = 2800271174] ------------------------------------- 1995063116880758384883742162683585083823496831886192454852008949852943883022194\ 6631919961684036194597899331129423209124271556491349413781117593785932096323957\ 8557300467937945267652465512660598955205500869181933115425086084606181046855090\ 7486608962488809048989483800925394163325785062156830947390255691238806522509664\ 3874441046759871626985453222868538161694315775629640762836880760732228535091641\ 4761839563814589694638994108409605362678210646214273333940365255656495306031426\ 8023496940033593431665145929777327966577560617258203140799419817960737824568376\ 2280037302885487251900834464581454650557929601414833921615734588139257095379769\ 1192778008269577356744441230620187578363255027283237892707103738028663930314281\ 3324140162419567169057406141965434232463880124885614730520743199225961179625013\ 0992860241708340807605932320161268492288496255841312844061536738951487114256315\ 1110897455142033138202029316409575964647560104058458415660720449628670165150619\ 2063100418642227590867090057460641785695191145605506825125040600751984226189805\ 9237118054444788072906395242548339221982707404473162376760846613033778706039803\ 4131971334936546227005631699374555082417809728109832913144035718775247685098572\ 7693792643322159939987688666080836883783802764328277517227365757274478411229438\ 9733810861607423253291974813120197604178281965697475898164531258434135959862784\ 1301281854062834766490886905210475808826158239619857701224070443305830758690393\ 1960460340497315658320867210591330090375282341553974539439771525745529051021231\ 0947321610753474825740775273986348298498340756937955646638621874569499279016572\ 1037013644331358172143117913982229838458473344402709641828510050729277483645505\ 7863450110085298781238947392869954083434615880704395911898581514577917714361969\ 8728131459483783202081474982171858011389071228250905826817436220577475921417653\ 7156877256149045829049924610286300815355833081301019876758562343435389554091756\ 2340084488752616264356864883351946372037729324009445624692325435040067802727383\ 7755376406726898636241037491410966718557050759098100246789880178271925953381282\ 4219540283027594084489550146766683896979968862416363133763939033734558014076367\ 4187771105538422573949911018646821969658165148513049422236994771476306915546821\ 7682876200362777257723781365331611196811280792669481887201298643660768551639860\ 5346022978715575179473852463694469230878942659482170080511203223654962881690357\ 3912136833839359175641873385051097027161391543959099159815465441733631165693603\ 1122249937969999226781732358023111862644575299135758175008199839236284615249881\ 0889602322443621737716180863570154684840586223297928538756234865564405369626220\ 1896357102881236156751254333830327002909766865056855715750551672751889919412971\ 1337690149916181315171544007728650573189557450920330185304847113818315407324053\ 3190384620840364217637039115506397890007428536721962809034779745333204683687958\ 6858023795221862912008074281955131794815762444829851846150970488802727472157468\ 8131594750409732115080498190455803416826949787141316063210686391511681774304792\ 596709376 Total time: 2.879 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host n032234.cs.kun.nl. (131.174.32.234) Time: Wed Jan 21 05:52:32 2004 Input: 2^100000 Output: Magma V2.10-6 Wed Jan 21 2004 05:52:29 on modular [Seed = 2950805110] ------------------------------------- 9990020930143845079440327643300335909804291390541816917715292738631458324642573\ 4832748733133244965040316439444555585493001879966076561765629084713542474928751\ 9888962987367109324635042737311247926580027853124108873708560528722839016456869\ 1026850675923517914697052857644696801524832345475543250292786520806957770971741\ 1022320429763512053307779968979251166198707717857759555217200813202952046179492\ 2925929562392096579787355815866752549579731314480624926026183794130508058268603\ 1535134178739622834990886357758062104606636372130587795322344972010808486369541\ 4018358513598580356035740218729081555665806071864612689728397946218422675793496\ 3889335724758876195913765676241112502070870487046517939639871010920036393474561\ 8090601613377898560296863598558024761448933047052222860131377095958357319485898\ 4964045723838751707022423326334368944232973818777331532869442179361253019078689\ 0360366328316150272613993415280407117191492390334187493539445589630129219725641\ 7717233543544751552379310892268182402452755752094704642185943862865632744231332\ 0847422215514933150027177500642288262118225493496005574573349646784832691809518\ 9595576917450967322441774043284045588210913790537564677213997662178526505716985\ 4834562487518322383250318645505472114369934167981678170255122812978065194806295\ 4053391546574799412974991903485075443364145056316573960066933824273164340395801\ 2128026098421224751420783471222483141030406860371964016185574165643947225346494\ 5249700314509890093162268952744428705476425472253167514521182231455388374308232\ 6422006330251375331293651643417252062561553117947386191429047614456549271284181\ 7518353132705297549537056143823957322793967303010607745684847742783219534922798\ 3836436163764742969545906672369124136325932123335643135894465219101882123829740\ 9079163860232354509593887667364032295779939011521544480036372150691155911119960\ 0153058910772942103223042426203569349321605292756962585844582235459464527692310\ 8197305806280326516736449343761732409753342333289730282959173569273013286423311\ 7596052304951716770331637095222569524604021433876551976440165281480223483318810\ 9755942196047647938852019854101734898594851100546924661723414313530993840592326\ 8953586538886974427008607028635502085562029549352480050796521564919683265106744\ 1009678229519541616177175429975200098873073778762106858907709694116104380286239\ 5044532378959187076028926039348982610077488767285291810646848914389364906478459\ 1211612193300707900537059042188012856559403699070888032966871611655961232331998\ 3109232250828661803218804394475729867620969358197843859279692501233269351946932\ 0772433552736556624822378783388807499927683163344031860446361870378978431303284\ 3823470410944306591471928341190975185239212327674384990561563688432939039442002\ 6175309768506051329371014490863961416205560535473355699267009413752718291424072\ 3426793756506976556747593410131022534283008040907958732954421355130730205017159\ 8424230760469209732907290141606353960880559202357376885647852240092777111489134\ 4924169956071717862984365339781808694741067511113535237115404365993108896974856\ 5880088786197493435792924620405176724601225061840401196628987267380307049836121\ 7974484679100747846356194664829224736134115135567179291781968056053726484141128\ 3478582412591219546011844124093497829633170420025304186616949623187358606524854\ 1022221186954422378828918971208051457514136196480536972316457056499847953765717\ 4548128597406077339158775332355215609435919275199351014222246963017013717419337\ 5049192953632951011152929518362828191918216516764559465158280489842561167481503\ 6780526787866271699964929694937704579487614662811092998202073701333032445100538\ 5378551188803474148198665114579322684900993000236736168555294173442059925371965\ 2449979254831593437063439703718096114703230741869850350547222890271748503333683\ 2830028113291084169315045738993318393459329299494279601530975611870891892952844\ 9074243284767006243171171622731766606796101967802204564589015899524704741001158\ 1109636337313293883568689494087593341769093878063985846473005889281759988444774\ 8613006315306876007008483726752778977735683004277890277210568383302147027972859\ 5336332110564064263909724579949686162908019604141753935768876587992428549912151\ 7379242703432486484142474568388895418932414509875057594030132496975416969553302\ 9688021930487416350109792003621023876827517636998097761497963609670434814012413\ 0683576879904997436596296495705459524735382000363770324894982103331332913562315\ 1698544104153170541939282347233988484535521732036880883121009439414349382822035\ 4965028153075108709860468122480297382563124498933196529620237260858650905030799\ 3308652001231671915182765742095689513136184095412121473786311042897717861448158\ 3169658487669495548262525049612270447147122296202746823629098038774693769873589\ 4212544179235529838747983045025390978873346973260309754415647480547373273276724\ 8652759034995336354126953900458854988683574927864615252040800490114785892289085\ 4433539969947808674716135197858385714564215831711930041179894407902683463575503\ 3988808672512788357729762649921382743657399292730223879257692423278548720129725\ 5386071968303782483063725899808484638503828356258403917311872694381464553651690\ 0625300232175913430847552159014752991492152969443623669108332336937679931382092\ 7587002424623833121823671523677209841718770386017230852244804317633360275973316\ 1201262248323085329288986154559221427378507410978822244729512663572225567169779\ 4097673415430172892683326350774512101678691213344656807397973727114619192999381\ 1817882754142179292688379028543090994244126051194584923790996632955026386570111\ 4884142266162969810073652710928504579470861508094054577797864301504899958634164\ 7005282205627860088640257094324442540440342431402038120748575379990160664655209\ 8698079058934732024305063590736382152128060004182752932548524792790423572759857\ 4209554632363830932428250711518801775633739811523761994686263270550635099851254\ 3338755946015409008620142936256737383316930823288543270014874766351188308851737\ 7526881952636016534590055616076771345361765545097442497907606390609330002841696\ 4847594027046669468486593636425428625241644836652173922586528474244952363302305\ 3114134493323398223365516114314691319001704882268365259163997239126266161402057\ 0799672738352959747912548896141928726125975756170159264582354115192217725391965\ 1034344793680369057003813056557866311011476313189571556336518727757991908862890\ 7654949520194749221488514170792523523942938017011494852390058443583297487692799\ 4158638464087726590174910493323885346542997925390056131156228824114719215813721\ 0120267399648622831610430287268739840335142120299516610846193164688075944526965\ 2485700705544521525474934504348529179875121859736471904615154135825821390401721\ 1829570232753702738978779350690404493855358765050355715587287320159688506133114\ 5477101575699375441097493374115991199114962726801718038950907803041184400075585\ 4685609769656695843256272833274164180445907278446800513607741542884127124563533\ 8362546906893643090206821675045981932174451336291385398315456061045969260450878\ 7700304184579153478291725762810632722108035826060904572460619204237580363147200\ 1587490753616337852434622987699178878086714539288465724172235048877668038694534\ 7458883190759735529280070924147137069664702953070050708309141249277140477619345\ 9007315206233634226128137074504162520473449597415678882003845446774388950379192\ 3445941712455102317389950303484219370880833297091081765610107086931580206950600\ 9642835204664733336116347666410631124706517380251059940926690898404666329861364\ 8854871230659903565772327667696057187057276814394932559371368029375974604116075\ 6415999194022667942306814857233613635929036768414803583280931275068011115716150\ 6276155660715823661226854426833027472584929487585208979085096283523552797849147\ 5563744318483993474633300330972497012808415900969455190375849945750379465019166\ 0098615027946061307947268985078496103038848460354233921754495058761571303447004\ 1582308022578669330051212683184600951020354317432378329217686597607627541242189\ 2808138872880175813109296020150746331979561488146333412674896256883784351178477\ 5926605772127342693283823847117460837822099396466123083439521695765810654237719\ 8189957384043031593097321505990137121839976258505543545951634005514908056562733\ 0475362528926945020226163130902420795006258931367813005222140742964756194053782\ 1824528330970215542109296386930054600119271783027615635057157354056726525241759\ 2543637186347183629201216245666209364207460550084244934728983061950607757052875\ 4845277680661218358066130291463288932240701043887535007851997159198390084654596\ 9961971383997234958637498065824393846150491840484858191935606671259680185748778\ 1956110433523842087341774338518573566310129275740928058684001180485499414947873\ 6882949368786637202682607198707656286436753775709560349718397405565505269425218\ 3543013489107852345177955197575164847115459284660037545584854709947374937966158\ 4104041423987576333520179551864485663220159855634193428666891252215344634879121\ 8159622744525372314219184738770596659942181275403613660438538829201810204850917\ 7177914852560262425298024923092295621770627700276592881584739948042550677309034\ 2004349163291358864462741531846851746258018090131447735863748652822127445066188\ 3667873545037139535563260349778209992416559111602097437491432360787879331015052\ 4170474378235535062056170175721753870617511929197156603630283023438195849465943\ 2846048293196051512486712360462565390356517332285675821093754122267422384704666\ 4733620292824834065137814475367747671882220098389682019784216724015491253360436\ 4378474797706336579054181335230108045599585473796858647089377916593402237955370\ 4527384943544110598388796974114305106940127106562850753703982330886781986829817\ 1415185218271493613110963984021912448323423901392553811725954153209435002954807\ 6402919827657415140429566669531773040033587015037034974248978981089394530269768\ 7 ** WARNING: Output too long, hence truncated. ************** MAGMA ***************** Host n032234.cs.kun.nl. (131.174.32.234) Time: Wed Jan 21 05:53:12 2004 Input: 3^100000/2^100000 Output: Magma V2.10-6 Wed Jan 21 2004 05:53:07 on modular [Seed = 2447346614] ------------------------------------- 1334971414230401469458914390489782292245248507606277355345627993984127414621589\ 6869522305980255798233239149889425419590524332428873537083020782279802984670783\ 1741929738848757721062024898109651957506705400177291046532531249067542250887334\ 2629571008941299300172233033166129544456836299498452579486504015455214736381320\ 7209965356768946943602282911944326154630492113002579642323048858295434770136138\ 1807531506158288312619405016500120857253910525756220107559776493580774834595066\ 4391476350300829536533954865604481712000952705040802828803086444633043581934923\ 3745903249195549325378269055546256255906921806226622155440527634094668066864913\ 6623767583909873402089078517647264604516160581720475547210448366081967137447991\ 8226442651928529699886492703878073655308269499457937484930238033529298447444330\ 5592397659315237841028937215223851003498757650130412927359617600578030416190379\ 6298302903624866963435298923914989181690433716204345541925220382491809472656081\ 5100985838795186158194775604404398151067087953994291069425659662679592924634171\ 4202829694934465304337015784361135937440940664714154737267519782717648220624437\ 7297495311363139117182846526847396011100256641964726915840529026133350440572152\ 8773250558502655312168986343564871064654334827513005332648722336798578355121274\ 6606106199891326833236919894249821574280609481988804468986557501778462928403152\ 8807251034659243061300457098151802838555328959349882183372411452749569160369571\ 4743361010656708814466807351536259662486169634113312883567962395107127472503411\ 6042262749977206507262437895238456653520219653531978179499712629802187572575395\ 6687297376185556357271688531139890579653883304482771789483031388421357481008509\ 8565935921766781917463457858769230646231584554088864174529684257142410973222364\ 9817540134839891873620127918668509134869736194958920383674812649484543522305782\ 2100302592646807575727578194260717181543935482870403359180749233077716153034001\ 1793589361924475858272465008394729371715225666239011244161943950834583986014699\ 7174686693257680063934668354311100491354219636350945161847892966360191444321041\ 5814538534529238970509876596798896164377609768509217186822053642712881560512260\ 8931134394917645728564527112075649899243588509896189777871982262490841773371456\ 3282280705117960125913614359871691670603977668478901681124754489210554082390746\ 8944197028644713521165393320189401484955745717592888716939502494769978142085727\ 9416589261535802589227216947994510155816971487967110284575709335449414531466148\ 7827312807482491775681483079035986821162264588779661180105819077546376651029290\ 7711997110626974295341783046136344293634320740538611689722973260771662996279029\ 0594693258720290527962515742948541908629615920387702713284405532221912639580505\ 7934699127235739861503038989250127304616711372778706981341392639654455238652201\ 7597218238761187391586599662062413539213518918645513578338850493396100319844660\ 5208670744749144430074910090059537659949842997826728577039649773069544827611866\ 7756543639772410681399983929270452748169361509813391108129985672725008227765388\ 5213638983701151082116587029152088099597676866999187286174366535315208022160397\ 7438626211594841556156961018093472784135886679204847504736973577572701881274901\ 6750931462912955125594990141946585753506471581028434134030334253795501120437081\ 5544893482812679643003407025461492617584333495534436165867788382504662944539048\ 8477556467905980634307147917907324010231216353890005861558147227617286591360275\ 7323014454633136379106944743507849778763582887527437449170717108602424789427423\ 4355538016716002066957451504280434714564531123845691200969031783298829274131199\ 9586824327799175771292478825777377168640034704639941266192370954227236366120326\ 5890314172863777680215765908406658926806646326817842515365371167556944030615284\ 3418579518627215615782318174869054982177438953670549959292281935795634816307186\ 9600441148786972830758543218792320712760035735487848071421875243850801279845349\ 1057359195756540776837477244064221930590143121983577298182656237987162764092981\ 5289234292533868773599625692945016310457215117554325069427871208178917592341317\ 7907055910603419879418725138782466192194904226294595706839605932337431233494629\ 4356669650495836863646061179558326934103380974998937492264627350053185617549472\ 5182154617056021251141479526577709631435946389382553489002507234840005564419979\ 8397611636958589582563067615424314091593835242358762107095442779316504216289376\ 5245650686307707212763130705657093765605944832005356656517514369489808699210259\ 0778607813704693284658981270561235460448718448868526049020018210678078465447276\ 9932811968492232580293770486523408319152137170374071112327031570327514487430519\ 4888994126792022738384085792232919851738923726460019795291895781083785682532241\ 0660197053207521147962288726832598906690938066795503989684267240497199944162010\ 2587002389055667070810316786601458582941570359373708315525780401241430070248873\ 0288149452569380882923587421428258970340997214682459415086807761182313990330758\ 2322997578299578657363484930382373188199149084726979933695431352177806126415524\ 7856275391133217083869277859968305367203603243060441431916049561622118488060739\ 9321315072111813308673783744452434556234137273517093201664640449765453517042831\ 5069923102237582553762833647922076684706723536313800601426921013889928581905936\ 3526419344006775798309414501256889071364557285302146843458961506093670297695754\ 9923043459213550580288565197182923237617256358806942894250764873424456953158127\ 7528867606210391411313046048850834217937973303617128444971859871599069013231716\ 9665961842234909776670587288821661651139948921457487140834846076973801304222950\ 4629877367228799354440270720238103482259479407771105100014641359796408059164038\ 0734396832157063050392563338171682883502037570557465637738936493706488029344926\ 5816539688572542746440669831417201261933866120750641748439942962043642095844763\ 4566173233824861969734665981026258879069389796035842980981978195801209204556935\ 8296811182977171849461912211870262255015472191879796123333702732308642716895453\ 0599802817401657993469292257129487969901266593493068148727684217569536396446003\ 3258410333729517266574619913957170757527085914212725614304749731787707661283667\ 4996774739526648338595429354974077264904919911066668919787202294856954581271540\ 8353034477721529527873023680998824005098060529330768524842394953639010703169832\ 5693499275600875271439688411524153169835134206457648001601913757246398917800483\ 8908277350637076404601772926009191022512391148104297894927339732899540427820539\ 5057818617768084014464787134781602124601084605012871297700574201445739342571183\ 5522774914697489379199011407890872461274425621513663890343008568873964862410662\ 5340069555129830501302507365972347187438333656996917932935218331379882921921935\ 8066632512330505982753224920270949856479726151109895867734980085820139985755461\ 4999655938395227808617048459846919382756038570105572337770195651317073145272491\ 9022955592599573988787436852840113428859046510655685808443916595581932537909065\ 5701524823432110002456567585197050701832617425631703221938485194731029800855574\ 2479373663302429056278626149941761647917637508044893881755330791064287334133384\ 1030292090426685240328073378172427807890484457090197682380462268873546396988199\ 4028929873779841027214400147177492414099043144303487317973521208466651501512232\ 3238893216982424280076917234107503861276205927377367185287432851342232757010642\ 0607588797091887203138123610646595800981955390232335256130838081965035617068532\ 7151570800176776979203356858700893316588686835813326673994567314913372820187372\ 6597496708946312560973160356684129728544946372294611958711750729130026958710952\ 1749715038257426057993403999933344247318125144822079210452393296177076423951006\ 1661516371346206436460008186609934412376199854355562969351803923656353243970817\ 0051749857738316313985893707659291972370187279309128741430326523422491151109050\ 1150396443016645330052023462851860297816657081191634082984107602122842947520729\ 2175481198462819094242041167442560153996413406957900827965574946523786905664663\ 7265960300498496780342902924717383508640912312874044250080553012881363962657304\ 8466362795234900377128566069109562498971814178550863326894320476419797600293064\ 1435248038590880978488813919119161940729099965902931480502232251690243453997185\ 6900875372513973604553767654950877489526448350324849795882039529551826068796753\ 0964850188123796012343279515006302388264219518380675742552567849332271710119137\ 1791385608432555648481983126822468787716619820803216979605115414238696910342784\ 1141050361004973761829430350559862396979945988500831480681600776379028931668735\ 4716440211402790799648515762956844596236585676101942227183812772209320431517182\ 2017816947879312788677431731050377520062182210827218697852645534260696275069914\ 4483557267776119064522878746969147634370638975366767436070675208212251922423671\ 7973266469860317229699253702035733823853947467763206656630609953068106798763682\ 2044778676790571526156752682098054008060114222048648235211088677652001733408972\ 3904040212348587337498166956391055169726819502134965644809188811214703082450567\ 4661432254495813032622478334872293769452151767150054404576681408107994962406006\ 4148141994717787006797204280361180807876033049761456459736601225700682679513329\ 3696671352803961223914709109598489933103263702275569203725595982540831266635392\ 7839853466911764727507808170177601072547287285970651032607461977529053857354086\ 7490363049236404542295177687297794359172552178522669357542909897340384086004138\ 4689245507547791562513587227152500782734563124006954754554171637939547310318754\ 8731671291477822677719948204266687600763155928248355933413026348454510166847294\ 3337107974636189072668256721441101751960657630930579890571217013133779253750178\ 8862346007151266814711927321948769679747053463999423708280575959959013839379892\ 6 ** WARNING: Output too long, hence truncated. ************** MAGMA ***************** Host n032234.cs.kun.nl. (131.174.32.234) Time: Wed Jan 21 05:53:50 2004 Input: 3^100000/2^1000000 Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Wed Jan 21 2004 05:53:27 on modular [Seed = 2597617801] ------------------------------------- 1334971414230401469458914390489782292245248507606277355345627993984127414621589\ 6869522305980255798233239149889425419590524332428873537083020782279802984670783\ 1741929738848757721062024898109651957506705400177291046532531249067542250887334\ 2629571008941299300172233033166129544456836299498452579486504015455214736381320\ 7209965356768946943602282911944326154630492113002579642323048858295434770136138\ 1807531506158288312619405016500120857253910525756220107559776493580774834595066\ 4391476350300829536533954865604481712000952705040802828803086444633043581934923\ 3745903249195549325378269055546256255906921806226622155440527634094668066864913\ 6623767583909873402089078517647264604516160581720475547210448366081967137447991\ 8226442651928529699886492703878073655308269499457937484930238033529298447444330\ 5592397659315237841028937215223851003498757650130412927359617600578030416190379\ 6298302903624866963435298923914989181690433716204345541925220382491809472656081\ 5100985838795186158194775604404398151067087953994291069425659662679592924634171\ 4202829694934465304337015784361135937440940664714154737267519782717648220624437\ 7297495311363139117182846526847396011100256641964726915840529026133350440572152\ 8773250558502655312168986343564871064654334827513005332648722336798578355121274\ 6606106199891326833236919894249821574280609481988804468986557501778462928403152\ 8807251034659243061300457098151802838555328959349882183372411452749569160369571\ 4743361010656708814466807351536259662486169634113312883567962395107127472503411\ 6042262749977206507262437895238456653520219653531978179499712629802187572575395\ 6687297376185556357271688531139890579653883304482771789483031388421357481008509\ 8565935921766781917463457858769230646231584554088864174529684257142410973222364\ 9817540134839891873620127918668509134869736194958920383674812649484543522305782\ 2100302592646807575727578194260717181543935482870403359180749233077716153034001\ 1793589361924475858272465008394729371715225666239011244161943950834583986014699\ 7174686693257680063934668354311100491354219636350945161847892966360191444321041\ 5814538534529238970509876596798896164377609768509217186822053642712881560512260\ 8931134394917645728564527112075649899243588509896189777871982262490841773371456\ 3282280705117960125913614359871691670603977668478901681124754489210554082390746\ 8944197028644713521165393320189401484955745717592888716939502494769978142085727\ 9416589261535802589227216947994510155816971487967110284575709335449414531466148\ 7827312807482491775681483079035986821162264588779661180105819077546376651029290\ 7711997110626974295341783046136344293634320740538611689722973260771662996279029\ 0594693258720290527962515742948541908629615920387702713284405532221912639580505\ 7934699127235739861503038989250127304616711372778706981341392639654455238652201\ 7597218238761187391586599662062413539213518918645513578338850493396100319844660\ 5208670744749144430074910090059537659949842997826728577039649773069544827611866\ 7756543639772410681399983929270452748169361509813391108129985672725008227765388\ 5213638983701151082116587029152088099597676866999187286174366535315208022160397\ 7438626211594841556156961018093472784135886679204847504736973577572701881274901\ 6750931462912955125594990141946585753506471581028434134030334253795501120437081\ 5544893482812679643003407025461492617584333495534436165867788382504662944539048\ 8477556467905980634307147917907324010231216353890005861558147227617286591360275\ 7323014454633136379106944743507849778763582887527437449170717108602424789427423\ 4355538016716002066957451504280434714564531123845691200969031783298829274131199\ 9586824327799175771292478825777377168640034704639941266192370954227236366120326\ 5890314172863777680215765908406658926806646326817842515365371167556944030615284\ 3418579518627215615782318174869054982177438953670549959292281935795634816307186\ 9600441148786972830758543218792320712760035735487848071421875243850801279845349\ 1057359195756540776837477244064221930590143121983577298182656237987162764092981\ 5289234292533868773599625692945016310457215117554325069427871208178917592341317\ 7907055910603419879418725138782466192194904226294595706839605932337431233494629\ 4356669650495836863646061179558326934103380974998937492264627350053185617549472\ 5182154617056021251141479526577709631435946389382553489002507234840005564419979\ 8397611636958589582563067615424314091593835242358762107095442779316504216289376\ 5245650686307707212763130705657093765605944832005356656517514369489808699210259\ 0778607813704693284658981270561235460448718448868526049020018210678078465447276\ 9932811968492232580293770486523408319152137170374071112327031570327514487430519\ 4888994126792022738384085792232919851738923726460019795291895781083785682532241\ 0660197053207521147962288726832598906690938066795503989684267240497199944162010\ 2587002389055667070810316786601458582941570359373708315525780401241430070248873\ 0288149452569380882923587421428258970340997214682459415086807761182313990330758\ 2322997578299578657363484930382373188199149084726979933695431352177806126415524\ 7856275391133217083869277859968305367203603243060441431916049561622118488060739\ 9321315072111813308673783744452434556234137273517093201664640449765453517042831\ 5069923102237582553762833647922076684706723536313800601426921013889928581905936\ 3526419344006775798309414501256889071364557285302146843458961506093670297695754\ 9923043459213550580288565197182923237617256358806942894250764873424456953158127\ 7528867606210391411313046048850834217937973303617128444971859871599069013231716\ 9665961842234909776670587288821661651139948921457487140834846076973801304222950\ 4629877367228799354440270720238103482259479407771105100014641359796408059164038\ 0734396832157063050392563338171682883502037570557465637738936493706488029344926\ 5816539688572542746440669831417201261933866120750641748439942962043642095844763\ 4566173233824861969734665981026258879069389796035842980981978195801209204556935\ 8296811182977171849461912211870262255015472191879796123333702732308642716895453\ 0599802817401657993469292257129487969901266593493068148727684217569536396446003\ 3258410333729517266574619913957170757527085914212725614304749731787707661283667\ 4996774739526648338595429354974077264904919911066668919787202294856954581271540\ 8353034477721529527873023680998824005098060529330768524842394953639010703169832\ 5693499275600875271439688411524153169835134206457648001601913757246398917800483\ 8908277350637076404601772926009191022512391148104297894927339732899540427820539\ 5057818617768084014464787134781602124601084605012871297700574201445739342571183\ 5522774914697489379199011407890872461274425621513663890343008568873964862410662\ 5340069555129830501302507365972347187438333656996917932935218331379882921921935\ 8066632512330505982753224920270949856479726151109895867734980085820139985755461\ 4999655938395227808617048459846919382756038570105572337770195651317073145272491\ 9022955592599573988787436852840113428859046510655685808443916595581932537909065\ 5701524823432110002456567585197050701832617425631703221938485194731029800855574\ 2479373663302429056278626149941761647917637508044893881755330791064287334133384\ 1030292090426685240328073378172427807890484457090197682380462268873546396988199\ 4028929873779841027214400147177492414099043144303487317973521208466651501512232\ 3238893216982424280076917234107503861276205927377367185287432851342232757010642\ 0607588797091887203138123610646595800981955390232335256130838081965035617068532\ 7151570800176776979203356858700893316588686835813326673994567314913372820187372\ 6597496708946312560973160356684129728544946372294611958711750729130026958710952\ 1749715038257426057993403999933344247318125144822079210452393296177076423951006\ 1661516371346206436460008186609934412376199854355562969351803923656353243970817\ 0051749857738316313985893707659291972370187279309128741430326523422491151109050\ 1150396443016645330052023462851860297816657081191634082984107602122842947520729\ 2175481198462819094242041167442560153996413406957900827965574946523786905664663\ 7265960300498496780342902924717383508640912312874044250080553012881363962657304\ 8466362795234900377128566069109562498971814178550863326894320476419797600293064\ 1435248038590880978488813919119161940729099965902931480502232251690243453997185\ 6900875372513973604553767654950877489526448350324849795882039529551826068796753\ 0964850188123796012343279515006302388264219518380675742552567849332271710119137\ 1791385608432555648481983126822468787716619820803216979605115414238696910342784\ 1141050361004973761829430350559862396979945988500831480681600776379028931668735\ 4716440211402790799648515762956844596236585676101942227183812772209320431517182\ 2017816947879312788677431731050377520062182210827218697852645534260696275069914\ 4483557267776119064522878746969147634370638975366767436070675208212251922423671\ 7973266469860317229699253702035733823853947467763206656630609953068106798763682\ 2044778676790571526156752682098054008060114222048648235211088677652001733408972\ 3904040212348587337498166956391055169726819502134965644809188811214703082450567\ 4661432254495813032622478334872293769452151767150054404576681408107994962406006\ 4148141994717787006797204280361180807876033049761456459736601225700682679513329\ 3696671352803961223914709109598489933103263702275569203725595982540831266635392\ 7839853466911764727507808170177601072547287285970651032607461977529053857354086\ 7490363049236404542295177687297794359172552178522669357542909897340384086004138\ 4689245507547791562513587227152500782734563124006954754554171637939547310318754\ 8731671291477822677719948204266687600763155928248355933413026348454510166847294\ 3337107974636189072668256721441101751960657630930579890571217013133779253750178\ 8862346007151266814711927321948769679747053463999423708280575959959013839379892\ 6 ** WARNING: Output too long, hence truncated. Errors: /home/mfd/gomagma: line 2: 29870 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host s02a.gnmipr.gm.com. (198.208.223.35) Time: Wed Jan 21 14:50:03 2004 Input: 2789*972 Output: Magma V2.10-6 Wed Jan 21 2004 14:49:59 on modular [Seed = 3733997826] ------------------------------------- 2710908 Total time: 3.169 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host s02a.gnmipr.gm.com. (198.208.223.35) Time: Wed Jan 21 14:50:05 2004 Input: 2789*972 Output: Magma V2.10-6 Wed Jan 21 2004 14:50:02 on modular [Seed = 3566879493] ------------------------------------- 2710908 Total time: 3.139 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host carroll.math.ubc.ca. (142.103.161.252) Time: Wed Jan 21 14:52:21 2004 Input: X=HyperellipticCurve(x^6+8*x^5+26*x^4+46*x^3+53*x^2+42*x+17, 0); Output: Magma V2.10-6 Wed Jan 21 2004 14:52:18 on modular [Seed = 980722292] ------------------------------------- >> X=HyperellipticCurve(x^6+8*x^5+26*x^4+46*x^3+53*x^2+42*x+17, 0);; ^ User error: Identifier 'x' has not been declared or assigned Total time: 2.869 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host carroll.math.ubc.ca. (142.103.161.252) Time: Wed Jan 21 14:54:51 2004 Input: X:=HyperellipticCurve(x^6+8*x^5+26*x^4+46*x^3+53*x^2+42*x+17, 0); Output: Magma V2.10-6 Wed Jan 21 2004 14:54:48 on modular [Seed = 1647115094] ------------------------------------- >> X:=HyperellipticCurve(x^6+8*x^5+26*x^4+46*x^3+53*x^2+42*x+17, 0);; ^ User error: Identifier 'x' has not been declared or assigned Total time: 3.019 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host carroll.math.ubc.ca. (142.103.161.252) Time: Wed Jan 21 14:55:25 2004 Input: X:=HyperellipticCurve([1, 8, 26, 46, 53, 42, 17], 0); Output: Magma V2.10-6 Wed Jan 21 2004 14:55:22 on modular [Seed = 1461308993] ------------------------------------- >> X:=HyperellipticCurve([1, 8, 26, 46, 53, 42, 17], 0);; ^ Runtime error in 'HyperellipticCurve': Bad argument types Argument types given: SeqEnum[RngIntElt], RngIntElt Total time: 3.069 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host carroll.math.ubc.ca. (142.103.161.252) Time: Wed Jan 21 14:57:40 2004 Input: P:=PolynomialRing(RationalField()); X:=HyperellipticCurve(x^6+8*x^5+ 26*x^4+ 46*x^3 53*x^2+ 42*x +17, 0); Output: Magma V2.10-6 Wed Jan 21 2004 14:57:37 on modular [Seed = 1208406469] ------------------------------------- >> X:=HyperellipticCurve(x^6+8*x^5+ 26*x^4+ 46*x^3 53*x^2+ 42*x +17, 0);; ^ User error: bad syntax Total time: 3.179 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host carroll.math.ubc.ca. (142.103.161.252) Time: Wed Jan 21 14:58:05 2004 Input: P:=PolynomialRing(RationalField()); X:=HyperellipticCurve(x^6+8*x^5+ 26*x^4+ 46*x^3+ 53*x^2+ 42*x +17); Output: Magma V2.10-6 Wed Jan 21 2004 14:58:02 on modular [Seed = 1091557559] ------------------------------------- Total time: 3.139 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host carroll.math.ubc.ca. (142.103.161.252) Time: Wed Jan 21 14:59:18 2004 Input: P:=PolynomialRing(RationalField()); X:=HyperellipticCurve(x^6+8*x^5+ 26*x^4+ 46*x^3+ 53*x^2+ 42*x +17); J:=Jacobian(X); Output: Magma V2.10-6 Wed Jan 21 2004 14:59:15 on modular [Seed = 3153404308] ------------------------------------- Total time: 3.139 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host carroll.math.ubc.ca. (142.103.161.252) Time: Wed Jan 21 14:59:45 2004 Input: P:=PolynomialRing(RationalField()); X:=HyperellipticCurve(x^6+8*x^5+ 26*x^4+ 46*x^3+ 53*x^2+ 42*x +17); J:=Jacobian(X); Curve(J); Output: Magma V2.10-6 Wed Jan 21 2004 14:59:42 on modular [Seed = 2900506302] ------------------------------------- Hyperelliptic Curve defined by y^2 = x^6 + 8*x^5 + 26*x^4 + 46*x^3 + 53*x^2 + 42*x + 17 over Rational Field Total time: 3.169 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host carroll.math.ubc.ca. (142.103.161.252) Time: Wed Jan 21 15:00:03 2004 Input: P:=PolynomialRing(RationalField()); X:=HyperellipticCurve(x^6+8*x^5+ 26*x^4+ 46*x^3+ 53*x^2+ 42*x +17); Jacobian(X); Output: Magma V2.10-6 Wed Jan 21 2004 15:00:00 on modular [Seed = 2783657945] ------------------------------------- Jacobian of Hyperelliptic Curve defined by y^2 = x^6 + 8*x^5 + 26*x^4 + 46*x^3 + 53*x^2 + 42*x + 17 over Rational Field Total time: 3.289 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host carroll.math.ubc.ca. (142.103.161.252) Time: Wed Jan 21 15:01:48 2004 Input: P:=PolynomialRing(RationalField()); X:=HyperellipticCurve(x^6+8*x^5+ 26*x^4+ 46*x^3+ 53*x^2+ 42*x +17); Random(X); Output: Magma V2.10-6 Wed Jan 21 2004 15:01:45 on modular [Seed = 2278104338] ------------------------------------- >> Random(X); ^ Runtime error in 'Random': Base field must be finite: Hyperelliptic Curve defined by y^2 = x^6 + 8*x^5 + 26*x^4 + 46*x^3 + 53*x^2 + 42*x + 17 over Rational Field Total time: 3.099 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host carroll.math.ubc.ca. (142.103.161.252) Time: Wed Jan 21 15:03:39 2004 Input: P:=PolynomialRing(GF(5)); X:=HyperellipticCurve(x^6+8*x^5+ 26*x^4+ 46*x^3+ 53*x^2+ 42*x +17); J:=Jacobian(X); Order(J); Output: Magma V2.10-6 Wed Jan 21 2004 15:03:35 on modular [Seed = 4189545170] ------------------------------------- 19 Total time: 3.069 seconds, Total memory usage: 2.03MB ************** MAGMA ***************** Host carroll.math.ubc.ca. (142.103.161.252) Time: Wed Jan 21 15:04:07 2004 Input: P:=PolynomialRing(GF(7)); X:=HyperellipticCurve(x^6+8*x^5+ 26*x^4+ 46*x^3+ 53*x^2+ 42*x +17); J:=Jacobian(X); Order(J); Output: Magma V2.10-6 Wed Jan 21 2004 15:04:04 on modular [Seed = 4072434170] ------------------------------------- 57 Total time: 3.219 seconds, Total memory usage: 2.01MB ************** MAGMA ***************** Host carroll.math.ubc.ca. (142.103.161.252) Time: Wed Jan 21 15:04:29 2004 Input: P:=PolynomialRing(GF(17 )); X:=HyperellipticCurve(x^6+8*x^5+ 26*x^4+ 46*x^3+ 53*x^2+ 42*x +17); J:=Jacobian(X); Order(J); Output: Magma V2.10-6 Wed Jan 21 2004 15:04:26 on modular [Seed = 3953488029] ------------------------------------- 228 Total time: 3.159 seconds, Total memory usage: 2.00MB ************** MAGMA ***************** Host carroll.math.ubc.ca. (142.103.161.252) Time: Wed Jan 21 15:05:06 2004 Input: P:=PolynomialRing(GF(101)); X:=HyperellipticCurve(x^6+8*x^5+ 26*x^4+ 46*x^3+ 53*x^2+ 42*x +17); J:=Jacobian(X); Order(J); Output: Magma V2.10-6 Wed Jan 21 2004 15:05:03 on modular [Seed = 3633726347] ------------------------------------- 9804 Total time: 3.079 seconds, Total memory usage: 2.19MB ************** MAGMA ***************** Host gauss02.uni-math.gwdg.de. (134.76.82.92) Time: Wed Jan 21 15:17:50 2004 Input: 1+2 Output: Magma V2.10-6 Wed Jan 21 2004 15:17:46 on modular [Seed = 1983440929] ------------------------------------- 3 Total time: 3.749 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host gauss02.uni-math.gwdg.de. (134.76.82.92) Time: Wed Jan 21 15:18:13 2004 Input: 1+2 Output: Magma V2.10-6 Wed Jan 21 2004 15:18:09 on modular [Seed = 1477887716] ------------------------------------- 3 Total time: 3.049 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host gauss02.uni-math.gwdg.de. (134.76.82.92) Time: Wed Jan 21 15:18:16 2004 Input: 1+2 Output: Magma V2.10-6 Wed Jan 21 2004 15:18:13 on modular [Seed = 1344196328] ------------------------------------- 3 Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host gauss02.uni-math.gwdg.de. (134.76.82.92) Time: Wed Jan 21 15:18:43 2004 Input: 1+2 Output: Magma V2.10-6 Wed Jan 21 2004 15:18:39 on modular [Seed = 1124982241] ------------------------------------- 3 Total time: 2.979 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host bluenote.ccrwest.org. (192.203.205.129) Time: Wed Jan 21 18:16:32 2004 Input: S:=SupersingularModule(13,22); HeckeOperator(S,11); Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Wed Jan 21 2004 18:16:07 on modular [Seed = 2850480594] ------------------------------------- Errors: /home/mfd/gomagma: line 2: 1002 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host bluenote.ccrwest.org. (192.203.205.129) Time: Wed Jan 21 18:17:08 2004 Input: S:=SupersingularModule(5,22); HeckeOperator(S,11); Output: Magma V2.10-6 Wed Jan 21 2004 18:16:59 on modular [Seed = 3119968657] ------------------------------------- [2 1 2 2 2 2 2 2 2 2 2 2] [1 2 2 2 2 2 2 2 2 2 2 2] [2 2 2 1 2 2 2 2 2 2 2 2] [2 2 1 2 2 2 2 2 2 2 2 2] [2 2 2 2 2 1 2 2 2 2 2 2] [2 2 2 2 1 2 2 2 2 2 2 2] [2 2 2 2 2 2 2 2 1 2 2 2] [2 2 2 2 2 2 2 2 2 1 2 2] [2 2 2 2 2 2 1 2 2 2 2 2] [2 2 2 2 2 2 2 1 2 2 2 2] [2 2 2 2 2 2 2 2 2 2 2 1] [2 2 2 2 2 2 2 2 2 2 1 2] Total time: 9.099 seconds, Total memory usage: 2.39MB ************** MAGMA ***************** Host bluenote.ccrwest.org. (192.203.205.129) Time: Wed Jan 21 18:18:08 2004 Input: time S := SupersingularModule(5,22); S; time T2 := HeckeOperator(S,11); T2; time CharacteristicPolynomial(T2); Output: Magma V2.10-6 Wed Jan 21 2004 18:17:58 on modular [Seed = 1091439011] ------------------------------------- Time: 0.010 Supersingular module associated to X_0(22)/GF(5) of dimension 12 Time: 0.020 [2 1 2 2 2 2 2 2 2 2 2 2] [1 2 2 2 2 2 2 2 2 2 2 2] [2 2 2 2 1 2 2 2 2 2 2 2] [2 2 2 2 2 1 2 2 2 2 2 2] [2 2 1 2 2 2 2 2 2 2 2 2] [2 2 2 1 2 2 2 2 2 2 2 2] [2 2 2 2 2 2 2 2 2 1 2 2] [2 2 2 2 2 2 2 2 1 2 2 2] [2 2 2 2 2 2 2 1 2 2 2 2] [2 2 2 2 2 2 1 2 2 2 2 2] [2 2 2 2 2 2 2 2 2 2 2 1] [2 2 2 2 2 2 2 2 2 2 1 2] $.1^12 - 24*$.1^11 + 18*$.1^10 + 120*$.1^9 - 105*$.1^8 - 240*$.1^7 + 220*$.1^6 + 240*$.1^5 - 225*$.1^4 - 120*$.1^3 + 114*$.1^2 + 24*$.1 - 23 Time: 0.000 Total time: 9.130 seconds, Total memory usage: 2.39MB ************** MAGMA ***************** Host bluenote.ccrwest.org. (192.203.205.129) Time: Wed Jan 21 18:20:05 2004 Input: time S := SupersingularModule(5,22); S; time T2s := HeckeOperator(S,11); T2s; time M := ModularForms(5*22); time T2m := HeckeOperator(S,11); T2m; time Factorization(CharacteristicPolynomial(T2s)); time Factorization(CharacteristicPolynomial(T2m)); Output: Magma V2.10-6 Wed Jan 21 2004 18:19:55 on modular [Seed = 1427774474] ------------------------------------- Time: 0.010 Supersingular module associated to X_0(22)/GF(5) of dimension 12 Time: 0.020 [2 1 2 2 2 2 2 2 2 2 2 2] [1 2 2 2 2 2 2 2 2 2 2 2] [2 2 2 2 2 1 2 2 2 2 2 2] [2 2 2 2 1 2 2 2 2 2 2 2] [2 2 2 1 2 2 2 2 2 2 2 2] [2 2 1 2 2 2 2 2 2 2 2 2] [2 2 2 2 2 2 2 2 2 1 2 2] [2 2 2 2 2 2 2 2 1 2 2 2] [2 2 2 2 2 2 2 1 2 2 2 2] [2 2 2 2 2 2 1 2 2 2 2 2] [2 2 2 2 2 2 2 2 2 2 2 1] [2 2 2 2 2 2 2 2 2 2 1 2] Time: 0.010 Time: 0.000 [2 1 2 2 2 2 2 2 2 2 2 2] [1 2 2 2 2 2 2 2 2 2 2 2] [2 2 2 2 2 1 2 2 2 2 2 2] [2 2 2 2 1 2 2 2 2 2 2 2] [2 2 2 1 2 2 2 2 2 2 2 2] [2 2 1 2 2 2 2 2 2 2 2 2] [2 2 2 2 2 2 2 2 2 1 2 2] [2 2 2 2 2 2 2 2 1 2 2 2] [2 2 2 2 2 2 2 1 2 2 2 2] [2 2 2 2 2 2 1 2 2 2 2 2] [2 2 2 2 2 2 2 2 2 2 2 1] [2 2 2 2 2 2 2 2 2 2 1 2] [ <$.1 - 23, 1>, <$.1 - 1, 6>, <$.1 + 1, 5> ] Time: 0.000 [ <$.1 - 23, 1>, <$.1 - 1, 6>, <$.1 + 1, 5> ] Time: 0.000 Total time: 9.289 seconds, Total memory usage: 2.39MB ************** MAGMA ***************** Host bluenote.ccrwest.org. (192.203.205.129) Time: Wed Jan 21 18:20:57 2004 Input: time S := SupersingularModule(5,22); S; time T2s := HeckeOperator(S,2); T2s; time M := ModularForms(5*22); time T2m := HeckeOperator(S,2); T2m; time Factorization(CharacteristicPolynomial(T2s)); time Factorization(CharacteristicPolynomial(T2m)); Output: Magma V2.10-6 Wed Jan 21 2004 18:20:48 on modular [Seed = 1814242680] ------------------------------------- Time: 0.010 Supersingular module associated to X_0(22)/GF(5) of dimension 12 Time: 0.020 [1 0 0 0 0 0 1 1 0 0 1 1] [0 1 0 0 0 0 0 0 1 1 1 1] [0 0 2 0 1 0 0 0 1 1 0 0] [0 0 0 2 0 1 1 1 0 0 0 0] [0 0 1 0 2 0 0 0 1 1 0 0] [0 0 0 1 0 2 1 1 0 0 0 0] [1 0 0 1 0 1 0 1 0 0 0 1] [1 0 0 1 0 1 1 0 0 0 1 0] [0 1 1 0 1 0 0 0 0 1 1 0] [0 1 1 0 1 0 0 0 1 0 0 1] [1 1 0 0 0 0 0 1 1 0 0 1] [1 1 0 0 0 0 1 0 0 1 1 0] Time: 0.020 Time: 0.000 [1 0 0 0 0 0 1 1 0 0 1 1] [0 1 0 0 0 0 0 0 1 1 1 1] [0 0 2 0 1 0 0 0 1 1 0 0] [0 0 0 2 0 1 1 1 0 0 0 0] [0 0 1 0 2 0 0 0 1 1 0 0] [0 0 0 1 0 2 1 1 0 0 0 0] [1 0 0 1 0 1 0 1 0 0 0 1] [1 0 0 1 0 1 1 0 0 0 1 0] [0 1 1 0 1 0 0 0 0 1 1 0] [0 1 1 0 1 0 0 0 1 0 0 1] [1 1 0 0 0 0 0 1 1 0 0 1] [1 1 0 0 0 0 1 0 0 1 1 0] [ <$.1 - 5, 1>, <$.1 - 3, 1>, <$.1 - 1, 2>, <$.1 + 1, 4>, <$.1^2 - 6*$.1 + 7, 1>, <$.1^2 + 2*$.1 - 1, 1> ] Time: 0.020 [ <$.1 - 5, 1>, <$.1 - 3, 1>, <$.1 - 1, 2>, <$.1 + 1, 4>, <$.1^2 - 6*$.1 + 7, 1>, <$.1^2 + 2*$.1 - 1, 1> ] Time: 0.010 Total time: 9.139 seconds, Total memory usage: 2.57MB ************** MAGMA ***************** Host bluenote.ccrwest.org. (192.203.205.129) Time: Wed Jan 21 18:21:32 2004 Input: time S := SupersingularModule(5,22); S; time T2s := HeckeOperator(S,2); T2s; time M := ModularForms(5*22); time T2m := HeckeOperator(M,2); T2m; time Factorization(CharacteristicPolynomial(T2s)); time Factorization(CharacteristicPolynomial(T2m)); Output: Magma V2.10-6 Wed Jan 21 2004 18:21:19 on modular [Seed = 2000174684] ------------------------------------- Time: 0.020 Supersingular module associated to X_0(22)/GF(5) of dimension 12 Time: 0.010 [1 0 0 0 0 0 1 0 1 0 1 1] [0 1 0 0 0 0 0 1 0 1 1 1] [0 0 2 1 0 0 0 1 0 1 0 0] [0 0 1 2 0 0 0 1 0 1 0 0] [0 0 0 0 2 1 1 0 1 0 0 0] [0 0 0 0 1 2 1 0 1 0 0 0] [1 0 0 0 1 1 0 0 1 0 0 1] [0 1 1 1 0 0 0 0 0 1 0 1] [1 0 0 0 1 1 1 0 0 0 1 0] [0 1 1 1 0 0 0 1 0 0 1 0] [1 1 0 0 0 0 0 0 1 1 0 1] [1 1 0 0 0 0 1 1 0 0 1 0] Time: 0.010 Time: 3.390 [1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0] [0 0 0 0 0 0 0 0 0 0 0 0 2 -1 0 2 -1 -4 -3 2 4 1] [0 1 0 0 0 0 0 0 0 0 0 0 -5 -1 6 -7 6 14 9 -4 -14 -2] [0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 -1 0 -3 0 0 1] [0 0 1 0 0 0 0 0 0 0 0 0 4 2 -4 5 -3 -6 -5 2 9 2] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 4 0] [0 0 0 1 0 0 0 0 0 0 0 0 3 1 -2 3 -2 -6 -5 2 6 1] [0 0 0 0 0 0 0 0 0 0 0 0 -2 -1 3 -3 2 4 3 0 -7 0] [0 0 0 0 1 0 0 0 0 0 0 0 2 2 -1 3 -2 -4 -2 2 4 1] [0 0 0 0 0 0 0 0 0 0 0 0 -2 -1 4 -4 3 8 5 -2 -8 -1] [0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 4 0] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -2] [0 0 0 0 0 0 1 0 0 0 0 0 2 1 0 1 -1 -2 -1 1 3 0] [0 0 0 0 0 0 0 0 0 0 0 0 -3 -1 2 -3 3 6 5 -2 -6 -1] [0 0 0 0 0 0 0 1 0 0 0 0 -2 -1 4 -5 5 9 6 -2 -11 0] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -2 0] [0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 2 0 0 -1] [0 0 0 0 0 0 0 0 0 0 0 0 3 2 -3 4 -3 -6 -4 2 7 1] [0 0 0 0 0 0 0 0 0 1 0 0 -1 -1 1 -1 1 2 1 0 -1 0] [0 0 0 0 0 0 0 0 0 0 0 0 2 1 -4 4 -4 -8 -5 2 9 0] [0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1 0] [0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 3] [ <$.1 - 5, 1>, <$.1 - 3, 1>, <$.1 - 1, 2>, <$.1 + 1, 4>, <$.1^2 - 6*$.1 + 7, 1>, <$.1^2 + 2*$.1 - 1, 1> ] Time: 0.010 [ <$.1 - 2, 3>, <$.1 - 1, 6>, <$.1 + 1, 3>, <$.1^2 - $.1 + 2, 1>, <$.1^2 + 2*$.1 + 2, 2>, <$.1^4 - 2*$.1^3 + 3*$.1^2 - 4*$.1 + 4, 1> ] Time: 0.020 Total time: 12.500 seconds, Total memory usage: 4.63MB ************** MAGMA ***************** Host bluenote.ccrwest.org. (192.203.205.129) Time: Wed Jan 21 18:23:29 2004 Input: time S := SupersingularModule(5,22); S; time T2s := HeckeOperator(S,11); T2s; time M := ModularForms(5*22); time T2m := HeckeOperator(M,11); T2m; time Factorization(CharacteristicPolynomial(T2s)); time Factorization(CharacteristicPolynomial(T2m)); Output: Magma V2.10-6 Wed Jan 21 2004 18:23:08 on modular [Seed = 2050307042] ------------------------------------- Time: 0.010 Supersingular module associated to X_0(22)/GF(5) of dimension 12 Time: 0.020 [2 1 2 2 2 2 2 2 2 2 2 2] [1 2 2 2 2 2 2 2 2 2 2 2] [2 2 2 2 2 1 2 2 2 2 2 2] [2 2 2 2 1 2 2 2 2 2 2 2] [2 2 2 1 2 2 2 2 2 2 2 2] [2 2 1 2 2 2 2 2 2 2 2 2] [2 2 2 2 2 2 2 2 2 1 2 2] [2 2 2 2 2 2 2 2 1 2 2 2] [2 2 2 2 2 2 2 1 2 2 2 2] [2 2 2 2 2 2 1 2 2 2 2 2] [2 2 2 2 2 2 2 2 2 2 2 1] [2 2 2 2 2 2 2 2 2 2 1 2] Time: 0.020 Time: 11.320 [1 0 0 0 0 24 0 0 0 0 24 0 0 0 0 96 0 0 0 0 24 0] [0 0 0 -1 1 -5 0 0 1 1 -4 0 3 -3 3 -22 2 0 3 0 -3 3] [0 0 0 -1 -2 14 0 -4 4 -10 13 -5 -4 -5 -8 65 4 -13 -1 -12 12 -7] [0 0 0 0 1 -2 2 0 3 0 -2 -1 5 -1 3 -10 8 0 5 -2 -1 5] [0 0 0 1 2 -7 1 4 -1 9 -7 5 5 5 8 -35 2 12 7 11 -6 9] [0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0] [0 0 0 1 1 -4 1 2 -1 6 -4 3 4 3 6 -21 1 7 4 8 -3 6] [0 0 0 -1 0 4 0 -3 3 -8 4 -5 1 -5 -3 20 5 -10 -1 -10 4 -3] [0 0 0 0 1 -4 0 0 1 2 -4 0 4 0 4 -20 3 2 2 2 -3 4] [0 0 0 -1 -1 8 0 -4 3 -9 8 -5 -1 -5 -5 38 4 -10 -1 -12 7 -5] [0 0 0 0 0 -4 0 0 0 0 -3 0 0 0 0 -16 0 0 0 0 -4 0] [0 1 0 4 -2 9 0 8 -6 13 8 12 -8 14 0 36 -14 18 0 20 6 0] [0 0 0 0 0 -1 0 1 -1 2 -1 1 1 1 1 -6 -1 3 0 2 -1 1] [0 0 0 0 -1 5 0 -1 1 -4 5 -1 -3 0 -4 25 -1 -4 -1 -4 4 -4] [0 0 0 -1 0 9 1 -4 5 -9 9 -5 1 -5 -3 43 7 -12 1 -11 9 -3] [0 0 0 0 0 4 0 0 0 0 4 0 0 0 0 17 0 0 0 0 4 0] [0 0 0 1 -1 3 -1 2 -3 3 3 3 -5 3 -2 13 -7 4 -3 5 2 -3] [0 0 0 1 1 -7 0 3 -2 8 -7 4 2 4 5 -33 -2 9 2 10 -6 5] [0 0 0 -1 0 0 0 -2 1 -4 0 -3 0 -3 -2 1 2 -5 -1 -6 0 -2] [0 0 0 1 0 -9 -1 4 -5 9 -9 5 -2 5 3 -42 -8 11 -2 12 -9 2] [0 0 0 0 0 -2 0 0 0 0 -2 0 0 0 0 -8 0 0 0 0 -1 0] [0 0 1 0 3 -4 4 0 7 0 -3 0 12 0 8 -16 15 0 13 0 -1 12] [ <$.1 - 23, 1>, <$.1 - 1, 6>, <$.1 + 1, 5> ] Time: 0.000 [ <$.1 - 11, 3>, <$.1 - 1, 14>, <$.1 + 1, 5> ] Time: 0.010 Total time: 20.600 seconds, Total memory usage: 10.03MB ************** MAGMA ***************** Host bluenote.ccrwest.org. (192.203.205.129) Time: Wed Jan 21 18:24:17 2004 Input: time S := SupersingularModule(5,22); S; time T2s := HeckeOperator(S,11); T2s; time M := ModularForms(5*22); time T2m := HeckeOperator(M,11); T2m; time Factorization(CharacteristicPolynomial(T2s)); time Factorization(CharacteristicPolynomial(T2m)); Output: Magma V2.10-6 Wed Jan 21 2004 18:23:57 on modular [Seed = 239158343] ------------------------------------- Time: 0.010 Supersingular module associated to X_0(22)/GF(5) of dimension 12 Time: 0.020 [2 1 2 2 2 2 2 2 2 2 2 2] [1 2 2 2 2 2 2 2 2 2 2 2] [2 2 2 1 2 2 2 2 2 2 2 2] [2 2 1 2 2 2 2 2 2 2 2 2] [2 2 2 2 2 1 2 2 2 2 2 2] [2 2 2 2 1 2 2 2 2 2 2 2] [2 2 2 2 2 2 2 2 2 1 2 2] [2 2 2 2 2 2 2 2 1 2 2 2] [2 2 2 2 2 2 2 1 2 2 2 2] [2 2 2 2 2 2 1 2 2 2 2 2] [2 2 2 2 2 2 2 2 2 2 2 1] [2 2 2 2 2 2 2 2 2 2 1 2] Time: 0.020 Time: 11.100 [1 0 0 0 0 24 0 0 0 0 24 0 0 0 0 96 0 0 0 0 24 0] [0 0 0 -1 1 -5 0 0 1 1 -4 0 3 -3 3 -22 2 0 3 0 -3 3] [0 0 0 -1 -2 14 0 -4 4 -10 13 -5 -4 -5 -8 65 4 -13 -1 -12 12 -7] [0 0 0 0 1 -2 2 0 3 0 -2 -1 5 -1 3 -10 8 0 5 -2 -1 5] [0 0 0 1 2 -7 1 4 -1 9 -7 5 5 5 8 -35 2 12 7 11 -6 9] [0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0] [0 0 0 1 1 -4 1 2 -1 6 -4 3 4 3 6 -21 1 7 4 8 -3 6] [0 0 0 -1 0 4 0 -3 3 -8 4 -5 1 -5 -3 20 5 -10 -1 -10 4 -3] [0 0 0 0 1 -4 0 0 1 2 -4 0 4 0 4 -20 3 2 2 2 -3 4] [0 0 0 -1 -1 8 0 -4 3 -9 8 -5 -1 -5 -5 38 4 -10 -1 -12 7 -5] [0 0 0 0 0 -4 0 0 0 0 -3 0 0 0 0 -16 0 0 0 0 -4 0] [0 1 0 4 -2 9 0 8 -6 13 8 12 -8 14 0 36 -14 18 0 20 6 0] [0 0 0 0 0 -1 0 1 -1 2 -1 1 1 1 1 -6 -1 3 0 2 -1 1] [0 0 0 0 -1 5 0 -1 1 -4 5 -1 -3 0 -4 25 -1 -4 -1 -4 4 -4] [0 0 0 -1 0 9 1 -4 5 -9 9 -5 1 -5 -3 43 7 -12 1 -11 9 -3] [0 0 0 0 0 4 0 0 0 0 4 0 0 0 0 17 0 0 0 0 4 0] [0 0 0 1 -1 3 -1 2 -3 3 3 3 -5 3 -2 13 -7 4 -3 5 2 -3] [0 0 0 1 1 -7 0 3 -2 8 -7 4 2 4 5 -33 -2 9 2 10 -6 5] [0 0 0 -1 0 0 0 -2 1 -4 0 -3 0 -3 -2 1 2 -5 -1 -6 0 -2] [0 0 0 1 0 -9 -1 4 -5 9 -9 5 -2 5 3 -42 -8 11 -2 12 -9 2] [0 0 0 0 0 -2 0 0 0 0 -2 0 0 0 0 -8 0 0 0 0 -1 0] [0 0 1 0 3 -4 4 0 7 0 -3 0 12 0 8 -16 15 0 13 0 -1 12] [ <$.1 - 23, 1>, <$.1 - 1, 6>, <$.1 + 1, 5> ] Time: 0.000 [ <$.1 - 11, 3>, <$.1 - 1, 14>, <$.1 + 1, 5> ] Time: 0.010 Total time: 20.289 seconds, Total memory usage: 10.04MB ************** MAGMA ***************** Host bluenote.ccrwest.org. (192.203.205.129) Time: Wed Jan 21 18:24:45 2004 Input: time S := SupersingularModule(5,30); S; time T2s := HeckeOperator(S,11); T2s; time M := ModularForms(5*22); time T2m := HeckeOperator(M,11); T2m; time Factorization(CharacteristicPolynomial(T2s)); time Factorization(CharacteristicPolynomial(T2m)); Output: Magma V2.10-6 Wed Jan 21 2004 18:24:30 on modular [Seed = 291396475] ------------------------------------- >> time S := SupersingularModule(5,30); S; ^ Runtime error in 'SupersingularModule': Arguments 1 and 2 must be coprime. >> time S := SupersingularModule(5,30); S; ^ User error: Identifier 'S' has not been declared or assigned >> time T2s := HeckeOperator(S,11); T2s; ^ User error: Identifier 'S' has not been declared or assigned >> time T2s := HeckeOperator(S,11); T2s; ^ User error: Identifier 'T2s' has not been declared or assigned Time: 0.020 Time: 11.670 [1 0 0 0 0 24 0 0 0 0 24 0 0 0 0 96 0 0 0 0 24 0] [0 0 0 -1 1 -5 0 0 1 1 -4 0 3 -3 3 -22 2 0 3 0 -3 3] [0 0 0 -1 -2 14 0 -4 4 -10 13 -5 -4 -5 -8 65 4 -13 -1 -12 12 -7] [0 0 0 0 1 -2 2 0 3 0 -2 -1 5 -1 3 -10 8 0 5 -2 -1 5] [0 0 0 1 2 -7 1 4 -1 9 -7 5 5 5 8 -35 2 12 7 11 -6 9] [0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0] [0 0 0 1 1 -4 1 2 -1 6 -4 3 4 3 6 -21 1 7 4 8 -3 6] [0 0 0 -1 0 4 0 -3 3 -8 4 -5 1 -5 -3 20 5 -10 -1 -10 4 -3] [0 0 0 0 1 -4 0 0 1 2 -4 0 4 0 4 -20 3 2 2 2 -3 4] [0 0 0 -1 -1 8 0 -4 3 -9 8 -5 -1 -5 -5 38 4 -10 -1 -12 7 -5] [0 0 0 0 0 -4 0 0 0 0 -3 0 0 0 0 -16 0 0 0 0 -4 0] [0 1 0 4 -2 9 0 8 -6 13 8 12 -8 14 0 36 -14 18 0 20 6 0] [0 0 0 0 0 -1 0 1 -1 2 -1 1 1 1 1 -6 -1 3 0 2 -1 1] [0 0 0 0 -1 5 0 -1 1 -4 5 -1 -3 0 -4 25 -1 -4 -1 -4 4 -4] [0 0 0 -1 0 9 1 -4 5 -9 9 -5 1 -5 -3 43 7 -12 1 -11 9 -3] [0 0 0 0 0 4 0 0 0 0 4 0 0 0 0 17 0 0 0 0 4 0] [0 0 0 1 -1 3 -1 2 -3 3 3 3 -5 3 -2 13 -7 4 -3 5 2 -3] [0 0 0 1 1 -7 0 3 -2 8 -7 4 2 4 5 -33 -2 9 2 10 -6 5] [0 0 0 -1 0 0 0 -2 1 -4 0 -3 0 -3 -2 1 2 -5 -1 -6 0 -2] [0 0 0 1 0 -9 -1 4 -5 9 -9 5 -2 5 3 -42 -8 11 -2 12 -9 2] [0 0 0 0 0 -2 0 0 0 0 -2 0 0 0 0 -8 0 0 0 0 -1 0] [0 0 1 0 3 -4 4 0 7 0 -3 0 12 0 8 -16 15 0 13 0 -1 12] >> time Factorization(CharacteristicPolynomial(T2s)); ^ User error: Identifier 'T2s' has not been declared or assigned [ <$.1 - 11, 3>, <$.1 - 1, 14>, <$.1 + 1, 5> ] Time: 0.000 Total time: 14.750 seconds, Total memory usage: 9.40MB ************** MAGMA ***************** Host bluenote.ccrwest.org. (192.203.205.129) Time: Wed Jan 21 18:25:35 2004 Input: time S := SupersingularModule(3,35); S; time T2s := HeckeOperator(S,11); T2s; time M := ModularForms(5*22); time T2m := HeckeOperator(M,11); T2m; time Factorization(CharacteristicPolynomial(T2s)); time Factorization(CharacteristicPolynomial(T2m)); Output: Magma V2.10-6 Wed Jan 21 2004 18:25:15 on modular [Seed = 847083565] ------------------------------------- Time: 0.010 Supersingular module associated to X_0(35)/GF(3) of dimension 8 Time: 0.010 [2 2 4 0 0 0 2 2] [2 2 0 4 2 2 0 0] [4 0 2 2 0 0 2 2] [0 4 2 2 2 2 0 0] [0 2 0 2 2 2 4 0] [0 2 0 2 2 2 0 4] [2 0 2 0 4 0 2 2] [2 0 2 0 0 4 2 2] Time: 0.020 Time: 11.410 [1 0 0 0 0 24 0 0 0 0 24 0 0 0 0 96 0 0 0 0 24 0] [0 0 0 -1 1 -5 0 0 1 1 -4 0 3 -3 3 -22 2 0 3 0 -3 3] [0 0 0 -1 -2 14 0 -4 4 -10 13 -5 -4 -5 -8 65 4 -13 -1 -12 12 -7] [0 0 0 0 1 -2 2 0 3 0 -2 -1 5 -1 3 -10 8 0 5 -2 -1 5] [0 0 0 1 2 -7 1 4 -1 9 -7 5 5 5 8 -35 2 12 7 11 -6 9] [0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0] [0 0 0 1 1 -4 1 2 -1 6 -4 3 4 3 6 -21 1 7 4 8 -3 6] [0 0 0 -1 0 4 0 -3 3 -8 4 -5 1 -5 -3 20 5 -10 -1 -10 4 -3] [0 0 0 0 1 -4 0 0 1 2 -4 0 4 0 4 -20 3 2 2 2 -3 4] [0 0 0 -1 -1 8 0 -4 3 -9 8 -5 -1 -5 -5 38 4 -10 -1 -12 7 -5] [0 0 0 0 0 -4 0 0 0 0 -3 0 0 0 0 -16 0 0 0 0 -4 0] [0 1 0 4 -2 9 0 8 -6 13 8 12 -8 14 0 36 -14 18 0 20 6 0] [0 0 0 0 0 -1 0 1 -1 2 -1 1 1 1 1 -6 -1 3 0 2 -1 1] [0 0 0 0 -1 5 0 -1 1 -4 5 -1 -3 0 -4 25 -1 -4 -1 -4 4 -4] [0 0 0 -1 0 9 1 -4 5 -9 9 -5 1 -5 -3 43 7 -12 1 -11 9 -3] [0 0 0 0 0 4 0 0 0 0 4 0 0 0 0 17 0 0 0 0 4 0] [0 0 0 1 -1 3 -1 2 -3 3 3 3 -5 3 -2 13 -7 4 -3 5 2 -3] [0 0 0 1 1 -7 0 3 -2 8 -7 4 2 4 5 -33 -2 9 2 10 -6 5] [0 0 0 -1 0 0 0 -2 1 -4 0 -3 0 -3 -2 1 2 -5 -1 -6 0 -2] [0 0 0 1 0 -9 -1 4 -5 9 -9 5 -2 5 3 -42 -8 11 -2 12 -9 2] [0 0 0 0 0 -2 0 0 0 0 -2 0 0 0 0 -8 0 0 0 0 -1 0] [0 0 1 0 3 -4 4 0 7 0 -3 0 12 0 8 -16 15 0 13 0 -1 12] [ <$.1 - 12, 1>, <$.1 - 4, 2>, <$.1, 1>, <$.1 + 4, 2>, <$.1^2 - 4*$.1 - 16, 1> ] Time: 0.010 [ <$.1 - 11, 3>, <$.1 - 1, 14>, <$.1 + 1, 5> ] Time: 0.000 Total time: 19.090 seconds, Total memory usage: 9.83MB ************** MAGMA ***************** Host bluenote.ccrwest.org. (192.203.205.129) Time: Wed Jan 21 18:27:59 2004 Input: p := 3; q1:= 5; q2:= 7; N := q1*q2; S := SupersingularModule(p,N); S; M := ModularForms(p*N); M; Ts := HeckeOperator(S,q2); Ts; Tm := HeckeOperator(M,q1); Tm; Factorization(CharacteristicPolynomial(Ts)); Factorization(CharacteristicPolynomial(Tm)); CharacteristicPolynomial(Ts) divides CharacteristicPolynomial(Tm); Output: Magma V2.10-6 Wed Jan 21 2004 18:27:46 on modular [Seed = 3397746812] ------------------------------------- Supersingular module associated to X_0(35)/GF(3) of dimension 8 Space of modular forms on Gamma_0(105) of weight 2 and dimension 20 over Integer Ring. [4 0 0 3 2 2 2 2] [0 4 3 0 2 2 2 2] [0 3 4 0 2 2 2 2] [3 0 0 4 2 2 2 2] [2 2 2 2 0 4 3 0] [2 2 2 2 4 0 0 3] [2 2 2 2 3 0 0 4] [2 2 2 2 0 3 4 0] [1 0 0 0 0 0 0 12 0 0 0 0 0 0 36 0 0 0 12 0] [0 0 0 0 -2 0 -1 -4 -3 0 -4 -4 0 -5 -10 -1 -7 6 -3 -2] [0 0 0 0 -1 0 -2 1 0 -2 0 2 -5 -1 5 -4 -2 -1 1 -2] [0 0 0 0 0 0 0 0 0 -1 0 0 2 0 0 1 0 0 -1 0] [0 0 0 0 -1 1 -1 -2 0 -2 -2 -2 0 0 -5 0 0 2 -2 2] [0 1 0 0 1 0 -3 4 6 -3 6 6 -6 2 15 -6 7 -8 3 6] [0 0 0 0 0 0 1 2 0 0 0 0 0 0 6 0 0 0 2 0] [0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0] [0 0 0 0 -1 0 -1 -2 1 -1 -1 -1 -1 -1 -5 -1 -1 1 -2 0] [0 0 0 0 0 0 1 1 0 2 0 0 3 0 3 2 0 0 1 0] [0 0 1 0 2 2 1 2 3 0 4 2 2 4 5 2 8 -3 2 10] [0 0 0 0 -2 -1 -2 -3 -2 -1 -4 -3 -3 -4 -8 -2 -6 4 -3 -6] [0 0 0 0 0 0 -1 1 0 -1 0 0 -2 0 3 -2 0 0 1 0] [0 0 0 0 -1 0 -1 -1 0 0 -2 -1 0 -2 -1 0 -3 1 -1 -2] [0 0 0 0 0 0 0 2 0 0 0 0 0 0 7 0 0 0 2 0] [0 0 0 1 0 0 3 -3 0 4 0 0 7 0 -9 6 0 0 -2 0] [0 0 0 0 1 0 0 1 1 0 2 2 -1 1 3 -1 3 -2 1 2] [0 0 0 0 -2 0 -2 -3 -1 -1 -4 -3 -2 -4 -7 -1 -5 4 -3 -4] [0 0 0 0 0 0 0 -2 0 0 0 0 0 0 -6 0 0 0 -1 0] [0 0 0 0 0 0 1 -1 -1 1 -1 -1 2 0 -4 2 -1 1 -1 -1] [ <$.1 - 15, 1>, <$.1 - 7, 1>, <$.1 - 1, 3>, <$.1 + 1, 2>, <$.1 + 7, 1> ] [ <$.1 - 5, 3>, <$.1 - 1, 11>, <$.1 + 1, 4>, <$.1^2 + 2*$.1 + 5, 1> ] >> CharacteristicPolynomial(Ts) divides CharacteristicPolynomial(Tm);; ^ User error: bad syntax Total time: 12.159 seconds, Total memory usage: 5.46MB ************** MAGMA ***************** Host bluenote.ccrwest.org. (192.203.205.129) Time: Wed Jan 21 18:29:21 2004 Input: p := 3; q1:= 5; q2:= 7; N := q1*q2; S := SupersingularModule(p,N); S; M := ModularForms(p*N); M; Ts := HeckeOperator(S,q1); Ts; Tm := HeckeOperator(M,q1); Tm; Factorization(CharacteristicPolynomial(Ts)); Factorization(CharacteristicPolynomial(Tm)); print "*****"; Ts := HeckeOperator(S,q2); Ts; Tm := HeckeOperator(M,q2); Tm; Factorization(CharacteristicPolynomial(Ts)); Factorization(CharacteristicPolynomial(Tm)); Output: Magma V2.10-6 Wed Jan 21 2004 18:29:06 on modular [Seed = 3734083032] ------------------------------------- Supersingular module associated to X_0(35)/GF(3) of dimension 8 Space of modular forms on Gamma_0(105) of weight 2 and dimension 20 over Integer Ring. [2 2 1 2 1 1 1 1] [2 2 2 1 1 1 1 1] [1 2 2 2 1 1 1 1] [2 1 2 2 1 1 1 1] [1 1 1 1 0 3 4 0] [1 1 1 1 3 0 0 4] [1 1 1 1 4 0 0 3] [1 1 1 1 0 4 3 0] [1 0 0 0 0 0 0 12 0 0 0 0 0 0 36 0 0 0 12 0] [0 0 0 0 -2 0 -1 -4 -3 0 -4 -4 0 -5 -10 -1 -7 6 -3 -2] [0 0 0 0 -1 0 -2 1 0 -2 0 2 -5 -1 5 -4 -2 -1 1 -2] [0 0 0 0 0 0 0 0 0 -1 0 0 2 0 0 1 0 0 -1 0] [0 0 0 0 -1 1 -1 -2 0 -2 -2 -2 0 0 -5 0 0 2 -2 2] [0 1 0 0 1 0 -3 4 6 -3 6 6 -6 2 15 -6 7 -8 3 6] [0 0 0 0 0 0 1 2 0 0 0 0 0 0 6 0 0 0 2 0] [0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0] [0 0 0 0 -1 0 -1 -2 1 -1 -1 -1 -1 -1 -5 -1 -1 1 -2 0] [0 0 0 0 0 0 1 1 0 2 0 0 3 0 3 2 0 0 1 0] [0 0 1 0 2 2 1 2 3 0 4 2 2 4 5 2 8 -3 2 10] [0 0 0 0 -2 -1 -2 -3 -2 -1 -4 -3 -3 -4 -8 -2 -6 4 -3 -6] [0 0 0 0 0 0 -1 1 0 -1 0 0 -2 0 3 -2 0 0 1 0] [0 0 0 0 -1 0 -1 -1 0 0 -2 -1 0 -2 -1 0 -3 1 -1 -2] [0 0 0 0 0 0 0 2 0 0 0 0 0 0 7 0 0 0 2 0] [0 0 0 1 0 0 3 -3 0 4 0 0 7 0 -9 6 0 0 -2 0] [0 0 0 0 1 0 0 1 1 0 2 2 -1 1 3 -1 3 -2 1 2] [0 0 0 0 -2 0 -2 -3 -1 -1 -4 -3 -2 -4 -7 -1 -5 4 -3 -4] [0 0 0 0 0 0 0 -2 0 0 0 0 0 0 -6 0 0 0 -1 0] [0 0 0 0 0 0 1 -1 -1 1 -1 -1 2 0 -4 2 -1 1 -1 -1] [ <$.1 - 11, 1>, <$.1 - 3, 1>, <$.1 - 1, 3>, <$.1 + 1, 2>, <$.1 + 7, 1> ] [ <$.1 - 5, 3>, <$.1 - 1, 11>, <$.1 + 1, 4>, <$.1^2 + 2*$.1 + 5, 1> ] ***** [4 0 0 3 2 2 2 2] [0 4 3 0 2 2 2 2] [0 3 4 0 2 2 2 2] [3 0 0 4 2 2 2 2] [2 2 2 2 0 4 0 3] [2 2 2 2 4 0 3 0] [2 2 2 2 0 3 0 4] [2 2 2 2 3 0 4 0] [1 0 0 0 0 12 0 0 0 0 36 0 0 0 0 12 0 0 0 0] [0 0 0 0 0 -4 0 -2 -3 -1 -10 1 -4 -1 0 -3 -1 1 1 -7] [0 0 0 0 0 1 -2 0 -3 -2 5 0 -4 -2 -3 1 -2 1 -5 -6] [0 0 0 0 0 0 0 0 0 1 0 0 -2 0 0 -1 0 0 1 0] [0 0 0 0 1 -2 0 -1 0 1 -5 3 -2 0 1 -2 0 -3 2 -3] [0 0 0 0 0 4 0 0 0 0 15 0 0 0 0 3 0 0 0 0] [0 0 0 0 0 2 -1 0 0 0 6 0 0 0 0 2 0 0 -2 0] [0 1 0 0 1 1 3 2 6 3 0 0 6 2 6 0 7 -2 6 12] [0 0 0 0 1 -2 0 -1 -1 0 -5 2 -1 1 1 -2 1 -2 2 -1] [0 0 0 0 0 1 -1 0 0 -2 3 0 -3 0 0 1 0 0 -4 0] [0 0 0 0 0 2 0 0 0 0 5 0 0 0 0 2 0 0 0 0] [0 0 0 0 1 -3 0 0 -1 -1 -8 3 -2 1 1 -3 2 -2 0 0] [0 0 0 0 0 1 1 0 0 1 3 0 2 0 0 1 0 0 2 0] [0 0 0 0 1 -1 -1 0 0 -2 -1 3 -4 2 2 -1 3 -3 -2 0] [0 0 1 0 2 2 -1 2 3 -2 7 4 -2 4 6 2 8 -5 -2 8] [0 0 0 0 0 -3 0 0 0 0 -9 0 0 0 0 -2 0 0 0 0] [0 0 0 0 -1 1 0 0 -1 0 3 -2 1 -1 -3 1 -3 2 -1 -2] [0 0 0 0 1 -3 -1 -1 -2 -2 -7 4 -5 1 1 -3 1 -3 -1 -3] [0 0 0 1 0 -2 3 0 0 4 -6 0 7 0 0 -1 0 0 8 0] [0 0 0 0 0 -1 0 0 1 0 -4 0 0 0 1 -1 1 0 0 2] [ <$.1 - 15, 1>, <$.1 - 7, 1>, <$.1 - 1, 3>, <$.1 + 1, 2>, <$.1 + 7, 1> ] [ <$.1 - 7, 3>, <$.1 - 1, 9>, <$.1 + 1, 6>, <$.1^2 + 7, 1> ] Total time: 15.050 seconds, Total memory usage: 6.34MB ************** MAGMA ***************** Host bluenote.ccrwest.org. (192.203.205.129) Time: Wed Jan 21 18:35:36 2004 Input: p := 3; q1:= 5; q2:= 7; N := q1*q2; S := CuspidalSubspace(SupersingularModule(p,N)); S; M := CuspidalSubspace(ModularForms(p*N)); M; Ts := HeckeOperator(S,q1); Ts; Tm := HeckeOperator(M,q1); Tm; Factorization(CharacteristicPolynomial(Ts)); Factorization(CharacteristicPolynomial(Tm)); print "*****"; Ts := HeckeOperator(S,q2); Ts; Tm := HeckeOperator(M,q2); Tm; Factorization(CharacteristicPolynomial(Ts)); Factorization(CharacteristicPolynomial(Tm)); Output: Magma V2.10-6 Wed Jan 21 2004 18:35:23 on modular [Seed = 4156078856] ------------------------------------- Supersingular module associated to X_0(35)/GF(3) of dimension 7 Space of modular forms on Gamma_0(105) of weight 2 and dimension 13 over Integer Ring. >> Ts := HeckeOperator(S,q1); Ts; ^ Runtime error in 'HeckeOperator': Argument 2 must be coprime to the level of argument 1. >> Ts := HeckeOperator(S,q1); Ts; ^ User error: Identifier 'Ts' has not been declared or assigned [ 0 0 2 -3 0 -3 -4 6 3 1 4 4 -4] [ 0 0 2 -3 0 -2 -3 5 2 1 5 2 -3] [ 0 0 0 0 0 0 0 0 -1 0 0 2 0] [ 0 0 0 -1 1 -1 -1 2 -1 -1 0 3 0] [ 1 0 -1 0 0 -1 0 2 -1 0 1 1 -1] [ 0 0 2 -3 0 -2 -3 6 2 0 3 2 -3] [ 0 0 0 0 0 0 1 0 0 0 0 0 0] [ 0 0 0 -1 0 -1 -1 3 0 0 1 2 -1] [ 0 0 1 -2 0 -2 -2 4 2 0 2 2 -2] [ 0 1 -2 1 2 0 1 -1 -2 -2 -3 2 1] [ 0 0 1 -1 -1 -1 -1 2 1 1 2 0 -1] [ 0 0 1 -1 0 -1 -1 2 1 0 1 1 -1] [ 0 0 1 -2 0 -3 -3 6 2 0 4 3 -3] >> Factorization(CharacteristicPolynomial(Ts)); ^ User error: Identifier 'Ts' has not been declared or assigned [ <$.1 - 1, 7>, <$.1 + 1, 4>, <$.1^2 + 2*$.1 + 5, 1> ] ***** >> Ts := HeckeOperator(S,q2); Ts; ^ Runtime error in 'HeckeOperator': Argument 2 must be coprime to the level of argument 1. >> Ts := HeckeOperator(S,q2); Ts; ^ User error: Identifier 'Ts' has not been declared or assigned [ 0 0 1 3 -4 0 0 -6 -3 3 8 -7 4] [ 0 0 1 3 -3 -1 1 -5 -2 2 7 -5 3] [ 0 0 0 0 0 0 0 0 1 0 0 -2 0] [ 0 -1 0 1 -1 0 -1 1 1 0 2 -3 0] [ 0 -2 0 -1 0 1 -2 4 2 -1 -3 0 -1] [ 0 0 1 3 -3 -1 0 -6 -2 3 9 -5 3] [ 1 -1 -1 -1 1 1 0 3 1 -1 -4 1 -2] [ 0 -1 0 1 -1 0 -1 0 0 0 1 -2 1] [ 0 0 1 2 -2 0 0 -4 -2 2 6 -4 2] [ 0 -2 0 -1 1 1 -2 4 2 -2 -3 0 -1] [ 0 0 0 1 -1 0 1 -2 -1 1 2 -1 1] [ 0 0 0 1 -1 0 0 -2 -1 1 3 -2 1] [ 0 -1 1 2 -3 0 0 -3 -2 2 6 -5 3] >> Factorization(CharacteristicPolynomial(Ts)); ^ User error: Identifier 'Ts' has not been declared or assigned [ <$.1 - 1, 5>, <$.1 + 1, 6>, <$.1^2 + 7, 1> ] Total time: 12.689 seconds, Total memory usage: 5.70MB ************** MAGMA ***************** Host h24-81-108-53.vc.shawcable.net. (24.81.108.53) Time: Wed Jan 21 23:50:50 2004 Input: E:=EllipticCurve[0,4]; S:=TorsionSubgroupScheme(E, 2); IsogenyFromKernel(S); Output: Magma V2.10-6 Wed Jan 21 2004 23:50:47 on modular [Seed = 189013483] ------------------------------------- >> E:=EllipticCurve[0,4]; ^ Runtime error in '[]': Bad argument types >> S:=TorsionSubgroupScheme(E, 2); ^ User error: Identifier 'E' has not been declared or assigned >> IsogenyFromKernel(S);; ^ User error: Identifier 'S' has not been declared or assigned Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host h24-81-108-53.vc.shawcable.net. (24.81.108.53) Time: Wed Jan 21 23:51:01 2004 Input: E:=EllipticCurve([0,4]); S:=TorsionSubgroupScheme(E, 2); IsogenyFromKernel(S); Output: Magma V2.10-6 Wed Jan 21 2004 23:50:58 on modular [Seed = 308085991] ------------------------------------- Elliptic Curve defined by y^2 = x^3 + 256 over Rational Field Elliptic curve isogeny from: CrvEll: E to Elliptic Curve defined by y^2 = x^3 + 256 over Rational Field taking (x : y : 1) to ((x^4 - 32*x) / (x^3 + 4) : (x^6*y + 80*x^3*y - 128*y) / (x^6 + 8*x^3 + 16) : 1) Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host h24-81-108-53.vc.shawcable.net. (24.81.108.53) Time: Wed Jan 21 23:51:40 2004 Input: E:=EllipticCurve([0,27]); S:=TorsionSubgroupScheme(E, 3); IsogenyFromKernel(S); Output: Magma V2.10-6 Wed Jan 21 2004 23:51:37 on modular [Seed = 408358534] ------------------------------------- Elliptic Curve defined by y^2 = x^3 + 19683 over Rational Field Elliptic curve isogeny from: CrvEll: E to Elliptic Curve defined by y^2 = x^3 + 19683 over Rational Field taking (x : y : 1) to ((x^9 - 2592*x^6 + 34992*x^3 + 1259712) / (x^8 + 216*x^5 + 11664*x^2) : (x^12*y + 5940*x^9*y - 1294704*x^6*y - 6298560*x^3*y - 272097792*y) / (x^12 + 324*x^9 + 34992*x^6 + 1259712*x^3) : 1) Total time: 2.909 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host h24-81-108-53.vc.shawcable.net. (24.81.108.53) Time: Wed Jan 21 23:52:57 2004 Input: E:=EllipticCurve([-4,16]); S:=TorsionSubgroupScheme(E, 5); IsogenyFromKernel(S); Output: Magma V2.10-6 Wed Jan 21 2004 23:52:54 on modular [Seed = 544159553] ------------------------------------- Elliptic Curve defined by y^2 = x^3 - 2500*x + 250000 over Rational Field Elliptic curve isogeny from: CrvEll: E to Elliptic Curve defined by y^2 = x^3 - 2500*x + 250000 over Rational Field taking (x : y : 1) to ((x^25 + 400*x^23 - 33280*x^22 + 36000*x^21 - 298496*x^20 + 12120320*x^19 + 7393280*x^18 - 297539840*x^17 + 1336483840*x^16 + 4716634112*x^15 - 52722401280*x^14 + 177576263680*x^13 + 277480734720*x^12 - 2064378101760*x^11 + 3096258281472*x^10 + 7705739591680*x^9 - 31978191585280*x^8 + 34893762396160*x^7 + 83362798632960*x^6 - 281565462528000*x^5 + 441278529536000*x^4 - 540066552217600*x^3 + 1189471059968000*x^2 - 1402682212352000*x + 129998459502592) / (x^24 - 496/5*x^22 + 2432*x^21 + 44704/25*x^20 - 633856/5*x^19 + 7475456/5*x^18 - 583680*x^17 - 28732672/5*x^16 - 438370304/25*x^15 - 551477248/5*x^14 + 5745082368/5*x^13 - 15527329792/5*x^12 - 7789346816/5*x^11 + 200882126848/25*x^10 - 69060263936/5*x^9 + 1174127968256/5*x^8 - 5010700107776/5*x^7 + 7212035473408/5*x^6 + 56827643428864/25*x^5 - 38480824500224/5*x^4 + 38307148857344/5*x^3 + 26362324713472/5*x^2 - 65490332418048/5*x + 264024541364224/25) : (x^36*y - 648*x^34*y + 75072*x^33*y - 170544*x^32*y + 6893568*x^31*y - 225311744*x^30*y + 142467072*x^29*y + 2684818432*x^28*y + 7008485376*x^27*y - 79627935744*x^26*y + 780136022016*x^25*y - 3766454894592*x^24*y - 39701978284032*x^23*y + 404262315884544*x^22*y - 1204462842544128*x^21*y - 4485758948868096*x^20*y + 29375645129637888*x^19*y - 26574146698739712*x^18*y - 326355693953089536*x^17*y + 1369504577772060672*x^16*y - 1286631249376444416*x^15*y - 8056450180712497152*x^14*y + 26676238718639013888*x^13*y - 19999305965634584576*x^12*y - 68786488400595124224*x^11*y + 167781483738881327104*x^10*y - 81611016878208057344*x^9*y - 217583008330561880064*x^8*y + 15131552757451849728*x^7*y + 2331876398517083701248*x^6*y - 8622123317308604547072*x^5*y + 16255701526795553603584*x^4*y - 15861203559382175973376*x^3*y + 5490595286299434811392*x^2*y - 4807365877147921022976*x*y + 4034435412498539610112*y) / (x^36 - 744/5*x^34 + 3648*x^33 + 159312/25*x^32 - 1855488/5*x^31 + 548574208/125*x^30 + 183263232/25*x^29 - 6022597632/25*x^28 + 46206091264/25*x^27 - 19706535936/25*x^26 - 910931853312/125*x^25 - 25787154432*x^24 - 1347375071232/5*x^23 + 61671070236672/25*x^22 - 5548718161920*x^21 - 624387286499328/125*x^20 + 448242533793792/25*x^19 - 1613925467553792/25*x^18 + 5110549431975936/5*x^17 - 100781082066026496/25*x^16 + 516505410006417408/125*x^15 + 315768118859268096/25*x^14 - 1007336799376244736/25*x^13 + 3559026639541108736/25*x^12 - 17755787932905504768/25*x^11 + 212449609090804482048/125*x^10 - 1805705616761552896/25*x^9 - 231288084861397499904/25*x^8 + 92775912160911949824/5*x^7 - 154294733752512806912/25*x^6 - 4573961417274553270272/125*x^5 + 1512653336390613860352/25*x^4 - 637525381807846981632/25*x^3 - 1137453779021060898816/25*x^2 + 1596212113627523579904/25*x - 4290090416504326586368/125) : 1) Total time: 2.979 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host h24-81-108-53.vc.shawcable.net. (24.81.108.53) Time: Wed Jan 21 23:57:15 2004 Input: E:=EllipticCurve([-3,62]); TorsionSubgroup(E); Output: Magma V2.10-6 Wed Jan 21 2004 23:57:12 on modular [Seed = 1014178899] ------------------------------------- Abelian Group of order 1 Total time: 2.939 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host h24-81-108-53.vc.shawcable.net. (24.81.108.53) Time: Thu Jan 22 00:01:24 2004 Input: E:=EllipticCurve([-3,62]); TorsionSubgroup(E); P:=PolynomialRing(RationalField()); K:=NumberField(x^3-3*x^2+1); BaseChange(E,K); TorsionSubgroup(E); Output: Magma V2.10-6 Thu Jan 22 2004 00:01:21 on modular [Seed = 4172800414] ------------------------------------- Abelian Group of order 1 Elliptic Curve defined by y^2 = x^3 - 3*x + 62 over K Abelian Group of order 1 Total time: 2.939 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host h24-81-108-53.vc.shawcable.net. (24.81.108.53) Time: Thu Jan 22 00:02:02 2004 Input: E:=EllipticCurve([0,7]); TorsionSubgroup(E); P:=PolynomialRing(RationalField()); K:=NumberField(x^3-7); BaseChange(E,K); TorsionSubgroup(E); Output: Magma V2.10-6 Thu Jan 22 2004 00:01:59 on modular [Seed = 2161088896] ------------------------------------- Abelian Group of order 1 Elliptic Curve defined by y^2 = x^3 + 7 over K Abelian Group of order 1 Total time: 2.939 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host h24-81-108-53.vc.shawcable.net. (24.81.108.53) Time: Thu Jan 22 00:02:38 2004 Input: E:=EllipticCurve([0,7]); TorsionSubgroup(E); P:=PolynomialRing(RationalField()); K:=NumberField(x^3+7); BaseChange(E,K); TorsionSubgroup(E); Output: Magma V2.10-6 Thu Jan 22 2004 00:02:35 on modular [Seed = 2294780324] ------------------------------------- Abelian Group of order 1 Elliptic Curve defined by y^2 = x^3 + 7 over K Abelian Group of order 1 Total time: 2.959 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host h24-81-108-53.vc.shawcable.net. (24.81.108.53) Time: Thu Jan 22 00:04:07 2004 Input: E:=EllipticCurve([0,7]); TorsionSubgroup(E); P:=PolynomialRing(RationalField()); K:=NumberField(x^2-7); BaseChange(E,K); TorsionSubgroup(E); Output: Magma V2.10-6 Thu Jan 22 2004 00:04:04 on modular [Seed = 2681243164] ------------------------------------- Abelian Group of order 1 Elliptic Curve defined by y^2 = x^3 + 7 over K Abelian Group of order 1 Total time: 3.009 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host h24-81-108-53.vc.shawcable.net. (24.81.108.53) Time: Thu Jan 22 00:04:42 2004 Input: E:=EllipticCurve([0,7]); TorsionSubgroup(E); P:=PolynomialRing(RationalField()); K:=QuadraticField(7); BaseChange(E,K); TorsionSubgroup(E); Output: Magma V2.10-6 Thu Jan 22 2004 00:04:39 on modular [Seed = 2817048071] ------------------------------------- Abelian Group of order 1 Elliptic Curve defined by y^2 = x^3 + 7 over K Abelian Group of order 1 Total time: 2.999 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host h24-81-108-53.vc.shawcable.net. (24.81.108.53) Time: Thu Jan 22 00:06:15 2004 Input: E:=EllipticCurve([0,7]); TorsionSubgroup(E); P:=PolynomialRing(RationalField()); K:=QuadraticField(7); E2:=BaseChange(E,K); TorsionSubgroup(E2); Output: Magma V2.10-6 Thu Jan 22 2004 00:06:11 on modular [Seed = 2883891624] ------------------------------------- Abelian Group of order 1 Abelian Group isomorphic to Z/3 Defined on 1 generator Relations: 3*$.1 = 0 Mapping from: Abelian Group isomorphic to Z/3 Defined on 1 generator Relations: 3*$.1 = 0 to CrvEll: E2 given by a rule [no inverse] Total time: 3.179 seconds, Total memory usage: 2.29MB ************** MAGMA ***************** Host h24-81-108-53.vc.shawcable.net. (24.81.108.53) Time: Thu Jan 22 00:07:05 2004 Input: E:=EllipticCurve([-3,62]); TorsionSubgroup(E); P:=PolynomialRing(RationalField()); K:=NumberField(x^3-3*x^2+1); E2:=BaseChange(E,K); TorsionSubgroup(E2); Output: Magma V2.10-6 Thu Jan 22 2004 00:07:01 on modular [Seed = 3019680129] ------------------------------------- Abelian Group of order 1 Abelian Group isomorphic to Z/7 Defined on 1 generator Relations: 7*$.1 = 0 Mapping from: Abelian Group isomorphic to Z/7 Defined on 1 generator Relations: 7*$.1 = 0 to CrvEll: E2 given by a rule [no inverse] Total time: 3.549 seconds, Total memory usage: 2.39MB ************** MAGMA ***************** Host h24-81-108-53.vc.shawcable.net. (24.81.108.53) Time: Thu Jan 22 00:08:57 2004 Input: E:=EllipticCurve([-3,62]); TorsionSubgroup(E); P:=PolynomialRing(RationalField()); K:=NumberField(x^3-3*x^2+1); E2:=BaseChange(E,K); G:=TorsionSubgroupScheme(E2, 7); IsogneyFromKernel(G); Output: Magma V2.10-6 Thu Jan 22 2004 00:08:54 on modular [Seed = 3136659483] ------------------------------------- Abelian Group of order 1 >> IsogneyFromKernel(G);; ^ User error: Identifier 'IsogneyFromKernel' has not been declared or assigned Total time: 2.979 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host h24-81-108-53.vc.shawcable.net. (24.81.108.53) Time: Thu Jan 22 00:09:17 2004 Input: E:=EllipticCurve([-3,62]); TorsionSubgroup(E); P:=PolynomialRing(RationalField()); K:=NumberField(x^3-3*x^2+1); E2:=BaseChange(E,K); G:=TorsionSubgroupScheme(E2, 7); IsogenyFromKernel(G); Output: Magma V2.10-6 Thu Jan 22 2004 00:09:14 on modular [Seed = 1291999231] ------------------------------------- Abelian Group of order 1 Elliptic Curve defined by y^2 = x^3 - 7203*x + 7294238 over K Elliptic curve isogeny from: CrvEll: E2 to Elliptic Curve defined by y^2 = x^3 - 7203*x + 7294238 over K taking (x : y : 1) to ((x^49 + 1176*x^47 - 972160*x^46 + 322308*x^45 - 44184672*x^44 + 11903170440*x^43 + 947135808*x^42 - 572457016782*x^41 + 27983913074656*x^40 + 26697365440200*x^39 - 3146769230545920*x^38 + 118855868832947540*x^37 + 26806777753353696*x^36 - 2330460924821715816*x^35 + 19761952740735412032*x^34 + 37278353633699308095*x^33 - 1207709206108978190688*x^32 + 18644070575465205572464*x^31 + 13839114826116625635072*x^30 - 384230344020130228559736*x^29 + 2897620653861889765444160*x^28 - 68473670657563786725936*x^27 + 21961130831743836673729152*x^26 - 444700526871186116177294340*x^25 - 1345290760664554849426403136*x^24 + 25501644510176793441173014800*x^23 - 183691849742947607089578651136*x^22 - 250093656475970312442940042680*x^21 + 3379807866711779436534301589952*x^20 - 16392398125383571185545003908688*x^19 - 14554465532985281426819834912640*x^18 + 142489066438554414176071928606607*x^17 - 471040274500893101323738816598208*x^16 + 41916773816371736165750719306104*x^15 - 1357037691645451394724955589324160*x^14 + 10344184138368368552120055553231220*x^13 + 28440942595788554019808864379604000*x^12 - 243689703808752302268732694663787736*x^11 + 856036733637364665499426983088422976*x^10 + 799841054321606069356114586706006258*x^9 - 5613867646827498667290811073442613920*x^8 + 14953172026995256569095508980420636328*x^7 + 22931351815260884895277368247196868096*x^6 - 145665682871979001674681011179962387612*x^5 + 412966632233158417219594002950567943776*x^4 + 94034153334835458592702418175215075640*x^3 - 587887508541747385643095647225707941824*x^2 + 1433243856070161096359031715880912566033*x - 14802352682262295701567495744891640800) / (x^48 - 264*x^46 + 489056/7*x^45 + 9828*x^44 - 64513728/7*x^43 + 57542086632/49*x^42 - 1966240224/7*x^41 + 58130394750/7*x^40 - 11864665735808/7*x^39 - 591863952024*x^38 + 515200325893152/7*x^37 - 10024539100639060/7*x^36 + 14469083036434368/49*x^35 - 199815852770109432/7*x^34 + 8216695696689835872/7*x^33 + 9807099632594542233/7*x^32 - 433028016010598616576/7*x^31 + 6063865296499490805328/7*x^30 + 4475872188484574837184/7*x^29 - 819912047292112486021176/49*x^28 + 805620217722340972248704/7*x^27 + 1067975136340132742439408/7*x^26 - 17657666522315373432616128/7*x^25 + 107767126399963569864355620/7*x^24 + 187444546542376022546419968/7*x^23 - 2597190224393022091234019280/7*x^22 + 96256311917532029775073628096/49*x^21 + 21143749443429276652000432824/7*x^20 - 236730076417796700150313454976/7*x^19 + 974956877252033466744243030928/7*x^18 + 1784550624698373845410367204544/7*x^17 - 17364069463895929023033803568471/7*x^16 + 66641463572177193336894096314880/7*x^15 + 933396768973694751883306587060696/49*x^14 - 1189526406295348575001002939404832/7*x^13 + 4387362565024056420102588595950668/7*x^12 + 4809089684437209402320836878719040/7*x^11 - 37798595996600766956232461414422344/7*x^10 + 121089370706766823564437382653960352/7*x^9 + 33231437265019248161722656954159678/7*x^8 - 33537077146970768381061245214259584*x^7 + 81961799449377961437561519590776008*x^6 - 101258314664322084018891288367868064*x^5 + 584645259222598153804250706191087748*x^4 - 1686297881626261932495159680348435776*x^3 + 281392737637663707533898441172169688*x^2 - 1408821466556824627466769987980308704*x + 203675229491944224207880989154534234081/49) : (x^72*y - 1836*x^70*y + 2188848*x^69*y - 1466802*x^68*y + 638825184*x^67*y - 195735089532*x^66*y + 50168722032*x^65*y + 2174462165601*x^64*y + 420473589285376*x^63*y - 568860814941408*x^62*y + 61307322287135616*x^61*y - 4752704315751921840*x^60*y - 7118106791619776256*x^59*y + 783705277335007962144*x^58*y - 27946359804901205420160*x^57*y - 16593985570867483412556*x^56*y + 1195966047893053528585728*x^55*y - 16664506550008717062397328*x^54*y - 43749721818538833426107328*x^53*y + 1786644044633653235951927688*x^52*y - 30437515019705257082744661888*x^51*y - 27358473403306743314180754384*x^50*y + 818409919235885650256598169920*x^49*y - 4441547059634217227973862573980*x^48*y - 8935031467838368610169683000832*x^47*y + 114459559986661323466604801274720*x^46*y - 496520227667101640797511793204608*x^45*y - 1886966313430563060118601612749776*x^44*y + 27719464230392184727056584614266624*x^43*y - 165045523654763275536743035316070048*x^42*y - 1538282624832815579602042861356230016*x^41*y + 25539148964698750240072027107688137006*x^40*y - 170071394615761051035031742736882719232*x^39*y - 782783939945793651308261853459138783432*x^38*y + 10681023178779278327818230816795491221536*x^37*y - 55476065081348948294731146814601807463212*x^36*y - 156528092896520261230047291890925349252800*x^35*y + 1648170467037732840955080536575866096758232*x^34*y - 6205982519965616971722951454953579780943968*x^33*y - 9767181609762272583388310277380579883162210*x^32*y + 65034467903982852594714130009435173992044032*x^31*y - 122786858269346395922868265452179340151515936*x^30*y + 922858021411669034088929140755812764291560576*x^29*y - 10014562841512820739757722924350814118551919824*x^28*y + 37341394204735816197476697116654377024715110144*x^27*y + 175035557863327385339608289566704231631269820896*x^26*y - 1327604493150068790664215360155441480731246346112*x^25*y + 3630299008045599994249206543235519708359643472580*x^24*y + 10362912085555841391480680594707884102850728276480*x^23*y - 64012766544074755173150763294262697103805101238544*x^22*y + 142629771371709974450951062654478912055403275209280*x^21*y + 291927427062425890738230362131239392854401625783944*x^20*y - 1505059743336838995280818840175920352615384521267072*x^19*y + 2737443394375708912811486566375076086669556415210928*x^18*y + 4956266260160717343100915431088471789630284206508864*x^17*y - 21984521322427539384852380839628579042633178743953452*x^16*y + 26617582173271059320526610105459615092568313575859712*x^15*y + 167130085998670141266936164776437397616007095737412256*x^14*y - 761998020303796401195167930948295339594002722069858944*x^13*y + 871697743584518002859400465542775998326294384221409872*x^12*y + 8850439492179825946690276642274523205635120083922084096*x^11*y - 40753964510677507928774012027156423312714660951369259360*x^10*y + 77755832465265665693583200461153475739335782779189745024*x^9*y + 112980321177708138889612139657357953789183405245303439449*x^8*y - 479662002094113553428294924881460054416805313064712506880*x^7*y + 814609836118303417826145560532761451679349410593205477524*x^6*y + 859617225100744532742646499339889023437459051177440572208*x^5*y - 3474243480868714925686361449324881263542395632592887016498*x^4*y + 6306167055809337204004814210180334169757251653552061885152*x^3*y + 368168040427996028168059786863596691481597420502770633668*x^2*y - 1899604272228849243647598374516771136451671220109843173008*x*y + 2911845048906783964453293477446155714014225397877172018121*y) / (x^72 - 396*x^70 + 733584/7*x^69 + 40878*x^68 - 193603680/7*x^67 + 175965042084/49*x^66 + 1005457968*x^65 - 22605822434511/49*x^64 + 12942342319822336/343*x^63 - 832302486933984/49*x^62 + 43206897651456384/49*x^61 - 4413180574282315440/49*x^60 - 1711590749504692992/49*x^59 + 191966917351033590048/49*x^58 - 2105647135752514593408/49*x^57 + 19771836959983108024620/343*x^56 - 220388321289077097177600/49*x^55 + 5870064618050264676897520/49*x^54 + 7312250090621746720187712/49*x^53 - 265074814534815422498061432/49*x^52 + 2284162170058161304083603072/49*x^51 - 1598752226731159707904649808/49*x^50 + 775902169377672792333548253120/343*x^49 - 311091069766921052270057698500/7*x^48 - 849382596081347521914029689344/7*x^47 + 3117763325222095677919006001760*x^46 - 1340374133042590765220199648363392/49*x^45 - 401322336023005447014864514423728/7*x^44 + 46867956540811741732437661209705216/49*x^43 - 1715745544759496611219117209855024480/343*x^42 - 737786158295236381783240826013295488/49*x^41 + 9008387778256312948694691828635561166/49*x^40 - 38832978691950561672854601654948131328/49*x^39 - 145663419106016669629251661072459696776/49*x^38 + 1502610689013535975643755177195547752608/49*x^37 - 5488951275341980463020955363526988571948/49*x^36 - 152106722340241925337832572134241283513920/343*x^35 + 188690488930357047678868589586939528305304/49*x^34 - 551827490621615296442345475315443812456416/49*x^33 - 2591192807248712343451339008302879461556994/49*x^32 + 19695304433506708916781661765326895757360640/49*x^31 - 50198017679382188575465847409125545584444960/49*x^30 - 265428227960796980185575712950210023857392000/49*x^29 + 12798994671660549435039176762894340722501804112/343*x^28 - 4218802101178413025261622753322885791694116096/49*x^27 - 21456720953177327152982649930040503150880314144/49*x^26 + 132841638023421694484729526801284502736942340736/49*x^25 - 38162822754907111135715561461085965903390671780/7*x^24 - 1403871780536812138693223645309785486758850598400/49*x^23 + 8023903749715782585396608869573404114953184303984/49*x^22 - 105318602420054027348094947863178004385262601410880/343*x^21 - 77095102342264934063648557796020292159710363478904/49*x^20 + 418382744102730161894409967732608656731 ** WARNING: Output too long, hence truncated. ************** MAGMA ***************** Host h24-81-108-53.vc.shawcable.net. (24.81.108.53) Time: Thu Jan 22 00:10:15 2004 Input: E:=EllipticCurve([-3,62]); TorsionSubgroup(E); P:=PolynomialRing(RationalField()); K:=NumberField(x^3-3*x^2+1); E2:=BaseChange(E,K); TorsionSubgroupScheme(E2, 7); Output: Magma V2.10-6 Thu Jan 22 2004 00:10:12 on modular [Seed = 1544767264] ------------------------------------- Abelian Group of order 1 Subgroup scheme of E2 defined by x^24 - 132*x^22 + 244528/7*x^21 - 3798*x^20 + 2976*x^19 - 23479460*x^18 - 7378992*x^17 + 941710599*x^16 - 28240934528*x^15 - 21269004408/7*x^14 + 217696617120*x^13 - 1955061444692*x^12 - 796544571456*x^11 + 20804996225112*x^10 - 200148360971744*x^9 - 134195225621985*x^8 + 2794653757461888*x^7 - 22669413664628276*x^6 - 4355232408254448*x^5 + 74051144317366986*x^4 - 406821347545608800*x^3 + 39734169977524428*x^2 - 345505446281792496*x + 14271483086629231759/7 Total time: 2.979 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host h24-81-108-53.vc.shawcable.net. (24.81.108.53) Time: Thu Jan 22 00:10:34 2004 Input: E:=EllipticCurve([-3,62]); TorsionSubgroup(E); P:=PolynomialRing(RationalField()); K:=NumberField(x^3-3*x^2+1); E2:=BaseChange(E,K); TorsionSubgroup(E2); Output: Magma V2.10-6 Thu Jan 22 2004 00:10:30 on modular [Seed = 1411075930] ------------------------------------- Abelian Group of order 1 Abelian Group isomorphic to Z/7 Defined on 1 generator Relations: 7*$.1 = 0 Mapping from: Abelian Group isomorphic to Z/7 Defined on 1 generator Relations: 7*$.1 = 0 to CrvEll: E2 given by a rule [no inverse] Total time: 3.629 seconds, Total memory usage: 2.39MB ************** MAGMA ***************** Host h24-81-108-53.vc.shawcable.net. (24.81.108.53) Time: Thu Jan 22 00:35:31 2004 Input: E:=EllipticCurve([-9747,-370386]); TorsionSubgroup(E); P:=PolynomialRing(RationalField()); K:=NumberField(x^3-6*x^2+3*x+1); E2:=BaseChange(E,K); TorsionSubgroup(E2); Output: Magma V2.10-6 Thu Jan 22 2004 00:35:28 on modular [Seed = 38609770] ------------------------------------- >> E:=EllipticCurve([-9747,-370386]); ^ Runtime error in 'EllipticCurve': Curve is singular >> TorsionSubgroup(E); ^ User error: Identifier 'E' has not been declared or assigned >> E2:=BaseChange(E,K); ^ User error: Identifier 'E' has not been declared or assigned >> TorsionSubgroup(E2);; ^ User error: Identifier 'E2' has not been declared or assigned Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host h24-81-108-53.vc.shawcable.net. (24.81.108.53) Time: Thu Jan 22 00:41:51 2004 Input: E:=EllipticCurve([-411253227,3210112702566]); TorsionSubgroup(E); P:=PolynomialRing(RationalField()); K:=NumberField(x^3+4*x^2-7*x+1); E2:=BaseChange(E,K); TorsionSubgroup(E2); Output: Magma V2.10-6 Thu Jan 22 2004 00:41:48 on modular [Seed = 324809159] ------------------------------------- Abelian Group of order 1 Abelian Group of order 1 Defined on 1 generator Relations: $.1 = 0 Mapping from: Abelian Group of order 1 Defined on 1 generator Relations: $.1 = 0 to CrvEll: E2 given by a rule [no inverse] Total time: 3.159 seconds, Total memory usage: 2.09MB ************** MAGMA ***************** Host h24-81-108-53.vc.shawcable.net. (24.81.108.53) Time: Thu Jan 22 00:43:28 2004 Input: E:=EllipticCurve([-432, 8208]); TorsionSubgroup(E); P:=PolynomialRing(RationalField()); K:=NumberField(x^3+4*x^2-7*x+1); E2:=BaseChange(E,K); TorsionSubgroup(E2); Output: Magma V2.10-6 Thu Jan 22 2004 00:43:25 on modular [Seed = 744689305] ------------------------------------- Abelian Group isomorphic to Z/5 Defined on 1 generator Relations: 5*$.1 = 0 Abelian Group isomorphic to Z/5 Defined on 1 generator Relations: 5*$.1 = 0 Mapping from: Abelian Group isomorphic to Z/5 Defined on 1 generator Relations: 5*$.1 = 0 to CrvEll: E2 given by a rule [no inverse] Total time: 3.239 seconds, Total memory usage: 2.19MB ************** MAGMA ***************** Host 3(NXDOMAIN) (193.226.4.152) Time: Thu Jan 22 01:37:51 2004 Input: P:=PolynomialRing(IntegerRing(),2); f1:=2*(x^2+y^2)+x-y-16; f2:=6*(x^4+y^4)+2*(x^3-y^3)+x-y-192; f3:=40*(x^6+y^6)+11*(x^5-y^5)+5*(x^3-y^3)+4*(x-y)-5120; f4:=(630*(x^8+y^8)+151*(x^7-y^7)+71*(x^5-y^5)+49*(x^3-y^3)+45*(x-y)-1024*315)*5040*64+ 2097152*x^7 + 1835008*x^6 - 1146880*x^5 - 1003520*x^4 + 132608*x^3 + 116032*x^2 - 1800*x - 1575; I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Factorization(14549535); Factorization(3011753745); Bn:=GroebnerBasis(ChangeRing(I,GF(11^4))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(13^4))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(19^4))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(23^4))); Bn; Output: Magma V2.10-6 Thu Jan 22 2004 01:37:41 on modular [Seed = 2800322907] ------------------------------------- [ x^2 + 8*x + y^2 + 14549527*y + 2648015362, x*y + 2*x + 14549533*y + 2648015366, 15*x + 14549520*y + 2648015370, y^3 + 9*y^2 + 14549531*y + 2648015334, 15*y^2 + 3011753685, 14549535*y + 2648015370, 3011753745 ] [ <3, 2>, <5, 1>, <7, 1>, <11, 1>, <13, 1>, <17, 1>, <19, 1> ] [ <3, 4>, <5, 1>, <7, 1>, <11, 1>, <13, 1>, <17, 1>, <19, 1>, <23, 1> ] [ x + 10*y, y^2 + 7 ] [ x + 12*y, y^2 + 9 ] [ x + 18*y, y^2 + 15 ] [ x + 21, y + 21 ] Total time: 3.319 seconds, Total memory usage: 7.41MB ************** MAGMA ***************** Host 3(NXDOMAIN) (193.226.4.152) Time: Thu Jan 22 01:39:18 2004 Input: P:=PolynomialRing(IntegerRing(),2); f1:=2*(x^2+y^2)+x-y-16; f2:=6*(x^4+y^4)+2*(x^3-y^3)+x-y-192; f3:=40*(x^6+y^6)+11*(x^5-y^5)+5*(x^3-y^3)+4*(x-y)-5120; f4:=(630*(x^8+y^8)+151*(x^7-y^7)+71*(x^5-y^5)+49*(x^3-y^3)+45*(x-y)-1024*315)*5040*64+ 2097152*x^7 + 1835008*x^6 - 1146880*x^5 - 1003520*x^4 + 132608*x^3 + 116032*x^2 - 1800*x - 1575; I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Factorization(14549535); Factorization(3011753745); Bn:=GroebnerBasis(ChangeRing(I,GF(11^4))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(13^4))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(17^4))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(19^4))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(23^4))); Bn; Output: Magma V2.10-6 Thu Jan 22 2004 01:39:14 on modular [Seed = 2969534698] ------------------------------------- [ x^2 + 8*x + y^2 + 14549527*y + 2648015362, x*y + 2*x + 14549533*y + 2648015366, 15*x + 14549520*y + 2648015370, y^3 + 9*y^2 + 14549531*y + 2648015334, 15*y^2 + 3011753685, 14549535*y + 2648015370, 3011753745 ] [ <3, 2>, <5, 1>, <7, 1>, <11, 1>, <13, 1>, <17, 1>, <19, 1> ] [ <3, 4>, <5, 1>, <7, 1>, <11, 1>, <13, 1>, <17, 1>, <19, 1>, <23, 1> ] [ x + 10*y, y^2 + 7 ] [ x + 12*y, y^2 + 9 ] [ x + 16*y, y^2 + 13 ] [ x + 18*y, y^2 + 15 ] [ x + 21, y + 21 ] Total time: 3.359 seconds, Total memory usage: 8.42MB ************** MAGMA ***************** Host 3(NXDOMAIN) (193.226.4.152) Time: Thu Jan 22 01:40:07 2004 Input: P:=PolynomialRing(IntegerRing(),2); f1:=2*(x^2+y^2)+x-y-16; f2:=6*(x^4+y^4)+2*(x^3-y^3)+x-y-192; f3:=40*(x^6+y^6)+11*(x^5-y^5)+5*(x^3-y^3)+4*(x-y)-5120; f4:=(630*(x^8+y^8)+151*(x^7-y^7)+71*(x^5-y^5)+49*(x^3-y^3)+45*(x-y)-1024*315)*5040*64+ 2097152*x^7 + 1835008*x^6 - 1146880*x^5 - 1003520*x^4 + 132608*x^3 + 116032*x^2 - 1800*x - 1575; I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Factorization(14549535); Factorization(3011753745); Bn:=GroebnerBasis(ChangeRing(I,GF(11^2))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(13^2))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(17^2))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(19^2))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(23^2))); Bn; Output: Magma V2.10-6 Thu Jan 22 2004 01:40:04 on modular [Seed = 1091465548] ------------------------------------- [ x^2 + 8*x + y^2 + 14549527*y + 2648015362, x*y + 2*x + 14549533*y + 2648015366, 15*x + 14549520*y + 2648015370, y^3 + 9*y^2 + 14549531*y + 2648015334, 15*y^2 + 3011753685, 14549535*y + 2648015370, 3011753745 ] [ <3, 2>, <5, 1>, <7, 1>, <11, 1>, <13, 1>, <17, 1>, <19, 1> ] [ <3, 4>, <5, 1>, <7, 1>, <11, 1>, <13, 1>, <17, 1>, <19, 1>, <23, 1> ] [ x + 10*y, y^2 + 7 ] [ x + 12*y, y^2 + 9 ] [ x + 16*y, y^2 + 13 ] [ x + 18*y, y^2 + 15 ] [ x + 21, y + 21 ] Total time: 2.989 seconds, Total memory usage: 2.23MB ************** MAGMA ***************** Host 3(NXDOMAIN) (193.226.4.152) Time: Thu Jan 22 01:41:09 2004 Input: P:=PolynomialRing(IntegerRing(),2); f1:=2*(x^2+y^2)+x-y-16; f2:=6*(x^4+y^4)+2*(x^3-y^3)+x-y-192; f3:=1280*(x^6+y^6)+352*(x^5-y^5)+160*(x^3-y^3)+128*(x-y)+2592*x^5+2160*x^4-720*x^3-600*x^2+18*x-163825; f4:=(630*(x^8+y^8)+151*(x^7-y^7)+71*(x^5-y^5)+49*(x^3-y^3)+45*(x-y)-1024*315)*5040*64+ -142336*x^7 - 777728*x^6 + 1030400*x^5 + 1536640*x^4 - 314944*x^3 - 406112*x^2 + 9000*x + 11025; I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Factorization(6435); Factorization(2297295); Bn:=GroebnerBasis(ChangeRing(I,GF(11^2))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(13^2))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(17^2))); Bn; Output: Magma V2.10-6 Thu Jan 22 2004 01:41:06 on modular [Seed = 1477929107] ------------------------------------- [ x^2 + 248*x + y^2 + 6187*y + 643492, x*y + 317*x + 6118*y + 2175026, 495*x + 5940*y + 1409265, y^3 + 9*y^2 + 6431*y + 643464, 15*y^2 + 2297235, 6435*y + 2175030, 2297295 ] [ <3, 2>, <5, 1>, <11, 1>, <13, 1> ] [ <3, 3>, <5, 1>, <7, 1>, <11, 1>, <13, 1>, <17, 1> ] [ x^2 + 6*x + 5*y + 7, x*y + 9*x + 2*y + 7, y^2 + 7 ] [ x + 12*y, y^2 + 9 ] [ x + 15, y + 15 ] Total time: 2.999 seconds, Total memory usage: 2.23MB ************** MAGMA ***************** Host 3(NXDOMAIN) (193.226.4.152) Time: Thu Jan 22 01:42:01 2004 Input: P:=PolynomialRing(IntegerRing(),2); f1:=2*(x^2+y^2)+x-y-16; f2:=6*(x^4+y^4)+2*(x^3-y^3)+x-y-192; f3:=1280*(x^6+y^6)+352*(x^5-y^5)+160*(x^3-y^3)+128*(x-y)+2592*x^5+2160*x^4-720*x^3-600*x^2+18*x-163825; f4:=(630*(x^8+y^8)+151*(x^7-y^7)+71*(x^5-y^5)+49*(x^3-y^3)+45*(x-y)-1024*315)*5040*64+ -142336*x^7 - 777728*x^6 + 1030400*x^5 + 1536640*x^4 - 314944*x^3 - 406112*x^2 + 9000*x + 11025; I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Factorization(6435); Factorization(2297295); Bn:=GroebnerBasis(ChangeRing(I,GF(11^4))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(13^4))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(17^4))); Bn; Output: Magma V2.10-6 Thu Jan 22 2004 01:41:58 on modular [Seed = 1394369452] ------------------------------------- [ x^2 + 248*x + y^2 + 6187*y + 643492, x*y + 317*x + 6118*y + 2175026, 495*x + 5940*y + 1409265, y^3 + 9*y^2 + 6431*y + 643464, 15*y^2 + 2297235, 6435*y + 2175030, 2297295 ] [ <3, 2>, <5, 1>, <11, 1>, <13, 1> ] [ <3, 3>, <5, 1>, <7, 1>, <11, 1>, <13, 1>, <17, 1> ] [ x^2 + 6*x + 5*y + 7, x*y + 9*x + 2*y + 7, y^2 + 7 ] [ x + 12*y, y^2 + 9 ] [ x + 15, y + 15 ] Total time: 3.029 seconds, Total memory usage: 3.48MB ************** MAGMA ***************** Host 3(NXDOMAIN) (193.226.4.152) Time: Thu Jan 22 01:42:32 2004 Input: P:=PolynomialRing(IntegerRing(),2); f1:=2*(x^2+y^2)+x-y-16; f2:=6*(x^4+y^4)+2*(x^3-y^3)+x-y-192; f3:=1280*(x^6+y^6)+352*(x^5-y^5)+160*(x^3-y^3)+128*(x-y)+2592*x^5+2160*x^4-720*x^3-600*x^2+18*x-163825; f4:=(630*(x^8+y^8)+151*(x^7-y^7)+71*(x^5-y^5)+49*(x^3-y^3)+45*(x-y)-1024*315)*5040*64+ -142336*x^7 - 777728*x^6 + 1030400*x^5 + 1536640*x^4 - 314944*x^3 - 406112*x^2 + 9000*x + 11025; I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Factorization(6435); Factorization(2297295); Bn:=GroebnerBasis(ChangeRing(I,GF(11))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(13))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(17))); Bn; Output: Magma V2.10-6 Thu Jan 22 2004 01:42:29 on modular [Seed = 1780833014] ------------------------------------- [ x^2 + 248*x + y^2 + 6187*y + 643492, x*y + 317*x + 6118*y + 2175026, 495*x + 5940*y + 1409265, y^3 + 9*y^2 + 6431*y + 643464, 15*y^2 + 2297235, 6435*y + 2175030, 2297295 ] [ <3, 2>, <5, 1>, <11, 1>, <13, 1> ] [ <3, 3>, <5, 1>, <7, 1>, <11, 1>, <13, 1>, <17, 1> ] [ x^2 + 6*x + 5*y + 7, x*y + 9*x + 2*y + 7, y^2 + 7 ] [ x + 12*y, y^2 + 9 ] [ x + 15, y + 15 ] Total time: 3.089 seconds, Total memory usage: 2.03MB ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Thu Jan 22 06:29:55 2004 Input: P := PolynomialRing(Rationals()); C := HyperellipticCurve(x^5 + 257); J := Jacobian(C); SetVerbose("JacHypSelmer", 2); TwoSelmerGroupData(J : Bound := 300); Output: Magma V2.10-6 Thu Jan 22 2004 06:29:47 on modular [Seed = 3566936233] ------------------------------------- TwoSelmerGroupData of Jacobian of Hyperelliptic Curve defined by y^2 = x^5 + 257 over Rational Field m= Mapping from: CrvHyp: C to CrvHyp: C1 with equations : $.1 $.2 $.3 and inverse $.1 $.2 $.3 Bad primes = [ 2, 5, 257 ] f is irreducible. For factor x^5 + 257, use field defined by x^5 + 257 and theta = K.1 The 2-torsion group has dimension 0. Determining local images... p = 2 x = 1/4 --> new generator (0 0 1 0 0 0 0 0 1) x = 2 --> new generator (0 1 1 0 1 1 1 0 1) p = 5 p = 257 p = infinity Computing class groups... Class group data of the fields: Field given by x^5 + 257: [ 2 ] Dimension of Cl[2] = 1. Signatures: [ 1, 2 ] Dimension of units mod squares = 3. Upper bound for Selmer group dimension: 4. ==> Upper bound for rank = 4. Computing unit groups... Class group and unit data of the fields: Field given by x^5 + 257: Class group = [ 2 ], units = [ 2, 0, 0 ] Time for local computations: 789 ms. Time for class groups: 1210 ms. Time for unit groups: 259 ms. Selmer group dimension = 4, Dimension of 2-torsion = 0, ==> Bound for the MW-rank = 4. Total time: 3019 ms. 4 4 <[ 6324*$.1^4 - 19200*$.1^3 + 58201*$.1^2 - 176674*$.1 + 535924, 4813226456041628140*$.1^4 + 36434957339645170375*$.1^3 + 134550883205234964034*$.1^2 + 325136991241356237462*$.1 + 357631773270138394448, -4765587902901*$.1^4 - 63798163626893*$.1^3 - 269309755742720*$.1^2 - 734788220557257*$.1 - 1128214191578602, 5935617327117/5*$.1^4 - 18007462569209/5*$.1^3 + 54630999497913/5*$.1^2 - 165739402654201/5*$.1 + 502819824492457/5 ], [], []> { Number Field with defining polynomial x^5 + 257 over the Rational Field } Total time: 6.229 seconds, Total memory usage: 3.39MB ************** MAGMA ***************** Host robbe.STUDFB.UniBw-Muenchen.de. (137.193.211.26) Time: Thu Jan 22 07:06:04 2004 Input: 3 5 Output: Magma V2.10-6 Thu Jan 22 2004 07:06:01 on modular [Seed = 761450967] ------------------------------------- >> 3 5; ^ User error: bad syntax Total time: 3.039 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (194.165.15.3) Time: Thu Jan 22 08:08:34 2004 Input: c := 31; IsPrime(c); Output: Magma V2.10-6 Thu Jan 22 2004 08:08:30 on modular [Seed = 3297464287] ------------------------------------- true Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (194.165.15.3) Time: Thu Jan 22 08:09:04 2004 Input: c := (2^31)-1; IsPrime(c); Output: Magma V2.10-6 Thu Jan 22 2004 08:09:01 on modular [Seed = 3364307952] ------------------------------------- true Total time: 2.939 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (194.165.15.3) Time: Thu Jan 22 08:09:27 2004 Input: c := (2^1001)-1; IsPrime(c); Output: Magma V2.10-6 Thu Jan 22 2004 08:09:24 on modular [Seed = 4206194987] ------------------------------------- false Total time: 2.999 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (194.165.15.3) Time: Thu Jan 22 08:11:26 2004 Input: c := (2^1001)-1; for n in [521..1500] do c := (2^n)-1 if IsPrime(c) then c; end if; end for; Output: Magma V2.10-6 Thu Jan 22 2004 08:11:23 on modular [Seed = 2597654836] ------------------------------------- >> if IsPrime(c) then ^ User error: bad syntax 2143017214372534641896850098120003621122809623411067214887500776740702102249872\ 2449863967576313917162551893458351062936503742905713846280871969155149397149607\ 8691355496484619708421492101247422837559083643060929499671638825347975351183310\ 87892154125829142392955373084335320859663305248773674411336138751 >> end if; ^ User error: bad syntax >> end for; ^ User error: bad syntax Total time: 2.999 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (194.165.15.3) Time: Thu Jan 22 08:11:43 2004 Input: c := (2^1001)-1; for n in [521..1500] do c := (2^n)-1 if IsPrime(c) then n; end if; end for; Output: Magma V2.10-6 Thu Jan 22 2004 08:11:39 on modular [Seed = 2378301907] ------------------------------------- >> if IsPrime(c) then ^ User error: bad syntax >> n; ^ User error: Identifier 'n' has not been declared or assigned >> end if; ^ User error: bad syntax >> end for; ^ User error: bad syntax Total time: 2.889 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (194.165.15.3) Time: Thu Jan 22 08:12:17 2004 Input: c := (2^1001)-1; for n in [521..1500] do c := (2^n)-1 if IsPrime(c) then c := n; c; end if; end for; Output: Magma V2.10-6 Thu Jan 22 2004 08:12:14 on modular [Seed = 3036362959] ------------------------------------- >> if IsPrime(c) then ^ User error: bad syntax >> c := n; ^ User error: Identifier 'n' has not been declared or assigned 2143017214372534641896850098120003621122809623411067214887500776740702102249872\ 2449863967576313917162551893458351062936503742905713846280871969155149397149607\ 8691355496484619708421492101247422837559083643060929499671638825347975351183310\ 87892154125829142392955373084335320859663305248773674411336138751 >> end if; ^ User error: bad syntax >> end for; ^ User error: bad syntax Total time: 3.429 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (194.165.15.3) Time: Thu Jan 22 08:12:51 2004 Input: c := (2^1001)-1; for n in [521..1500] do c := (2^n)-1; if IsPrime(c) then c := n; c; end if; end for; Output: Magma V2.10-6 Thu Jan 22 2004 08:12:31 on modular [Seed = 2750164937] ------------------------------------- 521 607 1279 Total time: 20.049 seconds, Total memory usage: 2.99MB ************** MAGMA ***************** Host 3(NXDOMAIN) (194.165.15.3) Time: Thu Jan 22 08:14:07 2004 Input: c := (2^1001)-1; for n in [521..1500] do c := (2^n)-1; if IsPrime(c) then n; end if; end for; Output: Magma V2.10-6 Thu Jan 22 2004 08:13:46 on modular [Seed = 2867144309] ------------------------------------- 521 607 1279 Total time: 20.170 seconds, Total memory usage: 2.99MB ************** MAGMA ***************** Host 3(NXDOMAIN) (194.165.15.3) Time: Thu Jan 22 08:14:49 2004 Input: c := (2^1001)-1; for n in [10..15000] do c := (2^n)-1; if IsPrime(c) then n; end if; end for; Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Thu Jan 22 2004 08:14:26 on modular [Seed = 1578226362] ------------------------------------- 13 17 19 31 61 89 107 127 521 607 1279 Errors: /home/mfd/gomagma: line 2: 5640 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host 3(NXDOMAIN) (194.165.15.3) Time: Thu Jan 22 09:24:23 2004 Input: k := GF(2); C := PrimitivePolynomial(k,9); C; for j in [11..17] do for k in [11..17] do for m in [11..17] do for n in [11..17] do C := ((1 + X^n)^8)*((1 + X^m)^8)*((1 + X^k)^8)*((1 + X^j)^8) + X^1279; if IsPrimitive(C) then C; n; m; k; j; end if; end for; end for; end for; end for; Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Thu Jan 22 2004 09:24:00 on modular [Seed = 1308742422] ------------------------------------- X^9 + X^4 + 1 X^1279 + X^456 + X^368 + X^344 + X^336 + X^320 + X^256 + X^248 + X^232 + X^224 + X^208 + X^200 + X^136 + X^120 + X^112 + X^88 + 1 17 15 14 11 X^1279 + X^456 + X^368 + X^344 + X^336 + X^320 + X^256 + X^248 + X^232 + X^224 + X^208 + X^200 + X^136 + X^120 + X^112 + X^88 + 1 15 17 14 11 X^1279 + X^456 + X^368 + X^344 + X^336 + X^320 + X^256 + X^248 + X^232 + X^224 + X^208 + X^200 + X^136 + X^120 + X^112 + X^88 + 1 17 14 15 11 X^1279 + X^456 + X^368 + X^344 + X^336 + X^320 + X^256 + X^248 + X^232 + X^224 + X^208 + X^200 + X^136 + X^120 + X^112 + X^88 + 1 14 17 15 11 X^1279 + X^456 + X^368 + X^344 + X^336 + X^320 + X^256 + X^248 + X^232 + X^224 + X^208 + X^200 + X^136 + X^120 + X^112 + X^88 + 1 15 14 17 11 X^1279 + X^456 + X^368 + X^344 + X^336 + X^320 + X^256 + X^248 + X^232 + X^224 + X^208 + X^200 + X^136 + X^120 + X^112 + X^88 + 1 14 15 17 11 X^1279 + X^464 + X^368 + X^352 + X^344 + X^328 + X^256 + X^248 + X^216 + X^208 + X^136 + X^120 + X^112 + X^96 + 1 17 15 14 12 X^1279 + X^464 + X^368 + X^352 + X^344 + X^328 + X^256 + X^248 + X^216 + X^208 + X^136 + X^120 + X^112 + X^96 + 1 15 17 14 12 X^1279 + X^464 + X^368 + X^352 + X^344 + X^328 + X^256 + X^248 + X^216 + X^208 + X^136 + X^120 + X^112 + X^96 + 1 17 14 15 12 X^1279 + X^464 + X^368 + X^352 + X^344 + X^328 + X^256 + X^248 + X^216 + X^208 + X^136 + X^120 + X^112 + X^96 + 1 14 17 15 12 X^1279 + X^464 + X^368 + X^352 + X^344 + X^328 + X^256 + X^248 + X^216 + X^208 + X^136 + X^120 + X^112 + X^96 + 1 15 14 17 12 X^1279 + X^464 + X^368 + X^352 + X^344 + X^328 + X^256 + X^248 + X^216 + X^208 + X^136 + X^120 + X^112 + X^96 + 1 14 15 17 12 X^1279 + X^504 + X^400 + X^376 + X^272 + X^232 + X^128 + X^104 + 1 17 17 16 13 X^1279 + X^504 + X^400 + X^376 + X^272 + X^232 + X^128 + X^104 + 1 17 16 17 13 X^1279 + X^504 + X^400 + X^376 + X^272 + X^232 + X^128 + X^104 + 1 16 17 17 13 X^1279 + X^456 + X^368 + X^344 + X^336 + X^320 + X^256 + X^248 + X^232 + X^224 + X^208 + X^200 + X^136 + X^120 + X^112 + X^88 + 1 17 15 11 14 X^1279 + X^456 + X^368 + X^344 + X^336 + X^320 + X^256 + X^248 + X^232 + X^224 + X^208 + X^200 + X^136 + X^120 + X^112 + X^88 + 1 15 17 11 14 X^1279 + X^464 + X^368 + X^352 + X^344 + X^328 + X^256 + X^248 + X^216 + X^208 + X^136 + X^120 + X^112 + X^96 + 1 17 15 12 14 X^1279 + X^464 + X^368 + X^352 + X^344 + X^328 + X^256 + X^248 + X^216 + X^208 + X^136 + X^120 + X^112 + X^96 + 1 15 17 12 14 X^1279 + X^456 + X^368 + X^344 + X^336 + X^320 + X^256 + X^248 + X^232 + X^224 + X^208 + X^200 + X^136 + X^120 + X^112 + X^88 + 1 17 11 15 14 X^1279 + X^464 + X^368 + X^352 + X^344 + X^328 + X^256 + X^248 + X^216 + X^208 + X^136 + X^120 + X^112 + X^96 + 1 17 12 15 14 X^1279 + X^456 + X^368 + X^344 + X^336 + X^320 + X^256 + X^248 + X^232 + X^224 + X^208 + X^200 + X^136 + X^120 + X^112 + X^88 + 1 11 17 15 14 X^1279 + X^464 + X^368 + X^352 + X^344 + X^328 + X^256 + X^248 + X^216 + X^208 + X^136 + X^120 + X^112 + X^96 + 1 12 17 15 14 X^1279 + X^456 + X^368 + X^344 + X^336 + X^320 + X^256 + X^248 + X^232 + X^224 + X^208 + X^200 + X^136 + X^120 + X^112 + X^88 + 1 15 11 17 14 X^1279 + X^464 + X^368 + X^352 + X^344 + X^328 + X^256 + X^248 + X^216 + X^208 + X^136 + X^120 + X^112 + X^96 + 1 15 12 17 14 X^1279 + X^456 + X^368 + X^344 + X^336 + X^320 + X^256 + X^248 + X^232 + X^224 + X^208 + X^200 + X^136 + X^120 + X^112 + X^88 + 1 11 15 17 14 X^1279 + X^464 + X^368 + X^352 + X^344 + X^328 + X^256 + X^248 + X^216 + X^208 + X^136 + X^120 + X^112 + X^96 + 1 12 15 17 14 X^1279 + X^456 + X^368 + X^344 + X^336 + X^320 + X^256 + X^248 + X^232 + X^224 + X^208 + X^200 + X^136 + X^120 + X^112 + X^88 + 1 17 14 11 15 X^1279 + X^456 + X^368 + X^344 + X^336 + X^320 + X^256 + X^248 + X^232 + X^224 + X^208 + X^200 + X^136 + X^120 + X^112 + X^88 + 1 14 17 11 15 X^1279 + X^464 + X^368 + X^352 + X^344 + X^328 + X^256 + X^248 + X^216 + X^208 + X^136 + X^120 + X^112 + X^96 + 1 17 14 12 15 X^1279 + X^464 + X^368 + X^352 + X^344 + X^328 + X^256 + X^248 + X^216 + X^208 + X^136 + X^120 + X^112 + X^96 + 1 14 17 12 15 X^1279 + X^456 + X^368 + X^344 + X^336 + X^320 + X^256 + X^248 + X^232 + X^224 + X^208 + X^200 + X^136 + X^120 + X^112 + X^88 + 1 17 11 14 15 X^1279 + X^464 + X^368 + X^352 + X^344 + X^328 + X^256 + X^248 + X^216 + X^208 + X^136 + X^120 + X^112 + X^96 + 1 17 12 14 15 X^1279 + X^456 + X^368 + X^344 + X^336 + X^320 + X^256 + X^248 + X^232 + X^224 + X^208 + X^200 + X^136 + X^120 + X^112 + X^88 + 1 11 17 14 15 X^1279 + X^464 + X^368 + X^352 + X^344 + X^328 + X^256 + X^248 + X^216 + X^208 + X^136 + X^120 + X^112 + X^96 + 1 12 17 14 15 X^1279 + X^456 + X^368 + X^344 + X^336 + X^320 + X^256 + X^248 + X^232 + X^224 + X^208 + X^200 + X^136 + X^120 + X^112 + X^88 + 1 14 11 17 15 X^1279 + X^464 + X^368 + X^352 + X^344 + X^328 + X^256 + X^248 + X^216 + X^208 + X^136 + X^120 + X^112 + X^96 + 1 14 12 17 15 X^1279 + X^456 + X^368 + X^344 + X^336 + X^320 + X^256 + X^248 + X^232 + X^224 + X^208 + X^200 + X^136 + X^120 + X^112 + X^88 + 1 11 14 17 15 X^1279 + X^464 + X^368 + X^352 + X^344 + X^328 + X^256 + X^248 + X^216 + X^208 + X^136 + X^120 + X^112 + X^96 + 1 12 14 17 15 X^1279 + X^504 + X^400 + X^376 + X^272 + X^232 + X^128 + X^104 + 1 17 17 13 16 X^1279 + X^504 + X^400 + X^376 + X^272 + X^232 + X^128 + X^104 + 1 17 13 17 16 X^1279 + X^504 + X^400 + X^376 + X^272 + X^232 + X^128 + X^104 + 1 13 17 17 16 X^1279 + X^456 + X^368 + X^344 + X^336 + X^320 + X^256 + X^248 + X^232 + X^224 + X^208 + X^200 + X^136 + X^120 + X^112 + X^88 + 1 15 14 11 17 X^1279 + X^456 + X^368 + X^344 + X^336 + X^320 + X^256 + X^248 + X^232 + X^224 + X^208 + X^200 + X^136 + X^120 + X^112 + X^88 + 1 14 15 11 17 X^1279 + X^464 + X^368 + X^352 + X^344 + X^328 + X^256 + X^248 + X^216 + X^208 + X^136 + X^120 + X^112 + X^96 + 1 15 14 12 17 X^1279 + X^464 + X^368 + X^352 + X^344 + X^328 + X^256 + X^248 + X^216 + X^208 + X^136 + X^120 + X^112 + X^96 + 1 14 15 12 17 X^1279 + X^504 + X^400 + X^376 + X^272 + X^232 + X^128 + X^104 + 1 17 16 13 17 X^1279 + X^504 + X^400 + X^376 + X^272 + X^232 + X^128 + X^104 + 1 16 17 13 17 Errors: /home/mfd/gomagma: line 2: 6166 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host 3(NXDOMAIN) (194.165.15.3) Time: Thu Jan 22 09:25:52 2004 Input: k := GF(2); C := PrimitivePolynomial(k,9); C; for j in [11..17] do for k in [11..17] do for m in [18..29] do for n in [17..23] do C := ((1 + X^n)^8)*((1 + X^m)^8)*((1 + X^k)^8)*((1 + X^j)^8) + X^1279; if IsPrimitive(C) then C; n; m; k; j; end if; end for; end for; end for; end for; Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Thu Jan 22 2004 09:25:29 on modular [Seed = 2000218742] ------------------------------------- X^9 + X^4 + 1 X^1279 + X^496 + X^320 + X^176 + 1 20 20 11 11 X^1279 + X^488 + X^400 + X^392 + X^304 + X^184 + X^96 + X^88 + 1 19 19 12 11 X^1279 + X^592 + X^504 + X^472 + X^440 + X^384 + X^360 + X^352 + X^320 + X^272 + X^240 + X^232 + X^208 + X^152 + X^120 + X^88 + 1 19 29 15 11 X^1279 + X^624 + X^536 + X^488 + X^448 + X^360 + X^264 + X^176 + X^136 + X^88 + 1 22 28 17 11 X^1279 + X^488 + X^400 + X^392 + X^304 + X^184 + X^96 + X^88 + 1 19 19 11 12 X^1279 + X^504 + X^408 + X^400 + X^304 + X^200 + X^104 + X^96 + 1 19 19 13 12 X^1279 + X^600 + X^504 + X^488 + X^416 + X^320 + X^304 + X^296 + X^280 + X^184 + X^112 + X^96 + 1 23 26 14 12 X^1279 + X^568 + X^472 + X^448 + X^424 + X^360 + X^352 + X^328 + X^304 + X^264 + X^240 + X^216 + X^208 + X^144 + X^120 + X^96 + 1 18 26 15 12 X^1279 + X^528 + X^432 + X^400 + X^384 + X^368 + X^304 + X^288 + X^272 + X^256 + X^240 + X^224 + X^160 + X^144 + X^128 + X^96 + 1 20 18 16 12 X^1279 + X^528 + X^432 + X^400 + X^384 + X^368 + X^304 + X^288 + X^272 + X^256 + X^240 + X^224 + X^160 + X^144 + X^128 + X^96 + 1 18 20 16 12 X^1279 + X^504 + X^408 + X^400 + X^304 + X^200 + X^104 + X^96 + 1 19 19 12 13 X^1279 + X^600 + X^496 + X^488 + X^424 + X^392 + X^384 + X^320 + X^312 + X^288 + X^280 + X^216 + X^208 + X^176 + X^112 + X^104 + 1 22 26 14 13 X^1279 + X^584 + X^480 + X^456 + X^416 + X^400 + X^352 + X^312 + X^296 + X^288 + X^272 + X^232 + X^184 + X^168 + X^128 + X^104 + 1 23 21 16 13 X^1279 + X^584 + X^480 + X^456 + X^416 + X^400 + X^352 + X^312 + X^296 + X^288 + X^272 + X^232 + X^184 + X^168 + X^128 + X^104 + 1 21 23 16 13 X^1279 + X^584 + X^480 + X^448 + X^440 + X^384 + X^344 + X^336 + X^304 + X^280 + X^248 + X^240 + X^200 + X^144 + X^136 + X^104 + 1 18 25 17 13 X^1279 + X^640 + X^536 + X^504 + X^472 + X^408 + X^400 + X^368 + X^336 + X^304 + X^272 + X^240 + X^232 + X^168 + X^136 + X^104 + 1 21 29 17 13 X^1279 + X^600 + X^504 + X^488 + X^416 + X^320 + X^304 + X^296 + X^280 + X^184 + X^112 + X^96 + 1 23 26 12 14 X^1279 + X^600 + X^496 + X^488 + X^424 + X^392 + X^384 + X^320 + X^312 + X^288 + X^280 + X^216 + X^208 + X^176 + X^112 + X^104 + 1 22 26 13 14 X^1279 + X^552 + X^408 + X^368 + X^328 + X^224 + X^184 + X^144 + 1 23 18 14 14 X^1279 + X^552 + X^408 + X^368 + X^328 + X^224 + X^184 + X^144 + 1 18 23 14 14 X^1279 + X^536 + X^424 + X^416 + X^304 + X^232 + X^120 + X^112 + 1 19 19 15 14 X^1279 + X^592 + X^480 + X^472 + X^440 + X^384 + X^360 + X^328 + X^320 + X^272 + X^264 + X^232 + X^208 + X^152 + X^120 + X^112 + 1 19 26 15 14 X^1279 + X^592 + X^504 + X^472 + X^440 + X^384 + X^360 + X^352 + X^320 + X^272 + X^240 + X^232 + X^208 + X^152 + X^120 + X^88 + 1 19 29 11 15 X^1279 + X^568 + X^472 + X^448 + X^424 + X^360 + X^352 + X^328 + X^304 + X^264 + X^240 + X^216 + X^208 + X^144 + X^120 + X^96 + 1 18 26 12 15 X^1279 + X^536 + X^424 + X^416 + X^304 + X^232 + X^120 + X^112 + 1 19 19 14 15 X^1279 + X^592 + X^480 + X^472 + X^440 + X^384 + X^360 + X^328 + X^320 + X^272 + X^264 + X^232 + X^208 + X^152 + X^120 + X^112 + 1 19 26 14 15 X^1279 + X^568 + X^432 + X^376 + X^328 + X^240 + X^192 + X^136 + 1 17 24 15 15 X^1279 + X^616 + X^496 + X^488 + X^440 + X^424 + X^368 + X^320 + X^312 + X^304 + X^296 + X^248 + X^192 + X^176 + X^128 + X^120 + 1 22 24 16 15 Errors: /home/mfd/gomagma: line 2: 6191 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host 3(NXDOMAIN) (194.165.15.3) Time: Thu Jan 22 09:27:25 2004 Input: k := GF(2); C := PrimitivePolynomial(k,9); C; for j in [23..31] do for k in [23..31] do for m in [18..29] do for n in [23..31] do C := ((1 + X^n)^8)*((1 + X^m)^8)*((1 + X^k)^8)*((1 + X^j)^8) + X^1279; if IsPrimitive(C) then C; n; m; k; j; end if; end for; end for; end for; end for; Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Thu Jan 22 2004 09:27:02 on modular [Seed = 324833021] ------------------------------------- X^9 + X^4 + 1 X^1279 + X^760 + X^592 + X^576 + X^560 + X^552 + X^408 + X^392 + X^384 + X^376 + X^368 + X^352 + X^208 + X^200 + X^184 + X^168 + 1 26 21 25 23 X^1279 + X^760 + X^592 + X^576 + X^560 + X^552 + X^408 + X^392 + X^384 + X^376 + X^368 + X^352 + X^208 + X^200 + X^184 + X^168 + 1 25 21 26 23 X^1279 + X^808 + X^616 + X^576 + X^424 + X^384 + X^232 + X^192 + 1 29 24 24 24 X^1279 + X^816 + X^624 + X^576 + X^432 + X^384 + X^240 + X^192 + 1 30 24 24 24 X^1279 + X^808 + X^616 + X^576 + X^424 + X^384 + X^232 + X^192 + 1 24 29 24 24 X^1279 + X^792 + X^632 + X^600 + X^592 + X^552 + X^440 + X^432 + X^400 + X^392 + X^360 + X^352 + X^240 + X^200 + X^192 + X^160 + 1 30 20 25 24 X^1279 + X^776 + X^608 + X^584 + X^576 + X^560 + X^416 + X^408 + X^392 + X^384 + X^368 + X^360 + X^216 + X^200 + X^192 + X^168 + 1 27 21 25 24 X^1279 + X^776 + X^632 + X^584 + X^568 + X^544 + X^440 + X^424 + X^400 + X^376 + X^352 + X^336 + X^232 + X^208 + X^192 + X^144 + 1 29 18 26 24 X^1279 + X^784 + X^640 + X^592 + X^568 + X^552 + X^448 + X^424 + X^408 + X^376 + X^360 + X^336 + X^232 + X^216 + X^192 + X^144 + 1 29 18 27 24 X^1279 + X^776 + X^608 + X^584 + X^576 + X^560 + X^416 + X^408 + X^392 + X^384 + X^368 + X^360 + X^216 + X^200 + X^192 + X^168 + 1 25 21 27 24 X^1279 + X^776 + X^632 + X^584 + X^568 + X^544 + X^440 + X^424 + X^400 + X^376 + X^352 + X^336 + X^232 + X^208 + X^192 + X^144 + 1 26 18 29 24 X^1279 + X^784 + X^640 + X^592 + X^568 + X^552 + X^448 + X^424 + X^408 + X^376 + X^360 + X^336 + X^232 + X^216 + X^192 + X^144 + 1 27 18 29 24 X^1279 + X^808 + X^616 + X^576 + X^424 + X^384 + X^232 + X^192 + 1 24 24 29 24 X^1279 + X^792 + X^632 + X^600 + X^592 + X^552 + X^440 + X^432 + X^400 + X^392 + X^360 + X^352 + X^240 + X^200 + X^192 + X^160 + 1 25 20 30 24 X^1279 + X^816 + X^624 + X^576 + X^432 + X^384 + X^240 + X^192 + 1 24 24 30 24 X^1279 + X^760 + X^592 + X^576 + X^560 + X^552 + X^408 + X^392 + X^384 + X^376 + X^368 + X^352 + X^208 + X^200 + X^184 + X^168 + 1 26 21 23 25 X^1279 + X^792 + X^632 + X^600 + X^592 + X^552 + X^440 + X^432 + X^400 + X^392 + X^360 + X^352 + X^240 + X^200 + X^192 + X^160 + 1 30 20 24 25 X^1279 + X^776 + X^608 + X^584 + X^576 + X^560 + X^416 + X^408 + X^392 + X^384 + X^368 + X^360 + X^216 + X^200 + X^192 + X^168 + 1 27 21 24 25 X^1279 + X^864 + X^640 + X^624 + X^464 + X^400 + X^240 + X^224 + 1 30 28 25 25 X^1279 + X^784 + X^632 + X^584 + X^576 + X^560 + X^432 + X^424 + X^408 + X^376 + X^360 + X^352 + X^224 + X^208 + X^200 + X^152 + 1 28 19 26 25 X^1279 + X^760 + X^592 + X^576 + X^560 + X^552 + X^408 + X^392 + X^384 + X^376 + X^368 + X^352 + X^208 + X^200 + X^184 + X^168 + 1 23 21 26 25 X^1279 + X^800 + X^624 + X^600 + X^592 + X^584 + X^424 + X^416 + X^408 + X^392 + X^384 + X^376 + X^216 + X^208 + X^200 + X^176 + 1 27 22 26 25 X^1279 + X^816 + X^640 + X^616 + X^608 + X^584 + X^440 + X^432 + X^384 + X^376 + X^232 + X^208 + X^200 + X^176 + 1 29 22 26 25 X^1279 + X^792 + X^648 + X^592 + X^576 + X^560 + X^448 + X^432 + X^416 + X^376 + X^360 + X^344 + X^232 + X^216 + X^200 + X^144 + 1 29 18 27 25 Errors: /home/mfd/gomagma: line 2: 6219 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host 3(NXDOMAIN) (194.165.15.3) Time: Thu Jan 22 09:28:53 2004 Input: k := GF(2); C := PrimitivePolynomial(k,9); C; for j in [23..31] do for k in [23..31] do for m in [18..23] do for n in [31..41] do C := ((1 + X^n)^8)*((1 + X^m)^8)*((1 + X^k)^8)*((1 + X^j)^8) + X^1279; if IsPrimitive(C) then C; n; m; k; j; end if; end for; end for; end for; end for; Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Thu Jan 22 2004 09:28:30 on modular [Seed = 255889753] ------------------------------------- X^9 + X^4 + 1 X^1279 + X^840 + X^664 + X^656 + X^632 + X^568 + X^480 + X^456 + X^448 + X^392 + X^384 + X^360 + X^272 + X^208 + X^184 + X^176 + 1 34 22 26 23 X^1279 + X^904 + X^688 + X^584 + X^536 + X^368 + X^320 + X^216 + 1 40 23 27 23 X^1279 + X^840 + X^680 + X^544 + X^456 + X^384 + X^296 + X^160 + 1 37 20 24 24 X^1279 + X^880 + X^720 + X^688 + X^664 + X^568 + X^528 + X^504 + X^472 + X^408 + X^376 + X^352 + X^312 + X^216 + X^192 + X^160 + 1 39 20 27 24 X^1279 + X^872 + X^712 + X^680 + X^640 + X^584 + X^520 + X^480 + X^448 + X^424 + X^392 + X^352 + X^288 + X^232 + X^192 + X^160 + 1 36 20 29 24 X^1279 + X^824 + X^656 + X^568 + X^424 + X^400 + X^256 + X^168 + 1 32 21 25 25 X^1279 + X^864 + X^688 + X^576 + X^464 + X^400 + X^288 + X^176 + 1 36 22 25 25 X^1279 + X^856 + X^704 + X^656 + X^640 + X^568 + X^504 + X^488 + X^440 + X^416 + X^368 + X^352 + X^288 + X^216 + X^200 + X^152 + 1 36 19 27 25 X^1279 + X^848 + X^688 + X^648 + X^632 + X^576 + X^488 + X^472 + X^432 + X^416 + X^376 + X^360 + X^272 + X^216 + X^200 + X^160 + 1 34 20 27 25 X^1279 + X^856 + X^680 + X^656 + X^632 + X^600 + X^480 + X^456 + X^432 + X^424 + X^400 + X^376 + X^256 + X^224 + X^200 + X^176 + 1 32 22 28 25 X^1279 + X^840 + X^696 + X^640 + X^600 + X^584 + X^496 + X^456 + X^440 + X^400 + X^384 + X^344 + X^256 + X^240 + X^200 + X^144 + 1 32 18 30 25 X^1279 + X^936 + X^752 + X^736 + X^688 + X^632 + X^552 + X^504 + X^488 + X^448 + X^432 + X^384 + X^304 + X^248 + X^200 + X^184 + 1 38 23 31 25 X^1279 + X^840 + X^664 + X^656 + X^632 + X^568 + X^480 + X^456 + X^448 + X^392 + X^384 + X^360 + X^272 + X^208 + X^184 + X^176 + 1 34 22 23 26 X^1279 + X^896 + X^752 + X^688 + X^680 + X^568 + X^544 + X^536 + X^472 + X^424 + X^360 + X^352 + X^328 + X^216 + X^208 + X^144 + 1 41 18 27 26 X^1279 + X^840 + X^688 + X^632 + X^616 + X^584 + X^480 + X^464 + X^432 + X^408 + X^376 + X^360 + X^256 + X^224 + X^208 + X^152 + 1 32 19 28 26 X^1279 + X^856 + X^704 + X^648 + X^496 + X^360 + X^208 + X^152 + 1 31 19 31 26 X^1279 + X^904 + X^688 + X^584 + X^536 + X^368 + X^320 + X^216 + 1 40 23 23 27 X^1279 + X^880 + X^720 + X^688 + X^664 + X^568 + X^528 + X^504 + X^472 + X^408 + X^376 + X^352 + X^312 + X^216 + X^192 + X^160 + 1 39 20 24 27 X^1279 + X^856 + X^704 + X^656 + X^640 + X^568 + X^504 + X^488 + X^440 + X^416 + X^368 + X^352 + X^288 + X^216 + X^200 + X^152 + 1 36 19 25 27 Errors: /home/mfd/gomagma: line 2: 6231 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host 3(NXDOMAIN) (194.165.15.3) Time: Thu Jan 22 09:30:05 2004 Input: k := GF(2); C := PrimitivePolynomial(k,9); C; for j in [23..31] do for k in [23..31] do for m in [41..53] do for n in [31..41] do C := ((1 + X^n)^8)*((1 + X^m)^8)*((1 + X^k)^8)*((1 + X^j)^8) + X^1279; if IsPrimitive(C) then C; n; m; k; j; end if; end for; end for; end for; end for; Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Thu Jan 22 2004 09:29:42 on modular [Seed = 930654521] ------------------------------------- X^9 + X^4 + 1 X^1279 + X^1072 + X^760 + X^704 + X^680 + X^392 + X^368 + X^312 + 1 39 49 23 23 X^1279 + X^1048 + X^864 + X^848 + X^792 + X^664 + X^640 + X^608 + X^592 + X^456 + X^440 + X^408 + X^384 + X^256 + X^200 + X^184 + 1 32 51 25 23 X^1279 + X^992 + X^808 + X^784 + X^728 + X^656 + X^600 + X^544 + X^520 + X^472 + X^448 + X^392 + X^336 + X^264 + X^208 + X^184 + 1 33 42 26 23 X^1279 + X^1008 + X^824 + X^792 + X^744 + X^664 + X^608 + X^560 + X^528 + X^480 + X^448 + X^400 + X^344 + X^264 + X^216 + X^184 + 1 33 43 27 23 X^1279 + X^1024 + X^840 + X^792 + X^760 + X^680 + X^608 + X^576 + X^528 + X^496 + X^448 + X^416 + X^344 + X^264 + X^232 + X^184 + 1 33 43 29 23 X^1279 + X^1072 + X^888 + X^840 + X^776 + X^712 + X^656 + X^592 + X^544 + X^528 + X^480 + X^416 + X^360 + X^296 + X^232 + X^184 + 1 37 45 29 23 X^1279 + X^1072 + X^888 + X^840 + X^808 + X^680 + X^656 + X^624 + X^576 + X^496 + X^448 + X^416 + X^392 + X^264 + X^232 + X^184 + 1 33 49 29 23 X^1279 + X^1032 + X^848 + X^792 + X^784 + X^672 + X^608 + X^600 + X^544 + X^488 + X^432 + X^424 + X^360 + X^248 + X^240 + X^184 + 1 31 45 30 23 X^1279 + X^1112 + X^928 + X^872 + X^832 + X^704 + X^688 + X^648 + X^592 + X^520 + X^464 + X^424 + X^408 + X^280 + X^240 + X^184 + 1 35 51 30 23 X^1279 + X^1120 + X^936 + X^872 + X^816 + X^736 + X^688 + X^632 + X^568 + X^552 + X^488 + X^432 + X^384 + X^304 + X^248 + X^184 + 1 38 48 31 23 X^1279 + X^1040 + X^848 + X^840 + X^736 + X^696 + X^648 + X^544 + X^536 + X^504 + X^496 + X^392 + X^344 + X^304 + X^200 + X^192 + 1 38 43 25 24 X^1279 + X^1040 + X^848 + X^840 + X^752 + X^680 + X^648 + X^560 + X^552 + X^488 + X^480 + X^392 + X^360 + X^288 + X^200 + X^192 + 1 36 45 25 24 X^1279 + X^1064 + X^872 + X^856 + X^784 + X^680 + X^664 + X^592 + X^576 + X^488 + X^472 + X^400 + X^384 + X^280 + X^208 + X^192 + 1 35 48 26 24 X^1279 + X^1080 + X^888 + X^872 + X^792 + X^688 + X^680 + X^600 + X^584 + X^496 + X^480 + X^400 + X^392 + X^288 + X^208 + X^192 + 1 36 49 26 24 X^1279 + X^1104 + X^912 + X^896 + X^816 + X^704 + X^688 + X^624 + X^608 + X^496 + X^480 + X^416 + X^400 + X^288 + X^208 + X^192 + 1 36 52 26 24 X^1279 + X^1024 + X^832 + X^808 + X^776 + X^656 + X^616 + X^584 + X^560 + X^464 + X^440 + X^408 + X^368 + X^248 + X^216 + X^192 + 1 31 46 27 24 X^1279 + X^1104 + X^912 + X^888 + X^776 + X^736 + X^696 + X^584 + X^560 + X^544 + X^520 + X^408 + X^368 + X^328 + X^216 + X^192 + 1 41 46 27 24 X^1279 + X^1056 + X^864 + X^824 + X^784 + X^696 + X^632 + X^592 + X^552 + X^504 + X^464 + X^424 + X^360 + X^272 + X^232 + X^192 + 1 34 45 29 24 Errors: /home/mfd/gomagma: line 2: 6255 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host 3(NXDOMAIN) (194.165.15.3) Time: Thu Jan 22 09:31:26 2004 Input: k := GF(2); C := PrimitivePolynomial(k,9); C; for j in [41..47] do for k in [23..31] do for m in [11..19] do for n in [31..41] do C := ((1 + X^n)^8)*((1 + X^m)^8)*((1 + X^k)^8)*((1 + X^j)^8) + X^1279; if IsPrimitive(C) then C; n; m; k; j; end if; end for; end for; end for; end for; Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Thu Jan 22 2004 09:31:03 on modular [Seed = 3683927332] ------------------------------------- X^9 + X^4 + 1 X^1279 + X^920 + X^800 + X^728 + X^640 + X^608 + X^592 + X^520 + X^472 + X^448 + X^400 + X^328 + X^312 + X^280 + X^192 + X^120 + 1 35 15 24 41 X^1279 + X^888 + X^800 + X^688 + X^616 + X^600 + X^560 + X^528 + X^472 + X^416 + X^360 + X^328 + X^288 + X^272 + X^200 + X^88 + 1 34 11 25 41 X^1279 + X^920 + X^792 + X^720 + X^656 + X^528 + X^464 + X^456 + X^392 + X^264 + X^200 + X^128 + 1 33 16 25 41 X^1279 + X^1000 + X^848 + X^776 + X^704 + X^672 + X^624 + X^552 + X^520 + X^480 + X^448 + X^376 + X^328 + X^296 + X^224 + X^152 + 1 37 19 28 41 X^1279 + X^912 + X^816 + X^680 + X^656 + X^560 + X^488 + X^424 + X^352 + X^256 + X^232 + X^96 + 1 32 12 29 41 X^1279 + X^984 + X^848 + X^744 + X^704 + X^656 + X^608 + X^568 + X^520 + X^464 + X^416 + X^376 + X^328 + X^280 + X^240 + X^136 + 1 35 17 30 41 X^1279 + X^1040 + X^896 + X^800 + X^656 + X^384 + X^240 + X^144 + 1 41 18 30 41 X^1279 + X^936 + X^832 + X^688 + X^680 + X^608 + X^584 + X^576 + X^504 + X^432 + X^360 + X^352 + X^328 + X^256 + X^248 + X^104 + 1 32 13 31 41 X^1279 + X^952 + X^856 + X^760 + X^664 + X^624 + X^616 + X^528 + X^520 + X^432 + X^424 + X^336 + X^328 + X^288 + X^192 + X^96 + 1 41 12 24 42 X^1279 + X^968 + X^816 + X^768 + X^688 + X^632 + X^616 + X^536 + X^488 + X^480 + X^432 + X^352 + X^336 + X^280 + X^200 + X^152 + 1 35 19 25 42 X^1279 + X^936 + X^840 + X^728 + X^640 + X^632 + X^600 + X^544 + X^504 + X^432 + X^392 + X^336 + X^304 + X^296 + X^208 + X^96 + 1 37 12 26 42 X^1279 + X^1024 + X^888 + X^800 + X^696 + X^688 + X^664 + X^560 + X^552 + X^472 + X^464 + X^360 + X^336 + X^328 + X^224 + X^136 + 1 41 17 28 42 X^1279 + X^952 + X^824 + X^720 + X^696 + X^616 + X^592 + X^568 + X^488 + X^464 + X^384 + X^360 + X^336 + X^256 + X^232 + X^128 + 1 32 16 29 42 X^1279 + X^984 + X^856 + X^752 + X^696 + X^648 + X^624 + X^568 + X^520 + X^464 + X^416 + X^360 + X^336 + X^288 + X^232 + X^128 + 1 36 16 29 42 X^1279 + X^968 + X^816 + X^736 + X^720 + X^632 + X^584 + X^568 + X^488 + X^480 + X^400 + X^384 + X^336 + X^248 + X^232 + X^152 + 1 31 19 29 42 X^1279 + X^984 + X^888 + X^736 + X^680 + X^648 + X^640 + X^584 + X^552 + X^432 + X^400 + X^344 + X^336 + X^304 + X^248 + X^96 + 1 38 12 31 42 X^1279 + X^1032 + X^896 + X^784 + X^720 + X^696 + X^648 + X^584 + X^560 + X^472 + X^448 + X^384 + X^336 + X^312 + X^248 + X^136 + 1 39 17 31 42 X^1279 + X^984 + X^832 + X^648 + X^496 + X^488 + X^336 + X^152 + 1 31 19 31 42 X^1279 + X^952 + X^856 + X^768 + X^672 + X^624 + X^608 + X^528 + X^512 + X^440 + X^424 + X^344 + X^328 + X^280 + X^184 + X^96 + 1 41 12 23 43 X^1279 + X^912 + X^800 + X^728 + X^640 + X^616 + X^568 + X^528 + X^384 + X^344 + X^296 + X^272 + X^184 + X^112 + 1 34 14 23 43 X^1279 + X^960 + X^848 + X^776 + X^664 + X^640 + X^616 + X^528 + X^504 + X^456 + X^432 + X^344 + X^320 + X^296 + X^184 + X^112 + 1 40 14 23 43 X^1279 + X^952 + X^864 + X^760 + X^672 + X^624 + X^608 + X^536 + X^520 + X^432 + X^416 + X^344 + X^328 + X^280 + X^192 + X^88 + 1 41 11 24 43 Errors: /home/mfd/gomagma: line 2: 6275 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host 3(NXDOMAIN) (194.165.15.3) Time: Thu Jan 22 09:32:53 2004 Input: k := GF(2); C := PrimitivePolynomial(k,9); C; for j in [41..47] do for k in [23..31] do for m in [11..19] do for n in [57..61] do C := ((1 + X^n)^8)*((1 + X^m)^8)*((1 + X^k)^8)*((1 + X^j)^8) + X^1279; if IsPrimitive(C) then C; n; m; k; j; end if; end for; end for; end for; end for; Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Thu Jan 22 2004 09:32:30 on modular [Seed = 3447870315] ------------------------------------- X^9 + X^4 + 1 X^1279 + X^1072 + X^968 + X^888 + X^784 + X^744 + X^640 + X^616 + X^560 + X^512 + X^456 + X^432 + X^328 + X^288 + X^184 + X^104 + 1 57 13 23 41 X^1279 + X^1064 + X^976 + X^872 + X^784 + X^736 + X^648 + X^608 + X^544 + X^520 + X^456 + X^416 + X^328 + X^280 + X^192 + X^88 + 1 57 11 24 41 X^1279 + X^1176 + X^1032 + X^960 + X^840 + X^816 + X^624 + X^552 + X^360 + X^336 + X^216 + X^144 + 1 60 18 27 42 X^1279 + X^1144 + X^1016 + X^920 + X^808 + X^792 + X^688 + X^680 + X^584 + X^560 + X^464 + X^456 + X^352 + X^336 + X^224 + X^128 + 1 57 16 28 42 X^1279 + X^1192 + X^1056 + X^960 + X^856 + X^824 + X^720 + X^704 + X^624 + X^568 + X^488 + X^472 + X^368 + X^336 + X^232 + X^136 + 1 61 17 29 42 X^1279 + X^1192 + X^1064 + X^944 + X^856 + X^816 + X^728 + X^712 + X^608 + X^584 + X^480 + X^464 + X^376 + X^336 + X^248 + X^128 + 1 60 16 31 42 X^1279 + X^1112 + X^1024 + X^920 + X^832 + X^768 + X^680 + X^624 + X^576 + X^536 + X^488 + X^432 + X^344 + X^280 + X^192 + X^88 + 1 61 11 24 43 X^1279 + X^1112 + X^1008 + X^920 + X^816 + X^768 + X^664 + X^640 + X^576 + X^536 + X^472 + X^448 + X^344 + X^296 + X^192 + X^104 + 1 59 13 24 43 X^1279 + X^1120 + X^1032 + X^896 + X^808 + X^776 + X^688 + X^656 + X^568 + X^552 + X^464 + X^432 + X^344 + X^312 + X^224 + X^88 + 1 58 11 28 43 X^1279 + X^1184 + X^1048 + X^936 + X^840 + X^800 + X^728 + X^704 + X^480 + X^456 + X^384 + X^344 + X^248 + X^136 + 1 57 17 31 43 X^1279 + X^1104 + X^1016 + X^920 + X^832 + X^752 + X^664 + X^624 + X^568 + X^536 + X^480 + X^440 + X^352 + X^272 + X^184 + X^88 + 1 60 11 23 44 X^1279 + X^1152 + X^1024 + X^968 + X^840 + X^800 + X^672 + X^664 + X^616 + X^536 + X^488 + X^480 + X^352 + X^312 + X^184 + X^128 + 1 61 16 23 44 X^1279 + X^1128 + X^1032 + X^920 + X^824 + X^776 + X^680 + X^656 + X^568 + X^560 + X^472 + X^448 + X^352 + X^304 + X^208 + X^96 + 1 59 12 26 44 X^1279 + X^1152 + X^1048 + X^928 + X^824 + X^800 + X^696 + X^680 + X^472 + X^456 + X^352 + X^328 + X^224 + X^104 + 1 59 13 28 44 X^1279 + X^1144 + X^1032 + X^960 + X^848 + X^784 + X^672 + X^656 + X^600 + X^544 + X^488 + X^472 + X^360 + X^296 + X^184 + X^112 + 1 61 14 23 45 X^1279 + X^1160 + X^1048 + X^952 + X^840 + X^800 + X^688 + X^680 + X^592 + X^568 + X^480 + X^472 + X^360 + X^320 + X^208 + X^112 + 1 60 14 26 45 X^1279 + X^1120 + X^1032 + X^904 + X^816 + X^760 + X^672 + X^664 + X^576 + X^544 + X^456 + X^448 + X^360 + X^304 + X^216 + X^88 + 1 57 11 27 45 X^1279 + X^1168 + X^1064 + X^936 + X^832 + X^808 + X^704 + X^696 + X^592 + X^576 + X^472 + X^464 + X^360 + X^336 + X^232 + X^104 + 1 59 13 29 45 Errors: /home/mfd/gomagma: line 2: 6293 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host 3(NXDOMAIN) (194.165.15.3) Time: Thu Jan 22 09:34:39 2004 Input: k := GF(2); C := PrimitivePolynomial(k,9); C; for j in [51..61] do for k in [27..31] do for m in [19..23] do for n in [13..17] do C := ((1 + X^n)^8)*((1 + X^m)^8)*((1 + X^k)^8)*((1 + X^j)^8) + X^1279; if IsPrimitive(C) then C; n; m; k; j; end if; end for; end for; end for; end for; Output: Magma V2.10-6 Thu Jan 22 2004 09:34:22 on modular [Seed = 3986846427] ------------------------------------- X^9 + X^4 + 1 X^1279 + X^944 + X^808 + X^776 + X^712 + X^640 + X^576 + X^544 + X^536 + X^408 + X^400 + X^368 + X^304 + X^232 + X^168 + X^136 + 1 17 21 29 51 X^1279 + X^920 + X^816 + X^760 + X^672 + X^656 + X^568 + X^352 + X^264 + X^248 + X^160 + X^104 + 1 13 20 31 51 X^1279 + X^912 + X^808 + X^752 + X^680 + X^648 + X^576 + X^520 + X^496 + X^416 + X^392 + X^336 + X^264 + X^232 + X^160 + X^104 + 1 13 20 29 52 X^1279 + X^920 + X^808 + X^752 + X^704 + X^640 + X^592 + X^536 + X^496 + X^424 + X^384 + X^328 + X^280 + X^216 + X^168 + X^112 + 1 14 21 27 53 X^1279 + X^936 + X^832 + X^784 + X^688 + X^680 + X^584 + X^536 + X^504 + X^432 + X^400 + X^352 + X^256 + X^248 + X^152 + X^104 + 1 13 19 31 54 X^1279 + X^952 + X^840 + X^792 + X^720 + X^680 + X^608 + X^560 + X^504 + X^448 + X^392 + X^344 + X^272 + X^232 + X^160 + X^112 + 1 14 20 29 56 X^1279 + X^960 + X^856 + X^776 + X^744 + X^672 + X^640 + X^560 + X^504 + X^456 + X^400 + X^320 + X^288 + X^216 + X^184 + X^104 + 1 13 23 27 57 X^1279 + X^968 + X^840 + X^816 + X^736 + X^688 + X^608 + X^584 + X^512 + X^456 + X^384 + X^360 + X^280 + X^232 + X^152 + X^128 + 1 16 19 29 57 X^1279 + X^976 + X^864 + X^800 + X^744 + X^688 + X^632 + X^568 + X^520 + X^456 + X^408 + X^344 + X^288 + X^232 + X^176 + X^112 + 1 14 22 29 57 X^1279 + X^992 + X^864 + X^824 + X^752 + X^696 + X^624 + X^584 + X^536 + X^456 + X^408 + X^368 + X^296 + X^240 + X^168 + X^128 + 1 16 21 30 57 X^1279 + X^976 + X^856 + X^816 + X^752 + X^696 + X^632 + X^592 + X^504 + X^472 + X^384 + X^344 + X^280 + X^224 + X^160 + X^120 + 1 15 20 28 59 X^1279 + X^992 + X^888 + X^832 + X^744 + X^728 + X^640 + X^584 + X^512 + X^480 + X^408 + X^352 + X^264 + X^248 + X^160 + X^104 + 1 13 20 31 60 X^1279 + X^1000 + X^864 + X^848 + X^776 + X^712 + X^640 + X^624 + X^512 + X^488 + X^376 + X^360 + X^288 + X^224 + X^152 + X^136 + 1 17 19 28 61 Total time: 17.029 seconds, Total memory usage: 2.23MB ************** MAGMA ***************** Host 3(NXDOMAIN) (194.165.15.3) Time: Thu Jan 22 09:35:50 2004 Input: k := GF(2); C := PrimitivePolynomial(k,9); C; for j in [61..71] do for k in [27..31] do for m in [19..23] do for n in [13..17] do C := ((1 + X^n)^8)*((1 + X^m)^8)*((1 + X^k)^8)*((1 + X^j)^8) + X^1279; if IsPrimitive(C) then C; n; m; k; j; end if; end for; end for; end for; end for; Output: Magma V2.10-6 Thu Jan 22 2004 09:35:32 on modular [Seed = 2480671871] ------------------------------------- X^9 + X^4 + 1 X^1279 + X^1000 + X^864 + X^848 + X^776 + X^712 + X^640 + X^624 + X^512 + X^488 + X^376 + X^360 + X^288 + X^224 + X^152 + X^136 + 1 17 19 28 61 X^1279 + X^984 + X^880 + X^824 + X^760 + X^720 + X^656 + X^600 + X^496 + X^488 + X^384 + X^328 + X^264 + X^224 + X^160 + X^104 + 1 13 20 28 62 X^1279 + X^1040 + X^904 + X^856 + X^824 + X^720 + X^688 + X^640 + X^536 + X^504 + X^400 + X^352 + X^320 + X^216 + X^184 + X^136 + 1 17 23 27 63 X^1279 + X^1056 + X^928 + X^872 + X^816 + X^744 + X^688 + X^632 + X^552 + X^504 + X^424 + X^368 + X^312 + X^240 + X^184 + X^128 + 1 16 23 30 63 X^1279 + X^1000 + X^888 + X^848 + X^784 + X^736 + X^672 + X^632 + X^520 + X^480 + X^368 + X^328 + X^264 + X^216 + X^152 + X^112 + 1 14 19 27 65 X^1279 + X^1024 + X^904 + X^872 + X^808 + X^752 + X^688 + X^656 + X^536 + X^488 + X^368 + X^336 + X^272 + X^216 + X^152 + X^120 + 1 15 19 27 67 X^1279 + X^1064 + X^944 + X^896 + X^824 + X^776 + X^704 + X^656 + X^536 + X^528 + X^408 + X^360 + X^288 + X^240 + X^168 + X^120 + 1 15 21 30 67 X^1279 + X^1056 + X^944 + X^880 + X^832 + X^768 + X^720 + X^656 + X^544 + X^512 + X^400 + X^336 + X^288 + X^224 + X^176 + X^112 + 1 14 22 28 68 X^1279 + X^1024 + X^920 + X^872 + X^808 + X^768 + X^704 + X^656 + X^552 + X^472 + X^368 + X^320 + X^256 + X^216 + X^152 + X^104 + 1 13 19 27 69 X^1279 + X^1032 + X^928 + X^872 + X^816 + X^768 + X^712 + X^656 + X^552 + X^480 + X^376 + X^320 + X^264 + X^216 + X^160 + X^104 + 1 13 20 27 69 X^1279 + X^1104 + X^976 + X^936 + X^856 + X^808 + X^728 + X^688 + X^560 + X^544 + X^416 + X^376 + X^296 + X^248 + X^168 + X^128 + 1 16 21 31 70 X^1279 + X^1096 + X^976 + X^928 + X^856 + X^808 + X^736 + X^688 + X^568 + X^528 + X^408 + X^360 + X^288 + X^240 + X^168 + X^120 + 1 15 21 30 71 X^1279 + X^1112 + X^984 + X^936 + X^872 + X^808 + X^744 + X^696 + X^568 + X^544 + X^416 + X^368 + X^304 + X^240 + X^176 + X^128 + 1 16 22 30 71 X^1279 + X^1104 + X^992 + X^920 + X^864 + X^808 + X^752 + X^680 + X^568 + X^536 + X^424 + X^352 + X^296 + X^240 + X^184 + X^112 + 1 14 23 30 71 Total time: 17.909 seconds, Total memory usage: 2.24MB ************** MAGMA ***************** Host 3(NXDOMAIN) (194.165.15.3) Time: Thu Jan 22 09:37:54 2004 Input: k := GF(2); C := PrimitivePolynomial(k,9); C; for t in [41..51] do for j in [61..71] do for k in [27..31] do for m in [19..23] do for n in [13..17] do C := ((1 + X^n)^8)*((1 + X^m)^8)*((1 + X^k)^8)*((1 + X^j)^8)*((1 + X^t)^8) + X^1279; if IsPrimitive(C) then C; n; m; k; j; t; end if; end for; end for; end for; end for; end for; Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Thu Jan 22 2004 09:37:31 on modular [Seed = 2969505987] ------------------------------------- X^9 + X^4 + 1 Errors: /home/mfd/gomagma: line 2: 6376 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host 3(NXDOMAIN) (194.165.15.3) Time: Thu Jan 22 09:38:51 2004 Input: k := GF(2); C := PrimitivePolynomial(k,9); C; for t in [17..19] do for j in [61..71] do for k in [27..31] do for m in [19..23] do for n in [13..16] do C := ((1 + X^n)^8)*((1 + X^m)^8)*((1 + X^k)^8)*((1 + X^j)^8)*((1 + X^t)^8) + X^1279; if IsPrimitive(C) then C; n; m; k; j; t; end if; end for; end for; end for; end for; end for; Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Thu Jan 22 2004 09:38:28 on modular [Seed = 2850425237] ------------------------------------- X^9 + X^4 + 1 X^1279 + X^1144 + X^1024 + X^1008 + X^960 + X^928 + X^888 + X^840 + X^824 + X^808 + X^792 + X^744 + X^704 + X^672 + X^656 + X^624 + X^608 + X^536 + X^520 + X^488 + X^472 + X^440 + X^400 + X^352 + X^336 + X^320 + X^304 + X^256 + X^216 + X^184 + X^136 + X^120 + 1 15 23 27 61 17 X^1279 + X^1136 + X^1024 + X^1000 + X^960 + X^920 + X^888 + X^848 + X^824 + X^808 + X^784 + X^744 + X^712 + X^672 + X^640 + X^632 + X^608 + X^528 + X^504 + X^496 + X^464 + X^424 + X^392 + X^352 + X^328 + X^312 + X^288 + X^248 + X^216 + X^176 + X^136 + X^112 + 1 14 22 27 62 17 X^1279 + X^1120 + X^1008 + X^984 + X^968 + X^896 + X^872 + X^856 + X^832 + X^784 + X^760 + X^744 + X^720 + X^648 + X^632 + X^624 + X^608 + X^512 + X^496 + X^488 + X^472 + X^400 + X^376 + X^360 + X^336 + X^288 + X^264 + X^248 + X^224 + X^152 + X^136 + X^112 + 1 14 19 28 62 17 X^1279 + X^1160 + X^1048 + X^1024 + X^984 + X^928 + X^912 + X^872 + X^848 + X^816 + X^792 + X^752 + X^736 + X^680 + X^656 + X^640 + X^616 + X^544 + X^520 + X^504 + X^480 + X^424 + X^408 + X^368 + X^344 + X^312 + X^288 + X^248 + X^232 + X^176 + X^136 + X^112 + 1 14 22 29 63 17 X^1279 + X^1168 + X^1048 + X^1032 + X^992 + X^936 + X^912 + X^872 + X^856 + X^816 + X^800 + X^760 + X^736 + X^680 + X^664 + X^640 + X^624 + X^544 + X^528 + X^504 + X^488 + X^432 + X^408 + X^368 + X^352 + X^312 + X^296 + X^256 + X^232 + X^176 + X^136 + X^120 + 1 15 22 29 63 17 X^1279 + X^1136 + X^1032 + X^1000 + X^976 + X^920 + X^896 + X^872 + X^840 + X^816 + X^784 + X^760 + X^736 + X^680 + X^656 + X^624 + X^616 + X^520 + X^512 + X^480 + X^456 + X^400 + X^376 + X^352 + X^320 + X^296 + X^264 + X^240 + X^216 + X^160 + X^136 + X^104 + 1 13 20 27 65 17 X^1279 + X^1184 + X^1064 + X^1048 + X^1008 + X^952 + X^928 + X^888 + X^872 + X^832 + X^816 + X^776 + X^752 + X^696 + X^664 + X^656 + X^640 + X^544 + X^528 + X^520 + X^488 + X^432 + X^408 + X^368 + X^352 + X^312 + X^296 + X^256 + X^232 + X^176 + X^136 + X^120 + 1 15 22 29 65 17 X^1279 + X^1200 + X^1088 + X^1064 + X^1016 + X^904 + X^880 + X^840 + X^816 + X^704 + X^680 + X^656 + X^632 + X^568 + X^544 + X^520 + X^496 + X^384 + X^360 + X^320 + X^296 + X^184 + X^136 + X^112 + 1 14 23 31 65 17 X^1279 + X^1200 + X^1080 + X^1064 + X^1024 + X^960 + X^944 + X^904 + X^888 + X^840 + X^824 + X^784 + X^768 + X^704 + X^672 + X^664 + X^648 + X^552 + X^536 + X^528 + X^496 + X^432 + X^416 + X^376 + X^360 + X^312 + X^296 + X^256 + X^240 + X^176 + X^136 + X^120 + 1 15 22 30 66 17 X^1279 + X^1200 + X^1088 + X^1064 + X^1016 + X^968 + X^952 + X^904 + X^880 + X^856 + X^832 + X^784 + X^768 + X^720 + X^672 + X^664 + X^648 + X^552 + X^536 + X^528 + X^480 + X^432 + X^416 + X^368 + X^344 + X^320 + X^296 + X^248 + X^232 + X^184 + X^136 + X^112 + 1 14 23 29 67 17 X^1279 + X^1208 + X^1088 + X^1072 + X^1040 + X^960 + X^952 + X^920 + X^904 + X^840 + X^824 + X^792 + X^784 + X^704 + X^656 + X^552 + X^504 + X^424 + X^416 + X^384 + X^368 + X^304 + X^288 + X^256 + X^248 + X^168 + X^136 + X^120 + 1 15 21 31 67 17 X^1279 + X^1192 + X^1072 + X^1056 + X^1024 + X^976 + X^936 + X^904 + X^888 + X^856 + X^840 + X^808 + X^768 + X^720 + X^688 + X^672 + X^640 + X^552 + X^520 + X^504 + X^472 + X^424 + X^384 + X^352 + X^336 + X^304 + X^288 + X^256 + X^216 + X^168 + X^136 + X^120 + 1 15 21 27 69 17 X^1279 + X^1232 + X^1104 + X^1096 + X^1056 + X^992 + X^968 + X^928 + X^920 + X^864 + X^856 + X^816 + X^792 + X^728 + X^688 + X^544 + X^504 + X^440 + X^416 + X^376 + X^368 + X^312 + X^304 + X^264 + X^240 + X^176 + X^136 + X^128 + 1 16 22 30 69 17 X^1279 + X^1232 + X^1112 + X^1096 + X^1064 + X^984 + X^976 + X^944 + X^928 + X^864 + X^848 + X^816 + X^808 + X^728 + X^696 + X^680 + X^672 + X^560 + X^552 + X^536 + X^504 + X^424 + X^416 + X^384 + X^368 + X^304 + X^288 + X^256 + X^248 + X^168 + X^136 + X^120 + 1 15 21 31 70 17 X^1279 + X^1240 + X^1136 + X^1104 + X^1056 + X^1000 + X^992 + X^952 + X^920 + X^888 + X^856 + X^816 + X^808 + X^752 + X^704 + X^536 + X^488 + X^432 + X^424 + X^384 + X^352 + X^320 + X^288 + X^248 + X^240 + X^184 + X^136 + X^104 + 1 13 23 31 71 17 X^1279 + X^1144 + X^1040 + X^1000 + X^992 + X^888 + X^848 + X^792 + X^752 + X^640 + X^600 + X^544 + X^504 + X^392 + X^352 + X^296 + X^256 + X^152 + X^144 + X^104 + 1 13 19 31 62 18 X^1279 + X^1152 + X^1032 + X^1008 + X^984 + X^936 + X^888 + X^864 + X^840 + X^816 + X^792 + X^768 + X^720 + X^672 + X^624 + X^528 + X^480 + X^432 + X^384 + X^360 + X^336 + X^312 + X^288 + X^264 + X^216 + X^168 + X^144 + X^120 + 1 15 21 27 63 18 X^1279 + X^1192 + X^1064 + X^1048 + X^1016 + X^960 + X^920 + X^888 + X^872 + X^832 + X^816 + X^784 + X^744 + X^688 + X^680 + X^656 + X^640 + X^552 + X^536 + X^512 + X^504 + X^448 + X^408 + X^376 + X^360 + X^320 + X^304 + X^272 + X^232 + X^176 + X^144 + X^128 + 1 16 22 29 64 18 X^1279 + X^1160 + X^1032 + X^1016 + X^1008 + X^944 + X^888 + X^880 + X^864 + X^816 + X^800 + X^792 + X^736 + X^672 + X^664 + X^648 + X^640 + X^520 + X^512 + X^496 + X^488 + X^424 + X^368 + X^360 + X^344 + X^296 + X^280 + X^272 + X^216 + X^152 + X^144 + X^128 + 1 16 19 27 65 18 Errors: /home/mfd/gomagma: line 2: 6385 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host 3(NXDOMAIN) (194.165.15.3) Time: Thu Jan 22 09:40:28 2004 Input: k := GF(2); C := PrimitivePolynomial(k,9); C; for t in [42..51] do for j in [32..41] do for k in [24..31] do for m in [20..23] do for n in [13..16] do C := ((1 + X^n)^8)*((1 + X^m)^8)*((1 + X^k)^8)*((1 + X^j)^8)*((1 + X^t)^8) + X^1279; if IsPrimitive(C) then C; n; m; k; j; t; end if; end for; end for; end for; end for; end for; Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Thu Jan 22 2004 09:40:05 on modular [Seed = 1394406351] ------------------------------------- X^9 + X^4 + 1 X^1279 + X^1056 + X^952 + X^896 + X^864 + X^760 + X^720 + X^704 + X^688 + X^632 + X^616 + X^560 + X^496 + X^440 + X^424 + X^368 + X^352 + X^336 + X^296 + X^192 + X^160 + X^104 + 1 13 20 24 33 42 X^1279 + X^1120 + X^1000 + X^952 + X^888 + X^856 + X^832 + X^784 + X^768 + X^736 + X^720 + X^688 + X^664 + X^624 + X^616 + X^600 + X^568 + X^552 + X^520 + X^504 + X^496 + X^456 + X^432 + X^400 + X^384 + X^352 + X^336 + X^288 + X^264 + X^232 + X^168 + X^120 + 1 15 21 29 33 42 X^1279 + X^1120 + X^1008 + X^944 + X^912 + X^800 + X^784 + X^736 + X^720 + X^672 + X^656 + X^608 + X^576 + X^544 + X^512 + X^464 + X^448 + X^400 + X^384 + X^336 + X^320 + X^208 + X^176 + X^112 + 1 14 22 26 36 42 X^1279 + X^1160 + X^1032 + X^976 + X^944 + X^864 + X^848 + X^824 + X^816 + X^760 + X^736 + X^696 + X^680 + X^648 + X^640 + X^632 + X^608 + X^552 + X^528 + X^520 + X^512 + X^480 + X^464 + X^424 + X^400 + X^344 + X^336 + X^312 + X^296 + X^216 + X^184 + X^128 + 1 16 23 27 37 42 X^1279 + X^1160 + X^1056 + X^984 + X^912 + X^880 + X^864 + X^824 + X^808 + X^760 + X^736 + X^720 + X^688 + X^648 + X^632 + X^616 + X^584 + X^576 + X^544 + X^528 + X^512 + X^472 + X^440 + X^424 + X^400 + X^352 + X^336 + X^296 + X^280 + X^248 + X^176 + X^104 + 1 13 22 31 37 42 X^1279 + X^1136 + X^1032 + X^952 + X^928 + X^848 + X^832 + X^824 + X^800 + X^744 + X^728 + X^696 + X^648 + X^640 + X^624 + X^616 + X^592 + X^544 + X^520 + X^512 + X^496 + X^488 + X^440 + X^408 + X^392 + X^336 + X^312 + X^304 + X^288 + X^208 + X^184 + X^104 + 1 13 23 26 38 42 X^1279 + X^1144 + X^1040 + X^960 + X^928 + X^856 + X^840 + X^824 + X^808 + X^744 + X^736 + X^704 + X^656 + X^640 + X^592 + X^552 + X^504 + X^488 + X^440 + X^408 + X^400 + X^336 + X^320 + X^304 + X^288 + X^216 + X^184 + X^104 + 1 13 23 27 38 42 X^1279 + X^1200 + X^1072 + X^1024 + X^952 + X^896 + X^888 + X^864 + X^824 + X^776 + X^760 + X^736 + X^712 + X^688 + X^648 + X^640 + X^616 + X^584 + X^560 + X^552 + X^512 + X^488 + X^464 + X^440 + X^424 + X^376 + X^336 + X^312 + X^304 + X^248 + X^176 + X^128 + 1 16 22 31 39 42 X^1279 + X^1160 + X^1056 + X^976 + X^944 + X^872 + X^824 + X^760 + X^736 + X^720 + X^640 + X^624 + X^608 + X^552 + X^536 + X^520 + X^440 + X^424 + X^400 + X^336 + X^288 + X^216 + X^184 + X^104 + 1 13 23 27 40 42 X^1279 + X^1064 + X^952 + X^904 + X^872 + X^808 + X^792 + X^760 + X^720 + X^712 + X^696 + X^648 + X^616 + X^608 + X^600 + X^560 + X^536 + X^528 + X^504 + X^464 + X^456 + X^448 + X^416 + X^368 + X^352 + X^344 + X^304 + X^272 + X^256 + X^192 + X^160 + X^112 + 1 14 20 24 32 43 X^1279 + X^1088 + X^968 + X^928 + X^880 + X^832 + X^808 + X^760 + X^744 + X^720 + X^712 + X^672 + X^600 + X^584 + X^552 + X^536 + X^504 + X^488 + X^416 + X^376 + X^368 + X^344 + X^328 + X^280 + X^256 + X^208 + X^160 + X^120 + 1 15 20 26 32 43 X^1279 + X^1112 + X^1008 + X^944 + X^872 + X^856 + X^840 + X^752 + X^704 + X^688 + X^664 + X^616 + X^584 + X^528 + X^496 + X^448 + X^424 + X^408 + X^360 + X^272 + X^256 + X^240 + X^168 + X^104 + 1 13 21 30 32 43 X^1279 + X^1112 + X^984 + X^928 + X^920 + X^848 + X^800 + X^792 + X^768 + X^736 + X^720 + X^664 + X^656 + X^640 + X^608 + X^584 + X^576 + X^536 + X^528 + X^504 + X^472 + X^456 + X^448 + X^392 + X^376 + X^344 + X^320 + X^312 + X^264 + X^192 + X^184 + X^128 + 1 16 23 24 33 43 X^1279 + X^1112 + X^1008 + X^944 + X^880 + X^848 + X^840 + X^776 + X^768 + X^744 + X^712 + X^680 + X^664 + X^616 + X^608 + X^600 + X^576 + X^536 + X^512 + X^504 + X^496 + X^448 + X^432 + X^400 + X^368 + X^344 + X^336 + X^272 + X^264 + X^232 + X^168 + X^104 + 1 13 21 29 33 43 Errors: /home/mfd/gomagma: line 2: 6410 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host 3(NXDOMAIN) (194.165.15.3) Time: Thu Jan 22 09:41:29 2004 Input: k := GF(2); C := PrimitivePolynomial(k,9); C; for t in [17..19] do for j in [32..41] do for k in [24..31] do for m in [20..23] do for n in [13..16] do C := ((1 + X^n)^8)*((1 + X^m)^8)*((1 + X^k)^8)*((1 + X^j)^8)*((1 + X^t)^8) + X^1279; if IsPrimitive(C) then C; n; m; k; j; t; end if; end for; end for; end for; end for; end for; Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Thu Jan 22 2004 09:41:05 on modular [Seed = 2133909031] ------------------------------------- X^9 + X^4 + 1 X^1279 + X^912 + X^808 + X^776 + X^728 + X^680 + X^672 + X^656 + X^624 + X^592 + X^576 + X^552 + X^544 + X^520 + X^496 + X^488 + X^472 + X^440 + X^424 + X^416 + X^392 + X^368 + X^360 + X^336 + X^320 + X^288 + X^256 + X^240 + X^232 + X^184 + X^136 + X^104 + 1 13 23 29 32 17 X^1279 + X^928 + X^808 + X^792 + X^760 + X^688 + X^672 + X^664 + X^640 + X^624 + X^568 + X^552 + X^544 + X^528 + X^520 + X^504 + X^496 + X^432 + X^424 + X^408 + X^400 + X^384 + X^376 + X^360 + X^304 + X^288 + X^264 + X^256 + X^240 + X^168 + X^136 + X^120 + 1 15 21 30 33 17 X^1279 + X^928 + X^816 + X^792 + X^760 + X^664 + X^648 + X^624 + X^568 + X^552 + X^544 + X^528 + X^496 + X^432 + X^400 + X^384 + X^376 + X^360 + X^304 + X^280 + X^264 + X^168 + X^136 + X^112 + 1 14 21 31 33 17 X^1279 + X^912 + X^784 + X^776 + X^728 + X^720 + X^648 + X^640 + X^600 + X^584 + X^536 + X^512 + X^504 + X^464 + X^448 + X^408 + X^400 + X^376 + X^328 + X^312 + X^272 + X^264 + X^192 + X^184 + X^136 + X^128 + 1 16 23 24 34 17 X^1279 + X^888 + X^776 + X^752 + X^728 + X^680 + X^640 + X^592 + X^568 + X^544 + X^520 + X^504 + X^456 + X^432 + X^384 + X^368 + X^344 + X^320 + X^296 + X^248 + X^208 + X^160 + X^136 + X^112 + 1 14 20 26 34 17 X^1279 + X^912 + X^808 + X^776 + X^736 + X^688 + X^672 + X^640 + X^632 + X^600 + X^584 + X^552 + X^536 + X^512 + X^504 + X^496 + X^464 + X^448 + X^416 + X^408 + X^400 + X^376 + X^360 + X^328 + X^312 + X^280 + X^272 + X^240 + X^224 + X^176 + X^136 + X^104 + 1 13 22 28 34 17 X^1279 + X^952 + X^832 + X^816 + X^792 + X^704 + X^696 + X^672 + X^664 + X^656 + X^584 + X^568 + X^536 + X^528 + X^504 + X^448 + X^424 + X^416 + X^384 + X^368 + X^296 + X^288 + X^280 + X^256 + X^248 + X^160 + X^136 + X^120 + 1 15 20 31 36 17 X^1279 + X^912 + X^800 + X^776 + X^736 + X^720 + X^664 + X^624 + X^616 + X^608 + X^600 + X^584 + X^544 + X^504 + X^488 + X^480 + X^472 + X^440 + X^432 + X^424 + X^408 + X^368 + X^328 + X^312 + X^304 + X^296 + X^288 + X^248 + X^192 + X^176 + X^136 + X^112 + 1 14 22 24 37 17 X^1279 + X^952 + X^840 + X^816 + X^792 + X^728 + X^704 + X^680 + X^656 + X^632 + X^616 + X^592 + X^568 + X^544 + X^520 + X^496 + X^480 + X^472 + X^456 + X^432 + X^408 + X^384 + X^360 + X^336 + X^320 + X^296 + X^272 + X^248 + X^224 + X^160 + X^136 + X^112 + 1 14 20 28 40 17 X^1279 + X^944 + X^824 + X^808 + X^776 + X^752 + X^688 + X^656 + X^640 + X^632 + X^584 + X^520 + X^480 + X^464 + X^424 + X^360 + X^312 + X^304 + X^288 + X^256 + X^192 + X^168 + X^136 + X^120 + 1 15 21 24 41 17 X^1279 + X^984 + X^864 + X^848 + X^800 + X^768 + X^728 + X^680 + X^664 + X^656 + X^648 + X^632 + X^584 + X^544 + X^536 + X^520 + X^512 + X^472 + X^464 + X^448 + X^440 + X^400 + X^352 + X^336 + X^328 + X^320 + X^304 + X^256 + X^216 + X^184 + X^136 + X^120 + 1 15 23 27 41 17 X^1279 + X^872 + X^752 + X^728 + X^712 + X^680 + X^616 + X^608 + X^592 + X^568 + X^560 + X^536 + X^520 + X^496 + X^472 + X^456 + X^448 + X^424 + X^416 + X^400 + X^376 + X^352 + X^336 + X^312 + X^304 + X^280 + X^264 + X^256 + X^192 + X^160 + X^144 + X^120 + 1 15 20 24 32 18 X^1279 + X^904 + X^784 + X^760 + X^728 + X^696 + X^648 + X^640 + X^608 + X^584 + X^576 + X^552 + X^528 + X^520 + X^504 + X^472 + X^464 + X^440 + X^432 + X^400 + X^384 + X^376 + X^352 + X^328 + X^320 + X^296 + X^264 + X^256 + X^208 + X^176 + X^144 + X^120 + 1 15 22 26 32 18 X^1279 + X^904 + X^792 + X^760 + X^736 + X^680 + X^624 + X^592 + X^568 + X^512 + X^504 + X^400 + X^392 + X^336 + X^312 + X^280 + X^224 + X^168 + X^144 + X^112 + 1 14 21 28 32 18 X^1279 + X^912 + X^808 + X^768 + X^744 + X^672 + X^664 + X^656 + X^640 + X^600 + X^568 + X^552 + X^528 + X^512 + X^504 + X^496 + X^488 + X^424 + X^416 + X^408 + X^400 + X^384 + X^360 + X^344 + X^312 + X^272 + X^256 + X^248 + X^240 + X^168 + X^144 + X^104 + 1 13 21 30 32 18 X^1279 + X^944 + X^816 + X^800 + X^776 + X^696 + X^688 + X^672 + X^648 + X^632 + X^568 + X^560 + X^552 + X^544 + X^528 + X^520 + X^504 + X^440 + X^424 + X^416 + X^400 + X^392 + X^384 + X^376 + X^312 + X^296 + X^272 + X^256 + X^248 + X^168 + X^144 + X^128 + 1 16 21 31 32 18 X^1279 + X^872 + X^768 + X^728 + X^704 + X^680 + X^624 + X^608 + X^600 + X^576 + X^560 + X^536 + X^512 + X^504 + X^464 + X^456 + X^440 + X^432 + X^416 + X^408 + X^368 + X^360 + X^336 + X^312 + X^296 + X^272 + X^264 + X^248 + X^192 + X^168 + X^144 + X^104 + 1 13 21 24 33 18 X^1279 + X^888 + X^784 + X^744 + X^720 + X^680 + X^640 + X^624 + X^616 + X^536 + X^520 + X^512 + X^480 + X^472 + X^456 + X^432 + X^416 + X^408 + X^376 + X^368 + X^352 + X^272 + X^264 + X^248 + X^208 + X^168 + X^144 + X^104 + 1 13 21 26 33 18 X^1279 + X^920 + X^800 + X^776 + X^760 + X^688 + X^640 + X^616 + X^568 + X^544 + X^536 + X^528 + X^512 + X^408 + X^392 + X^384 + X^376 + X^352 + X^304 + X^280 + X^232 + X^160 + X^144 + X^120 + 1 15 20 29 33 18 X^1279 + X^952 + X^824 + X^808 + X^776 + X^712 + X^688 + X^680 + X^648 + X^632 + X^584 + X^568 + X^560 + X^544 + X^536 + X^512 + X^504 + X^448 + X^440 + X^416 + X^408 + X^392 + X^384 + X^368 + X^320 + X^304 + X^272 + X^264 + X^240 + X^176 + X^144 + X^128 + 1 16 22 30 33 18 X^1279 + X^904 + X^800 + X^760 + X^728 + X^712 + X^656 + X^624 + X^616 + X^608 + X^584 + X^568 + X^536 + X^512 + X^480 + X^472 + X^464 + X^440 + X^432 + X^424 + X^392 + X^368 + X^336 + X^320 + X^296 + X^288 + X^280 + X^248 + X^192 + X^176 + X^144 + X^104 + 1 13 22 24 36 18 X^1279 + X^928 + X^808 + X^784 + X^744 + X^736 + X^664 + X^640 + X^624 + X^616 + X^600 + X^592 + X^552 + X^520 + X^496 + X^480 + X^472 + X^456 + X^448 + X^432 + X^408 + X^376 + X^336 + X^328 + X^312 + X^304 + X^288 + X^264 + X^192 + X^184 + X^144 + X^120 + 1 15 23 24 36 18 Errors: /home/mfd/gomagma: line 2: 6438 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host 3(NXDOMAIN) (194.165.15.3) Time: Thu Jan 22 09:42:57 2004 Input: k := GF(2); C := PrimitivePolynomial(k,9); C; for t in [17..19] do for j in [32..41] do for k in [24..31] do for m in [20..23] do for n in [41..51] do C := ((1 + X^n)^8)*((1 + X^m)^8)*((1 + X^k)^8)*((1 + X^j)^8)*((1 + X^t)^8) + X^1279; if IsPrimitive(C) then C; n; m; k; j; t; end if; end for; end for; end for; end for; end for; Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Thu Jan 22 2004 09:42:34 on modular [Seed = 1983502197] ------------------------------------- X^9 + X^4 + 1 X^1279 + X^1152 + X^1016 + X^968 + X^920 + X^896 + X^832 + X^808 + X^784 + X^760 + X^736 + X^712 + X^672 + X^664 + X^624 + X^600 + X^552 + X^528 + X^488 + X^480 + X^440 + X^416 + X^392 + X^368 + X^344 + X^320 + X^256 + X^232 + X^184 + X^136 + 1 43 23 29 32 17 X^1279 + X^1152 + X^1016 + X^992 + X^912 + X^896 + X^856 + X^792 + X^776 + X^760 + X^752 + X^736 + X^632 + X^616 + X^600 + X^552 + X^536 + X^520 + X^416 + X^400 + X^392 + X^376 + X^360 + X^296 + X^256 + X^240 + X^160 + X^136 + 1 45 20 30 32 17 X^1279 + X^1136 + X^1000 + X^960 + X^936 + X^872 + X^824 + X^800 + X^776 + X^760 + X^736 + X^696 + X^672 + X^640 + X^624 + X^600 + X^576 + X^560 + X^536 + X^512 + X^496 + X^464 + X^440 + X^400 + X^376 + X^360 + X^336 + X^312 + X^264 + X^200 + X^176 + X^136 + 1 45 22 25 33 17 X^1279 + X^1200 + X^1064 + X^1040 + X^968 + X^936 + X^904 + X^832 + X^808 + X^800 + X^792 + X^776 + X^704 + X^672 + X^656 + X^640 + X^632 + X^568 + X^560 + X^544 + X^528 + X^496 + X^424 + X^408 + X^400 + X^392 + X^368 + X^296 + X^264 + X^232 + X^160 + X^136 + 1 51 20 29 33 17 X^1279 + X^1160 + X^1024 + X^992 + X^928 + X^896 + X^856 + X^800 + X^792 + X^728 + X^632 + X^624 + X^592 + X^568 + X^536 + X^528 + X^432 + X^368 + X^360 + X^304 + X^264 + X^232 + X^168 + X^136 + 1 45 21 29 33 17 X^1279 + X^1160 + X^1024 + X^976 + X^920 + X^896 + X^840 + X^824 + X^784 + X^760 + X^736 + X^712 + X^688 + X^656 + X^640 + X^600 + X^584 + X^576 + X^560 + X^520 + X^504 + X^472 + X^448 + X^424 + X^400 + X^376 + X^336 + X^320 + X^264 + X^240 + X^184 + X^136 + 1 42 23 30 33 17 X^1279 + X^1176 + X^1040 + X^1008 + X^984 + X^904 + X^872 + X^848 + X^816 + X^736 + X^712 + X^680 + X^632 + X^544 + X^496 + X^464 + X^440 + X^360 + X^328 + X^304 + X^272 + X^192 + X^168 + X^136 + 1 51 21 24 34 17 X^1279 + X^1152 + X^1016 + X^968 + X^952 + X^880 + X^832 + X^816 + X^792 + X^768 + X^744 + X^696 + X^680 + X^656 + X^632 + X^608 + X^592 + X^560 + X^544 + X^520 + X^496 + X^472 + X^456 + X^408 + X^384 + X^360 + X^336 + X^320 + X^272 + X^200 + X^184 + X^136 + 1 45 23 25 34 17 X^1279 + X^1184 + X^1048 + X^1024 + X^944 + X^912 + X^888 + X^784 + X^776 + X^752 + X^616 + X^568 + X^432 + X^408 + X^400 + X^296 + X^272 + X^240 + X^160 + X^136 + 1 47 20 30 34 17 X^1279 + X^1216 + X^1080 + X^1040 + X^968 + X^944 + X^904 + X^808 + X^792 + X^768 + X^632 + X^584 + X^448 + X^424 + X^408 + X^312 + X^272 + X^248 + X^176 + X^136 + 1 48 22 31 34 17 X^1279 + X^1128 + X^992 + X^952 + X^920 + X^848 + X^816 + X^800 + X^784 + X^744 + X^712 + X^672 + X^664 + X^640 + X^624 + X^608 + X^592 + X^536 + X^520 + X^504 + X^488 + X^464 + X^456 + X^416 + X^384 + X^344 + X^328 + X^312 + X^280 + X^208 + X^176 + X^136 + 1 41 22 26 35 17 X^1279 + X^1208 + X^1072 + X^1040 + X^992 + X^928 + X^904 + X^856 + X^824 + X^800 + X^792 + X^760 + X^712 + X^688 + X^664 + X^632 + X^624 + X^584 + X^576 + X^544 + X^520 + X^496 + X^448 + X^416 + X^408 + X^384 + X^352 + X^304 + X^280 + X^216 + X^168 + X^136 + 1 51 21 27 35 17 X^1279 + X^1216 + X^1080 + X^1040 + X^984 + X^936 + X^904 + X^848 + X^824 + X^808 + X^800 + X^760 + X^704 + X^688 + X^672 + X^648 + X^624 + X^592 + X^568 + X^544 + X^528 + X^512 + X^456 + X^416 + X^408 + X^392 + X^368 + X^312 + X^280 + X^232 + X^176 + X^136 + 1 49 22 29 35 17 X^1279 + X^1216 + X^1080 + X^1056 + X^976 + X^936 + X^920 + X^840 + X^800 + X^776 + X^696 + X^656 + X^640 + X^576 + X^560 + X^520 + X^440 + X^416 + X^376 + X^296 + X^280 + X^240 + X^160 + X^136 + 1 50 20 30 35 17 X^1279 + X^1224 + X^1088 + X^1064 + X^984 + X^944 + X^928 + X^848 + X^824 + X^816 + X^808 + X^784 + X^704 + X^688 + X^680 + X^656 + X^648 + X^576 + X^568 + X^544 + X^536 + X^520 + X^440 + X^416 + X^408 + X^400 + X^376 + X^296 + X^280 + X^240 + X^160 + X^136 + 1 51 20 30 35 17 X^1279 + X^1160 + X^1024 + X^1000 + X^960 + X^872 + X^864 + X^824 + X^800 + X^784 + X^736 + X^712 + X^672 + X^664 + X^648 + X^624 + X^584 + X^576 + X^536 + X^512 + X^496 + X^488 + X^448 + X^424 + X^376 + X^360 + X^336 + X^296 + X^288 + X^200 + X^160 + X^136 + 1 47 20 25 36 17 Errors: /home/mfd/gomagma: line 2: 6447 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host 3(NXDOMAIN) (194.165.15.3) Time: Thu Jan 22 09:50:06 2004 Input: k := GF(2); C := PrimitivePolynomial(k,9); C; for t in [32..41] do for j in [24..31] do for k in [17..23] do for m in [14..17] do for n in [8..13] do C := ((1 + X^n)^16)*((1 + X^m)^16)*((1 + X^k)^8)*((1 + X^j)^8)*((1 + X^t)^8) + X^1279; if IsPrimitive(C) then C; n; m; k; j; t; end if; end for; end for; end for; end for; end for; Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Thu Jan 22 2004 09:49:43 on modular [Seed = 544179070] ------------------------------------- X^9 + X^4 + 1 X^1279 + X^976 + X^848 + X^816 + X^784 + X^736 + X^720 + X^688 + X^656 + X^624 + X^608 + X^592 + X^576 + X^560 + X^544 + X^528 + X^496 + X^480 + X^448 + X^432 + X^416 + X^400 + X^384 + X^368 + X^352 + X^320 + X^288 + X^256 + X^240 + X^192 + X^160 + X^128 + 1 8 15 20 24 32 X^1279 + X^1016 + X^872 + X^856 + X^816 + X^712 + X^672 + X^656 + X^512 + X^504 + X^360 + X^344 + X^304 + X^200 + X^160 + X^144 + 1 10 16 18 25 32 X^1279 + X^1016 + X^872 + X^856 + X^816 + X^712 + X^672 + X^656 + X^512 + X^504 + X^360 + X^344 + X^304 + X^200 + X^160 + X^144 + 1 9 16 20 25 32 X^1279 + X^1072 + X^888 + X^880 + X^872 + X^832 + X^816 + X^696 + X^688 + X^680 + X^648 + X^640 + X^624 + X^616 + X^576 + X^496 + X^456 + X^448 + X^432 + X^424 + X^392 + X^384 + X^376 + X^256 + X^240 + X^200 + X^192 + X^184 + 1 12 15 23 25 32 X^1279 + X^1016 + X^800 + X^728 + X^512 + X^504 + X^288 + X^216 + 1 9 16 18 27 32 X^1279 + X^1072 + X^920 + X^864 + X^856 + X^832 + X^816 + X^712 + X^704 + X^680 + X^664 + X^648 + X^624 + X^616 + X^608 + X^600 + X^576 + X^496 + X^472 + X^464 + X^456 + X^448 + X^424 + X^408 + X^392 + X^368 + X^360 + X^256 + X^240 + X^216 + X^208 + X^152 + 1 13 15 19 27 32 X^1279 + X^1072 + X^904 + X^880 + X^856 + X^832 + X^816 + X^712 + X^688 + X^648 + X^640 + X^624 + X^616 + X^600 + X^576 + X^496 + X^472 + X^456 + X^448 + X^432 + X^424 + X^384 + X^360 + X^256 + X^240 + X^216 + X^192 + X^168 + 1 12 15 21 27 32 X^1279 + X^1040 + X^896 + X^880 + X^816 + X^736 + X^672 + X^656 + X^528 + X^512 + X^384 + X^368 + X^304 + X^224 + X^160 + X^144 + 1 10 16 18 28 32 X^1279 + X^1048 + X^904 + X^896 + X^824 + X^792 + X^776 + X^752 + X^680 + X^672 + X^648 + X^640 + X^632 + X^624 + X^568 + X^552 + X^528 + X^520 + X^496 + X^480 + X^424 + X^416 + X^408 + X^400 + X^376 + X^368 + X^296 + X^272 + X^256 + X^224 + X^152 + X^144 + 1 9 17 19 28 32 X^1279 + X^1040 + X^896 + X^880 + X^816 + X^736 + X^672 + X^656 + X^528 + X^512 + X^384 + X^368 + X^304 + X^224 + X^160 + X^144 + 1 9 16 20 28 32 X^1279 + X^1056 + X^920 + X^848 + X^832 + X^824 + X^800 + X^712 + X^696 + X^688 + X^664 + X^624 + X^616 + X^600 + X^592 + X^576 + X^568 + X^488 + X^480 + X^464 + X^456 + X^440 + X^432 + X^392 + X^368 + X^360 + X^344 + X^256 + X^232 + X^224 + X^208 + X^136 + 1 13 14 17 29 32 X^1279 + X^1072 + X^920 + X^864 + X^848 + X^840 + X^816 + X^712 + X^696 + X^688 + X^664 + X^640 + X^632 + X^616 + X^608 + X^592 + X^584 + X^488 + X^480 + X^464 + X^456 + X^440 + X^432 + X^408 + X^384 + X^376 + X^360 + X^256 + X^232 + X^224 + X^208 + X^152 + 1 13 14 19 29 32 X^1279 + X^1096 + X^936 + X^904 + X^864 + X^744 + X^704 + X^672 + X^584 + X^512 + X^424 + X^392 + X^352 + X^232 + X^192 + X^160 + 1 12 16 20 29 32 X^1279 + X^1080 + X^928 + X^880 + X^872 + X^824 + X^816 + X^728 + X^720 + X^664 + X^624 + X^608 + X^560 + X^520 + X^472 + X^456 + X^416 + X^360 + X^352 + X^264 + X^256 + X^208 + X^200 + X^152 + 1 13 16 19 25 33 X^1279 + X^1032 + X^904 + X^872 + X^824 + X^768 + X^760 + X^744 + X^696 + X^664 + X^640 + X^632 + X^608 + X^600 + X^560 + X^552 + X^536 + X^496 + X^480 + X^472 + X^432 + X^424 + X^400 + X^392 + X^368 + X^336 + X^288 + X^272 + X^264 + X^208 + X^160 + X^128 + 1 8 17 20 26 33 X^1279 + X^1072 + X^904 + X^896 + X^864 + X^816 + X^808 + X^728 + X^696 + X^688 + X^648 + X^632 + X^608 + X^600 + X^552 + X^520 + X^472 + X^464 + X^440 + X^424 + X^384 + X^376 + X^344 + X^264 + X^256 + X^208 + X^176 + X^168 + 1 11 16 21 26 33 Errors: /home/mfd/gomagma: line 2: 6521 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host 3(NXDOMAIN) (194.165.15.3) Time: Thu Jan 22 09:51:27 2004 Input: k := GF(2); C := PrimitivePolynomial(k,9); C; for t in [32..41] do for j in [24..31] do for k in [17..23] do for m in [14..17] do for n in [8..13] do C := ((1 + X^n)^8)*((1 + X^m)^16)*((1 + X^k)^16)*((1 + X^j)^8)*((1 + X^t)^8) + X^1279; if IsPrimitive(C) then C; n; m; k; j; t; end if; end for; end for; end for; end for; end for; Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Thu Jan 22 2004 09:51:04 on modular [Seed = 3583669972] ------------------------------------- X^9 + X^4 + 1 X^1279 + X^1144 + X^1040 + X^952 + X^920 + X^888 + X^848 + X^816 + X^784 + X^776 + X^728 + X^696 + X^672 + X^664 + X^624 + X^592 + X^584 + X^560 + X^552 + X^520 + X^480 + X^472 + X^448 + X^416 + X^368 + X^360 + X^328 + X^296 + X^256 + X^224 + X^192 + X^104 + 1 13 14 23 24 32 X^1279 + X^1064 + X^1000 + X^864 + X^800 + X^776 + X^712 + X^576 + X^552 + X^512 + X^488 + X^352 + X^288 + X^264 + X^200 + X^64 + 1 8 16 18 25 32 X^1279 + X^1096 + X^1032 + X^896 + X^840 + X^832 + X^824 + X^792 + X^776 + X^760 + X^728 + X^640 + X^624 + X^592 + X^576 + X^568 + X^560 + X^536 + X^528 + X^520 + X^504 + X^472 + X^456 + X^368 + X^336 + X^320 + X^304 + X^272 + X^264 + X^256 + X^200 + X^64 + 1 8 17 19 25 32 X^1279 + X^1104 + X^1000 + X^904 + X^880 + X^848 + X^800 + X^784 + X^776 + X^744 + X^648 + X^624 + X^584 + X^576 + X^560 + X^544 + X^528 + X^520 + X^480 + X^456 + X^360 + X^328 + X^320 + X^304 + X^256 + X^224 + X^200 + X^104 + 1 13 14 20 25 32 X^1279 + X^1128 + X^1032 + X^928 + X^904 + X^872 + X^832 + X^808 + X^704 + X^680 + X^672 + X^648 + X^608 + X^520 + X^480 + X^456 + X^448 + X^424 + X^320 + X^296 + X^256 + X^224 + X^200 + X^96 + 1 12 14 22 25 32 X^1279 + X^1072 + X^992 + X^864 + X^848 + X^816 + X^784 + X^736 + X^688 + X^640 + X^608 + X^592 + X^544 + X^528 + X^480 + X^464 + X^432 + X^384 + X^336 + X^288 + X^256 + X^224 + X^208 + X^80 + 1 10 14 19 26 32 X^1279 + X^1104 + X^1024 + X^896 + X^880 + X^848 + X^816 + X^800 + X^688 + X^672 + X^640 + X^624 + X^592 + X^512 + X^480 + X^464 + X^432 + X^416 + X^304 + X^288 + X^256 + X^224 + X^208 + X^80 + 1 10 14 21 26 32 X^1279 + X^1064 + X^1000 + X^848 + X^792 + X^784 + X^728 + X^576 + X^552 + X^512 + X^488 + X^336 + X^280 + X^272 + X^216 + X^64 + 1 8 16 17 27 32 X^1279 + X^1056 + X^984 + X^840 + X^832 + X^800 + X^760 + X^728 + X^696 + X^616 + X^584 + X^576 + X^552 + X^504 + X^480 + X^472 + X^440 + X^360 + X^328 + X^296 + X^256 + X^224 + X^216 + X^72 + 1 9 14 18 27 32 X^1279 + X^1192 + X^1112 + X^976 + X^936 + X^920 + X^896 + X^856 + X^840 + X^824 + X^744 + X^720 + X^704 + X^664 + X^640 + X^624 + X^608 + X^584 + X^568 + X^552 + X^528 + X^488 + X^472 + X^448 + X^368 + X^352 + X^336 + X^296 + X^272 + X^256 + X^216 + X^80 + 1 10 17 23 27 32 X^1279 + X^1112 + X^1024 + X^888 + X^824 + X^800 + X^736 + X^376 + X^312 + X^288 + X^224 + X^88 + 1 11 16 18 28 32 X^1279 + X^1176 + X^1072 + X^952 + X^848 + X^840 + X^736 + X^664 + X^616 + X^560 + X^512 + X^440 + X^336 + X^328 + X^224 + X^104 + 1 13 16 21 28 32 X^1279 + X^1144 + X^1048 + X^912 + X^888 + X^872 + X^856 + X^816 + X^792 + X^776 + X^760 + X^656 + X^640 + X^624 + X^616 + X^600 + X^584 + X^560 + X^544 + X^528 + X^520 + X^504 + X^488 + X^384 + X^368 + X^352 + X^328 + X^288 + X^272 + X^256 + X^232 + X^96 + 1 12 17 18 29 32 X^1279 + X^1128 + X^1048 + X^896 + X^824 + X^816 + X^744 + X^616 + X^592 + X^536 + X^512 + X^384 + X^312 + X^304 + X^232 + X^80 + 1 10 16 19 29 32 X^1279 + X^1120 + X^1016 + X^896 + X^872 + X^864 + X^832 + X^792 + X^768 + X^760 + X^728 + X^648 + X^640 + X^616 + X^608 + X^584 + X^576 + X^544 + X^536 + X^512 + X^504 + X^480 + X^472 + X^392 + X^360 + X^352 + X^328 + X^288 + X^256 + X^248 + X^224 + X^104 + 1 13 14 18 31 32 X^1279 + X^1160 + X^1080 + X^920 + X^912 + X^904 + X^840 + X^832 + X^744 + X^672 + X^664 + X^656 + X^592 + X^568 + X^504 + X^496 + X^488 + X^416 + X^328 + X^320 + X^256 + X^248 + X^240 + X^80 + 1 10 15 21 31 32 X^1279 + X^1136 + X^1064 + X^944 + X^864 + X^792 + X^728 + X^680 + X^672 + X^464 + X^456 + X^408 + X^344 + X^272 + X^192 + X^72 + 1 9 17 21 24 33 X^1279 + X^1088 + X^1024 + X^888 + X^848 + X^784 + X^768 + X^760 + X^704 + X^648 + X^624 + X^568 + X^560 + X^528 + X^520 + X^464 + X^440 + X^384 + X^328 + X^320 + X^304 + X^240 + X^200 + X^64 + 1 8 15 20 25 33 Errors: /home/mfd/gomagma: line 2: 6540 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host 3(NXDOMAIN) (194.165.15.3) Time: Thu Jan 22 09:53:41 2004 Input: k := GF(2); C := PrimitivePolynomial(k,9); C; for t in [32..41] do for j in [24..31] do for k in [17..23] do for m in [14..17] do for n in [8..13] do C := ((1 + X^n)^11)*((1 + X^m)^13)*((1 + X^k)^17)*((1 + X^j)^8)*((1 + X^t)^8) + X^1279; if IsPrimitive(C) then C; n; m; k; j; t; end if; end for; end for; end for; end for; end for; Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Thu Jan 22 2004 09:53:17 on modular [Seed = 3903277932] ------------------------------------- X^9 + X^4 + 1 X^1279 + X^1042 + X^1032 + X^1027 + X^1025 + X^1022 + X^1017 + X^1015 + X^1012 + X^1010 + X^1007 + X^1005 + X^1000 + X^997 + X^995 + X^990 + X^982 + X^980 + X^972 + X^967 + X^965 + X^957 + X^955 + X^950 + X^942 + X^940 + X^932 + X^927 + X^925 + X^922 + X^917 + X^915 + X^912 + X^910 + X^907 + X^905 + X^900 + X^897 + X^895 + X^890 + X^882 + X^880 + X^872 + X^867 + X^865 + X^862 + X^857 + X^855 + X^852 + X^847 + X^845 + X^837 + X^833 + X^825 + X^823 + X^822 + X^818 + X^815 + X^813 + X^812 + X^808 + X^807 + X^803 + X^798 + X^797 + X^795 + X^788 + X^786 + X^782 + X^776 + X^775 + X^773 + X^772 + X^771 + X^770 + X^769 + X^767 + X^766 + X^763 + X^762 + X^761 + X^760 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X^797 + X^796 + X^793 + X^791 + X^789 + X^786 + X^785 + X^784 + X^783 + X^779 + X^778 + X^777 + X^775 + X^774 + X^773 + X^772 + X^771 + X^770 + X^766 + X^765 + X^764 + X^763 + X^761 + X^760 + X^759 + X^758 + X^756 + X^754 + X^753 + X^752 + X^751 + X^747 + X^746 + X^744 + X^742 + X^740 + X^739 + X^734 + X^733 + X^732 + X^728 + X^721 + X^720 + X^719 + X^714 + X^709 + X^707 + X^702 + X^700 + X^697 + X^695 + X^693 + X^690 + X^688 + X^683 + X^681 + X^679 + X^678 + X^677 + X^676 + X^674 + X^667 + X^665 + X^664 + X^663 + X^662 + X^660 + X^658 + X^653 + X^651 + X^648 + X^646 + X^645 + ** WARNING: Output too long, hence truncated. Errors: /home/mfd/gomagma: line 2: 6577 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host 3(NXDOMAIN) (194.165.15.3) Time: Thu Jan 22 09:56:14 2004 Input: k := GF(2); C := PrimitivePolynomial(k,9); C; for j in [24..31] do for k in [17..23] do for m in [14..17] do for n in [8..13] do C := ((1 + X^n)^11)*((1 + X^m)^13)*((1 + X^k)^17)*((1 + X^j)^19) + X^1279; if IsPrimitive(C) then C; n; m; k; j; end if; end for; end for; end for; end for; end for; Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Thu Jan 22 2004 09:55:51 on modular [Seed = 2480682941] ------------------------------------- X^9 + X^4 + 1 X^1279 + X^1037 + X^1027 + X^1023 + X^1020 + X^1017 + X^1010 + X^1007 + X^1006 + X^1000 + X^999 + X^990 + X^983 + X^982 + X^981 + X^975 + X^971 + X^967 + X^966 + X^964 + X^961 + X^959 + X^958 + X^957 + X^954 + X^950 + X^947 + X^944 + X^942 + X^941 + X^940 + X^937 + X^935 + X^931 + X^930 + 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truncated. Errors: /home/mfd/gomagma: line 2: 6602 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host 3(NXDOMAIN) (194.165.15.3) Time: Thu Jan 22 09:58:14 2004 Input: k := GF(2); C := PrimitivePolynomial(k,9); C; for j in [25..27] do for k in [17..23] do for m in [14..17] do for n in [8..13] do C := ((1 + X^n)^11)*((1 + X^m)^13)*((1 + X^k)^17)*((1 + X^j)^19) + X^1279; if IsPrimitive(C) then C; n; m; k; j; end if; end for; end for; end for; end for; end for; Output: Magma V2.10-6 Thu Jan 22 2004 09:58:05 on modular [Seed = 2378311977] ------------------------------------- X^9 + X^4 + 1 X^1279 + X^1154 + X^1143 + X^1140 + X^1133 + X^1132 + X^1129 + X^1128 + X^1122 + X^1121 + X^1119 + X^1118 + X^1117 + X^1114 + X^1111 + X^1108 + X^1106 + X^1103 + X^1102 + X^1100 + X^1098 + X^1097 + X^1096 + X^1095 + X^1093 + X^1092 + X^1091 + X^1088 + X^1087 + X^1086 + X^1085 + X^1084 + X^1082 + X^1080 + X^1074 + X^1073 + X^1072 + X^1071 + X^1070 + X^1069 + X^1067 + X^1066 + X^1063 + X^1061 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X^967 + X^966 + X^965 + X^964 + X^962 + X^961 + X^960 + X^959 + X^956 + X^955 + X^954 + X^953 + X^951 + X^950 + X^949 + X^948 + X^947 + X^943 + X^940 + X^939 + X^938 + X^936 + X^935 + X^934 + X^933 + X^932 + X^929 + X^928 + X^927 + X^926 + X^923 + X^922 + X^921 + X^920 + X^919 + X^917 + X^916 + X^915 + X^912 + X^908 + X^907 + X^906 + X^905 + X^904 + X^902 + X^901 + X^900 + X^899 + X^896 + X^895 + X^894 + X^893 + X^891 + X^890 + X^889 + X^888 + X^887 + X^883 + X^880 + X^878 + X^876 + X^875 + X^874 + X^873 + X^872 + X^871 + X^869 + X^868 + X^867 + X^866 + X^864 + X^862 + X^861 + X^859 + X^857 + X^852 + X^847 + X^846 + X^844 + X^842 + X^841 + X^839 + X^836 + X^835 + X^834 + X^831 + X^830 + X^829 + X^827 + X^823 + X^820 + X^816 + X^815 + X^814 + X^812 + X^811 + X^809 + X^808 + X^807 + X^804 + X^802 + X^799 + X^797 + X^792 + X^791 + X^787 + X^784 + X^782 + X^781 + X^776 + X^775 + X^770 + X^769 + X^767 + X^764 + X^760 + X^759 + X^754 + X^752 + X^749 + X^747 + X^744 + X^743 + X^742 + X^740 + X^739 + X^737 + X^736 + X^735 + X^731 + X^728 + X^724 + X^722 + X^721 + X^720 + X^717 + X^716 + X^715 + X^712 + X^710 + X^709 + X^707 + X^705 + X^704 + X^699 + X^694 + X^692 + X^690 + X^689 + X^685 + X^684 + X^683 + X^682 + X^680 + X^678 + X^677 + X^676 + X^675 + X^673 + X^672 + X^662 + X^661 + X^660 + X^658 + X^657 + X^655 + X^653 + X^652 + X^651 + X^650 + X^649 + X^648 + X^647 + X^646 + X^645 + X^644 + X^643 + X^641 + X^639 + X^635 + X^634 + X^632 + X^631 + X^630 + X^629 + X^628 + X^627 + X^626 + X^625 + X^624 + X^622 + X^621 + X^618 + X^617 + X^616 + X^614 + X^613 + X^609 + X^608 + X^607 + X^604 + X^602 + X^601 + X^598 + X^597 + X^595 + X^594 + X^593 + X^591 + X^590 + X^588 + X^586 + X^585 + X^583 + X^582 + X^581 + X^577 + X^574 + X^572 + X^570 + X^569 + X^568 + X^567 + X^566 + X^565 + X^563 + X^561 + X^560 + X^559 + X^558 + X^556 + X^554 + X^553 + X^552 + X^551 + X^550 + X^549 + X^547 + X^545 + X^542 + X^538 + X^537 + X^536 + X^534 + X^533 + X^531 + X^529 + X^528 + X^526 + X^525 + X^524 + X^522 + X^521 + X^518 + X^517 + X^515 + X^512 + X^511 + X^510 + X^506 + X^505 + X^503 + X^502 + X^501 + X^498 + X^497 + X^495 + X^494 + X^493 + X^492 + X^491 + X^490 + X^489 + X^488 + X^487 + X^485 + X^484 + X^480 + X^478 + X^476 + X^475 + X^474 + X^473 + X^472 + X^471 + X^470 + X^469 + X^468 + X^467 + X^466 + X^464 + X^462 + X^461 + X^459 + X^458 + X^457 + X^447 + X^446 + X^444 + X^443 + X^442 + X^441 + X^439 + X^437 + X^436 + X^435 + X^434 + X^430 + X^429 + X^427 + X^425 + X^420 + X^415 + X^414 + X^412 + X^410 + X^409 + X^407 + X^404 + X^403 + X^402 + X^399 + X^398 + X^397 + X^395 + X^391 + X^388 + X^384 + X^383 + X^382 + X^380 + X^379 + X^377 + X^376 + X^375 + X^372 + X^370 + X^367 + X^365 + X^360 + X^359 + X^355 + X^352 + X^350 + X^349 + X^344 + X^343 + X^338 + X^337 + X^335 + X^332 + X^328 + X^327 + X^322 + X^320 + X^317 + X^315 + X^312 + X^311 + X^310 + X^308 + X^307 + X^305 + X^304 + X^303 + X^299 + X^296 + X^292 + X^290 + X^289 + X^288 + X^285 + X^284 + X^283 + X^280 + X^278 + X^277 + X^275 + X^273 + X^272 + X^267 + X^262 + X^260 + X^258 + X^257 + X^255 + X^253 + X^252 + X^251 + X^250 + X^248 + X^247 + X^246 + X^245 + X^244 + X^243 + X^241 + X^239 + X^236 + X^232 + X^231 + X^230 + X^229 + X^228 + X^226 + X^225 + X^224 + X^223 + X^220 + X^219 + X^218 + X^217 + X^215 + X^214 + X^213 + X^212 + X^211 + X^207 + X^204 + X^203 + X^202 + X^200 + X^199 + X^198 + X^197 + X^196 + X^193 + X^192 + X^191 + X^190 + X^187 + X^186 + X^185 + X^184 + X^183 + X^181 + X^180 + X^179 + X^176 + X^172 + X^171 + X^170 + X^169 + X^168 + X^166 + X^165 + X^164 + X^163 + X^160 + X^159 + X^158 + X^157 + X^155 + X^154 + X^153 + X^152 + X^151 + X^147 + X^144 + X^142 + X^140 + X^139 + X^138 + X^137 + X^136 + X^135 + X^133 + X^132 + X^131 + X^130 + X^128 + X^126 + X^125 + X^123 + X^121 + X^116 + X^111 + X^110 + X^108 + X^106 + X^105 + X^ ** WARNING: Output too long, hence truncated. ************** MAGMA ***************** Host 3(NXDOMAIN) (194.165.15.3) Time: Thu Jan 22 10:00:19 2004 Input: k := GF(2); C := PrimitivePolynomial(k,9); C; for j in [31..32] do for k in [17..23] do for m in [14..17] do for n in [8..13] do C := ((1 + X^n)^11)*((1 + X^m)^13)*((1 + X^k)^19)*((1 + X^j)^17) + X^1279; if IsPrimitive(C) then C; n; m; k; j; end if; end for; end for; end for; end for; end for; Output: Magma V2.10-6 Thu Jan 22 2004 10:00:10 on modular [Seed = 3186759838] ------------------------------------- X^9 + X^4 + 1 X^1279 + X^1260 + X^1248 + X^1243 + X^1240 + X^1236 + X^1231 + X^1229 + X^1228 + X^1224 + X^1223 + X^1220 + X^1219 + X^1217 + X^1216 + X^1212 + X^1211 + X^1209 + X^1208 + X^1207 + X^1205 + X^1204 + X^1203 + X^1199 + X^1197 + X^1196 + X^1193 + X^1191 + X^1189 + X^1187 + X^1185 + X^1184 + X^1183 + X^1179 + X^1177 + X^1175 + X^1173 + X^1171 + X^1169 + X^1167 + X^1165 + X^1163 + X^1161 + X^1159 + X^1157 + X^1155 + X^1153 + X^1152 + X^1151 + X^1149 + X^1145 + X^1143 + X^1141 + X^1140 + X^1139 + X^1137 + X^1132 + X^1131 + X^1129 + X^1128 + X^1127 + X^1125 + X^1124 + X^1120 + X^1119 + X^1117 + X^1116 + X^1113 + X^1112 + X^1108 + X^1105 + X^1100 + X^1099 + X^1096 + X^1088 + X^1085 + X^1076 + X^1068 + X^1059 + X^1048 + X^1045 + X^1031 + X^1028 + X^1017 + X^1008 + X^1000 + X^991 + X^988 + X^980 + X^977 + X^976 + X^971 + X^968 + X^964 + X^963 + X^960 + X^959 + X^957 + X^956 + X^952 + X^951 + X^949 + X^948 + X^947 + X^945 + X^944 + X^940 + X^939 + X^937 + X^936 + X^935 + X^933 + X^931 + X^928 + X^927 + X^925 + X^924 + X^921 + X^920 + X^919 + X^917 + X^916 + X^915 + X^913 + X^908 + X^907 + X^905 + X^904 + X^901 + X^900 + X^896 + X^893 + X^888 + X^884 + X^880 + X^876 + X^872 + X^868 + X^863 + X^860 + X^856 + X^855 + X^852 + X^851 + X^849 + X^848 + X^843 + X^841 + X^840 + X^839 + X^837 + X^836 + X^835 + X^832 + X^831 + X^829 + X^828 + X^825 + X^823 + X^821 + X^820 + X^819 + X^817 + X^816 + X^812 + X^811 + X^809 + X^808 + X^807 + X^805 + X^804 + X^800 + X^799 + X^797 + X^796 + X^793 + X^792 + X^788 + X^785 + X^780 + X^779 + X^776 + X^768 + X^765 + X^764 + 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X^115 + X^111 + X^109 + X^108 + X^107 + X^105 + X^103 + X^101 + X^99 + X^97 + X^95 + X^93 + X^91 + X^89 + X^87 + X^85 + X^83 + X^81 + X^77 + X^76 + X^75 + X^73 + X^71 + X^69 + X^67 + X^64 + X^63 + X^61 + X^57 + X^56 + X^55 + X^53 + X^52 + X^51 + X^49 + X^48 + X^44 + X^43 + X^41 + X^40 + X^37 + X^36 + X^32 + X^31 + X^29 + X^24 + X^20 + X^17 + X^12 + 1 12 17 20 31 X^1279 + X^1196 + X^1188 + X^1182 + X^1180 + X^1175 + X^1174 + X^1172 + X^1167 + X^1166 + X^1165 + X^1161 + X^1159 + X^1158 + X^1157 + X^1154 + X^1153 + X^1149 + X^1146 + X^1145 + X^1144 + X^1143 + X^1141 + X^1138 + X^1137 + X^1136 + X^1135 + X^1133 + X^1132 + X^1128 + X^1127 + X^1126 + X^1125 + X^1124 + X^1123 + X^1122 + X^1120 + X^1117 + X^1116 + X^1115 + X^1114 + X^1111 + X^1109 + X^1108 + X^1107 + X^1106 + X^1105 + X^1103 + X^1102 + X^1101 + X^1099 + X^1098 + X^1093 + X^1087 + X^1086 + X^1085 + X^1080 + X^1078 + X^1074 + X^1073 + X^1072 + X^1070 + X^1067 + X^1066 + X^1064 + X^1063 + X^1056 + X^1049 + X^1046 + X^1045 + X^1039 + X^1038 + X^1035 + X^1021 + X^1018 + X^1017 + X^1011 + X^1010 + X^1007 + X^993 + X^990 + X^989 + X^983 + X^982 + X^979 + X^972 + X^965 + X^964 + X^962 + X^961 + X^958 + X^956 + X^955 + X^954 + X^950 + X^948 + X^943 + X^942 + X^941 + X^935 + X^930 + X^929 + X^927 + X^926 + X^925 + X^923 + X^922 + X^921 + X^920 + X^919 + X^917 + X^914 + X^913 + X^912 + X^911 + X^908 + X^906 + X^905 + X^904 + X^903 + X^902 + X^901 + X^900 + X^896 + X^895 + X^893 + X^892 + X^891 + X^890 + X^887 + X^885 + X^884 + X^883 + X^882 + X^879 + X^875 + X^874 + X^871 + X^870 + X^869 + X^867 + X^863 + X^862 + X^861 + X^860 + X^856 + X^854 + X^853 + X^852 + X^848 + X^844 + X^840 + X^839 + X^838 + X^836 + X^832 + X^831 + X^830 + X^829 + X^825 + X^823 + X^822 + X^821 + X^818 + X^817 + X^813 + X^810 + X^809 + X^808 + X^807 + X^805 + X^802 + X^801 + X^800 + X^799 + X^797 + X^796 + X^792 + X^791 + X^790 + X^789 + X^788 + X^787 + X^786 + X^784 + X^781 + X^780 + X^779 + X^778 + X^775 + X^773 + X^772 + X^771 + X^770 + X^769 + X^767 + X^766 + X^765 + X^763 + X^762 + X^757 + X^751 + X^750 + X^749 + X^744 + X^742 + X^738 + X^737 + X^736 + X^734 + X^731 + X^730 + X^728 + X^727 + X^720 + X^713 + X^710 + X^709 + X^703 + X^702 + X^700 + X^699 + X^692 + X^686 + X^685 + X^684 + X^682 + X^681 + X^679 + X^678 + X^676 + X^675 + X^674 + X^670 + X^669 + X^665 + X^663 + X^662 + X^661 + X^658 + X^654 + X^650 + X^649 + X^648 + X^646 + X^645 + X^643 + X^642 + X^641 + X^640 + X^639 + X^637 + X^632 + X^631 + X^630 + X^627 + X^625 + X^624 + X^622 + X^621 + X^615 + X^614 + X^613 + X^611 + X^610 + X^609 + X^603 + X^602 + X^599 + X^597 + X^594 + X^593 + X^587 + X^586 + X^585 + X^583 + X^582 + X^581 + X^575 + X^574 + X^572 + X^571 + X^569 + X^566 + X^565 + X^564 + X^559 + X^557 + X^556 + X^555 + X^554 + X^553 + X^551 + X^550 + X^548 + X^547 + X^546 + X^542 + X^538 + X^535 + X^534 + X^533 + X^531 + X^527 + X^526 + X^522 + X^521 + X^520 + X^518 + X^517 + X^515 + X^514 + X^512 + X^511 + X^510 + X^504 + X^497 + X^496 + X^494 + X^493 + X^487 + X^486 + X^483 + X^476 + X^469 + X^468 + X^466 + X^465 + X^462 + X^460 + X^459 + X^458 + X^454 + X^452 + X^447 + X^446 + X^445 + X^439 + X^434 + X^433 + X^431 + X^430 + X^429 + X^427 + X^426 + X^425 + X^424 + X^423 + X^421 + X^418 + X^417 + X^416 + X^415 + X^412 + X^410 + X^409 + X^408 + X^407 + X^406 + X^405 + X^404 + X^400 + X^399 + X^397 + X^396 + X^395 + X^394 + X^391 + X^389 + X^388 + X^387 + X^386 + X^383 + X^379 + X^378 + X^375 + X^374 + X^373 + X^371 + X^367 + X^366 + X^365 + X^364 + X^360 + X^358 + X^357 + X^356 + X^352 + X^348 + X^344 + X^343 + X^342 + X^340 + X^336 + X^335 + X^334 + X^333 + X^329 + X^327 + X^326 + X^325 + X^322 + X^321 + X^317 + X^314 + X^313 + X^312 + X^311 + X^309 + X^306 + X^305 + X^304 + X^303 + X^301 + X^300 + X^296 + X^295 + X^294 + X^293 + X^292 + X^291 + X^290 + X^288 + X^285 + X^284 + X^283 + X^282 + X^279 + X^277 + X^276 + X^275 + X^274 + X^273 + X^271 + X^270 + X^269 + X^267 + X^266 + X^261 + X^255 + X^254 + X^253 + X^248 + X^246 + X^242 + X^241 + X^240 + X^238 + X^235 + X^234 + X^232 + X^231 + X^224 + X^217 + X^214 + X^213 + X^207 + X^206 + X^203 + X^189 + X^186 + X^185 + X^179 + X^178 + X^175 + X^161 + X^158 + X^157 + X^151 + X^150 + X^147 + X^140 + X^133 + X^132 + X^130 + X^129 + X^126 + X^124 + X^123 + X^122 + X^118 + X^116 + X^111 + X^110 + X^109 + X^103 + X^98 + X^97 + X^95 + X^94 + X^93 + X^91 + X^90 + X^89 + X^88 + X^87 + X^85 + X^82 + X^81 + X^80 + X^79 + X^76 + X^74 + X^73 + X^72 + X^71 + X^70 + X^69 + X^68 + X^64 + X^63 + X^61 + X^60 + X^59 + X^58 + X^55 + X^53 + X^52 + X^51 + X^50 + X^47 + X^43 + X^42 + X^39 + X^38 + X^37 + X^35 + X^31 + X^30 + X^29 + X^24 + X^22 + X^21 + X^16 + X^14 + X^8 + 1 8 14 21 31 >> end for;; ^ User error: bad syntax Total time: 8.339 seconds, Total memory usage: 2.24MB ************** MAGMA ***************** Host 3(NXDOMAIN) (194.165.15.3) Time: Thu Jan 22 10:01:19 2004 Input: k := GF(2); C := PrimitivePolynomial(k,9); C; for j in [31..32] do for k in [17..23] do for m in [14..17] do for n in [8..13] do C := ((1 + X^n)^11)*((1 + X^m)^13)*((1 + X^k)^19)*((1 + X^j)^17) + X^1279; if IsPrimitive(C) then C; n; m; k; j; end if; end for; end for; end for; end for; Output: Magma V2.10-6 Thu Jan 22 2004 10:01:09 on modular [Seed = 1360983230] ------------------------------------- X^9 + X^4 + 1 X^1279 + X^1260 + X^1248 + X^1243 + X^1240 + X^1236 + X^1231 + X^1229 + X^1228 + X^1224 + X^1223 + X^1220 + X^1219 + X^1217 + X^1216 + X^1212 + X^1211 + X^1209 + X^1208 + X^1207 + X^1205 + X^1204 + X^1203 + X^1199 + X^1197 + X^1196 + X^1193 + X^1191 + X^1189 + X^1187 + X^1185 + X^1184 + X^1183 + X^1179 + X^1177 + X^1175 + X^1173 + X^1171 + X^1169 + X^1167 + X^1165 + X^1163 + X^1161 + X^1159 + X^1157 + X^1155 + X^1153 + X^1152 + X^1151 + X^1149 + X^1145 + X^1143 + X^1141 + X^1140 + X^1139 + X^1137 + X^1132 + X^1131 + X^1129 + X^1128 + X^1127 + X^1125 + X^1124 + X^1120 + X^1119 + X^1117 + X^1116 + X^1113 + X^1112 + X^1108 + X^1105 + X^1100 + X^1099 + X^1096 + X^1088 + X^1085 + X^1076 + X^1068 + X^1059 + X^1048 + X^1045 + X^1031 + X^1028 + X^1017 + X^1008 + X^1000 + X^991 + X^988 + X^980 + X^977 + X^976 + X^971 + X^968 + X^964 + X^963 + X^960 + X^959 + X^957 + X^956 + X^952 + X^951 + X^949 + X^948 + X^947 + X^945 + X^944 + X^940 + X^939 + X^937 + X^936 + X^935 + X^933 + X^931 + X^928 + X^927 + X^925 + X^924 + X^921 + X^920 + X^919 + X^917 + X^916 + X^915 + X^913 + X^908 + X^907 + X^905 + X^904 + X^901 + X^900 + X^896 + X^893 + X^888 + X^884 + X^880 + X^876 + X^872 + X^868 + X^863 + X^860 + X^856 + X^855 + X^852 + X^851 + X^849 + X^848 + X^843 + X^841 + X^840 + X^839 + X^837 + X^836 + X^835 + X^832 + X^831 + X^829 + X^828 + X^825 + X^823 + X^821 + X^820 + X^819 + X^817 + X^816 + X^812 + X^811 + X^809 + X^808 + X^807 + X^805 + X^804 + X^800 + X^799 + X^797 + X^796 + X^793 + X^792 + X^788 + X^785 + X^780 + X^779 + X^776 + X^768 + X^765 + X^764 + X^756 + X^752 + X^748 + X^747 + X^744 + X^740 + X^739 + X^735 + X^733 + X^732 + X^727 + X^725 + X^724 + X^723 + X^721 + X^720 + X^716 + X^715 + X^713 + X^712 + X^709 + X^707 + X^703 + X^701 + X^700 + X^695 + X^693 + X^691 + X^689 + X^687 + X^683 + X^681 + X^680 + X^679 + X^677 + X^675 + X^673 + X^669 + X^668 + X^667 + X^665 + X^663 + X^661 + X^660 + X^659 + X^655 + X^653 + X^651 + X^649 + X^648 + X^647 + X^645 + X^641 + X^640 + X^639 + X^637 + X^635 + X^633 + X^627 + X^625 + X^623 + X^621 + X^620 + X^619 + X^615 + X^613 + X^612 + X^611 + X^609 + X^607 + X^605 + X^601 + X^600 + X^599 + X^597 + X^595 + X^593 + X^592 + X^591 + X^587 + X^585 + X^583 + X^581 + X^580 + X^579 + X^577 + X^573 + X^571 + X^569 + X^567 + X^565 + X^560 + X^559 + X^557 + X^553 + X^551 + X^548 + X^547 + X^545 + X^544 + X^540 + X^539 + X^537 + X^536 + X^535 + X^533 + X^528 + X^527 + X^525 + X^521 + X^520 + X^516 + X^513 + X^512 + X^508 + X^504 + X^496 + X^495 + X^492 + X^484 + X^481 + X^480 + X^475 + X^472 + X^468 + X^467 + X^464 + X^463 + X^461 + X^460 + X^456 + X^455 + X^453 + X^452 + X^451 + X^449 + X^448 + X^444 + X^443 + X^441 + X^440 + X^439 + X^437 + X^435 + X^432 + X^431 + X^429 + X^428 + X^425 + X^424 + X^423 + X^421 + X^420 + X^419 + X^417 + X^412 + X^411 + X^409 + X^408 + X^405 + X^404 + X^400 + X^397 + X^392 + X^388 + X^384 + X^380 + X^376 + X^372 + X^367 + X^364 + X^360 + X^359 + X^356 + X^355 + X^353 + X^352 + X^347 + X^345 + X^344 + X^343 + X^341 + X^340 + X^339 + X^336 + X^335 + X^333 + X^332 + X^329 + X^327 + X^325 + X^324 + X^323 + X^321 + X^320 + X^316 + X^315 + X^313 + X^312 + X^311 + X^309 + X^308 + X^304 + X^303 + X^301 + X^300 + X^297 + X^296 + X^292 + X^289 + X^284 + X^283 + X^280 + X^272 + X^269 + X^260 + X^252 + X^243 + X^232 + X^229 + X^215 + X^212 + X^201 + X^192 + X^184 + X^175 + X^172 + X^164 + X^161 + X^160 + X^155 + X^152 + X^148 + X^147 + X^144 + X^143 + X^141 + X^140 + X^136 + X^135 + X^133 + X^132 + X^131 + X^129 + X^128 + X^123 + X^121 + X^120 + X^119 + X^117 + X^115 + X^111 + X^109 + X^108 + X^107 + X^105 + X^103 + X^101 + X^99 + X^97 + X^95 + X^93 + X^91 + X^89 + X^87 + X^85 + X^83 + X^81 + X^77 + X^76 + X^75 + X^73 + X^71 + X^69 + X^67 + X^64 + X^63 + X^61 + X^57 + X^56 + X^55 + X^53 + X^52 + X^51 + X^49 + X^48 + X^44 + X^43 + X^41 + X^40 + X^37 + X^36 + X^32 + X^31 + X^29 + X^24 + X^20 + X^17 + X^12 + 1 12 17 20 31 X^1279 + X^1196 + X^1188 + X^1182 + X^1180 + X^1175 + X^1174 + X^1172 + X^1167 + X^1166 + X^1165 + X^1161 + X^1159 + X^1158 + X^1157 + X^1154 + X^1153 + X^1149 + X^1146 + X^1145 + X^1144 + X^1143 + X^1141 + X^1138 + X^1137 + X^1136 + X^1135 + X^1133 + X^1132 + X^1128 + X^1127 + X^1126 + X^1125 + X^1124 + X^1123 + X^1122 + X^1120 + X^1117 + X^1116 + X^1115 + X^1114 + X^1111 + X^1109 + X^1108 + X^1107 + X^1106 + X^1105 + X^1103 + X^1102 + X^1101 + X^1099 + X^1098 + X^1093 + X^1087 + X^1086 + X^1085 + X^1080 + X^1078 + X^1074 + X^1073 + X^1072 + X^1070 + X^1067 + X^1066 + X^1064 + X^1063 + X^1056 + X^1049 + X^1046 + X^1045 + X^1039 + X^1038 + X^1035 + X^1021 + X^1018 + X^1017 + X^1011 + X^1010 + X^1007 + X^993 + X^990 + X^989 + X^983 + X^982 + X^979 + X^972 + X^965 + X^964 + X^962 + X^961 + X^958 + X^956 + X^955 + X^954 + X^950 + X^948 + X^943 + X^942 + X^941 + X^935 + X^930 + X^929 + X^927 + X^926 + X^925 + X^923 + X^922 + X^921 + X^920 + X^919 + X^917 + X^914 + X^913 + X^912 + X^911 + X^908 + X^906 + X^905 + X^904 + X^903 + X^902 + X^901 + X^900 + X^896 + X^895 + X^893 + X^892 + X^891 + X^890 + X^887 + X^885 + X^884 + X^883 + X^882 + X^879 + X^875 + X^874 + X^871 + X^870 + X^869 + X^867 + X^863 + X^862 + X^861 + X^860 + X^856 + X^854 + X^853 + X^852 + X^848 + X^844 + X^840 + X^839 + X^838 + X^836 + X^832 + X^831 + X^830 + X^829 + X^825 + X^823 + X^822 + X^821 + X^818 + X^817 + X^813 + X^810 + X^809 + X^808 + X^807 + X^805 + X^802 + X^801 + X^800 + X^799 + X^797 + X^796 + X^792 + X^791 + X^790 + X^789 + X^788 + X^787 + X^786 + X^784 + X^781 + X^780 + X^779 + X^778 + X^775 + X^773 + X^772 + X^771 + X^770 + X^769 + X^767 + X^766 + X^765 + X^763 + X^762 + X^757 + X^751 + X^750 + X^749 + X^744 + X^742 + X^738 + X^737 + X^736 + X^734 + X^731 + X^730 + X^728 + X^727 + X^720 + X^713 + X^710 + X^709 + X^703 + X^702 + X^700 + X^699 + X^692 + X^686 + X^685 + X^684 + X^682 + X^681 + X^679 + X^678 + X^676 + X^675 + X^674 + X^670 + X^669 + X^665 + X^663 + X^662 + X^661 + X^658 + X^654 + X^650 + X^649 + X^648 + X^646 + X^645 + X^643 + X^642 + X^641 + X^640 + X^639 + X^637 + X^632 + X^631 + X^630 + X^627 + X^625 + X^624 + X^622 + X^621 + X^615 + X^614 + X^613 + X^611 + X^610 + X^609 + X^603 + X^602 + X^599 + X^597 + X^594 + X^593 + X^587 + X^586 + X^585 + X^583 + X^582 + X^581 + X^575 + X^574 + X^572 + X^571 + X^569 + X^566 + X^565 + X^564 + X^559 + X^557 + X^556 + X^555 + X^554 + X^553 + X^551 + X^550 + X^548 + X^547 + X^546 + X^542 + X^538 + X^535 + X^534 + X^533 + X^531 + X^527 + X^526 + X^522 + X^521 + X^520 + X^518 + X^517 + X^515 + X^514 + X^512 + X^511 + X^510 + X^504 + X^497 + X^496 + X^494 + X^493 + X^487 + X^486 + X^483 + X^476 + X^469 + X^468 + X^466 + X^465 + X^462 + X^460 + X^459 + X^458 + X^454 + X^452 + X^447 + X^446 + X^445 + X^439 + X^434 + X^433 + X^431 + X^430 + X^429 + X^427 + X^426 + X^425 + X^424 + X^423 + X^421 + X^418 + X^417 + X^416 + X^415 + X^412 + X^410 + X^409 + X^408 + X^407 + X^406 + X^405 + X^404 + X^400 + X^399 + X^397 + X^396 + X^395 + X^394 + X^391 + X^389 + X^388 + X^387 + X^386 + X^383 + X^379 + X^378 + X^375 + X^374 + X^373 + X^371 + X^367 + X^366 + X^365 + X^364 + X^360 + X^358 + X^357 + X^356 + X^352 + X^348 + X^344 + X^343 + X^342 + X^340 + X^336 + X^335 + X^334 + X^333 + X^329 + X^327 + X^326 + X^325 + X^322 + X^321 + X^317 + X^314 + X^313 + X^312 + X^311 + X^309 + X^306 + X^305 + X^304 + X^303 + X^301 + X^300 + X^296 + X^295 + X^294 + X^293 + X^292 + X^291 + X^290 + X^288 + X^285 + X^284 + X^283 + X^282 + X^279 + X^277 + X^276 + X^275 + X^274 + X^273 + X^271 + X^270 + X^269 + X^267 + X^266 + X^261 + X^255 + X^254 + X^253 + X^248 + X^246 + X^242 + X^241 + X^240 + X^238 + X^235 + X^234 + X^232 + X^231 + X^224 + X^217 + X^214 + X^213 + X^207 + X^206 + X^203 + X^189 + X^186 + X^185 + X^179 + X^178 + X^175 + X^161 + X^158 + X^157 + X^151 + X^150 + X^147 + X^140 + X^133 + X^132 + X^130 + X^129 + X^126 + X^124 + X^123 + X^122 + X^118 + X^116 + X^111 + X^110 + X^109 + X^103 + X^98 + X^97 + X^95 + X^94 + X^93 + X^91 + X^90 + X^89 + X^88 + X^87 + X^85 + X^82 + X^81 + X^80 + X^79 + X^76 + X^74 + X^73 + X^72 + X^71 + X^70 + X^69 + X^68 + X^64 + X^63 + X^61 + X^60 + X^59 + X^58 + X^55 + X^53 + X^52 + X^51 + X^50 + X^47 + X^43 + X^42 + X^39 + X^38 + X^37 + X^35 + X^31 + X^30 + X^29 + X^24 + X^22 + X^21 + X^16 + X^14 + X^8 + 1 8 14 21 31 Total time: 8.409 seconds, Total memory usage: 2.24MB ************** MAGMA ***************** Host 3(NXDOMAIN) (194.165.15.3) Time: Thu Jan 22 10:03:05 2004 Input: k := GF(2); C := PrimitivePolynomial(k,9); C; for j in [31..32] do for k in [17..23] do for m in [14..17] do for n in [8..13] do C := ((1 + X^n)^19)*((1 + X^m)^17)*((1 + X^k)^13)*((1 + X^j)^11) + X^1279; if IsPrimitive(C) then C; n; m; k; j; end if; end for; end for; end for; end for; Output: Magma V2.10-6 Thu Jan 22 2004 10:02:55 on modular [Seed = 2067062078] ------------------------------------- X^9 + X^4 + 1 X^1279 + X^1146 + X^1133 + X^1130 + X^1124 + X^1120 + X^1117 + X^1115 + X^1111 + X^1108 + X^1107 + X^1104 + X^1102 + X^1099 + X^1098 + X^1095 + X^1093 + X^1091 + X^1089 + X^1086 + X^1085 + X^1084 + X^1082 + X^1080 + X^1077 + X^1076 + X^1073 + X^1071 + X^1069 + X^1068 + X^1067 + X^1064 + X^1062 + X^1060 + X^1055 + X^1054 + X^1053 + X^1051 + X^1049 + X^1046 + X^1040 + X^1038 + X^1037 + X^1033 + X^1032 + X^1031 + X^1024 + X^1019 + X^1018 + X^1016 + X^1015 + X^1010 + X^1003 + X^1002 + X^1001 + X^997 + X^996 + X^994 + X^988 + X^985 + X^983 + X^981 + X^980 + X^979 + X^974 + X^972 + X^967 + X^966 + X^965 + X^963 + X^961 + X^958 + X^952 + X^950 + X^949 + X^945 + X^944 + X^943 + X^938 + X^936 + X^931 + X^930 + X^928 + X^927 + X^925 + X^916 + X^915 + X^914 + X^913 + X^912 + X^908 + X^907 + X^906 + X^903 + X^899 + X^898 + X^897 + X^896 + X^895 + X^894 + X^893 + X^892 + X^887 + X^886 + X^884 + X^883 + X^882 + X^881 + X^879 + X^877 + X^875 + X^873 + X^870 + X^867 + X^865 + X^862 + X^861 + X^859 + X^857 + X^856 + X^850 + X^840 + X^836 + X^835 + X^833 + X^829 + X^827 + X^825 + X^821 + X^820 + X^819 + X^818 + X^817 + X^815 + X^814 + X^813 + X^812 + X^810 + X^809 + X^807 + X^802 + X^801 + X^799 + X^798 + X^797 + X^796 + X^792 + X^791 + X^790 + X^789 + X^788 + X^787 + X^786 + X^783 + X^780 + X^778 + X^776 + X^774 + X^770 + X^769 + X^766 + X^765 + X^764 + X^759 + X^758 + X^757 + X^756 + X^754 + X^751 + X^749 + X^748 + X^745 + X^744 + X^743 + X^742 + X^741 + X^736 + X^734 + X^733 + X^731 + X^729 + X^727 + X^726 + X^722 + X^720 + X^717 + X^716 + X^715 + X^714 + X^713 + X^712 + X^711 + X^709 + X^706 + X^704 + X^700 + X^698 + X^697 + X^695 + X^694 + X^693 + X^692 + X^690 + X^685 + X^684 + X^679 + X^678 + X^677 + X^676 + X^675 + X^674 + X^672 + X^670 + X^668 + X^666 + X^664 + X^662 + X^657 + X^655 + X^654 + X^653 + X^652 + X^650 + 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(148.60.40.28) Time: Thu Jan 22 11:58:12 2004 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: Magma V2.10-6 Thu Jan 22 2004 11:58:08 on modular [Seed = 3314910392] ------------------------------------- Replace this by some code, then click [PARI] or [MAGMA]! Total time: 3.059 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host penduick28.etu.univ-rennes1.fr. (148.60.40.28) Time: Thu Jan 22 11:58:14 2004 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: Magma V2.10-6 Thu Jan 22 2004 11:58:11 on modular [Seed = 3331753912] ------------------------------------- Replace this by some code, then click [PARI] or [MAGMA]! Total time: 3.089 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (194.165.15.3) Time: Thu Jan 22 12:51:24 2004 Input: k := GF(2); C := PrimitivePolynomial(k,9); C; for j in [22..31] do for k in [18..21] do for m in [14..17] do for n in [8..13] do C := ((1 + X^n)^19)*((1 + X^m)^17)*((1 + X^k)^13)*((1 + X^j)^11) + X^1279; if IsPrimitive(C) then C; n; m; k; j; end if; end for; end for; end for; end for; Output: Magma V2.10-6 Thu Jan 22 2004 12:51:08 on modular [Seed = 1175849876] ------------------------------------- X^9 + X^4 + 1 X^1279 + X^1003 + X^993 + X^986 + X^979 + X^976 + X^969 + X^963 + X^962 + X^955 + X^953 + X^952 + X^946 + X^945 + X^939 + X^938 + X^936 + X^931 + X^929 + X^928 + X^923 + X^922 + X^921 + X^915 + X^914 + X^913 + X^912 + X^906 + X^905 + X^904 + X^899 + X^898 + X^896 + X^891 + X^889 + X^888 + X^883 + X^882 + X^881 + X^875 + X^874 + X^873 + X^872 + X^866 + X^865 + X^864 + X^859 + X^858 + X^856 + X^851 + X^849 + X^848 + 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X^862 + X^859 + X^858 + X^857 + X^856 + X^855 + X^853 + X^852 + X^850 + X^848 + X^846 + X^845 + X^842 + X^841 + X^838 + X^837 + X^836 + X^834 + X^831 + X^829 + X^828 + X^827 + X^824 + X^822 + X^821 + X^820 + X^818 + X^817 + X^816 + X^815 + X^813 + X^812 + X^808 + X^807 + X^806 + X^803 + X^802 + X^800 + X^798 + X^797 + X^796 + X^795 + X^794 + X^792 + X^790 + X^789 + X^787 + X^786 + X^785 + X^784 + X^782 + X^780 + X^777 + X^776 + X^774 + X^773 + X^772 + X^770 + X^764 + X^763 + X^762 + X^761 + X^759 + X^756 + X^753 + X^751 + X^750 + X^749 + X^744 + X^743 + X^742 + X^741 + X^738 + X^732 + X^729 + X^728 + X^726 + X^725 + X^724 + X^723 + X^722 + X^720 + X^717 + X^715 + X^708 + X^707 + X^706 + X^705 + X^704 + X^703 + X^700 + X^699 + X^691 + X^687 + X^685 + X^684 + X^683 + X^678 + X^676 + X^674 + X^670 + X^669 + X^666 + X^663 + X^662 + X^660 + X^659 + X^658 + X^657 + X^655 + X^653 + X^648 + X^645 + X^641 + X^640 + X^638 + X^637 + X^636 + X^634 + X^632 + X^629 + X^627 + X^625 + X^620 + X^618 + X^617 + X^615 + X^614 + X^613 + X^612 + X^611 + X^610 + X^609 + X^608 + X^606 + X^602 + X^600 + X^599 + X^597 + X^596 + X^593 + X^591 + X^590 + X^589 + X^588 + X^587 + X^585 + X^581 + X^579 + X^578 + X^574 + X^569 + X^567 + X^566 + X^565 + X^564 + X^562 + X^561 + X^560 + X^559 + X^557 + X^555 + X^553 + X^552 + X^551 + X^549 + X^545 + X^543 + X^532 + X^529 + X^528 + X^524 + X^520 + X^519 + X^512 + X^511 + X^510 + X^509 + X^508 + X^507 + X^506 + X^505 + X^504 + X^503 + X^496 + X^495 + X^491 + X^487 + X^486 + X^483 + X^472 + X^470 + X^466 + X^464 + X^463 + X^462 + X^460 + X^458 + X^456 + X^455 + X^454 + X^453 + X^451 + X^450 + X^449 + X^448 + X^446 + X^441 + X^437 + X^436 + X^434 + X^430 + X^428 + X^427 + X^426 + X^425 + X^424 + X^422 + X^419 + X^418 + X^416 + X^415 + X^413 + X^409 + X^407 + X^406 + X^405 + X^404 + X^403 + X^402 + X^401 + X^400 + X^398 + X^397 + X^395 + X^390 + X^388 + X^386 + X^383 + X^381 + X^379 + X^378 + X^377 + X^375 + X^374 + X^370 + X^367 + X^362 + X^360 + X^358 + X^357 + X^356 + X^355 + X^353 + X^352 + X^349 + X^346 + X^345 + X^341 + X^339 + X^337 + X^332 + X^331 + X^330 + X^328 + X^324 + X^316 + X^315 + X^312 + X^311 + X^310 + X^309 + X^308 + X^307 + X^300 + X^298 + X^295 + X^293 + X^292 + X^291 + X^290 + X^289 + X^287 + X^286 + X^283 + X^277 + X^274 + X^273 + X^272 + X^271 + X^266 + X^265 + X^264 + X^262 + X^259 + X^256 + X^254 + X^253 + X^252 + X^251 + X^245 + X^243 + X^242 + X^241 + X^239 + X^238 + X^235 + X^233 + X^231 + X^230 + X^229 + X^228 + X^226 + X^225 + X^223 + X^221 + X^220 + X^219 + X^218 + X^217 + X^215 + X^213 + X^212 + X^209 + X^208 + X^207 + X^203 + X^202 + X^200 + X^199 + X^198 + X^197 + X^195 + X^194 + X^193 + X^191 + X^188 + X^187 + X^186 + X^184 + X^181 + X^179 + X^178 + X^177 + X^174 + X^173 + X^170 + X^169 + X^167 + X^165 + X^163 + X^162 + X^160 + X^159 + ** WARNING: Output too long, hence truncated. ************** MAGMA ***************** Host 3(NXDOMAIN) (194.165.15.3) Time: Thu Jan 22 12:53:20 2004 Input: k := GF(2); C := PrimitivePolynomial(k,9); C; for j in [22..31] do for k in [18..21] do for m in [14..17] do for n in [8..13] do C := ((1 + X^n)^23)*((1 + X^m)^19)*((1 + X^k)^17)*((1 + X^j)^13) + X^1279; if IsPrimitive(C) then C; n; m; k; j; end if; end for; end for; end for; end for; Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Thu Jan 22 2004 12:52:57 on modular [Seed = 2083271131] ------------------------------------- X^9 + X^4 + 1 X^1279 + X^1101 + X^1092 + X^1086 + X^1083 + X^1082 + X^1079 + X^1077 + X^1074 + X^1073 + X^1071 + X^1070 + X^1068 + X^1067 + X^1065 + X^1062 + X^1061 + X^1060 + X^1059 + X^1058 + X^1053 + X^1051 + X^1050 + X^1045 + X^1044 + X^1042 + X^1041 + X^1037 + X^1036 + X^1035 + X^1034 + X^1033 + X^1032 + X^1030 + X^1029 + X^1028 + X^1027 + X^1026 + X^1025 + X^1024 + X^1023 + X^1021 + X^1020 + X^1019 + X^1018 + X^1017 + X^1016 + X^1013 + X^1012 + X^1011 + X^1009 + X^1008 + X^1004 + X^1003 + X^1002 + X^1000 + X^998 + X^993 + X^992 + X^989 + X^988 + X^977 + X^976 + X^973 + X^972 + X^967 + X^965 + X^963 + X^962 + X^961 + X^956 + X^954 + X^953 + X^952 + X^949 + X^947 + X^946 + X^945 + X^944 + X^941 + X^940 + X^937 + X^936 + X^932 + X^931 + X^928 + X^927 + X^926 + X^925 + X^920 + X^918 + X^917 + X^912 + X^910 + X^909 + X^907 + X^906 + X^905 + X^904 + X^898 + X^897 + X^893 + X^892 + X^891 + X^890 + X^886 + X^883 + X^882 + X^881 + X^880 + X^876 + X^872 + X^867 + X^866 + X^857 + X^853 + X^851 + X^850 + X^847 + X^846 + X^841 + X^840 + X^839 + X^836 + X^835 + X^834 + X^833 + X^831 + X^830 + X^829 + X^828 + X^826 + X^825 + X^824 + X^823 + X^820 + X^816 + X^813 + X^811 + X^809 + X^808 + X^803 + X^801 + X^798 + X^796 + X^790 + X^789 + X^788 + X^787 + X^786 + X^785 + X^783 + X^782 + X^781 + X^780 + X^779 + X^778 + X^777 + X^776 + X^775 + X^773 + X^772 + X^771 + X^770 + X^769 + X^768 + X^767 + X^766 + X^765 + X^764 + X^763 + X^761 + X^760 + X^759 + X^757 + X^756 + X^746 + X^739 + X^735 + X^733 + 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+ X^1172 + X^1167 + X^1166 + X^1164 + X^1163 + X^1161 + X^1160 + X^1159 + X^1158 + X^1154 + X^1150 + X^1148 + X^1147 + X^1146 + X^1145 + X^1142 + X^1141 + X^1134 + X^1133 + X^1132 + X^1129 + X^1128 + X^1121 + X^1120 + X^1115 + X^1108 + X^1107 + X^1104 + X^1102 + X^1100 + X^1098 + X^1095 + X^1094 + X^1093 + X^1091 + X^1089 + X^1088 + X^1087 + X^1086 + X^1085 + X^1084 + X^1080 + X^1078 + X^1077 + X^1076 + X^1074 + X^1073 + X^1071 + X^1070 + X^1068 + X^1067 + X^1066 + X^1064 + X^1060 + X^1059 + X^1058 + X^1057 + X^1056 + X^1055 + X^1053 + X^1051 + X^1050 + X^1049 + X^1046 + X^1044 + X^1042 + X^1040 + X^1037 + X^1036 + X^1029 + X^1023 + X^1016 + X^1015 + X^1012 + X^1010 + X^1008 + X^1006 + X^1003 + X^1002 + X^1001 + X^1000 + X^999 + X^997 + X^996 + X^995 + X^994 + X^993 + X^992 + X^988 + X^987 + X^986 + X^985 + X^981 + X^979 + X^978 + X^977 + X^976 + X^975 + X^972 + X^971 + X^969 + X^967 + X^965 + X^963 + X^961 + X^957 + X^956 + X^955 + X^954 + X^953 + X^952 + X^951 + X^948 + X^946 + X^945 + X^944 + X^942 + X^940 + X^938 + X^936 + X^933 + X^931 + X^929 + X^925 + X^914 + X^913 + X^912 + X^909 + X^908 + X^904 + X^902 + X^901 + X^899 + X^898 + X^897 + X^893 + X^892 + X^890 + X^889 + X^888 + X^882 + X^881 + X^878 + X^874 + X^873 + X^868 + X^867 + X^866 + X^865 + X^864 + X^863 + X^862 + X^860 + X^859 + X^858 + X^857 + X^854 + X^852 + X^850 + X^849 + X^847 + X^845 + X^843 + X^837 + X^836 + X^835 + X^834 + X^830 + X^828 + X^826 + X^824 + X^822 + X^817 + X^816 + X^815 + X^814 + X^813 + X^812 + X^811 + X^810 + X^805 + X^802 + X^801 + X^799 + X^797 + X^794 + X^793 + X^792 + X^791 + X^787 + X^784 + X^782 + X^780 + X^779 + X^778 + X^777 + X^775 + X^774 + X^772 + X^770 + X^769 + X^768 + X^767 + X^766 + X^764 + X^763 + X^762 + X^761 + X^757 + X^756 + X^755 + X^753 + X^752 + X^751 + X^748 + X^747 + X^745 + X^743 + X^742 + X^739 + X^738 + X^735 + X^732 + X^731 + X^730 + X^728 + X^727 + X^725 + X^724 + X^721 + X^719 + X^718 + X^715 + X^714 + X^710 + X^704 + X^703 + X^702 + X^699 + X^697 + X^696 + X^694 + X^691 + X^688 + X^687 + X^685 + X^684 + X^676 + X^675 + X^674 + X^673 + X^672 + X^670 + X^667 + X^665 + X^662 + X^661 + X^659 + X^658 + X^657 + X^655 + X^654 + X^653 + X^649 + X^648 + X^647 + X^646 + X^645 + X^644 + X^641 + X^637 + X^633 + X^631 + X^629 + X^628 + X^622 + X^619 + X^617 + X^615 + X^614 + X^613 + X^612 + X^611 + X^597 + X^596 + X^595 + X^594 + X^593 + X^591 + X^589 + X^586 + X^580 + X^579 + X^577 + X^575 + X^571 + X^567 + X^564 + X^563 + X^562 + X^561 + X^560 + X^559 + X^555 + X^554 + X^553 + X^551 + X^550 + X^549 + X^547 + X^546 + X^543 + X^541 + X^538 + X^536 + X^535 + X^534 + X^533 + X^532 + X^524 + X^523 + X^521 + X^520 + X^517 + X^514 + X^512 + X^511 + X^509 + X^506 + X^505 + X^504 + X^498 + X^494 + X^493 + X^490 + X^489 + X^487 + X^484 + X^483 + X^481 + X^480 + X^478 + X^477 + X^476 + X^473 + X^470 + X^469 + X^466 + X^465 + X^463 + X^461 + X^460 + X^457 + X^456 + X^455 + X^453 + X^452 + X^451 + X^447 + X^446 + X^445 + X^444 + X^442 + X^441 + X^440 + X^439 + X^438 + X^436 + X^434 + X^433 + X^431 + X^430 + X^429 + X^428 + X^426 + X^424 + X^421 + X^417 + X^416 + X^415 + X^414 + X^411 + X^409 + X^407 + X^406 + X^403 + X^398 + X^397 + X^396 + X^395 + X^394 + X^393 + X^392 + X^391 + X^386 + X^384 + X^382 + X^380 + X^378 + X^374 + X^373 + X^372 + X^371 + X^365 + X^363 + X^361 + X^359 + X^358 + X^356 + X^354 + X^351 + X^350 + X^349 + X^348 + X^346 + X^345 + X^344 + X^343 + X^342 + X^341 + X^340 + X^335 + X^334 + X^330 + X^327 + X^326 + X^320 + X^319 + X^318 + X^316 + X^315 + X^311 + X^310 + X^309 + X^307 + X^306 + X^304 + X^300 + X^299 + X^296 + X^295 + X^294 + X^283 + X^279 + X^277 + X^275 + X^272 + X^270 + X^268 + X^266 + X^264 + X^263 + X^262 + X^260 + X^257 + X^256 + X^255 + X^254 + X^253 + X^252 + X^251 + X^247 + X^245 + X^243 + X^241 + X^239 + X^237 + X^236 + X^233 + X^232 + X^231 + X^230 + X^229 + X^227 + X^223 + X^222 + X^221 + X^220 + X^216 + X^215 + X^214 + X^213 + X^212 + X^211 + X^209 + X^208 + X^207 + X^206 + X^205 + X^202 + X^200 + X^198 + X^196 + X^193 + X^192 + X^185 + X^179 + X^172 + X^171 + X^168 + X^166 + X^164 + X^162 + X^159 + X^158 + X^157 + X^155 + X^153 + X^152 + X^151 + X^150 + X^149 + X^148 + X^144 + X^142 + X^141 + X^140 + X^138 + X^137 + X^135 + X^134 + X^132 + X^131 + X^130 + X^128 + X^124 + X^123 + X^122 + X^121 + X^120 + X^119 + X^117 + X^115 + X^114 + X^113 + X^110 + X^108 + X^106 + X^104 + X^101 + X^100 + X^93 + X^88 + X^87 + X^80 + X^79 + X^76 + X^75 + X^74 + X^67 + X^66 + X^63 + X^62 + X^61 + X^60 + X^58 + X^54 + X^50 + X^49 + X^48 + X^47 + X^45 + X^44 + X^42 + X^41 + X^36 + X^34 + X^32 + X^31 + X^29 + X^26 + X^23 + X^18 + X^16 + X^13 + 1 13 16 18 23 X^1279 + X^1218 + X^1208 + X^1201 + X^1193 + X^1191 + X^1184 + X^1183 + X^1176 + X^1174 + ** WARNING: Output too long, hence truncated. Errors: /home/mfd/gomagma: line 2: 7714 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host 3(NXDOMAIN) (194.165.15.3) Time: Thu Jan 22 12:55:38 2004 Input: k := GF(2); C := PrimitivePolynomial(k,9); C; for j in [22..31] do for k in [18..21] do for m in [16..19] do for n in [13..17] do C := ((1 + X^n)^23)*((1 + X^m)^19)*((1 + X^k)^17)*((1 + X^j)^13) + X^1279; if IsPrimitive(C) then C; n; m; k; j; end if; end for; end for; end for; end for; Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Thu Jan 22 2004 12:55:15 on modular [Seed = 1898004396] ------------------------------------- X^9 + X^4 + 1 X^1279 + X^1208 + X^1195 + X^1192 + X^1190 + X^1185 + X^1182 + X^1179 + X^1177 + X^1176 + X^1174 + X^1172 + X^1167 + X^1166 + X^1164 + X^1163 + X^1161 + X^1160 + X^1159 + X^1158 + X^1154 + X^1150 + X^1148 + X^1147 + X^1146 + X^1145 + X^1142 + X^1141 + X^1134 + X^1133 + X^1132 + X^1129 + X^1128 + X^1121 + X^1120 + X^1115 + X^1108 + X^1107 + X^1104 + X^1102 + X^1100 + X^1098 + X^1095 + X^1094 + X^1093 + X^1091 + X^1089 + X^1088 + X^1087 + X^1086 + X^1085 + X^1084 + X^1080 + X^1078 + X^1077 + X^1076 + X^1074 + X^1073 + X^1071 + X^1070 + X^1068 + X^1067 + X^1066 + X^1064 + X^1060 + X^1059 + X^1058 + X^1057 + X^1056 + X^1055 + X^1053 + X^1051 + X^1050 + X^1049 + X^1046 + X^1044 + X^1042 + X^1040 + X^1037 + X^1036 + X^1029 + X^1023 + X^1016 + X^1015 + X^1012 + X^1010 + X^1008 + X^1006 + X^1003 + X^1002 + X^1001 + X^1000 + X^999 + X^997 + X^996 + X^995 + X^994 + X^993 + X^992 + X^988 + X^987 + X^986 + X^985 + X^981 + X^979 + X^978 + X^977 + X^976 + X^975 + X^972 + X^971 + X^969 + X^967 + X^965 + X^963 + X^961 + X^957 + X^956 + X^955 + X^954 + X^953 + X^952 + X^951 + X^948 + X^946 + X^945 + X^944 + X^942 + X^940 + X^938 + X^936 + X^933 + X^931 + X^929 + X^925 + X^914 + X^913 + X^912 + X^909 + X^908 + X^904 + X^902 + X^901 + X^899 + X^898 + X^897 + X^893 + X^892 + X^890 + X^889 + X^888 + X^882 + X^881 + X^878 + X^874 + X^873 + X^868 + X^867 + X^866 + X^865 + X^864 + X^863 + X^862 + X^860 + X^859 + X^858 + X^857 + X^854 + X^852 + X^850 + X^849 + X^847 + X^845 + X^843 + X^837 + X^836 + X^835 + X^834 + X^830 + X^828 + X^826 + X^824 + X^822 + X^817 + X^816 + X^815 + X^814 + X^813 + X^812 + X^811 + X^810 + X^805 + X^802 + X^801 + X^799 + X^797 + X^794 + X^793 + X^792 + X^791 + X^787 + X^784 + X^782 + X^780 + X^779 + X^778 + X^777 + X^775 + X^774 + X^772 + X^770 + X^769 + X^768 + X^767 + X^766 + X^764 + X^763 + X^762 + X^761 + X^757 + X^756 + X^755 + X^753 + X^752 + X^751 + X^748 + X^747 + X^745 + X^743 + X^742 + X^739 + X^738 + X^735 + X^732 + X^731 + X^730 + X^728 + X^727 + X^725 + X^724 + X^721 + X^719 + X^718 + X^715 + X^714 + X^710 + X^704 + X^703 + X^702 + X^699 + X^697 + X^696 + X^694 + X^691 + X^688 + X^687 + X^685 + X^684 + X^676 + X^675 + X^674 + X^673 + X^672 + X^670 + X^667 + X^665 + X^662 + X^661 + X^659 + X^658 + X^657 + X^655 + X^654 + X^653 + X^649 + X^648 + X^647 + X^646 + X^645 + X^644 + X^641 + X^637 + X^633 + X^631 + X^629 + X^628 + X^622 + X^619 + X^617 + X^615 + X^614 + X^613 + X^612 + X^611 + X^597 + X^596 + X^595 + X^594 + X^593 + X^591 + X^589 + X^586 + X^580 + X^579 + X^577 + X^575 + X^571 + X^567 + X^564 + X^563 + X^562 + X^561 + X^560 + X^559 + X^555 + X^554 + X^553 + X^551 + X^550 + X^549 + X^547 + X^546 + X^543 + X^541 + X^538 + X^536 + X^535 + X^534 + X^533 + X^532 + X^524 + X^523 + X^521 + X^520 + X^517 + X^514 + X^512 + X^511 + X^509 + X^506 + X^505 + X^504 + X^498 + X^494 + X^493 + X^490 + X^489 + X^487 + X^484 + X^483 + X^481 + X^480 + X^478 + X^477 + X^476 + X^473 + X^470 + X^469 + X^466 + X^465 + X^463 + X^461 + X^460 + X^457 + X^456 + X^455 + X^453 + X^452 + X^451 + X^447 + X^446 + X^445 + X^444 + X^442 + X^441 + X^440 + X^439 + X^438 + X^436 + X^434 + X^433 + X^431 + X^430 + X^429 + X^428 + X^426 + X^424 + X^421 + X^417 + X^416 + X^415 + X^414 + X^411 + X^409 + X^407 + X^406 + X^403 + X^398 + X^397 + X^396 + X^395 + X^394 + X^393 + X^392 + X^391 + X^386 + X^384 + X^382 + X^380 + X^378 + X^374 + X^373 + X^372 + X^371 + X^365 + X^363 + X^361 + X^359 + X^358 + X^356 + X^354 + X^351 + X^350 + X^349 + X^348 + X^346 + X^345 + X^344 + X^343 + X^342 + X^341 + X^340 + X^335 + X^334 + X^330 + X^327 + X^326 + X^320 + X^319 + X^318 + X^316 + X^315 + X^311 + X^310 + X^309 + X^307 + X^306 + X^304 + X^300 + X^299 + X^296 + X^295 + X^294 + X^283 + X^279 + X^277 + X^275 + X^272 + X^270 + X^268 + X^266 + X^264 + X^263 + X^262 + X^260 + X^257 + X^256 + X^255 + X^254 + X^253 + X^252 + X^251 + X^247 + X^245 + X^243 + X^241 + X^239 + X^237 + X^236 + X^233 + X^232 + X^231 + X^230 + X^229 + X^227 + X^223 + X^222 + X^221 + X^220 + X^216 + X^215 + X^214 + X^213 + X^212 + X^211 + X^209 + X^208 + X^207 + X^206 + X^205 + X^202 + X^200 + X^198 + X^196 + X^193 + X^192 + X^185 + X^179 + X^172 + X^171 + X^168 + X^166 + X^164 + X^162 + X^159 + X^158 + X^157 + X^155 + X^153 + X^152 + X^151 + X^150 + X^149 + X^148 + X^144 + X^142 + X^141 + X^140 + X^138 + X^137 + X^135 + X^134 + X^132 + X^131 + X^130 + X^128 + X^124 + X^123 + X^122 + X^121 + X^120 + X^119 + X^117 + X^115 + X^114 + X^113 + X^110 + X^108 + X^106 + X^104 + X^101 + X^100 + X^93 + X^88 + X^87 + X^80 + X^79 + X^76 + X^75 + X^74 + X^67 + X^66 + X^63 + X^62 + X^61 + X^60 + X^58 + X^54 + X^50 + X^49 + X^48 + X^47 + X^45 + X^44 + X^42 + X^41 + X^36 + X^34 + X^32 + X^31 + X^29 + X^26 + X^23 + X^18 + X^16 + X^13 + 1 13 16 18 23 Errors: /home/mfd/gomagma: line 2: 7727 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host 3(NXDOMAIN) (194.165.15.3) Time: Thu Jan 22 12:57:25 2004 Input: k := GF(2); C := PrimitivePolynomial(k,9); C; for j in [23..31] do for k in [18..21] do for m in [16..19] do for n in [13..17] do C := ((1 + X^n)^23)*((1 + X^m)^19)*((1 + X^k)^17)*((1 + X^j)^13) + X^1279; if IsPrimitive(C) then C; n; m; k; j; end if; end for; end for; end for; end for; Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Thu Jan 22 2004 12:57:02 on modular [Seed = 1731668439] ------------------------------------- X^9 + X^4 + 1 X^1279 + X^1208 + X^1195 + X^1192 + X^1190 + X^1185 + X^1182 + X^1179 + X^1177 + X^1176 + X^1174 + X^1172 + X^1167 + X^1166 + X^1164 + X^1163 + X^1161 + X^1160 + X^1159 + X^1158 + X^1154 + X^1150 + X^1148 + X^1147 + X^1146 + X^1145 + X^1142 + X^1141 + X^1134 + X^1133 + X^1132 + X^1129 + X^1128 + X^1121 + X^1120 + X^1115 + X^1108 + X^1107 + X^1104 + X^1102 + X^1100 + X^1098 + X^1095 + X^1094 + X^1093 + X^1091 + X^1089 + X^1088 + X^1087 + X^1086 + X^1085 + X^1084 + X^1080 + X^1078 + X^1077 + X^1076 + X^1074 + X^1073 + X^1071 + X^1070 + X^1068 + X^1067 + X^1066 + X^1064 + X^1060 + X^1059 + X^1058 + X^1057 + X^1056 + X^1055 + X^1053 + X^1051 + X^1050 + X^1049 + X^1046 + X^1044 + X^1042 + X^1040 + X^1037 + X^1036 + X^1029 + X^1023 + X^1016 + X^1015 + X^1012 + X^1010 + X^1008 + X^1006 + X^1003 + X^1002 + X^1001 + X^1000 + X^999 + X^997 + X^996 + X^995 + X^994 + X^993 + X^992 + X^988 + X^987 + X^986 + X^985 + X^981 + X^979 + X^978 + X^977 + X^976 + X^975 + X^972 + X^971 + X^969 + X^967 + X^965 + X^963 + X^961 + X^957 + X^956 + X^955 + X^954 + X^953 + X^952 + X^951 + X^948 + X^946 + X^945 + X^944 + X^942 + X^940 + X^938 + X^936 + X^933 + X^931 + X^929 + X^925 + X^914 + X^913 + X^912 + X^909 + X^908 + X^904 + X^902 + X^901 + X^899 + X^898 + X^897 + X^893 + X^892 + X^890 + X^889 + X^888 + X^882 + X^881 + X^878 + X^874 + X^873 + X^868 + X^867 + X^866 + X^865 + X^864 + X^863 + X^862 + X^860 + X^859 + X^858 + X^857 + X^854 + X^852 + X^850 + X^849 + X^847 + X^845 + X^843 + X^837 + X^836 + X^835 + X^834 + X^830 + X^828 + X^826 + X^824 + X^822 + X^817 + X^816 + X^815 + X^814 + X^813 + X^812 + X^811 + X^810 + X^805 + X^802 + X^801 + X^799 + X^797 + X^794 + X^793 + X^792 + X^791 + X^787 + X^784 + X^782 + X^780 + X^779 + X^778 + X^777 + X^775 + X^774 + X^772 + X^770 + X^769 + X^768 + X^767 + X^766 + X^764 + X^763 + X^762 + X^761 + X^757 + X^756 + X^755 + X^753 + X^752 + X^751 + X^748 + X^747 + X^745 + X^743 + X^742 + X^739 + X^738 + X^735 + X^732 + X^731 + X^730 + X^728 + X^727 + X^725 + X^724 + X^721 + X^719 + X^718 + X^715 + X^714 + X^710 + X^704 + X^703 + X^702 + X^699 + X^697 + X^696 + X^694 + X^691 + X^688 + X^687 + X^685 + X^684 + X^676 + X^675 + X^674 + X^673 + X^672 + X^670 + X^667 + X^665 + X^662 + X^661 + X^659 + X^658 + X^657 + X^655 + X^654 + X^653 + X^649 + X^648 + X^647 + X^646 + X^645 + X^644 + X^641 + X^637 + X^633 + X^631 + X^629 + X^628 + X^622 + X^619 + X^617 + X^615 + X^614 + X^613 + X^612 + X^611 + X^597 + X^596 + X^595 + X^594 + X^593 + X^591 + X^589 + X^586 + X^580 + X^579 + X^577 + X^575 + X^571 + X^567 + X^564 + X^563 + X^562 + X^561 + X^560 + X^559 + X^555 + X^554 + X^553 + X^551 + X^550 + X^549 + X^547 + X^546 + X^543 + X^541 + X^538 + X^536 + X^535 + X^534 + X^533 + X^532 + X^524 + X^523 + X^521 + X^520 + X^517 + X^514 + X^512 + X^511 + X^509 + X^506 + X^505 + X^504 + X^498 + X^494 + X^493 + X^490 + X^489 + X^487 + X^484 + X^483 + X^481 + X^480 + X^478 + X^477 + X^476 + X^473 + X^470 + X^469 + X^466 + X^465 + X^463 + X^461 + X^460 + X^457 + X^456 + X^455 + X^453 + X^452 + X^451 + X^447 + X^446 + X^445 + X^444 + X^442 + X^441 + X^440 + X^439 + X^438 + X^436 + X^434 + X^433 + X^431 + X^430 + X^429 + X^428 + X^426 + X^424 + X^421 + X^417 + X^416 + X^415 + X^414 + X^411 + X^409 + X^407 + X^406 + X^403 + X^398 + X^397 + X^396 + X^395 + X^394 + X^393 + X^392 + X^391 + X^386 + X^384 + X^382 + X^380 + X^378 + X^374 + X^373 + X^372 + X^371 + X^365 + X^363 + X^361 + X^359 + X^358 + X^356 + X^354 + X^351 + X^350 + X^349 + X^348 + X^346 + X^345 + X^344 + X^343 + X^342 + X^341 + X^340 + X^335 + X^334 + X^330 + X^327 + X^326 + X^320 + X^319 + X^318 + X^316 + X^315 + X^311 + X^310 + X^309 + X^307 + X^306 + X^304 + X^300 + X^299 + X^296 + X^295 + X^294 + X^283 + X^279 + X^277 + X^275 + X^272 + X^270 + X^268 + X^266 + X^264 + X^263 + X^262 + X^260 + X^257 + X^256 + X^255 + X^254 + X^253 + X^252 + X^251 + X^247 + X^245 + X^243 + X^241 + X^239 + X^237 + X^236 + X^233 + X^232 + X^231 + X^230 + X^229 + X^227 + X^223 + X^222 + X^221 + X^220 + X^216 + X^215 + X^214 + X^213 + X^212 + X^211 + X^209 + X^208 + X^207 + X^206 + X^205 + X^202 + X^200 + X^198 + X^196 + X^193 + X^192 + X^185 + X^179 + X^172 + X^171 + X^168 + X^166 + X^164 + X^162 + X^159 + X^158 + X^157 + X^155 + X^153 + X^152 + X^151 + X^150 + X^149 + X^148 + X^144 + X^142 + X^141 + X^140 + X^138 + X^137 + X^135 + X^134 + X^132 + X^131 + X^130 + X^128 + X^124 + X^123 + X^122 + X^121 + X^120 + X^119 + X^117 + X^115 + X^114 + X^113 + X^110 + X^108 + X^106 + X^104 + X^101 + X^100 + X^93 + X^88 + X^87 + X^80 + X^79 + X^76 + X^75 + X^74 + X^67 + X^66 + X^63 + X^62 + X^61 + X^60 + X^58 + X^54 + X^50 + X^49 + X^48 + X^47 + X^45 + X^44 + X^42 + X^41 + X^36 + X^34 + X^32 + X^31 + X^29 + X^26 + X^23 + X^18 + X^16 + X^13 + 1 13 16 18 23 Errors: /home/mfd/gomagma: line 2: 7737 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host 3(NXDOMAIN) (194.165.15.3) Time: Thu Jan 22 12:58:41 2004 Input: k := GF(2); C := PrimitivePolynomial(k,9); C; for j in [23..31] do for k in [20..21] do for m in [16..19] do for n in [13..17] do C := ((1 + X^n)^23)*((1 + X^m)^19)*((1 + X^k)^17)*((1 + X^j)^13) + X^1279; if IsPrimitive(C) then C; n; m; k; j; end if; end for; end for; end for; end for; Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Thu Jan 22 2004 12:58:17 on modular [Seed = 491606649] ------------------------------------- X^9 + X^4 + 1 Errors: /home/mfd/gomagma: line 2: 7747 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host 3(NXDOMAIN) (194.165.15.3) Time: Thu Jan 22 12:59:24 2004 Input: k := GF(2); C := PrimitivePolynomial(k,9); C; for j in [23..31] do for k in [20..21] do for m in [18..19] do for n in [13..17] do C := ((1 + X^n)^23)*((1 + X^m)^19)*((1 + X^k)^17)*((1 + X^j)^13) + X^1279; if IsPrimitive(C) then C; n; m; k; j; end if; end for; end for; end for; end for; Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Thu Jan 22 2004 12:59:01 on modular [Seed = 306339113] ------------------------------------- X^9 + X^4 + 1 Errors: /home/mfd/gomagma: line 2: 7756 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host 3(NXDOMAIN) (194.165.15.3) Time: Thu Jan 22 13:00:31 2004 Input: k := GF(2); C := PrimitivePolynomial(k,9); C; for j in [22..31] do for k in [18..21] do for m in [12..17] do for n in [8..11] do C := ((1 + X^n)^23)*((1 + X^m)^19)*((1 + X^k)^17)*((1 + X^j)^13) + X^1279; if IsPrimitive(C) then C; n; m; k; j; end if; end for; end for; end for; end for; Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Thu Jan 22 2004 13:00:08 on modular [Seed = 55790837] 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Errors: /home/mfd/gomagma: line 2: 7773 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host 3(NXDOMAIN) (194.165.15.3) Time: Thu Jan 22 13:02:32 2004 Input: k := GF(2); C := PrimitivePolynomial(k,9); C; for j in [22..31] do for k in [18..21] do for m in [14..17] do for n in [8..13] do C := ((1 + X^n)^23)*((1 + X^m)^19)*((1 + X^k)^17)*((1 + X^j)^13) + X^1279; if IsPrimitive(C) then C; n; m; k; j; end if; end for; end for; end for; end for; Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Thu Jan 22 2004 13:02:09 on modular [Seed = 662140760] ------------------------------------- X^9 + X^4 + 1 X^1279 + X^1101 + X^1092 + X^1086 + X^1083 + X^1082 + X^1079 + X^1077 + X^1074 + X^1073 + X^1071 + X^1070 + X^1068 + X^1067 + X^1065 + X^1062 + X^1061 + X^1060 + X^1059 + X^1058 + X^1053 + X^1051 + X^1050 + X^1045 + X^1044 + X^1042 + X^1041 + X^1037 + X^1036 + X^1035 + X^1034 + X^1033 + X^1032 + 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Errors: /home/mfd/gomagma: line 2: 7801 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host 3(NXDOMAIN) (194.165.15.3) Time: Thu Jan 22 13:04:06 2004 Input: k := GF(2); C := PrimitivePolynomial(k,9); C; for j in [23..31] do for k in [18..21] do for m in [14..17] do for n in [8..13] do C := ((1 + X^n)^23)*((1 + X^m)^19)*((1 + X^k)^17)*((1 + X^j)^13) + X^1279; if IsPrimitive(C) then C; n; m; k; j; end if; end for; end for; end for; end for; Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Thu Jan 22 2004 13:03:43 on modular [Seed = 3700198653] ------------------------------------- X^9 + X^4 + 1 X^1279 + X^1208 + X^1195 + X^1192 + X^1190 + X^1185 + X^1182 + X^1179 + X^1177 + X^1176 + X^1174 + X^1172 + X^1167 + X^1166 + X^1164 + X^1163 + X^1161 + X^1160 + X^1159 + X^1158 + X^1154 + X^1150 + X^1148 + X^1147 + X^1146 + X^1145 + X^1142 + X^1141 + X^1134 + X^1133 + X^1132 + X^1129 + X^1128 + 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Errors: /home/mfd/gomagma: line 2: 7810 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host 3(NXDOMAIN) (194.165.15.3) Time: Thu Jan 22 13:05:35 2004 Input: k := GF(2); C := PrimitivePolynomial(k,9); C; for j in [23..31] do for k in [18..21] do for m in [14..17] do for n in [8..13] do C := ((1 + X^n)^23)*((1 + X^m)^19)*((1 + X^k)^17)*((1 + X^j)^13) + X^1279; if IsPrimitive(C) then n; m; k; j; C; end if; end for; end for; end for; end for; Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Thu Jan 22 2004 13:05:12 on modular [Seed = 3514925399] ------------------------------------- X^9 + X^4 + 1 13 16 18 23 X^1279 + X^1208 + X^1195 + X^1192 + X^1190 + X^1185 + X^1182 + X^1179 + X^1177 + X^1176 + X^1174 + X^1172 + X^1167 + X^1166 + X^1164 + X^1163 + X^1161 + X^1160 + X^1159 + X^1158 + X^1154 + X^1150 + X^1148 + X^1147 + X^1146 + X^1145 + X^1142 + X^1141 + X^1134 + X^1133 + X^1132 + X^1129 + 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Errors: /home/mfd/gomagma: line 2: 7823 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host 3(NXDOMAIN) (194.165.15.3) Time: Thu Jan 22 13:07:31 2004 Input: k := GF(2); C := PrimitivePolynomial(k,9); C; for j in [25..31] do for k in [20..21] do for m in [16..17] do for n in [10..13] do C := ((1 + X^n)^23)*((1 + X^m)^19)*((1 + X^k)^17)*((1 + X^j)^13) + X^1279; if IsPrimitive(C) then C; n; m; k; j; end if; end for; end for; end for; end for; Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Thu Jan 22 2004 13:07:08 on modular [Seed = 3348600533] ------------------------------------- X^9 + X^4 + 1 X^1279 + X^1218 + X^1208 + X^1201 + X^1193 + X^1191 + X^1184 + X^1183 + X^1176 + X^1174 + X^1167 + X^1166 + X^1159 + X^1157 + X^1149 + X^1142 + X^1138 + X^1132 + X^1128 + X^1121 + X^1118 + X^1113 + X^1111 + X^1108 + X^1104 + X^1103 + X^1101 + X^1096 + X^1094 + X^1093 + X^1091 + X^1087 + X^1086 + 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X^633 + X^630 + X^628 + X^625 + X^623 + X^620 + X^618 + X^615 + X^613 + X^610 + X^608 + X^605 + X^603 + X^600 + X^598 + X^595 + X^593 + X^590 + X^588 + X^585 + X^583 + X^580 + X^575 + X^573 + X^570 + X^565 + X^563 + X^561 + X^560 + X^558 + X^555 + X^551 + X^550 + X^548 + X^545 + X^544 + X^540 + X^538 + X^536 + X^535 + X^534 + X^533 + X^530 + X^528 + X^527 + X^526 + X^525 + X^523 + X^520 + X^519 + X^518 + X^517 + X^515 + X^513 + X^510 + X^509 + X^508 + X^505 + X^503 + X^502 + X^500 + X^495 + X^493 + X^492 + X^490 + X^485 + X^483 + X^481 + X^480 + X^475 + X^471 + X^470 + X^465 + X^464 + X^461 + X^460 + X^458 + X^456 + X^455 + X^454 + X^451 + X^450 + X^448 + X^447 + X^446 + X^445 + X^444 + X^440 + X^439 + X^438 + X^437 + X^436 + X^435 + X^434 + X^433 + X^430 + X^429 + X^428 + X^427 + X^426 + X^425 + X^423 + X^422 + X^420 + X^419 + X^417 + X^415 + X^413 + X^412 + X^410 + X^409 + X^405 + X^403 + X^402 + X^401 + X^400 + X^395 + X^392 + X^391 + X^390 + X^385 + X^384 + X^381 + X^380 + X^376 + X^375 + X^374 + X^371 + X^370 + X^367 + X^366 + X^365 + X^364 + X^361 + X^360 + X^359 + X^358 + X^357 + X^356 + X^355 + X^354 + X^351 + X^350 + X^349 + X^348 + X^347 + X^346 + X^345 + X^344 + X^342 + X^340 + X^339 + X^337 + X^336 + X^335 + X^334 + X^333 + X^332 + X^330 + X^329 + X^327 + X^326 + X^325 + X^323 + X^322 + X^321 + X^320 + X^319 + X^317 + X^315 + X^312 + X^311 + X^310 + X^309 + X^306 + X^305 + X^304 + X^302 + X^301 + X^300 + X^295 + X^294 + X^292 + X^291 + X^290 + X^289 + X^287 + X^286 + X^285 + X^284 + X^280 + X^277 + X^276 + X^275 + X^274 + X^272 + X^270 + X^269 + X^267 + X^266 + X^265 + X^261 + X^260 + X^259 + X^257 + X^256 + X^252 + X^251 + X^250 + X^249 + X^246 + X^244 + X^242 + X^241 + X^240 + X^239 + X^236 + X^235 + X^234 + X^232 + X^231 + X^229 + X^227 + X^225 + X^224 + X^222 + X^221 + X^219 + X^217 + X^215 + X^214 + X^212 + X^211 + X^210 + X^207 + X^205 + X^204 + X^202 + X^200 + X^197 + X^195 + X^194 + X^190 + X^187 + X^186 + X^185 + X^180 + X^177 + X^176 + X^170 + X^169 + X^166 + X^161 + X^160 + X^159 + X^156 + X^152 + X^151 + X^149 + X^144 + X^142 + X^141 + X^139 + X^135 + X^134 + X^132 + X^131 + X^127 + X^125 + X^124 + X^122 + X^117 + X^115 + X^114 + X^110 + X^107 + X^105 + X^100 + X^97 + X^90 + X^86 + X^80 + X^76 + X^69 + X^61 + X^59 + X^52 + X^51 + X^44 + X^42 + X^35 + X^34 + X^27 + X^25 + X^17 + X^10 + 1 10 17 20 25 Errors: /home/mfd/gomagma: line 2: 7833 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host 3(NXDOMAIN) (194.165.15.3) Time: Thu Jan 22 13:09:13 2004 Input: k := GF(2); C := PrimitivePolynomial(k,9); C; C := [(1 + X^12)^11]*[(1 + X^17)^13]*[(1 + X^31)^17]*[(1 + X^20)^19] + X^1279; if IsPrimitive(C) then C; end if; Output: Magma V2.10-6 Thu Jan 22 2004 13:09:10 on modular [Seed = 4239175012] ------------------------------------- X^9 + X^4 + 1 >> C := [(1 + X^12)^11]*[(1 + X^17)^13]*[(1 + X^31)^17]*[(1 + X^20)^19] + X^12 ^ Runtime error in '*': Bad argument types Argument types given: SeqEnum[RngUPolElt], SeqEnum[RngUPolElt] X^9 + X^4 + 1 Total time: 3.039 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (194.165.15.3) Time: Thu Jan 22 13:10:05 2004 Input: k := GF(2); C := PrimitivePolynomial(k,9); C; C := ((1 + X^12)^11)*((1 + X^17)^13)*((1 + X^31)^17)*((1 + X^20)^19) + X^1279; if IsPrimitive(C) then C; end if; Output: Magma V2.10-6 Thu Jan 22 2004 13:10:00 on modular [Seed = 3971792202] ------------------------------------- X^9 + X^4 + 1 X^1279 + X^1260 + X^1248 + X^1243 + X^1240 + X^1236 + X^1231 + X^1229 + X^1228 + X^1224 + X^1223 + X^1220 + X^1219 + X^1217 + X^1216 + X^1212 + X^1211 + X^1209 + X^1208 + X^1207 + X^1205 + X^1204 + X^1203 + X^1199 + X^1197 + X^1196 + X^1193 + X^1191 + X^1189 + X^1187 + X^1185 + X^1184 + X^1183 + X^1179 + X^1177 + X^1175 + X^1173 + X^1171 + X^1169 + X^1167 + X^1165 + X^1163 + X^1161 + X^1159 + X^1157 + X^1155 + X^1153 + X^1152 + X^1151 + X^1149 + X^1145 + X^1143 + X^1141 + X^1140 + X^1139 + X^1137 + X^1132 + X^1131 + X^1129 + X^1128 + X^1127 + X^1125 + X^1124 + X^1120 + X^1119 + X^1117 + X^1116 + X^1113 + X^1112 + X^1108 + X^1105 + X^1100 + X^1099 + X^1096 + X^1088 + X^1085 + X^1076 + X^1068 + X^1059 + X^1048 + X^1045 + X^1031 + X^1028 + X^1017 + X^1008 + X^1000 + X^991 + X^988 + X^980 + X^977 + X^976 + X^971 + X^968 + X^964 + X^963 + X^960 + X^959 + X^957 + X^956 + X^952 + X^951 + X^949 + X^948 + X^947 + X^945 + X^944 + X^940 + X^939 + X^937 + X^936 + X^935 + X^933 + X^931 + X^928 + X^927 + X^925 + X^924 + X^921 + X^920 + X^919 + X^917 + X^916 + X^915 + X^913 + X^908 + X^907 + X^905 + X^904 + X^901 + X^900 + X^896 + X^893 + X^888 + X^884 + X^880 + X^876 + X^872 + X^868 + X^863 + X^860 + X^856 + X^855 + X^852 + X^851 + X^849 + X^848 + X^843 + X^841 + X^840 + X^839 + X^837 + X^836 + X^835 + X^832 + X^831 + X^829 + X^828 + X^825 + X^823 + X^821 + X^820 + X^819 + X^817 + X^816 + X^812 + X^811 + X^809 + X^808 + X^807 + X^805 + X^804 + X^800 + X^799 + X^797 + X^796 + X^793 + X^792 + X^788 + X^785 + X^780 + X^779 + X^776 + X^768 + X^765 + X^764 + X^756 + X^752 + X^748 + X^747 + X^744 + X^740 + X^739 + X^735 + X^733 + X^732 + X^727 + X^725 + X^724 + X^723 + X^721 + X^720 + X^716 + X^715 + X^713 + X^712 + X^709 + X^707 + X^703 + X^701 + X^700 + X^695 + X^693 + X^691 + X^689 + X^687 + X^683 + X^681 + X^680 + X^679 + X^677 + X^675 + X^673 + X^669 + X^668 + X^667 + X^665 + X^663 + X^661 + X^660 + X^659 + X^655 + X^653 + X^651 + X^649 + X^648 + X^647 + X^645 + X^641 + X^640 + X^639 + X^637 + X^635 + X^633 + X^627 + X^625 + X^623 + X^621 + X^620 + X^619 + X^615 + X^613 + X^612 + X^611 + X^609 + X^607 + X^605 + X^601 + X^600 + X^599 + X^597 + X^595 + X^593 + X^592 + X^591 + X^587 + X^585 + X^583 + X^581 + X^580 + X^579 + X^577 + X^573 + X^571 + X^569 + X^567 + X^565 + X^560 + X^559 + X^557 + X^553 + X^551 + X^548 + X^547 + X^545 + X^544 + X^540 + X^539 + X^537 + X^536 + X^535 + X^533 + X^528 + X^527 + X^525 + X^521 + X^520 + X^516 + X^513 + X^512 + X^508 + X^504 + X^496 + X^495 + X^492 + X^484 + X^481 + X^480 + X^475 + X^472 + X^468 + X^467 + X^464 + X^463 + X^461 + X^460 + X^456 + X^455 + X^453 + X^452 + X^451 + X^449 + X^448 + X^444 + X^443 + X^441 + X^440 + X^439 + X^437 + X^435 + X^432 + X^431 + X^429 + X^428 + X^425 + X^424 + X^423 + X^421 + X^420 + X^419 + X^417 + X^412 + X^411 + X^409 + X^408 + X^405 + X^404 + X^400 + X^397 + X^392 + X^388 + X^384 + X^380 + X^376 + X^372 + X^367 + X^364 + X^360 + X^359 + X^356 + X^355 + X^353 + X^352 + X^347 + X^345 + X^344 + X^343 + X^341 + X^340 + X^339 + X^336 + X^335 + X^333 + X^332 + X^329 + X^327 + X^325 + X^324 + X^323 + X^321 + X^320 + X^316 + X^315 + X^313 + X^312 + X^311 + X^309 + X^308 + X^304 + X^303 + X^301 + X^300 + X^297 + X^296 + X^292 + X^289 + X^284 + X^283 + X^280 + X^272 + X^269 + X^260 + X^252 + X^243 + X^232 + X^229 + X^215 + X^212 + X^201 + X^192 + X^184 + X^175 + X^172 + X^164 + X^161 + X^160 + X^155 + X^152 + X^148 + X^147 + X^144 + X^143 + X^141 + X^140 + X^136 + X^135 + X^133 + X^132 + X^131 + X^129 + X^128 + X^123 + X^121 + X^120 + X^119 + X^117 + X^115 + X^111 + X^109 + X^108 + X^107 + X^105 + X^103 + X^101 + X^99 + X^97 + X^95 + X^93 + X^91 + X^89 + X^87 + X^85 + X^83 + X^81 + X^77 + X^76 + X^75 + X^73 + X^71 + X^69 + X^67 + X^64 + X^63 + X^61 + X^57 + X^56 + X^55 + X^53 + X^52 + X^51 + X^49 + X^48 + X^44 + X^43 + X^41 + X^40 + X^37 + X^36 + X^32 + X^31 + X^29 + X^24 + X^20 + X^17 + X^12 + 1 Total time: 4.229 seconds, Total memory usage: 2.14MB ************** MAGMA ***************** Host 3(NXDOMAIN) (194.165.15.3) Time: Thu Jan 22 13:12:04 2004 Input: k := GF(2); C := PrimitivePolynomial(k,9); C; for j in [22..31] do for k in [18..21] do for m in [14..17] do for n in [8..13] do C := ((1 + X^n)^19)*((1 + X^m)^17)*((1 + X^k)^13)*((1 + X^j)^23) + X^1279; if IsPrimitive(C) then C; n; m; k; j; end if; end for; end for; end for; end for; Output: Magma V2.10-6 Thu Jan 22 2004 13:11:43 on modular [Seed = 3853891556] ------------------------------------- X^9 + X^4 + 1 X^1279 + X^1215 + X^1207 + X^1201 + X^1199 + X^1194 + X^1193 + X^1186 + X^1185 + X^1183 + X^1180 + X^1178 + X^1175 + X^1172 + X^1169 + X^1164 + X^1162 + X^1161 + X^1159 + X^1154 + X^1151 + X^1148 + X^1145 + X^1140 + X^1138 + X^1137 + X^1135 + X^1131 + X^1130 + X^1127 + X^1124 + X^1123 + X^1121 + X^1117 + X^1116 + X^1115 + X^1114 + X^1113 + X^1111 + X^1110 + X^1109 + X^1106 + X^1103 + X^1102 + X^1101 + X^1100 + X^1099 + X^1097 + X^1096 + X^1094 + X^1092 + X^1091 + X^1090 + X^1089 + X^1088 + X^1085 + X^1082 + X^1080 + X^1078 + X^1077 + X^1076 + X^1075 + X^1071 + X^1070 + X^1068 + X^1067 + X^1064 + X^1063 + X^1061 + X^1057 + X^1056 + X^1054 + X^1053 + X^1051 + X^1050 + X^1049 + X^1046 + X^1043 + X^1042 + X^1040 + X^1037 + X^1036 + X^1032 + X^1031 + X^1030 + X^1029 + X^1028 + X^1027 + X^1022 + X^1019 + X^1017 + X^1016 + X^1015 + X^1013 + X^1010 + X^1008 + X^1006 + X^1005 + X^1001 + X^999 + X^998 + X^996 + X^994 + X^992 + X^987 + X^985 + X^984 + X^983 + X^980 + X^979 + X^978 + X^973 + X^969 + X^967 + X^966 + X^965 + X^964 + X^962 + X^959 + X^958 + X^953 + X^952 + X^948 + X^947 + X^946 + X^945 + X^944 + X^943 + X^938 + X^935 + X^933 + X^932 + X^931 + X^929 + X^926 + X^924 + X^922 + X^921 + X^917 + X^915 + X^914 + X^912 + X^910 + X^908 + X^903 + X^901 + X^900 + X^899 + X^896 + X^894 + X^889 + X^887 + X^885 + X^883 + X^882 + X^880 + X^878 + X^875 + X^873 + X^871 + X^869 + X^868 + X^866 + X^864 + X^862 + X^861 + X^859 + X^857 + X^854 + X^852 + X^851 + X^850 + X^848 + X^847 + X^845 + X^840 + X^838 + X^837 + X^836 + X^833 + X^830 + X^826 + X^824 + X^823 + X^819 + X^816 + X^812 + X^809 + X^805 + X^803 + X^802 + X^799 + X^798 + X^791 + X^789 + X^788 + X^787 + X^785 + X^784 + X^783 + X^782 + X^778 + X^777 + X^773 + X^770 + X^769 + X^768 + X^767 + X^766 + X^764 + X^763 + X^762 + X^759 + X^756 + X^753 + X^752 + X^749 + X^748 + X^746 + X^745 + X^743 + X^742 + X^739 + X^738 + X^735 + X^732 + X^729 + X^728 + X^727 + X^725 + X^724 + X^722 + X^721 + X^718 + X^715 + X^714 + X^713 + X^708 + X^707 + X^706 + X^704 + X^703 + X^701 + X^700 + X^699 + X^694 + X^693 + X^692 + X^689 + X^686 + X^685 + X^683 + X^682 + X^680 + X^679 + X^678 + X^675 + X^672 + X^669 + X^668 + X^665 + X^664 + X^662 + X^661 + X^659 + X^658 + X^655 + X^654 + X^651 + X^648 + X^645 + X^644 + X^643 + X^641 + X^640 + X^638 + X^637 + X^634 + X^631 + X^630 + X^629 + X^624 + X^622 + X^620 + X^619 + X^617 + X^616 + X^610 + X^608 + X^607 + X^605 + X^599 + X^598 + X^596 + X^595 + X^593 + X^591 + X^586 + X^585 + X^584 + X^581 + X^578 + X^577 + X^575 + X^574 + X^572 + X^571 + X^570 + X^567 + X^564 + X^561 + X^560 + X^557 + X^556 + X^554 + X^553 + X^551 + X^550 + X^547 + X^546 + X^543 + X^540 + X^537 + X^536 + X^535 + X^533 + X^532 + X^530 + X^529 + X^526 + X^523 + X^522 + X^521 + X^516 + X^515 + X^514 + X^512 + X^511 + X^509 + X^508 + X^507 + X^502 + X^501 + X^500 + X^497 + X^494 + X^493 + X^491 + X^490 + X^488 + X^487 + X^486 + X^483 + X^480 + X^477 + X^476 + X^473 + X^472 + X^470 + X^469 + X^467 + X^466 + X^463 + X^462 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X^308 + X^307 + X^306 + X^305 + X^304 + X^301 + X^300 + X^299 + X^298 + X^296 + X^295 + X^293 + X^291 + X^290 + X^289 + X^288 + X^287 + X^285 + X^284 + X^283 + X^282 + X^281 + X^280 + X^279 + X^276 + X^274 + X^273 + X^271 + X^26 ** WARNING: Output too long, hence truncated. ************** MAGMA ***************** Host 3(NXDOMAIN) (194.165.15.3) Time: Thu Jan 22 13:13:10 2004 Input: k := GF(2); C := PrimitivePolynomial(k,9); C; for j in [24..31] do for k in [18..21] do for m in [14..17] do for n in [8..13] do C := ((1 + X^n)^19)*((1 + X^m)^17)*((1 + X^k)^13)*((1 + X^j)^23) + X^1279; if IsPrimitive(C) then C; n; m; k; j; end if; end for; end for; end for; end for; Output: Magma V2.10-6 Thu Jan 22 2004 13:12:51 on modular [Seed = 2613823846] ------------------------------------- X^9 + X^4 + 1 X^1279 + X^1215 + X^1207 + X^1201 + X^1199 + X^1194 + X^1193 + X^1186 + X^1185 + X^1183 + X^1180 + X^1178 + X^1175 + X^1172 + X^1169 + X^1164 + X^1162 + X^1161 + X^1159 + X^1154 + X^1151 + X^1148 + 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X^490 + X^489 + X^485 + X^482 + X^481 + X^480 + X^479 + X^477 + X^474 + X^473 + X^471 + X^470 + X^466 + X^465 + X^464 + X^463 + X^462 + X^460 + X^459 + X^458 + X^457 + X^456 + X^455 + X^452 + X^451 + X^449 + X^448 + X^447 + X^445 + X^443 + X^442 + X^441 + X^440 + X^437 + X^435 + X^433 + X^432 + X^430 + X^424 + X^420 + X^419 + X^417 + X^416 + X^415 + X^414 + X^412 + X^411 + X^410 + X^408 + X^406 + X^405 + X^403 + X^398 + X^395 + X^392 + X^390 + X^389 + X^387 + X^385 + X^381 + X^380 + X^379 + X^374 + X^373 + X^371 + X^367 + X^366 + X^365 + X^364 + X^363 + X^360 + X^359 + X^358 + X^356 + X^354 + X^351 + X^350 + X^349 + X^348 + X^347 + X^346 + X^343 + X^341 + X^340 + X^339 + X^338 + X^334 + X^333 + X^331 + X^330 + X^329 + X^327 + X^326 + X^325 + X^324 + X^323 + X^321 + X^318 + X^316 + X^314 + X^313 + X^310 + X^309 + X^308 + X^307 + X^306 + X^305 + X^304 + X^301 + X^300 + X^299 + X^298 + X^296 + X^295 + X^293 + X^291 + X^290 + X^289 + X^288 + X^287 + X^285 + X^284 + X^283 + X^282 + X^281 + X^280 + X^279 + X^276 + X^274 + X^273 + X^271 + X^26 ** WARNING: Output too long, hence truncated. ************** MAGMA ***************** Host 3(NXDOMAIN) (194.165.15.3) Time: Thu Jan 22 13:14:25 2004 Input: k := GF(2); C := PrimitivePolynomial(k,9); C; for j in [20..31] do for k in [18..19] do for m in [14..17] do for n in [8..13] do C := ((1 + X^n)^13)*((1 + X^m)^17)*((1 + X^k)^19)*((1 + X^j)^23) + X^1279; if IsPrimitive(C) then C; n; m; k; j; end if; end for; end for; end for; end for; Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Thu Jan 22 2004 13:14:02 on modular [Seed = 2428551716] ------------------------------------- X^9 + X^4 + 1 X^1288 + X^1279 + X^1277 + X^1273 + X^1269 + X^1265 + X^1262 + X^1258 + X^1246 + X^1244 + X^1243 + X^1242 + X^1233 + X^1231 + X^1229 + X^1225 + X^1224 + X^1223 + X^1221 + X^1219 + X^1218 + X^1216 + X^1214 + X^1208 + X^1205 + X^1202 + X^1201 + X^1199 + X^1198 + X^1196 + X^1193 + X^1189 + X^1187 + X^1182 + X^1181 + X^1180 + X^1179 + X^1178 + X^1175 + X^1174 + X^1173 + X^1172 + X^1164 + X^1162 + X^1161 + X^1159 + X^1158 + X^1157 + X^1152 + X^1150 + X^1149 + X^1147 + X^1145 + X^1143 + X^1139 + X^1138 + X^1137 + X^1135 + X^1134 + X^1132 + X^1130 + X^1129 + X^1128 + X^1127 + X^1124 + X^1120 + X^1118 + X^1117 + X^1116 + X^1115 + X^1114 + X^1112 + X^1109 + X^1106 + X^1105 + X^1103 + X^1101 + X^1099 + X^1097 + X^1095 + X^1094 + X^1091 + X^1088 + X^1086 + X^1085 + X^1084 + X^1083 + X^1082 + X^1080 + X^1076 + X^1073 + X^1072 + X^1071 + X^1070 + X^1068 + X^1066 + X^1065 + X^1063 + X^1062 + X^1061 + X^1057 + X^1055 + X^1053 + X^1051 + X^1050 + X^1043 + X^1042 + X^1041 + X^1039 + X^1038 + X^1037 + X^1036 + X^1033 + X^1029 + X^1028 + X^1027 + X^1026 + X^1021 + X^1020 + X^1019 + X^1013 + X^1011 + X^1007 + X^1006 + X^1003 + X^1001 + X^999 + X^998 + X^995 + X^993 + X^992 + X^991 + X^989 + X^986 + X^985 + X^984 + X^983 + X^982 + X^978 + X^977 + X^975 + X^974 + X^973 + X^971 + X^968 + X^967 + X^962 + X^959 + X^958 + X^957 + X^953 + X^949 + X^947 + X^942 + X^941 + X^938 + X^934 + X^933 + X^932 + X^931 + X^929 + X^925 + X^924 + X^923 + X^922 + X^918 + X^915 + X^914 + X^912 + X^907 + X^904 + X^903 + X^899 + X^897 + X^894 + X^888 + X^887 + X^885 + X^884 + X^883 + X^880 + X^878 + X^876 + X^875 + X^874 + X^872 + X^871 + X^870 + X^868 + X^866 + X^860 + X^859 + X^858 + X^857 + X^856 + X^855 + X^850 + X^848 + X^846 + X^844 + X^842 + X^841 + X^839 + X^837 + X^836 + X^835 + X^833 + X^832 + X^831 + X^830 + X^828 + X^825 + X^824 + X^822 + X^820 + X^819 + X^817 + X^816 + X^815 + X^813 + X^811 + X^810 + X^807 + X^806 + X^804 + X^803 + X^798 + X^797 + X^795 + X^794 + X^789 + X^788 + X^786 + X^785 + X^782 + X^781 + X^779 + X^777 + X^776 + X^775 + X^773 + X^772 + X^770 + X^768 + X^767 + X^764 + X^762 + X^761 + X^760 + X^759 + X^757 + X^756 + X^755 + X^753 + X^751 + X^750 + X^748 + X^746 + X^742 + X^737 + X^736 + X^735 + X^734 + X^732 + X^729 + X^726 + X^725 + X^724 + X^722 + X^720 + X^717 + X^716 + X^712 + X^709 + X^708 + X^707 + X^705 + X^704 + X^702 + X^700 + X^699 + X^695 + X^693 + X^688 + X^687 + X^681 + X^679 + X^678 + X^675 + X^672 + X^669 + X^668 + X^667 + X^664 + X^663 + X^660 + X^659 + X^657 + X^655 + X^652 + X^651 + X^650 + X^649 + X^639 + X^638 + X^637 + X^636 + X^633 + X^631 + X^629 + X^628 + X^625 + X^624 + X^621 + X^620 + X^619 + X^616 + X^613 + X^610 + X^609 + X^607 + X^601 + X^600 + X^595 + X^593 + X^589 + X^588 + X^586 + X^584 + X^583 + X^581 + X^580 + X^579 + X^576 + X^572 + X^571 + X^568 + X^566 + X^564 + X^563 + X^562 + X^559 + X^556 + X^554 + X^553 + X^552 + X^551 + X^546 + X^542 + X^540 + X^538 + X^537 + X^535 + X^533 + X^532 + X^531 + X^529 + X^528 + X^527 + X^526 + X^524 + X^521 + X^520 + X^518 + X^516 + X^515 + X^513 + X^512 + X^511 + X^509 + X^507 + X^506 + X^503 + X^502 + X^500 + X^499 + X^494 + X^493 + X^491 + X^490 + X^485 + X^484 + X^482 + X^481 + X^478 + X^477 + X^475 + X^473 + X^472 + X^471 + X^469 + X^468 + X^466 + X^464 + X^463 + X^460 + X^458 + X^457 + X^456 + X^455 + X^453 + X^452 + X^451 + X^449 + X^447 + X^446 + X^444 + X^442 + X^440 + X^438 + X^433 + X^432 + X^431 + X^430 + X^429 + X^428 + X^422 + X^420 + X^418 + X^417 + X^416 + X^414 + X^413 + X^412 + X^410 + X^408 + X^405 + X^404 + X^403 + X^401 + X^400 + X^394 + X^391 + X^389 + X^385 + X^384 + X^381 + X^376 + X^374 + X^373 + X^370 + X^366 + X^365 + X^364 + X^363 + X^359 + X^357 + X^356 + X^355 + X^354 + X^350 + X^347 + X^346 + X^341 + X^339 + X^335 + X^331 + X^330 + X^329 + X^326 + X^321 + X^320 + X^317 + X^315 + X^314 + X^313 + X^311 + X^310 + X^306 + X^305 + X^304 + X^303 + X^302 + X^299 + X^297 + X^296 + X^295 + X^293 + X^290 + X^289 + X^287 + X^285 + X^282 + X^281 + X^277 + X^275 + X^269 + X^268 + X^267 + X^262 + X^261 + X^260 + X^259 + X^255 + X^252 + X^251 + X^250 + X^249 + X^247 + X^246 + X^245 + X^238 + X^237 + X^235 + X^233 + X^231 + X^227 + X^226 + X^225 + X^223 + X^222 + X^220 + X^218 + X^217 + X^216 + X^215 + X^212 + X^208 + X^206 + X^205 + X^204 + X^203 + X^202 + X^200 + X^197 + X^194 + X^193 + X^191 + X^189 + X^187 + X^185 + X^183 + X^182 + X^179 + X^176 + X^174 + X^173 + X^172 + X^171 + X^170 + X^168 + X^164 + X^161 + X^160 + X^159 + X^158 + X^156 + X^154 + X^153 + X^151 + X^150 + X^149 + X^145 + X^143 + X^141 + X^139 + X^138 + X^136 + X^131 + X^130 + X^129 + X^127 + X^126 + X^124 + X^116 + X^115 + X^114 + X^113 + X^110 + X^109 + X^108 + X^107 + X^106 + X^101 + X^99 + X^95 + X^92 + X^90 + X^89 + X^87 + X^86 + X^83 + X^80 + X^74 + X^72 + X^70 + X^69 + X^67 + X^65 + X^64 + X^63 + X^59 + X^57 + X^55 + X^46 + X^45 + X^44 + X^42 + X^30 + X^26 + X^23 + X^19 + X^15 + X^11 + 1 11 15 19 23 Errors: /home/mfd/gomagma: line 2: 7886 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host 3(NXDOMAIN) (194.165.15.3) Time: Thu Jan 22 13:15:37 2004 Input: k := GF(2); C := PrimitivePolynomial(k,9); C; for j in [19..31] do for k in [18..18] do for m in [14..17] do for n in [8..13] do C := ((1 + X^n)^13)*((1 + X^m)^17)*((1 + X^k)^19)*((1 + X^j)^23) + X^1279; if IsPrimitive(C) then C; n; m; k; j; end if; end for; end for; end for; end for; Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Thu Jan 22 2004 13:15:14 on modular [Seed = 2211696879] ------------------------------------- X^9 + X^4 + 1 Errors: /home/mfd/gomagma: line 2: 7901 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host 3(NXDOMAIN) (194.165.15.3) Time: Thu Jan 22 13:16:28 2004 Input: k := GF(2); C := PrimitivePolynomial(k,9); C; for j in [19..31] do for k in [16..18] do for m in [12..15] do for n in [8..11] do C := ((1 + X^n)^13)*((1 + X^m)^17)*((1 + X^k)^19)*((1 + X^j)^23) + X^1279; if IsPrimitive(C) then C; n; m; k; j; end if; end for; end for; end for; end for; Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Thu Jan 22 2004 13:16:05 on modular [Seed = 3102272387] ------------------------------------- X^9 + X^4 + 1 X^1279 + X^1113 + X^1104 + X^1098 + X^1097 + X^1094 + X^1089 + X^1088 + X^1085 + X^1082 + X^1081 + X^1079 + X^1078 + X^1077 + X^1075 + X^1073 + X^1072 + X^1070 + X^1069 + X^1068 + X^1065 + X^1063 + X^1061 + X^1060 + X^1059 + X^1058 + X^1057 + X^1054 + X^1052 + X^1051 + X^1049 + X^1045 + X^1044 + X^1042 + X^1041 + X^1040 + X^1039 + X^1038 + X^1037 + X^1036 + X^1035 + X^1033 + X^1029 + X^1023 + X^1022 + X^1019 + X^1018 + X^1009 + X^1004 + X^1003 + X^1001 + X^999 + X^996 + X^994 + X^993 + X^989 + X^982 + X^981 + X^978 + X^977 + X^975 + X^973 + X^970 + X^969 + X^965 + X^964 + X^963 + X^962 + X^961 + X^959 + X^957 + X^956 + X^954 + X^952 + X^951 + X^950 + X^949 + X^948 + X^944 + X^943 + X^940 + X^938 + X^936 + X^935 + X^932 + X^931 + X^924 + X^920 + X^919 + X^917 + X^914 + X^912 + X^910 + X^909 + X^904 + X^895 + X^894 + X^891 + X^890 + X^884 + X^880 + X^878 + X^877 + X^876 + X^875 + X^874 + X^872 + X^871 + X^869 + X^868 + X^862 + X^861 + X^859 + X^858 + X^856 + X^855 + X^853 + X^852 + X^850 + X^849 + X^848 + X^844 + X^843 + X^841 + X^840 + X^839 + X^838 + X^837 + X^836 + X^834 + X^832 + X^831 + X^830 + X^826 + X^825 + X^824 + X^822 + X^820 + X^819 + X^818 + X^815 + X^813 + X^811 + X^807 + X^803 + X^800 + X^799 + X^797 + X^794 + X^793 + X^790 + X^788 + X^786 + X^780 + X^775 + X^774 + X^771 + X^768 + X^767 + X^765 + X^762 + X^757 + X^755 + X^753 + X^750 + X^749 + X^743 + X^742 + X^738 + X^737 + X^736 + X^734 + X^733 + X^732 + X^731 + X^730 + X^726 + X^725 + X^724 + X^723 + X^719 + X^718 + X^716 + X^715 + X^714 + X^713 + X^712 + X^711 + X^710 + X^707 + X^706 + X^704 + X^701 + X^700 + X^699 + X^697 + X^695 + X^694 + X^693 + X^692 + X^691 + X^690 + X^689 + X^688 + X^687 + X^685 + X^682 + X^678 + X^676 + X^675 + X^673 + X^672 + X^671 + X^670 + X^668 + X^666 + X^665 + X^663 + X^660 + X^659 + X^657 + X^656 + X^652 + X^651 + X^647 + X^646 + X^645 + X^637 + X^634 + X^633 + X^629 + X^628 + X^627 + X^618 + X^616 + X^615 + X^614 + X^613 + X^605 + X^604 + X^602 + X^600 + X^599 + X^598 + X^597 + X^595 + X^593 + X^592 + X^590 + X^585 + X^583 + X^581 + X^579 + X^578 + X^577 + X^572 + X^571 + X^570 + X^569 + X^562 + X^561 + X^559 + X^557 + X^556 + X^554 + X^552 + X^551 + X^544 + X^543 + X^542 + X^541 + X^536 + X^535 + X^534 + X^532 + X^530 + X^528 + X^523 + X^521 + X^520 + X^518 + X^516 + X^515 + X^514 + X^513 + X^511 + X^509 + X^508 + X^500 + X^499 + X^498 + X^497 + X^495 + X^486 + X^485 + X^484 + X^480 + X^479 + X^476 + X^468 + X^467 + X^466 + X^462 + X^461 + X^457 + X^456 + X^454 + X^453 + X^450 + X^448 + X^447 + X^445 + X^443 + X^442 + X^441 + X^440 + X^438 + X^437 + X^435 + X^431 + X^428 + X^426 + X^425 + X^424 + X^423 + X^422 + X^421 + X^420 + X^419 + X^418 + X^416 + X^414 + X^413 + X^412 + X^409 + X^407 + X^406 + X^403 + X^402 + X^401 + X^400 + X^399 + X^398 + X^397 + X^395 + X^394 + X^390 + X^389 + X^388 + X^387 + X^383 + X^382 + X^381 + X^380 + X^379 + X^377 + X^376 + X^375 + X^371 + X^370 + X^364 + X^363 + X^360 + X^358 + X^356 + X^351 + X^348 + X^346 + X^345 + X^342 + X^339 + X^338 + X^333 + X^327 + X^325 + X^323 + X^320 + X^319 + X^316 + X^314 + X^313 + X^310 + X^306 + X^302 + X^300 + X^298 + X^295 + X^294 + X^293 + X^291 + X^289 + X^288 + X^287 + X^283 + X^282 + X^281 + X^279 + X^277 + X^276 + X^275 + X^274 + X^273 + X^272 + X^270 + X^269 + X^265 + X^264 + X^263 + X^261 + X^260 + X^258 + X^257 + X^255 + X^254 + X^252 + X^251 + X^245 + X^244 + X^242 + X^241 + X^239 + X^238 + X^237 + X^236 + X^235 + X^233 + X^229 + X^223 + X^222 + X^219 + X^218 + X^209 + X^204 + X^203 + X^201 + X^199 + X^196 + X^194 + X^193 + X^189 + X^182 + X^181 + X^178 + X^177 + X^175 + X^173 + X^170 + X^169 + X^165 + X^164 + X^163 + X^162 + X^161 + X^159 + X^157 + X^156 + X^154 + X^152 + X^151 + X^150 + X^149 + X^148 + X^144 + X^143 + X^140 + X^138 + X^136 + X^135 + X^132 + X^131 + X^124 + X^120 + X^119 + X^117 + X^114 + X^112 + X^110 + X^109 + X^104 + X^95 + X^94 + X^91 + X^90 + X^84 + X^80 + X^78 + X^77 + X^76 + X^75 + X^74 + X^73 + X^72 + X^71 + X^69 + X^68 + X^64 + X^62 + X^61 + X^59 + X^56 + X^55 + X^54 + X^53 + X^52 + X^50 + X^48 + X^45 + X^44 + X^43 + X^41 + X^40 + X^38 + X^36 + X^35 + X^34 + X^32 + X^31 + X^28 + X^25 + X^24 + X^19 + X^16 + X^15 + X^9 + 1 9 15 16 19 Errors: /home/mfd/gomagma: line 2: 7910 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host 3(NXDOMAIN) (194.165.15.3) Time: Thu Jan 22 13:17:26 2004 Input: k := GF(2); C := PrimitivePolynomial(k,9); C; for j in [19..31] do for k in [16..18] do for m in [12..15] do for n in [8..11] do C := ((1 + X^n)^13)*((1 + X^m)^17)*((1 + X^k)^19)*((1 + X^j)^31) + X^1279; if IsPrimitive(C) then C; n; m; k; j; end if; end for; end for; end for; end for; Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Thu Jan 22 2004 13:17:03 on modular [Seed = 2935946607] ------------------------------------- X^9 + X^4 + 1 Errors: /home/mfd/gomagma: line 2: 7920 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host 3(NXDOMAIN) (194.165.15.3) Time: Thu Jan 22 13:18:02 2004 Input: k := GF(2); C := PrimitivePolynomial(k,9); C; for j in [19..31] do for k in [16..18] do for m in [12..15] do for n in [8..11] do C := ((1 + X^n)^31)*((1 + X^m)^17)*((1 + X^k)^19)*((1 + X^j)^23) + X^1279; if IsPrimitive(C) then C; n; m; k; j; end if; end for; end for; end for; end for; Output: Magma V2.10-6 Thu Jan 22 2004 13:17:50 on modular [Seed = 2818044983] ------------------------------------- X^9 + X^4 + 1 Total time: 11.659 seconds, Total memory usage: 2.32MB ************** MAGMA ***************** Host 3(NXDOMAIN) (194.165.15.3) Time: Thu Jan 22 13:18:44 2004 Input: k := GF(2); C := PrimitivePolynomial(k,9); C; for j in [19..31] do for k in [16..18] do for m in [14..15] do for n in [8..13] do C := ((1 + X^n)^31)*((1 + X^m)^17)*((1 + X^k)^19)*((1 + X^j)^23) + X^1279; if IsPrimitive(C) then C; n; m; k; j; end if; end for; end for; end for; end for; Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Thu Jan 22 2004 13:18:21 on modular [Seed = 1561136879] ------------------------------------- X^9 + X^4 + 1 Errors: /home/mfd/gomagma: line 2: 7938 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host 3(NXDOMAIN) (194.165.15.3) Time: Thu Jan 22 13:19:16 2004 Input: k := GF(2); C := PrimitivePolynomial(k,9); C; for j in [19..31] do for k in [16..18] do for m in [14..15] do for n in [8..13] do C := ((1 + X^n)^24)*((1 + X^m)^17)*((1 + X^k)^19)*((1 + X^j)^23) + X^1279; if IsPrimitive(C) then C; n; m; k; j; end if; end for; end for; end for; end for; Output: Magma V2.10-6 Thu Jan 22 2004 13:19:04 on modular [Seed = 1409548307] ------------------------------------- X^9 + X^4 + 1 X^1290 + X^1279 + X^1276 + X^1274 + X^1270 + X^1260 + X^1258 + X^1256 + X^1254 + X^1250 + X^1244 + X^1242 + X^1240 + X^1238 + X^1236 + X^1234 + X^1230 + X^1228 + X^1224 + X^1222 + X^1220 + X^1218 + X^1216 + X^1214 + X^1210 + X^1208 + X^1204 + X^1202 + X^1200 + X^1198 + X^1196 + X^1190 + X^1188 + X^1184 + X^1182 + X^1176 + X^1170 + X^1168 + X^1156 + X^1150 + X^1146 + X^1136 + X^1132 + X^1126 + X^1114 + X^1112 + X^1106 + X^1100 + X^1094 + X^1092 + X^1086 + X^1080 + X^1074 + X^1072 + X^1066 + X^1060 + X^1054 + X^1052 + X^1046 + X^1040 + X^1032 + X^1026 + X^1018 + X^1012 + X^1006 + X^1004 + X^1002 + X^998 + X^992 + X^988 + X^984 + X^982 + X^978 + X^970 + X^968 + X^964 + X^962 + X^958 + X^956 + X^954 + X^950 + X^948 + X^944 + X^942 + X^940 + X^938 + X^936 + X^934 + X^930 + X^928 + X^924 + X^922 + X^920 + X^918 + X^916 + X^914 + X^910 + X^908 + X^906 + X^904 + X^902 + X^900 + X^898 + X^896 + X^894 + X^892 + X^888 + X^886 + X^884 + X^882 + X^880 + X^878 + X^874 + X^872 + X^868 + X^866 + X^864 + X^862 + X^860 + X^858 + X^854 + X^852 + X^848 + X^846 + X^844 + X^840 + X^838 + X^834 + X^832 + X^824 + X^820 + X^818 + X^814 + X^810 + X^804 + X^800 + X^798 + X^796 + X^790 + X^784 + X^778 + X^776 + X^770 + X^764 + X^758 + X^756 + X^750 + X^746 + X^744 + X^738 + X^736 + X^732 + X^726 + X^724 + X^718 + X^712 + X^706 + X^704 + X^698 + X^692 + X^686 + X^684 + X^678 + X^672 + X^666 + X^664 + X^658 + X^652 + X^646 + X^644 + X^638 + X^632 + X^626 + X^624 + X^618 + X^612 + X^606 + X^604 + X^598 + X^592 + X^586 + X^584 + X^578 + X^572 + X^566 + X^564 + X^558 + X^554 + X^552 + X^546 + X^544 + X^540 + X^534 + X^532 + X^526 + X^520 + X^514 + X^512 + X^506 + X^500 + X^494 + X^492 + X^490 + X^486 + X^480 + X^476 + X^472 + X^470 + X^466 + X^458 + X^456 + X^452 + X^450 + X^446 + X^444 + X^442 + X^438 + X^436 + X^432 + X^430 + X^428 + X^426 + X^424 + X^422 + X^418 + X^416 + X^412 + X^410 + X^408 + X^406 + X^404 + X^402 + X^398 + X^396 + X^394 + X^392 + X^390 + X^388 + X^386 + X^384 + X^382 + X^380 + X^376 + X^374 + X^372 + X^370 + X^368 + X^366 + X^362 + X^360 + X^356 + X^354 + X^352 + X^350 + X^348 + X^346 + X^342 + X^340 + X^336 + X^334 + X^332 + X^328 + X^326 + X^322 + X^320 + X^312 + X^308 + X^306 + X^302 + X^298 + X^292 + X^288 + X^286 + X^284 + X^278 + X^272 + X^264 + X^258 + X^250 + X^244 + X^238 + X^236 + X^230 + X^224 + X^218 + X^216 + X^210 + X^204 + X^198 + X^196 + X^190 + X^184 + X^178 + X^176 + X^164 + X^158 + X^154 + X^144 + X^140 + X^134 + X^122 + X^120 + X^114 + X^108 + X^106 + X^102 + X^100 + X^94 + X^92 + X^90 + X^88 + X^86 + X^82 + X^80 + X^76 + X^74 + X^72 + X^70 + X^68 + X^66 + X^62 + X^60 + X^56 + X^54 + X^52 + X^50 + X^48 + X^46 + X^40 + X^36 + X^34 + X^32 + X^30 + X^20 + X^16 + X^14 + 1 12 14 16 20 Total time: 12.210 seconds, Total memory usage: 2.42MB ************** MAGMA ***************** Host 3(NXDOMAIN) (194.165.15.3) Time: Thu Jan 22 13:20:01 2004 Input: k := GF(2); C := PrimitivePolynomial(k,9); C; for j in [19..31] do for k in [16..18] do for m in [14..15] do for n in [8..13] do C := ((1 + X^n)^21)*((1 + X^m)^17)*((1 + X^k)^19)*((1 + X^j)^23) + X^1279; if IsPrimitive(C) then C; n; m; k; j; end if; end for; end for; end for; end for; Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Thu Jan 22 2004 13:19:38 on modular [Seed = 1260068654] ------------------------------------- X^9 + X^4 + 1 X^1279 + X^1256 + X^1245 + X^1242 + X^1240 + X^1235 + X^1231 + X^1229 + X^1226 + X^1221 + X^1219 + X^1215 + X^1214 + X^1213 + X^1212 + X^1205 + X^1201 + X^1200 + X^1199 + X^1197 + X^1196 + X^1193 + X^1192 + X^1191 + X^1187 + X^1185 + X^1184 + X^1183 + X^1182 + X^1179 + X^1178 + X^1176 + X^1175 + X^1172 + X^1170 + X^1169 + X^1163 + X^1162 + X^1161 + X^1158 + X^1157 + X^1154 + X^1153 + X^1151 + X^1150 + X^1149 + X^1148 + X^1142 + X^1141 + X^1140 + X^1139 + X^1137 + X^1136 + X^1133 + X^1132 + X^1130 + X^1129 + X^1128 + X^1127 + X^1121 + X^1120 + X^1119 + X^1118 + X^1116 + X^1115 + X^1112 + X^1111 + X^1109 + X^1108 + X^1107 + X^1106 + X^1100 + X^1099 + X^1098 + X^1097 + X^1095 + X^1094 + X^1091 + X^1090 + X^1087 + X^1086 + X^1085 + X^1080 + X^1079 + X^1078 + X^1076 + X^1073 + X^1072 + X^1070 + X^1065 + X^1063 + X^1061 + X^1059 + X^1057 + X^1056 + X^1053 + X^1052 + X^1051 + X^1050 + X^1049 + X^1048 + X^1047 + X^1045 + X^1039 + X^1038 + X^1037 + X^1035 + X^1034 + X^1033 + X^1032 + X^1027 + X^1025 + X^1024 + X^1023 + X^1022 + X^1020 + X^1019 + X^1018 + X^1015 + X^1013 + X^1009 + X^1005 + X^999 + X^997 + X^996 + X^995 + X^994 + X^993 + X^992 + X^991 + X^990 + X^988 + X^987 + X^985 + X^984 + X^982 + X^979 + X^978 + X^976 + X^975 + X^974 + X^973 + X^970 + X^969 + X^968 + X^967 + X^966 + X^964 + X^963 + X^955 + X^953 + X^949 + X^948 + X^946 + X^945 + X^942 + X^941 + X^938 + X^934 + X^932 + X^928 + X^925 + X^921 + X^917 + X^912 + X^911 + X^910 + X^909 + X^908 + X^907 + X^906 + X^901 + X^900 + X^899 + X^898 + X^897 + X^895 + X^894 + X^893 + X^891 + X^889 + X^886 + X^883 + X^882 + X^878 + X^873 + X^871 + X^870 + X^869 + X^866 + X^863 + X^860 + X^858 + X^856 + X^855 + X^854 + X^851 + X^850 + X^847 + X^846 + X^844 + X^843 + X^841 + X^840 + X^839 + X^838 + X^836 + X^831 + X^828 + X^827 + X^820 + X^818 + X^814 + X^812 + X^811 + X^810 + X^807 + X^806 + X^804 + X^803 + X^801 + X^800 + X^799 + X^798 + X^797 + X^796 + X^792 + X^791 + X^787 + X^784 + X^783 + X^781 + X^780 + X^777 + X^776 + X^773 + X^767 + X^766 + X^763 + X^762 + X^755 + X^749 + X^748 + X^740 + X^738 + X^737 + X^736 + X^735 + X^731 + X^729 + X^728 + X^726 + X^725 + X^723 + X^722 + X^720 + X^719 + X^717 + X^714 + X^712 + X^711 + X^710 + X^709 + X^707 + X^706 + X^699 + X^697 + X^696 + X^695 + X^694 + X^692 + X^689 + X^687 + X^686 + X^685 + X^683 + X^681 + X^680 + X^679 + X^677 + X^675 + X^673 + X^672 + X^671 + X^669 + X^667 + X^664 + X^663 + X^661 + X^659 + X^657 + X^656 + X^655 + X^652 + X^650 + X^649 + X^648 + X^647 + X^644 + X^642 + X^640 + X^638 + X^634 + X^633 + X^632 + X^631 + X^630 + X^629 + X^627 + X^626 + X^625 + X^624 + X^623 + X^622 + X^618 + X^616 + X^614 + X^612 + X^609 + X^608 + X^607 + X^606 + X^604 + X^601 + X^600 + X^599 + X^597 + X^595 + X^593 + X^592 + X^589 + X^587 + X^585 + X^584 + X^583 + X^581 + X^579 + X^577 + X^576 + X^575 + X^573 + X^571 + X^570 + X^569 + X^567 + X^564 + X^562 + X^561 + X^560 + X^559 + X^557 + X^550 + X^549 + X^547 + X^546 + X^545 + X^544 + X^542 + X^539 + X^537 + X^536 + X^534 + X^533 + X^531 + X^530 + X^528 + X^527 + X^525 + X^521 + X^520 + X^519 + X^518 + X^516 + X^508 + X^507 + X^501 + X^494 + X^493 + X^490 + X^489 + X^483 + X^480 + X^479 + X^476 + X^475 + X^473 + X^472 + X^469 + X^465 + X^464 + X^460 + X^459 + X^458 + X^457 + X^456 + X^455 + X^453 + X^452 + X^450 + X^449 + X^446 + X^445 + X^444 + X^442 + X^438 + X^436 + X^429 + X^428 + X^425 + X^420 + X^418 + X^417 + X^416 + X^415 + X^413 + X^412 + X^410 + X^409 + X^406 + X^405 + X^402 + X^401 + X^400 + X^398 + X^396 + X^393 + X^390 + X^387 + X^386 + X^385 + X^383 + X^378 + X^374 + X^373 + X^370 + X^367 + X^365 + X^363 + X^362 + X^361 + X^359 + X^358 + X^357 + X^356 + X^355 + X^350 + X^349 + X^348 + X^347 + X^346 + X^345 + X^344 + X^339 + X^335 + X^331 + X^328 + X^324 + X^322 + X^318 + X^315 + X^314 + X^311 + X^310 + X^308 + X^307 + X^303 + X^301 + X^293 + X^292 + X^290 + X^289 + X^288 + X^287 + X^286 + X^283 + X^282 + X^281 + X^280 + X^278 + X^277 + X^274 + X^272 + X^271 + X^269 + X^268 + X^266 + X^265 + X^264 + X^263 + X^262 + X^261 + X^260 + X^259 + X^257 + X^251 + X^247 + X^243 + X^241 + X^238 + X^237 + X^236 + X^234 + X^233 + X^232 + X^231 + X^229 + X^224 + X^223 + X^222 + X^221 + X^219 + X^218 + X^217 + X^211 + X^209 + X^208 + X^207 + X^206 + X^205 + X^204 + X^203 + X^200 + X^199 + X^197 + X^195 + X^193 + X^191 + X^186 + X^184 + X^183 + X^180 + X^178 + X^177 + X^176 + X^171 + X^170 + X^169 + X^166 + X^165 + X^162 + X^161 + X^159 + X^158 + X^157 + X^156 + X^150 + X^149 + X^148 + X^147 + X^145 + X^144 + X^141 + X^140 + X^138 + X^137 + X^136 + X^135 + X^129 + X^128 + X^127 + X^126 + X^124 + X^123 + X^120 + X^119 + X^117 + X^116 + X^115 + X^114 + X^108 + X^107 + X^106 + X^105 + X^103 + X^102 + X^99 + X^98 + X^95 + X^94 + X^93 + X^87 + X^86 + X^84 + X^81 + X^80 + X^78 + X^77 + X^74 + X^73 + X^72 + X^71 + X^69 + X^65 + X^64 + X^63 + X^60 + X^59 + X^57 + X^56 + X^55 + X^51 + X^44 + X^43 + X^42 + X^41 + X^37 + X^35 + X^30 + X^27 + X^25 + X^21 + X^16 + X^14 + X^11 + 1 11 14 16 21 Errors: /home/mfd/gomagma: line 2: 7956 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host 3(NXDOMAIN) (194.165.15.3) Time: Thu Jan 22 13:21:53 2004 Input: k := GF(2); C := PrimitivePolynomial(k,9); C; for j in [19..31] do for k in [16..18] do for m in [14..15] do for n in [8..13] do C := ((1 + X^n)^21)*((1 + X^m)^19)*((1 + X^k)^17)*((1 + X^j)^23) + X^1279; if IsPrimitive(C) then C; n; m; k; j; end if; end for; end for; end for; end for; Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Thu Jan 22 2004 13:21:30 on modular [Seed = 1999053698] ------------------------------------- X^9 + X^4 + 1 X^1307 + X^1295 + X^1293 + X^1289 + X^1286 + X^1281 + X^1277 + X^1275 + X^1274 + X^1272 + X^1268 + X^1267 + X^1263 + X^1261 + X^1260 + X^1259 + X^1258 + X^1256 + X^1254 + X^1251 + X^1249 + X^1247 + X^1246 + X^1245 + X^1242 + X^1241 + X^1240 + X^1239 + X^1238 + X^1237 + X^1231 + X^1230 + X^1229 + X^1228 + X^1227 + X^1226 + X^1225 + X^1224 + X^1221 + X^1220 + X^1218 + X^1216 + X^1215 + X^1213 + X^1210 + X^1209 + X^1208 + X^1207 + X^1206 + X^1204 + X^1203 + X^1201 + X^1200 + X^1197 + X^1195 + X^1194 + X^1192 + X^1189 + X^1188 + X^1186 + X^1185 + X^1183 + X^1182 + X^1180 + X^1179 + X^1176 + X^1174 + X^1173 + X^1171 + X^1168 + X^1167 + X^1165 + X^1164 + X^1162 + X^1161 + X^1159 + X^1158 + X^1155 + X^1153 + X^1152 + X^1150 + X^1147 + X^1146 + X^1144 + X^1143 + X^1141 + X^1140 + X^1139 + X^1138 + X^1137 + X^1134 + X^1132 + X^1131 + X^1129 + X^1127 + X^1126 + X^1123 + X^1122 + X^1121 + X^1120 + X^1119 + X^1118 + X^1117 + X^1116 + X^1115 + X^1110 + X^1109 + X^1108 + X^1107 + X^1106 + X^1105 + X^1103 + X^1102 + X^1100 + X^1098 + X^1097 + X^1096 + X^1094 + X^1093 + X^1091 + X^1088 + X^1086 + X^1085 + X^1084 + X^1082 + X^1079 + X^1076 + X^1073 + X^1072 + X^1070 + X^1067 + X^1065 + X^1064 + X^1061 + X^1059 + X^1058 + X^1052 + X^1051 + X^1049 + X^1047 + X^1046 + X^1045 + X^1044 + X^1043 + X^1040 + X^1038 + X^1033 + X^1030 + X^1029 + X^1028 + X^1027 + X^1026 + X^1025 + X^1024 + X^1022 + X^1019 + X^1013 + X^1012 + X^1011 + X^1009 + X^1008 + X^1006 + X^1005 + X^1004 + X^998 + X^992 + X^991 + X^990 + X^988 + X^985 + X^984 + X^983 + X^981 + X^979 + X^977 + X^973 + X^971 + X^970 + X^969 + X^967 + X^965 + X^964 + X^962 + X^961 + X^960 + X^959 + X^958 + X^956 + X^952 + X^950 + X^949 + X^948 + X^946 + X^944 + X^943 + X^941 + X^940 + X^939 + X^938 + X^937 + X^933 + X^931 + X^928 + X^927 + X^925 + X^922 + X^921 + X^920 + X^918 + X^916 + X^912 + X^911 + X^910 + X^909 + X^906 + X^904 + X^901 + X^900 + X^897 + X^891 + X^890 + X^889 + X^888 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+ X^629 + X^628 + X^626 + X^625 + X^622 + X^620 + X^619 + X^618 + X^615 + X^614 + X^612 + X^609 + X^608 + X^605 + X^604 + X^603 + X^601 + X^599 + X^598 + X^594 + X^591 + X^588 + X^587 + X^584 + X^582 + X^580 + X^578 + X^577 + X^573 + X^571 + X^570 + X^569 + X^566 + X^556 + X^555 + X^552 + X^551 + X^550 + X^549 + X^548 + X^545 + X^543 + X^537 + X^534 + X^533 + X^530 + X^529 + X^528 + X^527 + X^524 + X^523 + X^522 + X^521 + X^516 + X^515 + X^512 + X^508 + X^506 + X^502 + X^501 + X^500 + X^499 + X^497 + X^494 + X^493 + X^489 + X^487 + X^485 + X^483 + X^480 + X^479 + X^478 + X^477 + X^476 + X^472 + X^469 + X^468 + X^466 + X^464 + X^462 + X^461 + X^458 + X^456 + X^455 + X^449 + X^448 + X^445 + X^443 + X^441 + X^440 + X^439 + X^437 + X^434 + X^431 + X^428 + X^427 + X^424 + X^422 + X^420 + X^419 + X^418 + X^417 + X^416 + X^410 + X^407 + X^406 + X^403 + X^401 + X^398 + X^397 + X^396 + X^395 + X^391 + X^389 + X^387 + X^386 + X^385 + X^382 + X^380 + X^379 + X^376 + X^374 + X^370 + X^369 + X^368 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X^616 + X^612 + X^610 + X^608 + X^606 + X^604 + X^602 + X^596 + X^594 + X^592 + X^590 + X^584 + X^578 + X^572 + X^570 + X^564 + X^562 + X^560 + X^558 + X^554 + X^550 + X^546 + X^544 + X^542 + X^540 + X^538 + X^536 + X^532 + X^530 + X^528 + X^522 + X^520 + X^518 + X^514 + X^508 + X^506 + X^502 + X^500 + X^498 + X^494 + X^492 + X^488 + X^482 + X^474 + X^470 + X^464 + X^460 + X^458 + X^452 + X^450 + X^448 + X^444 + X^442 + X^426 + X^424 + X^422 + X^420 + X^416 + X^412 + X^410 + X^406 + X^400 + X^394 + X^392 + X^382 + X^376 + X^374 + X^368 + X^366 + X^364 + X^362 + X^344 + X^342 + X^340 + X^338 + X^332 + X^326 + X^324 + X^322 + X^320 + X^312 + X^302 + X^300 + X^296 + X^294 + X^292 + X^282 + X^276 + X^274 + X^272 + X^270 + X^268 + X^266 + X^264 + X^260 + X^252 + X^248 + X^244 + X^242 + X^240 + X^232 + X^230 + X^228 + X^224 + X^220 + X^202 + X^194 + X^192 + X^190 + X^188 + X^184 + X^180 + X^178 + X^176 + X^172 + X^168 + X^158 + X^156 + X^154 + X^152 + X^150 + X^148 + X^146 + X^138 + X^136 + X^134 + X^132 + X^130 + X^128 + X^126 + X^124 + X^116 + X^114 + X^112 + X^110 + X^108 + X^106 + X^104 + X^102 + X^94 + X^92 + X^90 + X^88 + X^84 + X^82 + X^80 + X^76 + X^68 + X^66 + X^56 + X^54 + X^48 + X^46 + X^42 + X^36 + X^32 + X^30 + X^28 + X^26 + X^24 + X^22 + X^16 + X^14 + X^10 + 1 10 14 16 22 Errors: /home/mfd/gomagma: line 2: 7976 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host 3(NXDOMAIN) (194.165.15.3) Time: Thu Jan 22 13:23:16 2004 Input: k := GF(2); C := PrimitivePolynomial(k,9); C; for j in [19..31] do for k in [16..18] do for m in [14..15] do for n in [8..13] do C := ((1 + X^n)^21)*((1 + X^m)^19)*((1 + X^k)^15)*((1 + X^j)^23) + X^1279; if IsPrimitive(C) then C; n; m; k; j; end if; end for; end for; end for; end for; Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Thu Jan 22 2004 13:22:53 on modular [Seed = 1832729039] ------------------------------------- X^9 + X^4 + 1 X^1279 + X^1183 + X^1175 + X^1168 + X^1165 + X^1163 + X^1160 + X^1157 + X^1155 + X^1153 + X^1151 + X^1150 + X^1148 + X^1147 + X^1142 + X^1140 + X^1139 + X^1138 + X^1137 + X^1136 + X^1132 + X^1131 + X^1129 + X^1125 + X^1124 + X^1122 + X^1119 + X^1116 + X^1115 + X^1114 + X^1113 + X^1110 + X^1107 + X^1105 + X^1104 + X^1100 + X^1098 + X^1097 + X^1092 + X^1091 + X^1090 + X^1089 + X^1087 + X^1085 + X^1082 + X^1081 + X^1079 + X^1076 + X^1075 + X^1074 + X^1073 + X^1072 + X^1070 + X^1069 + X^1067 + X^1066 + X^1065 + X^1064 + X^1063 + X^1060 + X^1058 + X^1057 + X^1055 + X^1054 + X^1052 + X^1050 + X^1049 + X^1048 + X^1042 + X^1041 + X^1040 + X^1039 + X^1037 + X^1034 + X^1027 + X^1026 + X^1024 + X^1023 + X^1022 + X^1019 + X^1017 + X^1012 + X^1011 + X^1009 + X^1008 + X^1007 + X^1005 + X^1004 + X^1002 + X^999 + X^997 + X^996 + X^994 + X^993 + X^992 + X^991 + X^990 + X^989 + X^984 + X^983 + X^982 + X^979 + X^978 + X^977 + X^976 + X^975 + X^974 + X^973 + X^971 + X^968 + X^967 + X^965 + X^964 + X^963 + 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X^738 + X^735 + X^734 + X^733 + X^730 + X^729 + X^727 + X^726 + X^725 + X^723 + X^721 + X^720 + X^719 + X^718 + X^715 + X^714 + X^712 + X^710 + X^708 + X^707 + X^706 + X^705 + X^704 + X^700 + X^699 + X^697 + X^695 + X^692 + X^691 + X^690 + X^687 + X^684 + X^683 + X^682 + X^680 + X^677 + X^676 + X^675 + X^672 + X^668 + X^662 + X^661 + X^660 + X^657 + X^655 + X^653 + X^649 + X^646 + X^645 + X^643 + X^642 + X^640 + X^638 + X^637 + X^634 + X^631 + X^630 + X^629 + X^628 + X^627 + X^623 + X^622 + X^616 + X^614 + X^613 + X^612 + X^611 + X^608 + X^607 + X^603 + X^598 + X^596 + X^595 + X^592 + X^591 + X^588 + X^587 + X^585 + X^580 + X^576 + X^575 + X^572 + X^571 + X^570 + X^569 + X^567 + X^561 + X^560 + X^556 + X^555 + X^554 + X^553 + X^552 + X^549 + X^546 + X^545 + X^543 + X^541 + X^540 + X^538 + X^537 + X^534 + X^530 + X^528 + X^526 + X^523 + X^522 + X^521 + X^515 + X^511 + X^508 + X^507 + X^506 + X^503 + X^501 + X^500 + X^499 + X^496 + X^493 + X^492 + X^491 + X^488 + X^486 + X^484 + X^483 + 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X^255 + X^253 + X^252 + X^250 + X^249 + X^248 + X^243 + X^242 + X^240 + X^239 + X^238 + X^237 + X^235 + X^234 + X^233 + X^231 + X^228 + X^227 + X^225 + X^224 + X^223 + X^222 + X^221 + X^220 + X^219 + X^218 + X^216 + X^215 + X^212 + X^210 + X^209 + X^208 + X^207 + X^206 + X^205 + X^204 + X^201 + X^200 + X^199 + X^194 + X^193 + X^192 + X^191 + X^190 + X^189 + X^187 + X^186 + X^184 + X^181 + X^179 + X^178 + X^176 + X^175 + X^174 + X^172 + X^171 + X^166 + X^164 + X^161 + X^160 + X^159 + X^157 + X^156 + X^149 + X^146 + X^144 + X^143 + X^142 + X^141 + X^135 + X^134 + X^133 + X^131 + X^129 + X^128 + X^126 + X^125 + X^123 + X^120 + X^119 + X^118 + X^117 + X^116 + X^114 + X^113 + X^111 + X^110 + X^109 + X^108 + X^107 + X^104 + X^102 + X^101 + X^98 + X^96 + X^94 + X^93 + X^92 + X^91 + X^86 + X^85 + X^83 + X^79 + X^78 + X^76 + X^73 + X^70 + X^69 + X^68 + X^67 + X^64 + X^61 + X^59 + X^58 + X^54 + X^52 + X^51 + X^47 + X^46 + X^45 + X^44 + X^43 + X^41 + X^36 + X^35 + X^33 + X^32 + X^30 + X^28 + X^26 + X^23 + X^20 + X^18 + X^15 + X^8 + 1 8 15 18 20 Errors: /home/mfd/gomagma: line 2: 7986 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host 3(NXDOMAIN) (194.165.15.3) Time: Thu Jan 22 13:24:23 2004 Input: k := GF(2); C := PrimitivePolynomial(k,9); C; for j in [19..31] do for k in [17..18] do for m in [15..16] do for n in [8..13] do C := ((1 + X^n)^21)*((1 + X^m)^15)*((1 + X^k)^19)*((1 + X^j)^23) + X^1279; if IsPrimitive(C) then C; n; m; k; j; end if; end for; end for; end for; end for; Output: Magma V2.10-6 Thu Jan 22 2004 13:24:16 on modular [Seed = 1681142123] ------------------------------------- X^9 + X^4 + 1 Total time: 7.269 seconds, Total memory usage: 2.21MB ************** MAGMA ***************** Host 3(NXDOMAIN) (194.165.15.3) Time: Thu Jan 22 13:25:19 2004 Input: k := GF(2); C := PrimitivePolynomial(k,9); C; for j in [19..31] do for k in [17..18] do for m in [14..16] do for n in [8..13] do C := ((1 + X^n)^23)*((1 + X^m)^15)*((1 + X^k)^19)*((1 + X^j)^21) + X^1279; if IsPrimitive(C) then C; n; m; k; j; end if; end for; end for; end for; end for; Output: Magma V2.10-6 Thu Jan 22 2004 13:25:06 on modular [Seed = 340017609] ------------------------------------- X^9 + X^4 + 1 X^1279 + X^1250 + X^1237 + X^1236 + X^1232 + X^1231 + X^1224 + X^1223 + X^1222 + X^1219 + X^1217 + X^1214 + X^1213 + X^1211 + X^1210 + X^1209 + X^1208 + X^1206 + X^1203 + X^1201 + X^1199 + X^1198 + X^1197 + X^1194 + X^1193 + X^1189 + X^1188 + X^1184 + X^1182 + X^1177 + X^1174 + X^1172 + X^1169 + X^1168 + X^1167 + X^1166 + X^1164 + X^1163 + X^1162 + X^1160 + X^1159 + X^1158 + X^1157 + X^1152 + X^1151 + X^1150 + X^1148 + X^1146 + X^1145 + X^1143 + X^1142 + X^1141 + X^1140 + X^1138 + X^1134 + X^1132 + X^1128 + X^1127 + X^1126 + X^1123 + X^1119 + X^1116 + X^1114 + X^1113 + X^1112 + X^1111 + X^1107 + X^1106 + X^1103 + X^1102 + X^1101 + X^1100 + X^1099 + X^1097 + X^1096 + X^1094 + X^1092 + X^1091 + X^1090 + X^1089 + X^1087 + X^1086 + X^1082 + X^1081 + X^1076 + 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+ X^186 + X^181 + X^180 + X^178 + X^172 + X^171 + X^167 + X^164 + X^163 + X^159 + X^157 + X^154 + X^153 + X^151 + X^150 + X^149 + X^147 + X^146 + X^145 + X^142 + X^140 + X^137 + X^136 + X^135 + X^134 + X^133 + X^132 + X^130 + X^128 + X^127 + X^123 + X^120 + X^118 + X^116 + X^115 + X^110 + X^109 + X^107 + X^106 + X^103 + X^101 + X^98 + X^93 + X^92 + X^91 + X^90 + X^89 + X^86 + X^84 + X^83 + X^79 + X^77 + X^76 + X^74 + X^72 + X^71 + X^69 + X^66 + X^65 + X^62 + X^60 + X^59 + X^57 ** WARNING: Output too long, hence truncated. ************** MAGMA ***************** Host 3(NXDOMAIN) (194.165.15.3) Time: Thu Jan 22 13:26:39 2004 Input: k := GF(2); C := PrimitivePolynomial(k,9); C; for j in [19..31] do for k in [17..18] do for m in [14..16] do for n in [8..13] do C := ((1 + X^n)^23)*((1 + X^m)^15)*((1 + X^k)^19)*((1 + X^j)^21) + X^1279; if IsPrimitive(C) then n; m; k; j; C; end if; end for; end for; end for; end for; Output: Magma V2.10-6 Thu Jan 22 2004 13:26:26 on modular [Seed = 190537350] 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X^687 + X^684 + X^683 + X^681 + X^680 + X^678 + X^675 + X^672 + X^670 + X^669 + X^667 + X^666 + X^665 + X^664 + X^663 + X^661 + X^658 + X^657 + X^653 + X^652 + X^650 + X^648 + X^646 + X^644 + X^640 + X^636 + X^635 + X^631 + X^627 + X^625 + X^623 + X^621 + X^619 + X^618 + X^614 + X^613 + X^610 + X^608 + X^607 + X^606 + X^605 + X^604 + X^602 + X^601 + X^599 + X^596 + X^593 + X^591 + X^590 + X^588 + X^587 + X^584 + X^582 + X^579 + X^576 + X^575 + X^574 + X^573 + X^570 + X^569 + X^567 + X^565 + X^563 + X^562 + X^558 + X^556 + X^553 + X^552 + X^550 + X^549 + X^548 + X^547 + X^546 + X^543 + X^537 + X^536 + X^535 + X^533 + X^532 + X^531 + X^530 + X^526 + X^523 + X^520 + X^518 + X^517 + X^516 + X^514 + X^511 + X^509 + X^507 + X^506 + X^503 + X^500 + X^499 + X^497 + X^494 + X^493 + X^492 + X^490 + X^487 + X^486 + X^485 + X^482 + X^481 + X^480 + X^479 + X^476 + X^475 + X^470 + X^468 + X^467 + X^464 + X^462 + X^461 + X^459 + X^458 + X^453 + X^450 + X^447 + X^445 + X^444 + X^442 + X^441 + X^436 + X^430 + X^428 + X^424 + X^423 + X^419 + X^411 + X^409 + X^407 + X^406 + X^405 + X^402 + X^401 + X^399 + X^397 + X^394 + X^392 + X^391 + X^390 + X^388 + X^384 + X^382 + X^380 + X^375 + X^374 + X^371 + X^363 + X^361 + X^359 + X^358 + X^357 + X^354 + X^349 + X^346 + X^344 + X^342 + X^340 + X^337 + X^335 + X^332 + X^331 + X^327 + X^323 + X^321 + X^320 + X^318 + X^317 + X^315 + X^314 + X^311 + X^310 + X^309 + X^307 + X^306 + X^305 + X^304 + X^303 + X^301 + X^300 + X^299 + X^298 + X^295 + X^294 + X^293 + X^292 + X^291 + X^290 + X^289 + X^288 + X^286 + X^285 + X^284 + X^282 + X^281 + X^278 + X^277 + X^276 + X^274 + X^272 + X^271 + X^268 + X^264 + X^263 + X^260 + X^257 + X^255 + X^254 + X^246 + X^241 + X^240 + X^239 + X^238 + X^225 + X^224 + X^222 + X^217 + X^211 + X^209 + X^208 + X^203 + X^200 + X^197 + X^195 + X^194 + X^192 + X^189 + X^186 + X^181 + X^180 + X^178 + X^172 + X^171 + X^167 + X^164 + X^163 + X^159 + X^157 + X^154 + X^153 + X^151 + X^150 + X^149 + X^147 + X^146 + X^145 + X^142 + X^140 + X^137 + X^136 + X^135 + X^134 + X^133 + X^132 + X^130 + X^128 + X^127 + X^123 + X^120 + X^118 + X^116 + X^115 + X^110 + X^109 + X^107 + X^106 + X^103 + X^101 + X^98 + X^93 + X^92 + X^91 + X^90 + X^89 + X^86 + X^84 + X^83 + X^79 + X^77 + X^76 + X^74 + X^72 + X^71 + X^69 + X^66 + X^65 + X^62 + X^60 + ** WARNING: Output too long, hence truncated. ************** MAGMA ***************** Host 3(NXDOMAIN) (194.165.15.3) Time: Thu Jan 22 13:28:46 2004 Input: k := GF(2); C := PrimitivePolynomial(k,9); C; C := ((1 + X^12)^23)*((1 + X^14)^15)*((1 + X^17)^19)*((1 + X^22)^21) + X^1279; if IsPrimitive(C) then C; end if; Output: Magma V2.10-6 Thu Jan 22 2004 13:28:42 on modular [Seed = 22107908] ------------------------------------- X^9 + X^4 + 1 X^1279 + X^1271 + X^1259 + X^1257 + X^1254 + X^1249 + X^1247 + X^1245 + X^1243 + X^1242 + X^1240 + X^1233 + X^1232 + X^1231 + X^1230 + X^1229 + X^1228 + X^1226 + X^1223 + X^1219 + X^1217 + X^1216 + X^1214 + X^1212 + X^1211 + X^1209 + X^1206 + X^1205 + X^1202 + X^1200 + X^1199 + X^1197 + X^1195 + X^1194 + X^1192 + X^1188 + X^1187 + X^1185 + X^1182 + X^1181 + X^1180 + X^1179 + X^1178 + X^1173 + X^1170 + X^1168 + X^1165 + X^1164 + X^1162 + X^1161 + X^1156 + X^1155 + X^1153 + X^1151 + X^1148 + X^1144 + X^1143 + X^1141 + X^1139 + X^1138 + X^1137 + X^1136 + X^1135 + X^1134 + X^1131 + X^1129 + X^1126 + X^1125 + X^1124 + X^1122 + X^1121 + X^1120 + X^1118 + X^1117 + X^1114 + X^1112 + X^1108 + X^1107 + X^1104 + X^1100 + X^1099 + X^1093 + X^1091 + X^1090 + X^1085 + X^1082 + X^1079 + X^1077 + X^1076 + X^1074 + X^1071 + X^1068 + X^1063 + X^1062 + X^1060 + X^1054 + X^1049 + X^1047 + X^1046 + X^1033 + X^1032 + X^1031 + X^1030 + X^1025 + X^1017 + X^1016 + X^1014 + X^1011 + X^1008 + X^1007 + X^1003 + X^1000 + X^999 + X^997 + X^995 + X^994 + X^993 + X^990 + X^989 + X^987 + X^986 + X^985 + X^983 + X^982 + X^981 + X^980 + X^979 + X^978 + X^977 + X^976 + X^973 + X^972 + X^971 + X^970 + X^968 + X^967 + X^966 + X^965 + X^964 + X^962 + X^961 + X^960 + X^957 + X^956 + X^954 + X^953 + X^951 + X^950 + X^948 + X^944 + X^940 + X^939 + X^936 + X^934 + X^931 + X^929 + X^927 + X^925 + X^922 + X^917 + X^914 + X^913 + X^912 + X^910 + X^908 + X^900 + X^897 + X^896 + X^891 + X^889 + X^887 + X^883 + X^881 + X^880 + X^879 + X^877 + X^874 + X^872 + X^870 + X^869 + X^866 + X^865 + X^864 + X^862 + X^860 + X^852 + X^848 + X^847 + X^843 + X^841 + X^835 + X^830 + X^829 + X^827 + X^826 + X^824 + X^821 + X^818 + X^813 + X^812 + X^810 + X^809 + X^807 + X^804 + X^803 + X^801 + X^796 + X^795 + X^792 + X^791 + X^790 + X^789 + X^786 + X^785 + X^784 + X^781 + X^779 + X^778 + X^777 + X^774 + X^772 + X^771 + X^768 + X^765 + X^764 + X^762 + X^760 + X^757 + X^755 + X^754 + X^753 + X^751 + X^748 + X^745 + X^741 + X^740 + X^739 + X^738 + X^736 + X^735 + X^734 + X^728 + X^725 + X^724 + X^723 + X^722 + X^721 + X^719 + X^718 + X^715 + X^713 + X^709 + X^708 + X^706 + X^704 + X^702 + X^701 + X^698 + X^697 + X^696 + X^695 + X^692 + X^689 + X^687 + X^684 + X^683 + X^681 + X^680 + X^678 + X^675 + X^672 + X^670 + X^669 + X^667 + X^666 + X^665 + X^664 + X^663 + X^661 + X^658 + X^657 + X^653 + X^652 + X^650 + X^648 + X^646 + X^644 + X^640 + X^636 + X^635 + X^631 + X^627 + X^625 + X^623 + X^621 + X^619 + X^618 + X^614 + X^613 + X^610 + X^608 + X^607 + X^606 + X^605 + X^604 + X^602 + X^601 + X^599 + X^596 + X^593 + X^591 + X^590 + X^588 + X^587 + X^584 + X^582 + X^579 + X^576 + X^575 + X^574 + X^573 + X^570 + X^569 + X^567 + X^565 + X^563 + X^562 + X^558 + X^556 + X^553 + X^552 + X^550 + X^549 + X^548 + X^547 + X^546 + X^543 + X^537 + X^536 + X^535 + X^533 + X^532 + X^531 + X^530 + X^526 + X^523 + X^520 + X^518 + X^517 + X^516 + X^514 + X^511 + X^509 + X^507 + X^506 + X^503 + X^500 + X^499 + X^497 + X^494 + X^493 + X^492 + X^490 + X^487 + X^486 + X^485 + X^482 + X^481 + X^480 + X^479 + X^476 + X^475 + X^470 + X^468 + X^467 + X^464 + X^462 + X^461 + X^459 + X^458 + X^453 + X^450 + X^447 + X^445 + X^444 + X^442 + X^441 + X^436 + X^430 + X^428 + X^424 + X^423 + X^419 + X^411 + X^409 + X^407 + X^406 + X^405 + X^402 + X^401 + X^399 + X^397 + X^394 + X^392 + X^391 + X^390 + X^388 + X^384 + X^382 + X^380 + X^375 + X^374 + X^371 + X^363 + X^361 + X^359 + X^358 + X^357 + X^354 + X^349 + X^346 + X^344 + X^342 + X^340 + X^337 + X^335 + X^332 + X^331 + X^327 + X^323 + X^321 + X^320 + X^318 + X^317 + X^315 + X^314 + X^311 + X^310 + X^309 + X^307 + X^306 + X^305 + X^304 + X^303 + X^301 + X^300 + X^299 + X^298 + X^295 + X^294 + X^293 + X^292 + X^291 + X^290 + X^289 + X^288 + X^286 + X^285 + X^284 + X^282 + X^281 + X^278 + X^277 + X^276 + X^274 + X^272 + X^271 + X^268 + X^264 + X^263 + X^260 + X^257 + X^255 + X^254 + X^246 + X^241 + X^240 + X^239 + X^238 + X^225 + X^224 + X^222 + X^217 + X^211 + X^209 + X^208 + X^203 + X^200 + X^197 + X^195 + X^194 + X^192 + X^189 + X^186 + X^181 + X^180 + X^178 + X^172 + X^171 + X^167 + X^164 + X^163 + X^159 + X^157 + X^154 + X^153 + X^151 + X^150 + X^149 + X^147 + X^146 + X^145 + X^142 + X^140 + X^137 + X^136 + X^135 + X^134 + X^133 + X^132 + X^130 + X^128 + X^127 + X^123 + X^120 + X^118 + X^116 + X^115 + X^110 + X^109 + X^107 + X^106 + X^103 + X^101 + X^98 + X^93 + X^92 + X^91 + X^90 + X^89 + X^86 + X^84 + X^83 + X^79 + X^77 + X^76 + X^74 + X^72 + X^71 + X^69 + X^66 + X^65 + X^62 + X^60 + X^59 + X^57 + X^55 + X^54 + X^52 + X^48 + X^45 + X^43 + X^42 + X^41 + X^40 + X^39 + X^38 + X^31 + X^29 + X^28 + X^26 + X^24 + X^22 + X^17 + X^14 + X^12 + 1 Total time: 4.099 seconds, Total memory usage: 2.14MB ************** MAGMA ***************** Host customer-148-223-46-1.uninet.net.mx. (148.223.46.1) Time: Thu Jan 22 15:42:44 2004 Input: dx/dy Output: Magma V2.10-6 Thu Jan 22 2004 15:42:41 on modular [Seed = 3203320607] ------------------------------------- >> dx/dy; ^ User error: Identifier 'dx' has not been declared or assigned Total time: 2.929 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host carroll.math.ubc.ca. (142.103.161.252) Time: Thu Jan 22 16:30:22 2004 Input: F:=GF(5); E:=EllipticCurve([0,1]); AbelianGroup(E); Output: Magma V2.10-6 Thu Jan 22 2004 16:30:19 on modular [Seed = 1310609094] ------------------------------------- Abelian Group isomorphic to Z/6 Defined on 1 generator Relations: 6*$.1 = 0 Total time: 2.929 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host carroll.math.ubc.ca. (142.103.161.252) Time: Thu Jan 22 16:30:39 2004 Input: F:=GF(5); E:=EllipticCurve([0,2]); AbelianGroup(E); Output: Magma V2.10-6 Thu Jan 22 2004 16:30:36 on modular [Seed = 1426413002] ------------------------------------- Abelian Group isomorphic to Z Defined on 1 generator (free) Total time: 3.109 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host carroll.math.ubc.ca. (142.103.161.252) Time: Thu Jan 22 16:32:26 2004 Input: F:=GF(5); E:=EllipticCurve([0,2]); AbelianGroup(E); E:=ChangeRing(E, F); AbelianGroup(E); Output: Magma V2.10-6 Thu Jan 22 2004 16:32:23 on modular [Seed = 729492015] ------------------------------------- Abelian Group isomorphic to Z Defined on 1 generator (free) Abelian Group isomorphic to Z/6 Defined on 1 generator Relations: 6*$.1 = 0 Total time: 3.179 seconds, Total memory usage: 1.99MB ************** MAGMA ***************** Host carroll.math.ubc.ca. (142.103.161.252) Time: Thu Jan 22 16:32:45 2004 Input: F:=GF(17); E:=EllipticCurve([0,2]); AbelianGroup(E); E:=ChangeRing(E, F); AbelianGroup(E); Output: Magma V2.10-6 Thu Jan 22 2004 16:32:42 on modular [Seed = 845296427] ------------------------------------- Abelian Group isomorphic to Z Defined on 1 generator (free) Abelian Group isomorphic to Z/18 Defined on 1 generator Relations: 18*$.1 = 0 Total time: 3.249 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host carroll.math.ubc.ca. (142.103.161.252) Time: Thu Jan 22 16:33:00 2004 Input: F:=GF(17); E:=EllipticCurve([0,1]); AbelianGroup(E); E:=ChangeRing(E, F); AbelianGroup(E); Output: Magma V2.10-6 Thu Jan 22 2004 16:32:57 on modular [Seed = 946354642] ------------------------------------- Abelian Group isomorphic to Z/6 Defined on 1 generator Relations: 6*$.1 = 0 Abelian Group isomorphic to Z/18 Defined on 1 generator Relations: 18*$.1 = 0 Total time: 2.979 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host carroll.math.ubc.ca. (142.103.161.252) Time: Thu Jan 22 16:34:29 2004 Input: F:=GF(17); E:=EllipticCurve([0,1]); AbelianGroup(E); E:=ChangeRing(E, F); AbelianGroup(E); Generators(E); Output: Magma V2.10-6 Thu Jan 22 2004 16:34:26 on modular [Seed = 156829832] ------------------------------------- Abelian Group isomorphic to Z/6 Defined on 1 generator Relations: 6*$.1 = 0 Abelian Group isomorphic to Z/18 Defined on 1 generator Relations: 18*$.1 = 0 [ (9 : 4 : 1) ] Total time: 2.919 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host carroll.math.ubc.ca. (142.103.161.252) Time: Thu Jan 22 16:34:57 2004 Input: F:=GF(5); E:=EllipticCurve([0,1]); AbelianGroup(E); E:=ChangeRing(E, F); AbelianGroup(E); Generators(E); Output: Magma V2.10-6 Thu Jan 22 2004 16:34:54 on modular [Seed = 272634253] ------------------------------------- Abelian Group isomorphic to Z/6 Defined on 1 generator Relations: 6*$.1 = 0 Abelian Group isomorphic to Z/6 Defined on 1 generator Relations: 6*$.1 = 0 [ (2 : 2 : 1) ] Total time: 2.989 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host carroll.math.ubc.ca. (142.103.161.252) Time: Thu Jan 22 16:35:28 2004 Input: F:=GF(5); E:=EllipticCurve([1,0]); AbelianGroup(E); E:=ChangeRing(E, F); AbelianGroup(E); Generators(E); Output: Magma V2.10-6 Thu Jan 22 2004 16:35:25 on modular [Seed = 3820216733] ------------------------------------- Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Abelian Group isomorphic to Z/2 + Z/2 Defined on 2 generators Relations: 2*$.1 = 0 2*$.2 = 0 [ (3 : 0 : 1), (2 : 0 : 1) ] Total time: 2.979 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host carroll.math.ubc.ca. (142.103.161.252) Time: Thu Jan 22 16:36:37 2004 Input: F:=GF(5); E:=EllipticCurve([2,0]); AbelianGroup(E); E:=ChangeRing(E, F); AbelianGroup(E); Generators(E); Output: Magma V2.10-6 Thu Jan 22 2004 16:36:33 on modular [Seed = 4037079793] ------------------------------------- Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 [ (0 : 0 : 1) ] Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host carroll.math.ubc.ca. (142.103.161.252) Time: Thu Jan 22 16:37:32 2004 Input: F:=GF(17); E:=EllipticCurve([1,0]); AbelianGroup(E); E:=ChangeRing(E, F); AbelianGroup(E); Generators(E); Output: Magma V2.10-6 Thu Jan 22 2004 16:37:29 on modular [Seed = 4272880644] ------------------------------------- Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Abelian Group isomorphic to Z/4 + Z/4 Defined on 2 generators Relations: 4*$.1 = 0 4*$.2 = 0 [ (3 : 9 : 1), (1 : 6 : 1) ] Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host carroll.math.ubc.ca. (142.103.161.252) Time: Thu Jan 22 16:38:22 2004 Input: F:=GF(101); E:=EllipticCurve([0,1]); AbelianGroup(E); E:=ChangeRing(E, F); AbelianGroup(E); Generators(E); Output: Magma V2.10-6 Thu Jan 22 2004 16:38:17 on modular [Seed = 3399141472] ------------------------------------- Abelian Group isomorphic to Z/6 Defined on 1 generator Relations: 6*$.1 = 0 Abelian Group isomorphic to Z/102 Defined on 1 generator Relations: 102*$.1 = 0 [ (59 : 42 : 1) ] Total time: 2.989 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host carroll.math.ubc.ca. (142.103.161.252) Time: Thu Jan 22 16:38:35 2004 Input: F:=GF(101); E:=EllipticCurve([1,1]); AbelianGroup(E); E:=ChangeRing(E, F); AbelianGroup(E); Generators(E); Output: Magma V2.10-6 Thu Jan 22 2004 16:38:32 on modular [Seed = 3514946410] ------------------------------------- Abelian Group isomorphic to Z Defined on 1 generator (free) Abelian Group isomorphic to Z/105 Defined on 1 generator Relations: 105*$.1 = 0 [ (36 : 58 : 1) ] Total time: 3.159 seconds, Total memory usage: 2.09MB ************** MAGMA ***************** Host carroll.math.ubc.ca. (142.103.161.252) Time: Thu Jan 22 16:39:50 2004 Input: F:=GF(19); E:=EllipticCurve([+1,-2]); AbelianGroup(E); E:=ChangeRing(E, F); AbelianGroup(E); Generators(E); Output: Magma V2.10-6 Thu Jan 22 2004 16:39:47 on modular [Seed = 3733904798] ------------------------------------- Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Abelian Group isomorphic to Z/28 Defined on 1 generator Relations: 28*$.1 = 0 [ (15 : 14 : 1) ] Total time: 3.029 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host carroll.math.ubc.ca. (142.103.161.252) Time: Thu Jan 22 16:40:23 2004 Input: F:=GF(5); E:=EllipticCurve([+1,-2]); AbelianGroup(E); E:=ChangeRing(E, F); AbelianGroup(E); Generators(E); Output: Magma V2.10-6 Thu Jan 22 2004 16:40:20 on modular [Seed = 2935926153] ------------------------------------- Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Abelian Group isomorphic to Z/4 Defined on 1 generator Relations: 4*$.1 = 0 [ (4 : 4 : 1) ] Total time: 2.889 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host carroll.math.ubc.ca. (142.103.161.252) Time: Thu Jan 22 16:41:41 2004 Input: F:=GF(5); E:=EllipticCurve([0, 1,0, -2, 0]); AbelianGroup(E); E:=ChangeRing(E, F); AbelianGroup(E); Generators(E); Output: Magma V2.10-6 Thu Jan 22 2004 16:41:38 on modular [Seed = 3051730500] ------------------------------------- Abelian Group isomorphic to Z/2 + Z/2 Defined on 2 generators Relations: 2*$.1 = 0 2*$.2 = 0 Abelian Group isomorphic to Z/2 + Z/2 Defined on 2 generators Relations: 2*$.1 = 0 2*$.2 = 0 [ (0 : 0 : 1), (1 : 0 : 1) ] Total time: 2.979 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host carroll.math.ubc.ca. (142.103.161.252) Time: Thu Jan 22 16:41:53 2004 Input: F:=GF(7); E:=EllipticCurve([0, 1,0, -2, 0]); AbelianGroup(E); E:=ChangeRing(E, F); AbelianGroup(E); Generators(E); Output: Magma V2.10-6 Thu Jan 22 2004 16:41:50 on modular [Seed = 3169632065] ------------------------------------- Abelian Group isomorphic to Z/2 + Z/2 Defined on 2 generators Relations: 2*$.1 = 0 2*$.2 = 0 Abelian Group isomorphic to Z/2 + Z/6 Defined on 2 generators Relations: 2*$.1 = 0 6*$.2 = 0 [ (5 : 0 : 1), (4 : 3 : 1) ] Total time: 2.939 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host carroll.math.ubc.ca. (142.103.161.252) Time: Thu Jan 22 16:42:09 2004 Input: F:=GF(13); E:=EllipticCurve([0, 1,0, -2, 0]); AbelianGroup(E); E:=ChangeRing(E, F); AbelianGroup(E); Generators(E); Output: Magma V2.10-6 Thu Jan 22 2004 16:42:06 on modular [Seed = 2329577799] ------------------------------------- Abelian Group isomorphic to Z/2 + Z/2 Defined on 2 generators Relations: 2*$.1 = 0 2*$.2 = 0 Abelian Group isomorphic to Z/2 + Z/8 Defined on 2 generators Relations: 2*$.1 = 0 8*$.2 = 0 [ (11 : 0 : 1), (7 : 1 : 1) ] Total time: 2.969 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host carroll.math.ubc.ca. (142.103.161.252) Time: Thu Jan 22 16:42:21 2004 Input: F:=GF(17); E:=EllipticCurve([0, 1,0, -2, 0]); AbelianGroup(E); E:=ChangeRing(E, F); AbelianGroup(E); Generators(E); Output: Magma V2.10-6 Thu Jan 22 2004 16:42:18 on modular [Seed = 2428539721] ------------------------------------- Abelian Group isomorphic to Z/2 + Z/2 Defined on 2 generators Relations: 2*$.1 = 0 2*$.2 = 0 Abelian Group isomorphic to Z/2 + Z/12 Defined on 2 generators Relations: 2*$.1 = 0 12*$.2 = 0 [ (15 : 0 : 1), (6 : 6 : 1) ] Total time: 3.009 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host carroll.math.ubc.ca. (142.103.161.252) Time: Thu Jan 22 16:42:34 2004 Input: F:=GF(5); E:=EllipticCurve([0, 1,0, -2, 0]); AbelianGroup(E); E:=ChangeRing(E, F); AbelianGroup(E); Generators(E); Output: Magma V2.10-6 Thu Jan 22 2004 16:42:31 on modular [Seed = 2681183291] ------------------------------------- Abelian Group isomorphic to Z/2 + Z/2 Defined on 2 generators Relations: 2*$.1 = 0 2*$.2 = 0 Abelian Group isomorphic to Z/2 + Z/2 Defined on 2 generators Relations: 2*$.1 = 0 2*$.2 = 0 [ (1 : 0 : 1), (3 : 0 : 1) ] Total time: 2.989 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host carroll.math.ubc.ca. (142.103.161.252) Time: Thu Jan 22 16:43:33 2004 Input: F:=GF(5); E:=EllipticCurve([0, 1,0, -2, 0]); Discriminant(E); AbelianGroup(E); E:=ChangeRing(E, F); AbelianGroup(E); Generators(E); Output: Magma V2.10-6 Thu Jan 22 2004 16:43:30 on modular [Seed = 1630627079] ------------------------------------- 576 Abelian Group isomorphic to Z/2 + Z/2 Defined on 2 generators Relations: 2*$.1 = 0 2*$.2 = 0 Abelian Group isomorphic to Z/2 + Z/2 Defined on 2 generators Relations: 2*$.1 = 0 2*$.2 = 0 [ (0 : 0 : 1), (3 : 0 : 1) ] Total time: 2.989 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host carroll.math.ubc.ca. (142.103.161.252) Time: Thu Jan 22 16:44:03 2004 Input: F:=GF(5); E:=EllipticCurve([0, 5,0, 4, 0]); Discriminant(E); AbelianGroup(E); E:=ChangeRing(E, F); AbelianGroup(E); Generators(E); Output: Magma V2.10-6 Thu Jan 22 2004 16:44:00 on modular [Seed = 1782214190] ------------------------------------- 2304 Abelian Group isomorphic to Z/2 + Z/4 Defined on 2 generators Relations: 2*$.1 = 0 4*$.2 = 0 Abelian Group isomorphic to Z/2 + Z/4 Defined on 2 generators Relations: 2*$.1 = 0 4*$.2 = 0 [ (4 : 0 : 1), (3 : 3 : 1) ] Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host carroll.math.ubc.ca. (142.103.161.252) Time: Thu Jan 22 16:45:08 2004 Input: F:=GF(5); E:=EllipticCurve([0, 337,0, 20736, 0]); Discriminant(E); AbelianGroup(E); E:=ChangeRing(E, F); AbelianGroup(E); Generators(E); Output: Magma V2.10-6 Thu Jan 22 2004 16:45:04 on modular [Seed = 2015919228] ------------------------------------- 210691031040000 Abelian Group isomorphic to Z/2 + Z/8 Defined on 2 generators Relations: 2*$.1 = 0 8*$.2 = 0 >> AbelianGroup(E); ^ Runtime error in 'AbelianGroup': Bad argument types Argument types given: Crv >> Generators(E);; ^ Runtime error in 'Generators': Bad argument types Argument types given: Crv Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host carroll.math.ubc.ca. (142.103.161.252) Time: Thu Jan 22 16:46:44 2004 Input: F:=GF(5); E:=EllipticCurve([0, 337,0, 20736, 0]); Discriminant(E) mod 5; AbelianGroup(E); E:=ChangeRing(E, F); AbelianGroup(E); Generators(E); Output: Magma V2.10-6 Thu Jan 22 2004 16:46:41 on modular [Seed = 1091651044] ------------------------------------- >> Discriminant(E) mod 5; ^ Runtime error in 'mod': Bad argument types Argument types given: FldRatElt, FldRatElt Abelian Group isomorphic to Z/2 + Z/8 Defined on 2 generators Relations: 2*$.1 = 0 8*$.2 = 0 >> AbelianGroup(E); ^ Runtime error in 'AbelianGroup': Bad argument types Argument types given: Crv >> Generators(E);; ^ Runtime error in 'Generators': Bad argument types Argument types given: Crv Total time: 2.929 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host carroll.math.ubc.ca. (142.103.161.252) Time: Thu Jan 22 16:47:10 2004 Input: F:=GF(5); E:=EllipticCurve([0, 337,0, 20736, 0]); Discriminant(E) / 5; AbelianGroup(E); E:=ChangeRing(E, F); AbelianGroup(E); Generators(E); Output: Magma V2.10-6 Thu Jan 22 2004 16:47:07 on modular [Seed = 1243238133] ------------------------------------- 42138206208000 Abelian Group isomorphic to Z/2 + Z/8 Defined on 2 generators Relations: 2*$.1 = 0 8*$.2 = 0 >> AbelianGroup(E); ^ Runtime error in 'AbelianGroup': Bad argument types Argument types given: Crv >> Generators(E);; ^ Runtime error in 'Generators': Bad argument types Argument types given: Crv Total time: 2.999 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host carroll.math.ubc.ca. (142.103.161.252) Time: Thu Jan 22 16:47:23 2004 Input: F:=GF(17); E:=EllipticCurve([0, 337,0, 20736, 0]); Discriminant(E) / 17; AbelianGroup(E); E:=ChangeRing(E, F); AbelianGroup(E); Generators(E); Output: Magma V2.10-6 Thu Jan 22 2004 16:47:20 on modular [Seed = 1544313040] ------------------------------------- 210691031040000/17 Abelian Group isomorphic to Z/2 + Z/8 Defined on 2 generators Relations: 2*$.1 = 0 8*$.2 = 0 Abelian Group isomorphic to Z/2 + Z/8 Defined on 2 generators Relations: 2*$.1 = 0 8*$.2 = 0 [ (16 : 0 : 1), (5 : 8 : 1) ] Total time: 3.009 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host carroll.math.ubc.ca. (142.103.161.252) Time: Thu Jan 22 16:47:35 2004 Input: F:=GF(7); E:=EllipticCurve([0, 337,0, 20736, 0]); Discriminant(E) / 7; AbelianGroup(E); E:=ChangeRing(E, F); AbelianGroup(E); Generators(E); Output: Magma V2.10-6 Thu Jan 22 2004 16:47:32 on modular [Seed = 628433333] ------------------------------------- 30098718720000 Abelian Group isomorphic to Z/2 + Z/8 Defined on 2 generators Relations: 2*$.1 = 0 8*$.2 = 0 >> AbelianGroup(E); ^ Runtime error in 'AbelianGroup': Bad argument types Argument types given: Crv >> Generators(E);; ^ Runtime error in 'Generators': Bad argument types Argument types given: Crv Total time: 2.939 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host carroll.math.ubc.ca. (142.103.161.252) Time: Thu Jan 22 16:47:47 2004 Input: F:=GF(11); E:=EllipticCurve([0, 337,0, 20736, 0]); Discriminant(E) / 11; AbelianGroup(E); E:=ChangeRing(E, F); AbelianGroup(E); Generators(E); Output: Magma V2.10-6 Thu Jan 22 2004 16:47:44 on modular [Seed = 780020554] ------------------------------------- 210691031040000/11 Abelian Group isomorphic to Z/2 + Z/8 Defined on 2 generators Relations: 2*$.1 = 0 8*$.2 = 0 Abelian Group isomorphic to Z/2 + Z/8 Defined on 2 generators Relations: 2*$.1 = 0 8*$.2 = 0 [ (8 : 0 : 1), (2 : 7 : 1) ] Total time: 3.059 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host carroll.math.ubc.ca. (142.103.161.252) Time: Thu Jan 22 16:49:21 2004 Input: F:=GF(11); E:=EllipticCurve([0, 0,0, (-27*5^4-216*5), (-432=1080*5^3+54*5^6)]); Discriminant(E) / 11; AbelianGroup(E); E:=ChangeRing(E, F); AbelianGroup(E); Generators(E); Output: Magma V2.10-6 Thu Jan 22 2004 16:49:18 on modular [Seed = 811611402] ------------------------------------- >> E:=EllipticCurve([0, 0,0, (-27*5^4-216*5), (-432=1080*5^3+54*5^6)]); ^ Runtime error in [ ... ]: Could not find a valid universe >> Discriminant(E) / 11; ^ User error: Identifier 'E' has not been declared or assigned >> AbelianGroup(E); ^ User error: Identifier 'E' has not been declared or assigned >> E:=ChangeRing(E, F); ^ User error: Identifier 'E' has not been declared or assigned >> AbelianGroup(E); ^ User error: Identifier 'E' has not been declared or assigned >> Generators(E);; ^ User error: Identifier 'E' has not been declared or assigned Total time: 3.059 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host carroll.math.ubc.ca. (142.103.161.252) Time: Thu Jan 22 16:49:46 2004 Input: F:=GF(11); E:=EllipticCurve([(-27*5^4-216*5), (-432-1080*5^3+54*5^6)]); Discriminant(E) / 11; AbelianGroup(E); E:=ChangeRing(E, F); AbelianGroup(E); Generators(E); Output: Magma V2.10-6 Thu Jan 22 2004 16:49:43 on modular [Seed = 963197994] ------------------------------------- 153715016466432/11 Abelian Group isomorphic to Z/3 + Z Defined on 2 generators Relations: 3*$.1 = 0 Abelian Group isomorphic to Z/9 Defined on 1 generator Relations: 9*$.1 = 0 [ (9 : 2 : 1) ] Total time: 3.519 seconds, Total memory usage: 2.09MB ************** MAGMA ***************** Host carroll.math.ubc.ca. (142.103.161.252) Time: Thu Jan 22 16:50:01 2004 Input: F:=GF(5); E:=EllipticCurve([(-27*5^4-216*5), (-432-1080*5^3+54*5^6)]); Discriminant(E) / 11; AbelianGroup(E); E:=ChangeRing(E, F); AbelianGroup(E); Generators(E); Output: Magma V2.10-6 Thu Jan 22 2004 16:49:57 on modular [Seed = 38930403] ------------------------------------- 153715016466432/11 Abelian Group isomorphic to Z/3 + Z Defined on 2 generators Relations: 3*$.1 = 0 Abelian Group isomorphic to Z/6 Defined on 1 generator Relations: 6*$.1 = 0 [ (1 : 2 : 1) ] Total time: 3.459 seconds, Total memory usage: 2.09MB ************** MAGMA ***************** Host carroll.math.ubc.ca. (142.103.161.252) Time: Thu Jan 22 16:50:41 2004 Input: F:=GF(7); E:=EllipticCurve([(-27*5^4-216*5), (-432-1080*5^3+54*5^6)]); Discriminant(E) / 7; AbelianGroup(E); E:=ChangeRing(E, F); AbelianGroup(E); Generators(E); Output: Magma V2.10-6 Thu Jan 22 2004 16:50:38 on modular [Seed = 306321368] ------------------------------------- 153715016466432/7 Abelian Group isomorphic to Z/3 + Z Defined on 2 generators Relations: 3*$.1 = 0 Abelian Group isomorphic to Z/3 + Z/3 Defined on 2 generators Relations: 3*$.1 = 0 3*$.2 = 0 [ (0 : 4 : 1), (5 : 6 : 1) ] Total time: 3.449 seconds, Total memory usage: 1.99MB ************** MAGMA ***************** Host 219-89-142-151.jetstart.xtra.co.nz. (219.89.142.151) Time: Thu Jan 22 21:52:04 2004 Input: y := NormEquation(1, 1000); Output: Magma V2.10-6 Thu Jan 22 2004 21:52:00 on modular [Seed = 257934136] ------------------------------------- Total time: 3.019 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 219-89-142-151.jetstart.xtra.co.nz. (219.89.142.151) Time: Thu Jan 22 21:52:27 2004 Input: NormEquation(1, 1000) Output: Magma V2.10-6 Thu Jan 22 2004 21:52:24 on modular [Seed = 356899098] ------------------------------------- true 26 18 Total time: 2.889 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 219-89-142-151.jetstart.xtra.co.nz. (219.89.142.151) Time: Thu Jan 22 21:53:18 2004 Input: NormEquation(2, 1000) Output: Magma V2.10-6 Thu Jan 22 2004 21:53:15 on modular [Seed = 457955303] ------------------------------------- false Total time: 3.049 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 219-89-142-151.jetstart.xtra.co.nz. (219.89.142.151) Time: Thu Jan 22 21:53:35 2004 Input: NormEquation(-1, 1000) Output: Magma V2.10-6 Thu Jan 22 2004 21:53:32 on modular [Seed = 3803328041] ------------------------------------- >> NormEquation(-1, 1000); ^ Runtime error in 'NormEquation': Argument 1 must be positive and argument 2 non-negative Total time: 3.039 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host h24-81-108-53.vc.shawcable.net. (24.81.108.53) Time: Fri Jan 23 03:14:36 2004 Input: F:=GF(17); E:=EllipticCurve([1,0]); TorsionSubgroup(E); Output: Magma V2.10-6 Fri Jan 23 2004 03:14:33 on modular [Seed = 980069816] ------------------------------------- Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Total time: 2.889 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host h24-81-108-53.vc.shawcable.net. (24.81.108.53) Time: Fri Jan 23 03:14:45 2004 Input: F:=GF(17); E:=EllipticCurve([2,0]); TorsionSubgroup(E); Output: Magma V2.10-6 Fri Jan 23 2004 03:14:42 on modular [Seed = 828483240] ------------------------------------- Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Total time: 2.909 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host h24-81-108-53.vc.shawcable.net. (24.81.108.53) Time: Fri Jan 23 03:16:03 2004 Input: F:=GF(17); E:=EllipticCurve([2,0]); E:=ChangeRing(E, F); AbelianGroup(E); Output: Magma V2.10-6 Fri Jan 23 2004 03:16:00 on modular [Seed = 224236838] ------------------------------------- Abelian Group isomorphic to Z/2 + Z/10 Defined on 2 generators Relations: 2*$.1 = 0 10*$.2 = 0 Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host h24-81-108-53.vc.shawcable.net. (24.81.108.53) Time: Fri Jan 23 03:19:53 2004 Input: F:=GF(17); E:=EllipticCurve([-219,1654]); Discriminant(E); AbelianGroup(E); Output: Magma V2.10-6 Fri Jan 23 2004 03:19:48 on modular [Seed = 457933396] ------------------------------------- -509607936 Abelian Group isomorphic to Z/9 Defined on 1 generator Relations: 9*$.1 = 0 Total time: 2.979 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host h24-81-108-53.vc.shawcable.net. (24.81.108.53) Time: Fri Jan 23 03:21:24 2004 Input: F:=GF(5); E:=EllipticCurve([-219,1654]); Discriminant(E); E:=ChangeRing(F); AbelianGroup(E); Output: Magma V2.10-6 Fri Jan 23 2004 03:21:21 on modular [Seed = 340037118] ------------------------------------- -509607936 >> E:=ChangeRing(F); ^ Runtime error in 'ChangeRing': Bad argument types Argument types given: FldFin Abelian Group isomorphic to Z/9 Defined on 1 generator Relations: 9*$.1 = 0 Total time: 2.949 seconds, Total memory usage: 1.99MB ************** MAGMA ***************** Host h24-81-108-53.vc.shawcable.net. (24.81.108.53) Time: Fri Jan 23 03:21:35 2004 Input: F:=GF(5); E:=EllipticCurve([-219,1654]); Discriminant(E); E:=ChangeRing(E,F); AbelianGroup(E); Output: Magma V2.10-6 Fri Jan 23 2004 03:21:32 on modular [Seed = 3971773707] ------------------------------------- -509607936 Abelian Group isomorphic to Z/9 Defined on 1 generator Relations: 9*$.1 = 0 Total time: 2.889 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host h24-81-108-53.vc.shawcable.net. (24.81.108.53) Time: Fri Jan 23 03:22:37 2004 Input: F:=GF(5); E:=EllipticCurve([-219,1654]); Discriminant(E); Generators(E); Output: Magma V2.10-6 Fri Jan 23 2004 03:22:34 on modular [Seed = 4222313050] ------------------------------------- -509607936 [ (35 : -192 : 1) ] Total time: 2.989 seconds, Total memory usage: 1.99MB ************** MAGMA ***************** Host h24-81-108-53.vc.shawcable.net. (24.81.108.53) Time: Fri Jan 23 03:28:18 2004 Input: F:=GF(5); E:=EllipticCurve([0,5,0,4,0]); Discriminant(E); Generators(E); Output: Magma V2.10-6 Fri Jan 23 2004 03:28:15 on modular [Seed = 3399111102] ------------------------------------- 2304 [ (-4 : 0 : 1), (-2 : -2 : 1) ] Total time: 2.889 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host h24-81-108-53.vc.shawcable.net. (24.81.108.53) Time: Fri Jan 23 03:37:19 2004 Input: F:=GF(5); E:=EllipticCurve([-17955, 708318]); Discriminant(E); Generators(E); Output: Magma V2.10-6 Fri Jan 23 2004 03:37:16 on modular [Seed = 3548597892] ------------------------------------- 153715016466432 [ (147 : 1116 : 1), (1263 : 44640 : 1) ] Total time: 3.359 seconds, Total memory usage: 1.99MB ************** MAGMA ***************** Host h24-81-108-53.vc.shawcable.net. (24.81.108.53) Time: Fri Jan 23 03:42:34 2004 Input: F:=GF(5); E:=EllipticCurve([-432, 8208]); Conductor(E); Discriminant(E); Generators(E); Output: Magma V2.10-6 Fri Jan 23 2004 03:42:31 on modular [Seed = 2716942269] ------------------------------------- 11 -23944605696 [ (-12 : 108 : 1) ] Total time: 2.909 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host h24-81-108-53.vc.shawcable.net. (24.81.108.53) Time: Fri Jan 23 03:42:49 2004 Input: F:=GF(5); E:=EllipticCurve([-432, 8208]); Conductor(E); Discriminant(E); AbelianGroup(E); Output: Magma V2.10-6 Fri Jan 23 2004 03:42:46 on modular [Seed = 3119064916] ------------------------------------- 11 -23944605696 Abelian Group isomorphic to Z/5 Defined on 1 generator Relations: 5*$.1 = 0 Total time: 2.979 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host h24-81-108-53.vc.shawcable.net. (24.81.108.53) Time: Fri Jan 23 03:44:59 2004 Input: F:=GF(5); E:=EllipticCurve([-432, 8208]); Conductor(E); Discriminant(E); AbelianGroup(E); Generators(E); Output: Magma V2.10-6 Fri Jan 23 2004 03:44:56 on modular [Seed = 2967482323] ------------------------------------- 11 -23944605696 Abelian Group isomorphic to Z/5 Defined on 1 generator Relations: 5*$.1 = 0 [ (-12 : 108 : 1) ] Total time: 2.989 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host YahooBB218117016004.bbtec.net. (218.117.16.4) Time: Fri Jan 23 10:02:49 2004 Input: 2+3; Output: Magma V2.10-6 Fri Jan 23 2004 10:02:44 on modular [Seed = 2952714315] ------------------------------------- 5 Total time: 3.119 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host YahooBB218117016004.bbtec.net. (218.117.16.4) Time: Fri Jan 23 10:16:58 2004 Input: Factorial(20); Output: Magma V2.10-6 Fri Jan 23 2004 10:16:55 on modular [Seed = 1998982625] ------------------------------------- 2432902008176640000 Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host YahooBB218117016004.bbtec.net. (218.117.16.4) Time: Fri Jan 23 10:26:26 2004 Input: F:=GF(8); Output: Magma V2.10-6 Fri Jan 23 2004 10:26:23 on modular [Seed = 1866338817] ------------------------------------- Total time: 3.039 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host YahooBB218117016004.bbtec.net. (218.117.16.4) Time: Fri Jan 23 10:26:49 2004 Input: F:=GF(8); F; Output: Magma V2.10-6 Fri Jan 23 2004 10:26:46 on modular [Seed = 1443310353] ------------------------------------- Finite field of size 2^3 Total time: 3.039 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host YahooBB218117016004.bbtec.net. (218.117.16.4) Time: Fri Jan 23 10:27:56 2004 Input: F:=GF(8); "asdfghjkqwertyui", F; Output: Magma V2.10-6 Fri Jan 23 2004 10:27:52 on modular [Seed = 1074871625] ------------------------------------- asdfghjkqwertyui Finite field of size 2^3 Total time: 3.139 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host YahooBB218117016004.bbtec.net. (218.117.16.4) Time: Fri Jan 23 10:28:48 2004 Input: F:=GF(8); G:=SymplecticGroup(4, F); G; Output: Magma V2.10-6 Fri Jan 23 2004 10:28:44 on modular [Seed = 1243297686] ------------------------------------- MatrixGroup(4, GF(2^3)) Generators: [ F.1 0 0 0] [ 0 F.1 0 0] [ 0 0 F.1^6 0] [ 0 0 0 F.1^6] [ 1 1 1 0] [ 1 0 0 0] [ 0 1 0 1] [ 0 1 0 0] Total time: 3.059 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host YahooBB218117016004.bbtec.net. (218.117.16.4) Time: Fri Jan 23 10:29:37 2004 Input: F:=GF(8); G:=GeneralLinearGroup(4, F); G; Output: Magma V2.10-6 Fri Jan 23 2004 10:29:34 on modular [Seed = 895764634] ------------------------------------- GL(4, GF(2, 3)) Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host YahooBB218117016004.bbtec.net. (218.117.16.4) Time: Fri Jan 23 10:31:57 2004 Input: F:=GF(4); G:=SpecialLinearGroup(3, F); G; Output: Magma V2.10-6 Fri Jan 23 2004 10:31:52 on modular [Seed = 645355583] ------------------------------------- MatrixGroup(3, GF(2^2)) Generators: [ F.1 0 0] [ 0 F.1^2 0] [ 0 0 1] [ 1 0 1] [ 1 0 0] [ 0 1 0] Total time: 3.069 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host YahooBB218117016004.bbtec.net. (218.117.16.4) Time: Fri Jan 23 10:32:25 2004 Input: F:=GF(4); G:=SpecialLinearGroup(3, F); G; Output: Magma V2.10-6 Fri Jan 23 2004 10:32:21 on modular [Seed = 289435622] ------------------------------------- MatrixGroup(3, GF(2^2)) Generators: [ w 0 0] [ 0 w^2 0] [ 0 0 1] [ 1 0 1] [ 1 0 0] [ 0 1 0] Total time: 3.119 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host YahooBB218117016004.bbtec.net. (218.117.16.4) Time: Fri Jan 23 10:35:59 2004 Input: F:=GF(4); G:=SymplecticGroup(3, F); Order(G); Output: Magma V2.10-6 Fri Jan 23 2004 10:35:56 on modular [Seed = 5340973] ------------------------------------- >> G:=SymplecticGroup(3, F); ^ Runtime error in 'SymplecticGroup': Invalid dimension---should be even >> Order(G);; ^ User error: Identifier 'G' has not been declared or assigned Total time: 2.979 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host YahooBB218117016004.bbtec.net. (218.117.16.4) Time: Fri Jan 23 10:36:16 2004 Input: F:=GF(4); G:=SymplecticGroup(4, F); Order(G); Output: Magma V2.10-6 Fri Jan 23 2004 10:36:13 on modular [Seed = 190477335] ------------------------------------- 979200 Total time: 3.029 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host YahooBB218117016004.bbtec.net. (218.117.16.4) Time: Fri Jan 23 10:36:37 2004 Input: F:=GF(4); G:=SpecialLinearGroup(4, F); Order(G); Output: Magma V2.10-6 Fri Jan 23 2004 10:36:34 on modular [Seed = 4070804737] ------------------------------------- 987033600 Total time: 2.949 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host YahooBB218117016004.bbtec.net. (218.117.16.4) Time: Fri Jan 23 10:40:40 2004 Input: GCD(1234, 4567); Output: Magma V2.10-6 Fri Jan 23 2004 10:40:36 on modular [Seed = 3887523810] ------------------------------------- 1 Total time: 3.009 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host YahooBB218117016004.bbtec.net. (218.117.16.4) Time: Fri Jan 23 10:56:45 2004 Input: ?GL; Output: Magma V2.10-6 Fri Jan 23 2004 10:56:42 on modular [Seed = 2295958723] ------------------------------------- No references for word "GL;" Total time: 2.909 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host YahooBB218117016004.bbtec.net. (218.117.16.4) Time: Fri Jan 23 10:56:58 2004 Input: ?GL Output: Magma V2.10-6 Fri Jan 23 2004 10:56:55 on modular [Seed = 1881240645] ------------------------------------- 4 matches: 1 I /magma/group/matrix/creation-general-linear-group/magma/\ GeneralLinearGroup 2 I /magma/group/matrix/creation-general-linear-group/magma/\ GeneralLinearGroup 3 I /magma/group/matrix/standard/classical/linear/GeneralLinearGroup 4 I /magma/group/matrix/standard/classical/linear/GeneralLinearGroup To view an entry, type ? followed by the number next to it Total time: 2.999 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host YahooBB218117016004.bbtec.net. (218.117.16.4) Time: Fri Jan 23 10:58:02 2004 Input: ?GL ?1 Output: Magma V2.10-6 Fri Jan 23 2004 10:57:59 on modular [Seed = 1731617682] ------------------------------------- 4 matches: 1 I /magma/group/matrix/creation-general-linear-group/magma/\ GeneralLinearGroup 2 I /magma/group/matrix/creation-general-linear-group/magma/\ GeneralLinearGroup 3 I /magma/group/matrix/standard/classical/linear/GeneralLinearGroup 4 I /magma/group/matrix/standard/classical/linear/GeneralLinearGroup To view an entry, type ? followed by the number next to it =============================================================================== PATH: /magma/group/matrix/creation-general-linear-group/magma/\ GeneralLinearGroup KIND: Intrinsic =============================================================================== GeneralLinearGroup(n, R) : RngIntElt, Rng -> GrpMat GL(n, R) : RngIntElt, Rng -> GrpMat Given an integer n >= 1, create the generic matrix group, i.e. the general linear group GL(n, R). Initially, only a structure table is created for GL(n, R), so that, in particular, generators are not defined. This function is normally used to provide a context for the creation of elements and subgroups of GL(n, R). If structural computation is attempted with the group created by GeneralLinearGroup(n, R), then generators will be created where possible. At present, this is only permitted in the cases in which R is a finite field. =============================================================================== Total time: 2.919 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Fri Jan 23 12:40:08 2004 Input: P := PolynomialRing(Rationals()); C := HyperellipticCurve(x^5 + 257); J := Jacobian(C); SetVerbose("JacHypSelmer", 2); P := PolynomialRing(Rationals()); C := HyperellipticCurve(x^5 + 258); J := Jacobian(C); SetVerbose("JacHypSelmer", 2); Output: Magma V2.10-6 Fri Jan 23 2004 12:40:05 on modular [Seed = 912730679] ------------------------------------- Total time: 3.039 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Fri Jan 23 12:40:56 2004 Input: P := PolynomialRing(Rationals()); C := HyperellipticCurve(x^5 + 257); J := Jacobian(C); SetVerbose("JacHypSelmer", 2); TwoSelmerGroupData(J : Bound := 300); P := PolynomialRing(Rationals()); C := HyperellipticCurve(x^5 + 258); J := Jacobian(C); SetVerbose("JacHypSelmer", 2); TwoSelmerGroupData(J : Bound := 300); Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Fri Jan 23 2004 12:40:33 on modular [Seed = 1064182746] ------------------------------------- TwoSelmerGroupData of Jacobian of Hyperelliptic Curve defined by y^2 = x^5 + 257 over Rational Field m= Mapping from: CrvHyp: C to CrvHyp: C1 with equations : $.1 $.2 $.3 and inverse $.1 $.2 $.3 Bad primes = [ 2, 5, 257 ] f is irreducible. For factor x^5 + 257, use field defined by x^5 + 257 and theta = K.1 The 2-torsion group has dimension 0. Determining local images... p = 2 x = 1/4 --> new generator (0 0 1 0 0 0 0 0 1) x = 2 --> new generator (0 1 1 0 1 1 1 0 1) p = 5 p = 257 p = infinity Computing class groups... Class group data of the fields: Field given by x^5 + 257: [ 2 ] Dimension of Cl[2] = 1. Signatures: [ 1, 2 ] Dimension of units mod squares = 3. Upper bound for Selmer group dimension: 4. ==> Upper bound for rank = 4. Computing unit groups... Class group and unit data of the fields: Field given by x^5 + 257: Class group = [ 2 ], units = [ 2, 0, 0 ] Time for local computations: 750 ms. Time for class groups: 1400 ms. Time for unit groups: 370 ms. Selmer group dimension = 4, Dimension of 2-torsion = 0, ==> Bound for the MW-rank = 4. Total time: 3281 ms. 4 4 <[ 6324*$.1^4 - 19200*$.1^3 + 58201*$.1^2 - 176674*$.1 + 535924, 4813226456041628140*$.1^4 + 36434957339645170375*$.1^3 + 134550883205234964034*$.1^2 + 325136991241356237462*$.1 + 357631773270138394448, 1898945157296111119768004005861896951189113731493159631143905*$.1^4 - 5761015542398411283260475472857253473153837662142636183838143*$.1^3 + 17477755980596075244976664738473739735787278689402500394549187*$.1^2 - 53023976739713597727828199451673037316227792790503365996207432*$.1 + 160864021240202805022544738394785299697644164574703095412928724, 5935617327117/5*$.1^4 - 18007462569209/5*$.1^3 + 54630999497913/5*$.1^2 - 165739402654201/5*$.1 + 502819824492457/5 ], [], []> { Number Field with defining polynomial x^5 + 257 over the Rational Field } TwoSelmerGroupData of Jacobian of Hyperelliptic Curve defined by y^2 = x^5 + 258 over Rational Field m= Mapping from: CrvHyp: C to CrvHyp: C1 with equations : $.1 $.2 $.3 and inverse $.1 $.2 $.3 Bad primes = [ 2, 3, 5, 43 ] f is irreducible. For factor x^5 + 258, use field defined by x^5 + 258 and theta = K.1 The 2-torsion group has dimension 0. Determining local images... p = 2 x = 7 --> new generator (0 1 0 0 1 1 0) Errors: /home/mfd/gomagma: line 2: 13387 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Fri Jan 23 12:41:41 2004 Input: P := PolynomialRing(Rationals()); C := HyperellipticCurve(x^5 + 257); J := Jacobian(C); SetVerbose("JacHypSelmer", 2); TwoSelmerGroupData(J : Bound := 300); Output: Magma V2.10-6 Fri Jan 23 2004 12:41:35 on modular [Seed = 544291995] ------------------------------------- TwoSelmerGroupData of Jacobian of Hyperelliptic Curve defined by y^2 = x^5 + 257 over Rational Field m= Mapping from: CrvHyp: C to CrvHyp: C1 with equations : $.1 $.2 $.3 and inverse $.1 $.2 $.3 Bad primes = [ 2, 5, 257 ] f is irreducible. For factor x^5 + 257, use field defined by x^5 + 257 and theta = K.1 The 2-torsion group has dimension 0. Determining local images... p = 2 x = 1/4 --> new generator (0 0 1 0 0 0 0 0 1) x = 2 --> new generator (0 1 1 0 1 1 1 0 1) p = 5 p = 257 p = infinity Computing class groups... Class group data of the fields: Field given by x^5 + 257: [ 2 ] Dimension of Cl[2] = 1. Signatures: [ 1, 2 ] Dimension of units mod squares = 3. Upper bound for Selmer group dimension: 4. ==> Upper bound for rank = 4. Computing unit groups... Class group and unit data of the fields: Field given by x^5 + 257: Class group = [ 2 ], units = [ 2, 0, 0 ] Time for local computations: 750 ms. Time for class groups: 1669 ms. Time for unit groups: 370 ms. Selmer group dimension = 4, Dimension of 2-torsion = 0, ==> Bound for the MW-rank = 4. Total time: 3590 ms. 4 4 <[ 708711158630174206861435869376877169456490291809823030*$.1^4 - 2150086317265325367721413224155242086872423877990095040*$.1^3 + 6522927028024848746845077202090384185101639941777450765*$.1^2 - 19789241330112840384154682829351080020154171504531454933*$.1 + 60036555788364767049696812219348039883800501737327108765, 4608982659907306858072145919654527323151657358877026947/5*$.1^4 - 13982721215697714090534787431438586866996284632063423664/5*$.1^3 + 42420748139645869677654885626992288765520921800723857098/5*$.1^2 - 128695970188337586860684550304729758220384390330903328701/5*$.1 + 390437544575934550360748621620916384263901705453339168097/5, 5935617327117/5*$.1^4 - 18007462569209/5*$.1^3 + 54630999497913/5*$.1^2 - 165739402654201/5*$.1 + 502819824492457/5, 6324*$.1^4 - 19200*$.1^3 + 58201*$.1^2 - 176674*$.1 + 535924 ], [], []> { Number Field with defining polynomial x^5 + 257 over the Rational Field } Total time: 6.659 seconds, Total memory usage: 3.39MB ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Fri Jan 23 12:44:00 2004 Input: P := PolynomialRing(Rationals()); C := HyperellipticCurve(x^5 + 258); J := Jacobian(C); SetVerbose("JacHypSelmer", 2); TwoSelmerGroupData(J : Bound := 300); Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Fri Jan 23 2004 12:43:37 on modular [Seed = 729429526] ------------------------------------- TwoSelmerGroupData of Jacobian of Hyperelliptic Curve defined by y^2 = x^5 + 258 over Rational Field m= Mapping from: CrvHyp: C to CrvHyp: C1 with equations : $.1 $.2 $.3 and inverse $.1 $.2 $.3 Bad primes = [ 2, 3, 5, 43 ] f is irreducible. For factor x^5 + 258, use field defined by x^5 + 258 and theta = K.1 The 2-torsion group has dimension 0. Determining local images... p = 2 x = 7 --> new generator (0 1 0 0 1 1 0) x^2 + 55*x + 2831 --> new generator: (0 1 1 0 0 0 1) p = 3 p = 5 p = 43 p = infinity Computing class groups... Class group data of the fields: Field given by x^5 + 258: [ 5 ] Dimension of Cl[2] = 0. Signatures: [ 1, 2 ] Dimension of units mod squares = 3. Upper bound for Selmer group dimension: 2. ==> Upper bound for rank = 2. Computing unit groups... Errors: /home/mfd/gomagma: line 2: 13407 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host 3(NXDOMAIN) (65.241.52.198) Time: Fri Jan 23 14:31:21 2004 Input: floor(52!/60/60/24/365.25) Output: Magma V2.10-6 Fri Jan 23 2004 14:31:18 on modular [Seed = 207436540] ------------------------------------- >> floor(52!/60/60/24/365.25); ^ User error: bad syntax Total time: 2.919 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (65.241.52.198) Time: Fri Jan 23 14:32:10 2004 Input: floor(52!/(60*60*24*365.2425)) Output: Magma V2.10-6 Fri Jan 23 2004 14:32:06 on modular [Seed = 3803436067] ------------------------------------- >> floor(52!/(60*60*24*365.2425)); ^ User error: bad syntax Total time: 3.599 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host gw1.btc.transwitch.com. (63.149.68.2) Time: Fri Jan 23 15:52:56 2004 Input: Galois(x^2+1); Output: Magma V2.10-6 Fri Jan 23 2004 15:52:53 on modular [Seed = 3498121485] ------------------------------------- >> Galois(x^2+1);; ^ User error: Identifier 'x' has not been declared or assigned Total time: 2.929 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host gw1.btc.transwitch.com. (63.149.68.2) Time: Fri Jan 23 16:00:40 2004 Input: R := PolynomialRing(RationalField()); GaloisGroup(x^2+1); Output: Magma V2.10-6 Fri Jan 23 2004 16:00:36 on modular [Seed = 3152703671] ------------------------------------- Permutation group acting on a set of cardinality 2 (1, 2) [ 3, 2 ] 5 Total time: 2.999 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host gw1.btc.transwitch.com. (63.149.68.2) Time: Fri Jan 23 16:04:42 2004 Input: R := PolynomialRing(RationalField()); TransitiveGroupIdentification(GaloisGroup(x^8+3*x^4+1)); Output: Magma V2.10-6 Fri Jan 23 2004 16:04:39 on modular [Seed = 2563331207] ------------------------------------- 4 8 Total time: 3.459 seconds, Total memory usage: 7.71MB ************** MAGMA ***************** Host ip-221.net-81-220-87.toulouse.rev.numericable.fr. (81.220.87.221) Time: Fri Jan 23 16:04:57 2004 Input: 1+1 Output: Magma V2.10-6 Fri Jan 23 2004 16:04:53 on modular [Seed = 2329626247] ------------------------------------- 2 Total time: 2.999 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host gw1.btc.transwitch.com. (63.149.68.2) Time: Fri Jan 23 16:05:00 2004 Input: R := PolynomialRing(RationalField()); TransitiveGroupIdentification(GaloisGroup(16^8+8*x^4+1)); Output: Magma V2.10-6 Fri Jan 23 2004 16:04:56 on modular [Seed = 2380022157] ------------------------------------- 3 4 Total time: 3.029 seconds, Total memory usage: 1.99MB ************** MAGMA ***************** Host ip-221.net-81-220-87.toulouse.rev.numericable.fr. (81.220.87.221) Time: Fri Jan 23 16:05:07 2004 Input: 1+1 Output: Magma V2.10-6 Fri Jan 23 2004 16:05:04 on modular [Seed = 1897971080] ------------------------------------- 2 Total time: 2.909 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host gw1.btc.transwitch.com. (63.149.68.2) Time: Fri Jan 23 16:05:20 2004 Input: R := PolynomialRing(RationalField()); TransitiveGroupIdentification(GaloisGroup(x^16+8*x^8+1)); Output: Magma V2.10-6 Fri Jan 23 2004 16:05:12 on modular [Seed = 1748608153] ------------------------------------- 89 16 Total time: 7.849 seconds, Total memory usage: 6.80MB ************** MAGMA ***************** Host gw1.btc.transwitch.com. (63.149.68.2) Time: Fri Jan 23 16:09:41 2004 Input: R := PolynomialRing(RationalField()); TransitiveGroupIdentification(GaloisGroup(x^16+8*x^8+1)); Output: Magma V2.10-6 Fri Jan 23 2004 16:09:32 on modular [Seed = 1594790570] ------------------------------------- 89 16 Total time: 8.869 seconds, Total memory usage: 6.80MB ************** MAGMA ***************** Host gw1.btc.transwitch.com. (63.149.68.2) Time: Fri Jan 23 16:09:53 2004 Input: R := PolynomialRing(RationalField()); TransitiveGroupIdentification(GaloisGroup(x^16+8*x^7+1)); Output: Magma V2.10-6 Fri Jan 23 2004 16:09:48 on modular [Seed = 1327399594] ------------------------------------- 1954 16 Total time: 4.159 seconds, Total memory usage: 10.69MB ************** MAGMA ***************** Host gw1.btc.transwitch.com. (63.149.68.2) Time: Fri Jan 23 16:10:52 2004 Input: R := PolynomialRing(RationalField());TransitiveGroupIdentification(GaloisGroup(x^16 - 4*x^12 + 7*x^8 - 6*x^4 + 1)); Output: Magma V2.10-6 Fri Jan 23 2004 16:10:42 on modular [Seed = 796844676] ------------------------------------- 162 16 Total time: 9.479 seconds, Total memory usage: 11.48MB ************** MAGMA ***************** Host tow25dhcp183.towson01.md.comcast.net. (68.33.25.183) Time: Fri Jan 23 16:13:52 2004 Input: AHAH Output: Magma V2.10-6 Fri Jan 23 2004 16:13:48 on modular [Seed = 3837078033] ------------------------------------- >> AHAH; ^ User error: Identifier 'AHAH' has not been declared or assigned Total time: 2.999 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host tow25dhcp183.towson01.md.comcast.net. (68.33.25.183) Time: Fri Jan 23 16:13:55 2004 Input: AHAH Output: Magma V2.10-6 Fri Jan 23 2004 16:13:51 on modular [Seed = 3700232746] ------------------------------------- >> AHAH; ^ User error: Identifier 'AHAH' has not been declared or assigned Total time: 3.609 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 62-237-72-80.hpna.wlannet.com. (62.237.72.80) Time: Fri Jan 23 16:13:58 2004 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: Magma V2.10-6 Fri Jan 23 2004 16:13:51 on modular [Seed = 3514834744] ------------------------------------- Replace this by some code, then click [PARI] or [MAGMA]! Total time: 3.619 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host c6.nas9.dial.mels.ru. (62.109.179.6) Time: Fri Jan 23 16:14:33 2004 Input: 1 Output: Magma V2.10-6 Fri Jan 23 2004 16:14:22 on modular [Seed = 2984279910] ------------------------------------- 1 Total time: 2.919 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pD959076C.dip.t-dialin.net. (217.89.7.108) Time: Fri Jan 23 16:15:27 2004 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: Magma V2.10-6 Fri Jan 23 2004 16:15:23 on modular [Seed = 2902286910] ------------------------------------- Replace this by some code, then click [PARI] or [MAGMA]! Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host gw1.btc.transwitch.com. (63.149.68.2) Time: Fri Jan 23 17:25:27 2004 Input: R := PolynomialRing(RationalField());TransitiveGroupIdentification(GaloisGroup(x^16 - 594*x^8 + 9)); Output: Magma V2.10-6 Fri Jan 23 2004 17:25:18 on modular [Seed = 3365476349] ------------------------------------- 133 16 Total time: 9.389 seconds, Total memory usage: 4.20MB ************** MAGMA ***************** Host gw1.btc.transwitch.com. (63.149.68.2) Time: Fri Jan 23 17:39:24 2004 Input: R := PolynomialRing(RationalField());TransitiveGroupIdentification(GaloisGroup(x^16 - 57*x^14 + 1212*x^12 - 12385*x^10 + 64261*x^8 - 162395*x^6 + 159448*x^4 - 6131*x^2 + 1)); Output: Magma V2.10-6 Fri Jan 23 2004 17:39:16 on modular [Seed = 1815973508] ------------------------------------- 77 16 Total time: 7.579 seconds, Total memory usage: 5.39MB ************** MAGMA ***************** Host gw1.btc.transwitch.com. (63.149.68.2) Time: Fri Jan 23 17:46:48 2004 Input: R := PolynomialRing(RationalField());TransitiveGroupIdentification(GaloisGroup(x^16 - 32*x^14 + 378*x^12 - 2088*x^10 + 5778*x^8 - 8432*x^6 + 6426*x^4 - 2312*x^2 + 289)); Output: Magma V2.10-6 Fri Jan 23 2004 17:46:39 on modular [Seed = 628408598] ------------------------------------- 123 16 Total time: 8.590 seconds, Total memory usage: 7.97MB ************** MAGMA ***************** Host pcp486497pcs.howard01.md.comcast.net. (68.55.18.94) Time: Fri Jan 23 18:20:49 2004 Input: 2 + 2 Output: Magma V2.10-6 Fri Jan 23 2004 18:20:46 on modular [Seed = 323157792] ------------------------------------- 4 Total time: 3.069 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pcp486497pcs.howard01.md.comcast.net. (68.55.18.94) Time: Fri Jan 23 18:21:12 2004 Input: a + b Output: Magma V2.10-6 Fri Jan 23 2004 18:21:09 on modular [Seed = 4239200484] ------------------------------------- >> a + b; ^ User error: Identifier 'a' has not been declared or assigned Total time: 2.999 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pcp486497pcs.howard01.md.comcast.net. (68.55.18.94) Time: Fri Jan 23 18:21:28 2004 Input: a = 12 Output: Magma V2.10-6 Fri Jan 23 2004 18:21:24 on modular [Seed = 4154858494] ------------------------------------- >> a = 12; ^ User error: Identifier 'a' has not been declared or assigned Total time: 3.339 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 2(SERVFAIL) (63.107.36.10) Time: Fri Jan 23 23:22:56 2004 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: Magma V2.10-6 Fri Jan 23 2004 23:22:53 on modular [Seed = 946441005] ------------------------------------- Replace this by some code, then click [PARI] or [MAGMA]! Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host wc-36-10.wheaton.edu. (63.107.36.10) Time: Fri Jan 23 23:23:14 2004 Input: 2+4; Output: Magma V2.10-6 Fri Jan 23 2004 23:23:11 on modular [Seed = 1226373742] ------------------------------------- 6 Total time: 2.979 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Sat Jan 24 07:50:19 2004 Input: P := PolynomialRing(Rationals()); C := HyperellipticCurve(x^5 + 257); J := Jacobian(C); SetVerbose("JacHypSelmer", 2); TwoSelmerGroupData(J : Bound := 300); Output: Magma V2.10-6 Sat Jan 24 2004 07:50:11 on modular [Seed = 2049462381] ------------------------------------- TwoSelmerGroupData of Jacobian of Hyperelliptic Curve defined by y^2 = x^5 + 257 over Rational Field m= Mapping from: CrvHyp: C to CrvHyp: C1 with equations : $.1 $.2 $.3 and inverse $.1 $.2 $.3 Bad primes = [ 2, 5, 257 ] f is irreducible. For factor x^5 + 257, use field defined by x^5 + 257 and theta = K.1 The 2-torsion group has dimension 0. Determining local images... p = 2 x = 1/4 --> new generator (0 0 1 0 0 0 0 0 1) x = 2 --> new generator (0 1 1 0 1 1 1 0 1) p = 5 p = 257 p = infinity Computing class groups... Class group data of the fields: Field given by x^5 + 257: [ 2 ] Dimension of Cl[2] = 1. Signatures: [ 1, 2 ] Dimension of units mod squares = 3. Upper bound for Selmer group dimension: 4. ==> Upper bound for rank = 4. Computing unit groups... Class group and unit data of the fields: Field given by x^5 + 257: Class group = [ 2 ], units = [ 2, 0, 0 ] Time for local computations: 760 ms. Time for class groups: 1530 ms. Time for unit groups: 381 ms. Selmer group dimension = 4, Dimension of 2-torsion = 0, ==> Bound for the MW-rank = 4. Total time: 3459 ms. 4 4 <[ 6324*$.1^4 - 19200*$.1^3 + 58201*$.1^2 - 176674*$.1 + 535924, 122604583723030542/5*$.1^4 + 261859047053874576/5*$.1^3 + 156966657883052228/5*$.1^2 - 1639615992401178821/5*$.1 - 9493237037517256688/5, 708711158630174206861435869376877169456490291809823030*$.1^4 - 2150086317265325367721413224155242086872423877990095040*$.1^3 + 6522927028024848746845077202090384185101639941777450765*$.1^2 - 19789241330112840384154682829351080020154171504531454933*$.1 + 60036555788364767049696812219348039883800501737327108765, 3180819625039854751*$.1^4 - 9649963416275232927*$.1^3 + 29276037283718524351*$.1^2 - 88817575991236440979*$.1 + 269454562053935412631 ], [], []> { Number Field with defining polynomial x^5 + 257 over the Rational Field } Total time: 6.719 seconds, Total memory usage: 3.39MB ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Sat Jan 24 07:50:35 2004 Input: P := PolynomialRing(Rationals()); C := HyperellipticCurve(x^5 + 5); J := Jacobian(C); SetVerbose("JacHypSelmer", 2); TwoSelmerGroupData(J : Bound := 300); Output: Magma V2.10-6 Sat Jan 24 2004 07:50:31 on modular [Seed = 1664174432] ------------------------------------- TwoSelmerGroupData of Jacobian of Hyperelliptic Curve defined by y^2 = x^5 + 5 over Rational Field m= Mapping from: CrvHyp: C to CrvHyp: C1 with equations : $.1 $.2 $.3 and inverse $.1 $.2 $.3 Bad primes = [ 2, 5 ] f is irreducible. For factor x^5 + 5, use field defined by x^5 + 5 and theta = K.1 The 2-torsion group has dimension 0. Determining local images... p = 2 x = 1/4 --> new generator (0 0 1 0 0 0 0 0 1) x^2 + 25*x + 7387 --> new generator: (0 1 1 0 0 0 1 1 0) p = 5 p = infinity Computing class groups... Class group data of the fields: Field given by x^5 + 5: [] Dimension of Cl[2] = 0. Signatures: [ 1, 2 ] Dimension of units mod squares = 3. Upper bound for Selmer group dimension: 2. ==> Upper bound for rank = 2. Computing unit groups... Class group and unit data of the fields: Field given by x^5 + 5: Class group = [], units = [ 2, 0, 0 ] Time for local computations: 911 ms. Time for class groups: 370 ms. Time for unit groups: 80 ms. Selmer group dimension = 1, Dimension of 2-torsion = 0, ==> Bound for the MW-rank = 1. Total time: 1481 ms. 1 1 <[ 4*$.1^4 - 3*$.1^3 - 5*$.1^2 + 10*$.1 + 1 ], [], []> { Number Field with defining polynomial x^5 + 5 over the Rational Field } Total time: 4.669 seconds, Total memory usage: 2.99MB ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Sat Jan 24 07:53:06 2004 Input: P := PolynomialRing(Rationals()); C := HyperellipticCurve(x*(x-1)*(x-2)*(x-3)*(x-4)); J := Jacobian(C); SetVerbose("JacHypSelmer", 2); TwoSelmerGroupData(J : Bound := 300); Output: Magma V2.10-6 Sat Jan 24 2004 07:53:02 on modular [Seed = 2529475628] ------------------------------------- TwoSelmerGroupData of Jacobian of Hyperelliptic Curve defined by y^2 = x^5 - 10*x^4 + 35*x^3 - 50*x^2 + 24*x over Rational Field m= Mapping from: CrvHyp: C to CrvHyp: C1 with equations : $.1 $.2 $.3 and inverse $.1 $.2 $.3 Bad primes = [ 2, 3 ] f factors as (x - 4) (x - 3) (x - 2) (x - 1) (x). For factor x - 4, use field defined by x - 1 and theta = 4 For factor x - 3, use field defined by x - 1 and theta = 3 For factor x - 2, use field defined by x - 1 and theta = 2 For factor x - 1, use field defined by x - 1 and theta = 1 For factor x, use field defined by x - 1 and theta = 0 The 2-torsion group has dimension 4. Determining local images... p = 2 x = 1/4 --> new generator (0 0 0 0 0 1 0 0 0 0 0 1 0 0 0) x = 22 --> new generator (1 0 0 0 1 0 0 0 1 0 0 1 1 1 0) p = 3 x = 7 --> new generator (1 0 0 0 0 1 1 1 0 0) p = infinity Computing class groups... Class group data of the fields: Field given by x - 4: [] Field given by x - 3: [] Field given by x - 2: [] Field given by x - 1: [] Field given by x: [] Dimension of Cl[2] = 0. Signatures: [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] Dimension of units mod squares = 5. Upper bound for Selmer group dimension: 9. ==> Upper bound for rank = 5. Computing unit groups... Class group and unit data of the fields: Field given by x - 4: Class group = [], units = [ 2 ] Field given by x - 3: Class group = [], units = [ 2 ] Field given by x - 2: Class group = [], units = [ 2 ] Field given by x - 1: Class group = [], units = [ 2 ] Field given by x: Class group = [], units = [ 2 ] Time for local computations: 531 ms. Time for class groups: 0 ms. Time for unit groups: 0 ms. Selmer group dimension = 4, Dimension of 2-torsion = 4, ==> Bound for the MW-rank = 0. Total time: 590 ms. 0 4 <[ 1/8*$.1^4 - 3/4*$.1^3 + 3/8*$.1^2 + 5/4*$.1 + 2, -$.1^3 + 7*$.1^2 - 12*$.1 + 3, 1/4*$.1^4 - 3/2*$.1^3 + 11/4*$.1^2 - 5/2*$.1 + 4, -9/8*$.1^4 + 35/4*$.1^3 - 163/8*$.1^2 + 51/4*$.1 + 6 ], [], []> {} Total time: 3.759 seconds, Total memory usage: 2.69MB ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Sat Jan 24 07:56:57 2004 Input: P := PolynomialRing(Rationals()); C := HyperellipticCurve(x*(x-1)*(x-2)*(x-3)*(x-4)); D := QuadraticTwist(C,1); J := Jacobian(D); SetVerbose("JacHypSelmer", 2); TwoSelmerGroupData(J : Bound := 300); Output: Magma V2.10-6 Sat Jan 24 2004 07:56:53 on modular [Seed = 2228662021] ------------------------------------- TwoSelmerGroupData of Jacobian of Hyperelliptic Curve defined by y^2 = x^5 - 10*x^4 + 35*x^3 - 50*x^2 + 24*x over Rational Field m= Mapping from: CrvHyp: C to CrvHyp: C1 with equations : $.1 $.2 $.3 and inverse $.1 $.2 $.3 Bad primes = [ 2, 3 ] f factors as (x - 4) (x - 3) (x - 2) (x - 1) (x). For factor x - 4, use field defined by x - 1 and theta = 4 For factor x - 3, use field defined by x - 1 and theta = 3 For factor x - 2, use field defined by x - 1 and theta = 2 For factor x - 1, use field defined by x - 1 and theta = 1 For factor x, use field defined by x - 1 and theta = 0 The 2-torsion group has dimension 4. Determining local images... p = 2 x = 1/4 --> new generator (0 0 0 0 0 1 0 0 0 0 0 1 0 0 0) x = 22 --> new generator (1 0 0 0 1 0 0 0 1 0 0 1 1 1 0) p = 3 x = 7 --> new generator (1 0 0 0 0 1 1 1 0 0) p = infinity Computing class groups... Class group data of the fields: Field given by x - 4: [] Field given by x - 3: [] Field given by x - 2: [] Field given by x - 1: [] Field given by x: [] Dimension of Cl[2] = 0. Signatures: [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] Dimension of units mod squares = 5. Upper bound for Selmer group dimension: 9. ==> Upper bound for rank = 5. Computing unit groups... Class group and unit data of the fields: Field given by x - 4: Class group = [], units = [ 2 ] Field given by x - 3: Class group = [], units = [ 2 ] Field given by x - 2: Class group = [], units = [ 2 ] Field given by x - 1: Class group = [], units = [ 2 ] Field given by x: Class group = [], units = [ 2 ] Time for local computations: 511 ms. Time for class groups: 0 ms. Time for unit groups: 0 ms. Selmer group dimension = 4, Dimension of 2-torsion = 4, ==> Bound for the MW-rank = 0. Total time: 580 ms. 0 4 <[ 1/8*$.1^4 - 3/4*$.1^3 + 3/8*$.1^2 + 5/4*$.1 + 2, -$.1^3 + 7*$.1^2 - 12*$.1 + 3, 1/4*$.1^4 - 3/2*$.1^3 + 11/4*$.1^2 - 5/2*$.1 + 4, -9/8*$.1^4 + 35/4*$.1^3 - 163/8*$.1^2 + 51/4*$.1 + 6 ], [], []> {} Total time: 3.599 seconds, Total memory usage: 2.69MB ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Sat Jan 24 07:57:13 2004 Input: P := PolynomialRing(Rationals()); C := HyperellipticCurve(x*(x-1)*(x-2)*(x-3)*(x-4)); D := QuadraticTwist(C,2); J := Jacobian(D); SetVerbose("JacHypSelmer", 2); TwoSelmerGroupData(J : Bound := 300); Output: Magma V2.10-6 Sat Jan 24 2004 07:57:09 on modular [Seed = 2380244540] ------------------------------------- TwoSelmerGroupData of Jacobian of Hyperelliptic Curve defined by y^2 = 2*x^5 - 20*x^4 + 70*x^3 - 100*x^2 + 48*x over Rational Field m= Mapping from: CrvHyp: C to CrvHyp: C1 with equations : 2*$.1 4*$.2 $.3 and inverse 1/2*$.1 1/4*$.2 $.3 Change curve into Hyperelliptic Curve defined by y^2 = x^5 - 20*x^4 + 140*x^3 - 400*x^2 + 384*x over Rational Field Bad primes = [ 2, 3 ] f factors as (x - 8) (x - 6) (x - 4) (x - 2) (x). For factor x - 8, use field defined by x - 1 and theta = 8 For factor x - 6, use field defined by x - 1 and theta = 6 For factor x - 4, use field defined by x - 1 and theta = 4 For factor x - 2, use field defined by x - 1 and theta = 2 For factor x, use field defined by x - 1 and theta = 0 The 2-torsion group has dimension 4. Determining local images... p = 2 x = 1 --> new generator (0 0 0 0 1 0 0 0 1 0 1 1 0 0 0) x = 26 --> new generator (1 0 0 0 0 1 1 1 0 1 1 0 1 0 1) p = 3 x = 3 --> new generator (0 0 1 1 0 1 0 0 1 0) p = infinity Computing class groups... Class group data of the fields: Field given by x - 8: [] Field given by x - 6: [] Field given by x - 4: [] Field given by x - 2: [] Field given by x: [] Dimension of Cl[2] = 0. Signatures: [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] Dimension of units mod squares = 5. Upper bound for Selmer group dimension: 9. ==> Upper bound for rank = 5. Computing unit groups... Class group and unit data of the fields: Field given by x - 8: Class group = [], units = [ 2 ] Field given by x - 6: Class group = [], units = [ 2 ] Field given by x - 4: Class group = [], units = [ 2 ] Field given by x - 2: Class group = [], units = [ 2 ] Field given by x: Class group = [], units = [ 2 ] Time for local computations: 1059 ms. Time for class groups: 0 ms. Time for unit groups: 0 ms. Selmer group dimension = 4, Dimension of 2-torsion = 4, ==> Bound for the MW-rank = 0. Total time: 1119 ms. Transforming presentation of S back to model C. 0 4 <[ $.1^3 - 13/2*$.1^2 + 17/2*$.1 + 3, -1/4*$.1^4 + 3/2*$.1^3 - 5/4*$.1^2 - 3*$.1 + 1, -1/2*$.1^3 + 7/2*$.1^2 - 7*$.1 + 6, -9/4*$.1^4 + 19*$.1^3 - 203/4*$.1^2 + 43*$.1 + 3 ], [], []> {} Total time: 4.279 seconds, Total memory usage: 2.69MB ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Sat Jan 24 07:57:35 2004 Input: P := PolynomialRing(Rationals()); C := HyperellipticCurve(x*(x-1)*(x-2)*(x-3)*(x-4)); D := QuadraticTwist(C,20); J := Jacobian(D); SetVerbose("JacHypSelmer", 2); TwoSelmerGroupData(J : Bound := 300); Output: Magma V2.10-6 Sat Jan 24 2004 07:57:31 on modular [Seed = 3068435737] ------------------------------------- TwoSelmerGroupData of Jacobian of Hyperelliptic Curve defined by y^2 = 20*x^5 - 200*x^4 + 700*x^3 - 1000*x^2 + 480*x over Rational Field m= Mapping from: CrvHyp: C to CrvHyp: C1 with equations : 5*$.1 25/2*$.2 $.3 and inverse 1/5*$.1 2/25*$.2 $.3 Change curve into Hyperelliptic Curve defined by y^2 = x^5 - 50*x^4 + 875*x^3 - 6250*x^2 + 15000*x over Rational Field Bad primes = [ 2, 3, 5 ] f factors as (x - 20) (x - 15) (x - 10) (x - 5) (x). For factor x - 20, use field defined by x - 1 and theta = 20 For factor x - 15, use field defined by x - 1 and theta = 15 For factor x - 10, use field defined by x - 1 and theta = 10 For factor x - 5, use field defined by x - 1 and theta = 5 For factor x, use field defined by x - 1 and theta = 0 The 2-torsion group has dimension 4. Determining local images... p = 2 x = 1/4 --> new generator (0 0 0 0 0 1 0 0 0 0 0 1 0 0 0) x = 30 --> new generator (1 0 1 0 1 1 0 0 1 0 0 0 1 1 1) p = 3 x = 3 --> new generator (0 0 1 1 0 1 0 0 1 0) p = 5 p = infinity Computing class groups... Class group data of the fields: Field given by x - 20: [] Field given by x - 15: [] Field given by x - 10: [] Field given by x - 5: [] Field given by x: [] Dimension of Cl[2] = 0. Signatures: [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] Dimension of units mod squares = 5. Upper bound for Selmer group dimension: 13. ==> Upper bound for rank = 9. Computing unit groups... Class group and unit data of the fields: Field given by x - 20: Class group = [], units = [ 2 ] Field given by x - 15: Class group = [], units = [ 2 ] Field given by x - 10: Class group = [], units = [ 2 ] Field given by x - 5: Class group = [], units = [ 2 ] Field given by x: Class group = [], units = [ 2 ] Time for local computations: 531 ms. Time for class groups: 0 ms. Time for unit groups: 0 ms. Selmer group dimension = 5, Dimension of 2-torsion = 4, ==> Bound for the MW-rank = 1. Total time: 620 ms. Transforming presentation of S back to model C. 1 5 <[ 4*$.1^4 - 37*$.1^3 + 118*$.1^2 - 155*$.1 + 75, 3*$.1^4 - 35*$.1^3 + 136*$.1^2 - 194*$.1 + 75, 121/4*$.1^4 - 306*$.1^3 + 4331/4*$.1^2 - 1556*$.1 + 750, $.1^2 - 4*$.1 + 5, 35/8*$.1^4 - 177/4*$.1^3 + 1305/8*$.1^2 - 1033/4*$.1 + 150 ], [], []> {} Total time: 3.719 seconds, Total memory usage: 2.69MB ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Sat Jan 24 07:58:44 2004 Input: P := PolynomialRing(Rationals()); C := HyperellipticCurve(x*(x-1)*(x-2)*(x-3)*(x-4)); D := QuadraticTwist(C,21); J := Jacobian(D); SetVerbose("JacHypSelmer", 2); TwoSelmerGroupData(J : Bound := 300); Output: Magma V2.10-6 Sat Jan 24 2004 07:58:41 on modular [Seed = 3102381229] ------------------------------------- TwoSelmerGroupData of Jacobian of Hyperelliptic Curve defined by y^2 = 21*x^5 - 210*x^4 + 735*x^3 - 1050*x^2 + 504*x over Rational Field m= Mapping from: CrvHyp: C to CrvHyp: C1 with equations : 21*$.1 441*$.2 $.3 and inverse 1/21*$.1 1/441*$.2 $.3 Change curve into Hyperelliptic Curve defined by y^2 = x^5 - 210*x^4 + 15435*x^3 - 463050*x^2 + 4667544*x over Rational Field Bad primes = [ 2, 3, 7 ] f factors as (x - 84) (x - 63) (x - 42) (x - 21) (x). For factor x - 84, use field defined by x - 1 and theta = 84 For factor x - 63, use field defined by x - 1 and theta = 63 For factor x - 42, use field defined by x - 1 and theta = 42 For factor x - 21, use field defined by x - 1 and theta = 21 For factor x, use field defined by x - 1 and theta = 0 The 2-torsion group has dimension 4. Determining local images... p = 2 x = 1/4 --> new generator (0 0 0 0 0 1 0 0 0 0 0 1 0 0 0) x = 30 --> new generator (1 0 1 0 1 1 0 0 1 0 0 0 1 1 1) p = 3 p = 7 p = infinity Computing class groups... Class group data of the fields: Field given by x - 84: [] Field given by x - 63: [] Field given by x - 42: [] Field given by x - 21: [] Field given by x: [] Dimension of Cl[2] = 0. Signatures: [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] Dimension of units mod squares = 5. Upper bound for Selmer group dimension: 15. ==> Upper bound for rank = 11. Computing unit groups... Class group and unit data of the fields: Field given by x - 84: Class group = [], units = [ 2 ] Field given by x - 63: Class group = [], units = [ 2 ] Field given by x - 42: Class group = [], units = [ 2 ] Field given by x - 21: Class group = [], units = [ 2 ] Field given by x: Class group = [], units = [ 2 ] Time for local computations: 540 ms. Time for class groups: 0 ms. Time for unit groups: 0 ms. Selmer group dimension = 4, Dimension of 2-torsion = 4, ==> Bound for the MW-rank = 0. Total time: 659 ms. Transforming presentation of S back to model C. 0 4 <[ 373/8*$.1^4 - 5357/12*$.1^3 + 11775/8*$.1^2 - 23413/12*$.1 + 882, 6*$.1^4 - 187/3*$.1^3 + 225*$.1^2 - 968/3*$.1 + 147, 18595/12*$.1^4 - 30971/2*$.1^3 + 649745/12*$.1^2 - 154493/2*$.1 + 37044, 61/24*$.1^4 - 117/4*$.1^3 + 2879/24*$.1^2 - 821/4*$.1 + 126 ], [], []> {} Total time: 3.779 seconds, Total memory usage: 2.69MB ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Sat Jan 24 09:25:59 2004 Input: P := PolynomialRing(Rationals()); C := HyperellipticCurve(x*(x-1)*(x-2)*(x-3)*(x-4)); D := QuadraticTwist(C,1); J := Jacobian(D); SetVerbose("JacHypSelmer", 2); TwoSelmerGroupData(J : Bound := 300); Output: Magma V2.10-6 Sat Jan 24 2004 09:25:55 on modular [Seed = 1914745364] ------------------------------------- TwoSelmerGroupData of Jacobian of Hyperelliptic Curve defined by y^2 = x^5 - 10*x^4 + 35*x^3 - 50*x^2 + 24*x over Rational Field m= Mapping from: CrvHyp: C to CrvHyp: C1 with equations : $.1 $.2 $.3 and inverse $.1 $.2 $.3 Bad primes = [ 2, 3 ] f factors as (x - 4) (x - 3) (x - 2) (x - 1) (x). For factor x - 4, use field defined by x - 1 and theta = 4 For factor x - 3, use field defined by x - 1 and theta = 3 For factor x - 2, use field defined by x - 1 and theta = 2 For factor x - 1, use field defined by x - 1 and theta = 1 For factor x, use field defined by x - 1 and theta = 0 The 2-torsion group has dimension 4. Determining local images... p = 2 x = 1/4 --> new generator (0 0 0 0 0 1 0 0 0 0 0 1 0 0 0) x = 22 --> new generator (1 0 0 0 1 0 0 0 1 0 0 1 1 1 0) p = 3 x = 7 --> new generator (1 0 0 0 0 1 1 1 0 0) p = infinity Computing class groups... Class group data of the fields: Field given by x - 4: [] Field given by x - 3: [] Field given by x - 2: [] Field given by x - 1: [] Field given by x: [] Dimension of Cl[2] = 0. Signatures: [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] Dimension of units mod squares = 5. Upper bound for Selmer group dimension: 9. ==> Upper bound for rank = 5. Computing unit groups... Class group and unit data of the fields: Field given by x - 4: Class group = [], units = [ 2 ] Field given by x - 3: Class group = [], units = [ 2 ] Field given by x - 2: Class group = [], units = [ 2 ] Field given by x - 1: Class group = [], units = [ 2 ] Field given by x: Class group = [], units = [ 2 ] Time for local computations: 520 ms. Time for class groups: 0 ms. Time for unit groups: 0 ms. Selmer group dimension = 4, Dimension of 2-torsion = 4, ==> Bound for the MW-rank = 0. Total time: 569 ms. 0 4 <[ 1/8*$.1^4 - 3/4*$.1^3 + 3/8*$.1^2 + 5/4*$.1 + 2, -$.1^3 + 7*$.1^2 - 12*$.1 + 3, 1/4*$.1^4 - 3/2*$.1^3 + 11/4*$.1^2 - 5/2*$.1 + 4, -9/8*$.1^4 + 35/4*$.1^3 - 163/8*$.1^2 + 51/4*$.1 + 6 ], [], []> {} Total time: 3.629 seconds, Total memory usage: 2.69MB ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Sat Jan 24 09:27:14 2004 Input: P := PolynomialRing(Rationals()); C := HyperellipticCurve(x*(x-1)*(x-2)*(x-3)*(x-4)); D := QuadraticTwist(C,2); J := Jacobian(D); SetVerbose("JacHypSelmer", 2); TwoSelmerGroupData(J : Bound := 300); Output: Magma V2.10-6 Sat Jan 24 2004 09:27:09 on modular [Seed = 1698145741] ------------------------------------- TwoSelmerGroupData of Jacobian of Hyperelliptic Curve defined by y^2 = 2*x^5 - 20*x^4 + 70*x^3 - 100*x^2 + 48*x over Rational Field m= Mapping from: CrvHyp: C to CrvHyp: C1 with equations : 2*$.1 4*$.2 $.3 and inverse 1/2*$.1 1/4*$.2 $.3 Change curve into Hyperelliptic Curve defined by y^2 = x^5 - 20*x^4 + 140*x^3 - 400*x^2 + 384*x over Rational Field Bad primes = [ 2, 3 ] f factors as (x - 8) (x - 6) (x - 4) (x - 2) (x). For factor x - 8, use field defined by x - 1 and theta = 8 For factor x - 6, use field defined by x - 1 and theta = 6 For factor x - 4, use field defined by x - 1 and theta = 4 For factor x - 2, use field defined by x - 1 and theta = 2 For factor x, use field defined by x - 1 and theta = 0 The 2-torsion group has dimension 4. Determining local images... p = 2 x = 1 --> new generator (0 0 0 0 1 0 0 0 1 0 1 1 0 0 0) x = 26 --> new generator (1 0 0 0 0 1 1 1 0 1 1 0 1 0 1) p = 3 x = 3 --> new generator (0 0 1 1 0 1 0 0 1 0) p = infinity Computing class groups... Class group data of the fields: Field given by x - 8: [] Field given by x - 6: [] Field given by x - 4: [] Field given by x - 2: [] Field given by x: [] Dimension of Cl[2] = 0. Signatures: [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] Dimension of units mod squares = 5. Upper bound for Selmer group dimension: 9. ==> Upper bound for rank = 5. Computing unit groups... Class group and unit data of the fields: Field given by x - 8: Class group = [], units = [ 2 ] Field given by x - 6: Class group = [], units = [ 2 ] Field given by x - 4: Class group = [], units = [ 2 ] Field given by x - 2: Class group = [], units = [ 2 ] Field given by x: Class group = [], units = [ 2 ] Time for local computations: 1080 ms. Time for class groups: 0 ms. Time for unit groups: 9 ms. Selmer group dimension = 4, Dimension of 2-torsion = 4, ==> Bound for the MW-rank = 0. Total time: 1149 ms. Transforming presentation of S back to model C. 0 4 <[ $.1^3 - 13/2*$.1^2 + 17/2*$.1 + 3, -1/4*$.1^4 + 3/2*$.1^3 - 5/4*$.1^2 - 3*$.1 + 1, -1/2*$.1^3 + 7/2*$.1^2 - 7*$.1 + 6, -9/4*$.1^4 + 19*$.1^3 - 203/4*$.1^2 + 43*$.1 + 3 ], [], []> {} Total time: 4.299 seconds, Total memory usage: 2.69MB ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Sat Jan 24 09:28:51 2004 Input: P := PolynomialRing(Rationals()); C := HyperellipticCurve(x*(x-1)*(x-2)*(x-3)*(x-4)); D := QuadraticTwist(C,3); J := Jacobian(D); SetVerbose("JacHypSelmer", 2); TwoSelmerGroupData(J : Bound := 300); Output: Magma V2.10-6 Sat Jan 24 2004 09:28:47 on modular [Seed = 1866313317] ------------------------------------- TwoSelmerGroupData of Jacobian of Hyperelliptic Curve defined by y^2 = 3*x^5 - 30*x^4 + 105*x^3 - 150*x^2 + 72*x over Rational Field m= Mapping from: CrvHyp: C to CrvHyp: C1 with equations : 3*$.1 9*$.2 $.3 and inverse 1/3*$.1 1/9*$.2 $.3 Change curve into Hyperelliptic Curve defined by y^2 = x^5 - 30*x^4 + 315*x^3 - 1350*x^2 + 1944*x over Rational Field Bad primes = [ 2, 3 ] f factors as (x - 12) (x - 9) (x - 6) (x - 3) (x). For factor x - 12, use field defined by x - 1 and theta = 12 For factor x - 9, use field defined by x - 1 and theta = 9 For factor x - 6, use field defined by x - 1 and theta = 6 For factor x - 3, use field defined by x - 1 and theta = 3 For factor x, use field defined by x - 1 and theta = 0 The 2-torsion group has dimension 4. Determining local images... p = 2 x = 1/4 --> new generator (0 0 0 0 0 1 0 0 0 0 0 1 0 0 0) x = 26 --> new generator (1 1 1 0 0 0 0 0 1 0 1 1 1 0 1) p = 3 p = infinity Computing class groups... Class group data of the fields: Field given by x - 12: [] Field given by x - 9: [] Field given by x - 6: [] Field given by x - 3: [] Field given by x: [] Dimension of Cl[2] = 0. Signatures: [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] Dimension of units mod squares = 5. Upper bound for Selmer group dimension: 11. ==> Upper bound for rank = 7. Computing unit groups... Class group and unit data of the fields: Field given by x - 12: Class group = [], units = [ 2 ] Field given by x - 9: Class group = [], units = [ 2 ] Field given by x - 6: Class group = [], units = [ 2 ] Field given by x - 3: Class group = [], units = [ 2 ] Field given by x: Class group = [], units = [ 2 ] Time for local computations: 500 ms. Time for class groups: 0 ms. Time for unit groups: 0 ms. Selmer group dimension = 4, Dimension of 2-torsion = 4, ==> Bound for the MW-rank = 0. Total time: 580 ms. Transforming presentation of S back to model C. 0 4 <[ 15/8*$.1^4 - 191/12*$.1^3 + 349/8*$.1^2 - 535/12*$.1 + 18, -1/3*$.1^3 + 3*$.1^2 - 20/3*$.1 + 3, 67/12*$.1^4 - 107/2*$.1^3 + 2129/12*$.1^2 - 473/2*$.1 + 108, 1/24*$.1^4 - 9/4*$.1^3 + 347/24*$.1^2 - 113/4*$.1 + 18 ], [], []> {} Total time: 3.689 seconds, Total memory usage: 2.69MB ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Sat Jan 24 09:29:27 2004 Input: P := PolynomialRing(Rationals()); C := HyperellipticCurve(x*(x-1)*(x-2)*(x-3)*(x-4)); D := QuadraticTwist(C,4); J := Jacobian(D); SetVerbose("JacHypSelmer", 2); TwoSelmerGroupData(J : Bound := 300); Output: Magma V2.10-6 Sat Jan 24 2004 09:29:23 on modular [Seed = 2529449920] ------------------------------------- TwoSelmerGroupData of Jacobian of Hyperelliptic Curve defined by y^2 = 4*x^5 - 40*x^4 + 140*x^3 - 200*x^2 + 96*x over Rational Field m= Mapping from: CrvHyp: C to CrvHyp: C1 with equations : $.1 1/2*$.2 $.3 and inverse $.1 2*$.2 $.3 Change curve into Hyperelliptic Curve defined by y^2 = x^5 - 10*x^4 + 35*x^3 - 50*x^2 + 24*x over Rational Field Bad primes = [ 2, 3 ] f factors as (x - 4) (x - 3) (x - 2) (x - 1) (x). For factor x - 4, use field defined by x - 1 and theta = 4 For factor x - 3, use field defined by x - 1 and theta = 3 For factor x - 2, use field defined by x - 1 and theta = 2 For factor x - 1, use field defined by x - 1 and theta = 1 For factor x, use field defined by x - 1 and theta = 0 The 2-torsion group has dimension 4. Determining local images... p = 2 x = 1/4 --> new generator (0 0 0 0 0 1 0 0 0 0 0 1 0 0 0) x = 22 --> new generator (1 0 0 0 1 0 0 0 1 0 0 1 1 1 0) p = 3 x = 7 --> new generator (1 0 0 0 0 1 1 1 0 0) p = infinity Computing class groups... Class group data of the fields: Field given by x - 4: [] Field given by x - 3: [] Field given by x - 2: [] Field given by x - 1: [] Field given by x: [] Dimension of Cl[2] = 0. Signatures: [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] Dimension of units mod squares = 5. Upper bound for Selmer group dimension: 9. ==> Upper bound for rank = 5. Computing unit groups... Class group and unit data of the fields: Field given by x - 4: Class group = [], units = [ 2 ] Field given by x - 3: Class group = [], units = [ 2 ] Field given by x - 2: Class group = [], units = [ 2 ] Field given by x - 1: Class group = [], units = [ 2 ] Field given by x: Class group = [], units = [ 2 ] Time for local computations: 520 ms. Time for class groups: 0 ms. Time for unit groups: 0 ms. Selmer group dimension = 4, Dimension of 2-torsion = 4, ==> Bound for the MW-rank = 0. Total time: 580 ms. Transforming presentation of S back to model C. 0 4 <[ 1/8*$.1^4 - 3/4*$.1^3 + 3/8*$.1^2 + 5/4*$.1 + 2, -$.1^3 + 7*$.1^2 - 12*$.1 + 3, 1/4*$.1^4 - 3/2*$.1^3 + 11/4*$.1^2 - 5/2*$.1 + 4, -9/8*$.1^4 + 35/4*$.1^3 - 163/8*$.1^2 + 51/4*$.1 + 6 ], [], []> {} Total time: 3.669 seconds, Total memory usage: 2.69MB ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Sat Jan 24 09:29:43 2004 Input: P := PolynomialRing(Rationals()); C := HyperellipticCurve(x*(x-1)*(x-2)*(x-3)*(x-4)); D := QuadraticTwist(C,5); J := Jacobian(D); SetVerbose("JacHypSelmer", 2); TwoSelmerGroupData(J : Bound := 300); Output: Magma V2.10-6 Sat Jan 24 2004 09:29:39 on modular [Seed = 2580240607] ------------------------------------- TwoSelmerGroupData of Jacobian of Hyperelliptic Curve defined by y^2 = 5*x^5 - 50*x^4 + 175*x^3 - 250*x^2 + 120*x over Rational Field m= Mapping from: CrvHyp: C to CrvHyp: C1 with equations : 5*$.1 25*$.2 $.3 and inverse 1/5*$.1 1/25*$.2 $.3 Change curve into Hyperelliptic Curve defined by y^2 = x^5 - 50*x^4 + 875*x^3 - 6250*x^2 + 15000*x over Rational Field Bad primes = [ 2, 3, 5 ] f factors as (x - 20) (x - 15) (x - 10) (x - 5) (x). For factor x - 20, use field defined by x - 1 and theta = 20 For factor x - 15, use field defined by x - 1 and theta = 15 For factor x - 10, use field defined by x - 1 and theta = 10 For factor x - 5, use field defined by x - 1 and theta = 5 For factor x, use field defined by x - 1 and theta = 0 The 2-torsion group has dimension 4. Determining local images... p = 2 x = 1/4 --> new generator (0 0 0 0 0 1 0 0 0 0 0 1 0 0 0) x = 30 --> new generator (1 0 1 0 1 1 0 0 1 0 0 0 1 1 1) p = 3 x = 3 --> new generator (0 0 1 1 0 1 0 0 1 0) p = 5 p = infinity Computing class groups... Class group data of the fields: Field given by x - 20: [] Field given by x - 15: [] Field given by x - 10: [] Field given by x - 5: [] Field given by x: [] Dimension of Cl[2] = 0. Signatures: [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] Dimension of units mod squares = 5. Upper bound for Selmer group dimension: 13. ==> Upper bound for rank = 9. Computing unit groups... Class group and unit data of the fields: Field given by x - 20: Class group = [], units = [ 2 ] Field given by x - 15: Class group = [], units = [ 2 ] Field given by x - 10: Class group = [], units = [ 2 ] Field given by x - 5: Class group = [], units = [ 2 ] Field given by x: Class group = [], units = [ 2 ] Time for local computations: 540 ms. Time for class groups: 0 ms. Time for unit groups: 0 ms. Selmer group dimension = 5, Dimension of 2-torsion = 4, ==> Bound for the MW-rank = 1. Total time: 640 ms. Transforming presentation of S back to model C. 1 5 <[ 4*$.1^4 - 37*$.1^3 + 118*$.1^2 - 155*$.1 + 75, 3*$.1^4 - 35*$.1^3 + 136*$.1^2 - 194*$.1 + 75, 121/4*$.1^4 - 306*$.1^3 + 4331/4*$.1^2 - 1556*$.1 + 750, $.1^2 - 4*$.1 + 5, 35/8*$.1^4 - 177/4*$.1^3 + 1305/8*$.1^2 - 1033/4*$.1 + 150 ], [], []> {} Total time: 3.729 seconds, Total memory usage: 2.69MB ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Sat Jan 24 09:29:59 2004 Input: P := PolynomialRing(Rationals()); C := HyperellipticCurve(x*(x-1)*(x-2)*(x-3)*(x-4)); D := QuadraticTwist(C,6); J := Jacobian(D); SetVerbose("JacHypSelmer", 2); TwoSelmerGroupData(J : Bound := 300); Output: Magma V2.10-6 Sat Jan 24 2004 09:29:55 on modular [Seed = 2161263094] ------------------------------------- TwoSelmerGroupData of Jacobian of Hyperelliptic Curve defined by y^2 = 6*x^5 - 60*x^4 + 210*x^3 - 300*x^2 + 144*x over Rational Field m= Mapping from: CrvHyp: C to CrvHyp: C1 with equations : 6*$.1 36*$.2 $.3 and inverse 1/6*$.1 1/36*$.2 $.3 Change curve into Hyperelliptic Curve defined by y^2 = x^5 - 60*x^4 + 1260*x^3 - 10800*x^2 + 31104*x over Rational Field Bad primes = [ 2, 3 ] f factors as (x - 24) (x - 18) (x - 12) (x - 6) (x). For factor x - 24, use field defined by x - 1 and theta = 24 For factor x - 18, use field defined by x - 1 and theta = 18 For factor x - 12, use field defined by x - 1 and theta = 12 For factor x - 6, use field defined by x - 1 and theta = 6 For factor x, use field defined by x - 1 and theta = 0 The 2-torsion group has dimension 4. Determining local images... p = 2 x = 1 --> new generator (0 0 0 0 1 1 0 0 1 0 1 0 0 0 0) x = 42 --> new generator (1 0 0 1 1 0 1 1 1 0 0 0 1 0 1) p = 3 p = infinity Computing class groups... Class group data of the fields: Field given by x - 24: [] Field given by x - 18: [] Field given by x - 12: [] Field given by x - 6: [] Field given by x: [] Dimension of Cl[2] = 0. Signatures: [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] Dimension of units mod squares = 5. Upper bound for Selmer group dimension: 11. ==> Upper bound for rank = 7. Computing unit groups... Class group and unit data of the fields: Field given by x - 24: Class group = [], units = [ 2 ] Field given by x - 18: Class group = [], units = [ 2 ] Field given by x - 12: Class group = [], units = [ 2 ] Field given by x - 6: Class group = [], units = [ 2 ] Field given by x: Class group = [], units = [ 2 ] Time for local computations: 1080 ms. Time for class groups: 0 ms. Time for unit groups: 0 ms. Selmer group dimension = 4, Dimension of 2-torsion = 4, ==> Bound for the MW-rank = 0. Total time: 1149 ms. Transforming presentation of S back to model C. 0 4 <[ -1/4*$.1^4 + 17/6*$.1^3 - 41/4*$.1^2 + 32/3*$.1 + 3, -1/2*$.1^4 + 3*$.1^3 - 3*$.1^2 - 9/2*$.1 + 3, 4/3*$.1^4 - 65/6*$.1^3 + 163/6*$.1^2 - 65/3*$.1 + 6, -2/3*$.1^4 + 9/2*$.1^3 - 22/3*$.1^2 - 3/2*$.1 + 9 ], [], []> {} Total time: 4.299 seconds, Total memory usage: 2.69MB ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Sat Jan 24 09:30:17 2004 Input: P := PolynomialRing(Rationals()); C := HyperellipticCurve(x*(x-1)*(x-2)*(x-3)*(x-4)); D := QuadraticTwist(C,6); J := Jacobian(D); SetVerbose("JacHypSelmer", 2); TwoSelmerGroupData(J : Bound := 300); Output: Magma V2.10-6 Sat Jan 24 2004 09:30:11 on modular [Seed = 2967630294] ------------------------------------- TwoSelmerGroupData of Jacobian of Hyperelliptic Curve defined by y^2 = 6*x^5 - 60*x^4 + 210*x^3 - 300*x^2 + 144*x over Rational Field m= Mapping from: CrvHyp: C to CrvHyp: C1 with equations : 6*$.1 36*$.2 $.3 and inverse 1/6*$.1 1/36*$.2 $.3 Change curve into Hyperelliptic Curve defined by y^2 = x^5 - 60*x^4 + 1260*x^3 - 10800*x^2 + 31104*x over Rational Field Bad primes = [ 2, 3 ] f factors as (x - 24) (x - 18) (x - 12) (x - 6) (x). For factor x - 24, use field defined by x - 1 and theta = 24 For factor x - 18, use field defined by x - 1 and theta = 18 For factor x - 12, use field defined by x - 1 and theta = 12 For factor x - 6, use field defined by x - 1 and theta = 6 For factor x, use field defined by x - 1 and theta = 0 The 2-torsion group has dimension 4. Determining local images... p = 2 x = 1 --> new generator (0 0 0 0 1 1 0 0 1 0 1 0 0 0 0) x = 42 --> new generator (1 0 0 1 1 0 1 1 1 0 0 0 1 0 1) p = 3 p = infinity Computing class groups... Class group data of the fields: Field given by x - 24: [] Field given by x - 18: [] Field given by x - 12: [] Field given by x - 6: [] Field given by x: [] Dimension of Cl[2] = 0. Signatures: [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] Dimension of units mod squares = 5. Upper bound for Selmer group dimension: 11. ==> Upper bound for rank = 7. Computing unit groups... Class group and unit data of the fields: Field given by x - 24: Class group = [], units = [ 2 ] Field given by x - 18: Class group = [], units = [ 2 ] Field given by x - 12: Class group = [], units = [ 2 ] Field given by x - 6: Class group = [], units = [ 2 ] Field given by x: Class group = [], units = [ 2 ] Time for local computations: 1100 ms. Time for class groups: 0 ms. Time for unit groups: 0 ms. Selmer group dimension = 4, Dimension of 2-torsion = 4, ==> Bound for the MW-rank = 0. Total time: 1179 ms. Transforming presentation of S back to model C. 0 4 <[ -1/4*$.1^4 + 17/6*$.1^3 - 41/4*$.1^2 + 32/3*$.1 + 3, -1/2*$.1^4 + 3*$.1^3 - 3*$.1^2 - 9/2*$.1 + 3, 4/3*$.1^4 - 65/6*$.1^3 + 163/6*$.1^2 - 65/3*$.1 + 6, -2/3*$.1^4 + 9/2*$.1^3 - 22/3*$.1^2 - 3/2*$.1 + 9 ], [], []> {} Total time: 4.389 seconds, Total memory usage: 2.69MB ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Sat Jan 24 09:30:26 2004 Input: P := PolynomialRing(Rationals()); C := HyperellipticCurve(x*(x-1)*(x-2)*(x-3)*(x-4)); D := QuadraticTwist(C,5); J := Jacobian(D); SetVerbose("JacHypSelmer", 2); TwoSelmerGroupData(J : Bound := 300); Output: Magma V2.10-6 Sat Jan 24 2004 09:30:23 on modular [Seed = 3152640721] ------------------------------------- TwoSelmerGroupData of Jacobian of Hyperelliptic Curve defined by y^2 = 5*x^5 - 50*x^4 + 175*x^3 - 250*x^2 + 120*x over Rational Field m= Mapping from: CrvHyp: C to CrvHyp: C1 with equations : 5*$.1 25*$.2 $.3 and inverse 1/5*$.1 1/25*$.2 $.3 Change curve into Hyperelliptic Curve defined by y^2 = x^5 - 50*x^4 + 875*x^3 - 6250*x^2 + 15000*x over Rational Field Bad primes = [ 2, 3, 5 ] f factors as (x - 20) (x - 15) (x - 10) (x - 5) (x). For factor x - 20, use field defined by x - 1 and theta = 20 For factor x - 15, use field defined by x - 1 and theta = 15 For factor x - 10, use field defined by x - 1 and theta = 10 For factor x - 5, use field defined by x - 1 and theta = 5 For factor x, use field defined by x - 1 and theta = 0 The 2-torsion group has dimension 4. Determining local images... p = 2 x = 1/4 --> new generator (0 0 0 0 0 1 0 0 0 0 0 1 0 0 0) x = 30 --> new generator (1 0 1 0 1 1 0 0 1 0 0 0 1 1 1) p = 3 x = 3 --> new generator (0 0 1 1 0 1 0 0 1 0) p = 5 p = infinity Computing class groups... Class group data of the fields: Field given by x - 20: [] Field given by x - 15: [] Field given by x - 10: [] Field given by x - 5: [] Field given by x: [] Dimension of Cl[2] = 0. Signatures: [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] Dimension of units mod squares = 5. Upper bound for Selmer group dimension: 13. ==> Upper bound for rank = 9. Computing unit groups... Class group and unit data of the fields: Field given by x - 20: Class group = [], units = [ 2 ] Field given by x - 15: Class group = [], units = [ 2 ] Field given by x - 10: Class group = [], units = [ 2 ] Field given by x - 5: Class group = [], units = [ 2 ] Field given by x: Class group = [], units = [ 2 ] Time for local computations: 540 ms. Time for class groups: 0 ms. Time for unit groups: 0 ms. Selmer group dimension = 5, Dimension of 2-torsion = 4, ==> Bound for the MW-rank = 1. Total time: 630 ms. Transforming presentation of S back to model C. 1 5 <[ 4*$.1^4 - 37*$.1^3 + 118*$.1^2 - 155*$.1 + 75, 3*$.1^4 - 35*$.1^3 + 136*$.1^2 - 194*$.1 + 75, 121/4*$.1^4 - 306*$.1^3 + 4331/4*$.1^2 - 1556*$.1 + 750, $.1^2 - 4*$.1 + 5, 35/8*$.1^4 - 177/4*$.1^3 + 1305/8*$.1^2 - 1033/4*$.1 + 150 ], [], []> {} Total time: 3.759 seconds, Total memory usage: 2.69MB ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Sat Jan 24 09:31:55 2004 Input: P := PolynomialRing(Rationals()); C := HyperellipticCurve(x*(x-1)*(x-2)*(x-3)*(x-4)); D := QuadraticTwist(C,6); J := Jacobian(D); SetVerbose("JacHypSelmer", 2); TwoSelmerGroupData(J : Bound := 300); Output: Magma V2.10-6 Sat Jan 24 2004 09:31:51 on modular [Seed = 2919197807] ------------------------------------- TwoSelmerGroupData of Jacobian of Hyperelliptic Curve defined by y^2 = 6*x^5 - 60*x^4 + 210*x^3 - 300*x^2 + 144*x over Rational Field m= Mapping from: CrvHyp: C to CrvHyp: C1 with equations : 6*$.1 36*$.2 $.3 and inverse 1/6*$.1 1/36*$.2 $.3 Change curve into Hyperelliptic Curve defined by y^2 = x^5 - 60*x^4 + 1260*x^3 - 10800*x^2 + 31104*x over Rational Field Bad primes = [ 2, 3 ] f factors as (x - 24) (x - 18) (x - 12) (x - 6) (x). For factor x - 24, use field defined by x - 1 and theta = 24 For factor x - 18, use field defined by x - 1 and theta = 18 For factor x - 12, use field defined by x - 1 and theta = 12 For factor x - 6, use field defined by x - 1 and theta = 6 For factor x, use field defined by x - 1 and theta = 0 The 2-torsion group has dimension 4. Determining local images... p = 2 x = 1 --> new generator (0 0 0 0 1 1 0 0 1 0 1 0 0 0 0) x = 42 --> new generator (1 0 0 1 1 0 1 1 1 0 0 0 1 0 1) p = 3 p = infinity Computing class groups... Class group data of the fields: Field given by x - 24: [] Field given by x - 18: [] Field given by x - 12: [] Field given by x - 6: [] Field given by x: [] Dimension of Cl[2] = 0. Signatures: [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] Dimension of units mod squares = 5. Upper bound for Selmer group dimension: 11. ==> Upper bound for rank = 7. Computing unit groups... Class group and unit data of the fields: Field given by x - 24: Class group = [], units = [ 2 ] Field given by x - 18: Class group = [], units = [ 2 ] Field given by x - 12: Class group = [], units = [ 2 ] Field given by x - 6: Class group = [], units = [ 2 ] Field given by x: Class group = [], units = [ 2 ] Time for local computations: 1099 ms. Time for class groups: 0 ms. Time for unit groups: 0 ms. Selmer group dimension = 4, Dimension of 2-torsion = 4, ==> Bound for the MW-rank = 0. Total time: 1180 ms. Transforming presentation of S back to model C. 0 4 <[ -1/4*$.1^4 + 17/6*$.1^3 - 41/4*$.1^2 + 32/3*$.1 + 3, -1/2*$.1^4 + 3*$.1^3 - 3*$.1^2 - 9/2*$.1 + 3, 4/3*$.1^4 - 65/6*$.1^3 + 163/6*$.1^2 - 65/3*$.1 + 6, -2/3*$.1^4 + 9/2*$.1^3 - 22/3*$.1^2 - 3/2*$.1 + 9 ], [], []> {} Total time: 4.329 seconds, Total memory usage: 2.69MB ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Sat Jan 24 09:32:16 2004 Input: P := PolynomialRing(Rationals()); C := HyperellipticCurve(x*(x-1)*(x-2)*(x-3)*(x-4)); D := QuadraticTwist(C,7); J := Jacobian(D); SetVerbose("JacHypSelmer", 2); TwoSelmerGroupData(J : Bound := 300); Output: Magma V2.10-6 Sat Jan 24 2004 09:32:12 on modular [Seed = 3565557037] ------------------------------------- TwoSelmerGroupData of Jacobian of Hyperelliptic Curve defined by y^2 = 7*x^5 - 70*x^4 + 245*x^3 - 350*x^2 + 168*x over Rational Field m= Mapping from: CrvHyp: C to CrvHyp: C1 with equations : 7*$.1 49*$.2 $.3 and inverse 1/7*$.1 1/49*$.2 $.3 Change curve into Hyperelliptic Curve defined by y^2 = x^5 - 70*x^4 + 1715*x^3 - 17150*x^2 + 57624*x over Rational Field Bad primes = [ 2, 3, 7 ] f factors as (x - 28) (x - 21) (x - 14) (x - 7) (x). For factor x - 28, use field defined by x - 1 and theta = 28 For factor x - 21, use field defined by x - 1 and theta = 21 For factor x - 14, use field defined by x - 1 and theta = 14 For factor x - 7, use field defined by x - 1 and theta = 7 For factor x, use field defined by x - 1 and theta = 0 The 2-torsion group has dimension 4. Determining local images... p = 2 x = 1/4 --> new generator (0 0 0 0 0 1 0 0 0 0 0 1 0 0 0) x = 2 --> new generator (1 1 0 0 0 1 0 0 1 0 1 0 1 0 0) p = 3 x = 4 --> new generator (1 0 0 0 0 1 1 1 0 0) p = 7 p = infinity Computing class groups... Class group data of the fields: Field given by x - 28: [] Field given by x - 21: [] Field given by x - 14: [] Field given by x - 7: [] Field given by x: [] Dimension of Cl[2] = 0. Signatures: [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] Dimension of units mod squares = 5. Upper bound for Selmer group dimension: 13. ==> Upper bound for rank = 9. Computing unit groups... Class group and unit data of the fields: Field given by x - 28: Class group = [], units = [ 2 ] Field given by x - 21: Class group = [], units = [ 2 ] Field given by x - 14: Class group = [], units = [ 2 ] Field given by x - 7: Class group = [], units = [ 2 ] Field given by x: Class group = [], units = [ 2 ] Time for local computations: 511 ms. Time for class groups: 0 ms. Time for unit groups: 0 ms. Selmer group dimension = 4, Dimension of 2-torsion = 4, ==> Bound for the MW-rank = 0. Total time: 610 ms. Transforming presentation of S back to model C. 0 4 <[ 51/8*$.1^4 - 241/4*$.1^3 + 1513/8*$.1^2 - 921/4*$.1 + 98, 6*$.1^4 - 67*$.1^3 + 253*$.1^2 - 360*$.1 + 147, 225/4*$.1^4 - 1123/2*$.1^3 + 7851/4*$.1^2 - 5617/2*$.1 + 1372, -45/8*$.1^4 + 191/4*$.1^3 - 991/8*$.1^2 + 327/4*$.1 + 42 ], [], []> {} Total time: 3.779 seconds, Total memory usage: 2.69MB ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Sat Jan 24 09:32:36 2004 Input: P := PolynomialRing(Rationals()); C := HyperellipticCurve(x*(x-1)*(x-2)*(x-3)*(x-4)); D := QuadraticTwist(C,8); J := Jacobian(D); SetVerbose("JacHypSelmer", 2); TwoSelmerGroupData(J : Bound := 300); Output: Magma V2.10-6 Sat Jan 24 2004 09:32:31 on modular [Seed = 3750567477] ------------------------------------- TwoSelmerGroupData of Jacobian of Hyperelliptic Curve defined by y^2 = 8*x^5 - 80*x^4 + 280*x^3 - 400*x^2 + 192*x over Rational Field m= Mapping from: CrvHyp: C to CrvHyp: C1 with equations : 2*$.1 2*$.2 $.3 and inverse 1/2*$.1 1/2*$.2 $.3 Change curve into Hyperelliptic Curve defined by y^2 = x^5 - 20*x^4 + 140*x^3 - 400*x^2 + 384*x over Rational Field Bad primes = [ 2, 3 ] f factors as (x - 8) (x - 6) (x - 4) (x - 2) (x). For factor x - 8, use field defined by x - 1 and theta = 8 For factor x - 6, use field defined by x - 1 and theta = 6 For factor x - 4, use field defined by x - 1 and theta = 4 For factor x - 2, use field defined by x - 1 and theta = 2 For factor x, use field defined by x - 1 and theta = 0 The 2-torsion group has dimension 4. Determining local images... p = 2 x = 1 --> new generator (0 0 0 0 1 0 0 0 1 0 1 1 0 0 0) x = 26 --> new generator (1 0 0 0 0 1 1 1 0 1 1 0 1 0 1) p = 3 x = 3 --> new generator (0 0 1 1 0 1 0 0 1 0) p = infinity Computing class groups... Class group data of the fields: Field given by x - 8: [] Field given by x - 6: [] Field given by x - 4: [] Field given by x - 2: [] Field given by x: [] Dimension of Cl[2] = 0. Signatures: [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] Dimension of units mod squares = 5. Upper bound for Selmer group dimension: 9. ==> Upper bound for rank = 5. Computing unit groups... Class group and unit data of the fields: Field given by x - 8: Class group = [], units = [ 2 ] Field given by x - 6: Class group = [], units = [ 2 ] Field given by x - 4: Class group = [], units = [ 2 ] Field given by x - 2: Class group = [], units = [ 2 ] Field given by x: Class group = [], units = [ 2 ] Time for local computations: 1080 ms. Time for class groups: 0 ms. Time for unit groups: 0 ms. Selmer group dimension = 4, Dimension of 2-torsion = 4, ==> Bound for the MW-rank = 0. Total time: 1140 ms. Transforming presentation of S back to model C. 0 4 <[ $.1^3 - 13/2*$.1^2 + 17/2*$.1 + 3, -1/4*$.1^4 + 3/2*$.1^3 - 5/4*$.1^2 - 3*$.1 + 1, -1/2*$.1^3 + 7/2*$.1^2 - 7*$.1 + 6, -9/4*$.1^4 + 19*$.1^3 - 203/4*$.1^2 + 43*$.1 + 3 ], [], []> {} Total time: 4.329 seconds, Total memory usage: 2.69MB ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Sat Jan 24 09:32:51 2004 Input: P := PolynomialRing(Rationals()); C := HyperellipticCurve(x*(x-1)*(x-2)*(x-3)*(x-4)); D := QuadraticTwist(C,9); J := Jacobian(D); SetVerbose("JacHypSelmer", 2); TwoSelmerGroupData(J : Bound := 300); Output: Magma V2.10-6 Sat Jan 24 2004 09:32:47 on modular [Seed = 3331589340] ------------------------------------- TwoSelmerGroupData of Jacobian of Hyperelliptic Curve defined by y^2 = 9*x^5 - 90*x^4 + 315*x^3 - 450*x^2 + 216*x over Rational Field m= Mapping from: CrvHyp: C to CrvHyp: C1 with equations : $.1 1/3*$.2 $.3 and inverse $.1 3*$.2 $.3 Change curve into Hyperelliptic Curve defined by y^2 = x^5 - 10*x^4 + 35*x^3 - 50*x^2 + 24*x over Rational Field Bad primes = [ 2, 3 ] f factors as (x - 4) (x - 3) (x - 2) (x - 1) (x). For factor x - 4, use field defined by x - 1 and theta = 4 For factor x - 3, use field defined by x - 1 and theta = 3 For factor x - 2, use field defined by x - 1 and theta = 2 For factor x - 1, use field defined by x - 1 and theta = 1 For factor x, use field defined by x - 1 and theta = 0 The 2-torsion group has dimension 4. Determining local images... p = 2 x = 1/4 --> new generator (0 0 0 0 0 1 0 0 0 0 0 1 0 0 0) x = 22 --> new generator (1 0 0 0 1 0 0 0 1 0 0 1 1 1 0) p = 3 x = 7 --> new generator (1 0 0 0 0 1 1 1 0 0) p = infinity Computing class groups... Class group data of the fields: Field given by x - 4: [] Field given by x - 3: [] Field given by x - 2: [] Field given by x - 1: [] Field given by x: [] Dimension of Cl[2] = 0. Signatures: [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] Dimension of units mod squares = 5. Upper bound for Selmer group dimension: 9. ==> Upper bound for rank = 5. Computing unit groups... Class group and unit data of the fields: Field given by x - 4: Class group = [], units = [ 2 ] Field given by x - 3: Class group = [], units = [ 2 ] Field given by x - 2: Class group = [], units = [ 2 ] Field given by x - 1: Class group = [], units = [ 2 ] Field given by x: Class group = [], units = [ 2 ] Time for local computations: 520 ms. Time for class groups: 0 ms. Time for unit groups: 9 ms. Selmer group dimension = 4, Dimension of 2-torsion = 4, ==> Bound for the MW-rank = 0. Total time: 600 ms. Transforming presentation of S back to model C. 0 4 <[ 1/8*$.1^4 - 3/4*$.1^3 + 3/8*$.1^2 + 5/4*$.1 + 2, -$.1^3 + 7*$.1^2 - 12*$.1 + 3, 1/4*$.1^4 - 3/2*$.1^3 + 11/4*$.1^2 - 5/2*$.1 + 4, -9/8*$.1^4 + 35/4*$.1^3 - 163/8*$.1^2 + 51/4*$.1 + 6 ], [], []> {} Total time: 3.659 seconds, Total memory usage: 2.69MB ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Sat Jan 24 09:33:12 2004 Input: P := PolynomialRing(Rationals()); C := HyperellipticCurve(x*(x-1)*(x-2)*(x-3)*(x-4)); D := QuadraticTwist(C,10); J := Jacobian(D); SetVerbose("JacHypSelmer", 2); TwoSelmerGroupData(J : Bound := 300); Output: Magma V2.10-6 Sat Jan 24 2004 09:33:08 on modular [Seed = 3365538553] ------------------------------------- TwoSelmerGroupData of Jacobian of Hyperelliptic Curve defined by y^2 = 10*x^5 - 100*x^4 + 350*x^3 - 500*x^2 + 240*x over Rational Field m= Mapping from: CrvHyp: C to CrvHyp: C1 with equations : 10*$.1 100*$.2 $.3 and inverse 1/10*$.1 1/100*$.2 $.3 Change curve into Hyperelliptic Curve defined by y^2 = x^5 - 100*x^4 + 3500*x^3 - 50000*x^2 + 240000*x over Rational Field Bad primes = [ 2, 3, 5 ] f factors as (x - 40) (x - 30) (x - 20) (x - 10) (x). For factor x - 40, use field defined by x - 1 and theta = 40 For factor x - 30, use field defined by x - 1 and theta = 30 For factor x - 20, use field defined by x - 1 and theta = 20 For factor x - 10, use field defined by x - 1 and theta = 10 For factor x, use field defined by x - 1 and theta = 0 The 2-torsion group has dimension 4. Determining local images... p = 2 x = 1 --> new generator (0 0 0 0 1 0 0 0 1 0 1 1 0 0 0) x = 34 --> new generator (1 0 1 0 0 0 1 1 1 1 1 0 1 0 0) p = 3 x = 7 --> new generator (1 0 0 0 0 1 1 1 0 0) p = 5 p = infinity Computing class groups... Class group data of the fields: Field given by x - 40: [] Field given by x - 30: [] Field given by x - 20: [] Field given by x - 10: [] Field given by x: [] Dimension of Cl[2] = 0. Signatures: [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] Dimension of units mod squares = 5. Upper bound for Selmer group dimension: 13. ==> Upper bound for rank = 9. Computing unit groups... Class group and unit data of the fields: Field given by x - 40: Class group = [], units = [ 2 ] Field given by x - 30: Class group = [], units = [ 2 ] Field given by x - 20: Class group = [], units = [ 2 ] Field given by x - 10: Class group = [], units = [ 2 ] Field given by x: Class group = [], units = [ 2 ] Time for local computations: 1020 ms. Time for class groups: 0 ms. Time for unit groups: 0 ms. Selmer group dimension = 5, Dimension of 2-torsion = 4, ==> Bound for the MW-rank = 1. Total time: 1120 ms. Transforming presentation of S back to model C. 1 5 <[ 25*$.1^4 - 250*$.1^3 + 875*$.1^2 - 1260*$.1 + 625, 51/4*$.1^4 - 273/2*$.1^3 + 2041/4*$.1^2 - 1533/2*$.1 + 375, 3/4*$.1^4 - 10*$.1^3 + 181/4*$.1^2 - 81*$.1 + 50, 1/4*$.1^4 - 3/2*$.1^3 + 7/4*$.1^2 + 1/2*$.1 + 5, 7/2*$.1^4 - 33*$.1^3 + 107*$.1^2 - 285/2*$.1 + 75 ], [], []> {} Total time: 4.219 seconds, Total memory usage: 2.69MB ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Sat Jan 24 09:33:27 2004 Input: P := PolynomialRing(Rationals()); C := HyperellipticCurve(x*(x-1)*(x-2)*(x-3)*(x-4)); D := QuadraticTwist(C,11); J := Jacobian(D); SetVerbose("JacHypSelmer", 2); TwoSelmerGroupData(J : Bound := 300); Output: Magma V2.10-6 Sat Jan 24 2004 09:33:23 on modular [Seed = 4070584532] ------------------------------------- TwoSelmerGroupData of Jacobian of Hyperelliptic Curve defined by y^2 = 11*x^5 - 110*x^4 + 385*x^3 - 550*x^2 + 264*x over Rational Field m= Mapping from: CrvHyp: C to CrvHyp: C1 with equations : 11*$.1 121*$.2 $.3 and inverse 1/11*$.1 1/121*$.2 $.3 Change curve into Hyperelliptic Curve defined by y^2 = x^5 - 110*x^4 + 4235*x^3 - 66550*x^2 + 351384*x over Rational Field Bad primes = [ 2, 3, 11 ] f factors as (x - 44) (x - 33) (x - 22) (x - 11) (x). For factor x - 44, use field defined by x - 1 and theta = 44 For factor x - 33, use field defined by x - 1 and theta = 33 For factor x - 22, use field defined by x - 1 and theta = 22 For factor x - 11, use field defined by x - 1 and theta = 11 For factor x, use field defined by x - 1 and theta = 0 The 2-torsion group has dimension 4. Determining local images... p = 2 x = 1/4 --> new generator (0 0 0 0 0 1 0 0 0 0 0 1 0 0 0) x = 10 --> new generator (1 1 1 0 0 0 0 0 1 0 1 1 1 0 1) p = 3 x = 3 --> new generator (0 0 1 1 0 1 0 0 1 0) p = 11 p = infinity Computing class groups... Class group data of the fields: Field given by x - 44: [] Field given by x - 33: [] Field given by x - 22: [] Field given by x - 11: [] Field given by x: [] Dimension of Cl[2] = 0. Signatures: [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] Dimension of units mod squares = 5. Upper bound for Selmer group dimension: 13. ==> Upper bound for rank = 9. Computing unit groups... Class group and unit data of the fields: Field given by x - 44: Class group = [], units = [ 2 ] Field given by x - 33: Class group = [], units = [ 2 ] Field given by x - 22: Class group = [], units = [ 2 ] Field given by x - 11: Class group = [], units = [ 2 ] Field given by x: Class group = [], units = [ 2 ] Time for local computations: 511 ms. Time for class groups: 0 ms. Time for unit groups: 0 ms. Selmer group dimension = 5, Dimension of 2-torsion = 4, ==> Bound for the MW-rank = 1. Total time: 610 ms. Transforming presentation of S back to model C. 1 5 <[ 111/8*$.1^4 - 517/4*$.1^3 + 3293/8*$.1^2 - 2109/4*$.1 + 242, 10*$.1^4 - 115*$.1^3 + 457*$.1^2 - 716*$.1 + 363, 905/4*$.1^4 - 4507/2*$.1^3 + 31395/4*$.1^2 - 22289/2*$.1 + 5324, 19/8*$.1^4 - 97/4*$.1^3 + 705/8*$.1^2 - 521/4*$.1 + 66, $.1^4 - 10*$.1^3 + 51*$.1^2 - 130*$.1 + 121 ], [], []> {} Total time: 3.779 seconds, Total memory usage: 2.69MB ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Sat Jan 24 09:33:47 2004 Input: P := PolynomialRing(Rationals()); C := HyperellipticCurve(x*(x-1)*(x-2)*(x-3)*(x-4)); D := QuadraticTwist(C,12); J := Jacobian(D); SetVerbose("JacHypSelmer", 2); TwoSelmerGroupData(J : Bound := 300); Output: Magma V2.10-6 Sat Jan 24 2004 09:33:43 on modular [Seed = 3853985719] ------------------------------------- TwoSelmerGroupData of Jacobian of Hyperelliptic Curve defined by y^2 = 12*x^5 - 120*x^4 + 420*x^3 - 600*x^2 + 288*x over Rational Field m= Mapping from: CrvHyp: C to CrvHyp: C1 with equations : 3*$.1 9/2*$.2 $.3 and inverse 1/3*$.1 2/9*$.2 $.3 Change curve into Hyperelliptic Curve defined by y^2 = x^5 - 30*x^4 + 315*x^3 - 1350*x^2 + 1944*x over Rational Field Bad primes = [ 2, 3 ] f factors as (x - 12) (x - 9) (x - 6) (x - 3) (x). For factor x - 12, use field defined by x - 1 and theta = 12 For factor x - 9, use field defined by x - 1 and theta = 9 For factor x - 6, use field defined by x - 1 and theta = 6 For factor x - 3, use field defined by x - 1 and theta = 3 For factor x, use field defined by x - 1 and theta = 0 The 2-torsion group has dimension 4. Determining local images... p = 2 x = 1/4 --> new generator (0 0 0 0 0 1 0 0 0 0 0 1 0 0 0) x = 26 --> new generator (1 1 1 0 0 0 0 0 1 0 1 1 1 0 1) p = 3 p = infinity Computing class groups... Class group data of the fields: Field given by x - 12: [] Field given by x - 9: [] Field given by x - 6: [] Field given by x - 3: [] Field given by x: [] Dimension of Cl[2] = 0. Signatures: [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] Dimension of units mod squares = 5. Upper bound for Selmer group dimension: 11. ==> Upper bound for rank = 7. Computing unit groups... Class group and unit data of the fields: Field given by x - 12: Class group = [], units = [ 2 ] Field given by x - 9: Class group = [], units = [ 2 ] Field given by x - 6: Class group = [], units = [ 2 ] Field given by x - 3: Class group = [], units = [ 2 ] Field given by x: Class group = [], units = [ 2 ] Time for local computations: 500 ms. Time for class groups: 0 ms. Time for unit groups: 0 ms. Selmer group dimension = 4, Dimension of 2-torsion = 4, ==> Bound for the MW-rank = 0. Total time: 569 ms. Transforming presentation of S back to model C. 0 4 <[ 15/8*$.1^4 - 191/12*$.1^3 + 349/8*$.1^2 - 535/12*$.1 + 18, -1/3*$.1^3 + 3*$.1^2 - 20/3*$.1 + 3, 67/12*$.1^4 - 107/2*$.1^3 + 2129/12*$.1^2 - 473/2*$.1 + 108, 1/24*$.1^4 - 9/4*$.1^3 + 347/24*$.1^2 - 113/4*$.1 + 18 ], [], []> {} Total time: 3.769 seconds, Total memory usage: 2.69MB ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Sat Jan 24 09:34:11 2004 Input: P := PolynomialRing(Rationals()); C := HyperellipticCurve(x*(x-1)*(x-2)*(x-3)*(x-4)); D := QuadraticTwist(C,13); J := Jacobian(D); SetVerbose("JacHypSelmer", 2); TwoSelmerGroupData(J : Bound := 300); Output: Magma V2.10-6 Sat Jan 24 2004 09:34:08 on modular [Seed = 3971886745] ------------------------------------- TwoSelmerGroupData of Jacobian of Hyperelliptic Curve defined by y^2 = 13*x^5 - 130*x^4 + 455*x^3 - 650*x^2 + 312*x over Rational Field m= Mapping from: CrvHyp: C to CrvHyp: C1 with equations : 13*$.1 169*$.2 $.3 and inverse 1/13*$.1 1/169*$.2 $.3 Change curve into Hyperelliptic Curve defined by y^2 = x^5 - 130*x^4 + 5915*x^3 - 109850*x^2 + 685464*x over Rational Field Bad primes = [ 2, 3, 13 ] f factors as (x - 52) (x - 39) (x - 26) (x - 13) (x). For factor x - 52, use field defined by x - 1 and theta = 52 For factor x - 39, use field defined by x - 1 and theta = 39 For factor x - 26, use field defined by x - 1 and theta = 26 For factor x - 13, use field defined by x - 1 and theta = 13 For factor x, use field defined by x - 1 and theta = 0 The 2-torsion group has dimension 4. Determining local images... p = 2 x = 1/4 --> new generator (0 0 0 0 0 1 0 0 0 0 0 1 0 0 0) x = 14 --> new generator (1 0 1 0 1 1 0 0 1 0 0 0 1 1 1) p = 3 x = 1 --> new generator (1 0 0 0 0 1 1 1 0 0) p = 13 p = infinity Computing class groups... Class group data of the fields: Field given by x - 52: [] Field given by x - 39: [] Field given by x - 26: [] Field given by x - 13: [] Field given by x: [] Dimension of Cl[2] = 0. Signatures: [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] Dimension of units mod squares = 5. Upper bound for Selmer group dimension: 13. ==> Upper bound for rank = 9. Computing unit groups... Class group and unit data of the fields: Field given by x - 52: Class group = [], units = [ 2 ] Field given by x - 39: Class group = [], units = [ 2 ] Field given by x - 26: Class group = [], units = [ 2 ] Field given by x - 13: Class group = [], units = [ 2 ] Field given by x: Class group = [], units = [ 2 ] Time for local computations: 540 ms. Time for class groups: 0 ms. Time for unit groups: 0 ms. Selmer group dimension = 5, Dimension of 2-torsion = 4, ==> Bound for the MW-rank = 1. Total time: 629 ms. Transforming presentation of S back to model C. 1 5 <[ 149/8*$.1^4 - 719/4*$.1^3 + 4703/8*$.1^2 - 3047/4*$.1 + 338, -$.1^3 + 7*$.1^2 - 12*$.1 + 3, 33/4*$.1^4 - 139/2*$.1^3 + 747/4*$.1^2 - 349/2*$.1 + 52, -81/8*$.1^4 + 347/4*$.1^3 - 1819/8*$.1^2 + 603/4*$.1 + 78, 3*$.1^4 - 38*$.1^3 + 165*$.1^2 - 286*$.1 + 169 ], [], []> {} Total time: 3.749 seconds, Total memory usage: 2.79MB ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Sat Jan 24 09:34:36 2004 Input: P := PolynomialRing(Rationals()); C := HyperellipticCurve(x*(x-1)*(x-2)*(x-3)*(x-4)); D := QuadraticTwist(C,14); J := Jacobian(D); SetVerbose("JacHypSelmer", 2); TwoSelmerGroupData(J : Bound := 300); Output: Magma V2.10-6 Sat Jan 24 2004 09:34:31 on modular [Seed = 340186746] ------------------------------------- TwoSelmerGroupData of Jacobian of Hyperelliptic Curve defined by y^2 = 14*x^5 - 140*x^4 + 490*x^3 - 700*x^2 + 336*x over Rational Field m= Mapping from: CrvHyp: C to CrvHyp: C1 with equations : 14*$.1 196*$.2 $.3 and inverse 1/14*$.1 1/196*$.2 $.3 Change curve into Hyperelliptic Curve defined by y^2 = x^5 - 140*x^4 + 6860*x^3 - 137200*x^2 + 921984*x over Rational Field Bad primes = [ 2, 3, 7 ] f factors as (x - 56) (x - 42) (x - 28) (x - 14) (x). For factor x - 56, use field defined by x - 1 and theta = 56 For factor x - 42, use field defined by x - 1 and theta = 42 For factor x - 28, use field defined by x - 1 and theta = 28 For factor x - 14, use field defined by x - 1 and theta = 14 For factor x, use field defined by x - 1 and theta = 0 The 2-torsion group has dimension 4. Determining local images... p = 2 x = 1 --> new generator (0 0 0 0 1 1 0 0 1 0 1 0 0 0 0) x = 2 --> new generator (1 0 1 1 1 0 1 1 0 0 0 1 1 0 0) p = 3 x = 3 --> new generator (0 0 1 1 0 1 0 0 1 0) p = 7 p = infinity Computing class groups... Class group data of the fields: Field given by x - 56: [] Field given by x - 42: [] Field given by x - 28: [] Field given by x - 14: [] Field given by x: [] Dimension of Cl[2] = 0. Signatures: [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] Dimension of units mod squares = 5. Upper bound for Selmer group dimension: 13. ==> Upper bound for rank = 9. Computing unit groups... Class group and unit data of the fields: Field given by x - 56: Class group = [], units = [ 2 ] Field given by x - 42: Class group = [], units = [ 2 ] Field given by x - 28: Class group = [], units = [ 2 ] Field given by x - 14: Class group = [], units = [ 2 ] Field given by x: Class group = [], units = [ 2 ] Time for local computations: 1021 ms. Time for class groups: 0 ms. Time for unit groups: 0 ms. Selmer group dimension = 4, Dimension of 2-torsion = 4, ==> Bound for the MW-rank = 0. Total time: 1121 ms. Transforming presentation of S back to model C. 0 4 <[ 33/4*$.1^4 - 151/2*$.1^3 + 949/4*$.1^2 - 311*$.1 + 147, -$.1^4 + 6*$.1^3 - 13/2*$.1^2 - 15/2*$.1 + 7, 12*$.1^4 - 247/2*$.1^3 + 877/2*$.1^2 - 619*$.1 + 294, -27/2*$.1^4 + 239/2*$.1^3 - 673/2*$.1^2 + 587/2*$.1 + 21 ], [], []> {} Total time: 4.250 seconds, Total memory usage: 2.69MB ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Sat Jan 24 09:34:54 2004 Input: P := PolynomialRing(Rationals()); C := HyperellipticCurve(x*(x-1)*(x-2)*(x-3)*(x-4)); D := QuadraticTwist(C,15); J := Jacobian(D); SetVerbose("JacHypSelmer", 2); TwoSelmerGroupData(J : Bound := 300); Output: Magma V2.10-6 Sat Jan 24 2004 09:34:50 on modular [Seed = 440981638] ------------------------------------- TwoSelmerGroupData of Jacobian of Hyperelliptic Curve defined by y^2 = 15*x^5 - 150*x^4 + 525*x^3 - 750*x^2 + 360*x over Rational Field m= Mapping from: CrvHyp: C to CrvHyp: C1 with equations : 15*$.1 225*$.2 $.3 and inverse 1/15*$.1 1/225*$.2 $.3 Change curve into Hyperelliptic Curve defined by y^2 = x^5 - 150*x^4 + 7875*x^3 - 168750*x^2 + 1215000*x over Rational Field Bad primes = [ 2, 3, 5 ] f factors as (x - 60) (x - 45) (x - 30) (x - 15) (x). For factor x - 60, use field defined by x - 1 and theta = 60 For factor x - 45, use field defined by x - 1 and theta = 45 For factor x - 30, use field defined by x - 1 and theta = 30 For factor x - 15, use field defined by x - 1 and theta = 15 For factor x, use field defined by x - 1 and theta = 0 The 2-torsion group has dimension 4. Determining local images... p = 2 x = 1/4 --> new generator (0 0 0 0 0 1 0 0 0 0 0 1 0 0 0) x = 18 --> new generator (1 1 0 0 0 1 0 0 1 0 1 0 1 0 0) p = 3 p = 5 p = infinity Computing class groups... Class group data of the fields: Field given by x - 60: [] Field given by x - 45: [] Field given by x - 30: [] Field given by x - 15: [] Field given by x: [] Dimension of Cl[2] = 0. Signatures: [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] Dimension of units mod squares = 5. Upper bound for Selmer group dimension: 15. ==> Upper bound for rank = 11. Computing unit groups... Class group and unit data of the fields: Field given by x - 60: Class group = [], units = [ 2 ] Field given by x - 45: Class group = [], units = [ 2 ] Field given by x - 30: Class group = [], units = [ 2 ] Field given by x - 15: Class group = [], units = [ 2 ] Field given by x: Class group = [], units = [ 2 ] Time for local computations: 520 ms. Time for class groups: 0 ms. Time for unit groups: 0 ms. Selmer group dimension = 5, Dimension of 2-torsion = 4, ==> Bound for the MW-rank = 1. Total time: 630 ms. Transforming presentation of S back to model C. 1 5 <[ 107/8*$.1^4 - 509/4*$.1^3 + 3337/8*$.1^2 - 2209/4*$.1 + 250, 3*$.1^4 - 95/3*$.1^3 + 116*$.1^2 - 502/3*$.1 + 75, 449/4*$.1^4 - 2241/2*$.1^3 + 15663/4*$.1^2 - 11185/2*$.1 + 2700, 41/24*$.1^4 - 81/4*$.1^3 + 2035/24*$.1^2 - 585/4*$.1 + 90, 4/3*$.1^4 - 44/3*$.1^3 + 167/3*$.1^2 - 253/3*$.1 + 45 ], [], []> {} Total time: 3.759 seconds, Total memory usage: 2.69MB ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Sat Jan 24 09:35:23 2004 Input: P := PolynomialRing(Rationals()); C := HyperellipticCurve(x*(x-1)*(x-2)*(x-3)*(x-4)); D := QuadraticTwist(C,16); J := Jacobian(D); SetVerbose("JacHypSelmer", 2); TwoSelmerGroupData(J : Bound := 300); Output: Magma V2.10-6 Sat Jan 24 2004 09:35:19 on modular [Seed = 257805758] ------------------------------------- TwoSelmerGroupData of Jacobian of Hyperelliptic Curve defined by y^2 = 16*x^5 - 160*x^4 + 560*x^3 - 800*x^2 + 384*x over Rational Field m= Mapping from: CrvHyp: C to CrvHyp: C1 with equations : $.1 1/4*$.2 $.3 and inverse $.1 4*$.2 $.3 Change curve into Hyperelliptic Curve defined by y^2 = x^5 - 10*x^4 + 35*x^3 - 50*x^2 + 24*x over Rational Field Bad primes = [ 2, 3 ] f factors as (x - 4) (x - 3) (x - 2) (x - 1) (x). For factor x - 4, use field defined by x - 1 and theta = 4 For factor x - 3, use field defined by x - 1 and theta = 3 For factor x - 2, use field defined by x - 1 and theta = 2 For factor x - 1, use field defined by x - 1 and theta = 1 For factor x, use field defined by x - 1 and theta = 0 The 2-torsion group has dimension 4. Determining local images... p = 2 x = 1/4 --> new generator (0 0 0 0 0 1 0 0 0 0 0 1 0 0 0) x = 22 --> new generator (1 0 0 0 1 0 0 0 1 0 0 1 1 1 0) p = 3 x = 7 --> new generator (1 0 0 0 0 1 1 1 0 0) p = infinity Computing class groups... Class group data of the fields: Field given by x - 4: [] Field given by x - 3: [] Field given by x - 2: [] Field given by x - 1: [] Field given by x: [] Dimension of Cl[2] = 0. Signatures: [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] Dimension of units mod squares = 5. Upper bound for Selmer group dimension: 9. ==> Upper bound for rank = 5. Computing unit groups... Class group and unit data of the fields: Field given by x - 4: Class group = [], units = [ 2 ] Field given by x - 3: Class group = [], units = [ 2 ] Field given by x - 2: Class group = [], units = [ 2 ] Field given by x - 1: Class group = [], units = [ 2 ] Field given by x: Class group = [], units = [ 2 ] Time for local computations: 520 ms. Time for class groups: 0 ms. Time for unit groups: 0 ms. Selmer group dimension = 4, Dimension of 2-torsion = 4, ==> Bound for the MW-rank = 0. Total time: 590 ms. Transforming presentation of S back to model C. 0 4 <[ 1/8*$.1^4 - 3/4*$.1^3 + 3/8*$.1^2 + 5/4*$.1 + 2, -$.1^3 + 7*$.1^2 - 12*$.1 + 3, 1/4*$.1^4 - 3/2*$.1^3 + 11/4*$.1^2 - 5/2*$.1 + 4, -9/8*$.1^4 + 35/4*$.1^3 - 163/8*$.1^2 + 51/4*$.1 + 6 ], [], []> {} Total time: 3.749 seconds, Total memory usage: 2.69MB ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Sat Jan 24 09:35:43 2004 Input: P := PolynomialRing(Rationals()); C := HyperellipticCurve(x*(x-1)*(x-2)*(x-3)*(x-4)); D := QuadraticTwist(C,17); J := Jacobian(D); SetVerbose("JacHypSelmer", 2); TwoSelmerGroupData(J : Bound := 300); Output: Magma V2.10-6 Sat Jan 24 2004 09:35:39 on modular [Seed = 879163033] ------------------------------------- TwoSelmerGroupData of Jacobian of Hyperelliptic Curve defined by y^2 = 17*x^5 - 170*x^4 + 595*x^3 - 850*x^2 + 408*x over Rational Field m= Mapping from: CrvHyp: C to CrvHyp: C1 with equations : 17*$.1 289*$.2 $.3 and inverse 1/17*$.1 1/289*$.2 $.3 Change curve into Hyperelliptic Curve defined by y^2 = x^5 - 170*x^4 + 10115*x^3 - 245650*x^2 + 2004504*x over Rational Field Bad primes = [ 2, 3, 17 ] f factors as (x - 68) (x - 51) (x - 34) (x - 17) (x). For factor x - 68, use field defined by x - 1 and theta = 68 For factor x - 51, use field defined by x - 1 and theta = 51 For factor x - 34, use field defined by x - 1 and theta = 34 For factor x - 17, use field defined by x - 1 and theta = 17 For factor x, use field defined by x - 1 and theta = 0 The 2-torsion group has dimension 4. Determining local images... p = 2 x = 1/4 --> new generator (0 0 0 0 0 1 0 0 0 0 0 1 0 0 0) x = 22 --> new generator (1 0 0 0 1 0 0 0 1 0 0 1 1 1 0) p = 3 x = 3 --> new generator (0 0 1 1 0 1 0 0 1 0) p = 17 p = infinity Computing class groups... Class group data of the fields: Field given by x - 68: [] Field given by x - 51: [] Field given by x - 34: [] Field given by x - 17: [] Field given by x: [] Dimension of Cl[2] = 0. Signatures: [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] Dimension of units mod squares = 5. Upper bound for Selmer group dimension: 13. ==> Upper bound for rank = 9. Computing unit groups... Class group and unit data of the fields: Field given by x - 68: Class group = [], units = [ 2 ] Field given by x - 51: Class group = [], units = [ 2 ] Field given by x - 34: Class group = [], units = [ 2 ] Field given by x - 17: Class group = [], units = [ 2 ] Field given by x: Class group = [], units = [ 2 ] Time for local computations: 540 ms. Time for class groups: 0 ms. Time for unit groups: 0 ms. Selmer group dimension = 6, Dimension of 2-torsion = 4, ==> Bound for the MW-rank = 2. Total time: 629 ms. Transforming presentation of S back to model C. 2 6 <[ 193/8*$.1^4 - 931/4*$.1^3 + 6275/8*$.1^2 - 4411/4*$.1 + 578, 10*$.1^4 - 93*$.1^3 + 285*$.1^2 - 304*$.1 + 51, 193/4*$.1^4 - 947/2*$.1^3 + 6507/4*$.1^2 - 4613/2*$.1 + 1156, -105/8*$.1^4 + 451/4*$.1^3 - 2371/8*$.1^2 + 787/4*$.1 + 102, 10*$.1^4 - 100*$.1^3 + 358*$.1^2 - 540*$.1 + 289, -2*$.1^4 + 12*$.1^3 - 14*$.1^2 - 12*$.1 + 17 ], [], []> {} Total time: 3.799 seconds, Total memory usage: 2.69MB ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Sat Jan 24 09:36:10 2004 Input: P := PolynomialRing(Rationals()); C := HyperellipticCurve(x*(x-1)*(x-2)*(x-3)*(x-4)); D := QuadraticTwist(C,18); J := Jacobian(D); SetVerbose("JacHypSelmer", 2); TwoSelmerGroupData(J : Bound := 300); Output: Magma V2.10-6 Sat Jan 24 2004 09:36:05 on modular [Seed = 979958009] ------------------------------------- TwoSelmerGroupData of Jacobian of Hyperelliptic Curve defined by y^2 = 18*x^5 - 180*x^4 + 630*x^3 - 900*x^2 + 432*x over Rational Field m= Mapping from: CrvHyp: C to CrvHyp: C1 with equations : 2*$.1 4/3*$.2 $.3 and inverse 1/2*$.1 3/4*$.2 $.3 Change curve into Hyperelliptic Curve defined by y^2 = x^5 - 20*x^4 + 140*x^3 - 400*x^2 + 384*x over Rational Field Bad primes = [ 2, 3 ] f factors as (x - 8) (x - 6) (x - 4) (x - 2) (x). For factor x - 8, use field defined by x - 1 and theta = 8 For factor x - 6, use field defined by x - 1 and theta = 6 For factor x - 4, use field defined by x - 1 and theta = 4 For factor x - 2, use field defined by x - 1 and theta = 2 For factor x, use field defined by x - 1 and theta = 0 The 2-torsion group has dimension 4. Determining local images... p = 2 x = 1 --> new generator (0 0 0 0 1 0 0 0 1 0 1 1 0 0 0) x = 26 --> new generator (1 0 0 0 0 1 1 1 0 1 1 0 1 0 1) p = 3 x = 3 --> new generator (0 0 1 1 0 1 0 0 1 0) p = infinity Computing class groups... Class group data of the fields: Field given by x - 8: [] Field given by x - 6: [] Field given by x - 4: [] Field given by x - 2: [] Field given by x: [] Dimension of Cl[2] = 0. Signatures: [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] Dimension of units mod squares = 5. Upper bound for Selmer group dimension: 9. ==> Upper bound for rank = 5. Computing unit groups... Class group and unit data of the fields: Field given by x - 8: Class group = [], units = [ 2 ] Field given by x - 6: Class group = [], units = [ 2 ] Field given by x - 4: Class group = [], units = [ 2 ] Field given by x - 2: Class group = [], units = [ 2 ] Field given by x: Class group = [], units = [ 2 ] Time for local computations: 1060 ms. Time for class groups: 0 ms. Time for unit groups: 1 ms. Selmer group dimension = 4, Dimension of 2-torsion = 4, ==> Bound for the MW-rank = 0. Total time: 1129 ms. Transforming presentation of S back to model C. 0 4 <[ $.1^3 - 13/2*$.1^2 + 17/2*$.1 + 3, -1/4*$.1^4 + 3/2*$.1^3 - 5/4*$.1^2 - 3*$.1 + 1, -1/2*$.1^3 + 7/2*$.1^2 - 7*$.1 + 6, -9/4*$.1^4 + 19*$.1^3 - 203/4*$.1^2 + 43*$.1 + 3 ], [], []> {} Total time: 4.219 seconds, Total memory usage: 2.69MB ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Sat Jan 24 09:36:32 2004 Input: P := PolynomialRing(Rationals()); C := HyperellipticCurve(x*(x-1)*(x-2)*(x-3)*(x-4)); D := QuadraticTwist(C,19); J := Jacobian(D); SetVerbose("JacHypSelmer", 2); TwoSelmerGroupData(J : Bound := 300); Output: Magma V2.10-6 Sat Jan 24 2004 09:36:28 on modular [Seed = 594665945] ------------------------------------- TwoSelmerGroupData of Jacobian of Hyperelliptic Curve defined by y^2 = 19*x^5 - 190*x^4 + 665*x^3 - 950*x^2 + 456*x over Rational Field m= Mapping from: CrvHyp: C to CrvHyp: C1 with equations : 19*$.1 361*$.2 $.3 and inverse 1/19*$.1 1/361*$.2 $.3 Change curve into Hyperelliptic Curve defined by y^2 = x^5 - 190*x^4 + 12635*x^3 - 342950*x^2 + 3127704*x over Rational Field Bad primes = [ 2, 3, 19 ] f factors as (x - 76) (x - 57) (x - 38) (x - 19) (x). For factor x - 76, use field defined by x - 1 and theta = 76 For factor x - 57, use field defined by x - 1 and theta = 57 For factor x - 38, use field defined by x - 1 and theta = 38 For factor x - 19, use field defined by x - 1 and theta = 19 For factor x, use field defined by x - 1 and theta = 0 The 2-torsion group has dimension 4. Determining local images... p = 2 x = 1/4 --> new generator (0 0 0 0 0 1 0 0 0 0 0 1 0 0 0) x = 26 --> new generator (1 1 1 0 0 0 0 0 1 0 1 1 1 0 1) p = 3 x = 7 --> new generator (1 0 0 0 0 1 1 1 0 0) p = 19 p = infinity Computing class groups... Class group data of the fields: Field given by x - 76: [] Field given by x - 57: [] Field given by x - 38: [] Field given by x - 19: [] Field given by x: [] Dimension of Cl[2] = 0. Signatures: [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] Dimension of units mod squares = 5. Upper bound for Selmer group dimension: 13. ==> Upper bound for rank = 9. Computing unit groups... Class group and unit data of the fields: Field given by x - 76: Class group = [], units = [ 2 ] Field given by x - 57: Class group = [], units = [ 2 ] Field given by x - 38: Class group = [], units = [ 2 ] Field given by x - 19: Class group = [], units = [ 2 ] Field given by x: Class group = [], units = [ 2 ] Time for local computations: 500 ms. Time for class groups: 0 ms. Time for unit groups: 11 ms. Selmer group dimension = 5, Dimension of 2-torsion = 4, ==> Bound for the MW-rank = 1. Total time: 589 ms. Transforming presentation of S back to model C. 1 5 <[ 295/8*$.1^4 - 1437/4*$.1^3 + 9573/8*$.1^2 - 6373/4*$.1 + 722, 10*$.1^4 - 91*$.1^3 + 269*$.1^2 - 264*$.1 + 19, 4561/4*$.1^4 - 22803/2*$.1^3 + 159611/4*$.1^2 - 114041/2*$.1 + 27436, 43/8*$.1^4 - 361/4*$.1^3 + 3849/8*$.1^2 - 4017/4*$.1 + 722, -7*$.1^4 + 42*$.1^3 - 49*$.1^2 - 42*$.1 + 57 ], [], []> {} Total time: 3.659 seconds, Total memory usage: 2.69MB ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Sat Jan 24 09:36:57 2004 Input: P := PolynomialRing(Rationals()); C := HyperellipticCurve(x*(x-1)*(x-2)*(x-3)*(x-4)); D := QuadraticTwist(C,20); J := Jacobian(D); SetVerbose("JacHypSelmer", 2); TwoSelmerGroupData(J : Bound := 300); Output: Magma V2.10-6 Sat Jan 24 2004 09:36:53 on modular [Seed = 679144251] ------------------------------------- TwoSelmerGroupData of Jacobian of Hyperelliptic Curve defined by y^2 = 20*x^5 - 200*x^4 + 700*x^3 - 1000*x^2 + 480*x over Rational Field m= Mapping from: CrvHyp: C to CrvHyp: C1 with equations : 5*$.1 25/2*$.2 $.3 and inverse 1/5*$.1 2/25*$.2 $.3 Change curve into Hyperelliptic Curve defined by y^2 = x^5 - 50*x^4 + 875*x^3 - 6250*x^2 + 15000*x over Rational Field Bad primes = [ 2, 3, 5 ] f factors as (x - 20) (x - 15) (x - 10) (x - 5) (x). For factor x - 20, use field defined by x - 1 and theta = 20 For factor x - 15, use field defined by x - 1 and theta = 15 For factor x - 10, use field defined by x - 1 and theta = 10 For factor x - 5, use field defined by x - 1 and theta = 5 For factor x, use field defined by x - 1 and theta = 0 The 2-torsion group has dimension 4. Determining local images... p = 2 x = 1/4 --> new generator (0 0 0 0 0 1 0 0 0 0 0 1 0 0 0) x = 30 --> new generator (1 0 1 0 1 1 0 0 1 0 0 0 1 1 1) p = 3 x = 3 --> new generator (0 0 1 1 0 1 0 0 1 0) p = 5 p = infinity Computing class groups... Class group data of the fields: Field given by x - 20: [] Field given by x - 15: [] Field given by x - 10: [] Field given by x - 5: [] Field given by x: [] Dimension of Cl[2] = 0. Signatures: [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] Dimension of units mod squares = 5. Upper bound for Selmer group dimension: 13. ==> Upper bound for rank = 9. Computing unit groups... Class group and unit data of the fields: Field given by x - 20: Class group = [], units = [ 2 ] Field given by x - 15: Class group = [], units = [ 2 ] Field given by x - 10: Class group = [], units = [ 2 ] Field given by x - 5: Class group = [], units = [ 2 ] Field given by x: Class group = [], units = [ 2 ] Time for local computations: 539 ms. Time for class groups: 0 ms. Time for unit groups: 0 ms. Selmer group dimension = 5, Dimension of 2-torsion = 4, ==> Bound for the MW-rank = 1. Total time: 639 ms. Transforming presentation of S back to model C. 1 5 <[ 4*$.1^4 - 37*$.1^3 + 118*$.1^2 - 155*$.1 + 75, 3*$.1^4 - 35*$.1^3 + 136*$.1^2 - 194*$.1 + 75, 121/4*$.1^4 - 306*$.1^3 + 4331/4*$.1^2 - 1556*$.1 + 750, $.1^2 - 4*$.1 + 5, 35/8*$.1^4 - 177/4*$.1^3 + 1305/8*$.1^2 - 1033/4*$.1 + 150 ], [], []> {} Total time: 3.839 seconds, Total memory usage: 2.69MB ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Sat Jan 24 09:37:19 2004 Input: P := PolynomialRing(Rationals()); C := HyperellipticCurve(x*(x-1)*(x-2)*(x-3)*(x-4)); D := QuadraticTwist(C,21); J := Jacobian(D); SetVerbose("JacHypSelmer", 2); TwoSelmerGroupData(J : Bound := 300); Output: Magma V2.10-6 Sat Jan 24 2004 09:37:15 on modular [Seed = 1359188572] ------------------------------------- TwoSelmerGroupData of Jacobian of Hyperelliptic Curve defined by y^2 = 21*x^5 - 210*x^4 + 735*x^3 - 1050*x^2 + 504*x over Rational Field m= Mapping from: CrvHyp: C to CrvHyp: C1 with equations : 21*$.1 441*$.2 $.3 and inverse 1/21*$.1 1/441*$.2 $.3 Change curve into Hyperelliptic Curve defined by y^2 = x^5 - 210*x^4 + 15435*x^3 - 463050*x^2 + 4667544*x over Rational Field Bad primes = [ 2, 3, 7 ] f factors as (x - 84) (x - 63) (x - 42) (x - 21) (x). For factor x - 84, use field defined by x - 1 and theta = 84 For factor x - 63, use field defined by x - 1 and theta = 63 For factor x - 42, use field defined by x - 1 and theta = 42 For factor x - 21, use field defined by x - 1 and theta = 21 For factor x, use field defined by x - 1 and theta = 0 The 2-torsion group has dimension 4. Determining local images... p = 2 x = 1/4 --> new generator (0 0 0 0 0 1 0 0 0 0 0 1 0 0 0) x = 30 --> new generator (1 0 1 0 1 1 0 0 1 0 0 0 1 1 1) p = 3 p = 7 p = infinity Computing class groups... Class group data of the fields: Field given by x - 84: [] Field given by x - 63: [] Field given by x - 42: [] Field given by x - 21: [] Field given by x: [] Dimension of Cl[2] = 0. Signatures: [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] Dimension of units mod squares = 5. Upper bound for Selmer group dimension: 15. ==> Upper bound for rank = 11. Computing unit groups... Class group and unit data of the fields: Field given by x - 84: Class group = [], units = [ 2 ] Field given by x - 63: Class group = [], units = [ 2 ] Field given by x - 42: Class group = [], units = [ 2 ] Field given by x - 21: Class group = [], units = [ 2 ] Field given by x: Class group = [], units = [ 2 ] Time for local computations: 549 ms. Time for class groups: 0 ms. Time for unit groups: 0 ms. Selmer group dimension = 4, Dimension of 2-torsion = 4, ==> Bound for the MW-rank = 0. Total time: 659 ms. Transforming presentation of S back to model C. 0 4 <[ 373/8*$.1^4 - 5357/12*$.1^3 + 11775/8*$.1^2 - 23413/12*$.1 + 882, 6*$.1^4 - 187/3*$.1^3 + 225*$.1^2 - 968/3*$.1 + 147, 18595/12*$.1^4 - 30971/2*$.1^3 + 649745/12*$.1^2 - 154493/2*$.1 + 37044, 61/24*$.1^4 - 117/4*$.1^3 + 2879/24*$.1^2 - 821/4*$.1 + 126 ], [], []> {} Total time: 3.789 seconds, Total memory usage: 2.69MB ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Sat Jan 24 09:37:41 2004 Input: P := PolynomialRing(Rationals()); C := HyperellipticCurve(x*(x-1)*(x-2)*(x-3)*(x-4)); D := QuadraticTwist(C,22); J := Jacobian(D); SetVerbose("JacHypSelmer", 2); TwoSelmerGroupData(J : Bound := 300); Output: Magma V2.10-6 Sat Jan 24 2004 09:37:37 on modular [Seed = 1175749985] ------------------------------------- TwoSelmerGroupData of Jacobian of Hyperelliptic Curve defined by y^2 = 22*x^5 - 220*x^4 + 770*x^3 - 1100*x^2 + 528*x over Rational Field m= Mapping from: CrvHyp: C to CrvHyp: C1 with equations : 22*$.1 484*$.2 $.3 and inverse 1/22*$.1 1/484*$.2 $.3 Change curve into Hyperelliptic Curve defined by y^2 = x^5 - 220*x^4 + 16940*x^3 - 532400*x^2 + 5622144*x over Rational Field Bad primes = [ 2, 3, 11 ] f factors as (x - 88) (x - 66) (x - 44) (x - 22) (x). For factor x - 88, use field defined by x - 1 and theta = 88 For factor x - 66, use field defined by x - 1 and theta = 66 For factor x - 44, use field defined by x - 1 and theta = 44 For factor x - 22, use field defined by x - 1 and theta = 22 For factor x, use field defined by x - 1 and theta = 0 The 2-torsion group has dimension 4. Determining local images... p = 2 x = 1 --> new generator (0 0 0 0 1 1 0 0 1 0 1 0 0 0 0) x = 26 --> new generator (1 0 0 1 1 0 1 1 1 0 0 0 1 0 1) p = 3 x = 1 --> new generator (1 0 0 0 0 1 1 1 0 0) p = 11 p = infinity Computing class groups... Class group data of the fields: Field given by x - 88: [] Field given by x - 66: [] Field given by x - 44: [] Field given by x - 22: [] Field given by x: [] Dimension of Cl[2] = 0. Signatures: [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] Dimension of units mod squares = 5. Upper bound for Selmer group dimension: 13. ==> Upper bound for rank = 9. Computing unit groups... Class group and unit data of the fields: Field given by x - 88: Class group = [], units = [ 2 ] Field given by x - 66: Class group = [], units = [ 2 ] Field given by x - 44: Class group = [], units = [ 2 ] Field given by x - 22: Class group = [], units = [ 2 ] Field given by x: Class group = [], units = [ 2 ] Time for local computations: 1081 ms. Time for class groups: 0 ms. Time for unit groups: 0 ms. Selmer group dimension = 5, Dimension of 2-torsion = 4, ==> Bound for the MW-rank = 1. Total time: 1189 ms. Transforming presentation of S back to model C. 1 5 <[ -5/4*$.1^4 + 15/2*$.1^3 - 53/4*$.1^2 + 2*$.1 + 11, -3/2*$.1^4 + 9*$.1^3 - 10*$.1^2 - 21/2*$.1 + 11, 6*$.1^4 - 99/2*$.1^3 + 253/2*$.1^2 - 103*$.1 + 22, -20*$.1^4 + 337/2*$.1^3 - 436*$.1^2 + 597/2*$.1 + 121, -4*$.1^4 + 24*$.1^3 - 28*$.1^2 - 24*$.1 + 33 ], [], []> {} Total time: 4.279 seconds, Total memory usage: 2.69MB ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Sat Jan 24 09:38:00 2004 Input: P := PolynomialRing(Rationals()); C := HyperellipticCurve(x*(x-1)*(x-2)*(x-3)*(x-4)); D := QuadraticTwist(C,23); J := Jacobian(D); SetVerbose("JacHypSelmer", 2); TwoSelmerGroupData(J : Bound := 300); Output: Magma V2.10-6 Sat Jan 24 2004 09:37:56 on modular [Seed = 1277071134] ------------------------------------- TwoSelmerGroupData of Jacobian of Hyperelliptic Curve defined by y^2 = 23*x^5 - 230*x^4 + 805*x^3 - 1150*x^2 + 552*x over Rational Field m= Mapping from: CrvHyp: C to CrvHyp: C1 with equations : 23*$.1 529*$.2 $.3 and inverse 1/23*$.1 1/529*$.2 $.3 Change curve into Hyperelliptic Curve defined by y^2 = x^5 - 230*x^4 + 18515*x^3 - 608350*x^2 + 6716184*x over Rational Field Bad primes = [ 2, 3, 23 ] f factors as (x - 92) (x - 69) (x - 46) (x - 23) (x). For factor x - 92, use field defined by x - 1 and theta = 92 For factor x - 69, use field defined by x - 1 and theta = 69 For factor x - 46, use field defined by x - 1 and theta = 46 For factor x - 23, use field defined by x - 1 and theta = 23 For factor x, use field defined by x - 1 and theta = 0 The 2-torsion group has dimension 4. Determining local images... p = 2 x = 1/4 --> new generator (0 0 0 0 0 1 0 0 0 0 0 1 0 0 0) x = 2 --> new generator (1 1 0 0 0 1 0 0 1 0 1 0 1 0 0) p = 3 x = 3 --> new generator (0 0 1 1 0 1 0 0 1 0) p = 23 p = infinity Computing class groups... Class group data of the fields: Field given by x - 92: [] Field given by x - 69: [] Field given by x - 46: [] Field given by x - 23: [] Field given by x: [] Dimension of Cl[2] = 0. Signatures: [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] Dimension of units mod squares = 5. Upper bound for Selmer group dimension: 13. ==> Upper bound for rank = 9. Computing unit groups... Class group and unit data of the fields: Field given by x - 92: Class group = [], units = [ 2 ] Field given by x - 69: Class group = [], units = [ 2 ] Field given by x - 46: Class group = [], units = [ 2 ] Field given by x - 23: Class group = [], units = [ 2 ] Field given by x: Class group = [], units = [ 2 ] Time for local computations: 520 ms. Time for class groups: 0 ms. Time for unit groups: 0 ms. Selmer group dimension = 6, Dimension of 2-torsion = 4, ==> Bound for the MW-rank = 2. Total time: 610 ms. Transforming presentation of S back to model C. 2 6 <[ 25*$.1^4 - 242*$.1^3 + 815*$.1^2 - 1126*$.1 + 529, 20*$.1^4 - 208*$.1^3 + 760*$.1^2 - 1124*$.1 + 529, -7/4*$.1^4 + 14*$.1^3 - 117/4*$.1^2 - 6*$.1 + 46, 1496*$.1^4 - 15025*$.1^3 + 52819*$.1^2 - 75745*$.1 + 36501, 1/8*$.1^4 - 7/4*$.1^3 + 59/8*$.1^2 - 43/4*$.1 + 6, 60*$.1^4 - 623*$.1^3 + 2251*$.1^2 - 3272*$.1 + 1587 ], [], []> {} Total time: 3.819 seconds, Total memory usage: 2.69MB ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Sat Jan 24 09:38:23 2004 Input: P := PolynomialRing(Rationals()); C := HyperellipticCurve(x*(x-1)*(x-2)*(x-3)*(x-4)); D := QuadraticTwist(C,24); J := Jacobian(D); SetVerbose("JacHypSelmer", 2); TwoSelmerGroupData(J : Bound := 300); Output: Magma V2.10-6 Sat Jan 24 2004 09:38:19 on modular [Seed = 1965536824] ------------------------------------- TwoSelmerGroupData of Jacobian of Hyperelliptic Curve defined by y^2 = 24*x^5 - 240*x^4 + 840*x^3 - 1200*x^2 + 576*x over Rational Field m= Mapping from: CrvHyp: C to CrvHyp: C1 with equations : 6*$.1 18*$.2 $.3 and inverse 1/6*$.1 1/18*$.2 $.3 Change curve into Hyperelliptic Curve defined by y^2 = x^5 - 60*x^4 + 1260*x^3 - 10800*x^2 + 31104*x over Rational Field Bad primes = [ 2, 3 ] f factors as (x - 24) (x - 18) (x - 12) (x - 6) (x). For factor x - 24, use field defined by x - 1 and theta = 24 For factor x - 18, use field defined by x - 1 and theta = 18 For factor x - 12, use field defined by x - 1 and theta = 12 For factor x - 6, use field defined by x - 1 and theta = 6 For factor x, use field defined by x - 1 and theta = 0 The 2-torsion group has dimension 4. Determining local images... p = 2 x = 1 --> new generator (0 0 0 0 1 1 0 0 1 0 1 0 0 0 0) x = 42 --> new generator (1 0 0 1 1 0 1 1 1 0 0 0 1 0 1) p = 3 p = infinity Computing class groups... Class group data of the fields: Field given by x - 24: [] Field given by x - 18: [] Field given by x - 12: [] Field given by x - 6: [] Field given by x: [] Dimension of Cl[2] = 0. Signatures: [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] Dimension of units mod squares = 5. Upper bound for Selmer group dimension: 11. ==> Upper bound for rank = 7. Computing unit groups... Class group and unit data of the fields: Field given by x - 24: Class group = [], units = [ 2 ] Field given by x - 18: Class group = [], units = [ 2 ] Field given by x - 12: Class group = [], units = [ 2 ] Field given by x - 6: Class group = [], units = [ 2 ] Field given by x: Class group = [], units = [ 2 ] Time for local computations: 1159 ms. Time for class groups: 0 ms. Time for unit groups: 10 ms. Selmer group dimension = 4, Dimension of 2-torsion = 4, ==> Bound for the MW-rank = 0. Total time: 1240 ms. Transforming presentation of S back to model C. 0 4 <[ -1/4*$.1^4 + 17/6*$.1^3 - 41/4*$.1^2 + 32/3*$.1 + 3, -1/2*$.1^4 + 3*$.1^3 - 3*$.1^2 - 9/2*$.1 + 3, 4/3*$.1^4 - 65/6*$.1^3 + 163/6*$.1^2 - 65/3*$.1 + 6, -2/3*$.1^4 + 9/2*$.1^3 - 22/3*$.1^2 - 3/2*$.1 + 9 ], [], []> {} Total time: 4.329 seconds, Total memory usage: 2.69MB ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Sat Jan 24 09:38:40 2004 Input: P := PolynomialRing(Rationals()); C := HyperellipticCurve(x*(x-1)*(x-2)*(x-3)*(x-4)); D := QuadraticTwist(C,25); J := Jacobian(D); SetVerbose("JacHypSelmer", 2); TwoSelmerGroupData(J : Bound := 300); Output: Magma V2.10-6 Sat Jan 24 2004 09:38:36 on modular [Seed = 2049489152] ------------------------------------- TwoSelmerGroupData of Jacobian of Hyperelliptic Curve defined by y^2 = 25*x^5 - 250*x^4 + 875*x^3 - 1250*x^2 + 600*x over Rational Field m= Mapping from: CrvHyp: C to CrvHyp: C1 with equations : $.1 1/5*$.2 $.3 and inverse $.1 5*$.2 $.3 Change curve into Hyperelliptic Curve defined by y^2 = x^5 - 10*x^4 + 35*x^3 - 50*x^2 + 24*x over Rational Field Bad primes = [ 2, 3 ] f factors as (x - 4) (x - 3) (x - 2) (x - 1) (x). For factor x - 4, use field defined by x - 1 and theta = 4 For factor x - 3, use field defined by x - 1 and theta = 3 For factor x - 2, use field defined by x - 1 and theta = 2 For factor x - 1, use field defined by x - 1 and theta = 1 For factor x, use field defined by x - 1 and theta = 0 The 2-torsion group has dimension 4. Determining local images... p = 2 x = 1/4 --> new generator (0 0 0 0 0 1 0 0 0 0 0 1 0 0 0) x = 22 --> new generator (1 0 0 0 1 0 0 0 1 0 0 1 1 1 0) p = 3 x = 7 --> new generator (1 0 0 0 0 1 1 1 0 0) p = infinity Computing class groups... Class group data of the fields: Field given by x - 4: [] Field given by x - 3: [] Field given by x - 2: [] Field given by x - 1: [] Field given by x: [] Dimension of Cl[2] = 0. Signatures: [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] Dimension of units mod squares = 5. Upper bound for Selmer group dimension: 9. ==> Upper bound for rank = 5. Computing unit groups... Class group and unit data of the fields: Field given by x - 4: Class group = [], units = [ 2 ] Field given by x - 3: Class group = [], units = [ 2 ] Field given by x - 2: Class group = [], units = [ 2 ] Field given by x - 1: Class group = [], units = [ 2 ] Field given by x: Class group = [], units = [ 2 ] Time for local computations: 520 ms. Time for class groups: 0 ms. Time for unit groups: 0 ms. Selmer group dimension = 4, Dimension of 2-torsion = 4, ==> Bound for the MW-rank = 0. Total time: 590 ms. Transforming presentation of S back to model C. 0 4 <[ 1/8*$.1^4 - 3/4*$.1^3 + 3/8*$.1^2 + 5/4*$.1 + 2, -$.1^3 + 7*$.1^2 - 12*$.1 + 3, 1/4*$.1^4 - 3/2*$.1^3 + 11/4*$.1^2 - 5/2*$.1 + 4, -9/8*$.1^4 + 35/4*$.1^3 - 163/8*$.1^2 + 51/4*$.1 + 6 ], [], []> {} Total time: 3.749 seconds, Total memory usage: 2.69MB ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Sat Jan 24 09:39:04 2004 Input: P := PolynomialRing(Rationals()); C := HyperellipticCurve(x*(x-1)*(x-2)*(x-3)*(x-4)); D := QuadraticTwist(C,26); J := Jacobian(D); SetVerbose("JacHypSelmer", 2); TwoSelmerGroupData(J : Bound := 300); Output: Magma V2.10-6 Sat Jan 24 2004 09:38:59 on modular [Seed = 1664196854] ------------------------------------- TwoSelmerGroupData of Jacobian of Hyperelliptic Curve defined by y^2 = 26*x^5 - 260*x^4 + 910*x^3 - 1300*x^2 + 624*x over Rational Field m= Mapping from: CrvHyp: C to CrvHyp: C1 with equations : 26*$.1 676*$.2 $.3 and inverse 1/26*$.1 1/676*$.2 $.3 Change curve into Hyperelliptic Curve defined by y^2 = x^5 - 260*x^4 + 23660*x^3 - 878800*x^2 + 10967424*x over Rational Field Bad primes = [ 2, 3, 13 ] f factors as (x - 104) (x - 78) (x - 52) (x - 26) (x). For factor x - 104, use field defined by x - 1 and theta = 104 For factor x - 78, use field defined by x - 1 and theta = 78 For factor x - 52, use field defined by x - 1 and theta = 52 For factor x - 26, use field defined by x - 1 and theta = 26 For factor x, use field defined by x - 1 and theta = 0 The 2-torsion group has dimension 4. Determining local images... p = 2 x = 1 --> new generator (0 0 0 0 1 0 0 0 1 0 1 1 0 0 0) x = 50 --> new generator (1 0 1 0 0 0 1 1 1 1 1 0 1 0 0) p = 3 x = 3 --> new generator (0 0 1 1 0 1 0 0 1 0) p = 13 p = infinity Computing class groups... Class group data of the fields: Field given by x - 104: [] Field given by x - 78: [] Field given by x - 52: [] Field given by x - 26: [] Field given by x: [] Dimension of Cl[2] = 0. Signatures: [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] Dimension of units mod squares = 5. Upper bound for Selmer group dimension: 13. ==> Upper bound for rank = 9. Computing unit groups... Class group and unit data of the fields: Field given by x - 104: Class group = [], units = [ 2 ] Field given by x - 78: Class group = [], units = [ 2 ] Field given by x - 52: Class group = [], units = [ 2 ] Field given by x - 26: Class group = [], units = [ 2 ] Field given by x: Class group = [], units = [ 2 ] Time for local computations: 1021 ms. Time for class groups: 0 ms. Time for unit groups: 0 ms. Selmer group dimension = 5, Dimension of 2-torsion = 4, ==> Bound for the MW-rank = 1. Total time: 1121 ms. Transforming presentation of S back to model C. 1 5 <[ 15/2*$.1^4 - 56*$.1^3 + 130*$.1^2 - 229/2*$.1 + 39, -7/4*$.1^4 + 21/2*$.1^3 - 47/4*$.1^2 - 12*$.1 + 13, 42*$.1^4 - 853/2*$.1^3 + 3007/2*$.1^2 - 2131*$.1 + 1014, -99/4*$.1^4 + 220*$.1^3 - 2489/4*$.1^2 + 544*$.1 + 39, $.1^4 - 8*$.1^3 + 23*$.1^2 - 28*$.1 + 13 ], [], []> {} Total time: 4.199 seconds, Total memory usage: 2.79MB ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Sat Jan 24 09:39:23 2004 Input: P := PolynomialRing(Rationals()); C := HyperellipticCurve(x*(x-1)*(x-2)*(x-3)*(x-4)); D := QuadraticTwist(C,27); J := Jacobian(D); SetVerbose("JacHypSelmer", 2); TwoSelmerGroupData(J : Bound := 300); Output: Magma V2.10-6 Sat Jan 24 2004 09:39:19 on modular [Seed = 1748675561] ------------------------------------- TwoSelmerGroupData of Jacobian of Hyperelliptic Curve defined by y^2 = 27*x^5 - 270*x^4 + 945*x^3 - 1350*x^2 + 648*x over Rational Field m= Mapping from: CrvHyp: C to CrvHyp: C1 with equations : 3*$.1 3*$.2 $.3 and inverse 1/3*$.1 1/3*$.2 $.3 Change curve into Hyperelliptic Curve defined by y^2 = x^5 - 30*x^4 + 315*x^3 - 1350*x^2 + 1944*x over Rational Field Bad primes = [ 2, 3 ] f factors as (x - 12) (x - 9) (x - 6) (x - 3) (x). For factor x - 12, use field defined by x - 1 and theta = 12 For factor x - 9, use field defined by x - 1 and theta = 9 For factor x - 6, use field defined by x - 1 and theta = 6 For factor x - 3, use field defined by x - 1 and theta = 3 For factor x, use field defined by x - 1 and theta = 0 The 2-torsion group has dimension 4. Determining local images... p = 2 x = 1/4 --> new generator (0 0 0 0 0 1 0 0 0 0 0 1 0 0 0) x = 26 --> new generator (1 1 1 0 0 0 0 0 1 0 1 1 1 0 1) p = 3 p = infinity Computing class groups... Class group data of the fields: Field given by x - 12: [] Field given by x - 9: [] Field given by x - 6: [] Field given by x - 3: [] Field given by x: [] Dimension of Cl[2] = 0. Signatures: [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] Dimension of units mod squares = 5. Upper bound for Selmer group dimension: 11. ==> Upper bound for rank = 7. Computing unit groups... Class group and unit data of the fields: Field given by x - 12: Class group = [], units = [ 2 ] Field given by x - 9: Class group = [], units = [ 2 ] Field given by x - 6: Class group = [], units = [ 2 ] Field given by x - 3: Class group = [], units = [ 2 ] Field given by x: Class group = [], units = [ 2 ] Time for local computations: 489 ms. Time for class groups: 0 ms. Time for unit groups: 0 ms. Selmer group dimension = 4, Dimension of 2-torsion = 4, ==> Bound for the MW-rank = 0. Total time: 569 ms. Transforming presentation of S back to model C. 0 4 <[ 15/8*$.1^4 - 191/12*$.1^3 + 349/8*$.1^2 - 535/12*$.1 + 18, -1/3*$.1^3 + 3*$.1^2 - 20/3*$.1 + 3, 67/12*$.1^4 - 107/2*$.1^3 + 2129/12*$.1^2 - 473/2*$.1 + 108, 1/24*$.1^4 - 9/4*$.1^3 + 347/24*$.1^2 - 113/4*$.1 + 18 ], [], []> {} Total time: 3.639 seconds, Total memory usage: 2.69MB ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Sat Jan 24 09:39:46 2004 Input: P := PolynomialRing(Rationals()); C := HyperellipticCurve(x*(x-1)*(x-2)*(x-3)*(x-4)); D := QuadraticTwist(C,28); J := Jacobian(D); SetVerbose("JacHypSelmer", 2); TwoSelmerGroupData(J : Bound := 300); Output: Magma V2.10-6 Sat Jan 24 2004 09:39:43 on modular [Seed = 2445496872] ------------------------------------- TwoSelmerGroupData of Jacobian of Hyperelliptic Curve defined by y^2 = 28*x^5 - 280*x^4 + 980*x^3 - 1400*x^2 + 672*x over Rational Field m= Mapping from: CrvHyp: C to CrvHyp: C1 with equations : 7*$.1 49/2*$.2 $.3 and inverse 1/7*$.1 2/49*$.2 $.3 Change curve into Hyperelliptic Curve defined by y^2 = x^5 - 70*x^4 + 1715*x^3 - 17150*x^2 + 57624*x over Rational Field Bad primes = [ 2, 3, 7 ] f factors as (x - 28) (x - 21) (x - 14) (x - 7) (x). For factor x - 28, use field defined by x - 1 and theta = 28 For factor x - 21, use field defined by x - 1 and theta = 21 For factor x - 14, use field defined by x - 1 and theta = 14 For factor x - 7, use field defined by x - 1 and theta = 7 For factor x, use field defined by x - 1 and theta = 0 The 2-torsion group has dimension 4. Determining local images... p = 2 x = 1/4 --> new generator (0 0 0 0 0 1 0 0 0 0 0 1 0 0 0) x = 2 --> new generator (1 1 0 0 0 1 0 0 1 0 1 0 1 0 0) p = 3 x = 4 --> new generator (1 0 0 0 0 1 1 1 0 0) p = 7 p = infinity Computing class groups... Class group data of the fields: Field given by x - 28: [] Field given by x - 21: [] Field given by x - 14: [] Field given by x - 7: [] Field given by x: [] Dimension of Cl[2] = 0. Signatures: [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] Dimension of units mod squares = 5. Upper bound for Selmer group dimension: 13. ==> Upper bound for rank = 9. Computing unit groups... Class group and unit data of the fields: Field given by x - 28: Class group = [], units = [ 2 ] Field given by x - 21: Class group = [], units = [ 2 ] Field given by x - 14: Class group = [], units = [ 2 ] Field given by x - 7: Class group = [], units = [ 2 ] Field given by x: Class group = [], units = [ 2 ] Time for local computations: 500 ms. Time for class groups: 0 ms. Time for unit groups: 0 ms. Selmer group dimension = 4, Dimension of 2-torsion = 4, ==> Bound for the MW-rank = 0. Total time: 600 ms. Transforming presentation of S back to model C. 0 4 <[ 51/8*$.1^4 - 241/4*$.1^3 + 1513/8*$.1^2 - 921/4*$.1 + 98, 6*$.1^4 - 67*$.1^3 + 253*$.1^2 - 360*$.1 + 147, 225/4*$.1^4 - 1123/2*$.1^3 + 7851/4*$.1^2 - 5617/2*$.1 + 1372, -45/8*$.1^4 + 191/4*$.1^3 - 991/8*$.1^2 + 327/4*$.1 + 42 ], [], []> {} Total time: 3.699 seconds, Total memory usage: 2.69MB ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Sat Jan 24 09:40:10 2004 Input: P := PolynomialRing(Rationals()); C := HyperellipticCurve(x*(x-1)*(x-2)*(x-3)*(x-4)); D := QuadraticTwist(C,29); J := Jacobian(D); SetVerbose("JacHypSelmer", 2); TwoSelmerGroupData(J : Bound := 300); Output: Magma V2.10-6 Sat Jan 24 2004 09:40:06 on modular [Seed = 2178105937] ------------------------------------- TwoSelmerGroupData of Jacobian of Hyperelliptic Curve defined by y^2 = 29*x^5 - 290*x^4 + 1015*x^3 - 1450*x^2 + 696*x over Rational Field m= Mapping from: CrvHyp: C to CrvHyp: C1 with equations : 29*$.1 841*$.2 $.3 and inverse 1/29*$.1 1/841*$.2 $.3 Change curve into Hyperelliptic Curve defined by y^2 = x^5 - 290*x^4 + 29435*x^3 - 1219450*x^2 + 16974744*x over Rational Field Bad primes = [ 2, 3, 29 ] f factors as (x - 116) (x - 87) (x - 58) (x - 29) (x). For factor x - 116, use field defined by x - 1 and theta = 116 For factor x - 87, use field defined by x - 1 and theta = 87 For factor x - 58, use field defined by x - 1 and theta = 58 For factor x - 29, use field defined by x - 1 and theta = 29 For factor x, use field defined by x - 1 and theta = 0 The 2-torsion group has dimension 4. Determining local images... p = 2 x = 1/4 --> new generator (0 0 0 0 0 1 0 0 0 0 0 1 0 0 0) x = 14 --> new generator (1 0 1 0 1 1 0 0 1 0 0 0 1 1 1) p = 3 x = 3 --> new generator (0 0 1 1 0 1 0 0 1 0) p = 29 p = infinity Computing class groups... Class group data of the fields: Field given by x - 116: [] Field given by x - 87: [] Field given by x - 58: [] Field given by x - 29: [] Field given by x: [] Dimension of Cl[2] = 0. Signatures: [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] Dimension of units mod squares = 5. Upper bound for Selmer group dimension: 13. ==> Upper bound for rank = 9. Computing unit groups... Class group and unit data of the fields: Field given by x - 116: Class group = [], units = [ 2 ] Field given by x - 87: Class group = [], units = [ 2 ] Field given by x - 58: Class group = [], units = [ 2 ] Field given by x - 29: Class group = [], units = [ 2 ] Field given by x: Class group = [], units = [ 2 ] Time for local computations: 551 ms. Time for class groups: 0 ms. Time for unit groups: 0 ms. Selmer group dimension = 5, Dimension of 2-torsion = 4, ==> Bound for the MW-rank = 1. Total time: 651 ms. Transforming presentation of S back to model C. 1 5 <[ 108*$.1^4 - 1069*$.1^3 + 3698*$.1^2 - 5231*$.1 + 2523, 105*$.1^4 - 1079*$.1^3 + 3850*$.1^2 - 5486*$.1 + 2523, 24369/4*$.1^4 - 60942*$.1^3 + 853443/4*$.1^2 - 304844*$.1 + 146334, 2*$.1^4 - 16*$.1^3 + 47*$.1^2 - 60*$.1 + 29, 1595/8*$.1^4 - 7977/4*$.1^3 + 56193/8*$.1^2 - 40753/4*$.1 + 5046 ], [], []> {} Total time: 3.729 seconds, Total memory usage: 2.69MB ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Sat Jan 24 09:40:29 2004 Input: P := PolynomialRing(Rationals()); C := HyperellipticCurve(x*(x-1)*(x-2)*(x-3)*(x-4)); D := QuadraticTwist(C,30); J := Jacobian(D); SetVerbose("JacHypSelmer", 2); TwoSelmerGroupData(J : Bound := 300); Output: Magma V2.10-6 Sat Jan 24 2004 09:40:24 on modular [Seed = 3068425592] ------------------------------------- TwoSelmerGroupData of Jacobian of Hyperelliptic Curve defined by y^2 = 30*x^5 - 300*x^4 + 1050*x^3 - 1500*x^2 + 720*x over Rational Field m= Mapping from: CrvHyp: C to CrvHyp: C1 with equations : 30*$.1 900*$.2 $.3 and inverse 1/30*$.1 1/900*$.2 $.3 Change curve into Hyperelliptic Curve defined by y^2 = x^5 - 300*x^4 + 31500*x^3 - 1350000*x^2 + 19440000*x over Rational Field Bad primes = [ 2, 3, 5 ] f factors as (x - 120) (x - 90) (x - 60) (x - 30) (x). For factor x - 120, use field defined by x - 1 and theta = 120 For factor x - 90, use field defined by x - 1 and theta = 90 For factor x - 60, use field defined by x - 1 and theta = 60 For factor x - 30, use field defined by x - 1 and theta = 30 For factor x, use field defined by x - 1 and theta = 0 The 2-torsion group has dimension 4. Determining local images... p = 2 x = 1 --> new generator (0 0 0 0 1 1 0 0 1 0 1 0 0 0 0) x = 50 --> new generator (1 0 1 1 1 0 1 1 0 0 0 1 1 0 0) p = 3 p = 5 p = infinity Computing class groups... Class group data of the fields: Field given by x - 120: [] Field given by x - 90: [] Field given by x - 60: [] Field given by x - 30: [] Field given by x: [] Dimension of Cl[2] = 0. Signatures: [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] Dimension of units mod squares = 5. Upper bound for Selmer group dimension: 15. ==> Upper bound for rank = 11. Computing unit groups... Class group and unit data of the fields: Field given by x - 120: Class group = [], units = [ 2 ] Field given by x - 90: Class group = [], units = [ 2 ] Field given by x - 60: Class group = [], units = [ 2 ] Field given by x - 30: Class group = [], units = [ 2 ] Field given by x: Class group = [], units = [ 2 ] Time for local computations: 1050 ms. Time for class groups: 0 ms. Time for unit groups: 0 ms. Selmer group dimension = 5, Dimension of 2-torsion = 4, ==> Bound for the MW-rank = 1. Total time: 1160 ms. Transforming presentation of S back to model C. 1 5 <[ 13/4*$.1^4 - 185/6*$.1^3 + 409/4*$.1^2 - 431/3*$.1 + 75, -2*$.1^4 + 12*$.1^3 - 27/2*$.1^2 - 27/2*$.1 + 15, 38/3*$.1^4 - 685/6*$.1^3 + 2051/6*$.1^2 - 1165/3*$.1 + 150, 5/4*$.1^4 - 35/3*$.1^3 + 159/4*$.1^2 - 187/3*$.1 + 45, 331/4*$.1^4 - 1655/2*$.1^3 + 11609/4*$.1^2 - 8335/2*$.1 + 2025 ], [], []> {} Total time: 4.299 seconds, Total memory usage: 2.79MB ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Sat Jan 24 09:40:49 2004 Input: P := PolynomialRing(Rationals()); C := HyperellipticCurve(x*(x-1)*(x-2)*(x-3)*(x-4)); D := QuadraticTwist(C,31); J := Jacobian(D); SetVerbose("JacHypSelmer", 2); TwoSelmerGroupData(J : Bound := 300); Output: Magma V2.10-6 Sat Jan 24 2004 09:40:45 on modular [Seed = 3220012100] ------------------------------------- TwoSelmerGroupData of Jacobian of Hyperelliptic Curve defined by y^2 = 31*x^5 - 310*x^4 + 1085*x^3 - 1550*x^2 + 744*x over Rational Field m= Mapping from: CrvHyp: C to CrvHyp: C1 with equations : 31*$.1 961*$.2 $.3 and inverse 1/31*$.1 1/961*$.2 $.3 Change curve into Hyperelliptic Curve defined by y^2 = x^5 - 310*x^4 + 33635*x^3 - 1489550*x^2 + 22164504*x over Rational Field Bad primes = [ 2, 3, 31 ] f factors as (x - 124) (x - 93) (x - 62) (x - 31) (x). For factor x - 124, use field defined by x - 1 and theta = 124 For factor x - 93, use field defined by x - 1 and theta = 93 For factor x - 62, use field defined by x - 1 and theta = 62 For factor x - 31, use field defined by x - 1 and theta = 31 For factor x, use field defined by x - 1 and theta = 0 The 2-torsion group has dimension 4. Determining local images... p = 2 x = 1/4 --> new generator (0 0 0 0 0 1 0 0 0 0 0 1 0 0 0) x = 18 --> new generator (1 1 0 0 0 1 0 0 1 0 1 0 1 0 0) p = 3 x = 1 --> new generator (1 0 0 0 0 1 1 1 0 0) p = 31 p = infinity Computing class groups... Class group data of the fields: Field given by x - 124: [] Field given by x - 93: [] Field given by x - 62: [] Field given by x - 31: [] Field given by x: [] Dimension of Cl[2] = 0. Signatures: [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] Dimension of units mod squares = 5. Upper bound for Selmer group dimension: 13. ==> Upper bound for rank = 9. Computing unit groups... Class group and unit data of the fields: Field given by x - 124: Class group = [], units = [ 2 ] Field given by x - 93: Class group = [], units = [ 2 ] Field given by x - 62: Class group = [], units = [ 2 ] Field given by x - 31: Class group = [], units = [ 2 ] Field given by x: Class group = [], units = [ 2 ] Time for local computations: 511 ms. Time for class groups: 0 ms. Time for unit groups: 0 ms. Selmer group dimension = 4, Dimension of 2-torsion = 4, ==> Bound for the MW-rank = 0. Total time: 610 ms. Transforming presentation of S back to model C. 0 4 <[ 731/8*$.1^4 - 3593/4*$.1^3 + 24353/8*$.1^2 - 16625/4*$.1 + 1922, 120*$.1^4 - 1231*$.1^3 + 4387*$.1^2 - 6252*$.1 + 2883, 19841/4*$.1^4 - 99203/2*$.1^3 + 694411/4*$.1^2 - 496065/2*$.1 + 119164, -189/8*$.1^4 + 815/4*$.1^3 - 4303/8*$.1^2 + 1431/4*$.1 + 186 ], [], []> {} Total time: 3.759 seconds, Total memory usage: 2.69MB ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Sat Jan 24 09:41:09 2004 Input: P := PolynomialRing(Rationals()); C := HyperellipticCurve(x*(x-1)*(x-2)*(x-3)*(x-4)); D := QuadraticTwist(C,32); J := Jacobian(D); SetVerbose("JacHypSelmer", 2); TwoSelmerGroupData(J : Bound := 300); Output: Magma V2.10-6 Sat Jan 24 2004 09:41:04 on modular [Seed = 2784453043] ------------------------------------- TwoSelmerGroupData of Jacobian of Hyperelliptic Curve defined by y^2 = 32*x^5 - 320*x^4 + 1120*x^3 - 1600*x^2 + 768*x over Rational Field m= Mapping from: CrvHyp: C to CrvHyp: C1 with equations : 2*$.1 $.2 $.3 and inverse 1/2*$.1 $.2 $.3 Change curve into Hyperelliptic Curve defined by y^2 = x^5 - 20*x^4 + 140*x^3 - 400*x^2 + 384*x over Rational Field Bad primes = [ 2, 3 ] f factors as (x - 8) (x - 6) (x - 4) (x - 2) (x). For factor x - 8, use field defined by x - 1 and theta = 8 For factor x - 6, use field defined by x - 1 and theta = 6 For factor x - 4, use field defined by x - 1 and theta = 4 For factor x - 2, use field defined by x - 1 and theta = 2 For factor x, use field defined by x - 1 and theta = 0 The 2-torsion group has dimension 4. Determining local images... p = 2 x = 1 --> new generator (0 0 0 0 1 0 0 0 1 0 1 1 0 0 0) x = 26 --> new generator (1 0 0 0 0 1 1 1 0 1 1 0 1 0 1) p = 3 x = 3 --> new generator (0 0 1 1 0 1 0 0 1 0) p = infinity Computing class groups... Class group data of the fields: Field given by x - 8: [] Field given by x - 6: [] Field given by x - 4: [] Field given by x - 2: [] Field given by x: [] Dimension of Cl[2] = 0. Signatures: [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] Dimension of units mod squares = 5. Upper bound for Selmer group dimension: 9. ==> Upper bound for rank = 5. Computing unit groups... Class group and unit data of the fields: Field given by x - 8: Class group = [], units = [ 2 ] Field given by x - 6: Class group = [], units = [ 2 ] Field given by x - 4: Class group = [], units = [ 2 ] Field given by x - 2: Class group = [], units = [ 2 ] Field given by x: Class group = [], units = [ 2 ] Time for local computations: 1060 ms. Time for class groups: 0 ms. Time for unit groups: 1 ms. Selmer group dimension = 4, Dimension of 2-torsion = 4, ==> Bound for the MW-rank = 0. Total time: 1129 ms. Transforming presentation of S back to model C. 0 4 <[ $.1^3 - 13/2*$.1^2 + 17/2*$.1 + 3, -1/4*$.1^4 + 3/2*$.1^3 - 5/4*$.1^2 - 3*$.1 + 1, -1/2*$.1^3 + 7/2*$.1^2 - 7*$.1 + 6, -9/4*$.1^4 + 19*$.1^3 - 203/4*$.1^2 + 43*$.1 + 3 ], [], []> {} Total time: 4.259 seconds, Total memory usage: 2.69MB ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Sat Jan 24 09:41:24 2004 Input: P := PolynomialRing(Rationals()); C := HyperellipticCurve(x*(x-1)*(x-2)*(x-3)*(x-4)); D := QuadraticTwist(C,33); J := Jacobian(D); SetVerbose("JacHypSelmer", 2); TwoSelmerGroupData(J : Bound := 300); Output: Magma V2.10-6 Sat Jan 24 2004 09:41:20 on modular [Seed = 2868407980] ------------------------------------- TwoSelmerGroupData of Jacobian of Hyperelliptic Curve defined by y^2 = 33*x^5 - 330*x^4 + 1155*x^3 - 1650*x^2 + 792*x over Rational Field m= Mapping from: CrvHyp: C to CrvHyp: C1 with equations : 33*$.1 1089*$.2 $.3 and inverse 1/33*$.1 1/1089*$.2 $.3 Change curve into Hyperelliptic Curve defined by y^2 = x^5 - 330*x^4 + 38115*x^3 - 1796850*x^2 + 28462104*x over Rational Field Bad primes = [ 2, 3, 11 ] f factors as (x - 132) (x - 99) (x - 66) (x - 33) (x). For factor x - 132, use field defined by x - 1 and theta = 132 For factor x - 99, use field defined by x - 1 and theta = 99 For factor x - 66, use field defined by x - 1 and theta = 66 For factor x - 33, use field defined by x - 1 and theta = 33 For factor x, use field defined by x - 1 and theta = 0 The 2-torsion group has dimension 4. Determining local images... p = 2 x = 1/4 --> new generator (0 0 0 0 0 1 0 0 0 0 0 1 0 0 0) x = 22 --> new generator (1 0 0 0 1 0 0 0 1 0 0 1 1 1 0) p = 3 p = 11 p = infinity Computing class groups... Class group data of the fields: Field given by x - 132: [] Field given by x - 99: [] Field given by x - 66: [] Field given by x - 33: [] Field given by x: [] Dimension of Cl[2] = 0. Signatures: [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] Dimension of units mod squares = 5. Upper bound for Selmer group dimension: 15. ==> Upper bound for rank = 11. Computing unit groups... Class group and unit data of the fields: Field given by x - 132: Class group = [], units = [ 2 ] Field given by x - 99: Class group = [], units = [ 2 ] Field given by x - 66: Class group = [], units = [ 2 ] Field given by x - 33: Class group = [], units = [ 2 ] Field given by x: Class group = [], units = [ 2 ] Time for local computations: 551 ms. Time for class groups: 0 ms. Time for unit groups: 0 ms. Selmer group dimension = 5, Dimension of 2-torsion = 4, ==> Bound for the MW-rank = 1. Total time: 661 ms. Transforming presentation of S back to model C. 1 5 <[ 2555/24*$.1^4 - 12401/12*$.1^3 + 83377/24*$.1^2 - 56665/12*$.1 + 2178, 14*$.1^4 - 431/3*$.1^3 + 517*$.1^2 - 2260/3*$.1 + 363, 72011/12*$.1^4 - 119979/2*$.1^3 + 2518393/12*$.1^2 - 599245/2*$.1 + 143748, 173/24*$.1^4 - 293/4*$.1^3 + 6319/24*$.1^2 - 1557/4*$.1 + 198, 124/3*$.1^4 - 1240/3*$.1^3 + 4388/3*$.1^2 - 6440/3*$.1 + 1089 ], [], []> {} Total time: 3.799 seconds, Total memory usage: 2.79MB ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Sat Jan 24 09:41:39 2004 Input: P := PolynomialRing(Rationals()); C := HyperellipticCurve(x*(x-1)*(x-2)*(x-3)*(x-4)); D := QuadraticTwist(C,34); J := Jacobian(D); SetVerbose("JacHypSelmer", 2); TwoSelmerGroupData(J : Bound := 300); Output: Magma V2.10-6 Sat Jan 24 2004 09:41:34 on modular [Seed = 3548452827] ------------------------------------- TwoSelmerGroupData of Jacobian of Hyperelliptic Curve defined by y^2 = 34*x^5 - 340*x^4 + 1190*x^3 - 1700*x^2 + 816*x over Rational Field m= Mapping from: CrvHyp: C to CrvHyp: C1 with equations : 34*$.1 1156*$.2 $.3 and inverse 1/34*$.1 1/1156*$.2 $.3 Change curve into Hyperelliptic Curve defined by y^2 = x^5 - 340*x^4 + 40460*x^3 - 1965200*x^2 + 32072064*x over Rational Field Bad primes = [ 2, 3, 17 ] f factors as (x - 136) (x - 102) (x - 68) (x - 34) (x). For factor x - 136, use field defined by x - 1 and theta = 136 For factor x - 102, use field defined by x - 1 and theta = 102 For factor x - 68, use field defined by x - 1 and theta = 68 For factor x - 34, use field defined by x - 1 and theta = 34 For factor x, use field defined by x - 1 and theta = 0 The 2-torsion group has dimension 4. Determining local images... p = 2 x = 1 --> new generator (0 0 0 0 1 0 0 0 1 0 1 1 0 0 0) x = 58 --> new generator (1 0 0 0 0 1 1 1 0 1 1 0 1 0 1) p = 3 x = 4 --> new generator (1 0 0 0 0 1 1 1 0 0) p = 17 p = infinity Computing class groups... Class group data of the fields: Field given by x - 136: [] Field given by x - 102: [] Field given by x - 68: [] Field given by x - 34: [] Field given by x: [] Dimension of Cl[2] = 0. Signatures: [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] Dimension of units mod squares = 5. Upper bound for Selmer group dimension: 13. ==> Upper bound for rank = 9. Computing unit groups... Class group and unit data of the fields: Field given by x - 136: Class group = [], units = [ 2 ] Field given by x - 102: Class group = [], units = [ 2 ] Field given by x - 68: Class group = [], units = [ 2 ] Field given by x - 34: Class group = [], units = [ 2 ] Field given by x: Class group = [], units = [ 2 ] Time for local computations: 1081 ms. Time for class groups: 0 ms. Time for unit groups: 0 ms. Selmer group dimension = 6, Dimension of 2-torsion = 4, ==> Bound for the MW-rank = 2. Total time: 1190 ms. Transforming presentation of S back to model C. 2 6 <[ -14*$.1^4 + 125*$.1^3 - 705/2*$.1^2 + 585/2*$.1 + 51, -1/4*$.1^4 + 3/2*$.1^3 - 5/4*$.1^2 - 3*$.1 + 1, 12*$.1^4 - 209/2*$.1^3 + 591/2*$.1^2 - 303*$.1 + 102, -129/4*$.1^4 + 287*$.1^3 - 3251/4*$.1^2 + 711*$.1 + 51, 10*$.1^4 - 100*$.1^3 + 358*$.1^2 - 540*$.1 + 289, -2*$.1^4 + 12*$.1^3 - 14*$.1^2 - 12*$.1 + 17 ], [], []> {} Total time: 4.309 seconds, Total memory usage: 2.69MB ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Sat Jan 24 09:41:54 2004 Input: P := PolynomialRing(Rationals()); C := HyperellipticCurve(x*(x-1)*(x-2)*(x-3)*(x-4)); D := QuadraticTwist(C,35); J := Jacobian(D); SetVerbose("JacHypSelmer", 2); TwoSelmerGroupData(J : Bound := 300); Output: Magma V2.10-6 Sat Jan 24 2004 09:41:50 on modular [Seed = 3632930016] ------------------------------------- TwoSelmerGroupData of Jacobian of Hyperelliptic Curve defined by y^2 = 35*x^5 - 350*x^4 + 1225*x^3 - 1750*x^2 + 840*x over Rational Field m= Mapping from: CrvHyp: C to CrvHyp: C1 with equations : 35*$.1 1225*$.2 $.3 and inverse 1/35*$.1 1/1225*$.2 $.3 Change curve into Hyperelliptic Curve defined by y^2 = x^5 - 350*x^4 + 42875*x^3 - 2143750*x^2 + 36015000*x over Rational Field Bad primes = [ 2, 3, 5, 7 ] f factors as (x - 140) (x - 105) (x - 70) (x - 35) (x). For factor x - 140, use field defined by x - 1 and theta = 140 For factor x - 105, use field defined by x - 1 and theta = 105 For factor x - 70, use field defined by x - 1 and theta = 70 For factor x - 35, use field defined by x - 1 and theta = 35 For factor x, use field defined by x - 1 and theta = 0 The 2-torsion group has dimension 4. Determining local images... p = 2 x = 1/4 --> new generator (0 0 0 0 0 1 0 0 0 0 0 1 0 0 0) x = 26 --> new generator (1 1 1 0 0 0 0 0 1 0 1 1 1 0 1) p = 3 x = 3 --> new generator (0 0 1 1 0 1 0 0 1 0) p = 5 p = 7 p = infinity Computing class groups... Class group data of the fields: Field given by x - 140: [] Field given by x - 105: [] Field given by x - 70: [] Field given by x - 35: [] Field given by x: [] Dimension of Cl[2] = 0. Signatures: [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] Dimension of units mod squares = 5. Upper bound for Selmer group dimension: 17. ==> Upper bound for rank = 13. Computing unit groups... Class group and unit data of the fields: Field given by x - 140: Class group = [], units = [ 2 ] Field given by x - 105: Class group = [], units = [ 2 ] Field given by x - 70: Class group = [], units = [ 2 ] Field given by x - 35: Class group = [], units = [ 2 ] Field given by x: Class group = [], units = [ 2 ] Time for local computations: 529 ms. Time for class groups: 0 ms. Time for unit groups: 0 ms. Selmer group dimension = 5, Dimension of 2-torsion = 4, ==> Bound for the MW-rank = 1. Total time: 670 ms. Transforming presentation of S back to model C. 1 5 <[ 751*$.1^4 - 7521*$.1^3 + 26391*$.1^2 - 37891*$.1 + 18375, 153*$.1^4 - 1565*$.1^3 + 5566*$.1^2 - 7934*$.1 + 3675, 169/4*$.1^4 - 426*$.1^3 + 6027/4*$.1^2 - 2170*$.1 + 1050, 7*$.1^4 - 70*$.1^3 + 246*$.1^2 - 352*$.1 + 175, 12213/8*$.1^4 - 61087/4*$.1^3 + 427807/8*$.1^2 - 305783/4*$.1 + 36750 ], [], []> {} Total time: 3.819 seconds, Total memory usage: 2.79MB ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Sat Jan 24 09:42:14 2004 Input: P := PolynomialRing(Rationals()); C := HyperellipticCurve(x*(x-1)*(x-2)*(x-3)*(x-4)); D := QuadraticTwist(C,36); J := Jacobian(D); SetVerbose("JacHypSelmer", 2); TwoSelmerGroupData(J : Bound := 300); Output: Magma V2.10-6 Sat Jan 24 2004 09:42:11 on modular [Seed = 3247637908] ------------------------------------- TwoSelmerGroupData of Jacobian of Hyperelliptic Curve defined by y^2 = 36*x^5 - 360*x^4 + 1260*x^3 - 1800*x^2 + 864*x over Rational Field m= Mapping from: CrvHyp: C to CrvHyp: C1 with equations : $.1 1/6*$.2 $.3 and inverse $.1 6*$.2 $.3 Change curve into Hyperelliptic Curve defined by y^2 = x^5 - 10*x^4 + 35*x^3 - 50*x^2 + 24*x over Rational Field Bad primes = [ 2, 3 ] f factors as (x - 4) (x - 3) (x - 2) (x - 1) (x). For factor x - 4, use field defined by x - 1 and theta = 4 For factor x - 3, use field defined by x - 1 and theta = 3 For factor x - 2, use field defined by x - 1 and theta = 2 For factor x - 1, use field defined by x - 1 and theta = 1 For factor x, use field defined by x - 1 and theta = 0 The 2-torsion group has dimension 4. Determining local images... p = 2 x = 1/4 --> new generator (0 0 0 0 0 1 0 0 0 0 0 1 0 0 0) x = 22 --> new generator (1 0 0 0 1 0 0 0 1 0 0 1 1 1 0) p = 3 x = 7 --> new generator (1 0 0 0 0 1 1 1 0 0) p = infinity Computing class groups... Class group data of the fields: Field given by x - 4: [] Field given by x - 3: [] Field given by x - 2: [] Field given by x - 1: [] Field given by x: [] Dimension of Cl[2] = 0. Signatures: [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] Dimension of units mod squares = 5. Upper bound for Selmer group dimension: 9. ==> Upper bound for rank = 5. Computing unit groups... Class group and unit data of the fields: Field given by x - 4: Class group = [], units = [ 2 ] Field given by x - 3: Class group = [], units = [ 2 ] Field given by x - 2: Class group = [], units = [ 2 ] Field given by x - 1: Class group = [], units = [ 2 ] Field given by x: Class group = [], units = [ 2 ] Time for local computations: 509 ms. Time for class groups: 0 ms. Time for unit groups: 11 ms. Selmer group dimension = 4, Dimension of 2-torsion = 4, ==> Bound for the MW-rank = 0. Total time: 580 ms. Transforming presentation of S back to model C. 0 4 <[ 1/8*$.1^4 - 3/4*$.1^3 + 3/8*$.1^2 + 5/4*$.1 + 2, -$.1^3 + 7*$.1^2 - 12*$.1 + 3, 1/4*$.1^4 - 3/2*$.1^3 + 11/4*$.1^2 - 5/2*$.1 + 4, -9/8*$.1^4 + 35/4*$.1^3 - 163/8*$.1^2 + 51/4*$.1 + 6 ], [], []> {} Total time: 3.669 seconds, Total memory usage: 2.69MB ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Sat Jan 24 09:42:32 2004 Input: P := PolynomialRing(Rationals()); C := HyperellipticCurve(x*(x-1)*(x-2)*(x-3)*(x-4)); D := QuadraticTwist(C,37); J := Jacobian(D); SetVerbose("JacHypSelmer", 2); TwoSelmerGroupData(J : Bound := 300); Output: Magma V2.10-6 Sat Jan 24 2004 09:42:28 on modular [Seed = 4137956020] ------------------------------------- TwoSelmerGroupData of Jacobian of Hyperelliptic Curve defined by y^2 = 37*x^5 - 370*x^4 + 1295*x^3 - 1850*x^2 + 888*x over Rational Field m= Mapping from: CrvHyp: C to CrvHyp: C1 with equations : 37*$.1 1369*$.2 $.3 and inverse 1/37*$.1 1/1369*$.2 $.3 Change curve into Hyperelliptic Curve defined by y^2 = x^5 - 370*x^4 + 47915*x^3 - 2532650*x^2 + 44979864*x over Rational Field Bad primes = [ 2, 3, 37 ] f factors as (x - 148) (x - 111) (x - 74) (x - 37) (x). For factor x - 148, use field defined by x - 1 and theta = 148 For factor x - 111, use field defined by x - 1 and theta = 111 For factor x - 74, use field defined by x - 1 and theta = 74 For factor x - 37, use field defined by x - 1 and theta = 37 For factor x, use field defined by x - 1 and theta = 0 The 2-torsion group has dimension 4. Determining local images... p = 2 x = 1/4 --> new generator (0 0 0 0 0 1 0 0 0 0 0 1 0 0 0) x = 30 --> new generator (1 0 1 0 1 1 0 0 1 0 0 0 1 1 1) p = 3 x = 7 --> new generator (1 0 0 0 0 1 1 1 0 0) p = 37 p = infinity Computing class groups... Class group data of the fields: Field given by x - 148: [] Field given by x - 111: [] Field given by x - 74: [] Field given by x - 37: [] Field given by x: [] Dimension of Cl[2] = 0. Signatures: [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] Dimension of units mod squares = 5. Upper bound for Selmer group dimension: 13. ==> Upper bound for rank = 9. Computing unit groups... Class group and unit data of the fields: Field given by x - 148: Class group = [], units = [ 2 ] Field given by x - 111: Class group = [], units = [ 2 ] Field given by x - 74: Class group = [], units = [ 2 ] Field given by x - 37: Class group = [], units = [ 2 ] Field given by x: Class group = [], units = [ 2 ] Time for local computations: 540 ms. Time for class groups: 0 ms. Time for unit groups: 9 ms. Selmer group dimension = 5, Dimension of 2-torsion = 4, ==> Bound for the MW-rank = 1. Total time: 659 ms. Transforming presentation of S back to model C. 1 5 <[ 1021/8*$.1^4 - 5031/4*$.1^3 + 34263/8*$.1^2 - 23551/4*$.1 + 2738, -$.1^3 + 7*$.1^2 - 12*$.1 + 3, 97/4*$.1^4 - 411/2*$.1^3 + 2219/4*$.1^2 - 1037/2*$.1 + 148, -225/8*$.1^4 + 971/4*$.1^3 - 5131/8*$.1^2 + 1707/4*$.1 + 222, 45*$.1^4 - 474*$.1^3 + 1755*$.1^2 - 2658*$.1 + 1369 ], [], []> {} Total time: 3.789 seconds, Total memory usage: 2.69MB ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Sat Jan 24 09:42:49 2004 Input: P := PolynomialRing(Rationals()); C := HyperellipticCurve(x*(x-1)*(x-2)*(x-3)*(x-4)); D := QuadraticTwist(C,38); J := Jacobian(D); SetVerbose("JacHypSelmer", 2); TwoSelmerGroupData(J : Bound := 300); Output: Magma V2.10-6 Sat Jan 24 2004 09:42:45 on modular [Seed = 4289543052] ------------------------------------- TwoSelmerGroupData of Jacobian of Hyperelliptic Curve defined by y^2 = 38*x^5 - 380*x^4 + 1330*x^3 - 1900*x^2 + 912*x over Rational Field m= Mapping from: CrvHyp: C to CrvHyp: C1 with equations : 38*$.1 1444*$.2 $.3 and inverse 1/38*$.1 1/1444*$.2 $.3 Change curve into Hyperelliptic Curve defined by y^2 = x^5 - 380*x^4 + 50540*x^3 - 2743600*x^2 + 50043264*x over Rational Field Bad primes = [ 2, 3, 19 ] f factors as (x - 152) (x - 114) (x - 76) (x - 38) (x). For factor x - 152, use field defined by x - 1 and theta = 152 For factor x - 114, use field defined by x - 1 and theta = 114 For factor x - 76, use field defined by x - 1 and theta = 76 For factor x - 38, use field defined by x - 1 and theta = 38 For factor x, use field defined by x - 1 and theta = 0 The 2-torsion group has dimension 4. Determining local images... p = 2 x = 1 --> new generator (0 0 0 0 1 1 0 0 1 0 1 0 0 0 0) x = 10 --> new generator (1 0 0 1 1 0 1 1 1 0 0 0 1 0 1) p = 3 x = 3 --> new generator (0 0 1 1 0 1 0 0 1 0) p = 19 p = infinity Computing class groups... Class group data of the fields: Field given by x - 152: [] Field given by x - 114: [] Field given by x - 76: [] Field given by x - 38: [] Field given by x: [] Dimension of Cl[2] = 0. Signatures: [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] Dimension of units mod squares = 5. Upper bound for Selmer group dimension: 13. ==> Upper bound for rank = 9. Computing unit groups... Class group and unit data of the fields: Field given by x - 152: Class group = [], units = [ 2 ] Field given by x - 114: Class group = [], units = [ 2 ] Field given by x - 76: Class group = [], units = [ 2 ] Field given by x - 38: Class group = [], units = [ 2 ] Field given by x: Class group = [], units = [ 2 ] Time for local computations: 1120 ms. Time for class groups: 0 ms. Time for unit groups: 9 ms. Selmer group dimension = 5, Dimension of 2-torsion = 4, ==> Bound for the MW-rank = 1. Total time: 1241 ms. Transforming presentation of S back to model C. 1 5 <[ 195/4*$.1^4 - 929/2*$.1^3 + 6227/4*$.1^2 - 2186*$.1 + 1083, -5/2*$.1^4 + 15*$.1^3 - 17*$.1^2 - 33/2*$.1 + 19, 90*$.1^4 - 1819/2*$.1^3 + 6397/2*$.1^2 - 4543*$.1 + 2166, 2*$.1^4 - 39/2*$.1^3 + 70*$.1^2 - 211/2*$.1 + 57, 8*$.1^4 - 80*$.1^3 + 308*$.1^2 - 540*$.1 + 361 ], [], []> {} Total time: 4.379 seconds, Total memory usage: 2.69MB ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Sat Jan 24 09:43:10 2004 Input: P := PolynomialRing(Rationals()); C := HyperellipticCurve(x*(x-1)*(x-2)*(x-3)*(x-4)); D := QuadraticTwist(C,39); J := Jacobian(D); SetVerbose("JacHypSelmer", 2); TwoSelmerGroupData(J : Bound := 300); Output: Magma V2.10-6 Sat Jan 24 2004 09:43:06 on modular [Seed = 3853984137] ------------------------------------- TwoSelmerGroupData of Jacobian of Hyperelliptic Curve defined by y^2 = 39*x^5 - 390*x^4 + 1365*x^3 - 1950*x^2 + 936*x over Rational Field m= Mapping from: CrvHyp: C to CrvHyp: C1 with equations : 39*$.1 1521*$.2 $.3 and inverse 1/39*$.1 1/1521*$.2 $.3 Change curve into Hyperelliptic Curve defined by y^2 = x^5 - 390*x^4 + 53235*x^3 - 2965950*x^2 + 55522584*x over Rational Field Bad primes = [ 2, 3, 13 ] f factors as (x - 156) (x - 117) (x - 78) (x - 39) (x). For factor x - 156, use field defined by x - 1 and theta = 156 For factor x - 117, use field defined by x - 1 and theta = 117 For factor x - 78, use field defined by x - 1 and theta = 78 For factor x - 39, use field defined by x - 1 and theta = 39 For factor x, use field defined by x - 1 and theta = 0 The 2-torsion group has dimension 4. Determining local images... p = 2 x = 1/4 --> new generator (0 0 0 0 0 1 0 0 0 0 0 1 0 0 0) x = 2 --> new generator (1 1 0 0 0 1 0 0 1 0 1 0 1 0 0) p = 3 p = 13 p = infinity Computing class groups... Class group data of the fields: Field given by x - 156: [] Field given by x - 117: [] Field given by x - 78: [] Field given by x - 39: [] Field given by x: [] Dimension of Cl[2] = 0. Signatures: [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] Dimension of units mod squares = 5. Upper bound for Selmer group dimension: 15. ==> Upper bound for rank = 11. Computing unit groups... Class group and unit data of the fields: Field given by x - 156: Class group = [], units = [ 2 ] Field given by x - 117: Class group = [], units = [ 2 ] Field given by x - 78: Class group = [], units = [ 2 ] Field given by x - 39: Class group = [], units = [ 2 ] Field given by x: Class group = [], units = [ 2 ] Time for local computations: 520 ms. Time for class groups: 0 ms. Time for unit groups: 0 ms. Selmer group dimension = 5, Dimension of 2-torsion = 4, ==> Bound for the MW-rank = 1. Total time: 641 ms. Transforming presentation of S back to model C. 1 5 <[ 1163/8*$.1^4 - 17003/12*$.1^3 + 38321/8*$.1^2 - 78691/12*$.1 + 3042, -1/3*$.1^3 + 3*$.1^2 - 20/3*$.1 + 3, 931/12*$.1^4 - 1475/2*$.1^3 + 28913/12*$.1^2 - 6305/2*$.1 + 1404, 121/24*$.1^4 - 225/4*$.1^3 + 5411/24*$.1^2 - 1529/4*$.1 + 234, 3*$.1^4 - 38*$.1^3 + 165*$.1^2 - 286*$.1 + 169 ], [], []> {} Total time: 3.719 seconds, Total memory usage: 2.79MB ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Sat Jan 24 09:43:24 2004 Input: P := PolynomialRing(Rationals()); C := HyperellipticCurve(x*(x-1)*(x-2)*(x-3)*(x-4)); D := QuadraticTwist(C,40); J := Jacobian(D); SetVerbose("JacHypSelmer", 2); TwoSelmerGroupData(J : Bound := 300); Output: Magma V2.10-6 Sat Jan 24 2004 09:43:20 on modular [Seed = 3954782069] ------------------------------------- TwoSelmerGroupData of Jacobian of Hyperelliptic Curve defined by y^2 = 40*x^5 - 400*x^4 + 1400*x^3 - 2000*x^2 + 960*x over Rational Field m= Mapping from: CrvHyp: C to CrvHyp: C1 with equations : 10*$.1 50*$.2 $.3 and inverse 1/10*$.1 1/50*$.2 $.3 Change curve into Hyperelliptic Curve defined by y^2 = x^5 - 100*x^4 + 3500*x^3 - 50000*x^2 + 240000*x over Rational Field Bad primes = [ 2, 3, 5 ] f factors as (x - 40) (x - 30) (x - 20) (x - 10) (x). For factor x - 40, use field defined by x - 1 and theta = 40 For factor x - 30, use field defined by x - 1 and theta = 30 For factor x - 20, use field defined by x - 1 and theta = 20 For factor x - 10, use field defined by x - 1 and theta = 10 For factor x, use field defined by x - 1 and theta = 0 The 2-torsion group has dimension 4. Determining local images... p = 2 x = 1 --> new generator (0 0 0 0 1 0 0 0 1 0 1 1 0 0 0) x = 34 --> new generator (1 0 1 0 0 0 1 1 1 1 1 0 1 0 0) p = 3 x = 7 --> new generator (1 0 0 0 0 1 1 1 0 0) p = 5 p = infinity Computing class groups... Class group data of the fields: Field given by x - 40: [] Field given by x - 30: [] Field given by x - 20: [] Field given by x - 10: [] Field given by x: [] Dimension of Cl[2] = 0. Signatures: [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] Dimension of units mod squares = 5. Upper bound for Selmer group dimension: 13. ==> Upper bound for rank = 9. Computing unit groups... Class group and unit data of the fields: Field given by x - 40: Class group = [], units = [ 2 ] Field given by x - 30: Class group = [], units = [ 2 ] Field given by x - 20: Class group = [], units = [ 2 ] Field given by x - 10: Class group = [], units = [ 2 ] Field given by x: Class group = [], units = [ 2 ] Time for local computations: 1070 ms. Time for class groups: 0 ms. Time for unit groups: 0 ms. Selmer group dimension = 5, Dimension of 2-torsion = 4, ==> Bound for the MW-rank = 1. Total time: 1169 ms. Transforming presentation of S back to model C. 1 5 <[ 25*$.1^4 - 250*$.1^3 + 875*$.1^2 - 1260*$.1 + 625, 51/4*$.1^4 - 273/2*$.1^3 + 2041/4*$.1^2 - 1533/2*$.1 + 375, 3/4*$.1^4 - 10*$.1^3 + 181/4*$.1^2 - 81*$.1 + 50, 1/4*$.1^4 - 3/2*$.1^3 + 7/4*$.1^2 + 1/2*$.1 + 5, 7/2*$.1^4 - 33*$.1^3 + 107*$.1^2 - 285/2*$.1 + 75 ], [], []> {} Total time: 4.319 seconds, Total memory usage: 2.69MB ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Sat Jan 24 09:43:48 2004 Input: P := PolynomialRing(Rationals()); C := HyperellipticCurve(x*(x-1)*(x-2)*(x-3)*(x-4)); D := QuadraticTwist(C,41); J := Jacobian(D); SetVerbose("JacHypSelmer", 2); TwoSelmerGroupData(J : Bound := 300); Output: Magma V2.10-6 Sat Jan 24 2004 09:43:44 on modular [Seed = 289658278] ------------------------------------- TwoSelmerGroupData of Jacobian of Hyperelliptic Curve defined by y^2 = 41*x^5 - 410*x^4 + 1435*x^3 - 2050*x^2 + 984*x over Rational Field m= Mapping from: CrvHyp: C to CrvHyp: C1 with equations : 41*$.1 1681*$.2 $.3 and inverse 1/41*$.1 1/1681*$.2 $.3 Change curve into Hyperelliptic Curve defined by y^2 = x^5 - 410*x^4 + 58835*x^3 - 3446050*x^2 + 67818264*x over Rational Field Bad primes = [ 2, 3, 41 ] f factors as (x - 164) (x - 123) (x - 82) (x - 41) (x). For factor x - 164, use field defined by x - 1 and theta = 164 For factor x - 123, use field defined by x - 1 and theta = 123 For factor x - 82, use field defined by x - 1 and theta = 82 For factor x - 41, use field defined by x - 1 and theta = 41 For factor x, use field defined by x - 1 and theta = 0 The 2-torsion group has dimension 4. Determining local images... p = 2 x = 1/4 --> new generator (0 0 0 0 0 1 0 0 0 0 0 1 0 0 0) x = 6 --> new generator (1 0 0 0 1 0 0 0 1 0 0 1 1 1 0) p = 3 x = 3 --> new generator (0 0 1 1 0 1 0 0 1 0) p = 41 p = infinity Computing class groups... Class group data of the fields: Field given by x - 164: [] Field given by x - 123: [] Field given by x - 82: [] Field given by x - 41: [] Field given by x: [] Dimension of Cl[2] = 0. Signatures: [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] Dimension of units mod squares = 5. Upper bound for Selmer group dimension: 13. ==> Upper bound for rank = 9. Computing unit groups... Class group and unit data of the fields: Field given by x - 164: Class group = [], units = [ 2 ] Field given by x - 123: Class group = [], units = [ 2 ] Field given by x - 82: Class group = [], units = [ 2 ] Field given by x - 41: Class group = [], units = [ 2 ] Field given by x: Class group = [], units = [ 2 ] Time for local computations: 540 ms. Time for class groups: 0 ms. Time for unit groups: 0 ms. Selmer group dimension = 6, Dimension of 2-torsion = 4, ==> Bound for the MW-rank = 2. Total time: 649 ms. Transforming presentation of S back to model C. 2 6 <[ 1121/8*$.1^4 - 5523/4*$.1^3 + 38083/8*$.1^2 - 27035/4*$.1 + 3362, 25*$.1^4 - 231*$.1^3 + 702*$.1^2 - 742*$.1 + 123, 1121/4*$.1^4 - 5563/2*$.1^3 + 38651/4*$.1^2 - 27525/2*$.1 + 6724, -249/8*$.1^4 + 1075/4*$.1^3 - 5683/8*$.1^2 + 1891/4*$.1 + 246, 65*$.1^4 - 650*$.1^3 + 2295*$.1^2 - 3350*$.1 + 1681, -5*$.1^4 + 30*$.1^3 - 35*$.1^2 - 30*$.1 + 41 ], [], []> {} Total time: 3.799 seconds, Total memory usage: 2.69MB ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Sat Jan 24 09:44:02 2004 Input: P := PolynomialRing(Rationals()); C := HyperellipticCurve(x*(x-1)*(x-2)*(x-3)*(x-4)); D := QuadraticTwist(C,42); J := Jacobian(D); SetVerbose("JacHypSelmer", 2); TwoSelmerGroupData(J : Bound := 300); Output: Magma V2.10-6 Sat Jan 24 2004 09:43:57 on modular [Seed = 407559330] ------------------------------------- TwoSelmerGroupData of Jacobian of Hyperelliptic Curve defined by y^2 = 42*x^5 - 420*x^4 + 1470*x^3 - 2100*x^2 + 1008*x over Rational Field m= Mapping from: CrvHyp: C to CrvHyp: C1 with equations : 42*$.1 1764*$.2 $.3 and inverse 1/42*$.1 1/1764*$.2 $.3 Change curve into Hyperelliptic Curve defined by y^2 = x^5 - 420*x^4 + 61740*x^3 - 3704400*x^2 + 74680704*x over Rational Field Bad primes = [ 2, 3, 7 ] f factors as (x - 168) (x - 126) (x - 84) (x - 42) (x). For factor x - 168, use field defined by x - 1 and theta = 168 For factor x - 126, use field defined by x - 1 and theta = 126 For factor x - 84, use field defined by x - 1 and theta = 84 For factor x - 42, use field defined by x - 1 and theta = 42 For factor x, use field defined by x - 1 and theta = 0 The 2-torsion group has dimension 4. Determining local images... p = 2 x = 1 --> new generator (0 0 0 0 1 0 0 0 1 0 1 1 0 0 0) x = 2 --> new generator (1 0 1 0 0 0 1 1 1 1 1 0 1 0 0) p = 3 p = 7 p = infinity Computing class groups... Class group data of the fields: Field given by x - 168: [] Field given by x - 126: [] Field given by x - 84: [] Field given by x - 42: [] Field given by x: [] Dimension of Cl[2] = 0. Signatures: [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] Dimension of units mod squares = 5. Upper bound for Selmer group dimension: 15. ==> Upper bound for rank = 11. Computing unit groups... Class group and unit data of the fields: Field given by x - 168: Class group = [], units = [ 2 ] Field given by x - 126: Class group = [], units = [ 2 ] Field given by x - 84: Class group = [], units = [ 2 ] Field given by x - 42: Class group = [], units = [ 2 ] Field given by x: Class group = [], units = [ 2 ] Time for local computations: 1051 ms. Time for class groups: 0 ms. Time for unit groups: 0 ms. Selmer group dimension = 4, Dimension of 2-torsion = 4, ==> Bound for the MW-rank = 0. Total time: 1169 ms. Transforming presentation of S back to model C. 0 4 <[ 13/2*$.1^4 - 188/3*$.1^3 + 211*$.1^2 - 1775/6*$.1 + 147, -11/4*$.1^4 + 33/2*$.1^3 - 75/4*$.1^2 - 18*$.1 + 21, 64/3*$.1^4 - 1175/6*$.1^3 + 3625/6*$.1^2 - 2165/3*$.1 + 294, -29/12*$.1^4 + 18*$.1^3 - 391/12*$.1^2 - 18*$.1 + 63 ], [], []> {} Total time: 4.299 seconds, Total memory usage: 2.69MB ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Sat Jan 24 09:44:20 2004 Input: P := PolynomialRing(Rationals()); C := HyperellipticCurve(x*(x-1)*(x-2)*(x-3)*(x-4)); D := QuadraticTwist(C,43); J := Jacobian(D); SetVerbose("JacHypSelmer", 2); TwoSelmerGroupData(J : Bound := 300); Output: Magma V2.10-6 Sat Jan 24 2004 09:44:16 on modular [Seed = 257805272] ------------------------------------- TwoSelmerGroupData of Jacobian of Hyperelliptic Curve defined by y^2 = 43*x^5 - 430*x^4 + 1505*x^3 - 2150*x^2 + 1032*x over Rational Field m= Mapping from: CrvHyp: C to CrvHyp: C1 with equations : 43*$.1 1849*$.2 $.3 and inverse 1/43*$.1 1/1849*$.2 $.3 Change curve into Hyperelliptic Curve defined by y^2 = x^5 - 430*x^4 + 64715*x^3 - 3975350*x^2 + 82051224*x over Rational Field Bad primes = [ 2, 3, 43 ] f factors as (x - 172) (x - 129) (x - 86) (x - 43) (x). For factor x - 172, use field defined by x - 1 and theta = 172 For factor x - 129, use field defined by x - 1 and theta = 129 For factor x - 86, use field defined by x - 1 and theta = 86 For factor x - 43, use field defined by x - 1 and theta = 43 For factor x, use field defined by x - 1 and theta = 0 The 2-torsion group has dimension 4. Determining local images... p = 2 x = 1/4 --> new generator (0 0 0 0 0 1 0 0 0 0 0 1 0 0 0) x = 10 --> new generator (1 1 1 0 0 0 0 0 1 0 1 1 1 0 1) p = 3 x = 4 --> new generator (1 0 0 0 0 1 1 1 0 0) p = 43 p = infinity Computing class groups... Class group data of the fields: Field given by x - 172: [] Field given by x - 129: [] Field given by x - 86: [] Field given by x - 43: [] Field given by x: [] Dimension of Cl[2] = 0. Signatures: [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] Dimension of units mod squares = 5. Upper bound for Selmer group dimension: 13. ==> Upper bound for rank = 9. Computing unit groups... Class group and unit data of the fields: Field given by x - 172: Class group = [], units = [ 2 ] Field given by x - 129: Class group = [], units = [ 2 ] Field given by x - 86: Class group = [], units = [ 2 ] Field given by x - 43: Class group = [], units = [ 2 ] Field given by x: Class group = [], units = [ 2 ] Time for local computations: 520 ms. Time for class groups: 0 ms. Time for unit groups: 0 ms. Selmer group dimension = 5, Dimension of 2-torsion = 4, ==> Bound for the MW-rank = 1. Total time: 631 ms. Transforming presentation of S back to model C. 1 5 <[ 1359/8*$.1^4 - 6709/4*$.1^3 + 45853/8*$.1^2 - 31677/4*$.1 + 3698, 23*$.1^4 - 209*$.1^3 + 616*$.1^2 - 602*$.1 + 43, 52977/4*$.1^4 - 264883/2*$.1^3 + 1854171/4*$.1^2 - 1324489/2*$.1 + 318028, 779/8*$.1^4 - 4233/4*$.1^3 + 32681/8*$.1^2 - 26257/4*$.1 + 3698, -16*$.1^4 + 96*$.1^3 - 112*$.1^2 - 96*$.1 + 129 ], [], []> {} Total time: 3.729 seconds, Total memory usage: 2.69MB ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Sat Jan 24 09:44:47 2004 Input: P := PolynomialRing(Rationals()); C := HyperellipticCurve(x*(x-1)*(x-2)*(x-3)*(x-4)); D := QuadraticTwist(C,44); J := Jacobian(D); SetVerbose("JacHypSelmer", 2); TwoSelmerGroupData(J : Bound := 300); Output: Magma V2.10-6 Sat Jan 24 2004 09:44:43 on modular [Seed = 912585466] ------------------------------------- TwoSelmerGroupData of Jacobian of Hyperelliptic Curve defined by y^2 = 44*x^5 - 440*x^4 + 1540*x^3 - 2200*x^2 + 1056*x over Rational Field m= Mapping from: CrvHyp: C to CrvHyp: C1 with equations : 11*$.1 121/2*$.2 $.3 and inverse 1/11*$.1 2/121*$.2 $.3 Change curve into Hyperelliptic Curve defined by y^2 = x^5 - 110*x^4 + 4235*x^3 - 66550*x^2 + 351384*x over Rational Field Bad primes = [ 2, 3, 11 ] f factors as (x - 44) (x - 33) (x - 22) (x - 11) (x). For factor x - 44, use field defined by x - 1 and theta = 44 For factor x - 33, use field defined by x - 1 and theta = 33 For factor x - 22, use field defined by x - 1 and theta = 22 For factor x - 11, use field defined by x - 1 and theta = 11 For factor x, use field defined by x - 1 and theta = 0 The 2-torsion group has dimension 4. Determining local images... p = 2 x = 1/4 --> new generator (0 0 0 0 0 1 0 0 0 0 0 1 0 0 0) x = 10 --> new generator (1 1 1 0 0 0 0 0 1 0 1 1 1 0 1) p = 3 x = 3 --> new generator (0 0 1 1 0 1 0 0 1 0) p = 11 p = infinity Computing class groups... Class group data of the fields: Field given by x - 44: [] Field given by x - 33: [] Field given by x - 22: [] Field given by x - 11: [] Field given by x: [] Dimension of Cl[2] = 0. Signatures: [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] Dimension of units mod squares = 5. Upper bound for Selmer group dimension: 13. ==> Upper bound for rank = 9. Computing unit groups... Class group and unit data of the fields: Field given by x - 44: Class group = [], units = [ 2 ] Field given by x - 33: Class group = [], units = [ 2 ] Field given by x - 22: Class group = [], units = [ 2 ] Field given by x - 11: Class group = [], units = [ 2 ] Field given by x: Class group = [], units = [ 2 ] Time for local computations: 500 ms. Time for class groups: 0 ms. Time for unit groups: 0 ms. Selmer group dimension = 5, Dimension of 2-torsion = 4, ==> Bound for the MW-rank = 1. Total time: 600 ms. Transforming presentation of S back to model C. 1 5 <[ 111/8*$.1^4 - 517/4*$.1^3 + 3293/8*$.1^2 - 2109/4*$.1 + 242, 10*$.1^4 - 115*$.1^3 + 457*$.1^2 - 716*$.1 + 363, 905/4*$.1^4 - 4507/2*$.1^3 + 31395/4*$.1^2 - 22289/2*$.1 + 5324, 19/8*$.1^4 - 97/4*$.1^3 + 705/8*$.1^2 - 521/4*$.1 + 66, $.1^4 - 10*$.1^3 + 51*$.1^2 - 130*$.1 + 121 ], [], []> {} Total time: 3.739 seconds, Total memory usage: 2.69MB ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Sat Jan 24 09:45:04 2004 Input: P := PolynomialRing(Rationals()); C := HyperellipticCurve(x*(x-1)*(x-2)*(x-3)*(x-4)); D := QuadraticTwist(C,45); J := Jacobian(D); SetVerbose("JacHypSelmer", 2); TwoSelmerGroupData(J : Bound := 300); Output: Magma V2.10-6 Sat Jan 24 2004 09:45:00 on modular [Seed = 963378626] ------------------------------------- TwoSelmerGroupData of Jacobian of Hyperelliptic Curve defined by y^2 = 45*x^5 - 450*x^4 + 1575*x^3 - 2250*x^2 + 1080*x over Rational Field m= Mapping from: CrvHyp: C to CrvHyp: C1 with equations : 5*$.1 25/3*$.2 $.3 and inverse 1/5*$.1 3/25*$.2 $.3 Change curve into Hyperelliptic Curve defined by y^2 = x^5 - 50*x^4 + 875*x^3 - 6250*x^2 + 15000*x over Rational Field Bad primes = [ 2, 3, 5 ] f factors as (x - 20) (x - 15) (x - 10) (x - 5) (x). For factor x - 20, use field defined by x - 1 and theta = 20 For factor x - 15, use field defined by x - 1 and theta = 15 For factor x - 10, use field defined by x - 1 and theta = 10 For factor x - 5, use field defined by x - 1 and theta = 5 For factor x, use field defined by x - 1 and theta = 0 The 2-torsion group has dimension 4. Determining local images... p = 2 x = 1/4 --> new generator (0 0 0 0 0 1 0 0 0 0 0 1 0 0 0) x = 30 --> new generator (1 0 1 0 1 1 0 0 1 0 0 0 1 1 1) p = 3 x = 3 --> new generator (0 0 1 1 0 1 0 0 1 0) p = 5 p = infinity Computing class groups... Class group data of the fields: Field given by x - 20: [] Field given by x - 15: [] Field given by x - 10: [] Field given by x - 5: [] Field given by x: [] Dimension of Cl[2] = 0. Signatures: [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] Dimension of units mod squares = 5. Upper bound for Selmer group dimension: 13. ==> Upper bound for rank = 9. Computing unit groups... Class group and unit data of the fields: Field given by x - 20: Class group = [], units = [ 2 ] Field given by x - 15: Class group = [], units = [ 2 ] Field given by x - 10: Class group = [], units = [ 2 ] Field given by x - 5: Class group = [], units = [ 2 ] Field given by x: Class group = [], units = [ 2 ] Time for local computations: 529 ms. Time for class groups: 0 ms. Time for unit groups: 0 ms. Selmer group dimension = 5, Dimension of 2-torsion = 4, ==> Bound for the MW-rank = 1. Total time: 629 ms. Transforming presentation of S back to model C. 1 5 <[ 4*$.1^4 - 37*$.1^3 + 118*$.1^2 - 155*$.1 + 75, 3*$.1^4 - 35*$.1^3 + 136*$.1^2 - 194*$.1 + 75, 121/4*$.1^4 - 306*$.1^3 + 4331/4*$.1^2 - 1556*$.1 + 750, $.1^2 - 4*$.1 + 5, 35/8*$.1^4 - 177/4*$.1^3 + 1305/8*$.1^2 - 1033/4*$.1 + 150 ], [], []> {} Total time: 3.719 seconds, Total memory usage: 2.69MB ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Sat Jan 24 09:45:26 2004 Input: P := PolynomialRing(Rationals()); C := HyperellipticCurve(x*(x-1)*(x-2)*(x-3)*(x-4)); D := QuadraticTwist(C,46); J := Jacobian(D); SetVerbose("JacHypSelmer", 2); TwoSelmerGroupData(J : Bound := 300); Output: Magma V2.10-6 Sat Jan 24 2004 09:45:21 on modular [Seed = 544400694] ------------------------------------- TwoSelmerGroupData of Jacobian of Hyperelliptic Curve defined by y^2 = 46*x^5 - 460*x^4 + 1610*x^3 - 2300*x^2 + 1104*x over Rational Field m= Mapping from: CrvHyp: C to CrvHyp: C1 with equations : 46*$.1 2116*$.2 $.3 and inverse 1/46*$.1 1/2116*$.2 $.3 Change curve into Hyperelliptic Curve defined by y^2 = x^5 - 460*x^4 + 74060*x^3 - 4866800*x^2 + 107458944*x over Rational Field Bad primes = [ 2, 3, 23 ] f factors as (x - 184) (x - 138) (x - 92) (x - 46) (x). For factor x - 184, use field defined by x - 1 and theta = 184 For factor x - 138, use field defined by x - 1 and theta = 138 For factor x - 92, use field defined by x - 1 and theta = 92 For factor x - 46, use field defined by x - 1 and theta = 46 For factor x, use field defined by x - 1 and theta = 0 The 2-torsion group has dimension 4. Determining local images... p = 2 x = 1 --> new generator (0 0 0 0 1 1 0 0 1 0 1 0 0 0 0) x = 34 --> new generator (1 0 1 1 1 0 1 1 0 0 0 1 1 0 0) p = 3 x = 7 --> new generator (1 0 0 0 0 1 1 1 0 0) p = 23 p = infinity Computing class groups... Class group data of the fields: Field given by x - 184: [] Field given by x - 138: [] Field given by x - 92: [] Field given by x - 46: [] Field given by x: [] Dimension of Cl[2] = 0. Signatures: [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] Dimension of units mod squares = 5. Upper bound for Selmer group dimension: 13. ==> Upper bound for rank = 9. Computing unit groups... Class group and unit data of the fields: Field given by x - 184: Class group = [], units = [ 2 ] Field given by x - 138: Class group = [], units = [ 2 ] Field given by x - 92: Class group = [], units = [ 2 ] Field given by x - 46: Class group = [], units = [ 2 ] Field given by x: Class group = [], units = [ 2 ] Time for local computations: 1060 ms. Time for class groups: 0 ms. Time for unit groups: 0 ms. Selmer group dimension = 6, Dimension of 2-torsion = 4, ==> Bound for the MW-rank = 2. Total time: 1181 ms. Transforming presentation of S back to model C. 2 6 <[ 25*$.1^4 - 242*$.1^3 + 815*$.1^2 - 1126*$.1 + 529, 20*$.1^4 - 208*$.1^3 + 760*$.1^2 - 1124*$.1 + 529, 7/4*$.1^4 - 22*$.1^3 + 401/4*$.1^2 - 195*$.1 + 138, -27/4*$.1^4 + 119/2*$.1^3 - 661/4*$.1^2 + 271/2*$.1 + 23, 507*$.1^4 - 5066*$.1^3 + 35419/2*$.1^2 - 50543/2*$.1 + 12167, 6015/4*$.1^4 - 30143/2*$.1^3 + 211525/4*$.1^2 - 151491/2*$.1 + 36501 ], [], []> {} Total time: 4.369 seconds, Total memory usage: 2.69MB ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Sat Jan 24 09:45:40 2004 Input: P := PolynomialRing(Rationals()); C := HyperellipticCurve(x*(x-1)*(x-2)*(x-3)*(x-4)); D := QuadraticTwist(C,47); J := Jacobian(D); SetVerbose("JacHypSelmer", 2); TwoSelmerGroupData(J : Bound := 300); Output: Magma V2.10-6 Sat Jan 24 2004 09:45:37 on modular [Seed = 1459982929] ------------------------------------- TwoSelmerGroupData of Jacobian of Hyperelliptic Curve defined by y^2 = 47*x^5 - 470*x^4 + 1645*x^3 - 2350*x^2 + 1128*x over Rational Field m= Mapping from: CrvHyp: C to CrvHyp: C1 with equations : 47*$.1 2209*$.2 $.3 and inverse 1/47*$.1 1/2209*$.2 $.3 Change curve into Hyperelliptic Curve defined by y^2 = x^5 - 470*x^4 + 77315*x^3 - 5191150*x^2 + 117112344*x over Rational Field Bad primes = [ 2, 3, 47 ] f factors as (x - 188) (x - 141) (x - 94) (x - 47) (x). For factor x - 188, use field defined by x - 1 and theta = 188 For factor x - 141, use field defined by x - 1 and theta = 141 For factor x - 94, use field defined by x - 1 and theta = 94 For factor x - 47, use field defined by x - 1 and theta = 47 For factor x, use field defined by x - 1 and theta = 0 The 2-torsion group has dimension 4. Determining local images... p = 2 x = 1/4 --> new generator (0 0 0 0 0 1 0 0 0 0 0 1 0 0 0) x = 18 --> new generator (1 1 0 0 0 1 0 0 1 0 1 0 1 0 0) p = 3 x = 3 --> new generator (0 0 1 1 0 1 0 0 1 0) p = 47 p = infinity Computing class groups... Class group data of the fields: Field given by x - 188: [] Field given by x - 141: [] Field given by x - 94: [] Field given by x - 47: [] Field given by x: [] Dimension of Cl[2] = 0. Signatures: [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] Dimension of units mod squares = 5. Upper bound for Selmer group dimension: 13. ==> Upper bound for rank = 9. Computing unit groups... Class group and unit data of the fields: Field given by x - 188: Class group = [], units = [ 2 ] Field given by x - 141: Class group = [], units = [ 2 ] Field given by x - 94: Class group = [], units = [ 2 ] Field given by x - 47: Class group = [], units = [ 2 ] Field given by x: Class group = [], units = [ 2 ] Time for local computations: 511 ms. Time for class groups: 0 ms. Time for unit groups: 0 ms. Selmer group dimension = 6, Dimension of 2-torsion = 4, ==> Bound for the MW-rank = 2. Total time: 619 ms. Transforming presentation of S back to model C. 2 6 <[ 98*$.1^4 - 964*$.1^3 + 3310*$.1^2 - 4652*$.1 + 2209, 88*$.1^4 - 896*$.1^3 + 3200*$.1^2 - 4648*$.1 + 2209, -15/4*$.1^4 + 30*$.1^3 - 253/4*$.1^2 - 10*$.1 + 94, 12927*$.1^4 - 129403*$.1^3 + 453384*$.1^2 - 648283*$.1 + 311469, 1/8*$.1^4 - 7/4*$.1^3 + 59/8*$.1^2 - 43/4*$.1 + 6, 264*$.1^4 - 2687*$.1^3 + 9547*$.1^2 - 13748*$.1 + 6627 ], [], []> {} Total time: 3.749 seconds, Total memory usage: 2.69MB ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Sat Jan 24 09:46:02 2004 Input: P := PolynomialRing(Rationals()); C := HyperellipticCurve(x*(x-1)*(x-2)*(x-3)*(x-4)); D := QuadraticTwist(C,48); J := Jacobian(D); SetVerbose("JacHypSelmer", 2); TwoSelmerGroupData(J : Bound := 300); Output: Magma V2.10-6 Sat Jan 24 2004 09:45:58 on modular [Seed = 1561303148] ------------------------------------- TwoSelmerGroupData of Jacobian of Hyperelliptic Curve defined by y^2 = 48*x^5 - 480*x^4 + 1680*x^3 - 2400*x^2 + 1152*x over Rational Field m= Mapping from: CrvHyp: C to CrvHyp: C1 with equations : 3*$.1 9/4*$.2 $.3 and inverse 1/3*$.1 4/9*$.2 $.3 Change curve into Hyperelliptic Curve defined by y^2 = x^5 - 30*x^4 + 315*x^3 - 1350*x^2 + 1944*x over Rational Field Bad primes = [ 2, 3 ] f factors as (x - 12) (x - 9) (x - 6) (x - 3) (x). For factor x - 12, use field defined by x - 1 and theta = 12 For factor x - 9, use field defined by x - 1 and theta = 9 For factor x - 6, use field defined by x - 1 and theta = 6 For factor x - 3, use field defined by x - 1 and theta = 3 For factor x, use field defined by x - 1 and theta = 0 The 2-torsion group has dimension 4. Determining local images... p = 2 x = 1/4 --> new generator (0 0 0 0 0 1 0 0 0 0 0 1 0 0 0) x = 26 --> new generator (1 1 1 0 0 0 0 0 1 0 1 1 1 0 1) p = 3 p = infinity Computing class groups... Class group data of the fields: Field given by x - 12: [] Field given by x - 9: [] Field given by x - 6: [] Field given by x - 3: [] Field given by x: [] Dimension of Cl[2] = 0. Signatures: [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] Dimension of units mod squares = 5. Upper bound for Selmer group dimension: 11. ==> Upper bound for rank = 7. Computing unit groups... Class group and unit data of the fields: Field given by x - 12: Class group = [], units = [ 2 ] Field given by x - 9: Class group = [], units = [ 2 ] Field given by x - 6: Class group = [], units = [ 2 ] Field given by x - 3: Class group = [], units = [ 2 ] Field given by x: Class group = [], units = [ 2 ] Time for local computations: 491 ms. Time for class groups: 0 ms. Time for unit groups: 0 ms. Selmer group dimension = 4, Dimension of 2-torsion = 4, ==> Bound for the MW-rank = 0. Total time: 560 ms. Transforming presentation of S back to model C. 0 4 <[ 15/8*$.1^4 - 191/12*$.1^3 + 349/8*$.1^2 - 535/12*$.1 + 18, -1/3*$.1^3 + 3*$.1^2 - 20/3*$.1 + 3, 67/12*$.1^4 - 107/2*$.1^3 + 2129/12*$.1^2 - 473/2*$.1 + 108, 1/24*$.1^4 - 9/4*$.1^3 + 347/24*$.1^2 - 113/4*$.1 + 18 ], [], []> {} Total time: 3.669 seconds, Total memory usage: 2.69MB ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Sat Jan 24 09:46:20 2004 Input: P := PolynomialRing(Rationals()); C := HyperellipticCurve(x*(x-1)*(x-2)*(x-3)*(x-4)); D := QuadraticTwist(C,49); J := Jacobian(D); SetVerbose("JacHypSelmer", 2); TwoSelmerGroupData(J : Bound := 300); Output: Magma V2.10-6 Sat Jan 24 2004 09:46:16 on modular [Seed = 1142325611] ------------------------------------- TwoSelmerGroupData of Jacobian of Hyperelliptic Curve defined by y^2 = 49*x^5 - 490*x^4 + 1715*x^3 - 2450*x^2 + 1176*x over Rational Field m= Mapping from: CrvHyp: C to CrvHyp: C1 with equations : $.1 1/7*$.2 $.3 and inverse $.1 7*$.2 $.3 Change curve into Hyperelliptic Curve defined by y^2 = x^5 - 10*x^4 + 35*x^3 - 50*x^2 + 24*x over Rational Field Bad primes = [ 2, 3 ] f factors as (x - 4) (x - 3) (x - 2) (x - 1) (x). For factor x - 4, use field defined by x - 1 and theta = 4 For factor x - 3, use field defined by x - 1 and theta = 3 For factor x - 2, use field defined by x - 1 and theta = 2 For factor x - 1, use field defined by x - 1 and theta = 1 For factor x, use field defined by x - 1 and theta = 0 The 2-torsion group has dimension 4. Determining local images... p = 2 x = 1/4 --> new generator (0 0 0 0 0 1 0 0 0 0 0 1 0 0 0) x = 22 --> new generator (1 0 0 0 1 0 0 0 1 0 0 1 1 1 0) p = 3 x = 7 --> new generator (1 0 0 0 0 1 1 1 0 0) p = infinity Computing class groups... Class group data of the fields: Field given by x - 4: [] Field given by x - 3: [] Field given by x - 2: [] Field given by x - 1: [] Field given by x: [] Dimension of Cl[2] = 0. Signatures: [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] Dimension of units mod squares = 5. Upper bound for Selmer group dimension: 9. ==> Upper bound for rank = 5. Computing unit groups... Class group and unit data of the fields: Field given by x - 4: Class group = [], units = [ 2 ] Field given by x - 3: Class group = [], units = [ 2 ] Field given by x - 2: Class group = [], units = [ 2 ] Field given by x - 1: Class group = [], units = [ 2 ] Field given by x: Class group = [], units = [ 2 ] Time for local computations: 520 ms. Time for class groups: 0 ms. Time for unit groups: 0 ms. Selmer group dimension = 4, Dimension of 2-torsion = 4, ==> Bound for the MW-rank = 0. Total time: 591 ms. Transforming presentation of S back to model C. 0 4 <[ 1/8*$.1^4 - 3/4*$.1^3 + 3/8*$.1^2 + 5/4*$.1 + 2, -$.1^3 + 7*$.1^2 - 12*$.1 + 3, 1/4*$.1^4 - 3/2*$.1^3 + 11/4*$.1^2 - 5/2*$.1 + 4, -9/8*$.1^4 + 35/4*$.1^3 - 163/8*$.1^2 + 51/4*$.1 + 6 ], [], []> {} Total time: 3.709 seconds, Total memory usage: 2.69MB ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Sat Jan 24 09:46:38 2004 Input: P := PolynomialRing(Rationals()); C := HyperellipticCurve(x*(x-1)*(x-2)*(x-3)*(x-4)); D := QuadraticTwist(C,50); J := Jacobian(D); SetVerbose("JacHypSelmer", 2); TwoSelmerGroupData(J : Bound := 300); Output: Magma V2.10-6 Sat Jan 24 2004 09:46:34 on modular [Seed = 1259965974] ------------------------------------- TwoSelmerGroupData of Jacobian of Hyperelliptic Curve defined by y^2 = 50*x^5 - 500*x^4 + 1750*x^3 - 2500*x^2 + 1200*x over Rational Field m= Mapping from: CrvHyp: C to CrvHyp: C1 with equations : 2*$.1 4/5*$.2 $.3 and inverse 1/2*$.1 5/4*$.2 $.3 Change curve into Hyperelliptic Curve defined by y^2 = x^5 - 20*x^4 + 140*x^3 - 400*x^2 + 384*x over Rational Field Bad primes = [ 2, 3 ] f factors as (x - 8) (x - 6) (x - 4) (x - 2) (x). For factor x - 8, use field defined by x - 1 and theta = 8 For factor x - 6, use field defined by x - 1 and theta = 6 For factor x - 4, use field defined by x - 1 and theta = 4 For factor x - 2, use field defined by x - 1 and theta = 2 For factor x, use field defined by x - 1 and theta = 0 The 2-torsion group has dimension 4. Determining local images... p = 2 x = 1 --> new generator (0 0 0 0 1 0 0 0 1 0 1 1 0 0 0) x = 26 --> new generator (1 0 0 0 0 1 1 1 0 1 1 0 1 0 1) p = 3 x = 3 --> new generator (0 0 1 1 0 1 0 0 1 0) p = infinity Computing class groups... Class group data of the fields: Field given by x - 8: [] Field given by x - 6: [] Field given by x - 4: [] Field given by x - 2: [] Field given by x: [] Dimension of Cl[2] = 0. Signatures: [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] Dimension of units mod squares = 5. Upper bound for Selmer group dimension: 9. ==> Upper bound for rank = 5. Computing unit groups... Class group and unit data of the fields: Field given by x - 8: Class group = [], units = [ 2 ] Field given by x - 6: Class group = [], units = [ 2 ] Field given by x - 4: Class group = [], units = [ 2 ] Field given by x - 2: Class group = [], units = [ 2 ] Field given by x: Class group = [], units = [ 2 ] Time for local computations: 1059 ms. Time for class groups: 0 ms. Time for unit groups: 0 ms. Selmer group dimension = 4, Dimension of 2-torsion = 4, ==> Bound for the MW-rank = 0. Total time: 1129 ms. Transforming presentation of S back to model C. 0 4 <[ $.1^3 - 13/2*$.1^2 + 17/2*$.1 + 3, -1/4*$.1^4 + 3/2*$.1^3 - 5/4*$.1^2 - 3*$.1 + 1, -1/2*$.1^3 + 7/2*$.1^2 - 7*$.1 + 6, -9/4*$.1^4 + 19*$.1^3 - 203/4*$.1^2 + 43*$.1 + 3 ], [], []> {} Total time: 4.339 seconds, Total memory usage: 2.69MB ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Sat Jan 24 09:46:58 2004 Input: P := PolynomialRing(Rationals()); C := HyperellipticCurve(x*(x-1)*(x-2)*(x-3)*(x-4)); D := QuadraticTwist(C,51); J := Jacobian(D); SetVerbose("JacHypSelmer", 2); TwoSelmerGroupData(J : Bound := 300); Output: Magma V2.10-6 Sat Jan 24 2004 09:46:54 on modular [Seed = 1914746683] ------------------------------------- TwoSelmerGroupData of Jacobian of Hyperelliptic Curve defined by y^2 = 51*x^5 - 510*x^4 + 1785*x^3 - 2550*x^2 + 1224*x over Rational Field m= Mapping from: CrvHyp: C to CrvHyp: C1 with equations : 51*$.1 2601*$.2 $.3 and inverse 1/51*$.1 1/2601*$.2 $.3 Change curve into Hyperelliptic Curve defined by y^2 = x^5 - 510*x^4 + 91035*x^3 - 6632550*x^2 + 162364824*x over Rational Field Bad primes = [ 2, 3, 17 ] f factors as (x - 204) (x - 153) (x - 102) (x - 51) (x). For factor x - 204, use field defined by x - 1 and theta = 204 For factor x - 153, use field defined by x - 1 and theta = 153 For factor x - 102, use field defined by x - 1 and theta = 102 For factor x - 51, use field defined by x - 1 and theta = 51 For factor x, use field defined by x - 1 and theta = 0 The 2-torsion group has dimension 4. Determining local images... p = 2 x = 1/4 --> new generator (0 0 0 0 0 1 0 0 0 0 0 1 0 0 0) x = 26 --> new generator (1 1 1 0 0 0 0 0 1 0 1 1 1 0 1) p = 3 p = 17 p = infinity Computing class groups... Class group data of the fields: Field given by x - 204: [] Field given by x - 153: [] Field given by x - 102: [] Field given by x - 51: [] Field given by x: [] Dimension of Cl[2] = 0. Signatures: [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] Dimension of units mod squares = 5. Upper bound for Selmer group dimension: 15. ==> Upper bound for rank = 11. Computing unit groups... Class group and unit data of the fields: Field given by x - 204: Class group = [], units = [ 2 ] Field given by x - 153: Class group = [], units = [ 2 ] Field given by x - 102: Class group = [], units = [ 2 ] Field given by x - 51: Class group = [], units = [ 2 ] Field given by x: Class group = [], units = [ 2 ] Time for local computations: 520 ms. Time for class groups: 0 ms. Time for unit groups: 0 ms. Selmer group dimension = 4, Dimension of 2-torsion = 4, ==> Bound for the MW-rank = 0. Total time: 639 ms. Transforming presentation of S back to model C. 0 4 <[ 5789/24*$.1^4 - 28367/12*$.1^3 + 193255/24*$.1^2 - 133543/12*$.1 + 5202, 36*$.1^4 - 1097/3*$.1^3 + 1295*$.1^2 - 5548/3*$.1 + 867, 265475/12*$.1^4 - 442411/2*$.1^3 + 9289105/12*$.1^2 - 2211193/2*$.1 + 530604, 161/24*$.1^4 - 297/4*$.1^3 + 7099/24*$.1^2 - 2001/4*$.1 + 306 ], [], []> {} Total time: 3.779 seconds, Total memory usage: 2.69MB ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Sat Jan 24 09:47:12 2004 Input: P := PolynomialRing(Rationals()); C := HyperellipticCurve(x*(x-1)*(x-2)*(x-3)*(x-4)); D := QuadraticTwist(C,50); J := Jacobian(D); SetVerbose("JacHypSelmer", 2); TwoSelmerGroupData(J : Bound := 300); Output: Magma V2.10-6 Sat Jan 24 2004 09:47:07 on modular [Seed = 2032909317] ------------------------------------- TwoSelmerGroupData of Jacobian of Hyperelliptic Curve defined by y^2 = 50*x^5 - 500*x^4 + 1750*x^3 - 2500*x^2 + 1200*x over Rational Field m= Mapping from: CrvHyp: C to CrvHyp: C1 with equations : 2*$.1 4/5*$.2 $.3 and inverse 1/2*$.1 5/4*$.2 $.3 Change curve into Hyperelliptic Curve defined by y^2 = x^5 - 20*x^4 + 140*x^3 - 400*x^2 + 384*x over Rational Field Bad primes = [ 2, 3 ] f factors as (x - 8) (x - 6) (x - 4) (x - 2) (x). For factor x - 8, use field defined by x - 1 and theta = 8 For factor x - 6, use field defined by x - 1 and theta = 6 For factor x - 4, use field defined by x - 1 and theta = 4 For factor x - 2, use field defined by x - 1 and theta = 2 For factor x, use field defined by x - 1 and theta = 0 The 2-torsion group has dimension 4. Determining local images... p = 2 x = 1 --> new generator (0 0 0 0 1 0 0 0 1 0 1 1 0 0 0) x = 26 --> new generator (1 0 0 0 0 1 1 1 0 1 1 0 1 0 1) p = 3 x = 3 --> new generator (0 0 1 1 0 1 0 0 1 0) p = infinity Computing class groups... Class group data of the fields: Field given by x - 8: [] Field given by x - 6: [] Field given by x - 4: [] Field given by x - 2: [] Field given by x: [] Dimension of Cl[2] = 0. Signatures: [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] Dimension of units mod squares = 5. Upper bound for Selmer group dimension: 9. ==> Upper bound for rank = 5. Computing unit groups... Class group and unit data of the fields: Field given by x - 8: Class group = [], units = [ 2 ] Field given by x - 6: Class group = [], units = [ 2 ] Field given by x - 4: Class group = [], units = [ 2 ] Field given by x - 2: Class group = [], units = [ 2 ] Field given by x: Class group = [], units = [ 2 ] Time for local computations: 1049 ms. Time for class groups: 0 ms. Time for unit groups: 0 ms. Selmer group dimension = 4, Dimension of 2-torsion = 4, ==> Bound for the MW-rank = 0. Total time: 1120 ms. Transforming presentation of S back to model C. 0 4 <[ $.1^3 - 13/2*$.1^2 + 17/2*$.1 + 3, -1/4*$.1^4 + 3/2*$.1^3 - 5/4*$.1^2 - 3*$.1 + 1, -1/2*$.1^3 + 7/2*$.1^2 - 7*$.1 + 6, -9/4*$.1^4 + 19*$.1^3 - 203/4*$.1^2 + 43*$.1 + 3 ], [], []> {} Total time: 4.329 seconds, Total memory usage: 2.69MB ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Sat Jan 24 09:47:26 2004 Input: P := PolynomialRing(Rationals()); C := HyperellipticCurve(x*(x-1)*(x-2)*(x-3)*(x-4)); D := QuadraticTwist(C,51); J := Jacobian(D); SetVerbose("JacHypSelmer", 2); TwoSelmerGroupData(J : Bound := 300); Output: Magma V2.10-6 Sat Jan 24 2004 09:47:22 on modular [Seed = 1613931789] ------------------------------------- TwoSelmerGroupData of Jacobian of Hyperelliptic Curve defined by y^2 = 51*x^5 - 510*x^4 + 1785*x^3 - 2550*x^2 + 1224*x over Rational Field m= Mapping from: CrvHyp: C to CrvHyp: C1 with equations : 51*$.1 2601*$.2 $.3 and inverse 1/51*$.1 1/2601*$.2 $.3 Change curve into Hyperelliptic Curve defined by y^2 = x^5 - 510*x^4 + 91035*x^3 - 6632550*x^2 + 162364824*x over Rational Field Bad primes = [ 2, 3, 17 ] f factors as (x - 204) (x - 153) (x - 102) (x - 51) (x). For factor x - 204, use field defined by x - 1 and theta = 204 For factor x - 153, use field defined by x - 1 and theta = 153 For factor x - 102, use field defined by x - 1 and theta = 102 For factor x - 51, use field defined by x - 1 and theta = 51 For factor x, use field defined by x - 1 and theta = 0 The 2-torsion group has dimension 4. Determining local images... p = 2 x = 1/4 --> new generator (0 0 0 0 0 1 0 0 0 0 0 1 0 0 0) x = 26 --> new generator (1 1 1 0 0 0 0 0 1 0 1 1 1 0 1) p = 3 p = 17 p = infinity Computing class groups... Class group data of the fields: Field given by x - 204: [] Field given by x - 153: [] Field given by x - 102: [] Field given by x - 51: [] Field given by x: [] Dimension of Cl[2] = 0. Signatures: [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] Dimension of units mod squares = 5. Upper bound for Selmer group dimension: 15. ==> Upper bound for rank = 11. Computing unit groups... Class group and unit data of the fields: Field given by x - 204: Class group = [], units = [ 2 ] Field given by x - 153: Class group = [], units = [ 2 ] Field given by x - 102: Class group = [], units = [ 2 ] Field given by x - 51: Class group = [], units = [ 2 ] Field given by x: Class group = [], units = [ 2 ] Time for local computations: 520 ms. Time for class groups: 0 ms. Time for unit groups: 11 ms. Selmer group dimension = 4, Dimension of 2-torsion = 4, ==> Bound for the MW-rank = 0. Total time: 630 ms. Transforming presentation of S back to model C. 0 4 <[ 5789/24*$.1^4 - 28367/12*$.1^3 + 193255/24*$.1^2 - 133543/12*$.1 + 5202, 36*$.1^4 - 1097/3*$.1^3 + 1295*$.1^2 - 5548/3*$.1 + 867, 265475/12*$.1^4 - 442411/2*$.1^3 + 9289105/12*$.1^2 - 2211193/2*$.1 + 530604, 161/24*$.1^4 - 297/4*$.1^3 + 7099/24*$.1^2 - 2001/4*$.1 + 306 ], [], []> {} Total time: 3.769 seconds, Total memory usage: 2.69MB ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Sat Jan 24 09:47:41 2004 Input: P := PolynomialRing(Rationals()); C := HyperellipticCurve(x*(x-1)*(x-2)*(x-3)*(x-4)); D := QuadraticTwist(C,52); J := Jacobian(D); SetVerbose("JacHypSelmer", 2); TwoSelmerGroupData(J : Bound := 300); Output: Magma V2.10-6 Sat Jan 24 2004 09:47:38 on modular [Seed = 2546291210] ------------------------------------- TwoSelmerGroupData of Jacobian of Hyperelliptic Curve defined by y^2 = 52*x^5 - 520*x^4 + 1820*x^3 - 2600*x^2 + 1248*x over Rational Field m= Mapping from: CrvHyp: C to CrvHyp: C1 with equations : 13*$.1 169/2*$.2 $.3 and inverse 1/13*$.1 2/169*$.2 $.3 Change curve into Hyperelliptic Curve defined by y^2 = x^5 - 130*x^4 + 5915*x^3 - 109850*x^2 + 685464*x over Rational Field Bad primes = [ 2, 3, 13 ] f factors as (x - 52) (x - 39) (x - 26) (x - 13) (x). For factor x - 52, use field defined by x - 1 and theta = 52 For factor x - 39, use field defined by x - 1 and theta = 39 For factor x - 26, use field defined by x - 1 and theta = 26 For factor x - 13, use field defined by x - 1 and theta = 13 For factor x, use field defined by x - 1 and theta = 0 The 2-torsion group has dimension 4. Determining local images... p = 2 x = 1/4 --> new generator (0 0 0 0 0 1 0 0 0 0 0 1 0 0 0) x = 14 --> new generator (1 0 1 0 1 1 0 0 1 0 0 0 1 1 1) p = 3 x = 1 --> new generator (1 0 0 0 0 1 1 1 0 0) p = 13 p = infinity Computing class groups... Class group data of the fields: Field given by x - 52: [] Field given by x - 39: [] Field given by x - 26: [] Field given by x - 13: [] Field given by x: [] Dimension of Cl[2] = 0. Signatures: [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] Dimension of units mod squares = 5. Upper bound for Selmer group dimension: 13. ==> Upper bound for rank = 9. Computing unit groups... Class group and unit data of the fields: Field given by x - 52: Class group = [], units = [ 2 ] Field given by x - 39: Class group = [], units = [ 2 ] Field given by x - 26: Class group = [], units = [ 2 ] Field given by x - 13: Class group = [], units = [ 2 ] Field given by x: Class group = [], units = [ 2 ] Time for local computations: 551 ms. Time for class groups: 0 ms. Time for unit groups: 0 ms. Selmer group dimension = 5, Dimension of 2-torsion = 4, ==> Bound for the MW-rank = 1. Total time: 641 ms. Transforming presentation of S back to model C. 1 5 <[ 149/8*$.1^4 - 719/4*$.1^3 + 4703/8*$.1^2 - 3047/4*$.1 + 338, -$.1^3 + 7*$.1^2 - 12*$.1 + 3, 33/4*$.1^4 - 139/2*$.1^3 + 747/4*$.1^2 - 349/2*$.1 + 52, -81/8*$.1^4 + 347/4*$.1^3 - 1819/8*$.1^2 + 603/4*$.1 + 78, 3*$.1^4 - 38*$.1^3 + 165*$.1^2 - 286*$.1 + 169 ], [], []> {} Total time: 3.789 seconds, Total memory usage: 2.79MB ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Sat Jan 24 09:47:57 2004 Input: P := PolynomialRing(Rationals()); C := HyperellipticCurve(x*(x-1)*(x-2)*(x-3)*(x-4)); D := QuadraticTwist(C,53); J := Jacobian(D); SetVerbose("JacHypSelmer", 2); TwoSelmerGroupData(J : Bound := 300); Output: Magma V2.10-6 Sat Jan 24 2004 09:47:53 on modular [Seed = 2647611411] ------------------------------------- TwoSelmerGroupData of Jacobian of Hyperelliptic Curve defined by y^2 = 53*x^5 - 530*x^4 + 1855*x^3 - 2650*x^2 + 1272*x over Rational Field m= Mapping from: CrvHyp: C to CrvHyp: C1 with equations : 53*$.1 2809*$.2 $.3 and inverse 1/53*$.1 1/2809*$.2 $.3 Change curve into Hyperelliptic Curve defined by y^2 = x^5 - 530*x^4 + 98315*x^3 - 7443850*x^2 + 189371544*x over Rational Field Bad primes = [ 2, 3, 53 ] f factors as (x - 212) (x - 159) (x - 106) (x - 53) (x). For factor x - 212, use field defined by x - 1 and theta = 212 For factor x - 159, use field defined by x - 1 and theta = 159 For factor x - 106, use field defined by x - 1 and theta = 106 For factor x - 53, use field defined by x - 1 and theta = 53 For factor x, use field defined by x - 1 and theta = 0 The 2-torsion group has dimension 4. Determining local images... p = 2 x = 1/4 --> new generator (0 0 0 0 0 1 0 0 0 0 0 1 0 0 0) x = 30 --> new generator (1 0 1 0 1 1 0 0 1 0 0 0 1 1 1) p = 3 x = 3 --> new generator (0 0 1 1 0 1 0 0 1 0) p = 53 p = infinity Computing class groups... Class group data of the fields: Field given by x - 212: [] Field given by x - 159: [] Field given by x - 106: [] Field given by x - 53: [] Field given by x: [] Dimension of Cl[2] = 0. Signatures: [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] Dimension of units mod squares = 5. Upper bound for Selmer group dimension: 13. ==> Upper bound for rank = 9. Computing unit groups... Class group and unit data of the fields: Field given by x - 212: Class group = [], units = [ 2 ] Field given by x - 159: Class group = [], units = [ 2 ] Field given by x - 106: Class group = [], units = [ 2 ] Field given by x - 53: Class group = [], units = [ 2 ] Field given by x: Class group = [], units = [ 2 ] Time for local computations: 540 ms. Time for class groups: 0 ms. Time for unit groups: 0 ms. Selmer group dimension = 5, Dimension of 2-torsion = 4, ==> Bound for the MW-rank = 1. Total time: 661 ms. Transforming presentation of S back to model C. 1 5 <[ 356*$.1^4 - 3541*$.1^3 + 12318*$.1^2 - 17507*$.1 + 8427, 351*$.1^4 - 3563*$.1^3 + 12604*$.1^2 - 17978*$.1 + 8427, 148841/4*$.1^4 - 372138*$.1^3 + 5210395/4*$.1^2 - 1860932*$.1 + 893262, 4*$.1^4 - 32*$.1^3 + 93*$.1^2 - 116*$.1 + 53, 5459/8*$.1^4 - 27297/4*$.1^3 + 191721/8*$.1^2 - 138073/4*$.1 + 16854 ], [], []> {} Total time: 3.759 seconds, Total memory usage: 2.79MB ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Sat Jan 24 09:48:11 2004 Input: P := PolynomialRing(Rationals()); C := HyperellipticCurve(x*(x-1)*(x-2)*(x-3)*(x-4)); D := QuadraticTwist(C,54); J := Jacobian(D); SetVerbose("JacHypSelmer", 2); TwoSelmerGroupData(J : Bound := 300); Output: Magma V2.10-6 Sat Jan 24 2004 09:48:07 on modular [Seed = 2228633908] ------------------------------------- TwoSelmerGroupData of Jacobian of Hyperelliptic Curve defined by y^2 = 54*x^5 - 540*x^4 + 1890*x^3 - 2700*x^2 + 1296*x over Rational Field m= Mapping from: CrvHyp: C to CrvHyp: C1 with equations : 6*$.1 12*$.2 $.3 and inverse 1/6*$.1 1/12*$.2 $.3 Change curve into Hyperelliptic Curve defined by y^2 = x^5 - 60*x^4 + 1260*x^3 - 10800*x^2 + 31104*x over Rational Field Bad primes = [ 2, 3 ] f factors as (x - 24) (x - 18) (x - 12) (x - 6) (x). For factor x - 24, use field defined by x - 1 and theta = 24 For factor x - 18, use field defined by x - 1 and theta = 18 For factor x - 12, use field defined by x - 1 and theta = 12 For factor x - 6, use field defined by x - 1 and theta = 6 For factor x, use field defined by x - 1 and theta = 0 The 2-torsion group has dimension 4. Determining local images... p = 2 x = 1 --> new generator (0 0 0 0 1 1 0 0 1 0 1 0 0 0 0) x = 42 --> new generator (1 0 0 1 1 0 1 1 1 0 0 0 1 0 1) p = 3 p = infinity Computing class groups... Class group data of the fields: Field given by x - 24: [] Field given by x - 18: [] Field given by x - 12: [] Field given by x - 6: [] Field given by x: [] Dimension of Cl[2] = 0. Signatures: [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] Dimension of units mod squares = 5. Upper bound for Selmer group dimension: 11. ==> Upper bound for rank = 7. Computing unit groups... Class group and unit data of the fields: Field given by x - 24: Class group = [], units = [ 2 ] Field given by x - 18: Class group = [], units = [ 2 ] Field given by x - 12: Class group = [], units = [ 2 ] Field given by x - 6: Class group = [], units = [ 2 ] Field given by x: Class group = [], units = [ 2 ] Time for local computations: 1071 ms. Time for class groups: 0 ms. Time for unit groups: 0 ms. Selmer group dimension = 4, Dimension of 2-torsion = 4, ==> Bound for the MW-rank = 0. Total time: 1150 ms. Transforming presentation of S back to model C. 0 4 <[ -1/4*$.1^4 + 17/6*$.1^3 - 41/4*$.1^2 + 32/3*$.1 + 3, -1/2*$.1^4 + 3*$.1^3 - 3*$.1^2 - 9/2*$.1 + 3, 4/3*$.1^4 - 65/6*$.1^3 + 163/6*$.1^2 - 65/3*$.1 + 6, -2/3*$.1^4 + 9/2*$.1^3 - 22/3*$.1^2 - 3/2*$.1 + 9 ], [], []> {} Total time: 4.269 seconds, Total memory usage: 2.69MB ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Sat Jan 24 09:48:25 2004 Input: P := PolynomialRing(Rationals()); C := HyperellipticCurve(x*(x-1)*(x-2)*(x-3)*(x-4)); D := QuadraticTwist(C,53); J := Jacobian(D); SetVerbose("JacHypSelmer", 2); TwoSelmerGroupData(J : Bound := 300); Output: Magma V2.10-6 Sat Jan 24 2004 09:48:21 on modular [Seed = 2346274345] ------------------------------------- TwoSelmerGroupData of Jacobian of Hyperelliptic Curve defined by y^2 = 53*x^5 - 530*x^4 + 1855*x^3 - 2650*x^2 + 1272*x over Rational Field m= Mapping from: CrvHyp: C to CrvHyp: C1 with equations : 53*$.1 2809*$.2 $.3 and inverse 1/53*$.1 1/2809*$.2 $.3 Change curve into Hyperelliptic Curve defined by y^2 = x^5 - 530*x^4 + 98315*x^3 - 7443850*x^2 + 189371544*x over Rational Field Bad primes = [ 2, 3, 53 ] f factors as (x - 212) (x - 159) (x - 106) (x - 53) (x). For factor x - 212, use field defined by x - 1 and theta = 212 For factor x - 159, use field defined by x - 1 and theta = 159 For factor x - 106, use field defined by x - 1 and theta = 106 For factor x - 53, use field defined by x - 1 and theta = 53 For factor x, use field defined by x - 1 and theta = 0 The 2-torsion group has dimension 4. Determining local images... p = 2 x = 1/4 --> new generator (0 0 0 0 0 1 0 0 0 0 0 1 0 0 0) x = 30 --> new generator (1 0 1 0 1 1 0 0 1 0 0 0 1 1 1) p = 3 x = 3 --> new generator (0 0 1 1 0 1 0 0 1 0) p = 53 p = infinity Computing class groups... Class group data of the fields: Field given by x - 212: [] Field given by x - 159: [] Field given by x - 106: [] Field given by x - 53: [] Field given by x: [] Dimension of Cl[2] = 0. Signatures: [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] Dimension of units mod squares = 5. Upper bound for Selmer group dimension: 13. ==> Upper bound for rank = 9. Computing unit groups... Class group and unit data of the fields: Field given by x - 212: Class group = [], units = [ 2 ] Field given by x - 159: Class group = [], units = [ 2 ] Field given by x - 106: Class group = [], units = [ 2 ] Field given by x - 53: Class group = [], units = [ 2 ] Field given by x: Class group = [], units = [ 2 ] Time for local computations: 540 ms. Time for class groups: 0 ms. Time for unit groups: 0 ms. Selmer group dimension = 5, Dimension of 2-torsion = 4, ==> Bound for the MW-rank = 1. Total time: 660 ms. Transforming presentation of S back to model C. 1 5 <[ 356*$.1^4 - 3541*$.1^3 + 12318*$.1^2 - 17507*$.1 + 8427, 351*$.1^4 - 3563*$.1^3 + 12604*$.1^2 - 17978*$.1 + 8427, 148841/4*$.1^4 - 372138*$.1^3 + 5210395/4*$.1^2 - 1860932*$.1 + 893262, 4*$.1^4 - 32*$.1^3 + 93*$.1^2 - 116*$.1 + 53, 5459/8*$.1^4 - 27297/4*$.1^3 + 191721/8*$.1^2 - 138073/4*$.1 + 16854 ], [], []> {} Total time: 3.899 seconds, Total memory usage: 2.79MB ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Sat Jan 24 09:48:39 2004 Input: P := PolynomialRing(Rationals()); C := HyperellipticCurve(x*(x-1)*(x-2)*(x-3)*(x-4)); D := QuadraticTwist(C,54); J := Jacobian(D); SetVerbose("JacHypSelmer", 2); TwoSelmerGroupData(J : Bound := 300); Output: Magma V2.10-6 Sat Jan 24 2004 09:48:34 on modular [Seed = 3001055079] ------------------------------------- TwoSelmerGroupData of Jacobian of Hyperelliptic Curve defined by y^2 = 54*x^5 - 540*x^4 + 1890*x^3 - 2700*x^2 + 1296*x over Rational Field m= Mapping from: CrvHyp: C to CrvHyp: C1 with equations : 6*$.1 12*$.2 $.3 and inverse 1/6*$.1 1/12*$.2 $.3 Change curve into Hyperelliptic Curve defined by y^2 = x^5 - 60*x^4 + 1260*x^3 - 10800*x^2 + 31104*x over Rational Field Bad primes = [ 2, 3 ] f factors as (x - 24) (x - 18) (x - 12) (x - 6) (x). For factor x - 24, use field defined by x - 1 and theta = 24 For factor x - 18, use field defined by x - 1 and theta = 18 For factor x - 12, use field defined by x - 1 and theta = 12 For factor x - 6, use field defined by x - 1 and theta = 6 For factor x, use field defined by x - 1 and theta = 0 The 2-torsion group has dimension 4. Determining local images... p = 2 x = 1 --> new generator (0 0 0 0 1 1 0 0 1 0 1 0 0 0 0) x = 42 --> new generator (1 0 0 1 1 0 1 1 1 0 0 0 1 0 1) p = 3 p = infinity Computing class groups... Class group data of the fields: Field given by x - 24: [] Field given by x - 18: [] Field given by x - 12: [] Field given by x - 6: [] Field given by x: [] Dimension of Cl[2] = 0. Signatures: [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] Dimension of units mod squares = 5. Upper bound for Selmer group dimension: 11. ==> Upper bound for rank = 7. Computing unit groups... Class group and unit data of the fields: Field given by x - 24: Class group = [], units = [ 2 ] Field given by x - 18: Class group = [], units = [ 2 ] Field given by x - 12: Class group = [], units = [ 2 ] Field given by x - 6: Class group = [], units = [ 2 ] Field given by x: Class group = [], units = [ 2 ] Time for local computations: 1069 ms. Time for class groups: 0 ms. Time for unit groups: 0 ms. Selmer group dimension = 4, Dimension of 2-torsion = 4, ==> Bound for the MW-rank = 0. Total time: 1149 ms. Transforming presentation of S back to model C. 0 4 <[ -1/4*$.1^4 + 17/6*$.1^3 - 41/4*$.1^2 + 32/3*$.1 + 3, -1/2*$.1^4 + 3*$.1^3 - 3*$.1^2 - 9/2*$.1 + 3, 4/3*$.1^4 - 65/6*$.1^3 + 163/6*$.1^2 - 65/3*$.1 + 6, -2/3*$.1^4 + 9/2*$.1^3 - 22/3*$.1^2 - 3/2*$.1 + 9 ], [], []> {} Total time: 4.339 seconds, Total memory usage: 2.69MB ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Sat Jan 24 09:49:04 2004 Input: P := PolynomialRing(Rationals()); C := HyperellipticCurve(x*(x-1)*(x-2)*(x-3)*(x-4)); D := QuadraticTwist(C,55); J := Jacobian(D); SetVerbose("JacHypSelmer", 2); TwoSelmerGroupData(J : Bound := 300); Output: Magma V2.10-6 Sat Jan 24 2004 09:49:01 on modular [Seed = 3119217779] ------------------------------------- TwoSelmerGroupData of Jacobian of Hyperelliptic Curve defined by y^2 = 55*x^5 - 550*x^4 + 1925*x^3 - 2750*x^2 + 1320*x over Rational Field m= Mapping from: CrvHyp: C to CrvHyp: C1 with equations : 55*$.1 3025*$.2 $.3 and inverse 1/55*$.1 1/3025*$.2 $.3 Change curve into Hyperelliptic Curve defined by y^2 = x^5 - 550*x^4 + 105875*x^3 - 8318750*x^2 + 219615000*x over Rational Field Bad primes = [ 2, 3, 5, 11 ] f factors as (x - 220) (x - 165) (x - 110) (x - 55) (x). For factor x - 220, use field defined by x - 1 and theta = 220 For factor x - 165, use field defined by x - 1 and theta = 165 For factor x - 110, use field defined by x - 1 and theta = 110 For factor x - 55, use field defined by x - 1 and theta = 55 For factor x, use field defined by x - 1 and theta = 0 The 2-torsion group has dimension 4. Determining local images... p = 2 x = 1/4 --> new generator (0 0 0 0 0 1 0 0 0 0 0 1 0 0 0) x = 2 --> new generator (1 1 0 0 0 1 0 0 1 0 1 0 1 0 0) p = 3 x = 7 --> new generator (1 0 0 0 0 1 1 1 0 0) p = 5 p = 11 p = infinity Computing class groups... Class group data of the fields: Field given by x - 220: [] Field given by x - 165: [] Field given by x - 110: [] Field given by x - 55: [] Field given by x: [] Dimension of Cl[2] = 0. Signatures: [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] Dimension of units mod squares = 5. Upper bound for Selmer group dimension: 17. ==> Upper bound for rank = 13. Computing unit groups... Class group and unit data of the fields: Field given by x - 220: Class group = [], units = [ 2 ] Field given by x - 165: Class group = [], units = [ 2 ] Field given by x - 110: Class group = [], units = [ 2 ] Field given by x - 55: Class group = [], units = [ 2 ] Field given by x: Class group = [], units = [ 2 ] Time for local computations: 520 ms. Time for class groups: 0 ms. Time for unit groups: 0 ms. Selmer group dimension = 4, Dimension of 2-torsion = 4, ==> Bound for the MW-rank = 0. Total time: 679 ms. Transforming presentation of S back to model C. 0 4 <[ 2179/8*$.1^4 - 10785/4*$.1^3 + 74073/8*$.1^2 - 51529/4*$.1 + 6050, 378*$.1^4 - 3835*$.1^3 + 13561*$.1^2 - 19344*$.1 + 9075, 110881/4*$.1^4 - 554403/2*$.1^3 + 3880811/4*$.1^2 - 2772113/2*$.1 + 665500, -333/8*$.1^4 + 1439/4*$.1^3 - 7615/8*$.1^2 + 2535/4*$.1 + 330 ], [], []> {} Total time: 3.779 seconds, Total memory usage: 2.79MB ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Sat Jan 24 09:49:24 2004 Input: P := PolynomialRing(Rationals()); C := HyperellipticCurve(x*(x-1)*(x-2)*(x-3)*(x-4)); D := QuadraticTwist(C,56); J := Jacobian(D); SetVerbose("JacHypSelmer", 2); TwoSelmerGroupData(J : Bound := 300); Output: Magma V2.10-6 Sat Jan 24 2004 09:49:20 on modular [Seed = 2700240199] ------------------------------------- TwoSelmerGroupData of Jacobian of Hyperelliptic Curve defined by y^2 = 56*x^5 - 560*x^4 + 1960*x^3 - 2800*x^2 + 1344*x over Rational Field m= Mapping from: CrvHyp: C to CrvHyp: C1 with equations : 14*$.1 98*$.2 $.3 and inverse 1/14*$.1 1/98*$.2 $.3 Change curve into Hyperelliptic Curve defined by y^2 = x^5 - 140*x^4 + 6860*x^3 - 137200*x^2 + 921984*x over Rational Field Bad primes = [ 2, 3, 7 ] f factors as (x - 56) (x - 42) (x - 28) (x - 14) (x). For factor x - 56, use field defined by x - 1 and theta = 56 For factor x - 42, use field defined by x - 1 and theta = 42 For factor x - 28, use field defined by x - 1 and theta = 28 For factor x - 14, use field defined by x - 1 and theta = 14 For factor x, use field defined by x - 1 and theta = 0 The 2-torsion group has dimension 4. Determining local images... p = 2 x = 1 --> new generator (0 0 0 0 1 1 0 0 1 0 1 0 0 0 0) x = 2 --> new generator (1 0 1 1 1 0 1 1 0 0 0 1 1 0 0) p = 3 x = 3 --> new generator (0 0 1 1 0 1 0 0 1 0) p = 7 p = infinity Computing class groups... Class group data of the fields: Field given by x - 56: [] Field given by x - 42: [] Field given by x - 28: [] Field given by x - 14: [] Field given by x: [] Dimension of Cl[2] = 0. Signatures: [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] Dimension of units mod squares = 5. Upper bound for Selmer group dimension: 13. ==> Upper bound for rank = 9. Computing unit groups... Class group and unit data of the fields: Field given by x - 56: Class group = [], units = [ 2 ] Field given by x - 42: Class group = [], units = [ 2 ] Field given by x - 28: Class group = [], units = [ 2 ] Field given by x - 14: Class group = [], units = [ 2 ] Field given by x: Class group = [], units = [ 2 ] Time for local computations: 1021 ms. Time for class groups: 0 ms. Time for unit groups: 0 ms. Selmer group dimension = 4, Dimension of 2-torsion = 4, ==> Bound for the MW-rank = 0. Total time: 1129 ms. Transforming presentation of S back to model C. 0 4 <[ 33/4*$.1^4 - 151/2*$.1^3 + 949/4*$.1^2 - 311*$.1 + 147, -$.1^4 + 6*$.1^3 - 13/2*$.1^2 - 15/2*$.1 + 7, 12*$.1^4 - 247/2*$.1^3 + 877/2*$.1^2 - 619*$.1 + 294, -27/2*$.1^4 + 239/2*$.1^3 - 673/2*$.1^2 + 587/2*$.1 + 21 ], [], []> {} Total time: 4.279 seconds, Total memory usage: 2.69MB ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Sat Jan 24 09:49:45 2004 Input: P := PolynomialRing(Rationals()); C := HyperellipticCurve(x*(x-1)*(x-2)*(x-3)*(x-4)); D := QuadraticTwist(C,57); J := Jacobian(D); SetVerbose("JacHypSelmer", 2); TwoSelmerGroupData(J : Bound := 300); Output: Magma V2.10-6 Sat Jan 24 2004 09:49:41 on modular [Seed = 3615822277] ------------------------------------- TwoSelmerGroupData of Jacobian of Hyperelliptic Curve defined by y^2 = 57*x^5 - 570*x^4 + 1995*x^3 - 2850*x^2 + 1368*x over Rational Field m= Mapping from: CrvHyp: C to CrvHyp: C1 with equations : 57*$.1 3249*$.2 $.3 and inverse 1/57*$.1 1/3249*$.2 $.3 Change curve into Hyperelliptic Curve defined by y^2 = x^5 - 570*x^4 + 113715*x^3 - 9259650*x^2 + 253344024*x over Rational Field Bad primes = [ 2, 3, 19 ] f factors as (x - 228) (x - 171) (x - 114) (x - 57) (x). For factor x - 228, use field defined by x - 1 and theta = 228 For factor x - 171, use field defined by x - 1 and theta = 171 For factor x - 114, use field defined by x - 1 and theta = 114 For factor x - 57, use field defined by x - 1 and theta = 57 For factor x, use field defined by x - 1 and theta = 0 The 2-torsion group has dimension 4. Determining local images... p = 2 x = 1/4 --> new generator (0 0 0 0 0 1 0 0 0 0 0 1 0 0 0) x = 6 --> new generator (1 0 0 0 1 0 0 0 1 0 0 1 1 1 0) p = 3 p = 19 p = infinity Computing class groups... Class group data of the fields: Field given by x - 228: [] Field given by x - 171: [] Field given by x - 114: [] Field given by x - 57: [] Field given by x: [] Dimension of Cl[2] = 0. Signatures: [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] Dimension of units mod squares = 5. Upper bound for Selmer group dimension: 15. ==> Upper bound for rank = 11. Computing unit groups... Class group and unit data of the fields: Field given by x - 228: Class group = [], units = [ 2 ] Field given by x - 171: Class group = [], units = [ 2 ] Field given by x - 114: Class group = [], units = [ 2 ] Field given by x - 57: Class group = [], units = [ 2 ] Field given by x: Class group = [], units = [ 2 ] Time for local computations: 551 ms. Time for class groups: 0 ms. Time for unit groups: 0 ms. Selmer group dimension = 5, Dimension of 2-torsion = 4, ==> Bound for the MW-rank = 1. Total time: 669 ms. Transforming presentation of S back to model C. 1 5 <[ 2385/8*$.1^4 - 35129/12*$.1^3 + 79987/8*$.1^2 - 166369/12*$.1 + 6498, 43*$.1^4 - 1309/3*$.1^3 + 1552*$.1^2 - 6734/3*$.1 + 1083, 370627/12*$.1^4 - 617643/2*$.1^3 + 12968465/12*$.1^2 - 3087077/2*$.1 + 740772, 325/24*$.1^4 - 541/4*$.1^3 + 11447/24*$.1^2 - 2765/4*$.1 + 342, 385/3*$.1^4 - 3850/3*$.1^3 + 13559/3*$.1^2 - 19670/3*$.1 + 3249 ], [], []> {} Total time: 3.779 seconds, Total memory usage: 2.69MB ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Sat Jan 24 09:50:09 2004 Input: P := PolynomialRing(Rationals()); C := HyperellipticCurve(x*(x-1)*(x-2)*(x-3)*(x-4)); D := QuadraticTwist(C,58); J := Jacobian(D); SetVerbose("JacHypSelmer", 2); TwoSelmerGroupData(J : Bound := 300); Output: Magma V2.10-6 Sat Jan 24 2004 09:50:04 on modular [Seed = 3348431308] ------------------------------------- TwoSelmerGroupData of Jacobian of Hyperelliptic Curve defined by y^2 = 58*x^5 - 580*x^4 + 2030*x^3 - 2900*x^2 + 1392*x over Rational Field m= Mapping from: CrvHyp: C to CrvHyp: C1 with equations : 58*$.1 3364*$.2 $.3 and inverse 1/58*$.1 1/3364*$.2 $.3 Change curve into Hyperelliptic Curve defined by y^2 = x^5 - 580*x^4 + 117740*x^3 - 9755600*x^2 + 271595904*x over Rational Field Bad primes = [ 2, 3, 29 ] f factors as (x - 232) (x - 174) (x - 116) (x - 58) (x). For factor x - 232, use field defined by x - 1 and theta = 232 For factor x - 174, use field defined by x - 1 and theta = 174 For factor x - 116, use field defined by x - 1 and theta = 116 For factor x - 58, use field defined by x - 1 and theta = 58 For factor x, use field defined by x - 1 and theta = 0 The 2-torsion group has dimension 4. Determining local images... p = 2 x = 1 --> new generator (0 0 0 0 1 0 0 0 1 0 1 1 0 0 0) x = 18 --> new generator (1 0 1 0 0 0 1 1 1 1 1 0 1 0 0) p = 3 x = 1 --> new generator (1 0 0 0 0 1 1 1 0 0) p = 29 p = infinity Computing class groups... Class group data of the fields: Field given by x - 232: [] Field given by x - 174: [] Field given by x - 116: [] Field given by x - 58: [] Field given by x: [] Dimension of Cl[2] = 0. Signatures: [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] Dimension of units mod squares = 5. Upper bound for Selmer group dimension: 13. ==> Upper bound for rank = 9. Computing unit groups... Class group and unit data of the fields: Field given by x - 232: Class group = [], units = [ 2 ] Field given by x - 174: Class group = [], units = [ 2 ] Field given by x - 116: Class group = [], units = [ 2 ] Field given by x - 58: Class group = [], units = [ 2 ] Field given by x: Class group = [], units = [ 2 ] Time for local computations: 1030 ms. Time for class groups: 0 ms. Time for unit groups: 0 ms. Selmer group dimension = 5, Dimension of 2-torsion = 4, ==> Bound for the MW-rank = 1. Total time: 1160 ms. Transforming presentation of S back to model C. 1 5 <[ 29464*$.1^4 - 294640*$.1^3 + 1031240*$.1^2 - 1473258*$.1 + 707281, 12127/4*$.1^4 - 60741/2*$.1^3 + 425949/4*$.1^2 - 304689/2*$.1 + 73167, 243/4*$.1^4 - 626*$.1^3 + 9061/4*$.1^2 - 3353*$.1 + 1682, 29/4*$.1^4 - 119/2*$.1^3 + 603/4*$.1^2 - 243/2*$.1 + 29, 219/2*$.1^4 - 1077*$.1^3 + 3697*$.1^2 - 10389/2*$.1 + 2523 ], [], []> {} Total time: 4.289 seconds, Total memory usage: 2.79MB ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Sat Jan 24 09:50:30 2004 Input: P := PolynomialRing(Rationals()); C := HyperellipticCurve(x*(x-1)*(x-2)*(x-3)*(x-4)); D := QuadraticTwist(C,59); J := Jacobian(D); SetVerbose("JacHypSelmer", 2); TwoSelmerGroupData(J : Bound := 300); Output: Magma V2.10-6 Sat Jan 24 2004 09:50:26 on modular [Seed = 3466332394] ------------------------------------- TwoSelmerGroupData of Jacobian of Hyperelliptic Curve defined by y^2 = 59*x^5 - 590*x^4 + 2065*x^3 - 2950*x^2 + 1416*x over Rational Field m= Mapping from: CrvHyp: C to CrvHyp: C1 with equations : 59*$.1 3481*$.2 $.3 and inverse 1/59*$.1 1/3481*$.2 $.3 Change curve into Hyperelliptic Curve defined by y^2 = x^5 - 590*x^4 + 121835*x^3 - 10268950*x^2 + 290816664*x over Rational Field Bad primes = [ 2, 3, 59 ] f factors as (x - 236) (x - 177) (x - 118) (x - 59) (x). For factor x - 236, use field defined by x - 1 and theta = 236 For factor x - 177, use field defined by x - 1 and theta = 177 For factor x - 118, use field defined by x - 1 and theta = 118 For factor x - 59, use field defined by x - 1 and theta = 59 For factor x, use field defined by x - 1 and theta = 0 The 2-torsion group has dimension 4. Determining local images... p = 2 x = 1/4 --> new generator (0 0 0 0 0 1 0 0 0 0 0 1 0 0 0) x = 10 --> new generator (1 1 1 0 0 0 0 0 1 0 1 1 1 0 1) p = 3 x = 3 --> new generator (0 0 1 1 0 1 0 0 1 0) p = 59 p = infinity Computing class groups... Class group data of the fields: Field given by x - 236: [] Field given by x - 177: [] Field given by x - 118: [] Field given by x - 59: [] Field given by x: [] Dimension of Cl[2] = 0. Signatures: [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] Dimension of units mod squares = 5. Upper bound for Selmer group dimension: 13. ==> Upper bound for rank = 9. Computing unit groups... Class group and unit data of the fields: Field given by x - 236: Class group = [], units = [ 2 ] Field given by x - 177: Class group = [], units = [ 2 ] Field given by x - 118: Class group = [], units = [ 2 ] Field given by x - 59: Class group = [], units = [ 2 ] Field given by x: Class group = [], units = [ 2 ] Time for local computations: 520 ms. Time for class groups: 0 ms. Time for unit groups: 0 ms. Selmer group dimension = 5, Dimension of 2-torsion = 4, ==> Bound for the MW-rank = 1. Total time: 630 ms. Transforming presentation of S back to model C. 1 5 <[ 2479/8*$.1^4 - 12197/4*$.1^3 + 83677/8*$.1^2 - 58493/4*$.1 + 6962, 408*$.1^4 - 4159*$.1^3 + 14843*$.1^2 - 21536*$.1 + 10443, 137017/4*$.1^4 - 684987/2*$.1^3 + 4794067/4*$.1^2 - 3423585/2*$.1 + 821516, 131/8*$.1^4 - 625/4*$.1^3 + 4241/8*$.1^2 - 2969/4*$.1 + 354, 123*$.1^4 - 1230*$.1^3 + 4393*$.1^2 - 6590*$.1 + 3481 ], [], []> {} Total time: 3.809 seconds, Total memory usage: 2.79MB ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Sat Jan 24 09:50:55 2004 Input: P := PolynomialRing(Rationals()); C := HyperellipticCurve(x*(x-1)*(x-2)*(x-3)*(x-4)); D := QuadraticTwist(C,60); J := Jacobian(D); SetVerbose("JacHypSelmer", 2); TwoSelmerGroupData(J : Bound := 300); Output: Magma V2.10-6 Sat Jan 24 2004 09:50:51 on modular [Seed = 4104532648] ------------------------------------- TwoSelmerGroupData of Jacobian of Hyperelliptic Curve defined by y^2 = 60*x^5 - 600*x^4 + 2100*x^3 - 3000*x^2 + 1440*x over Rational Field m= Mapping from: CrvHyp: C to CrvHyp: C1 with equations : 15*$.1 225/2*$.2 $.3 and inverse 1/15*$.1 2/225*$.2 $.3 Change curve into Hyperelliptic Curve defined by y^2 = x^5 - 150*x^4 + 7875*x^3 - 168750*x^2 + 1215000*x over Rational Field Bad primes = [ 2, 3, 5 ] f factors as (x - 60) (x - 45) (x - 30) (x - 15) (x). For factor x - 60, use field defined by x - 1 and theta = 60 For factor x - 45, use field defined by x - 1 and theta = 45 For factor x - 30, use field defined by x - 1 and theta = 30 For factor x - 15, use field defined by x - 1 and theta = 15 For factor x, use field defined by x - 1 and theta = 0 The 2-torsion group has dimension 4. Determining local images... p = 2 x = 1/4 --> new generator (0 0 0 0 0 1 0 0 0 0 0 1 0 0 0) x = 18 --> new generator (1 1 0 0 0 1 0 0 1 0 1 0 1 0 0) p = 3 p = 5 p = infinity Computing class groups... Class group data of the fields: Field given by x - 60: [] Field given by x - 45: [] Field given by x - 30: [] Field given by x - 15: [] Field given by x: [] Dimension of Cl[2] = 0. Signatures: [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] Dimension of units mod squares = 5. Upper bound for Selmer group dimension: 15. ==> Upper bound for rank = 11. Computing unit groups... Class group and unit data of the fields: Field given by x - 60: Class group = [], units = [ 2 ] Field given by x - 45: Class group = [], units = [ 2 ] Field given by x - 30: Class group = [], units = [ 2 ] Field given by x - 15: Class group = [], units = [ 2 ] Field given by x: Class group = [], units = [ 2 ] Time for local computations: 531 ms. Time for class groups: 0 ms. Time for unit groups: 0 ms. Selmer group dimension = 5, Dimension of 2-torsion = 4, ==> Bound for the MW-rank = 1. Total time: 641 ms. Transforming presentation of S back to model C. 1 5 <[ 107/8*$.1^4 - 509/4*$.1^3 + 3337/8*$.1^2 - 2209/4*$.1 + 250, 3*$.1^4 - 95/3*$.1^3 + 116*$.1^2 - 502/3*$.1 + 75, 449/4*$.1^4 - 2241/2*$.1^3 + 15663/4*$.1^2 - 11185/2*$.1 + 2700, 41/24*$.1^4 - 81/4*$.1^3 + 2035/24*$.1^2 - 585/4*$.1 + 90, 4/3*$.1^4 - 44/3*$.1^3 + 167/3*$.1^2 - 253/3*$.1 + 45 ], [], []> {} Total time: 3.769 seconds, Total memory usage: 2.69MB ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Sat Jan 24 09:51:15 2004 Input: P := PolynomialRing(Rationals()); C := HyperellipticCurve(x*(x-1)*(x-2)*(x-3)*(x-4)); D := QuadraticTwist(C,61); J := Jacobian(D); SetVerbose("JacHypSelmer", 2); TwoSelmerGroupData(J : Bound := 300); Output: Magma V2.10-6 Sat Jan 24 2004 09:51:11 on modular [Seed = 4222172595] ------------------------------------- TwoSelmerGroupData of Jacobian of Hyperelliptic Curve defined by y^2 = 61*x^5 - 610*x^4 + 2135*x^3 - 3050*x^2 + 1464*x over Rational Field m= Mapping from: CrvHyp: C to CrvHyp: C1 with equations : 61*$.1 3721*$.2 $.3 and inverse 1/61*$.1 1/3721*$.2 $.3 Change curve into Hyperelliptic Curve defined by y^2 = x^5 - 610*x^4 + 130235*x^3 - 11349050*x^2 + 332300184*x over Rational Field Bad primes = [ 2, 3, 61 ] f factors as (x - 244) (x - 183) (x - 122) (x - 61) (x). For factor x - 244, use field defined by x - 1 and theta = 244 For factor x - 183, use field defined by x - 1 and theta = 183 For factor x - 122, use field defined by x - 1 and theta = 122 For factor x - 61, use field defined by x - 1 and theta = 61 For factor x, use field defined by x - 1 and theta = 0 The 2-torsion group has dimension 4. Determining local images... p = 2 x = 1/4 --> new generator (0 0 0 0 0 1 0 0 0 0 0 1 0 0 0) x = 14 --> new generator (1 0 1 0 1 1 0 0 1 0 0 0 1 1 1) p = 3 x = 4 --> new generator (1 0 0 0 0 1 1 1 0 0) p = 61 p = infinity Computing class groups... Class group data of the fields: Field given by x - 244: [] Field given by x - 183: [] Field given by x - 122: [] Field given by x - 61: [] Field given by x: [] Dimension of Cl[2] = 0. Signatures: [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] Dimension of units mod squares = 5. Upper bound for Selmer group dimension: 13. ==> Upper bound for rank = 9. Computing unit groups... Class group and unit data of the fields: Field given by x - 244: Class group = [], units = [ 2 ] Field given by x - 183: Class group = [], units = [ 2 ] Field given by x - 122: Class group = [], units = [ 2 ] Field given by x - 61: Class group = [], units = [ 2 ] Field given by x: Class group = [], units = [ 2 ] Time for local computations: 540 ms. Time for class groups: 0 ms. Time for unit groups: 0 ms. Selmer group dimension = 5, Dimension of 2-torsion = 4, ==> Bound for the MW-rank = 1. Total time: 650 ms. Transforming presentation of S back to model C. 1 5 <[ 2661/8*$.1^4 - 13183/4*$.1^3 + 90703/8*$.1^2 - 63255/4*$.1 + 7442, -$.1^3 + 7*$.1^2 - 12*$.1 + 3, 161/4*$.1^4 - 683/2*$.1^3 + 3691/4*$.1^2 - 1725/2*$.1 + 244, -369/8*$.1^4 + 1595/4*$.1^3 - 8443/8*$.1^2 + 2811/4*$.1 + 366, 135*$.1^4 - 1390*$.1^3 + 5025*$.1^2 - 7430*$.1 + 3721 ], [], []> {} Total time: 3.799 seconds, Total memory usage: 2.79MB ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Sat Jan 24 09:51:35 2004 Input: P := PolynomialRing(Rationals()); C := HyperellipticCurve(x*(x-1)*(x-2)*(x-3)*(x-4)); D := QuadraticTwist(C,62); J := Jacobian(D); SetVerbose("JacHypSelmer", 2); TwoSelmerGroupData(J : Bound := 300); Output: Magma V2.10-6 Sat Jan 24 2004 09:51:30 on modular [Seed = 3803194503] ------------------------------------- TwoSelmerGroupData of Jacobian of Hyperelliptic Curve defined by y^2 = 62*x^5 - 620*x^4 + 2170*x^3 - 3100*x^2 + 1488*x over Rational Field m= Mapping from: CrvHyp: C to CrvHyp: C1 with equations : 62*$.1 3844*$.2 $.3 and inverse 1/62*$.1 1/3844*$.2 $.3 Change curve into Hyperelliptic Curve defined by y^2 = x^5 - 620*x^4 + 134540*x^3 - 11916400*x^2 + 354632064*x over Rational Field Bad primes = [ 2, 3, 31 ] f factors as (x - 248) (x - 186) (x - 124) (x - 62) (x). For factor x - 248, use field defined by x - 1 and theta = 248 For factor x - 186, use field defined by x - 1 and theta = 186 For factor x - 124, use field defined by x - 1 and theta = 124 For factor x - 62, use field defined by x - 1 and theta = 62 For factor x, use field defined by x - 1 and theta = 0 The 2-torsion group has dimension 4. Determining local images... p = 2 x = 1 --> new generator (0 0 0 0 1 1 0 0 1 0 1 0 0 0 0) x = 18 --> new generator (1 0 1 1 1 0 1 1 0 0 0 1 1 0 0) p = 3 x = 3 --> new generator (0 0 1 1 0 1 0 0 1 0) p = 31 p = infinity Computing class groups... Class group data of the fields: Field given by x - 248: [] Field given by x - 186: [] Field given by x - 124: [] Field given by x - 62: [] Field given by x: [] Dimension of Cl[2] = 0. Signatures: [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] Dimension of units mod squares = 5. Upper bound for Selmer group dimension: 13. ==> Upper bound for rank = 9. Computing unit groups... Class group and unit data of the fields: Field given by x - 248: Class group = [], units = [ 2 ] Field given by x - 186: Class group = [], units = [ 2 ] Field given by x - 124: Class group = [], units = [ 2 ] Field given by x - 62: Class group = [], units = [ 2 ] Field given by x: Class group = [], units = [ 2 ] Time for local computations: 1050 ms. Time for class groups: 0 ms. Time for unit groups: 9 ms. Selmer group dimension = 4, Dimension of 2-torsion = 4, ==> Bound for the MW-rank = 0. Total time: 1169 ms. Transforming presentation of S back to model C. 0 4 <[ 525/4*$.1^4 - 2563/2*$.1^3 + 17449/4*$.1^2 - 6089*$.1 + 2883, -4*$.1^4 + 24*$.1^3 - 55/2*$.1^2 - 51/2*$.1 + 31, 240*$.1^4 - 4831/2*$.1^3 + 16957/2*$.1^2 - 12067*$.1 + 5766, -117/2*$.1^4 + 1043/2*$.1^3 - 2959/2*$.1^2 + 2591/2*$.1 + 93 ], [], []> {} Total time: 4.319 seconds, Total memory usage: 2.79MB ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Sat Jan 24 09:51:52 2004 Input: P := PolynomialRing(Rationals()); C := HyperellipticCurve(x*(x-1)*(x-2)*(x-3)*(x-4)); D := QuadraticTwist(C,63); J := Jacobian(D); SetVerbose("JacHypSelmer", 2); TwoSelmerGroupData(J : Bound := 300); Output: Magma V2.10-6 Sat Jan 24 2004 09:51:49 on modular [Seed = 3921358715] ------------------------------------- TwoSelmerGroupData of Jacobian of Hyperelliptic Curve defined by y^2 = 63*x^5 - 630*x^4 + 2205*x^3 - 3150*x^2 + 1512*x over Rational Field m= Mapping from: CrvHyp: C to CrvHyp: C1 with equations : 7*$.1 49/3*$.2 $.3 and inverse 1/7*$.1 3/49*$.2 $.3 Change curve into Hyperelliptic Curve defined by y^2 = x^5 - 70*x^4 + 1715*x^3 - 17150*x^2 + 57624*x over Rational Field Bad primes = [ 2, 3, 7 ] f factors as (x - 28) (x - 21) (x - 14) (x - 7) (x). For factor x - 28, use field defined by x - 1 and theta = 28 For factor x - 21, use field defined by x - 1 and theta = 21 For factor x - 14, use field defined by x - 1 and theta = 14 For factor x - 7, use field defined by x - 1 and theta = 7 For factor x, use field defined by x - 1 and theta = 0 The 2-torsion group has dimension 4. Determining local images... p = 2 x = 1/4 --> new generator (0 0 0 0 0 1 0 0 0 0 0 1 0 0 0) x = 2 --> new generator (1 1 0 0 0 1 0 0 1 0 1 0 1 0 0) p = 3 x = 4 --> new generator (1 0 0 0 0 1 1 1 0 0) p = 7 p = infinity Computing class groups... Class group data of the fields: Field given by x - 28: [] Field given by x - 21: [] Field given by x - 14: [] Field given by x - 7: [] Field given by x: [] Dimension of Cl[2] = 0. Signatures: [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] Dimension of units mod squares = 5. Upper bound for Selmer group dimension: 13. ==> Upper bound for rank = 9. Computing unit groups... Class group and unit data of the fields: Field given by x - 28: Class group = [], units = [ 2 ] Field given by x - 21: Class group = [], units = [ 2 ] Field given by x - 14: Class group = [], units = [ 2 ] Field given by x - 7: Class group = [], units = [ 2 ] Field given by x: Class group = [], units = [ 2 ] Time for local computations: 500 ms. Time for class groups: 0 ms. Time for unit groups: 9 ms. Selmer group dimension = 4, Dimension of 2-torsion = 4, ==> Bound for the MW-rank = 0. Total time: 600 ms. Transforming presentation of S back to model C. 0 4 <[ 51/8*$.1^4 - 241/4*$.1^3 + 1513/8*$.1^2 - 921/4*$.1 + 98, 6*$.1^4 - 67*$.1^3 + 253*$.1^2 - 360*$.1 + 147, 225/4*$.1^4 - 1123/2*$.1^3 + 7851/4*$.1^2 - 5617/2*$.1 + 1372, -45/8*$.1^4 + 191/4*$.1^3 - 991/8*$.1^2 + 327/4*$.1 + 42 ], [], []> {} Total time: 3.699 seconds, Total memory usage: 2.69MB ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Sat Jan 24 09:52:12 2004 Input: P := PolynomialRing(Rationals()); C := HyperellipticCurve(x*(x-1)*(x-2)*(x-3)*(x-4)); D := QuadraticTwist(C,64); J := Jacobian(D); SetVerbose("JacHypSelmer", 2); TwoSelmerGroupData(J : Bound := 300); Output: Magma V2.10-6 Sat Jan 24 2004 09:52:08 on modular [Seed = 525195679] ------------------------------------- TwoSelmerGroupData of Jacobian of Hyperelliptic Curve defined by y^2 = 64*x^5 - 640*x^4 + 2240*x^3 - 3200*x^2 + 1536*x over Rational Field m= Mapping from: CrvHyp: C to CrvHyp: C1 with equations : $.1 1/8*$.2 $.3 and inverse $.1 8*$.2 $.3 Change curve into Hyperelliptic Curve defined by y^2 = x^5 - 10*x^4 + 35*x^3 - 50*x^2 + 24*x over Rational Field Bad primes = [ 2, 3 ] f factors as (x - 4) (x - 3) (x - 2) (x - 1) (x). For factor x - 4, use field defined by x - 1 and theta = 4 For factor x - 3, use field defined by x - 1 and theta = 3 For factor x - 2, use field defined by x - 1 and theta = 2 For factor x - 1, use field defined by x - 1 and theta = 1 For factor x, use field defined by x - 1 and theta = 0 The 2-torsion group has dimension 4. Determining local images... p = 2 x = 1/4 --> new generator (0 0 0 0 0 1 0 0 0 0 0 1 0 0 0) x = 22 --> new generator (1 0 0 0 1 0 0 0 1 0 0 1 1 1 0) p = 3 x = 7 --> new generator (1 0 0 0 0 1 1 1 0 0) p = infinity Computing class groups... Class group data of the fields: Field given by x - 4: [] Field given by x - 3: [] Field given by x - 2: [] Field given by x - 1: [] Field given by x: [] Dimension of Cl[2] = 0. Signatures: [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] Dimension of units mod squares = 5. Upper bound for Selmer group dimension: 9. ==> Upper bound for rank = 5. Computing unit groups... Class group and unit data of the fields: Field given by x - 4: Class group = [], units = [ 2 ] Field given by x - 3: Class group = [], units = [ 2 ] Field given by x - 2: Class group = [], units = [ 2 ] Field given by x - 1: Class group = [], units = [ 2 ] Field given by x: Class group = [], units = [ 2 ] Time for local computations: 509 ms. Time for class groups: 0 ms. Time for unit groups: 0 ms. Selmer group dimension = 4, Dimension of 2-torsion = 4, ==> Bound for the MW-rank = 0. Total time: 580 ms. Transforming presentation of S back to model C. 0 4 <[ 1/8*$.1^4 - 3/4*$.1^3 + 3/8*$.1^2 + 5/4*$.1 + 2, -$.1^3 + 7*$.1^2 - 12*$.1 + 3, 1/4*$.1^4 - 3/2*$.1^3 + 11/4*$.1^2 - 5/2*$.1 + 4, -9/8*$.1^4 + 35/4*$.1^3 - 163/8*$.1^2 + 51/4*$.1 + 6 ], [], []> {} Total time: 3.789 seconds, Total memory usage: 2.69MB ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Sat Jan 24 09:52:32 2004 Input: P := PolynomialRing(Rationals()); C := HyperellipticCurve(x*(x-1)*(x-2)*(x-3)*(x-4)); D := QuadraticTwist(C,65); J := Jacobian(D); SetVerbose("JacHypSelmer", 2); TwoSelmerGroupData(J : Bound := 300); Output: Magma V2.10-6 Sat Jan 24 2004 09:52:29 on modular [Seed = 140168893] ------------------------------------- TwoSelmerGroupData of Jacobian of Hyperelliptic Curve defined by y^2 = 65*x^5 - 650*x^4 + 2275*x^3 - 3250*x^2 + 1560*x over Rational Field m= Mapping from: CrvHyp: C to CrvHyp: C1 with equations : 65*$.1 4225*$.2 $.3 and inverse 1/65*$.1 1/4225*$.2 $.3 Change curve into Hyperelliptic Curve defined by y^2 = x^5 - 650*x^4 + 147875*x^3 - 13731250*x^2 + 428415000*x over Rational Field Bad primes = [ 2, 3, 5, 13 ] f factors as (x - 260) (x - 195) (x - 130) (x - 65) (x). For factor x - 260, use field defined by x - 1 and theta = 260 For factor x - 195, use field defined by x - 1 and theta = 195 For factor x - 130, use field defined by x - 1 and theta = 130 For factor x - 65, use field defined by x - 1 and theta = 65 For factor x, use field defined by x - 1 and theta = 0 The 2-torsion group has dimension 4. Determining local images... p = 2 x = 1/4 --> new generator (0 0 0 0 0 1 0 0 0 0 0 1 0 0 0) x = 22 --> new generator (1 0 0 0 1 0 0 0 1 0 0 1 1 1 0) p = 3 x = 3 --> new generator (0 0 1 1 0 1 0 0 1 0) p = 5 p = 13 p = infinity Computing class groups... Class group data of the fields: Field given by x - 260: [] Field given by x - 195: [] Field given by x - 130: [] Field given by x - 65: [] Field given by x: [] Dimension of Cl[2] = 0. Signatures: [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] Dimension of units mod squares = 5. Upper bound for Selmer group dimension: 17. ==> Upper bound for rank = 13. Computing unit groups... Class group and unit data of the fields: Field given by x - 260: Class group = [], units = [ 2 ] Field given by x - 195: Class group = [], units = [ 2 ] Field given by x - 130: Class group = [], units = [ 2 ] Field given by x - 65: Class group = [], units = [ 2 ] Field given by x: Class group = [], units = [ 2 ] Time for local computations: 560 ms. Time for class groups: 0 ms. Time for unit groups: 0 ms. Selmer group dimension = 4, Dimension of 2-torsion = 4, ==> Bound for the MW-rank = 0. Total time: 721 ms. Transforming presentation of S back to model C. 0 4 <[ 3009/8*$.1^4 - 14915/4*$.1^3 + 102723/8*$.1^2 - 71739/4*$.1 + 8450, 528*$.1^4 - 5345*$.1^3 + 18871*$.1^2 - 26924*$.1 + 12675, 183041/4*$.1^4 - 915203/2*$.1^3 + 6406411/4*$.1^2 - 4576133/2*$.1 + 1098500, -393/8*$.1^4 + 1699/4*$.1^3 - 8995/8*$.1^2 + 2995/4*$.1 + 390 ], [], []> {} Total time: 3.829 seconds, Total memory usage: 2.89MB ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Sat Jan 24 09:52:53 2004 Input: P := PolynomialRing(Rationals()); C := HyperellipticCurve(x*(x-1)*(x-2)*(x-3)*(x-4)); D := QuadraticTwist(C,66); J := Jacobian(D); SetVerbose("JacHypSelmer", 2); TwoSelmerGroupData(J : Bound := 300); Output: Magma V2.10-6 Sat Jan 24 2004 09:52:48 on modular [Seed = 22267865] ------------------------------------- TwoSelmerGroupData of Jacobian of Hyperelliptic Curve defined by y^2 = 66*x^5 - 660*x^4 + 2310*x^3 - 3300*x^2 + 1584*x over Rational Field m= Mapping from: CrvHyp: C to CrvHyp: C1 with equations : 66*$.1 4356*$.2 $.3 and inverse 1/66*$.1 1/4356*$.2 $.3 Change curve into Hyperelliptic Curve defined by y^2 = x^5 - 660*x^4 + 152460*x^3 - 14374800*x^2 + 455393664*x over Rational Field Bad primes = [ 2, 3, 11 ] f factors as (x - 264) (x - 198) (x - 132) (x - 66) (x). For factor x - 264, use field defined by x - 1 and theta = 264 For factor x - 198, use field defined by x - 1 and theta = 198 For factor x - 132, use field defined by x - 1 and theta = 132 For factor x - 66, use field defined by x - 1 and theta = 66 For factor x, use field defined by x - 1 and theta = 0 The 2-torsion group has dimension 4. Determining local images... p = 2 x = 1 --> new generator (0 0 0 0 1 0 0 0 1 0 1 1 0 0 0) x = 26 --> new generator (1 0 0 0 0 1 1 1 0 1 1 0 1 0 1) p = 3 p = 11 p = infinity Computing class groups... Class group data of the fields: Field given by x - 264: [] Field given by x - 198: [] Field given by x - 132: [] Field given by x - 66: [] Field given by x: [] Dimension of Cl[2] = 0. Signatures: [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] Dimension of units mod squares = 5. Upper bound for Selmer group dimension: 15. ==> Upper bound for rank = 11. Computing unit groups... Class group and unit data of the fields: Field given by x - 264: Class group = [], units = [ 2 ] Field given by x - 198: Class group = [], units = [ 2 ] Field given by x - 132: Class group = [], units = [ 2 ] Field given by x - 66: Class group = [], units = [ 2 ] Field given by x: Class group = [], units = [ 2 ] Time for local computations: 1100 ms. Time for class groups: 0 ms. Time for unit groups: 0 ms. Selmer group dimension = 5, Dimension of 2-torsion = 4, ==> Bound for the MW-rank = 1. Total time: 1220 ms. Transforming presentation of S back to model C. 1 5 <[ 16*$.1^4 - 469/3*$.1^3 + 1067/2*$.1^2 - 4501/6*$.1 + 363, -1/4*$.1^4 + 3/2*$.1^3 - 5/4*$.1^2 - 3*$.1 + 1, 134/3*$.1^4 - 2515/6*$.1^3 + 8033/6*$.1^2 - 5065/3*$.1 + 726, 19/4*$.1^4 - 193/3*$.1^3 + 1193/4*$.1^2 - 1673/3*$.1 + 363, -4*$.1^4 + 24*$.1^3 - 28*$.1^2 - 24*$.1 + 33 ], [], []> {} Total time: 4.369 seconds, Total memory usage: 2.79MB ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Sat Jan 24 09:53:08 2004 Input: P := PolynomialRing(Rationals()); C := HyperellipticCurve(x*(x-1)*(x-2)*(x-3)*(x-4)); D := QuadraticTwist(C,67); J := Jacobian(D); SetVerbose("JacHypSelmer", 2); TwoSelmerGroupData(J : Bound := 300); Output: Magma V2.10-6 Sat Jan 24 2004 09:53:04 on modular [Seed = 1030749173] ------------------------------------- TwoSelmerGroupData of Jacobian of Hyperelliptic Curve defined by y^2 = 67*x^5 - 670*x^4 + 2345*x^3 - 3350*x^2 + 1608*x over Rational Field m= Mapping from: CrvHyp: C to CrvHyp: C1 with equations : 67*$.1 4489*$.2 $.3 and inverse 1/67*$.1 1/4489*$.2 $.3 Change curve into Hyperelliptic Curve defined by y^2 = x^5 - 670*x^4 + 157115*x^3 - 15038150*x^2 + 483626904*x over Rational Field Bad primes = [ 2, 3, 67 ] f factors as (x - 268) (x - 201) (x - 134) (x - 67) (x). For factor x - 268, use field defined by x - 1 and theta = 268 For factor x - 201, use field defined by x - 1 and theta = 201 For factor x - 134, use field defined by x - 1 and theta = 134 For factor x - 67, use field defined by x - 1 and theta = 67 For factor x, use field defined by x - 1 and theta = 0 The 2-torsion group has dimension 4. Determining local images... p = 2 x = 1/4 --> new generator (0 0 0 0 0 1 0 0 0 0 0 1 0 0 0) x = 26 --> new generator (1 1 1 0 0 0 0 0 1 0 1 1 1 0 1) p = 3 x = 1 --> new generator (1 0 0 0 0 1 1 1 0 0) p = 67 p = infinity Computing class groups... Class group data of the fields: Field given by x - 268: [] Field given by x - 201: [] Field given by x - 134: [] Field given by x - 67: [] Field given by x: [] Dimension of Cl[2] = 0. Signatures: [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] Dimension of units mod squares = 5. Upper bound for Selmer group dimension: 13. ==> Upper bound for rank = 9. Computing unit groups... Class group and unit data of the fields: Field given by x - 268: Class group = [], units = [ 2 ] Field given by x - 201: Class group = [], units = [ 2 ] Field given by x - 134: Class group = [], units = [ 2 ] Field given by x - 67: Class group = [], units = [ 2 ] Field given by x: Class group = [], units = [ 2 ] Time for local computations: 509 ms. Time for class groups: 0 ms. Time for unit groups: 0 ms. Selmer group dimension = 5, Dimension of 2-torsion = 4, ==> Bound for the MW-rank = 1. Total time: 620 ms. Transforming presentation of S back to model C. 1 5 <[ 3191/8*$.1^4 - 15821/4*$.1^3 + 109013/8*$.1^2 - 76181/4*$.1 + 8978, 36*$.1^4 - 327*$.1^3 + 963*$.1^2 - 940*$.1 + 67, 200465/4*$.1^4 - 1002323/2*$.1^3 + 7016251/4*$.1^2 - 5011737/2*$.1 + 1203052, 2283/8*$.1^4 - 11945/4*$.1^3 + 88393/8*$.1^2 - 67697/4*$.1 + 8978, -25*$.1^4 + 150*$.1^3 - 175*$.1^2 - 150*$.1 + 201 ], [], []> {} Total time: 3.709 seconds, Total memory usage: 2.79MB ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Sat Jan 24 09:53:23 2004 Input: P := PolynomialRing(Rationals()); C := HyperellipticCurve(x*(x-1)*(x-2)*(x-3)*(x-4)); D := QuadraticTwist(C,68); J := Jacobian(D); SetVerbose("JacHypSelmer", 2); TwoSelmerGroupData(J : Bound := 300); Output: Magma V2.10-6 Sat Jan 24 2004 09:53:20 on modular [Seed = 912584910] ------------------------------------- TwoSelmerGroupData of Jacobian of Hyperelliptic Curve defined by y^2 = 68*x^5 - 680*x^4 + 2380*x^3 - 3400*x^2 + 1632*x over Rational Field m= Mapping from: CrvHyp: C to CrvHyp: C1 with equations : 17*$.1 289/2*$.2 $.3 and inverse 1/17*$.1 2/289*$.2 $.3 Change curve into Hyperelliptic Curve defined by y^2 = x^5 - 170*x^4 + 10115*x^3 - 245650*x^2 + 2004504*x over Rational Field Bad primes = [ 2, 3, 17 ] f factors as (x - 68) (x - 51) (x - 34) (x - 17) (x). For factor x - 68, use field defined by x - 1 and theta = 68 For factor x - 51, use field defined by x - 1 and theta = 51 For factor x - 34, use field defined by x - 1 and theta = 34 For factor x - 17, use field defined by x - 1 and theta = 17 For factor x, use field defined by x - 1 and theta = 0 The 2-torsion group has dimension 4. Determining local images... p = 2 x = 1/4 --> new generator (0 0 0 0 0 1 0 0 0 0 0 1 0 0 0) x = 22 --> new generator (1 0 0 0 1 0 0 0 1 0 0 1 1 1 0) p = 3 x = 3 --> new generator (0 0 1 1 0 1 0 0 1 0) p = 17 p = infinity Computing class groups... Class group data of the fields: Field given by x - 68: [] Field given by x - 51: [] Field given by x - 34: [] Field given by x - 17: [] Field given by x: [] Dimension of Cl[2] = 0. Signatures: [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] Dimension of units mod squares = 5. Upper bound for Selmer group dimension: 13. ==> Upper bound for rank = 9. Computing unit groups... Class group and unit data of the fields: Field given by x - 68: Class group = [], units = [ 2 ] Field given by x - 51: Class group = [], units = [ 2 ] Field given by x - 34: Class group = [], units = [ 2 ] Field given by x - 17: Class group = [], units = [ 2 ] Field given by x: Class group = [], units = [ 2 ] Time for local computations: 531 ms. Time for class groups: 0 ms. Time for unit groups: 0 ms. Selmer group dimension = 6, Dimension of 2-torsion = 4, ==> Bound for the MW-rank = 2. Total time: 630 ms. Transforming presentation of S back to model C. 2 6 <[ 193/8*$.1^4 - 931/4*$.1^3 + 6275/8*$.1^2 - 4411/4*$.1 + 578, 10*$.1^4 - 93*$.1^3 + 285*$.1^2 - 304*$.1 + 51, 193/4*$.1^4 - 947/2*$.1^3 + 6507/4*$.1^2 - 4613/2*$.1 + 1156, -105/8*$.1^4 + 451/4*$.1^3 - 2371/8*$.1^2 + 787/4*$.1 + 102, 10*$.1^4 - 100*$.1^3 + 358*$.1^2 - 540*$.1 + 289, -2*$.1^4 + 12*$.1^3 - 14*$.1^2 - 12*$.1 + 17 ], [], []> {} Total time: 3.769 seconds, Total memory usage: 2.69MB ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Sat Jan 24 09:53:40 2004 Input: P := PolynomialRing(Rationals()); C := HyperellipticCurve(x*(x-1)*(x-2)*(x-3)*(x-4)); D := QuadraticTwist(C,69); J := Jacobian(D); SetVerbose("JacHypSelmer", 2); TwoSelmerGroupData(J : Bound := 300); Output: Magma V2.10-6 Sat Jan 24 2004 09:53:36 on modular [Seed = 796780999] ------------------------------------- TwoSelmerGroupData of Jacobian of Hyperelliptic Curve defined by y^2 = 69*x^5 - 690*x^4 + 2415*x^3 - 3450*x^2 + 1656*x over Rational Field m= Mapping from: CrvHyp: C to CrvHyp: C1 with equations : 69*$.1 4761*$.2 $.3 and inverse 1/69*$.1 1/4761*$.2 $.3 Change curve into Hyperelliptic Curve defined by y^2 = x^5 - 690*x^4 + 166635*x^3 - 16425450*x^2 + 544010904*x over Rational Field Bad primes = [ 2, 3, 23 ] f factors as (x - 276) (x - 207) (x - 138) (x - 69) (x). For factor x - 276, use field defined by x - 1 and theta = 276 For factor x - 207, use field defined by x - 1 and theta = 207 For factor x - 138, use field defined by x - 1 and theta = 138 For factor x - 69, use field defined by x - 1 and theta = 69 For factor x, use field defined by x - 1 and theta = 0 The 2-torsion group has dimension 4. Determining local images... p = 2 x = 1/4 --> new generator (0 0 0 0 0 1 0 0 0 0 0 1 0 0 0) x = 30 --> new generator (1 0 1 0 1 1 0 0 1 0 0 0 1 1 1) p = 3 p = 23 p = infinity Computing class groups... Class group data of the fields: Field given by x - 276: [] Field given by x - 207: [] Field given by x - 138: [] Field given by x - 69: [] Field given by x: [] Dimension of Cl[2] = 0. Signatures: [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] Dimension of units mod squares = 5. Upper bound for Selmer group dimension: 15. ==> Upper bound for rank = 11. Computing unit groups... Class group and unit data of the fields: Field given by x - 276: Class group = [], units = [ 2 ] Field given by x - 207: Class group = [], units = [ 2 ] Field given by x - 138: Class group = [], units = [ 2 ] Field given by x - 69: Class group = [], units = [ 2 ] Field given by x: Class group = [], units = [ 2 ] Time for local computations: 560 ms. Time for class groups: 0 ms. Time for unit groups: 11 ms. Selmer group dimension = 6, Dimension of 2-torsion = 4, ==> Bound for the MW-rank = 2. Total time: 689 ms. Transforming presentation of S back to model C. 2 6 <[ 25*$.1^4 - 242*$.1^3 + 815*$.1^2 - 1126*$.1 + 529, 20*$.1^4 - 208*$.1^3 + 760*$.1^2 - 1124*$.1 + 529, 109297/12*$.1^4 - 91115*$.1^3 + 3828407/12*$.1^2 - 455964*$.1 + 219006, 8/3*$.1^4 - 51*$.1^3 + 925/3*$.1^2 - 743*$.1 + 621, 10247/24*$.1^4 - 50549/12*$.1^3 + 347413/24*$.1^2 - 242509/12*$.1 + 9522, 68*$.1^4 - 2039/3*$.1^3 + 2367*$.1^2 - 10024/3*$.1 + 1587 ], [], []> {} Total time: 3.789 seconds, Total memory usage: 2.69MB ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Sat Jan 24 09:54:02 2004 Input: P := PolynomialRing(Rationals()); C := HyperellipticCurve(x*(x-1)*(x-2)*(x-3)*(x-4)); D := QuadraticTwist(C,70); J := Jacobian(D); SetVerbose("JacHypSelmer", 2); TwoSelmerGroupData(J : Bound := 300); Output: Magma V2.10-6 Sat Jan 24 2004 09:53:58 on modular [Seed = 1477091142] ------------------------------------- TwoSelmerGroupData of Jacobian of Hyperelliptic Curve defined by y^2 = 70*x^5 - 700*x^4 + 2450*x^3 - 3500*x^2 + 1680*x over Rational Field m= Mapping from: CrvHyp: C to CrvHyp: C1 with equations : 70*$.1 4900*$.2 $.3 and inverse 1/70*$.1 1/4900*$.2 $.3 Change curve into Hyperelliptic Curve defined by y^2 = x^5 - 700*x^4 + 171500*x^3 - 17150000*x^2 + 576240000*x over Rational Field Bad primes = [ 2, 3, 5, 7 ] f factors as (x - 280) (x - 210) (x - 140) (x - 70) (x). For factor x - 280, use field defined by x - 1 and theta = 280 For factor x - 210, use field defined by x - 1 and theta = 210 For factor x - 140, use field defined by x - 1 and theta = 140 For factor x - 70, use field defined by x - 1 and theta = 70 For factor x, use field defined by x - 1 and theta = 0 The 2-torsion group has dimension 4. Determining local images... p = 2 x = 1 --> new generator (0 0 0 0 1 1 0 0 1 0 1 0 0 0 0) x = 42 --> new generator (1 0 0 1 1 0 1 1 1 0 0 0 1 0 1) p = 3 x = 4 --> new generator (1 0 0 0 0 1 1 1 0 0) p = 5 p = 7 p = infinity Computing class groups... Class group data of the fields: Field given by x - 280: [] Field given by x - 210: [] Field given by x - 140: [] Field given by x - 70: [] Field given by x: [] Dimension of Cl[2] = 0. Signatures: [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] Dimension of units mod squares = 5. Upper bound for Selmer group dimension: 17. ==> Upper bound for rank = 13. Computing unit groups... Class group and unit data of the fields: Field given by x - 280: Class group = [], units = [ 2 ] Field given by x - 210: Class group = [], units = [ 2 ] Field given by x - 140: Class group = [], units = [ 2 ] Field given by x - 70: Class group = [], units = [ 2 ] Field given by x: Class group = [], units = [ 2 ] Time for local computations: 1109 ms. Time for class groups: 0 ms. Time for unit groups: 0 ms. Selmer group dimension = 5, Dimension of 2-torsion = 4, ==> Bound for the MW-rank = 1. Total time: 1270 ms. Transforming presentation of S back to model C. 1 5 <[ 40*$.1^4 - 346*$.1^3 + 1020*$.1^2 - 1236*$.1 + 525, 999/4*$.1^4 - 5023/2*$.1^3 + 35389/4*$.1^2 - 25423/2*$.1 + 6125, 8523/4*$.1^4 - 21345*$.1^3 + 299389/4*$.1^2 - 107082*$.1 + 51450, 2941/4*$.1^4 - 14741/2*$.1^3 + 103779/4*$.1^2 - 74949/2*$.1 + 18375, 43/4*$.1^4 - 195/2*$.1^3 + 1231/4*$.1^2 - 394*$.1 + 175 ], [], []> {} Total time: 4.469 seconds, Total memory usage: 2.79MB ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Sat Jan 24 09:54:17 2004 Input: P := PolynomialRing(Rationals()); C := HyperellipticCurve(x*(x-1)*(x-2)*(x-3)*(x-4)); D := QuadraticTwist(C,71); J := Jacobian(D); SetVerbose("JacHypSelmer", 2); TwoSelmerGroupData(J : Bound := 300); Output: Magma V2.10-6 Sat Jan 24 2004 09:54:13 on modular [Seed = 1359189596] ------------------------------------- TwoSelmerGroupData of Jacobian of Hyperelliptic Curve defined by y^2 = 71*x^5 - 710*x^4 + 2485*x^3 - 3550*x^2 + 1704*x over Rational Field m= Mapping from: CrvHyp: C to CrvHyp: C1 with equations : 71*$.1 5041*$.2 $.3 and inverse 1/71*$.1 1/5041*$.2 $.3 Change curve into Hyperelliptic Curve defined by y^2 = x^5 - 710*x^4 + 176435*x^3 - 17895550*x^2 + 609880344*x over Rational Field Bad primes = [ 2, 3, 71 ] f factors as (x - 284) (x - 213) (x - 142) (x - 71) (x). For factor x - 284, use field defined by x - 1 and theta = 284 For factor x - 213, use field defined by x - 1 and theta = 213 For factor x - 142, use field defined by x - 1 and theta = 142 For factor x - 71, use field defined by x - 1 and theta = 71 For factor x, use field defined by x - 1 and theta = 0 The 2-torsion group has dimension 4. Determining local images... p = 2 x = 1/4 --> new generator (0 0 0 0 0 1 0 0 0 0 0 1 0 0 0) x = 2 --> new generator (1 1 0 0 0 1 0 0 1 0 1 0 1 0 0) p = 3 x = 3 --> new generator (0 0 1 1 0 1 0 0 1 0) p = 71 p = infinity Computing class groups... Class group data of the fields: Field given by x - 284: [] Field given by x - 213: [] Field given by x - 142: [] Field given by x - 71: [] Field given by x: [] Dimension of Cl[2] = 0. Signatures: [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] Dimension of units mod squares = 5. Upper bound for Selmer group dimension: 13. ==> Upper bound for rank = 9. Computing unit groups... Class group and unit data of the fields: Field given by x - 284: Class group = [], units = [ 2 ] Field given by x - 213: Class group = [], units = [ 2 ] Field given by x - 142: Class group = [], units = [ 2 ] Field given by x - 71: Class group = [], units = [ 2 ] Field given by x: Class group = [], units = [ 2 ] Time for local computations: 511 ms. Time for class groups: 0 ms. Time for unit groups: 9 ms. Selmer group dimension = 6, Dimension of 2-torsion = 4, ==> Bound for the MW-rank = 2. Total time: 641 ms. Transforming presentation of S back to model C. 2 6 <[ 219*$.1^4 - 2166*$.1^3 + 7485*$.1^2 - 10578*$.1 + 5041, 204*$.1^4 - 2064*$.1^3 + 7320*$.1^2 - 10572*$.1 + 5041, -23/4*$.1^4 + 46*$.1^3 - 389/4*$.1^2 - 14*$.1 + 142, 44662*$.1^4 - 446821*$.1^3 + 1564589*$.1^2 - 2236021*$.1 + 1073733, 1/8*$.1^4 - 7/4*$.1^3 + 59/8*$.1^2 - 43/4*$.1 + 6, 612*$.1^4 - 6191*$.1^3 + 21883*$.1^2 - 31424*$.1 + 15123 ], [], []> {} Total time: 3.839 seconds, Total memory usage: 2.79MB ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Sat Jan 24 09:54:32 2004 Input: P := PolynomialRing(Rationals()); C := HyperellipticCurve(x*(x-1)*(x-2)*(x-3)*(x-4)); D := QuadraticTwist(C,72); J := Jacobian(D); SetVerbose("JacHypSelmer", 2); TwoSelmerGroupData(J : Bound := 300); Output: Magma V2.10-6 Sat Jan 24 2004 09:54:28 on modular [Seed = 1243123062] ------------------------------------- TwoSelmerGroupData of Jacobian of Hyperelliptic Curve defined by y^2 = 72*x^5 - 720*x^4 + 2520*x^3 - 3600*x^2 + 1728*x over Rational Field m= Mapping from: CrvHyp: C to CrvHyp: C1 with equations : 2*$.1 2/3*$.2 $.3 and inverse 1/2*$.1 3/2*$.2 $.3 Change curve into Hyperelliptic Curve defined by y^2 = x^5 - 20*x^4 + 140*x^3 - 400*x^2 + 384*x over Rational Field Bad primes = [ 2, 3 ] f factors as (x - 8) (x - 6) (x - 4) (x - 2) (x). For factor x - 8, use field defined by x - 1 and theta = 8 For factor x - 6, use field defined by x - 1 and theta = 6 For factor x - 4, use field defined by x - 1 and theta = 4 For factor x - 2, use field defined by x - 1 and theta = 2 For factor x, use field defined by x - 1 and theta = 0 The 2-torsion group has dimension 4. Determining local images... p = 2 x = 1 --> new generator (0 0 0 0 1 0 0 0 1 0 1 1 0 0 0) x = 26 --> new generator (1 0 0 0 0 1 1 1 0 1 1 0 1 0 1) p = 3 x = 3 --> new generator (0 0 1 1 0 1 0 0 1 0) p = infinity Computing class groups... Class group data of the fields: Field given by x - 8: [] Field given by x - 6: [] Field given by x - 4: [] Field given by x - 2: [] Field given by x: [] Dimension of Cl[2] = 0. Signatures: [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] Dimension of units mod squares = 5. Upper bound for Selmer group dimension: 9. ==> Upper bound for rank = 5. Computing unit groups... Class group and unit data of the fields: Field given by x - 8: Class group = [], units = [ 2 ] Field given by x - 6: Class group = [], units = [ 2 ] Field given by x - 4: Class group = [], units = [ 2 ] Field given by x - 2: Class group = [], units = [ 2 ] Field given by x: Class group = [], units = [ 2 ] Time for local computations: 1079 ms. Time for class groups: 0 ms. Time for unit groups: 0 ms. Selmer group dimension = 4, Dimension of 2-torsion = 4, ==> Bound for the MW-rank = 0. Total time: 1130 ms. Transforming presentation of S back to model C. 0 4 <[ $.1^3 - 13/2*$.1^2 + 17/2*$.1 + 3, -1/4*$.1^4 + 3/2*$.1^3 - 5/4*$.1^2 - 3*$.1 + 1, -1/2*$.1^3 + 7/2*$.1^2 - 7*$.1 + 6, -9/4*$.1^4 + 19*$.1^3 - 203/4*$.1^2 + 43*$.1 + 3 ], [], []> {} Total time: 4.309 seconds, Total memory usage: 2.69MB ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Sat Jan 24 09:54:52 2004 Input: P := PolynomialRing(Rationals()); C := HyperellipticCurve(x*(x-1)*(x-2)*(x-3)*(x-4)); D := QuadraticTwist(C,73); J := Jacobian(D); SetVerbose("JacHypSelmer", 2); TwoSelmerGroupData(J : Bound := 300); Output: Magma V2.10-6 Sat Jan 24 2004 09:54:48 on modular [Seed = 1125221475] ------------------------------------- TwoSelmerGroupData of Jacobian of Hyperelliptic Curve defined by y^2 = 73*x^5 - 730*x^4 + 2555*x^3 - 3650*x^2 + 1752*x over Rational Field m= Mapping from: CrvHyp: C to CrvHyp: C1 with equations : 73*$.1 5329*$.2 $.3 and inverse 1/73*$.1 1/5329*$.2 $.3 Change curve into Hyperelliptic Curve defined by y^2 = x^5 - 730*x^4 + 186515*x^3 - 19450850*x^2 + 681557784*x over Rational Field Bad primes = [ 2, 3, 73 ] f factors as (x - 292) (x - 219) (x - 146) (x - 73) (x). For factor x - 292, use field defined by x - 1 and theta = 292 For factor x - 219, use field defined by x - 1 and theta = 219 For factor x - 146, use field defined by x - 1 and theta = 146 For factor x - 73, use field defined by x - 1 and theta = 73 For factor x, use field defined by x - 1 and theta = 0 The 2-torsion group has dimension 4. Determining local images... p = 2 x = 1/4 --> new generator (0 0 0 0 0 1 0 0 0 0 0 1 0 0 0) x = 6 --> new generator (1 0 0 0 1 0 0 0 1 0 0 1 1 1 0) p = 3 x = 7 --> new generator (1 0 0 0 0 1 1 1 0 0) p = 73 p = infinity Computing class groups... Class group data of the fields: Field given by x - 292: [] Field given by x - 219: [] Field given by x - 146: [] Field given by x - 73: [] Field given by x: [] Dimension of Cl[2] = 0. Signatures: [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] Dimension of units mod squares = 5. Upper bound for Selmer group dimension: 13. ==> Upper bound for rank = 9. Computing unit groups... Class group and unit data of the fields: Field given by x - 292: Class group = [], units = [ 2 ] Field given by x - 219: Class group = [], units = [ 2 ] Field given by x - 146: Class group = [], units = [ 2 ] Field given by x - 73: Class group = [], units = [ 2 ] Field given by x: Class group = [], units = [ 2 ] Time for local computations: 549 ms. Time for class groups: 0 ms. Time for unit groups: 11 ms. Selmer group dimension = 8, Dimension of 2-torsion = 4, ==> Bound for the MW-rank = 4. Total time: 669 ms. Transforming presentation of S back to model C. 4 8 <[ 1/8*$.1^4 - 3/4*$.1^3 + 3/8*$.1^2 + 5/4*$.1 + 2, -$.1^3 + 7*$.1^2 - 12*$.1 + 3, 1/4*$.1^4 - 3/2*$.1^3 + 11/4*$.1^2 - 5/2*$.1 + 4, -9/8*$.1^4 + 35/4*$.1^3 - 163/8*$.1^2 + 51/4*$.1 + 6, 6*$.1^4 - 48*$.1^3 + 138*$.1^2 - 168*$.1 + 73, -9*$.1^4 + 54*$.1^3 - 63*$.1^2 - 54*$.1 + 73, 21*$.1^4 - 174*$.1^3 + 447*$.1^2 - 366*$.1 + 73, -9*$.1^4 + 78*$.1^3 - 207*$.1^2 + 138*$.1 + 73 ], [], []> {} Total time: 3.789 seconds, Total memory usage: 2.79MB ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Sat Jan 24 09:55:07 2004 Input: P := PolynomialRing(Rationals()); C := HyperellipticCurve(x*(x-1)*(x-2)*(x-3)*(x-4)); D := QuadraticTwist(C,74); J := Jacobian(D); SetVerbose("JacHypSelmer", 2); TwoSelmerGroupData(J : Bound := 300); Output: Magma V2.10-6 Sat Jan 24 2004 09:55:03 on modular [Seed = 1881323311] ------------------------------------- TwoSelmerGroupData of Jacobian of Hyperelliptic Curve defined by y^2 = 74*x^5 - 740*x^4 + 2590*x^3 - 3700*x^2 + 1776*x over Rational Field m= Mapping from: CrvHyp: C to CrvHyp: C1 with equations : 74*$.1 5476*$.2 $.3 and inverse 1/74*$.1 1/5476*$.2 $.3 Change curve into Hyperelliptic Curve defined by y^2 = x^5 - 740*x^4 + 191660*x^3 - 20261200*x^2 + 719677824*x over Rational Field Bad primes = [ 2, 3, 37 ] f factors as (x - 296) (x - 222) (x - 148) (x - 74) (x). For factor x - 296, use field defined by x - 1 and theta = 296 For factor x - 222, use field defined by x - 1 and theta = 222 For factor x - 148, use field defined by x - 1 and theta = 148 For factor x - 74, use field defined by x - 1 and theta = 74 For factor x, use field defined by x - 1 and theta = 0 The 2-torsion group has dimension 4. Determining local images... p = 2 x = 1 --> new generator (0 0 0 0 1 0 0 0 1 0 1 1 0 0 0) x = 34 --> new generator (1 0 1 0 0 0 1 1 1 1 1 0 1 0 0) p = 3 x = 3 --> new generator (0 0 1 1 0 1 0 0 1 0) p = 37 p = infinity Computing class groups... Class group data of the fields: Field given by x - 296: [] Field given by x - 222: [] Field given by x - 148: [] Field given by x - 74: [] Field given by x: [] Dimension of Cl[2] = 0. Signatures: [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] Dimension of units mod squares = 5. Upper bound for Selmer group dimension: 13. ==> Upper bound for rank = 9. Computing unit groups... Class group and unit data of the fields: Field given by x - 296: Class group = [], units = [ 2 ] Field given by x - 222: Class group = [], units = [ 2 ] Field given by x - 148: Class group = [], units = [ 2 ] Field given by x - 74: Class group = [], units = [ 2 ] Field given by x: Class group = [], units = [ 2 ] Time for local computations: 1060 ms. Time for class groups: 11 ms. Time for unit groups: 0 ms. Selmer group dimension = 5, Dimension of 2-torsion = 4, ==> Bound for the MW-rank = 1. Total time: 1191 ms. Transforming presentation of S back to model C. 1 5 <[ 45/2*$.1^4 - 170*$.1^3 + 403*$.1^2 - 721/2*$.1 + 111, -19/4*$.1^4 + 57/2*$.1^3 - 131/4*$.1^2 - 30*$.1 + 37, 342*$.1^4 - 6877/2*$.1^3 + 24127/2*$.1^2 - 17179*$.1 + 8214, -279/4*$.1^4 + 622*$.1^3 - 7061/4*$.1^2 + 1546*$.1 + 111, 3*$.1^4 - 24*$.1^3 + 69*$.1^2 - 84*$.1 + 37 ], [], []> {} Total time: 4.359 seconds, Total memory usage: 2.79MB ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Sat Jan 24 09:55:22 2004 Input: P := PolynomialRing(Rationals()); C := HyperellipticCurve(x*(x-1)*(x-2)*(x-3)*(x-4)); D := QuadraticTwist(C,75); J := Jacobian(D); SetVerbose("JacHypSelmer", 2); TwoSelmerGroupData(J : Bound := 300); Output: Magma V2.10-6 Sat Jan 24 2004 09:55:19 on modular [Seed = 1765518886] ------------------------------------- TwoSelmerGroupData of Jacobian of Hyperelliptic Curve defined by y^2 = 75*x^5 - 750*x^4 + 2625*x^3 - 3750*x^2 + 1800*x over Rational Field m= Mapping from: CrvHyp: C to CrvHyp: C1 with equations : 3*$.1 9/5*$.2 $.3 and inverse 1/3*$.1 5/9*$.2 $.3 Change curve into Hyperelliptic Curve defined by y^2 = x^5 - 30*x^4 + 315*x^3 - 1350*x^2 + 1944*x over Rational Field Bad primes = [ 2, 3 ] f factors as (x - 12) (x - 9) (x - 6) (x - 3) (x). For factor x - 12, use field defined by x - 1 and theta = 12 For factor x - 9, use field defined by x - 1 and theta = 9 For factor x - 6, use field defined by x - 1 and theta = 6 For factor x - 3, use field defined by x - 1 and theta = 3 For factor x, use field defined by x - 1 and theta = 0 The 2-torsion group has dimension 4. Determining local images... p = 2 x = 1/4 --> new generator (0 0 0 0 0 1 0 0 0 0 0 1 0 0 0) x = 26 --> new generator (1 1 1 0 0 0 0 0 1 0 1 1 1 0 1) p = 3 p = infinity Computing class groups... Class group data of the fields: Field given by x - 12: [] Field given by x - 9: [] Field given by x - 6: [] Field given by x - 3: [] Field given by x: [] Dimension of Cl[2] = 0. Signatures: [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] Dimension of units mod squares = 5. Upper bound for Selmer group dimension: 11. ==> Upper bound for rank = 7. Computing unit groups... Class group and unit data of the fields: Field given by x - 12: Class group = [], units = [ 2 ] Field given by x - 9: Class group = [], units = [ 2 ] Field given by x - 6: Class group = [], units = [ 2 ] Field given by x - 3: Class group = [], units = [ 2 ] Field given by x: Class group = [], units = [ 2 ] Time for local computations: 500 ms. Time for class groups: 0 ms. Time for unit groups: 0 ms. Selmer group dimension = 4, Dimension of 2-torsion = 4, ==> Bound for the MW-rank = 0. Total time: 560 ms. Transforming presentation of S back to model C. 0 4 <[ 15/8*$.1^4 - 191/12*$.1^3 + 349/8*$.1^2 - 535/12*$.1 + 18, -1/3*$.1^3 + 3*$.1^2 - 20/3*$.1 + 3, 67/12*$.1^4 - 107/2*$.1^3 + 2129/12*$.1^2 - 473/2*$.1 + 108, 1/24*$.1^4 - 9/4*$.1^3 + 347/24*$.1^2 - 113/4*$.1 + 18 ], [], []> {} Total time: 3.659 seconds, Total memory usage: 2.69MB ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Sat Jan 24 09:55:54 2004 Input: P := PolynomialRing(Rationals()); C := HyperellipticCurve(x*(x-1)*(x-2)*(x-3)*(x-4)); D := QuadraticTwist(C,76); J := Jacobian(D); SetVerbose("JacHypSelmer", 2); TwoSelmerGroupData(J : Bound := 300); Output: Magma V2.10-6 Sat Jan 24 2004 09:55:51 on modular [Seed = 1664197644] ------------------------------------- TwoSelmerGroupData of Jacobian of Hyperelliptic Curve defined by y^2 = 76*x^5 - 760*x^4 + 2660*x^3 - 3800*x^2 + 1824*x over Rational Field m= Mapping from: CrvHyp: C to CrvHyp: C1 with equations : 19*$.1 361/2*$.2 $.3 and inverse 1/19*$.1 2/361*$.2 $.3 Change curve into Hyperelliptic Curve defined by y^2 = x^5 - 190*x^4 + 12635*x^3 - 342950*x^2 + 3127704*x over Rational Field Bad primes = [ 2, 3, 19 ] f factors as (x - 76) (x - 57) (x - 38) (x - 19) (x). For factor x - 76, use field defined by x - 1 and theta = 76 For factor x - 57, use field defined by x - 1 and theta = 57 For factor x - 38, use field defined by x - 1 and theta = 38 For factor x - 19, use field defined by x - 1 and theta = 19 For factor x, use field defined by x - 1 and theta = 0 The 2-torsion group has dimension 4. Determining local images... p = 2 x = 1/4 --> new generator (0 0 0 0 0 1 0 0 0 0 0 1 0 0 0) x = 26 --> new generator (1 1 1 0 0 0 0 0 1 0 1 1 1 0 1) p = 3 x = 7 --> new generator (1 0 0 0 0 1 1 1 0 0) p = 19 p = infinity Computing class groups... Class group data of the fields: Field given by x - 76: [] Field given by x - 57: [] Field given by x - 38: [] Field given by x - 19: [] Field given by x: [] Dimension of Cl[2] = 0. Signatures: [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] Dimension of units mod squares = 5. Upper bound for Selmer group dimension: 13. ==> Upper bound for rank = 9. Computing unit groups... Class group and unit data of the fields: Field given by x - 76: Class group = [], units = [ 2 ] Field given by x - 57: Class group = [], units = [ 2 ] Field given by x - 38: Class group = [], units = [ 2 ] Field given by x - 19: Class group = [], units = [ 2 ] Field given by x: Class group = [], units = [ 2 ] Time for local computations: 511 ms. Time for class groups: 0 ms. Time for unit groups: 9 ms. Selmer group dimension = 5, Dimension of 2-torsion = 4, ==> Bound for the MW-rank = 1. Total time: 611 ms. Transforming presentation of S back to model C. 1 5 <[ 295/8*$.1^4 - 1437/4*$.1^3 + 9573/8*$.1^2 - 6373/4*$.1 + 722, 10*$.1^4 - 91*$.1^3 + 269*$.1^2 - 264*$.1 + 19, 4561/4*$.1^4 - 22803/2*$.1^3 + 159611/4*$.1^2 - 114041/2*$.1 + 27436, 43/8*$.1^4 - 361/4*$.1^3 + 3849/8*$.1^2 - 4017/4*$.1 + 722, -7*$.1^4 + 42*$.1^3 - 49*$.1^2 - 42*$.1 + 57 ], [], []> {} Total time: 3.729 seconds, Total memory usage: 2.69MB ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Sat Jan 24 09:56:08 2004 Input: P := PolynomialRing(Rationals()); C := HyperellipticCurve(x*(x-1)*(x-2)*(x-3)*(x-4)); D := QuadraticTwist(C,77); J := Jacobian(D); SetVerbose("JacHypSelmer", 2); TwoSelmerGroupData(J : Bound := 300); Output: Magma V2.10-6 Sat Jan 24 2004 09:56:04 on modular [Seed = 2630769408] ------------------------------------- TwoSelmerGroupData of Jacobian of Hyperelliptic Curve defined by y^2 = 77*x^5 - 770*x^4 + 2695*x^3 - 3850*x^2 + 1848*x over Rational Field m= Mapping from: CrvHyp: C to CrvHyp: C1 with equations : 77*$.1 5929*$.2 $.3 and inverse 1/77*$.1 1/5929*$.2 $.3 Change curve into Hyperelliptic Curve defined by y^2 = x^5 - 770*x^4 + 207515*x^3 - 22826650*x^2 + 843672984*x over Rational Field Bad primes = [ 2, 3, 7, 11 ] f factors as (x - 308) (x - 231) (x - 154) (x - 77) (x). For factor x - 308, use field defined by x - 1 and theta = 308 For factor x - 231, use field defined by x - 1 and theta = 231 For factor x - 154, use field defined by x - 1 and theta = 154 For factor x - 77, use field defined by x - 1 and theta = 77 For factor x, use field defined by x - 1 and theta = 0 The 2-torsion group has dimension 4. Determining local images... p = 2 x = 1/4 --> new generator (0 0 0 0 0 1 0 0 0 0 0 1 0 0 0) x = 14 --> new generator (1 0 1 0 1 1 0 0 1 0 0 0 1 1 1) p = 3 x = 3 --> new generator (0 0 1 1 0 1 0 0 1 0) p = 7 p = 11 p = infinity Computing class groups... Class group data of the fields: Field given by x - 308: [] Field given by x - 231: [] Field given by x - 154: [] Field given by x - 77: [] Field given by x: [] Dimension of Cl[2] = 0. Signatures: [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] Dimension of units mod squares = 5. Upper bound for Selmer group dimension: 17. ==> Upper bound for rank = 13. Computing unit groups... Class group and unit data of the fields: Field given by x - 308: Class group = [], units = [ 2 ] Field given by x - 231: Class group = [], units = [ 2 ] Field given by x - 154: Class group = [], units = [ 2 ] Field given by x - 77: Class group = [], units = [ 2 ] Field given by x: Class group = [], units = [ 2 ] Time for local computations: 569 ms. Time for class groups: 0 ms. Time for unit groups: 0 ms. Selmer group dimension = 5, Dimension of 2-torsion = 4, ==> Bound for the MW-rank = 1. Total time: 729 ms. Transforming presentation of S back to model C. 1 5 <[ 18*$.1^4 - 185*$.1^3 + 669*$.1^2 - 1008*$.1 + 539, 741*$.1^4 - 7487*$.1^3 + 26398*$.1^2 - 37670*$.1 + 17787, 13787/4*$.1^4 - 34495*$.1^3 + 483373/4*$.1^2 - 172780*$.1 + 83006, 102*$.1^4 - 1019*$.1^3 + 3577*$.1^2 - 5159*$.1 + 2541, 919/8*$.1^4 - 4553/4*$.1^3 + 31533/8*$.1^2 - 22277/4*$.1 + 2662 ], [], []> {} Total time: 3.859 seconds, Total memory usage: 2.79MB ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Sat Jan 24 09:56:22 2004 Input: P := PolynomialRing(Rationals()); C := HyperellipticCurve(x*(x-1)*(x-2)*(x-3)*(x-4)); D := QuadraticTwist(C,78); J := Jacobian(D); SetVerbose("JacHypSelmer", 2); TwoSelmerGroupData(J : Bound := 300); Output: Magma V2.10-6 Sat Jan 24 2004 09:56:18 on modular [Seed = 2512867871] ------------------------------------- TwoSelmerGroupData of Jacobian of Hyperelliptic Curve defined by y^2 = 78*x^5 - 780*x^4 + 2730*x^3 - 3900*x^2 + 1872*x over Rational Field m= Mapping from: CrvHyp: C to CrvHyp: C1 with equations : 78*$.1 6084*$.2 $.3 and inverse 1/78*$.1 1/6084*$.2 $.3 Change curve into Hyperelliptic Curve defined by y^2 = x^5 - 780*x^4 + 212940*x^3 - 23727600*x^2 + 888361344*x over Rational Field Bad primes = [ 2, 3, 13 ] f factors as (x - 312) (x - 234) (x - 156) (x - 78) (x). For factor x - 312, use field defined by x - 1 and theta = 312 For factor x - 234, use field defined by x - 1 and theta = 234 For factor x - 156, use field defined by x - 1 and theta = 156 For factor x - 78, use field defined by x - 1 and theta = 78 For factor x, use field defined by x - 1 and theta = 0 The 2-torsion group has dimension 4. Determining local images... p = 2 x = 1 --> new generator (0 0 0 0 1 1 0 0 1 0 1 0 0 0 0) x = 2 --> new generator (1 0 1 1 1 0 1 1 0 0 0 1 1 0 0) p = 3 p = 13 p = infinity Computing class groups... Class group data of the fields: Field given by x - 312: [] Field given by x - 234: [] Field given by x - 156: [] Field given by x - 78: [] Field given by x: [] Dimension of Cl[2] = 0. Signatures: [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] Dimension of units mod squares = 5. Upper bound for Selmer group dimension: 15. ==> Upper bound for rank = 11. Computing unit groups... Class group and unit data of the fields: Field given by x - 312: Class group = [], units = [ 2 ] Field given by x - 234: Class group = [], units = [ 2 ] Field given by x - 156: Class group = [], units = [ 2 ] Field given by x - 78: Class group = [], units = [ 2 ] Field given by x: Class group = [], units = [ 2 ] Time for local computations: 1050 ms. Time for class groups: 0 ms. Time for unit groups: 0 ms. Selmer group dimension = 5, Dimension of 2-torsion = 4, ==> Bound for the MW-rank = 1. Total time: 1169 ms. Transforming presentation of S back to model C. 1 5 <[ 13/4*$.1^4 - 157/6*$.1^3 + 281/4*$.1^2 - 241/3*$.1 + 39, -5*$.1^4 + 30*$.1^3 - 69/2*$.1^2 - 63/2*$.1 + 39, 178/3*$.1^4 - 3365/6*$.1^3 + 10867/6*$.1^2 - 6965/3*$.1 + 1014, -25/6*$.1^4 + 63/2*$.1^3 - 347/6*$.1^2 - 69/2*$.1 + 117, $.1^4 - 8*$.1^3 + 23*$.1^2 - 28*$.1 + 13 ], [], []> {} Total time: 4.379 seconds, Total memory usage: 2.79MB ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Sat Jan 24 09:56:36 2004 Input: P := PolynomialRing(Rationals()); C := HyperellipticCurve(x*(x-1)*(x-2)*(x-3)*(x-4)); D := QuadraticTwist(C,79); J := Jacobian(D); SetVerbose("JacHypSelmer", 2); TwoSelmerGroupData(J : Bound := 300); Output: Magma V2.10-6 Sat Jan 24 2004 09:56:33 on modular [Seed = 2396801335] ------------------------------------- TwoSelmerGroupData of Jacobian of Hyperelliptic Curve defined by y^2 = 79*x^5 - 790*x^4 + 2765*x^3 - 3950*x^2 + 1896*x over Rational Field m= Mapping from: CrvHyp: C to CrvHyp: C1 with equations : 79*$.1 6241*$.2 $.3 and inverse 1/79*$.1 1/6241*$.2 $.3 Change curve into Hyperelliptic Curve defined by y^2 = x^5 - 790*x^4 + 218435*x^3 - 24651950*x^2 + 934801944*x over Rational Field Bad primes = [ 2, 3, 79 ] f factors as (x - 316) (x - 237) (x - 158) (x - 79) (x). For factor x - 316, use field defined by x - 1 and theta = 316 For factor x - 237, use field defined by x - 1 and theta = 237 For factor x - 158, use field defined by x - 1 and theta = 158 For factor x - 79, use field defined by x - 1 and theta = 79 For factor x, use field defined by x - 1 and theta = 0 The 2-torsion group has dimension 4. Determining local images... p = 2 x = 1/4 --> new generator (0 0 0 0 0 1 0 0 0 0 0 1 0 0 0) x = 18 --> new generator (1 1 0 0 0 1 0 0 1 0 1 0 1 0 0) p = 3 x = 4 --> new generator (1 0 0 0 0 1 1 1 0 0) p = 79 p = infinity Computing class groups... Class group data of the fields: Field given by x - 316: [] Field given by x - 237: [] Field given by x - 158: [] Field given by x - 79: [] Field given by x: [] Dimension of Cl[2] = 0. Signatures: [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] Dimension of units mod squares = 5. Upper bound for Selmer group dimension: 13. ==> Upper bound for rank = 9. Computing unit groups... Class group and unit data of the fields: Field given by x - 316: Class group = [], units = [ 2 ] Field given by x - 237: Class group = [], units = [ 2 ] Field given by x - 158: Class group = [], units = [ 2 ] Field given by x - 79: Class group = [], units = [ 2 ] Field given by x: Class group = [], units = [ 2 ] Time for local computations: 511 ms. Time for class groups: 0 ms. Time for unit groups: 0 ms. Selmer group dimension = 4, Dimension of 2-torsion = 4, ==> Bound for the MW-rank = 0. Total time: 630 ms. Transforming presentation of S back to model C. 0 4 <[ 4395/8*$.1^4 - 21817/4*$.1^3 + 150673/8*$.1^2 - 105633/4*$.1 + 12482, 780*$.1^4 - 7879*$.1^3 + 27775*$.1^2 - 39636*$.1 + 18723, 328641/4*$.1^4 - 1643203/2*$.1^3 + 11502411/4*$.1^2 - 8216161/2*$.1 + 1972156, -477/8*$.1^4 + 2063/4*$.1^3 - 10927/8*$.1^2 + 3639/4*$.1 + 474 ], [], []> {} Total time: 3.769 seconds, Total memory usage: 2.79MB ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Sat Jan 24 09:56:51 2004 Input: P := PolynomialRing(Rationals()); C := HyperellipticCurve(x*(x-1)*(x-2)*(x-3)*(x-4)); D := QuadraticTwist(C,80); J := Jacobian(D); SetVerbose("JacHypSelmer", 2); TwoSelmerGroupData(J : Bound := 300); Output: Magma V2.10-6 Sat Jan 24 2004 09:56:47 on modular [Seed = 2278899760] ------------------------------------- TwoSelmerGroupData of Jacobian of Hyperelliptic Curve defined by y^2 = 80*x^5 - 800*x^4 + 2800*x^3 - 4000*x^2 + 1920*x over Rational Field m= Mapping from: CrvHyp: C to CrvHyp: C1 with equations : 5*$.1 25/4*$.2 $.3 and inverse 1/5*$.1 4/25*$.2 $.3 Change curve into Hyperelliptic Curve defined by y^2 = x^5 - 50*x^4 + 875*x^3 - 6250*x^2 + 15000*x over Rational Field Bad primes = [ 2, 3, 5 ] f factors as (x - 20) (x - 15) (x - 10) (x - 5) (x). For factor x - 20, use field defined by x - 1 and theta = 20 For factor x - 15, use field defined by x - 1 and theta = 15 For factor x - 10, use field defined by x - 1 and theta = 10 For factor x - 5, use field defined by x - 1 and theta = 5 For factor x, use field defined by x - 1 and theta = 0 The 2-torsion group has dimension 4. Determining local images... p = 2 x = 1/4 --> new generator (0 0 0 0 0 1 0 0 0 0 0 1 0 0 0) x = 30 --> new generator (1 0 1 0 1 1 0 0 1 0 0 0 1 1 1) p = 3 x = 3 --> new generator (0 0 1 1 0 1 0 0 1 0) p = 5 p = infinity Computing class groups... Class group data of the fields: Field given by x - 20: [] Field given by x - 15: [] Field given by x - 10: [] Field given by x - 5: [] Field given by x: [] Dimension of Cl[2] = 0. Signatures: [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] Dimension of units mod squares = 5. Upper bound for Selmer group dimension: 13. ==> Upper bound for rank = 9. Computing unit groups... Class group and unit data of the fields: Field given by x - 20: Class group = [], units = [ 2 ] Field given by x - 15: Class group = [], units = [ 2 ] Field given by x - 10: Class group = [], units = [ 2 ] Field given by x - 5: Class group = [], units = [ 2 ] Field given by x: Class group = [], units = [ 2 ] Time for local computations: 540 ms. Time for class groups: 0 ms. Time for unit groups: 0 ms. Selmer group dimension = 5, Dimension of 2-torsion = 4, ==> Bound for the MW-rank = 1. Total time: 649 ms. Transforming presentation of S back to model C. 1 5 <[ 4*$.1^4 - 37*$.1^3 + 118*$.1^2 - 155*$.1 + 75, 3*$.1^4 - 35*$.1^3 + 136*$.1^2 - 194*$.1 + 75, 121/4*$.1^4 - 306*$.1^3 + 4331/4*$.1^2 - 1556*$.1 + 750, $.1^2 - 4*$.1 + 5, 35/8*$.1^4 - 177/4*$.1^3 + 1305/8*$.1^2 - 1033/4*$.1 + 150 ], [], []> {} Total time: 3.849 seconds, Total memory usage: 2.69MB ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Sat Jan 24 09:57:10 2004 Input: P := PolynomialRing(Rationals()); C := HyperellipticCurve(x*(x-1)*(x-2)*(x-3)*(x-4)); D := QuadraticTwist(C,81); J := Jacobian(D); SetVerbose("JacHypSelmer", 2); TwoSelmerGroupData(J : Bound := 300); Output: Magma V2.10-6 Sat Jan 24 2004 09:57:06 on modular [Seed = 2967631722] ------------------------------------- TwoSelmerGroupData of Jacobian of Hyperelliptic Curve defined by y^2 = 81*x^5 - 810*x^4 + 2835*x^3 - 4050*x^2 + 1944*x over Rational Field m= Mapping from: CrvHyp: C to CrvHyp: C1 with equations : $.1 1/9*$.2 $.3 and inverse $.1 9*$.2 $.3 Change curve into Hyperelliptic Curve defined by y^2 = x^5 - 10*x^4 + 35*x^3 - 50*x^2 + 24*x over Rational Field Bad primes = [ 2, 3 ] f factors as (x - 4) (x - 3) (x - 2) (x - 1) (x). For factor x - 4, use field defined by x - 1 and theta = 4 For factor x - 3, use field defined by x - 1 and theta = 3 For factor x - 2, use field defined by x - 1 and theta = 2 For factor x - 1, use field defined by x - 1 and theta = 1 For factor x, use field defined by x - 1 and theta = 0 The 2-torsion group has dimension 4. Determining local images... p = 2 x = 1/4 --> new generator (0 0 0 0 0 1 0 0 0 0 0 1 0 0 0) x = 22 --> new generator (1 0 0 0 1 0 0 0 1 0 0 1 1 1 0) p = 3 x = 7 --> new generator (1 0 0 0 0 1 1 1 0 0) p = infinity Computing class groups... Class group data of the fields: Field given by x - 4: [] Field given by x - 3: [] Field given by x - 2: [] Field given by x - 1: [] Field given by x: [] Dimension of Cl[2] = 0. Signatures: [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] Dimension of units mod squares = 5. Upper bound for Selmer group dimension: 9. ==> Upper bound for rank = 5. Computing unit groups... Class group and unit data of the fields: Field given by x - 4: Class group = [], units = [ 2 ] Field given by x - 3: Class group = [], units = [ 2 ] Field given by x - 2: Class group = [], units = [ 2 ] Field given by x - 1: Class group = [], units = [ 2 ] Field given by x: Class group = [], units = [ 2 ] Time for local computations: 531 ms. Time for class groups: 0 ms. Time for unit groups: 0 ms. Selmer group dimension = 4, Dimension of 2-torsion = 4, ==> Bound for the MW-rank = 0. Total time: 591 ms. Transforming presentation of S back to model C. 0 4 <[ 1/8*$.1^4 - 3/4*$.1^3 + 3/8*$.1^2 + 5/4*$.1 + 2, -$.1^3 + 7*$.1^2 - 12*$.1 + 3, 1/4*$.1^4 - 3/2*$.1^3 + 11/4*$.1^2 - 5/2*$.1 + 4, -9/8*$.1^4 + 35/4*$.1^3 - 163/8*$.1^2 + 51/4*$.1 + 6 ], [], []> {} Total time: 3.739 seconds, Total memory usage: 2.69MB ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Sat Jan 24 09:57:25 2004 Input: P := PolynomialRing(Rationals()); C := HyperellipticCurve(x*(x-1)*(x-2)*(x-3)*(x-4)); D := QuadraticTwist(C,82); J := Jacobian(D); SetVerbose("JacHypSelmer", 2); TwoSelmerGroupData(J : Bound := 300); Output: Magma V2.10-6 Sat Jan 24 2004 09:57:20 on modular [Seed = 2851827297] ------------------------------------- TwoSelmerGroupData of Jacobian of Hyperelliptic Curve defined by y^2 = 82*x^5 - 820*x^4 + 2870*x^3 - 4100*x^2 + 1968*x over Rational Field m= Mapping from: CrvHyp: C to CrvHyp: C1 with equations : 82*$.1 6724*$.2 $.3 and inverse 1/82*$.1 1/6724*$.2 $.3 Change curve into Hyperelliptic Curve defined by y^2 = x^5 - 820*x^4 + 235340*x^3 - 27568400*x^2 + 1085092224*x over Rational Field Bad primes = [ 2, 3, 41 ] f factors as (x - 328) (x - 246) (x - 164) (x - 82) (x). For factor x - 328, use field defined by x - 1 and theta = 328 For factor x - 246, use field defined by x - 1 and theta = 246 For factor x - 164, use field defined by x - 1 and theta = 164 For factor x - 82, use field defined by x - 1 and theta = 82 For factor x, use field defined by x - 1 and theta = 0 The 2-torsion group has dimension 4. Determining local images... p = 2 x = 1 --> new generator (0 0 0 0 1 0 0 0 1 0 1 1 0 0 0) x = 42 --> new generator (1 0 0 0 0 1 1 1 0 1 1 0 1 0 1) p = 3 x = 7 --> new generator (1 0 0 0 0 1 1 1 0 0) p = 41 p = infinity Computing class groups... Class group data of the fields: Field given by x - 328: [] Field given by x - 246: [] Field given by x - 164: [] Field given by x - 82: [] Field given by x: [] Dimension of Cl[2] = 0. Signatures: [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] Dimension of units mod squares = 5. Upper bound for Selmer group dimension: 13. ==> Upper bound for rank = 9. Computing unit groups... Class group and unit data of the fields: Field given by x - 328: Class group = [], units = [ 2 ] Field given by x - 246: Class group = [], units = [ 2 ] Field given by x - 164: Class group = [], units = [ 2 ] Field given by x - 82: Class group = [], units = [ 2 ] Field given by x: Class group = [], units = [ 2 ] Time for local computations: 1100 ms. Time for class groups: 0 ms. Time for unit groups: 0 ms. Selmer group dimension = 6, Dimension of 2-torsion = 4, ==> Bound for the MW-rank = 2. Total time: 1220 ms. Transforming presentation of S back to model C. 2 6 <[ -35*$.1^4 + 311*$.1^3 - 1743/2*$.1^2 + 1437/2*$.1 + 123, -1/4*$.1^4 + 3/2*$.1^3 - 5/4*$.1^2 - 3*$.1 + 1, 30*$.1^4 - 521/2*$.1^3 + 1467/2*$.1^2 - 747*$.1 + 246, -309/4*$.1^4 + 689*$.1^3 - 7823/4*$.1^2 + 1713*$.1 + 123, 65*$.1^4 - 650*$.1^3 + 2295*$.1^2 - 3350*$.1 + 1681, -5*$.1^4 + 30*$.1^3 - 35*$.1^2 - 30*$.1 + 41 ], [], []> {} Total time: 4.419 seconds, Total memory usage: 2.79MB ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Sat Jan 24 09:57:44 2004 Input: P := PolynomialRing(Rationals()); C := HyperellipticCurve(x*(x-1)*(x-2)*(x-3)*(x-4)); D := QuadraticTwist(C,83); J := Jacobian(D); SetVerbose("JacHypSelmer", 2); TwoSelmerGroupData(J : Bound := 300); Output: Magma V2.10-6 Sat Jan 24 2004 09:57:40 on modular [Seed = 2733663582] ------------------------------------- TwoSelmerGroupData of Jacobian of Hyperelliptic Curve defined by y^2 = 83*x^5 - 830*x^4 + 2905*x^3 - 4150*x^2 + 1992*x over Rational Field m= Mapping from: CrvHyp: C to CrvHyp: C1 with equations : 83*$.1 6889*$.2 $.3 and inverse 1/83*$.1 1/6889*$.2 $.3 Change curve into Hyperelliptic Curve defined by y^2 = x^5 - 830*x^4 + 241115*x^3 - 28589350*x^2 + 1138999704*x over Rational Field Bad primes = [ 2, 3, 83 ] f factors as (x - 332) (x - 249) (x - 166) (x - 83) (x). For factor x - 332, use field defined by x - 1 and theta = 332 For factor x - 249, use field defined by x - 1 and theta = 249 For factor x - 166, use field defined by x - 1 and theta = 166 For factor x - 83, use field defined by x - 1 and theta = 83 For factor x, use field defined by x - 1 and theta = 0 The 2-torsion group has dimension 4. Determining local images... p = 2 x = 1/4 --> new generator (0 0 0 0 0 1 0 0 0 0 0 1 0 0 0) x = 26 --> new generator (1 1 1 0 0 0 0 0 1 0 1 1 1 0 1) p = 3 x = 3 --> new generator (0 0 1 1 0 1 0 0 1 0) p = 83 p = infinity Computing class groups... Class group data of the fields: Field given by x - 332: [] Field given by x - 249: [] Field given by x - 166: [] Field given by x - 83: [] Field given by x: [] Dimension of Cl[2] = 0. Signatures: [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] Dimension of units mod squares = 5. Upper bound for Selmer group dimension: 13. ==> Upper bound for rank = 9. Computing unit groups... Class group and unit data of the fields: Field given by x - 332: Class group = [], units = [ 2 ] Field given by x - 249: Class group = [], units = [ 2 ] Field given by x - 166: Class group = [], units = [ 2 ] Field given by x - 83: Class group = [], units = [ 2 ] Field given by x: Class group = [], units = [ 2 ] Time for local computations: 509 ms. Time for class groups: 0 ms. Time for unit groups: 11 ms. Selmer group dimension = 5, Dimension of 2-torsion = 4, ==> Bound for the MW-rank = 1. Total time: 630 ms. Transforming presentation of S back to model C. 1 5 <[ 4815/8*$.1^4 - 23797/4*$.1^3 + 164189/8*$.1^2 - 115485/4*$.1 + 13778, 823*$.1^4 - 8341*$.1^3 + 29596*$.1^2 - 42746*$.1 + 20667, 381329/4*$.1^4 - 1906507/2*$.1^3 + 13344363/4*$.1^2 - 9530633/2*$.1 + 2287148, 187/8*$.1^4 - 889/4*$.1^3 + 6009/8*$.1^2 - 4193/4*$.1 + 498, 256*$.1^4 - 2560*$.1^3 + 9084*$.1^2 - 13420*$.1 + 6889 ], [], []> {} Total time: 3.829 seconds, Total memory usage: 2.79MB ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Sat Jan 24 09:58:03 2004 Input: P := PolynomialRing(Rationals()); C := HyperellipticCurve(x*(x-1)*(x-2)*(x-3)*(x-4)); D := QuadraticTwist(C,84); J := Jacobian(D); SetVerbose("JacHypSelmer", 2); TwoSelmerGroupData(J : Bound := 300); Output: Magma V2.10-6 Sat Jan 24 2004 09:57:59 on modular [Seed = 3700300595] ------------------------------------- TwoSelmerGroupData of Jacobian of Hyperelliptic Curve defined by y^2 = 84*x^5 - 840*x^4 + 2940*x^3 - 4200*x^2 + 2016*x over Rational Field m= Mapping from: CrvHyp: C to CrvHyp: C1 with equations : 21*$.1 441/2*$.2 $.3 and inverse 1/21*$.1 2/441*$.2 $.3 Change curve into Hyperelliptic Curve defined by y^2 = x^5 - 210*x^4 + 15435*x^3 - 463050*x^2 + 4667544*x over Rational Field Bad primes = [ 2, 3, 7 ] f factors as (x - 84) (x - 63) (x - 42) (x - 21) (x). For factor x - 84, use field defined by x - 1 and theta = 84 For factor x - 63, use field defined by x - 1 and theta = 63 For factor x - 42, use field defined by x - 1 and theta = 42 For factor x - 21, use field defined by x - 1 and theta = 21 For factor x, use field defined by x - 1 and theta = 0 The 2-torsion group has dimension 4. Determining local images... p = 2 x = 1/4 --> new generator (0 0 0 0 0 1 0 0 0 0 0 1 0 0 0) x = 30 --> new generator (1 0 1 0 1 1 0 0 1 0 0 0 1 1 1) p = 3 p = 7 p = infinity Computing class groups... Class group data of the fields: Field given by x - 84: [] Field given by x - 63: [] Field given by x - 42: [] Field given by x - 21: [] Field given by x: [] Dimension of Cl[2] = 0. Signatures: [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] Dimension of units mod squares = 5. Upper bound for Selmer group dimension: 15. ==> Upper bound for rank = 11. Computing unit groups... Class group and unit data of the fields: Field given by x - 84: Class group = [], units = [ 2 ] Field given by x - 63: Class group = [], units = [ 2 ] Field given by x - 42: Class group = [], units = [ 2 ] Field given by x - 21: Class group = [], units = [ 2 ] Field given by x: Class group = [], units = [ 2 ] Time for local computations: 571 ms. Time for class groups: 0 ms. Time for unit groups: 0 ms. Selmer group dimension = 4, Dimension of 2-torsion = 4, ==> Bound for the MW-rank = 0. Total time: 679 ms. Transforming presentation of S back to model C. 0 4 <[ 373/8*$.1^4 - 5357/12*$.1^3 + 11775/8*$.1^2 - 23413/12*$.1 + 882, 6*$.1^4 - 187/3*$.1^3 + 225*$.1^2 - 968/3*$.1 + 147, 18595/12*$.1^4 - 30971/2*$.1^3 + 649745/12*$.1^2 - 154493/2*$.1 + 37044, 61/24*$.1^4 - 117/4*$.1^3 + 2879/24*$.1^2 - 821/4*$.1 + 126 ], [], []> {} Total time: 3.919 seconds, Total memory usage: 2.69MB ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Sat Jan 24 09:58:22 2004 Input: P := PolynomialRing(Rationals()); C := HyperellipticCurve(x*(x-1)*(x-2)*(x-3)*(x-4)); D := QuadraticTwist(C,85); J := Jacobian(D); SetVerbose("JacHypSelmer", 2); TwoSelmerGroupData(J : Bound := 300); Output: Magma V2.10-6 Sat Jan 24 2004 09:58:18 on modular [Seed = 3582401991] ------------------------------------- TwoSelmerGroupData of Jacobian of Hyperelliptic Curve defined by y^2 = 85*x^5 - 850*x^4 + 2975*x^3 - 4250*x^2 + 2040*x over Rational Field m= Mapping from: CrvHyp: C to CrvHyp: C1 with equations : 85*$.1 7225*$.2 $.3 and inverse 1/85*$.1 1/7225*$.2 $.3 Change curve into Hyperelliptic Curve defined by y^2 = x^5 - 850*x^4 + 252875*x^3 - 30706250*x^2 + 1252815000*x over Rational Field Bad primes = [ 2, 3, 5, 17 ] f factors as (x - 340) (x - 255) (x - 170) (x - 85) (x). For factor x - 340, use field defined by x - 1 and theta = 340 For factor x - 255, use field defined by x - 1 and theta = 255 For factor x - 170, use field defined by x - 1 and theta = 170 For factor x - 85, use field defined by x - 1 and theta = 85 For factor x, use field defined by x - 1 and theta = 0 The 2-torsion group has dimension 4. Determining local images... p = 2 x = 1/4 --> new generator (0 0 0 0 0 1 0 0 0 0 0 1 0 0 0) x = 30 --> new generator (1 0 1 0 1 1 0 0 1 0 0 0 1 1 1) p = 3 x = 1 --> new generator (1 0 0 0 0 1 1 1 0 0) p = 5 p = 17 p = infinity Computing class groups... Class group data of the fields: Field given by x - 340: [] Field given by x - 255: [] Field given by x - 170: [] Field given by x - 85: [] Field given by x: [] Dimension of Cl[2] = 0. Signatures: [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] Dimension of units mod squares = 5. Upper bound for Selmer group dimension: 17. ==> Upper bound for rank = 13. Computing unit groups... Class group and unit data of the fields: Field given by x - 340: Class group = [], units = [ 2 ] Field given by x - 255: Class group = [], units = [ 2 ] Field given by x - 170: Class group = [], units = [ 2 ] Field given by x - 85: Class group = [], units = [ 2 ] Field given by x: Class group = [], units = [ 2 ] Time for local computations: 551 ms. Time for class groups: 0 ms. Time for unit groups: 11 ms. Selmer group dimension = 5, Dimension of 2-torsion = 4, ==> Bound for the MW-rank = 1. Total time: 730 ms. Transforming presentation of S back to model C. 1 5 <[ 5069/8*$.1^4 - 25175/4*$.1^3 + 174023/8*$.1^2 - 122159/4*$.1 + 14450, 616*$.1^4 - 6169*$.1^3 + 21615*$.1^2 - 30852*$.1 + 14739, 278545/4*$.1^4 - 1392555/2*$.1^3 + 9746491/4*$.1^2 - 6960701/2*$.1 + 1670420, -513/8*$.1^4 + 2219/4*$.1^3 - 11755/8*$.1^2 + 3915/4*$.1 + 510, 17*$.1^4 - 170*$.1^3 + 599*$.1^2 - 866*$.1 + 425 ], [], []> {} Total time: 3.789 seconds, Total memory usage: 2.79MB ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Sat Jan 24 09:58:36 2004 Input: P := PolynomialRing(Rationals()); C := HyperellipticCurve(x*(x-1)*(x-2)*(x-3)*(x-4)); D := QuadraticTwist(C,86); J := Jacobian(D); SetVerbose("JacHypSelmer", 2); TwoSelmerGroupData(J : Bound := 300); Output: Magma V2.10-6 Sat Jan 24 2004 09:58:32 on modular [Seed = 3466331854] ------------------------------------- TwoSelmerGroupData of Jacobian of Hyperelliptic Curve defined by y^2 = 86*x^5 - 860*x^4 + 3010*x^3 - 4300*x^2 + 2064*x over Rational Field m= Mapping from: CrvHyp: C to CrvHyp: C1 with equations : 86*$.1 7396*$.2 $.3 and inverse 1/86*$.1 1/7396*$.2 $.3 Change curve into Hyperelliptic Curve defined by y^2 = x^5 - 860*x^4 + 258860*x^3 - 31802800*x^2 + 1312819584*x over Rational Field Bad primes = [ 2, 3, 43 ] f factors as (x - 344) (x - 258) (x - 172) (x - 86) (x). For factor x - 344, use field defined by x - 1 and theta = 344 For factor x - 258, use field defined by x - 1 and theta = 258 For factor x - 172, use field defined by x - 1 and theta = 172 For factor x - 86, use field defined by x - 1 and theta = 86 For factor x, use field defined by x - 1 and theta = 0 The 2-torsion group has dimension 4. Determining local images... p = 2 x = 1 --> new generator (0 0 0 0 1 1 0 0 1 0 1 0 0 0 0) x = 26 --> new generator (1 0 0 1 1 0 1 1 1 0 0 0 1 0 1) p = 3 x = 3 --> new generator (0 0 1 1 0 1 0 0 1 0) p = 43 p = infinity Computing class groups... Class group data of the fields: Field given by x - 344: [] Field given by x - 258: [] Field given by x - 172: [] Field given by x - 86: [] Field given by x: [] Dimension of Cl[2] = 0. Signatures: [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] Dimension of units mod squares = 5. Upper bound for Selmer group dimension: 13. ==> Upper bound for rank = 9. Computing unit groups... Class group and unit data of the fields: Field given by x - 344: Class group = [], units = [ 2 ] Field given by x - 258: Class group = [], units = [ 2 ] Field given by x - 172: Class group = [], units = [ 2 ] Field given by x - 86: Class group = [], units = [ 2 ] Field given by x: Class group = [], units = [ 2 ] Time for local computations: 1140 ms. Time for class groups: 0 ms. Time for unit groups: 9 ms. Selmer group dimension = 5, Dimension of 2-torsion = 4, ==> Bound for the MW-rank = 1. Total time: 1260 ms. Transforming presentation of S back to model C. 1 5 <[ 955/4*$.1^4 - 4673/2*$.1^3 + 32107/4*$.1^2 - 11390*$.1 + 5547, -11/2*$.1^4 + 33*$.1^3 - 38*$.1^2 - 69/2*$.1 + 43, 462*$.1^4 - 9283/2*$.1^3 + 32557/2*$.1^2 - 23191*$.1 + 11094, 6*$.1^4 - 111/2*$.1^3 + 186*$.1^2 - 523/2*$.1 + 129, 61*$.1^4 - 610*$.1^3 + 2199*$.1^2 - 3370*$.1 + 1849 ], [], []> {} Total time: 4.459 seconds, Total memory usage: 2.79MB ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Sat Jan 24 09:58:55 2004 Input: P := PolynomialRing(Rationals()); C := HyperellipticCurve(x*(x-1)*(x-2)*(x-3)*(x-4)); D := QuadraticTwist(C,87); J := Jacobian(D); SetVerbose("JacHypSelmer", 2); TwoSelmerGroupData(J : Bound := 300); Output: Magma V2.10-6 Sat Jan 24 2004 09:58:51 on modular [Seed = 3348434932] ------------------------------------- TwoSelmerGroupData of Jacobian of Hyperelliptic Curve defined by y^2 = 87*x^5 - 870*x^4 + 3045*x^3 - 4350*x^2 + 2088*x over Rational Field m= Mapping from: CrvHyp: C to CrvHyp: C1 with equations : 87*$.1 7569*$.2 $.3 and inverse 1/87*$.1 1/7569*$.2 $.3 Change curve into Hyperelliptic Curve defined by y^2 = x^5 - 870*x^4 + 264915*x^3 - 32925150*x^2 + 1374954264*x over Rational Field Bad primes = [ 2, 3, 29 ] f factors as (x - 348) (x - 261) (x - 174) (x - 87) (x). For factor x - 348, use field defined by x - 1 and theta = 348 For factor x - 261, use field defined by x - 1 and theta = 261 For factor x - 174, use field defined by x - 1 and theta = 174 For factor x - 87, use field defined by x - 1 and theta = 87 For factor x, use field defined by x - 1 and theta = 0 The 2-torsion group has dimension 4. Determining local images... p = 2 x = 1/4 --> new generator (0 0 0 0 0 1 0 0 0 0 0 1 0 0 0) x = 2 --> new generator (1 1 0 0 0 1 0 0 1 0 1 0 1 0 0) p = 3 p = 29 p = infinity Computing class groups... Class group data of the fields: Field given by x - 348: [] Field given by x - 261: [] Field given by x - 174: [] Field given by x - 87: [] Field given by x: [] Dimension of Cl[2] = 0. Signatures: [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] Dimension of units mod squares = 5. Upper bound for Selmer group dimension: 15. ==> Upper bound for rank = 11. Computing unit groups... Class group and unit data of the fields: Field given by x - 348: Class group = [], units = [ 2 ] Field given by x - 261: Class group = [], units = [ 2 ] Field given by x - 174: Class group = [], units = [ 2 ] Field given by x - 87: Class group = [], units = [ 2 ] Field given by x: Class group = [], units = [ 2 ] Time for local computations: 529 ms. Time for class groups: 0 ms. Time for unit groups: 0 ms. Selmer group dimension = 5, Dimension of 2-torsion = 4, ==> Bound for the MW-rank = 1. Total time: 651 ms. Transforming presentation of S back to model C. 1 5 <[ 16403/8*$.1^4 - 81861/4*$.1^3 + 571681/8*$.1^2 - 407289/4*$.1 + 48778, 105*$.1^4 - 3179/3*$.1^3 + 3734*$.1^2 - 15994/3*$.1 + 2523, 15137/4*$.1^4 - 75657/2*$.1^3 + 529407/4*$.1^2 - 378097/2*$.1 + 90828, 281/24*$.1^4 - 513/4*$.1^3 + 12163/24*$.1^2 - 3417/4*$.1 + 522, 19/3*$.1^4 - 230/3*$.1^3 + 944/3*$.1^2 - 1507/3*$.1 + 261 ], [], []> {} Total time: 3.739 seconds, Total memory usage: 2.69MB ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Sat Jan 24 09:59:11 2004 Input: P := PolynomialRing(Rationals()); C := HyperellipticCurve(x*(x-1)*(x-2)*(x-3)*(x-4)); D := QuadraticTwist(C,88); J := Jacobian(D); SetVerbose("JacHypSelmer", 2); TwoSelmerGroupData(J : Bound := 300); Output: Magma V2.10-6 Sat Jan 24 2004 09:59:06 on modular [Seed = 4037163218] ------------------------------------- TwoSelmerGroupData of Jacobian of Hyperelliptic Curve defined by y^2 = 88*x^5 - 880*x^4 + 3080*x^3 - 4400*x^2 + 2112*x over Rational Field m= Mapping from: CrvHyp: C to CrvHyp: C1 with equations : 22*$.1 242*$.2 $.3 and inverse 1/22*$.1 1/242*$.2 $.3 Change curve into Hyperelliptic Curve defined by y^2 = x^5 - 220*x^4 + 16940*x^3 - 532400*x^2 + 5622144*x over Rational Field Bad primes = [ 2, 3, 11 ] f factors as (x - 88) (x - 66) (x - 44) (x - 22) (x). For factor x - 88, use field defined by x - 1 and theta = 88 For factor x - 66, use field defined by x - 1 and theta = 66 For factor x - 44, use field defined by x - 1 and theta = 44 For factor x - 22, use field defined by x - 1 and theta = 22 For factor x, use field defined by x - 1 and theta = 0 The 2-torsion group has dimension 4. Determining local images... p = 2 x = 1 --> new generator (0 0 0 0 1 1 0 0 1 0 1 0 0 0 0) x = 26 --> new generator (1 0 0 1 1 0 1 1 1 0 0 0 1 0 1) p = 3 x = 1 --> new generator (1 0 0 0 0 1 1 1 0 0) p = 11 p = infinity Computing class groups... Class group data of the fields: Field given by x - 88: [] Field given by x - 66: [] Field given by x - 44: [] Field given by x - 22: [] Field given by x: [] Dimension of Cl[2] = 0. Signatures: [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] Dimension of units mod squares = 5. Upper bound for Selmer group dimension: 13. ==> Upper bound for rank = 9. Computing unit groups... Class group and unit data of the fields: Field given by x - 88: Class group = [], units = [ 2 ] Field given by x - 66: Class group = [], units = [ 2 ] Field given by x - 44: Class group = [], units = [ 2 ] Field given by x - 22: Class group = [], units = [ 2 ] Field given by x: Class group = [], units = [ 2 ] Time for local computations: 1090 ms. Time for class groups: 0 ms. Time for unit groups: 9 ms. Selmer group dimension = 5, Dimension of 2-torsion = 4, ==> Bound for the MW-rank = 1. Total time: 1189 ms. Transforming presentation of S back to model C. 1 5 <[ -5/4*$.1^4 + 15/2*$.1^3 - 53/4*$.1^2 + 2*$.1 + 11, -3/2*$.1^4 + 9*$.1^3 - 10*$.1^2 - 21/2*$.1 + 11, 6*$.1^4 - 99/2*$.1^3 + 253/2*$.1^2 - 103*$.1 + 22, -20*$.1^4 + 337/2*$.1^3 - 436*$.1^2 + 597/2*$.1 + 121, -4*$.1^4 + 24*$.1^3 - 28*$.1^2 - 24*$.1 + 33 ], [], []> {} Total time: 4.279 seconds, Total memory usage: 2.69MB ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Sat Jan 24 09:59:24 2004 Input: P := PolynomialRing(Rationals()); C := HyperellipticCurve(x*(x-1)*(x-2)*(x-3)*(x-4)); D := QuadraticTwist(C,89); J := Jacobian(D); SetVerbose("JacHypSelmer", 2); TwoSelmerGroupData(J : Bound := 300); Output: Magma V2.10-6 Sat Jan 24 2004 09:59:20 on modular [Seed = 3921355193] ------------------------------------- TwoSelmerGroupData of Jacobian of Hyperelliptic Curve defined by y^2 = 89*x^5 - 890*x^4 + 3115*x^3 - 4450*x^2 + 2136*x over Rational Field m= Mapping from: CrvHyp: C to CrvHyp: C1 with equations : 89*$.1 7921*$.2 $.3 and inverse 1/89*$.1 1/7921*$.2 $.3 Change curve into Hyperelliptic Curve defined by y^2 = x^5 - 890*x^4 + 277235*x^3 - 35248450*x^2 + 1505813784*x over Rational Field Bad primes = [ 2, 3, 89 ] f factors as (x - 356) (x - 267) (x - 178) (x - 89) (x). For factor x - 356, use field defined by x - 1 and theta = 356 For factor x - 267, use field defined by x - 1 and theta = 267 For factor x - 178, use field defined by x - 1 and theta = 178 For factor x - 89, use field defined by x - 1 and theta = 89 For factor x, use field defined by x - 1 and theta = 0 The 2-torsion group has dimension 4. Determining local images... p = 2 x = 1/4 --> new generator (0 0 0 0 0 1 0 0 0 0 0 1 0 0 0) x = 6 --> new generator (1 0 0 0 1 0 0 0 1 0 0 1 1 1 0) p = 3 x = 3 --> new generator (0 0 1 1 0 1 0 0 1 0) p = 89 p = infinity Computing class groups... Class group data of the fields: Field given by x - 356: [] Field given by x - 267: [] Field given by x - 178: [] Field given by x - 89: [] Field given by x: [] Dimension of Cl[2] = 0. Signatures: [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] Dimension of units mod squares = 5. Upper bound for Selmer group dimension: 13. ==> Upper bound for rank = 9. Computing unit groups... Class group and unit data of the fields: Field given by x - 356: Class group = [], units = [ 2 ] Field given by x - 267: Class group = [], units = [ 2 ] Field given by x - 178: Class group = [], units = [ 2 ] Field given by x - 89: Class group = [], units = [ 2 ] Field given by x: Class group = [], units = [ 2 ] Time for local computations: 559 ms. Time for class groups: 0 ms. Time for unit groups: 0 ms. Selmer group dimension = 6, Dimension of 2-torsion = 4, ==> Bound for the MW-rank = 2. Total time: 701 ms. Transforming presentation of S back to model C. 2 6 <[ 5281/8*$.1^4 - 26227/4*$.1^3 + 182339/8*$.1^2 - 129883/4*$.1 + 15842, 55*$.1^4 - 507*$.1^3 + 1536*$.1^2 - 1618*$.1 + 267, 5281/4*$.1^4 - 26315/2*$.1^3 + 183579/4*$.1^2 - 130949/2*$.1 + 31684, -537/8*$.1^4 + 2323/4*$.1^3 - 12307/8*$.1^2 + 4099/4*$.1 + 534, 319*$.1^4 - 3190*$.1^3 + 11209*$.1^2 - 16170*$.1 + 7921, -11*$.1^4 + 66*$.1^3 - 77*$.1^2 - 66*$.1 + 89 ], [], []> {} Total time: 3.879 seconds, Total memory usage: 2.79MB ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Sat Jan 24 09:59:41 2004 Input: P := PolynomialRing(Rationals()); C := HyperellipticCurve(x*(x-1)*(x-2)*(x-3)*(x-4)); D := QuadraticTwist(C,90); J := Jacobian(D); SetVerbose("JacHypSelmer", 2); TwoSelmerGroupData(J : Bound := 300); Output: Magma V2.10-6 Sat Jan 24 2004 09:59:36 on modular [Seed = 3803196066] ------------------------------------- TwoSelmerGroupData of Jacobian of Hyperelliptic Curve defined by y^2 = 90*x^5 - 900*x^4 + 3150*x^3 - 4500*x^2 + 2160*x over Rational Field m= Mapping from: CrvHyp: C to CrvHyp: C1 with equations : 10*$.1 100/3*$.2 $.3 and inverse 1/10*$.1 3/100*$.2 $.3 Change curve into Hyperelliptic Curve defined by y^2 = x^5 - 100*x^4 + 3500*x^3 - 50000*x^2 + 240000*x over Rational Field Bad primes = [ 2, 3, 5 ] f factors as (x - 40) (x - 30) (x - 20) (x - 10) (x). For factor x - 40, use field defined by x - 1 and theta = 40 For factor x - 30, use field defined by x - 1 and theta = 30 For factor x - 20, use field defined by x - 1 and theta = 20 For factor x - 10, use field defined by x - 1 and theta = 10 For factor x, use field defined by x - 1 and theta = 0 The 2-torsion group has dimension 4. Determining local images... p = 2 x = 1 --> new generator (0 0 0 0 1 0 0 0 1 0 1 1 0 0 0) x = 34 --> new generator (1 0 1 0 0 0 1 1 1 1 1 0 1 0 0) p = 3 x = 7 --> new generator (1 0 0 0 0 1 1 1 0 0) p = 5 p = infinity Computing class groups... Class group data of the fields: Field given by x - 40: [] Field given by x - 30: [] Field given by x - 20: [] Field given by x - 10: [] Field given by x: [] Dimension of Cl[2] = 0. Signatures: [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] Dimension of units mod squares = 5. Upper bound for Selmer group dimension: 13. ==> Upper bound for rank = 9. Computing unit groups... Class group and unit data of the fields: Field given by x - 40: Class group = [], units = [ 2 ] Field given by x - 30: Class group = [], units = [ 2 ] Field given by x - 20: Class group = [], units = [ 2 ] Field given by x - 10: Class group = [], units = [ 2 ] Field given by x: Class group = [], units = [ 2 ] Time for local computations: 1030 ms. Time for class groups: 0 ms. Time for unit groups: 11 ms. Selmer group dimension = 5, Dimension of 2-torsion = 4, ==> Bound for the MW-rank = 1. Total time: 1130 ms. Transforming presentation of S back to model C. 1 5 <[ 25*$.1^4 - 250*$.1^3 + 875*$.1^2 - 1260*$.1 + 625, 51/4*$.1^4 - 273/2*$.1^3 + 2041/4*$.1^2 - 1533/2*$.1 + 375, 3/4*$.1^4 - 10*$.1^3 + 181/4*$.1^2 - 81*$.1 + 50, 1/4*$.1^4 - 3/2*$.1^3 + 7/4*$.1^2 + 1/2*$.1 + 5, 7/2*$.1^4 - 33*$.1^3 + 107*$.1^2 - 285/2*$.1 + 75 ], [], []> {} Total time: 4.319 seconds, Total memory usage: 2.69MB ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Sat Jan 24 10:00:01 2004 Input: P := PolynomialRing(Rationals()); C := HyperellipticCurve(x*(x-1)*(x-2)*(x-3)*(x-4)); D := QuadraticTwist(C,91); J := Jacobian(D); SetVerbose("JacHypSelmer", 2); TwoSelmerGroupData(J : Bound := 300); Output: Magma V2.10-6 Sat Jan 24 2004 09:59:57 on modular [Seed = 440980078] ------------------------------------- TwoSelmerGroupData of Jacobian of Hyperelliptic Curve defined by y^2 = 91*x^5 - 910*x^4 + 3185*x^3 - 4550*x^2 + 2184*x over Rational Field m= Mapping from: CrvHyp: C to CrvHyp: C1 with equations : 91*$.1 8281*$.2 $.3 and inverse 1/91*$.1 1/8281*$.2 $.3 Change curve into Hyperelliptic Curve defined by y^2 = x^5 - 910*x^4 + 289835*x^3 - 37678550*x^2 + 1645799064*x over Rational Field Bad primes = [ 2, 3, 7, 13 ] f factors as (x - 364) (x - 273) (x - 182) (x - 91) (x). For factor x - 364, use field defined by x - 1 and theta = 364 For factor x - 273, use field defined by x - 1 and theta = 273 For factor x - 182, use field defined by x - 1 and theta = 182 For factor x - 91, use field defined by x - 1 and theta = 91 For factor x, use field defined by x - 1 and theta = 0 The 2-torsion group has dimension 4. Determining local images... p = 2 x = 1/4 --> new generator (0 0 0 0 0 1 0 0 0 0 0 1 0 0 0) x = 10 --> new generator (1 1 1 0 0 0 0 0 1 0 1 1 1 0 1) p = 3 x = 7 --> new generator (1 0 0 0 0 1 1 1 0 0) p = 7 p = 13 p = infinity Computing class groups... Class group data of the fields: Field given by x - 364: [] Field given by x - 273: [] Field given by x - 182: [] Field given by x - 91: [] Field given by x: [] Dimension of Cl[2] = 0. Signatures: [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] Dimension of units mod squares = 5. Upper bound for Selmer group dimension: 17. ==> Upper bound for rank = 13. Computing unit groups... Class group and unit data of the fields: Field given by x - 364: Class group = [], units = [ 2 ] Field given by x - 273: Class group = [], units = [ 2 ] Field given by x - 182: Class group = [], units = [ 2 ] Field given by x - 91: Class group = [], units = [ 2 ] Field given by x: Class group = [], units = [ 2 ] Time for local computations: 551 ms. Time for class groups: 0 ms. Time for unit groups: 9 ms. Selmer group dimension = 5, Dimension of 2-torsion = 4, ==> Bound for the MW-rank = 1. Total time: 710 ms. Transforming presentation of S back to model C. 1 5 <[ 29/8*$.1^4 - 119/4*$.1^3 + 599/8*$.1^2 - 239/4*$.1 + 14, 1035*$.1^4 - 10441*$.1^3 + 36772*$.1^2 - 52482*$.1 + 24843, 502321/4*$.1^4 - 2511603/2*$.1^3 + 17581211/4*$.1^2 - 12558185/2*$.1 + 3014284, -549/8*$.1^4 + 2375/4*$.1^3 - 12583/8*$.1^2 + 4191/4*$.1 + 546, 56*$.1^4 - 539*$.1^3 + 1822*$.1^2 - 2521*$.1 + 1183 ], [], []> {} Total time: 3.809 seconds, Total memory usage: 2.79MB ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Sat Jan 24 10:00:14 2004 Input: P := PolynomialRing(Rationals()); C := HyperellipticCurve(x*(x-1)*(x-2)*(x-3)*(x-4)); D := QuadraticTwist(C,92); J := Jacobian(D); SetVerbose("JacHypSelmer", 2); TwoSelmerGroupData(J : Bound := 300); Output: Magma V2.10-6 Sat Jan 24 2004 10:00:10 on modular [Seed = 173589097] ------------------------------------- TwoSelmerGroupData of Jacobian of Hyperelliptic Curve defined by y^2 = 92*x^5 - 920*x^4 + 3220*x^3 - 4600*x^2 + 2208*x over Rational Field m= Mapping from: CrvHyp: C to CrvHyp: C1 with equations : 23*$.1 529/2*$.2 $.3 and inverse 1/23*$.1 2/529*$.2 $.3 Change curve into Hyperelliptic Curve defined by y^2 = x^5 - 230*x^4 + 18515*x^3 - 608350*x^2 + 6716184*x over Rational Field Bad primes = [ 2, 3, 23 ] f factors as (x - 92) (x - 69) (x - 46) (x - 23) (x). For factor x - 92, use field defined by x - 1 and theta = 92 For factor x - 69, use field defined by x - 1 and theta = 69 For factor x - 46, use field defined by x - 1 and theta = 46 For factor x - 23, use field defined by x - 1 and theta = 23 For factor x, use field defined by x - 1 and theta = 0 The 2-torsion group has dimension 4. Determining local images... p = 2 x = 1/4 --> new generator (0 0 0 0 0 1 0 0 0 0 0 1 0 0 0) x = 2 --> new generator (1 1 0 0 0 1 0 0 1 0 1 0 1 0 0) p = 3 x = 3 --> new generator (0 0 1 1 0 1 0 0 1 0) p = 23 p = infinity Computing class groups... Class group data of the fields: Field given by x - 92: [] Field given by x - 69: [] Field given by x - 46: [] Field given by x - 23: [] Field given by x: [] Dimension of Cl[2] = 0. Signatures: [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] Dimension of units mod squares = 5. Upper bound for Selmer group dimension: 13. ==> Upper bound for rank = 9. Computing unit groups... Class group and unit data of the fields: Field given by x - 92: Class group = [], units = [ 2 ] Field given by x - 69: Class group = [], units = [ 2 ] Field given by x - 46: Class group = [], units = [ 2 ] Field given by x - 23: Class group = [], units = [ 2 ] Field given by x: Class group = [], units = [ 2 ] Time for local computations: 509 ms. Time for class groups: 0 ms. Time for unit groups: 0 ms. Selmer group dimension = 6, Dimension of 2-torsion = 4, ==> Bound for the MW-rank = 2. Total time: 620 ms. Transforming presentation of S back to model C. 2 6 <[ 25*$.1^4 - 242*$.1^3 + 815*$.1^2 - 1126*$.1 + 529, 20*$.1^4 - 208*$.1^3 + 760*$.1^2 - 1124*$.1 + 529, -7/4*$.1^4 + 14*$.1^3 - 117/4*$.1^2 - 6*$.1 + 46, 1496*$.1^4 - 15025*$.1^3 + 52819*$.1^2 - 75745*$.1 + 36501, 1/8*$.1^4 - 7/4*$.1^3 + 59/8*$.1^2 - 43/4*$.1 + 6, 60*$.1^4 - 623*$.1^3 + 2251*$.1^2 - 3272*$.1 + 1587 ], [], []> {} Total time: 3.709 seconds, Total memory usage: 2.69MB ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Sat Jan 24 10:00:29 2004 Input: P := PolynomialRing(Rationals()); C := HyperellipticCurve(x*(x-1)*(x-2)*(x-3)*(x-4)); D := QuadraticTwist(C,93); J := Jacobian(D); SetVerbose("JacHypSelmer", 2); TwoSelmerGroupData(J : Bound := 300); Output: Magma V2.10-6 Sat Jan 24 2004 10:00:25 on modular [Seed = 89640341] ------------------------------------- TwoSelmerGroupData of Jacobian of Hyperelliptic Curve defined by y^2 = 93*x^5 - 930*x^4 + 3255*x^3 - 4650*x^2 + 2232*x over Rational Field m= Mapping from: CrvHyp: C to CrvHyp: C1 with equations : 93*$.1 8649*$.2 $.3 and inverse 1/93*$.1 1/8649*$.2 $.3 Change curve into Hyperelliptic Curve defined by y^2 = x^5 - 930*x^4 + 302715*x^3 - 40217850*x^2 + 1795324824*x over Rational Field Bad primes = [ 2, 3, 31 ] f factors as (x - 372) (x - 279) (x - 186) (x - 93) (x). For factor x - 372, use field defined by x - 1 and theta = 372 For factor x - 279, use field defined by x - 1 and theta = 279 For factor x - 186, use field defined by x - 1 and theta = 186 For factor x - 93, use field defined by x - 1 and theta = 93 For factor x, use field defined by x - 1 and theta = 0 The 2-torsion group has dimension 4. Determining local images... p = 2 x = 1/4 --> new generator (0 0 0 0 0 1 0 0 0 0 0 1 0 0 0) x = 14 --> new generator (1 0 1 0 1 1 0 0 1 0 0 0 1 1 1) p = 3 p = 31 p = infinity Computing class groups... Class group data of the fields: Field given by x - 372: [] Field given by x - 279: [] Field given by x - 186: [] Field given by x - 93: [] Field given by x: [] Dimension of Cl[2] = 0. Signatures: [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] Dimension of units mod squares = 5. Upper bound for Selmer group dimension: 15. ==> Upper bound for rank = 11. Computing unit groups... Class group and unit data of the fields: Field given by x - 372: Class group = [], units = [ 2 ] Field given by x - 279: Class group = [], units = [ 2 ] Field given by x - 186: Class group = [], units = [ 2 ] Field given by x - 93: Class group = [], units = [ 2 ] Field given by x: Class group = [], units = [ 2 ] Time for local computations: 589 ms. Time for class groups: 0 ms. Time for unit groups: 9 ms. Selmer group dimension = 4, Dimension of 2-torsion = 4, ==> Bound for the MW-rank = 0. Total time: 721 ms. Transforming presentation of S back to model C. 0 4 <[ 6125/8*$.1^4 - 90821/12*$.1^3 + 208679/8*$.1^2 - 438925/12*$.1 + 17298, 120*$.1^4 - 3631/3*$.1^3 + 4263*$.1^2 - 18260/3*$.1 + 2883, 1609027/12*$.1^4 - 2681627/2*$.1^3 + 56311409/12*$.1^2 - 13406573/2*$.1 + 3217428, 301/24*$.1^4 - 549/4*$.1^3 + 13007/24*$.1^2 - 3653/4*$.1 + 558 ], [], []> {} Total time: 3.889 seconds, Total memory usage: 2.69MB ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Sat Jan 24 10:00:42 2004 Input: P := PolynomialRing(Rationals()); C := HyperellipticCurve(x*(x-1)*(x-2)*(x-3)*(x-4)); D := QuadraticTwist(C,94); J := Jacobian(D); SetVerbose("JacHypSelmer", 2); TwoSelmerGroupData(J : Bound := 300); Output: Magma V2.10-6 Sat Jan 24 2004 10:00:37 on modular [Seed = 1013904560] ------------------------------------- TwoSelmerGroupData of Jacobian of Hyperelliptic Curve defined by y^2 = 94*x^5 - 940*x^4 + 3290*x^3 - 4700*x^2 + 2256*x over Rational Field m= Mapping from: CrvHyp: C to CrvHyp: C1 with equations : 94*$.1 8836*$.2 $.3 and inverse 1/94*$.1 1/8836*$.2 $.3 Change curve into Hyperelliptic Curve defined by y^2 = x^5 - 940*x^4 + 309260*x^3 - 41529200*x^2 + 1873797504*x over Rational Field Bad primes = [ 2, 3, 47 ] f factors as (x - 376) (x - 282) (x - 188) (x - 94) (x). For factor x - 376, use field defined by x - 1 and theta = 376 For factor x - 282, use field defined by x - 1 and theta = 282 For factor x - 188, use field defined by x - 1 and theta = 188 For factor x - 94, use field defined by x - 1 and theta = 94 For factor x, use field defined by x - 1 and theta = 0 The 2-torsion group has dimension 4. Determining local images... p = 2 x = 1 --> new generator (0 0 0 0 1 1 0 0 1 0 1 0 0 0 0) x = 50 --> new generator (1 0 1 1 1 0 1 1 0 0 0 1 1 0 0) p = 3 x = 1 --> new generator (1 0 0 0 0 1 1 1 0 0) p = 47 p = infinity Computing class groups... Class group data of the fields: Field given by x - 376: [] Field given by x - 282: [] Field given by x - 188: [] Field given by x - 94: [] Field given by x: [] Dimension of Cl[2] = 0. Signatures: [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] Dimension of units mod squares = 5. Upper bound for Selmer group dimension: 13. ==> Upper bound for rank = 9. Computing unit groups... Class group and unit data of the fields: Field given by x - 376: Class group = [], units = [ 2 ] Field given by x - 282: Class group = [], units = [ 2 ] Field given by x - 188: Class group = [], units = [ 2 ] Field given by x - 94: Class group = [], units = [ 2 ] Field given by x: Class group = [], units = [ 2 ] Time for local computations: 1011 ms. Time for class groups: 0 ms. Time for unit groups: 0 ms. Selmer group dimension = 6, Dimension of 2-torsion = 4, ==> Bound for the MW-rank = 2. Total time: 1131 ms. Transforming presentation of S back to model C. 2 6 <[ 98*$.1^4 - 964*$.1^3 + 3310*$.1^2 - 4652*$.1 + 2209, 88*$.1^4 - 896*$.1^3 + 3200*$.1^2 - 4648*$.1 + 2209, 15/4*$.1^4 - 46*$.1^3 + 825/4*$.1^2 - 399*$.1 + 282, -55/4*$.1^4 + 243/2*$.1^3 - 1353/4*$.1^2 + 555/2*$.1 + 47, 4326*$.1^4 - 43252*$.1^3 + 302677/2*$.1^2 - 432283/2*$.1 + 103823, 51771/4*$.1^4 - 258995/2*$.1^3 + 1814041/4*$.1^2 - 1296567/2*$.1 + 311469 ], [], []> {} Total time: 4.199 seconds, Total memory usage: 2.79MB ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Sat Jan 24 10:00:55 2004 Input: P := PolynomialRing(Rationals()); C := HyperellipticCurve(x*(x-1)*(x-2)*(x-3)*(x-4)); D := QuadraticTwist(C,95); J := Jacobian(D); SetVerbose("JacHypSelmer", 2); TwoSelmerGroupData(J : Bound := 300); Output: Magma V2.10-6 Sat Jan 24 2004 10:00:51 on modular [Seed = 912588428] ------------------------------------- TwoSelmerGroupData of Jacobian of Hyperelliptic Curve defined by y^2 = 95*x^5 - 950*x^4 + 3325*x^3 - 4750*x^2 + 2280*x over Rational Field m= Mapping from: CrvHyp: C to CrvHyp: C1 with equations : 95*$.1 9025*$.2 $.3 and inverse 1/95*$.1 1/9025*$.2 $.3 Change curve into Hyperelliptic Curve defined by y^2 = x^5 - 950*x^4 + 315875*x^3 - 42868750*x^2 + 1954815000*x over Rational Field Bad primes = [ 2, 3, 5, 19 ] f factors as (x - 380) (x - 285) (x - 190) (x - 95) (x). For factor x - 380, use field defined by x - 1 and theta = 380 For factor x - 285, use field defined by x - 1 and theta = 285 For factor x - 190, use field defined by x - 1 and theta = 190 For factor x - 95, use field defined by x - 1 and theta = 95 For factor x, use field defined by x - 1 and theta = 0 The 2-torsion group has dimension 4. Determining local images... p = 2 x = 1/4 --> new generator (0 0 0 0 0 1 0 0 0 0 0 1 0 0 0) x = 18 --> new generator (1 1 0 0 0 1 0 0 1 0 1 0 1 0 0) p = 3 x = 3 --> new generator (0 0 1 1 0 1 0 0 1 0) p = 5 p = 19 p = infinity Computing class groups... Class group data of the fields: Field given by x - 380: [] Field given by x - 285: [] Field given by x - 190: [] Field given by x - 95: [] Field given by x: [] Dimension of Cl[2] = 0. Signatures: [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] Dimension of units mod squares = 5. Upper bound for Selmer group dimension: 17. ==> Upper bound for rank = 13. Computing unit groups... Class group and unit data of the fields: Field given by x - 380: Class group = [], units = [ 2 ] Field given by x - 285: Class group = [], units = [ 2 ] Field given by x - 190: Class group = [], units = [ 2 ] Field given by x - 95: Class group = [], units = [ 2 ] Field given by x: Class group = [], units = [ 2 ] Time for local computations: 531 ms. Time for class groups: 0 ms. Time for unit groups: 0 ms. Selmer group dimension = 4, Dimension of 2-torsion = 4, ==> Bound for the MW-rank = 0. Total time: 701 ms. Transforming presentation of S back to model C. 0 4 <[ 6299/8*$.1^4 - 31305/4*$.1^3 + 216673/8*$.1^2 - 152369/4*$.1 + 18050, 1128*$.1^4 - 11375*$.1^3 + 40051*$.1^2 - 57164*$.1 + 27075, 571521/4*$.1^4 - 2857603/2*$.1^3 + 20003211/4*$.1^2 - 14288193/2*$.1 + 3429500, -573/8*$.1^4 + 2479/4*$.1^3 - 13135/8*$.1^2 + 4375/4*$.1 + 570 ], [], []> {} Total time: 3.859 seconds, Total memory usage: 2.79MB ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Sat Jan 24 10:01:08 2004 Input: P := PolynomialRing(Rationals()); C := HyperellipticCurve(x*(x-1)*(x-2)*(x-3)*(x-4)); D := QuadraticTwist(C,96); J := Jacobian(D); SetVerbose("JacHypSelmer", 2); TwoSelmerGroupData(J : Bound := 300); Output: Magma V2.10-6 Sat Jan 24 2004 10:01:04 on modular [Seed = 1392614394] ------------------------------------- TwoSelmerGroupData of Jacobian of Hyperelliptic Curve defined by y^2 = 96*x^5 - 960*x^4 + 3360*x^3 - 4800*x^2 + 2304*x over Rational Field m= Mapping from: CrvHyp: C to CrvHyp: C1 with equations : 6*$.1 9*$.2 $.3 and inverse 1/6*$.1 1/9*$.2 $.3 Change curve into Hyperelliptic Curve defined by y^2 = x^5 - 60*x^4 + 1260*x^3 - 10800*x^2 + 31104*x over Rational Field Bad primes = [ 2, 3 ] f factors as (x - 24) (x - 18) (x - 12) (x - 6) (x). For factor x - 24, use field defined by x - 1 and theta = 24 For factor x - 18, use field defined by x - 1 and theta = 18 For factor x - 12, use field defined by x - 1 and theta = 12 For factor x - 6, use field defined by x - 1 and theta = 6 For factor x, use field defined by x - 1 and theta = 0 The 2-torsion group has dimension 4. Determining local images... p = 2 x = 1 --> new generator (0 0 0 0 1 1 0 0 1 0 1 0 0 0 0) x = 42 --> new generator (1 0 0 1 1 0 1 1 1 0 0 0 1 0 1) p = 3 p = infinity Computing class groups... Class group data of the fields: Field given by x - 24: [] Field given by x - 18: [] Field given by x - 12: [] Field given by x - 6: [] Field given by x: [] Dimension of Cl[2] = 0. Signatures: [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] Dimension of units mod squares = 5. Upper bound for Selmer group dimension: 11. ==> Upper bound for rank = 7. Computing unit groups... Class group and unit data of the fields: Field given by x - 24: Class group = [], units = [ 2 ] Field given by x - 18: Class group = [], units = [ 2 ] Field given by x - 12: Class group = [], units = [ 2 ] Field given by x - 6: Class group = [], units = [ 2 ] Field given by x: Class group = [], units = [ 2 ] Time for local computations: 1080 ms. Time for class groups: 0 ms. Time for unit groups: 9 ms. Selmer group dimension = 4, Dimension of 2-torsion = 4, ==> Bound for the MW-rank = 0. Total time: 1159 ms. Transforming presentation of S back to model C. 0 4 <[ -1/4*$.1^4 + 17/6*$.1^3 - 41/4*$.1^2 + 32/3*$.1 + 3, -1/2*$.1^4 + 3*$.1^3 - 3*$.1^2 - 9/2*$.1 + 3, 4/3*$.1^4 - 65/6*$.1^3 + 163/6*$.1^2 - 65/3*$.1 + 6, -2/3*$.1^4 + 9/2*$.1^3 - 22/3*$.1^2 - 3/2*$.1 + 9 ], [], []> {} Total time: 4.379 seconds, Total memory usage: 2.69MB ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Sat Jan 24 10:01:21 2004 Input: P := PolynomialRing(Rationals()); C := HyperellipticCurve(x*(x-1)*(x-2)*(x-3)*(x-4)); D := QuadraticTwist(C,97); J := Jacobian(D); SetVerbose("JacHypSelmer", 2); TwoSelmerGroupData(J : Bound := 300); Output: Magma V2.10-6 Sat Jan 24 2004 10:01:17 on modular [Seed = 1243120366] ------------------------------------- TwoSelmerGroupData of Jacobian of Hyperelliptic Curve defined by y^2 = 97*x^5 - 970*x^4 + 3395*x^3 - 4850*x^2 + 2328*x over Rational Field m= Mapping from: CrvHyp: C to CrvHyp: C1 with equations : 97*$.1 9409*$.2 $.3 and inverse 1/97*$.1 1/9409*$.2 $.3 Change curve into Hyperelliptic Curve defined by y^2 = x^5 - 970*x^4 + 329315*x^3 - 45633650*x^2 + 2124702744*x over Rational Field Bad primes = [ 2, 3, 97 ] f factors as (x - 388) (x - 291) (x - 194) (x - 97) (x). For factor x - 388, use field defined by x - 1 and theta = 388 For factor x - 291, use field defined by x - 1 and theta = 291 For factor x - 194, use field defined by x - 1 and theta = 194 For factor x - 97, use field defined by x - 1 and theta = 97 For factor x, use field defined by x - 1 and theta = 0 The 2-torsion group has dimension 4. Determining local images... p = 2 x = 1/4 --> new generator (0 0 0 0 0 1 0 0 0 0 0 1 0 0 0) x = 22 --> new generator (1 0 0 0 1 0 0 0 1 0 0 1 1 1 0) p = 3 x = 4 --> new generator (1 0 0 0 0 1 1 1 0 0) p = 97 p = infinity Computing class groups... Class group data of the fields: Field given by x - 388: [] Field given by x - 291: [] Field given by x - 194: [] Field given by x - 97: [] Field given by x: [] Dimension of Cl[2] = 0. Signatures: [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] Dimension of units mod squares = 5. Upper bound for Selmer group dimension: 13. ==> Upper bound for rank = 9. Computing unit groups... Class group and unit data of the fields: Field given by x - 388: Class group = [], units = [ 2 ] Field given by x - 291: Class group = [], units = [ 2 ] Field given by x - 194: Class group = [], units = [ 2 ] Field given by x - 97: Class group = [], units = [ 2 ] Field given by x: Class group = [], units = [ 2 ] Time for local computations: 549 ms. Time for class groups: 0 ms. Time for unit groups: 0 ms. Selmer group dimension = 8, Dimension of 2-torsion = 4, ==> Bound for the MW-rank = 4. Total time: 670 ms. Transforming presentation of S back to model C. 4 8 <[ 1/8*$.1^4 - 3/4*$.1^3 + 3/8*$.1^2 + 5/4*$.1 + 2, -$.1^3 + 7*$.1^2 - 12*$.1 + 3, 1/4*$.1^4 - 3/2*$.1^3 + 11/4*$.1^2 - 5/2*$.1 + 4, -9/8*$.1^4 + 35/4*$.1^3 - 163/8*$.1^2 + 51/4*$.1 + 6, 8*$.1^4 - 64*$.1^3 + 184*$.1^2 - 224*$.1 + 97, -12*$.1^4 + 72*$.1^3 - 84*$.1^2 - 72*$.1 + 97, 28*$.1^4 - 232*$.1^3 + 596*$.1^2 - 488*$.1 + 97, -12*$.1^4 + 104*$.1^3 - 276*$.1^2 + 184*$.1 + 97 ], [], []> {} Total time: 3.819 seconds, Total memory usage: 2.79MB ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Sat Jan 24 10:01:34 2004 Input: P := PolynomialRing(Rationals()); C := HyperellipticCurve(x*(x-1)*(x-2)*(x-3)*(x-4)); D := QuadraticTwist(C,98); J := Jacobian(D); SetVerbose("JacHypSelmer", 2); TwoSelmerGroupData(J : Bound := 300); Output: Magma V2.10-6 Sat Jan 24 2004 10:01:30 on modular [Seed = 1159171478] ------------------------------------- TwoSelmerGroupData of Jacobian of Hyperelliptic Curve defined by y^2 = 98*x^5 - 980*x^4 + 3430*x^3 - 4900*x^2 + 2352*x over Rational Field m= Mapping from: CrvHyp: C to CrvHyp: C1 with equations : 2*$.1 4/7*$.2 $.3 and inverse 1/2*$.1 7/4*$.2 $.3 Change curve into Hyperelliptic Curve defined by y^2 = x^5 - 20*x^4 + 140*x^3 - 400*x^2 + 384*x over Rational Field Bad primes = [ 2, 3 ] f factors as (x - 8) (x - 6) (x - 4) (x - 2) (x). For factor x - 8, use field defined by x - 1 and theta = 8 For factor x - 6, use field defined by x - 1 and theta = 6 For factor x - 4, use field defined by x - 1 and theta = 4 For factor x - 2, use field defined by x - 1 and theta = 2 For factor x, use field defined by x - 1 and theta = 0 The 2-torsion group has dimension 4. Determining local images... p = 2 x = 1 --> new generator (0 0 0 0 1 0 0 0 1 0 1 1 0 0 0) x = 26 --> new generator (1 0 0 0 0 1 1 1 0 1 1 0 1 0 1) p = 3 x = 3 --> new generator (0 0 1 1 0 1 0 0 1 0) p = infinity Computing class groups... Class group data of the fields: Field given by x - 8: [] Field given by x - 6: [] Field given by x - 4: [] Field given by x - 2: [] Field given by x: [] Dimension of Cl[2] = 0. Signatures: [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] Dimension of units mod squares = 5. Upper bound for Selmer group dimension: 9. ==> Upper bound for rank = 5. Computing unit groups... Class group and unit data of the fields: Field given by x - 8: Class group = [], units = [ 2 ] Field given by x - 6: Class group = [], units = [ 2 ] Field given by x - 4: Class group = [], units = [ 2 ] Field given by x - 2: Class group = [], units = [ 2 ] Field given by x: Class group = [], units = [ 2 ] Time for local computations: 1079 ms. Time for class groups: 0 ms. Time for unit groups: 0 ms. Selmer group dimension = 4, Dimension of 2-torsion = 4, ==> Bound for the MW-rank = 0. Total time: 1139 ms. Transforming presentation of S back to model C. 0 4 <[ $.1^3 - 13/2*$.1^2 + 17/2*$.1 + 3, -1/4*$.1^4 + 3/2*$.1^3 - 5/4*$.1^2 - 3*$.1 + 1, -1/2*$.1^3 + 7/2*$.1^2 - 7*$.1 + 6, -9/4*$.1^4 + 19*$.1^3 - 203/4*$.1^2 + 43*$.1 + 3 ], [], []> {} Total time: 4.359 seconds, Total memory usage: 2.69MB ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Sat Jan 24 10:01:47 2004 Input: P := PolynomialRing(Rationals()); C := HyperellipticCurve(x*(x-1)*(x-2)*(x-3)*(x-4)); D := QuadraticTwist(C,99); J := Jacobian(D); SetVerbose("JacHypSelmer", 2); TwoSelmerGroupData(J : Bound := 300); Output: Magma V2.10-6 Sat Jan 24 2004 10:01:43 on modular [Seed = 2083435698] ------------------------------------- TwoSelmerGroupData of Jacobian of Hyperelliptic Curve defined by y^2 = 99*x^5 - 990*x^4 + 3465*x^3 - 4950*x^2 + 2376*x over Rational Field m= Mapping from: CrvHyp: C to CrvHyp: C1 with equations : 11*$.1 121/3*$.2 $.3 and inverse 1/11*$.1 3/121*$.2 $.3 Change curve into Hyperelliptic Curve defined by y^2 = x^5 - 110*x^4 + 4235*x^3 - 66550*x^2 + 351384*x over Rational Field Bad primes = [ 2, 3, 11 ] f factors as (x - 44) (x - 33) (x - 22) (x - 11) (x). For factor x - 44, use field defined by x - 1 and theta = 44 For factor x - 33, use field defined by x - 1 and theta = 33 For factor x - 22, use field defined by x - 1 and theta = 22 For factor x - 11, use field defined by x - 1 and theta = 11 For factor x, use field defined by x - 1 and theta = 0 The 2-torsion group has dimension 4. Determining local images... p = 2 x = 1/4 --> new generator (0 0 0 0 0 1 0 0 0 0 0 1 0 0 0) x = 10 --> new generator (1 1 1 0 0 0 0 0 1 0 1 1 1 0 1) p = 3 x = 3 --> new generator (0 0 1 1 0 1 0 0 1 0) p = 11 p = infinity Computing class groups... Class group data of the fields: Field given by x - 44: [] Field given by x - 33: [] Field given by x - 22: [] Field given by x - 11: [] Field given by x: [] Dimension of Cl[2] = 0. Signatures: [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] Dimension of units mod squares = 5. Upper bound for Selmer group dimension: 13. ==> Upper bound for rank = 9. Computing unit groups... Class group and unit data of the fields: Field given by x - 44: Class group = [], units = [ 2 ] Field given by x - 33: Class group = [], units = [ 2 ] Field given by x - 22: Class group = [], units = [ 2 ] Field given by x - 11: Class group = [], units = [ 2 ] Field given by x: Class group = [], units = [ 2 ] Time for local computations: 519 ms. Time for class groups: 0 ms. Time for unit groups: 0 ms. Selmer group dimension = 5, Dimension of 2-torsion = 4, ==> Bound for the MW-rank = 1. Total time: 619 ms. Transforming presentation of S back to model C. 1 5 <[ 111/8*$.1^4 - 517/4*$.1^3 + 3293/8*$.1^2 - 2109/4*$.1 + 242, 10*$.1^4 - 115*$.1^3 + 457*$.1^2 - 716*$.1 + 363, 905/4*$.1^4 - 4507/2*$.1^3 + 31395/4*$.1^2 - 22289/2*$.1 + 5324, 19/8*$.1^4 - 97/4*$.1^3 + 705/8*$.1^2 - 521/4*$.1 + 66, $.1^4 - 10*$.1^3 + 51*$.1^2 - 130*$.1 + 121 ], [], []> {} Total time: 3.819 seconds, Total memory usage: 2.69MB ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Sat Jan 24 10:02:01 2004 Input: P := PolynomialRing(Rationals()); C := HyperellipticCurve(x*(x-1)*(x-2)*(x-3)*(x-4)); D := QuadraticTwist(C,100); J := Jacobian(D); SetVerbose("JacHypSelmer", 2); TwoSelmerGroupData(J : Bound := 300); Output: Magma V2.10-6 Sat Jan 24 2004 10:01:58 on modular [Seed = 1998962568] ------------------------------------- TwoSelmerGroupData of Jacobian of Hyperelliptic Curve defined by y^2 = 100*x^5 - 1000*x^4 + 3500*x^3 - 5000*x^2 + 2400*x over Rational Field m= Mapping from: CrvHyp: C to CrvHyp: C1 with equations : $.1 1/10*$.2 $.3 and inverse $.1 10*$.2 $.3 Change curve into Hyperelliptic Curve defined by y^2 = x^5 - 10*x^4 + 35*x^3 - 50*x^2 + 24*x over Rational Field Bad primes = [ 2, 3 ] f factors as (x - 4) (x - 3) (x - 2) (x - 1) (x). For factor x - 4, use field defined by x - 1 and theta = 4 For factor x - 3, use field defined by x - 1 and theta = 3 For factor x - 2, use field defined by x - 1 and theta = 2 For factor x - 1, use field defined by x - 1 and theta = 1 For factor x, use field defined by x - 1 and theta = 0 The 2-torsion group has dimension 4. Determining local images... p = 2 x = 1/4 --> new generator (0 0 0 0 0 1 0 0 0 0 0 1 0 0 0) x = 22 --> new generator (1 0 0 0 1 0 0 0 1 0 0 1 1 1 0) p = 3 x = 7 --> new generator (1 0 0 0 0 1 1 1 0 0) p = infinity Computing class groups... Class group data of the fields: Field given by x - 4: [] Field given by x - 3: [] Field given by x - 2: [] Field given by x - 1: [] Field given by x: [] Dimension of Cl[2] = 0. Signatures: [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] Dimension of units mod squares = 5. Upper bound for Selmer group dimension: 9. ==> Upper bound for rank = 5. Computing unit groups... Class group and unit data of the fields: Field given by x - 4: Class group = [], units = [ 2 ] Field given by x - 3: Class group = [], units = [ 2 ] Field given by x - 2: Class group = [], units = [ 2 ] Field given by x - 1: Class group = [], units = [ 2 ] Field given by x: Class group = [], units = [ 2 ] Time for local computations: 520 ms. Time for class groups: 0 ms. Time for unit groups: 0 ms. Selmer group dimension = 4, Dimension of 2-torsion = 4, ==> Bound for the MW-rank = 0. Total time: 589 ms. Transforming presentation of S back to model C. 0 4 <[ 1/8*$.1^4 - 3/4*$.1^3 + 3/8*$.1^2 + 5/4*$.1 + 2, -$.1^3 + 7*$.1^2 - 12*$.1 + 3, 1/4*$.1^4 - 3/2*$.1^3 + 11/4*$.1^2 - 5/2*$.1 + 4, -9/8*$.1^4 + 35/4*$.1^3 - 163/8*$.1^2 + 51/4*$.1 + 6 ], [], []> {} Total time: 3.669 seconds, Total memory usage: 2.69MB ************** MAGMA ***************** Host YahooBB218117016004.bbtec.net. (218.117.16.4) Time: Sat Jan 24 13:09:37 2004 Input: x := 3; case < x^3 + x + 23 gt 1234 | true : "Yes", default : "No" >; Output: Magma V2.10-6 Sat Jan 24 2004 13:09:33 on modular [Seed = 3937934893] ------------------------------------- No Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host YahooBB218117016004.bbtec.net. (218.117.16.4) Time: Sat Jan 24 13:09:50 2004 Input: x := 13; case < x^3 + x + 23 gt 1234 | true : "Yes", default : "No" >; Output: Magma V2.10-6 Sat Jan 24 2004 13:09:47 on modular [Seed = 3820033810] ------------------------------------- Yes Total time: 2.929 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host YahooBB218117016004.bbtec.net. (218.117.16.4) Time: Sat Jan 24 13:10:09 2004 Input: x := 10; case < x^3 + x + 23 gt 1234 | true : "Yes", default : "No" >; Output: Magma V2.10-6 Sat Jan 24 2004 13:10:06 on modular [Seed = 306243319] ------------------------------------- No Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host YahooBB218117016004.bbtec.net. (218.117.16.4) Time: Sat Jan 24 13:17:38 2004 Input: gaussians := sub< MatrixRing(Integers(), 2) | [0, 1, -1, 0] >; i; Output: Magma V2.10-6 Sat Jan 24 2004 13:17:35 on modular [Seed = 5437092] ------------------------------------- [ 0 1] [-1 0] Total time: 2.909 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host YahooBB218117016004.bbtec.net. (218.117.16.4) Time: Sat Jan 24 13:18:57 2004 Input: F := FreeGroup(2); G := quo; Category(G); Output: Magma V2.10-6 Sat Jan 24 2004 13:18:54 on modular [Seed = 1047316779] ------------------------------------- GrpFP Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host YahooBB218117016004.bbtec.net. (218.117.16.4) Time: Sat Jan 24 13:19:15 2004 Input: F := FreeGroup(2); G := quo; Category(F); Output: Magma V2.10-6 Sat Jan 24 2004 13:19:11 on modular [Seed = 895992369] ------------------------------------- GrpFP Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host YahooBB218117016004.bbtec.net. (218.117.16.4) Time: Sat Jan 24 13:19:35 2004 Input: F := FreeGroup(2); G := quo; Category(G); Output: Magma V2.10-6 Sat Jan 24 2004 13:19:32 on modular [Seed = 746511107] ------------------------------------- GrpFP Total time: 2.909 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host YahooBB218117016004.bbtec.net. (218.117.16.4) Time: Sat Jan 24 13:19:55 2004 Input: F := FreeGroup(2); G := quo; Category(G); Category(F); Output: Magma V2.10-6 Sat Jan 24 2004 13:19:52 on modular [Seed = 1510518025] ------------------------------------- GrpFP GrpFP Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host YahooBB218117016004.bbtec.net. (218.117.16.4) Time: Sat Jan 24 13:20:10 2004 Input: F := FreeGroup(2); G := quo; Parent(G); Category(F); Output: Magma V2.10-6 Sat Jan 24 2004 13:20:07 on modular [Seed = 1243135238] ------------------------------------- Power Structure of GrpFP GrpFP Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host YahooBB218117016004.bbtec.net. (218.117.16.4) Time: Sat Jan 24 13:20:40 2004 Input: F := FreeGroup(2); G := quo; Parent(G); Category(F); G; Output: Magma V2.10-6 Sat Jan 24 2004 13:20:37 on modular [Seed = 1091810863] ------------------------------------- Power Structure of GrpFP GrpFP Finitely presented group G on 2 generators Relations c^2 = Id(G) d^3 = Id(G) (c * d)^4 = Id(G) Total time: 2.869 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host YahooBB218117016004.bbtec.net. (218.117.16.4) Time: Sat Jan 24 13:21:02 2004 Input: F := FreeGroup(2); G := quo; F; Output: Magma V2.10-6 Sat Jan 24 2004 13:20:59 on modular [Seed = 2133690607] ------------------------------------- Finitely presented group F on 2 generators (free) Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host YahooBB218117016004.bbtec.net. (218.117.16.4) Time: Sat Jan 24 13:24:15 2004 Input: G := Group< a,b | a^5, b^2, a*b*a*b >; Output: Magma V2.10-6 Sat Jan 24 2004 13:24:12 on modular [Seed = 1965526306] ------------------------------------- Total time: 2.939 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host YahooBB218117016004.bbtec.net. (218.117.16.4) Time: Sat Jan 24 13:24:34 2004 Input: G := Group< a,b | a^5, b^2, a*b*a*b >; Order(G); Output: Magma V2.10-6 Sat Jan 24 2004 13:24:31 on modular [Seed = 1816040488] ------------------------------------- 10 Total time: 3.009 seconds, Total memory usage: 17.80MB ************** MAGMA ***************** Host YahooBB218117016004.bbtec.net. (218.117.16.4) Time: Sat Jan 24 13:25:00 2004 Input: G := Group< a,b | a^5, b^2, a*b*a*b >; Order(G); G; Output: Magma V2.10-6 Sat Jan 24 2004 13:24:57 on modular [Seed = 2613666809] ------------------------------------- 10 Finitely presented group G on 2 generators Relations a^5 = Id(G) b^2 = Id(G) (a * b)^2 = Id(G) Total time: 3.039 seconds, Total memory usage: 17.80MB ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Sun Jan 25 09:57:12 2004 Input: P := PolynomialRing(Rationals()); C := HyperellipticCurve(x*(x-1)*(x-2)*(x-3)*(x-4)); D := QuadraticTwist(C,101); J := Jacobian(D); SetVerbose("JacHypSelmer", 2); TwoSelmerGroupData(J : Bound := 300); Output: Magma V2.10-6 Sun Jan 25 2004 09:57:06 on modular [Seed = 2496073138] ------------------------------------- TwoSelmerGroupData of Jacobian of Hyperelliptic Curve defined by y^2 = 101*x^5 - 1010*x^4 + 3535*x^3 - 5050*x^2 + 2424*x over Rational Field m= Mapping from: CrvHyp: C to CrvHyp: C1 with equations : 101*$.1 10201*$.2 $.3 and inverse 1/101*$.1 1/10201*$.2 $.3 Change curve into Hyperelliptic Curve defined by y^2 = x^5 - 1010*x^4 + 357035*x^3 - 51515050*x^2 + 2497449624*x over Rational Field Bad primes = [ 2, 3, 101 ] f factors as (x - 404) (x - 303) (x - 202) (x - 101) (x). For factor x - 404, use field defined by x - 1 and theta = 404 For factor x - 303, use field defined by x - 1 and theta = 303 For factor x - 202, use field defined by x - 1 and theta = 202 For factor x - 101, use field defined by x - 1 and theta = 101 For factor x, use field defined by x - 1 and theta = 0 The 2-torsion group has dimension 4. Determining local images... p = 2 x = 1/4 --> new generator (0 0 0 0 0 1 0 0 0 0 0 1 0 0 0) x = 30 --> new generator (1 0 1 0 1 1 0 0 1 0 0 0 1 1 1) p = 3 x = 3 --> new generator (0 0 1 1 0 1 0 0 1 0) p = 101 p = infinity Computing class groups... Class group data of the fields: Field given by x - 404: [] Field given by x - 303: [] Field given by x - 202: [] Field given by x - 101: [] Field given by x: [] Dimension of Cl[2] = 0. Signatures: [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] Dimension of units mod squares = 5. Upper bound for Selmer group dimension: 13. ==> Upper bound for rank = 9. Computing unit groups... Class group and unit data of the fields: Field given by x - 404: Class group = [], units = [ 2 ] Field given by x - 303: Class group = [], units = [ 2 ] Field given by x - 202: Class group = [], units = [ 2 ] Field given by x - 101: Class group = [], units = [ 2 ] Field given by x: Class group = [], units = [ 2 ] Time for local computations: 571 ms. Time for class groups: 0 ms. Time for unit groups: 0 ms. Selmer group dimension = 5, Dimension of 2-torsion = 4, ==> Bound for the MW-rank = 1. Total time: 671 ms. Transforming presentation of S back to model C. 1 5 <[ 1284*$.1^4 - 12805*$.1^3 + 44678*$.1^2 - 63659*$.1 + 30603, 1275*$.1^4 - 12851*$.1^3 + 45232*$.1^2 - 64562*$.1 + 30603, 1030233/4*$.1^4 - 2575650*$.1^3 + 36059979/4*$.1^2 - 12878708*$.1 + 6181806, 8*$.1^4 - 64*$.1^3 + 185*$.1^2 - 228*$.1 + 101, 20099/8*$.1^4 - 100497/4*$.1^3 + 704697/8*$.1^2 - 505513/4*$.1 + 61206 ], [], []> {} Total time: 4.040 seconds, Total memory usage: 2.79MB ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Sun Jan 25 09:58:08 2004 Input: P := PolynomialRing(Rationals()); C := HyperellipticCurve(x*(x-1)*(x-2)*(x-3)*(x-4)); D := QuadraticTwist(C,102); J := Jacobian(D); SetVerbose("JacHypSelmer", 2); TwoSelmerGroupData(J : Bound := 300); Output: Magma V2.10-6 Sun Jan 25 2004 09:58:04 on modular [Seed = 2664236935] ------------------------------------- TwoSelmerGroupData of Jacobian of Hyperelliptic Curve defined by y^2 = 102*x^5 - 1020*x^4 + 3570*x^3 - 5100*x^2 + 2448*x over Rational Field m= Mapping from: CrvHyp: C to CrvHyp: C1 with equations : 102*$.1 10404*$.2 $.3 and inverse 1/102*$.1 1/10404*$.2 $.3 Change curve into Hyperelliptic Curve defined by y^2 = x^5 - 1020*x^4 + 364140*x^3 - 53060400*x^2 + 2597837184*x over Rational Field Bad primes = [ 2, 3, 17 ] f factors as (x - 408) (x - 306) (x - 204) (x - 102) (x). For factor x - 408, use field defined by x - 1 and theta = 408 For factor x - 306, use field defined by x - 1 and theta = 306 For factor x - 204, use field defined by x - 1 and theta = 204 For factor x - 102, use field defined by x - 1 and theta = 102 For factor x, use field defined by x - 1 and theta = 0 The 2-torsion group has dimension 4. Determining local images... p = 2 x = 1 --> new generator (0 0 0 0 1 1 0 0 1 0 1 0 0 0 0) x = 10 --> new generator (1 0 0 1 1 0 1 1 1 0 0 0 1 0 1) p = 3 p = 17 p = infinity Computing class groups... Class group data of the fields: Field given by x - 408: [] Field given by x - 306: [] Field given by x - 204: [] Field given by x - 102: [] Field given by x: [] Dimension of Cl[2] = 0. Signatures: [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] Dimension of units mod squares = 5. Upper bound for Selmer group dimension: 15. ==> Upper bound for rank = 11. Computing unit groups... Class group and unit data of the fields: Field given by x - 408: Class group = [], units = [ 2 ] Field given by x - 306: Class group = [], units = [ 2 ] Field given by x - 204: Class group = [], units = [ 2 ] Field given by x - 102: Class group = [], units = [ 2 ] Field given by x: Class group = [], units = [ 2 ] Time for local computations: 1111 ms. Time for class groups: 0 ms. Time for unit groups: 0 ms. Selmer group dimension = 4, Dimension of 2-torsion = 4, ==> Bound for the MW-rank = 0. Total time: 1229 ms. Transforming presentation of S back to model C. 0 4 <[ 151/4*$.1^4 - 2231/6*$.1^3 + 5119/4*$.1^2 - 5420/3*$.1 + 867, -13/2*$.1^4 + 39*$.1^3 - 45*$.1^2 - 81/2*$.1 + 51, 284/3*$.1^4 - 5425/6*$.1^3 + 17795/6*$.1^2 - 11665/3*$.1 + 1734, -16/3*$.1^4 + 81/2*$.1^3 - 224/3*$.1^2 - 91/2*$.1 + 153 ], [], []> {} Total time: 4.379 seconds, Total memory usage: 2.69MB ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Sun Jan 25 09:58:31 2004 Input: P := PolynomialRing(Rationals()); C := HyperellipticCurve(x*(x-1)*(x-2)*(x-3)*(x-4)); D := QuadraticTwist(C,103); J := Jacobian(D); SetVerbose("JacHypSelmer", 2); TwoSelmerGroupData(J : Bound := 300); Output: Magma V2.10-6 Sun Jan 25 2004 09:58:27 on modular [Seed = 1647442839] ------------------------------------- TwoSelmerGroupData of Jacobian of Hyperelliptic Curve defined by y^2 = 103*x^5 - 1030*x^4 + 3605*x^3 - 5150*x^2 + 2472*x over Rational Field m= Mapping from: CrvHyp: C to CrvHyp: C1 with equations : 103*$.1 10609*$.2 $.3 and inverse 1/103*$.1 1/10609*$.2 $.3 Change curve into Hyperelliptic Curve defined by y^2 = x^5 - 1030*x^4 + 371315*x^3 - 54636350*x^2 + 2701221144*x over Rational Field Bad primes = [ 2, 3, 103 ] f factors as (x - 412) (x - 309) (x - 206) (x - 103) (x). For factor x - 412, use field defined by x - 1 and theta = 412 For factor x - 309, use field defined by x - 1 and theta = 309 For factor x - 206, use field defined by x - 1 and theta = 206 For factor x - 103, use field defined by x - 1 and theta = 103 For factor x, use field defined by x - 1 and theta = 0 The 2-torsion group has dimension 4. Determining local images... p = 2 x = 1/4 --> new generator (0 0 0 0 0 1 0 0 0 0 0 1 0 0 0) x = 2 --> new generator (1 1 0 0 0 1 0 0 1 0 1 0 1 0 0) p = 3 x = 1 --> new generator (1 0 0 0 0 1 1 1 0 0) p = 103 p = infinity Computing class groups... Class group data of the fields: Field given by x - 412: [] Field given by x - 309: [] Field given by x - 206: [] Field given by x - 103: [] Field given by x: [] Dimension of Cl[2] = 0. Signatures: [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] Dimension of units mod squares = 5. Upper bound for Selmer group dimension: 13. ==> Upper bound for rank = 9. Computing unit groups... Class group and unit data of the fields: Field given by x - 412: Class group = [], units = [ 2 ] Field given by x - 309: Class group = [], units = [ 2 ] Field given by x - 206: Class group = [], units = [ 2 ] Field given by x - 103: Class group = [], units = [ 2 ] Field given by x: Class group = [], units = [ 2 ] Time for local computations: 509 ms. Time for class groups: 0 ms. Time for unit groups: 0 ms. Selmer group dimension = 4, Dimension of 2-torsion = 4, ==> Bound for the MW-rank = 0. Total time: 630 ms. Transforming presentation of S back to model C. 0 4 <[ 7379/8*$.1^4 - 36689/4*$.1^3 + 254153/8*$.1^2 - 178937/4*$.1 + 21218, 1326*$.1^4 - 13363*$.1^3 + 47029*$.1^2 - 67128*$.1 + 31827, 728417/4*$.1^4 - 3642083/2*$.1^3 + 25494571/4*$.1^2 - 18210609/2*$.1 + 4370908, -621/8*$.1^4 + 2687/4*$.1^3 - 14239/8*$.1^2 + 4743/4*$.1 + 618 ], [], []> {} Total time: 3.779 seconds, Total memory usage: 2.79MB ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Sun Jan 25 09:58:51 2004 Input: P := PolynomialRing(Rationals()); C := HyperellipticCurve(x*(x-1)*(x-2)*(x-3)*(x-4)); D := QuadraticTwist(C,105); J := Jacobian(D); SetVerbose("JacHypSelmer", 2); TwoSelmerGroupData(J : Bound := 300); Output: Magma V2.10-6 Sun Jan 25 2004 09:58:47 on modular [Seed = 1798894250] ------------------------------------- TwoSelmerGroupData of Jacobian of Hyperelliptic Curve defined by y^2 = 105*x^5 - 1050*x^4 + 3675*x^3 - 5250*x^2 + 2520*x over Rational Field m= Mapping from: CrvHyp: C to CrvHyp: C1 with equations : 105*$.1 11025*$.2 $.3 and inverse 1/105*$.1 1/11025*$.2 $.3 Change curve into Hyperelliptic Curve defined by y^2 = x^5 - 1050*x^4 + 385875*x^3 - 57881250*x^2 + 2917215000*x over Rational Field Bad primes = [ 2, 3, 5, 7 ] f factors as (x - 420) (x - 315) (x - 210) (x - 105) (x). For factor x - 420, use field defined by x - 1 and theta = 420 For factor x - 315, use field defined by x - 1 and theta = 315 For factor x - 210, use field defined by x - 1 and theta = 210 For factor x - 105, use field defined by x - 1 and theta = 105 For factor x, use field defined by x - 1 and theta = 0 The 2-torsion group has dimension 4. Determining local images... p = 2 x = 1/4 --> new generator (0 0 0 0 0 1 0 0 0 0 0 1 0 0 0) x = 6 --> new generator (1 0 0 0 1 0 0 0 1 0 0 1 1 1 0) p = 3 p = 5 p = 7 p = infinity Computing class groups... Class group data of the fields: Field given by x - 420: [] Field given by x - 315: [] Field given by x - 210: [] Field given by x - 105: [] Field given by x: [] Dimension of Cl[2] = 0. Signatures: [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] Dimension of units mod squares = 5. Upper bound for Selmer group dimension: 19. ==> Upper bound for rank = 15. Computing unit groups... Class group and unit data of the fields: Field given by x - 420: Class group = [], units = [ 2 ] Field given by x - 315: Class group = [], units = [ 2 ] Field given by x - 210: Class group = [], units = [ 2 ] Field given by x - 105: Class group = [], units = [ 2 ] Field given by x: Class group = [], units = [ 2 ] Time for local computations: 580 ms. Time for class groups: 0 ms. Time for unit groups: 9 ms. Selmer group dimension = 7, Dimension of 2-torsion = 4, ==> Bound for the MW-rank = 3. Total time: 750 ms. Transforming presentation of S back to model C. 3 7 <[ 138*$.1^4 - 4175/3*$.1^3 + 4944*$.1^2 - 21781/3*$.1 + 3675, 628/3*$.1^4 - 6316/3*$.1^3 + 22259/3*$.1^2 - 32027/3*$.1 + 5145, 11017/12*$.1^4 - 27521/3*$.1^3 + 385199/12*$.1^2 - 137620/3*$.1 + 22050, 7504*$.1^4 - 225092/3*$.1^3 + 262577*$.1^2 - 1125250/3*$.1 + 180075, 360269/24*$.1^4 - 1801135/12*$.1^3 + 12606391/24*$.1^2 - 9003575/12*$.1 + 360150, 997/3*$.1^4 - 9941/3*$.1^3 + 34673/3*$.1^2 - 49339/3*$.1 + 7875, 34420/3*$.1^4 - 114740*$.1^3 + 1204895/3*$.1^2 - 573885*$.1 + 275625 ], [], []> {} Total time: 3.969 seconds, Total memory usage: 2.79MB ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Sun Jan 25 09:59:13 2004 Input: P := PolynomialRing(Rationals()); C := HyperellipticCurve(x*(x-1)*(x-2)*(x-3)*(x-4)); D := QuadraticTwist(C,106); J := Jacobian(D); SetVerbose("JacHypSelmer", 2); TwoSelmerGroupData(J : Bound := 300); Output: Magma V2.10-6 Sun Jan 25 2004 09:59:08 on modular [Seed = 1881401770] ------------------------------------- TwoSelmerGroupData of Jacobian of Hyperelliptic Curve defined by y^2 = 106*x^5 - 1060*x^4 + 3710*x^3 - 5300*x^2 + 2544*x over Rational Field m= Mapping from: CrvHyp: C to CrvHyp: C1 with equations : 106*$.1 11236*$.2 $.3 and inverse 1/106*$.1 1/11236*$.2 $.3 Change curve into Hyperelliptic Curve defined by y^2 = x^5 - 1060*x^4 + 393260*x^3 - 59550800*x^2 + 3029944704*x over Rational Field Bad primes = [ 2, 3, 53 ] f factors as (x - 424) (x - 318) (x - 212) (x - 106) (x). For factor x - 424, use field defined by x - 1 and theta = 424 For factor x - 318, use field defined by x - 1 and theta = 318 For factor x - 212, use field defined by x - 1 and theta = 212 For factor x - 106, use field defined by x - 1 and theta = 106 For factor x, use field defined by x - 1 and theta = 0 The 2-torsion group has dimension 4. Determining local images... p = 2 x = 1 --> new generator (0 0 0 0 1 0 0 0 1 0 1 1 0 0 0) x = 2 --> new generator (1 0 1 0 0 0 1 1 1 1 1 0 1 0 0) p = 3 x = 4 --> new generator (1 0 0 0 0 1 1 1 0 0) p = 53 p = infinity Computing class groups... Class group data of the fields: Field given by x - 424: [] Field given by x - 318: [] Field given by x - 212: [] Field given by x - 106: [] Field given by x: [] Dimension of Cl[2] = 0. Signatures: [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] Dimension of units mod squares = 5. Upper bound for Selmer group dimension: 13. ==> Upper bound for rank = 9. Computing unit groups... Class group and unit data of the fields: Field given by x - 424: Class group = [], units = [ 2 ] Field given by x - 318: Class group = [], units = [ 2 ] Field given by x - 212: Class group = [], units = [ 2 ] Field given by x - 106: Class group = [], units = [ 2 ] Field given by x: Class group = [], units = [ 2 ] Time for local computations: 1040 ms. Time for class groups: 0 ms. Time for unit groups: 9 ms. Selmer group dimension = 5, Dimension of 2-torsion = 4, ==> Bound for the MW-rank = 1. Total time: 1151 ms. Transforming presentation of S back to model C. 1 5 <[ 328759*$.1^4 - 3287590*$.1^3 + 11506565*$.1^2 - 16438056*$.1 + 7890481, 74315/4*$.1^4 - 371769/2*$.1^3 + 2603777/4*$.1^2 - 1860645/2*$.1 + 446631, 867/4*$.1^4 - 2202*$.1^3 + 31381/4*$.1^2 - 11425*$.1 + 5618, 57/4*$.1^4 - 235/2*$.1^3 + 1199/4*$.1^2 - 487/2*$.1 + 53, 719/2*$.1^4 - 3561*$.1^3 + 12327*$.1^2 - 34893/2*$.1 + 8427 ], [], []> {} Total time: 4.289 seconds, Total memory usage: 2.69MB ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Sun Jan 25 09:59:27 2004 Input: P := PolynomialRing(Rationals()); C := HyperellipticCurve(x*(x-1)*(x-2)*(x-3)*(x-4)); D := QuadraticTwist(C,107); J := Jacobian(D); SetVerbose("JacHypSelmer", 2); TwoSelmerGroupData(J : Bound := 300); Output: Magma V2.10-6 Sun Jan 25 2004 09:59:23 on modular [Seed = 2032853204] ------------------------------------- TwoSelmerGroupData of Jacobian of Hyperelliptic Curve defined by y^2 = 107*x^5 - 1070*x^4 + 3745*x^3 - 5350*x^2 + 2568*x over Rational Field m= Mapping from: CrvHyp: C to CrvHyp: C1 with equations : 107*$.1 11449*$.2 $.3 and inverse 1/107*$.1 1/11449*$.2 $.3 Change curve into Hyperelliptic Curve defined by y^2 = x^5 - 1070*x^4 + 400715*x^3 - 61252150*x^2 + 3145910424*x over Rational Field Bad primes = [ 2, 3, 107 ] f factors as (x - 428) (x - 321) (x - 214) (x - 107) (x). For factor x - 428, use field defined by x - 1 and theta = 428 For factor x - 321, use field defined by x - 1 and theta = 321 For factor x - 214, use field defined by x - 1 and theta = 214 For factor x - 107, use field defined by x - 1 and theta = 107 For factor x, use field defined by x - 1 and theta = 0 The 2-torsion group has dimension 4. Determining local images... p = 2 x = 1/4 --> new generator (0 0 0 0 0 1 0 0 0 0 0 1 0 0 0) x = 10 --> new generator (1 1 1 0 0 0 0 0 1 0 1 1 1 0 1) p = 3 x = 3 --> new generator (0 0 1 1 0 1 0 0 1 0) p = 107 p = infinity Computing class groups... Class group data of the fields: Field given by x - 428: [] Field given by x - 321: [] Field given by x - 214: [] Field given by x - 107: [] Field given by x: [] Dimension of Cl[2] = 0. Signatures: [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] Dimension of units mod squares = 5. Upper bound for Selmer group dimension: 13. ==> Upper bound for rank = 9. Computing unit groups... Class group and unit data of the fields: Field given by x - 428: Class group = [], units = [ 2 ] Field given by x - 321: Class group = [], units = [ 2 ] Field given by x - 214: Class group = [], units = [ 2 ] Field given by x - 107: Class group = [], units = [ 2 ] Field given by x: Class group = [], units = [ 2 ] Time for local computations: 511 ms. Time for class groups: 0 ms. Time for unit groups: 9 ms. Selmer group dimension = 5, Dimension of 2-torsion = 4, ==> Bound for the MW-rank = 1. Total time: 619 ms. Transforming presentation of S back to model C. 1 5 <[ 7919/8*$.1^4 - 39237/4*$.1^3 + 271581/8*$.1^2 - 191677/4*$.1 + 22898, 1382*$.1^4 - 13963*$.1^3 + 49389*$.1^2 - 71156*$.1 + 34347, 816873/4*$.1^4 - 4084187/2*$.1^3 + 28587779/4*$.1^2 - 20418481/2*$.1 + 4900172, 243/8*$.1^4 - 1153/4*$.1^3 + 7777/8*$.1^2 - 5417/4*$.1 + 642, 437*$.1^4 - 4370*$.1^3 + 15455*$.1^2 - 22650*$.1 + 11449 ], [], []> {} Total time: 3.749 seconds, Total memory usage: 2.79MB ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Sun Jan 25 09:59:43 2004 Input: P := PolynomialRing(Rationals()); C := HyperellipticCurve(x*(x-1)*(x-2)*(x-3)*(x-4)); D := QuadraticTwist(C,109); J := Jacobian(D); SetVerbose("JacHypSelmer", 2); TwoSelmerGroupData(J : Bound := 300); Output: Magma V2.10-6 Sun Jan 25 2004 09:59:39 on modular [Seed = 1310578675] ------------------------------------- TwoSelmerGroupData of Jacobian of Hyperelliptic Curve defined by y^2 = 109*x^5 - 1090*x^4 + 3815*x^3 - 5450*x^2 + 2616*x over Rational Field m= Mapping from: CrvHyp: C to CrvHyp: C1 with equations : 109*$.1 11881*$.2 $.3 and inverse 1/109*$.1 1/11881*$.2 $.3 Change curve into Hyperelliptic Curve defined by y^2 = x^5 - 1090*x^4 + 415835*x^3 - 64751450*x^2 + 3387795864*x over Rational Field Bad primes = [ 2, 3, 109 ] f factors as (x - 436) (x - 327) (x - 218) (x - 109) (x). For factor x - 436, use field defined by x - 1 and theta = 436 For factor x - 327, use field defined by x - 1 and theta = 327 For factor x - 218, use field defined by x - 1 and theta = 218 For factor x - 109, use field defined by x - 1 and theta = 109 For factor x, use field defined by x - 1 and theta = 0 The 2-torsion group has dimension 4. Determining local images... p = 2 x = 1/4 --> new generator (0 0 0 0 0 1 0 0 0 0 0 1 0 0 0) x = 14 --> new generator (1 0 1 0 1 1 0 0 1 0 0 0 1 1 1) p = 3 x = 7 --> new generator (1 0 0 0 0 1 1 1 0 0) p = 109 p = infinity Computing class groups... Class group data of the fields: Field given by x - 436: [] Field given by x - 327: [] Field given by x - 218: [] Field given by x - 109: [] Field given by x: [] Dimension of Cl[2] = 0. Signatures: [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] Dimension of units mod squares = 5. Upper bound for Selmer group dimension: 13. ==> Upper bound for rank = 9. Computing unit groups... Class group and unit data of the fields: Field given by x - 436: Class group = [], units = [ 2 ] Field given by x - 327: Class group = [], units = [ 2 ] Field given by x - 218: Class group = [], units = [ 2 ] Field given by x - 109: Class group = [], units = [ 2 ] Field given by x: Class group = [], units = [ 2 ] Time for local computations: 551 ms. Time for class groups: 0 ms. Time for unit groups: 0 ms. Selmer group dimension = 5, Dimension of 2-torsion = 4, ==> Bound for the MW-rank = 1. Total time: 650 ms. Transforming presentation of S back to model C. 1 5 <[ 8245/8*$.1^4 - 41007/4*$.1^3 + 284223/8*$.1^2 - 200263/4*$.1 + 23762, -$.1^3 + 7*$.1^2 - 12*$.1 + 3, 289/4*$.1^4 - 1227/2*$.1^3 + 6635/4*$.1^2 - 3101/2*$.1 + 436, -657/8*$.1^4 + 2843/4*$.1^3 - 15067/8*$.1^2 + 5019/4*$.1 + 654, 459*$.1^4 - 4662*$.1^3 + 16605*$.1^2 - 24174*$.1 + 11881 ], [], []> {} Total time: 3.759 seconds, Total memory usage: 2.79MB ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Sun Jan 25 10:00:01 2004 Input: P := PolynomialRing(Rationals()); C := HyperellipticCurve(x*(x-1)*(x-2)*(x-3)*(x-4)); D := QuadraticTwist(C,110); J := Jacobian(D); SetVerbose("JacHypSelmer", 2); TwoSelmerGroupData(J : Bound := 300); Output: Magma V2.10-6 Sun Jan 25 2004 09:59:56 on modular [Seed = 1459932893] ------------------------------------- TwoSelmerGroupData of Jacobian of Hyperelliptic Curve defined by y^2 = 110*x^5 - 1100*x^4 + 3850*x^3 - 5500*x^2 + 2640*x over Rational Field m= Mapping from: CrvHyp: C to CrvHyp: C1 with equations : 110*$.1 12100*$.2 $.3 and inverse 1/110*$.1 1/12100*$.2 $.3 Change curve into Hyperelliptic Curve defined by y^2 = x^5 - 1100*x^4 + 423500*x^3 - 66550000*x^2 + 3513840000*x over Rational Field Bad primes = [ 2, 3, 5, 11 ] f factors as (x - 440) (x - 330) (x - 220) (x - 110) (x). For factor x - 440, use field defined by x - 1 and theta = 440 For factor x - 330, use field defined by x - 1 and theta = 330 For factor x - 220, use field defined by x - 1 and theta = 220 For factor x - 110, use field defined by x - 1 and theta = 110 For factor x, use field defined by x - 1 and theta = 0 The 2-torsion group has dimension 4. Determining local images... p = 2 x = 1 --> new generator (0 0 0 0 1 1 0 0 1 0 1 0 0 0 0) x = 34 --> new generator (1 0 1 1 1 0 1 1 0 0 0 1 1 0 0) p = 3 x = 3 --> new generator (0 0 1 1 0 1 0 0 1 0) p = 5 p = 11 p = infinity Computing class groups... Class group data of the fields: Field given by x - 440: [] Field given by x - 330: [] Field given by x - 220: [] Field given by x - 110: [] Field given by x: [] Dimension of Cl[2] = 0. Signatures: [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] Dimension of units mod squares = 5. Upper bound for Selmer group dimension: 17. ==> Upper bound for rank = 13. Computing unit groups... Class group and unit data of the fields: Field given by x - 440: Class group = [], units = [ 2 ] Field given by x - 330: Class group = [], units = [ 2 ] Field given by x - 220: Class group = [], units = [ 2 ] Field given by x - 110: Class group = [], units = [ 2 ] Field given by x: Class group = [], units = [ 2 ] Time for local computations: 1049 ms. Time for class groups: 0 ms. Time for unit groups: 0 ms. Selmer group dimension = 4, Dimension of 2-torsion = 4, ==> Bound for the MW-rank = 0. Total time: 1210 ms. Transforming presentation of S back to model C. 0 4 <[ 1593/4*$.1^4 - 7855/2*$.1^3 + 54109/4*$.1^2 - 19067*$.1 + 9075, -7*$.1^4 + 42*$.1^3 - 97/2*$.1^2 - 87/2*$.1 + 55, 756*$.1^4 - 15175/2*$.1^3 + 53197/2*$.1^2 - 37915*$.1 + 18150, -207/2*$.1^4 + 1847/2*$.1^3 - 5245/2*$.1^2 + 4595/2*$.1 + 165 ], [], []> {} Total time: 4.359 seconds, Total memory usage: 2.79MB ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Sun Jan 25 10:00:27 2004 Input: P := PolynomialRing(Rationals()); C := HyperellipticCurve(x*(x-1)*(x-2)*(x-3)*(x-4)); D := QuadraticTwist(C,111); J := Jacobian(D); SetVerbose("JacHypSelmer", 2); TwoSelmerGroupData(J : Bound := 300); Output: Magma V2.10-6 Sun Jan 25 2004 10:00:23 on modular [Seed = 661962054] ------------------------------------- TwoSelmerGroupData of Jacobian of Hyperelliptic Curve defined by y^2 = 111*x^5 - 1110*x^4 + 3885*x^3 - 5550*x^2 + 2664*x over Rational Field m= Mapping from: CrvHyp: C to CrvHyp: C1 with equations : 111*$.1 12321*$.2 $.3 and inverse 1/111*$.1 1/12321*$.2 $.3 Change curve into Hyperelliptic Curve defined by y^2 = x^5 - 1110*x^4 + 431235*x^3 - 68381550*x^2 + 3643368984*x over Rational Field Bad primes = [ 2, 3, 37 ] f factors as (x - 444) (x - 333) (x - 222) (x - 111) (x). For factor x - 444, use field defined by x - 1 and theta = 444 For factor x - 333, use field defined by x - 1 and theta = 333 For factor x - 222, use field defined by x - 1 and theta = 222 For factor x - 111, use field defined by x - 1 and theta = 111 For factor x, use field defined by x - 1 and theta = 0 The 2-torsion group has dimension 4. Determining local images... p = 2 x = 1/4 --> new generator (0 0 0 0 0 1 0 0 0 0 0 1 0 0 0) x = 18 --> new generator (1 1 0 0 0 1 0 0 1 0 1 0 1 0 0) p = 3 p = 37 p = infinity Computing class groups... Class group data of the fields: Field given by x - 444: [] Field given by x - 333: [] Field given by x - 222: [] Field given by x - 111: [] Field given by x: [] Dimension of Cl[2] = 0. Signatures: [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] Dimension of units mod squares = 5. Upper bound for Selmer group dimension: 15. ==> Upper bound for rank = 11. Computing unit groups... Class group and unit data of the fields: Field given by x - 444: Class group = [], units = [ 2 ] Field given by x - 333: Class group = [], units = [ 2 ] Field given by x - 222: Class group = [], units = [ 2 ] Field given by x - 111: Class group = [], units = [ 2 ] Field given by x: Class group = [], units = [ 2 ] Time for local computations: 540 ms. Time for class groups: 0 ms. Time for unit groups: 0 ms. Selmer group dimension = 5, Dimension of 2-torsion = 4, ==> Bound for the MW-rank = 1. Total time: 650 ms. Transforming presentation of S back to model C. 1 5 <[ 8643/8*$.1^4 - 128387/12*$.1^3 + 295705/8*$.1^2 - 623803/12*$.1 + 24642, -1/3*$.1^3 + 3*$.1^2 - 20/3*$.1 + 3, 2659/12*$.1^4 - 4211/2*$.1^3 + 82481/12*$.1^2 - 17969/2*$.1 + 3996, 361/24*$.1^4 - 657/4*$.1^3 + 15539/24*$.1^2 - 4361/4*$.1 + 666, 45*$.1^4 - 474*$.1^3 + 1755*$.1^2 - 2658*$.1 + 1369 ], [], []> {} Total time: 3.759 seconds, Total memory usage: 2.69MB ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Sun Jan 25 10:00:44 2004 Input: P := PolynomialRing(Rationals()); C := HyperellipticCurve(x*(x-1)*(x-2)*(x-3)*(x-4)); D := QuadraticTwist(C,113); J := Jacobian(D); SetVerbose("JacHypSelmer", 2); TwoSelmerGroupData(J : Bound := 300); Output: Magma V2.10-6 Sun Jan 25 2004 10:00:40 on modular [Seed = 746567250] ------------------------------------- TwoSelmerGroupData of Jacobian of Hyperelliptic Curve defined by y^2 = 113*x^5 - 1130*x^4 + 3955*x^3 - 5650*x^2 + 2712*x over Rational Field m= Mapping from: CrvHyp: C to CrvHyp: C1 with equations : 113*$.1 12769*$.2 $.3 and inverse 1/113*$.1 1/12769*$.2 $.3 Change curve into Hyperelliptic Curve defined by y^2 = x^5 - 1130*x^4 + 446915*x^3 - 72144850*x^2 + 3913136664*x over Rational Field Bad primes = [ 2, 3, 113 ] f factors as (x - 452) (x - 339) (x - 226) (x - 113) (x). For factor x - 452, use field defined by x - 1 and theta = 452 For factor x - 339, use field defined by x - 1 and theta = 339 For factor x - 226, use field defined by x - 1 and theta = 226 For factor x - 113, use field defined by x - 1 and theta = 113 For factor x, use field defined by x - 1 and theta = 0 The 2-torsion group has dimension 4. Determining local images... p = 2 x = 1/4 --> new generator (0 0 0 0 0 1 0 0 0 0 0 1 0 0 0) x = 22 --> new generator (1 0 0 0 1 0 0 0 1 0 0 1 1 1 0) p = 3 x = 3 --> new generator (0 0 1 1 0 1 0 0 1 0) p = 113 p = infinity Computing class groups... Class group data of the fields: Field given by x - 452: [] Field given by x - 339: [] Field given by x - 226: [] Field given by x - 113: [] Field given by x: [] Dimension of Cl[2] = 0. Signatures: [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] Dimension of units mod squares = 5. Upper bound for Selmer group dimension: 13. ==> Upper bound for rank = 9. Computing unit groups... Class group and unit data of the fields: Field given by x - 452: Class group = [], units = [ 2 ] Field given by x - 339: Class group = [], units = [ 2 ] Field given by x - 226: Class group = [], units = [ 2 ] Field given by x - 113: Class group = [], units = [ 2 ] Field given by x: Class group = [], units = [ 2 ] Time for local computations: 540 ms. Time for class groups: 0 ms. Time for unit groups: 0 ms. Selmer group dimension = 6, Dimension of 2-torsion = 4, ==> Bound for the MW-rank = 2. Total time: 650 ms. Transforming presentation of S back to model C. 2 6 <[ 8513/8*$.1^4 - 42339/4*$.1^3 + 294787/8*$.1^2 - 210107/4*$.1 + 25538, 70*$.1^4 - 645*$.1^3 + 1953*$.1^2 - 2056*$.1 + 339, 8513/4*$.1^4 - 42451/2*$.1^3 + 296363/4*$.1^2 - 211461/2*$.1 + 51076, -681/8*$.1^4 + 2947/4*$.1^3 - 15619/8*$.1^2 + 5203/4*$.1 + 678, 518*$.1^4 - 5180*$.1^3 + 18186*$.1^2 - 26180*$.1 + 12769, -14*$.1^4 + 84*$.1^3 - 98*$.1^2 - 84*$.1 + 113 ], [], []> {} Total time: 3.799 seconds, Total memory usage: 2.79MB ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Sun Jan 25 10:01:04 2004 Input: P := PolynomialRing(Rationals()); C := HyperellipticCurve(x*(x-1)*(x-2)*(x-3)*(x-4)); D := QuadraticTwist(C,114); J := Jacobian(D); SetVerbose("JacHypSelmer", 2); TwoSelmerGroupData(J : Bound := 300); Output: Magma V2.10-6 Sun Jan 25 2004 10:00:59 on modular [Seed = 845260927] ------------------------------------- TwoSelmerGroupData of Jacobian of Hyperelliptic Curve defined by y^2 = 114*x^5 - 1140*x^4 + 3990*x^3 - 5700*x^2 + 2736*x over Rational Field m= Mapping from: CrvHyp: C to CrvHyp: C1 with equations : 114*$.1 12996*$.2 $.3 and inverse 1/114*$.1 1/12996*$.2 $.3 Change curve into Hyperelliptic Curve defined by y^2 = x^5 - 1140*x^4 + 454860*x^3 - 74077200*x^2 + 4053504384*x over Rational Field Bad primes = [ 2, 3, 19 ] f factors as (x - 456) (x - 342) (x - 228) (x - 114) (x). For factor x - 456, use field defined by x - 1 and theta = 456 For factor x - 342, use field defined by x - 1 and theta = 342 For factor x - 228, use field defined by x - 1 and theta = 228 For factor x - 114, use field defined by x - 1 and theta = 114 For factor x, use field defined by x - 1 and theta = 0 The 2-torsion group has dimension 4. Determining local images... p = 2 x = 1 --> new generator (0 0 0 0 1 0 0 0 1 0 1 1 0 0 0) x = 10 --> new generator (1 0 0 0 0 1 1 1 0 1 1 0 1 0 1) p = 3 p = 19 p = infinity Computing class groups... Class group data of the fields: Field given by x - 456: [] Field given by x - 342: [] Field given by x - 228: [] Field given by x - 114: [] Field given by x: [] Dimension of Cl[2] = 0. Signatures: [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] Dimension of units mod squares = 5. Upper bound for Selmer group dimension: 15. ==> Upper bound for rank = 11. Computing unit groups... Class group and unit data of the fields: Field given by x - 456: Class group = [], units = [ 2 ] Field given by x - 342: Class group = [], units = [ 2 ] Field given by x - 228: Class group = [], units = [ 2 ] Field given by x - 114: Class group = [], units = [ 2 ] Field given by x: Class group = [], units = [ 2 ] Time for local computations: 1131 ms. Time for class groups: 0 ms. Time for unit groups: 0 ms. Selmer group dimension = 5, Dimension of 2-torsion = 4, ==> Bound for the MW-rank = 1. Total time: 1241 ms. Transforming presentation of S back to model C. 1 5 <[ 47*$.1^4 - 1391/3*$.1^3 + 3197/2*$.1^2 - 13553/6*$.1 + 1083, -1/4*$.1^4 + 3/2*$.1^3 - 5/4*$.1^2 - 3*$.1 + 1, 346/3*$.1^4 - 6635/6*$.1^3 + 21889/6*$.1^2 - 14465/3*$.1 + 2166, 107/4*$.1^4 - 893/3*$.1^3 + 4689/4*$.1^2 - 5725/3*$.1 + 1083, -7*$.1^4 + 42*$.1^3 - 49*$.1^2 - 42*$.1 + 57 ], [], []> {} Total time: 4.469 seconds, Total memory usage: 2.69MB ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Sun Jan 25 10:01:16 2004 Input: P := PolynomialRing(Rationals()); C := HyperellipticCurve(x*(x-1)*(x-2)*(x-3)*(x-4)); D := QuadraticTwist(C,115); J := Jacobian(D); SetVerbose("JacHypSelmer", 2); TwoSelmerGroupData(J : Bound := 300); Output: Magma V2.10-6 Sun Jan 25 2004 10:01:13 on modular [Seed = 156930902] ------------------------------------- TwoSelmerGroupData of Jacobian of Hyperelliptic Curve defined by y^2 = 115*x^5 - 1150*x^4 + 4025*x^3 - 5750*x^2 + 2760*x over Rational Field m= Mapping from: CrvHyp: C to CrvHyp: C1 with equations : 115*$.1 13225*$.2 $.3 and inverse 1/115*$.1 1/13225*$.2 $.3 Change curve into Hyperelliptic Curve defined by y^2 = x^5 - 1150*x^4 + 462875*x^3 - 76043750*x^2 + 4197615000*x over Rational Field Bad primes = [ 2, 3, 5, 23 ] f factors as (x - 460) (x - 345) (x - 230) (x - 115) (x). For factor x - 460, use field defined by x - 1 and theta = 460 For factor x - 345, use field defined by x - 1 and theta = 345 For factor x - 230, use field defined by x - 1 and theta = 230 For factor x - 115, use field defined by x - 1 and theta = 115 For factor x, use field defined by x - 1 and theta = 0 The 2-torsion group has dimension 4. Determining local images... p = 2 x = 1/4 --> new generator (0 0 0 0 0 1 0 0 0 0 0 1 0 0 0) x = 26 --> new generator (1 1 1 0 0 0 0 0 1 0 1 1 1 0 1) p = 3 x = 4 --> new generator (1 0 0 0 0 1 1 1 0 0) p = 5 p = 23 p = infinity Computing class groups... Class group data of the fields: Field given by x - 460: [] Field given by x - 345: [] Field given by x - 230: [] Field given by x - 115: [] Field given by x: [] Dimension of Cl[2] = 0. Signatures: [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] Dimension of units mod squares = 5. Upper bound for Selmer group dimension: 17. ==> Upper bound for rank = 13. Computing unit groups... Class group and unit data of the fields: Field given by x - 460: Class group = [], units = [ 2 ] Field given by x - 345: Class group = [], units = [ 2 ] Field given by x - 230: Class group = [], units = [ 2 ] Field given by x - 115: Class group = [], units = [ 2 ] Field given by x: Class group = [], units = [ 2 ] Time for local computations: 551 ms. Time for class groups: 0 ms. Time for unit groups: 9 ms. Selmer group dimension = 5, Dimension of 2-torsion = 4, ==> Bound for the MW-rank = 1. Total time: 690 ms. Transforming presentation of S back to model C. 1 5 <[ 1893/8*$.1^4 - 9523/4*$.1^3 + 66887/8*$.1^2 - 47847/4*$.1 + 5750, 7545*$.1^4 - 75630*$.1^3 + 265339*$.1^2 - 379782*$.1 + 182505, 8735/4*$.1^4 - 43787/2*$.1^3 + 307305/4*$.1^2 - 219987/2*$.1 + 52900, 1081/8*$.1^4 - 5355/4*$.1^3 + 37075/8*$.1^2 - 26235/4*$.1 + 3174, 8*$.1^4 - 71*$.1^3 + 211*$.1^2 - 248*$.1 + 115 ], [], []> {} Total time: 3.799 seconds, Total memory usage: 2.79MB ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Sun Jan 25 10:01:33 2004 Input: P := PolynomialRing(Rationals()); C := HyperellipticCurve(x*(x-1)*(x-2)*(x-3)*(x-4)); D := QuadraticTwist(C,118); J := Jacobian(D); SetVerbose("JacHypSelmer", 2); TwoSelmerGroupData(J : Bound := 300); Output: Magma V2.10-6 Sun Jan 25 2004 10:01:28 on modular [Seed = 508396592] ------------------------------------- TwoSelmerGroupData of Jacobian of Hyperelliptic Curve defined by y^2 = 118*x^5 - 1180*x^4 + 4130*x^3 - 5900*x^2 + 2832*x over Rational Field m= Mapping from: CrvHyp: C to CrvHyp: C1 with equations : 118*$.1 13924*$.2 $.3 and inverse 1/118*$.1 1/13924*$.2 $.3 Change curve into Hyperelliptic Curve defined by y^2 = x^5 - 1180*x^4 + 487340*x^3 - 82151600*x^2 + 4653066624*x over Rational Field Bad primes = [ 2, 3, 59 ] f factors as (x - 472) (x - 354) (x - 236) (x - 118) (x). For factor x - 472, use field defined by x - 1 and theta = 472 For factor x - 354, use field defined by x - 1 and theta = 354 For factor x - 236, use field defined by x - 1 and theta = 236 For factor x - 118, use field defined by x - 1 and theta = 118 For factor x, use field defined by x - 1 and theta = 0 The 2-torsion group has dimension 4. Determining local images... p = 2 x = 1 --> new generator (0 0 0 0 1 1 0 0 1 0 1 0 0 0 0) x = 58 --> new generator (1 0 0 1 1 0 1 1 1 0 0 0 1 0 1) p = 3 x = 7 --> new generator (1 0 0 0 0 1 1 1 0 0) p = 59 p = infinity Computing class groups... Class group data of the fields: Field given by x - 472: [] Field given by x - 354: [] Field given by x - 236: [] Field given by x - 118: [] Field given by x: [] Dimension of Cl[2] = 0. Signatures: [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] Dimension of units mod squares = 5. Upper bound for Selmer group dimension: 13. ==> Upper bound for rank = 9. Computing unit groups... Class group and unit data of the fields: Field given by x - 472: Class group = [], units = [ 2 ] Field given by x - 354: Class group = [], units = [ 2 ] Field given by x - 236: Class group = [], units = [ 2 ] Field given by x - 118: Class group = [], units = [ 2 ] Field given by x: Class group = [], units = [ 2 ] Time for local computations: 1120 ms. Time for class groups: 0 ms. Time for unit groups: 11 ms. Selmer group dimension = 5, Dimension of 2-torsion = 4, ==> Bound for the MW-rank = 1. Total time: 1229 ms. Transforming presentation of S back to model C. 1 5 <[ -21/4*$.1^4 + 47/2*$.1^3 - 37/4*$.1^2 - 62*$.1 + 59, -15/2*$.1^4 + 45*$.1^3 - 52*$.1^2 - 93/2*$.1 + 59, 34*$.1^4 - 563/2*$.1^3 + 1445/2*$.1^2 - 591*$.1 + 118, 8*$.1^4 - 511/2*$.1^3 + 1744*$.1^2 - 8539/2*$.1 + 3481, -22*$.1^4 + 132*$.1^3 - 154*$.1^2 - 132*$.1 + 177 ], [], []> {} Total time: 4.399 seconds, Total memory usage: 2.69MB ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Sun Jan 25 10:01:47 2004 Input: P := PolynomialRing(Rationals()); C := HyperellipticCurve(x*(x-1)*(x-2)*(x-3)*(x-4)); D := QuadraticTwist(C,119); J := Jacobian(D); SetVerbose("JacHypSelmer", 2); TwoSelmerGroupData(J : Bound := 300); Output: Magma V2.10-6 Sun Jan 25 2004 10:01:43 on modular [Seed = 3887365590] ------------------------------------- TwoSelmerGroupData of Jacobian of Hyperelliptic Curve defined by y^2 = 119*x^5 - 1190*x^4 + 4165*x^3 - 5950*x^2 + 2856*x over Rational Field m= Mapping from: CrvHyp: C to CrvHyp: C1 with equations : 119*$.1 14161*$.2 $.3 and inverse 1/119*$.1 1/14161*$.2 $.3 Change curve into Hyperelliptic Curve defined by y^2 = x^5 - 1190*x^4 + 495635*x^3 - 84257950*x^2 + 4812814104*x over Rational Field Bad primes = [ 2, 3, 7, 17 ] f factors as (x - 476) (x - 357) (x - 238) (x - 119) (x). For factor x - 476, use field defined by x - 1 and theta = 476 For factor x - 357, use field defined by x - 1 and theta = 357 For factor x - 238, use field defined by x - 1 and theta = 238 For factor x - 119, use field defined by x - 1 and theta = 119 For factor x, use field defined by x - 1 and theta = 0 The 2-torsion group has dimension 4. Determining local images... p = 2 x = 1/4 --> new generator (0 0 0 0 0 1 0 0 0 0 0 1 0 0 0) x = 2 --> new generator (1 1 0 0 0 1 0 0 1 0 1 0 1 0 0) p = 3 x = 3 --> new generator (0 0 1 1 0 1 0 0 1 0) p = 7 p = 17 p = infinity Computing class groups... Class group data of the fields: Field given by x - 476: [] Field given by x - 357: [] Field given by x - 238: [] Field given by x - 119: [] Field given by x: [] Dimension of Cl[2] = 0. Signatures: [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] Dimension of units mod squares = 5. Upper bound for Selmer group dimension: 17. ==> Upper bound for rank = 13. Computing unit groups... Class group and unit data of the fields: Field given by x - 476: Class group = [], units = [ 2 ] Field given by x - 357: Class group = [], units = [ 2 ] Field given by x - 238: Class group = [], units = [ 2 ] Field given by x - 119: Class group = [], units = [ 2 ] Field given by x: Class group = [], units = [ 2 ] Time for local computations: 540 ms. Time for class groups: 0 ms. Time for unit groups: 0 ms. Selmer group dimension = 6, Dimension of 2-torsion = 4, ==> Bound for the MW-rank = 2. Total time: 689 ms. Transforming presentation of S back to model C. 2 6 <[ 33*$.1^4 - 330*$.1^3 + 1159*$.1^2 - 1678*$.1 + 833, 562*$.1^4 - 5676*$.1^3 + 20122*$.1^2 - 29176*$.1 + 14161, 665/4*$.1^4 - 1666*$.1^3 + 23403/4*$.1^2 - 8390*$.1 + 4046, 12412*$.1^4 - 124081*$.1^3 + 434095*$.1^2 - 619793*$.1 + 297381, -31/8*$.1^4 + 57/4*$.1^3 + 283/8*$.1^2 - 587/4*$.1 + 102, 511530*$.1^4 - 5115419*$.1^3 + 17904349*$.1^2 - 25577996*$.1 + 12277587 ], [], []> {} Total time: 3.779 seconds, Total memory usage: 2.69MB ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Sun Jan 25 10:02:01 2004 Input: P := PolynomialRing(Rationals()); C := HyperellipticCurve(x*(x-1)*(x-2)*(x-3)*(x-4)); D := QuadraticTwist(C,122); J := Jacobian(D); SetVerbose("JacHypSelmer", 2); TwoSelmerGroupData(J : Bound := 300); Output: Magma V2.10-6 Sun Jan 25 2004 10:01:56 on modular [Seed = 3971970798] ------------------------------------- TwoSelmerGroupData of Jacobian of Hyperelliptic Curve defined by y^2 = 122*x^5 - 1220*x^4 + 4270*x^3 - 6100*x^2 + 2928*x over Rational Field m= Mapping from: CrvHyp: C to CrvHyp: C1 with equations : 122*$.1 14884*$.2 $.3 and inverse 1/122*$.1 1/14884*$.2 $.3 Change curve into Hyperelliptic Curve defined by y^2 = x^5 - 1220*x^4 + 520940*x^3 - 90792400*x^2 + 5316802944*x over Rational Field Bad primes = [ 2, 3, 61 ] f factors as (x - 488) (x - 366) (x - 244) (x - 122) (x). For factor x - 488, use field defined by x - 1 and theta = 488 For factor x - 366, use field defined by x - 1 and theta = 366 For factor x - 244, use field defined by x - 1 and theta = 244 For factor x - 122, use field defined by x - 1 and theta = 122 For factor x, use field defined by x - 1 and theta = 0 The 2-torsion group has dimension 4. Determining local images... p = 2 x = 1 --> new generator (0 0 0 0 1 0 0 0 1 0 1 1 0 0 0) x = 18 --> new generator (1 0 1 0 0 0 1 1 1 1 1 0 1 0 0) p = 3 x = 3 --> new generator (0 0 1 1 0 1 0 0 1 0) p = 61 p = infinity Computing class groups... Class group data of the fields: Field given by x - 488: [] Field given by x - 366: [] Field given by x - 244: [] Field given by x - 122: [] Field given by x: [] Dimension of Cl[2] = 0. Signatures: [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] Dimension of units mod squares = 5. Upper bound for Selmer group dimension: 13. ==> Upper bound for rank = 9. Computing unit groups... Class group and unit data of the fields: Field given by x - 488: Class group = [], units = [ 2 ] Field given by x - 366: Class group = [], units = [ 2 ] Field given by x - 244: Class group = [], units = [ 2 ] Field given by x - 122: Class group = [], units = [ 2 ] Field given by x: Class group = [], units = [ 2 ] Time for local computations: 1051 ms. Time for class groups: 0 ms. Time for unit groups: 9 ms. Selmer group dimension = 5, Dimension of 2-torsion = 4, ==> Bound for the MW-rank = 1. Total time: 1151 ms. Transforming presentation of S back to model C. 1 5 <[ 75/2*$.1^4 - 284*$.1^3 + 676*$.1^2 - 1213/2*$.1 + 183, -31/4*$.1^4 + 93/2*$.1^3 - 215/4*$.1^2 - 48*$.1 + 61, 930*$.1^4 - 18661/2*$.1^3 + 65407/2*$.1^2 - 46627*$.1 + 22326, -459/4*$.1^4 + 1024*$.1^3 - 11633/4*$.1^2 + 2548*$.1 + 183, 5*$.1^4 - 40*$.1^3 + 115*$.1^2 - 140*$.1 + 61 ], [], []> {} Total time: 4.299 seconds, Total memory usage: 2.69MB ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Sun Jan 25 10:02:17 2004 Input: P := PolynomialRing(Rationals()); C := HyperellipticCurve(x*(x-1)*(x-2)*(x-3)*(x-4)); D := QuadraticTwist(C,123); J := Jacobian(D); SetVerbose("JacHypSelmer", 2); TwoSelmerGroupData(J : Bound := 300); Output: Magma V2.10-6 Sun Jan 25 2004 10:02:13 on modular [Seed = 4121325542] ------------------------------------- TwoSelmerGroupData of Jacobian of Hyperelliptic Curve defined by y^2 = 123*x^5 - 1230*x^4 + 4305*x^3 - 6150*x^2 + 2952*x over Rational Field m= Mapping from: CrvHyp: C to CrvHyp: C1 with equations : 123*$.1 15129*$.2 $.3 and inverse 1/123*$.1 1/15129*$.2 $.3 Change curve into Hyperelliptic Curve defined by y^2 = x^5 - 1230*x^4 + 529515*x^3 - 93043350*x^2 + 5493279384*x over Rational Field Bad primes = [ 2, 3, 41 ] f factors as (x - 492) (x - 369) (x - 246) (x - 123) (x). For factor x - 492, use field defined by x - 1 and theta = 492 For factor x - 369, use field defined by x - 1 and theta = 369 For factor x - 246, use field defined by x - 1 and theta = 246 For factor x - 123, use field defined by x - 1 and theta = 123 For factor x, use field defined by x - 1 and theta = 0 The 2-torsion group has dimension 4. Determining local images... p = 2 x = 1/4 --> new generator (0 0 0 0 0 1 0 0 0 0 0 1 0 0 0) x = 10 --> new generator (1 1 1 0 0 0 0 0 1 0 1 1 1 0 1) p = 3 p = 41 p = infinity Computing class groups... Class group data of the fields: Field given by x - 492: [] Field given by x - 369: [] Field given by x - 246: [] Field given by x - 123: [] Field given by x: [] Dimension of Cl[2] = 0. Signatures: [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] Dimension of units mod squares = 5. Upper bound for Selmer group dimension: 15. ==> Upper bound for rank = 11. Computing unit groups... Class group and unit data of the fields: Field given by x - 492: Class group = [], units = [ 2 ] Field given by x - 369: Class group = [], units = [ 2 ] Field given by x - 246: Class group = [], units = [ 2 ] Field given by x - 123: Class group = [], units = [ 2 ] Field given by x: Class group = [], units = [ 2 ] Time for local computations: 531 ms. Time for class groups: 0 ms. Time for unit groups: 9 ms. Selmer group dimension = 4, Dimension of 2-torsion = 4, ==> Bound for the MW-rank = 0. Total time: 669 ms. Transforming presentation of S back to model C. 0 4 <[ 31685/24*$.1^4 - 157031/12*$.1^3 + 1086367/24*$.1^2 - 765055/12*$.1 + 30258, 210*$.1^4 - 6341/3*$.1^3 + 7433*$.1^2 - 31840/3*$.1 + 5043, 3722147/12*$.1^4 - 6203467/2*$.1^3 + 130269169/12*$.1^2 - 31015273/2*$.1 + 7443468, 401/24*$.1^4 - 729/4*$.1^3 + 17227/24*$.1^2 - 4833/4*$.1 + 738 ], [], []> {} Total time: 3.789 seconds, Total memory usage: 2.69MB ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Sun Jan 25 10:02:36 2004 Input: P := PolynomialRing(Rationals()); C := HyperellipticCurve(x*(x-1)*(x-2)*(x-3)*(x-4)); D := QuadraticTwist(C,127); J := Jacobian(D); SetVerbose("JacHypSelmer", 2); TwoSelmerGroupData(J : Bound := 300); Output: Magma V2.10-6 Sun Jan 25 2004 10:02:32 on modular [Seed = 4205404180] ------------------------------------- TwoSelmerGroupData of Jacobian of Hyperelliptic Curve defined by y^2 = 127*x^5 - 1270*x^4 + 4445*x^3 - 6350*x^2 + 3048*x over Rational Field m= Mapping from: CrvHyp: C to CrvHyp: C1 with equations : 127*$.1 16129*$.2 $.3 and inverse 1/127*$.1 1/16129*$.2 $.3 Change curve into Hyperelliptic Curve defined by y^2 = x^5 - 1270*x^4 + 564515*x^3 - 102419150*x^2 + 6243471384*x over Rational Field Bad primes = [ 2, 3, 127 ] f factors as (x - 508) (x - 381) (x - 254) (x - 127) (x). For factor x - 508, use field defined by x - 1 and theta = 508 For factor x - 381, use field defined by x - 1 and theta = 381 For factor x - 254, use field defined by x - 1 and theta = 254 For factor x - 127, use field defined by x - 1 and theta = 127 For factor x, use field defined by x - 1 and theta = 0 The 2-torsion group has dimension 4. Determining local images... p = 2 x = 1/4 --> new generator (0 0 0 0 0 1 0 0 0 0 0 1 0 0 0) x = 18 --> new generator (1 1 0 0 0 1 0 0 1 0 1 0 1 0 0) p = 3 x = 7 --> new generator (1 0 0 0 0 1 1 1 0 0) p = 127 p = infinity Computing class groups... Class group data of the fields: Field given by x - 508: [] Field given by x - 381: [] Field given by x - 254: [] Field given by x - 127: [] Field given by x: [] Dimension of Cl[2] = 0. Signatures: [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] Dimension of units mod squares = 5. Upper bound for Selmer group dimension: 13. ==> Upper bound for rank = 9. Computing unit groups... Class group and unit data of the fields: Field given by x - 508: Class group = [], units = [ 2 ] Field given by x - 381: Class group = [], units = [ 2 ] Field given by x - 254: Class group = [], units = [ 2 ] Field given by x - 127: Class group = [], units = [ 2 ] Field given by x: Class group = [], units = [ 2 ] Time for local computations: 540 ms. Time for class groups: 0 ms. Time for unit groups: 0 ms. Selmer group dimension = 4, Dimension of 2-torsion = 4, ==> Bound for the MW-rank = 0. Total time: 651 ms. Transforming presentation of S back to model C. 0 4 <[ 11131/8*$.1^4 - 55401/4*$.1^3 + 384513/8*$.1^2 - 271441/4*$.1 + 32258, 2016*$.1^4 - 20287*$.1^3 + 71323*$.1^2 - 101820*$.1 + 48387, 1365505/4*$.1^4 - 6827523/2*$.1^3 + 47792651/4*$.1^2 - 34137857/2*$.1 + 8193532, -765/8*$.1^4 + 3311/4*$.1^3 - 17551/8*$.1^2 + 5847/4*$.1 + 762 ], [], []> {} Total time: 3.889 seconds, Total memory usage: 2.79MB ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Sun Jan 25 10:02:58 2004 Input: P := PolynomialRing(Rationals()); C := HyperellipticCurve(x*(x-1)*(x-2)*(x-3)*(x-4)); D := QuadraticTwist(C,129); J := Jacobian(D); SetVerbose("JacHypSelmer", 2); TwoSelmerGroupData(J : Bound := 300); Output: Magma V2.10-6 Sun Jan 25 2004 10:02:54 on modular [Seed = 3281017147] ------------------------------------- TwoSelmerGroupData of Jacobian of Hyperelliptic Curve defined by y^2 = 129*x^5 - 1290*x^4 + 4515*x^3 - 6450*x^2 + 3096*x over Rational Field m= Mapping from: CrvHyp: C to CrvHyp: C1 with equations : 129*$.1 16641*$.2 $.3 and inverse 1/129*$.1 1/16641*$.2 $.3 Change curve into Hyperelliptic Curve defined by y^2 = x^5 - 1290*x^4 + 582435*x^3 - 107334450*x^2 + 6646149144*x over Rational Field Bad primes = [ 2, 3, 43 ] f factors as (x - 516) (x - 387) (x - 258) (x - 129) (x). For factor x - 516, use field defined by x - 1 and theta = 516 For factor x - 387, use field defined by x - 1 and theta = 387 For factor x - 258, use field defined by x - 1 and theta = 258 For factor x - 129, use field defined by x - 1 and theta = 129 For factor x, use field defined by x - 1 and theta = 0 The 2-torsion group has dimension 4. Determining local images... p = 2 x = 1/4 --> new generator (0 0 0 0 0 1 0 0 0 0 0 1 0 0 0) x = 22 --> new generator (1 0 0 0 1 0 0 0 1 0 0 1 1 1 0) p = 3 p = 43 p = infinity Computing class groups... Class group data of the fields: Field given by x - 516: [] Field given by x - 387: [] Field given by x - 258: [] Field given by x - 129: [] Field given by x: [] Dimension of Cl[2] = 0. Signatures: [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] Dimension of units mod squares = 5. Upper bound for Selmer group dimension: 15. ==> Upper bound for rank = 11. Computing unit groups... Class group and unit data of the fields: Field given by x - 516: Class group = [], units = [ 2 ] Field given by x - 387: Class group = [], units = [ 2 ] Field given by x - 258: Class group = [], units = [ 2 ] Field given by x - 129: Class group = [], units = [ 2 ] Field given by x: Class group = [], units = [ 2 ] Time for local computations: 560 ms. Time for class groups: 0 ms. Time for unit groups: 0 ms. Selmer group dimension = 5, Dimension of 2-torsion = 4, ==> Bound for the MW-rank = 1. Total time: 681 ms. Transforming presentation of S back to model C. 1 5 <[ 11593/8*$.1^4 - 172433/12*$.1^3 + 397851/8*$.1^2 - 841081/12*$.1 + 33282, 226*$.1^4 - 6823/3*$.1^3 + 8017*$.1^2 - 34556/3*$.1 + 5547, 4293931/12*$.1^4 - 7156395/2*$.1^3 + 150279641/12*$.1^2 - 35779373/2*$.1 + 8586756, 781/24*$.1^4 - 1285/4*$.1^3 + 26831/24*$.1^2 - 6389/4*$.1 + 774, 2032/3*$.1^4 - 20320/3*$.1^3 + 71312/3*$.1^2 - 102560/3*$.1 + 16641 ], [], []> {} Total time: 3.779 seconds, Total memory usage: 2.69MB ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Sun Jan 25 10:03:14 2004 Input: P := PolynomialRing(Rationals()); C := HyperellipticCurve(x*(x-1)*(x-2)*(x-3)*(x-4)); D := QuadraticTwist(C,130); J := Jacobian(D); SetVerbose("JacHypSelmer", 2); TwoSelmerGroupData(J : Bound := 300); Output: Magma V2.10-6 Sun Jan 25 2004 10:03:09 on modular [Seed = 3382334210] ------------------------------------- TwoSelmerGroupData of Jacobian of Hyperelliptic Curve defined by y^2 = 130*x^5 - 1300*x^4 + 4550*x^3 - 6500*x^2 + 3120*x over Rational Field m= Mapping from: CrvHyp: C to CrvHyp: C1 with equations : 130*$.1 16900*$.2 $.3 and inverse 1/130*$.1 1/16900*$.2 $.3 Change curve into Hyperelliptic Curve defined by y^2 = x^5 - 1300*x^4 + 591500*x^3 - 109850000*x^2 + 6854640000*x over Rational Field Bad primes = [ 2, 3, 5, 13 ] f factors as (x - 520) (x - 390) (x - 260) (x - 130) (x). For factor x - 520, use field defined by x - 1 and theta = 520 For factor x - 390, use field defined by x - 1 and theta = 390 For factor x - 260, use field defined by x - 1 and theta = 260 For factor x - 130, use field defined by x - 1 and theta = 130 For factor x, use field defined by x - 1 and theta = 0 The 2-torsion group has dimension 4. Determining local images... p = 2 x = 1 --> new generator (0 0 0 0 1 0 0 0 1 0 1 1 0 0 0) x = 26 --> new generator (1 0 0 0 0 1 1 1 0 1 1 0 1 0 1) p = 3 x = 1 --> new generator (1 0 0 0 0 1 1 1 0 0) p = 5 p = 13 p = infinity Computing class groups... Class group data of the fields: Field given by x - 520: [] Field given by x - 390: [] Field given by x - 260: [] Field given by x - 130: [] Field given by x: [] Dimension of Cl[2] = 0. Signatures: [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] Dimension of units mod squares = 5. Upper bound for Selmer group dimension: 17. ==> Upper bound for rank = 13. Computing unit groups... Class group and unit data of the fields: Field given by x - 520: Class group = [], units = [ 2 ] Field given by x - 390: Class group = [], units = [ 2 ] Field given by x - 260: Class group = [], units = [ 2 ] Field given by x - 130: Class group = [], units = [ 2 ] Field given by x: Class group = [], units = [ 2 ] Time for local computations: 1140 ms. Time for class groups: 0 ms. Time for unit groups: 0 ms. Selmer group dimension = 4, Dimension of 2-torsion = 4, ==> Bound for the MW-rank = 0. Total time: 1280 ms. Transforming presentation of S back to model C. 0 4 <[ 552*$.1^4 - 5455*$.1^3 + 37667/2*$.1^2 - 53199/2*$.1 + 12675, -33/4*$.1^4 + 99/2*$.1^3 - 229/4*$.1^2 - 51*$.1 + 65, 1056*$.1^4 - 21185/2*$.1^3 + 74247/2*$.1^2 - 52935*$.1 + 25350, -489/4*$.1^4 + 1091*$.1^3 - 12395/4*$.1^2 + 2715*$.1 + 195 ], [], []> {} Total time: 4.439 seconds, Total memory usage: 2.89MB ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Sun Jan 25 10:03:35 2004 Input: P := PolynomialRing(Rationals()); C := HyperellipticCurve(x*(x-1)*(x-2)*(x-3)*(x-4)); D := QuadraticTwist(C,131); J := Jacobian(D); SetVerbose("JacHypSelmer", 2); TwoSelmerGroupData(J : Bound := 300); Output: Magma V2.10-6 Sun Jan 25 2004 10:03:31 on modular [Seed = 3733800059] ------------------------------------- TwoSelmerGroupData of Jacobian of Hyperelliptic Curve defined by y^2 = 131*x^5 - 1310*x^4 + 4585*x^3 - 6550*x^2 + 3144*x over Rational Field m= Mapping from: CrvHyp: C to CrvHyp: C1 with equations : 131*$.1 17161*$.2 $.3 and inverse 1/131*$.1 1/17161*$.2 $.3 Change curve into Hyperelliptic Curve defined by y^2 = x^5 - 1310*x^4 + 600635*x^3 - 112404550*x^2 + 7067998104*x over Rational Field Bad primes = [ 2, 3, 131 ] f factors as (x - 524) (x - 393) (x - 262) (x - 131) (x). For factor x - 524, use field defined by x - 1 and theta = 524 For factor x - 393, use field defined by x - 1 and theta = 393 For factor x - 262, use field defined by x - 1 and theta = 262 For factor x - 131, use field defined by x - 1 and theta = 131 For factor x, use field defined by x - 1 and theta = 0 The 2-torsion group has dimension 4. Determining local images... p = 2 x = 1/4 --> new generator (0 0 0 0 0 1 0 0 0 0 0 1 0 0 0) x = 26 --> new generator (1 1 1 0 0 0 0 0 1 0 1 1 1 0 1) p = 3 x = 3 --> new generator (0 0 1 1 0 1 0 0 1 0) p = 131 p = infinity Computing class groups... Class group data of the fields: Field given by x - 524: [] Field given by x - 393: [] Field given by x - 262: [] Field given by x - 131: [] Field given by x: [] Dimension of Cl[2] = 0. Signatures: [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] Dimension of units mod squares = 5. Upper bound for Selmer group dimension: 13. ==> Upper bound for rank = 9. Computing unit groups... Class group and unit data of the fields: Field given by x - 524: Class group = [], units = [ 2 ] Field given by x - 393: Class group = [], units = [ 2 ] Field given by x - 262: Class group = [], units = [ 2 ] Field given by x - 131: Class group = [], units = [ 2 ] Field given by x: Class group = [], units = [ 2 ] Time for local computations: 511 ms. Time for class groups: 0 ms. Time for unit groups: 0 ms. Selmer group dimension = 5, Dimension of 2-torsion = 4, ==> Bound for the MW-rank = 1. Total time: 629 ms. Transforming presentation of S back to model C. 1 5 <[ 11791/8*$.1^4 - 58517/4*$.1^3 + 405853/8*$.1^2 - 287069/4*$.1 + 34322, 2085*$.1^4 - 21025*$.1^3 + 74222*$.1^2 - 106766*$.1 + 51483, 1498945/4*$.1^4 - 7494507/2*$.1^3 + 52459675/4*$.1^2 - 37469529/2*$.1 + 8992364, 299/8*$.1^4 - 1417/4*$.1^3 + 9545/8*$.1^2 - 6641/4*$.1 + 786, 666*$.1^4 - 6660*$.1^3 + 23506*$.1^2 - 34280*$.1 + 17161 ], [], []> {} Total time: 3.779 seconds, Total memory usage: 2.79MB ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Sun Jan 25 10:03:48 2004 Input: P := PolynomialRing(Rationals()); C := HyperellipticCurve(x*(x-1)*(x-2)*(x-3)*(x-4)); D := QuadraticTwist(C,133); J := Jacobian(D); SetVerbose("JacHypSelmer", 2); TwoSelmerGroupData(J : Bound := 300); Output: Magma V2.10-6 Sun Jan 25 2004 10:03:44 on modular [Seed = 2817801489] ------------------------------------- TwoSelmerGroupData of Jacobian of Hyperelliptic Curve defined by y^2 = 133*x^5 - 1330*x^4 + 4655*x^3 - 6650*x^2 + 3192*x over Rational Field m= Mapping from: CrvHyp: C to CrvHyp: C1 with equations : 133*$.1 17689*$.2 $.3 and inverse 1/133*$.1 1/17689*$.2 $.3 Change curve into Hyperelliptic Curve defined by y^2 = x^5 - 1330*x^4 + 619115*x^3 - 117631850*x^2 + 7509617304*x over Rational Field Bad primes = [ 2, 3, 7, 19 ] f factors as (x - 532) (x - 399) (x - 266) (x - 133) (x). For factor x - 532, use field defined by x - 1 and theta = 532 For factor x - 399, use field defined by x - 1 and theta = 399 For factor x - 266, use field defined by x - 1 and theta = 266 For factor x - 133, use field defined by x - 1 and theta = 133 For factor x, use field defined by x - 1 and theta = 0 The 2-torsion group has dimension 4. Determining local images... p = 2 x = 1/4 --> new generator (0 0 0 0 0 1 0 0 0 0 0 1 0 0 0) x = 30 --> new generator (1 0 1 0 1 1 0 0 1 0 0 0 1 1 1) p = 3 x = 4 --> new generator (1 0 0 0 0 1 1 1 0 0) p = 7 p = 19 p = infinity Computing class groups... Class group data of the fields: Field given by x - 532: [] Field given by x - 399: [] Field given by x - 266: [] Field given by x - 133: [] Field given by x: [] Dimension of Cl[2] = 0. Signatures: [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] Dimension of units mod squares = 5. Upper bound for Selmer group dimension: 17. ==> Upper bound for rank = 13. Computing unit groups... Class group and unit data of the fields: Field given by x - 532: Class group = [], units = [ 2 ] Field given by x - 399: Class group = [], units = [ 2 ] Field given by x - 266: Class group = [], units = [ 2 ] Field given by x - 133: Class group = [], units = [ 2 ] Field given by x: Class group = [], units = [ 2 ] Time for local computations: 569 ms. Time for class groups: 0 ms. Time for unit groups: 9 ms. Selmer group dimension = 5, Dimension of 2-torsion = 4, ==> Bound for the MW-rank = 1. Total time: 721 ms. Transforming presentation of S back to model C. 1 5 <[ 12189/8*$.1^4 - 60679/4*$.1^3 + 421303/8*$.1^2 - 297567/4*$.1 + 35378, 104*$.1^4 - 977*$.1^3 + 3067*$.1^2 - 3524*$.1 + 931, 1568337/4*$.1^4 - 7841683/2*$.1^3 + 54891771/4*$.1^2 - 39208669/2*$.1 + 9410548, 575/8*$.1^4 - 3477/4*$.1^3 + 30677/8*$.1^2 - 29173/4*$.1 + 5054, -7*$.1^4 + 42*$.1^3 - 49*$.1^2 - 42*$.1 + 57 ], [], []> {} Total time: 3.859 seconds, Total memory usage: 2.69MB ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Sun Jan 25 10:04:17 2004 Input: P := PolynomialRing(Rationals()); C := HyperellipticCurve(x*(x-1)*(x-2)*(x-3)*(x-4)); D := QuadraticTwist(C,134); J := Jacobian(D); SetVerbose("JacHypSelmer", 2); TwoSelmerGroupData(J : Bound := 300); Output: Magma V2.10-6 Sun Jan 25 2004 10:04:13 on modular [Seed = 2902406695] ------------------------------------- TwoSelmerGroupData of Jacobian of Hyperelliptic Curve defined by y^2 = 134*x^5 - 1340*x^4 + 4690*x^3 - 6700*x^2 + 3216*x over Rational Field m= Mapping from: CrvHyp: C to CrvHyp: C1 with equations : 134*$.1 17956*$.2 $.3 and inverse 1/134*$.1 1/17956*$.2 $.3 Change curve into Hyperelliptic Curve defined by y^2 = x^5 - 1340*x^4 + 628460*x^3 - 120305200*x^2 + 7738030464*x over Rational Field Bad primes = [ 2, 3, 67 ] f factors as (x - 536) (x - 402) (x - 268) (x - 134) (x). For factor x - 536, use field defined by x - 1 and theta = 536 For factor x - 402, use field defined by x - 1 and theta = 402 For factor x - 268, use field defined by x - 1 and theta = 268 For factor x - 134, use field defined by x - 1 and theta = 134 For factor x, use field defined by x - 1 and theta = 0 The 2-torsion group has dimension 4. Determining local images... p = 2 x = 1 --> new generator (0 0 0 0 1 1 0 0 1 0 1 0 0 0 0) x = 42 --> new generator (1 0 0 1 1 0 1 1 1 0 0 0 1 0 1) p = 3 x = 3 --> new generator (0 0 1 1 0 1 0 0 1 0) p = 67 p = infinity Computing class groups... Class group data of the fields: Field given by x - 536: [] Field given by x - 402: [] Field given by x - 268: [] Field given by x - 134: [] Field given by x: [] Dimension of Cl[2] = 0. Signatures: [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] Dimension of units mod squares = 5. Upper bound for Selmer group dimension: 13. ==> Upper bound for rank = 9. Computing unit groups... Class group and unit data of the fields: Field given by x - 536: Class group = [], units = [ 2 ] Field given by x - 402: Class group = [], units = [ 2 ] Field given by x - 268: Class group = [], units = [ 2 ] Field given by x - 134: Class group = [], units = [ 2 ] Field given by x: Class group = [], units = [ 2 ] Time for local computations: 1121 ms. Time for class groups: 0 ms. Time for unit groups: 0 ms. Selmer group dimension = 5, Dimension of 2-torsion = 4, ==> Bound for the MW-rank = 1. Total time: 1221 ms. Transforming presentation of S back to model C. 1 5 <[ 2291/4*$.1^4 - 11297/2*$.1^3 + 78147/4*$.1^2 - 27794*$.1 + 13467, -17/2*$.1^4 + 51*$.1^3 - 59*$.1^2 - 105/2*$.1 + 67, 1122*$.1^4 - 22507/2*$.1^3 + 78877/2*$.1^2 - 56239*$.1 + 26934, 10*$.1^4 - 183/2*$.1^3 + 302*$.1^2 - 835/2*$.1 + 201, 162*$.1^4 - 1620*$.1^3 + 5770*$.1^2 - 8600*$.1 + 4489 ], [], []> {} Total time: 4.489 seconds, Total memory usage: 2.69MB ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Sun Jan 25 10:04:33 2004 Input: P := PolynomialRing(Rationals()); C := HyperellipticCurve(x*(x-1)*(x-2)*(x-3)*(x-4)); D := QuadraticTwist(C,137); J := Jacobian(D); SetVerbose("JacHypSelmer", 2); TwoSelmerGroupData(J : Bound := 300); Output: Magma V2.10-6 Sun Jan 25 2004 10:04:30 on modular [Seed = 3051761453] ------------------------------------- TwoSelmerGroupData of Jacobian of Hyperelliptic Curve defined by y^2 = 137*x^5 - 1370*x^4 + 4795*x^3 - 6850*x^2 + 3288*x over Rational Field m= Mapping from: CrvHyp: C to CrvHyp: C1 with equations : 137*$.1 18769*$.2 $.3 and inverse 1/137*$.1 1/18769*$.2 $.3 Change curve into Hyperelliptic Curve defined by y^2 = x^5 - 1370*x^4 + 656915*x^3 - 128567650*x^2 + 8454608664*x over Rational Field Bad primes = [ 2, 3, 137 ] f factors as (x - 548) (x - 411) (x - 274) (x - 137) (x). For factor x - 548, use field defined by x - 1 and theta = 548 For factor x - 411, use field defined by x - 1 and theta = 411 For factor x - 274, use field defined by x - 1 and theta = 274 For factor x - 137, use field defined by x - 1 and theta = 137 For factor x, use field defined by x - 1 and theta = 0 The 2-torsion group has dimension 4. Determining local images... p = 2 x = 1/4 --> new generator (0 0 0 0 0 1 0 0 0 0 0 1 0 0 0) x = 6 --> new generator (1 0 0 0 1 0 0 0 1 0 0 1 1 1 0) p = 3 x = 3 --> new generator (0 0 1 1 0 1 0 0 1 0) p = 137 p = infinity Computing class groups... Class group data of the fields: Field given by x - 548: [] Field given by x - 411: [] Field given by x - 274: [] Field given by x - 137: [] Field given by x: [] Dimension of Cl[2] = 0. Signatures: [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] Dimension of units mod squares = 5. Upper bound for Selmer group dimension: 13. ==> Upper bound for rank = 9. Computing unit groups... Class group and unit data of the fields: Field given by x - 548: Class group = [], units = [ 2 ] Field given by x - 411: Class group = [], units = [ 2 ] Field given by x - 274: Class group = [], units = [ 2 ] Field given by x - 137: Class group = [], units = [ 2 ] Field given by x: Class group = [], units = [ 2 ] Time for local computations: 551 ms. Time for class groups: 0 ms. Time for unit groups: 9 ms. Selmer group dimension = 6, Dimension of 2-torsion = 4, ==> Bound for the MW-rank = 2. Total time: 650 ms. Transforming presentation of S back to model C. 2 6 <[ 12513/8*$.1^4 - 62291/4*$.1^3 + 434115/8*$.1^2 - 309531/4*$.1 + 37538, 85*$.1^4 - 783*$.1^3 + 2370*$.1^2 - 2494*$.1 + 411, 12513/4*$.1^4 - 62427/2*$.1^3 + 436027/4*$.1^2 - 311173/2*$.1 + 75076, -825/8*$.1^4 + 3571/4*$.1^3 - 18931/8*$.1^2 + 6307/4*$.1 + 822, 765*$.1^4 - 7650*$.1^3 + 26843*$.1^2 - 38590*$.1 + 18769, -17*$.1^4 + 102*$.1^3 - 119*$.1^2 - 102*$.1 + 137 ], [], []> {} Total time: 3.769 seconds, Total memory usage: 2.79MB ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Sun Jan 25 10:04:54 2004 Input: P := PolynomialRing(Rationals()); C := HyperellipticCurve(x*(x-1)*(x-2)*(x-3)*(x-4)); D := QuadraticTwist(C,138); J := Jacobian(D); SetVerbose("JacHypSelmer", 2); TwoSelmerGroupData(J : Bound := 300); Output: Magma V2.10-6 Sun Jan 25 2004 10:04:50 on modular [Seed = 3135840718] ------------------------------------- TwoSelmerGroupData of Jacobian of Hyperelliptic Curve defined by y^2 = 138*x^5 - 1380*x^4 + 4830*x^3 - 6900*x^2 + 3312*x over Rational Field m= Mapping from: CrvHyp: C to CrvHyp: C1 with equations : 138*$.1 19044*$.2 $.3 and inverse 1/138*$.1 1/19044*$.2 $.3 Change curve into Hyperelliptic Curve defined by y^2 = x^5 - 1380*x^4 + 666540*x^3 - 131403600*x^2 + 8704174464*x over Rational Field Bad primes = [ 2, 3, 23 ] f factors as (x - 552) (x - 414) (x - 276) (x - 138) (x). For factor x - 552, use field defined by x - 1 and theta = 552 For factor x - 414, use field defined by x - 1 and theta = 414 For factor x - 276, use field defined by x - 1 and theta = 276 For factor x - 138, use field defined by x - 1 and theta = 138 For factor x, use field defined by x - 1 and theta = 0 The 2-torsion group has dimension 4. Determining local images... p = 2 x = 1 --> new generator (0 0 0 0 1 0 0 0 1 0 1 1 0 0 0) x = 34 --> new generator (1 0 1 0 0 0 1 1 1 1 1 0 1 0 0) p = 3 p = 23 p = infinity Computing class groups... Class group data of the fields: Field given by x - 552: [] Field given by x - 414: [] Field given by x - 276: [] Field given by x - 138: [] Field given by x: [] Dimension of Cl[2] = 0. Signatures: [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] Dimension of units mod squares = 5. Upper bound for Selmer group dimension: 15. ==> Upper bound for rank = 11. Computing unit groups... Class group and unit data of the fields: Field given by x - 552: Class group = [], units = [ 2 ] Field given by x - 414: Class group = [], units = [ 2 ] Field given by x - 276: Class group = [], units = [ 2 ] Field given by x - 138: Class group = [], units = [ 2 ] Field given by x: Class group = [], units = [ 2 ] Time for local computations: 1060 ms. Time for class groups: 0 ms. Time for unit groups: 1 ms. Selmer group dimension = 6, Dimension of 2-torsion = 4, ==> Bound for the MW-rank = 2. Total time: 1170 ms. Transforming presentation of S back to model C. 2 6 <[ 25*$.1^4 - 242*$.1^3 + 815*$.1^2 - 1126*$.1 + 529, 20*$.1^4 - 208*$.1^3 + 760*$.1^2 - 1124*$.1 + 529, 1639/4*$.1^4 - 12224/3*$.1^3 + 56593/4*$.1^2 - 60007/3*$.1 + 9522, 64*$.1^4 - 1954/3*$.1^3 + 2309*$.1^2 - 9920/3*$.1 + 1587, -1/2*$.1^4 + 14/3*$.1^3 - 14*$.1^2 + 77/6*$.1 + 3, 54545/12*$.1^4 - 90977/2*$.1^3 + 1912099/12*$.1^2 - 455665/2*$.1 + 109503 ], [], []> {} Total time: 4.309 seconds, Total memory usage: 2.69MB ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Sun Jan 25 10:05:08 2004 Input: P := PolynomialRing(Rationals()); C := HyperellipticCurve(x*(x-1)*(x-2)*(x-3)*(x-4)); D := QuadraticTwist(C,139); J := Jacobian(D); SetVerbose("JacHypSelmer", 2); TwoSelmerGroupData(J : Bound := 300); Output: Magma V2.10-6 Sun Jan 25 2004 10:05:04 on modular [Seed = 2413565129] ------------------------------------- TwoSelmerGroupData of Jacobian of Hyperelliptic Curve defined by y^2 = 139*x^5 - 1390*x^4 + 4865*x^3 - 6950*x^2 + 3336*x over Rational Field m= Mapping from: CrvHyp: C to CrvHyp: C1 with equations : 139*$.1 19321*$.2 $.3 and inverse 1/139*$.1 1/19321*$.2 $.3 Change curve into Hyperelliptic Curve defined by y^2 = x^5 - 1390*x^4 + 676235*x^3 - 134280950*x^2 + 8959224984*x over Rational Field Bad primes = [ 2, 3, 139 ] f factors as (x - 556) (x - 417) (x - 278) (x - 139) (x). For factor x - 556, use field defined by x - 1 and theta = 556 For factor x - 417, use field defined by x - 1 and theta = 417 For factor x - 278, use field defined by x - 1 and theta = 278 For factor x - 139, use field defined by x - 1 and theta = 139 For factor x, use field defined by x - 1 and theta = 0 The 2-torsion group has dimension 4. Determining local images... p = 2 x = 1/4 --> new generator (0 0 0 0 0 1 0 0 0 0 0 1 0 0 0) x = 10 --> new generator (1 1 1 0 0 0 0 0 1 0 1 1 1 0 1) p = 3 x = 1 --> new generator (1 0 0 0 0 1 1 1 0 0) p = 139 p = infinity Computing class groups... Class group data of the fields: Field given by x - 556: [] Field given by x - 417: [] Field given by x - 278: [] Field given by x - 139: [] Field given by x: [] Dimension of Cl[2] = 0. Signatures: [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] Dimension of units mod squares = 5. Upper bound for Selmer group dimension: 13. ==> Upper bound for rank = 9. Computing unit groups... Class group and unit data of the fields: Field given by x - 556: Class group = [], units = [ 2 ] Field given by x - 417: Class group = [], units = [ 2 ] Field given by x - 278: Class group = [], units = [ 2 ] Field given by x - 139: Class group = [], units = [ 2 ] Field given by x: Class group = [], units = [ 2 ] Time for local computations: 531 ms. Time for class groups: 0 ms. Time for unit groups: 0 ms. Selmer group dimension = 5, Dimension of 2-torsion = 4, ==> Bound for the MW-rank = 1. Total time: 639 ms. Transforming presentation of S back to model C. 1 5 <[ 13295/8*$.1^4 - 66197/4*$.1^3 + 459773/8*$.1^2 - 324893/4*$.1 + 38642, 75*$.1^4 - 681*$.1^3 + 2004*$.1^2 - 1954*$.1 + 139, 1790321/4*$.1^4 - 8951603/2*$.1^3 + 62661211/4*$.1^2 - 44758281/2*$.1 + 10742476, 11403/8*$.1^4 - 58121/4*$.1^3 + 416809/8*$.1^2 - 307217/4*$.1 + 38642, -52*$.1^4 + 312*$.1^3 - 364*$.1^2 - 312*$.1 + 417 ], [], []> {} Total time: 3.759 seconds, Total memory usage: 2.79MB ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Sun Jan 25 10:05:23 2004 Input: P := PolynomialRing(Rationals()); C := HyperellipticCurve(x*(x-1)*(x-2)*(x-3)*(x-4)); D := QuadraticTwist(C,141); J := Jacobian(D); SetVerbose("JacHypSelmer", 2); TwoSelmerGroupData(J : Bound := 300); Output: Magma V2.10-6 Sun Jan 25 2004 10:05:19 on modular [Seed = 2496073693] ------------------------------------- TwoSelmerGroupData of Jacobian of Hyperelliptic Curve defined by y^2 = 141*x^5 - 1410*x^4 + 4935*x^3 - 7050*x^2 + 3384*x over Rational Field m= Mapping from: CrvHyp: C to CrvHyp: C1 with equations : 141*$.1 19881*$.2 $.3 and inverse 1/141*$.1 1/19881*$.2 $.3 Change curve into Hyperelliptic Curve defined by y^2 = x^5 - 1410*x^4 + 695835*x^3 - 140161050*x^2 + 9486099864*x over Rational Field Bad primes = [ 2, 3, 47 ] f factors as (x - 564) (x - 423) (x - 282) (x - 141) (x). For factor x - 564, use field defined by x - 1 and theta = 564 For factor x - 423, use field defined by x - 1 and theta = 423 For factor x - 282, use field defined by x - 1 and theta = 282 For factor x - 141, use field defined by x - 1 and theta = 141 For factor x, use field defined by x - 1 and theta = 0 The 2-torsion group has dimension 4. Determining local images... p = 2 x = 1/4 --> new generator (0 0 0 0 0 1 0 0 0 0 0 1 0 0 0) x = 14 --> new generator (1 0 1 0 1 1 0 0 1 0 0 0 1 1 1) p = 3 p = 47 p = infinity Computing class groups... Class group data of the fields: Field given by x - 564: [] Field given by x - 423: [] Field given by x - 282: [] Field given by x - 141: [] Field given by x: [] Dimension of Cl[2] = 0. Signatures: [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] Dimension of units mod squares = 5. Upper bound for Selmer group dimension: 15. ==> Upper bound for rank = 11. Computing unit groups... Class group and unit data of the fields: Field given by x - 564: Class group = [], units = [ 2 ] Field given by x - 423: Class group = [], units = [ 2 ] Field given by x - 282: Class group = [], units = [ 2 ] Field given by x - 141: Class group = [], units = [ 2 ] Field given by x: Class group = [], units = [ 2 ] Time for local computations: 549 ms. Time for class groups: 0 ms. Time for unit groups: 0 ms. Selmer group dimension = 6, Dimension of 2-torsion = 4, ==> Bound for the MW-rank = 2. Total time: 670 ms. Transforming presentation of S back to model C. 2 6 <[ 98*$.1^4 - 964*$.1^3 + 3310*$.1^2 - 4652*$.1 + 2209, 88*$.1^4 - 896*$.1^3 + 3200*$.1^2 - 4648*$.1 + 2209, 933985/12*$.1^4 - 778391*$.1^3 + 32695655/12*$.1^2 - 3892752*$.1 + 1868814, 17/3*$.1^4 - 105*$.1^3 + 1888/3*$.1^2 - 1517*$.1 + 1269, 41255/24*$.1^4 - 204869/12*$.1^3 + 1420885/24*$.1^2 - 1003309/12*$.1 + 39762, 280*$.1^4 - 8399/3*$.1^3 + 9775*$.1^2 - 41644/3*$.1 + 6627 ], [], []> {} Total time: 3.829 seconds, Total memory usage: 2.69MB ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Sun Jan 25 10:05:39 2004 Input: P := PolynomialRing(Rationals()); C := HyperellipticCurve(x*(x-1)*(x-2)*(x-3)*(x-4)); D := QuadraticTwist(C,142); J := Jacobian(D); SetVerbose("JacHypSelmer", 2); TwoSelmerGroupData(J : Bound := 300); Output: Magma V2.10-6 Sun Jan 25 2004 10:05:34 on modular [Seed = 2647525061] ------------------------------------- TwoSelmerGroupData of Jacobian of Hyperelliptic Curve defined by y^2 = 142*x^5 - 1420*x^4 + 4970*x^3 - 7100*x^2 + 3408*x over Rational Field m= Mapping from: CrvHyp: C to CrvHyp: C1 with equations : 142*$.1 20164*$.2 $.3 and inverse 1/142*$.1 1/20164*$.2 $.3 Change curve into Hyperelliptic Curve defined by y^2 = x^5 - 1420*x^4 + 705740*x^3 - 143164400*x^2 + 9758085504*x over Rational Field Bad primes = [ 2, 3, 71 ] f factors as (x - 568) (x - 426) (x - 284) (x - 142) (x). For factor x - 568, use field defined by x - 1 and theta = 568 For factor x - 426, use field defined by x - 1 and theta = 426 For factor x - 284, use field defined by x - 1 and theta = 284 For factor x - 142, use field defined by x - 1 and theta = 142 For factor x, use field defined by x - 1 and theta = 0 The 2-torsion group has dimension 4. Determining local images... p = 2 x = 1 --> new generator (0 0 0 0 1 1 0 0 1 0 1 0 0 0 0) x = 2 --> new generator (1 0 1 1 1 0 1 1 0 0 0 1 1 0 0) p = 3 x = 4 --> new generator (1 0 0 0 0 1 1 1 0 0) p = 71 p = infinity Computing class groups... Class group data of the fields: Field given by x - 568: [] Field given by x - 426: [] Field given by x - 284: [] Field given by x - 142: [] Field given by x: [] Dimension of Cl[2] = 0. Signatures: [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] Dimension of units mod squares = 5. Upper bound for Selmer group dimension: 13. ==> Upper bound for rank = 9. Computing unit groups... Class group and unit data of the fields: Field given by x - 568: Class group = [], units = [ 2 ] Field given by x - 426: Class group = [], units = [ 2 ] Field given by x - 284: Class group = [], units = [ 2 ] Field given by x - 142: Class group = [], units = [ 2 ] Field given by x: Class group = [], units = [ 2 ] Time for local computations: 1060 ms. Time for class groups: 0 ms. Time for unit groups: 0 ms. Selmer group dimension = 6, Dimension of 2-torsion = 4, ==> Bound for the MW-rank = 2. Total time: 1160 ms. Transforming presentation of S back to model C. 2 6 <[ 219*$.1^4 - 2166*$.1^3 + 7485*$.1^2 - 10578*$.1 + 5041, 204*$.1^4 - 2064*$.1^3 + 7320*$.1^2 - 10572*$.1 + 5041, 23/4*$.1^4 - 70*$.1^3 + 1249/4*$.1^2 - 603*$.1 + 426, -83/4*$.1^4 + 367/2*$.1^3 - 2045/4*$.1^2 + 839/2*$.1 + 71, 14913*$.1^4 - 149118*$.1^3 + 1043695/2*$.1^2 - 1490823/2*$.1 + 357911, 178743/4*$.1^4 - 893927/2*$.1^3 + 6259117/4*$.1^2 - 4472043/2*$.1 + 1073733 ], [], []> {} Total time: 4.329 seconds, Total memory usage: 2.79MB ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Sun Jan 25 10:05:51 2004 Input: P := PolynomialRing(Rationals()); C := HyperellipticCurve(x*(x-1)*(x-2)*(x-3)*(x-4)); D := QuadraticTwist(C,143); J := Jacobian(D); SetVerbose("JacHypSelmer", 2); TwoSelmerGroupData(J : Bound := 300); Output: Magma V2.10-6 Sun Jan 25 2004 10:05:47 on modular [Seed = 1664153679] ------------------------------------- TwoSelmerGroupData of Jacobian of Hyperelliptic Curve defined by y^2 = 143*x^5 - 1430*x^4 + 5005*x^3 - 7150*x^2 + 3432*x over Rational Field m= Mapping from: CrvHyp: C to CrvHyp: C1 with equations : 143*$.1 20449*$.2 $.3 and inverse 1/143*$.1 1/20449*$.2 $.3 Change curve into Hyperelliptic Curve defined by y^2 = x^5 - 1430*x^4 + 715715*x^3 - 146210350*x^2 + 10035878424*x over Rational Field Bad primes = [ 2, 3, 11, 13 ] f factors as (x - 572) (x - 429) (x - 286) (x - 143) (x). For factor x - 572, use field defined by x - 1 and theta = 572 For factor x - 429, use field defined by x - 1 and theta = 429 For factor x - 286, use field defined by x - 1 and theta = 286 For factor x - 143, use field defined by x - 1 and theta = 143 For factor x, use field defined by x - 1 and theta = 0 The 2-torsion group has dimension 4. Determining local images... p = 2 x = 1/4 --> new generator (0 0 0 0 0 1 0 0 0 0 0 1 0 0 0) x = 18 --> new generator (1 1 0 0 0 1 0 0 1 0 1 0 1 0 0) p = 3 x = 3 --> new generator (0 0 1 1 0 1 0 0 1 0) p = 11 p = 13 p = infinity Computing class groups... Class group data of the fields: Field given by x - 572: [] Field given by x - 429: [] Field given by x - 286: [] Field given by x - 143: [] Field given by x: [] Dimension of Cl[2] = 0. Signatures: [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] Dimension of units mod squares = 5. Upper bound for Selmer group dimension: 17. ==> Upper bound for rank = 13. Computing unit groups... Class group and unit data of the fields: Field given by x - 572: Class group = [], units = [ 2 ] Field given by x - 429: Class group = [], units = [ 2 ] Field given by x - 286: Class group = [], units = [ 2 ] Field given by x - 143: Class group = [], units = [ 2 ] Field given by x: Class group = [], units = [ 2 ] Time for local computations: 560 ms. Time for class groups: 0 ms. Time for unit groups: 0 ms. Selmer group dimension = 4, Dimension of 2-torsion = 4, ==> Bound for the MW-rank = 0. Total time: 710 ms. Transforming presentation of S back to model C. 0 4 <[ 14059/8*$.1^4 - 70009/4*$.1^3 + 486353/8*$.1^2 - 343777/4*$.1 + 40898, 2556*$.1^4 - 25703*$.1^3 + 90319*$.1^2 - 128948*$.1 + 61347, 1949377/4*$.1^4 - 9746883/2*$.1^3 + 68228171/4*$.1^2 - 48734689/2*$.1 + 11696828, -861/8*$.1^4 + 3727/4*$.1^3 - 19759/8*$.1^2 + 6583/4*$.1 + 858 ], [], []> {} Total time: 3.829 seconds, Total memory usage: 2.89MB ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Sun Jan 25 10:06:06 2004 Input: P := PolynomialRing(Rationals()); C := HyperellipticCurve(x*(x-1)*(x-2)*(x-3)*(x-4)); D := QuadraticTwist(C,145); J := Jacobian(D); SetVerbose("JacHypSelmer", 2); TwoSelmerGroupData(J : Bound := 300); Output: Magma V2.10-6 Sun Jan 25 2004 10:06:02 on modular [Seed = 1765470804] ------------------------------------- TwoSelmerGroupData of Jacobian of Hyperelliptic Curve defined by y^2 = 145*x^5 - 1450*x^4 + 5075*x^3 - 7250*x^2 + 3480*x over Rational Field m= Mapping from: CrvHyp: C to CrvHyp: C1 with equations : 145*$.1 21025*$.2 $.3 and inverse 1/145*$.1 1/21025*$.2 $.3 Change curve into Hyperelliptic Curve defined by y^2 = x^5 - 1450*x^4 + 735875*x^3 - 152431250*x^2 + 10609215000*x over Rational Field Bad primes = [ 2, 3, 5, 29 ] f factors as (x - 580) (x - 435) (x - 290) (x - 145) (x). For factor x - 580, use field defined by x - 1 and theta = 580 For factor x - 435, use field defined by x - 1 and theta = 435 For factor x - 290, use field defined by x - 1 and theta = 290 For factor x - 145, use field defined by x - 1 and theta = 145 For factor x, use field defined by x - 1 and theta = 0 The 2-torsion group has dimension 4. Determining local images... p = 2 x = 1/4 --> new generator (0 0 0 0 0 1 0 0 0 0 0 1 0 0 0) x = 22 --> new generator (1 0 0 0 1 0 0 0 1 0 0 1 1 1 0) p = 3 x = 7 --> new generator (1 0 0 0 0 1 1 1 0 0) p = 5 p = 29 p = infinity Computing class groups... Class group data of the fields: Field given by x - 580: [] Field given by x - 435: [] Field given by x - 290: [] Field given by x - 145: [] Field given by x: [] Dimension of Cl[2] = 0. Signatures: [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] Dimension of units mod squares = 5. Upper bound for Selmer group dimension: 17. ==> Upper bound for rank = 13. Computing unit groups... Class group and unit data of the fields: Field given by x - 580: Class group = [], units = [ 2 ] Field given by x - 435: Class group = [], units = [ 2 ] Field given by x - 290: Class group = [], units = [ 2 ] Field given by x - 145: Class group = [], units = [ 2 ] Field given by x: Class group = [], units = [ 2 ] Time for local computations: 580 ms. Time for class groups: 0 ms. Time for unit groups: 0 ms. Selmer group dimension = 4, Dimension of 2-torsion = 4, ==> Bound for the MW-rank = 0. Total time: 719 ms. Transforming presentation of S back to model C. 0 4 <[ 14449/8*$.1^4 - 71955/4*$.1^3 + 499923/8*$.1^2 - 353419/4*$.1 + 42050, 2628*$.1^4 - 26425*$.1^3 + 92851*$.1^2 - 132564*$.1 + 63075, 2032321/4*$.1^4 - 10161603/2*$.1^3 + 71131211/4*$.1^2 - 50808293/2*$.1 + 12194500, -873/8*$.1^4 + 3779/4*$.1^3 - 20035/8*$.1^2 + 6675/4*$.1 + 870 ], [], []> {} Total time: 3.819 seconds, Total memory usage: 2.79MB ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Sun Jan 25 10:06:20 2004 Input: P := PolynomialRing(Rationals()); C := HyperellipticCurve(x*(x-1)*(x-2)*(x-3)*(x-4)); D := QuadraticTwist(C,146); J := Jacobian(D); SetVerbose("JacHypSelmer", 2); TwoSelmerGroupData(J : Bound := 300); Output: Magma V2.10-6 Sun Jan 25 2004 10:06:16 on modular [Seed = 1881402239] ------------------------------------- TwoSelmerGroupData of Jacobian of Hyperelliptic Curve defined by y^2 = 146*x^5 - 1460*x^4 + 5110*x^3 - 7300*x^2 + 3504*x over Rational Field m= Mapping from: CrvHyp: C to CrvHyp: C1 with equations : 146*$.1 21316*$.2 $.3 and inverse 1/146*$.1 1/21316*$.2 $.3 Change curve into Hyperelliptic Curve defined by y^2 = x^5 - 1460*x^4 + 746060*x^3 - 155606800*x^2 + 10904924544*x over Rational Field Bad primes = [ 2, 3, 73 ] f factors as (x - 584) (x - 438) (x - 292) (x - 146) (x). For factor x - 584, use field defined by x - 1 and theta = 584 For factor x - 438, use field defined by x - 1 and theta = 438 For factor x - 292, use field defined by x - 1 and theta = 292 For factor x - 146, use field defined by x - 1 and theta = 146 For factor x, use field defined by x - 1 and theta = 0 The 2-torsion group has dimension 4. Determining local images... p = 2 x = 1 --> new generator (0 0 0 0 1 0 0 0 1 0 1 1 0 0 0) x = 42 --> new generator (1 0 0 0 0 1 1 1 0 1 1 0 1 0 1) p = 3 x = 3 --> new generator (0 0 1 1 0 1 0 0 1 0) p = 73 p = infinity Computing class groups... Class group data of the fields: Field given by x - 584: [] Field given by x - 438: [] Field given by x - 292: [] Field given by x - 146: [] Field given by x: [] Dimension of Cl[2] = 0. Signatures: [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] Dimension of units mod squares = 5. Upper bound for Selmer group dimension: 13. ==> Upper bound for rank = 9. Computing unit groups... Class group and unit data of the fields: Field given by x - 584: Class group = [], units = [ 2 ] Field given by x - 438: Class group = [], units = [ 2 ] Field given by x - 292: Class group = [], units = [ 2 ] Field given by x - 146: Class group = [], units = [ 2 ] Field given by x: Class group = [], units = [ 2 ] Time for local computations: 1100 ms. Time for class groups: 0 ms. Time for unit groups: 0 ms. Selmer group dimension = 8, Dimension of 2-torsion = 4, ==> Bound for the MW-rank = 4. Total time: 1200 ms. Transforming presentation of S back to model C. 4 8 <[ $.1^3 - 13/2*$.1^2 + 17/2*$.1 + 3, -1/4*$.1^4 + 3/2*$.1^3 - 5/4*$.1^2 - 3*$.1 + 1, -1/2*$.1^3 + 7/2*$.1^2 - 7*$.1 + 6, -9/4*$.1^4 + 19*$.1^3 - 203/4*$.1^2 + 43*$.1 + 3, 6*$.1^4 - 48*$.1^3 + 138*$.1^2 - 168*$.1 + 73, -9*$.1^4 + 54*$.1^3 - 63*$.1^2 - 54*$.1 + 73, 21*$.1^4 - 174*$.1^3 + 447*$.1^2 - 366*$.1 + 73, -9*$.1^4 + 78*$.1^3 - 207*$.1^2 + 138*$.1 + 73 ], [], []> {} Total time: 4.369 seconds, Total memory usage: 2.79MB ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Sun Jan 25 10:06:39 2004 Input: P := PolynomialRing(Rationals()); C := HyperellipticCurve(x*(x-1)*(x-2)*(x-3)*(x-4)); D := QuadraticTwist(C,149); J := Jacobian(D); SetVerbose("JacHypSelmer", 2); TwoSelmerGroupData(J : Bound := 300); Output: Magma V2.10-6 Sun Jan 25 2004 10:06:35 on modular [Seed = 1192549467] ------------------------------------- TwoSelmerGroupData of Jacobian of Hyperelliptic Curve defined by y^2 = 149*x^5 - 1490*x^4 + 5215*x^3 - 7450*x^2 + 3576*x over Rational Field m= Mapping from: CrvHyp: C to CrvHyp: C1 with equations : 149*$.1 22201*$.2 $.3 and inverse 1/149*$.1 1/22201*$.2 $.3 Change curve into Hyperelliptic Curve defined by y^2 = x^5 - 1490*x^4 + 777035*x^3 - 165397450*x^2 + 11829225624*x over Rational Field Bad primes = [ 2, 3, 149 ] f factors as (x - 596) (x - 447) (x - 298) (x - 149) (x). For factor x - 596, use field defined by x - 1 and theta = 596 For factor x - 447, use field defined by x - 1 and theta = 447 For factor x - 298, use field defined by x - 1 and theta = 298 For factor x - 149, use field defined by x - 1 and theta = 149 For factor x, use field defined by x - 1 and theta = 0 The 2-torsion group has dimension 4. Determining local images... p = 2 x = 1/4 --> new generator (0 0 0 0 0 1 0 0 0 0 0 1 0 0 0) x = 30 --> new generator (1 0 1 0 1 1 0 0 1 0 0 0 1 1 1) p = 3 x = 3 --> new generator (0 0 1 1 0 1 0 0 1 0) p = 149 p = infinity Computing class groups... Class group data of the fields: Field given by x - 596: [] Field given by x - 447: [] Field given by x - 298: [] Field given by x - 149: [] Field given by x: [] Dimension of Cl[2] = 0. Signatures: [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] Dimension of units mod squares = 5. Upper bound for Selmer group dimension: 13. ==> Upper bound for rank = 9. Computing unit groups... Class group and unit data of the fields: Field given by x - 596: Class group = [], units = [ 2 ] Field given by x - 447: Class group = [], units = [ 2 ] Field given by x - 298: Class group = [], units = [ 2 ] Field given by x - 149: Class group = [], units = [ 2 ] Field given by x: Class group = [], units = [ 2 ] Time for local computations: 540 ms. Time for class groups: 0 ms. Time for unit groups: 0 ms. Selmer group dimension = 5, Dimension of 2-torsion = 4, ==> Bound for the MW-rank = 1. Total time: 649 ms. Transforming presentation of S back to model C. 1 5 <[ 2788*$.1^4 - 27829*$.1^3 + 97198*$.1^2 - 138611*$.1 + 66603, 2775*$.1^4 - 27899*$.1^3 + 98020*$.1^2 - 139946*$.1 + 66603, 3307849/4*$.1^4 - 8269722*$.1^3 + 115777403/4*$.1^2 - 41349284*$.1 + 19847694, 12*$.1^4 - 96*$.1^3 + 277*$.1^2 - 340*$.1 + 149, 43955/8*$.1^4 - 219777/4*$.1^3 + 1540233/8*$.1^2 - 1103353/4*$.1 + 133206 ], [], []> {} Total time: 3.749 seconds, Total memory usage: 2.89MB ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Sun Jan 25 10:06:53 2004 Input: P := PolynomialRing(Rationals()); C := HyperellipticCurve(x*(x-1)*(x-2)*(x-3)*(x-4)); D := QuadraticTwist(C,151); J := Jacobian(D); SetVerbose("JacHypSelmer", 2); TwoSelmerGroupData(J : Bound := 300); Output: Magma V2.10-6 Sun Jan 25 2004 10:06:50 on modular [Seed = 1310578083] ------------------------------------- TwoSelmerGroupData of Jacobian of Hyperelliptic Curve defined by y^2 = 151*x^5 - 1510*x^4 + 5285*x^3 - 7550*x^2 + 3624*x over Rational Field m= Mapping from: CrvHyp: C to CrvHyp: C1 with equations : 151*$.1 22801*$.2 $.3 and inverse 1/151*$.1 1/22801*$.2 $.3 Change curve into Hyperelliptic Curve defined by y^2 = x^5 - 1510*x^4 + 798035*x^3 - 172147550*x^2 + 12477254424*x over Rational Field Bad primes = [ 2, 3, 151 ] f factors as (x - 604) (x - 453) (x - 302) (x - 151) (x). For factor x - 604, use field defined by x - 1 and theta = 604 For factor x - 453, use field defined by x - 1 and theta = 453 For factor x - 302, use field defined by x - 1 and theta = 302 For factor x - 151, use field defined by x - 1 and theta = 151 For factor x, use field defined by x - 1 and theta = 0 The 2-torsion group has dimension 4. Determining local images... p = 2 x = 1/4 --> new generator (0 0 0 0 0 1 0 0 0 0 0 1 0 0 0) x = 2 --> new generator (1 1 0 0 0 1 0 0 1 0 1 0 1 0 0) p = 3 x = 4 --> new generator (1 0 0 0 0 1 1 1 0 0) p = 151 p = infinity Computing class groups... Class group data of the fields: Field given by x - 604: [] Field given by x - 453: [] Field given by x - 302: [] Field given by x - 151: [] Field given by x: [] Dimension of Cl[2] = 0. Signatures: [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] Dimension of units mod squares = 5. Upper bound for Selmer group dimension: 13. ==> Upper bound for rank = 9. Computing unit groups... Class group and unit data of the fields: Field given by x - 604: Class group = [], units = [ 2 ] Field given by x - 453: Class group = [], units = [ 2 ] Field given by x - 302: Class group = [], units = [ 2 ] Field given by x - 151: Class group = [], units = [ 2 ] Field given by x: Class group = [], units = [ 2 ] Time for local computations: 511 ms. Time for class groups: 0 ms. Time for unit groups: 0 ms. Selmer group dimension = 4, Dimension of 2-torsion = 4, ==> Bound for the MW-rank = 0. Total time: 619 ms. Transforming presentation of S back to model C. 0 4 <[ 15651/8*$.1^4 - 77953/4*$.1^3 + 541753/8*$.1^2 - 383145/4*$.1 + 45602, 2850*$.1^4 - 28651*$.1^3 + 100657*$.1^2 - 143712*$.1 + 68403, 2295201/4*$.1^4 - 11476003/2*$.1^3 + 80332011/4*$.1^2 - 57380305/2*$.1 + 13771804, -909/8*$.1^4 + 3935/4*$.1^3 - 20863/8*$.1^2 + 6951/4*$.1 + 906 ], [], []> {} Total time: 3.779 seconds, Total memory usage: 2.89MB ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Sun Jan 25 10:07:10 2004 Input: P := PolynomialRing(Rationals()); C := HyperellipticCurve(x*(x-1)*(x-2)*(x-3)*(x-4)); D := QuadraticTwist(C,154); J := Jacobian(D); SetVerbose("JacHypSelmer", 2); TwoSelmerGroupData(J : Bound := 300); Output: Magma V2.10-6 Sun Jan 25 2004 10:07:05 on modular [Seed = 1426509483] ------------------------------------- TwoSelmerGroupData of Jacobian of Hyperelliptic Curve defined by y^2 = 154*x^5 - 1540*x^4 + 5390*x^3 - 7700*x^2 + 3696*x over Rational Field m= Mapping from: CrvHyp: C to CrvHyp: C1 with equations : 154*$.1 23716*$.2 $.3 and inverse 1/154*$.1 1/23716*$.2 $.3 Change curve into Hyperelliptic Curve defined by y^2 = x^5 - 1540*x^4 + 830060*x^3 - 182613200*x^2 + 13498767744*x over Rational Field Bad primes = [ 2, 3, 7, 11 ] f factors as (x - 616) (x - 462) (x - 308) (x - 154) (x). For factor x - 616, use field defined by x - 1 and theta = 616 For factor x - 462, use field defined by x - 1 and theta = 462 For factor x - 308, use field defined by x - 1 and theta = 308 For factor x - 154, use field defined by x - 1 and theta = 154 For factor x, use field defined by x - 1 and theta = 0 The 2-torsion group has dimension 4. Determining local images... p = 2 x = 1 --> new generator (0 0 0 0 1 0 0 0 1 0 1 1 0 0 0) x = 50 --> new generator (1 0 1 0 0 0 1 1 1 1 1 0 1 0 0) p = 3 x = 7 --> new generator (1 0 0 0 0 1 1 1 0 0) p = 7 p = 11 p = infinity Computing class groups... Class group data of the fields: Field given by x - 616: [] Field given by x - 462: [] Field given by x - 308: [] Field given by x - 154: [] Field given by x: [] Dimension of Cl[2] = 0. Signatures: [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] Dimension of units mod squares = 5. Upper bound for Selmer group dimension: 17. ==> Upper bound for rank = 13. Computing unit groups... Class group and unit data of the fields: Field given by x - 616: Class group = [], units = [ 2 ] Field given by x - 462: Class group = [], units = [ 2 ] Field given by x - 308: Class group = [], units = [ 2 ] Field given by x - 154: Class group = [], units = [ 2 ] Field given by x: Class group = [], units = [ 2 ] Time for local computations: 1139 ms. Time for class groups: 0 ms. Time for unit groups: 0 ms. Selmer group dimension = 5, Dimension of 2-torsion = 4, ==> Bound for the MW-rank = 1. Total time: 1309 ms. Transforming presentation of S back to model C. 1 5 <[ 1843/4*$.1^4 - 9233/2*$.1^3 + 64841/4*$.1^2 - 46593/2*$.1 + 11319, 285*$.1^4 - 2810*$.1^3 + 9627*$.1^2 - 13262*$.1 + 5929, 9183/4*$.1^4 - 22981*$.1^3 + 322393/4*$.1^2 - 115584*$.1 + 55902, 666*$.1^4 - 6886*$.1^3 + 24891*$.1^2 - 36456*$.1 + 17787, 75749/4*$.1^4 - 378951/2*$.1^3 + 2654709/4*$.1^2 - 949210*$.1 + 456533 ], [], []> {} Total time: 4.449 seconds, Total memory usage: 2.79MB ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Sun Jan 25 10:07:22 2004 Input: P := PolynomialRing(Rationals()); C := HyperellipticCurve(x*(x-1)*(x-2)*(x-3)*(x-4)); D := QuadraticTwist(C,155); J := Jacobian(D); SetVerbose("JacHypSelmer", 2); TwoSelmerGroupData(J : Bound := 300); Output: Magma V2.10-6 Sun Jan 25 2004 10:07:18 on modular [Seed = 1544538013] ------------------------------------- TwoSelmerGroupData of Jacobian of Hyperelliptic Curve defined by y^2 = 155*x^5 - 1550*x^4 + 5425*x^3 - 7750*x^2 + 3720*x over Rational Field m= Mapping from: CrvHyp: C to CrvHyp: C1 with equations : 155*$.1 24025*$.2 $.3 and inverse 1/155*$.1 1/24025*$.2 $.3 Change curve into Hyperelliptic Curve defined by y^2 = x^5 - 1550*x^4 + 840875*x^3 - 186193750*x^2 + 13852815000*x over Rational Field Bad primes = [ 2, 3, 5, 31 ] f factors as (x - 620) (x - 465) (x - 310) (x - 155) (x). For factor x - 620, use field defined by x - 1 and theta = 620 For factor x - 465, use field defined by x - 1 and theta = 465 For factor x - 310, use field defined by x - 1 and theta = 310 For factor x - 155, use field defined by x - 1 and theta = 155 For factor x, use field defined by x - 1 and theta = 0 The 2-torsion group has dimension 4. Determining local images... p = 2 x = 1/4 --> new generator (0 0 0 0 0 1 0 0 0 0 0 1 0 0 0) x = 10 --> new generator (1 1 1 0 0 0 0 0 1 0 1 1 1 0 1) p = 3 x = 3 --> new generator (0 0 1 1 0 1 0 0 1 0) p = 5 p = 31 p = infinity Computing class groups... Class group data of the fields: Field given by x - 620: [] Field given by x - 465: [] Field given by x - 310: [] Field given by x - 155: [] Field given by x: [] Dimension of Cl[2] = 0. Signatures: [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] Dimension of units mod squares = 5. Upper bound for Selmer group dimension: 17. ==> Upper bound for rank = 13. Computing unit groups... Class group and unit data of the fields: Field given by x - 620: Class group = [], units = [ 2 ] Field given by x - 465: Class group = [], units = [ 2 ] Field given by x - 310: Class group = [], units = [ 2 ] Field given by x - 155: Class group = [], units = [ 2 ] Field given by x: Class group = [], units = [ 2 ] Time for local computations: 531 ms. Time for class groups: 0 ms. Time for unit groups: 0 ms. Selmer group dimension = 5, Dimension of 2-torsion = 4, ==> Bound for the MW-rank = 1. Total time: 679 ms. Transforming presentation of S back to model C. 1 5 <[ 93109*$.1^4 - 931042*$.1^3 + 3258448*$.1^2 - 4654685*$.1 + 2234325, 3003*$.1^4 - 30185*$.1^3 + 106036*$.1^2 - 151394*$.1 + 72075, 119971/4*$.1^4 - 300081*$.1^3 + 4202981/4*$.1^2 - 1501406*$.1 + 720750, $.1^2 - 4*$.1 + 5, 935/8*$.1^4 - 4977/4*$.1^3 + 38205/8*$.1^2 - 31333/4*$.1 + 4650 ], [], []> {} Total time: 3.809 seconds, Total memory usage: 2.79MB ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Sun Jan 25 10:07:36 2004 Input: P := PolynomialRing(Rationals()); C := HyperellipticCurve(x*(x-1)*(x-2)*(x-3)*(x-4)); D := QuadraticTwist(C,157); J := Jacobian(D); SetVerbose("JacHypSelmer", 2); TwoSelmerGroupData(J : Bound := 300); Output: Magma V2.10-6 Sun Jan 25 2004 10:07:32 on modular [Seed = 594589936] ------------------------------------- TwoSelmerGroupData of Jacobian of Hyperelliptic Curve defined by y^2 = 157*x^5 - 1570*x^4 + 5495*x^3 - 7850*x^2 + 3768*x over Rational Field m= Mapping from: CrvHyp: C to CrvHyp: C1 with equations : 157*$.1 24649*$.2 $.3 and inverse 1/157*$.1 1/24649*$.2 $.3 Change curve into Hyperelliptic Curve defined by y^2 = x^5 - 1570*x^4 + 862715*x^3 - 193494650*x^2 + 14581756824*x over Rational Field Bad primes = [ 2, 3, 157 ] f factors as (x - 628) (x - 471) (x - 314) (x - 157) (x). For factor x - 628, use field defined by x - 1 and theta = 628 For factor x - 471, use field defined by x - 1 and theta = 471 For factor x - 314, use field defined by x - 1 and theta = 314 For factor x - 157, use field defined by x - 1 and theta = 157 For factor x, use field defined by x - 1 and theta = 0 The 2-torsion group has dimension 4. Determining local images... p = 2 x = 1/4 --> new generator (0 0 0 0 0 1 0 0 0 0 0 1 0 0 0) x = 14 --> new generator (1 0 1 0 1 1 0 0 1 0 0 0 1 1 1) p = 3 x = 1 --> new generator (1 0 0 0 0 1 1 1 0 0) p = 157 p = infinity Computing class groups... Class group data of the fields: Field given by x - 628: [] Field given by x - 471: [] Field given by x - 314: [] Field given by x - 157: [] Field given by x: [] Dimension of Cl[2] = 0. Signatures: [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] Dimension of units mod squares = 5. Upper bound for Selmer group dimension: 13. ==> Upper bound for rank = 9. Computing unit groups... Class group and unit data of the fields: Field given by x - 628: Class group = [], units = [ 2 ] Field given by x - 471: Class group = [], units = [ 2 ] Field given by x - 314: Class group = [], units = [ 2 ] Field given by x - 157: Class group = [], units = [ 2 ] Field given by x: Class group = [], units = [ 2 ] Time for local computations: 550 ms. Time for class groups: 0 ms. Time for unit groups: 11 ms. Selmer group dimension = 5, Dimension of 2-torsion = 4, ==> Bound for the MW-rank = 1. Total time: 659 ms. Transforming presentation of S back to model C. 1 5 <[ 16901/8*$.1^4 - 84191/4*$.1^3 + 585263/8*$.1^2 - 414071/4*$.1 + 49298, -$.1^3 + 7*$.1^2 - 12*$.1 + 3, 417/4*$.1^4 - 1771/2*$.1^3 + 9579/4*$.1^2 - 4477/2*$.1 + 628, -945/8*$.1^4 + 4091/4*$.1^3 - 21691/8*$.1^2 + 7227/4*$.1 + 942, 975*$.1^4 - 9854*$.1^3 + 34905*$.1^2 - 50518*$.1 + 24649 ], [], []> {} Total time: 3.829 seconds, Total memory usage: 2.89MB ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Sun Jan 25 10:07:59 2004 Input: P := PolynomialRing(Rationals()); C := HyperellipticCurve(x*(x-1)*(x-2)*(x-3)*(x-4)); D := QuadraticTwist(C,158); J := Jacobian(D); SetVerbose("JacHypSelmer", 2); TwoSelmerGroupData(J : Bound := 300); Output: Magma V2.10-6 Sun Jan 25 2004 10:07:54 on modular [Seed = 712618375] ------------------------------------- TwoSelmerGroupData of Jacobian of Hyperelliptic Curve defined by y^2 = 158*x^5 - 1580*x^4 + 5530*x^3 - 7900*x^2 + 3792*x over Rational Field m= Mapping from: CrvHyp: C to CrvHyp: C1 with equations : 158*$.1 24964*$.2 $.3 and inverse 1/158*$.1 1/24964*$.2 $.3 Change curve into Hyperelliptic Curve defined by y^2 = x^5 - 1580*x^4 + 873740*x^3 - 197215600*x^2 + 14956831104*x over Rational Field Bad primes = [ 2, 3, 79 ] f factors as (x - 632) (x - 474) (x - 316) (x - 158) (x). For factor x - 632, use field defined by x - 1 and theta = 632 For factor x - 474, use field defined by x - 1 and theta = 474 For factor x - 316, use field defined by x - 1 and theta = 316 For factor x - 158, use field defined by x - 1 and theta = 158 For factor x, use field defined by x - 1 and theta = 0 The 2-torsion group has dimension 4. Determining local images... p = 2 x = 1 --> new generator (0 0 0 0 1 1 0 0 1 0 1 0 0 0 0) x = 50 --> new generator (1 0 1 1 1 0 1 1 0 0 0 1 1 0 0) p = 3 x = 3 --> new generator (0 0 1 1 0 1 0 0 1 0) p = 79 p = infinity Computing class groups... Class group data of the fields: Field given by x - 632: [] Field given by x - 474: [] Field given by x - 316: [] Field given by x - 158: [] Field given by x: [] Dimension of Cl[2] = 0. Signatures: [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] Dimension of units mod squares = 5. Upper bound for Selmer group dimension: 13. ==> Upper bound for rank = 9. Computing unit groups... Class group and unit data of the fields: Field given by x - 632: Class group = [], units = [ 2 ] Field given by x - 474: Class group = [], units = [ 2 ] Field given by x - 316: Class group = [], units = [ 2 ] Field given by x - 158: Class group = [], units = [ 2 ] Field given by x: Class group = [], units = [ 2 ] Time for local computations: 1061 ms. Time for class groups: 0 ms. Time for unit groups: 0 ms. Selmer group dimension = 4, Dimension of 2-torsion = 4, ==> Bound for the MW-rank = 0. Total time: 1169 ms. Transforming presentation of S back to model C. 0 4 <[ 3237/4*$.1^4 - 16027/2*$.1^3 + 110929/4*$.1^2 - 39245*$.1 + 18723, -10*$.1^4 + 60*$.1^3 - 139/2*$.1^2 - 123/2*$.1 + 79, 1560*$.1^4 - 31279/2*$.1^3 + 109597/2*$.1^2 - 78163*$.1 + 37446, -297/2*$.1^4 + 2651/2*$.1^3 - 7531/2*$.1^2 + 6599/2*$.1 + 237 ], [], []> {} Total time: 4.329 seconds, Total memory usage: 2.79MB ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Sun Jan 25 10:10:57 2004 Input: P := PolynomialRing(Rationals()); C := HyperellipticCurve(x*(x-1)*(x-2)*(x-3)*(x-4)); D := QuadraticTwist(C,159); J := Jacobian(D); SetVerbose("JacHypSelmer", 2); TwoSelmerGroupData(J : Bound := 300); Output: Magma V2.10-6 Sun Jan 25 2004 10:10:53 on modular [Seed = 963290403] ------------------------------------- TwoSelmerGroupData of Jacobian of Hyperelliptic Curve defined by y^2 = 159*x^5 - 1590*x^4 + 5565*x^3 - 7950*x^2 + 3816*x over Rational Field m= Mapping from: CrvHyp: C to CrvHyp: C1 with equations : 159*$.1 25281*$.2 $.3 and inverse 1/159*$.1 1/25281*$.2 $.3 Change curve into Hyperelliptic Curve defined by y^2 = x^5 - 1590*x^4 + 884835*x^3 - 200983950*x^2 + 15339095064*x over Rational Field Bad primes = [ 2, 3, 53 ] f factors as (x - 636) (x - 477) (x - 318) (x - 159) (x). For factor x - 636, use field defined by x - 1 and theta = 636 For factor x - 477, use field defined by x - 1 and theta = 477 For factor x - 318, use field defined by x - 1 and theta = 318 For factor x - 159, use field defined by x - 1 and theta = 159 For factor x, use field defined by x - 1 and theta = 0 The 2-torsion group has dimension 4. Determining local images... p = 2 x = 1/4 --> new generator (0 0 0 0 0 1 0 0 0 0 0 1 0 0 0) x = 18 --> new generator (1 1 0 0 0 1 0 0 1 0 1 0 1 0 0) p = 3 p = 53 p = infinity Computing class groups... Class group data of the fields: Field given by x - 636: [] Field given by x - 477: [] Field given by x - 318: [] Field given by x - 159: [] Field given by x: [] Dimension of Cl[2] = 0. Signatures: [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] Dimension of units mod squares = 5. Upper bound for Selmer group dimension: 15. ==> Upper bound for rank = 11. Computing unit groups... Class group and unit data of the fields: Field given by x - 636: Class group = [], units = [ 2 ] Field given by x - 477: Class group = [], units = [ 2 ] Field given by x - 318: Class group = [], units = [ 2 ] Field given by x - 159: Class group = [], units = [ 2 ] Field given by x: Class group = [], units = [ 2 ] Time for local computations: 540 ms. Time for class groups: 0 ms. Time for unit groups: 0 ms. Selmer group dimension = 5, Dimension of 2-torsion = 4, ==> Bound for the MW-rank = 1. Total time: 651 ms. Transforming presentation of S back to model C. 1 5 <[ 99515/8*$.1^4 - 497293/4*$.1^3 + 3478585/8*$.1^2 - 2482769/4*$.1 + 297754, 351*$.1^4 - 10583/3*$.1^3 + 12392*$.1^2 - 53086/3*$.1 + 8427, 50561/4*$.1^4 - 252753/2*$.1^3 + 1768911/4*$.1^2 - 1263409/2*$.1 + 303372, 521/24*$.1^4 - 945/4*$.1^3 + 22291/24*$.1^2 - 6249/4*$.1 + 954, 34/3*$.1^4 - 416/3*$.1^3 + 1721/3*$.1^2 - 2761/3*$.1 + 477 ], [], []> {} Total time: 3.899 seconds, Total memory usage: 2.69MB ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Sun Jan 25 10:11:21 2004 Input: P := PolynomialRing(Rationals()); C := HyperellipticCurve(x*(x-1)*(x-2)*(x-3)*(x-4)); D := QuadraticTwist(C,161); J := Jacobian(D); SetVerbose("JacHypSelmer", 2); TwoSelmerGroupData(J : Bound := 300); Output: Magma V2.10-6 Sun Jan 25 2004 10:11:17 on modular [Seed = 257725437] ------------------------------------- TwoSelmerGroupData of Jacobian of Hyperelliptic Curve defined by y^2 = 161*x^5 - 1610*x^4 + 5635*x^3 - 8050*x^2 + 3864*x over Rational Field m= Mapping from: CrvHyp: C to CrvHyp: C1 with equations : 161*$.1 25921*$.2 $.3 and inverse 1/161*$.1 1/25921*$.2 $.3 Change curve into Hyperelliptic Curve defined by y^2 = x^5 - 1610*x^4 + 907235*x^3 - 208664050*x^2 + 16125557784*x over Rational Field Bad primes = [ 2, 3, 7, 23 ] f factors as (x - 644) (x - 483) (x - 322) (x - 161) (x). For factor x - 644, use field defined by x - 1 and theta = 644 For factor x - 483, use field defined by x - 1 and theta = 483 For factor x - 322, use field defined by x - 1 and theta = 322 For factor x - 161, use field defined by x - 1 and theta = 161 For factor x, use field defined by x - 1 and theta = 0 The 2-torsion group has dimension 4. Determining local images... p = 2 x = 1/4 --> new generator (0 0 0 0 0 1 0 0 0 0 0 1 0 0 0) x = 22 --> new generator (1 0 0 0 1 0 0 0 1 0 0 1 1 1 0) p = 3 x = 3 --> new generator (0 0 1 1 0 1 0 0 1 0) p = 7 p = 23 p = infinity Computing class groups... Class group data of the fields: Field given by x - 644: [] Field given by x - 483: [] Field given by x - 322: [] Field given by x - 161: [] Field given by x: [] Dimension of Cl[2] = 0. Signatures: [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] Dimension of units mod squares = 5. Upper bound for Selmer group dimension: 17. ==> Upper bound for rank = 13. Computing unit groups... Class group and unit data of the fields: Field given by x - 644: Class group = [], units = [ 2 ] Field given by x - 483: Class group = [], units = [ 2 ] Field given by x - 322: Class group = [], units = [ 2 ] Field given by x - 161: Class group = [], units = [ 2 ] Field given by x: Class group = [], units = [ 2 ] Time for local computations: 589 ms. Time for class groups: 0 ms. Time for unit groups: 0 ms. Selmer group dimension = 6, Dimension of 2-torsion = 4, ==> Bound for the MW-rank = 2. Total time: 750 ms. Transforming presentation of S back to model C. 2 6 <[ 303*$.1^4 - 3054*$.1^3 + 10825*$.1^2 - 15802*$.1 + 7889, 3520*$.1^4 - 35288*$.1^3 + 123820*$.1^2 - 177244*$.1 + 85169, 169/4*$.1^4 - 426*$.1^3 + 6043/4*$.1^2 - 2184*$.1 + 1058, 3274*$.1^4 - 32677*$.1^3 + 114073*$.1^2 - 162431*$.1 + 77763, 51819/8*$.1^4 - 259109/4*$.1^3 + 1813897/8*$.1^2 - 1295761/4*$.1 + 155526, 22*$.1^4 - 213*$.1^3 + 717*$.1^2 - 988*$.1 + 483 ], [], []> {} Total time: 3.859 seconds, Total memory usage: 2.69MB ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Sun Jan 25 10:11:34 2004 Input: P := PolynomialRing(Rationals()); C := HyperellipticCurve(x*(x-1)*(x-2)*(x-3)*(x-4)); D := QuadraticTwist(C,163); J := Jacobian(D); SetVerbose("JacHypSelmer", 2); TwoSelmerGroupData(J : Bound := 300); Output: Magma V2.10-6 Sun Jan 25 2004 10:11:31 on modular [Seed = 373656274] ------------------------------------- TwoSelmerGroupData of Jacobian of Hyperelliptic Curve defined by y^2 = 163*x^5 - 1630*x^4 + 5705*x^3 - 8150*x^2 + 3912*x over Rational Field m= Mapping from: CrvHyp: C to CrvHyp: C1 with equations : 163*$.1 26569*$.2 $.3 and inverse 1/163*$.1 1/26569*$.2 $.3 Change curve into Hyperelliptic Curve defined by y^2 = x^5 - 1630*x^4 + 929915*x^3 - 216537350*x^2 + 16941882264*x over Rational Field Bad primes = [ 2, 3, 163 ] f factors as (x - 652) (x - 489) (x - 326) (x - 163) (x). For factor x - 652, use field defined by x - 1 and theta = 652 For factor x - 489, use field defined by x - 1 and theta = 489 For factor x - 326, use field defined by x - 1 and theta = 326 For factor x - 163, use field defined by x - 1 and theta = 163 For factor x, use field defined by x - 1 and theta = 0 The 2-torsion group has dimension 4. Determining local images... p = 2 x = 1/4 --> new generator (0 0 0 0 0 1 0 0 0 0 0 1 0 0 0) x = 26 --> new generator (1 1 1 0 0 0 0 0 1 0 1 1 1 0 1) p = 3 x = 7 --> new generator (1 0 0 0 0 1 1 1 0 0) p = 163 p = infinity Computing class groups... Class group data of the fields: Field given by x - 652: [] Field given by x - 489: [] Field given by x - 326: [] Field given by x - 163: [] Field given by x: [] Dimension of Cl[2] = 0. Signatures: [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] Dimension of units mod squares = 5. Upper bound for Selmer group dimension: 13. ==> Upper bound for rank = 9. Computing unit groups... Class group and unit data of the fields: Field given by x - 652: Class group = [], units = [ 2 ] Field given by x - 489: Class group = [], units = [ 2 ] Field given by x - 326: Class group = [], units = [ 2 ] Field given by x - 163: Class group = [], units = [ 2 ] Field given by x: Class group = [], units = [ 2 ] Time for local computations: 509 ms. Time for class groups: 0 ms. Time for unit groups: 0 ms. Selmer group dimension = 5, Dimension of 2-torsion = 4, ==> Bound for the MW-rank = 1. Total time: 629 ms. Transforming presentation of S back to model C. 1 5 <[ 18199/8*$.1^4 - 90669/4*$.1^3 + 630453/8*$.1^2 - 446197/4*$.1 + 53138, 88*$.1^4 - 799*$.1^3 + 2351*$.1^2 - 2292*$.1 + 163, 2887057/4*$.1^4 - 14435283/2*$.1^3 + 101046971/4*$.1^2 - 72176729/2*$.1 + 17322988, 15979/8*$.1^4 - 81193/4*$.1^3 + 580041/8*$.1^2 - 425457/4*$.1 + 53138, -61*$.1^4 + 366*$.1^3 - 427*$.1^2 - 366*$.1 + 489 ], [], []> {} Total time: 3.739 seconds, Total memory usage: 2.89MB ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Sun Jan 25 10:11:50 2004 Input: P := PolynomialRing(Rationals()); C := HyperellipticCurve(x*(x-1)*(x-2)*(x-3)*(x-4)); D := QuadraticTwist(C,165); J := Jacobian(D); SetVerbose("JacHypSelmer", 2); TwoSelmerGroupData(J : Bound := 300); Output: Magma V2.10-6 Sun Jan 25 2004 10:11:46 on modular [Seed = 491684296] ------------------------------------- TwoSelmerGroupData of Jacobian of Hyperelliptic Curve defined by y^2 = 165*x^5 - 1650*x^4 + 5775*x^3 - 8250*x^2 + 3960*x over Rational Field m= Mapping from: CrvHyp: C to CrvHyp: C1 with equations : 165*$.1 27225*$.2 $.3 and inverse 1/165*$.1 1/27225*$.2 $.3 Change curve into Hyperelliptic Curve defined by y^2 = x^5 - 1650*x^4 + 952875*x^3 - 224606250*x^2 + 17788815000*x over Rational Field Bad primes = [ 2, 3, 5, 11 ] f factors as (x - 660) (x - 495) (x - 330) (x - 165) (x). For factor x - 660, use field defined by x - 1 and theta = 660 For factor x - 495, use field defined by x - 1 and theta = 495 For factor x - 330, use field defined by x - 1 and theta = 330 For factor x - 165, use field defined by x - 1 and theta = 165 For factor x, use field defined by x - 1 and theta = 0 The 2-torsion group has dimension 4. Determining local images... p = 2 x = 1/4 --> new generator (0 0 0 0 0 1 0 0 0 0 0 1 0 0 0) x = 30 --> new generator (1 0 1 0 1 1 0 0 1 0 0 0 1 1 1) p = 3 p = 5 p = 11 p = infinity Computing class groups... Class group data of the fields: Field given by x - 660: [] Field given by x - 495: [] Field given by x - 330: [] Field given by x - 165: [] Field given by x: [] Dimension of Cl[2] = 0. Signatures: [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] Dimension of units mod squares = 5. Upper bound for Selmer group dimension: 19. ==> Upper bound for rank = 15. Computing unit groups... Class group and unit data of the fields: Field given by x - 660: Class group = [], units = [ 2 ] Field given by x - 495: Class group = [], units = [ 2 ] Field given by x - 330: Class group = [], units = [ 2 ] Field given by x - 165: Class group = [], units = [ 2 ] Field given by x: Class group = [], units = [ 2 ] Time for local computations: 599 ms. Time for class groups: 0 ms. Time for unit groups: 0 ms. Selmer group dimension = 6, Dimension of 2-torsion = 4, ==> Bound for the MW-rank = 2. Total time: 759 ms. Transforming presentation of S back to model C. 2 6 <[ 1081/24*$.1^4 - 5027/12*$.1^3 + 31835/24*$.1^2 - 20011/12*$.1 + 726, 378*$.1^4 - 11395/3*$.1^3 + 13341*$.1^2 - 57152/3*$.1 + 9075, 332821/4*$.1^4 - 4992131/6*$.1^3 + 11647691/4*$.1^2 - 24957571/6*$.1 + 1996500, 315/8*$.1^4 - 4715/12*$.1^3 + 11033/8*$.1^2 - 23923/12*$.1 + 990, 9*$.1^4 - 90*$.1^3 + 316*$.1^2 - 455*$.1 + 225, 376*$.1^4 - 11263/3*$.1^3 + 13138*$.1^2 - 56405/3*$.1 + 9075 ], [], []> {} Total time: 3.940 seconds, Total memory usage: 2.79MB ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Sun Jan 25 10:12:03 2004 Input: P := PolynomialRing(Rationals()); C := HyperellipticCurve(x*(x-1)*(x-2)*(x-3)*(x-4)); D := QuadraticTwist(C,166); J := Jacobian(D); SetVerbose("JacHypSelmer", 2); TwoSelmerGroupData(J : Bound := 300); Output: Magma V2.10-6 Sun Jan 25 2004 10:11:59 on modular [Seed = 3837229116] ------------------------------------- TwoSelmerGroupData of Jacobian of Hyperelliptic Curve defined by y^2 = 166*x^5 - 1660*x^4 + 5810*x^3 - 8300*x^2 + 3984*x over Rational Field m= Mapping from: CrvHyp: C to CrvHyp: C1 with equations : 166*$.1 27556*$.2 $.3 and inverse 1/166*$.1 1/27556*$.2 $.3 Change curve into Hyperelliptic Curve defined by y^2 = x^5 - 1660*x^4 + 964460*x^3 - 228714800*x^2 + 18223995264*x over Rational Field Bad primes = [ 2, 3, 83 ] f factors as (x - 664) (x - 498) (x - 332) (x - 166) (x). For factor x - 664, use field defined by x - 1 and theta = 664 For factor x - 498, use field defined by x - 1 and theta = 498 For factor x - 332, use field defined by x - 1 and theta = 332 For factor x - 166, use field defined by x - 1 and theta = 166 For factor x, use field defined by x - 1 and theta = 0 The 2-torsion group has dimension 4. Determining local images... p = 2 x = 1 --> new generator (0 0 0 0 1 1 0 0 1 0 1 0 0 0 0) x = 10 --> new generator (1 0 0 1 1 0 1 1 1 0 0 0 1 0 1) p = 3 x = 1 --> new generator (1 0 0 0 0 1 1 1 0 0) p = 83 p = infinity Computing class groups... Class group data of the fields: Field given by x - 664: [] Field given by x - 498: [] Field given by x - 332: [] Field given by x - 166: [] Field given by x: [] Dimension of Cl[2] = 0. Signatures: [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] Dimension of units mod squares = 5. Upper bound for Selmer group dimension: 13. ==> Upper bound for rank = 9. Computing unit groups... Class group and unit data of the fields: Field given by x - 664: Class group = [], units = [ 2 ] Field given by x - 498: Class group = [], units = [ 2 ] Field given by x - 332: Class group = [], units = [ 2 ] Field given by x - 166: Class group = [], units = [ 2 ] Field given by x: Class group = [], units = [ 2 ] Time for local computations: 1119 ms. Time for class groups: 0 ms. Time for unit groups: 0 ms. Selmer group dimension = 5, Dimension of 2-torsion = 4, ==> Bound for the MW-rank = 1. Total time: 1229 ms. Transforming presentation of S back to model C. 1 5 <[ -29/4*$.1^4 + 63/2*$.1^3 - 29/4*$.1^2 - 94*$.1 + 83, -21/2*$.1^4 + 63*$.1^3 - 73*$.1^2 - 129/2*$.1 + 83, 48*$.1^4 - 795/2*$.1^3 + 2041/2*$.1^2 - 835*$.1 + 166, 94*$.1^4 - 2375/2*$.1^3 + 5354*$.1^2 - 20307/2*$.1 + 6889, -31*$.1^4 + 186*$.1^3 - 217*$.1^2 - 186*$.1 + 249 ], [], []> {} Total time: 4.409 seconds, Total memory usage: 2.79MB ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Sun Jan 25 10:12:19 2004 Input: P := PolynomialRing(Rationals()); C := HyperellipticCurve(x*(x-1)*(x-2)*(x-3)*(x-4)); D := QuadraticTwist(C,167); J := Jacobian(D); SetVerbose("JacHypSelmer", 2); TwoSelmerGroupData(J : Bound := 300); Output: Magma V2.10-6 Sun Jan 25 2004 10:12:15 on modular [Seed = 3954734915] ------------------------------------- TwoSelmerGroupData of Jacobian of Hyperelliptic Curve defined by y^2 = 167*x^5 - 1670*x^4 + 5845*x^3 - 8350*x^2 + 4008*x over Rational Field m= Mapping from: CrvHyp: C to CrvHyp: C1 with equations : 167*$.1 27889*$.2 $.3 and inverse 1/167*$.1 1/27889*$.2 $.3 Change curve into Hyperelliptic Curve defined by y^2 = x^5 - 1670*x^4 + 976115*x^3 - 232873150*x^2 + 18667111704*x over Rational Field Bad primes = [ 2, 3, 167 ] f factors as (x - 668) (x - 501) (x - 334) (x - 167) (x). For factor x - 668, use field defined by x - 1 and theta = 668 For factor x - 501, use field defined by x - 1 and theta = 501 For factor x - 334, use field defined by x - 1 and theta = 334 For factor x - 167, use field defined by x - 1 and theta = 167 For factor x, use field defined by x - 1 and theta = 0 The 2-torsion group has dimension 4. Determining local images... p = 2 x = 1/4 --> new generator (0 0 0 0 0 1 0 0 0 0 0 1 0 0 0) x = 2 --> new generator (1 1 0 0 0 1 0 0 1 0 1 0 1 0 0) p = 3 x = 3 --> new generator (0 0 1 1 0 1 0 0 1 0) p = 167 p = infinity Computing class groups... Class group data of the fields: Field given by x - 668: [] Field given by x - 501: [] Field given by x - 334: [] Field given by x - 167: [] Field given by x: [] Dimension of Cl[2] = 0. Signatures: [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] Dimension of units mod squares = 5. Upper bound for Selmer group dimension: 13. ==> Upper bound for rank = 9. Computing unit groups... Class group and unit data of the fields: Field given by x - 668: Class group = [], units = [ 2 ] Field given by x - 501: Class group = [], units = [ 2 ] Field given by x - 334: Class group = [], units = [ 2 ] Field given by x - 167: Class group = [], units = [ 2 ] Field given by x: Class group = [], units = [ 2 ] Time for local computations: 520 ms. Time for class groups: 0 ms. Time for unit groups: 0 ms. Selmer group dimension = 6, Dimension of 2-torsion = 4, ==> Bound for the MW-rank = 2. Total time: 639 ms. Transforming presentation of S back to model C. 2 6 <[ 1183*$.1^4 - 11774*$.1^3 + 40985*$.1^2 - 58282*$.1 + 27889, 1148*$.1^4 - 11536*$.1^3 + 40600*$.1^2 - 58268*$.1 + 27889, -55/4*$.1^4 + 110*$.1^3 - 933/4*$.1^2 - 30*$.1 + 334, 582002*$.1^4 - 5820493*$.1^3 + 20373409*$.1^2 - 29106973*$.1 + 13972389, 1/8*$.1^4 - 7/4*$.1^3 + 59/8*$.1^2 - 43/4*$.1 + 6, 3444*$.1^4 - 34607*$.1^3 + 121627*$.1^2 - 174128*$.1 + 83667 ], [], []> {} Total time: 3.779 seconds, Total memory usage: 2.89MB ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Sun Jan 25 10:12:39 2004 Input: P := PolynomialRing(Rationals()); C := HyperellipticCurve(x*(x-1)*(x-2)*(x-3)*(x-4)); D := QuadraticTwist(C,170); J := Jacobian(D); SetVerbose("JacHypSelmer", 2); TwoSelmerGroupData(J : Bound := 300); Output: Magma V2.10-6 Sun Jan 25 2004 10:12:34 on modular [Seed = 4070665847] ------------------------------------- TwoSelmerGroupData of Jacobian of Hyperelliptic Curve defined by y^2 = 170*x^5 - 1700*x^4 + 5950*x^3 - 8500*x^2 + 4080*x over Rational Field m= Mapping from: CrvHyp: C to CrvHyp: C1 with equations : 170*$.1 28900*$.2 $.3 and inverse 1/170*$.1 1/28900*$.2 $.3 Change curve into Hyperelliptic Curve defined by y^2 = x^5 - 1700*x^4 + 1011500*x^3 - 245650000*x^2 + 20045040000*x over Rational Field Bad primes = [ 2, 3, 5, 17 ] f factors as (x - 680) (x - 510) (x - 340) (x - 170) (x). For factor x - 680, use field defined by x - 1 and theta = 680 For factor x - 510, use field defined by x - 1 and theta = 510 For factor x - 340, use field defined by x - 1 and theta = 340 For factor x - 170, use field defined by x - 1 and theta = 170 For factor x, use field defined by x - 1 and theta = 0 The 2-torsion group has dimension 4. Determining local images... p = 2 x = 1 --> new generator (0 0 0 0 1 0 0 0 1 0 1 1 0 0 0) x = 2 --> new generator (1 0 1 0 0 0 1 1 1 1 1 0 1 0 0) p = 3 x = 3 --> new generator (0 0 1 1 0 1 0 0 1 0) p = 5 p = 17 p = infinity Computing class groups... Class group data of the fields: Field given by x - 680: [] Field given by x - 510: [] Field given by x - 340: [] Field given by x - 170: [] Field given by x: [] Dimension of Cl[2] = 0. Signatures: [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] Dimension of units mod squares = 5. Upper bound for Selmer group dimension: 17. ==> Upper bound for rank = 13. Computing unit groups... Class group and unit data of the fields: Field given by x - 680: Class group = [], units = [ 2 ] Field given by x - 510: Class group = [], units = [ 2 ] Field given by x - 340: Class group = [], units = [ 2 ] Field given by x - 170: Class group = [], units = [ 2 ] Field given by x: Class group = [], units = [ 2 ] Time for local computations: 1069 ms. Time for class groups: 0 ms. Time for unit groups: 0 ms. Selmer group dimension = 5, Dimension of 2-torsion = 4, ==> Bound for the MW-rank = 1. Total time: 1219 ms. Transforming presentation of S back to model C. 1 5 <[ 329/2*$.1^4 - 1662*$.1^3 + 5901*$.1^2 - 17273/2*$.1 + 4335, -43/4*$.1^4 + 129/2*$.1^3 - 299/4*$.1^2 - 66*$.1 + 85, 1806*$.1^4 - 36205/2*$.1^3 + 126847/2*$.1^2 - 90475*$.1 + 43350, -639/4*$.1^4 + 1426*$.1^3 - 16205/4*$.1^2 + 3550*$.1 + 255, 55*$.1^4 - 560*$.1^3 + 2001*$.1^2 - 2924*$.1 + 1445 ], [], []> {} Total time: 4.479 seconds, Total memory usage: 2.79MB ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Sun Jan 25 10:12:53 2004 Input: P := PolynomialRing(Rationals()); C := HyperellipticCurve(x*(x-1)*(x-2)*(x-3)*(x-4)); D := QuadraticTwist(C,173); J := Jacobian(D); SetVerbose("JacHypSelmer", 2); TwoSelmerGroupData(J : Bound := 300); Output: Magma V2.10-6 Sun Jan 25 2004 10:12:49 on modular [Seed = 4188693871] ------------------------------------- TwoSelmerGroupData of Jacobian of Hyperelliptic Curve defined by y^2 = 173*x^5 - 1730*x^4 + 6055*x^3 - 8650*x^2 + 4152*x over Rational Field m= Mapping from: CrvHyp: C to CrvHyp: C1 with equations : 173*$.1 29929*$.2 $.3 and inverse 1/173*$.1 1/29929*$.2 $.3 Change curve into Hyperelliptic Curve defined by y^2 = x^5 - 1730*x^4 + 1047515*x^3 - 258885850*x^2 + 21497880984*x over Rational Field Bad primes = [ 2, 3, 173 ] f factors as (x - 692) (x - 519) (x - 346) (x - 173) (x). For factor x - 692, use field defined by x - 1 and theta = 692 For factor x - 519, use field defined by x - 1 and theta = 519 For factor x - 346, use field defined by x - 1 and theta = 346 For factor x - 173, use field defined by x - 1 and theta = 173 For factor x, use field defined by x - 1 and theta = 0 The 2-torsion group has dimension 4. Determining local images... p = 2 x = 1/4 --> new generator (0 0 0 0 0 1 0 0 0 0 0 1 0 0 0) x = 14 --> new generator (1 0 1 0 1 1 0 0 1 0 0 0 1 1 1) p = 3 x = 3 --> new generator (0 0 1 1 0 1 0 0 1 0) p = 173 p = infinity Computing class groups... Class group data of the fields: Field given by x - 692: [] Field given by x - 519: [] Field given by x - 346: [] Field given by x - 173: [] Field given by x: [] Dimension of Cl[2] = 0. Signatures: [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] Dimension of units mod squares = 5. Upper bound for Selmer group dimension: 13. ==> Upper bound for rank = 9. Computing unit groups... Class group and unit data of the fields: Field given by x - 692: Class group = [], units = [ 2 ] Field given by x - 519: Class group = [], units = [ 2 ] Field given by x - 346: Class group = [], units = [ 2 ] Field given by x - 173: Class group = [], units = [ 2 ] Field given by x: Class group = [], units = [ 2 ] Time for local computations: 549 ms. Time for class groups: 0 ms. Time for unit groups: 11 ms. Selmer group dimension = 5, Dimension of 2-torsion = 4, ==> Bound for the MW-rank = 1. Total time: 661 ms. Transforming presentation of S back to model C. 1 5 <[ 3756*$.1^4 - 37501*$.1^3 + 131018*$.1^2 - 186887*$.1 + 89787, 3741*$.1^4 - 37583*$.1^3 + 131974*$.1^2 - 188438*$.1 + 89787, 5177601/4*$.1^4 - 12944118*$.1^3 + 181219155/4*$.1^2 - 64721372*$.1 + 31066302, 14*$.1^4 - 112*$.1^3 + 323*$.1^2 - 396*$.1 + 173, 59339/8*$.1^4 - 296697/4*$.1^3 + 2078961/8*$.1^2 - 1488673/4*$.1 + 179574 ], [], []> {} Total time: 3.769 seconds, Total memory usage: 2.89MB ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Sun Jan 25 10:13:06 2004 Input: P := PolynomialRing(Rationals()); C := HyperellipticCurve(x*(x-1)*(x-2)*(x-3)*(x-4)); D := QuadraticTwist(C,174); J := Jacobian(D); SetVerbose("JacHypSelmer", 2); TwoSelmerGroupData(J : Bound := 300); Output: Magma V2.10-6 Sun Jan 25 2004 10:13:02 on modular [Seed = 3230882905] ------------------------------------- TwoSelmerGroupData of Jacobian of Hyperelliptic Curve defined by y^2 = 174*x^5 - 1740*x^4 + 6090*x^3 - 8700*x^2 + 4176*x over Rational Field m= Mapping from: CrvHyp: C to CrvHyp: C1 with equations : 174*$.1 30276*$.2 $.3 and inverse 1/174*$.1 1/30276*$.2 $.3 Change curve into Hyperelliptic Curve defined by y^2 = x^5 - 1740*x^4 + 1059660*x^3 - 263401200*x^2 + 21999268224*x over Rational Field Bad primes = [ 2, 3, 29 ] f factors as (x - 696) (x - 522) (x - 348) (x - 174) (x). For factor x - 696, use field defined by x - 1 and theta = 696 For factor x - 522, use field defined by x - 1 and theta = 522 For factor x - 348, use field defined by x - 1 and theta = 348 For factor x - 174, use field defined by x - 1 and theta = 174 For factor x, use field defined by x - 1 and theta = 0 The 2-torsion group has dimension 4. Determining local images... p = 2 x = 1 --> new generator (0 0 0 0 1 1 0 0 1 0 1 0 0 0 0) x = 34 --> new generator (1 0 1 1 1 0 1 1 0 0 0 1 1 0 0) p = 3 p = 29 p = infinity Computing class groups... Class group data of the fields: Field given by x - 696: [] Field given by x - 522: [] Field given by x - 348: [] Field given by x - 174: [] Field given by x: [] Dimension of Cl[2] = 0. Signatures: [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] Dimension of units mod squares = 5. Upper bound for Selmer group dimension: 15. ==> Upper bound for rank = 11. Computing unit groups... Class group and unit data of the fields: Field given by x - 696: Class group = [], units = [ 2 ] Field given by x - 522: Class group = [], units = [ 2 ] Field given by x - 348: Class group = [], units = [ 2 ] Field given by x - 174: Class group = [], units = [ 2 ] Field given by x: Class group = [], units = [ 2 ] Time for local computations: 1059 ms. Time for class groups: 0 ms. Time for unit groups: 10 ms. Selmer group dimension = 5, Dimension of 2-torsion = 4, ==> Bound for the MW-rank = 1. Total time: 1180 ms. Transforming presentation of S back to model C. 1 5 <[ 433/4*$.1^4 - 6437/6*$.1^3 + 14869/4*$.1^2 - 15809/3*$.1 + 2523, -11*$.1^4 + 66*$.1^3 - 153/2*$.1^2 - 135/2*$.1 + 87, 746/3*$.1^4 - 14485/6*$.1^3 + 48659/6*$.1^2 - 32965/3*$.1 + 5046, 45/4*$.1^4 - 323/3*$.1^3 + 1463/4*$.1^2 - 1555/3*$.1 + 261, 11311/4*$.1^4 - 56555/2*$.1^3 + 396053/4*$.1^2 - 283195/2*$.1 + 68121 ], [], []> {} Total time: 4.409 seconds, Total memory usage: 2.69MB ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Sun Jan 25 10:13:26 2004 Input: P := PolynomialRing(Rationals()); C := HyperellipticCurve(x*(x-1)*(x-2)*(x-3)*(x-4)); D := QuadraticTwist(C,177); J := Jacobian(D); SetVerbose("JacHypSelmer", 2); TwoSelmerGroupData(J : Bound := 300); Output: Magma V2.10-6 Sun Jan 25 2004 10:13:22 on modular [Seed = 3599059874] ------------------------------------- TwoSelmerGroupData of Jacobian of Hyperelliptic Curve defined by y^2 = 177*x^5 - 1770*x^4 + 6195*x^3 - 8850*x^2 + 4248*x over Rational Field m= Mapping from: CrvHyp: C to CrvHyp: C1 with equations : 177*$.1 31329*$.2 $.3 and inverse 1/177*$.1 1/31329*$.2 $.3 Change curve into Hyperelliptic Curve defined by y^2 = x^5 - 1770*x^4 + 1096515*x^3 - 277261650*x^2 + 23556149784*x over Rational Field Bad primes = [ 2, 3, 59 ] f factors as (x - 708) (x - 531) (x - 354) (x - 177) (x). For factor x - 708, use field defined by x - 1 and theta = 708 For factor x - 531, use field defined by x - 1 and theta = 531 For factor x - 354, use field defined by x - 1 and theta = 354 For factor x - 177, use field defined by x - 1 and theta = 177 For factor x, use field defined by x - 1 and theta = 0 The 2-torsion group has dimension 4. Determining local images... p = 2 x = 1/4 --> new generator (0 0 0 0 0 1 0 0 0 0 0 1 0 0 0) x = 22 --> new generator (1 0 0 0 1 0 0 0 1 0 0 1 1 1 0) p = 3 p = 59 p = infinity Computing class groups... Class group data of the fields: Field given by x - 708: [] Field given by x - 531: [] Field given by x - 354: [] Field given by x - 177: [] Field given by x: [] Dimension of Cl[2] = 0. Signatures: [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] Dimension of units mod squares = 5. Upper bound for Selmer group dimension: 15. ==> Upper bound for rank = 11. Computing unit groups... Class group and unit data of the fields: Field given by x - 708: Class group = [], units = [ 2 ] Field given by x - 531: Class group = [], units = [ 2 ] Field given by x - 354: Class group = [], units = [ 2 ] Field given by x - 177: Class group = [], units = [ 2 ] Field given by x: Class group = [], units = [ 2 ] Time for local computations: 569 ms. Time for class groups: 0 ms. Time for unit groups: 0 ms. Selmer group dimension = 5, Dimension of 2-torsion = 4, ==> Bound for the MW-rank = 1. Total time: 689 ms. Transforming presentation of S back to model C. 1 5 <[ 64715/24*$.1^4 - 321569/12*$.1^3 + 2232481/24*$.1^2 - 1578889/12*$.1 + 62658, 428*$.1^4 - 12899/3*$.1^3 + 15127*$.1^2 - 65104/3*$.1 + 10443, 11091227/12*$.1^4 - 18485163/2*$.1^3 + 388182025/12*$.1^2 - 92422237/2*$.1 + 22180932, 1085/24*$.1^4 - 1781/4*$.1^3 + 37087/24*$.1^2 - 8805/4*$.1 + 1062, 3850/3*$.1^4 - 38500/3*$.1^3 + 135014/3*$.1^2 - 193820/3*$.1 + 31329 ], [], []> {} Total time: 3.869 seconds, Total memory usage: 2.69MB ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Sun Jan 25 10:13:41 2004 Input: P := PolynomialRing(Rationals()); C := HyperellipticCurve(x*(x-1)*(x-2)*(x-3)*(x-4)); D := QuadraticTwist(C,178); J := Jacobian(D); SetVerbose("JacHypSelmer", 2); TwoSelmerGroupData(J : Bound := 300); Output: Magma V2.10-6 Sun Jan 25 2004 10:13:37 on modular [Seed = 3717087387] ------------------------------------- TwoSelmerGroupData of Jacobian of Hyperelliptic Curve defined by y^2 = 178*x^5 - 1780*x^4 + 6230*x^3 - 8900*x^2 + 4272*x over Rational Field m= Mapping from: CrvHyp: C to CrvHyp: C1 with equations : 178*$.1 31684*$.2 $.3 and inverse 1/178*$.1 1/31684*$.2 $.3 Change curve into Hyperelliptic Curve defined by y^2 = x^5 - 1780*x^4 + 1108940*x^3 - 281987600*x^2 + 24093020544*x over Rational Field Bad primes = [ 2, 3, 89 ] f factors as (x - 712) (x - 534) (x - 356) (x - 178) (x). For factor x - 712, use field defined by x - 1 and theta = 712 For factor x - 534, use field defined by x - 1 and theta = 534 For factor x - 356, use field defined by x - 1 and theta = 356 For factor x - 178, use field defined by x - 1 and theta = 178 For factor x, use field defined by x - 1 and theta = 0 The 2-torsion group has dimension 4. Determining local images... p = 2 x = 1 --> new generator (0 0 0 0 1 0 0 0 1 0 1 1 0 0 0) x = 10 --> new generator (1 0 0 0 0 1 1 1 0 1 1 0 1 0 1) p = 3 x = 4 --> new generator (1 0 0 0 0 1 1 1 0 0) p = 89 p = infinity Computing class groups... Class group data of the fields: Field given by x - 712: [] Field given by x - 534: [] Field given by x - 356: [] Field given by x - 178: [] Field given by x: [] Dimension of Cl[2] = 0. Signatures: [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] Dimension of units mod squares = 5. Upper bound for Selmer group dimension: 13. ==> Upper bound for rank = 9. Computing unit groups... Class group and unit data of the fields: Field given by x - 712: Class group = [], units = [ 2 ] Field given by x - 534: Class group = [], units = [ 2 ] Field given by x - 356: Class group = [], units = [ 2 ] Field given by x - 178: Class group = [], units = [ 2 ] Field given by x: Class group = [], units = [ 2 ] Time for local computations: 1099 ms. Time for class groups: 0 ms. Time for unit groups: 0 ms. Selmer group dimension = 6, Dimension of 2-torsion = 4, ==> Bound for the MW-rank = 2. Total time: 1220 ms. Transforming presentation of S back to model C. 2 6 <[ -77*$.1^4 + 683*$.1^3 - 3819/2*$.1^2 + 3141/2*$.1 + 267, -1/4*$.1^4 + 3/2*$.1^3 - 5/4*$.1^2 - 3*$.1 + 1, 66*$.1^4 - 1145/2*$.1^3 + 3219/2*$.1^2 - 1635*$.1 + 534, -669/4*$.1^4 + 1493*$.1^3 - 16967/4*$.1^2 + 3717*$.1 + 267, 319*$.1^4 - 3190*$.1^3 + 11209*$.1^2 - 16170*$.1 + 7921, -11*$.1^4 + 66*$.1^3 - 77*$.1^2 - 66*$.1 + 89 ], [], []> {} Total time: 4.399 seconds, Total memory usage: 2.79MB ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Sun Jan 25 10:13:55 2004 Input: P := PolynomialRing(Rationals()); C := HyperellipticCurve(x*(x-1)*(x-2)*(x-3)*(x-4)); D := QuadraticTwist(C,179); J := Jacobian(D); SetVerbose("JacHypSelmer", 2); TwoSelmerGroupData(J : Bound := 300); Output: Magma V2.10-6 Sun Jan 25 2004 10:13:51 on modular [Seed = 2767665644] ------------------------------------- TwoSelmerGroupData of Jacobian of Hyperelliptic Curve defined by y^2 = 179*x^5 - 1790*x^4 + 6265*x^3 - 8950*x^2 + 4296*x over Rational Field m= Mapping from: CrvHyp: C to CrvHyp: C1 with equations : 179*$.1 32041*$.2 $.3 and inverse 1/179*$.1 1/32041*$.2 $.3 Change curve into Hyperelliptic Curve defined by y^2 = x^5 - 1790*x^4 + 1121435*x^3 - 286766950*x^2 + 24639016344*x over Rational Field Bad primes = [ 2, 3, 179 ] f factors as (x - 716) (x - 537) (x - 358) (x - 179) (x). For factor x - 716, use field defined by x - 1 and theta = 716 For factor x - 537, use field defined by x - 1 and theta = 537 For factor x - 358, use field defined by x - 1 and theta = 358 For factor x - 179, use field defined by x - 1 and theta = 179 For factor x, use field defined by x - 1 and theta = 0 The 2-torsion group has dimension 4. Determining local images... p = 2 x = 1/4 --> new generator (0 0 0 0 0 1 0 0 0 0 0 1 0 0 0) x = 26 --> new generator (1 1 1 0 0 0 0 0 1 0 1 1 1 0 1) p = 3 x = 3 --> new generator (0 0 1 1 0 1 0 0 1 0) p = 179 p = infinity Computing class groups... Class group data of the fields: Field given by x - 716: [] Field given by x - 537: [] Field given by x - 358: [] Field given by x - 179: [] Field given by x: [] Dimension of Cl[2] = 0. Signatures: [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] Dimension of units mod squares = 5. Upper bound for Selmer group dimension: 13. ==> Upper bound for rank = 9. Computing unit groups... Class group and unit data of the fields: Field given by x - 716: Class group = [], units = [ 2 ] Field given by x - 537: Class group = [], units = [ 2 ] Field given by x - 358: Class group = [], units = [ 2 ] Field given by x - 179: Class group = [], units = [ 2 ] Field given by x: Class group = [], units = [ 2 ] Time for local computations: 520 ms. Time for class groups: 0 ms. Time for unit groups: 9 ms. Selmer group dimension = 5, Dimension of 2-torsion = 4, ==> Bound for the MW-rank = 1. Total time: 639 ms. Transforming presentation of S back to model C. 1 5 <[ 21839/8*$.1^4 - 108597/4*$.1^3 + 755037/8*$.1^2 - 535453/4*$.1 + 64082, 3923*$.1^4 - 39469*$.1^3 + 139008*$.1^2 - 199586*$.1 + 96123, 3823857/4*$.1^4 - 19118987/2*$.1^3 + 133830347/4*$.1^2 - 95590825/2*$.1 + 22941356, 411/8*$.1^4 - 1945/4*$.1^3 + 13081/8*$.1^2 - 9089/4*$.1 + 1074, 1268*$.1^4 - 12680*$.1^3 + 44648*$.1^2 - 64740*$.1 + 32041 ], [], []> {} Total time: 3.839 seconds, Total memory usage: 2.89MB ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Sun Jan 25 10:14:12 2004 Input: P := PolynomialRing(Rationals()); C := HyperellipticCurve(x*(x-1)*(x-2)*(x-3)*(x-4)); D := QuadraticTwist(C,181); J := Jacobian(D); SetVerbose("JacHypSelmer", 2); TwoSelmerGroupData(J : Bound := 300); Output: Magma V2.10-6 Sun Jan 25 2004 10:14:08 on modular [Seed = 2885170828] ------------------------------------- TwoSelmerGroupData of Jacobian of Hyperelliptic Curve defined by y^2 = 181*x^5 - 1810*x^4 + 6335*x^3 - 9050*x^2 + 4344*x over Rational Field m= Mapping from: CrvHyp: C to CrvHyp: C1 with equations : 181*$.1 32761*$.2 $.3 and inverse 1/181*$.1 1/32761*$.2 $.3 Change curve into Hyperelliptic Curve defined by y^2 = x^5 - 1810*x^4 + 1146635*x^3 - 296487050*x^2 + 25758794904*x over Rational Field Bad primes = [ 2, 3, 181 ] f factors as (x - 724) (x - 543) (x - 362) (x - 181) (x). For factor x - 724, use field defined by x - 1 and theta = 724 For factor x - 543, use field defined by x - 1 and theta = 543 For factor x - 362, use field defined by x - 1 and theta = 362 For factor x - 181, use field defined by x - 1 and theta = 181 For factor x, use field defined by x - 1 and theta = 0 The 2-torsion group has dimension 4. Determining local images... p = 2 x = 1/4 --> new generator (0 0 0 0 0 1 0 0 0 0 0 1 0 0 0) x = 30 --> new generator (1 0 1 0 1 1 0 0 1 0 0 0 1 1 1) p = 3 x = 7 --> new generator (1 0 0 0 0 1 1 1 0 0) p = 181 p = infinity Computing class groups... Class group data of the fields: Field given by x - 724: [] Field given by x - 543: [] Field given by x - 362: [] Field given by x - 181: [] Field given by x: [] Dimension of Cl[2] = 0. Signatures: [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] Dimension of units mod squares = 5. Upper bound for Selmer group dimension: 13. ==> Upper bound for rank = 9. Computing unit groups... Class group and unit data of the fields: Field given by x - 724: Class group = [], units = [ 2 ] Field given by x - 543: Class group = [], units = [ 2 ] Field given by x - 362: Class group = [], units = [ 2 ] Field given by x - 181: Class group = [], units = [ 2 ] Field given by x: Class group = [], units = [ 2 ] Time for local computations: 560 ms. Time for class groups: 0 ms. Time for unit groups: 9 ms. Selmer group dimension = 5, Dimension of 2-torsion = 4, ==> Bound for the MW-rank = 1. Total time: 661 ms. Transforming presentation of S back to model C. 1 5 <[ 22381/8*$.1^4 - 111543/4*$.1^3 + 776103/8*$.1^2 - 549775/4*$.1 + 65522, -$.1^3 + 7*$.1^2 - 12*$.1 + 3, 481/4*$.1^4 - 2043/2*$.1^3 + 11051/4*$.1^2 - 5165/2*$.1 + 724, -1089/8*$.1^4 + 4715/4*$.1^3 - 25003/8*$.1^2 + 8331/4*$.1 + 1086, 1305*$.1^4 - 13170*$.1^3 + 46575*$.1^2 - 67290*$.1 + 32761 ], [], []> {} Total time: 3.869 seconds, Total memory usage: 2.89MB ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Sun Jan 25 10:14:25 2004 Input: P := PolynomialRing(Rationals()); C := HyperellipticCurve(x*(x-1)*(x-2)*(x-3)*(x-4)); D := QuadraticTwist(C,182); J := Jacobian(D); SetVerbose("JacHypSelmer", 2); TwoSelmerGroupData(J : Bound := 300); Output: Magma V2.10-6 Sun Jan 25 2004 10:14:20 on modular [Seed = 3001102233] ------------------------------------- TwoSelmerGroupData of Jacobian of Hyperelliptic Curve defined by y^2 = 182*x^5 - 1820*x^4 + 6370*x^3 - 9100*x^2 + 4368*x over Rational Field m= Mapping from: CrvHyp: C to CrvHyp: C1 with equations : 182*$.1 33124*$.2 $.3 and inverse 1/182*$.1 1/33124*$.2 $.3 Change curve into Hyperelliptic Curve defined by y^2 = x^5 - 1820*x^4 + 1159340*x^3 - 301428400*x^2 + 26332785024*x over Rational Field Bad primes = [ 2, 3, 7, 13 ] f factors as (x - 728) (x - 546) (x - 364) (x - 182) (x). For factor x - 728, use field defined by x - 1 and theta = 728 For factor x - 546, use field defined by x - 1 and theta = 546 For factor x - 364, use field defined by x - 1 and theta = 364 For factor x - 182, use field defined by x - 1 and theta = 182 For factor x, use field defined by x - 1 and theta = 0 The 2-torsion group has dimension 4. Determining local images... p = 2 x = 1 --> new generator (0 0 0 0 1 1 0 0 1 0 1 0 0 0 0) x = 58 --> new generator (1 0 0 1 1 0 1 1 1 0 0 0 1 0 1) p = 3 x = 3 --> new generator (0 0 1 1 0 1 0 0 1 0) p = 7 p = 13 p = infinity Computing class groups... Class group data of the fields: Field given by x - 728: [] Field given by x - 546: [] Field given by x - 364: [] Field given by x - 182: [] Field given by x: [] Dimension of Cl[2] = 0. Signatures: [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] Dimension of units mod squares = 5. Upper bound for Selmer group dimension: 17. ==> Upper bound for rank = 13. Computing unit groups... Class group and unit data of the fields: Field given by x - 728: Class group = [], units = [ 2 ] Field given by x - 546: Class group = [], units = [ 2 ] Field given by x - 364: Class group = [], units = [ 2 ] Field given by x - 182: Class group = [], units = [ 2 ] Field given by x: Class group = [], units = [ 2 ] Time for local computations: 1141 ms. Time for class groups: 0 ms. Time for unit groups: 0 ms. Selmer group dimension = 5, Dimension of 2-torsion = 4, ==> Bound for the MW-rank = 1. Total time: 1299 ms. Transforming presentation of S back to model C. 1 5 <[ 53511/4*$.1^4 - 267679/2*$.1^3 + 1875283/4*$.1^2 - 670772*$.1 + 322959, 16705/2*$.1^4 - 83512*$.1^3 + 292201*$.1^2 - 834301/2*$.1 + 199927, 26881*$.1^4 - 537697/2*$.1^3 + 1882325/2*$.1^2 - 1344931*$.1 + 645918, -171*$.1^4 + 3053/2*$.1^3 - 4337*$.1^2 + 7601/2*$.1 + 273, 4473*$.1^4 - 44740*$.1^3 + 156651*$.1^2 - 223946*$.1 + 107653 ], [], []> {} Total time: 4.479 seconds, Total memory usage: 2.79MB ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Sun Jan 25 10:14:37 2004 Input: P := PolynomialRing(Rationals()); C := HyperellipticCurve(x*(x-1)*(x-2)*(x-3)*(x-4)); D := QuadraticTwist(C,183); J := Jacobian(D); SetVerbose("JacHypSelmer", 2); TwoSelmerGroupData(J : Bound := 300); Output: Magma V2.10-6 Sun Jan 25 2004 10:14:33 on modular [Seed = 3119129735] ------------------------------------- TwoSelmerGroupData of Jacobian of Hyperelliptic Curve defined by y^2 = 183*x^5 - 1830*x^4 + 6405*x^3 - 9150*x^2 + 4392*x over Rational Field m= Mapping from: CrvHyp: C to CrvHyp: C1 with equations : 183*$.1 33489*$.2 $.3 and inverse 1/183*$.1 1/33489*$.2 $.3 Change curve into Hyperelliptic Curve defined by y^2 = x^5 - 1830*x^4 + 1172115*x^3 - 306424350*x^2 + 26916314904*x over Rational Field Bad primes = [ 2, 3, 61 ] f factors as (x - 732) (x - 549) (x - 366) (x - 183) (x). For factor x - 732, use field defined by x - 1 and theta = 732 For factor x - 549, use field defined by x - 1 and theta = 549 For factor x - 366, use field defined by x - 1 and theta = 366 For factor x - 183, use field defined by x - 1 and theta = 183 For factor x, use field defined by x - 1 and theta = 0 The 2-torsion group has dimension 4. Determining local images... p = 2 x = 1/4 --> new generator (0 0 0 0 0 1 0 0 0 0 0 1 0 0 0) x = 2 --> new generator (1 1 0 0 0 1 0 0 1 0 1 0 1 0 0) p = 3 p = 61 p = infinity Computing class groups... Class group data of the fields: Field given by x - 732: [] Field given by x - 549: [] Field given by x - 366: [] Field given by x - 183: [] Field given by x: [] Dimension of Cl[2] = 0. Signatures: [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] Dimension of units mod squares = 5. Upper bound for Selmer group dimension: 15. ==> Upper bound for rank = 11. Computing unit groups... Class group and unit data of the fields: Field given by x - 732: Class group = [], units = [ 2 ] Field given by x - 549: Class group = [], units = [ 2 ] Field given by x - 366: Class group = [], units = [ 2 ] Field given by x - 183: Class group = [], units = [ 2 ] Field given by x: Class group = [], units = [ 2 ] Time for local computations: 540 ms. Time for class groups: 0 ms. Time for unit groups: 0 ms. Selmer group dimension = 5, Dimension of 2-torsion = 4, ==> Bound for the MW-rank = 1. Total time: 659 ms. Transforming presentation of S back to model C. 1 5 <[ 23035/8*$.1^4 - 343451/12*$.1^3 + 795009/8*$.1^2 - 1687315/12*$.1 + 66978, -1/3*$.1^3 + 3*$.1^2 - 20/3*$.1 + 3, 4387/12*$.1^4 - 6947/2*$.1^3 + 136049/12*$.1^2 - 29633/2*$.1 + 6588, 601/24*$.1^4 - 1089/4*$.1^3 + 25667/24*$.1^2 - 7193/4*$.1 + 1098, 135*$.1^4 - 1390*$.1^3 + 5025*$.1^2 - 7430*$.1 + 3721 ], [], []> {} Total time: 3.829 seconds, Total memory usage: 2.69MB ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Sun Jan 25 10:14:52 2004 Input: P := PolynomialRing(Rationals()); C := HyperellipticCurve(x*(x-1)*(x-2)*(x-3)*(x-4)); D := QuadraticTwist(C,185); J := Jacobian(D); SetVerbose("JacHypSelmer", 2); TwoSelmerGroupData(J : Bound := 300); Output: Magma V2.10-6 Sun Jan 25 2004 10:14:48 on modular [Seed = 2161319311] ------------------------------------- TwoSelmerGroupData of Jacobian of Hyperelliptic Curve defined by y^2 = 185*x^5 - 1850*x^4 + 6475*x^3 - 9250*x^2 + 4440*x over Rational Field m= Mapping from: CrvHyp: C to CrvHyp: C1 with equations : 185*$.1 34225*$.2 $.3 and inverse 1/185*$.1 1/34225*$.2 $.3 Change curve into Hyperelliptic Curve defined by y^2 = x^5 - 1850*x^4 + 1197875*x^3 - 316581250*x^2 + 28112415000*x over Rational Field Bad primes = [ 2, 3, 5, 37 ] f factors as (x - 740) (x - 555) (x - 370) (x - 185) (x). For factor x - 740, use field defined by x - 1 and theta = 740 For factor x - 555, use field defined by x - 1 and theta = 555 For factor x - 370, use field defined by x - 1 and theta = 370 For factor x - 185, use field defined by x - 1 and theta = 185 For factor x, use field defined by x - 1 and theta = 0 The 2-torsion group has dimension 4. Determining local images... p = 2 x = 1/4 --> new generator (0 0 0 0 0 1 0 0 0 0 0 1 0 0 0) x = 6 --> new generator (1 0 0 0 1 0 0 0 1 0 0 1 1 1 0) p = 3 x = 3 --> new generator (0 0 1 1 0 1 0 0 1 0) p = 5 p = 37 p = infinity Computing class groups... Class group data of the fields: Field given by x - 740: [] Field given by x - 555: [] Field given by x - 370: [] Field given by x - 185: [] Field given by x: [] Dimension of Cl[2] = 0. Signatures: [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] Dimension of units mod squares = 5. Upper bound for Selmer group dimension: 17. ==> Upper bound for rank = 13. Computing unit groups... Class group and unit data of the fields: Field given by x - 740: Class group = [], units = [ 2 ] Field given by x - 555: Class group = [], units = [ 2 ] Field given by x - 370: Class group = [], units = [ 2 ] Field given by x - 185: Class group = [], units = [ 2 ] Field given by x: Class group = [], units = [ 2 ] Time for local computations: 570 ms. Time for class groups: 0 ms. Time for unit groups: 0 ms. Selmer group dimension = 4, Dimension of 2-torsion = 4, ==> Bound for the MW-rank = 0. Total time: 729 ms. Transforming presentation of S back to model C. 0 4 <[ 23369/8*$.1^4 - 116475/4*$.1^3 + 810523/8*$.1^2 - 574259/4*$.1 + 68450, 4278*$.1^4 - 42965*$.1^3 + 150841*$.1^2 - 215384*$.1 + 102675, 4220961/4*$.1^4 - 21104803/2*$.1^3 + 147733611/4*$.1^2 - 105524373/2*$.1 + 25326500, -1113/8*$.1^4 + 4819/4*$.1^3 - 25555/8*$.1^2 + 8515/4*$.1 + 1110 ], [], []> {} Total time: 3.909 seconds, Total memory usage: 2.79MB ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Sun Jan 25 10:15:09 2004 Input: P := PolynomialRing(Rationals()); C := HyperellipticCurve(x*(x-1)*(x-2)*(x-3)*(x-4)); D := QuadraticTwist(C,186); J := Jacobian(D); SetVerbose("JacHypSelmer", 2); TwoSelmerGroupData(J : Bound := 300); Output: Magma V2.10-6 Sun Jan 25 2004 10:15:04 on modular [Seed = 2478837388] ------------------------------------- TwoSelmerGroupData of Jacobian of Hyperelliptic Curve defined by y^2 = 186*x^5 - 1860*x^4 + 6510*x^3 - 9300*x^2 + 4464*x over Rational Field m= Mapping from: CrvHyp: C to CrvHyp: C1 with equations : 186*$.1 34596*$.2 $.3 and inverse 1/186*$.1 1/34596*$.2 $.3 Change curve into Hyperelliptic Curve defined by y^2 = x^5 - 1860*x^4 + 1210860*x^3 - 321742800*x^2 + 28725197184*x over Rational Field Bad primes = [ 2, 3, 31 ] f factors as (x - 744) (x - 558) (x - 372) (x - 186) (x). For factor x - 744, use field defined by x - 1 and theta = 744 For factor x - 558, use field defined by x - 1 and theta = 558 For factor x - 372, use field defined by x - 1 and theta = 372 For factor x - 186, use field defined by x - 1 and theta = 186 For factor x, use field defined by x - 1 and theta = 0 The 2-torsion group has dimension 4. Determining local images... p = 2 x = 1 --> new generator (0 0 0 0 1 0 0 0 1 0 1 1 0 0 0) x = 18 --> new generator (1 0 1 0 0 0 1 1 1 1 1 0 1 0 0) p = 3 p = 31 p = infinity Computing class groups... Class group data of the fields: Field given by x - 744: [] Field given by x - 558: [] Field given by x - 372: [] Field given by x - 186: [] Field given by x: [] Dimension of Cl[2] = 0. Signatures: [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] Dimension of units mod squares = 5. Upper bound for Selmer group dimension: 15. ==> Upper bound for rank = 11. Computing unit groups... Class group and unit data of the fields: Field given by x - 744: Class group = [], units = [ 2 ] Field given by x - 558: Class group = [], units = [ 2 ] Field given by x - 372: Class group = [], units = [ 2 ] Field given by x - 186: Class group = [], units = [ 2 ] Field given by x: Class group = [], units = [ 2 ] Time for local computations: 1060 ms. Time for class groups: 0 ms. Time for unit groups: 11 ms. Selmer group dimension = 4, Dimension of 2-torsion = 4, ==> Bound for the MW-rank = 0. Total time: 1189 ms. Transforming presentation of S back to model C. 0 4 <[ 247/2*$.1^4 - 3674/3*$.1^3 + 4246*$.1^2 - 36131/6*$.1 + 2883, -47/4*$.1^4 + 141/2*$.1^3 - 327/4*$.1^2 - 72*$.1 + 93, 844/3*$.1^4 - 16415/6*$.1^3 + 55273/6*$.1^2 - 37565/3*$.1 + 5766, -113/12*$.1^4 + 72*$.1^3 - 1603/12*$.1^2 - 84*$.1 + 279 ], [], []> {} Total time: 4.369 seconds, Total memory usage: 2.69MB ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Sun Jan 25 10:15:46 2004 Input: P := PolynomialRing(Rationals()); C := HyperellipticCurve(x*(x-1)*(x-2)*(x-3)*(x-4)); D := QuadraticTwist(C,187); J := Jacobian(D); SetVerbose("JacHypSelmer", 2); TwoSelmerGroupData(J : Bound := 300); Output: Magma V2.10-6 Sun Jan 25 2004 10:15:42 on modular [Seed = 2596865891] ------------------------------------- TwoSelmerGroupData of Jacobian of Hyperelliptic Curve defined by y^2 = 187*x^5 - 1870*x^4 + 6545*x^3 - 9350*x^2 + 4488*x over Rational Field m= Mapping from: CrvHyp: C to CrvHyp: C1 with equations : 187*$.1 34969*$.2 $.3 and inverse 1/187*$.1 1/34969*$.2 $.3 Change curve into Hyperelliptic Curve defined by y^2 = x^5 - 1870*x^4 + 1223915*x^3 - 326960150*x^2 + 29347943064*x over Rational Field Bad primes = [ 2, 3, 11, 17 ] f factors as (x - 748) (x - 561) (x - 374) (x - 187) (x). For factor x - 748, use field defined by x - 1 and theta = 748 For factor x - 561, use field defined by x - 1 and theta = 561 For factor x - 374, use field defined by x - 1 and theta = 374 For factor x - 187, use field defined by x - 1 and theta = 187 For factor x, use field defined by x - 1 and theta = 0 The 2-torsion group has dimension 4. Determining local images... p = 2 x = 1/4 --> new generator (0 0 0 0 0 1 0 0 0 0 0 1 0 0 0) x = 10 --> new generator (1 1 1 0 0 0 0 0 1 0 1 1 1 0 1) p = 3 x = 4 --> new generator (1 0 0 0 0 1 1 1 0 0) p = 11 p = 17 p = infinity Computing class groups... Class group data of the fields: Field given by x - 748: [] Field given by x - 561: [] Field given by x - 374: [] Field given by x - 187: [] Field given by x: [] Dimension of Cl[2] = 0. Signatures: [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] Dimension of units mod squares = 5. Upper bound for Selmer group dimension: 17. ==> Upper bound for rank = 13. Computing unit groups... Class group and unit data of the fields: Field given by x - 748: Class group = [], units = [ 2 ] Field given by x - 561: Class group = [], units = [ 2 ] Field given by x - 374: Class group = [], units = [ 2 ] Field given by x - 187: Class group = [], units = [ 2 ] Field given by x: Class group = [], units = [ 2 ] Time for local computations: 549 ms. Time for class groups: 0 ms. Time for unit groups: 11 ms. Selmer group dimension = 5, Dimension of 2-torsion = 4, ==> Bound for the MW-rank = 1. Total time: 699 ms. Transforming presentation of S back to model C. 1 5 <[ 23871/8*$.1^4 - 118981/4*$.1^3 + 828013/8*$.1^2 - 586701/4*$.1 + 69938, 223*$.1^4 - 2145*$.1^3 + 7024*$.1^2 - 8842*$.1 + 3179, 4359345/4*$.1^4 - 21796723/2*$.1^3 + 152577051/4*$.1^2 - 108983977/2*$.1 + 26156812, -149/8*$.1^4 - 41/4*$.1^3 + 8777/8*$.1^2 - 16241/4*$.1 + 4114, -4*$.1^4 + 24*$.1^3 - 28*$.1^2 - 24*$.1 + 33 ], [], []> {} Total time: 3.849 seconds, Total memory usage: 2.79MB ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Sun Jan 25 10:16:03 2004 Input: P := PolynomialRing(Rationals()); C := HyperellipticCurve(x*(x-1)*(x-2)*(x-3)*(x-4)); D := QuadraticTwist(C,190); J := Jacobian(D); SetVerbose("JacHypSelmer", 2); TwoSelmerGroupData(J : Bound := 300); Output: Magma V2.10-6 Sun Jan 25 2004 10:15:58 on modular [Seed = 1866265257] ------------------------------------- TwoSelmerGroupData of Jacobian of Hyperelliptic Curve defined by y^2 = 190*x^5 - 1900*x^4 + 6650*x^3 - 9500*x^2 + 4560*x over Rational Field m= Mapping from: CrvHyp: C to CrvHyp: C1 with equations : 190*$.1 36100*$.2 $.3 and inverse 1/190*$.1 1/36100*$.2 $.3 Change curve into Hyperelliptic Curve defined by y^2 = x^5 - 1900*x^4 + 1263500*x^3 - 342950000*x^2 + 31277040000*x over Rational Field Bad primes = [ 2, 3, 5, 19 ] f factors as (x - 760) (x - 570) (x - 380) (x - 190) (x). For factor x - 760, use field defined by x - 1 and theta = 760 For factor x - 570, use field defined by x - 1 and theta = 570 For factor x - 380, use field defined by x - 1 and theta = 380 For factor x - 190, use field defined by x - 1 and theta = 190 For factor x, use field defined by x - 1 and theta = 0 The 2-torsion group has dimension 4. Determining local images... p = 2 x = 1 --> new generator (0 0 0 0 1 1 0 0 1 0 1 0 0 0 0) x = 18 --> new generator (1 0 1 1 1 0 1 1 0 0 0 1 1 0 0) p = 3 x = 7 --> new generator (1 0 0 0 0 1 1 1 0 0) p = 5 p = 19 p = infinity Computing class groups... Class group data of the fields: Field given by x - 760: [] Field given by x - 570: [] Field given by x - 380: [] Field given by x - 190: [] Field given by x: [] Dimension of Cl[2] = 0. Signatures: [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] Dimension of units mod squares = 5. Upper bound for Selmer group dimension: 17. ==> Upper bound for rank = 13. Computing unit groups... Class group and unit data of the fields: Field given by x - 760: Class group = [], units = [ 2 ] Field given by x - 570: Class group = [], units = [ 2 ] Field given by x - 380: Class group = [], units = [ 2 ] Field given by x - 190: Class group = [], units = [ 2 ] Field given by x: Class group = [], units = [ 2 ] Time for local computations: 1071 ms. Time for class groups: 0 ms. Time for unit groups: 0 ms. Selmer group dimension = 4, Dimension of 2-torsion = 4, ==> Bound for the MW-rank = 0. Total time: 1230 ms. Transforming presentation of S back to model C. 0 4 <[ 4653/4*$.1^4 - 23075/2*$.1^3 + 160009/4*$.1^2 - 56697*$.1 + 27075, -12*$.1^4 + 72*$.1^3 - 167/2*$.1^2 - 147/2*$.1 + 95, 2256*$.1^4 - 45215/2*$.1^3 + 158397/2*$.1^2 - 112995*$.1 + 54150, -357/2*$.1^4 + 3187/2*$.1^3 - 9055/2*$.1^2 + 7935/2*$.1 + 285 ], [], []> {} Total time: 4.479 seconds, Total memory usage: 2.79MB ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Sun Jan 25 10:16:16 2004 Input: P := PolynomialRing(Rationals()); C := HyperellipticCurve(x*(x-1)*(x-2)*(x-3)*(x-4)); D := QuadraticTwist(C,191); J := Jacobian(D); SetVerbose("JacHypSelmer", 2); TwoSelmerGroupData(J : Bound := 300); Output: Magma V2.10-6 Sun Jan 25 2004 10:16:12 on modular [Seed = 2016142764] ------------------------------------- TwoSelmerGroupData of Jacobian of Hyperelliptic Curve defined by y^2 = 191*x^5 - 1910*x^4 + 6685*x^3 - 9550*x^2 + 4584*x over Rational Field m= Mapping from: CrvHyp: C to CrvHyp: C1 with equations : 191*$.1 36481*$.2 $.3 and inverse 1/191*$.1 1/36481*$.2 $.3 Change curve into Hyperelliptic Curve defined by y^2 = x^5 - 1910*x^4 + 1276835*x^3 - 348393550*x^2 + 31940720664*x over Rational Field Bad primes = [ 2, 3, 191 ] f factors as (x - 764) (x - 573) (x - 382) (x - 191) (x). For factor x - 764, use field defined by x - 1 and theta = 764 For factor x - 573, use field defined by x - 1 and theta = 573 For factor x - 382, use field defined by x - 1 and theta = 382 For factor x - 191, use field defined by x - 1 and theta = 191 For factor x, use field defined by x - 1 and theta = 0 The 2-torsion group has dimension 4. Determining local images... p = 2 x = 1/4 --> new generator (0 0 0 0 0 1 0 0 0 0 0 1 0 0 0) x = 18 --> new generator (1 1 0 0 0 1 0 0 1 0 1 0 1 0 0) p = 3 x = 3 --> new generator (0 0 1 1 0 1 0 0 1 0) p = 191 p = infinity Computing class groups... Class group data of the fields: Field given by x - 764: [] Field given by x - 573: [] Field given by x - 382: [] Field given by x - 191: [] Field given by x: [] Dimension of Cl[2] = 0. Signatures: [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] Dimension of units mod squares = 5. Upper bound for Selmer group dimension: 13. ==> Upper bound for rank = 9. Computing unit groups... Class group and unit data of the fields: Field given by x - 764: Class group = [], units = [ 2 ] Field given by x - 573: Class group = [], units = [ 2 ] Field given by x - 382: Class group = [], units = [ 2 ] Field given by x - 191: Class group = [], units = [ 2 ] Field given by x: Class group = [], units = [ 2 ] Time for local computations: 520 ms. Time for class groups: 0 ms. Time for unit groups: 0 ms. Selmer group dimension = 6, Dimension of 2-torsion = 4, ==> Bound for the MW-rank = 2. Total time: 641 ms. Transforming presentation of S back to model C. 2 6 <[ 1544*$.1^4 - 15376*$.1^3 + 53560*$.1^2 - 76208*$.1 + 36481, 1504*$.1^4 - 15104*$.1^3 + 53120*$.1^2 - 76192*$.1 + 36481, -63/4*$.1^4 + 126*$.1^3 - 1069/4*$.1^2 - 34*$.1 + 382, 870777*$.1^4 - 8708311*$.1^3 + 30481014*$.1^2 - 43546711*$.1 + 20903613, 1/8*$.1^4 - 7/4*$.1^3 + 59/8*$.1^2 - 43/4*$.1 + 6, 4512*$.1^4 - 45311*$.1^3 + 159163*$.1^2 - 227804*$.1 + 109443 ], [], []> {} Total time: 3.819 seconds, Total memory usage: 2.89MB ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Sun Jan 25 10:16:30 2004 Input: P := PolynomialRing(Rationals()); C := HyperellipticCurve(x*(x-1)*(x-2)*(x-3)*(x-4)); D := QuadraticTwist(C,193); J := Jacobian(D); SetVerbose("JacHypSelmer", 2); TwoSelmerGroupData(J : Bound := 300); Output: Magma V2.10-6 Sun Jan 25 2004 10:16:26 on modular [Seed = 1898114259] ------------------------------------- TwoSelmerGroupData of Jacobian of Hyperelliptic Curve defined by y^2 = 193*x^5 - 1930*x^4 + 6755*x^3 - 9650*x^2 + 4632*x over Rational Field m= Mapping from: CrvHyp: C to CrvHyp: C1 with equations : 193*$.1 37249*$.2 $.3 and inverse 1/193*$.1 1/37249*$.2 $.3 Change curve into Hyperelliptic Curve defined by y^2 = x^5 - 1930*x^4 + 1303715*x^3 - 359452850*x^2 + 33299712024*x over Rational Field Bad primes = [ 2, 3, 193 ] f factors as (x - 772) (x - 579) (x - 386) (x - 193) (x). For factor x - 772, use field defined by x - 1 and theta = 772 For factor x - 579, use field defined by x - 1 and theta = 579 For factor x - 386, use field defined by x - 1 and theta = 386 For factor x - 193, use field defined by x - 1 and theta = 193 For factor x, use field defined by x - 1 and theta = 0 The 2-torsion group has dimension 4. Determining local images... p = 2 x = 1/4 --> new generator (0 0 0 0 0 1 0 0 0 0 0 1 0 0 0) x = 22 --> new generator (1 0 0 0 1 0 0 0 1 0 0 1 1 1 0) p = 3 x = 1 --> new generator (1 0 0 0 0 1 1 1 0 0) p = 193 p = infinity Computing class groups... Class group data of the fields: Field given by x - 772: [] Field given by x - 579: [] Field given by x - 386: [] Field given by x - 193: [] Field given by x: [] Dimension of Cl[2] = 0. Signatures: [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] Dimension of units mod squares = 5. Upper bound for Selmer group dimension: 13. ==> Upper bound for rank = 9. Computing unit groups... Class group and unit data of the fields: Field given by x - 772: Class group = [], units = [ 2 ] Field given by x - 579: Class group = [], units = [ 2 ] Field given by x - 386: Class group = [], units = [ 2 ] Field given by x - 193: Class group = [], units = [ 2 ] Field given by x: Class group = [], units = [ 2 ] Time for local computations: 549 ms. Time for class groups: 0 ms. Time for unit groups: 0 ms. Selmer group dimension = 8, Dimension of 2-torsion = 4, ==> Bound for the MW-rank = 4. Total time: 649 ms. Transforming presentation of S back to model C. 4 8 <[ 1/8*$.1^4 - 3/4*$.1^3 + 3/8*$.1^2 + 5/4*$.1 + 2, -$.1^3 + 7*$.1^2 - 12*$.1 + 3, 1/4*$.1^4 - 3/2*$.1^3 + 11/4*$.1^2 - 5/2*$.1 + 4, -9/8*$.1^4 + 35/4*$.1^3 - 163/8*$.1^2 + 51/4*$.1 + 6, 16*$.1^4 - 128*$.1^3 + 368*$.1^2 - 448*$.1 + 193, -24*$.1^4 + 144*$.1^3 - 168*$.1^2 - 144*$.1 + 193, 56*$.1^4 - 464*$.1^3 + 1192*$.1^2 - 976*$.1 + 193, -24*$.1^4 + 208*$.1^3 - 552*$.1^2 + 368*$.1 + 193 ], [], []> {} Total time: 3.749 seconds, Total memory usage: 2.89MB ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Sun Jan 25 10:16:47 2004 Input: P := PolynomialRing(Rationals()); C := HyperellipticCurve(x*(x-1)*(x-2)*(x-3)*(x-4)); D := QuadraticTwist(C,194); J := Jacobian(D); SetVerbose("JacHypSelmer", 2); TwoSelmerGroupData(J : Bound := 300); Output: Magma V2.10-6 Sun Jan 25 2004 10:16:42 on modular [Seed = 1243207672] ------------------------------------- TwoSelmerGroupData of Jacobian of Hyperelliptic Curve defined by y^2 = 194*x^5 - 1940*x^4 + 6790*x^3 - 9700*x^2 + 4656*x over Rational Field m= Mapping from: CrvHyp: C to CrvHyp: C1 with equations : 194*$.1 37636*$.2 $.3 and inverse 1/194*$.1 1/37636*$.2 $.3 Change curve into Hyperelliptic Curve defined by y^2 = x^5 - 1940*x^4 + 1317260*x^3 - 365069200*x^2 + 33995243904*x over Rational Field Bad primes = [ 2, 3, 97 ] f factors as (x - 776) (x - 582) (x - 388) (x - 194) (x). For factor x - 776, use field defined by x - 1 and theta = 776 For factor x - 582, use field defined by x - 1 and theta = 582 For factor x - 388, use field defined by x - 1 and theta = 388 For factor x - 194, use field defined by x - 1 and theta = 194 For factor x, use field defined by x - 1 and theta = 0 The 2-torsion group has dimension 4. Determining local images... p = 2 x = 1 --> new generator (0 0 0 0 1 0 0 0 1 0 1 1 0 0 0) x = 26 --> new generator (1 0 0 0 0 1 1 1 0 1 1 0 1 0 1) p = 3 x = 3 --> new generator (0 0 1 1 0 1 0 0 1 0) p = 97 p = infinity Computing class groups... Class group data of the fields: Field given by x - 776: [] Field given by x - 582: [] Field given by x - 388: [] Field given by x - 194: [] Field given by x: [] Dimension of Cl[2] = 0. Signatures: [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] Dimension of units mod squares = 5. Upper bound for Selmer group dimension: 13. ==> Upper bound for rank = 9. Computing unit groups... Class group and unit data of the fields: Field given by x - 776: Class group = [], units = [ 2 ] Field given by x - 582: Class group = [], units = [ 2 ] Field given by x - 388: Class group = [], units = [ 2 ] Field given by x - 194: Class group = [], units = [ 2 ] Field given by x: Class group = [], units = [ 2 ] Time for local computations: 1120 ms. Time for class groups: 0 ms. Time for unit groups: 19 ms. Selmer group dimension = 8, Dimension of 2-torsion = 4, ==> Bound for the MW-rank = 4. Total time: 1290 ms. Transforming presentation of S back to model C. 4 8 <[ $.1^3 - 13/2*$.1^2 + 17/2*$.1 + 3, -1/4*$.1^4 + 3/2*$.1^3 - 5/4*$.1^2 - 3*$.1 + 1, -1/2*$.1^3 + 7/2*$.1^2 - 7*$.1 + 6, -9/4*$.1^4 + 19*$.1^3 - 203/4*$.1^2 + 43*$.1 + 3, 8*$.1^4 - 64*$.1^3 + 184*$.1^2 - 224*$.1 + 97, -12*$.1^4 + 72*$.1^3 - 84*$.1^2 - 72*$.1 + 97, 28*$.1^4 - 232*$.1^3 + 596*$.1^2 - 488*$.1 + 97, -12*$.1^4 + 104*$.1^3 - 276*$.1^2 + 184*$.1 + 97 ], [], []> {} Total time: 4.469 seconds, Total memory usage: 2.79MB ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Sun Jan 25 10:17:02 2004 Input: P := PolynomialRing(Rationals()); C := HyperellipticCurve(x*(x-1)*(x-2)*(x-3)*(x-4)); D := QuadraticTwist(C,195); J := Jacobian(D); SetVerbose("JacHypSelmer", 2); TwoSelmerGroupData(J : Bound := 300); Output: Magma V2.10-6 Sun Jan 25 2004 10:16:58 on modular [Seed = 1125179073] ------------------------------------- TwoSelmerGroupData of Jacobian of Hyperelliptic Curve defined by y^2 = 195*x^5 - 1950*x^4 + 6825*x^3 - 9750*x^2 + 4680*x over Rational Field m= Mapping from: CrvHyp: C to CrvHyp: C1 with equations : 195*$.1 38025*$.2 $.3 and inverse 1/195*$.1 1/38025*$.2 $.3 Change curve into Hyperelliptic Curve defined by y^2 = x^5 - 1950*x^4 + 1330875*x^3 - 370743750*x^2 + 34701615000*x over Rational Field Bad primes = [ 2, 3, 5, 13 ] f factors as (x - 780) (x - 585) (x - 390) (x - 195) (x). For factor x - 780, use field defined by x - 1 and theta = 780 For factor x - 585, use field defined by x - 1 and theta = 585 For factor x - 390, use field defined by x - 1 and theta = 390 For factor x - 195, use field defined by x - 1 and theta = 195 For factor x, use field defined by x - 1 and theta = 0 The 2-torsion group has dimension 4. Determining local images... p = 2 x = 1/4 --> new generator (0 0 0 0 0 1 0 0 0 0 0 1 0 0 0) x = 26 --> new generator (1 1 1 0 0 0 0 0 1 0 1 1 1 0 1) p = 3 p = 5 p = 13 p = infinity Computing class groups... Class group data of the fields: Field given by x - 780: [] Field given by x - 585: [] Field given by x - 390: [] Field given by x - 195: [] Field given by x: [] Dimension of Cl[2] = 0. Signatures: [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] Dimension of units mod squares = 5. Upper bound for Selmer group dimension: 19. ==> Upper bound for rank = 15. Computing unit groups... Class group and unit data of the fields: Field given by x - 780: Class group = [], units = [ 2 ] Field given by x - 585: Class group = [], units = [ 2 ] Field given by x - 390: Class group = [], units = [ 2 ] Field given by x - 195: Class group = [], units = [ 2 ] Field given by x: Class group = [], units = [ 2 ] Time for local computations: 560 ms. Time for class groups: 0 ms. Time for unit groups: 0 ms. Selmer group dimension = 6, Dimension of 2-torsion = 4, ==> Bound for the MW-rank = 2. Total time: 721 ms. Transforming presentation of S back to model C. 2 6 <[ 248/3*$.1^4 - 807*$.1^3 + 8209/3*$.1^2 - 3764*$.1 + 1755, 11*$.1^4 - 118*$.1^3 + 442*$.1^2 - 665*$.1 + 325, 165337/12*$.1^4 - 413059/3*$.1^3 + 5777759/12*$.1^2 - 2061350/3*$.1 + 329550, 11*$.1^4 - 114*$.1^3 + 418*$.1^2 - 630*$.1 + 325, 149/8*$.1^4 - 723/4*$.1^3 + 4887/8*$.1^2 - 3351/4*$.1 + 390, 39*$.1^4 - 1175/3*$.1^3 + 1379*$.1^2 - 5965/3*$.1 + 975 ], [], []> {} Total time: 3.829 seconds, Total memory usage: 2.89MB ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Sun Jan 25 10:17:15 2004 Input: P := PolynomialRing(Rationals()); C := HyperellipticCurve(x*(x-1)*(x-2)*(x-3)*(x-4)); D := QuadraticTwist(C,197); J := Jacobian(D); SetVerbose("JacHypSelmer", 2); TwoSelmerGroupData(J : Bound := 300); Output: Magma V2.10-6 Sun Jan 25 2004 10:17:11 on modular [Seed = 1544536515] ------------------------------------- TwoSelmerGroupData of Jacobian of Hyperelliptic Curve defined by y^2 = 197*x^5 - 1970*x^4 + 6895*x^3 - 9850*x^2 + 4728*x over Rational Field m= Mapping from: CrvHyp: C to CrvHyp: C1 with equations : 197*$.1 38809*$.2 $.3 and inverse 1/197*$.1 1/38809*$.2 $.3 Change curve into Hyperelliptic Curve defined by y^2 = x^5 - 1970*x^4 + 1358315*x^3 - 382268650*x^2 + 36147323544*x over Rational Field Bad primes = [ 2, 3, 197 ] f factors as (x - 788) (x - 591) (x - 394) (x - 197) (x). For factor x - 788, use field defined by x - 1 and theta = 788 For factor x - 591, use field defined by x - 1 and theta = 591 For factor x - 394, use field defined by x - 1 and theta = 394 For factor x - 197, use field defined by x - 1 and theta = 197 For factor x, use field defined by x - 1 and theta = 0 The 2-torsion group has dimension 4. Determining local images... p = 2 x = 1/4 --> new generator (0 0 0 0 0 1 0 0 0 0 0 1 0 0 0) x = 30 --> new generator (1 0 1 0 1 1 0 0 1 0 0 0 1 1 1) p = 3 x = 3 --> new generator (0 0 1 1 0 1 0 0 1 0) p = 197 p = infinity Computing class groups... Class group data of the fields: Field given by x - 788: [] Field given by x - 591: [] Field given by x - 394: [] Field given by x - 197: [] Field given by x: [] Dimension of Cl[2] = 0. Signatures: [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] Dimension of units mod squares = 5. Upper bound for Selmer group dimension: 13. ==> Upper bound for rank = 9. Computing unit groups... Class group and unit data of the fields: Field given by x - 788: Class group = [], units = [ 2 ] Field given by x - 591: Class group = [], units = [ 2 ] Field given by x - 394: Class group = [], units = [ 2 ] Field given by x - 197: Class group = [], units = [ 2 ] Field given by x: Class group = [], units = [ 2 ] Time for local computations: 549 ms. Time for class groups: 0 ms. Time for unit groups: 0 ms. Selmer group dimension = 5, Dimension of 2-torsion = 4, ==> Bound for the MW-rank = 1. Total time: 661 ms. Transforming presentation of S back to model C. 1 5 <[ 4868*$.1^4 - 48613*$.1^3 + 169878*$.1^2 - 242363*$.1 + 116427, 4851*$.1^4 - 48707*$.1^3 + 170968*$.1^2 - 244130*$.1 + 116427, 7645241/4*$.1^4 - 19113234*$.1^3 + 267586987/4*$.1^2 - 95567060*$.1 + 45872238, 16*$.1^4 - 128*$.1^3 + 369*$.1^2 - 452*$.1 + 197, 77027/8*$.1^4 - 385137/4*$.1^3 + 2698329/8*$.1^2 - 1931593/4*$.1 + 232854 ], [], []> {} Total time: 3.819 seconds, Total memory usage: 2.89MB ************** MAGMA ***************** Host robserve.STUDFB.UniBw-Muenchen.de. (137.193.211.43) Time: Sun Jan 25 10:17:31 2004 Input: P := PolynomialRing(Rationals()); C := HyperellipticCurve(x*(x-1)*(x-2)*(x-3)*(x-4)); D := QuadraticTwist(C,199); J := Jacobian(D); SetVerbose("JacHypSelmer", 2); TwoSelmerGroupData(J : Bound := 300); Output: Magma V2.10-6 Sun Jan 25 2004 10:17:27 on modular [Seed = 1426508602] ------------------------------------- TwoSelmerGroupData of Jacobian of Hyperelliptic Curve defined by y^2 = 199*x^5 - 1990*x^4 + 6965*x^3 - 9950*x^2 + 4776*x over Rational Field m= Mapping from: CrvHyp: C to CrvHyp: C1 with equations : 199*$.1 39601*$.2 $.3 and inverse 1/199*$.1 1/39601*$.2 $.3 Change curve into Hyperelliptic Curve defined by y^2 = x^5 - 1990*x^4 + 1386035*x^3 - 394029950*x^2 + 37637740824*x over Rational Field Bad primes = [ 2, 3, 199 ] f factors as (x - 796) (x - 597) (x - 398) (x - 199) (x). For factor x - 796, use field defined by x - 1 and theta = 796 For factor x - 597, use field defined by x - 1 and theta = 597 For factor x - 398, use field defined by x - 1 and theta = 398 For factor x - 199, use field defined by x - 1 and theta = 199 For factor x, use field defined by x - 1 and theta = 0 The 2-torsion group has dimension 4. Determining local images... p = 2 x = 1/4 --> new generator (0 0 0 0 0 1 0 0 0 0 0 1 0 0 0) x = 2 --> new generator (1 1 0 0 0 1 0 0 1 0 1 0 1 0 0) p = 3 x = 7 --> new generator (1 0 0 0 0 1 1 1 0 0) p = 199 p = infinity Computing class groups... Class group data of the fields: Field given by x - 796: [] Field given by x - 597: [] Field given by x - 398: [] Field given by x - 199: [] Field given by x: [] Dimension of Cl[2] = 0. Signatures: [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] Dimension of units mod squares = 5. Upper bound for Selmer group dimension: 13. ==> Upper bound for rank = 9. Computing unit groups... Class group and unit data of the fields: Field given by x - 796: Class group = [], units = [ 2 ] Field given by x - 597: Class group = [], units = [ 2 ] Field given by x - 398: Class group = [], units = [ 2 ] Field given by x - 199: Class group = [], units = [ 2 ] Field given by x: Class group = [], units = [ 2 ] Time for local computations: 519 ms. Time for class groups: 0 ms. Time for unit groups: 0 ms. Selmer group dimension = 4, Dimension of 2-torsion = 4, ==> Bound for the MW-rank = 0. Total time: 641 ms. Transforming presentation of S back to model C. 0 4 <[ 26995/8*$.1^4 - 134577/4*$.1^3 + 936873/8*$.1^2 - 664153/4*$.1 + 79202, 4950*$.1^4 - 49699*$.1^3 + 174445*$.1^2 - 249096*$.1 + 118803, 5253601/4*$.1^4 - 26268003/2*$.1^3 + 183876011/4*$.1^2 - 131340401/2*$.1 + 31522396, -1197/8*$.1^4 + 5183/4*$.1^3 - 27487/8*$.1^2 + 9159/4*$.1 + 1194 ], [], []> {} Total time: 3.829 seconds, Total memory usage: 2.89MB ************** MAGMA ***************** Host du-011-0088.freeuk.com. (212.126.154.88) Time: Sun Jan 25 13:03:44 2004 Input: 44^44 Output: Magma V2.10-6 Sun Jan 25 2004 13:03:41 on modular [Seed = 3247801685] ------------------------------------- 2050773823560610053645205609172376035486179836520607547294916966189367296 Total time: 3.029 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host core-dr00.proxy.nacamar.net. (194.162.162.68) Time: Mon Jan 26 04:40:47 2004 Input: H:=HammingCode(GF(7),2); GeneratorMatrix(H); Output: Magma V2.10-6 Mon Jan 26 2004 04:40:43 on modular [Seed = 3001422417] ------------------------------------- [1 0 0 0 0 0 1 6] [0 1 0 0 0 0 1 5] [0 0 1 0 0 0 2 4] [0 0 0 1 0 0 3 3] [0 0 0 0 1 0 4 2] [0 0 0 0 0 1 5 1] Total time: 3.039 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host core-dr00.proxy.nacamar.net. (194.162.162.68) Time: Mon Jan 26 04:41:58 2004 Input: H:=HammingCode(GF(8),2); GeneratorMatrix(H); Output: Magma V2.10-6 Mon Jan 26 2004 04:41:55 on modular [Seed = 2901937207] ------------------------------------- [ 1 0 0 0 0 0 0 1 $.1] [ 0 1 0 0 0 0 0 $.1 $.1^6] [ 0 0 1 0 0 0 0 $.1^6 $.1^3] [ 0 0 0 1 0 0 0 $.1^3 $.1^3] [ 0 0 0 0 1 0 0 $.1^3 $.1^6] [ 0 0 0 0 0 1 0 $.1^6 $.1] [ 0 0 0 0 0 0 1 $.1 1] Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host core-dr00.proxy.nacamar.net. (194.162.162.68) Time: Mon Jan 26 04:57:18 2004 Input: H:=HammingCode(GF(16),2); GeneratorMatrix(H); Output: Magma V2.10-6 Mon Jan 26 2004 04:57:15 on modular [Seed = 1359344979] ------------------------------------- [1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 $.1^3] [0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 $.1^3 $.1^13] [0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 $.1^13 $.1^9] [0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 $.1^9 $.1] [0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 $.1 $.1^14] [0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 $.1^14 $.1^5] [0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 $.1^5 $.1^6] [0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 $.1^6 $.1^6] [0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 $.1^6 $.1^5] [0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 $.1^5 $.1^14] [0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 $.1^14 $.1] [0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 $.1 $.1^9] [0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 $.1^9 $.1^13] [0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 $.1^13 $.1^3] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 $.1^3 1] Total time: 3.009 seconds, Total memory usage: 2.19MB ************** MAGMA ***************** Host core-dr00.proxy.nacamar.net. (194.162.162.68) Time: Mon Jan 26 04:58:04 2004 Input: H:=HammingCode(GF(2),1); GeneratorMatrix(H); Output: Magma V2.10-6 Mon Jan 26 2004 04:58:01 on modular [Seed = 1209855128] ------------------------------------- Matrix with 0 rows and 1 column Total time: 3.019 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host core-dr00.proxy.nacamar.net. (194.162.162.68) Time: Mon Jan 26 04:58:37 2004 Input: H:=HammingCode(GF(2),2); GeneratorMatrix(H); Output: Magma V2.10-6 Mon Jan 26 2004 04:58:34 on modular [Seed = 1108797169] ------------------------------------- [1 1 1] Total time: 2.899 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host core-dr00.proxy.nacamar.net. (194.162.162.68) Time: Mon Jan 26 04:59:30 2004 Input: H:=HammingCode(GF(16),2); GeneratorMatrix(H); Output: Magma V2.10-6 Mon Jan 26 2004 04:59:27 on modular [Seed = 1047173816] ------------------------------------- [1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 $.1^3] [0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 $.1^3 $.1^13] [0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 $.1^13 $.1^9] [0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 $.1^9 $.1] [0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 $.1 $.1^14] [0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 $.1^14 $.1^5] [0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 $.1^5 $.1^6] [0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 $.1^6 $.1^6] [0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 $.1^6 $.1^5] [0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 $.1^5 $.1^14] [0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 $.1^14 $.1] [0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 $.1 $.1^9] [0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 $.1^9 $.1^13] [0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 $.1^13 $.1^3] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 $.1^3 1] Total time: 2.909 seconds, Total memory usage: 2.19MB ************** MAGMA ***************** Host core-dr00.proxy.nacamar.net. (194.162.162.68) Time: Mon Jan 26 05:00:11 2004 Input: H:=HammingCode(GF(8),2); GeneratorMatrix(H); Output: Magma V2.10-6 Mon Jan 26 2004 05:00:09 on modular [Seed = 779783038] ------------------------------------- [ 1 0 0 0 0 0 0 1 $.1] [ 0 1 0 0 0 0 0 $.1 $.1^6] [ 0 0 1 0 0 0 0 $.1^6 $.1^3] [ 0 0 0 1 0 0 0 $.1^3 $.1^3] [ 0 0 0 0 1 0 0 $.1^3 $.1^6] [ 0 0 0 0 0 1 0 $.1^6 $.1] [ 0 0 0 0 0 0 1 $.1 1] Total time: 2.909 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host core-dr00.proxy.nacamar.net. (194.162.162.68) Time: Mon Jan 26 05:00:32 2004 Input: H:=HammingCode(GF(33),2); GeneratorMatrix(H); Output: Magma V2.10-6 Mon Jan 26 2004 05:00:29 on modular [Seed = 424524893] ------------------------------------- >> H:=HammingCode(GF(33),2); ^ Runtime error in 'GF': Argument 1 (33) is not a prime power >> GeneratorMatrix(H); ^ User error: Identifier 'H' has not been declared or assigned Total time: 2.939 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host core-dr00.proxy.nacamar.net. (194.162.162.68) Time: Mon Jan 26 05:00:44 2004 Input: H:=HammingCode(GF(32),2); GeneratorMatrix(H); Output: Magma V2.10-6 Mon Jan 26 2004 05:00:41 on modular [Seed = 272938272] ------------------------------------- [1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 $.1^7] [0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 $.1^7 $.1^13] [0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 $.1^13 $.1^21] [0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 $.1^21 $.1^6] [0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 $.1^6 $.1^2] [0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 $.1^2 $.1^4] [0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 $.1^4 $.1^18] [0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 $.1^18 $.1^29] [0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 $.1^29 $.1^19] [0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 $.1^19 $.1^24] [0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 $.1^24 $.1^11] [0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 $.1^11 $.1^14] [0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 $.1^14 $.1^15] [0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 $.1^15 $.1^3] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 $.1^3 $.1^12] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 $.1^12 $.1^12] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 $.1^12 $.1^3] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 $.1^3 $.1^15] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 $.1^15 $.1^14] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 $.1^14 $.1^11] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 $.1^11 $.1^24] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 $.1^24 $.1^19] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 $.1^19 $.1^29] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 $.1^29 $.1^18] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 $.1^18 $.1^4] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 $.1^4 $.1^2] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 $.1^2 $.1^6] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 $.1^6 $.1^21] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 $.1^21 $.1^13] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 $.1^13 $.1^7] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 $.1^7 1] Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host core-dr00.proxy.nacamar.net. (194.162.162.68) Time: Mon Jan 26 05:01:15 2004 Input: H:=HammingCode(GF(16),2); GeneratorMatrix(H); Output: Magma V2.10-6 Mon Jan 26 2004 05:01:12 on modular [Seed = 4054144224] ------------------------------------- [1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 $.1^3] [0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 $.1^3 $.1^13] [0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 $.1^13 $.1^9] [0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 $.1^9 $.1] [0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 $.1 $.1^14] [0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 $.1^14 $.1^5] [0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 $.1^5 $.1^6] [0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 $.1^6 $.1^6] [0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 $.1^6 $.1^5] [0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 $.1^5 $.1^14] [0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 $.1^14 $.1] [0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 $.1 $.1^9] [0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 $.1^9 $.1^13] [0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 $.1^13 $.1^3] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 $.1^3 1] Total time: 2.889 seconds, Total memory usage: 2.19MB ************** MAGMA ***************** Host core-dr00.proxy.nacamar.net. (194.162.162.68) Time: Mon Jan 26 05:03:53 2004 Input: H:=HammingCode(GF(8),2); GeneratorMatrix(H); Output: Magma V2.10-6 Mon Jan 26 2004 05:03:50 on modular [Seed = 3786753950] ------------------------------------- [ 1 0 0 0 0 0 0 1 $.1] [ 0 1 0 0 0 0 0 $.1 $.1^6] [ 0 0 1 0 0 0 0 $.1^6 $.1^3] [ 0 0 0 1 0 0 0 $.1^3 $.1^3] [ 0 0 0 0 1 0 0 $.1^3 $.1^6] [ 0 0 0 0 0 1 0 $.1^6 $.1] [ 0 0 0 0 0 0 1 $.1 1] Total time: 2.979 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host core-dr00.proxy.nacamar.net. (194.162.162.68) Time: Mon Jan 26 05:17:15 2004 Input: H:=HammingCode(GF(7),2); GeneratorMatrix(H); Output: Magma V2.10-6 Mon Jan 26 2004 05:17:12 on modular [Seed = 3085115110] ------------------------------------- [1 0 0 0 0 0 1 6] [0 1 0 0 0 0 1 5] [0 0 1 0 0 0 2 4] [0 0 0 1 0 0 3 3] [0 0 0 0 1 0 4 2] [0 0 0 0 0 1 5 1] Total time: 2.919 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host core-dr00.proxy.nacamar.net. (194.162.162.68) Time: Mon Jan 26 05:17:20 2004 Input: H:=HammingCode(GF(7),2); GeneratorMatrix(H); Output: Magma V2.10-6 Mon Jan 26 2004 05:17:17 on modular [Seed = 2935621626] ------------------------------------- [1 0 0 0 0 0 1 6] [0 1 0 0 0 0 1 5] [0 0 1 0 0 0 2 4] [0 0 0 1 0 0 3 3] [0 0 0 0 1 0 4 2] [0 0 0 0 0 1 5 1] Total time: 2.939 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host core-dr00.proxy.nacamar.net. (194.162.162.68) Time: Mon Jan 26 05:35:22 2004 Input: H:=HammingCode(GF(8),3); GeneratorMatrix(H); Output: Magma V2.10-6 Mon Jan 26 2004 05:35:19 on modular [Seed = 1614073213] ------------------------------------- [1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 $.1^4] [0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 $.1^4 1 $.1] [0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 $.1 $.1^4 $.1^4] [0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 $.1^4 $.1 $.1^2] [0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 $.1^2 $.1^4 $.1^5] [0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 $.1^5 $.1^2 $.1] [0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 $.1 $.1^5 $.1^3] [0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 $.1^3 $.1 $.1^4] [0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 $.1^4 $.1^3 0] [0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 $.1^4 $.1^3] [0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 $.1^3 0 $.1^5] [0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 $.1^5 $.1^3 $.1^2] [0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 $.1^2 $.1^5 $.1^4] [0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 $.1^4 $.1^2 $.1^6] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 $.1^6 $.1^4 $.1^5] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 $.1^5 $.1^6 $.1] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 $.1 $.1^5 $.1] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 $.1 $.1 0] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 $.1 $.1] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 $.1 0 $.1^6] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 $.1^6 $.1 $.1^3] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 $.1^3 $.1^6 $.1^3] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 $.1^3 $.1^3 $.1^2] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 $.1^2 $.1^3 $.1^4] [0 0 0 0 0 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0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 $.1^3 $.1^4 $.1^4] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 $.1^4 $.1^3 $.1^2] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 $.1^2 $.1^4 $.1^4] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 $.1^4 $.1^2 $.1^2] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 $.1^2 $.1^4 1] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 $.1^2 0] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 $.1^2] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 $.1^2 0 $.1^2] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 $.1^2 $.1^2 $.1^6] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 $.1^6 $.1^2 $.1^5] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 $.1^5 $.1^6 0] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 $.1^5 $.1^6] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 $.1^6 0 $.1^2] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 $.1^2 $.1^6 $.1^6] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 $.1^6 $.1^2 $.1^4] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 $.1^4 $.1^6 $.1^4] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 $.1^4 $.1^4 $.1^5] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 $.1^5 $.1^4 $.1] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 $.1 $.1^5 1] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 $.1 1] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 $.1^2] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 $.1^2 1 $.1^2] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 $.1^2 $.1^2 $.1^2] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 $.1^2 $.1^2 1] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 $.1^2 $.1] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 $.1 1 $.1^3] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 $.1^3 $.1 0] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 $.1^3 $.1] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 $.1 0 $.1^2] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 $.1^2 $.1 $.1^6] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 ** WARNING: Output too long, hence truncated. ************** MAGMA ***************** Host p2182-adsau04yokonib2-acca.kanagawa.ocn.ne.jp. (220.104.197.182) Time: Mon Jan 26 08:45:41 2004 Input: prime element Output: Magma V2.10-6 Mon Jan 26 2004 08:45:38 on modular [Seed = 1158684474] ------------------------------------- >> prime element; ^ User error: bad syntax Total time: 3.009 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host p2182-adsau04yokonib2-acca.kanagawa.ocn.ne.jp. (220.104.197.182) Time: Mon Jan 26 08:46:08 2004 Input: prime element Output: Magma V2.10-6 Mon Jan 26 2004 08:46:05 on modular [Seed = 862349651] ------------------------------------- >> prime element; ^ User error: bad syntax Total time: 2.979 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 2(SERVFAIL) (203.91.149.163) Time: Mon Jan 26 09:53:57 2004 Input: k := GF(2); C := PrimitivePolynomial(k,9); C; for j in [19..31] do for k in [16..18] do for m in [14..15] do for n in [8..13] do C := ((1 + X^11)^n)*((1 + X^13)^m)*((1 + X^17)^k)*((1 + X^19)^j) + X^1279; if IsPrimitive(C) then C; n; m; k; j; end if; end for; end for; end for; end for; Output: Magma V2.10-6 Mon Jan 26 2004 09:53:51 on modular [Seed = 779831215] ------------------------------------- X^9 + X^4 + 1 Total time: 6.209 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 2(SERVFAIL) (203.91.149.163) Time: Mon Jan 26 09:55:20 2004 Input: k := GF(2); C := PrimitivePolynomial(k,9); C; for j in [8..31] do for k in [8..21] do for m in [8..21] do for n in [8..21] do C := ((1 + X^11)^n)*((1 + X^13)^m)*((1 + X^17)^k)*((1 + X^19)^j) + X^1279; if IsPrimitive(C) then C; n; m; k; j; end if; end for; end for; end for; end for; Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Mon Jan 26 2004 09:54:57 on modular [Seed = 661802264] ------------------------------------- X^9 + X^4 + 1 X^1279 + X^781 + X^768 + X^737 + X^729 + X^724 + X^716 + X^685 + X^672 + X^645 + X^632 + X^629 + X^616 + X^605 + X^601 + X^593 + X^592 + X^588 + X^585 + X^580 + X^577 + X^573 + X^572 + X^564 + X^561 + X^560 + X^553 + X^549 + X^548 + X^540 + X^536 + X^533 + X^529 + X^521 + X^520 + X^516 + X^509 + X^508 + X^496 + X^493 + X^480 + X^477 + X^469 + X^464 + X^456 + X^453 + X^449 + X^441 + X^440 + X^437 + X^436 + X^428 + X^425 + X^424 + X^421 + X^417 + X^412 + X^409 + X^408 + X^404 + X^401 + X^396 + X^393 + X^388 + X^385 + X^380 + X^377 + X^373 + X^372 + X^369 + X^364 + X^360 + X^357 + X^356 + X^353 + X^345 + X^344 + X^341 + X^340 + X^332 + X^328 + X^325 + X^317 + X^312 + X^304 + X^301 + X^288 + X^285 + X^273 + X^272 + X^265 + X^261 + X^260 + X^252 + X^248 + X^245 + X^241 + X^233 + X^232 + X^228 + X^221 + X^220 + X^217 + X^209 + X^208 + X^204 + X^201 + X^196 + X^193 + X^189 + X^188 + X^180 + X^176 + X^165 + X^152 + X^149 + X^136 + X^109 + X^96 + X^65 + X^57 + X^52 + X^44 + X^13 + 1 20 21 8 8 X^1279 + X^661 + X^650 + X^639 + X^635 + X^628 + X^627 + X^624 + X^616 + X^613 + X^605 + X^602 + X^601 + X^594 + X^590 + X^579 + X^568 + X^557 + X^546 + X^535 + X^531 + X^525 + X^524 + X^523 + X^520 + X^514 + X^512 + X^503 + X^501 + X^499 + X^497 + X^492 + X^491 + X^490 + X^488 + X^487 + X^486 + X^485 + X^483 + X^480 + X^477 + X^476 + X^474 + X^472 + X^469 + X^466 + X^465 + X^463 + X^461 + X^459 + X^458 + X^454 + X^453 + X^452 + X^451 + X^450 + X^449 + X^448 + X^443 + X^442 + X^440 + X^438 + X^437 + X^432 + X^429 + X^427 + X^426 + X^425 + X^421 + X^418 + X^416 + X^414 + X^410 + X^405 + X^403 + X^399 + X^395 + X^394 + X^392 + X^388 + X^387 + X^384 + X^383 + X^381 + X^379 + X^376 + X^372 + X^371 + X^370 + X^368 + X^365 + X^361 + X^360 + X^359 + X^357 + X^355 + X^354 + X^351 + X^350 + X^348 + X^346 + X^345 + X^344 + X^340 + X^334 + X^327 + X^321 + X^317 + X^316 + X^315 + X^313 + X^311 + X^310 + X^307 + X^306 + X^304 + X^302 + X^301 + X^300 + X^296 + X^293 + X^291 + X^290 + X^289 + X^285 + X^282 + X^280 + X^278 + X^277 + X^274 + X^273 + X^269 + X^267 + X^266 + X^262 + X^258 + X^256 + X^251 + X^247 + X^245 + X^243 + X^240 + X^236 + X^235 + X^234 + X^232 + X^229 + X^224 + X^223 + X^221 + X^219 + X^218 + X^213 + X^212 + X^211 + X^210 + X^209 + X^208 + X^207 + X^203 + X^202 + X^200 + X^198 + X^196 + X^195 + X^192 + X^189 + X^187 + X^185 + X^184 + X^181 + X^178 + X^176 + X^175 + X^174 + X^173 + X^171 + X^170 + X^169 + X^164 + X^162 + X^160 + X^158 + X^149 + X^147 + X^141 + X^138 + X^137 + X^136 + X^130 + X^126 + X^115 + X^104 + X^93 + X^82 + X^71 + X^67 + X^60 + X^59 + X^56 + X^48 + X^45 + X^37 + X^34 + X^33 + X^26 + X^22 + X^11 + 1 19 10 10 8 X^1279 + X^799 + X^782 + X^765 + X^755 + X^748 + X^747 + X^738 + X^731 + X^730 + X^721 + X^714 + X^713 + X^711 + X^704 + X^703 + X^697 + X^696 + X^694 + X^687 + X^686 + X^680 + X^679 + X^677 + X^670 + X^669 + X^667 + X^663 + X^662 + X^660 + X^659 + X^653 + X^652 + X^650 + X^647 + X^646 + X^645 + X^643 + X^642 + X^636 + X^635 + X^633 + X^630 + X^629 + X^628 + X^626 + X^625 + X^619 + X^618 + X^616 + X^615 + X^613 + X^612 + X^611 + X^609 + X^608 + X^603 + X^602 + X^601 + X^599 + X^598 + X^596 + X^594 + X^592 + X^586 + X^585 + X^584 + X^582 + X^581 + X^579 + X^577 + X^575 + X^569 + X^568 + X^567 + X^565 + X^564 + X^562 + X^560 + X^559 + X^558 + X^552 + X^550 + X^548 + X^545 + X^543 + X^542 + X^541 + X^539 + X^535 + X^533 + X^531 + X^528 + X^527 + X^526 + X^525 + X^524 + X^522 + X^518 + X^516 + X^515 + X^514 + X^511 + X^510 + X^509 + X^508 + X^505 + X^503 + X^501 + X^499 + X^498 + X^497 + X^495 + X^494 + X^493 + X^492 + X^491 + X^488 + X^486 + X^484 + X^483 + X^482 + X^481 + X^480 + X^478 + X^477 + X^476 + X^474 + X^471 + X^469 + X^467 + X^466 + X^465 + X^464 + X^461 + X^460 + X^457 + X^454 + X^452 + X^451 + X^450 + X^449 + X^448 + X^447 + X^444 + X^443 + X^440 + X^437 + X^435 + X^434 + X^433 + X^432 + X^430 + X^427 + X^426 + X^423 + X^420 + X^418 + X^417 + X^416 + X^415 + X^413 + X^410 + X^409 + X^407 + X^406 + X^403 + X^401 + X^400 + X^399 + X^398 + X^396 + X^393 + X^392 + X^390 + X^389 + X^386 + X^384 + X^383 + X^382 + X^381 + X^379 + X^376 + X^373 + X^372 + X^369 + X^367 + X^366 + X^365 + X^364 + X^362 + X^359 + X^356 + X^355 + X^352 + X^351 + X^350 + X^349 + X^348 + X^347 + X^345 + X^342 + X^339 + X^338 + X^335 + X^334 + X^333 + X^332 + X^330 + X^328 + X^325 + X^323 + X^322 + X^321 + X^319 + X^318 + X^317 + X^316 + X^315 + X^313 + X^311 + X^308 + X^307 + X^306 + X^305 + X^304 + X^302 + X^301 + X^300 + X^298 + X^296 + X^294 + X^291 + X^290 + X^289 + X^288 + X^285 + X^284 + X^283 + X^281 + X^277 + X^275 + X^274 + X^273 + X^272 + X^271 + X^268 + X^266 + X^264 + X^260 + X^258 + X^257 + X^256 + X^254 + X^251 + X^249 + X^247 + X^241 + X^240 + X^239 + X^237 + X^235 + X^234 + X^232 + X^231 + X^230 + X^224 + X^222 + X^220 + X^218 + X^217 + X^215 + X^214 + X^213 + X^207 + X^205 + X^203 + X^201 + X^200 + X^198 + X^197 + X^196 + X^191 + X^190 + X^188 + X^187 + X^186 + X^184 + X^183 + X^181 + X^180 + X^174 + X^173 + X^171 + X^170 + X^169 + X^166 + X^164 + X^163 + X^157 + X^156 + X^154 + X^153 + X^152 + X^149 + X^147 + X^146 + X^140 + X^139 + X^137 + X^136 + X^132 + X^130 + X^129 + X^122 + X^120 + X^119 + X^113 + X^112 + X^105 + X^103 + X^102 + X^96 + X^95 + X^88 + X^86 + X^85 + X^78 + X^69 + X^68 + X^61 + X^52 + X^51 + X^44 + X^34 + X^17 + 1 12 20 15 8 X^1279 + X^775 + X^764 + X^749 + X^741 + X^738 + X^730 + X^715 + X^704 + X^671 + X^660 + X^645 + X^637 + X^634 + X^626 + X^623 + X^612 + X^611 + X^600 + X^599 + X^597 + X^589 + X^588 + X^586 + X^578 + X^573 + X^565 + X^563 + X^562 + X^554 + X^552 + X^539 + X^528 + X^519 + X^508 + X^503 + X^495 + X^493 + X^492 + X^485 + X^484 + X^482 + X^477 + X^474 + X^466 + X^461 + X^459 + X^450 + X^448 + X^447 + X^443 + X^436 + X^435 + X^432 + X^424 + X^421 + X^413 + X^410 + X^402 + X^399 + X^388 + X^387 + X^376 + X^373 + X^365 + X^362 + X^354 + X^351 + X^343 + X^340 + X^339 + X^332 + X^328 + X^327 + X^325 + X^316 + X^314 + X^309 + X^301 + X^298 + X^293 + X^291 + X^290 + X^283 + X^282 + X^280 + X^272 + X^267 + X^256 + X^247 + X^236 + X^223 + X^221 + X^213 + X^212 + X^210 + X^202 + X^197 + X^189 + X^187 + X^186 + X^178 + X^176 + X^175 + X^164 + X^163 + X^152 + X^149 + X^141 + X^138 + X^130 + X^115 + X^104 + X^71 + X^60 + X^45 + X^37 + X^34 + X^26 + X^11 + 1 17 10 18 8 X^1279 + X^906 + X^884 + X^862 + X^854 + X^840 + X^838 + X^832 + X^818 + X^816 + X^810 + X^796 + X^794 + X^788 + X^786 + X^774 + X^772 + X^766 + X^764 + X^754 + X^752 + X^750 + X^744 + X^742 + X^732 + X^728 + X^722 + X^720 + X^710 + X^706 + X^702 + X^700 + X^688 + X^686 + X^684 + X^680 + X^666 + X^664 + X^658 + X^646 + X^644 + X^642 + X^636 + X^630 + X^624 + X^622 + X^620 + X^614 + X^610 + X^608 + X^602 + X^600 + X^598 + X^592 + X^588 + X^586 + X^582 + X^580 + X^578 + X^576 + X^570 + X^564 + X^560 + X^558 + X^556 + X^554 + X^548 + X^546 + X^542 + X^538 + X^536 + X^534 + X^532 + X^524 + X^522 + X^520 + X^516 + X^512 + X^502 + X^500 + X^498 + X^490 + X^482 + X^480 + X^476 + X^470 + X^468 + X^460 + X^458 + X^448 + X^446 + X^438 + X^436 + X^430 + X^426 + X^424 + X^416 + X^408 + X^406 + X^404 + X^394 + X^390 + X^386 + X^384 + X^382 + X^374 + X^372 + X^370 + X^368 + X^364 + X^360 + X^358 + X^352 + X^350 + X^348 + X^346 + X^342 + X^336 + X^330 + X^328 + X^326 + X^324 + X^320 + X^318 + X^314 + X^308 + X^306 + X^304 + X^298 + X^296 + X^292 + X^286 + X^284 + X^282 + X^276 + X^270 + X^264 + X^262 + X^260 + X^248 + X^242 + X^240 + X^226 + X^222 + X^220 + X^218 + X^206 + X^204 + X^200 + X^196 + X^186 + X^184 + X^178 + X^174 + X^164 + X^162 + X^156 + X^154 + X^152 + X^142 + X^140 + X^134 + X^132 + X^120 + X^118 + X^112 + X^110 + X^96 + X^90 + X^88 + X^74 + X^68 + X^66 + X^52 + X^44 + X^22 + 1 14 20 20 8 X^1279 + X^745 + X^728 + X^701 + X^684 + X^677 + X^660 + X^657 + X^641 + X^640 + X^633 + X^624 + X^616 + X^613 + X^597 + X^596 + X^593 + X^589 + X^580 + X^576 + X^573 + X^572 + X^556 + X^553 + X^549 + X^545 + X^536 + X^532 + X^529 + X^528 + X^525 + X^512 + X^509 + X^508 + X^505 + X^492 + X^489 + X^488 + X^485 + X^481 + X^473 + X^472 + X^468 + X^464 + X^461 + X^456 + X^445 + X^444 + X^441 + X^437 + X^429 + X^428 + X^424 + X^421 + X^420 + X^412 + X^405 + X^404 + X^401 + X^393 + X^388 + X^385 + X^384 + X^377 + X^376 + X^369 + X^368 + X^361 + X^360 + X^357 + X^352 + X^344 + X^341 + X^340 + X^333 + X^325 + X^324 + X^321 + X^317 + X^316 + X^308 + X^304 + X^301 + X^300 + X^289 + X^284 + X^281 + X^277 + X^273 + X^272 + X^264 + X^260 + X^257 + X^256 + X^253 + X^240 + X^237 + X^236 + X^233 + X^220 + X^217 + X^216 + X^213 + X^209 + X^200 + X^196 + X^192 + X^189 + X^173 + X^172 + X^169 + X^165 + X^156 + X^152 + X^149 + X^148 + X^132 + X^129 + X^121 + X^112 + X^105 + X^104 + X^88 + X^85 + X^68 + X^61 + X^44 + X^17 + 1 12 8 21 8 X^1279 + X^766 + X^753 + X^749 + X^736 + X^714 + X^701 + X^698 + X^697 + X^685 + X^684 + X^681 + X^678 + X^668 + X^665 + X^662 + X^661 + X^649 + X^648 + X^646 + X^645 + X^633 + X^632 + X^629 + X^626 + X^616 + X^614 + X^613 + X^609 + X^601 + X^597 + X^596 + X^594 + X^584 + X^581 + X^577 + X^574 + X^564 + X^562 + X^561 + X^558 + X^557 + X^549 + X^546 + X^544 + X^542 + X^541 + X^533 + X^532 + X^528 + X^526 + X^525 + X^522 + X^516 + X^513 + X^512 + X^510 + X^506 + X^505 + X^497 + X^496 + X^492 + X^489 + X^ ** WARNING: Output too long, hence truncated. Errors: /home/mfd/gomagma: line 2: 15961 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host dirichlet.math.umass.edu. (128.119.47.126) Time: Mon Jan 26 13:59:39 2004 Input: P:=PolynomialRing(Rational());C:=HyperellipticCurve(10x^6-20x^5+55x^2-30x+9);Points(C:Bound:=1); Output: Magma V2.10-6 Mon Jan 26 2004 13:59:36 on modular [Seed = 2445586952] ------------------------------------- >> P:=PolynomialRing(Rational());C:=HyperellipticCurve(10x^6-20x^5+55x^2-30 ^ User error: Identifier 'Rational' has not been declared or assigned >> P:=PolynomialRing(Rational());C:=HyperellipticCurve(10x^6-20x^5+55x^2-30 ^ User error: bad syntax Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host dirichlet.math.umass.edu. (128.119.47.126) Time: Mon Jan 26 13:59:53 2004 Input: P:=PolynomialRing(Rationals());C:=HyperellipticCurve(10x^6-20x^5+55x^2-30x+9);Points(C:Bound:=1); Output: Magma V2.10-6 Mon Jan 26 2004 13:59:50 on modular [Seed = 2563619647] ------------------------------------- >> P:=PolynomialRing(Rationals());C:=HyperellipticCurve(10x^6-20x^5+55x^2-3 ^ User error: bad syntax Total time: 2.929 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host dirichlet.math.umass.edu. (128.119.47.126) Time: Mon Jan 26 14:00:19 2004 Input: P:=PolynomialRing(Rationals());C:=HyperellipticCurve(10*x^6-20*x^5+55*x^2-30*x+9);Points(C:Bound:=1); Output: Magma V2.10-6 Mon Jan 26 2004 14:00:16 on modular [Seed = 2835188585] ------------------------------------- {@ (0 : -3 : 1), (0 : 3 : 1) @} Total time: 2.959 seconds, Total memory usage: 29.52MB ************** MAGMA ***************** Host dirichlet.math.umass.edu. (128.119.47.126) Time: Mon Jan 26 14:00:44 2004 Input: P:=PolynomialRing(Rationals());C:=HyperellipticCurve(10*x^6-20*x^5+55*x^2-30*x+9);Points(C:Bound:=2); Output: Magma V2.10-6 Mon Jan 26 2004 14:00:40 on modular [Seed = 3018231914] ------------------------------------- {@ (0 : -3 : 1), (0 : 3 : 1), (2 : -13 : 1), (2 : 13 : 1) @} Total time: 3.009 seconds, Total memory usage: 29.52MB ************** MAGMA ***************** Host dirichlet.math.umass.edu. (128.119.47.126) Time: Mon Jan 26 14:01:03 2004 Input: P:=PolynomialRing(Rationals());C:=HyperellipticCurve(10*x^6-20*x^5+55*x^2-30*x+9);Points(C:Bound:=3); Output: Magma V2.10-6 Mon Jan 26 2004 14:01:00 on modular [Seed = 3136264535] ------------------------------------- {@ (0 : -3 : 1), (0 : 3 : 1), (2 : -13 : 1), (2 : 13 : 1) @} Total time: 2.979 seconds, Total memory usage: 29.52MB ************** MAGMA ***************** Host dirichlet.math.umass.edu. (128.119.47.126) Time: Mon Jan 26 14:01:17 2004 Input: P:=PolynomialRing(Rationals());C:=HyperellipticCurve(10*x^6-20*x^5+55*x^2-30*x+9);Points(C:Bound:=4); Output: Magma V2.10-6 Mon Jan 26 2004 14:01:14 on modular [Seed = 3615683628] ------------------------------------- {@ (0 : -3 : 1), (0 : 3 : 1), (2 : -13 : 1), (2 : 13 : 1) @} Total time: 3.019 seconds, Total memory usage: 29.52MB ************** MAGMA ***************** Host dirichlet.math.umass.edu. (128.119.47.126) Time: Mon Jan 26 14:01:31 2004 Input: P:=PolynomialRing(Rationals());C:=HyperellipticCurve(10*x^6-20*x^5+55*x^2-30*x+9);Points(C:Bound:=10); Output: Magma V2.10-6 Mon Jan 26 2004 14:01:28 on modular [Seed = 3786720744] ------------------------------------- {@ (0 : -3 : 1), (0 : 3 : 1), (2 : -13 : 1), (2 : 13 : 1) @} Total time: 2.929 seconds, Total memory usage: 29.52MB ************** MAGMA ***************** Host dirichlet.math.umass.edu. (128.119.47.126) Time: Mon Jan 26 14:01:43 2004 Input: P:=PolynomialRing(Rationals());C:=HyperellipticCurve(10*x^6-20*x^5+55*x^2-30*x+9);Points(C:Bound:=100); Output: Magma V2.10-6 Mon Jan 26 2004 14:01:40 on modular [Seed = 3904752893] ------------------------------------- {@ (0 : -3 : 1), (0 : 3 : 1), (2 : -13 : 1), (2 : 13 : 1) @} Total time: 3.039 seconds, Total memory usage: 29.52MB ************** MAGMA ***************** Host naifmac.jpl.nasa.gov. (137.78.102.97) Time: Mon Jan 26 20:37:00 2004 Input: 12! Output: Magma V2.10-6 Mon Jan 26 2004 20:36:57 on modular [Seed = 407738535] ------------------------------------- >> 12!; ^ User error: bad syntax Total time: 3.099 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host ip3-127.eyrkonaeac01.dialup.ca.telus.com. (209.29.82.127) Time: Mon Jan 26 21:16:19 2004 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: Magma V2.10-6 Mon Jan 26 2004 21:16:16 on modular [Seed = 3532086052] ------------------------------------- Replace this by some code, then click [PARI] or [MAGMA]! Total time: 3.009 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host adsl-67-127-52-39.dsl.pltn13.pacbell.net. (67.127.52.39) Time: Tue Jan 27 00:33:16 2004 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: Magma V2.10-6 Tue Jan 27 2004 00:33:06 on modular [Seed = 1192427359] ------------------------------------- Replace this by some code, then click [PARI] or [MAGMA]! Total time: 3.019 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host c-24-17-30-82.client.comcast.net. (24.17.30.82) Time: Tue Jan 27 11:35:07 2004 Input: IsPrime(7) Output: Magma V2.10-6 Tue Jan 27 2004 11:35:04 on modular [Seed = 407817012] ------------------------------------- true Total time: 3.549 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host c-24-17-30-82.client.comcast.net. (24.17.30.82) Time: Tue Jan 27 11:36:35 2004 Input: IsPrime(2^(2^14) + 2775) Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Tue Jan 27 2004 11:36:11 on modular [Seed = 39113069] ------------------------------------- Errors: /home/mfd/gomagma: line 2: 21526 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host c-24-17-30-82.client.comcast.net. (24.17.30.82) Time: Tue Jan 27 11:37:55 2004 Input: IsPrime(2^(2^10) + 643) Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Tue Jan 27 2004 11:37:31 on modular [Seed = 812049391] ------------------------------------- Errors: /home/mfd/gomagma: line 2: 21540 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host c-24-17-30-82.client.comcast.net. (24.17.30.82) Time: Tue Jan 27 11:38:51 2004 Input: IsPrime(2^(2^8) + 297) Output: Magma V2.10-6 Tue Jan 27 2004 11:38:46 on modular [Seed = 679410730] ------------------------------------- true Total time: 4.329 seconds, Total memory usage: 2.99MB ************** MAGMA ***************** Host c-24-17-30-82.client.comcast.net. (24.17.30.82) Time: Tue Jan 27 11:39:28 2004 Input: IsPrime(2^(2^9) + 75) Output: Magma V2.10-6 Tue Jan 27 2004 11:39:19 on modular [Seed = 1510772345] ------------------------------------- true Total time: 8.089 seconds, Total memory usage: 2.99MB ************** MAGMA ***************** Host c-24-17-30-82.client.comcast.net. (24.17.30.82) Time: Tue Jan 27 11:40:28 2004 Input: IsPrime(2^(2^9) - 569) Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Tue Jan 27 2004 11:40:05 on modular [Seed = 1243389499] ------------------------------------- Errors: /home/mfd/gomagma: line 2: 21598 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host c-24-17-30-82.client.comcast.net. (24.17.30.82) Time: Tue Jan 27 11:41:01 2004 Input: IsPrime(2^(2^9) - 569) Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Tue Jan 27 2004 11:40:38 on modular [Seed = 2033167851] ------------------------------------- Errors: /home/mfd/gomagma: line 2: 21613 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host c-24-17-30-82.client.comcast.net. (24.17.30.82) Time: Tue Jan 27 11:42:04 2004 Input: IsPrime(2^(2^9) + 145) Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Tue Jan 27 2004 11:41:40 on modular [Seed = 1832630717] ------------------------------------- Errors: /home/mfd/gomagma: line 2: 21625 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host escher.math.ubc.ca. (142.103.161.251) Time: Tue Jan 27 14:43:21 2004 Input: E:=EllipticCurve([0, 148176]); TorsionSubgroup(E); Output: Magma V2.10-6 Tue Jan 27 2004 14:43:18 on modular [Seed = 1714460968] ------------------------------------- Abelian Group of order 1 Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host escher.math.ubc.ca. (142.103.161.251) Time: Tue Jan 27 14:44:28 2004 Input: P:=PolynomialRing(RationalField()); F:=NumberField(x^3-3*x^2+1); E:=EllipticCurve([0, 148176]); TorsionSubgroup(E); E:=ChangeBase(E, F); TorsionSubgroup(E); Output: Magma V2.10-6 Tue Jan 27 2004 14:44:24 on modular [Seed = 2428923664] ------------------------------------- Abelian Group of order 1 >> E:=ChangeBase(E, F); ^ Runtime error in 'ChangeBase': Bad argument types Argument types given: CrvEll, FldNum Abelian Group of order 1 Total time: 3.029 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host escher.math.ubc.ca. (142.103.161.251) Time: Tue Jan 27 14:44:56 2004 Input: P:=PolynomialRing(RationalField()); F:=NumberField(x^3-3*x^2+1); E:=EllipticCurve([0, 148176]); TorsionSubgroup(E); E:=BaseChange(E, F); TorsionSubgroup(E); Output: Magma V2.10-6 Tue Jan 27 2004 14:44:53 on modular [Seed = 2313123364] ------------------------------------- Abelian Group of order 1 Abelian Group of order 1 Defined on 1 generator Relations: $.1 = 0 Mapping from: Abelian Group of order 1 Defined on 1 generator Relations: $.1 = 0 to CrvEll: E given by a rule [no inverse] Total time: 3.219 seconds, Total memory usage: 2.09MB ************** MAGMA ***************** Host escher.math.ubc.ca. (142.103.161.251) Time: Tue Jan 27 14:45:30 2004 Input: P:=PolynomialRing(RationalField()); F:=NumberField(x^3-3*x^2+1); E:=EllipticCurve([0, 148176]); AbelianGroup(E); E:=BaseChange(E, F); AbelianGroup(E); Output: Magma V2.10-6 Tue Jan 27 2004 14:45:25 on modular [Seed = 3119466100] ------------------------------------- Abelian Group of order 1 >> AbelianGroup(E);; ^ Runtime error in 'AbelianGroup': Curve must be defined over a (FldFin) finite field or the rationals Total time: 3.509 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host escher.math.ubc.ca. (142.103.161.251) Time: Tue Jan 27 14:45:52 2004 Input: P:=PolynomialRing(RationalField()); F:=NumberField(x^3-3*x^2+1); E:=EllipticCurve([0, 148176]); AbelianGroup(E); E:=BaseChange(E, F); TorsionSubgroup(E); Output: Magma V2.10-6 Tue Jan 27 2004 14:45:48 on modular [Seed = 2868663646] ------------------------------------- Abelian Group of order 1 Abelian Group of order 1 Defined on 1 generator Relations: $.1 = 0 Mapping from: Abelian Group of order 1 Defined on 1 generator Relations: $.1 = 0 to CrvEll: E given by a rule [no inverse] Total time: 3.779 seconds, Total memory usage: 2.14MB ************** MAGMA ***************** Host escher.math.ubc.ca. (142.103.161.251) Time: Tue Jan 27 14:52:34 2004 Input: P:=PolynomialRing(RationalField()); F:=NumberField(x^3-x^2-2*x+1); E:=EllipticCurve([-499392, 150691536]); AbelianGroup(E); E:=BaseChange(E, F); TorsionSubgroup(E); Output: Magma V2.10-6 Tue Jan 27 2004 14:52:26 on modular [Seed = 3331344292] ------------------------------------- Abelian Group of order 1 Abelian Group of order 1 Defined on 1 generator Relations: $.1 = 0 Mapping from: Abelian Group of order 1 Defined on 1 generator Relations: $.1 = 0 to CrvEll: E given by a rule [no inverse] Total time: 3.899 seconds, Total memory usage: 2.24MB ************** MAGMA ***************** Host escher.math.ubc.ca. (142.103.161.251) Time: Tue Jan 27 14:53:07 2004 Input: P:=PolynomialRing(RationalField()); F:=NumberField(x^3-2); E:=EllipticCurve([0, 2]); AbelianGroup(E); E:=BaseChange(E, F); TorsionSubgroup(E); Output: Magma V2.10-6 Tue Jan 27 2004 14:52:57 on modular [Seed = 4289298046] ------------------------------------- Abelian Group isomorphic to Z Defined on 1 generator (free) Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 Mapping from: Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 to CrvEll: E given by a rule [no inverse] Total time: 3.789 seconds, Total memory usage: 2.63MB ************** MAGMA ***************** Host escher.math.ubc.ca. (142.103.161.251) Time: Tue Jan 27 14:57:00 2004 Input: P:=PolynomialRing(RationalField()); F:=NumberField(x^3-3*x^2+1); E:=EllipticCurve([-3, 62]); AbelianGroup(E); E:=BaseChange(E, F); TorsionSubgroup(E); Output: Magma V2.10-6 Tue Jan 27 2004 14:56:55 on modular [Seed = 458070405] ------------------------------------- Abelian Group isomorphic to Z Defined on 1 generator (free) Abelian Group isomorphic to Z/7 Defined on 1 generator Relations: 7*$.1 = 0 Mapping from: Abelian Group isomorphic to Z/7 Defined on 1 generator Relations: 7*$.1 = 0 to CrvEll: E given by a rule [no inverse] Total time: 4.339 seconds, Total memory usage: 2.50MB ************** MAGMA ***************** Host escher.math.ubc.ca. (142.103.161.251) Time: Tue Jan 27 14:57:40 2004 Input: P:=PolynomialRing(RationalField()); F:=NumberField(x^3-3*x^2+1); E:=EllipticCurve([-3, 62]); AbelianGroup(E); E:=BaseChange(E, F); G:=TorsionSubgroupScheme(E); IsogenyFromKernel(G); Output: Magma V2.10-6 Tue Jan 27 2004 14:57:36 on modular [Seed = 306483386] ------------------------------------- Abelian Group isomorphic to Z Defined on 1 generator (free) >> G:=TorsionSubgroupScheme(E); ^ Runtime error in 'TorsionSubgroupScheme': Bad argument types Argument types given: CrvEll >> IsogenyFromKernel(G);; ^ User error: Identifier 'G' has not been declared or assigned Total time: 3.839 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host escher.math.ubc.ca. (142.103.161.251) Time: Tue Jan 27 14:58:37 2004 Input: P:=PolynomialRing(RationalField()); F:=NumberField(x^3-3*x^2+1); E:=EllipticCurve([-3, 62]); AbelianGroup(E); E:=BaseChange(E, F); G:=TorsionSubgroupScheme(E, 7); IsogenyFromKernel(G); Output: Magma V2.10-6 Tue Jan 27 2004 14:58:33 on modular [Seed = 55935475] ------------------------------------- Abelian Group isomorphic to Z Defined on 1 generator (free) Elliptic Curve defined by y^2 = x^3 - 7203*x + 7294238 over F Elliptic curve isogeny from: CrvEll: E to Elliptic Curve defined by y^2 = x^3 - 7203*x + 7294238 over F taking (x : y : 1) to ((x^49 + 1176*x^47 - 972160*x^46 + 322308*x^45 - 44184672*x^44 + 11903170440*x^43 + 947135808*x^42 - 572457016782*x^41 + 27983913074656*x^40 + 26697365440200*x^39 - 3146769230545920*x^38 + 118855868832947540*x^37 + 26806777753353696*x^36 - 2330460924821715816*x^35 + 19761952740735412032*x^34 + 37278353633699308095*x^33 - 1207709206108978190688*x^32 + 18644070575465205572464*x^31 + 13839114826116625635072*x^30 - 384230344020130228559736*x^29 + 2897620653861889765444160*x^28 - 68473670657563786725936*x^27 + 21961130831743836673729152*x^26 - 444700526871186116177294340*x^25 - 1345290760664554849426403136*x^24 + 25501644510176793441173014800*x^23 - 183691849742947607089578651136*x^22 - 250093656475970312442940042680*x^21 + 3379807866711779436534301589952*x^20 - 16392398125383571185545003908688*x^19 - 14554465532985281426819834912640*x^18 + 142489066438554414176071928606607*x^17 - 471040274500893101323738816598208*x^16 + 41916773816371736165750719306104*x^15 - 1357037691645451394724955589324160*x^14 + 10344184138368368552120055553231220*x^13 + 28440942595788554019808864379604000*x^12 - 243689703808752302268732694663787736*x^11 + 856036733637364665499426983088422976*x^10 + 799841054321606069356114586706006258*x^9 - 5613867646827498667290811073442613920*x^8 + 14953172026995256569095508980420636328*x^7 + 22931351815260884895277368247196868096*x^6 - 145665682871979001674681011179962387612*x^5 + 412966632233158417219594002950567943776*x^4 + 94034153334835458592702418175215075640*x^3 - 587887508541747385643095647225707941824*x^2 + 1433243856070161096359031715880912566033*x - 14802352682262295701567495744891640800) / (x^48 - 264*x^46 + 489056/7*x^45 + 9828*x^44 - 64513728/7*x^43 + 57542086632/49*x^42 - 1966240224/7*x^41 + 58130394750/7*x^40 - 11864665735808/7*x^39 - 591863952024*x^38 + 515200325893152/7*x^37 - 10024539100639060/7*x^36 + 14469083036434368/49*x^35 - 199815852770109432/7*x^34 + 8216695696689835872/7*x^33 + 9807099632594542233/7*x^32 - 433028016010598616576/7*x^31 + 6063865296499490805328/7*x^30 + 4475872188484574837184/7*x^29 - 819912047292112486021176/49*x^28 + 805620217722340972248704/7*x^27 + 1067975136340132742439408/7*x^26 - 17657666522315373432616128/7*x^25 + 107767126399963569864355620/7*x^24 + 187444546542376022546419968/7*x^23 - 2597190224393022091234019280/7*x^22 + 96256311917532029775073628096/49*x^21 + 21143749443429276652000432824/7*x^20 - 236730076417796700150313454976/7*x^19 + 974956877252033466744243030928/7*x^18 + 1784550624698373845410367204544/7*x^17 - 17364069463895929023033803568471/7*x^16 + 66641463572177193336894096314880/7*x^15 + 933396768973694751883306587060696/49*x^14 - 1189526406295348575001002939404832/7*x^13 + 4387362565024056420102588595950668/7*x^12 + 4809089684437209402320836878719040/7*x^11 - 37798595996600766956232461414422344/7*x^10 + 121089370706766823564437382653960352/7*x^9 + 33231437265019248161722656954159678/7*x^8 - 33537077146970768381061245214259584*x^7 + 81961799449377961437561519590776008*x^6 - 101258314664322084018891288367868064*x^5 + 584645259222598153804250706191087748*x^4 - 1686297881626261932495159680348435776*x^3 + 281392737637663707533898441172169688*x^2 - 1408821466556824627466769987980308704*x + 203675229491944224207880989154534234081/49) : (x^72*y - 1836*x^70*y + 2188848*x^69*y - 1466802*x^68*y + 638825184*x^67*y - 195735089532*x^66*y + 50168722032*x^65*y + 2174462165601*x^64*y + 420473589285376*x^63*y - 568860814941408*x^62*y + 61307322287135616*x^61*y - 4752704315751921840*x^60*y - 7118106791619776256*x^59*y + 783705277335007962144*x^58*y - 27946359804901205420160*x^57*y - 16593985570867483412556*x^56*y + 1195966047893053528585728*x^55*y - 16664506550008717062397328*x^54*y - 43749721818538833426107328*x^53*y + 1786644044633653235951927688*x^52*y - 30437515019705257082744661888*x^51*y - 27358473403306743314180754384*x^50*y + 818409919235885650256598169920*x^49*y - 4441547059634217227973862573980*x^48*y - 8935031467838368610169683000832*x^47*y + 114459559986661323466604801274720*x^46*y - 496520227667101640797511793204608*x^45*y - 1886966313430563060118601612749776*x^44*y + 27719464230392184727056584614266624*x^43*y - 165045523654763275536743035316070048*x^42*y - 1538282624832815579602042861356230016*x^41*y + 25539148964698750240072027107688137006*x^40*y - 170071394615761051035031742736882719232*x^39*y - 782783939945793651308261853459138783432*x^38*y + 10681023178779278327818230816795491221536*x^37*y - 55476065081348948294731146814601807463212*x^36*y - 156528092896520261230047291890925349252800*x^35*y + 1648170467037732840955080536575866096758232*x^34*y - 6205982519965616971722951454953579780943968*x^33*y - 9767181609762272583388310277380579883162210*x^32*y + 65034467903982852594714130009435173992044032*x^31*y - 122786858269346395922868265452179340151515936*x^30*y + 922858021411669034088929140755812764291560576*x^29*y - 10014562841512820739757722924350814118551919824*x^28*y + 37341394204735816197476697116654377024715110144*x^27*y + 175035557863327385339608289566704231631269820896*x^26*y - 1327604493150068790664215360155441480731246346112*x^25*y + 3630299008045599994249206543235519708359643472580*x^24*y + 10362912085555841391480680594707884102850728276480*x^23*y - 64012766544074755173150763294262697103805101238544*x^22*y + 142629771371709974450951062654478912055403275209280*x^21*y + 291927427062425890738230362131239392854401625783944*x^20*y - 1505059743336838995280818840175920352615384521267072*x^19*y + 2737443394375708912811486566375076086669556415210928*x^18*y + 4956266260160717343100915431088471789630284206508864*x^17*y - 21984521322427539384852380839628579042633178743953452*x^16*y + 26617582173271059320526610105459615092568313575859712*x^15*y + 167130085998670141266936164776437397616007095737412256*x^14*y - 761998020303796401195167930948295339594002722069858944*x^13*y + 871697743584518002859400465542775998326294384221409872*x^12*y + 8850439492179825946690276642274523205635120083922084096*x^11*y - 40753964510677507928774012027156423312714660951369259360*x^10*y + 77755832465265665693583200461153475739335782779189745024*x^9*y + 112980321177708138889612139657357953789183405245303439449*x^8*y - 479662002094113553428294924881460054416805313064712506880*x^7*y + 814609836118303417826145560532761451679349410593205477524*x^6*y + 859617225100744532742646499339889023437459051177440572208*x^5*y - 3474243480868714925686361449324881263542395632592887016498*x^4*y + 6306167055809337204004814210180334169757251653552061885152*x^3*y + 368168040427996028168059786863596691481597420502770633668*x^2*y - 1899604272228849243647598374516771136451671220109843173008*x*y + 2911845048906783964453293477446155714014225397877172018121*y) / (x^72 - 396*x^70 + 733584/7*x^69 + 40878*x^68 - 193603680/7*x^67 + 175965042084/49*x^66 + 1005457968*x^65 - 22605822434511/49*x^64 + 12942342319822336/343*x^63 - 832302486933984/49*x^62 + 43206897651456384/49*x^61 - 4413180574282315440/49*x^60 - 1711590749504692992/49*x^59 + 191966917351033590048/49*x^58 - 2105647135752514593408/49*x^57 + 19771836959983108024620/343*x^56 - 220388321289077097177600/49*x^55 + 5870064618050264676897520/49*x^54 + 7312250090621746720187712/49*x^53 - 265074814534815422498061432/49*x^52 + 2284162170058161304083603072/49*x^51 - 1598752226731159707904649808/49*x^50 + 775902169377672792333548253120/343*x^49 - 311091069766921052270057698500/7*x^48 - 849382596081347521914029689344/7*x^47 + 3117763325222095677919006001760*x^46 - 1340374133042590765220199648363392/49*x^45 - 401322336023005447014864514423728/7*x^44 + 46867956540811741732437661209705216/49*x^43 - 1715745544759496611219117209855024480/343*x^42 - 737786158295236381783240826013295488/49*x^41 + 9008387778256312948694691828635561166/49*x^40 - 38832978691950561672854601654948131328/49*x^39 - 145663419106016669629251661072459696776/49*x^38 + 1502610689013535975643755177195547752608/49*x^37 - 5488951275341980463020955363526988571948/49*x^36 - 152106722340241925337832572134241283513920/343*x^35 + 188690488930357047678868589586939528305304/49*x^34 - 551827490621615296442345475315443812456416/49*x^33 - 2591192807248712343451339008302879461556994/49*x^32 + 19695304433506708916781661765326895757360640/49*x^31 - 50198017679382188575465847409125545584444960/49*x^30 - 265428227960796980185575712950210023857392000/49*x^29 + 12798994671660549435039176762894340722501804112/343*x^28 - 4218802101178413025261622753322885791694116096/49*x^27 - 21456720953177327152982649930040503150880314144/49*x^26 + 132841638023421694484729526801284502736942340736/49*x^25 - 38162822754907111135715561461085965903390671780/7*x^24 - 1403871780536812138693223645309785486758850598400/49*x^23 + 8023903749715782585396608869573404114953184303984/49*x^22 - 105318602420054027348094947863178004385262601410880/343*x^21 - 77095102342264934063648557796020292159710363478904/49*x^20 + 418382 ** WARNING: Output too long, hence truncated. ************** MAGMA ***************** Host escher.math.ubc.ca. (142.103.161.251) Time: Tue Jan 27 14:59:08 2004 Input: P:=PolynomialRing(RationalField()); F:=NumberField(t^3-3*t^2+1); E:=EllipticCurve([-3, 62]); E:=BaseChange(E, F); G:=TorsionSubgroupScheme(E, 7); IsogenyFromKernel(G); Output: Magma V2.10-6 Tue Jan 27 2004 14:59:05 on modular [Seed = 1030471213] ------------------------------------- Elliptic Curve defined by y^2 = x^3 - 7203*x + 7294238 over F Elliptic curve isogeny from: CrvEll: E to Elliptic Curve defined by y^2 = x^3 - 7203*x + 7294238 over F taking (x : y : 1) to ((x^49 + 1176*x^47 - 972160*x^46 + 322308*x^45 - 44184672*x^44 + 11903170440*x^43 + 947135808*x^42 - 572457016782*x^41 + 27983913074656*x^40 + 26697365440200*x^39 - 3146769230545920*x^38 + 118855868832947540*x^37 + 26806777753353696*x^36 - 2330460924821715816*x^35 + 19761952740735412032*x^34 + 37278353633699308095*x^33 - 1207709206108978190688*x^32 + 18644070575465205572464*x^31 + 13839114826116625635072*x^30 - 384230344020130228559736*x^29 + 2897620653861889765444160*x^28 - 68473670657563786725936*x^27 + 21961130831743836673729152*x^26 - 444700526871186116177294340*x^25 - 1345290760664554849426403136*x^24 + 25501644510176793441173014800*x^23 - 183691849742947607089578651136*x^22 - 250093656475970312442940042680*x^21 + 3379807866711779436534301589952*x^20 - 16392398125383571185545003908688*x^19 - 14554465532985281426819834912640*x^18 + 142489066438554414176071928606607*x^17 - 471040274500893101323738816598208*x^16 + 41916773816371736165750719306104*x^15 - 1357037691645451394724955589324160*x^14 + 10344184138368368552120055553231220*x^13 + 28440942595788554019808864379604000*x^12 - 243689703808752302268732694663787736*x^11 + 856036733637364665499426983088422976*x^10 + 799841054321606069356114586706006258*x^9 - 5613867646827498667290811073442613920*x^8 + 14953172026995256569095508980420636328*x^7 + 22931351815260884895277368247196868096*x^6 - 145665682871979001674681011179962387612*x^5 + 412966632233158417219594002950567943776*x^4 + 94034153334835458592702418175215075640*x^3 - 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5488951275341980463020955363526988571948/49*x^36 - 152106722340241925337832572134241283513920/343*x^35 + 188690488930357047678868589586939528305304/49*x^34 - 551827490621615296442345475315443812456416/49*x^33 - 2591192807248712343451339008302879461556994/49*x^32 + 19695304433506708916781661765326895757360640/49*x^31 - 50198017679382188575465847409125545584444960/49*x^30 - 265428227960796980185575712950210023857392000/49*x^29 + 12798994671660549435039176762894340722501804112/343*x^28 - 4218802101178413025261622753322885791694116096/49*x^27 - 21456720953177327152982649930040503150880314144/49*x^26 + 132841638023421694484729526801284502736942340736/49*x^25 - 38162822754907111135715561461085965903390671780/7*x^24 - 1403871780536812138693223645309785486758850598400/49*x^23 + 8023903749715782585396608869573404114953184303984/49*x^22 - 105318602420054027348094947863178004385262601410880/343*x^21 - 77095102342264934063648557796020292159710363478904/49*x^20 + 418382744102730161894409967732608656731383337070208/49*x^19 - ** WARNING: Output too long, hence truncated. ************** MAGMA ***************** Host escher.math.ubc.ca. (142.103.161.251) Time: Tue Jan 27 15:01:31 2004 Input: P:=PolynomialRing(RationalField()); F:=NumberField(t^3-3*t^2+1); E:=EllipticCurve([-3, 62]); E:=BaseChange(E, F); G:=TorsionSubgroupScheme(E, 7); f:=IsogenyFromKernel(G); Output: Magma V2.10-6 Tue Jan 27 2004 15:01:27 on modular [Seed = 1392890077] ------------------------------------- Total time: 3.559 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host escher.math.ubc.ca. (142.103.161.251) Time: Tue Jan 27 15:01:53 2004 Input: P:=PolynomialRing(RationalField()); F:=NumberField(t^3-3*t^2+1); E:=EllipticCurve([-3, 62]); E:=BaseChange(E, F); G:=TorsionSubgroupScheme(E, 7); IsogenyFromKernel(G); Output: Magma V2.10-6 Tue Jan 27 2004 15:01:50 on modular [Seed = 1092076278] ------------------------------------- Elliptic Curve defined by y^2 = x^3 - 7203*x + 7294238 over F Elliptic curve isogeny from: CrvEll: E to Elliptic Curve defined by y^2 = x^3 - 7203*x + 7294238 over F taking (x : y : 1) to ((x^49 + 1176*x^47 - 972160*x^46 + 322308*x^45 - 44184672*x^44 + 11903170440*x^43 + 947135808*x^42 - 572457016782*x^41 + 27983913074656*x^40 + 26697365440200*x^39 - 3146769230545920*x^38 + 118855868832947540*x^37 + 26806777753353696*x^36 - 2330460924821715816*x^35 + 19761952740735412032*x^34 + 37278353633699308095*x^33 - 1207709206108978190688*x^32 + 18644070575465205572464*x^31 + 13839114826116625635072*x^30 - 384230344020130228559736*x^29 + 2897620653861889765444160*x^28 - 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** WARNING: Output too long, hence truncated. ************** MAGMA ***************** Host du-003-0053.freeuk.com. (212.126.145.53) Time: Tue Jan 27 15:27:55 2004 Input: 4444^4444 Output: Magma V2.10-6 Tue Jan 27 2004 15:27:51 on modular [Seed = 2817601145] ------------------------------------- 5103632503725508048204025019552439592478247548228451474782897598673947907686253\ 1615833001864027197875434172496782212810360936998814871028023280409517604289704\ 2329972500598176514520339025649810534743421439824344770100550779029713858795780\ 9702679504701392721044806973761259973536289419464535239969236107882490228631837\ 4845566910211826792995098340076750261275207380564696757508258866109492489008027\ 0547456803873740320864945594128706961297090655436915863348251354398963931589475\ 8112711565503724716691291451231939073859064049863419562587944620889495591463503\ 4539916382798196213477934038238442489518643389819322763837231638995434876736816\ 6197701384461213907138885227915369469036344596322022836858321727168424358555102\ 8145573990606847177420753847223304260265490698750202012535598517490507323002100\ 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8322021167977131912613038625008119849405429846694204887183172236242862288336790\ 9477121490619012206914630546550893640068987662807001110340851060691959426999963\ 8625770005626017492523797890236162873818398973726653672765659018643008643410406\ 6899555984970430626699113393427759387535749682565485768733441976884012572940596\ 8561088870844930327298262384766100598122878415316818577429986646232585929190348\ 5003475620155889277543198895554594051171715895055495486034595904571029634647547\ 7063086888136584311637100547898320415124284265050681611051509889545401120651624\ 4391221497649639685865746613599904551431103519132165219232384299800607864707270\ 8181697496966241035548875930875115568893160317567583836193538432689661991040144\ 9935129538122817672871284002069273657674924148759715545901520947799114857656365\ 4045173182167157523650652433679807488706825534249579941824724777137214284123485\ 0010132319343743177056148129377153581570970068560101898874969988379653338032155\ 1925970404211930703722814870147383043024350899076127839345055871818704915007022\ 7746230795835272945695192813801661478856551200048085236743108277259088743550025\ 4665714845790505371032347103281992340947593930321523400969614546891287784544415\ 7428705725324269845118873307464750432702122363395708402813809266954445176416954\ 0 ** WARNING: Output too long, hence truncated. ************** MAGMA ***************** Host user-vc8frgq.biz.mindspring.com. (216.135.238.26) Time: Tue Jan 27 16:39:19 2004 Input: 36!*(1/4) Output: Magma V2.10-6 Tue Jan 27 2004 16:39:15 on modular [Seed = 729657779] ------------------------------------- >> 36!*(1/4); ^ User error: bad syntax Total time: 3.289 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host user-vc8frgq.biz.mindspring.com. (216.135.238.26) Time: Tue Jan 27 16:39:34 2004 Input: 36!^(1/4) Output: Magma V2.10-6 Tue Jan 27 2004 16:39:30 on modular [Seed = 578074795] ------------------------------------- >> 36!^(1/4); ^ User error: bad syntax Total time: 3.209 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host user-vc8frgq.biz.mindspring.com. (216.135.238.26) Time: Tue Jan 27 16:44:18 2004 Input: 36!^(1/4) Output: Magma V2.10-6 Tue Jan 27 2004 16:44:15 on modular [Seed = 1948446656] ------------------------------------- >> 36!^(1/4); ^ User error: bad syntax Total time: 2.929 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host user-vc8frgq.biz.mindspring.com. (216.135.238.26) Time: Tue Jan 27 16:44:36 2004 Input: (36!)^(1/4) Output: Magma V2.10-6 Tue Jan 27 2004 16:44:33 on modular [Seed = 1664481465] ------------------------------------- >> (36!)^(1/4); ^ User error: bad syntax Total time: 2.909 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host user-vc8frgq.biz.mindspring.com. (216.135.238.26) Time: Tue Jan 27 16:45:41 2004 Input: factorial(36)^(1/4) Output: Magma V2.10-6 Tue Jan 27 2004 16:45:38 on modular [Seed = 2663907975] ------------------------------------- >> factorial(36)^(1/4); ^ User error: Identifier 'factorial' has not been declared or assigned Total time: 2.879 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host user-vc8frgq.biz.mindspring.com. (216.135.238.26) Time: Tue Jan 27 16:46:12 2004 Input: Factorial(36)^(1/4) Output: Magma V2.10-6 Tue Jan 27 2004 16:46:08 on modular [Seed = 2512587182] ------------------------------------- 24696407768.642268938484229 Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host user-vc8frgq.biz.mindspring.com. (216.135.238.26) Time: Tue Jan 27 16:47:22 2004 Input: Factorial(36)^(1/8) Output: Magma V2.10-6 Tue Jan 27 2004 16:47:19 on modular [Seed = 2363101424] ------------------------------------- 157150.90762907565510502605 Total time: 2.989 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host user-vc8frgq.biz.mindspring.com. (216.135.238.26) Time: Tue Jan 27 16:48:04 2004 Input: Factorial(36)^(1/16) Output: Magma V2.10-6 Tue Jan 27 2004 16:48:00 on modular [Seed = 3152881457] ------------------------------------- 396.422637634476741173669805 Total time: 2.939 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host user-vc8frgq.biz.mindspring.com. (216.135.238.26) Time: Tue Jan 27 16:50:50 2004 Input: Factorial(36)^(1/32) Output: Magma V2.10-6 Tue Jan 27 2004 16:50:47 on modular [Seed = 2868656006] ------------------------------------- 19.910365080391588368944073 Total time: 3.039 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host user-vc8frgq.biz.mindspring.com. (216.135.238.26) Time: Tue Jan 27 16:51:12 2004 Input: Factorial(81)^(1/32) Output: Magma V2.10-6 Tue Jan 27 2004 16:51:09 on modular [Seed = 2717334775] ------------------------------------- 5940.874774876290626272698777 Total time: 2.889 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host user-vc8frgq.biz.mindspring.com. (216.135.238.26) Time: Tue Jan 27 16:52:16 2004 Input: Factorial(81)^(1/64) Output: Magma V2.10-6 Tue Jan 27 2004 16:52:13 on modular [Seed = 3633202510] ------------------------------------- 77.077070357378598450571851 Total time: 2.879 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host user-vc8frgq.biz.mindspring.com. (216.135.238.26) Time: Tue Jan 27 16:53:42 2004 Input: Factorial(99)^(1/64) Output: Magma V2.10-6 Tue Jan 27 2004 16:53:39 on modular [Seed = 3615574575] ------------------------------------- 273.546591147764442036242319 Total time: 3.009 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host user-vc8frgq.biz.mindspring.com. (216.135.238.26) Time: Tue Jan 27 16:56:14 2004 Input: Factorial(99)^(1/32) Output: Magma V2.10-6 Tue Jan 27 2004 16:56:11 on modular [Seed = 3247923105] ------------------------------------- 74827.7375285621998018967 Total time: 2.929 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host user-vc8frgq.biz.mindspring.com. (216.135.238.26) Time: Tue Jan 27 16:56:32 2004 Input: Factorial(999)^(1/128) Output: Magma V2.10-6 Tue Jan 27 2004 16:56:29 on modular [Seed = 4172179054] ------------------------------------- 108636004144203001522.0699 Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host user-vc8frgq.biz.mindspring.com. (216.135.238.26) Time: Tue Jan 27 16:56:46 2004 Input: Factorial(999)^(1/256) Output: Magma V2.10-6 Tue Jan 27 2004 16:56:42 on modular [Seed = 4154550646] ------------------------------------- 10422859691.284489392393422 Total time: 3.069 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host user-vc8frgq.biz.mindspring.com. (216.135.238.26) Time: Tue Jan 27 16:56:57 2004 Input: Factorial(999)^(1/512) Output: Magma V2.10-6 Tue Jan 27 2004 16:56:54 on modular [Seed = 4005064787] ------------------------------------- 102092.40760842350412119415 Total time: 2.909 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host user-vc8frgq.biz.mindspring.com. (216.135.238.26) Time: Tue Jan 27 16:57:11 2004 Input: Factorial(999)^(1/1024) Output: Magma V2.10-6 Tue Jan 27 2004 16:57:08 on modular [Seed = 3853744970] ------------------------------------- 319.519025424814890037809896 Total time: 2.939 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host user-vc8frgq.biz.mindspring.com. (216.135.238.26) Time: Tue Jan 27 16:59:35 2004 Input: Factorial(9999)^(1/4096) Output: Magma V2.10-6 Tue Jan 27 2004 16:59:32 on modular [Seed = 339905356] ------------------------------------- 506926378.9828945090352843 Total time: 2.989 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host user-vc8frgq.biz.mindspring.com. (216.135.238.26) Time: Tue Jan 27 16:59:50 2004 Input: Factorial(9999)^(1/8192) Output: Magma V2.10-6 Tue Jan 27 2004 16:59:47 on modular [Seed = 224105026] ------------------------------------- 22515.02562696508478116428 Total time: 3.069 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host user-vc8frgq.biz.mindspring.com. (216.135.238.26) Time: Tue Jan 27 17:00:42 2004 Input: Factorial(9999)^(1/16384) Output: Magma V2.10-6 Tue Jan 27 2004 17:00:39 on modular [Seed = 1030464166] ------------------------------------- 150.050077064175761059575319 Total time: 2.989 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host user-vc8frgq.biz.mindspring.com. (216.135.238.26) Time: Tue Jan 27 17:04:19 2004 Input: Factorial(100)^(1/64) Output: Magma V2.10-6 Tue Jan 27 2004 17:04:16 on modular [Seed = 561480029] ------------------------------------- 293.955308257998480151750358 Total time: 2.979 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host user-vc8frgq.biz.mindspring.com. (216.135.238.26) Time: Tue Jan 27 17:08:33 2004 Input: Factorial(2)^(1/64) Output: Magma V2.10-6 Tue Jan 27 2004 17:08:30 on modular [Seed = 2512598231] ------------------------------------- 1.01088928605170046002041 Total time: 2.979 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host user-vc8frgq.biz.mindspring.com. (216.135.238.26) Time: Tue Jan 27 17:08:56 2004 Input: Factorial(3)^(1/64) Output: Magma V2.10-6 Tue Jan 27 2004 17:08:53 on modular [Seed = 2261788655] ------------------------------------- 1.028391819416065480657163 Total time: 2.939 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host user-vc8frgq.biz.mindspring.com. (216.135.238.26) Time: Tue Jan 27 17:09:21 2004 Input: Factorial(4)^(1/64) Output: Magma V2.10-6 Tue Jan 27 2004 17:09:18 on modular [Seed = 3102611754] ------------------------------------- 1.050910667960496580904754 Total time: 2.939 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host user-vc8frgq.biz.mindspring.com. (216.135.238.26) Time: Tue Jan 27 17:09:55 2004 Input: Factorial(5)^(1/64) Output: Magma V2.10-6 Tue Jan 27 2004 17:09:51 on modular [Seed = 2984710146] ------------------------------------- 1.077673508153681863804689 Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host user-vc8frgq.biz.mindspring.com. (216.135.238.26) Time: Tue Jan 27 17:10:19 2004 Input: Factorial(6)^(1/64) Output: Magma V2.10-6 Tue Jan 27 2004 17:10:16 on modular [Seed = 2717319285] ------------------------------------- 1.108270619786658969626867 Total time: 2.939 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host user-vc8frgq.biz.mindspring.com. (216.135.238.26) Time: Tue Jan 27 17:11:14 2004 Input: Factorial(7)^(1/64) Output: Magma V2.10-6 Tue Jan 27 2004 17:11:12 on modular [Seed = 3399248086] ------------------------------------- 1.142484921933381619669629 Total time: 2.909 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host user-vc8frgq.biz.mindspring.com. (216.135.238.26) Time: Tue Jan 27 17:11:34 2004 Input: Factorial(8)^(1/64) Output: Magma V2.10-6 Tue Jan 27 2004 17:11:31 on modular [Seed = 3281347020] ------------------------------------- 1.180215348263809146342848 Total time: 2.919 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host user-vc8frgq.biz.mindspring.com. (216.135.238.26) Time: Tue Jan 27 17:11:51 2004 Input: Factorial(9)^(1/64) Output: Magma V2.10-6 Tue Jan 27 2004 17:11:48 on modular [Seed = 4104279756] ------------------------------------- 1.221437635052048751067548 Total time: 2.929 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host user-vc8frgq.biz.mindspring.com. (216.135.238.26) Time: Tue Jan 27 17:12:12 2004 Input: Factorial(10)^(1/64) Output: Magma V2.10-6 Tue Jan 27 2004 17:12:09 on modular [Seed = 3988475848] ------------------------------------- 1.266182472528021535896829 Total time: 2.929 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host user-vc8frgq.biz.mindspring.com. (216.135.238.26) Time: Tue Jan 27 17:12:29 2004 Input: Factorial(11)^(1/64) Output: Magma V2.10-6 Tue Jan 27 2004 17:12:26 on modular [Seed = 3870311600] ------------------------------------- 1.3145226028956092735685 Total time: 2.909 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host user-vc8frgq.biz.mindspring.com. (216.135.238.26) Time: Tue Jan 27 17:13:25 2004 Input: Factorial(12)^(1/64) Output: Magma V2.10-6 Tue Jan 27 2004 17:13:22 on modular [Seed = 508083329] ------------------------------------- 1.36656491044019562805318 Total time: 2.999 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host user-vc8frgq.biz.mindspring.com. (216.135.238.26) Time: Tue Jan 27 17:13:45 2004 Input: Factorial(13)^(1/64) Output: Magma V2.10-6 Tue Jan 27 2004 17:13:42 on modular [Seed = 306491545] ------------------------------------- 1.422445481152860731665044 Total time: 2.919 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host user-vc8frgq.biz.mindspring.com. (216.135.238.26) Time: Tue Jan 27 17:14:04 2004 Input: Factorial(14)^(1/64) Output: Magma V2.10-6 Tue Jan 27 2004 17:14:01 on modular [Seed = 89368497] ------------------------------------- 1.482326526651940489796017 Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host user-vc8frgq.biz.mindspring.com. (216.135.238.26) Time: Tue Jan 27 17:14:22 2004 Input: Factorial(15)^(1/64) Output: Magma V2.10-6 Tue Jan 27 2004 17:14:19 on modular [Seed = 1063886233] ------------------------------------- 1.546394535744217433772063 Total time: 2.929 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host user-vc8frgq.biz.mindspring.com. (216.135.238.26) Time: Tue Jan 27 17:14:39 2004 Input: Factorial(16)^(1/64) Output: Magma V2.10-6 Tue Jan 27 2004 17:14:36 on modular [Seed = 912299239] ------------------------------------- 1.614859270966698551370827 Total time: 2.929 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host user-vc8frgq.biz.mindspring.com. (216.135.238.26) Time: Tue Jan 27 17:14:57 2004 Input: Factorial(17)^(1/64) Output: Magma V2.10-6 Tue Jan 27 2004 17:14:54 on modular [Seed = 696224746] ------------------------------------- 1.687953372150060026357968 Total time: 3.029 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host user-vc8frgq.biz.mindspring.com. (216.135.238.26) Time: Tue Jan 27 17:15:15 2004 Input: Factorial(18)^(1/64) Output: Magma V2.10-6 Tue Jan 27 2004 17:15:12 on modular [Seed = 1544224433] ------------------------------------- 1.765932415049432829128674 Total time: 2.939 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host user-vc8frgq.biz.mindspring.com. (216.135.238.26) Time: Tue Jan 27 17:15:43 2004 Input: Factorial(19)^(1/64) Output: Magma V2.10-6 Tue Jan 27 2004 17:15:40 on modular [Seed = 1459745862] ------------------------------------- 1.849075326133296294652945 Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host user-vc8frgq.biz.mindspring.com. (216.135.238.26) Time: Tue Jan 27 17:16:03 2004 Input: Factorial(20)^(1/64) Output: Magma V2.10-6 Tue Jan 27 2004 17:16:00 on modular [Seed = 1310256499] ------------------------------------- 1.93768508843833865447558 Total time: 2.909 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host user-vc8frgq.biz.mindspring.com. (216.135.238.26) Time: Tue Jan 27 17:16:21 2004 Input: Factorial(21)^(1/64) Output: Magma V2.10-6 Tue Jan 27 2004 17:16:18 on modular [Seed = 1092084334] ------------------------------------- 2.032089695622844884367124 Total time: 3.019 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host user-vc8frgq.biz.mindspring.com. (216.135.238.26) Time: Tue Jan 27 17:16:53 2004 Input: Factorial(22)^(1/64) Output: Magma V2.10-6 Tue Jan 27 2004 17:16:50 on modular [Seed = 2066602036] ------------------------------------- 2.132643326385390989045722 Total time: 2.919 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host user-vc8frgq.biz.mindspring.com. (216.135.238.26) Time: Tue Jan 27 17:17:20 2004 Input: Factorial(23)^(1/64) Output: Magma V2.10-6 Tue Jan 27 2004 17:17:17 on modular [Seed = 1915015426] ------------------------------------- 2.239727721879204359596827 Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host user-vc8frgq.biz.mindspring.com. (216.135.238.26) Time: Tue Jan 27 17:17:38 2004 Input: Factorial(24)^(1/64) Output: Magma V2.10-6 Tue Jan 27 2004 17:17:35 on modular [Seed = 1697891847] ------------------------------------- 2.353753756249715965995779 Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host user-vc8frgq.biz.mindspring.com. (216.135.238.26) Time: Tue Jan 27 17:18:00 2004 Input: Factorial(25)^(1/64) Output: Magma V2.10-6 Tue Jan 27 2004 17:17:57 on modular [Seed = 2630500116] ------------------------------------- 2.475163195961483824422867 Total time: 2.929 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host user-vc8frgq.biz.mindspring.com. (216.135.238.26) Time: Tue Jan 27 17:18:16 2004 Input: Factorial(25)^(1/64) Output: Magma V2.10-6 Tue Jan 27 2004 17:18:13 on modular [Seed = 2546021423] ------------------------------------- 2.475163195961483824422867 Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host user-vc8frgq.biz.mindspring.com. (216.135.238.26) Time: Tue Jan 27 17:18:24 2004 Input: Factorial(26)^(1/64) Output: Magma V2.10-6 Tue Jan 27 2004 17:18:21 on modular [Seed = 2278630455] ------------------------------------- 2.604430647809144596096964 Total time: 2.919 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host user-vc8frgq.biz.mindspring.com. (216.135.238.26) Time: Tue Jan 27 17:18:44 2004 Input: Factorial(27)^(1/64) Output: Magma V2.10-6 Tue Jan 27 2004 17:18:41 on modular [Seed = 3202882914] ------------------------------------- 2.742065698851652235517823 Total time: 2.919 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host user-vc8frgq.biz.mindspring.com. (216.135.238.26) Time: Tue Jan 27 17:19:03 2004 Input: Factorial(28)^(1/64) Output: Magma V2.10-6 Tue Jan 27 2004 17:19:00 on modular [Seed = 2918911588] ------------------------------------- 2.888615254256018612358656 Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host user-vc8frgq.biz.mindspring.com. (216.135.238.26) Time: Tue Jan 27 17:19:20 2004 Input: Factorial(29)^(1/64) Output: Magma V2.10-6 Tue Jan 27 2004 17:19:17 on modular [Seed = 2817590367] ------------------------------------- 3.04466608138223693358935 Total time: 2.929 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host user-vc8frgq.biz.mindspring.com. (216.135.238.26) Time: Tue Jan 27 17:19:41 2004 Input: Factorial(30)^(1/64) Output: Magma V2.10-6 Tue Jan 27 2004 17:19:38 on modular [Seed = 3598742833] ------------------------------------- 3.210847570522282909836297 Total time: 3.009 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host user-vc8frgq.biz.mindspring.com. (216.135.238.26) Time: Tue Jan 27 17:19:59 2004 Input: Factorial(31)^(1/64) Output: Magma V2.10-6 Tue Jan 27 2004 17:19:55 on modular [Seed = 3399249628] ------------------------------------- 3.38783472462117063794704 Total time: 3.699 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host user-vc8frgq.biz.mindspring.com. (216.135.238.26) Time: Tue Jan 27 17:20:17 2004 Input: Factorial(32)^(1/64) Output: Magma V2.10-6 Tue Jan 27 2004 17:20:14 on modular [Seed = 4070856433] ------------------------------------- 3.576351392128804723485626 Total time: 2.989 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host user-vc8frgq.biz.mindspring.com. (216.135.238.26) Time: Tue Jan 27 17:20:38 2004 Input: Factorial(33)^(1/64) Output: Magma V2.10-6 Tue Jan 27 2004 17:20:35 on modular [Seed = 491501872] ------------------------------------- 3.777173758911762733447587 Total time: 2.929 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host user-vc8frgq.biz.mindspring.com. (216.135.238.26) Time: Tue Jan 27 17:21:01 2004 Input: Factorial(34)^(1/64) Output: Magma V2.10-6 Tue Jan 27 2004 17:20:58 on modular [Seed = 173846110] ------------------------------------- 3.991134116935884326175667 Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host user-vc8frgq.biz.mindspring.com. (216.135.238.26) Time: Tue Jan 27 17:21:21 2004 Input: Factorial(35)^(1/64) Output: Magma V2.10-6 Tue Jan 27 2004 17:21:17 on modular [Seed = 55945024] ------------------------------------- 4.219124929246971352812845 Total time: 3.659 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host user-vc8frgq.biz.mindspring.com. (216.135.238.26) Time: Tue Jan 27 17:21:43 2004 Input: Factorial(36)^(1/64) Output: Magma V2.10-6 Tue Jan 27 2004 17:21:40 on modular [Seed = 812029018] ------------------------------------- 4.462103212655618118467027 Total time: 2.919 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host user-vc8frgq.biz.mindspring.com. (216.135.238.26) Time: Tue Jan 27 17:22:02 2004 Input: Factorial(37)^(1/64) Output: Magma V2.10-6 Tue Jan 27 2004 17:21:59 on modular [Seed = 561481144] ------------------------------------- 4.721095261496920106207866 Total time: 2.929 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host user-vc8frgq.biz.mindspring.com. (216.135.238.26) Time: Tue Jan 27 17:22:20 2004 Input: Factorial(38)^(1/64) Output: Magma V2.10-6 Tue Jan 27 2004 17:22:17 on modular [Seed = 1442902737] ------------------------------------- 4.997201737907734789815046 Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host user-vc8frgq.biz.mindspring.com. (216.135.238.26) Time: Tue Jan 27 17:22:39 2004 Input: Factorial(39)^(1/64) Output: Magma V2.10-6 Tue Jan 27 2004 17:22:36 on modular [Seed = 1158930935] ------------------------------------- 5.291603156262893164272289 Total time: 3.009 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host user-vc8frgq.biz.mindspring.com. (216.135.238.26) Time: Tue Jan 27 17:22:59 2004 Input: Factorial(40)^(1/64) Output: Magma V2.10-6 Tue Jan 27 2004 17:22:56 on modular [Seed = 1948438698] ------------------------------------- 5.605565791756028805012281 Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host user-vc8frgq.biz.mindspring.com. (216.135.238.26) Time: Tue Jan 27 17:23:16 2004 Input: Factorial(41)^(1/64) Output: Magma V2.10-6 Tue Jan 27 2004 17:23:13 on modular [Seed = 1832634786] ------------------------------------- 5.940448045618933410938831 Total time: 2.909 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host user-vc8frgq.biz.mindspring.com. (216.135.238.26) Time: Tue Jan 27 17:23:33 2004 Input: Factorial(42)^(1/64) Output: Magma V2.10-6 Tue Jan 27 2004 17:23:30 on modular [Seed = 2597076582] ------------------------------------- 6.297707302164110687771323 Total time: 2.939 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host user-vc8frgq.biz.mindspring.com. (216.135.238.26) Time: Tue Jan 27 17:23:55 2004 Input: Factorial(43)^(1/64) Output: Magma V2.10-6 Tue Jan 27 2004 17:23:52 on modular [Seed = 2346528621] ------------------------------------- 6.678907315727493721768039 Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host user-vc8frgq.biz.mindspring.com. (216.135.238.26) Time: Tue Jan 27 17:24:13 2004 Input: Factorial(44)^(1/64) Output: Magma V2.10-6 Tue Jan 27 2004 17:24:09 on modular [Seed = 3119455406] ------------------------------------- 7.085726168701877850040196 Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host user-vc8frgq.biz.mindspring.com. (216.135.238.26) Time: Tue Jan 27 17:24:31 2004 Input: Factorial(45)^(1/64) Output: Magma V2.10-6 Tue Jan 27 2004 17:24:28 on modular [Seed = 2935491500] ------------------------------------- 7.519964845207271118369766 Total time: 3.329 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host user-vc8frgq.biz.mindspring.com. (216.135.238.26) Time: Tue Jan 27 17:24:49 2004 Input: Factorial(46)^(1/64) Output: Magma V2.10-6 Tue Jan 27 2004 17:24:46 on modular [Seed = 3750329071] ------------------------------------- 7.983556468564082444608309 Total time: 2.979 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host user-vc8frgq.biz.mindspring.com. (216.135.238.26) Time: Tue Jan 27 17:25:08 2004 Input: Factorial(47)^(1/64) Output: Magma V2.10-6 Tue Jan 27 2004 17:25:05 on modular [Seed = 3348193944] ------------------------------------- 8.478576254642307322425305 Total time: 3.119 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host user-vc8frgq.biz.mindspring.com. (216.135.238.26) Time: Tue Jan 27 17:25:34 2004 Input: Factorial(48)^(1/64) Output: Magma V2.10-6 Tue Jan 27 2004 17:25:30 on modular [Seed = 4121120945] ------------------------------------- 9.007252237379741918746347 Total time: 3.619 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host user-vc8frgq.biz.mindspring.com. (216.135.238.26) Time: Tue Jan 27 17:25:54 2004 Input: Factorial(49)^(1/64) Output: Magma V2.10-6 Tue Jan 27 2004 17:25:51 on modular [Seed = 3770041745] ------------------------------------- 9.571976827321729623197215 Total time: 2.979 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host user-vc8frgq.biz.mindspring.com. (216.135.238.26) Time: Tue Jan 27 17:26:12 2004 Input: Factorial(50)^(1/64) Output: Magma V2.10-6 Tue Jan 27 2004 17:26:09 on modular [Seed = 407813510] ------------------------------------- 10.175319268963060192222964 Total time: 2.989 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host user-vc8frgq.biz.mindspring.com. (216.135.238.26) Time: Tue Jan 27 17:26:30 2004 Input: Factorial(51)^(1/64) Output: Magma V2.10-6 Tue Jan 27 2004 17:26:27 on modular [Seed = 257534595] ------------------------------------- 10.820039068000726505206814 Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host user-vc8frgq.biz.mindspring.com. (216.135.238.26) Time: Tue Jan 27 17:26:53 2004 Input: Factorial(52)^(1/64) Output: Magma V2.10-6 Tue Jan 27 2004 17:26:50 on modular [Seed = 105948083] ------------------------------------- 11.509100465368134217882802 Total time: 2.929 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host user-vc8frgq.biz.mindspring.com. (216.135.238.26) Time: Tue Jan 27 17:27:11 2004 Input: Factorial(53)^(1/64) Output: Magma V2.10-6 Tue Jan 27 2004 17:27:08 on modular [Seed = 1030461598] ------------------------------------- 12.245688041153640919379652 Total time: 2.999 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host user-vc8frgq.biz.mindspring.com. (216.135.238.26) Time: Tue Jan 27 17:27:34 2004 Input: Factorial(54)^(1/64) Output: Magma V2.10-6 Tue Jan 27 2004 17:27:31 on modular [Seed = 878875128] ------------------------------------- 13.033223538248562342706487 Total time: 2.889 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host user-vc8frgq.biz.mindspring.com. (216.135.238.26) Time: Tue Jan 27 17:27:58 2004 Input: Factorial(55)^(1/64) Output: Magma V2.10-6 Tue Jan 27 2004 17:27:55 on modular [Seed = 729648863] ------------------------------------- 13.875384002864887036454025 Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host user-vc8frgq.biz.mindspring.com. (216.135.238.26) Time: Tue Jan 27 17:28:22 2004 Input: Factorial(56)^(1/64) Output: Magma V2.10-6 Tue Jan 27 2004 17:28:19 on modular [Seed = 578061374] ------------------------------------- 14.776121346957317891150614 Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host user-vc8frgq.biz.mindspring.com. (216.135.238.26) Time: Tue Jan 27 17:28:48 2004 Input: Factorial(57)^(1/64) Output: Magma V2.10-6 Tue Jan 27 2004 17:28:45 on modular [Seed = 1494220635] ------------------------------------- 15.739683446128221184951541 Total time: 2.929 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host user-vc8frgq.biz.mindspring.com. (216.135.238.26) Time: Tue Jan 27 17:29:07 2004 Input: Factorial(58)^(1/64) Output: Magma V2.10-6 Tue Jan 27 2004 17:29:04 on modular [Seed = 1342633599] ------------------------------------- 16.770636895842145825577778 Total time: 2.919 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host user-vc8frgq.biz.mindspring.com. (216.135.238.26) Time: Tue Jan 27 17:29:27 2004 Input: Factorial(59)^(1/64) Output: Magma V2.10-6 Tue Jan 27 2004 17:29:24 on modular [Seed = 1125508376] ------------------------------------- 17.873891558787902264782558 Total time: 2.989 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host user-vc8frgq.biz.mindspring.com. (216.135.238.26) Time: Tue Jan 27 17:29:52 2004 Input: Factorial(60)^(1/64) Output: Magma V2.10-6 Tue Jan 27 2004 17:29:49 on modular [Seed = 1881593394] ------------------------------------- 19.054727047064876772222701 Total time: 3.289 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host user-vc8frgq.biz.mindspring.com. (216.135.238.26) Time: Tue Jan 27 17:30:12 2004 Input: Factorial(61)^(1/64) Output: Magma V2.10-6 Tue Jan 27 2004 17:30:08 on modular [Seed = 2495755003] ------------------------------------- 20.31882129460583919096651 Total time: 3.219 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host user-vc8frgq.biz.mindspring.com. (216.135.238.26) Time: Tue Jan 27 17:30:30 2004 Input: Factorial(62)^(1/64) Output: Magma V2.10-6 Tue Jan 27 2004 17:30:27 on modular [Seed = 2261786650] ------------------------------------- 21.672281387956409332607937 Total time: 2.939 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host user-vc8frgq.biz.mindspring.com. (216.135.238.26) Time: Tue Jan 27 17:30:50 2004 Input: Factorial(63)^(1/64) Output: Magma V2.10-6 Tue Jan 27 2004 17:30:46 on modular [Seed = 3186301748] ------------------------------------- 23.121676837293408252224053 Total time: 3.439 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host user-vc8frgq.biz.mindspring.com. (216.135.238.26) Time: Tue Jan 27 17:31:09 2004 Input: Factorial(64)^(1/64) Output: Magma V2.10-6 Tue Jan 27 2004 17:31:06 on modular [Seed = 2852065052] ------------------------------------- 24.674075484469319574805011 Total time: 2.909 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host user-vc8frgq.biz.mindspring.com. (216.135.238.26) Time: Tue Jan 27 17:31:31 2004 Input: Factorial(65)^(1/64) Output: Magma V2.10-6 Tue Jan 27 2004 17:31:28 on modular [Seed = 2700478079] ------------------------------------- 26.33708226101436198767626 Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host user-vc8frgq.biz.mindspring.com. (216.135.238.26) Time: Tue Jan 27 17:31:49 2004 Input: Factorial(66)^(1/64) Output: Magma V2.10-6 Tue Jan 27 2004 17:31:46 on modular [Seed = 3482937602] ------------------------------------- 28.118881026515774480557189 Total time: 2.989 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host user-vc8frgq.biz.mindspring.com. (216.135.238.26) Time: Tue Jan 27 17:32:09 2004 Input: Factorial(67)^(1/64) Output: Magma V2.10-6 Tue Jan 27 2004 17:32:06 on modular [Seed = 4222442754] ------------------------------------- 30.02827973673930638060468 Total time: 2.939 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host user-vc8frgq.biz.mindspring.com. (216.135.238.26) Time: Tue Jan 27 17:32:27 2004 Input: Factorial(68)^(1/64) Output: Magma V2.10-6 Tue Jan 27 2004 17:32:23 on modular [Seed = 4021897480] ------------------------------------- 32.074759211383739394602638 Total time: 2.929 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host user-vc8frgq.biz.mindspring.com. (216.135.238.26) Time: Tue Jan 27 17:32:48 2004 Input: Factorial(69)^(1/64) Output: Magma V2.10-6 Tue Jan 27 2004 17:32:45 on modular [Seed = 3820307697] ------------------------------------- 34.268525793599231049113815 Total time: 2.919 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host user-vc8frgq.biz.mindspring.com. (216.135.238.26) Time: Tue Jan 27 17:33:14 2004 Input: Factorial(70)^(1/64) Output: Magma V2.10-6 Tue Jan 27 2004 17:33:11 on modular [Seed = 763071018] ------------------------------------- 36.620568217499479501051672 Total time: 2.909 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host user-vc8frgq.biz.mindspring.com. (216.135.238.26) Time: Tue Jan 27 17:33:32 2004 Input: Factorial(71)^(1/64) Output: Magma V2.10-6 Tue Jan 27 2004 17:33:29 on modular [Seed = 929140782] ------------------------------------- 39.142719026013720143458443 Total time: 2.939 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host user-vc8frgq.biz.mindspring.com. (216.135.238.26) Time: Tue Jan 27 17:33:50 2004 Input: Factorial(72)^(1/64) Output: Magma V2.10-6 Tue Jan 27 2004 17:33:47 on modular [Seed = 5678955] ------------------------------------- 41.84772090972843389157061 Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host user-vc8frgq.biz.mindspring.com. (216.135.238.26) Time: Tue Jan 27 17:34:10 2004 Input: Factorial(73)^(1/64) Output: Magma V2.10-6 Tue Jan 27 2004 17:34:07 on modular [Seed = 173845877] ------------------------------------- 44.749298368046114153593271 Total time: 2.909 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host user-vc8frgq.biz.mindspring.com. (216.135.238.26) Time: Tue Jan 27 17:34:28 2004 Input: Factorial(74)^(1/64) Output: Magma V2.10-6 Tue Jan 27 2004 17:34:25 on modular [Seed = 373338439] ------------------------------------- 47.862235127241196877770519 Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host user-vc8frgq.biz.mindspring.com. (216.135.238.26) Time: Tue Jan 27 17:34:47 2004 Input: Factorial(75)^(1/64) Output: Magma V2.10-6 Tue Jan 27 2004 17:34:43 on modular [Seed = 524925115] ------------------------------------- 51.202457786040338420790706 Total time: 3.039 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host user-vc8frgq.biz.mindspring.com. (216.135.238.26) Time: Tue Jan 27 17:35:05 2004 Input: Factorial(76)^(1/64) Output: Magma V2.10-6 Tue Jan 27 2004 17:35:01 on modular [Seed = 1998704834] ------------------------------------- 54.787126198433509808028658 Total time: 3.469 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host user-vc8frgq.biz.mindspring.com. (216.135.238.26) Time: Tue Jan 27 17:35:23 2004 Input: Factorial(77)^(1/64) Output: Magma V2.10-6 Tue Jan 27 2004 17:35:20 on modular [Seed = 1158931149] ------------------------------------- 58.634731145792231649667205 Total time: 2.939 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host user-vc8frgq.biz.mindspring.com. (216.135.238.26) Time: Tue Jan 27 17:35:44 2004 Input: Factorial(78)^(1/64) Output: Magma V2.10-6 Tue Jan 27 2004 17:35:41 on modular [Seed = 1442902475] ------------------------------------- 62.765199896312342015375392 Total time: 2.879 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host user-vc8frgq.biz.mindspring.com. (216.135.238.26) Time: Tue Jan 27 17:36:02 2004 Input: Factorial(79)^(1/64) Output: Magma V2.10-6 Tue Jan 27 2004 17:35:59 on modular [Seed = 2817589320] ------------------------------------- 67.20001029961582360123767 Total time: 3.029 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host user-vc8frgq.biz.mindspring.com. (216.135.238.26) Time: Tue Jan 27 17:36:21 2004 Input: Factorial(80)^(1/64) Output: Magma V2.10-6 Tue Jan 27 2004 17:36:18 on modular [Seed = 2984711795] ------------------------------------- 71.962314118370595286747377 Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host user-vc8frgq.biz.mindspring.com. (216.135.238.26) Time: Tue Jan 27 17:36:44 2004 Input: Factorial(81)^(1/64) Output: Magma V2.10-6 Tue Jan 27 2004 17:36:41 on modular [Seed = 2194941275] ------------------------------------- 77.077070357378598450571851 Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host user-vc8frgq.biz.mindspring.com. (216.135.238.26) Time: Tue Jan 27 17:37:01 2004 Input: Factorial(82)^(1/64) Output: Magma V2.10-6 Tue Jan 27 2004 17:36:58 on modular [Seed = 2346525601] ------------------------------------- 82.57118941413190549665091 Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host user-vc8frgq.biz.mindspring.com. (216.135.238.26) Time: Tue Jan 27 17:37:22 2004 Input: Factorial(83)^(1/64) Output: Magma V2.10-6 Tue Jan 27 2004 17:37:19 on modular [Seed = 2495757483] ------------------------------------- 88.473688943768716857178638 Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host user-vc8frgq.biz.mindspring.com. (216.135.238.26) Time: Tue Jan 27 17:37:42 2004 Input: Factorial(84)^(1/64) Output: Magma V2.10-6 Tue Jan 27 2004 17:37:39 on modular [Seed = 2647340430] ------------------------------------- 94.815862406137569132987825 Total time: 3.009 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host user-vc8frgq.biz.mindspring.com. (216.135.238.26) Time: Tue Jan 27 17:38:08 2004 Input: Factorial(85)^(1/64) Output: Magma V2.10-6 Tue Jan 27 2004 17:38:03 on modular [Seed = 3870314125] ------------------------------------- 101.631461343800455725359454 Total time: 3.059 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host user-vc8frgq.biz.mindspring.com. (216.135.238.26) Time: Tue Jan 27 17:38:26 2004 Input: Factorial(86)^(1/64) Output: Magma V2.10-6 Tue Jan 27 2004 17:38:23 on modular [Seed = 4021897104] ------------------------------------- 108.95689252781900381370143 Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host user-vc8frgq.biz.mindspring.com. (216.135.238.26) Time: Tue Jan 27 17:38:46 2004 Input: Factorial(87)^(1/64) Output: Magma V2.10-6 Tue Jan 27 2004 17:38:42 on modular [Seed = 3231082643] ------------------------------------- 116.831431203664854443025132 Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host user-vc8frgq.biz.mindspring.com. (216.135.238.26) Time: Tue Jan 27 17:39:09 2004 Input: Factorial(88)^(1/64) Output: Magma V2.10-6 Tue Jan 27 2004 17:39:06 on modular [Seed = 3382665571] ------------------------------------- 125.297451773219963920220391 Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host user-vc8frgq.biz.mindspring.com. (216.135.238.26) Time: Tue Jan 27 17:39:29 2004 Input: Factorial(89)^(1/64) Output: Magma V2.10-6 Tue Jan 27 2004 17:39:25 on modular [Seed = 3548740462] ------------------------------------- 134.400677361284729053726748 Total time: 3.229 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host user-vc8frgq.biz.mindspring.com. (216.135.238.26) Time: Tue Jan 27 17:39:49 2004 Input: Factorial(90)^(1/64) Output: Magma V2.10-6 Tue Jan 27 2004 17:39:46 on modular [Seed = 729646008] ------------------------------------- 144.190449837052642644224922 Total time: 2.939 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host user-vc8frgq.biz.mindspring.com. (216.135.238.26) Time: Tue Jan 27 17:40:07 2004 Input: Factorial(91)^(1/64) Output: Magma V2.10-6 Tue Jan 27 2004 17:40:04 on modular [Seed = 122793954] ------------------------------------- 154.720021993466941111202238 Total time: 2.939 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host user-vc8frgq.biz.mindspring.com. (216.135.238.26) Time: Tue Jan 27 17:40:26 2004 Input: Factorial(92)^(1/64) Output: Magma V2.10-6 Tue Jan 27 2004 17:40:23 on modular [Seed = 240690936] ------------------------------------- 166.046873731146910195059966 Total time: 2.939 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host user-vc8frgq.biz.mindspring.com. (216.135.238.26) Time: Tue Jan 27 17:40:44 2004 Input: Factorial(93)^(1/64) Output: Magma V2.10-6 Tue Jan 27 2004 17:40:41 on modular [Seed = 1631046057] ------------------------------------- 178.233054249637187651165102 Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host user-vc8frgq.biz.mindspring.com. (216.135.238.26) Time: Tue Jan 27 17:41:03 2004 Input: Factorial(94)^(1/64) Output: Magma V2.10-6 Tue Jan 27 2004 17:41:00 on modular [Seed = 1748943029] ------------------------------------- 191.345552418156011452906751 Total time: 3.659 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host user-vc8frgq.biz.mindspring.com. (216.135.238.26) Time: Tue Jan 27 17:41:30 2004 Input: Factorial(95)^(1/64) Output: Magma V2.10-6 Tue Jan 27 2004 17:41:27 on modular [Seed = 1092085879] ------------------------------------- 205.456697681954363555979278 Total time: 2.929 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host user-vc8frgq.biz.mindspring.com. (216.135.238.26) Time: Tue Jan 27 17:41:50 2004 Input: Factorial(96)^(1/64) Output: Magma V2.10-6 Tue Jan 27 2004 17:41:47 on modular [Seed = 1293673543] ------------------------------------- 220.644594060105007512347241 Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host user-vc8frgq.biz.mindspring.com. (216.135.238.26) Time: Tue Jan 27 17:42:07 2004 Input: Factorial(97)^(1/64) Output: Magma V2.10-6 Tue Jan 27 2004 17:42:04 on modular [Seed = 1409482057] ------------------------------------- 236.993590007386311167374808 Total time: 2.889 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host user-vc8frgq.biz.mindspring.com. (216.135.238.26) Time: Tue Jan 27 17:42:26 2004 Input: Factorial(98)^(1/64) Output: Magma V2.10-6 Tue Jan 27 2004 17:42:21 on modular [Seed = 2700478924] ------------------------------------- 254.594787148398166106488028 Total time: 4.489 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host user-vc8frgq.biz.mindspring.com. (216.135.238.26) Time: Tue Jan 27 17:42:44 2004 Input: Factorial(99)^(1/64) Output: Magma V2.10-6 Tue Jan 27 2004 17:42:41 on modular [Seed = 2935490542] ------------------------------------- 273.546591147764442036242319 Total time: 2.999 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host user-vc8frgq.biz.mindspring.com. (216.135.238.26) Time: Tue Jan 27 17:43:03 2004 Input: Factorial(100)^(1/64) Output: Magma V2.10-6 Tue Jan 27 2004 17:43:00 on modular [Seed = 3119452396] ------------------------------------- 293.955308257998480151750358 Total time: 2.999 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host user-vc8frgq.biz.mindspring.com. (216.135.238.26) Time: Tue Jan 27 17:46:04 2004 Input: Factorial(101)^(1/64) Output: Magma V2.10-6 Tue Jan 27 2004 17:46:01 on modular [Seed = 3803465962] ------------------------------------- 315.935791388250014718628873 Total time: 3.069 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host user-vc8frgq.biz.mindspring.com. (216.135.238.26) Time: Tue Jan 27 17:46:22 2004 Input: Factorial(102)^(1/64) Output: Magma V2.10-6 Tue Jan 27 2004 17:46:19 on modular [Seed = 4021896693] ------------------------------------- 339.612139864796861600602076 Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host user-vc8frgq.biz.mindspring.com. (216.135.238.26) Time: Tue Jan 27 17:46:41 2004 Input: Factorial(103)^(1/64) Output: Magma V2.10-6 Tue Jan 27 2004 17:46:38 on modular [Seed = 4137704601] ------------------------------------- 365.118457410059282660522316 Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host user-vc8frgq.biz.mindspring.com. (216.135.238.26) Time: Tue Jan 27 17:47:00 2004 Input: Factorial(104)^(1/64) Output: Magma V2.10-6 Tue Jan 27 2004 17:46:57 on modular [Seed = 3247926145] ------------------------------------- 392.599673253565278638163227 Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host user-vc8frgq.biz.mindspring.com. (216.135.238.26) Time: Tue Jan 27 17:47:19 2004 Input: Factorial(105)^(1/64) Output: Magma V2.10-6 Tue Jan 27 2004 17:47:15 on modular [Seed = 3365823133] ------------------------------------- 422.21243170836467424311042 Total time: 2.989 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host user-vc8frgq.biz.mindspring.com. (216.135.238.26) Time: Tue Jan 27 17:47:37 2004 Input: Factorial(106)^(1/64) Output: Magma V2.10-6 Tue Jan 27 2004 17:47:34 on modular [Seed = 3548739956] ------------------------------------- 454.126056002798909395372626 Total time: 2.869 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host user-vc8frgq.biz.mindspring.com. (216.135.238.26) Time: Tue Jan 27 17:47:55 2004 Input: Factorial(107)^(1/64) Output: Magma V2.10-6 Tue Jan 27 2004 17:47:52 on modular [Seed = 3666636899] ------------------------------------- 488.523592653459861052465836 Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host user-vc8frgq.biz.mindspring.com. (216.135.238.26) Time: Tue Jan 27 17:48:17 2004 Input: Factorial(108)^(1/64) Output: Magma V2.10-6 Tue Jan 27 2004 17:48:14 on modular [Seed = 644910250] ------------------------------------- 525.602943204073426510453245 Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host user-vc8frgq.biz.mindspring.com. (216.135.238.26) Time: Tue Jan 27 17:48:34 2004 Input: Factorial(109)^(1/64) Output: Magma V2.10-6 Tue Jan 27 2004 17:48:31 on modular [Seed = 796493234] ------------------------------------- 565.578090740686380298084712 Total time: 2.929 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host user-vc8frgq.biz.mindspring.com. (216.135.238.26) Time: Tue Jan 27 17:48:54 2004 Input: Factorial(110)^(1/64) Output: Magma V2.10-6 Tue Jan 27 2004 17:48:51 on modular [Seed = 878878405] ------------------------------------- 608.680429230015574842872567 Total time: 3.059 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host user-vc8frgq.biz.mindspring.com. (216.135.238.26) Time: Tue Jan 27 17:49:12 2004 Input: Factorial(111)^(1/64) Output: Magma V2.10-6 Tue Jan 27 2004 17:49:09 on modular [Seed = 39102661] ------------------------------------- 655.160204419597050526971724 Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host user-vc8frgq.biz.mindspring.com. (216.135.238.26) Time: Tue Jan 27 17:49:30 2004 Input: Factorial(112)^(1/64) Output: Magma V2.10-6 Tue Jan 27 2004 17:49:27 on modular [Seed = 190685662] ------------------------------------- 705.288075790304386032319082 Total time: 2.909 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host user-vc8frgq.biz.mindspring.com. (216.135.238.26) Time: Tue Jan 27 17:50:41 2004 Input: Factorial(113)^(1/64) Output: Magma V2.10-6 Tue Jan 27 2004 17:50:38 on modular [Seed = 508081410] ------------------------------------- 759.356809869176494054934843 Total time: 3.009 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host user-vc8frgq.biz.mindspring.com. (216.135.238.26) Time: Tue Jan 27 17:51:02 2004 Input: Factorial(114)^(1/64) Output: Magma V2.10-6 Tue Jan 27 2004 17:50:59 on modular [Seed = 1799208986] ------------------------------------- 817.683116099059917574465605 Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host user-vc8frgq.biz.mindspring.com. (216.135.238.26) Time: Tue Jan 27 17:51:22 2004 Input: Factorial(115)^(1/64) Output: Magma V2.10-6 Tue Jan 27 2004 17:51:19 on modular [Seed = 1881594677] ------------------------------------- 880.60963742759540068931044 Total time: 2.919 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host user-vc8frgq.biz.mindspring.com. (216.135.238.26) Time: Tue Jan 27 17:51:41 2004 Input: Factorial(116)^(1/64) Output: Magma V2.10-6 Tue Jan 27 2004 17:51:38 on modular [Seed = 2033177121] ------------------------------------- 948.507108828385804602538238 Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host user-vc8frgq.biz.mindspring.com. (216.135.238.26) Time: Tue Jan 27 17:52:16 2004 Input: Factorial(117)^(1/64) Output: Magma V2.10-6 Tue Jan 27 2004 17:52:13 on modular [Seed = 1158934266] ------------------------------------- 1021.776698109201767348851991 Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host user-vc8frgq.biz.mindspring.com. (216.135.238.26) Time: Tue Jan 27 17:52:36 2004 Input: Factorial(118)^(1/64) Output: Magma V2.10-6 Tue Jan 27 2004 17:52:33 on modular [Seed = 1376057793] ------------------------------------- 1100.852544603903506872913795 Total time: 2.989 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host user-vc8frgq.biz.mindspring.com. (216.135.238.26) Time: Tue Jan 27 17:52:55 2004 Input: Factorial(119)^(1/64) Output: Magma V2.10-6 Tue Jan 27 2004 17:52:51 on modular [Seed = 2800749888] ------------------------------------- 1186.204512695193040214969611 Total time: 3.509 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host user-vc8frgq.biz.mindspring.com. (216.135.238.26) Time: Tue Jan 27 17:53:13 2004 Input: Factorial(120)^(1/64) Output: Magma V2.10-6 Tue Jan 27 2004 17:53:10 on modular [Seed = 2967870276] ------------------------------------- 1278.341178583957338750181678 Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host user-vc8frgq.biz.mindspring.com. (216.135.238.26) Time: Tue Jan 27 17:53:32 2004 Input: Factorial(121)^(1/64) Output: Magma V2.10-6 Tue Jan 27 2004 17:53:29 on modular [Seed = 3119452786] ------------------------------------- 1377.813070318271976921166486 Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host user-vc8frgq.biz.mindspring.com. (216.135.238.26) Time: Tue Jan 27 17:54:13 2004 Input: Factorial(122)^(1/64) Output: Magma V2.10-6 Tue Jan 27 2004 17:54:10 on modular [Seed = 2413372351] ------------------------------------- 1485.21618283249200376049539 Total time: 3.139 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host user-vc8frgq.biz.mindspring.com. (216.135.238.26) Time: Tue Jan 27 17:54:31 2004 Input: Factorial(123)^(1/64) Output: Magma V2.10-6 Tue Jan 27 2004 17:54:28 on modular [Seed = 2630496410] ------------------------------------- 1601.195791636664344956549683 Total time: 2.869 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host user-vc8frgq.biz.mindspring.com. (216.135.238.26) Time: Tue Jan 27 17:54:49 2004 Input: Factorial(124)^(1/64) Output: Magma V2.10-6 Tue Jan 27 2004 17:54:46 on modular [Seed = 3904783612] ------------------------------------- 1726.450590852264854770574812 Total time: 2.989 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host user-vc8frgq.biz.mindspring.com. (216.135.238.26) Time: Tue Jan 27 17:55:10 2004 Input: Factorial(125)^(1/64) Output: Magma V2.10-6 Tue Jan 27 2004 17:55:07 on modular [Seed = 3416090530] ------------------------------------- 1861.737183526712511988114237 Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host user-vc8frgq.biz.mindspring.com. (216.135.238.26) Time: Tue Jan 27 17:55:27 2004 Input: Factorial(126)^(1/64) Output: Magma V2.10-6 Tue Jan 27 2004 17:55:24 on modular [Seed = 3498474670] ------------------------------------- 2007.874954592280061011159322 Total time: 3.379 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host user-vc8frgq.biz.mindspring.com. (216.135.238.26) Time: Tue Jan 27 17:55:45 2004 Input: Factorial(127)^(1/64) Output: Magma V2.10-6 Tue Jan 27 2004 17:55:42 on modular [Seed = 544640109] ------------------------------------- 2165.751359482377997702624153 Total time: 3.019 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host user-vc8frgq.biz.mindspring.com. (216.135.238.26) Time: Tue Jan 27 17:56:04 2004 Input: Factorial(128)^(1/64) Output: Magma V2.10-6 Tue Jan 27 2004 17:56:01 on modular [Seed = 746225806] ------------------------------------- 2336.327664298776818841842402 Total time: 3.179 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host user-vc8frgq.biz.mindspring.com. (216.135.238.26) Time: Tue Jan 27 17:56:25 2004 Input: Factorial(129)^(1/64) Output: Magma V2.10-6 Tue Jan 27 2004 17:56:22 on modular [Seed = 1047040651] ------------------------------------- 2520.64517655789839106399892 Total time: 2.869 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host user-vc8frgq.biz.mindspring.com. (216.135.238.26) Time: Tue Jan 27 17:56:44 2004 Input: Factorial(130)^(1/64) Output: Magma V2.10-6 Tue Jan 27 2004 17:56:41 on modular [Seed = 89368975] ------------------------------------- 2719.832008955461017116491442 Total time: 2.889 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host user-vc8frgq.biz.mindspring.com. (216.135.238.26) Time: Tue Jan 27 17:57:01 2004 Input: Factorial(131)^(1/64) Output: Magma V2.10-6 Tue Jan 27 2004 17:56:58 on modular [Seed = 339916941] ------------------------------------- 2935.11042230114511271201955 Total time: 2.979 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host user-vc8frgq.biz.mindspring.com. (216.135.238.26) Time: Tue Jan 27 17:57:19 2004 Input: Factorial(132)^(1/64) Output: Magma V2.10-6 Tue Jan 27 2004 17:57:15 on modular [Seed = 1614204040] ------------------------------------- 3167.804797815413120674355445 Total time: 3.679 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host user-vc8frgq.biz.mindspring.com. (216.135.238.26) Time: Tue Jan 27 17:57:37 2004 Input: Factorial(133)^(1/64) Output: Magma V2.10-6 Tue Jan 27 2004 17:57:34 on modular [Seed = 1915018895] ------------------------------------- 3419.350293378439853062519211 Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host user-vc8frgq.biz.mindspring.com. (216.135.238.26) Time: Tue Jan 27 17:57:55 2004 Input: Factorial(134)^(1/64) Output: Magma V2.10-6 Tue Jan 27 2004 17:57:52 on modular [Seed = 2033178026] ------------------------------------- 3691.302243108194162195290781 Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host user-vc8frgq.biz.mindspring.com. (216.135.238.26) Time: Tue Jan 27 17:58:35 2004 Input: Factorial(135)^(1/64) Output: Magma V2.10-6 Tue Jan 27 2004 17:58:31 on modular [Seed = 1209984380] ------------------------------------- 3985.346364855839962745541225 Total time: 3.389 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host user-vc8frgq.biz.mindspring.com. (216.135.238.26) Time: Tue Jan 27 17:58:55 2004 Input: Factorial(136)^(1/64) Output: Magma V2.10-6 Tue Jan 27 2004 17:58:52 on modular [Seed = 1594487376] ------------------------------------- 4303.309845879709415091305653 Total time: 2.889 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host user-vc8frgq.biz.mindspring.com. (216.135.238.26) Time: Tue Jan 27 17:59:14 2004 Input: Factorial(137)^(1/64) Output: Magma V2.10-6 Tue Jan 27 2004 17:59:11 on modular [Seed = 3001294766] ------------------------------------- 4647.173383135478695326043293 Total time: 2.929 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host user-vc8frgq.biz.mindspring.com. (216.135.238.26) Time: Tue Jan 27 17:59:36 2004 Input: Factorial(138)^(1/64) Output: Magma V2.10-6 Tue Jan 27 2004 17:59:32 on modular [Seed = 3119453390] ------------------------------------- 5019.084261344913293257375725 Total time: 3.589 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host user-vc8frgq.biz.mindspring.com. (216.135.238.26) Time: Tue Jan 27 17:59:54 2004 Input: Factorial(139)^(1/64) Output: Magma V2.10-6 Tue Jan 27 2004 17:59:51 on modular [Seed = 2296260044] ------------------------------------- 5421.370559327781693623324623 Total time: 2.989 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host user-vc8frgq.biz.mindspring.com. (216.135.238.26) Time: Tue Jan 27 18:00:13 2004 Input: Factorial(140)^(1/64) Output: Magma V2.10-6 Tue Jan 27 2004 18:00:09 on modular [Seed = 3770043834] ------------------------------------- 5856.556583054841172718012597 Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host user-vc8frgq.biz.mindspring.com. (216.135.238.26) Time: Tue Jan 27 18:00:29 2004 Input: Factorial(141)^(1/64) Output: Magma V2.10-6 Tue Jan 27 2004 18:00:26 on modular [Seed = 4154546783] ------------------------------------- 6327.379632562600568807484063 Total time: 2.909 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host user-vc8frgq.biz.mindspring.com. (216.135.238.26) Time: Tue Jan 27 18:01:44 2004 Input: Factorial(141)^(1/64) Output: Magma V2.10-6 Tue Jan 27 2004 18:01:41 on modular [Seed = 1013617101] ------------------------------------- 6327.379632562600568807484063 Total time: 2.909 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host user-vc8frgq.biz.mindspring.com. (216.135.238.26) Time: Tue Jan 27 18:02:08 2004 Input: Factorial(143)^(1/64) Output: Magma V2.10-6 Tue Jan 27 2004 18:02:05 on modular [Seed = 89368780] ------------------------------------- 7388.0618609884280706067248 Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host user-vc8frgq.biz.mindspring.com. (216.135.238.26) Time: Tue Jan 27 18:02:30 2004 Input: Factorial(142)^(1/64) Output: Magma V2.10-6 Tue Jan 27 2004 18:02:26 on modular [Seed = 373340208] ------------------------------------- 6836.808219326573072977631296 Total time: 2.939 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host user-vc8frgq.biz.mindspring.com. (216.135.238.26) Time: Tue Jan 27 18:03:20 2004 Input: Factorial(143)^(1/64) Output: Magma V2.10-6 Tue Jan 27 2004 18:03:17 on modular [Seed = 1731316086] ------------------------------------- 7388.0618609884280706067248 Total time: 3.009 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host user-vc8frgq.biz.mindspring.com. (216.135.238.26) Time: Tue Jan 27 18:03:37 2004 Input: Factorial(144)^(1/64) Output: Magma V2.10-6 Tue Jan 27 2004 18:03:34 on modular [Seed = 2083181086] ------------------------------------- 7984.63259154961223343839412 Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host user-vc8frgq.biz.mindspring.com. (216.135.238.26) Time: Tue Jan 27 18:03:58 2004 Input: Factorial(145)^(1/64) Output: Magma V2.10-6 Tue Jan 27 2004 18:03:54 on modular [Seed = 1075244606] ------------------------------------- 8630.308337362285653420954858 Total time: 3.209 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host user-vc8frgq.biz.mindspring.com. (216.135.238.26) Time: Tue Jan 27 18:04:17 2004 Input: Factorial(146)^(1/64) Output: Magma V2.10-6 Tue Jan 27 2004 18:04:14 on modular [Seed = 1376058392] ------------------------------------- 9329.198322557958025281454791 Total time: 2.909 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host user-vc8frgq.biz.mindspring.com. (216.135.238.26) Time: Tue Jan 27 18:04:35 2004 Input: Factorial(147)^(1/64) Output: Magma V2.10-6 Tue Jan 27 2004 18:04:32 on modular [Seed = 2750745863] ------------------------------------- 10085.76068205334786428857 Total time: 2.919 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host user-vc8frgq.biz.mindspring.com. (216.135.238.26) Time: Tue Jan 27 18:04:54 2004 Input: Factorial(148)^(1/64) Output: Magma V2.10-6 Tue Jan 27 2004 18:04:51 on modular [Seed = 3084982528] ------------------------------------- 10904.83247606899474023186 Total time: 3.029 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host user-vc8frgq.biz.mindspring.com. (216.135.238.26) Time: Tue Jan 27 18:05:13 2004 Input: Factorial(149)^(1/64) Output: Magma V2.10-6 Tue Jan 27 2004 18:05:10 on modular [Seed = 2363105806] ------------------------------------- 11791.66231730605413261924 Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host user-vc8frgq.biz.mindspring.com. (216.135.238.26) Time: Tue Jan 27 18:05:34 2004 Input: Factorial(150)^(1/64) Output: Magma V2.10-6 Tue Jan 27 2004 18:05:31 on modular [Seed = 2647339778] ------------------------------------- 12751.9458406781674807812 Total time: 2.979 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host user-vc8frgq.biz.mindspring.com. (216.135.238.26) Time: Tue Jan 27 18:05:52 2004 Input: Factorial(151)^(1/64) Output: Magma V2.10-6 Tue Jan 27 2004 18:05:49 on modular [Seed = 4005052423] ------------------------------------- 13791.86426592762037072822 Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host user-vc8frgq.biz.mindspring.com. (216.135.238.26) Time: Tue Jan 27 18:06:30 2004 Input: Factorial(152)^(1/64) Output: Magma V2.10-6 Tue Jan 27 2004 18:06:26 on modular [Seed = 4205597740] ------------------------------------- 14918.12632572016336993448 Total time: 3.579 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host user-vc8frgq.biz.mindspring.com. (216.135.238.26) Time: Tue Jan 27 18:06:49 2004 Input: Factorial(153)^(1/64) Output: Magma V2.10-6 Tue Jan 27 2004 18:06:46 on modular [Seed = 3365824490] ------------------------------------- 16138.0138560767113031068 Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host user-vc8frgq.biz.mindspring.com. (216.135.238.26) Time: Tue Jan 27 18:07:08 2004 Input: Factorial(154)^(1/64) Output: Magma V2.10-6 Tue Jan 27 2004 18:07:05 on modular [Seed = 3650057956] ------------------------------------- 17459.43137244362366688015 Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host user-vc8frgq.biz.mindspring.com. (216.135.238.26) Time: Tue Jan 27 18:07:31 2004 Input: Factorial(155)^(1/64) Output: Magma V2.10-6 Tue Jan 27 2004 18:07:28 on modular [Seed = 594906166] ------------------------------------- 18890.9599835238851651108 Total time: 2.939 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host user-vc8frgq.biz.mindspring.com. (216.135.238.26) Time: Tue Jan 27 18:07:52 2004 Input: Factorial(156)^(1/64) Output: Magma V2.10-6 Tue Jan 27 2004 18:07:49 on modular [Seed = 845454674] ------------------------------------- 20441.91602640477178410255 Total time: 2.879 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host user-vc8frgq.biz.mindspring.com. (216.135.238.26) Time: Tue Jan 27 18:08:11 2004 Input: Factorial(157)^(1/64) Output: Magma V2.10-6 Tue Jan 27 2004 18:08:08 on modular [Seed = 105949563] ------------------------------------- 22122.41484075872211346726 Total time: 2.989 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host user-vc8frgq.biz.mindspring.com. (216.135.238.26) Time: Tue Jan 27 18:08:29 2004 Input: Factorial(158)^(1/64) Output: Magma V2.10-6 Tue Jan 27 2004 18:08:26 on modular [Seed = 289914462] ------------------------------------- 23943.4401372198641197842 Total time: 2.979 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host user-vc8frgq.biz.mindspring.com. (216.135.238.26) Time: Tue Jan 27 18:08:47 2004 Input: Factorial(159)^(1/64) Output: Magma V2.10-6 Tue Jan 27 2004 18:08:44 on modular [Seed = 407811905] ------------------------------------- 25916.91945572919529521056 Total time: 2.889 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host user-vc8frgq.biz.mindspring.com. (216.135.238.26) Time: Tue Jan 27 18:09:06 2004 Input: Factorial(160)^(1/64) Output: Magma V2.10-6 Tue Jan 27 2004 18:09:03 on modular [Seed = 1799210177] ------------------------------------- 28055.8062540026585363227 Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host user-vc8frgq.biz.mindspring.com. (216.135.238.26) Time: Tue Jan 27 18:09:24 2004 Input: Factorial(161)^(1/64) Output: Magma V2.10-6 Tue Jan 27 2004 18:09:21 on modular [Seed = 2100024057] ------------------------------------- 30374.16921464220223958654 Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host user-vc8frgq.biz.mindspring.com. (216.135.238.26) Time: Tue Jan 27 18:09:42 2004 Input: Factorial(162)^(1/64) Output: Magma V2.10-6 Tue Jan 27 2004 18:09:39 on modular [Seed = 1276830682] ------------------------------------- 32887.28941214487824444445 Total time: 2.939 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host user-vc8frgq.biz.mindspring.com. (216.135.238.26) Time: Tue Jan 27 18:10:01 2004 Input: Factorial(163)^(1/64) Output: Magma V2.10-6 Tue Jan 27 2004 18:09:58 on modular [Seed = 1459746996] ------------------------------------- 35611.76603856707238049904 Total time: 3.089 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host user-vc8frgq.biz.mindspring.com. (216.135.238.26) Time: Tue Jan 27 18:10:20 2004 Input: Factorial(164)^(1/64) Output: Magma V2.10-6 Tue Jan 27 2004 18:10:17 on modular [Seed = 2952331347] ------------------------------------- 38565.63144930456637338925 Total time: 2.979 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host user-vc8frgq.biz.mindspring.com. (216.135.238.26) Time: Tue Jan 27 18:10:38 2004 Input: Factorial(165)^(1/64) Output: Magma V2.10-6 Tue Jan 27 2004 18:10:35 on modular [Seed = 3202879856] ------------------------------------- 41768.47635882869139780451 Total time: 2.909 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host user-vc8frgq.biz.mindspring.com. (216.135.238.26) Time: Tue Jan 27 18:11:15 2004 Input: Factorial(166)^(1/64) Output: Magma V2.10-6 Tue Jan 27 2004 18:11:12 on modular [Seed = 2512594336] ------------------------------------- 45241.58609079234743032652 Total time: 2.989 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host user-vc8frgq.biz.mindspring.com. (216.135.238.26) Time: Tue Jan 27 18:11:33 2004 Input: Factorial(167)^(1/64) Output: Magma V2.10-6 Tue Jan 27 2004 18:11:30 on modular [Seed = 2630495387] ------------------------------------- 49008.08886825276002633338 Total time: 2.919 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host user-vc8frgq.biz.mindspring.com. (216.135.238.26) Time: Tue Jan 27 18:11:49 2004 Input: Factorial(168)^(1/64) Output: Magma V2.10-6 Tue Jan 27 2004 18:11:46 on modular [Seed = 4021903352] ------------------------------------- 53093.11721846820758209562 Total time: 2.999 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host user-vc8frgq.biz.mindspring.com. (216.135.238.26) Time: Tue Jan 27 18:12:07 2004 Input: Factorial(169)^(1/64) Output: Magma V2.10-6 Tue Jan 27 2004 18:12:04 on modular [Seed = 4037427345] ------------------------------------- 57523.98366348813113316985 Total time: 2.999 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host user-vc8frgq.biz.mindspring.com. (216.135.238.26) Time: Tue Jan 27 18:12:29 2004 Input: Factorial(170)^(1/64) Output: Magma V2.10-6 Tue Jan 27 2004 18:12:26 on modular [Seed = 3281351612] ------------------------------------- 62330.37197330673643312539 Total time: 2.929 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host user-vc8frgq.biz.mindspring.com. (216.135.238.26) Time: Tue Jan 27 18:12:47 2004 Input: Factorial(171)^(1/64) Output: Magma V2.10-6 Tue Jan 27 2004 18:12:44 on modular [Seed = 3683478418] ------------------------------------- 67544.54537349402996445971 Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host user-vc8frgq.biz.mindspring.com. (216.135.238.26) Time: Tue Jan 27 18:13:06 2004 Input: Factorial(172)^(1/64) Output: Magma V2.10-6 Tue Jan 27 2004 18:13:03 on modular [Seed = 561484152] ------------------------------------- 73201.57322483403207726799 Total time: 3.029 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host user-vc8frgq.biz.mindspring.com. (216.135.238.26) Time: Tue Jan 27 18:13:27 2004 Input: Factorial(173)^(1/64) Output: Magma V2.10-6 Tue Jan 27 2004 18:13:23 on modular [Seed = 812023938] ------------------------------------- 79339.57782954763191046863 Total time: 3.599 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host user-vc8frgq.biz.mindspring.com. (216.135.238.26) Time: Tue Jan 27 18:13:45 2004 Input: Factorial(174)^(1/64) Output: Magma V2.10-6 Tue Jan 27 2004 18:13:42 on modular [Seed = 39105154] ------------------------------------- 86000.00316820579506323757 Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host user-vc8frgq.biz.mindspring.com. (216.135.238.26) Time: Tue Jan 27 18:14:05 2004 Input: Factorial(175)^(1/64) Output: Magma V2.10-6 Tue Jan 27 2004 18:14:01 on modular [Seed = 190692247] ------------------------------------- 93227.90753459311109307655 Total time: 3.049 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host user-vc8frgq.biz.mindspring.com. (216.135.238.26) Time: Tue Jan 27 18:14:35 2004 Input: Factorial(176)^(1/64) Output: Magma V2.10-6 Tue Jan 27 2004 18:14:32 on modular [Seed = 424651239] ------------------------------------- 101072.28221381339610340011 Total time: 2.989 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host user-vc8frgq.biz.mindspring.com. (216.135.238.26) Time: Tue Jan 27 18:14:53 2004 Input: Factorial(177)^(1/64) Output: Magma V2.10-6 Tue Jan 27 2004 18:14:50 on modular [Seed = 1981859514] ------------------------------------- 109586.39854320544763230648 Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host user-vc8frgq.biz.mindspring.com. (216.135.238.26) Time: Tue Jan 27 18:15:10 2004 Input: Factorial(178)^(1/64) Output: Magma V2.10-6 Tue Jan 27 2004 18:15:07 on modular [Seed = 1158935960] ------------------------------------- 118828.18590765185227820796 Total time: 2.909 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host user-vc8frgq.biz.mindspring.com. (216.135.238.26) Time: Tue Jan 27 18:15:30 2004 Input: Factorial(179)^(1/64) Output: Magma V2.10-6 Tue Jan 27 2004 18:15:27 on modular [Seed = 1376052091] ------------------------------------- 128860.6434522491023121466 Total time: 2.909 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host user-vc8frgq.biz.mindspring.com. (216.135.238.26) Time: Tue Jan 27 18:15:49 2004 Input: Factorial(180)^(1/64) Output: Magma V2.10-6 Tue Jan 27 2004 18:15:46 on modular [Seed = 2800752546] ------------------------------------- 139752.28854784658602912009 Total time: 2.919 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host user-vc8frgq.biz.mindspring.com. (216.135.238.26) Time: Tue Jan 27 18:16:10 2004 Input: Factorial(181)^(1/64) Output: Magma V2.10-6 Tue Jan 27 2004 18:16:06 on modular [Seed = 3084977831] ------------------------------------- 151577.64532060406317360571 Total time: 3.049 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host user-vc8frgq.biz.mindspring.com. (216.135.238.26) Time: Tue Jan 27 18:16:28 2004 Input: Factorial(182)^(1/64) Output: Magma V2.10-6 Tue Jan 27 2004 18:16:25 on modular [Seed = 3169455571] ------------------------------------- 164417.77685759163461260094 Total time: 2.929 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host user-vc8frgq.biz.mindspring.com. (216.135.238.26) Time: Tue Jan 27 18:16:46 2004 Input: Factorial(183)^(1/64) Output: Magma V2.10-6 Tue Jan 27 2004 18:16:43 on modular [Seed = 2245211384] ------------------------------------- 178360.86502889029927368032 Total time: 2.929 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host user-vc8frgq.biz.mindspring.com. (216.135.238.26) Time: Tue Jan 27 18:17:03 2004 Input: Factorial(184)^(1/64) Output: Magma V2.10-6 Tue Jan 27 2004 18:17:00 on modular [Seed = 2329689024] ------------------------------------- 193502.84222518849988015981 Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host user-vc8frgq.biz.mindspring.com. (216.135.238.26) Time: Tue Jan 27 18:17:20 2004 Input: Factorial(185)^(1/64) Output: Magma V2.10-6 Tue Jan 27 2004 18:17:17 on modular [Seed = 2479170248] ------------------------------------- 209948.07970129055595630556 Total time: 2.919 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host user-vc8frgq.biz.mindspring.com. (216.135.238.26) Time: Tue Jan 27 18:17:36 2004 Input: Factorial(186)^(1/64) Output: Magma V2.10-6 Tue Jan 27 2004 18:17:33 on modular [Seed = 2563647795] ------------------------------------- 227810.13764329508140710124 Total time: 2.919 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host user-vc8frgq.biz.mindspring.com. (216.135.238.26) Time: Tue Jan 27 18:17:54 2004 Input: Factorial(187)^(1/64) Output: Magma V2.10-6 Tue Jan 27 2004 18:17:51 on modular [Seed = 3786887256] ------------------------------------- 247212.58254378665620040398 Total time: 2.929 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host user-vc8frgq.biz.mindspring.com. (216.135.238.26) Time: Tue Jan 27 18:18:11 2004 Input: Factorial(188)^(1/64) Output: Magma V2.10-6 Tue Jan 27 2004 18:18:08 on modular [Seed = 4137699168] ------------------------------------- 268289.87797884268631515599 Total time: 2.909 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host user-vc8frgq.biz.mindspring.com. (216.135.238.26) Time: Tue Jan 27 18:18:28 2004 Input: Factorial(189)^(1/64) Output: Magma V2.10-6 Tue Jan 27 2004 18:18:25 on modular [Seed = 4289285656] ------------------------------------- 291188.35543695829660962082 Total time: 2.939 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host user-vc8frgq.biz.mindspring.com. (216.135.238.26) Time: Tue Jan 27 18:18:46 2004 Input: Factorial(190)^(1/64) Output: Magma V2.10-6 Tue Jan 27 2004 18:18:43 on modular [Seed = 3432676665] ------------------------------------- 316067.27245747396667556909 Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host user-vc8frgq.biz.mindspring.com. (216.135.238.26) Time: Tue Jan 27 18:19:05 2004 Input: Factorial(191)^(1/64) Output: Magma V2.10-6 Tue Jan 27 2004 18:19:01 on modular [Seed = 3750325788] ------------------------------------- 343099.9659994968197607604 Total time: 3.469 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host user-vc8frgq.biz.mindspring.com. (216.135.238.26) Time: Tue Jan 27 18:19:43 2004 Input: Factorial(192)^(1/64) Output: Magma V2.10-6 Tue Jan 27 2004 18:19:40 on modular [Seed = 878872095] ------------------------------------- 372475.10968682305278863695 Total time: 2.909 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host user-vc8frgq.biz.mindspring.com. (216.135.238.26) Time: Tue Jan 27 18:20:02 2004 Input: Factorial(193)^(1/64) Output: Magma V2.10-6 Tue Jan 27 2004 18:19:59 on modular [Seed = 997034243] ------------------------------------- 404398.08436566624080806793 Total time: 3.089 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host user-vc8frgq.biz.mindspring.com. (216.135.238.26) Time: Tue Jan 27 18:20:19 2004 Input: Factorial(194)^(1/64) Output: Magma V2.10-6 Tue Jan 27 2004 18:20:16 on modular [Seed = 323330308] ------------------------------------- 439092.4722762742104308869 Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host user-vc8frgq.biz.mindspring.com. (216.135.238.26) Time: Tue Jan 27 18:20:36 2004 Input: Factorial(195)^(1/64) Output: Magma V2.10-6 Tue Jan 27 2004 18:20:33 on modular [Seed = 1631048455] ------------------------------------- 476801.68608355547902504056 Total time: 2.909 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host user-vc8frgq.biz.mindspring.com. (216.135.238.26) Time: Tue Jan 27 18:20:55 2004 Input: Factorial(196)^(1/64) Output: Magma V2.10-6 Tue Jan 27 2004 18:20:52 on modular [Seed = 1748949531] ------------------------------------- 517790.7450430486323796668 Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host user-vc8frgq.biz.mindspring.com. (216.135.238.26) Time: Tue Jan 27 18:21:13 2004 Input: Factorial(197)^(1/64) Output: Magma V2.10-6 Tue Jan 27 2004 18:21:10 on modular [Seed = 1142093317] ------------------------------------- 562348.21170506199737429891 Total time: 3.029 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host user-vc8frgq.biz.mindspring.com. (216.135.238.26) Time: Tue Jan 27 18:21:33 2004 Input: Factorial(198)^(1/64) Output: Magma V2.10-6 Tue Jan 27 2004 18:21:30 on modular [Seed = 1392894222] ------------------------------------- 610788.30379045324117847642 Total time: 3.009 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host user-vc8frgq.biz.mindspring.com. (216.135.238.26) Time: Tue Jan 27 18:21:52 2004 Input: Factorial(199)^(1/64) Output: Magma V2.10-6 Tue Jan 27 2004 18:21:48 on modular [Seed = 2750746888] ------------------------------------- 663453.19721600646780083174 Total time: 3.339 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host user-vc8frgq.biz.mindspring.com. (216.135.238.26) Time: Tue Jan 27 18:22:10 2004 Input: Factorial(200)^(1/64) Output: Magma V2.10-6 Tue Jan 27 2004 18:22:07 on modular [Seed = 3136030722] ------------------------------------- 720715.53771630437309387299 Total time: 2.939 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host user-vc8frgq.biz.mindspring.com. (216.135.238.26) Time: Tue Jan 27 18:26:49 2004 Input: Factorial(10)^(1/128) Output: Magma V2.10-6 Tue Jan 27 2004 18:26:46 on modular [Seed = 4137698663] ------------------------------------- 1.125247738290560411600847 Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host user-vc8frgq.biz.mindspring.com. (216.135.238.26) Time: Tue Jan 27 18:27:27 2004 Input: Factorial(20)^(1/128) Output: Magma V2.10-6 Tue Jan 27 2004 18:27:24 on modular [Seed = 3449519670] ------------------------------------- 1.392007574849482869894916 Total time: 2.989 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host user-vc8frgq.biz.mindspring.com. (216.135.238.26) Time: Tue Jan 27 18:27:50 2004 Input: Factorial(30)^(1/128) Output: Magma V2.10-6 Tue Jan 27 2004 18:27:47 on modular [Seed = 3733482762] ------------------------------------- 1.791883804972376803984657 Total time: 2.939 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host user-vc8frgq.biz.mindspring.com. (216.135.238.26) Time: Tue Jan 27 18:28:12 2004 Input: Factorial(40)^(1/128) Output: Magma V2.10-6 Tue Jan 27 2004 18:28:09 on modular [Seed = 712809995] ------------------------------------- 2.367607609329727763580515 Total time: 2.909 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host user-vc8frgq.biz.mindspring.com. (216.135.238.26) Time: Tue Jan 27 18:28:40 2004 Input: Factorial(50)^(1/128) Output: Magma V2.10-6 Tue Jan 27 2004 18:28:37 on modular [Seed = 644911659] ------------------------------------- 3.189877626016875932064781 Total time: 3.529 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host user-vc8frgq.biz.mindspring.com. (216.135.238.26) Time: Tue Jan 27 18:29:11 2004 Input: Factorial(60)^(1/128) Output: Magma V2.10-6 Tue Jan 27 2004 18:29:08 on modular [Seed = 140426340] ------------------------------------- 4.36517205240124261155488 Total time: 2.939 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host user-vc8frgq.biz.mindspring.com. (216.135.238.26) Time: Tue Jan 27 18:29:32 2004 Input: Factorial(70)^(1/128) Output: Magma V2.10-6 Tue Jan 27 2004 18:29:28 on modular [Seed = 72527988] ------------------------------------- 6.051493056882696242514908 Total time: 2.989 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host user-vc8frgq.biz.mindspring.com. (216.135.238.26) Time: Tue Jan 27 18:29:53 2004 Input: Factorial(80)^(1/128) Output: Magma V2.10-6 Tue Jan 27 2004 18:29:50 on modular [Seed = 491497819] ------------------------------------- 8.483060421709289893506718 Total time: 2.999 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host user-vc8frgq.biz.mindspring.com. (216.135.238.26) Time: Tue Jan 27 18:31:16 2004 Input: Factorial(81)^(1/128) Output: Magma V2.10-6 Tue Jan 27 2004 18:31:13 on modular [Seed = 2016332945] ------------------------------------- 8.779354780243169922933261 Total time: 3.019 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host user-vc8frgq.biz.mindspring.com. (216.135.238.26) Time: Tue Jan 27 18:31:40 2004 Input: Factorial(90)^(1/128) Output: Magma V2.10-6 Tue Jan 27 2004 18:31:37 on modular [Seed = 1948434565] ------------------------------------- 12.007932787830411679857421 Total time: 2.989 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host user-vc8frgq.biz.mindspring.com. (216.135.238.26) Time: Tue Jan 27 18:32:02 2004 Input: Factorial(99)^(1/128) Output: Magma V2.10-6 Tue Jan 27 2004 18:31:59 on modular [Seed = 1075246215] ------------------------------------- 16.539243971468721340050623 Total time: 2.979 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host user-vc8frgq.biz.mindspring.com. (216.135.238.26) Time: Tue Jan 27 18:32:21 2004 Input: Factorial(100)^(1/128) Output: Magma V2.10-6 Tue Jan 27 2004 18:32:18 on modular [Seed = 1494215795] ------------------------------------- 17.145124912289163026182645 Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host user-vc8frgq.biz.mindspring.com. (216.135.238.26) Time: Tue Jan 27 18:32:45 2004 Input: Factorial(101)^(1/128) Output: Magma V2.10-6 Tue Jan 27 2004 18:32:42 on modular [Seed = 1376053088] ------------------------------------- 17.77458273457495301769311 Total time: 2.909 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host user-vc8frgq.biz.mindspring.com. (216.135.238.26) Time: Tue Jan 27 18:33:07 2004 Input: Factorial(102)^(1/128) Output: Magma V2.10-6 Tue Jan 27 2004 18:33:04 on modular [Seed = 2885492403] ------------------------------------- 18.428568578834246007381521 Total time: 2.919 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host user-vc8frgq.biz.mindspring.com. (216.135.238.26) Time: Tue Jan 27 18:33:23 2004 Input: Factorial(103)^(1/128) Output: Magma V2.10-6 Tue Jan 27 2004 18:33:20 on modular [Seed = 2784170189] ------------------------------------- 19.108073095162140986291219 Total time: 2.939 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host user-vc8frgq.biz.mindspring.com. (216.135.238.26) Time: Tue Jan 27 18:33:40 2004 Input: Factorial(104)^(1/128) Output: Magma V2.10-6 Tue Jan 27 2004 18:33:37 on modular [Seed = 3202878407] ------------------------------------- 19.814128122467697383398006 Total time: 2.919 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host user-vc8frgq.biz.mindspring.com. (216.135.238.26) Time: Tue Jan 27 18:33:58 2004 Input: Factorial(105)^(1/128) Output: Magma V2.10-6 Tue Jan 27 2004 18:33:55 on modular [Seed = 3084976892] ------------------------------------- 20.547808440521453193059807 Total time: 2.919 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host user-vc8frgq.biz.mindspring.com. (216.135.238.26) Time: Tue Jan 27 18:34:16 2004 Input: Factorial(106)^(1/128) Output: Magma V2.10-6 Tue Jan 27 2004 18:34:13 on modular [Seed = 2178364636] ------------------------------------- 21.310233598034511207599092 Total time: 2.919 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host user-vc8frgq.biz.mindspring.com. (216.135.238.26) Time: Tue Jan 27 18:34:32 2004 Input: Factorial(107)^(1/128) Output: Magma V2.10-6 Tue Jan 27 2004 18:34:29 on modular [Seed = 2597072695] ------------------------------------- 22.102569820124081242523374 Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host user-vc8frgq.biz.mindspring.com. (216.135.238.26) Time: Tue Jan 27 18:34:57 2004 Input: Factorial(108)^(1/128) Output: Magma V2.10-6 Tue Jan 27 2004 18:34:54 on modular [Seed = 2529174304] ------------------------------------- 22.926031998670712544340125 Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host user-vc8frgq.biz.mindspring.com. (216.135.238.26) Time: Tue Jan 27 18:35:14 2004 Input: Factorial(109)^(1/128) Output: Magma V2.10-6 Tue Jan 27 2004 18:35:11 on modular [Seed = 3870315361] ------------------------------------- 23.781885769229621381649821 Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host user-vc8frgq.biz.mindspring.com. (216.135.238.26) Time: Tue Jan 27 18:35:31 2004 Input: Factorial(110)^(1/128) Output: Magma V2.10-6 Tue Jan 27 2004 18:35:28 on modular [Seed = 4289284631] ------------------------------------- 24.671449678322828033347647 Total time: 2.939 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host user-vc8frgq.biz.mindspring.com. (216.135.238.26) Time: Tue Jan 27 18:35:46 2004 Input: Factorial(111)^(1/128) Output: Magma V2.10-6 Tue Jan 27 2004 18:35:43 on modular [Seed = 3365829935] ------------------------------------- 25.596097445110593470628184 Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host user-vc8frgq.biz.mindspring.com. (216.135.238.26) Time: Tue Jan 27 18:36:05 2004 Input: Factorial(112)^(1/128) Output: Magma V2.10-6 Tue Jan 27 2004 18:36:02 on modular [Seed = 3264509704] ------------------------------------- 26.557260321620232708358185 Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host user-vc8frgq.biz.mindspring.com. (216.135.238.26) Time: Tue Jan 27 18:36:21 2004 Input: Factorial(113)^(1/128) Output: Magma V2.10-6 Tue Jan 27 2004 18:36:18 on modular [Seed = 3683479041] ------------------------------------- 27.556429555898138779741637 Total time: 2.979 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host user-vc8frgq.biz.mindspring.com. (216.135.238.26) Time: Tue Jan 27 18:36:37 2004 Input: Factorial(114)^(1/128) Output: Magma V2.10-6 Tue Jan 27 2004 18:36:34 on modular [Seed = 3565314814] ------------------------------------- 28.595158962647154998844919 Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host user-vc8frgq.biz.mindspring.com. (216.135.238.26) Time: Tue Jan 27 18:36:55 2004 Input: Factorial(115)^(1/128) Output: Magma V2.10-6 Tue Jan 27 2004 18:36:51 on modular [Seed = 561485595] ------------------------------------- 29.675067606116677568274464 Total time: 3.919 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host user-vc8frgq.biz.mindspring.com. (216.135.238.26) Time: Tue Jan 27 18:37:36 2004 Input: Factorial(116)^(1/128) Output: Magma V2.10-6 Tue Jan 27 2004 18:37:33 on modular [Seed = 1063881003] ------------------------------------- 30.797842600227467955864001 Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host user-vc8frgq.biz.mindspring.com. (216.135.238.26) Time: Tue Jan 27 18:37:53 2004 Input: Factorial(117)^(1/128) Output: Magma V2.10-6 Tue Jan 27 2004 18:37:49 on modular [Seed = 912293970] ------------------------------------- 31.965242031137536302389105 Total time: 2.979 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host user-vc8frgq.biz.mindspring.com. (216.135.238.26) Time: Tue Jan 27 18:38:10 2004 Input: Factorial(118)^(1/128) Output: Magma V2.10-6 Tue Jan 27 2004 18:38:06 on modular [Seed = 22525814] ------------------------------------- 33.179098007690075040825048 Total time: 2.919 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host user-vc8frgq.biz.mindspring.com. (216.135.238.26) Time: Tue Jan 27 18:38:30 2004 Input: Factorial(119)^(1/128) Output: Magma V2.10-6 Tue Jan 27 2004 18:38:27 on modular [Seed = 407809602] ------------------------------------- 34.441319845429748574140117 Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host user-vc8frgq.biz.mindspring.com. (216.135.238.26) Time: Tue Jan 27 18:38:46 2004 Input: Factorial(120)^(1/128) Output: Magma V2.10-6 Tue Jan 27 2004 18:38:43 on modular [Seed = 323331513] ------------------------------------- 35.753897390130174992513798 Total time: 2.999 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host user-vc8frgq.biz.mindspring.com. (216.135.238.26) Time: Tue Jan 27 18:39:03 2004 Input: Factorial(121)^(1/128) Output: Magma V2.10-6 Tue Jan 27 2004 18:39:00 on modular [Seed = 1849219283] ------------------------------------- 37.118904487043687223491475 Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host user-vc8frgq.biz.mindspring.com. (216.135.238.26) Time: Tue Jan 27 18:39:20 2004 Input: Factorial(122)^(1/128) Output: Magma V2.10-6 Tue Jan 27 2004 18:39:17 on modular [Seed = 2016333556] ------------------------------------- 38.538502602364975692580519 Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host user-vc8frgq.biz.mindspring.com. (216.135.238.26) Time: Tue Jan 27 18:39:38 2004 Input: Factorial(123)^(1/128) Output: Magma V2.10-6 Tue Jan 27 2004 18:39:35 on modular [Seed = 1931855341] ------------------------------------- 40.014944603693559842425813 Total time: 3.039 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host user-vc8frgq.biz.mindspring.com. (216.135.238.26) Time: Tue Jan 27 18:39:57 2004 Input: Factorial(124)^(1/128) Output: Magma V2.10-6 Tue Jan 27 2004 18:39:54 on modular [Seed = 1243413673] ------------------------------------- 41.550578706586805549439782 Total time: 2.989 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host user-vc8frgq.biz.mindspring.com. (216.135.238.26) Time: Tue Jan 27 18:40:15 2004 Input: Factorial(125)^(1/128) Output: Magma V2.10-6 Tue Jan 27 2004 18:40:12 on modular [Seed = 1594485162] ------------------------------------- 43.147852594616021191737442 Total time: 2.929 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host user-vc8frgq.biz.mindspring.com. (216.135.238.26) Time: Tue Jan 27 18:40:36 2004 Input: Factorial(126)^(1/128) Output: Magma V2.10-6 Tue Jan 27 2004 18:40:33 on modular [Seed = 1442898062] ------------------------------------- 44.809317720673677548361313 Total time: 2.979 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host user-vc8frgq.biz.mindspring.com. (216.135.238.26) Time: Tue Jan 27 18:40:53 2004 Input: Factorial(127)^(1/128) Output: Magma V2.10-6 Tue Jan 27 2004 18:40:50 on modular [Seed = 2733905289] ------------------------------------- 46.537633797630686991406625 Total time: 3.029 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host user-vc8frgq.biz.mindspring.com. (216.135.238.26) Time: Tue Jan 27 18:41:09 2004 Input: Factorial(128)^(1/128) Output: Magma V2.10-6 Tue Jan 27 2004 18:41:06 on modular [Seed = 3001288073] ------------------------------------- 48.335573486809658611662664 Total time: 2.929 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host user-vc8frgq.biz.mindspring.com. (216.135.238.26) Time: Tue Jan 27 18:41:27 2004 Input: Factorial(129)^(1/128) Output: Magma V2.10-6 Tue Jan 27 2004 18:41:24 on modular [Seed = 2379954816] ------------------------------------- 50.206027293123864443031899 Total time: 2.929 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host user-vc8frgq.biz.mindspring.com. (216.135.238.26) Time: Tue Jan 27 18:42:09 2004 Input: Factorial(130)^(1/128) Output: Magma V2.10-6 Tue Jan 27 2004 18:42:05 on modular [Seed = 2647337721] ------------------------------------- 52.152008676133089256702609 Total time: 4.499 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host user-vc8frgq.biz.mindspring.com. (216.135.238.26) Time: Tue Jan 27 18:42:26 2004 Input: Factorial(131)^(1/128) Output: Magma V2.10-6 Tue Jan 27 2004 18:42:23 on modular [Seed = 3955055773] ------------------------------------- 54.176659386687410561667028 Total time: 2.909 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host user-vc8frgq.biz.mindspring.com. (216.135.238.26) Time: Tue Jan 27 18:42:44 2004 Input: Factorial(132)^(1/128) Output: Magma V2.10-6 Tue Jan 27 2004 18:42:41 on modular [Seed = 3803469242] ------------------------------------- 56.283255039269122931254522 Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host user-vc8frgq.biz.mindspring.com. (216.135.238.26) Time: Tue Jan 27 18:43:01 2004 Input: Factorial(133)^(1/128) Output: Magma V2.10-6 Tue Jan 27 2004 18:42:58 on modular [Seed = 4255861334] ------------------------------------- 58.475210930602378230379445 Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host user-vc8frgq.biz.mindspring.com. (216.135.238.26) Time: Tue Jan 27 18:43:22 2004 Input: Factorial(134)^(1/128) Output: Magma V2.10-6 Tue Jan 27 2004 18:43:19 on modular [Seed = 4104274762] ------------------------------------- 60.756088115580599501702741 Total time: 3.009 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host user-vc8frgq.biz.mindspring.com. (216.135.238.26) Time: Tue Jan 27 18:43:49 2004 Input: Factorial(135)^(1/128) Output: Magma V2.10-6 Tue Jan 27 2004 18:43:46 on modular [Seed = 3482941524] ------------------------------------- 63.129599752064324035582689 Total time: 2.989 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host user-vc8frgq.biz.mindspring.com. (216.135.238.26) Time: Tue Jan 27 18:44:05 2004 Input: Factorial(136)^(1/128) Output: Magma V2.10-6 Tue Jan 27 2004 18:44:02 on modular [Seed = 3683478576] ------------------------------------- 65.599617726627869543074046 Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host user-vc8frgq.biz.mindspring.com. (216.135.238.26) Time: Tue Jan 27 18:44:23 2004 Input: Factorial(137)^(1/128) Output: Magma V2.10-6 Tue Jan 27 2004 18:44:20 on modular [Seed = 3582157352] ------------------------------------- 68.17017957388317379938335 Total time: 2.909 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host user-vc8frgq.biz.mindspring.com. (216.135.238.26) Time: Tue Jan 27 18:44:40 2004 Input: Factorial(138)^(1/128) Output: Magma V2.10-6 Tue Jan 27 2004 18:44:37 on modular [Seed = 796498144] ------------------------------------- 70.845495702584460731288922 Total time: 2.889 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host user-vc8frgq.biz.mindspring.com. (216.135.238.26) Time: Tue Jan 27 18:44:56 2004 Input: Factorial(139)^(1/128) Output: Magma V2.10-6 Tue Jan 27 2004 18:44:53 on modular [Seed = 611488763] ------------------------------------- 73.62995694231921587497499 Total time: 2.929 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host user-vc8frgq.biz.mindspring.com. (216.135.238.26) Time: Tue Jan 27 18:45:14 2004 Input: Factorial(140)^(1/128) Output: Magma V2.10-6 Tue Jan 27 2004 18:45:11 on modular [Seed = 828868892] ------------------------------------- 76.528142425220548225942151 Total time: 2.939 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host user-vc8frgq.biz.mindspring.com. (216.135.238.26) Time: Tue Jan 27 18:45:35 2004 Input: Factorial(141)^(1/128) Output: Magma V2.10-6 Tue Jan 27 2004 18:45:32 on modular [Seed = 240694840] ------------------------------------- 79.544827817794668784805854 Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host user-vc8frgq.biz.mindspring.com. (216.135.238.26) Time: Tue Jan 27 18:45:54 2004 Input: Factorial(142)^(1/128) Output: Magma V2.10-6 Tue Jan 27 2004 18:45:51 on modular [Seed = 441229855] ------------------------------------- 82.68499391864628463514918 Total time: 3.009 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host user-vc8frgq.biz.mindspring.com. (216.135.238.26) Time: Tue Jan 27 18:46:15 2004 Input: Factorial(143)^(1/128) Output: Magma V2.10-6 Tue Jan 27 2004 18:46:10 on modular [Seed = 373337726] ------------------------------------- 85.953835638605611156207272 Total time: 4.399 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host user-vc8frgq.biz.mindspring.com. (216.135.238.26) Time: Tue Jan 27 18:46:32 2004 Input: Factorial(144)^(1/128) Output: Magma V2.10-6 Tue Jan 27 2004 18:46:29 on modular [Seed = 1731321624] ------------------------------------- 89.356771380514930920270057 Total time: 2.909 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host user-vc8frgq.biz.mindspring.com. (216.135.238.26) Time: Tue Jan 27 18:46:48 2004 Input: Factorial(145)^(1/128) Output: Magma V2.10-6 Tue Jan 27 2004 18:46:45 on modular [Seed = 2083177523] ------------------------------------- 92.899452836721733048100737 Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host user-vc8frgq.biz.mindspring.com. (216.135.238.26) Time: Tue Jan 27 18:47:06 2004 Input: Factorial(146)^(1/128) Output: Magma V2.10-6 Tue Jan 27 2004 18:47:02 on modular [Seed = 1965280553] ------------------------------------- 96.587775223151081881144117 Total time: 2.999 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host user-vc8frgq.biz.mindspring.com. (216.135.238.26) Time: Tue Jan 27 18:47:22 2004 Input: Factorial(147)^(1/128) Output: Magma V2.10-6 Tue Jan 27 2004 18:47:19 on modular [Seed = 1108671215] ------------------------------------- 100.427887969693696353397879 Total time: 2.939 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host user-vc8frgq.biz.mindspring.com. (216.135.238.26) Time: Tue Jan 27 18:48:03 2004 Input: Factorial(148)^(1/128) Output: Magma V2.10-6 Tue Jan 27 2004 18:48:00 on modular [Seed = 1359473099] ------------------------------------- 104.426205887550059644927032 Total time: 2.929 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host user-vc8frgq.biz.mindspring.com. (216.135.238.26) Time: Tue Jan 27 18:48:31 2004 Input: Factorial(149)^(1/128) Output: Magma V2.10-6 Tue Jan 27 2004 18:48:28 on modular [Seed = 2935494216] ------------------------------------- 108.589420835116595314716261 Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host user-vc8frgq.biz.mindspring.com. (216.135.238.26) Time: Tue Jan 27 18:48:49 2004 Input: Factorial(150)^(1/128) Output: Magma V2.10-6 Tue Jan 27 2004 18:48:46 on modular [Seed = 2817597267] ------------------------------------- 112.924513904989502419971474 Total time: 3.009 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host user-vc8frgq.biz.mindspring.com. (216.135.238.26) Time: Tue Jan 27 18:49:07 2004 Input: Factorial(151)^(1/128) Output: Magma V2.10-6 Tue Jan 27 2004 18:49:04 on modular [Seed = 3169453158] ------------------------------------- 117.438768155697292168828654 Total time: 3.019 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host user-vc8frgq.biz.mindspring.com. (216.135.238.26) Time: Tue Jan 27 18:49:25 2004 Input: Factorial(152)^(1/128) Output: Magma V2.10-6 Tue Jan 27 2004 18:49:22 on modular [Seed = 2313105569] ------------------------------------- 122.139781912856563647462959 Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host hecate.telcordia.com. (192.4.209.5) Time: Tue Jan 27 18:49:29 2004 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: Magma V2.10-6 Tue Jan 27 2004 18:49:26 on modular [Seed = 2261794730] ------------------------------------- Replace this by some code, then click [PARI] or [MAGMA]! Total time: 3.059 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host user-vc8frgq.biz.mindspring.com. (216.135.238.26) Time: Tue Jan 27 18:49:42 2004 Input: Factorial(153)^(1/128) Output: Magma V2.10-6 Tue Jan 27 2004 18:49:39 on modular [Seed = 3938210771] ------------------------------------- 127.035482665579349162114122 Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host user-vc8frgq.biz.mindspring.com. (216.135.238.26) Time: Tue Jan 27 18:49:59 2004 Input: Factorial(154)^(1/128) Output: Magma V2.10-6 Tue Jan 27 2004 18:49:56 on modular [Seed = 3820313325] ------------------------------------- 132.134141585146810484367384 Total time: 2.989 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host user-vc8frgq.biz.mindspring.com. (216.135.238.26) Time: Tue Jan 27 18:50:17 2004 Input: Factorial(155)^(1/128) Output: Magma V2.10-6 Tue Jan 27 2004 18:50:14 on modular [Seed = 4087696111] ------------------------------------- 137.444388694205647316750812 Total time: 2.919 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host user-vc8frgq.biz.mindspring.com. (216.135.238.26) Time: Tue Jan 27 18:50:35 2004 Input: Factorial(156)^(1/128) Output: Magma V2.10-6 Tue Jan 27 2004 18:50:32 on modular [Seed = 3365826986] ------------------------------------- 142.975228716042877271666769 Total time: 2.849 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host user-vc8frgq.biz.mindspring.com. (216.135.238.26) Time: Tue Jan 27 18:50:52 2004 Input: Factorial(157)^(1/128) Output: Magma V2.10-6 Tue Jan 27 2004 18:50:49 on modular [Seed = 3247929522] ------------------------------------- 148.736057634854373981512706 Total time: 2.989 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host user-vc8frgq.biz.mindspring.com. (216.135.238.26) Time: Tue Jan 27 18:51:10 2004 Input: Factorial(158)^(1/128) Output: Magma V2.10-6 Tue Jan 27 2004 18:51:07 on modular [Seed = 3733481375] ------------------------------------- 154.736679999345546640214103 Total time: 2.929 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host user-vc8frgq.biz.mindspring.com. (216.135.238.26) Time: Tue Jan 27 18:51:27 2004 Input: Factorial(159)^(1/128) Output: Magma V2.10-6 Tue Jan 27 2004 18:51:24 on modular [Seed = 594909812] ------------------------------------- 160.987327003491785086904301 Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host user-vc8frgq.biz.mindspring.com. (216.135.238.26) Time: Tue Jan 27 18:51:46 2004 Input: Factorial(160)^(1/128) Output: Magma V2.10-6 Tue Jan 27 2004 18:51:43 on modular [Seed = 929140371] ------------------------------------- 167.498675379844895465712057 Total time: 2.889 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host user-vc8frgq.biz.mindspring.com. (216.135.238.26) Time: Tue Jan 27 18:52:09 2004 Input: Factorial(161)^(1/128) Output: Magma V2.10-6 Tue Jan 27 2004 18:52:06 on modular [Seed = 105955211] ------------------------------------- 174.2818671424029764935555 Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host user-vc8frgq.biz.mindspring.com. (216.135.238.26) Time: Tue Jan 27 18:52:26 2004 Input: Factorial(162)^(1/128) Output: Magma V2.10-6 Tue Jan 27 2004 18:52:22 on modular [Seed = 306490255] ------------------------------------- 181.348530217768454470023421 Total time: 3.489 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host user-vc8frgq.biz.mindspring.com. (216.135.238.26) Time: Tue Jan 27 18:52:46 2004 Input: Factorial(163)^(1/128) Output: Magma V2.10-6 Tue Jan 27 2004 18:52:43 on modular [Seed = 1631049857] ------------------------------------- 188.710800005105887899561056 Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host user-vc8frgq.biz.mindspring.com. (216.135.238.26) Time: Tue Jan 27 18:53:04 2004 Input: Factorial(164)^(1/128) Output: Magma V2.10-6 Tue Jan 27 2004 18:53:00 on modular [Seed = 1881590150] ------------------------------------- 196.381341907281421788003958 Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host user-vc8frgq.biz.mindspring.com. (216.135.238.26) Time: Tue Jan 27 18:54:03 2004 Input: Factorial(165)^(1/128) Output: Magma V2.10-6 Tue Jan 27 2004 18:53:59 on modular [Seed = 1392896367] ------------------------------------- 204.373374877523347605342368 Total time: 3.499 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host user-vc8frgq.biz.mindspring.com. (216.135.238.26) Time: Tue Jan 27 18:54:21 2004 Input: Factorial(166)^(1/128) Output: Magma V2.10-6 Tue Jan 27 2004 18:54:18 on modular [Seed = 2902070957] ------------------------------------- 212.700696027992224880973014 Total time: 2.929 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host user-vc8frgq.biz.mindspring.com. (216.135.238.26) Time: Tue Jan 27 18:54:38 2004 Input: Factorial(167)^(1/128) Output: Magma V2.10-6 Tue Jan 27 2004 18:54:35 on modular [Seed = 3152871851] ------------------------------------- 221.377706348793757725261403 Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host user-vc8frgq.biz.mindspring.com. (216.135.238.26) Time: Tue Jan 27 18:54:55 2004 Input: Factorial(168)^(1/128) Output: Magma V2.10-6 Tue Jan 27 2004 18:54:52 on modular [Seed = 3084979664] ------------------------------------- 230.419437588212612975227299 Total time: 2.909 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host user-vc8frgq.biz.mindspring.com. (216.135.238.26) Time: Tue Jan 27 18:55:12 2004 Input: Factorial(169)^(1/128) Output: Magma V2.10-6 Tue Jan 27 2004 18:55:09 on modular [Seed = 2194946292] ------------------------------------- 239.841580347295350148535117 Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host user-vc8frgq.biz.mindspring.com. (216.135.238.26) Time: Tue Jan 27 18:55:30 2004 Input: Factorial(170)^(1/128) Output: Magma V2.10-6 Tue Jan 27 2004 18:55:26 on modular [Seed = 2647336921] ------------------------------------- 249.66051344437056659348487 Total time: 3.609 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host user-vc8frgq.biz.mindspring.com. (216.135.238.26) Time: Tue Jan 27 18:55:49 2004 Input: Factorial(171)^(1/128) Output: Magma V2.10-6 Tue Jan 27 2004 18:55:46 on modular [Seed = 3971634757] ------------------------------------- 259.893334607669440254280545 Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host user-vc8frgq.biz.mindspring.com. (216.135.238.26) Time: Tue Jan 27 18:56:15 2004 Input: Factorial(172)^(1/128) Output: Magma V2.10-6 Tue Jan 27 2004 18:56:11 on modular [Seed = 4255860557] ------------------------------------- 270.557892556905521290660091 Total time: 3.649 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host user-vc8frgq.biz.mindspring.com. (216.135.238.26) Time: Tue Jan 27 18:56:33 2004 Input: Factorial(173)^(1/128) Output: Magma V2.10-6 Tue Jan 27 2004 18:56:30 on modular [Seed = 3482940746] ------------------------------------- 281.672820537494586132890285 Total time: 2.939 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host user-vc8frgq.biz.mindspring.com. (216.135.238.26) Time: Tue Jan 27 18:56:53 2004 Input: Factorial(174)^(1/128) Output: Magma V2.10-6 Tue Jan 27 2004 18:56:50 on modular [Seed = 3331357743] ------------------------------------- 293.257571374049599427604313 Total time: 2.979 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host user-vc8frgq.biz.mindspring.com. (216.135.238.26) Time: Tue Jan 27 18:57:13 2004 Input: Factorial(175)^(1/128) Output: Magma V2.10-6 Tue Jan 27 2004 18:57:10 on modular [Seed = 3582160680] ------------------------------------- 305.332454112878592133437235 Total time: 3.019 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host user-vc8frgq.biz.mindspring.com. (216.135.238.26) Time: Tue Jan 27 18:57:31 2004 Input: Factorial(176)^(1/128) Output: Magma V2.10-6 Tue Jan 27 2004 18:57:28 on modular [Seed = 729649647] ------------------------------------- 317.918672326451118286046714 Total time: 3.009 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host user-vc8frgq.biz.mindspring.com. (216.135.238.26) Time: Tue Jan 27 18:57:48 2004 Input: Factorial(177)^(1/128) Output: Magma V2.10-6 Tue Jan 27 2004 18:57:45 on modular [Seed = 878874337] ------------------------------------- 331.038364156188772742834652 Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host user-vc8frgq.biz.mindspring.com. (216.135.238.26) Time: Tue Jan 27 18:58:05 2004 Input: Factorial(178)^(1/128) Output: Magma V2.10-6 Tue Jan 27 2004 18:58:02 on modular [Seed = 224114219] ------------------------------------- 344.714644173484240269338805 Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host user-vc8frgq.biz.mindspring.com. (216.135.238.26) Time: Tue Jan 27 18:58:21 2004 Input: Factorial(179)^(1/128) Output: Magma V2.10-6 Tue Jan 27 2004 18:58:18 on modular [Seed = 105954608] ------------------------------------- 358.971647142569049877942955 Total time: 2.909 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host user-vc8frgq.biz.mindspring.com. (216.135.238.26) Time: Tue Jan 27 18:58:38 2004 Input: Factorial(180)^(1/128) Output: Magma V2.10-6 Tue Jan 27 2004 18:58:35 on modular [Seed = 524919832] ------------------------------------- 373.83457377274053573422723 Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host user-vc8frgq.biz.mindspring.com. (216.135.238.26) Time: Tue Jan 27 18:58:56 2004 Input: Factorial(181)^(1/128) Output: Magma V2.10-6 Tue Jan 27 2004 18:58:53 on modular [Seed = 1748947834] ------------------------------------- 389.329738551531744114314798 Total time: 2.869 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host user-vc8frgq.biz.mindspring.com. (216.135.238.26) Time: Tue Jan 27 18:59:13 2004 Input: Factorial(182)^(1/128) Output: Magma V2.10-6 Tue Jan 27 2004 18:59:10 on modular [Seed = 1647630592] ------------------------------------- 405.48461975467285855677526 Total time: 2.989 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host user-vc8frgq.biz.mindspring.com. (216.135.238.26) Time: Tue Jan 27 18:59:32 2004 Input: Factorial(183)^(1/128) Output: Magma V2.10-6 Tue Jan 27 2004 18:59:29 on modular [Seed = 1142095625] ------------------------------------- 422.327911733158242217336322 Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host user-vc8frgq.biz.mindspring.com. (216.135.238.26) Time: Tue Jan 27 18:59:54 2004 Input: Factorial(184)^(1/128) Output: Magma V2.10-6 Tue Jan 27 2004 18:59:51 on modular [Seed = 1561060870] ------------------------------------- 439.889579582408953294344374 Total time: 2.979 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host user-vc8frgq.biz.mindspring.com. (216.135.238.26) Time: Tue Jan 27 19:00:35 2004 Input: Factorial(185)^(1/128) Output: Magma V2.10-6 Tue Jan 27 2004 19:00:32 on modular [Seed = 2800753962] ------------------------------------- 458.200916303416569189316004 Total time: 2.989 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host user-vc8frgq.biz.mindspring.com. (216.135.238.26) Time: Tue Jan 27 19:00:52 2004 Input: Factorial(186)^(1/128) Output: Magma V2.10-6 Tue Jan 27 2004 19:00:49 on modular [Seed = 3219719202] ------------------------------------- 477.294602570880829992286734 Total time: 3.239 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host user-vc8frgq.biz.mindspring.com. (216.135.238.26) Time: Tue Jan 27 19:01:10 2004 Input: Factorial(187)^(1/128) Output: Magma V2.10-6 Tue Jan 27 2004 19:01:07 on modular [Seed = 2613911668] ------------------------------------- 497.204769228721956554775372 Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host user-vc8frgq.biz.mindspring.com. (216.135.238.26) Time: Tue Jan 27 19:01:28 2004 Input: Factorial(188)^(1/128) Output: Magma V2.10-6 Tue Jan 27 2004 19:01:25 on modular [Seed = 3836895005] ------------------------------------- 517.967062638970014184872348 Total time: 3.009 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host user-vc8frgq.biz.mindspring.com. (216.135.238.26) Time: Tue Jan 27 19:01:46 2004 Input: Factorial(189)^(1/128) Output: Magma V2.10-6 Tue Jan 27 2004 19:01:43 on modular [Seed = 4255860278] ------------------------------------- 539.618713015920433442573514 Total time: 3.019 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host user-vc8frgq.biz.mindspring.com. (216.135.238.26) Time: Tue Jan 27 19:02:03 2004 Input: Factorial(190)^(1/128) Output: Magma V2.10-6 Tue Jan 27 2004 19:02:00 on modular [Seed = 4137700642] ------------------------------------- 562.198605883609397158503735 Total time: 3.019 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host user-vc8frgq.biz.mindspring.com. (216.135.238.26) Time: Tue Jan 27 19:02:21 2004 Input: Factorial(191)^(1/128) Output: Magma V2.10-6 Tue Jan 27 2004 19:02:18 on modular [Seed = 3482940393] ------------------------------------- 585.747356801118497169084577 Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host user-vc8frgq.biz.mindspring.com. (216.135.238.26) Time: Tue Jan 27 19:02:37 2004 Input: Factorial(192)^(1/128) Output: Magma V2.10-6 Tue Jan 27 2004 19:02:34 on modular [Seed = 3633210606] ------------------------------------- 610.307389506978731279631873 Total time: 2.979 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host user-vc8frgq.biz.mindspring.com. (216.135.238.26) Time: Tue Jan 27 19:02:54 2004 Input: Factorial(193)^(1/128) Output: Magma V2.10-6 Tue Jan 27 2004 19:02:51 on modular [Seed = 3515313622] ------------------------------------- 635.923017641024093799356883 Total time: 2.989 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host user-vc8frgq.biz.mindspring.com. (216.135.238.26) Time: Tue Jan 27 19:03:15 2004 Input: Factorial(194)^(1/128) Output: Magma V2.10-6 Tue Jan 27 2004 19:03:12 on modular [Seed = 963609940] ------------------------------------- 662.640530209459954394136914 Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host user-vc8frgq.biz.mindspring.com. (216.135.238.26) Time: Tue Jan 27 19:03:33 2004 Input: Factorial(195)^(1/128) Output: Magma V2.10-6 Tue Jan 27 2004 19:03:30 on modular [Seed = 140424311] ------------------------------------- 690.508280966677096247546772 Total time: 2.919 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host user-vc8frgq.biz.mindspring.com. (216.135.238.26) Time: Tue Jan 27 19:03:51 2004 Input: Factorial(196)^(1/128) Output: Magma V2.10-6 Tue Jan 27 2004 19:03:48 on modular [Seed = 339912797] ------------------------------------- 719.576781895475440985491259 Total time: 3.009 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host user-vc8frgq.biz.mindspring.com. (216.135.238.26) Time: Tue Jan 27 19:04:09 2004 Input: Factorial(197)^(1/128) Output: Magma V2.10-6 Tue Jan 27 2004 19:04:05 on modular [Seed = 1748948016] ------------------------------------- 749.898800975879676312295583 Total time: 3.739 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host user-vc8frgq.biz.mindspring.com. (216.135.238.26) Time: Tue Jan 27 19:04:27 2004 Input: Factorial(198)^(1/128) Output: Magma V2.10-6 Tue Jan 27 2004 19:04:24 on modular [Seed = 2033173980] ------------------------------------- 781.529464441650620214762079 Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host user-vc8frgq.biz.mindspring.com. (216.135.238.26) Time: Tue Jan 27 19:04:44 2004 Input: Factorial(199)^(1/128) Output: Magma V2.10-6 Tue Jan 27 2004 19:04:41 on modular [Seed = 1158937073] ------------------------------------- 814.526363732940486951206255 Total time: 3.079 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host user-vc8frgq.biz.mindspring.com. (216.135.238.26) Time: Tue Jan 27 19:05:02 2004 Input: Factorial(200)^(1/128) Output: Magma V2.10-6 Tue Jan 27 2004 19:04:59 on modular [Seed = 1544216794] ------------------------------------- 848.949667363327478613561984 Total time: 3.119 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host user-vc8frgq.biz.mindspring.com. (216.135.238.26) Time: Tue Jan 27 19:05:42 2004 Input: Factorial(201)^(1/128) Output: Magma V2.10-6 Tue Jan 27 2004 19:05:39 on modular [Seed = 2767329370] ------------------------------------- 884.862237929716500498320101 Total time: 2.929 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host user-vc8frgq.biz.mindspring.com. (216.135.238.26) Time: Tue Jan 27 19:06:01 2004 Input: Factorial(202)^(1/128) Output: Magma V2.10-6 Tue Jan 27 2004 19:05:58 on modular [Seed = 3084979068] ------------------------------------- 922.329754504330499816472492 Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host user-vc8frgq.biz.mindspring.com. (216.135.238.26) Time: Tue Jan 27 19:06:17 2004 Input: Factorial(203)^(1/128) Output: Magma V2.10-6 Tue Jan 27 2004 19:06:14 on modular [Seed = 2396533333] ------------------------------------- 961.420840659264238406432987 Total time: 2.909 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host user-vc8frgq.biz.mindspring.com. (216.135.238.26) Time: Tue Jan 27 19:06:36 2004 Input: Factorial(204)^(1/128) Output: Magma V2.10-6 Tue Jan 27 2004 19:06:32 on modular [Seed = 2178366628] ------------------------------------- 1002.207198385853638256824977 Total time: 3.549 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host user-vc8frgq.biz.mindspring.com. (216.135.238.26) Time: Tue Jan 27 19:07:05 2004 Input: Factorial(205)^(1/128) Output: Magma V2.10-6 Tue Jan 27 2004 19:07:02 on modular [Seed = 2428906907] ------------------------------------- 1044.763748183454769855738409 Total time: 3.039 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host user-vc8frgq.biz.mindspring.com. (216.135.238.26) Time: Tue Jan 27 19:07:33 2004 Input: Factorial(206)^(1/128) Output: Magma V2.10-6 Tue Jan 27 2004 19:07:30 on modular [Seed = 3820314252] ------------------------------------- 1089.16877560515390999860282 Total time: 2.939 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host user-vc8frgq.biz.mindspring.com. (216.135.238.26) Time: Tue Jan 27 19:07:50 2004 Input: Factorial(207)^(1/128) Output: Magma V2.10-6 Tue Jan 27 2004 19:07:47 on modular [Seed = 4205594500] ------------------------------------- 1135.504084561471996536967682 Total time: 2.919 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host user-vc8frgq.biz.mindspring.com. (216.135.238.26) Time: Tue Jan 27 19:08:11 2004 Input: Factorial(208)^(1/128) Output: Magma V2.10-6 Tue Jan 27 2004 19:08:08 on modular [Seed = 3449516168] ------------------------------------- 1183.85515769731273111612198 Total time: 2.879 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host user-vc8frgq.biz.mindspring.com. (216.135.238.26) Time: Tue Jan 27 19:08:29 2004 Input: Factorial(209)^(1/128) Output: Magma V2.10-6 Tue Jan 27 2004 19:08:26 on modular [Seed = 3297933715] ------------------------------------- 1234.311324172264431625979151 Total time: 3.009 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host user-vc8frgq.biz.mindspring.com. (216.135.238.26) Time: Tue Jan 27 19:08:49 2004 Input: Factorial(210)^(1/128) Output: Magma V2.10-6 Tue Jan 27 2004 19:08:46 on modular [Seed = 3750322812] ------------------------------------- 1286.965935189933913702323884 Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host user-vc8frgq.biz.mindspring.com. (216.135.238.26) Time: Tue Jan 27 19:09:07 2004 Input: Factorial(211)^(1/128) Output: Magma V2.10-6 Tue Jan 27 2004 19:09:04 on modular [Seed = 3598740315] ------------------------------------- 1341.916547638300153349136925 Total time: 2.929 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host user-vc8frgq.biz.mindspring.com. (216.135.238.26) Time: Tue Jan 27 19:09:26 2004 Input: Factorial(212)^(1/128) Output: Magma V2.10-6 Tue Jan 27 2004 19:09:23 on modular [Seed = 729650870] ------------------------------------- 1399.265116220161863663811679 Total time: 2.909 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host user-vc8frgq.biz.mindspring.com. (216.135.238.26) Time: Tue Jan 27 19:09:44 2004 Input: Factorial(213)^(1/128) Output: Magma V2.10-6 Tue Jan 27 2004 19:09:41 on modular [Seed = 544644555] ------------------------------------- 1459.118194470653745936288638 Total time: 3.059 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host user-vc8frgq.biz.mindspring.com. (216.135.238.26) Time: Tue Jan 27 19:10:03 2004 Input: Factorial(214)^(1/128) Output: Magma V2.10-6 Tue Jan 27 2004 19:10:00 on modular [Seed = 963609807] ------------------------------------- 1521.587145077560196623670178 Total time: 3.069 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host user-vc8frgq.biz.mindspring.com. (216.135.238.26) Time: Tue Jan 27 19:10:21 2004 Input: Factorial(215)^(1/128) Output: Magma V2.10-6 Tue Jan 27 2004 19:10:18 on modular [Seed = 157267149] ------------------------------------- 1586.788359939803712159423172 Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host user-vc8frgq.biz.mindspring.com. (216.135.238.26) Time: Tue Jan 27 19:10:39 2004 Input: Factorial(216)^(1/128) Output: Magma V2.10-6 Tue Jan 27 2004 19:10:36 on modular [Seed = 508077004] ------------------------------------- 1654.843490420071168955374672 Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host user-vc8frgq.biz.mindspring.com. (216.135.238.26) Time: Tue Jan 27 19:12:00 2004 Input: Factorial(217)^(1/128) Output: Magma V2.10-6 Tue Jan 27 2004 19:11:57 on modular [Seed = 1731320068] ------------------------------------- 1725.879688269109689706931954 Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host user-vc8frgq.biz.mindspring.com. (216.135.238.26) Time: Tue Jan 27 19:12:20 2004 Input: Factorial(218)^(1/128) Output: Magma V2.10-6 Tue Jan 27 2004 19:12:17 on modular [Seed = 2066597172] ------------------------------------- 1800.029857721822252381851233 Total time: 3.159 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host user-vc8frgq.biz.mindspring.com. (216.135.238.26) Time: Tue Jan 27 19:13:44 2004 Input: Factorial(219)^(1/128) Output: Magma V2.10-6 Tue Jan 27 2004 19:13:41 on modular [Seed = 1510794433] ------------------------------------- 1877.432919288971165058938278 Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host user-vc8frgq.biz.mindspring.com. (216.135.238.26) Time: Tue Jan 27 19:15:02 2004 Input: Factorial(220)^(1/128) Output: Magma V2.10-6 Tue Jan 27 2004 19:14:59 on modular [Seed = 1342631805] ------------------------------------- 1958.234085793107037272914801 Total time: 3.009 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host user-vc8frgq.biz.mindspring.com. (216.135.238.26) Time: Tue Jan 27 19:15:33 2004 Input: Factorial(221)^(1/128) Output: Magma V2.10-6 Tue Jan 27 2004 19:15:30 on modular [Seed = 2784172713] ------------------------------------- 2042.585151223336472982954504 Total time: 2.979 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host user-vc8frgq.biz.mindspring.com. (216.135.238.26) Time: Tue Jan 27 19:15:54 2004 Input: Factorial(222)^(1/128) Output: Magma V2.10-6 Tue Jan 27 2004 19:15:51 on modular [Seed = 3136030115] ------------------------------------- 2130.644793010780588763896522 Total time: 2.989 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host user-vc8frgq.biz.mindspring.com. (216.135.238.26) Time: Tue Jan 27 19:16:46 2004 Input: Factorial(223)^(1/128) Output: Magma V2.10-6 Tue Jan 27 2004 19:16:42 on modular [Seed = 3018132727] ------------------------------------- 2222.578888355118600950684397 Total time: 2.989 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host user-vc8frgq.biz.mindspring.com. (216.135.238.26) Time: Tue Jan 27 19:17:25 2004 Input: Factorial(224)^(1/128) Output: Magma V2.10-6 Tue Jan 27 2004 19:17:22 on modular [Seed = 2296264500] ------------------------------------- 2318.560845262519021660059423 Total time: 2.979 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host user-vc8frgq.biz.mindspring.com. (216.135.238.26) Time: Tue Jan 27 19:17:55 2004 Input: Factorial(225)^(1/128) Output: Magma V2.10-6 Tue Jan 27 2004 19:17:52 on modular [Seed = 2178367007] ------------------------------------- 2418.771948986601409983220424 Total time: 2.979 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host user-vc8frgq.biz.mindspring.com. (216.135.238.26) Time: Tue Jan 27 19:18:13 2004 Input: Factorial(226)^(1/128) Output: Magma V2.10-6 Tue Jan 27 2004 19:18:10 on modular [Seed = 2512595577] ------------------------------------- 2523.401724596913304978762541 Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host user-vc8frgq.biz.mindspring.com. (216.135.238.26) Time: Tue Jan 27 19:18:31 2004 Input: Factorial(227)^(1/128) Output: Magma V2.10-6 Tue Jan 27 2004 19:18:28 on modular [Seed = 3938211088] ------------------------------------- 2632.648316433822452238216735 Total time: 3.059 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host user-vc8frgq.biz.mindspring.com. (216.135.238.26) Time: Tue Jan 27 19:19:27 2004 Input: Factorial(228)^(1/128) Output: Magma V2.10-6 Tue Jan 27 2004 19:19:24 on modular [Seed = 4289249245] ------------------------------------- 2746.718885244789788787649094 Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host user-vc8frgq.biz.mindspring.com. (216.135.238.26) Time: Tue Jan 27 19:19:55 2004 Input: Factorial(229)^(1/128) Output: Magma V2.10-6 Tue Jan 27 2004 19:19:52 on modular [Seed = 4087657461] ------------------------------------- 2865.830023834783640472856676 Total time: 3.009 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host user-vc8frgq.biz.mindspring.com. (216.135.238.26) Time: Tue Jan 27 19:20:15 2004 Input: Factorial(230)^(1/128) Output: Magma V2.10-6 Tue Jan 27 2004 19:20:12 on modular [Seed = 3281290193] ------------------------------------- 2990.208192103203867669551399 Total time: 2.979 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host user-vc8frgq.biz.mindspring.com. (216.135.238.26) Time: Tue Jan 27 19:20:41 2004 Input: Factorial(231)^(1/128) Output: Magma V2.10-6 Tue Jan 27 2004 19:20:38 on modular [Seed = 3633289376] ------------------------------------- 3120.090172381194003309293225 Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host user-vc8frgq.biz.mindspring.com. (216.135.238.26) Time: Tue Jan 27 19:24:32 2004 Input: Factorial(232)^(1/128) Output: Magma V2.10-6 Tue Jan 27 2004 19:24:29 on modular [Seed = 746286398] ------------------------------------- 3255.723546026721774484559627 Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host user-vc8frgq.biz.mindspring.com. (216.135.238.26) Time: Tue Jan 27 19:24:50 2004 Input: Factorial(233)^(1/128) Output: Magma V2.10-6 Tue Jan 27 2004 19:24:47 on modular [Seed = 594829891] ------------------------------------- 3397.367192280400286680891806 Total time: 2.929 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host user-vc8frgq.biz.mindspring.com. (216.135.238.26) Time: Tue Jan 27 19:25:08 2004 Input: Factorial(234)^(1/128) Output: Magma V2.10-6 Tue Jan 27 2004 19:25:05 on modular [Seed = 240734016] ------------------------------------- 3545.291810432804788688063351 Total time: 2.919 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host user-vc8frgq.biz.mindspring.com. (216.135.238.26) Time: Tue Jan 27 19:25:27 2004 Input: Factorial(235)^(1/128) Output: Magma V2.10-6 Tue Jan 27 2004 19:25:24 on modular [Seed = 39142233] ------------------------------------- 3699.780466404119478006800315 Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host user-vc8frgq.biz.mindspring.com. (216.135.238.26) Time: Tue Jan 27 19:25:42 2004 Input: Factorial(236)^(1/128) Output: Magma V2.10-6 Tue Jan 27 2004 19:25:39 on modular [Seed = 424564917] ------------------------------------- 3861.129164889436586442895975 Total time: 2.979 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host user-vc8frgq.biz.mindspring.com. (216.135.238.26) Time: Tue Jan 27 19:26:00 2004 Input: Factorial(237)^(1/128) Output: Magma V2.10-6 Tue Jan 27 2004 19:25:57 on modular [Seed = 273109418] ------------------------------------- 4029.647448278042777732889766 Total time: 2.919 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host user-vc8frgq.biz.mindspring.com. (216.135.238.26) Time: Tue Jan 27 19:26:19 2004 Input: Factorial(238)^(1/128) Output: Magma V2.10-6 Tue Jan 27 2004 19:26:16 on modular [Seed = 1731208928] ------------------------------------- 4205.659023612688174095752673 Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host user-vc8frgq.biz.mindspring.com. (216.135.238.26) Time: Tue Jan 27 19:26:37 2004 Input: Factorial(239)^(1/128) Output: Magma V2.10-6 Tue Jan 27 2004 19:26:34 on modular [Seed = 2116632555] ------------------------------------- 4389.50241891526957452853368 Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host user-vc8frgq.biz.mindspring.com. (216.135.238.26) Time: Tue Jan 27 19:26:55 2004 Input: Factorial(240)^(1/128) Output: Magma V2.10-6 Tue Jan 27 2004 19:26:52 on modular [Seed = 1965175958] ------------------------------------- 4581.531670268706384612544737 Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host user-vc8frgq.biz.mindspring.com. (216.135.238.26) Time: Tue Jan 27 19:27:13 2004 Input: Factorial(241)^(1/128) Output: Magma V2.10-6 Tue Jan 27 2004 19:27:10 on modular [Seed = 1276841405] ------------------------------------- 4782.117041111186787338190561 Total time: 2.979 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host user-vc8frgq.biz.mindspring.com. (216.135.238.26) Time: Tue Jan 27 19:27:30 2004 Input: Factorial(242)^(1/128) Output: Magma V2.10-6 Tue Jan 27 2004 19:27:27 on modular [Seed = 1125384835] ------------------------------------- 4991.64577526856100516052125 Total time: 2.889 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host user-vc8frgq.biz.mindspring.com. (216.135.238.26) Time: Tue Jan 27 19:27:49 2004 Input: Factorial(243)^(1/128) Output: Magma V2.10-6 Tue Jan 27 2004 19:27:46 on modular [Seed = 1376063615] ------------------------------------- 5210.522885323613650633676322 Total time: 2.879 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (202.128.229.42) Time: Tue Jan 27 22:17:35 2004 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: Magma V2.10-6 Tue Jan 27 2004 22:17:32 on modular [Seed = 3466176304] ------------------------------------- Replace this by some code, then click [PARI] or [MAGMA]! Total time: 2.989 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host core-dr00.proxy.nacamar.net. (194.162.162.68) Time: Wed Jan 28 02:04:00 2004 Input: H:=HammingCode(GF(7),2); GeneratorMatrix(H); Output: Magma V2.10-6 Wed Jan 28 2004 02:03:56 on modular [Seed = 3051531103] ------------------------------------- [1 0 0 0 0 0 1 6] [0 1 0 0 0 0 1 5] [0 0 1 0 0 0 2 4] [0 0 0 1 0 0 3 3] [0 0 0 0 1 0 4 2] [0 0 0 0 0 1 5 1] Total time: 2.939 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host core-dr00.proxy.nacamar.net. (194.162.162.68) Time: Wed Jan 28 02:04:30 2004 Input: GF(7); Output: Magma V2.10-6 Wed Jan 28 2004 02:04:27 on modular [Seed = 3152848246] ------------------------------------- Finite field of size 7 Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host core-dr00.proxy.nacamar.net. (194.162.162.68) Time: Wed Jan 28 02:05:05 2004 Input: print GF(7); Output: Magma V2.10-6 Wed Jan 28 2004 02:05:02 on modular [Seed = 2902176644] ------------------------------------- Finite field of size 7 Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host spc-14.csse.uwa.edu.au. (130.95.1.14) Time: Wed Jan 28 03:57:49 2004 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: Magma V2.10-6 Wed Jan 28 2004 03:57:46 on modular [Seed = 2967963917] ------------------------------------- Replace this by some code, then click [PARI] or [MAGMA]! Total time: 2.999 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host core-dr00.proxy.nacamar.net. (194.162.162.68) Time: Wed Jan 28 05:14:12 2004 Input: HammingCode(GF(8),2); Output: Magma V2.10-6 Wed Jan 28 2004 05:14:09 on modular [Seed = 763029094] ------------------------------------- [9, 7, 3] Hamming code (r = 2) over GF(2^3) Generator matrix: [ 1 0 0 0 0 0 0 1 $.1] [ 0 1 0 0 0 0 0 $.1 $.1^6] [ 0 0 1 0 0 0 0 $.1^6 $.1^3] [ 0 0 0 1 0 0 0 $.1^3 $.1^3] [ 0 0 0 0 1 0 0 $.1^3 $.1^6] [ 0 0 0 0 0 1 0 $.1^6 $.1] [ 0 0 0 0 0 0 1 $.1 1] Total time: 3.019 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host core-dr00.proxy.nacamar.net. (194.162.162.68) Time: Wed Jan 28 05:23:17 2004 Input: HammingCode(GF(4),2); Output: Magma V2.10-6 Wed Jan 28 2004 05:23:14 on modular [Seed = 390126271] ------------------------------------- [5, 3, 3] Hamming code (r = 2) over GF(2^2) Generator matrix: [ 1 0 0 1 $.1^2] [ 0 1 0 $.1^2 $.1^2] [ 0 0 1 $.1^2 1] Total time: 3.039 seconds, Total memory usage: 1.99MB ************** MAGMA ***************** Host core-dr00.proxy.nacamar.net. (194.162.162.68) Time: Wed Jan 28 05:23:36 2004 Input: HammingCode(GF(3),2); Output: Magma V2.10-6 Wed Jan 28 2004 05:23:33 on modular [Seed = 207339923] ------------------------------------- [4, 2, 3] Hamming code (r = 2) over GF(3) Generator matrix: [1 0 1 2] [0 1 1 1] Total time: 3.009 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host core-dr00.proxy.nacamar.net. (194.162.162.68) Time: Wed Jan 28 05:23:49 2004 Input: HammingCode(GF(9),2); Output: Magma V2.10-6 Wed Jan 28 2004 05:23:46 on modular [Seed = 89311373] ------------------------------------- [10, 8, 3] Hamming code (r = 2) over GF(3^2) Generator matrix: [ 1 0 0 0 0 0 0 0 $.1^5 $.1] [ 0 1 0 0 0 0 0 0 $.1^5 $.1^7] [ 0 0 1 0 0 0 0 0 $.1^6 $.1] [ 0 0 0 1 0 0 0 0 $.1^7 $.1^5] [ 0 0 0 0 1 0 0 0 1 1] [ 0 0 0 0 0 1 0 0 $.1 $.1^6] [ 0 0 0 0 0 0 1 0 $.1^2 $.1^3] [ 0 0 0 0 0 0 0 1 $.1^3 $.1^2] Total time: 2.949 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host core-dr00.proxy.nacamar.net. (194.162.162.68) Time: Wed Jan 28 05:24:03 2004 Input: HammingCode(GF(11),2); Output: Magma V2.10-6 Wed Jan 28 2004 05:24:00 on modular [Seed = 1915076488] ------------------------------------- [12, 10, 3] Hamming code (r = 2) over GF(11) Generator matrix: [ 1 0 0 0 0 0 0 0 0 0 1 10] [ 0 1 0 0 0 0 0 0 0 0 1 9] [ 0 0 1 0 0 0 0 0 0 0 2 8] [ 0 0 0 1 0 0 0 0 0 0 3 7] [ 0 0 0 0 1 0 0 0 0 0 4 6] [ 0 0 0 0 0 1 0 0 0 0 5 5] [ 0 0 0 0 0 0 1 0 0 0 6 4] [ 0 0 0 0 0 0 0 1 0 0 7 3] [ 0 0 0 0 0 0 0 0 1 0 8 2] [ 0 0 0 0 0 0 0 0 0 1 9 1] Total time: 2.929 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host core-dr00.proxy.nacamar.net. (194.162.162.68) Time: Wed Jan 28 05:24:49 2004 Input: HammingCode(GF(8),2); Output: Magma V2.10-6 Wed Jan 28 2004 05:24:46 on modular [Seed = 1849271226] ------------------------------------- [9, 7, 3] Hamming code (r = 2) over GF(2^3) Generator matrix: [ 1 0 0 0 0 0 0 1 $.1] [ 0 1 0 0 0 0 0 $.1 $.1^6] [ 0 0 1 0 0 0 0 $.1^6 $.1^3] [ 0 0 0 1 0 0 0 $.1^3 $.1^3] [ 0 0 0 0 1 0 0 $.1^3 $.1^6] [ 0 0 0 0 0 1 0 $.1^6 $.1] [ 0 0 0 0 0 0 1 $.1 1] Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host core-dr00.proxy.nacamar.net. (194.162.162.68) Time: Wed Jan 28 05:25:35 2004 Input: HammingCode(GF(11),2); Output: Magma V2.10-6 Wed Jan 28 2004 05:25:32 on modular [Seed = 1527551357] ------------------------------------- [12, 10, 3] Hamming code (r = 2) over GF(11) Generator matrix: [ 1 0 0 0 0 0 0 0 0 0 1 10] [ 0 1 0 0 0 0 0 0 0 0 1 9] [ 0 0 1 0 0 0 0 0 0 0 2 8] [ 0 0 0 1 0 0 0 0 0 0 3 7] [ 0 0 0 0 1 0 0 0 0 0 4 6] [ 0 0 0 0 0 1 0 0 0 0 5 5] [ 0 0 0 0 0 0 1 0 0 0 6 4] [ 0 0 0 0 0 0 0 1 0 0 7 3] [ 0 0 0 0 0 0 0 0 1 0 8 2] [ 0 0 0 0 0 0 0 0 0 1 9 1] Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (218.52.49.253) Time: Wed Jan 28 07:20:28 2004 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: Magma V2.10-6 Wed Jan 28 2004 07:20:24 on modular [Seed = 1981914949] ------------------------------------- Replace this by some code, then click [PARI] or [MAGMA]! Total time: 3.019 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (218.39.19.105) Time: Wed Jan 28 07:25:49 2004 Input: 1./7 Output: Magma V2.10-6 Wed Jan 28 2004 07:25:45 on modular [Seed = 1577694252] ------------------------------------- >> 1./7 ^ User error: Real literal has no digits after decimal point Total time: 2.939 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (205.204.1.17) Time: Wed Jan 28 07:54:01 2004 Input: > knapsack := function(Q, t) > R := [IntegerRing() | x : x in Q | x le t]; > if &+R lt t then > return [ ]; > elif t in R then > return [t]; > else > for x in R do > RR := Exclude(R, x); > s := $$(RR, t - x); > if not IsEmpty(s) then > return Append(s, x); > end if; > end for; > return [ ]; > end if; > end function; Output: Magma V2.10-6 Wed Jan 28 2004 07:53:58 on modular [Seed = 3786805564] ------------------------------------- Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 24-205-83-208.pas-eres.charterpipeline.net. (24.205.83.208) Time: Wed Jan 28 12:28:08 2004 Input: 99^9 Output: Magma V2.10-6 Wed Jan 28 2004 12:28:04 on modular [Seed = 1965212782] ------------------------------------- 913517247483640899 Total time: 2.999 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 24-205-83-208.pas-eres.charterpipeline.net. (24.205.83.208) Time: Wed Jan 28 12:28:38 2004 Input: (99^9)^(1/4) Output: Magma V2.10-6 Wed Jan 28 2004 12:28:35 on modular [Seed = 1815862544] ------------------------------------- 30915.70736833859140648157 Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 24-205-83-208.pas-eres.charterpipeline.net. (24.205.83.208) Time: Wed Jan 28 12:28:49 2004 Input: (99^9)^(1/8) Output: Magma V2.10-6 Wed Jan 28 2004 12:28:46 on modular [Seed = 1664406034] ------------------------------------- 175.8286306843643465177628 Total time: 2.989 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 24-205-83-208.pas-eres.charterpipeline.net. (24.205.83.208) Time: Wed Jan 28 12:35:55 2004 Input: (999^9)^(1/1024) Output: Magma V2.10-6 Wed Jan 28 2004 12:35:52 on modular [Seed = 1142158979] ------------------------------------- 1.062584235794572938091453 Total time: 2.989 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 24-205-83-208.pas-eres.charterpipeline.net. (24.205.83.208) Time: Wed Jan 28 12:36:09 2004 Input: (999^9)^(1/128) Output: Magma V2.10-6 Wed Jan 28 2004 12:36:05 on modular [Seed = 3136096640] ------------------------------------- 1.625200504205850828952607 Total time: 3.019 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 24-205-83-208.pas-eres.charterpipeline.net. (24.205.83.208) Time: Wed Jan 28 12:36:25 2004 Input: (999^9)^(1/32) Output: Magma V2.10-6 Wed Jan 28 2004 12:36:22 on modular [Seed = 2984641176] ------------------------------------- 6.976342494347564816724216 Total time: 3.019 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 24-205-83-208.pas-eres.charterpipeline.net. (24.205.83.208) Time: Wed Jan 28 12:36:46 2004 Input: (999^9)^(1/16) Output: Magma V2.10-6 Wed Jan 28 2004 12:36:42 on modular [Seed = 2835291069] ------------------------------------- 48.669354598439602436785737 Total time: 2.989 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 24-205-83-208.pas-eres.charterpipeline.net. (24.205.83.208) Time: Wed Jan 28 12:37:00 2004 Input: (999^9)^(1/8) Output: Magma V2.10-6 Wed Jan 28 2004 12:36:57 on modular [Seed = 2680695961] ------------------------------------- 2368.706077028654075360333058 Total time: 2.989 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 24-205-83-208.pas-eres.charterpipeline.net. (24.205.83.208) Time: Wed Jan 28 12:37:54 2004 Input: (9^99)^(1/8) Output: Magma V2.10-6 Wed Jan 28 2004 12:37:51 on modular [Seed = 2529240518] ------------------------------------- 643800121500.9063168066642144 Total time: 2.979 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 24-205-83-208.pas-eres.charterpipeline.net. (24.205.83.208) Time: Wed Jan 28 12:38:05 2004 Input: (9^99)^(1/16) Output: Magma V2.10-6 Wed Jan 28 2004 12:38:02 on modular [Seed = 2379890376] ------------------------------------- 802371.56075032115809518621 Total time: 2.939 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 24-205-83-208.pas-eres.charterpipeline.net. (24.205.83.208) Time: Wed Jan 28 12:38:18 2004 Input: (9^99)^(1/32) Output: Magma V2.10-6 Wed Jan 28 2004 12:38:15 on modular [Seed = 2228434748] ------------------------------------- 895.751952691324674678049936 Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 24-205-83-208.pas-eres.charterpipeline.net. (24.205.83.208) Time: Wed Jan 28 12:39:24 2004 Input: (9^99)^(1/64) Output: Magma V2.10-6 Wed Jan 28 2004 12:39:20 on modular [Seed = 4205660429] ------------------------------------- 29.929115467907244429727717 Total time: 2.979 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 24-205-83-208.pas-eres.charterpipeline.net. (24.205.83.208) Time: Wed Jan 28 12:41:37 2004 Input: (9^99)^(1/32) Output: Magma V2.10-6 Wed Jan 28 2004 12:41:33 on modular [Seed = 3921567131] ------------------------------------- 895.751952691324674678049936 Total time: 3.069 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 24-205-83-208.pas-eres.charterpipeline.net. (24.205.83.208) Time: Wed Jan 28 12:41:57 2004 Input: ((9^99)^(1/32))/3 Output: Magma V2.10-6 Wed Jan 28 2004 12:41:54 on modular [Seed = 3770111165] ------------------------------------- 298.583984230441558226016645 Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 24-205-83-208.pas-eres.charterpipeline.net. (24.205.83.208) Time: Wed Jan 28 12:42:37 2004 Input: ((9^99)^(1/32))/6 Output: Magma V2.10-6 Wed Jan 28 2004 12:42:34 on modular [Seed = 3615515490] ------------------------------------- 149.291992115220779113008323 Total time: 2.889 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 24-205-83-208.pas-eres.charterpipeline.net. (24.205.83.208) Time: Wed Jan 28 12:42:58 2004 Input: ((9^99)^(1/32))/9 Output: Magma V2.10-6 Wed Jan 28 2004 12:42:55 on modular [Seed = 3466164846] ------------------------------------- 99.527994743480519408672215 Total time: 3.009 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 24-205-83-208.pas-eres.charterpipeline.net. (24.205.83.208) Time: Wed Jan 28 12:47:04 2004 Input: ((6^99)^(1/32)) Output: Magma V2.10-6 Wed Jan 28 2004 12:47:01 on modular [Seed = 1832573113] ------------------------------------- 255.508546178603649625918158 Total time: 2.989 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 24-205-83-208.pas-eres.charterpipeline.net. (24.205.83.208) Time: Wed Jan 28 12:47:56 2004 Input: ((3^99)^(1/16)) Output: Magma V2.10-6 Wed Jan 28 2004 12:47:53 on modular [Seed = 1948500476] ------------------------------------- 895.751952691324674678049944 Total time: 3.019 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 24-205-83-208.pas-eres.charterpipeline.net. (24.205.83.208) Time: Wed Jan 28 12:48:41 2004 Input: ((99^3)^(1) Output: Magma V2.10-6 Wed Jan 28 2004 12:48:38 on modular [Seed = 2133379784] ------------------------------------- >> ((99^3)^(1); ^ User error: bad syntax Total time: 2.889 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 24-205-83-208.pas-eres.charterpipeline.net. (24.205.83.208) Time: Wed Jan 28 12:48:56 2004 Input: 99^3 Output: Magma V2.10-6 Wed Jan 28 2004 12:48:53 on modular [Seed = 106016834] ------------------------------------- 970299 Total time: 2.979 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 24-205-83-208.pas-eres.charterpipeline.net. (24.205.83.208) Time: Wed Jan 28 12:49:29 2004 Input: (99^3)^(1/2) Output: Magma V2.10-6 Wed Jan 28 2004 12:49:26 on modular [Seed = 273131127] ------------------------------------- 985.037562735553755187135023 Total time: 2.989 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 24-205-83-208.pas-eres.charterpipeline.net. (24.205.83.208) Time: Wed Jan 28 12:50:30 2004 Input: (6^999)^(1/512) Output: Magma V2.10-6 Wed Jan 28 2004 12:50:27 on modular [Seed = 644976644] ------------------------------------- 32.984266766372904111456188 Total time: 2.929 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 24-205-83-208.pas-eres.charterpipeline.net. (24.205.83.208) Time: Wed Jan 28 12:50:42 2004 Input: (6^999)^(1/256) Output: Magma V2.10-6 Wed Jan 28 2004 12:50:39 on modular [Seed = 828802847] ------------------------------------- 1087.961854115252036136957235 Total time: 3.129 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 24-205-83-208.pas-eres.charterpipeline.net. (24.205.83.208) Time: Wed Jan 28 12:54:02 2004 Input: (9^(9!))^(1/1024) Output: Magma V2.10-6 Wed Jan 28 2004 12:53:59 on modular [Seed = 1013680970] ------------------------------------- >> (9^(9!))^(1/1024); ^ User error: bad syntax Total time: 3.029 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 24-205-83-208.pas-eres.charterpipeline.net. (24.205.83.208) Time: Wed Jan 28 12:54:23 2004 Input: (9^9!)^(1/1024) Output: Magma V2.10-6 Wed Jan 28 2004 12:54:19 on modular [Seed = 3348132042] ------------------------------------- >> (9^9!)^(1/1024); ^ User error: bad syntax Total time: 2.999 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 24-205-83-208.pas-eres.charterpipeline.net. (24.205.83.208) Time: Wed Jan 28 12:54:48 2004 Input: 9^9! Output: Magma V2.10-6 Wed Jan 28 2004 12:54:45 on modular [Seed = 3515246325] ------------------------------------- >> 9^9!; ^ User error: bad syntax Total time: 3.009 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 24-205-83-208.pas-eres.charterpipeline.net. (24.205.83.208) Time: Wed Jan 28 12:55:11 2004 Input: 9^720 Output: Magma V2.10-6 Wed Jan 28 2004 12:55:08 on modular [Seed = 3700124641] ------------------------------------- 1133983659022391894791539490976876837450923531762737284195820365480118798633708\ 8892923817785292263252742811567055615871043164666065261092921663215977742658797\ 4417515209011054823046575119044855973781029685904112753078907546187438722747935\ 8875707758885836558970881755540532237300372314045471133881119497171163878347739\ 2881933869561154710250304580500414222467563368669009361645462160202744696437809\ 4332484688801958867407365865592677779842267636596019843144626640171599345493073\ 8790906842265095185106303414900094692138509660665263316952327541210968996895100\ 5666040186528373441197010934371128984929948693638910131425522266796461143551605\ 77997696582597104581636235640285573984700815829876636801 Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 24-205-83-208.pas-eres.charterpipeline.net. (24.205.83.208) Time: Wed Jan 28 12:55:38 2004 Input: (9^720)^(1/1024) Output: Magma V2.10-6 Wed Jan 28 2004 12:55:35 on modular [Seed = 3887091761] ------------------------------------- 4.687613155942329267878731 Total time: 2.979 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 24-205-83-208.pas-eres.charterpipeline.net. (24.205.83.208) Time: Wed Jan 28 12:55:51 2004 Input: (9^720)^(1/256) Output: Magma V2.10-6 Wed Jan 28 2004 12:55:48 on modular [Seed = 4005124363] ------------------------------------- 482.84424318044341985059387 Total time: 2.889 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 24-205-83-208.pas-eres.charterpipeline.net. (24.205.83.208) Time: Wed Jan 28 12:56:57 2004 Input: 9! Output: Magma V2.10-6 Wed Jan 28 2004 12:56:53 on modular [Seed = 4188950109] ------------------------------------- >> 9!; ^ User error: bad syntax Total time: 3.069 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 24-205-83-208.pas-eres.charterpipeline.net. (24.205.83.208) Time: Wed Jan 28 12:57:28 2004 Input: (9^Factorial(9))^(1/1024) Output: Magma V2.10-6 Wed Jan 28 2004 12:57:24 on modular [Seed = 2161588421] ------------------------------------- 1.44440599588170419273061675e338 Total time: 3.659 seconds, Total memory usage: 3.96MB ************** MAGMA ***************** Host 24-205-83-208.pas-eres.charterpipeline.net. (24.205.83.208) Time: Wed Jan 28 12:57:42 2004 Input: (9^Factorial(9))^(1/256) Output: Magma V2.10-6 Wed Jan 28 2004 12:57:39 on modular [Seed = 2346464217] ------------------------------------- 4.352683912161503829445423e1352 Total time: 3.579 seconds, Total memory usage: 3.96MB ************** MAGMA ***************** Host 24-205-83-208.pas-eres.charterpipeline.net. (24.205.83.208) Time: Wed Jan 28 12:58:02 2004 Input: (9^Factorial(9))^(1/512) Output: Magma V2.10-6 Wed Jan 28 2004 12:57:59 on modular [Seed = 2462395124] ------------------------------------- 2.086308680939017669370879e676 Total time: 3.559 seconds, Total memory usage: 3.96MB ************** MAGMA ***************** Host 24-205-83-208.pas-eres.charterpipeline.net. (24.205.83.208) Time: Wed Jan 28 12:58:17 2004 Input: (9^Factorial(9))^(1/2048) Output: Magma V2.10-6 Wed Jan 28 2004 12:58:13 on modular [Seed = 2647270889] ------------------------------------- 1.2018344294792457778312408e169 Total time: 3.639 seconds, Total memory usage: 3.96MB ************** MAGMA ***************** Host 24-205-83-208.pas-eres.charterpipeline.net. (24.205.83.208) Time: Wed Jan 28 12:58:32 2004 Input: (9^Factorial(9))^(1/32768) Output: Magma V2.10-6 Wed Jan 28 2004 12:58:29 on modular [Seed = 2767396000] ------------------------------------- 36939438537.6951419485070031 Total time: 3.639 seconds, Total memory usage: 3.96MB ************** MAGMA ***************** Host 24-205-83-208.pas-eres.charterpipeline.net. (24.205.83.208) Time: Wed Jan 28 12:58:49 2004 Input: (9^Factorial(9))^(1/65536) Output: Magma V2.10-6 Wed Jan 28 2004 12:58:45 on modular [Seed = 2952271803] ------------------------------------- 192196.3541217552387431935 Total time: 3.529 seconds, Total memory usage: 3.96MB ************** MAGMA ***************** Host 24-205-83-208.pas-eres.charterpipeline.net. (24.205.83.208) Time: Wed Jan 28 12:59:26 2004 Input: (9^Factorial(9))^(1/131072) Output: Magma V2.10-6 Wed Jan 28 2004 12:59:22 on modular [Seed = 3119382914] ------------------------------------- 438.402046210730223985754699 Total time: 3.679 seconds, Total memory usage: 3.96MB ************** MAGMA ***************** Host 24-205-83-208.pas-eres.charterpipeline.net. (24.205.83.208) Time: Wed Jan 28 13:00:20 2004 Input: (9^Factorial(9))^(2^-16) Output: Magma V2.10-6 Wed Jan 28 2004 13:00:16 on modular [Seed = 1210052794] ------------------------------------- 192196.3541217552387431935 Total time: 3.649 seconds, Total memory usage: 3.96MB ************** MAGMA ***************** Host 24-205-83-208.pas-eres.charterpipeline.net. (24.205.83.208) Time: Wed Jan 28 13:00:33 2004 Input: (9^Factorial(9))^(2^-17) Output: Magma V2.10-6 Wed Jan 28 2004 13:00:30 on modular [Seed = 1359407533] ------------------------------------- 438.402046210730223985754699 Total time: 3.609 seconds, Total memory usage: 3.96MB ************** MAGMA ***************** Host 3(NXDOMAIN) (144.138.141.225) Time: Wed Jan 28 19:40:01 2004 Input: K := GF(9); M := MatrixGroup< 2, K | [w,w,1,2*w], [0,2*w,1,1], [1,0,1,2] >; M; Output: Magma V2.10-6 Wed Jan 28 2004 19:39:57 on modular [Seed = 524749060] ------------------------------------- MatrixGroup(2, GF(3^2)) Generators: [ w w] [ 1 w^5] [ 0 w^5] [ 1 1] [ 1 0] [ 1 2] Total time: 2.959 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 3(NXDOMAIN) (144.138.141.225) Time: Wed Jan 28 19:41:22 2004 Input: M := MatrixGroup< 2, K | [w,w,1,2*w], [0,2*w,1,1], [1,0,1,2] >; M; Output: Magma V2.10-6 Wed Jan 28 2004 19:41:19 on modular [Seed = 796342726] ------------------------------------- >> M := MatrixGroup< 2, K | [w,w,1,2*w], [0,2*w,1,1], [1,0,1,2] >; ^ User error: Identifier 'K' has not been declared or assigned >> M; ^ User error: Identifier 'M' has not been declared or assigned Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (144.138.141.225) Time: Wed Jan 28 19:41:34 2004 Input: M := MatrixGroup< 2, [w,w,1,2*w], [0,2*w,1,1], [1,0,1,2] >; M; Output: Magma V2.10-6 Wed Jan 28 2004 19:41:31 on modular [Seed = 879502025] ------------------------------------- >> M := MatrixGroup< 2, [w,w,1,2*w], [0,2*w,1,1], [1,0,1,2] >; ^ User error: bad syntax >> M; ^ User error: Identifier 'M' has not been declared or assigned Total time: 2.999 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (144.138.141.225) Time: Wed Jan 28 19:42:47 2004 Input: > K := GeneralLinearGroup(3, K); M := MatrixGroup< 2,K|[w,w,1,2*w], [0,2*w,1,1], [1,0,1,2] >; M; Output: Magma V2.10-6 Wed Jan 28 2004 19:42:44 on modular [Seed = 979512696] ------------------------------------- >> K := GeneralLinearGroup(3, K); ^ User error: Identifier 'K' has not been declared or assigned >> M := MatrixGroup< 2,K|[w,w,1,2*w], [0,2*w,1,1], [1,0,1,2] >; ^ User error: Identifier 'K' has not been declared or assigned >> M; ^ User error: Identifier 'M' has not been declared or assigned Total time: 2.999 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (144.138.141.225) Time: Wed Jan 28 19:42:59 2004 Input: K := GeneralLinearGroup(3, K); M := MatrixGroup< 2,K|[w,w,1,2*w], [0,2*w,1,1], [1,0,1,2] >; M; Output: Magma V2.10-6 Wed Jan 28 2004 19:42:56 on modular [Seed = 3281769621] ------------------------------------- >> K := GeneralLinearGroup(3, K); ^ User error: Identifier 'K' has not been declared or assigned >> M := MatrixGroup< 2,K|[w,w,1,2*w], [0,2*w,1,1], [1,0,1,2] >; ^ User error: Identifier 'K' has not been declared or assigned >> M; ^ User error: Identifier 'M' has not been declared or assigned Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (144.138.141.225) Time: Wed Jan 28 19:44:03 2004 Input: K := FiniteField(2); GL2 := GeneralLinearGroup(2, K); M := MatrixGroup< 2,GL2 |[w,w,1,2*w], [0,2*w,1,1], [1,0,1,2] >; M; Output: Magma V2.10-6 Wed Jan 28 2004 19:44:00 on modular [Seed = 3364937694] ------------------------------------- >> M := MatrixGroup< 2,GL2 |[w,w,1,2*w], [0,2*w,1,1], [1,0,1,2] >; ^ Runtime error in 'GeneralLinearGroup': Bad argument types Argument types given: RngIntElt, GrpMat >> M; ^ User error: Identifier 'M' has not been declared or assigned Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (144.138.141.225) Time: Wed Jan 28 19:44:30 2004 Input: K := FiniteField(4); GL2 := GeneralLinearGroup(2, K); M := MatrixGroup< 2,GL2 |[w,w,1,2*w], [0,2*w,1,1], [1,0,1,2] >; M; Output: Magma V2.10-6 Wed Jan 28 2004 19:44:27 on modular [Seed = 3515467516] ------------------------------------- >> M := MatrixGroup< 2,GL2 |[w,w,1,2*w], [0,2*w,1,1], [1,0,1,2] >; ^ Runtime error in 'GeneralLinearGroup': Bad argument types Argument types given: RngIntElt, GrpMat >> M; ^ User error: Identifier 'M' has not been declared or assigned Total time: 2.949 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 3(NXDOMAIN) (144.138.141.225) Time: Wed Jan 28 19:47:13 2004 Input: M := MatrixGroup< 2,GL2 |[w,w,1,2*w], [0,2*w,1,1], [1,0,1,2] >; M; Output: Magma V2.10-6 Wed Jan 28 2004 19:47:10 on modular [Seed = 3820747691] ------------------------------------- >> M := MatrixGroup< 2,GL2 |[w,w,1,2*w], [0,2*w,1,1], [1,0,1,2] >; ^ User error: Identifier 'GL2' has not been declared or assigned >> M; ^ User error: Identifier 'M' has not been declared or assigned Total time: 2.939 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (144.138.141.225) Time: Wed Jan 28 19:47:39 2004 Input: M := MatrixGroup< 2,R|[w,w,1,2*w], [0,2*w,1,1], [1,0,1,2] >; M; Output: Magma V2.10-6 Wed Jan 28 2004 19:47:36 on modular [Seed = 3920753031] ------------------------------------- >> M := MatrixGroup< 2,R|[w,w,1,2*w], [0,2*w,1,1], [1,0,1,2] >; ^ User error: Identifier 'R' has not been declared or assigned >> M; ^ User error: Identifier 'M' has not been declared or assigned Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (144.138.141.225) Time: Wed Jan 28 19:48:22 2004 Input: M := MatrixGroup< 2,R|[1,0,0,0], [0,0,0,1]>; M; Output: Magma V2.10-6 Wed Jan 28 2004 19:48:19 on modular [Seed = 4272350955] ------------------------------------- >> M := MatrixGroup< 2,R|[1,0,0,0], [0,0,0,1]>; ^ User error: Identifier 'R' has not been declared or assigned >> M; ^ User error: Identifier 'M' has not been declared or assigned Total time: 2.979 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (144.138.141.225) Time: Wed Jan 28 19:49:19 2004 Input: M := MatrixGroup< 2,[1,0,0,0], [0,0,0,1]>; M; Output: Magma V2.10-6 Wed Jan 28 2004 19:49:16 on modular [Seed = 2279579469] ------------------------------------- >> M := MatrixGroup< 2,[1,0,0,0], [0,0,0,1]>; ^ User error: bad syntax >> M; ^ User error: Identifier 'M' has not been declared or assigned Total time: 2.939 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (144.138.141.225) Time: Wed Jan 28 19:52:39 2004 Input: R=FiniteField(4); M := MatrixGroup< 2,R|[1,0,0,0], [0,0,0,1]>; M; Output: Magma V2.10-6 Wed Jan 28 2004 19:52:35 on modular [Seed = 2663810956] ------------------------------------- >> R=FiniteField(4); ^ User error: Identifier 'R' has not been declared or assigned >> M := MatrixGroup< 2,R|[1,0,0,0], [0,0,0,1]>; ^ User error: Identifier 'R' has not been declared or assigned >> M; ^ User error: Identifier 'M' has not been declared or assigned Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (144.138.141.225) Time: Wed Jan 28 19:52:51 2004 Input: R:=FiniteField(4); M := MatrixGroup< 2,R|[1,0,0,0], [0,0,0,1]>; M; Output: Magma V2.10-6 Wed Jan 28 2004 19:52:48 on modular [Seed = 2818555521] ------------------------------------- >> M := MatrixGroup< 2,R|[1,0,0,0], [0,0,0,1]>; ^ Runtime error in MatrixGroup< ... >: Can not build a generator from the arguments given >> M; ^ User error: Identifier 'M' has not been declared or assigned Total time: 2.979 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 3(NXDOMAIN) (144.138.141.225) Time: Wed Jan 28 19:53:25 2004 Input: R:=FiniteField(4); M := MatrixGroup< 2,R|[1,0,0,1], [0,0,0,1]>; M; Output: Magma V2.10-6 Wed Jan 28 2004 19:53:22 on modular [Seed = 2918560873] ------------------------------------- >> M := MatrixGroup< 2,R|[1,0,0,1], [0,0,0,1]>; ^ Runtime error in MatrixGroup< ... >: Can not build a generator from the arguments given >> M; ^ User error: Identifier 'M' has not been declared or assigned Total time: 2.989 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 3(NXDOMAIN) (144.138.141.225) Time: Wed Jan 28 19:58:09 2004 Input: R:=IntegerRing() M := MatrixGroup< 2,R|[1,0,0,1], [0,0,0,1]>; M; Output: Magma V2.10-6 Wed Jan 28 2004 19:58:06 on modular [Seed = 1142709917] ------------------------------------- >> M := MatrixGroup< 2,R|[1,0,0,1], [0,0,0,1]>; ^ User error: bad syntax >> M; ^ User error: Identifier 'M' has not been declared or assigned Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (144.138.141.225) Time: Wed Jan 28 19:58:22 2004 Input: R:=IntegerRing(); M := MatrixGroup< 2,R|[1,0,0,1], [0,0,0,1]>; M; Output: Magma V2.10-6 Wed Jan 28 2004 19:58:19 on modular [Seed = 1209029284] ------------------------------------- >> M := MatrixGroup< 2,R|[1,0,0,1], [0,0,0,1]>; ^ Runtime error in MatrixGroup< ... >: Can not build a generator from the arguments given >> M; ^ User error: Identifier 'M' has not been declared or assigned Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (144.138.141.225) Time: Wed Jan 28 20:00:01 2004 Input: R:=IntegerRing(); M := MatrixGroup< 2,R M; Output: Magma V2.10-6 Wed Jan 28 2004 19:59:58 on modular [Seed = 1732213806] ------------------------------------- >> M; ^ User error: bad syntax Total time: 3.149 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (144.138.141.225) Time: Wed Jan 28 20:00:11 2004 Input: R:=IntegerRing(); M := MatrixGroup< 2,R>; M; Output: Magma V2.10-6 Wed Jan 28 2004 20:00:08 on modular [Seed = 1999596584] ------------------------------------- >> M := MatrixGroup< 2,R>; ^ User error: bad syntax >> M; ^ User error: Identifier 'M' has not been declared or assigned Total time: 2.989 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (144.138.141.225) Time: Wed Jan 28 20:00:36 2004 Input: R:=IntegerRing(); M := MatrixGroup< 2,R|[1,0,0,0]>; M; Output: Magma V2.10-6 Wed Jan 28 2004 20:00:33 on modular [Seed = 2116445448] ------------------------------------- >> M := MatrixGroup< 2,R|[1,0,0,0]>; ^ Runtime error in MatrixGroup< ... >: Can not build a generator from the arguments given >> M; ^ User error: Identifier 'M' has not been declared or assigned Total time: 2.879 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host ade-ce4.chariot.net.au. (203.87.94.182) Time: Thu Jan 29 04:21:09 2004 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: Magma V2.10-6 Thu Jan 29 2004 04:21:06 on modular [Seed = 2935373436] ------------------------------------- Replace this by some code, then click [PARI] or [MAGMA]! Total time: 2.909 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host ade-ce4.chariot.net.au. (203.87.94.182) Time: Thu Jan 29 04:21:33 2004 Input: sun + fun = swim Output: Magma V2.10-6 Thu Jan 29 2004 04:21:30 on modular [Seed = 1443808925] ------------------------------------- >> sun + fun = swim; ^ User error: Identifier 'swim' has not been declared or assigned Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host ade-ce4.chariot.net.au. (203.87.94.182) Time: Thu Jan 29 04:22:02 2004 Input: sun + fun = swim Output: Magma V2.10-6 Thu Jan 29 2004 04:21:59 on modular [Seed = 1209063598] ------------------------------------- >> sun + fun = swim; ^ User error: Identifier 'swim' has not been declared or assigned Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host massena-2-81-57-129-182.fbx.proxad.net. (81.57.129.182) Time: Thu Jan 29 10:08:22 2004 Input: ifactor(25) Output: Magma V2.10-6 Thu Jan 29 2004 10:08:17 on modular [Seed = 1460549345] ------------------------------------- >> ifactor(25); ^ User error: Identifier 'ifactor' has not been declared or assigned Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host massena-2-81-57-129-182.fbx.proxad.net. (81.57.129.182) Time: Thu Jan 29 10:08:39 2004 Input: factor(25) Output: Magma V2.10-6 Thu Jan 29 2004 10:08:36 on modular [Seed = 1577533437] ------------------------------------- [ <5, 2> ] 1 Total time: 3.039 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host massena-2-81-57-129-182.fbx.proxad.net. (81.57.129.182) Time: Thu Jan 29 10:09:35 2004 Input: factor(250) Output: Magma V2.10-6 Thu Jan 29 2004 10:09:32 on modular [Seed = 1932136712] ------------------------------------- [ <2, 1>, <5, 3> ] 1 Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host massena-2-81-57-129-182.fbx.proxad.net. (81.57.129.182) Time: Thu Jan 29 10:09:46 2004 Input: factor(2500) Output: Magma V2.10-6 Thu Jan 29 2004 10:09:43 on modular [Seed = 2049120282] ------------------------------------- [ <2, 2>, <5, 4> ] 1 Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host massena-2-81-57-129-182.fbx.proxad.net. (81.57.129.182) Time: Thu Jan 29 10:10:06 2004 Input: factor(250002454) Output: Magma V2.10-6 Thu Jan 29 2004 10:10:03 on modular [Seed = 374305802] ------------------------------------- [ <2, 1>, <13, 1>, <9615479, 1> ] 1 Total time: 2.939 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host massena-2-81-57-129-182.fbx.proxad.net. (81.57.129.182) Time: Thu Jan 29 10:10:32 2004 Input: factor(250002454455424513216854) Output: Magma V2.10-6 Thu Jan 29 2004 10:10:29 on modular [Seed = 189950265] ------------------------------------- [ <2, 1>, <3, 2>, <211, 1>, <65824764206272910273, 1> ] 1 Total time: 2.939 seconds, Total memory usage: 3.00MB ************** MAGMA ***************** Host massena-2-81-57-129-182.fbx.proxad.net. (81.57.129.182) Time: Thu Jan 29 10:10:47 2004 Input: factor(25000245445542451321685465345345435454542) Output: Magma V2.10-6 Thu Jan 29 2004 10:10:43 on modular [Seed = 845893654] ------------------------------------- [ <2, 1>, <11, 2>, <577, 1>, <37489, 1>, <98561, 1>, <25072337, 1>, <1932632682625324831, 1> ] 1 Total time: 3.099 seconds, Total memory usage: 3.00MB ************** MAGMA ***************** Host massena-2-81-57-129-182.fbx.proxad.net. (81.57.129.182) Time: Thu Jan 29 10:12:09 2004 Input: factor(250002454455424513216854653453454354452565638534548534546545345) Output: Magma V2.10-6 Thu Jan 29 2004 10:12:05 on modular [Seed = 3264979024] ------------------------------------- [ <3, 1>, <5, 1>, <197591189, 1>, <1967507429, 1>, <42871537410379677915586797717246201629363383, 1> ] 1 Total time: 3.769 seconds, Total memory usage: 3.00MB ************** MAGMA ***************** Host massena-2-81-57-129-182.fbx.proxad.net. (81.57.129.182) Time: Thu Jan 29 10:12:22 2004 Input: factor(25000245445542451321685465345345435445256563853454853454654534511) Output: Magma V2.10-6 Thu Jan 29 2004 10:12:18 on modular [Seed = 3364989517] ------------------------------------- [ <139, 1>, <163, 2>, <127399, 1>, <5313592488678110303500943898903204255602897\ 1767548979, 1> ] 1 Total time: 3.299 seconds, Total memory usage: 3.00MB ************** MAGMA ***************** Host h24-81-108-53.vc.shawcable.net. (24.81.108.53) Time: Thu Jan 29 13:12:01 2004 Input: R:=PolynomailRing(RationalField()); X:=HyperellipticCurve([x^2-x,x^3-x^2-1]); Jacobian(X); Output: Magma V2.10-6 Thu Jan 29 2004 13:11:58 on modular [Seed = 1276461311] ------------------------------------- >> R:=PolynomailRing(RationalField()); ^ User error: Identifier 'PolynomailRing' has not been declared or assigned >> X:=HyperellipticCurve([x^2-x,x^3-x^2-1]); ^ User error: Identifier 'x' has not been declared or assigned >> Jacobian(X);; ^ User error: Identifier 'X' has not been declared or assigned Total time: 3.049 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host h24-81-108-53.vc.shawcable.net. (24.81.108.53) Time: Thu Jan 29 13:12:13 2004 Input: R:=PolynomialRing(RationalField()); X:=HyperellipticCurve([x^2-x,x^3-x^2-1]); Jacobian(X); Output: Magma V2.10-6 Thu Jan 29 2004 13:12:10 on modular [Seed = 1075399911] ------------------------------------- Jacobian of Hyperelliptic Curve defined by y^2 + (x^3 - x^2 - 1)*y = x^2 - x over Rational Field Total time: 3.009 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host h24-81-108-53.vc.shawcable.net. (24.81.108.53) Time: Thu Jan 29 13:13:50 2004 Input: R:=PolynomialRing(RationalField()); X:=HyperellipticCurve([x^2-x,x^3-x^2-1]); J:=Jacobian(X); AbelianGroup(J); Output: Magma V2.10-6 Thu Jan 29 2004 13:13:47 on modular [Seed = 1949137266] ------------------------------------- >> AbelianGroup(J);; ^ Runtime error in 'AbelianGroup': The base field of the Jacobian must be finite Total time: 3.009 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host h24-81-108-53.vc.shawcable.net. (24.81.108.53) Time: Thu Jan 29 13:14:41 2004 Input: R:=PolynomialRing(RationalField()); X:=HyperellipticCurve([x^2-x,x^3-x^2-1]); J:=Jacobian(X); TorsionSubgroup(J); Output: Magma V2.10-6 Thu Jan 29 2004 13:14:37 on modular [Seed = 1815437756] ------------------------------------- >> TorsionSubgroup(J);; ^ Runtime error in 'TorsionSubgroup': TorsionSubgroup needs a curve of the form y^2 = f(x), where f has integral coefficients. Total time: 2.979 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host h24-81-108-53.vc.shawcable.net. (24.81.108.53) Time: Thu Jan 29 13:15:17 2004 Input: R:=PolynomialRing(RationalField()); X:=HyperellipticCurve([x^6-2*x^5+x^4-2*x^3+6*x^2-4*x+1,0]); J:=Jacobian(X); TorsionSubgroup(J); Output: Magma V2.10-6 Thu Jan 29 2004 13:15:12 on modular [Seed = 474288625] ------------------------------------- Abelian Group isomorphic to Z/19 Defined on 1 generator Relations: 19*P[1] = 0 Mapping from: Abelian Group isomorphic to Z/19 Defined on 1 generator Relations: 19*P[1] = 0 to JacHyp: J given by a rule [no inverse] Total time: 3.509 seconds, Total memory usage: 3.09MB ************** MAGMA ***************** Host h24-81-108-53.vc.shawcable.net. (24.81.108.53) Time: Thu Jan 29 13:15:38 2004 Input: R:=PolynomialRing(RationalField()); X:=HyperellipticCurve([x^6-2*x^5+x^4-2*x^3+6*x^2-4*x+1,0]); J:=Jacobian(X); Generators(TorsionSubgroup(J)); Output: Magma V2.10-6 Thu Jan 29 2004 13:15:35 on modular [Seed = 340597134] ------------------------------------- { P[1] } Total time: 3.569 seconds, Total memory usage: 3.09MB ************** MAGMA ***************** Host h24-81-108-53.vc.shawcable.net. (24.81.108.53) Time: Thu Jan 29 13:16:57 2004 Input: R:=PolynomialRing(RationalField()); X:=HyperellipticCurve([x^6-2*x^5+x^4-2*x^3+6*x^2-4*x+1,0]); J:=Jacobian(X); Chabauty0(TorsionSubgroup(J)); Output: Magma V2.10-6 Thu Jan 29 2004 13:16:53 on modular [Seed = 206897732] ------------------------------------- >> Chabauty0(TorsionSubgroup(J));; ^ Runtime error in 'Chabauty0': Bad argument types Argument types given: GrpAb Total time: 3.509 seconds, Total memory usage: 3.09MB ************** MAGMA ***************** Host h24-81-108-53.vc.shawcable.net. (24.81.108.53) Time: Thu Jan 29 13:17:11 2004 Input: R:=PolynomialRing(RationalField()); X:=HyperellipticCurve([x^6-2*x^5+x^4-2*x^3+6*x^2-4*x+1,0]); J:=Jacobian(X); Chabauty0(J); Output: Magma V2.10-6 Thu Jan 29 2004 13:17:07 on modular [Seed = 5836414] ------------------------------------- {@ (1 : -1 : 0), (1 : 1 : 0), (0 : 1 : 1), (0 : -1 : 1), (1 : 1 : 1), (1 : -1 : 1) @} Total time: 3.569 seconds, Total memory usage: 3.11MB ************** MAGMA ***************** Host h24-81-108-53.vc.shawcable.net. (24.81.108.53) Time: Thu Jan 29 13:25:39 2004 Input: X:=EllipticCurve([-432,8208]); AbelianGroup(X); Output: Magma V2.10-6 Thu Jan 29 2004 13:25:36 on modular [Seed = 3616458666] ------------------------------------- Abelian Group isomorphic to Z/5 Defined on 1 generator Relations: 5*$.1 = 0 Total time: 2.969 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host h24-81-108-53.vc.shawcable.net. (24.81.108.53) Time: Thu Jan 29 13:26:08 2004 Input: X:=EllipticCurve([-432,8208]); G:=TorsionSubgroupScheme(X); IsogneyFromKernel(G); Output: Magma V2.10-6 Thu Jan 29 2004 13:26:05 on modular [Seed = 3365001384] ------------------------------------- >> G:=TorsionSubgroupScheme(X); ^ Runtime error in 'TorsionSubgroupScheme': Bad argument types Argument types given: CrvEll >> IsogneyFromKernel(G);; ^ User error: Identifier 'G' has not been declared or assigned Total time: 2.989 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host h24-81-108-53.vc.shawcable.net. (24.81.108.53) Time: Thu Jan 29 13:26:40 2004 Input: X:=EllipticCurve([-432,8208]); G:=TorsionSubgroupScheme(X, 5); IsogneyFromKernel(G); Output: Magma V2.10-6 Thu Jan 29 2004 13:26:37 on modular [Seed = 3231305920] ------------------------------------- >> IsogneyFromKernel(G);; ^ User error: Identifier 'IsogneyFromKernel' has not been declared or assigned Total time: 2.989 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host h24-81-108-53.vc.shawcable.net. (24.81.108.53) Time: Thu Jan 29 13:28:28 2004 Input: X:=EllipticCurve([-432,8208]); G:=TorsionSubgroupScheme(X, 5); IsogenyFromKernel(G); Output: Magma V2.10-6 Thu Jan 29 2004 13:28:25 on modular [Seed = 4037664868] ------------------------------------- Elliptic Curve defined by y^2 + y = x^3 - x^2 - 208*x + 2818 over Rational Field Elliptic curve isogeny from: CrvEll: X to Elliptic Curve defined by y^2 + y = x^3 - x^2 - 208*x + 2818 over Rational Field taking (x : y : 1) to ((1/36*x^25 + 1/3*x^24 + 1200*x^23 - 2389056/5*x^22 + 12079872*x^21 - 11310824448/25*x^20 + 325894689792/5*x^19 + 6868144410624/5*x^18 - 201315817635840*x^17 + 12886171038646272/5*x^16 + 9390610168091246592/25*x^15 - 99810490458367328256/5*x^14 + 1299376112980142850048/5*x^13 + 10551038051249547116544*x^12 - 1928148901296086162866176/5*x^11 + 39811001888659119575924736/25*x^10 + 693253441680160077127876608/5*x^9 - 13534352942995665019390132224/5*x^8 - 4977820052567467820228542464*x^7 + 4863382419863666410707650347008/5*x^6 - 472435391759981657955812776083456/25*x^5 + 1172961840579846320869370763411456/5*x^4 - 13532470915043783925363070161911808/5*x^3 + 144227471965630628381682482257330176/5*x^2 - 888922351684018721468991552947748864/5*x + 7427964960020962449373953985974632448/25) / (x^24 - 53568/5*x^22 + 1247616*x^21 + 521427456/25*x^20 - 35118157824/5*x^19 + 2171655401472/5*x^18 - 3492526325760*x^17 - 967772272656384/5*x^16 + 132157392238411776/25*x^15 - 1804701204656160768/5*x^14 + 79073765324325126144/5*x^13 - 208722015157777072128*x^12 - 18596694881863653654528/5*x^11 + 4295428982731079216529408/25*x^10 - 26069499110070435578904576/5*x^9 + 843861137039464665635094528/5*x^8 - 3089181183834298811355758592*x^7 + 35543918544634983099477786624/5*x^6 + 18671499306985380196755997458432/25*x\ ^5 - 60565473749514057205374026514432/5*x^4 + 213996707199567259227624598142976/5*x^3 + 3979643934960756362174242360393728/5*x^2 - 48808003315774106140261433204539392/5*x + 963626566674454861979826642688671744/25) : (1/216*x^36*y - 1/2*x^36 - 324*x^34*y + 40176/5*x^34 + 178296*x^33*y - 935712*x^33 - 9209376*x^32*y - 929107584/25*x^32 + 1768200192*x^31*y + 51400728576/5*x^31 - 269293787136*x^30*y - 71529237762048/125*x^30 + 3946622828544*x^29*y - 548289869709312/25*x^29 + 272136060370944*x^28*y + 90031713547124736/25*x^28 + 2739580313665536*x^27*y - 4037866199408443392/25*x^27 - 889832118670589952*x^26*y + 29412199782838960128/25*x^26 + 34622904298075324416*x^25*y + 12157804361841993842688/125*x^25 + 1402788491184996089856*x^24*y - 21453741145550500134912/5*x^24 - 260301725475541912387584*x^23*y + 1190654760169595599847424/5*x^23 + 11551991628424766621220864*x^22*y - 222156935980457449758916608/25*x^22 - 45407114352081982992678912*x^21*y + 427716569980191522127085568/5*x^21 - 13451079112692648877171408896*x^20*y + 527530514909750576088210210816/125*x^20 + 359862414790836048773051842560*x^19*y - 4811011654572799837798152536064/25*x^19 + 6347178162588039681343425085440*x^18*y + 157251228536227649073309120724992/25*x^18 - 531048357069877285798010683392000*x^17*y - 184406290462486956758675037880320*x^17 + 9593412876206052980523614613798912*x^16*y + 64147091233592521992668083258392576/25*x^16 + 91446914862206861296323103618498560*x^15*y + 5119936591515747922500010059723964416/125*x^15 - 7154133720163028414018121127100940288*x^14*y - 66998395478387737850606710894035468288/25*x^14 + 115521764509186530644889320217894715392*x^13*y + 1772464753223118748902842673808281698304/25*x^13 + 109329733309173293442738048125494099968*x^12*y - 38628511034431531322213310631695756558336/25*x^12 - 31171077465069942412416775055764396965888*x^11*y + 630311922036518754270652566862265950666752/25*x^11 + 464085711807438527979693846725178811219968*x^10*y - 9500481865729430688128011380886770221580288/125*x^10 - 3006004048755435241984404417706385467244544*x^9*y - 196390463420242805225800686898110875465416704/25*x^9 + 54427136497661805365768823285970053655166976*x^8*y + 4607194533008657954961806318254876737983741952/25*x^8 - 2489951927276799046059772567418624042908778496*x^7*y - 33865133817529449125588951614411786273809235968/25*x^7 + 63781612274721685177590271876496494284496699392*x^6*y - 323556867970303936920778365006098789120977403904/25*x^6 - 1006077119762222221070339423629313336942385954816*x^5*y + 44274235162632887954283228051653662608872662106112/125*x^5 + 10273778504019751940642101643620677032810731536384*x^4*y - 63784862048522104155696171947371218300164596826112/25*x^4 - 66293175187135144046057897370984340295140283252736*x^3*y - 117426997649741104891874978381224801321202372050944/25*x^3 + 274839701535089724267380526128270951279061626781696*x^2*y + 5205039733659429026600599407335412416137974584967168/25*x^2 - 1061366047200988695899704742666637642596857380077568*x*y - 35934092983913747628400224112297266399132373192015872/25*x + 3355219333443312903445643101070742758941180135735296*y + 472969517241153147002792417503894848741645120738164736/125) / (x^36 - 80352/5*x^34 + 1871424*x^33 + 1858215168/25*x^32 - 102801457152/5*x^31 + 143058475524096/125*x^30 + 1096579739418624/25*x^29 - 180063427094249472/25*x^28 + 8075732398816886784/25*x^27 - 58824399565677920256/25*x^26 - 24315608723683987685376/125*x^25 + 42907482291101000269824/5*x^24 - 2381309520339191199694848/5*x^23 + 444313871960914899517833216/25*x^22 - 855433139960383044254171136/5*x^21 - 1055061029819501152176420421632/125*x^20 + 9622023309145599675596305072128/25*x^19 - 314502457072455298146618241449984/25*x^18 + 368812580924973913517350075760640*x^17 - 128294182467185043985336166516785152/25*x^16 - 10239873183031495845000020119447928832/125*x^15 + 133996790956775475701213421788070936576/25*x^14 - 3544929506446237497805685347616563396608/25*x^13 + 77257022068863062644426621263391513116672/25*x^12 - 1260623844073037508541305133724531901333504/25*x^11 + 19000963731458861376256022761773540443160576/125*x^10 + 392780926840485610451601373796221750930833408/25*x^9 - 9214389066017315909923612636509753475967483904/25*x^8 + 67730267635058898251177903228823572547618471936/25*x^7 + 647113735940607873841556730012197578241954807808/25*x^6 - 88548470325265775908566456103307325217745324212224/125*x^5 + 127569724097044208311392343894742436600329193652224/25*x^4 + 234853995299482209783749956762449602642404744101888/25*x^3 - 10410079467318858053201198814670824832275949169934336/25*x^2 + 71868185967827495256800448224594532798264746384031744/25*x - 945939034482306294005584835007789697483290241476329472/125) : 1) Total time: 3.049 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (80.232.193.34) Time: Thu Jan 29 16:04:43 2004 Input: (1+xy)/(1-xy-xyy-xxyyy) Output: Magma V2.10-6 Thu Jan 29 2004 16:04:40 on modular [Seed = 106902321] ------------------------------------- >> (1+xy)/(1-xy-xyy-xxyyy) ^ User error: Identifier 'xy' has not been declared or assigned Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (80.232.193.34) Time: Thu Jan 29 16:05:27 2004 Input: (1+x*y)/(1-x*y-x*y*y-x*x*y*y*y) Output: Magma V2.10-6 Thu Jan 29 2004 16:05:24 on modular [Seed = 796269284] ------------------------------------- >> (1+x*y)/(1-x*y-x*y*y-x*x*y*y*y) ^ User error: Identifier 'x' has not been declared or assigned Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (80.232.193.34) Time: Thu Jan 29 16:06:11 2004 Input: Integer x Integer y (1+x*y)/(1-x*y-x*y*y-x*x*y*y*y) Output: Magma V2.10-6 Thu Jan 29 2004 16:06:08 on modular [Seed = 3716474946] ------------------------------------- >> Integer x ^ User error: bad syntax >> Integer y ^ User error: bad syntax >> (1+x*y)/(1-x*y-x*y*y-x*x*y*y*y) ^ User error: Identifier 'x' has not been declared or assigned Total time: 3.019 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (80.232.193.34) Time: Thu Jan 29 16:06:39 2004 Input: Int x Int y (1+x*y)/(1-x*y-x*y*y-x*x*y*y*y) Output: Magma V2.10-6 Thu Jan 29 2004 16:06:35 on modular [Seed = 3415408207] ------------------------------------- >> Int x ^ User error: bad syntax >> Int y ^ User error: bad syntax >> (1+x*y)/(1-x*y-x*y*y-x*x*y*y*y) ^ User error: Identifier 'x' has not been declared or assigned Total time: 3.019 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (80.232.193.34) Time: Thu Jan 29 16:06:55 2004 Input: x y (1+x*y)/(1-x*y-x*y*y-x*x*y*y*y) Output: Magma V2.10-6 Thu Jan 29 2004 16:06:52 on modular [Seed = 3265001329] ------------------------------------- >> y ^ User error: bad syntax >> (1+x*y)/(1-x*y-x*y*y-x*x*y*y*y) ^ User error: Identifier 'x' has not been declared or assigned Total time: 2.979 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host h68-144-29-100.cg.shawcable.net. (68.144.29.100) Time: Thu Jan 29 23:04:31 2004 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: Magma V2.10-6 Thu Jan 29 2004 23:04:28 on modular [Seed = 1075435499] ------------------------------------- Replace this by some code, then click [PARI] or [MAGMA]! Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host h68-144-29-100.cg.shawcable.net. (68.144.29.100) Time: Thu Jan 29 23:10:10 2004 Input: ModularCurve(X,Canonical,2) : Sch, MonStgElt, RngIntElt -> CrvMod Output: Magma V2.10-6 Thu Jan 29 2004 23:10:07 on modular [Seed = 1510196002] ------------------------------------- >> ModularCurve(X,Canonical,2) : Sch, MonStgElt, RngIntElt -> CrvMod ^ User error: bad syntax Total time: 2.879 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host h68-144-29-100.cg.shawcable.net. (68.144.29.100) Time: Thu Jan 29 23:10:26 2004 Input: ModularCurve(X,Canonical,2) Output: Magma V2.10-6 Thu Jan 29 2004 23:10:23 on modular [Seed = 561559657] ------------------------------------- >> ModularCurve(X,Canonical,2) ^ User error: Identifier 'X' has not been declared or assigned Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 24-205-83-208.pas-eres.charterpipeline.net. (24.205.83.208) Time: Thu Jan 29 23:11:43 2004 Input: (99^9)^(1/8) Output: Magma V2.10-6 Thu Jan 29 2004 23:11:40 on modular [Seed = 896314414] ------------------------------------- 175.8286306843643465177628 Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 24-205-83-208.pas-eres.charterpipeline.net. (24.205.83.208) Time: Thu Jan 29 23:12:31 2004 Input: (99^9)^(1/4) Output: Magma V2.10-6 Thu Jan 29 2004 23:12:28 on modular [Seed = 1013294583] ------------------------------------- 30915.70736833859140648157 Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host h68-144-29-100.cg.shawcable.net. (68.144.29.100) Time: Thu Jan 29 23:12:41 2004 Input: ModularCurve(A1,"Caonical",2) : Sch, MonStgElt, RngIntElt -> CrvMod Output: Magma V2.10-6 Thu Jan 29 2004 23:12:38 on modular [Seed = 56269522] ------------------------------------- >> ModularCurve(A1,"Caonical",2) : Sch, MonStgElt, RngIntElt -> CrvMod ^ User error: bad syntax Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host h68-144-29-100.cg.shawcable.net. (68.144.29.100) Time: Thu Jan 29 23:13:07 2004 Input: ModularCurve(A1,"Caonical",2) Output: Magma V2.10-6 Thu Jan 29 2004 23:13:04 on modular [Seed = 173249469] ------------------------------------- >> ModularCurve(A1,"Caonical",2); ^ User error: Identifier 'A1' has not been declared or assigned Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 24-205-83-208.pas-eres.charterpipeline.net. (24.205.83.208) Time: Thu Jan 29 23:13:43 2004 Input: 30916^(1/2) Output: Magma V2.10-6 Thu Jan 29 2004 23:13:40 on modular [Seed = 289966210] ------------------------------------- 175.829462832598109487420226 Total time: 2.889 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 24-205-83-208.pas-eres.charterpipeline.net. (24.205.83.208) Time: Thu Jan 29 23:14:42 2004 Input: (99^9)^(1/2) Output: Magma V2.10-6 Thu Jan 29 2004 23:14:39 on modular [Seed = 406946384] ------------------------------------- 955780962.0847450731043219 Total time: 2.989 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host h68-144-29-100.cg.shawcable.net. (68.144.29.100) Time: Thu Jan 29 23:15:08 2004 Input: P2 := PolynomialRing(Integers(),2); P2!CanonicalModularPolynomial(2); Output: Magma V2.10-6 Thu Jan 29 2004 23:15:05 on modular [Seed = 3954340293] ------------------------------------- x^3 + 48*x^2 - x*j + 768*x + 4096 Total time: 2.979 seconds, Total memory usage: 2.54MB ************** MAGMA ***************** Host 24-205-83-208.pas-eres.charterpipeline.net. (24.205.83.208) Time: Thu Jan 29 23:15:16 2004 Input: (955780963)^(1/2) Output: Magma V2.10-6 Thu Jan 29 2004 23:15:13 on modular [Seed = 4071319748] ------------------------------------- 30915.70738314101717296908 Total time: 3.019 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 24-205-83-208.pas-eres.charterpipeline.net. (24.205.83.208) Time: Thu Jan 29 23:15:31 2004 Input: (30916)^(1/2) Output: Magma V2.10-6 Thu Jan 29 2004 23:15:28 on modular [Seed = 4188038142] ------------------------------------- 175.829462832598109487420226 Total time: 2.979 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 24-205-83-208.pas-eres.charterpipeline.net. (24.205.83.208) Time: Thu Jan 29 23:17:20 2004 Input: (9^(9^9))^(1/(2^32)) Output: ** WARNING: Computation used more memory than allowed. ** Magma V2.10-6 Thu Jan 29 2004 23:17:17 on modular [Seed = 3482735973] ------------------------------------- Current total memory usage: 1.7MB, failed memory request: 1208.6MB System Error: User memory limit has been reached Total time: 2.999 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 24-205-83-208.pas-eres.charterpipeline.net. (24.205.83.208) Time: Thu Jan 29 23:17:54 2004 Input: (9^(9^3))^(1/1024) Output: Magma V2.10-6 Thu Jan 29 2004 23:17:51 on modular [Seed = 3599715422] ------------------------------------- 4.779017947473825958608107 Total time: 2.879 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 24-205-83-208.pas-eres.charterpipeline.net. (24.205.83.208) Time: Thu Jan 29 23:18:08 2004 Input: (9^(9^3))^(1/256) Output: Magma V2.10-6 Thu Jan 29 2004 23:18:05 on modular [Seed = 3716433735] ------------------------------------- 521.620493906283389063923557 Total time: 2.889 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 24-205-83-208.pas-eres.charterpipeline.net. (24.205.83.208) Time: Thu Jan 29 23:19:59 2004 Input: (9^(9^6))^(1/1024) Output: Magma V2.10-6 Thu Jan 29 2004 23:19:56 on modular [Seed = 2768060335] ------------------------------------- 1.729355331915474402596842614e495 Total time: 3.619 seconds, Total memory usage: 4.26MB ************** MAGMA ***************** Host 24-205-83-208.pas-eres.charterpipeline.net. (24.205.83.208) Time: Thu Jan 29 23:20:15 2004 Input: (9^(9^6))^(1/512) Output: Magma V2.10-6 Thu Jan 29 2004 23:20:11 on modular [Seed = 3035443112] ------------------------------------- 2.99066986402448063888787342e990 Total time: 3.699 seconds, Total memory usage: 4.26MB ************** MAGMA ***************** Host 24-205-83-208.pas-eres.charterpipeline.net. (24.205.83.208) Time: Thu Jan 29 23:20:29 2004 Input: (9^(9^6))^(1/256) Output: Magma V2.10-6 Thu Jan 29 2004 23:20:25 on modular [Seed = 3152158805] ------------------------------------- 8.944106235584205513947458e1980 Total time: 3.679 seconds, Total memory usage: 4.26MB ************** MAGMA ***************** Host 24-205-83-208.pas-eres.charterpipeline.net. (24.205.83.208) Time: Thu Jan 29 23:20:42 2004 Input: (9^(9^6))^(1/64) Output: Magma V2.10-6 Thu Jan 29 2004 23:20:37 on modular [Seed = 2195396976] ------------------------------------- 6.399525825329803886865451074e7923 Total time: 3.679 seconds, Total memory usage: 4.26MB ************** MAGMA ***************** Host 24-205-83-208.pas-eres.charterpipeline.net. (24.205.83.208) Time: Thu Jan 29 23:20:58 2004 Input: (9^(9^6))^(1/4096) Output: Magma V2.10-6 Thu Jan 29 2004 23:20:54 on modular [Seed = 2295403337] ------------------------------------- 6.448683454444135362812443992e123 Total time: 3.629 seconds, Total memory usage: 4.26MB ************** MAGMA ***************** Host 24-205-83-208.pas-eres.charterpipeline.net. (24.205.83.208) Time: Thu Jan 29 23:21:17 2004 Input: (9^(9^6))^(1/(2^20)) Output: Magma V2.10-6 Thu Jan 29 2004 23:21:13 on modular [Seed = 2680554561] ------------------------------------- 3.045304654824346360754921 Total time: 3.689 seconds, Total memory usage: 4.26MB ************** MAGMA ***************** Host h68-144-29-100.cg.shawcable.net. (68.144.29.100) Time: Thu Jan 29 23:21:28 2004 Input: P2 := PolynomialRing(Integers(),3); P2!CanonicalModularPolynomial(2); Output: Magma V2.10-6 Thu Jan 29 2004 23:21:24 on modular [Seed = 1764815557] ------------------------------------- >> P2!CanonicalModularPolynomial(2); ^ Runtime error in '!': LHS rank (3) does not equal RHS rank (2) Total time: 3.449 seconds, Total memory usage: 2.54MB ************** MAGMA ***************** Host 24-205-83-208.pas-eres.charterpipeline.net. (24.205.83.208) Time: Thu Jan 29 23:21:30 2004 Input: (9^(9^6))^(1/(2^18)) Output: Magma V2.10-6 Thu Jan 29 2004 23:21:26 on modular [Seed = 1815476162] ------------------------------------- 86.004858428302159044894282 Total time: 4.129 seconds, Total memory usage: 4.26MB ************** MAGMA ***************** Host 24-205-83-208.pas-eres.charterpipeline.net. (24.205.83.208) Time: Thu Jan 29 23:21:44 2004 Input: (9^(9^6))^(1/(2^17)) Output: Magma V2.10-6 Thu Jan 29 2004 23:21:40 on modular [Seed = 2065883335] ------------------------------------- 7396.835673272296922941836103 Total time: 3.729 seconds, Total memory usage: 4.26MB ************** MAGMA ***************** Host h68-144-29-100.cg.shawcable.net. (68.144.29.100) Time: Thu Jan 29 23:21:49 2004 Input: P2 := PolynomialRing(Integers(),2); P2!CanonicalModularPolynomial(2); Output: Magma V2.10-6 Thu Jan 29 2004 23:21:46 on modular [Seed = 1949167559] ------------------------------------- x^3 + 48*x^2 - x*j + 768*x + 4096 Total time: 2.859 seconds, Total memory usage: 2.54MB ************** MAGMA ***************** Host h68-144-29-100.cg.shawcable.net. (68.144.29.100) Time: Thu Jan 29 23:25:15 2004 Input: ModularCurve("Canonical",2); Output: Magma V2.10-6 Thu Jan 29 2004 23:25:12 on modular [Seed = 1092148609] ------------------------------------- >> ModularCurve("Canonical",2);; ^ Runtime error in 'ModularCurve': Bad argument types Argument types given: MonStgElt, RngIntElt Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 24-205-83-208.pas-eres.charterpipeline.net. (24.205.83.208) Time: Thu Jan 29 23:27:00 2004 Input: (9^(9^9)) Output: ** WARNING: Computation used more memory than allowed. ** Magma V2.10-6 Thu Jan 29 2004 23:26:57 on modular [Seed = 1526908450] ------------------------------------- Current total memory usage: 1.7MB, failed memory request: 1208.6MB System Error: User memory limit has been reached Total time: 2.979 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 24-205-83-208.pas-eres.charterpipeline.net. (24.205.83.208) Time: Thu Jan 29 23:27:37 2004 Input: (9^(6^9)) Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Thu Jan 29 2004 23:27:14 on modular [Seed = 1410189598] ------------------------------------- Errors: /home/mfd/gomagma: line 2: 10300 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host 24-205-83-208.pas-eres.charterpipeline.net. (24.205.83.208) Time: Thu Jan 29 23:28:25 2004 Input: (9^(6^9))(1/(2^30)) Output: Magma V2.10-6 Thu Jan 29 2004 23:28:08 on modular [Seed = 762621981] ------------------------------------- >> (9^(6^9))(1/(2^30)); ^ Runtime error: Bad argument types Argument types given: FldRatElt, RngIntElt Total time: 16.879 seconds, Total memory usage: 34.40MB ************** MAGMA ***************** Host 24-205-83-208.pas-eres.charterpipeline.net. (24.205.83.208) Time: Thu Jan 29 23:28:46 2004 Input: (9^(6^9))^(1/(2^30)) Output: Magma V2.10-6 Thu Jan 29 2004 23:28:25 on modular [Seed = 544849185] ------------------------------------- 1.020836347405948820338572 Total time: 21.219 seconds, Total memory usage: 34.40MB ************** MAGMA ***************** Host 24-205-83-208.pas-eres.charterpipeline.net. (24.205.83.208) Time: Thu Jan 29 23:29:28 2004 Input: (9^(6^9))^(1/(2^24)) Output: Magma V2.10-6 Thu Jan 29 2004 23:29:06 on modular [Seed = 1046979524] ------------------------------------- 3.742760140050927086532344 Total time: 21.219 seconds, Total memory usage: 34.40MB ************** MAGMA ***************** Host 24-205-83-208.pas-eres.charterpipeline.net. (24.205.83.208) Time: Thu Jan 29 23:29:57 2004 Input: (9^(6^9))^(1/(2^21)) Output: Magma V2.10-6 Thu Jan 29 2004 23:29:36 on modular [Seed = 929999599] ------------------------------------- 38506.67018256815447689838 Total time: 21.199 seconds, Total memory usage: 34.40MB ************** MAGMA ***************** Host h68-144-29-100.cg.shawcable.net. (68.144.29.100) Time: Thu Jan 29 23:30:21 2004 Input: P2 := PolynomialRing(Integers(),2); P2!CanonicalModularPolynomial(3); Output: Magma V2.10-6 Thu Jan 29 2004 23:30:18 on modular [Seed = 123640501] ------------------------------------- x^4 + 36*x^3 + 270*x^2 - x*j + 756*x + 729 Total time: 3.019 seconds, Total memory usage: 2.54MB ************** MAGMA ***************** Host 24-205-83-208.pas-eres.charterpipeline.net. (24.205.83.208) Time: Thu Jan 29 23:30:57 2004 Input: (9^(6^9))^(1/(2^22)) Output: Magma V2.10-6 Thu Jan 29 2004 23:30:36 on modular [Seed = 273255828] ------------------------------------- 196.231165166413243913638815 Total time: 21.180 seconds, Total memory usage: 34.40MB ************** MAGMA ***************** Host pxy-2a.kyoto-u.ac.jp. (130.54.130.227) Time: Fri Jan 30 01:56:43 2004 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: Magma V2.10-6 Fri Jan 30 2004 01:56:39 on modular [Seed = 2801592045] ------------------------------------- Replace this by some code, then click [PARI] or [MAGMA]! Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 24-205-83-208.pas-eres.charterpipeline.net. (24.205.83.208) Time: Fri Jan 30 03:19:19 2004 Input: (9^(6^9))^(1/(2^21)) Output: Magma V2.10-6 Fri Jan 30 2004 03:18:57 on modular [Seed = 862543917] ------------------------------------- 38506.67018256815447689838 Total time: 21.409 seconds, Total memory usage: 34.40MB ************** MAGMA ***************** Host 24-205-83-208.pas-eres.charterpipeline.net. (24.205.83.208) Time: Fri Jan 30 03:20:25 2004 Input: (9^(3^3))^(1024) Output: Magma V2.10-6 Fri Jan 30 2004 03:20:22 on modular [Seed = 4289047638] ------------------------------------- 7886802736485710362916352260419090317211756201805319082292073090892355771340960\ 4425716587389666526094806708271490686178810128885857376058552459583365323419979\ 8660677817621043369077201143963669962309343349612522805208367827663778767395210\ 5899928091531236178829922273130756035555221888795825043657180778069427454334827\ 5429715784441742881651659953888190038467616218083795448558938745488077698835073\ 1863201586951987216785731007806291211496107635696238335727807075934369058857918\ 5230000936018184252755077480510507350007350758604626397767893747844786417464080\ 2179991493646554806574234315643627996785493351949216372248833427452412868994393\ 1290491034166770472295071168652905728195005961365149953232042664544470950871737\ 9865995635939401269520838583172558656149550346305891758760417336916466359126042\ 1505935012009518413933258139192462642795870571903417275130636204942053928960809\ 3809208363676852960970732363984508488645603879435257574330985134414092086147937\ 4082305466437654518752092138368768998921370024310602261396953518405307820778102\ 8523005432483153493840320455229126448903009823483062896626063284900976856055798\ 1545672473564430094059725617777810197826540706404468118052509908528170460189036\ 4876645597051206346645068959154186736100216022687077586075721649582299479372029\ 0494352666299590242918824000706489550526714206640648882611935653767614707593897\ 6576909885600579795950351289226386467378716652732441813108106604795197990102243\ 6218407282299810694966504994401432702863049100144473573634374815929525509858849\ 2307362573910235910693472255265216305871843656646314486725097406558308988198857\ 9239585580033485951998564072363487971074733208453969051059023310457374711694474\ 0590508001108430773387433951141016102136576837720509914051623977060872917781692\ 6109769551138216339224482073239314737484998025450129649112217264596131906856345\ 1351975747720909390686554584004053397152646770470546219934334858345661903634709\ 2292313723336693709145685460311528667508962102687914609252121008641757953471811\ 3327002466969636129899292192609532869848241492523847513188596931832249406925347\ 3771508515295386518221109411910641636428886160121416075124031068148119906476829\ 4537788408482459676076736667600238016821018262644504397244776388916638522088313\ 3661495454058020698247917948693544821722793127243558177025461372933728200743731\ 6857885949779794939281373022435042101956470285956981713399232055503822828320088\ 2797200917210613711608200384037001935444757899999000653102074665929412638209228\ 9720376480366656651260967080772394483222169474759558070709437102868484353133767\ 6507820750348981500583718300526763312531378412790595107410208054686754646366801\ 0730684102060910036241426250367741412828567930525140200234045779616980718321539\ 3661118796951211594631894448981528440091419849992374047021118528134350781321179\ 7898088465661113173365539773686162038923606856566164475266571726866899035135863\ 5925548290571524666012530119250244397605018060363657776956753023380508996957196\ 5631569910882262166048544786088776596983309019469281349898360258606558201498830\ 0263954325077797099544156856571115012467187300315200061738327795259969114833137\ 4652203627818539713450103560943932179238215313825232339634262783495385038887629\ 4485674549744636840793505890803535462669999325590041696059271445279217504581446\ 7537516838618004241756392384471158440137176930313783806674626294628364615628599\ 3492610153581424161449259602864332145999607633673977391774870451716662112433936\ 1707931640162970952352402873197437734357709709074134856345246486379942383572338\ 9695307555638397577982434356706740891007583342623463441195779834188527400367743\ 7793559200320171721876192311906813940468215276650107526216894445744392501610153\ 1866777358152135535050851261386622638930940698858330973744197083466821744588398\ 0099151794526911223924270767145921656510529046415046207770071813570971697789589\ 0312409927451199855040175807456508671731255597479576568491534596290210835055931\ 0002705544662986395621234198458737478625880399678497818060691451825145961361047\ 3486290457119798869693668888477428123214311581147989077403493573972141663697469\ 5509560728932386194231176045679832780376781121926410706205730366505701720508603\ 6918640908325243645540194524700064222168278965231487410195362030303583734468157\ 4165755149918478157866904086520298890238654362190121223682645475926816040422138\ 1754081666516051203316107832587842864717224482642957853532853038803116468710060\ 5622582447223876017519132529900283016816512805615247650960111163582173823821413\ 7986812082198086428671772698532829516577891605436645177444050460495819314791369\ 3356546419424804974471058949215206979588775980072995581728382542505876949944418\ 5818459037580483466565093582312631461000843728243848956644214455713276422203985\ 1171724134411422708432705455755399515864697920271111751326390761767061763391828\ 7180106806014622402537214056501489096048030783085861569082375478012286814281311\ 2343716854032316282500966117021378715553351683682205182349435234750734053548408\ 0428849227928476233015241857920716365990719492425619961398181350154447340281145\ 4803175889411702306968524299104425200850580158907199423820586675300760088964482\ 6965482593428489325486608757979770045103653753961118634078138456814082762412877\ 5723347477265100126625944887864108050123954481497301538169735122313481671990165\ 3792086520928585656947668005868532329827459529147521432862529669828765181954502\ 1006878549379253317540077376941881326948465827567125221483070909047142739688865\ 3081475107051989817749152300284879997880699364632126174535257616330807687172799\ 0817130198166705835556046140812649870918649693772398420078433403014034173754930\ 6856779795309158773917273296046402124850977996538794061471700939009967188534580\ 1307068575065387844719132085208326978908376886239955707312270086066085208292257\ 8993887174032827834190588510375400239015484531076768480950607706401844590764363\ 5309182549879020362256164907584598670794891279475116526574030564700694534638653\ 1512313710706748130929988485693262722733033384313082067641572323236619904062107\ 7809192022284292583789866979016700021607918030804635049504806237314631795043105\ 9022178590361573063039051710430922004524578368127279177469466254869031118375599\ 3878812542880436830915189845079052567789135996588224286994483803415381112689550\ 4892512895242458779855435473262495447097725719609165568260718618419698430041997\ 0258286787768582468037034049282383816493870419058612843253995574775347664103957\ 8006763848223783451896117758621971331243263797649043780979657811627194208351510\ 7843099268903214900585751552105654128800192896011835257660927741943085154945170\ 9474025896538751789927916380925798933818887147712680729444025983445754904849169\ 8308295758755909142484658762746239230845224016440751184431099512337298984563775\ 1609154025260996601801196383273766021711677659213327026537128561009257438966251\ 8017197532262634177614931699248706811081904184722066346321250899005947054627184\ 4173354263761152941597013925286814607846137670171784012563584436689616834922746\ 7446932210312190978370321246489928576000232594477398629382926933776842755252041\ 6172541098301718833966707052242100341659646858552549017098332136916365693833510\ 9513518547126429244596462476984622666164088823754410934315948914748360227521186\ 7357019593315453072563675179656473575333880252467480876911897280514736397894033\ 4439418861153486093971102277709053240148679100537787706015404542882477518031150\ 7512792849538736258868378729050061498179939935515286224476956729019216259751065\ 9344172221480417380728071838206485766237047719388226870057955248034904729436042\ 3965452975546435965923512060364543656247645064581441441629126414419856339943545\ 6555661177804740383374933806564963330790173657719640382018256517481424719451427\ 2975916690208975446552459372535676086611352746576308920465974569069135485694329\ 9597936999872765640339461720684804230248616493578708683094626837319672824579855\ 8411773707157428357467695430175304805675211072413250214022802850362864893169063\ 2219204454316007151284426852825972260963242357735400326029330623286113904686258\ 1564414757331936463450880700726207729133964377287048422190875496936496771330382\ 0821792546078255985752273682824987297116690910201146867901570134632662088672935\ 7307360012758153634510273131831753983504565652674474497337222821031244641398568\ 0319449900821826588396853262756070417371280875872555965051646631219504609099594\ 2900307075450528109972595376566513608572819971656457097625815225984059485667378\ 2537727187437064561716145566746342807932919311923580476050976588757102480062616\ 2842539364063130903696735635426964026784982136304596501298587632495441945929306\ 8331909791582929734217416695840951308178222108276697863826750294715320855905320\ 1282614623630944753216629916605408604772564879827985584004814138182755264996172\ 6494380788361199554394817062672164399927130458554002654658742326882695972048786\ 2160846867017389964809522459540419303777433286255408230421361685587187198813746\ 3287383101417179965234882733347436514324151357460893887678993135794223315586076\ 5641772670491875321249721911521991382351150397763822981793757742096703069956918\ 4934299732961327077787526084198137198483779308976135294851609214231848315798075\ 9652288189796652512570920285523974587948847363527872010310236948704303622660138\ 8051950828181423482168215192899111319785586215047593319334994408206431817163152\ 8109612723199182438096033084331095823075091336259247533238381184089779205295366\ 8854871748703235011602781424901760828978924533510927228094307947697282760504743\ 8905177859837042871929962786075539329831190840968168531280128987165972334057104\ 2780988260318308431694111137520753199376101208475448197956249258872033509555448\ 1144882955494874197806782019992240192771126444263462979509942135302581497204515\ 8029877051831515195331131989453897948473381495592338567500841594061968873130213\ 0 ** WARNING: Output too long, hence truncated. ************** MAGMA ***************** Host 24-205-83-208.pas-eres.charterpipeline.net. (24.205.83.208) Time: Fri Jan 30 03:20:45 2004 Input: (9^(3^3))^(1/1024) Output: Magma V2.10-6 Fri Jan 30 2004 03:20:42 on modular [Seed = 3733228907] ------------------------------------- 1.059645726959167637839055 Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 24-205-83-208.pas-eres.charterpipeline.net. (24.205.83.208) Time: Fri Jan 30 03:21:05 2004 Input: (9^(3^3))^(1/64) Output: Magma V2.10-6 Fri Jan 30 2004 03:21:02 on modular [Seed = 2851338792] ------------------------------------- 2.526801108055887241647503 Total time: 2.889 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 24-205-83-208.pas-eres.charterpipeline.net. (24.205.83.208) Time: Fri Jan 30 03:21:18 2004 Input: (9^(9^3))^(1/64) Output: Magma V2.10-6 Fri Jan 30 2004 03:21:14 on modular [Seed = 3035555617] ------------------------------------- 74031846910.0753889797150712 Total time: 3.039 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 24-205-83-208.pas-eres.charterpipeline.net. (24.205.83.208) Time: Fri Jan 30 03:21:31 2004 Input: (9^(9^3))^(1/256) Output: Magma V2.10-6 Fri Jan 30 2004 03:21:28 on modular [Seed = 2663697145] ------------------------------------- 521.620493906283389063923557 Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 24-205-83-208.pas-eres.charterpipeline.net. (24.205.83.208) Time: Fri Jan 30 03:22:16 2004 Input: (9^(3^9))^(1/256) Output: Magma V2.10-6 Fri Jan 30 2004 03:22:13 on modular [Seed = 2133142330] ------------------------------------- 2.336551956192259300588926e73 Total time: 2.989 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 24-205-83-208.pas-eres.charterpipeline.net. (24.205.83.208) Time: Fri Jan 30 03:22:28 2004 Input: (9^(3^9))^(1/1024) Output: Magma V2.10-6 Fri Jan 30 2004 03:22:25 on modular [Seed = 1748122713] ------------------------------------- 2198588037458589676.92117443 Total time: 2.989 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 24-205-83-208.pas-eres.charterpipeline.net. (24.205.83.208) Time: Fri Jan 30 03:22:40 2004 Input: (9^(3^9))^(1/2048) Output: Magma V2.10-6 Fri Jan 30 2004 03:22:37 on modular [Seed = 1359676780] ------------------------------------- 1482763648.5490833872330278 Total time: 2.979 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 24-205-83-208.pas-eres.charterpipeline.net. (24.205.83.208) Time: Fri Jan 30 03:22:55 2004 Input: (9^(3^9))^(1/4096) Output: Magma V2.10-6 Fri Jan 30 2004 03:22:52 on modular [Seed = 1509953142] ------------------------------------- 38506.67018256815447689838 Total time: 2.989 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 24-205-83-208.pas-eres.charterpipeline.net. (24.205.83.208) Time: Fri Jan 30 03:32:02 2004 Input: (9^(3^(3^3)))^(2^-30) Output: Magma V2.10-6 Fri Jan 30 2004 03:31:59 on modular [Seed = 728857892] ------------------------------------- >> (9^(3^(3^3)))^(2^-30); ^ Runtime error in '^': Argument 2 (7625597484987) is too large Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 24-205-83-208.pas-eres.charterpipeline.net. (24.205.83.208) Time: Fri Jan 30 03:32:43 2004 Input: (3^(3^(3^3)))^(2^(-30)) Output: Magma V2.10-6 Fri Jan 30 2004 03:32:40 on modular [Seed = 340673228] ------------------------------------- >> (3^(3^(3^3)))^(2^(-30)); ^ Runtime error in '^': Argument 2 (7625597484987) is too large Total time: 2.889 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 24-205-83-208.pas-eres.charterpipeline.net. (24.205.83.208) Time: Fri Jan 30 03:33:07 2004 Input: (3^(3^(3^2)))^(2^(-30)) Output: Magma V2.10-6 Fri Jan 30 2004 03:33:04 on modular [Seed = 491211693] ------------------------------------- 1.00002013910880407665029 Total time: 2.919 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 24-205-83-208.pas-eres.charterpipeline.net. (24.205.83.208) Time: Fri Jan 30 03:33:17 2004 Input: (3^(3^(3^2)))^(2^(-20)) Output: Magma V2.10-6 Fri Jan 30 2004 03:33:14 on modular [Seed = 106713276] ------------------------------------- 1.020836347405948820338572 Total time: 2.929 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 24-205-83-208.pas-eres.charterpipeline.net. (24.205.83.208) Time: Fri Jan 30 03:33:30 2004 Input: (3^(3^(3^2)))^(2^(-16)) Output: Magma V2.10-6 Fri Jan 30 2004 03:33:27 on modular [Seed = 4037715543] ------------------------------------- 1.39090669931095587649339 Total time: 2.979 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 24-205-83-208.pas-eres.charterpipeline.net. (24.205.83.208) Time: Fri Jan 30 03:33:39 2004 Input: (3^(3^(3^2)))^(2^(-10)) Output: Magma V2.10-6 Fri Jan 30 2004 03:33:36 on modular [Seed = 4188254057] ------------------------------------- 1482763648.5490833872330278 Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 24-205-83-208.pas-eres.charterpipeline.net. (24.205.83.208) Time: Fri Jan 30 03:33:48 2004 Input: (3^(3^(3^2)))^(2^(-11)) Output: Magma V2.10-6 Fri Jan 30 2004 03:33:45 on modular [Seed = 3803755643] ------------------------------------- 38506.67018256815447689838 Total time: 3.029 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 24-205-83-208.pas-eres.charterpipeline.net. (24.205.83.208) Time: Fri Jan 30 03:34:19 2004 Input: (3^(2^(3^3)))^(2^(-11)) Output: ** WARNING: Computation used more memory than allowed. ** Magma V2.10-6 Fri Jan 30 2004 03:34:16 on modular [Seed = 3954293907] ------------------------------------- Current total memory usage: 65.6MB, failed memory request: 32.0MB System Error: User memory limit has been reached Total time: 2.909 seconds, Total memory usage: 68.80MB ************** MAGMA ***************** Host 24-205-83-208.pas-eres.charterpipeline.net. (24.205.83.208) Time: Fri Jan 30 03:34:46 2004 Input: (2^(2^(3^3)))^(2^(-11)) Output: Magma V2.10-6 Fri Jan 30 2004 03:34:30 on modular [Seed = 3566109618] ------------------------------------- 2.003529930406846464979072e19728 Total time: 15.789 seconds, Total memory usage: 18.47MB ************** MAGMA ***************** Host 24-205-83-208.pas-eres.charterpipeline.net. (24.205.83.208) Time: Fri Jan 30 03:35:11 2004 Input: (2^(2^(3^3)))^(2^(-16)) Output: Magma V2.10-6 Fri Jan 30 2004 03:34:54 on modular [Seed = 3716647555] ------------------------------------- 3.231700607131100730071488e616 Total time: 16.489 seconds, Total memory usage: 18.47MB ************** MAGMA ***************** Host 24-205-83-208.pas-eres.charterpipeline.net. (24.205.83.208) Time: Fri Jan 30 03:35:35 2004 Input: (2^(2^(3^3)))^(2^(-20)) Output: Magma V2.10-6 Fri Jan 30 2004 03:35:18 on modular [Seed = 3398475260] ------------------------------------- 3.40282366920938463463374607e38 Total time: 16.430 seconds, Total memory usage: 18.47MB ************** MAGMA ***************** Host 24-205-83-208.pas-eres.charterpipeline.net. (24.205.83.208) Time: Fri Jan 30 03:36:03 2004 Input: (2^(2^(3^3)))^(2^(-22)) Output: Magma V2.10-6 Fri Jan 30 2004 03:35:46 on modular [Seed = 3018450081] ------------------------------------- 4294967296 Total time: 16.359 seconds, Total memory usage: 18.47MB ************** MAGMA ***************** Host 24-205-83-208.pas-eres.charterpipeline.net. (24.205.83.208) Time: Fri Jan 30 03:36:34 2004 Input: (2^(2^(3^3)))^(2^(-24)) Output: Magma V2.10-6 Fri Jan 30 2004 03:36:17 on modular [Seed = 3186092620] ------------------------------------- 256 Total time: 16.489 seconds, Total memory usage: 18.47MB ************** MAGMA ***************** Host 24-205-83-208.pas-eres.charterpipeline.net. (24.205.83.208) Time: Fri Jan 30 03:36:46 2004 Input: (3^(2^(3^3)))^(2^(-24)) Output: ** WARNING: Computation used more memory than allowed. ** Magma V2.10-6 Fri Jan 30 2004 03:36:43 on modular [Seed = 2818437196] ------------------------------------- Current total memory usage: 65.6MB, failed memory request: 32.0MB System Error: User memory limit has been reached Total time: 3.049 seconds, Total memory usage: 68.80MB ************** MAGMA ***************** Host 24-205-83-208.pas-eres.charterpipeline.net. (24.205.83.208) Time: Fri Jan 30 03:37:00 2004 Input: (3^(2^(2^3)))^(2^(-24)) Output: Magma V2.10-6 Fri Jan 30 2004 03:36:57 on modular [Seed = 2429208393] ------------------------------------- 1.000016763633682393881167 Total time: 2.919 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 24-205-83-208.pas-eres.charterpipeline.net. (24.205.83.208) Time: Fri Jan 30 03:37:09 2004 Input: (3^(2^(2^3)))^(2^(-16)) Output: Magma V2.10-6 Fri Jan 30 2004 03:37:06 on modular [Seed = 2579746395] ------------------------------------- 1.004300675728873305270798 Total time: 2.999 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 24-205-83-208.pas-eres.charterpipeline.net. (24.205.83.208) Time: Fri Jan 30 03:37:19 2004 Input: (3^(2^(2^3)))^(2^(-12)) Output: Magma V2.10-6 Fri Jan 30 2004 03:37:16 on modular [Seed = 2195248462] ------------------------------------- 1.071075483072914469123248 Total time: 2.919 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 24-205-83-208.pas-eres.charterpipeline.net. (24.205.83.208) Time: Fri Jan 30 03:37:29 2004 Input: (3^(2^(2^3)))^(2^(-9)) Output: Magma V2.10-6 Fri Jan 30 2004 03:37:26 on modular [Seed = 2345786429] ------------------------------------- 1.732050807568877293527446 Total time: 2.939 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 24-205-83-208.pas-eres.charterpipeline.net. (24.205.83.208) Time: Fri Jan 30 03:37:41 2004 Input: (3^(2^(2^3)))^(2^(-5)) Output: Magma V2.10-6 Fri Jan 30 2004 03:37:38 on modular [Seed = 1966023382] ------------------------------------- 6560.999999999999999999999932 Total time: 2.939 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 24-205-83-208.pas-eres.charterpipeline.net. (24.205.83.208) Time: Fri Jan 30 03:40:15 2004 Input: (3^(2^(2^6)))^(2^(-10)) Output: Magma V2.10-6 Fri Jan 30 2004 03:40:12 on modular [Seed = 1698643320] ------------------------------------- >> (3^(2^(2^6)))^(2^(-10)); ^ Runtime error in '^': Argument 2 (18446744073709551616) is too large Total time: 2.909 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 24-205-83-208.pas-eres.charterpipeline.net. (24.205.83.208) Time: Fri Jan 30 03:40:36 2004 Input: (3^(3^(2^3)))^(2^(-10)) Output: Magma V2.10-6 Fri Jan 30 2004 03:40:33 on modular [Seed = 1815491740] ------------------------------------- 1140.312740848237585651407008 Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 24-205-83-208.pas-eres.charterpipeline.net. (24.205.83.208) Time: Fri Jan 30 03:41:58 2004 Input: (3^(3^(3^2)))^(2^(-10)) Output: Magma V2.10-6 Fri Jan 30 2004 03:41:55 on modular [Seed = 1443630836] ------------------------------------- 1482763648.5490833872330278 Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 24-205-83-208.pas-eres.charterpipeline.net. (24.205.83.208) Time: Fri Jan 30 03:42:10 2004 Input: (3^(3^(3^2)))^(2^(-12)) Output: Magma V2.10-6 Fri Jan 30 2004 03:42:07 on modular [Seed = 1092295151] ------------------------------------- 196.231165166413243913638815 Total time: 2.979 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 24-205-83-208.pas-eres.charterpipeline.net. (24.205.83.208) Time: Fri Jan 30 03:46:05 2004 Input: (3^(3^(3^3)))^(2^(-12)) Output: Magma V2.10-6 Fri Jan 30 2004 03:46:02 on modular [Seed = 1276515831] ------------------------------------- >> (3^(3^(3^3)))^(2^(-12)); ^ Runtime error in '^': Argument 2 (7625597484987) is too large Total time: 2.939 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 24-205-83-208.pas-eres.charterpipeline.net. (24.205.83.208) Time: Fri Jan 30 03:47:42 2004 Input: (3^(2^(3^3)))^(2^(-12)) Output: ** WARNING: Computation used more memory than allowed. ** Magma V2.10-6 Fri Jan 30 2004 03:47:39 on modular [Seed = 913075308] ------------------------------------- Current total memory usage: 65.6MB, failed memory request: 32.0MB System Error: User memory limit has been reached Total time: 2.859 seconds, Total memory usage: 68.80MB ************** MAGMA ***************** Host 24-205-83-208.pas-eres.charterpipeline.net. (24.205.83.208) Time: Fri Jan 30 03:48:01 2004 Input: (3^(2^(3^3)))^(2^(-20)) Output: ** WARNING: Computation used more memory than allowed. ** Magma V2.10-6 Fri Jan 30 2004 03:47:58 on modular [Seed = 561740654] ------------------------------------- Current total memory usage: 65.6MB, failed memory request: 32.0MB System Error: User memory limit has been reached Total time: 2.959 seconds, Total memory usage: 68.80MB ************** MAGMA ***************** Host 24-205-83-208.pas-eres.charterpipeline.net. (24.205.83.208) Time: Fri Jan 30 03:48:20 2004 Input: (3^(2^(3^2)))^(2^(-20)) Output: Magma V2.10-6 Fri Jan 30 2004 03:48:17 on modular [Seed = 678588936] ------------------------------------- 1.000536575686835002418113 Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 24-205-83-208.pas-eres.charterpipeline.net. (24.205.83.208) Time: Fri Jan 30 03:48:31 2004 Input: (3^(2^(3^2)))^(2^(-12)) Output: Magma V2.10-6 Fri Jan 30 2004 03:48:28 on modular [Seed = 323569982] ------------------------------------- 1.147202690439877089473059 Total time: 2.939 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 24-205-83-208.pas-eres.charterpipeline.net. (24.205.83.208) Time: Fri Jan 30 03:48:40 2004 Input: (3^(2^(3^2)))^(2^(-8)) Output: Magma V2.10-6 Fri Jan 30 2004 03:48:37 on modular [Seed = 440418318] ------------------------------------- 9 Total time: 2.919 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 24-205-83-208.pas-eres.charterpipeline.net. (24.205.83.208) Time: Fri Jan 30 03:49:01 2004 Input: (3^(2^(3^2)))^(2^(-6)) Output: Magma V2.10-6 Fri Jan 30 2004 03:48:58 on modular [Seed = 90136334] ------------------------------------- 6560.999999999999999999999954 Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host dhcpra25.sogang.ac.kr. (163.239.41.75) Time: Fri Jan 30 07:46:50 2004 Input: 2+3 Output: Magma V2.10-6 Fri Jan 30 2004 07:46:46 on modular [Seed = 2935274733] ------------------------------------- 5 Total time: 3.199 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host p6094-ipad86marunouchi.tokyo.ocn.ne.jp. (221.188.33.94) Time: Fri Jan 30 09:10:29 2004 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: Magma V2.10-6 Fri Jan 30 2004 09:10:26 on modular [Seed = 3904032076] ------------------------------------- Replace this by some code, then click [PARI] or [MAGMA]! Total time: 2.989 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host p6094-ipad86marunouchi.tokyo.ocn.ne.jp. (221.188.33.94) Time: Fri Jan 30 09:10:39 2004 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: Magma V2.10-6 Fri Jan 30 2004 09:10:36 on modular [Seed = 3515610235] ------------------------------------- Replace this by some code, then click [PARI] or [MAGMA]! Total time: 2.889 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Fri Jan 30 14:29:32 2004 Input: //Rubin/Silverberg mod 3 formula derivation for y^2=x^3-d^2*x in Magma R:=PolynomialRing(Integers()); W:=NumberField(z^2-2*z-2);w:=W![0,1]; R:=PolynomialRing(W); Y:=NumberField(y^2-(1+2*w)); y:=Y![0,1]; P:=PolynomialRing(Y,2); a:=(4-w)*y*d; g:=(1-w)*y*d; m:=18*y/d; un:=a*t+w; ud:=1+g*t; u:=un/ud; a4:=(1/m^2)*(1+g*t)^4*(-27*u*(u^3 + 8 )); a4; a6:=(1/m^3)*(1+g*t)^6*54*(u^6-20*u^3-8); a6; Output: Magma V2.10-6 Fri Jan 30 2004 14:29:29 on modular [Seed = 962841053] ------------------------------------- 27*$.1^4*$.2^6 - 18*$.1^2*$.2^4 - $.2^2 108*$.1^5*$.2^8 + 4*$.1*$.2^4 Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Fri Jan 30 18:02:07 2004 Input: //A combination mod 7 demo of E-level-raising and M-level-raising. //Program for Kraus mod 7 Elliptic curves : v:=487/512 ; k:=(49/54)*(v-1); print [ v, k ]; a4:=(7*k^3+7*k^2-19*k-16); a6:=-k^5+14*k^4+63*k^3+77*k^2+38*k+20; E:=EllipticCurve([0,1,0,a4,a6]); F:=QuadraticTwist(E,1/7); Conductor(F); G:=SimplifiedModel(F); G; Factorization(Numerator(Discriminant(G))); print []; //Program confirming M-level-raising formula for above: A:=SortDecomposition(NewformDecomposition(NewSubspace (CuspidalSubspace(ModularSymbols(185,2,+1))))); EllipticCurve(A[3]); for q in [1..36] do if IsPrime(q) and q ne 5 then print q; Factorization(Numerator(Evaluate(CharacteristicPolynomial( DualHeckeOperator(A[3],q)),(q+1)))); Factorization(Numerator(Evaluate(CharacteristicPolynomial( DualHeckeOperator(A[3],q)),-(q+1)))); end if; end for; Output: Magma V2.10-6 Fri Jan 30 2004 18:02:03 on modular [Seed = 2596288753] ------------------------------------- [ 487/512, -1225/27648 ] 15118015 Elliptic Curve defined by y^2 + y = x^3 - x^2 - 8901413362985*x + 10285544326980788148 over Rational Field [ <5, 4>, <11, 7>, <17, 7>, <19, 7>, <23, 7>, <37, 1> ] [] Elliptic Curve defined by y^2 + y = x^3 - x^2 - 5*x + 6 over Rational Field 2 [ <3, 1> ] [ <3, 1> ] 3 [ <5, 1> ] [ <3, 1> ] 7 [ <11, 1> ] [ <5, 1> ] 11 [ <17, 1> ] [ <7, 1> ] 13 [ <2, 1>, <5, 1> ] [ <2, 1>, <3, 2> ] 17 [ <2, 1>, <11, 1> ] [ <2, 1>, <7, 1> ] 19 [ <2, 2>, <7, 1> ] [ <2, 2>, <3, 1> ] 23 [ <2, 2>, <5, 1> ] [ <2, 2>, <7, 1> ] 29 [ <2, 1>, <13, 1> ] [ <2, 1>, <17, 1> ] 31 [ <2, 1>, <3, 1>, <5, 1> ] [ <2, 1>, <17, 1> ] Total time: 4.039 seconds, Total memory usage: 3.85MB ************** MAGMA ***************** Host adsl-64-161-26-182.dsl.sntc01.pacbell.net. (64.161.26.182) Time: Sat Jan 31 06:03:18 2004 Input: factor((Mod(1,2)*(x^1279-1))) Output: Magma V2.10-6 Sat Jan 31 2004 06:03:12 on modular [Seed = 3770362758] ------------------------------------- >> factor((Mod(1,2)*(x^1279-1))) ^ User error: Identifier 'x' has not been declared or assigned Total time: 3.069 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host p508B2E97.dip.t-dialin.net. (80.139.46.151) Time: Sat Jan 31 08:29:01 2004 Input: 1+1 Output: Magma V2.10-6 Sat Jan 31 2004 08:28:58 on modular [Seed = 1030148287] ------------------------------------- 2 Total time: 3.059 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host p508B2E97.dip.t-dialin.net. (80.139.46.151) Time: Sat Jan 31 08:29:23 2004 Input: 2^8 + 2^8 Output: Magma V2.10-6 Sat Jan 31 2004 08:29:20 on modular [Seed = 913169310] ------------------------------------- 512 Total time: 2.889 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host TYO111.gate.nec.co.jp. (202.32.8.233) Time: Mon Feb 2 00:48:52 2004 Input: 8^9; Output: Magma V2.10-6 Mon Feb 2 2004 00:48:49 on modular [Seed = 3348783985] ------------------------------------- 134217728 Total time: 2.929 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host TYO108.gate.nec.co.jp. (210.143.35.18) Time: Mon Feb 2 00:49:51 2004 Input: G:=Sym(4); x:=G!(1,2,3); Order(x); Output: Magma V2.10-6 Mon Feb 2 2004 00:49:48 on modular [Seed = 3448793414] ------------------------------------- 3 Total time: 2.979 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host mail.provigent.com. (62.219.165.202) Time: Mon Feb 2 02:21:20 2004 Input: sin(x) Output: Magma V2.10-6 Mon Feb 2 2004 02:21:17 on modular [Seed = 4221977070] ------------------------------------- >> sin(x); ^ User error: Identifier 'x' has not been declared or assigned Total time: 2.929 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host wessel.mat.dtu.dk. (130.225.84.3) Time: Mon Feb 2 04:31:23 2004 Input: F2:=FiniteField(2); F4:=ext; AllIrreduciblePolynomials(F4,4); Output: Magma V2.10-6 Mon Feb 2 2004 04:31:19 on modular [Seed = 3152405287] ------------------------------------- { $.1^4 + a*$.1^3 + $.1 + a^2, $.1^4 + a*$.1^3 + $.1^2 + a*$.1 + 1, $.1^4 + $.1^3 + a*$.1^2 + a^2, $.1^4 + a*$.1^3 + a^2*$.1^2 + a^2*$.1 + 1, $.1^4 + a*$.1^3 + a*$.1^2 + a^2*$.1 + a^2, $.1^4 + a*$.1^3 + $.1^2 + 1, $.1^4 + a*$.1^3 + a^2*$.1^2 + 1, $.1^4 + a^2*$.1^3 + a^2*$.1^2 + a*$.1 + 1, $.1^4 + a*$.1^3 + a*$.1^2 + a^2, $.1^4 + a^2*$.1^3 + a*$.1 + a^2, $.1^4 + a^2*$.1^3 + $.1^2 + a^2*$.1 + 1, $.1^4 + a^2*$.1^3 + a^2*$.1 + a^2, $.1^4 + $.1^2 + a*$.1 + 1, $.1^4 + a^2*$.1^3 + $.1^2 + 1, $.1^4 + a*$.1^2 + a*$.1 + a^2, $.1^4 + a^2*$.1^2 + a*$.1 + 1, $.1^4 + $.1^2 + a^2*$.1 + 1, $.1^4 + a*$.1^2 + a^2*$.1 + a^2, $.1^4 + $.1^3 + $.1^2 + a*$.1 + a, $.1^4 + a*$.1^3 + $.1^2 + $.1 + a, $.1^4 + $.1^3 + a^2*$.1^2 + a^2*$.1 + a, $.1^4 + $.1^3 + $.1^2 + a, $.1^4 + $.1^3 + a^2*$.1^2 + a, $.1^4 + a^2*$.1^3 + a^2*$.1^2 + a*$.1 + a, $.1^4 + a^2*$.1^3 + $.1^2 + a^2*$.1 + a, $.1^4 + a^2*$.1^2 + a*$.1 + a, $.1^4 + a^2*$.1^3 + a^2*$.1^2 + a, $.1^4 + $.1^3 + a*$.1^2 + $.1 + 1, $.1^4 + $.1^2 + a^2*$.1 + a, $.1^4 + a^2*$.1^2 + a^2*$.1 + a, $.1^4 + $.1^3 + a*$.1 + 1, $.1^4 + $.1^3 + $.1^2 + a^2*$.1 + a^2, $.1^4 + a*$.1^3 + $.1 + 1, $.1^4 + $.1^3 + a^2*$.1^2 + a^2*$.1 + a^2, $.1^4 + $.1^3 + a^2*$.1 + 1, $.1^4 + a*$.1^3 + $.1^2 + a*$.1 + a^2, $.1^4 + $.1^3 + $.1^2 + a^2, $.1^4 + a*$.1^3 + a^2*$.1^2 + a*$.1 + a^2, $.1^4 + a^2*$.1^3 + $.1^2 + $.1 + a^2, $.1^4 + a*$.1^3 + a*$.1^2 + a^2*$.1 + 1, $.1^4 + a^2*$.1^3 + $.1 + 1, $.1^4 + a^2*$.1^3 + a^2*$.1^2 + $.1 + a^2, $.1^4 + a^2*$.1^3 + a*$.1^2 + a*$.1 + 1, $.1^4 + a*$.1^3 + a^2*$.1^2 + a^2, $.1^4 + a^2*$.1^3 + a*$.1^2 + 1, $.1^4 + $.1^2 + a*$.1 + a^2, $.1^4 + a*$.1^2 + a^2*$.1 + 1, $.1^4 + a^2*$.1^2 + a^2*$.1 + a^2, $.1^4 + $.1^3 + $.1 + a, $.1^4 + $.1^3 + a*$.1^2 + a*$.1 + a, $.1^4 + a*$.1^3 + a*$.1^2 + $.1 + a, $.1^4 + a*$.1^3 + a*$.1 + a, $.1^4 + a^2*$.1^3 + $.1 + a, $.1^4 + a*$.1^3 + a^2*$.1 + a, $.1^4 + a^2*$.1^3 + a*$.1^2 + a^2*$.1 + a, $.1^4 + a*$.1^2 + a*$.1 + a, $.1^4 + a^2*$.1^3 + a*$.1^2 + a, $.1^4 + $.1^3 + a^2*$.1^2 + $.1 + 1, $.1^4 + $.1^3 + $.1 + a^2, $.1^4 + $.1^3 + a*$.1^2 + a*$.1 + a^2 } Total time: 3.079 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host wessel.mat.dtu.dk. (130.225.84.3) Time: Mon Feb 2 04:34:10 2004 Input: F2:=FiniteField(2); F4:=ext; (a^2+1)*a^2; Output: Magma V2.10-6 Mon Feb 2 2004 04:34:06 on modular [Seed = 2834755933] ------------------------------------- 1 Total time: 3.049 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host wessel.mat.dtu.dk. (130.225.84.3) Time: Mon Feb 2 04:36:17 2004 Input: F2:=FiniteField(2); F4:=ext; P:=PolynomialRing(F4); AllIrreduciblePolynomials(F4); Output: Magma V2.10-6 Mon Feb 2 2004 04:36:13 on modular [Seed = 2563162862] ------------------------------------- >> AllIrreduciblePolynomials(F4); ^ Runtime error in 'AllIrreduciblePolynomials': Bad argument types Argument types given: FldFin Total time: 2.939 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host wessel.mat.dtu.dk. (130.225.84.3) Time: Mon Feb 2 04:36:26 2004 Input: F2:=FiniteField(2); F4:=ext; P:=PolynomialRing(F4); AllIrreduciblePolynomials(F4,4); Output: Magma V2.10-6 Mon Feb 2 2004 04:36:23 on modular [Seed = 2546585083] ------------------------------------- { x^4 + a*x^3 + x + a^2, x^4 + a*x^3 + x^2 + a*x + 1, x^4 + x^3 + a*x^2 + a^2, x^4 + a*x^3 + a^2*x^2 + a^2*x + 1, x^4 + a*x^3 + a*x^2 + a^2*x + a^2, x^4 + a*x^3 + x^2 + 1, x^4 + a*x^3 + a^2*x^2 + 1, x^4 + a^2*x^3 + a^2*x^2 + a*x + 1, x^4 + a*x^3 + a*x^2 + a^2, x^4 + a^2*x^3 + a*x + a^2, x^4 + a^2*x^3 + x^2 + a^2*x + 1, x^4 + a^2*x^3 + a^2*x + a^2, x^4 + x^2 + a*x + 1, x^4 + a^2*x^3 + x^2 + 1, x^4 + a*x^2 + a*x + a^2, x^4 + a^2*x^2 + a*x + 1, x^4 + x^2 + a^2*x + 1, x^4 + a*x^2 + a^2*x + a^2, x^4 + x^3 + x^2 + a*x + a, x^4 + a*x^3 + x^2 + x + a, x^4 + x^3 + a^2*x^2 + a^2*x + a, x^4 + x^3 + x^2 + a, x^4 + x^3 + a^2*x^2 + a, x^4 + a^2*x^3 + a^2*x^2 + a*x + a, x^4 + a^2*x^3 + x^2 + a^2*x + a, x^4 + a^2*x^2 + a*x + a, x^4 + a^2*x^3 + a^2*x^2 + a, x^4 + x^3 + a*x^2 + x + 1, x^4 + x^2 + a^2*x + a, x^4 + a^2*x^2 + a^2*x + a, x^4 + x^3 + a*x + 1, x^4 + x^3 + x^2 + a^2*x + a^2, x^4 + a*x^3 + x + 1, x^4 + x^3 + a^2*x^2 + a^2*x + a^2, x^4 + x^3 + a^2*x + 1, x^4 + a*x^3 + x^2 + a*x + a^2, x^4 + x^3 + x^2 + a^2, x^4 + a*x^3 + a^2*x^2 + a*x + a^2, x^4 + a^2*x^3 + x^2 + x + a^2, x^4 + a*x^3 + a*x^2 + a^2*x + 1, x^4 + a^2*x^3 + x + 1, x^4 + a^2*x^3 + a^2*x^2 + x + a^2, x^4 + a^2*x^3 + a*x^2 + a*x + 1, x^4 + a*x^3 + a^2*x^2 + a^2, x^4 + a^2*x^3 + a*x^2 + 1, x^4 + x^2 + a*x + a^2, x^4 + a*x^2 + a^2*x + 1, x^4 + a^2*x^2 + a^2*x + a^2, x^4 + x^3 + x + a, x^4 + x^3 + a*x^2 + a*x + a, x^4 + a*x^3 + a*x^2 + x + a, x^4 + a*x^3 + a*x + a, x^4 + a^2*x^3 + x + a, x^4 + a*x^3 + a^2*x + a, x^4 + a^2*x^3 + a*x^2 + a^2*x + a, x^4 + a*x^2 + a*x + a, x^4 + a^2*x^3 + a*x^2 + a, x^4 + x^3 + a^2*x^2 + x + 1, x^4 + x^3 + x + a^2, x^4 + x^3 + a*x^2 + a*x + a^2 } Total time: 3.009 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host wessel.mat.dtu.dk. (130.225.84.3) Time: Mon Feb 2 04:40:26 2004 Input: F2:=FiniteField(2); F16:=ext; P:=PolynomialRing(F16); AllIrreduciblePolynomials(F16,2); Output: Magma V2.10-6 Mon Feb 2 2004 04:40:22 on modular [Seed = 2262359547] ------------------------------------- { x^2 + a^4*x + a^14, x^2 + a*x + a^5, x^2 + a^2*x + a^11, x^2 + a^10*x + a^4, x^2 + a^11*x + a^10, x^2 + a*x + a^8, x^2 + a^9*x + a^9, x^2 + a^3*x + a^5, x^2 + a^11*x + a^4, x^2 + a^4*x + a^11, x^2 + a^4*x + a^5, x^2 + a^13*x + a^10, x^2 + a^2*x + a^2, x^2 + a^10*x + a^3, x^2 + a^8*x + a^14, x^2 + a^6*x + a^11, x^2 + a^14*x + a^10, x^2 + a^3*x + a^2, x^2 + a^11*x + a^3, x^2 + a^9*x + a^14, x^2 + a^14*x + a^4, x^2 + a^7*x + a^11, x^2 + a^4*x + a^2, x^2 + a^12*x + a^3, x^2 + a^5*x + a^8, x^2 + a^13*x + a^9, x^2 + a^10*x + a^14, x^2 + a^7*x + a^5, x^2 + a^8*x + a^13, x^2 + x + a^12, x^2 + a^13*x + a^3, x^2 + a^5*x + a^2, x^2 + a^14*x + a^9, x^2 + a^6*x + a^8, x^2 + a^11*x + a^14, x^2 + x + a^6, x^2 + a^8*x + a^7, x^2 + a^7*x + a^8, x^2 + a^7*x + a^2, x^2 + a^8*x + a^8, x^2 + x + a^9, x^2 + a^13*x + a^14, x^2 + a^3*x + a^12, x^2 + a^11*x + a^13, x^2 + x + a^3, x^2 + a*x + a^9, x^2 + a^9*x + a^2, x^2 + a^10*x + a^8, x^2 + a^4*x + a^6, x^2 + a^12*x + a^7, x^2 + a^2*x + a^3, x^2 + a^10*x + a^2, x^2 + a^3*x + a^9, x^2 + a^13*x + a^7, x^2 + a^5*x + a^6, x^2 + a^3*x + a^3, x^2 + a^12*x + a^8, x^2 + a*x + 1, x^2 + a^9*x + a, x^2 + a^6*x + a^6, x^2 + a^14*x + a^7, x^2 + a^7*x + a^12, x^2 + a^5*x + a^9, x^2 + a^13*x + a^8, x^2 + a^10*x + a, x^2 + a^2*x + 1, x^2 + a^7*x + a^6, x^2 + a^8*x + a^12, x^2 + x + a^13, x^2 + a^13*x + a^2, x^2 + a^6*x + a^9, x^2 + a^3*x + 1, x^2 + a^11*x + a, x^2 + x + a^7, x^2 + a*x + a^13, x^2 + a^9*x + a^12, x^2 + a^6*x + a^3, x^2 + a^4*x + 1, x^2 + a^12*x + a, x^2 + a^9*x + a^6, x^2 + a^10*x + a^12, x^2 + a^2*x + a^13, x^2 + a^2*x + a^7, x^2 + a^3*x + a^13, x^2 + a^6*x + 1, x^2 + a^14*x + a, x^2 + a^11*x + a^6, x^2 + a^12*x + a^12, x^2 + a^10*x + a^11, x^2 + a^2*x + a^10, x^2 + a^4*x + a^7, x^2 + a^12*x + a^6, x^2 + a^5*x + a^13, x^2 + a^8*x + 1, x^2 + a^5*x + a^7, x^2 + a^14*x + a^12, x^2 + a^3*x + a^4, x^2 + a^11*x + a^5, x^2 + a^9*x + 1, x^2 + a*x + a, x^2 + a^7*x + a^13, x^2 + a^12*x + a^5, x^2 + a^4*x + a^4, x^2 + a^2*x + a, x^2 + x + a^14, x^2 + a^5*x + a^4, x^2 + a^13*x + a^5, x^2 + a^6*x + a^10, x^2 + a^14*x + a^11, x^2 + a*x + a^14, x^2 + a^6*x + a^4, x^2 + a^14*x + a^5, x^2 + a^7*x + a^10, x^2 + a^12*x + 1, x^2 + x + a^11, x^2 + a^8*x + a^10, x^2 + a^5*x + a, x^2 + a^8*x + a^4, x^2 + a^9*x + a^10, x^2 + a*x + a^11 } Total time: 3.169 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host wessel.mat.dtu.dk. (130.225.84.3) Time: Mon Feb 2 04:42:17 2004 Input: F2:=FiniteField(2); F16:=ext; a^4; Output: Magma V2.10-6 Mon Feb 2 2004 04:42:14 on modular [Seed = 2066030705] ------------------------------------- a^4 Total time: 2.979 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host wessel.mat.dtu.dk. (130.225.84.3) Time: Mon Feb 2 04:42:44 2004 Input: F2:=FiniteField(2); F16:=ext; a^4*a; Output: Magma V2.10-6 Mon Feb 2 2004 04:42:41 on modular [Seed = 1815230337] ------------------------------------- a^5 Total time: 2.919 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host wessel.mat.dtu.dk. (130.225.84.3) Time: Mon Feb 2 04:45:32 2004 Input: F2:=FiniteField(2); F16:=ext; P:=PolynomialRing(F16); DefiningPolynomial(F16); AllIrreduciblePolynomials(F16,2); Output: Magma V2.10-6 Mon Feb 2 2004 04:45:29 on modular [Seed = 1664958246] ------------------------------------- $.1^4 + $.1 + 1 { x^2 + a^4*x + a^14, x^2 + a*x + a^5, x^2 + a^2*x + a^11, x^2 + a^10*x + a^4, x^2 + a^11*x + a^10, x^2 + a*x + a^8, x^2 + a^9*x + a^9, x^2 + a^3*x + a^5, x^2 + a^11*x + a^4, x^2 + a^4*x + a^11, x^2 + a^4*x + a^5, x^2 + a^13*x + a^10, x^2 + a^2*x + a^2, x^2 + a^10*x + a^3, x^2 + a^8*x + a^14, x^2 + a^6*x + a^11, x^2 + a^14*x + a^10, x^2 + a^3*x + a^2, x^2 + a^11*x + a^3, x^2 + a^9*x + a^14, x^2 + a^14*x + a^4, x^2 + a^7*x + a^11, x^2 + a^4*x + a^2, x^2 + a^12*x + a^3, x^2 + a^5*x + a^8, x^2 + a^13*x + a^9, x^2 + a^10*x + a^14, x^2 + a^7*x + a^5, x^2 + a^8*x + a^13, x^2 + x + a^12, x^2 + a^13*x + a^3, x^2 + a^5*x + a^2, x^2 + a^14*x + a^9, x^2 + a^6*x + a^8, x^2 + a^11*x + a^14, x^2 + x + a^6, x^2 + a^8*x + a^7, x^2 + a^7*x + a^8, x^2 + a^7*x + a^2, x^2 + a^8*x + a^8, x^2 + x + a^9, x^2 + a^13*x + a^14, x^2 + a^3*x + a^12, x^2 + a^11*x + a^13, x^2 + x + a^3, x^2 + a*x + a^9, x^2 + a^9*x + a^2, x^2 + a^10*x + a^8, x^2 + a^4*x + a^6, x^2 + a^12*x + a^7, x^2 + a^2*x + a^3, x^2 + a^10*x + a^2, x^2 + a^3*x + a^9, x^2 + a^13*x + a^7, x^2 + a^5*x + a^6, x^2 + a^3*x + a^3, x^2 + a^12*x + a^8, x^2 + a*x + 1, x^2 + a^9*x + a, x^2 + a^6*x + a^6, x^2 + a^14*x + a^7, x^2 + a^7*x + a^12, x^2 + a^5*x + a^9, x^2 + a^13*x + a^8, x^2 + a^10*x + a, x^2 + a^2*x + 1, x^2 + a^7*x + a^6, x^2 + a^8*x + a^12, x^2 + x + a^13, x^2 + a^13*x + a^2, x^2 + a^6*x + a^9, x^2 + a^3*x + 1, x^2 + a^11*x + a, x^2 + x + a^7, x^2 + a*x + a^13, x^2 + a^9*x + a^12, x^2 + a^6*x + a^3, x^2 + a^4*x + 1, x^2 + a^12*x + a, x^2 + a^9*x + a^6, x^2 + a^10*x + a^12, x^2 + a^2*x + a^13, x^2 + a^2*x + a^7, x^2 + a^3*x + a^13, x^2 + a^6*x + 1, x^2 + a^14*x + a, x^2 + a^11*x + a^6, x^2 + a^12*x + a^12, x^2 + a^10*x + a^11, x^2 + a^2*x + a^10, x^2 + a^4*x + a^7, x^2 + a^12*x + a^6, x^2 + a^5*x + a^13, x^2 + a^8*x + 1, x^2 + a^5*x + a^7, x^2 + a^14*x + a^12, x^2 + a^3*x + a^4, x^2 + a^11*x + a^5, x^2 + a^9*x + 1, x^2 + a*x + a, x^2 + a^7*x + a^13, x^2 + a^12*x + a^5, x^2 + a^4*x + a^4, x^2 + a^2*x + a, x^2 + x + a^14, x^2 + a^5*x + a^4, x^2 + a^13*x + a^5, x^2 + a^6*x + a^10, x^2 + a^14*x + a^11, x^2 + a*x + a^14, x^2 + a^6*x + a^4, x^2 + a^14*x + a^5, x^2 + a^7*x + a^10, x^2 + a^12*x + 1, x^2 + x + a^11, x^2 + a^8*x + a^10, x^2 + a^5*x + a, x^2 + a^8*x + a^4, x^2 + a^9*x + a^10, x^2 + a*x + a^11 } Total time: 2.949 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host cache4.nottingham.ac.uk. (128.243.220.42) Time: Mon Feb 2 06:17:36 2004 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: Magma V2.10-6 Mon Feb 2 2004 06:17:32 on modular [Seed = 2178936881] ------------------------------------- Replace this by some code, then click [PARI] or [MAGMA]! Total time: 2.999 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host cache4.nottingham.ac.uk. (128.243.220.42) Time: Mon Feb 2 06:18:04 2004 Input: d:=2 Output: Magma V2.10-6 Mon Feb 2 2004 06:18:01 on modular [Seed = 2066025196] ------------------------------------- Total time: 2.889 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host cache4.nottingham.ac.uk. (128.243.220.42) Time: Mon Feb 2 06:18:31 2004 Input: d; Output: Magma V2.10-6 Mon Feb 2 2004 06:18:28 on modular [Seed = 1915486219] ------------------------------------- >> d;; ^ User error: Identifier 'd' has not been declared or assigned Total time: 2.889 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host cache4.nottingham.ac.uk. (128.243.220.42) Time: Mon Feb 2 06:19:50 2004 Input: Q:=Rationals(); QT:=FunctionField(Q); EC:=EllipticCurve([QT|0,0,0,T^2,-1]); EC; Output: Magma V2.10-6 Mon Feb 2 2004 06:19:47 on modular [Seed = 1698371403] ------------------------------------- Elliptic Curve defined by y^2 = x^3 + T^2*x - 1 over Univariate rational function field over Rational Field Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (212.201.49.123) Time: Mon Feb 2 10:43:09 2004 Input: Rationals() Output: Magma V2.10-6 Mon Feb 2 2004 10:43:05 on modular [Seed = 3770601622] ------------------------------------- Rational Field Total time: 2.919 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host cass25.ast.cam.ac.uk. (131.111.68.94) Time: Mon Feb 2 12:03:09 2004 Input: help; Output: Magma V2.10-6 Mon Feb 2 2004 12:03:06 on modular [Seed = 1159432079] ------------------------------------- >> help;; ^ User error: Identifier 'help' has not been declared or assigned Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host cass25.ast.cam.ac.uk. (131.111.68.94) Time: Mon Feb 2 12:03:19 2004 Input: help Output: Magma V2.10-6 Mon Feb 2 2004 12:03:16 on modular [Seed = 1309707418] ------------------------------------- >> help; ^ User error: Identifier 'help' has not been declared or assigned Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host cache-dl09.proxy.aol.com. (205.188.209.45) Time: Mon Feb 2 21:34:02 2004 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: Magma V2.10-6 Mon Feb 2 2004 21:33:59 on modular [Seed = 56380305] ------------------------------------- Replace this by some code, then click [PARI] or [MAGMA]! Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host genoa.ucc.usyd.edu.au. (129.78.228.114) Time: Mon Feb 2 23:20:24 2004 Input: cos^2 + sin^2 Output: Magma V2.10-6 Mon Feb 2 2004 23:20:21 on modular [Seed = 3971190124] ------------------------------------- >> cos^2 + sin^2; ^ User error: Identifier 'cos' has not been declared or assigned Total time: 3.039 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host wessel.mat.dtu.dk. (130.225.84.3) Time: Tue Feb 3 04:52:15 2004 Input: F2:=GF(2); F4:=ext; P:=PolynomialRing(F4); AllIrreduciblePolynomials(F4,2); Output: Magma V2.10-6 Tue Feb 3 2004 04:52:12 on modular [Seed = 2446245591] ------------------------------------- { x^2 + a^2*x + a^2, x^2 + a^2*x + 1, x^2 + a*x + a, x^2 + x + a^2, x^2 + a*x + 1, x^2 + x + a } Total time: 3.079 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host c-24-17-30-82.client.comcast.net. (24.17.30.82) Time: Tue Feb 3 06:23:51 2004 Input: 2^((2^64 - 258)/2) mod (2^64 - 257) Output: Magma V2.10-6 Tue Feb 3 2004 06:23:47 on modular [Seed = 1276348547] ------------------------------------- Runtime error: Overflow in real computation Total time: 3.009 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host amande.loria.fr. (152.81.8.166) Time: Tue Feb 3 07:09:04 2004 Input: Q:=RationalField(); P3:=ProjectiveSpace(Q,3); V:=Scheme(P3,2*X2+3*Y2-5*Z2-7*W2); IsLocallySolvable(V,2); Output: Magma V2.10-6 Tue Feb 3 2004 07:09:00 on modular [Seed = 2918343421] ------------------------------------- >> V:=Scheme(P3,2*X2+3*Y2-5*Z2-7*W2); ^ User error: Identifier 'X2' has not been declared or assigned >> IsLocallySolvable(V,2); ; ^ User error: Identifier 'V' has not been declared or assigned Total time: 3.029 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host amande.loria.fr. (152.81.8.166) Time: Tue Feb 3 07:09:33 2004 Input: Q:=RationalField(); P3:=ProjectiveSpace(Q,3); V:=Scheme(P3,2*X^2+3*Y^2-5*Z^2-7*W^2); IsLocallySolvable(V,2); Output: Magma V2.10-6 Tue Feb 3 2004 07:09:29 on modular [Seed = 2818074833] ------------------------------------- true (1 + O(2^50) : 1 + O(2^2) : 1 + O(2^2) : O(2^2)) Total time: 3.009 seconds, Total memory usage: 2.11MB ************** MAGMA ***************** Host amande.loria.fr. (152.81.8.166) Time: Tue Feb 3 07:10:03 2004 Input: Q:=RationalField(); P3:=ProjectiveSpace(Q,3); V:=Scheme(P3,2*X^2+3*Y^2-5*Z^2-7*W^2); IsLocallySolvable(V,2); IsLocallySolvable(V,3); IsLocallySolvable(V,5); IsLocallySolvable(V,7); Output: Magma V2.10-6 Tue Feb 3 2004 07:10:00 on modular [Seed = 3085465635] ------------------------------------- true (1 + O(2^50) : 1 + O(2^2) : 1 + O(2^2) : O(2^2)) true (1 + O(3^50) : O(3) : 1 + O(3) : O(3)) true (1 + O(5^50) : 1 + O(5) : O(5) : O(5)) true (-3 + O(7) : 1 + O(7^50) : O(7) : O(7)) Total time: 3.119 seconds, Total memory usage: 2.31MB ************** MAGMA ***************** Host zmd1.math3.us.edu.pl. (155.158.26.81) Time: Tue Feb 3 07:17:26 2004 Input: 1+2 Output: Magma V2.10-6 Tue Feb 3 2004 07:17:23 on modular [Seed = 3532456845] ------------------------------------- 3 Total time: 2.919 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host zmd1.math3.us.edu.pl. (155.158.26.81) Time: Tue Feb 3 07:19:29 2004 Input: Solve(x^2-3*x+2=0) Output: Magma V2.10-6 Tue Feb 3 2004 07:19:25 on modular [Seed = 4171704634] ------------------------------------- >> Solve(x^2-3*x+2=0); ^ User error: Identifier 'x' has not been declared or assigned Total time: 3.019 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (61.0.177.45) Time: Tue Feb 3 08:47:13 2004 Input: 3*4 Output: Magma V2.10-6 Tue Feb 3 2004 08:47:10 on modular [Seed = 2734507249] ------------------------------------- 12 Total time: 2.989 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host amande.loria.fr. (152.81.8.166) Time: Tue Feb 3 10:51:20 2004 Input: Q:=RationalField(); P3:=ProjectiveSpace(Q,3); V:=Scheme(P3,2*X^2+6*Y^2-267*Z^2-81613*W^2); IsLocallySolvable(V,2); IsLocallySolvable(V,3); IsLocallySolvable(V,5); IsLocallySolvable(V,7); Output: Magma V2.10-6 Tue Feb 3 2004 10:51:15 on modular [Seed = 3582613160] ------------------------------------- true (1 + O(2^50) : 1 + O(2^2) : 1 + O(2^2) : 1 + O(2^2)) true (O(3^3) : -2 + O(3^2) : 1 + O(3^50) : O(3^2)) true (1 + O(5^50) : 1 + O(5) : O(5) : 1 + O(5)) true (-2 + O(7) : 1 + O(7^50) : O(7) : O(7)) Total time: 3.149 seconds, Total memory usage: 2.31MB ************** MAGMA ***************** Host amande.loria.fr. (152.81.8.166) Time: Tue Feb 3 10:57:20 2004 Input: Q:=RationalField(); P3:=ProjectiveSpace(Q,3); V:=Scheme(P3,2*X^2+6*Y^2-267*Z^2-81613*W^2); IsLocallySolvable(V,3); IsLocallySolvable(V,7); IsLocallySolvable(V,89); IsLocallySolvable(V,131); Output: Magma V2.10-6 Tue Feb 3 2004 10:57:16 on modular [Seed = 3770639410] ------------------------------------- true (O(3^3) : -2 + O(3^2) : 1 + O(3^50) : O(3^2)) true (-2 + O(7) : 1 + O(7^50) : O(7) : O(7)) true (O(89^2) : O(89^2) : -13 + O(89) : 1 + O(89^50)) true (-65 + O(131) : 19 + O(131) : 1 + O(131^50) : O(131)) Total time: 3.729 seconds, Total memory usage: 6.44MB ************** MAGMA ***************** Host amande.loria.fr. (152.81.8.166) Time: Tue Feb 3 10:57:58 2004 Input: Q:=RationalField(); P3:=ProjectiveSpace(Q,3); V:=Scheme(P3,2*X^2+6*Y^2-267*Z^2-81613*W^2); IsLocallySolvable(V,3); IsLocallySolvable(V,7); IsLocallySolvable(V,89); IsLocallySolvable(V,131); IsLocallySolvable(V,2); Output: Magma V2.10-6 Tue Feb 3 2004 10:57:54 on modular [Seed = 4088166143] ------------------------------------- true (O(3^3) : -2 + O(3^2) : 1 + O(3^50) : O(3^2)) true (-2 + O(7) : 1 + O(7^50) : O(7) : O(7)) true (O(89^2) : O(89^2) : -13 + O(89) : 1 + O(89^50)) true (-65 + O(131) : 19 + O(131) : 1 + O(131^50) : O(131)) true (1 + O(2^50) : 1 + O(2^2) : 1 + O(2^2) : 1 + O(2^2)) Total time: 3.669 seconds, Total memory usage: 6.44MB ************** MAGMA ***************** Host amande.loria.fr. (152.81.8.166) Time: Tue Feb 3 12:37:00 2004 Input: Q:=RationalField(); P3:=ProjectiveSpace(Q,3); V:=Scheme(P3,2*X^2+6*Y^2-267*Z^2-81613*W^2); IsLocallySolvable(V,3); IsLocallySolvable(V,7); IsLocallySolvable(V,89); IsLocallySolvable(V,133); IsLocallySolvable(V,2); Output: Magma V2.10-6 Tue Feb 3 2004 12:36:57 on modular [Seed = 424052016] ------------------------------------- true (O(3^3) : -2 + O(3^2) : 1 + O(3^50) : O(3^2)) true (-2 + O(7) : 1 + O(7^50) : O(7) : O(7)) true (O(89^2) : O(89^2) : -13 + O(89) : 1 + O(89^50)) >> IsLocallySolvable(V,133); ^ Runtime error in 'IsLocallySolvable': p must be prime true (1 + O(2^50) : 1 + O(2^2) : 1 + O(2^2) : 1 + O(2^2)) Total time: 3.369 seconds, Total memory usage: 6.44MB ************** MAGMA ***************** Host amande.loria.fr. (152.81.8.166) Time: Tue Feb 3 12:37:22 2004 Input: Q:=RationalField(); P3:=ProjectiveSpace(Q,3); V:=Scheme(P3,2*X^2+6*Y^2-267*Z^2-81613*W^2); IsLocallySolvable(V,3); IsLocallySolvable(V,7); IsLocallySolvable(V,89); IsLocallySolvable(V,131); IsLocallySolvable(V,2); Output: Magma V2.10-6 Tue Feb 3 2004 12:37:17 on modular [Seed = 39689820] ------------------------------------- true (O(3^3) : -2 + O(3^2) : 1 + O(3^50) : O(3^2)) true (-2 + O(7) : 1 + O(7^50) : O(7) : O(7)) true (O(89^2) : O(89^2) : -13 + O(89) : 1 + O(89^50)) true (-65 + O(131) : 19 + O(131) : 1 + O(131^50) : O(131)) true (1 + O(2^50) : 1 + O(2^2) : 1 + O(2^2) : 1 + O(2^2)) Total time: 3.739 seconds, Total memory usage: 6.44MB ************** MAGMA ***************** Host amande.loria.fr. (152.81.8.166) Time: Tue Feb 3 12:46:52 2004 Input: Q:=RationalField(); P3:=ProjectiveSpace(Q,3); V:=Scheme(P3,1985603095*X^2+13769004378196145*Y^2-34*Z^2-23086*W^2); IsLocallySolvable(V,3); IsLocallySolvable(V,7); IsLocallySolvable(V,5); IsLocallySolvable(V,13); IsLocallySolvable(V,2); Output: Magma V2.10-6 Tue Feb 3 2004 12:46:49 on modular [Seed = 1046585511] ------------------------------------- true (1 + O(3^50) : 1 + O(3) : O(3) : O(3)) true (1 + O(7^50) : O(7^2) : O(7^2) : 1 + O(7^2)) true (1 + O(5^50) : O(5) : 1 + O(5) : 1 + O(5)) true (1 + O(13^50) : O(13) : 1 + O(13) : O(13)) true (1 + O(2^50) : 1 + O(2^2) : O(2^2) : O(2^2)) Total time: 3.079 seconds, Total memory usage: 2.41MB ************** MAGMA ***************** Host amande.loria.fr. (152.81.8.166) Time: Tue Feb 3 12:47:36 2004 Input: Q:=RationalField(); P3:=ProjectiveSpace(Q,3); V:=Scheme(P3,1985603095*X^2+13769004378196145*Y^2-34*Z^2-23086*W^2); IsLocallySolvable(V,17); IsLocallySolvable(V,97); IsLocallySolvable(V,191); IsLocallySolvable(V,199); IsLocallySolvable(V,1327); Output: ** WARNING: Computation used more memory than allowed. ** Magma V2.10-6 Tue Feb 3 2004 12:47:18 on modular [Seed = 662223249] ------------------------------------- true (1 + O(17^50) : 1 + O(17) : O(17) : O(17)) true (1 + O(97^50) : 32 + O(97) : 1 + O(97) : O(97)) true (82 + O(191) : O(191) : 1 + O(191^50) : O(191)) true (1 + O(199^50) : O(199) : 52 + O(199) : 1 + O(199)) Current total memory usage: 91.7MB, failed memory request: 4.9MB System Error: User memory limit has been reached Total time: 18.649 seconds, Total memory usage: 96.21MB ************** MAGMA ***************** Host amande.loria.fr. (152.81.8.166) Time: Tue Feb 3 12:48:01 2004 Input: Q:=RationalField(); P3:=ProjectiveSpace(Q,3); V:=Scheme(P3,1985603095*X^2+13769004378196145*Y^2-34*Z^2-23086*W^2); IsLocallySolvable(V,17); IsLocallySolvable(V,97); IsLocallySolvable(V,191); Output: Magma V2.10-6 Tue Feb 3 2004 12:47:57 on modular [Seed = 1343213197] ------------------------------------- true (1 + O(17^50) : 1 + O(17) : O(17) : O(17)) true (1 + O(97^50) : 32 + O(97) : 1 + O(97) : O(97)) true (82 + O(191) : O(191) : 1 + O(191^50) : O(191)) Total time: 4.069 seconds, Total memory usage: 11.18MB ************** MAGMA ***************** Host amande.loria.fr. (152.81.8.166) Time: Tue Feb 3 12:48:15 2004 Input: Q:=RationalField(); P3:=ProjectiveSpace(Q,3); V:=Scheme(P3,1985603095*X^2+13769004378196145*Y^2-34*Z^2-23086*W^2); IsLocallySolvable(V,199); Output: Magma V2.10-6 Tue Feb 3 2004 12:48:11 on modular [Seed = 1510327441] ------------------------------------- true (1 + O(199^50) : O(199) : 52 + O(199) : 1 + O(199)) Total time: 4.239 seconds, Total memory usage: 22.21MB ************** MAGMA ***************** Host amande.loria.fr. (152.81.8.166) Time: Tue Feb 3 12:50:44 2004 Input: Q:=RationalField(); P3:=ProjectiveSpace(Q,3); V:=Scheme(P3,1985603095*X^2+13769004378196145*Y^2-34*Z^2-23086*W^2); IsLocallySolvable(V,1327); Output: ** WARNING: Computation used more memory than allowed. ** Magma V2.10-6 Tue Feb 3 2004 12:50:28 on modular [Seed = 1259656255] ------------------------------------- Current total memory usage: 92.8MB, failed memory request: 3.6MB System Error: User memory limit has been reached Total time: 16.209 seconds, Total memory usage: 97.36MB ************** MAGMA ***************** Host amande.loria.fr. (152.81.8.166) Time: Tue Feb 3 12:51:08 2004 Input: Q:=RationalField(); P3:=ProjectiveSpace(Q,3); V:=Scheme(P3,1985603095*X^2+13769004378196145*Y^2-34*Z^2-23086*W^2); IsLocallySolvable(V,1327); Output: ** WARNING: Computation used more memory than allowed. ** Magma V2.10-6 Tue Feb 3 2004 12:50:52 on modular [Seed = 1949035288] ------------------------------------- Current total memory usage: 92.8MB, failed memory request: 3.6MB System Error: User memory limit has been reached Total time: 16.170 seconds, Total memory usage: 97.36MB ************** MAGMA ***************** Host finotti.math.ucsb.edu. (128.111.88.112) Time: Tue Feb 3 12:54:05 2004 Input: P:=PolynomailRing(GF(5)); (x+2)^125; Output: Magma V2.10-6 Tue Feb 3 2004 12:54:01 on modular [Seed = 2132860757] ------------------------------------- >> P:=PolynomailRing(GF(5)); ^ User error: Identifier 'PolynomailRing' has not been declared or assigned >> (x+2)^125;; ^ User error: Identifier 'x' has not been declared or assigned Total time: 3.059 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host finotti.math.ucsb.edu. (128.111.88.112) Time: Tue Feb 3 12:54:22 2004 Input: P:=PolynomialRing(GF(5)); (x+2)^125; Output: Magma V2.10-6 Tue Feb 3 2004 12:54:19 on modular [Seed = 1748486195] ------------------------------------- x^125 + 2 Total time: 3.069 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host user-vc8frgq.biz.mindspring.com. (216.135.238.26) Time: Tue Feb 3 14:29:14 2004 Input: gamma[3i] Output: Magma V2.10-6 Tue Feb 3 2004 14:29:10 on modular [Seed = 3035300387] ------------------------------------- >> gamma[3i]; ^ User error: bad syntax Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host user-vc8frgq.biz.mindspring.com. (216.135.238.26) Time: Tue Feb 3 14:29:28 2004 Input: gamma[3*i] Output: Magma V2.10-6 Tue Feb 3 2004 14:29:25 on modular [Seed = 3219130683] ------------------------------------- >> gamma[3*i]; ^ User error: Identifier 'gamma' has not been declared or assigned Total time: 2.939 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host user-vc8frgq.biz.mindspring.com. (216.135.238.26) Time: Tue Feb 3 14:29:38 2004 Input: Gamma[3*i] Output: Magma V2.10-6 Tue Feb 3 2004 14:29:35 on modular [Seed = 2801340456] ------------------------------------- >> Gamma[3*i]; ^ User error: Identifier 'i' has not been declared or assigned Total time: 2.989 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host user-vc8frgq.biz.mindspring.com. (216.135.238.26) Time: Tue Feb 3 14:39:10 2004 Input: Gamma[3*i] Output: Magma V2.10-6 Tue Feb 3 2004 14:39:07 on modular [Seed = 3315236111] ------------------------------------- >> Gamma[3*i]; ^ User error: Identifier 'i' has not been declared or assigned Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host user-vc8frgq.biz.mindspring.com. (216.135.238.26) Time: Tue Feb 3 14:39:33 2004 Input: Gamma[3*(-1)^(1/2)] Output: Magma V2.10-6 Tue Feb 3 2004 14:39:30 on modular [Seed = 3482351404] ------------------------------------- >> Gamma[3*(-1)^(1/2)]; ^ Runtime error in '^': Argument 1 is negative Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host user-vc8frgq.biz.mindspring.com. (216.135.238.26) Time: Tue Feb 3 14:54:32 2004 Input: Gamma[3*I] Output: Magma V2.10-6 Tue Feb 3 2004 14:54:29 on modular [Seed = 912886353] ------------------------------------- >> Gamma[3*I]; ^ User error: Identifier 'I' has not been declared or assigned Total time: 3.019 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host proxye.west.saic.com. (198.151.12.10) Time: Tue Feb 3 16:36:42 2004 Input: z = Integers(); P = PolynomialRing(z); a = PrimitiveRoot(P); Output: Magma V2.10-6 Tue Feb 3 2004 16:36:39 on modular [Seed = 1711682066] ------------------------------------- >> z = Integers(); ^ User error: Identifier 'z' has not been declared or assigned >> P = PolynomialRing(z); ^ User error: Identifier 'z' has not been declared or assigned >> a = PrimitiveRoot(P); ^ User error: Identifier 'P' has not been declared or assigned Total time: 2.879 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host proxye.west.saic.com. (198.151.12.10) Time: Tue Feb 3 16:36:45 2004 Input: z = Integers(); P = PolynomialRing(z); a = PrimitiveRoot(P); Output: Magma V2.10-6 Tue Feb 3 2004 16:36:42 on modular [Seed = 1846426135] ------------------------------------- >> z = Integers(); ^ User error: Identifier 'z' has not been declared or assigned >> P = PolynomialRing(z); ^ User error: Identifier 'z' has not been declared or assigned >> a = PrimitiveRoot(P); ^ User error: Identifier 'P' has not been declared or assigned Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host proxye.west.saic.com. (198.151.12.10) Time: Tue Feb 3 16:37:03 2004 Input: z := Integers(); P := PolynomialRing(z); a := PrimitiveRoot(P); Output: Magma V2.10-6 Tue Feb 3 2004 16:37:00 on modular [Seed = 2515911162] ------------------------------------- >> a := PrimitiveRoot(P); ^ Runtime error in 'PrimitiveRoot': Bad argument types Argument types given: RngUPol Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host CPE0020188e89e7-CM400026065536.cpe.net.cable.rogers.com. (24.100.224.195) Time: Tue Feb 3 20:05:37 2004 Input: 2x + 3x Output: Magma V2.10-6 Tue Feb 3 2004 20:05:34 on modular [Seed = 3602305950] ------------------------------------- >> 2x + 3x; ^ User error: bad syntax Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host i-195-137-81-190.freedom2surf.net. (195.137.81.190) Time: Tue Feb 3 20:26:37 2004 Input: 3+4 Output: Magma V2.10-6 Tue Feb 3 2004 20:26:34 on modular [Seed = 4052876205] ------------------------------------- 7 Total time: 2.889 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host i-195-137-81-190.freedom2surf.net. (195.137.81.190) Time: Tue Feb 3 20:27:00 2004 Input: 3+4 Output: Magma V2.10-6 Tue Feb 3 2004 20:26:57 on modular [Seed = 3968657051] ------------------------------------- 7 Total time: 2.989 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host i-195-137-81-190.freedom2surf.net. (195.137.81.190) Time: Tue Feb 3 20:27:12 2004 Input: 3+4 Output: Magma V2.10-6 Tue Feb 3 2004 20:27:09 on modular [Seed = 461050209] ------------------------------------- 7 Total time: 3.009 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host adsl-67-112-77-106.dsl.lsan03.pacbell.net. (67.112.77.106) Time: Tue Feb 3 21:54:21 2004 Input: 4x + 5 = 2 Output: Magma V2.10-6 Tue Feb 3 2004 21:54:18 on modular [Seed = 3417036038] ------------------------------------- >> 4x + 5 = 2; ^ User error: bad syntax Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host adsl-67-112-77-106.dsl.lsan03.pacbell.net. (67.112.77.106) Time: Tue Feb 3 21:54:36 2004 Input: 4 * x + 5 = 2 Output: Magma V2.10-6 Tue Feb 3 2004 21:54:33 on modular [Seed = 4069714956] ------------------------------------- >> 4 * x + 5 = 2; ^ User error: Identifier 'x' has not been declared or assigned Total time: 2.929 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host adsl-67-112-77-106.dsl.lsan03.pacbell.net. (67.112.77.106) Time: Tue Feb 3 21:54:50 2004 Input: x = 1 4 * x + 5 = 2 Output: Magma V2.10-6 Tue Feb 3 2004 21:54:47 on modular [Seed = 4187612953] ------------------------------------- >> 4 * x + 5 = 2; ^ User error: bad syntax Total time: 2.989 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 66-214-245-21.gln-eres.charterpipeline.net. (66.214.245.21) Time: Tue Feb 3 23:45:33 2004 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: Magma V2.10-6 Tue Feb 3 2004 23:45:30 on modular [Seed = 1261138872] ------------------------------------- Replace this by some code, then click [PARI] or [MAGMA]! Total time: 3.009 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host dsl-203-33-160-63.NSW.netspace.net.au. (203.33.160.63) Time: Wed Feb 4 07:07:46 2004 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: Magma V2.10-6 Wed Feb 4 2004 07:07:41 on modular [Seed = 4069675619] ------------------------------------- Replace this by some code, then click [PARI] or [MAGMA]! Total time: 3.209 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host wessel.mat.dtu.dk. (130.225.84.3) Time: Wed Feb 4 08:07:16 2004 Input: F2:=GF(2); P:=PolynomialRing(F2); F256:=ext; AllIrreduciblePolynomials(F2,8); Output: Magma V2.10-6 Wed Feb 4 2004 08:07:13 on modular [Seed = 2499033653] ------------------------------------- { x^8 + x^7 + x^6 + x^5 + x^4 + x + 1, x^8 + x^6 + x^3 + x^2 + 1, x^8 + x^6 + x^5 + x^3 + 1, x^8 + x^7 + x^4 + x^3 + x^2 + x + 1, x^8 + x^6 + x^5 + x^4 + 1, x^8 + x^7 + x^3 + x^2 + 1, x^8 + x^4 + x^3 + x^2 + 1, x^8 + x^7 + x^5 + x^3 + 1, x^8 + x^7 + x^6 + x + 1, x^8 + x^5 + x^4 + x^3 + 1, x^8 + x^7 + x^6 + x^4 + x^3 + x^2 + 1, x^8 + x^7 + x^5 + x^4 + 1, x^8 + x^7 + x^6 + x^5 + x^4 + x^3 + 1, x^8 + x^7 + x^3 + x + 1, x^8 + x^4 + x^3 + x + 1, x^8 + x^7 + x^6 + x^5 + x^2 + x + 1, x^8 + x^6 + x^5 + x^4 + x^2 + x + 1, x^8 + x^6 + x^5 + x^2 + 1, x^8 + x^5 + x^4 + x^3 + x^2 + x + 1, x^8 + x^5 + x^3 + x^2 + 1, x^8 + x^6 + x^5 + x + 1, x^8 + x^7 + x^6 + x^5 + x^4 + x^2 + 1, x^8 + x^7 + x^2 + x + 1, x^8 + x^5 + x^3 + x + 1, x^8 + x^7 + x^6 + x^3 + x^2 + x + 1, x^8 + x^7 + x^5 + x + 1, x^8 + x^6 + x^4 + x^3 + x^2 + x + 1, x^8 + x^7 + x^5 + x^4 + x^3 + x^2 + 1, x^8 + x^7 + x^6 + x^4 + x^2 + x + 1, x^8 + x^6 + x^5 + x^4 + x^3 + x + 1 } Total time: 2.979 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 2(SERVFAIL) (63.197.170.253) Time: Wed Feb 4 11:53:03 2004 Input: zx>=ajhlchfg1 Output: Magma V2.10-6 Wed Feb 4 2004 11:53:00 on modular [Seed = 1429485082] ------------------------------------- >> zx>=ajhlchfg1; ^ User error: bad syntax Total time: 2.909 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 2(SERVFAIL) (63.197.170.253) Time: Wed Feb 4 11:53:43 2004 Input: 159831 Output: Magma V2.10-6 Wed Feb 4 2004 11:53:40 on modular [Seed = 1547517931] ------------------------------------- 159831 Total time: 2.979 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 2(SERVFAIL) (63.197.170.253) Time: Wed Feb 4 11:54:34 2004 Input: 1547517931 Output: Magma V2.10-6 Wed Feb 4 2004 11:54:31 on modular [Seed = 2882193487] ------------------------------------- 1547517931 Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 2(SERVFAIL) (63.197.170.253) Time: Wed Feb 4 11:54:53 2004 Input: 159831 Output: Magma V2.10-6 Wed Feb 4 2004 11:54:50 on modular [Seed = 3000226123] ------------------------------------- 159831 Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host mathdhcp41.ces.clemson.edu. (130.127.112.170) Time: Wed Feb 4 14:04:01 2004 Input: kd1:=MultipartiteGraph([3,3,3]); kd2:=LineGraph(kd1); kd2; AutomorphismGroup(kd2); Output: Magma V2.10-6 Wed Feb 4 2004 14:03:50 on modular [Seed = 1012743692] ------------------------------------- Graph Vertex Neighbours 1 2 3 4 7 10 13 16 19 22 25 ; 2 1 3 5 8 11 13 17 19 23 25 ; 3 1 2 6 9 12 13 18 19 24 25 ; 4 1 5 6 7 10 14 16 20 22 26 ; 5 2 4 6 8 11 14 17 20 23 26 ; 6 3 4 5 9 12 14 18 20 24 26 ; 7 1 4 8 9 10 15 16 21 22 27 ; 8 2 5 7 9 11 15 17 21 23 27 ; 9 3 6 7 8 12 15 18 21 24 27 ; 10 1 4 7 11 12 13 14 15 16 22 ; 11 2 5 8 10 12 13 14 15 17 23 ; 12 3 6 9 10 11 13 14 15 18 24 ; 13 1 2 3 10 11 12 14 15 19 25 ; 14 4 5 6 10 11 12 13 15 20 26 ; 15 7 8 9 10 11 12 13 14 21 27 ; 16 1 4 7 10 17 18 19 20 21 22 ; 17 2 5 8 11 16 18 19 20 21 23 ; 18 3 6 9 12 16 17 19 20 21 24 ; 19 1 2 3 13 16 17 18 20 21 25 ; 20 4 5 6 14 16 17 18 19 21 26 ; 21 7 8 9 15 16 17 18 19 20 27 ; 22 1 4 7 10 16 23 24 25 26 27 ; 23 2 5 8 11 17 22 24 25 26 27 ; 24 3 6 9 12 18 22 23 25 26 27 ; 25 1 2 3 13 19 22 23 24 26 27 ; 26 4 5 6 14 20 22 23 24 25 27 ; 27 7 8 9 15 21 22 23 24 25 26 ; Permutation group acting on a set of cardinality 27 Order = 1296 = 2^4 * 3^4 (16, 22)(17, 23)(18, 24)(19, 25)(20, 26)(21, 27) (4, 7)(5, 8)(6, 9)(14, 15)(20, 21)(26, 27) (10, 16)(11, 17)(12, 18)(13, 19)(14, 20)(15, 21) (2, 3)(5, 6)(8, 9)(11, 12)(17, 18)(23, 24) (2, 4)(3, 7)(6, 8)(10, 13)(11, 14)(12, 15)(16, 19)(17, 20)(18, 21)(22, 25)(23, 26)(24, 27) (1, 2)(4, 5)(7, 8)(10, 11)(16, 17)(22, 23) (1, 10)(2, 11)(3, 12)(4, 16)(5, 17)(6, 18)(7, 22)(8, 23)(9, 24)(14, 19)(15, 25)(21, 26) Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host mathdhcp41.ces.clemson.edu. (130.127.112.170) Time: Wed Feb 4 14:06:14 2004 Input: kd1:=MultipartiteGraph([5,5,5]); kd2:=LineGraph(kd1); kd2; AutomorphismGroup(kd2); Output: Magma V2.10-6 Wed Feb 4 2004 14:06:10 on modular [Seed = 174786702] ------------------------------------- Graph Vertex Neighbours 1 2 3 4 5 6 11 16 21 26 31 36 41 46 51 56 61 66 71 ; 2 1 3 4 5 7 12 17 22 27 31 37 41 47 51 57 61 67 71 ; 3 1 2 4 5 8 13 18 23 28 31 38 41 48 51 58 61 68 71 ; 4 1 2 3 5 9 14 19 24 29 31 39 41 49 51 59 61 69 71 ; 5 1 2 3 4 10 15 20 25 30 31 40 41 50 51 60 61 70 71 ; 6 1 7 8 9 10 11 16 21 26 32 36 42 46 52 56 62 66 72 ; 7 2 6 8 9 10 12 17 22 27 32 37 42 47 52 57 62 67 72 ; 8 3 6 7 9 10 13 18 23 28 32 38 42 48 52 58 62 68 72 ; 9 4 6 7 8 10 14 19 24 29 32 39 42 49 52 59 62 69 72 ; 10 5 6 7 8 9 15 20 25 30 32 40 42 50 52 60 62 70 72 ; 11 1 6 12 13 14 15 16 21 26 33 36 43 46 53 56 63 66 73 ; 12 2 7 11 13 14 15 17 22 27 33 37 43 47 53 57 63 67 73 ; 13 3 8 11 12 14 15 18 23 28 33 38 43 48 53 58 63 68 73 ; 14 4 9 11 12 13 15 19 24 29 33 39 43 49 53 59 63 69 73 ; 15 5 10 11 12 13 14 20 25 30 33 40 43 50 53 60 63 70 73 ; 16 1 6 11 17 18 19 20 21 26 34 36 44 46 54 56 64 66 74 ; 17 2 7 12 16 18 19 20 22 27 34 37 44 47 54 57 64 67 74 ; 18 3 8 13 16 17 19 20 23 28 34 38 44 48 54 58 64 68 74 ; 19 4 9 14 16 17 18 20 24 29 34 39 44 49 54 59 64 69 74 ; 20 5 10 15 16 17 18 19 25 30 34 40 44 50 54 60 64 70 74 ; 21 1 6 11 16 22 23 24 25 26 35 36 45 46 55 56 65 66 75 ; 22 2 7 12 17 21 23 24 25 27 35 37 45 47 55 57 65 67 75 ; 23 3 8 13 18 21 22 24 25 28 35 38 45 48 55 58 65 68 75 ; 24 4 9 14 19 21 22 23 25 29 35 39 45 49 55 59 65 69 75 ; 25 5 10 15 20 21 22 23 24 30 35 40 45 50 55 60 65 70 75 ; 26 1 6 11 16 21 27 28 29 30 31 32 33 34 35 36 46 56 66 ; 27 2 7 12 17 22 26 28 29 30 31 32 33 34 35 37 47 57 67 ; 28 3 8 13 18 23 26 27 29 30 31 32 33 34 35 38 48 58 68 ; 29 4 9 14 19 24 26 27 28 30 31 32 33 34 35 39 49 59 69 ; 30 5 10 15 20 25 26 27 28 29 31 32 33 34 35 40 50 60 70 ; 31 1 2 3 4 5 26 27 28 29 30 32 33 34 35 41 51 61 71 ; 32 6 7 8 9 10 26 27 28 29 30 31 33 34 35 42 52 62 72 ; 33 11 12 13 14 15 26 27 28 29 30 31 32 34 35 43 53 63 73 ; 34 16 17 18 19 20 26 27 28 29 30 31 32 33 35 44 54 64 74 ; 35 21 22 23 24 25 26 27 28 29 30 31 32 33 34 45 55 65 75 ; 36 1 6 11 16 21 26 37 38 39 40 41 42 43 44 45 46 56 66 ; 37 2 7 12 17 22 27 36 38 39 40 41 42 43 44 45 47 57 67 ; 38 3 8 13 18 23 28 36 37 39 40 41 42 43 44 45 48 58 68 ; 39 4 9 14 19 24 29 36 37 38 40 41 42 43 44 45 49 59 69 ; 40 5 10 15 20 25 30 36 37 38 39 41 42 43 44 45 50 60 70 ; 41 1 2 3 4 5 31 36 37 38 39 40 42 43 44 45 51 61 71 ; 42 6 7 8 9 10 32 36 37 38 39 40 41 43 44 45 52 62 72 ; 43 11 12 13 14 15 33 36 37 38 39 40 41 42 44 45 53 63 73 ; 44 16 17 18 19 20 34 36 37 38 39 40 41 42 43 45 54 64 74 ; 45 21 22 23 24 25 35 36 37 38 39 40 41 42 43 44 55 65 75 ; 46 1 6 11 16 21 26 36 47 48 49 50 51 52 53 54 55 56 66 ; 47 2 7 12 17 22 27 37 46 48 49 50 51 52 53 54 55 57 67 ; 48 3 8 13 18 23 28 38 46 47 49 50 51 52 53 54 55 58 68 ; 49 4 9 14 19 24 29 39 46 47 48 50 51 52 53 54 55 59 69 ; 50 5 10 15 20 25 30 40 46 47 48 49 51 52 53 54 55 60 70 ; 51 1 2 3 4 5 31 41 46 47 48 49 50 52 53 54 55 61 71 ; 52 6 7 8 9 10 32 42 46 47 48 49 50 51 53 54 55 62 72 ; 53 11 12 13 14 15 33 43 46 47 48 49 50 51 52 54 55 63 73 ; 54 16 17 18 19 20 34 44 46 47 48 49 50 51 52 53 55 64 74 ; 55 21 22 23 24 25 35 45 46 47 48 49 50 51 52 53 54 65 75 ; 56 1 6 11 16 21 26 36 46 57 58 59 60 61 62 63 64 65 66 ; 57 2 7 12 17 22 27 37 47 56 58 59 60 61 62 63 64 65 67 ; 58 3 8 13 18 23 28 38 48 56 57 59 60 61 62 63 64 65 68 ; 59 4 9 14 19 24 29 39 49 56 57 58 60 61 62 63 64 65 69 ; 60 5 10 15 20 25 30 40 50 56 57 58 59 61 62 63 64 65 70 ; 61 1 2 3 4 5 31 41 51 56 57 58 59 60 62 63 64 65 71 ; 62 6 7 8 9 10 32 42 52 56 57 58 59 60 61 63 64 65 72 ; 63 11 12 13 14 15 33 43 53 56 57 58 59 60 61 62 64 65 73 ; 64 16 17 18 19 20 34 44 54 56 57 58 59 60 61 62 63 65 74 ; 65 21 22 23 24 25 35 45 55 56 57 58 59 60 61 62 63 64 75 ; 66 1 6 11 16 21 26 36 46 56 67 68 69 70 71 72 73 74 75 ; 67 2 7 12 17 22 27 37 47 57 66 68 69 70 71 72 73 74 75 ; 68 3 8 13 18 23 28 38 48 58 66 67 69 70 71 72 73 74 75 ; 69 4 9 14 19 24 29 39 49 59 66 67 68 70 71 72 73 74 75 ; 70 5 10 15 20 25 30 40 50 60 66 67 68 69 71 72 73 74 75 ; 71 1 2 3 4 5 31 41 51 61 66 67 68 69 70 72 73 74 75 ; 72 6 7 8 9 10 32 42 52 62 66 67 68 69 70 71 73 74 75 ; 73 11 12 13 14 15 33 43 53 63 66 67 68 69 70 71 72 74 75 ; 74 16 17 18 19 20 34 44 54 64 66 67 68 69 70 71 72 73 75 ; 75 21 22 23 24 25 35 45 55 65 66 67 68 69 70 71 72 73 74 ; Permutation group acting on a set of cardinality 75 Order = 10368000 = 2^10 * 3^4 * 5^3 (56, 66)(57, 67)(58, 68)(59, 69)(60, 70)(61, 71)(62, 72)(63, 73)(64, 74)(65, 75) (4, 5)(9, 10)(14, 15)(19, 20)(24, 25)(29, 30)(39, 40)(49, 50)(59, 60)(69, 70) (16, 21)(17, 22)(18, 23)(19, 24)(20, 25)(34, 35)(44, 45)(54, 55)(64, 65)(74, 75) (3, 4)(8, 9)(13, 14)(18, 19)(23, 24)(28, 29)(38, 39)(48, 49)(58, 59)(68, 69) (46, 56)(47, 57)(48, 58)(49, 59)(50, 60)(51, 61)(52, 62)(53, 63)(54, 64)(55, 65) (11, 16)(12, 17)(13, 18)(14, 19)(15, 20)(33, 34)(43, 44)(53, 54)(63, 64)(73, 74) (36, 46)(37, 47)(38, 48)(39, 49)(40, 50)(41, 51)(42, 52)(43, 53)(44, 54)(45, 55) (6, 11)(7, 12)(8, 13)(9, 14)(10, 15)(32, 33)(42, 43)(52, 53)(62, 63)(72, 73) (26, 36)(27, 37)(28, 38)(29, 39)(30, 40)(31, 41)(32, 42)(33, 43)(34, 44)(35, 45) (2, 3)(7, 8)(12, 13)(17, 18)(22, 23)(27, 28)(37, 38)(47, 48)(57, 58)(67, 68) (2, 6)(3, 11)(4, 16)(5, 21)(8, 12)(9, 17)(10, 22)(14, 18)(15, 23)(20, 24)(26, 31)(27, 32)(28, 33)(29, 34)(30, 35)(36, 41)(37, 42)(38, 43)(39, 44)(40, 45)(46, 51)(47, 52)(48, 53)(49, 54)(50, 55)(56, 61)(57, 62)(58, 63)(59, 64)(60, 65)(66, 71)(67, 72)(68, 73)(69, 74)(70, 75) (1, 2)(6, 7)(11, 12)(16, 17)(21, 22)(26, 27)(36, 37)(46, 47)(56, 57)(66, 67) (1, 26)(2, 27)(3, 28)(4, 29)(5, 30)(6, 36)(7, 37)(8, 38)(9, 39)(10, 40)(11, 46)(12, 47)(13, 48)(14, 49)(15, 50)(16, 56)(17, 57)(18, 58)(19, 59)(20, 60)(21, 66)(22, 67)(23, 68)(24, 69)(25, 70)(32, 41)(33, 51)(34, 61)(35, 71)(43, 52)(44, 62)(45, 72)(54, 63)(55, 73)(65, 74) Total time: 3.039 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host mathdhcp41.ces.clemson.edu. (130.127.112.170) Time: Wed Feb 4 14:09:20 2004 Input: kd1:=MultipartiteGraph([2,2,2]); kd2:=LineGraph(kd1); kd2; AutomorphismGroup(kd2); Output: Magma V2.10-6 Wed Feb 4 2004 14:09:16 on modular [Seed = 326242409] ------------------------------------- Graph Vertex Neighbours 1 2 3 5 7 9 11 ; 2 1 4 6 7 10 11 ; 3 1 4 5 8 9 12 ; 4 2 3 6 8 10 12 ; 5 1 3 6 7 8 9 ; 6 2 4 5 7 8 10 ; 7 1 2 5 6 8 11 ; 8 3 4 5 6 7 12 ; 9 1 3 5 10 11 12 ; 10 2 4 6 9 11 12 ; 11 1 2 7 9 10 12 ; 12 3 4 8 9 10 11 ; Permutation group acting on a set of cardinality 12 Order = 48 = 2^4 * 3 (2, 3)(5, 7)(6, 8)(9, 11)(10, 12) (5, 9)(6, 10)(7, 11)(8, 12) (1, 2)(3, 4)(5, 6)(9, 10) (1, 5)(2, 6)(3, 9)(4, 10)(8, 11) Total time: 2.889 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host mathdhcp41.ces.clemson.edu. (130.127.112.170) Time: Wed Feb 4 14:10:13 2004 Input: kd1:=MultipartiteGraph([4,4,4]); kd2:=LineGraph(kd1); kd2; AutomorphismGroup(kd2); Output: Magma V2.10-6 Wed Feb 4 2004 14:10:10 on modular [Seed = 1661100247] ------------------------------------- Graph Vertex Neighbours 1 2 3 4 5 9 13 17 21 25 29 33 37 41 45 ; 2 1 3 4 6 10 14 18 21 26 29 34 37 42 45 ; 3 1 2 4 7 11 15 19 21 27 29 35 37 43 45 ; 4 1 2 3 8 12 16 20 21 28 29 36 37 44 45 ; 5 1 6 7 8 9 13 17 22 25 30 33 38 41 46 ; 6 2 5 7 8 10 14 18 22 26 30 34 38 42 46 ; 7 3 5 6 8 11 15 19 22 27 30 35 38 43 46 ; 8 4 5 6 7 12 16 20 22 28 30 36 38 44 46 ; 9 1 5 10 11 12 13 17 23 25 31 33 39 41 47 ; 10 2 6 9 11 12 14 18 23 26 31 34 39 42 47 ; 11 3 7 9 10 12 15 19 23 27 31 35 39 43 47 ; 12 4 8 9 10 11 16 20 23 28 31 36 39 44 47 ; 13 1 5 9 14 15 16 17 24 25 32 33 40 41 48 ; 14 2 6 10 13 15 16 18 24 26 32 34 40 42 48 ; 15 3 7 11 13 14 16 19 24 27 32 35 40 43 48 ; 16 4 8 12 13 14 15 20 24 28 32 36 40 44 48 ; 17 1 5 9 13 18 19 20 21 22 23 24 25 33 41 ; 18 2 6 10 14 17 19 20 21 22 23 24 26 34 42 ; 19 3 7 11 15 17 18 20 21 22 23 24 27 35 43 ; 20 4 8 12 16 17 18 19 21 22 23 24 28 36 44 ; 21 1 2 3 4 17 18 19 20 22 23 24 29 37 45 ; 22 5 6 7 8 17 18 19 20 21 23 24 30 38 46 ; 23 9 10 11 12 17 18 19 20 21 22 24 31 39 47 ; 24 13 14 15 16 17 18 19 20 21 22 23 32 40 48 ; 25 1 5 9 13 17 26 27 28 29 30 31 32 33 41 ; 26 2 6 10 14 18 25 27 28 29 30 31 32 34 42 ; 27 3 7 11 15 19 25 26 28 29 30 31 32 35 43 ; 28 4 8 12 16 20 25 26 27 29 30 31 32 36 44 ; 29 1 2 3 4 21 25 26 27 28 30 31 32 37 45 ; 30 5 6 7 8 22 25 26 27 28 29 31 32 38 46 ; 31 9 10 11 12 23 25 26 27 28 29 30 32 39 47 ; 32 13 14 15 16 24 25 26 27 28 29 30 31 40 48 ; 33 1 5 9 13 17 25 34 35 36 37 38 39 40 41 ; 34 2 6 10 14 18 26 33 35 36 37 38 39 40 42 ; 35 3 7 11 15 19 27 33 34 36 37 38 39 40 43 ; 36 4 8 12 16 20 28 33 34 35 37 38 39 40 44 ; 37 1 2 3 4 21 29 33 34 35 36 38 39 40 45 ; 38 5 6 7 8 22 30 33 34 35 36 37 39 40 46 ; 39 9 10 11 12 23 31 33 34 35 36 37 38 40 47 ; 40 13 14 15 16 24 32 33 34 35 36 37 38 39 48 ; 41 1 5 9 13 17 25 33 42 43 44 45 46 47 48 ; 42 2 6 10 14 18 26 34 41 43 44 45 46 47 48 ; 43 3 7 11 15 19 27 35 41 42 44 45 46 47 48 ; 44 4 8 12 16 20 28 36 41 42 43 45 46 47 48 ; 45 1 2 3 4 21 29 37 41 42 43 44 46 47 48 ; 46 5 6 7 8 22 30 38 41 42 43 44 45 47 48 ; 47 9 10 11 12 23 31 39 41 42 43 44 45 46 48 ; 48 13 14 15 16 24 32 40 41 42 43 44 45 46 47 ; Permutation group acting on a set of cardinality 48 Order = 82944 = 2^10 * 3^4 (3, 4)(7, 8)(11, 12)(15, 16)(19, 20)(27, 28)(35, 36)(43, 44) (33, 41)(34, 42)(35, 43)(36, 44)(37, 45)(38, 46)(39, 47)(40, 48) (9, 13)(10, 14)(11, 15)(12, 16)(23, 24)(31, 32)(39, 40)(47, 48) (25, 33)(26, 34)(27, 35)(28, 36)(29, 37)(30, 38)(31, 39)(32, 40) (5, 9)(6, 10)(7, 11)(8, 12)(22, 23)(30, 31)(38, 39)(46, 47) (17, 25)(18, 26)(19, 27)(20, 28)(21, 29)(22, 30)(23, 31)(24, 32) (2, 3)(6, 7)(10, 11)(14, 15)(18, 19)(26, 27)(34, 35)(42, 43) (2, 5)(3, 9)(4, 13)(7, 10)(8, 14)(12, 15)(17, 21)(18, 22)(19, 23)(20, 24)(25, 29)(26, 30)(27, 31)(28, 32)(33, 37)(34, 38)(35, 39)(36, 40)(41, 45)(42, 46)(43, 47)(44, 48) (1, 2)(5, 6)(9, 10)(13, 14)(17, 18)(25, 26)(33, 34)(41, 42) (1, 17)(2, 18)(3, 19)(4, 20)(5, 25)(6, 26)(7, 27)(8, 28)(9, 33)(10, 34)(11, 35)(12, 36)(13, 41)(14, 42)(15, 43)(16, 44)(22, 29)(23, 37)(24, 45)(31, 38)(32, 46)(40, 47) Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host reached (130.127.112.170) Time: Wed Feb 4 14:11:31 2004 Input: kd1:=MultipartiteGraph([6,6,6]); kd2:=LineGraph(kd1); kd2; AutomorphismGroup(kd2); Output: Magma V2.10-6 Wed Feb 4 2004 14:11:14 on modular [Seed = 1762159261] ------------------------------------- Graph Vertex Neighbours 1 2 3 4 5 6 7 13 19 25 31 37 43 49 55 61 67 73 79 85 91 97 103 ; 2 1 3 4 5 6 8 14 20 26 32 38 43 50 55 62 67 74 79 86 91 98 103 ; 3 1 2 4 5 6 9 15 21 27 33 39 43 51 55 63 67 75 79 87 91 99 103 ; 4 1 2 3 5 6 10 16 22 28 34 40 43 52 55 64 67 76 79 88 91 100 103 ; 5 1 2 3 4 6 11 17 23 29 35 41 43 53 55 65 67 77 79 89 91 101 103 ; 6 1 2 3 4 5 12 18 24 30 36 42 43 54 55 66 67 78 79 90 91 102 103 ; 7 1 8 9 10 11 12 13 19 25 31 37 44 49 56 61 68 73 80 85 92 97 104 ; 8 2 7 9 10 11 12 14 20 26 32 38 44 50 56 62 68 74 80 86 92 98 104 ; 9 3 7 8 10 11 12 15 21 27 33 39 44 51 56 63 68 75 80 87 92 99 104 ; 10 4 7 8 9 11 12 16 22 28 34 40 44 52 56 64 68 76 80 88 92 100 104 ; 11 5 7 8 9 10 12 17 23 29 35 41 44 53 56 65 68 77 80 89 92 101 104 ; 12 6 7 8 9 10 11 18 24 30 36 42 44 54 56 66 68 78 80 90 92 102 104 ; 13 1 7 14 15 16 17 18 19 25 31 37 45 49 57 61 69 73 81 85 93 97 105 ; 14 2 8 13 15 16 17 18 20 26 32 38 45 50 57 62 69 74 81 86 93 98 105 ; 15 3 9 13 14 16 17 18 21 27 33 39 45 51 57 63 69 75 81 87 93 99 105 ; 16 4 10 13 14 15 17 18 22 28 34 40 45 52 57 64 69 76 81 88 93 100 105 ; 17 5 11 13 14 15 16 18 23 29 35 41 45 53 57 65 69 77 81 89 93 101 105 ; 18 6 12 13 14 15 16 17 24 30 36 42 45 54 57 66 69 78 81 90 93 102 105 ; 19 1 7 13 20 21 22 23 24 25 31 37 46 49 58 61 70 73 82 85 94 97 106 ; 20 2 8 14 19 21 22 23 24 26 32 38 46 50 58 62 70 74 82 86 94 98 106 ; 21 3 9 15 19 20 22 23 24 27 33 39 46 51 58 63 70 75 82 87 94 99 106 ; 22 4 10 16 19 20 21 23 24 28 34 40 46 52 58 64 70 76 82 88 94 100 106 ; 23 5 11 17 19 20 21 22 24 29 35 41 46 53 58 65 70 77 82 89 94 101 106 ; 24 6 12 18 19 20 21 22 23 30 36 42 46 54 58 66 70 78 82 90 94 102 106 ; 25 1 7 13 19 26 27 28 29 30 31 37 47 49 59 61 71 73 83 85 95 97 107 ; 26 2 8 14 20 25 27 28 29 30 32 38 47 50 59 62 71 74 83 86 95 98 107 ; 27 3 9 15 21 25 26 28 29 30 33 39 47 51 59 63 71 75 83 87 95 99 107 ; 28 4 10 16 22 25 26 27 29 30 34 40 47 52 59 64 71 76 83 88 95 100 107 ; 29 5 11 17 23 25 26 27 28 30 35 41 47 53 59 65 71 77 83 89 95 101 107 ; 30 6 12 18 24 25 26 27 28 29 36 42 47 54 59 66 71 78 83 90 95 102 107 ; 31 1 7 13 19 25 32 33 34 35 36 37 48 49 60 61 72 73 84 85 96 97 108 ; 32 2 8 14 20 26 31 33 34 35 36 38 48 50 60 62 72 74 84 86 96 98 108 ; 33 3 9 15 21 27 31 32 34 35 36 39 48 51 60 63 72 75 84 87 96 99 108 ; 34 4 10 16 22 28 31 32 33 35 36 40 48 52 60 64 72 76 84 88 96 100 108 ; 35 5 11 17 23 29 31 32 33 34 36 41 48 53 60 65 72 77 84 89 96 101 108 ; 36 6 12 18 24 30 31 32 33 34 35 42 48 54 60 66 72 78 84 90 96 102 108 ; 37 1 7 13 19 25 31 38 39 40 41 42 43 44 45 46 47 48 49 61 73 85 97 ; 38 2 8 14 20 26 32 37 39 40 41 42 43 44 45 46 47 48 50 62 74 86 98 ; 39 3 9 15 21 27 33 37 38 40 41 42 43 44 45 46 47 48 51 63 75 87 99 ; 40 4 10 16 22 28 34 37 38 39 41 42 43 44 45 46 47 48 52 64 76 88 100 ; 41 5 11 17 23 29 35 37 38 39 40 42 43 44 45 46 47 48 53 65 77 89 101 ; 42 6 12 18 24 30 36 37 38 39 40 41 43 44 45 46 47 48 54 66 78 90 102 ; 43 1 2 3 4 5 6 37 38 39 40 41 42 44 45 46 47 48 55 67 79 91 103 ; 44 7 8 9 10 11 12 37 38 39 40 41 42 43 45 46 47 48 56 68 80 92 104 ; 45 13 14 15 16 17 18 37 38 39 40 41 42 43 44 46 47 48 57 69 81 93 105 ; 46 19 20 21 22 23 24 37 38 39 40 41 42 43 44 45 47 48 58 70 82 94 106 ; 47 25 26 27 28 29 30 37 38 39 40 41 42 43 44 45 46 48 59 71 83 95 107 ; 48 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 60 72 84 96 108 ; 49 1 7 13 19 25 31 37 50 51 52 53 54 55 56 57 58 59 60 61 73 85 97 ; 50 2 8 14 20 26 32 38 49 51 52 53 54 55 56 57 58 59 60 62 74 86 98 ; 51 3 9 15 21 27 33 39 49 50 52 53 54 55 56 57 58 59 60 63 75 87 99 ; 52 4 10 16 22 28 34 40 49 50 51 53 54 55 56 57 58 59 60 64 76 88 100 ; 53 5 11 17 23 29 35 41 49 50 51 52 54 55 56 57 58 59 60 65 77 89 101 ; 54 6 12 18 24 30 36 42 49 50 51 52 53 55 56 57 58 59 60 66 78 90 102 ; 55 1 2 3 4 5 6 43 49 50 51 52 53 54 56 57 58 59 60 67 79 91 103 ; 56 7 8 9 10 11 12 44 49 50 51 52 53 54 55 57 58 59 60 68 80 92 104 ; 57 13 14 15 16 17 18 45 49 50 51 52 53 54 55 56 58 59 60 69 81 93 105 ; 58 19 20 21 22 23 24 46 49 50 51 52 53 54 55 56 57 59 60 70 82 94 106 ; 59 25 26 27 28 29 30 47 49 50 51 52 53 54 55 56 57 58 60 71 83 95 107 ; 60 31 32 33 34 35 36 48 49 50 51 52 53 54 55 56 57 58 59 72 84 96 108 ; 61 1 7 13 19 25 31 37 49 62 63 64 65 66 67 68 69 70 71 72 73 85 97 ; 62 2 8 14 20 26 32 38 50 61 63 64 65 66 67 68 69 70 71 72 74 86 98 ; 63 3 9 15 21 27 33 39 51 61 62 64 65 66 67 68 69 70 71 72 75 87 99 ; 64 4 10 16 22 28 34 40 52 61 62 63 65 66 67 68 69 70 71 72 76 88 100 ; 65 5 11 17 23 29 35 41 53 61 62 63 64 66 67 68 69 70 71 72 77 89 101 ; 66 6 12 18 24 30 36 42 54 61 62 63 64 65 67 68 69 70 71 72 78 90 102 ; 67 1 2 3 4 5 6 43 55 61 62 63 64 65 66 68 69 70 71 72 79 91 103 ; 68 7 8 9 10 11 12 44 56 61 62 63 64 65 66 67 69 70 71 72 80 92 104 ; 69 13 14 15 16 17 18 45 57 61 62 63 64 65 66 67 68 70 71 72 81 93 105 ; 70 19 20 21 22 23 24 46 58 61 62 63 64 65 66 67 68 69 71 72 82 94 106 ; 71 25 26 27 28 29 30 47 59 61 62 63 64 65 66 67 68 69 70 72 83 95 107 ; 72 31 32 33 34 35 36 48 60 61 62 63 64 65 66 67 68 69 70 71 84 96 108 ; 73 1 7 13 19 25 31 37 49 61 74 75 76 77 78 79 80 81 82 83 84 85 97 ; 74 2 8 14 20 26 32 38 50 62 73 75 76 77 78 79 80 81 82 83 84 86 98 ; 75 3 9 15 21 27 33 39 51 63 73 74 76 77 78 79 80 81 82 83 84 87 99 ; 76 4 10 16 22 28 34 40 52 64 73 74 75 77 78 79 80 81 82 83 84 88 100 ; 77 5 11 17 23 29 35 41 53 65 73 74 75 76 78 79 80 81 82 83 84 89 101 ; 78 6 12 18 24 30 36 42 54 66 73 74 75 76 77 79 80 81 82 83 84 90 102 ; 79 1 2 3 4 5 6 43 55 67 73 74 75 76 77 78 80 81 82 83 84 91 103 ; 80 7 8 9 10 11 12 44 56 68 73 74 75 76 77 78 79 81 82 83 84 92 104 ; 81 13 14 15 16 17 18 45 57 69 73 74 75 76 77 78 79 80 82 83 84 93 105 ; 82 19 20 21 22 23 24 46 58 70 73 74 75 76 77 78 79 80 81 83 84 94 106 ; 83 25 26 27 28 29 30 47 59 71 73 74 75 76 77 78 79 80 81 82 84 95 107 ; 84 31 32 33 34 35 36 48 60 72 73 74 75 76 77 78 79 80 81 82 83 96 108 ; 85 1 7 13 19 25 31 37 49 61 73 86 87 88 89 90 91 92 93 94 95 96 97 ; 86 2 8 14 20 26 32 38 50 62 74 85 87 88 89 90 91 92 93 94 95 96 98 ; 87 3 9 15 21 27 33 39 51 63 75 85 86 88 89 90 91 92 93 94 95 96 99 ; 88 4 10 16 22 28 34 40 52 64 76 85 86 87 89 90 91 92 93 94 95 96 100 ; 89 5 11 17 23 29 35 41 53 65 77 85 86 87 88 90 91 92 93 94 95 96 101 ; 90 6 12 18 24 30 36 42 54 66 78 85 86 87 88 89 91 92 93 94 95 96 102 ; 91 1 2 3 4 5 6 43 55 67 79 85 86 87 88 89 90 92 93 94 95 96 103 ; 92 7 8 9 10 11 12 44 56 68 80 85 86 87 88 89 90 91 93 94 95 96 104 ; 93 13 14 15 16 17 18 45 57 69 81 85 86 87 88 89 90 91 92 94 95 96 105 ; 94 19 20 21 22 23 24 46 58 70 82 85 86 87 88 89 90 91 92 93 95 96 106 ; 95 25 26 27 28 29 30 47 59 71 83 85 86 87 88 89 90 91 92 93 94 96 107 ; 96 31 32 33 34 35 36 48 60 72 84 85 86 87 88 89 90 91 92 93 94 95 108 ; 97 1 7 13 19 25 31 37 49 61 73 85 98 99 100 101 102 103 104 105 106 107 108 ; 98 2 8 14 20 26 32 38 50 62 74 86 97 99 100 101 102 103 104 105 106 107 108 ; 99 3 9 15 21 27 33 39 51 63 75 87 97 98 100 101 102 103 104 105 106 107 108 ; 100 4 10 16 22 28 34 40 52 64 76 88 97 98 99 101 102 103 104 105 106 107 108 ; 101 5 11 17 23 29 35 41 53 65 77 89 97 98 99 100 102 103 104 105 106 107 108 ; 102 6 12 18 24 30 36 42 54 66 78 90 97 98 99 100 101 103 104 105 106 107 108 ; 103 1 2 3 4 5 6 43 55 67 79 91 97 98 99 100 101 102 104 105 106 107 108 ; 104 7 8 9 10 11 12 44 56 68 80 92 97 98 99 100 101 102 103 105 106 107 108 ; 105 13 14 15 16 17 18 45 57 69 81 93 97 98 99 100 101 102 103 104 106 107 108 ; 106 19 20 21 22 23 24 46 58 70 82 94 97 98 99 100 101 102 103 104 105 107 108 ; 107 25 26 27 28 29 30 47 59 71 83 95 97 98 99 100 101 102 103 104 105 106 108 ; 108 31 32 33 34 35 36 48 60 72 84 96 97 98 99 100 101 102 103 104 105 106 107 ; Permutation group acting on a set of cardinality 108 Order = 2^13 * 3^7 * 5^3 Total time: 2.939 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host mathdhcp41.ces.clemson.edu. (130.127.112.170) Time: Wed Feb 4 14:16:00 2004 Input: kd1:=MultipartiteGraph([3,3,3,3]); kd2:=LineGraph(kd1); kd2; AutomorphismGroup(kd2); Output: Magma V2.10-6 Wed Feb 4 2004 14:15:48 on modular [Seed = 1109608064] ------------------------------------- Graph Vertex Neighbours 1 2 3 4 7 10 13 16 19 22 25 28 31 37 40 46 49 ; 2 1 3 5 8 11 13 17 19 23 25 29 31 38 40 47 49 ; 3 1 2 6 9 12 13 18 19 24 25 30 31 39 40 48 49 ; 4 1 5 6 7 10 14 16 20 22 26 28 32 37 41 46 50 ; 5 2 4 6 8 11 14 17 20 23 26 29 32 38 41 47 50 ; 6 3 4 5 9 12 14 18 20 24 26 30 32 39 41 48 50 ; 7 1 4 8 9 10 15 16 21 22 27 28 33 37 42 46 51 ; 8 2 5 7 9 11 15 17 21 23 27 29 33 38 42 47 51 ; 9 3 6 7 8 12 15 18 21 24 27 30 33 39 42 48 51 ; 10 1 4 7 11 12 13 14 15 16 22 28 34 37 43 46 52 ; 11 2 5 8 10 12 13 14 15 17 23 29 34 38 43 47 52 ; 12 3 6 9 10 11 13 14 15 18 24 30 34 39 43 48 52 ; 13 1 2 3 10 11 12 14 15 19 25 31 34 40 43 49 52 ; 14 4 5 6 10 11 12 13 15 20 26 32 34 41 43 50 52 ; 15 7 8 9 10 11 12 13 14 21 27 33 34 42 43 51 52 ; 16 1 4 7 10 17 18 19 20 21 22 28 35 37 44 46 53 ; 17 2 5 8 11 16 18 19 20 21 23 29 35 38 44 47 53 ; 18 3 6 9 12 16 17 19 20 21 24 30 35 39 44 48 53 ; 19 1 2 3 13 16 17 18 20 21 25 31 35 40 44 49 53 ; 20 4 5 6 14 16 17 18 19 21 26 32 35 41 44 50 53 ; 21 7 8 9 15 16 17 18 19 20 27 33 35 42 44 51 53 ; 22 1 4 7 10 16 23 24 25 26 27 28 36 37 45 46 54 ; 23 2 5 8 11 17 22 24 25 26 27 29 36 38 45 47 54 ; 24 3 6 9 12 18 22 23 25 26 27 30 36 39 45 48 54 ; 25 1 2 3 13 19 22 23 24 26 27 31 36 40 45 49 54 ; 26 4 5 6 14 20 22 23 24 25 27 32 36 41 45 50 54 ; 27 7 8 9 15 21 22 23 24 25 26 33 36 42 45 51 54 ; 28 1 4 7 10 16 22 29 30 31 32 33 34 35 36 37 46 ; 29 2 5 8 11 17 23 28 30 31 32 33 34 35 36 38 47 ; 30 3 6 9 12 18 24 28 29 31 32 33 34 35 36 39 48 ; 31 1 2 3 13 19 25 28 29 30 32 33 34 35 36 40 49 ; 32 4 5 6 14 20 26 28 29 30 31 33 34 35 36 41 50 ; 33 7 8 9 15 21 27 28 29 30 31 32 34 35 36 42 51 ; 34 10 11 12 13 14 15 28 29 30 31 32 33 35 36 43 52 ; 35 16 17 18 19 20 21 28 29 30 31 32 33 34 36 44 53 ; 36 22 23 24 25 26 27 28 29 30 31 32 33 34 35 45 54 ; 37 1 4 7 10 16 22 28 38 39 40 41 42 43 44 45 46 ; 38 2 5 8 11 17 23 29 37 39 40 41 42 43 44 45 47 ; 39 3 6 9 12 18 24 30 37 38 40 41 42 43 44 45 48 ; 40 1 2 3 13 19 25 31 37 38 39 41 42 43 44 45 49 ; 41 4 5 6 14 20 26 32 37 38 39 40 42 43 44 45 50 ; 42 7 8 9 15 21 27 33 37 38 39 40 41 43 44 45 51 ; 43 10 11 12 13 14 15 34 37 38 39 40 41 42 44 45 52 ; 44 16 17 18 19 20 21 35 37 38 39 40 41 42 43 45 53 ; 45 22 23 24 25 26 27 36 37 38 39 40 41 42 43 44 54 ; 46 1 4 7 10 16 22 28 37 47 48 49 50 51 52 53 54 ; 47 2 5 8 11 17 23 29 38 46 48 49 50 51 52 53 54 ; 48 3 6 9 12 18 24 30 39 46 47 49 50 51 52 53 54 ; 49 1 2 3 13 19 25 31 40 46 47 48 50 51 52 53 54 ; 50 4 5 6 14 20 26 32 41 46 47 48 49 51 52 53 54 ; 51 7 8 9 15 21 27 33 42 46 47 48 49 50 52 53 54 ; 52 10 11 12 13 14 15 34 43 46 47 48 49 50 51 53 54 ; 53 16 17 18 19 20 21 35 44 46 47 48 49 50 51 52 54 ; 54 22 23 24 25 26 27 36 45 46 47 48 49 50 51 52 53 ; Permutation group acting on a set of cardinality 54 Order = 31104 = 2^7 * 3^5 (16, 22)(17, 23)(18, 24)(19, 25)(20, 26)(21, 27)(35, 36)(44, 45)(53, 54) (37, 46)(38, 47)(39, 48)(40, 49)(41, 50)(42, 51)(43, 52)(44, 53)(45, 54) (4, 7)(5, 8)(6, 9)(14, 15)(20, 21)(26, 27)(32, 33)(41, 42)(50, 51) (28, 37)(29, 38)(30, 39)(31, 40)(32, 41)(33, 42)(34, 43)(35, 44)(36, 45) (2, 3)(5, 6)(8, 9)(11, 12)(17, 18)(23, 24)(29, 30)(38, 39)(47, 48) (2, 4)(3, 7)(6, 8)(10, 13)(11, 14)(12, 15)(16, 19)(17, 20)(18, 21)(22, 25)(23, 26)(24, 27)(28, 31)(29, 32)(30, 33)(37, 40)(38, 41)(39, 42)(46, 49)(47, 50)(48, 51) (10, 16)(11, 17)(12, 18)(13, 19)(14, 20)(15, 21)(34, 35)(43, 44)(52, 53) (10, 28)(11, 29)(12, 30)(13, 31)(14, 32)(15, 33)(16, 37)(17, 38)(18, 39)(19, 40)(20, 41)(21, 42)(22, 46)(23, 47)(24, 48)(25, 49)(26, 50)(27, 51)(35, 43)(36, 52)(45, 53) (1, 2)(4, 5)(7, 8)(10, 11)(16, 17)(22, 23)(28, 29)(37, 38)(46, 47) (1, 10)(2, 11)(3, 12)(4, 16)(5, 17)(6, 18)(7, 22)(8, 23)(9, 24)(14, 19)(15, 25)(21, 26)(31, 34)(32, 35)(33, 36)(40, 43)(41, 44)(42, 45)(49, 52)(50, 53)(51, 54) Total time: 3.059 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host mathdhcp41.ces.clemson.edu. (130.127.112.170) Time: Wed Feb 4 14:18:04 2004 Input: kd1:=MultipartiteGraph([2,2,2,2]); kd2:=LineGraph(kd1); kd2; AutomorphismGroup(kd2); Output: Magma V2.10-6 Wed Feb 4 2004 14:18:01 on modular [Seed = 1261063684] ------------------------------------- Graph Vertex Neighbours 1 2 3 5 7 9 11 13 15 19 21 ; 2 1 4 6 7 10 11 14 15 20 21 ; 3 1 4 5 8 9 12 13 16 19 22 ; 4 2 3 6 8 10 12 14 16 20 22 ; 5 1 3 6 7 8 9 13 17 19 23 ; 6 2 4 5 7 8 10 14 17 20 23 ; 7 1 2 5 6 8 11 15 17 21 23 ; 8 3 4 5 6 7 12 16 17 22 23 ; 9 1 3 5 10 11 12 13 18 19 24 ; 10 2 4 6 9 11 12 14 18 20 24 ; 11 1 2 7 9 10 12 15 18 21 24 ; 12 3 4 8 9 10 11 16 18 22 24 ; 13 1 3 5 9 14 15 16 17 18 19 ; 14 2 4 6 10 13 15 16 17 18 20 ; 15 1 2 7 11 13 14 16 17 18 21 ; 16 3 4 8 12 13 14 15 17 18 22 ; 17 5 6 7 8 13 14 15 16 18 23 ; 18 9 10 11 12 13 14 15 16 17 24 ; 19 1 3 5 9 13 20 21 22 23 24 ; 20 2 4 6 10 14 19 21 22 23 24 ; 21 1 2 7 11 15 19 20 22 23 24 ; 22 3 4 8 12 16 19 20 21 23 24 ; 23 5 6 7 8 17 19 20 21 22 24 ; 24 9 10 11 12 18 19 20 21 22 23 ; Permutation group acting on a set of cardinality 24 Order = 384 = 2^7 * 3 (13, 19)(14, 20)(15, 21)(16, 22)(17, 23)(18, 24) (2, 3)(5, 7)(6, 8)(9, 11)(10, 12)(13, 15)(14, 16)(19, 21)(20, 22) (5, 9)(6, 10)(7, 11)(8, 12)(17, 18)(23, 24) (5, 13)(6, 14)(7, 15)(8, 16)(9, 19)(10, 20)(11, 21)(12, 22)(18, 23) (1, 2)(3, 4)(5, 6)(9, 10)(13, 14)(19, 20) (1, 5)(2, 6)(3, 9)(4, 10)(8, 11)(15, 17)(16, 18)(21, 23)(22, 24) Total time: 3.049 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host mathdhcp41.ces.clemson.edu. (130.127.112.170) Time: Wed Feb 4 14:19:49 2004 Input: kd1:=MultipartiteGraph([3,3,3,3,3]); kd2:=LineGraph(kd1); kd2; AutomorphismGroup(kd2); Output: Magma V2.10-6 Wed Feb 4 2004 14:19:45 on modular [Seed = 1345410471] ------------------------------------- Graph Vertex Neighbours 1 2 3 4 7 10 13 16 19 22 25 28 31 37 40 46 49 55 58 67 70 79 82 ; 2 1 3 5 8 11 13 17 19 23 25 29 31 38 40 47 49 56 58 68 70 80 82 ; 3 1 2 6 9 12 13 18 19 24 25 30 31 39 40 48 49 57 58 69 70 81 82 ; 4 1 5 6 7 10 14 16 20 22 26 28 32 37 41 46 50 55 59 67 71 79 83 ; 5 2 4 6 8 11 14 17 20 23 26 29 32 38 41 47 50 56 59 68 71 80 83 ; 6 3 4 5 9 12 14 18 20 24 26 30 32 39 41 48 50 57 59 69 71 81 83 ; 7 1 4 8 9 10 15 16 21 22 27 28 33 37 42 46 51 55 60 67 72 79 84 ; 8 2 5 7 9 11 15 17 21 23 27 29 33 38 42 47 51 56 60 68 72 80 84 ; 9 3 6 7 8 12 15 18 21 24 27 30 33 39 42 48 51 57 60 69 72 81 84 ; 10 1 4 7 11 12 13 14 15 16 22 28 34 37 43 46 52 55 61 67 73 79 85 ; 11 2 5 8 10 12 13 14 15 17 23 29 34 38 43 47 52 56 61 68 73 80 85 ; 12 3 6 9 10 11 13 14 15 18 24 30 34 39 43 48 52 57 61 69 73 81 85 ; 13 1 2 3 10 11 12 14 15 19 25 31 34 40 43 49 52 58 61 70 73 82 85 ; 14 4 5 6 10 11 12 13 15 20 26 32 34 41 43 50 52 59 61 71 73 83 85 ; 15 7 8 9 10 11 12 13 14 21 27 33 34 42 43 51 52 60 61 72 73 84 85 ; 16 1 4 7 10 17 18 19 20 21 22 28 35 37 44 46 53 55 62 67 74 79 86 ; 17 2 5 8 11 16 18 19 20 21 23 29 35 38 44 47 53 56 62 68 74 80 86 ; 18 3 6 9 12 16 17 19 20 21 24 30 35 39 44 48 53 57 62 69 74 81 86 ; 19 1 2 3 13 16 17 18 20 21 25 31 35 40 44 49 53 58 62 70 74 82 86 ; 20 4 5 6 14 16 17 18 19 21 26 32 35 41 44 50 53 59 62 71 74 83 86 ; 21 7 8 9 15 16 17 18 19 20 27 33 35 42 44 51 53 60 62 72 74 84 86 ; 22 1 4 7 10 16 23 24 25 26 27 28 36 37 45 46 54 55 63 67 75 79 87 ; 23 2 5 8 11 17 22 24 25 26 27 29 36 38 45 47 54 56 63 68 75 80 87 ; 24 3 6 9 12 18 22 23 25 26 27 30 36 39 45 48 54 57 63 69 75 81 87 ; 25 1 2 3 13 19 22 23 24 26 27 31 36 40 45 49 54 58 63 70 75 82 87 ; 26 4 5 6 14 20 22 23 24 25 27 32 36 41 45 50 54 59 63 71 75 83 87 ; 27 7 8 9 15 21 22 23 24 25 26 33 36 42 45 51 54 60 63 72 75 84 87 ; 28 1 4 7 10 16 22 29 30 31 32 33 34 35 36 37 46 55 64 67 76 79 88 ; 29 2 5 8 11 17 23 28 30 31 32 33 34 35 36 38 47 56 64 68 76 80 88 ; 30 3 6 9 12 18 24 28 29 31 32 33 34 35 36 39 48 57 64 69 76 81 88 ; 31 1 2 3 13 19 25 28 29 30 32 33 34 35 36 40 49 58 64 70 76 82 88 ; 32 4 5 6 14 20 26 28 29 30 31 33 34 35 36 41 50 59 64 71 76 83 88 ; 33 7 8 9 15 21 27 28 29 30 31 32 34 35 36 42 51 60 64 72 76 84 88 ; 34 10 11 12 13 14 15 28 29 30 31 32 33 35 36 43 52 61 64 73 76 85 88 ; 35 16 17 18 19 20 21 28 29 30 31 32 33 34 36 44 53 62 64 74 76 86 88 ; 36 22 23 24 25 26 27 28 29 30 31 32 33 34 35 45 54 63 64 75 76 87 88 ; 37 1 4 7 10 16 22 28 38 39 40 41 42 43 44 45 46 55 65 67 77 79 89 ; 38 2 5 8 11 17 23 29 37 39 40 41 42 43 44 45 47 56 65 68 77 80 89 ; 39 3 6 9 12 18 24 30 37 38 40 41 42 43 44 45 48 57 65 69 77 81 89 ; 40 1 2 3 13 19 25 31 37 38 39 41 42 43 44 45 49 58 65 70 77 82 89 ; 41 4 5 6 14 20 26 32 37 38 39 40 42 43 44 45 50 59 65 71 77 83 89 ; 42 7 8 9 15 21 27 33 37 38 39 40 41 43 44 45 51 60 65 72 77 84 89 ; 43 10 11 12 13 14 15 34 37 38 39 40 41 42 44 45 52 61 65 73 77 85 89 ; 44 16 17 18 19 20 21 35 37 38 39 40 41 42 43 45 53 62 65 74 77 86 89 ; 45 22 23 24 25 26 27 36 37 38 39 40 41 42 43 44 54 63 65 75 77 87 89 ; 46 1 4 7 10 16 22 28 37 47 48 49 50 51 52 53 54 55 66 67 78 79 90 ; 47 2 5 8 11 17 23 29 38 46 48 49 50 51 52 53 54 56 66 68 78 80 90 ; 48 3 6 9 12 18 24 30 39 46 47 49 50 51 52 53 54 57 66 69 78 81 90 ; 49 1 2 3 13 19 25 31 40 46 47 48 50 51 52 53 54 58 66 70 78 82 90 ; 50 4 5 6 14 20 26 32 41 46 47 48 49 51 52 53 54 59 66 71 78 83 90 ; 51 7 8 9 15 21 27 33 42 46 47 48 49 50 52 53 54 60 66 72 78 84 90 ; 52 10 11 12 13 14 15 34 43 46 47 48 49 50 51 53 54 61 66 73 78 85 90 ; 53 16 17 18 19 20 21 35 44 46 47 48 49 50 51 52 54 62 66 74 78 86 90 ; 54 22 23 24 25 26 27 36 45 46 47 48 49 50 51 52 53 63 66 75 78 87 90 ; 55 1 4 7 10 16 22 28 37 46 56 57 58 59 60 61 62 63 64 65 66 67 79 ; 56 2 5 8 11 17 23 29 38 47 55 57 58 59 60 61 62 63 64 65 66 68 80 ; 57 3 6 9 12 18 24 30 39 48 55 56 58 59 60 61 62 63 64 65 66 69 81 ; 58 1 2 3 13 19 25 31 40 49 55 56 57 59 60 61 62 63 64 65 66 70 82 ; 59 4 5 6 14 20 26 32 41 50 55 56 57 58 60 61 62 63 64 65 66 71 83 ; 60 7 8 9 15 21 27 33 42 51 55 56 57 58 59 61 62 63 64 65 66 72 84 ; 61 10 11 12 13 14 15 34 43 52 55 56 57 58 59 60 62 63 64 65 66 73 85 ; 62 16 17 18 19 20 21 35 44 53 55 56 57 58 59 60 61 63 64 65 66 74 86 ; 63 22 23 24 25 26 27 36 45 54 55 56 57 58 59 60 61 62 64 65 66 75 87 ; 64 28 29 30 31 32 33 34 35 36 55 56 57 58 59 60 61 62 63 65 66 76 88 ; 65 37 38 39 40 41 42 43 44 45 55 56 57 58 59 60 61 62 63 64 66 77 89 ; 66 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 78 90 ; 67 1 4 7 10 16 22 28 37 46 55 68 69 70 71 72 73 74 75 76 77 78 79 ; 68 2 5 8 11 17 23 29 38 47 56 67 69 70 71 72 73 74 75 76 77 78 80 ; 69 3 6 9 12 18 24 30 39 48 57 67 68 70 71 72 73 74 75 76 77 78 81 ; 70 1 2 3 13 19 25 31 40 49 58 67 68 69 71 72 73 74 75 76 77 78 82 ; 71 4 5 6 14 20 26 32 41 50 59 67 68 69 70 72 73 74 75 76 77 78 83 ; 72 7 8 9 15 21 27 33 42 51 60 67 68 69 70 71 73 74 75 76 77 78 84 ; 73 10 11 12 13 14 15 34 43 52 61 67 68 69 70 71 72 74 75 76 77 78 85 ; 74 16 17 18 19 20 21 35 44 53 62 67 68 69 70 71 72 73 75 76 77 78 86 ; 75 22 23 24 25 26 27 36 45 54 63 67 68 69 70 71 72 73 74 76 77 78 87 ; 76 28 29 30 31 32 33 34 35 36 64 67 68 69 70 71 72 73 74 75 77 78 88 ; 77 37 38 39 40 41 42 43 44 45 65 67 68 69 70 71 72 73 74 75 76 78 89 ; 78 46 47 48 49 50 51 52 53 54 66 67 68 69 70 71 72 73 74 75 76 77 90 ; 79 1 4 7 10 16 22 28 37 46 55 67 80 81 82 83 84 85 86 87 88 89 90 ; 80 2 5 8 11 17 23 29 38 47 56 68 79 81 82 83 84 85 86 87 88 89 90 ; 81 3 6 9 12 18 24 30 39 48 57 69 79 80 82 83 84 85 86 87 88 89 90 ; 82 1 2 3 13 19 25 31 40 49 58 70 79 80 81 83 84 85 86 87 88 89 90 ; 83 4 5 6 14 20 26 32 41 50 59 71 79 80 81 82 84 85 86 87 88 89 90 ; 84 7 8 9 15 21 27 33 42 51 60 72 79 80 81 82 83 85 86 87 88 89 90 ; 85 10 11 12 13 14 15 34 43 52 61 73 79 80 81 82 83 84 86 87 88 89 90 ; 86 16 17 18 19 20 21 35 44 53 62 74 79 80 81 82 83 84 85 87 88 89 90 ; 87 22 23 24 25 26 27 36 45 54 63 75 79 80 81 82 83 84 85 86 88 89 90 ; 88 28 29 30 31 32 33 34 35 36 64 76 79 80 81 82 83 84 85 86 87 89 90 ; 89 37 38 39 40 41 42 43 44 45 65 77 79 80 81 82 83 84 85 86 87 88 90 ; 90 46 47 48 49 50 51 52 53 54 66 78 79 80 81 82 83 84 85 86 87 88 89 ; Permutation group acting on a set of cardinality 90 Order = 933120 = 2^8 * 3^6 * 5 (37, 46)(38, 47)(39, 48)(40, 49)(41, 50)(42, 51)(43, 52)(44, 53)(45, 54)(65, 66)(77, 78)(89, 90) (67, 79)(68, 80)(69, 81)(70, 82)(71, 83)(72, 84)(73, 85)(74, 86)(75, 87)(76, 88)(77, 89)(78, 90) (16, 22)(17, 23)(18, 24)(19, 25)(20, 26)(21, 27)(35, 36)(44, 45)(53, 54)(62, 63)(74, 75)(86, 87) (55, 67)(56, 68)(57, 69)(58, 70)(59, 71)(60, 72)(61, 73)(62, 74)(63, 75)(64, 76)(65, 77)(66, 78) (4, 7)(5, 8)(6, 9)(14, 15)(20, 21)(26, 27)(32, 33)(41, 42)(50, 51)(59, 60)(71, 72)(83, 84) (28, 37)(29, 38)(30, 39)(31, 40)(32, 41)(33, 42)(34, 43)(35, 44)(36, 45)(64, 65)(76, 77)(88, 89) (28, 55)(29, 56)(30, 57)(31, 58)(32, 59)(33, 60)(34, 61)(35, 62)(36, 63)(37, 67)(38, 68)(39, 69)(40, 70)(41, 71)(42, 72)(43, 73)(44, 74)(45, 75)(46, 79)(47, 80)(48, 81)(49, 82)(50, 83)(51, 84)(52, 85)(53, 86)(54, 87)(65, 76)(66, 88)(78, 89) (2, 3)(5, 6)(8, 9)(11, 12)(17, 18)(23, 24)(29, 30)(38, 39)(47, 48)(56, 57)(68, 69)(80, 81) (2, 4)(3, 7)(6, 8)(10, 13)(11, 14)(12, 15)(16, 19)(17, 20)(18, 21)(22, 25)(23, 26)(24, 27)(28, 31)(29, 32)(30, 33)(37, 40)(38, 41)(39, 42)(46, 49)(47, 50)(48, 51)(55, 58)(56, 59)(57, 60)(67, 70)(68, 71)(69, 72)(79, 82)(80, 83)(81, 84) (10, 16)(11, 17)(12, 18)(13, 19)(14, 20)(15, 21)(34, 35)(43, 44)(52, 53)(61, 62)(73, 74)(85, 86) (10, 28)(11, 29)(12, 30)(13, 31)(14, 32)(15, 33)(16, 37)(17, 38)(18, 39)(19, 40)(20, 41)(21, 42)(22, 46)(23, 47)(24, 48)(25, 49)(26, 50)(27, 51)(35, 43)(36, 52)(45, 53)(61, 64)(62, 65)(63, 66)(73, 76)(74, 77)(75, 78)(85, 88)(86, 89)(87, 90) (1, 2)(4, 5)(7, 8)(10, 11)(16, 17)(22, 23)(28, 29)(37, 38)(46, 47)(55, 56)(67, 68)(79, 80) (1, 10)(2, 11)(3, 12)(4, 16)(5, 17)(6, 18)(7, 22)(8, 23)(9, 24)(14, 19)(15, 25)(21, 26)(31, 34)(32, 35)(33, 36)(40, 43)(41, 44)(42, 45)(49, 52)(50, 53)(51, 54)(58, 61)(59, 62)(60, 63)(70, 73)(71, 74)(72, 75)(82, 85)(83, 86)(84, 87) Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 2(SERVFAIL) (203.91.149.163) Time: Wed Feb 4 16:29:29 2004 Input: F2:=GF(2); P:=PolynomialRing(F2); F256:=ext; AllIrreduciblePolynomials(F2,8); Output: Magma V2.10-6 Wed Feb 4 2004 16:29:25 on modular [Seed = 1880183916] ------------------------------------- { x^8 + x^7 + x^6 + x^5 + x^4 + x + 1, x^8 + x^6 + x^3 + x^2 + 1, x^8 + x^6 + x^5 + x^3 + 1, x^8 + x^7 + x^4 + x^3 + x^2 + x + 1, x^8 + x^6 + x^5 + x^4 + 1, x^8 + x^7 + x^3 + x^2 + 1, x^8 + x^4 + x^3 + x^2 + 1, x^8 + x^7 + x^5 + x^3 + 1, x^8 + x^7 + x^6 + x + 1, x^8 + x^5 + x^4 + x^3 + 1, x^8 + x^7 + x^6 + x^4 + x^3 + x^2 + 1, x^8 + x^7 + x^5 + x^4 + 1, x^8 + x^7 + x^6 + x^5 + x^4 + x^3 + 1, x^8 + x^7 + x^3 + x + 1, x^8 + x^4 + x^3 + x + 1, x^8 + x^7 + x^6 + x^5 + x^2 + x + 1, x^8 + x^6 + x^5 + x^4 + x^2 + x + 1, x^8 + x^6 + x^5 + x^2 + 1, x^8 + x^5 + x^4 + x^3 + x^2 + x + 1, x^8 + x^5 + x^3 + x^2 + 1, x^8 + x^6 + x^5 + x + 1, x^8 + x^7 + x^6 + x^5 + x^4 + x^2 + 1, x^8 + x^7 + x^2 + x + 1, x^8 + x^5 + x^3 + x + 1, x^8 + x^7 + x^6 + x^3 + x^2 + x + 1, x^8 + x^7 + x^5 + x + 1, x^8 + x^6 + x^4 + x^3 + x^2 + x + 1, x^8 + x^7 + x^5 + x^4 + x^3 + x^2 + 1, x^8 + x^7 + x^6 + x^4 + x^2 + x + 1, x^8 + x^6 + x^5 + x^4 + x^3 + x + 1 } Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 2(SERVFAIL) (203.91.149.163) Time: Wed Feb 4 16:30:04 2004 Input: F2:=GF(2); P:=PolynomialRing(F2); F256:=ext; AllPrimitivePolynomials(F2,8); Output: Magma V2.10-6 Wed Feb 4 2004 16:30:01 on modular [Seed = 1126328115] ------------------------------------- >> AllPrimitivePolynomials(F2,8); ^ User error: Identifier 'AllPrimitivePolynomials' has not been declared or assigned Total time: 2.939 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host wessel.mat.dtu.dk. (130.225.84.3) Time: Thu Feb 5 04:28:29 2004 Input: F2:=GF(2); P:=PolynomialRing(F2); AllIrredusiblePolynomials(F2,8); Output: Magma V2.10-6 Thu Feb 5 2004 04:28:25 on modular [Seed = 3218993972] ------------------------------------- >> AllIrredusiblePolynomials(F2,8);; ^ User error: Identifier 'AllIrredusiblePolynomials' has not been declared or assigned Total time: 3.019 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host wessel.mat.dtu.dk. (130.225.84.3) Time: Thu Feb 5 04:28:52 2004 Input: F2:=GF(2); P:=PolynomialRing(F2); AllIrreduciblePolynomials(F2,8); Output: Magma V2.10-6 Thu Feb 5 2004 04:28:49 on modular [Seed = 2781342022] ------------------------------------- { x^8 + x^7 + x^6 + x^5 + x^4 + x + 1, x^8 + x^6 + x^3 + x^2 + 1, x^8 + x^6 + x^5 + x^3 + 1, x^8 + x^7 + x^4 + x^3 + x^2 + x + 1, x^8 + x^6 + x^5 + x^4 + 1, x^8 + x^7 + x^3 + x^2 + 1, x^8 + x^4 + x^3 + x^2 + 1, x^8 + x^7 + x^5 + x^3 + 1, x^8 + x^7 + x^6 + x + 1, x^8 + x^5 + x^4 + x^3 + 1, x^8 + x^7 + x^6 + x^4 + x^3 + x^2 + 1, x^8 + x^7 + x^5 + x^4 + 1, x^8 + x^7 + x^6 + x^5 + x^4 + x^3 + 1, x^8 + x^7 + x^3 + x + 1, x^8 + x^4 + x^3 + x + 1, x^8 + x^7 + x^6 + x^5 + x^2 + x + 1, x^8 + x^6 + x^5 + x^4 + x^2 + x + 1, x^8 + x^6 + x^5 + x^2 + 1, x^8 + x^5 + x^4 + x^3 + x^2 + x + 1, x^8 + x^5 + x^3 + x^2 + 1, x^8 + x^6 + x^5 + x + 1, x^8 + x^7 + x^6 + x^5 + x^4 + x^2 + 1, x^8 + x^7 + x^2 + x + 1, x^8 + x^5 + x^3 + x + 1, x^8 + x^7 + x^6 + x^3 + x^2 + x + 1, x^8 + x^7 + x^5 + x + 1, x^8 + x^6 + x^4 + x^3 + x^2 + x + 1, x^8 + x^7 + x^5 + x^4 + x^3 + x^2 + 1, x^8 + x^7 + x^6 + x^4 + x^2 + x + 1, x^8 + x^6 + x^5 + x^4 + x^3 + x + 1 } Total time: 3.029 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host wessel.mat.dtu.dk. (130.225.84.3) Time: Thu Feb 5 04:32:50 2004 Input: F2:=GF(2); F16:=ext; P:=PolynomialRing(F16); AllIrreduciblePolynomials(F16,2); Output: Magma V2.10-6 Thu Feb 5 2004 04:32:47 on modular [Seed = 2599999255] ------------------------------------- { x^2 + b^4*x + b^14, x^2 + b*x + b^5, x^2 + b^2*x + b^11, x^2 + b^10*x + b^4, x^2 + b^11*x + b^10, x^2 + b*x + b^8, x^2 + b^9*x + b^9, x^2 + b^3*x + b^5, x^2 + b^11*x + b^4, x^2 + b^4*x + b^11, x^2 + b^4*x + b^5, x^2 + b^13*x + b^10, x^2 + b^2*x + b^2, x^2 + b^10*x + b^3, x^2 + b^8*x + b^14, x^2 + b^6*x + b^11, x^2 + b^14*x + b^10, x^2 + b^3*x + b^2, x^2 + b^11*x + b^3, x^2 + b^9*x + b^14, x^2 + b^14*x + b^4, x^2 + b^7*x + b^11, x^2 + b^4*x + b^2, x^2 + b^12*x + b^3, x^2 + b^5*x + b^8, x^2 + b^13*x + b^9, x^2 + b^10*x + b^14, x^2 + b^7*x + b^5, x^2 + b^8*x + b^13, x^2 + x + b^12, x^2 + b^13*x + b^3, x^2 + b^5*x + b^2, x^2 + b^14*x + b^9, x^2 + b^6*x + b^8, x^2 + b^11*x + b^14, x^2 + x + b^6, x^2 + b^8*x + b^7, x^2 + b^7*x + b^8, x^2 + b^7*x + b^2, x^2 + b^8*x + b^8, x^2 + x + b^9, x^2 + b^13*x + b^14, x^2 + b^3*x + b^12, x^2 + b^11*x + b^13, x^2 + x + b^3, x^2 + b*x + b^9, x^2 + b^9*x + b^2, x^2 + b^10*x + b^8, x^2 + b^4*x + b^6, x^2 + b^12*x + b^7, x^2 + b^2*x + b^3, x^2 + b^10*x + b^2, x^2 + b^3*x + b^9, x^2 + b^13*x + b^7, x^2 + b^5*x + b^6, x^2 + b^3*x + b^3, x^2 + b^12*x + b^8, x^2 + b*x + 1, x^2 + b^9*x + b, x^2 + b^6*x + b^6, x^2 + b^14*x + b^7, x^2 + b^7*x + b^12, x^2 + b^5*x + b^9, x^2 + b^13*x + b^8, x^2 + b^10*x + b, x^2 + b^2*x + 1, x^2 + b^7*x + b^6, x^2 + b^8*x + b^12, x^2 + x + b^13, x^2 + b^13*x + b^2, x^2 + b^6*x + b^9, x^2 + b^3*x + 1, x^2 + b^11*x + b, x^2 + x + b^7, x^2 + b*x + b^13, x^2 + b^9*x + b^12, x^2 + b^6*x + b^3, x^2 + b^4*x + 1, x^2 + b^12*x + b, x^2 + b^9*x + b^6, x^2 + b^10*x + b^12, x^2 + b^2*x + b^13, x^2 + b^2*x + b^7, x^2 + b^3*x + b^13, x^2 + b^6*x + 1, x^2 + b^14*x + b, x^2 + b^11*x + b^6, x^2 + b^12*x + b^12, x^2 + b^10*x + b^11, x^2 + b^2*x + b^10, x^2 + b^4*x + b^7, x^2 + b^12*x + b^6, x^2 + b^5*x + b^13, x^2 + b^8*x + 1, x^2 + b^5*x + b^7, x^2 + b^14*x + b^12, x^2 + b^3*x + b^4, x^2 + b^11*x + b^5, x^2 + b^9*x + 1, x^2 + b*x + b, x^2 + b^7*x + b^13, x^2 + b^12*x + b^5, x^2 + b^4*x + b^4, x^2 + b^2*x + b, x^2 + x + b^14, x^2 + b^5*x + b^4, x^2 + b^13*x + b^5, x^2 + b^6*x + b^10, x^2 + b^14*x + b^11, x^2 + b*x + b^14, x^2 + b^6*x + b^4, x^2 + b^14*x + b^5, x^2 + b^7*x + b^10, x^2 + b^12*x + 1, x^2 + x + b^11, x^2 + b^8*x + b^10, x^2 + b^5*x + b, x^2 + b^8*x + b^4, x^2 + b^9*x + b^10, x^2 + b*x + b^11 } Total time: 2.959 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host roam27-53.fas.harvard.edu. (140.247.27.53) Time: Thu Feb 5 10:13:02 2004 Input: Factorization(2004); Output: Magma V2.10-6 Thu Feb 5 2004 10:12:57 on modular [Seed = 3850893481] ------------------------------------- [ <2, 2>, <3, 1>, <167, 1> ] Total time: 3.039 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host cache3.nottingham.ac.uk. (128.243.220.41) Time: Thu Feb 5 10:31:14 2004 Input: Q:=Rationals(); QT:=FunctionField(Q); EC:=EllipticCurve([QT|0,0,0,T^2,-1]); EC; Output: Magma V2.10-6 Thu Feb 5 2004 10:31:11 on modular [Seed = 3450858567] ------------------------------------- Elliptic Curve defined by y^2 = x^3 + T^2*x - 1 over Univariate rational function field over Rational Field Total time: 2.939 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host cache3.nottingham.ac.uk. (128.243.220.41) Time: Thu Feb 5 10:33:27 2004 Input: Q:=Rationals(); QT:=FunctionField(Q); EC:=EllipticCurve([QT|0,0,0,T^2,-1]); EC; P2QT:=:=ProjectivePlane(QT); F:=CoordinateRing(P2QT)!DefiningPolynomial(EC); F; Output: Magma V2.10-6 Thu Feb 5 2004 10:33:24 on modular [Seed = 878057030] ------------------------------------- Elliptic Curve defined by y^2 = x^3 + T^2*x - 1 over Univariate rational function field over Rational Field >> P2QT:=:=ProjectivePlane(QT); ^ User error: bad syntax >> F:=CoordinateRing(P2QT)!DefiningPolynomial(EC); ^ User error: Identifier 'P2QT' has not been declared or assigned >> F; ^ User error: Identifier 'F' has not been declared or assigned Total time: 3.059 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host cache3.nottingham.ac.uk. (128.243.220.41) Time: Thu Feb 5 10:33:42 2004 Input: Q:=Rationals(); QT:=FunctionField(Q); EC:=EllipticCurve([QT|0,0,0,T^2,-1]); EC; P2QT:=ProjectivePlane(QT); F:=CoordinateRing(P2QT)!DefiningPolynomial(EC); F; Output: Magma V2.10-6 Thu Feb 5 2004 10:33:39 on modular [Seed = 1029644120] ------------------------------------- Elliptic Curve defined by y^2 = x^3 + T^2*x - 1 over Univariate rational function field over Rational Field -X^3 - T^2*X*Z^2 + Y^2*Z + Z^3 Total time: 3.029 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host cache3.nottingham.ac.uk. (128.243.220.41) Time: Thu Feb 5 10:36:33 2004 Input: Q:=Rationals(); QT:=FunctionField(Q); EC:=EllipticCurve([QT|0,0,0,T^2,-1]); EC; P2QT:=ProjectivePlane(QT); F:=CoordinateRing(P2QT)!DefiningPolynomial(EC); F; L:=AffineSpace(QT,6); fx:=a0+a1*T; fy:=b0+b1*T; fz:=c0+c1*T; FT:=Evaluate(F,[fx,fy,fz]); Output: Magma V2.10-6 Thu Feb 5 2004 10:36:30 on modular [Seed = 743313124] ------------------------------------- Elliptic Curve defined by y^2 = x^3 + T^2*x - 1 over Univariate rational function field over Rational Field -X^3 - T^2*X*Z^2 + Y^2*Z + Z^3 Total time: 3.069 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host cache3.nottingham.ac.uk. (128.243.220.41) Time: Thu Feb 5 10:36:55 2004 Input: Q:=Rationals(); QT:=FunctionField(Q); EC:=EllipticCurve([QT|0,0,0,T^2,-1]); EC; P2QT:=ProjectivePlane(QT); F:=CoordinateRing(P2QT)!DefiningPolynomial(EC); F; L:=AffineSpace(QT,6); fx:=a0+a1*T; fy:=b0+b1*T; fz:=c0+c1*T; FT:=Evaluate(F,[fx,fy,fz]); FT; Output: Magma V2.10-6 Thu Feb 5 2004 10:36:52 on modular [Seed = 360134199] ------------------------------------- Elliptic Curve defined by y^2 = x^3 + T^2*x - 1 over Univariate rational function field over Rational Field -X^3 - T^2*X*Z^2 + Y^2*Z + Z^3 -a0^3 - 3*T*a0^2*a1 - 3*T^2*a0*a1^2 - T^2*a0*c0^2 - 2*T^3*a0*c0*c1 - T^4*a0*c1^2 - T^3*a1^3 - T^3*a1*c0^2 - 2*T^4*a1*c0*c1 - T^5*a1*c1^2 + b0^2*c0 + T*b0^2*c1 + 2*T*b0*b1*c0 + 2*T^2*b0*b1*c1 + T^2*b1^2*c0 + T^3*b1^2*c1 + c0^3 + 3*T*c0^2*c1 + 3*T^2*c0*c1^2 + T^3*c1^3 Total time: 3.059 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host reached (12.146.247.3) Time: Thu Feb 5 10:59:58 2004 Input: 52+53 1982 Output: Magma V2.10-6 Thu Feb 5 2004 10:59:41 on modular [Seed = 2014990371] ------------------------------------- >> 1982; ^ User error: bad syntax Total time: 3.059 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host dhcp9536062.columbus.rr.com. (24.95.36.62) Time: Thu Feb 5 20:16:24 2004 Input: (x^2+1)*(x+3) Output: Magma V2.10-6 Thu Feb 5 2004 20:16:21 on modular [Seed = 4002169911] ------------------------------------- >> (x^2+1)*(x+3) ^ User error: Identifier 'x' has not been declared or assigned Total time: 3.109 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host dhcp9536062.columbus.rr.com. (24.95.36.62) Time: Thu Feb 5 20:17:02 2004 Input: x*(x+1)*(x+5)*(x+10) Output: Magma V2.10-6 Thu Feb 5 2004 20:16:59 on modular [Seed = 3753735400] ------------------------------------- >> x*(x+1)*(x+5)*(x+10); ^ User error: Identifier 'x' has not been declared or assigned Total time: 3.129 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host dhcp9536062.columbus.rr.com. (24.95.36.62) Time: Thu Feb 5 20:24:45 2004 Input: (x^2+8x+12)*(4x^3+48x^2+130x+50)-(x^4+16x^3+65x^2+50x)*(2x+8) Output: Magma V2.10-6 Thu Feb 5 2004 20:24:42 on modular [Seed = 945460447] ------------------------------------- >> (x^2+8x+12)*(4x^3+48x^2+130x+50)-(x^4+16x^3+65x^2+50x)*(2x+8); ^ User error: bad syntax Total time: 3.119 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host dhcp9536062.columbus.rr.com. (24.95.36.62) Time: Thu Feb 5 20:24:54 2004 Input: (x^2+8x+12)*(4x^3+48x^2+130x+50)-(x^4+16x^3+65x^2+50x)*(2x+8) Output: Magma V2.10-6 Thu Feb 5 2004 20:24:51 on modular [Seed = 709396212] ------------------------------------- >> (x^2+8x+12)*(4x^3+48x^2+130x+50)-(x^4+16x^3+65x^2+50x)*(2x+8); ^ User error: bad syntax Total time: 3.029 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host dhcp9536062.columbus.rr.com. (24.95.36.62) Time: Thu Feb 5 20:25:16 2004 Input: (x^2+8*x+12)*(4*x^3+48*x^2+130*x+50)-(x^4+16*x^3+65*x^2+50*x)*(2*x+8) Output: Magma V2.10-6 Thu Feb 5 2004 20:25:12 on modular [Seed = 427537885] ------------------------------------- >> (x^2+8*x+12)*(4*x^3+48*x^2+130*x+50)-(x^4+16*x^3+65*x^2+50*x)*(2*x+8); ^ User error: Identifier 'x' has not been declared or assigned Total time: 3.099 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host dhcp9536062.columbus.rr.com. (24.95.36.62) Time: Thu Feb 5 20:31:38 2004 Input: (x+2)*(x+6) Output: Magma V2.10-6 Thu Feb 5 2004 20:31:35 on modular [Seed = 39889992] ------------------------------------- >> (x+2)*(x+6); ^ User error: Identifier 'x' has not been declared or assigned Total time: 3.009 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pa-murraysville-3e-1-10.pittpa.adelphia.net. (68.232.212.10) Time: Thu Feb 5 20:32:28 2004 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" a*(b+c) Output: Magma V2.10-6 Thu Feb 5 2004 20:32:25 on modular [Seed = 1581052106] ------------------------------------- >> a*(b+c); ^ User error: bad syntax Total time: 3.039 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 69-162-40-105.stcgpa.adelphia.net. (69.162.40.105) Time: Thu Feb 5 22:58:15 2004 Input: A := QuaternionAlgebra< RationalField() | -1, -5 >; RamifiedPrimes(A); Output: Magma V2.10-6 Thu Feb 5 2004 22:58:11 on modular [Seed = 3050759463] ------------------------------------- [ 2 ] Total time: 3.139 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 69-162-40-105.stcgpa.adelphia.net. (69.162.40.105) Time: Thu Feb 5 22:58:36 2004 Input: A := QuaternionAlgebra< RationalField() | -1, -5 >; i*i; RamifiedPrimes(A); Output: Magma V2.10-6 Thu Feb 5 2004 22:58:33 on modular [Seed = 3168791572] ------------------------------------- -1 [ 2 ] Total time: 3.049 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 69-162-40-105.stcgpa.adelphia.net. (69.162.40.105) Time: Thu Feb 5 22:59:27 2004 Input: A := QuaternionAlgebra< RationalField() | -1, -5 >; i*i; RamifiedPrimes(A); Discriminant(A); IsDefinite(A); Output: Magma V2.10-6 Thu Feb 5 2004 22:59:24 on modular [Seed = 1143411994] ------------------------------------- -1 [ 2 ] 2 true Total time: 3.139 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 69-162-40-105.stcgpa.adelphia.net. (69.162.40.105) Time: Thu Feb 5 22:59:31 2004 Input: A := QuaternionAlgebra< RationalField() | -1, -5 >; i*i; RamifiedPrimes(A); Discriminant(A); IsDefinite(A); Output: Magma V2.10-6 Thu Feb 5 2004 22:59:28 on modular [Seed = 1294867503] ------------------------------------- -1 [ 2 ] 2 true Total time: 3.029 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 69-162-40-105.stcgpa.adelphia.net. (69.162.40.105) Time: Thu Feb 5 22:59:40 2004 Input: A := QuaternionAlgebra< RationalField() | -1, -10 >; i*i; RamifiedPrimes(A); Discriminant(A); IsDefinite(A); Output: Magma V2.10-6 Thu Feb 5 2004 22:59:36 on modular [Seed = 1513687856] ------------------------------------- -1 [ 2 ] 2 true Total time: 3.119 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 69-162-40-105.stcgpa.adelphia.net. (69.162.40.105) Time: Thu Feb 5 22:59:49 2004 Input: A := QuaternionAlgebra< RationalField() | -1, -7 >; i*i; RamifiedPrimes(A); Discriminant(A); IsDefinite(A); Output: Magma V2.10-6 Thu Feb 5 2004 22:59:45 on modular [Seed = 1660957200] ------------------------------------- -1 [ 7 ] 7 true Total time: 3.089 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 69-162-40-105.stcgpa.adelphia.net. (69.162.40.105) Time: Thu Feb 5 22:59:59 2004 Input: A := QuaternionAlgebra< RationalField() | -1, -3>; i*i; RamifiedPrimes(A); Discriminant(A); IsDefinite(A); Output: Magma V2.10-6 Thu Feb 5 2004 22:59:56 on modular [Seed = 1745565974] ------------------------------------- -1 [ 3 ] 3 true Total time: 3.069 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 69-162-40-105.stcgpa.adelphia.net. (69.162.40.105) Time: Thu Feb 5 23:00:12 2004 Input: A := QuaternionAlgebra< RationalField() | -1, 5>; RamifiedPrimes(A); Discriminant(A); IsDefinite(A); Output: Magma V2.10-6 Thu Feb 5 2004 23:00:07 on modular [Seed = 2015046013] ------------------------------------- [] 1 false Total time: 2.999 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 69-162-40-105.stcgpa.adelphia.net. (69.162.40.105) Time: Thu Feb 5 23:00:24 2004 Input: A := QuaternionAlgebra< RationalField() | -1, -5>; RamifiedPrimes(A); Discriminant(A); IsDefinite(A); Output: Magma V2.10-6 Thu Feb 5 2004 23:00:20 on modular [Seed = 23220247] ------------------------------------- [ 2 ] 2 true Total time: 3.059 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 69-162-40-105.stcgpa.adelphia.net. (69.162.40.105) Time: Thu Feb 5 23:00:35 2004 Input: A := QuaternionAlgebra< RationalField() | -3, -5>; RamifiedPrimes(A); Discriminant(A); IsDefinite(A); Output: Magma V2.10-6 Thu Feb 5 2004 23:00:31 on modular [Seed = 242048787] ------------------------------------- [ 5 ] 5 true Total time: 3.109 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 69-162-40-105.stcgpa.adelphia.net. (69.162.40.105) Time: Thu Feb 5 23:00:59 2004 Input: A := QuaternionAlgebra< RationalField() | -2, -5>; RamifiedPrimes(A); Discriminant(A); IsDefinite(A); Output: Magma V2.10-6 Thu Feb 5 2004 23:00:56 on modular [Seed = 343360814] ------------------------------------- [ 5 ] 5 true Total time: 3.109 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 69-162-40-105.stcgpa.adelphia.net. (69.162.40.105) Time: Thu Feb 5 23:01:13 2004 Input: A := QuaternionAlgebra< RationalField() | -1, -5>; RamifiedPrimes(A); Discriminant(A); IsDefinite(A); Output: Magma V2.10-6 Thu Feb 5 2004 23:01:10 on modular [Seed = 860906231] ------------------------------------- [ 2 ] 2 true Total time: 3.069 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 69-162-40-105.stcgpa.adelphia.net. (69.162.40.105) Time: Thu Feb 5 23:01:52 2004 Input: A := QuaternionAlgebra< RationalField() | -2, -5>; RamifiedPrimes(A); Discriminant(A); IsDefinite(A); Units(A); UnitGroup(A); Output: Magma V2.10-6 Thu Feb 5 2004 23:01:49 on modular [Seed = 945514967] ------------------------------------- [ 5 ] 5 true >> Units(A); ^ Runtime error in 'Units': Bad argument types Argument types given: AlgQuat >> UnitGroup(A);; ^ Runtime error in 'UnitGroup': Bad argument types Argument types given: AlgQuat Total time: 3.029 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 69-162-40-105.stcgpa.adelphia.net. (69.162.40.105) Time: Thu Feb 5 23:02:53 2004 Input: A := QuaternionAlgebra< RationalField() | -2, -5>; RamifiedPrimes(A); Discriminant(A); IsDefinite(A); S:=MaximalOrder(A); Units(S); UnitGroup(S); Output: Magma V2.10-6 Thu Feb 5 2004 23:02:50 on modular [Seed = 3248656489] ------------------------------------- [ 5 ] 5 true [ 1, -1, 1/2 + 1/4*i - 1/4*k, -1/2 - 1/4*i + 1/4*k, -1/2 + 1/4*i - 1/4*k, 1/2 - 1/4*i + 1/4*k ] Permutation group acting on a set of cardinality 6 Order = 6 = 2 * 3 Id($) (1, 2)(3, 4)(5, 6) (1, 3, 5, 2, 4, 6) (1, 4, 5)(2, 3, 6) (1, 5, 4)(2, 6, 3) (1, 6, 4, 2, 5, 3) Mapping from: GrpPerm: $, Degree 6, Order 2 * 3 to [ (1 0 0 0), (-1 0 0 0), ( 1 -1 0 0), (-1 1 0 0), ( 0 -1 0 0), (0 1 0 0) ] <(1, 2)(3, 4)(5, 6), -1> <(1, 3, 5, 2, 4, 6), 1/2 + 1/4*i - 1/4*k> <(1, 4, 5)(2, 3, 6), -1/2 - 1/4*i + 1/4*k> <(1, 5, 4)(2, 6, 3), -1/2 + 1/4*i - 1/4*k> <(1, 6, 4, 2, 5, 3), 1/2 - 1/4*i + 1/4*k> Total time: 3.109 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 69-162-40-105.stcgpa.adelphia.net. (69.162.40.105) Time: Thu Feb 5 23:09:30 2004 Input: A := QuaternionAlgebra< RationalField() | -2, -5>; RamifiedPrimes(A); Discriminant(A); IsDefinite(A); S:=MaximalOrder(A); Units(S); UnitGroup(S); (1/2 + 1/4*i - 1/4*k)*(1/2 + 1/4*i - 1/4*k) Output: Magma V2.10-6 Thu Feb 5 2004 23:09:26 on modular [Seed = 3602220514] ------------------------------------- [ 5 ] 5 true [ 1, -1, 1/2 + 1/4*i - 1/4*k, -1/2 - 1/4*i + 1/4*k, -1/2 + 1/4*i - 1/4*k, 1/2 - 1/4*i + 1/4*k ] Permutation group acting on a set of cardinality 6 Order = 6 = 2 * 3 Id($) (1, 2)(3, 4)(5, 6) (1, 3, 5, 2, 4, 6) (1, 4, 5)(2, 3, 6) (1, 5, 4)(2, 6, 3) (1, 6, 4, 2, 5, 3) Mapping from: GrpPerm: $, Degree 6, Order 2 * 3 to [ (1 0 0 0), (-1 0 0 0), ( 1 -1 0 0), (-1 1 0 0), ( 0 -1 0 0), (0 1 0 0) ] <(1, 2)(3, 4)(5, 6), -1> <(1, 3, 5, 2, 4, 6), 1/2 + 1/4*i - 1/4*k> <(1, 4, 5)(2, 3, 6), -1/2 - 1/4*i + 1/4*k> <(1, 5, 4)(2, 6, 3), -1/2 + 1/4*i - 1/4*k> <(1, 6, 4, 2, 5, 3), 1/2 - 1/4*i + 1/4*k> -1/2 + 1/4*i - 1/4*k Total time: 3.209 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 12-222-60-125.client.insightBB.com. (12.222.60.125) Time: Thu Feb 5 23:40:14 2004 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: Magma V2.10-6 Thu Feb 5 2004 23:40:10 on modular [Seed = 2448608121] ------------------------------------- Replace this by some code, then click [PARI] or [MAGMA]! Total time: 3.239 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 69-162-40-105.stcgpa.adelphia.net. (69.162.40.105) Time: Fri Feb 6 00:51:14 2004 Input: A := QuaternionAlgebra< RationalField() | -2, -5>; RamifiedPrimes(A); Discriminant(A); IsDefinite(A); S:=MaximalOrder(A); Units(S); UnitGroup(S); M := MatrixAlgebra(A, 2); Output: Magma V2.10-6 Fri Feb 6 2004 00:51:11 on modular [Seed = 911564090] ------------------------------------- [ 5 ] 5 true [ 1, -1, 1/2 + 1/4*i - 1/4*k, -1/2 - 1/4*i + 1/4*k, -1/2 + 1/4*i - 1/4*k, 1/2 - 1/4*i + 1/4*k ] Permutation group acting on a set of cardinality 6 Order = 6 = 2 * 3 Id($) (1, 2)(3, 4)(5, 6) (1, 3, 5, 2, 4, 6) (1, 4, 5)(2, 3, 6) (1, 5, 4)(2, 6, 3) (1, 6, 4, 2, 5, 3) Mapping from: GrpPerm: $, Degree 6, Order 2 * 3 to [ (1 0 0 0), (-1 0 0 0), ( 1 -1 0 0), (-1 1 0 0), ( 0 -1 0 0), (0 1 0 0) ] <(1, 2)(3, 4)(5, 6), -1> <(1, 3, 5, 2, 4, 6), 1/2 + 1/4*i - 1/4*k> <(1, 4, 5)(2, 3, 6), -1/2 - 1/4*i + 1/4*k> <(1, 5, 4)(2, 6, 3), -1/2 + 1/4*i - 1/4*k> <(1, 6, 4, 2, 5, 3), 1/2 - 1/4*i + 1/4*k> Total time: 3.289 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 69-162-40-105.stcgpa.adelphia.net. (69.162.40.105) Time: Fri Feb 6 00:52:33 2004 Input: A := QuaternionAlgebra< RationalField() | -2, -5>; RamifiedPrimes(A); Discriminant(A); IsDefinite(A); S:=MaximalOrder(A); Units(S); UnitGroup(S); M := MatrixAlgebra(A, 2); Units(M); Output: Magma V2.10-6 Fri Feb 6 2004 00:52:30 on modular [Seed = 1029592800] ------------------------------------- [ 5 ] 5 true [ 1, -1, 1/2 + 1/4*i - 1/4*k, -1/2 - 1/4*i + 1/4*k, -1/2 + 1/4*i - 1/4*k, 1/2 - 1/4*i + 1/4*k ] Permutation group acting on a set of cardinality 6 Order = 6 = 2 * 3 Id($) (1, 2)(3, 4)(5, 6) (1, 3, 5, 2, 4, 6) (1, 4, 5)(2, 3, 6) (1, 5, 4)(2, 6, 3) (1, 6, 4, 2, 5, 3) Mapping from: GrpPerm: $, Degree 6, Order 2 * 3 to [ (1 0 0 0), (-1 0 0 0), ( 1 -1 0 0), (-1 1 0 0), ( 0 -1 0 0), (0 1 0 0) ] <(1, 2)(3, 4)(5, 6), -1> <(1, 3, 5, 2, 4, 6), 1/2 + 1/4*i - 1/4*k> <(1, 4, 5)(2, 3, 6), -1/2 - 1/4*i + 1/4*k> <(1, 5, 4)(2, 6, 3), -1/2 + 1/4*i - 1/4*k> <(1, 6, 4, 2, 5, 3), 1/2 - 1/4*i + 1/4*k> >> Units(M);; ^ Runtime error in 'Units': Bad argument types Argument types given: AlgMat Total time: 3.099 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 69-162-40-105.stcgpa.adelphia.net. (69.162.40.105) Time: Fri Feb 6 00:53:16 2004 Input: A := QuaternionAlgebra< RationalField() | -2, -5>; RamifiedPrimes(A); Discriminant(A); IsDefinite(A); S:=MaximalOrder(A); Units(S); UnitGroup(S); M := MatrixAlgebra(S, 2); Units(M); Output: Magma V2.10-6 Fri Feb 6 2004 00:53:13 on modular [Seed = 3299323726] ------------------------------------- [ 5 ] 5 true [ 1, -1, 1/2 + 1/4*i - 1/4*k, -1/2 - 1/4*i + 1/4*k, -1/2 + 1/4*i - 1/4*k, 1/2 - 1/4*i + 1/4*k ] Permutation group acting on a set of cardinality 6 Order = 6 = 2 * 3 Id($) (1, 2)(3, 4)(5, 6) (1, 3, 5, 2, 4, 6) (1, 4, 5)(2, 3, 6) (1, 5, 4)(2, 6, 3) (1, 6, 4, 2, 5, 3) Mapping from: GrpPerm: $, Degree 6, Order 2 * 3 to [ (1 0 0 0), (-1 0 0 0), ( 1 -1 0 0), (-1 1 0 0), ( 0 -1 0 0), (0 1 0 0) ] <(1, 2)(3, 4)(5, 6), -1> <(1, 3, 5, 2, 4, 6), 1/2 + 1/4*i - 1/4*k> <(1, 4, 5)(2, 3, 6), -1/2 - 1/4*i + 1/4*k> <(1, 5, 4)(2, 6, 3), -1/2 + 1/4*i - 1/4*k> <(1, 6, 4, 2, 5, 3), 1/2 - 1/4*i + 1/4*k> >> Units(M);; ^ Runtime error in 'Units': Bad argument types Argument types given: AlgMat Total time: 2.979 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 69-162-40-105.stcgpa.adelphia.net. (69.162.40.105) Time: Fri Feb 6 00:53:38 2004 Input: A := QuaternionAlgebra< RationalField() | -2, -5>; RamifiedPrimes(A); Discriminant(A); IsDefinite(A); S:=MaximalOrder(A); Units(S); UnitGroup(S); M := MatrixAlgebra(S, 2); UnitGroup(M); Output: Magma V2.10-6 Fri Feb 6 2004 00:53:34 on modular [Seed = 3551574094] ------------------------------------- [ 5 ] 5 true [ 1, -1, 1/2 + 1/4*i - 1/4*k, -1/2 - 1/4*i + 1/4*k, -1/2 + 1/4*i - 1/4*k, 1/2 - 1/4*i + 1/4*k ] Permutation group acting on a set of cardinality 6 Order = 6 = 2 * 3 Id($) (1, 2)(3, 4)(5, 6) (1, 3, 5, 2, 4, 6) (1, 4, 5)(2, 3, 6) (1, 5, 4)(2, 6, 3) (1, 6, 4, 2, 5, 3) Mapping from: GrpPerm: $, Degree 6, Order 2 * 3 to [ (1 0 0 0), (-1 0 0 0), ( 1 -1 0 0), (-1 1 0 0), ( 0 -1 0 0), (0 1 0 0) ] <(1, 2)(3, 4)(5, 6), -1> <(1, 3, 5, 2, 4, 6), 1/2 + 1/4*i - 1/4*k> <(1, 4, 5)(2, 3, 6), -1/2 - 1/4*i + 1/4*k> <(1, 5, 4)(2, 6, 3), -1/2 + 1/4*i - 1/4*k> <(1, 6, 4, 2, 5, 3), 1/2 - 1/4*i + 1/4*k> >> UnitGroup(M);; ^ Runtime error in 'UnitGroup': Bad argument types Argument types given: AlgMat Total time: 3.109 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 69-162-40-105.stcgpa.adelphia.net. (69.162.40.105) Time: Fri Feb 6 00:53:55 2004 Input: A := QuaternionAlgebra< RationalField() | -2, -5>; RamifiedPrimes(A); Discriminant(A); IsDefinite(A); S:=MaximalOrder(A); Units(S); UnitGroup(S); M := MatrixAlgebra(S, 2); M; Output: Magma V2.10-6 Fri Feb 6 2004 00:53:52 on modular [Seed = 3669602665] ------------------------------------- [ 5 ] 5 true [ 1, -1, 1/2 + 1/4*i - 1/4*k, -1/2 - 1/4*i + 1/4*k, -1/2 + 1/4*i - 1/4*k, 1/2 - 1/4*i + 1/4*k ] Permutation group acting on a set of cardinality 6 Order = 6 = 2 * 3 Id($) (1, 2)(3, 4)(5, 6) (1, 3, 5, 2, 4, 6) (1, 4, 5)(2, 3, 6) (1, 5, 4)(2, 6, 3) (1, 6, 4, 2, 5, 3) Mapping from: GrpPerm: $, Degree 6, Order 2 * 3 to [ (1 0 0 0), (-1 0 0 0), ( 1 -1 0 0), (-1 1 0 0), ( 0 -1 0 0), (0 1 0 0) ] <(1, 2)(3, 4)(5, 6), -1> <(1, 3, 5, 2, 4, 6), 1/2 + 1/4*i - 1/4*k> <(1, 4, 5)(2, 3, 6), -1/2 - 1/4*i + 1/4*k> <(1, 5, 4)(2, 6, 3), -1/2 + 1/4*i - 1/4*k> <(1, 6, 4, 2, 5, 3), 1/2 - 1/4*i + 1/4*k> Full Matrix Algebra of degree 2 over Quaternion Order of level (5, 1) with base ring Integer Ring Total time: 3.139 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 69-162-40-105.stcgpa.adelphia.net. (69.162.40.105) Time: Fri Feb 6 00:59:13 2004 Input: A := QuaternionAlgebra< RationalField() | -2, -5>; RamifiedPrimes(A); Discriminant(A); IsDefinite(A); S:=MaximalOrder(A); Units(S); UnitGroup(S); M := MatrixAlgebra(S, 2); GeneratorsOfAlgebraWithOne(M); Output: Magma V2.10-6 Fri Feb 6 2004 00:59:10 on modular [Seed = 3834087817] ------------------------------------- [ 5 ] 5 true [ 1, -1, 1/2 + 1/4*i - 1/4*k, -1/2 - 1/4*i + 1/4*k, -1/2 + 1/4*i - 1/4*k, 1/2 - 1/4*i + 1/4*k ] Permutation group acting on a set of cardinality 6 Order = 6 = 2 * 3 Id($) (1, 2)(3, 4)(5, 6) (1, 3, 5, 2, 4, 6) (1, 4, 5)(2, 3, 6) (1, 5, 4)(2, 6, 3) (1, 6, 4, 2, 5, 3) Mapping from: GrpPerm: $, Degree 6, Order 2 * 3 to [ (1 0 0 0), (-1 0 0 0), ( 1 -1 0 0), (-1 1 0 0), ( 0 -1 0 0), (0 1 0 0) ] <(1, 2)(3, 4)(5, 6), -1> <(1, 3, 5, 2, 4, 6), 1/2 + 1/4*i - 1/4*k> <(1, 4, 5)(2, 3, 6), -1/2 - 1/4*i + 1/4*k> <(1, 5, 4)(2, 6, 3), -1/2 + 1/4*i - 1/4*k> <(1, 6, 4, 2, 5, 3), 1/2 - 1/4*i + 1/4*k> >> GeneratorsOfAlgebraWithOne(M);; ^ User error: Identifier 'GeneratorsOfAlgebraWithOne' has not been declared or assigned Total time: 3.119 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 69-162-40-105.stcgpa.adelphia.net. (69.162.40.105) Time: Fri Feb 6 01:00:41 2004 Input: A := QuaternionAlgebra< RationalField() | -2, -5>; RamifiedPrimes(A); Discriminant(A); IsDefinite(A); S:=MaximalOrder(A); Units(S); UnitGroup(S); M := MatrixRing(S, 2); Output: Magma V2.10-6 Fri Feb 6 2004 01:00:38 on modular [Seed = 4221081150] ------------------------------------- [ 5 ] 5 true [ 1, -1, 1/2 + 1/4*i - 1/4*k, -1/2 - 1/4*i + 1/4*k, -1/2 + 1/4*i - 1/4*k, 1/2 - 1/4*i + 1/4*k ] Permutation group acting on a set of cardinality 6 Order = 6 = 2 * 3 Id($) (1, 2)(3, 4)(5, 6) (1, 3, 5, 2, 4, 6) (1, 4, 5)(2, 3, 6) (1, 5, 4)(2, 6, 3) (1, 6, 4, 2, 5, 3) Mapping from: GrpPerm: $, Degree 6, Order 2 * 3 to [ (1 0 0 0), (-1 0 0 0), ( 1 -1 0 0), (-1 1 0 0), ( 0 -1 0 0), (0 1 0 0) ] <(1, 2)(3, 4)(5, 6), -1> <(1, 3, 5, 2, 4, 6), 1/2 + 1/4*i - 1/4*k> <(1, 4, 5)(2, 3, 6), -1/2 - 1/4*i + 1/4*k> <(1, 5, 4)(2, 6, 3), -1/2 + 1/4*i - 1/4*k> <(1, 6, 4, 2, 5, 3), 1/2 - 1/4*i + 1/4*k> Total time: 3.059 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 69-162-40-105.stcgpa.adelphia.net. (69.162.40.105) Time: Fri Feb 6 01:07:45 2004 Input: A := QuaternionAlgebra< RationalField() | -2, -5>; RamifiedPrimes(A); Discriminant(A); IsDefinite(A); S:=MaximalOrder(A); # Units(S); # UnitGroup(S); M := MatrixRing(S, 2); Output: Magma V2.10-6 Fri Feb 6 2004 01:07:41 on modular [Seed = 2684154097] ------------------------------------- [ 5 ] 5 true 6 6 Total time: 3.029 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 69-162-40-105.stcgpa.adelphia.net. (69.162.40.105) Time: Fri Feb 6 01:07:59 2004 Input: A := QuaternionAlgebra< RationalField() | -2, -5>; # RamifiedPrimes(A); # Discriminant(A); # IsDefinite(A); S:=MaximalOrder(A); # Units(S); # UnitGroup(S); M := MatrixRing(S, 2); Output: Magma V2.10-6 Fri Feb 6 2004 01:07:56 on modular [Seed = 2797980121] ------------------------------------- 1 >> # Discriminant(A); ^ Runtime error in '#': Bad argument types Argument types given: FldRatElt >> # IsDefinite(A); ^ Runtime error in '#': Bad argument types Argument types given: BoolElt 6 6 Total time: 3.019 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 69-162-40-105.stcgpa.adelphia.net. (69.162.40.105) Time: Fri Feb 6 01:08:30 2004 Input: A := QuaternionAlgebra< RationalField() | -2, -5>; # RamifiedPrimes(A); Discriminant(A); # IsDefinite(A); S:=MaximalOrder(A); # Units(S); # UnitGroup(S); M := MatrixRing(S, 2); Output: Magma V2.10-6 Fri Feb 6 2004 01:08:27 on modular [Seed = 2916008629] ------------------------------------- 1 5 >> # IsDefinite(A); ^ Runtime error in '#': Bad argument types Argument types given: BoolElt 6 6 Total time: 3.089 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 69-162-40-105.stcgpa.adelphia.net. (69.162.40.105) Time: Fri Feb 6 01:08:49 2004 Input: A := QuaternionAlgebra< RationalField() | -2, -5>; # RamifiedPrimes(A); # Discriminant(A); # IsDefinite(A); S:=MaximalOrder(A); # Units(S); # UnitGroup(S); M := MatrixRing(S, 2); Output: Magma V2.10-6 Fri Feb 6 2004 01:08:45 on modular [Seed = 3034045338] ------------------------------------- 1 >> # Discriminant(A); ^ Runtime error in '#': Bad argument types Argument types given: FldRatElt >> # IsDefinite(A); ^ Runtime error in '#': Bad argument types Argument types given: BoolElt 6 6 Total time: 3.099 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 69-162-40-105.stcgpa.adelphia.net. (69.162.40.105) Time: Fri Feb 6 01:11:46 2004 Input: A := QuaternionAlgebra< RationalField() | -2, -5>; // RamifiedPrimes(A); // Discriminant(A); // IsDefinite(A); S:=MaximalOrder(A); // Units(S); // UnitGroup(S); M := MatrixRing(S, 2); Output: Magma V2.10-6 Fri Feb 6 2004 01:11:43 on modular [Seed = 1278163991] ------------------------------------- Total time: 3.019 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 69-162-40-105.stcgpa.adelphia.net. (69.162.40.105) Time: Fri Feb 6 01:18:47 2004 Input: A := QuaternionAlgebra< RationalField() | -2, -5>; // RamifiedPrimes(A); // Discriminant(A); // IsDefinite(A); S:=MaximalOrder(A); // Units(S); // UnitGroup(S); M := MatrixRing(S, 2); Random(M); Output: Magma V2.10-6 Fri Feb 6 2004 01:18:43 on modular [Seed = 1597779672] ------------------------------------- >> Random(M);; ^ Runtime error in 'Random': Coefficient ring of argument 1 has no random algorithm Total time: 3.029 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 69-162-40-105.stcgpa.adelphia.net. (69.162.40.105) Time: Fri Feb 6 01:19:04 2004 Input: A := QuaternionAlgebra< RationalField() | -2, -5>; // RamifiedPrimes(A); // Discriminant(A); // IsDefinite(A); S:=MaximalOrder(A); // Units(S); // UnitGroup(S); M := MatrixAlgebra(S, 2); Random(M); Output: Magma V2.10-6 Fri Feb 6 2004 01:19:01 on modular [Seed = 1610813937] ------------------------------------- >> Random(M);; ^ Runtime error in 'Random': Coefficient ring of argument 1 has no random algorithm Total time: 2.989 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 69-162-40-105.stcgpa.adelphia.net. (69.162.40.105) Time: Fri Feb 6 01:19:56 2004 Input: A := QuaternionAlgebra< RationalField() | -2, -5>; // RamifiedPrimes(A); // Discriminant(A); // IsDefinite(A); S:=MaximalOrder(A); // Units(S); // UnitGroup(S); M := MatrixRing(S, 2); M!1; Output: Magma V2.10-6 Fri Feb 6 2004 01:19:52 on modular [Seed = 1762269989] ------------------------------------- [1 0] [0 1] Total time: 3.069 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 69-162-40-105.stcgpa.adelphia.net. (69.162.40.105) Time: Fri Feb 6 01:20:08 2004 Input: A := QuaternionAlgebra< RationalField() | -2, -5>; // RamifiedPrimes(A); // Discriminant(A); // IsDefinite(A); S:=MaximalOrder(A); // Units(S); // UnitGroup(S); M := MatrixAlgebra(S, 2); M!1; Output: Magma V2.10-6 Fri Feb 6 2004 01:20:05 on modular [Seed = 2031749928] ------------------------------------- [1 0] [0 1] Total time: 2.969 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 69-162-40-105.stcgpa.adelphia.net. (69.162.40.105) Time: Fri Feb 6 01:21:42 2004 Input: A := QuaternionAlgebra< RationalField() | -2, -5>; // RamifiedPrimes(A); // Discriminant(A); // IsDefinite(A); S:=MaximalOrder(A); // Units(S); // UnitGroup(S); M := MatrixRing(S, 2); N := MatrixAlgebra(S, 2); M:Units; Output: Magma V2.10-6 Fri Feb 6 2004 01:21:39 on modular [Seed = 56652084] ------------------------------------- >> M:Units;; ^ User error: Bad print level "Units" Total time: 3.039 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 69-162-40-105.stcgpa.adelphia.net. (69.162.40.105) Time: Fri Feb 6 01:22:42 2004 Input: A := QuaternionAlgebra< RationalField() | -2, -5>; // RamifiedPrimes(A); // Discriminant(A); // IsDefinite(A); S:=MaximalOrder(A); // Units(S); // UnitGroup(S); M := MatrixAlgebra(S, 2); BaseRing(M); Output: Magma V2.10-6 Fri Feb 6 2004 01:22:39 on modular [Seed = 343369471] ------------------------------------- Quaternion Order of level (5, 1) with base ring Integer Ring Total time: 2.979 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 69-162-40-105.stcgpa.adelphia.net. (69.162.40.105) Time: Fri Feb 6 01:23:00 2004 Input: A := QuaternionAlgebra< RationalField() | -2, -5>; // RamifiedPrimes(A); // Discriminant(A); // IsDefinite(A); S:=MaximalOrder(A); // Units(S); // UnitGroup(S); M := MatrixAlgebra(S, 2); BaseRing(M); CoefficientRing(M); Output: Magma V2.10-6 Fri Feb 6 2004 01:22:57 on modular [Seed = 494825368] ------------------------------------- Quaternion Order of level (5, 1) with base ring Integer Ring Quaternion Order of level (5, 1) with base ring Integer Ring Total time: 3.059 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 69-162-40-105.stcgpa.adelphia.net. (69.162.40.105) Time: Fri Feb 6 01:23:18 2004 Input: A := QuaternionAlgebra< RationalField() | -2, -5>; // RamifiedPrimes(A); // Discriminant(A); // IsDefinite(A); S:=MaximalOrder(A); // Units(S); // UnitGroup(S); M := MatrixAlgebra(S, 2); Degree(M); Output: Magma V2.10-6 Fri Feb 6 2004 01:23:15 on modular [Seed = 642077873] ------------------------------------- 2 Total time: 3.059 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 69-162-40-105.stcgpa.adelphia.net. (69.162.40.105) Time: Fri Feb 6 01:23:39 2004 Input: A := QuaternionAlgebra< RationalField() | -2, -5>; // RamifiedPrimes(A); // Discriminant(A); // IsDefinite(A); S:=MaximalOrder(A); // Units(S); // UnitGroup(S); M := MatrixAlgebra(S, 2); Generators(M); Output: Magma V2.10-6 Fri Feb 6 2004 01:23:36 on modular [Seed = 793533827] ------------------------------------- { [0 1] [1 0], [1 0] [0 0] } Total time: 2.979 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 69-162-40-105.stcgpa.adelphia.net. (69.162.40.105) Time: Fri Feb 6 01:24:09 2004 Input: A := QuaternionAlgebra< RationalField() | -2, -5>; // RamifiedPrimes(A); // Discriminant(A); // IsDefinite(A); S:=MaximalOrder(A); // Units(S); // UnitGroup(S); M := MatrixAlgebra(S, 2); Generic(M); Output: Magma V2.10-6 Fri Feb 6 2004 01:24:06 on modular [Seed = 810763122] ------------------------------------- Full Matrix Algebra of degree 2 over Quaternion Order of level (5, 1) with base ring Integer Ring Total time: 3.099 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 69-162-40-105.stcgpa.adelphia.net. (69.162.40.105) Time: Fri Feb 6 01:24:51 2004 Input: A := QuaternionAlgebra< RationalField() | -2, -5>; // RamifiedPrimes(A); // Discriminant(A); // IsDefinite(A); S:=MaximalOrder(A); // Units(S); // UnitGroup(S); M := MatrixAlgebra(S, 2); Dimension(M); Output: Magma V2.10-6 Fri Feb 6 2004 01:24:48 on modular [Seed = 962218573] ------------------------------------- 4 Total time: 3.169 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 69-162-40-105.stcgpa.adelphia.net. (69.162.40.105) Time: Fri Feb 6 01:25:48 2004 Input: A := QuaternionAlgebra< RationalField() | -2, -5>; // RamifiedPrimes(A); // Discriminant(A); // IsDefinite(A); S:=MaximalOrder(A); // Units(S); // UnitGroup(S); M := MatrixAlgebra(S, 2); Center(M); Output: Magma V2.10-6 Fri Feb 6 2004 01:25:45 on modular [Seed = 3467492835] ------------------------------------- >> Center(M);; ^ Runtime error in 'Center': Argument 1 has no echelon algorithm Total time: 2.999 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 69-162-40-105.stcgpa.adelphia.net. (69.162.40.105) Time: Fri Feb 6 01:26:17 2004 Input: A := QuaternionAlgebra< RationalField() | -2, -5>; // RamifiedPrimes(A); // Discriminant(A); // IsDefinite(A); S:=MaximalOrder(A); // Units(S); // UnitGroup(S); M := MatrixAlgebra(S, 2); N := MatrixAlgebra(A, 2); Center(N); Output: Magma V2.10-6 Fri Feb 6 2004 01:26:14 on modular [Seed = 3501433618] ------------------------------------- >> Center(N);; ^ Runtime error in 'Center': Argument 1 has no echelon algorithm Total time: 3.139 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 69-162-40-105.stcgpa.adelphia.net. (69.162.40.105) Time: Fri Feb 6 01:27:23 2004 Input: A := QuaternionAlgebra< RationalField() | -2, -5>; // RamifiedPrimes(A); // Discriminant(A); // IsDefinite(A); S:=MaximalOrder(A); // Units(S); // UnitGroup(S); M := MatrixAlgebra(S, 2); N := MatrixAlgebra(A, 2); Basis(N); Output: Magma V2.10-6 Fri Feb 6 2004 01:27:20 on modular [Seed = 3652889173] ------------------------------------- [ [1 0] [0 0], [0 1] [0 0], [0 0] [1 0], [0 0] [0 1] ] Total time: 3.049 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 69-162-40-105.stcgpa.adelphia.net. (69.162.40.105) Time: Fri Feb 6 01:27:37 2004 Input: A := QuaternionAlgebra< RationalField() | -2, -5>; // RamifiedPrimes(A); // Discriminant(A); // IsDefinite(A); S:=MaximalOrder(A); // Units(S); // UnitGroup(S); M := MatrixAlgebra(S, 2); N := MatrixAlgebra(A, 2); Basis(M); Output: Magma V2.10-6 Fri Feb 6 2004 01:27:34 on modular [Seed = 3800142192] ------------------------------------- [ [1 0] [0 0], [0 1] [0 0], [0 0] [1 0], [0 0] [0 1] ] Total time: 3.019 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 69-162-40-105.stcgpa.adelphia.net. (69.162.40.105) Time: Fri Feb 6 01:29:28 2004 Input: A := QuaternionAlgebra< RationalField() | -2, -5>; // RamifiedPrimes(A); // Discriminant(A); // IsDefinite(A); S:=MaximalOrder(A); // Units(S); // UnitGroup(S); M := MatrixAlgebra(S, 2); N := MatrixAlgebra(A, 2); Center(M); Output: Magma V2.10-6 Fri Feb 6 2004 01:29:25 on modular [Seed = 3951599594] ------------------------------------- >> Center(M);; ^ Runtime error in 'Center': Argument 1 has no echelon algorithm Total time: 3.059 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host baboen.math.kun.nl. (131.174.132.109) Time: Fri Feb 6 03:42:12 2004 Input: P := [ p : p in [1..1000] | IsPrime(p) ]; R := []; for i in [1..10] do Q := [ P[j] : j in [1..#P-i] | IsPrime(P[j]) and IsPrime(P[j+i]) ]; Append( ~R, Q ); end for; for i in R do print i; end for; Output: Magma V2.10-6 Fri Feb 6 2004 03:42:08 on modular [Seed = 3185487512] ------------------------------------- [ 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229, 233, 239, 241, 251, 257, 263, 269, 271, 277, 281, 283, 293, 307, 311, 313, 317, 331, 337, 347, 349, 353, 359, 367, 373, 379, 383, 389, 397, 401, 409, 419, 421, 431, 433, 439, 443, 449, 457, 461, 463, 467, 479, 487, 491, 499, 503, 509, 521, 523, 541, 547, 557, 563, 569, 571, 577, 587, 593, 599, 601, 607, 613, 617, 619, 631, 641, 643, 647, 653, 659, 661, 673, 677, 683, 691, 701, 709, 719, 727, 733, 739, 743, 751, 757, 761, 769, 773, 787, 797, 809, 811, 821, 823, 827, 829, 839, 853, 857, 859, 863, 877, 881, 883, 887, 907, 911, 919, 929, 937, 941, 947, 953, 967, 971, 977, 983, 991 ] [ 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229, 233, 239, 241, 251, 257, 263, 269, 271, 277, 281, 283, 293, 307, 311, 313, 317, 331, 337, 347, 349, 353, 359, 367, 373, 379, 383, 389, 397, 401, 409, 419, 421, 431, 433, 439, 443, 449, 457, 461, 463, 467, 479, 487, 491, 499, 503, 509, 521, 523, 541, 547, 557, 563, 569, 571, 577, 587, 593, 599, 601, 607, 613, 617, 619, 631, 641, 643, 647, 653, 659, 661, 673, 677, 683, 691, 701, 709, 719, 727, 733, 739, 743, 751, 757, 761, 769, 773, 787, 797, 809, 811, 821, 823, 827, 829, 839, 853, 857, 859, 863, 877, 881, 883, 887, 907, 911, 919, 929, 937, 941, 947, 953, 967, 971, 977, 983 ] [ 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229, 233, 239, 241, 251, 257, 263, 269, 271, 277, 281, 283, 293, 307, 311, 313, 317, 331, 337, 347, 349, 353, 359, 367, 373, 379, 383, 389, 397, 401, 409, 419, 421, 431, 433, 439, 443, 449, 457, 461, 463, 467, 479, 487, 491, 499, 503, 509, 521, 523, 541, 547, 557, 563, 569, 571, 577, 587, 593, 599, 601, 607, 613, 617, 619, 631, 641, 643, 647, 653, 659, 661, 673, 677, 683, 691, 701, 709, 719, 727, 733, 739, 743, 751, 757, 761, 769, 773, 787, 797, 809, 811, 821, 823, 827, 829, 839, 853, 857, 859, 863, 877, 881, 883, 887, 907, 911, 919, 929, 937, 941, 947, 953, 967, 971, 977 ] [ 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229, 233, 239, 241, 251, 257, 263, 269, 271, 277, 281, 283, 293, 307, 311, 313, 317, 331, 337, 347, 349, 353, 359, 367, 373, 379, 383, 389, 397, 401, 409, 419, 421, 431, 433, 439, 443, 449, 457, 461, 463, 467, 479, 487, 491, 499, 503, 509, 521, 523, 541, 547, 557, 563, 569, 571, 577, 587, 593, 599, 601, 607, 613, 617, 619, 631, 641, 643, 647, 653, 659, 661, 673, 677, 683, 691, 701, 709, 719, 727, 733, 739, 743, 751, 757, 761, 769, 773, 787, 797, 809, 811, 821, 823, 827, 829, 839, 853, 857, 859, 863, 877, 881, 883, 887, 907, 911, 919, 929, 937, 941, 947, 953, 967, 971 ] [ 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229, 233, 239, 241, 251, 257, 263, 269, 271, 277, 281, 283, 293, 307, 311, 313, 317, 331, 337, 347, 349, 353, 359, 367, 373, 379, 383, 389, 397, 401, 409, 419, 421, 431, 433, 439, 443, 449, 457, 461, 463, 467, 479, 487, 491, 499, 503, 509, 521, 523, 541, 547, 557, 563, 569, 571, 577, 587, 593, 599, 601, 607, 613, 617, 619, 631, 641, 643, 647, 653, 659, 661, 673, 677, 683, 691, 701, 709, 719, 727, 733, 739, 743, 751, 757, 761, 769, 773, 787, 797, 809, 811, 821, 823, 827, 829, 839, 853, 857, 859, 863, 877, 881, 883, 887, 907, 911, 919, 929, 937, 941, 947, 953, 967 ] [ 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229, 233, 239, 241, 251, 257, 263, 269, 271, 277, 281, 283, 293, 307, 311, 313, 317, 331, 337, 347, 349, 353, 359, 367, 373, 379, 383, 389, 397, 401, 409, 419, 421, 431, 433, 439, 443, 449, 457, 461, 463, 467, 479, 487, 491, 499, 503, 509, 521, 523, 541, 547, 557, 563, 569, 571, 577, 587, 593, 599, 601, 607, 613, 617, 619, 631, 641, 643, 647, 653, 659, 661, 673, 677, 683, 691, 701, 709, 719, 727, 733, 739, 743, 751, 757, 761, 769, 773, 787, 797, 809, 811, 821, 823, 827, 829, 839, 853, 857, 859, 863, 877, 881, 883, 887, 907, 911, 919, 929, 937, 941, 947, 953 ] [ 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229, 233, 239, 241, 251, 257, 263, 269, 271, 277, 281, 283, 293, 307, 311, 313, 317, 331, 337, 347, 349, 353, 359, 367, 373, 379, 383, 389, 397, 401, 409, 419, 421, 431, 433, 439, 443, 449, 457, 461, 463, 467, 479, 487, 491, 499, 503, 509, 521, 523, 541, 547, 557, 563, 569, 571, 577, 587, 593, 599, 601, 607, 613, 617, 619, 631, 641, 643, 647, 653, 659, 661, 673, 677, 683, 691, 701, 709, 719, 727, 733, 739, 743, 751, 757, 761, 769, 773, 787, 797, 809, 811, 821, 823, 827, 829, 839, 853, 857, 859, 863, 877, 881, 883, 887, 907, 911, 919, 929, 937, 941, 947 ] [ 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229, 233, 239, 241, 251, 257, 263, 269, 271, 277, 281, 283, 293, 307, 311, 313, 317, 331, 337, 347, 349, 353, 359, 367, 373, 379, 383, 389, 397, 401, 409, 419, 421, 431, 433, 439, 443, 449, 457, 461, 463, 467, 479, 487, 491, 499, 503, 509, 521, 523, 541, 547, 557, 563, 569, 571, 577, 587, 593, 599, 601, 607, 613, 617, 619, 631, 641, 643, 647, 653, 659, 661, 673, 677, 683, 691, 701, 709, 719, 727, 733, 739, 743, 751, 757, 761, 769, 773, 787, 797, 809, 811, 821, 823, 827, 829, 839, 853, 857, 859, 863, 877, 881, 883, 887, 907, 911, 919, 929, 937, 941 ] [ 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229, 233, 239, 241, 251, 257, 263, 269, 271, 277, 281, 283, 293, 307, 311, 313, 317, 331, 337, 347, 349, 353, 359, 367, 373, 379, 383, 389, 397, 401, 409, 419, 421, 431, 433, 439, 443, 449, 457, 461, 463, 467, 479, 487, 491, 499, 503, 509, 521, 523, 541, 547, 557, 563, 569, 571, 577, 587, 593, 599, 601, 607, 613, 617, 619, 631, 641, 643, 647, 653, 659, 661, 673, 677, 683, 691, 701, 709, 719, 727, 733, 739, 743, 751, 757, 761, 769, 773, 787, 797, 809, 811, 821, 823, 827, 829, 839, 853, 857, 859, 863, 877, 881, 883, 887, 907, 911, 919, 929, 937 ] [ 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229, 233, 239, 241, 251, 257, 263, 269, 271, 277, 281, 283, 293, 307, 311, 313, 317, 331, 337, 347, 349, 353, 359, 367, 373, 379, 383, 389, 397, 401, 409, 419, 421, 431, 433, 439, 443, 449, 457, 461, 463, 467, 479, 487, 491, 499, 503, 509, 521, 523, 541, 547, 557, 563, 569, 571, 577, 587, 593, 599, 601, 607, 613, 617, 619, 631, 641, 643, 647, 653, 659, 661, 673, 677, 683, 691, 701, 709, 719, 727, 733, 739, 743, 751, 757, 761, 769, 773, 787, 797, 809, 811, 821, 823, 827, 829, 839, 853, 857, 859, 863, 877, 881, 883, 887, 907, 911, 919, 929 ] Total time: 3.189 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host baboen.math.kun.nl. (131.174.132.109) Time: Fri Feb 6 03:43:43 2004 Input: P := [ p : p in [1..1000] | IsPrime(p) ]; R := []; for i in [1..10] do Q := [ P[j] : j in [1..#P-i] | P[j]+i in P ]; Append( ~R, Q ); end for; for i in R do print i; end for; Output: Magma V2.10-6 Fri Feb 6 2004 03:43:40 on modular [Seed = 1193563325] ------------------------------------- [ 2 ] [ 3, 5, 11, 17, 29, 41, 59, 71, 101, 107, 137, 149, 179, 191, 197, 227, 239, 269, 281, 311, 347, 419, 431, 461, 521, 569, 599, 617, 641, 659, 809, 821, 827, 857, 881 ] [ 2 ] [ 3, 7, 13, 19, 37, 43, 67, 79, 97, 103, 109, 127, 163, 193, 223, 229, 277, 307, 313, 349, 379, 397, 439, 457, 463, 487, 499, 613, 643, 673, 739, 757, 769, 823, 853, 859, 877, 883, 907, 937, 967 ] [ 2 ] [ 5, 7, 11, 13, 17, 23, 31, 37, 41, 47, 53, 61, 67, 73, 83, 97, 101, 103, 107, 131, 151, 157, 167, 173, 191, 193, 223, 227, 233, 251, 257, 263, 271, 277, 307, 311, 331, 347, 353, 367, 373, 383, 433, 443, 457, 461, 503, 541, 557, 563, 571, 587, 593, 601, 607, 613, 641, 647, 653, 677, 727, 733, 751, 821, 823, 853, 857, 877, 881, 941, 947 ] [] [ 3, 5, 11, 23, 29, 53, 59, 71, 89, 101, 131, 149, 173, 191, 233, 263, 269, 359, 389, 401, 431, 449, 479, 491, 563, 569, 593, 599, 653, 683, 701, 719, 743, 761, 821, 911, 929 ] [ 2 ] [ 3, 7, 13, 19, 31, 37, 43, 61, 73, 79, 97, 103, 127, 139, 157, 163, 181, 223, 229, 241, 271, 283, 307, 337, 349, 373, 379, 409, 421, 433, 439, 457, 499, 547, 577, 607, 631, 643, 673, 691, 709, 733, 751, 787, 811, 829, 853, 877, 919 ] Total time: 3.079 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (217.218.127.70) Time: Fri Feb 6 07:21:36 2004 Input: k := GF(2); C := PrimitivePolynomial(k,9); C; for j in [31..32] do for k in [17..23] do for m in [14..17] do for n in [8..13] do C := ((1 + X^n)^21)*((1 + X^m)^23)*((1 + X^k)^27)*((1 + X^j)^29) + X^1279; if IsPrimitive(C) then C; n; m; k; j; end if; end for; end for; end for; end for; Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Fri Feb 6 2004 07:21:12 on modular [Seed = 3968805405] ------------------------------------- X^9 + X^4 + 1 Errors: /home/mfd/gomagma: line 2: 2469 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host 3(NXDOMAIN) (217.218.127.70) Time: Fri Feb 6 07:22:49 2004 Input: k := GF(2); C := PrimitivePolynomial(k,9); C; for j in [21..32] do for k in [16..20] do for m in [12..15] do for n in [5..11] do C := ((1 + X^n)^21)*((1 + X^m)^23)*((1 + X^k)^27)*((1 + X^j)^29) + X^1279; if IsPrimitive(C) then C; n; m; k; j; end if; end for; end for; end for; end for; Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Fri Feb 6 2004 07:22:26 on modular [Seed = 3867484589] ------------------------------------- X^9 + X^4 + 1 Errors: /home/mfd/gomagma: line 2: 2479 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host 3(NXDOMAIN) (217.218.127.70) Time: Fri Feb 6 07:25:05 2004 Input: k := GF(2); C := PrimitivePolynomial(k,9); C; for j in [21..32] do for k in [16..20] do for m in [12..15] do for n in [9..11] do C := ((1 + X^n)^17)*((1 + X^m)^19)*((1 + X^k)^21)*((1 + X^j)^23) + X^1279; if IsPrimitive(C) then C; n; m; k; j; end if; end for; end for; end for; end for; Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Fri Feb 6 2004 07:24:41 on modular [Seed = 4120261173] ------------------------------------- X^9 + X^4 + 1 X^1324 + X^1314 + X^1310 + X^1308 + X^1298 + X^1296 + X^1294 + X^1290 + X^1282 + X^1280 + X^1279 + X^1274 + X^1260 + X^1258 + X^1246 + X^1244 + X^1232 + X^1230 + X^1218 + X^1216 + X^1202 + X^1194 + X^1178 + X^1170 + X^1164 + X^1150 + X^1148 + X^1146 + X^1138 + X^1136 + X^1134 + X^1132 + X^1122 + X^1120 + X^1118 + X^1116 + X^1114 + X^1104 + X^1102 + X^1098 + X^1088 + X^1036 + X^1026 + X^1022 + X^1020 + X^1010 + X^1008 + X^1006 + X^1004 + X^1002 + X^992 + X^990 + X^988 + X^986 + X^978 + X^976 + X^974 + X^972 + X^962 + X^960 + X^958 + X^956 + X^954 + X^944 + X^942 + X^938 + X^928 + X^908 + X^898 + X^894 + X^892 + X^882 + X^880 + X^878 + X^876 + X^874 + X^864 + X^862 + X^860 + X^858 + X^850 + X^848 + X^846 + X^844 + X^834 + X^832 + X^830 + X^828 + X^826 + X^816 + X^814 + X^812 + X^810 + X^802 + X^800 + X^798 + X^796 + X^786 + X^784 + X^782 + X^778 + X^770 + X^768 + X^762 + X^746 + X^738 + X^722 + X^716 + X^714 + X^706 + X^702 + X^700 + X^698 + X^688 + X^686 + X^682 + X^672 + X^652 + X^642 + X^638 + X^636 + X^626 + X^624 + X^622 + X^618 + X^610 + X^608 + X^602 + X^586 + X^578 + X^562 + X^556 + X^554 + X^546 + X^542 + X^540 + X^538 + X^528 + X^526 + X^524 + X^522 + X^514 + X^512 + X^510 + X^508 + X^498 + X^496 + X^494 + X^492 + X^490 + X^480 + X^478 + X^476 + X^474 + X^466 + X^464 + X^462 + X^460 + X^450 + X^448 + X^446 + X^444 + X^442 + X^432 + X^430 + X^426 + X^416 + X^396 + X^386 + X^382 + X^380 + X^370 + X^368 + X^366 + X^364 + X^362 + X^352 + X^350 + X^348 + X^346 + X^338 + X^336 + X^334 + X^332 + X^322 + X^320 + X^318 + X^316 + X^314 + X^304 + X^302 + X^298 + X^288 + X^236 + X^226 + X^222 + X^220 + X^210 + X^208 + X^206 + X^204 + X^202 + X^192 + X^190 + X^188 + X^186 + X^178 + X^176 + X^174 + X^160 + X^154 + X^146 + X^130 + X^122 + X^108 + X^106 + X^94 + X^92 + X^80 + X^78 + X^66 + X^64 + X^50 + X^44 + X^42 + X^34 + X^30 + X^28 + X^26 + X^16 + X^14 + X^10 + 1 10 14 16 24 Errors: /home/mfd/gomagma: line 2: 2492 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host 3(NXDOMAIN) (217.218.127.70) Time: Fri Feb 6 07:26:54 2004 Input: k := GF(2); C := PrimitivePolynomial(k,9); C; for j in [21..32] do for k in [16..20] do for m in [12..15] do for n in [9..11] do C := ((1 + X^n)^21)*((1 + X^m)^17)*((1 + X^k)^19)*((1 + X^j)^23) + X^1279; if IsPrimitive(C) then C; n; m; k; j; end if; end for; end for; end for; end for; Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Fri Feb 6 2004 07:26:31 on modular [Seed = 2263171384] ------------------------------------- X^9 + X^4 + 1 X^1279 + X^1256 + X^1245 + X^1242 + X^1240 + X^1235 + X^1231 + X^1229 + X^1226 + X^1221 + X^1219 + X^1215 + X^1214 + X^1213 + X^1212 + X^1205 + X^1201 + X^1200 + X^1199 + X^1197 + X^1196 + X^1193 + X^1192 + X^1191 + X^1187 + X^1185 + X^1184 + X^1183 + X^1182 + X^1179 + X^1178 + X^1176 + X^1175 + X^1172 + X^1170 + X^1169 + X^1163 + X^1162 + X^1161 + X^1158 + X^1157 + X^1154 + X^1153 + X^1151 + X^1150 + X^1149 + X^1148 + X^1142 + X^1141 + X^1140 + X^1139 + X^1137 + X^1136 + X^1133 + X^1132 + X^1130 + X^1129 + X^1128 + X^1127 + X^1121 + X^1120 + X^1119 + X^1118 + X^1116 + X^1115 + X^1112 + X^1111 + X^1109 + X^1108 + X^1107 + X^1106 + X^1100 + X^1099 + X^1098 + X^1097 + X^1095 + X^1094 + X^1091 + X^1090 + X^1087 + X^1086 + X^1085 + X^1080 + X^1079 + X^1078 + X^1076 + X^1073 + X^1072 + X^1070 + X^1065 + X^1063 + X^1061 + X^1059 + X^1057 + X^1056 + X^1053 + X^1052 + X^1051 + X^1050 + X^1049 + X^1048 + X^1047 + X^1045 + X^1039 + X^1038 + X^1037 + X^1035 + X^1034 + X^1033 + X^1032 + X^1027 + X^1025 + X^1024 + X^1023 + X^1022 + X^1020 + X^1019 + X^1018 + X^1015 + X^1013 + X^1009 + X^1005 + X^999 + X^997 + X^996 + X^995 + X^994 + X^993 + X^992 + X^991 + X^990 + X^988 + X^987 + X^985 + X^984 + X^982 + X^979 + X^978 + X^976 + X^975 + X^974 + X^973 + X^970 + X^969 + X^968 + X^967 + X^966 + X^964 + X^963 + X^955 + X^953 + X^949 + X^948 + X^946 + X^945 + X^942 + X^941 + X^938 + X^934 + X^932 + X^928 + X^925 + X^921 + X^917 + X^912 + X^911 + X^910 + X^909 + X^908 + X^907 + X^906 + X^901 + X^900 + X^899 + X^898 + X^897 + X^895 + X^894 + X^893 + X^891 + X^889 + X^886 + X^883 + X^882 + X^878 + X^873 + X^871 + X^870 + X^869 + X^866 + X^863 + X^860 + X^858 + X^856 + X^855 + X^854 + X^851 + X^850 + X^847 + X^846 + X^844 + X^843 + X^841 + X^840 + X^839 + X^838 + X^836 + X^831 + X^828 + X^827 + X^820 + X^818 + X^814 + X^812 + X^811 + X^810 + X^807 + X^806 + X^804 + X^803 + X^801 + X^800 + X^799 + X^798 + X^797 + X^796 + X^792 + X^791 + X^787 + X^784 + X^783 + X^781 + X^780 + X^777 + X^776 + X^773 + X^767 + X^766 + X^763 + X^762 + X^755 + X^749 + X^748 + X^740 + X^738 + X^737 + X^736 + X^735 + X^731 + X^729 + X^728 + X^726 + X^725 + X^723 + X^722 + X^720 + X^719 + X^717 + X^714 + X^712 + X^711 + X^710 + X^709 + X^707 + X^706 + X^699 + X^697 + X^696 + X^695 + X^694 + X^692 + X^689 + X^687 + X^686 + X^685 + X^683 + X^681 + X^680 + X^679 + X^677 + X^675 + X^673 + X^672 + X^671 + X^669 + X^667 + X^664 + X^663 + X^661 + X^659 + X^657 + X^656 + X^655 + X^652 + X^650 + X^649 + X^648 + X^647 + X^644 + X^642 + X^640 + X^638 + X^634 + X^633 + X^632 + X^631 + X^630 + X^629 + X^627 + X^626 + X^625 + X^624 + X^623 + X^622 + X^618 + X^616 + X^614 + X^612 + X^609 + X^608 + X^607 + X^606 + X^604 + X^601 + X^600 + X^599 + X^597 + X^595 + X^593 + X^592 + X^589 + X^587 + X^585 + X^584 + X^583 + X^581 + X^579 + X^577 + X^576 + X^575 + X^573 + X^571 + X^570 + X^569 + X^567 + X^564 + X^562 + X^561 + X^560 + X^559 + X^557 + X^550 + X^549 + X^547 + X^546 + X^545 + X^544 + X^542 + X^539 + X^537 + X^536 + X^534 + X^533 + X^531 + X^530 + X^528 + X^527 + X^525 + X^521 + X^520 + X^519 + X^518 + X^516 + X^508 + X^507 + X^501 + X^494 + X^493 + X^490 + X^489 + X^483 + X^480 + X^479 + X^476 + X^475 + X^473 + X^472 + X^469 + X^465 + X^464 + X^460 + X^459 + X^458 + X^457 + X^456 + X^455 + X^453 + X^452 + X^450 + X^449 + X^446 + X^445 + X^444 + X^442 + X^438 + X^436 + X^429 + X^428 + X^425 + X^420 + X^418 + X^417 + X^416 + X^415 + X^413 + X^412 + X^410 + X^409 + X^406 + X^405 + X^402 + X^401 + X^400 + X^398 + X^396 + X^393 + X^390 + X^387 + X^386 + X^385 + X^383 + X^378 + X^374 + X^373 + X^370 + X^367 + X^365 + X^363 + X^362 + X^361 + X^359 + X^358 + X^357 + X^356 + X^355 + X^350 + X^349 + X^348 + X^347 + X^346 + X^345 + X^344 + X^339 + X^335 + X^331 + X^328 + X^324 + X^322 + X^318 + X^315 + X^314 + X^311 + X^310 + X^308 + X^307 + X^303 + X^301 + X^293 + X^292 + X^290 + X^289 + X^288 + X^287 + X^286 + X^283 + X^282 + X^281 + X^280 + X^278 + X^277 + X^274 + X^272 + X^271 + X^269 + X^268 + X^266 + X^265 + X^264 + X^263 + X^262 + X^261 + X^260 + X^259 + X^257 + X^251 + X^247 + X^243 + X^241 + X^238 + X^237 + X^236 + X^234 + X^233 + X^232 + X^231 + X^229 + X^224 + X^223 + X^222 + X^221 + X^219 + X^218 + X^217 + X^211 + X^209 + X^208 + X^207 + X^206 + X^205 + X^204 + X^203 + X^200 + X^199 + X^197 + X^195 + X^193 + X^191 + X^186 + X^184 + X^183 + X^180 + X^178 + X^177 + X^176 + X^171 + X^170 + X^169 + X^166 + X^165 + X^162 + X^161 + X^159 + X^158 + X^157 + X^156 + X^150 + X^149 + X^148 + X^147 + X^145 + X^144 + X^141 + X^140 + X^138 + X^137 + X^136 + X^135 + X^129 + X^128 + X^127 + X^126 + X^124 + X^123 + X^120 + X^119 + X^117 + X^116 + X^115 + X^114 + X^108 + X^107 + X^106 + X^105 + X^103 + X^102 + X^99 + X^98 + X^95 + X^94 + X^93 + X^87 + X^86 + X^84 + X^81 + X^80 + X^78 + X^77 + X^74 + X^73 + X^72 + X^71 + X^69 + X^65 + X^64 + X^63 + X^60 + X^59 + X^57 + X^56 + X^55 + X^51 + X^44 + X^43 + X^42 + X^41 + X^37 + X^35 + X^30 + X^27 + X^25 + X^21 + X^16 + X^14 + X^11 + 1 11 14 16 21 Errors: /home/mfd/gomagma: line 2: 2511 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host 3(NXDOMAIN) (217.218.127.70) Time: Fri Feb 6 07:28:09 2004 Input: k := GF(2); C := PrimitivePolynomial(k,9); C; for j in [21..32] do for k in [16..20] do for m in [12..15] do for n in [9..11] do C := ((1 + X^n)^21)*((1 + X^m)^17)*((1 + X^k)^29)*((1 + X^j)^23) + X^1279; if IsPrimitive(C) then C; n; m; k; j; end if; end for; end for; end for; end for; Output: Magma V2.10-6 Fri Feb 6 2004 07:27:52 on modular [Seed = 2448578960] ------------------------------------- X^9 + X^4 + 1 Total time: 16.750 seconds, Total memory usage: 2.55MB ************** MAGMA ***************** Host 3(NXDOMAIN) (217.218.127.70) Time: Fri Feb 6 07:28:45 2004 Input: k := GF(2); C := PrimitivePolynomial(k,9); C; for j in [21..32] do for k in [16..20] do for m in [12..15] do for n in [9..11] do C := ((1 + X^n)^29)*((1 + X^m)^17)*((1 + X^k)^21)*((1 + X^j)^23) + X^1279; if IsPrimitive(C) then C; n; m; k; j; end if; end for; end for; end for; end for; Output: Magma V2.10-6 Fri Feb 6 2004 07:28:29 on modular [Seed = 2831900812] ------------------------------------- X^9 + X^4 + 1 Total time: 15.719 seconds, Total memory usage: 2.35MB ************** MAGMA ***************** Host 3(NXDOMAIN) (217.218.127.70) Time: Fri Feb 6 07:29:45 2004 Input: k := GF(2); C := PrimitivePolynomial(k,9); C; for j in [21..32] do for k in [16..20] do for m in [12..15] do for n in [9..11] do C := ((1 + X^n)^23)*((1 + X^m)^19)*((1 + X^k)^17)*((1 + X^j)^23) + X^1279; if IsPrimitive(C) then C; n; m; k; j; end if; end for; end for; end for; end for; Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Fri Feb 6 2004 07:29:22 on modular [Seed = 2747296584] ------------------------------------- X^9 + X^4 + 1 X^1279 + X^1268 + X^1259 + X^1254 + X^1251 + X^1250 + X^1246 + X^1245 + X^1242 + X^1241 + X^1240 + X^1236 + X^1233 + X^1231 + X^1229 + X^1227 + X^1226 + X^1223 + X^1222 + X^1220 + X^1217 + X^1215 + X^1214 + X^1213 + X^1211 + X^1210 + X^1209 + X^1208 + X^1207 + X^1206 + X^1205 + X^1200 + X^1199 + X^1198 + X^1197 + X^1196 + X^1193 + X^1191 + X^1190 + X^1189 + X^1185 + X^1184 + X^1182 + X^1181 + X^1176 + X^1175 + X^1173 + X^1172 + X^1171 + X^1168 + X^1167 + X^1164 + X^1162 + X^1159 + X^1155 + X^1154 + X^1153 + X^1151 + X^1150 + X^1149 + X^1145 + X^1142 + X^1140 + X^1137 + X^1133 + X^1132 + X^1131 + X^1129 + X^1128 + X^1127 + X^1124 + X^1123 + X^1120 + X^1118 + X^1111 + X^1109 + X^1105 + X^1102 + X^1097 + X^1093 + X^1088 + X^1084 + X^1083 + X^1082 + X^1075 + X^1073 + X^1066 + X^1065 + X^1060 + X^1056 + X^1051 + X^1050 + X^1044 + X^1043 + X^1041 + X^1035 + X^1034 + X^1033 + X^1032 + X^1030 + X^1028 + X^1027 + X^1026 + X^1023 + X^1022 + X^1021 + X^1019 + X^1018 + X^1017 + X^1016 + X^1014 + X^1012 + X^1011 + X^1009 + X^1003 + X^1002 + X^999 + X^996 + X^992 + X^991 + X^990 + X^988 + X^987 + X^986 + X^981 + X^978 + X^975 + X^974 + X^972 + X^971 + X^970 + X^968 + X^964 + X^963 + X^962 + X^961 + X^960 + X^959 + X^958 + X^957 + X^955 + X^950 + X^948 + X^947 + X^943 + X^942 + X^939 + X^937 + X^936 + X^935 + X^933 + X^932 + X^930 + X^929 + X^928 + X^927 + X^926 + X^925 + X^924 + X^923 + X^920 + X^918 + X^916 + X^912 + X^911 + X^909 + X^907 + X^906 + X^903 + X^898 + X^896 + X^895 + X^894 + X^892 + X^890 + X^888 + X^887 + X^884 + X^882 + X^881 + X^880 + X^876 + X^870 + X^869 + X^866 + X^865 + X^864 + X^863 + X^859 + X^857 + X^854 + X^853 + X^852 + X^849 + X^848 + X^847 + X^845 + X^844 + X^842 + X^838 + X^836 + X^829 + X^827 + X^826 + X^825 + X^824 + X^823 + X^820 + X^817 + X^815 + X^811 + X^810 + X^809 + X^808 + X^807 + X^804 + X^802 + X^798 + X^797 + X^795 + X^794 + X^787 + X^785 + X^784 + X^783 + X^780 + X^778 + X^777 + X^776 + X^775 + X^774 + X^772 + X^766 + X^765 + X^764 + X^762 + X^758 + X^757 + X^756 + X^754 + X^753 + X^752 + X^751 + X^750 + X^749 + X^746 + X^744 + X^743 + X^740 + X^738 + X^736 + X^733 + X^732 + X^730 + X^728 + X^727 + X^725 + X^724 + X^723 + X^718 + X^717 + X^713 + X^711 + X^709 + X^704 + X^702 + X^700 + X^699 + X^698 + X^697 + X^696 + X^695 + X^694 + X^693 + X^690 + X^689 + X^688 + X^687 + X^685 + X^684 + X^682 + X^680 + X^677 + X^676 + X^675 + X^674 + X^673 + X^672 + X^671 + X^669 + X^667 + X^666 + X^664 + X^663 + X^661 + X^658 + X^656 + X^652 + X^651 + X^649 + X^648 + X^647 + X^646 + X^645 + X^644 + X^642 + X^640 + X^638 + X^636 + X^635 + X^633 + X^632 + X^630 + X^628 + X^626 + X^624 + X^623 + X^622 + X^621 + X^620 + X^619 + X^617 + X^616 + X^612 + X^610 + X^607 + X^605 + X^604 + X^602 + X^601 + X^599 + X^597 + X^596 + X^595 + X^594 + X^593 + X^592 + X^591 + X^588 + X^586 + X^584 + X^583 + X^581 + X^580 + X^579 + X^578 + X^575 + X^574 + X^573 + X^572 + X^571 + X^570 + X^569 + X^568 + X^566 + X^564 + X^559 + X^557 + X^555 + X^551 + X^550 + X^545 + X^544 + X^543 + X^541 + X^540 + X^538 + X^536 + X^535 + X^532 + X^530 + X^528 + X^525 + X^524 + X^522 + X^519 + X^518 + X^517 + X^516 + X^515 + X^514 + X^512 + X^511 + X^510 + X^506 + X^504 + X^503 + X^502 + X^496 + X^494 + X^493 + X^492 + X^491 + X^490 + X^488 + X^485 + X^484 + X^483 + X^481 + X^474 + X^473 + X^471 + X^470 + X^466 + X^464 + X^461 + X^460 + X^459 + X^458 + X^457 + X^453 + X^451 + X^448 + X^445 + X^444 + X^443 + X^442 + X^441 + X^439 + X^432 + X^430 + X^426 + X^424 + X^423 + X^421 + X^420 + X^419 + X^416 + X^415 + X^414 + X^411 + X^409 + X^405 + X^404 + X^403 + X^402 + X^399 + X^398 + X^392 + X^388 + X^387 + X^386 + X^384 + X^381 + X^380 + X^378 + X^376 + X^374 + X^373 + X^372 + X^370 + X^365 + X^362 + X^361 + X^359 + X^357 + X^356 + X^352 + X^350 + X^348 + X^345 + X^344 + X^343 + X^342 + X^341 + X^340 + X^339 + X^338 + X^336 + X^335 + X^333 + X^332 + X^331 + X^329 + X^326 + X^325 + X^321 + X^320 + X^318 + X^313 + X^311 + X^310 + X^309 + X^308 + X^307 + X^306 + X^305 + X^304 + X^300 + X^298 + X^297 + X^296 + X^294 + X^293 + X^290 + X^287 + X^282 + X^281 + X^280 + X^278 + X^277 + X^276 + X^272 + X^269 + X^266 + X^265 + X^259 + X^257 + X^256 + X^254 + X^252 + X^251 + X^250 + X^249 + X^247 + X^246 + X^245 + X^242 + X^241 + X^240 + X^238 + X^236 + X^235 + X^234 + X^233 + X^227 + X^225 + X^224 + X^218 + X^217 + X^212 + X^208 + X^203 + X^202 + X^195 + X^193 + X^186 + X^185 + X^184 + X^180 + X^175 + X^171 + X^166 + X^163 + X^159 + X^157 + X^150 + X^148 + X^145 + X^144 + X^141 + X^140 + X^139 + X^137 + X^136 + X^135 + X^131 + X^128 + X^126 + X^123 + X^119 + X^118 + X^117 + X^115 + X^114 + X^113 + X^109 + X^106 + X^104 + X^101 + X^100 + X^97 + X^96 + X^95 + X^93 + X^92 + X^87 + X^86 + X^84 + X^83 + X^79 + X^78 + X^77 + X^75 + X^72 + X^71 + X^70 + X^69 + X^68 + X^63 + X^62 + X^61 + X^60 + X^59 + X^58 + X^57 + X^55 + X^54 + X^53 + X^51 + X^48 + X^46 + X^45 + X^42 + X^41 + X^39 + X^37 + X^35 + X^32 + X^28 + X^27 + X^26 + X^23 + X^22 + X^18 + X^17 + X^14 + X^9 + 1 9 14 17 22 Errors: /home/mfd/gomagma: line 2: 2538 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host 3(NXDOMAIN) (217.218.127.70) Time: Fri Feb 6 07:31:35 2004 Input: k := GF(2); C := PrimitivePolynomial(k,9); C; for j in [21..32] do for k in [16..20] do for m in [12..15] do for n in [7..11] do C := ((1 + X^n)^29)*((1 + X^m)^19)*((1 + X^k)^17)*((1 + X^j)^23) + X^1279; if IsPrimitive(C) then C; n; m; k; j; end if; end for; end for; end for; end for; Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Fri Feb 6 2004 07:31:11 on modular [Seed = 3050732787] ------------------------------------- X^9 + X^4 + 1 Errors: /home/mfd/gomagma: line 2: 2556 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host 3(NXDOMAIN) (217.218.127.70) Time: Fri Feb 6 07:32:11 2004 Input: k := GF(2); C := PrimitivePolynomial(k,9); C; for j in [21..32] do for k in [16..20] do for m in [12..15] do for n in [9..11] do C := ((1 + X^n)^29)*((1 + X^m)^19)*((1 + X^k)^17)*((1 + X^j)^23) + X^1279; if IsPrimitive(C) then C; n; m; k; j; end if; end for; end for; end for; end for; Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Fri Feb 6 2004 07:31:48 on modular [Seed = 1278182706] ------------------------------------- X^9 + X^4 + 1 Errors: /home/mfd/gomagma: line 2: 2566 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host 3(NXDOMAIN) (217.218.127.70) Time: Fri Feb 6 07:32:45 2004 Input: k := GF(2); C := PrimitivePolynomial(k,9); C; for j in [21..32] do for k in [16..20] do for m in [12..15] do for n in [9..11] do C := ((1 + X^n)^25)*((1 + X^m)^19)*((1 + X^k)^17)*((1 + X^j)^23) + X^1279; if IsPrimitive(C) then C; n; m; k; j; end if; end for; end for; end for; end for; Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Fri Feb 6 2004 07:32:22 on modular [Seed = 1160154201] ------------------------------------- X^9 + X^4 + 1 X^1298 + X^1287 + X^1286 + X^1281 + X^1279 + X^1276 + X^1275 + X^1274 + X^1270 + X^1269 + X^1265 + X^1264 + X^1263 + X^1262 + X^1259 + X^1258 + X^1257 + X^1254 + X^1253 + X^1252 + X^1251 + X^1248 + X^1247 + X^1246 + X^1245 + X^1243 + X^1242 + X^1241 + X^1240 + X^1237 + X^1236 + X^1235 + X^1234 + X^1232 + X^1231 + X^1230 + X^1229 + X^1226 + X^1225 + X^1224 + X^1223 + X^1221 + X^1220 + X^1219 + X^1218 + X^1215 + X^1214 + X^1213 + X^1212 + X^1209 + X^1208 + X^1207 + X^1204 + X^1203 + X^1202 + X^1201 + X^1197 + X^1196 + X^1192 + X^1191 + X^1190 + X^1185 + X^1180 + X^1179 + X^1168 + X^1106 + X^1095 + X^1094 + X^1089 + X^1084 + X^1083 + X^1082 + X^1078 + X^1077 + X^1073 + X^1072 + X^1071 + X^1070 + X^1067 + X^1066 + X^1065 + X^1062 + X^1061 + X^1060 + X^1059 + X^1056 + X^1055 + X^1054 + X^1053 + X^1051 + X^1050 + X^1049 + X^1048 + X^1045 + X^1044 + X^1043 + X^1042 + X^1040 + X^1039 + X^1038 + X^1037 + X^1034 + X^1033 + X^1032 + X^1031 + X^1029 + X^1028 + X^1027 + X^1023 + X^1022 + X^1021 + X^1020 + X^1017 + X^1016 + X^1014 + X^1012 + X^1011 + X^1010 + X^1005 + X^1003 + X^1002 + X^1000 + X^999 + X^997 + X^992 + X^991 + X^990 + X^988 + X^986 + X^985 + X^982 + X^981 + X^980 + X^979 + X^975 + X^974 + X^973 + X^971 + X^970 + X^969 + X^968 + X^965 + X^964 + X^963 + X^962 + X^960 + X^959 + X^958 + X^957 + X^954 + X^953 + X^952 + X^951 + X^949 + X^948 + X^947 + X^946 + X^943 + X^942 + X^941 + X^940 + X^937 + X^936 + X^935 + X^932 + X^931 + X^930 + X^929 + X^925 + X^924 + X^920 + X^919 + X^918 + X^913 + X^908 + X^907 + X^896 + X^834 + X^823 + X^822 + X^817 + X^812 + X^811 + X^810 + X^806 + X^805 + X^801 + X^800 + X^799 + X^798 + X^795 + X^794 + X^793 + X^790 + X^789 + X^788 + X^787 + X^784 + X^783 + X^782 + X^781 + X^779 + X^778 + X^777 + X^776 + X^773 + X^772 + X^771 + X^770 + X^768 + 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X^41 + X^40 + X^39 + X^36 + X^35 + X^34 + X^33 + X^29 + X^28 + X^24 + X^23 + X^22 + X^17 + X^12 + X^11 + 1 11 12 17 22 Errors: /home/mfd/gomagma: line 2: 2575 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host 3(NXDOMAIN) (217.218.127.70) Time: Fri Feb 6 07:33:45 2004 Input: k := GF(2); C := PrimitivePolynomial(k,9); C; for j in [21..32] do for k in [16..20] do for m in [12..15] do for n in [9..11] do C := ((1 + X^n)^23)*((1 + X^m)^17)*((1 + X^k)^19)*((1 + X^j)^23) + X^1279; if IsPrimitive(C) then C; n; m; k; j; end if; end for; end for; end for; end for; Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Fri Feb 6 2004 07:33:21 on modular [Seed = 1345558923] ------------------------------------- X^9 + X^4 + 1 X^1356 + X^1347 + X^1341 + X^1323 + X^1320 + X^1317 + X^1311 + X^1305 + X^1299 + X^1293 + X^1287 + X^1284 + X^1281 + X^1279 + X^1263 + X^1257 + X^1248 + X^1212 + X^1203 + X^1197 + 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X^441 + X^434 + X^426 + X^424 + X^416 + X^407 + X^406 + X^404 + X^399 + X^397 + X^396 + X^394 + X^389 + X^386 + X^384 + X^382 + X^379 + X^378 + X^376 + X^375 + X^374 + X^372 + X^369 + X^368 + X^366 + X^364 + X^362 + X^359 + X^356 + X^354 + X^352 + X^344 + X^342 + X^334 + X^332 + X^329 + X^322 + X^320 + X^317 + X^312 + X^310 + X^295 + X^291 + X^288 + X^281 + X^266 + X^264 + X^262 + X^259 + X^256 + X^254 + X^247 + X^246 + X^242 + X^239 + X^236 + X^233 + X^232 + X^229 + X^227 + X^226 + X^220 + X^219 + X^217 + X^215 + X^210 + X^209 + X^208 + X^207 + X^201 + X^200 + X^197 + X^194 + X^190 + X^187 + X^186 + X^182 + X^180 + X^179 + X^177 + X^172 + X^170 + X^160 + X^157 + X^150 + X^128 + X^121 + X^104 + X^99 + X^94 + X^87 + X^84 + X^82 + X^77 + X^74 + X^72 + X^67 + X^64 + X^62 + X^60 + X^57 + X^54 + X^52 + X^50 + X^47 + X^44 + X^42 + X^41 + X^40 + X^37 + X^34 + X^32 + X^30 + X^27 + X^22 + X^20 + X^17 + X^12 + X^10 + 1 10 12 17 29 Errors: /home/mfd/gomagma: line 2: 2586 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host mat227.bham.ac.uk. (147.188.56.208) Time: Fri Feb 6 10:33:26 2004 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: Magma V2.10-6 Fri Feb 6 2004 10:33:21 on modular [Seed = 1530439894] ------------------------------------- Replace this by some code, then click [PARI] or [MAGMA]! Total time: 3.259 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (219.237.59.57) Time: Fri Feb 6 11:06:04 2004 Input: (x+y)^5 Output: Magma V2.10-6 Fri Feb 6 2004 11:06:01 on modular [Seed = 658824194] ------------------------------------- >> (x+y)^5; ^ User error: Identifier 'x' has not been declared or assigned Total time: 3.039 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host dhcp65-157.ureg.ohio-state.edu. (128.146.65.157) Time: Fri Feb 6 12:52:01 2004 Input: (x+2)*(3*x^2+20*x-1)-(x^3+10*x^2-x-10) Output: Magma V2.10-6 Fri Feb 6 2004 12:51:57 on modular [Seed = 360087909] ------------------------------------- >> (x+2)*(3*x^2+20*x-1)-(x^3+10*x^2-x-10); ^ User error: Identifier 'x' has not been declared or assigned Total time: 3.049 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host Buttercup.EGR.UH.EDU. (129.7.202.153) Time: Fri Feb 6 13:43:44 2004 Input: 1+2 Output: Magma V2.10-6 Fri Feb 6 2004 13:43:41 on modular [Seed = 2381196701] ------------------------------------- 3 Total time: 3.129 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host Buttercup.EGR.UH.EDU. (129.7.202.153) Time: Fri Feb 6 13:55:29 2004 Input: Ser(log(-x)) Output: Magma V2.10-6 Fri Feb 6 2004 13:55:26 on modular [Seed = 1463088135] ------------------------------------- >> Ser(log(-x)) ^ User error: Identifier 'x' has not been declared or assigned Total time: 2.979 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 69-162-40-105.stcgpa.adelphia.net. (69.162.40.105) Time: Fri Feb 6 14:40:07 2004 Input: A := QuaternionAlgebra< RationalField() | -2, -5>; // RamifiedPrimes(A); // Discriminant(A); // IsDefinite(A); S:=MaximalOrder(A); // Units(S); // UnitGroup(S); T:=MatrixAlgebra(S,2); B:=MatrixAgebra(A,2); Output: Magma V2.10-6 Fri Feb 6 2004 14:40:03 on modular [Seed = 2414617170] ------------------------------------- >> B:=MatrixAgebra(A,2);; ^ User error: Identifier 'MatrixAgebra' has not been declared or assigned Total time: 3.139 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host 69-162-40-105.stcgpa.adelphia.net. (69.162.40.105) Time: Fri Feb 6 14:40:29 2004 Input: A := QuaternionAlgebra< RationalField() | -2, -5>; // RamifiedPrimes(A); // Discriminant(A); // IsDefinite(A); S:=MaximalOrder(A); // Units(S); // UnitGroup(S); T:=MatrixAlgebra(S,2); B:=MatrixAlgebra(A,2); Output: Magma V2.10-6 Fri Feb 6 2004 14:40:26 on modular [Seed = 2229741920] ------------------------------------- Total time: 2.999 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host p23.mat.univ.szczecin.pl. (212.14.9.46) Time: Fri Feb 6 16:50:08 2004 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: Magma V2.10-6 Fri Feb 6 2004 16:50:04 on modular [Seed = 3033594103] ------------------------------------- Replace this by some code, then click [PARI] or [MAGMA]! Total time: 3.149 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (61.136.9.23) Time: Sat Feb 7 02:27:39 2004 Input: 1745264755423825474573924809951949066708882319246693921995410289 Output: Magma V2.10-6 Sat Feb 7 2004 02:27:36 on modular [Seed = 73455416] ------------------------------------- 1745264755423825474573924809951949066708882319246693921995410289 Total time: 2.989 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host h9n1c1o994.bredband.skanova.com. (81.225.40.9) Time: Sat Feb 7 15:53:04 2004 Input: ?BCHCode Output: Magma V2.10-6 Sat Feb 7 2004 15:53:01 on modular [Seed = 1914135040] ------------------------------------- 3 matches: 1 I /magma/combinatorial-geometrical-incidence/\ error-correcting-linear-code/families/BCH/BCHCode 2 I /magma/combinatorial-geometrical-incidence/\ error-correcting-linear-code/families/BCH/BCHCode 3 E /magma/combinatorial-geometrical-incidence/\ error-correcting-linear-code/families/BCH/Example-BCHCode To view an entry, type ? followed by the number next to it Total time: 3.059 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host h9n1c1o994.bredband.skanova.com. (81.225.40.9) Time: Sat Feb 7 15:53:48 2004 Input: 3 Output: Magma V2.10-6 Sat Feb 7 2004 15:53:45 on modular [Seed = 1762425199] ------------------------------------- 3 Total time: 3.019 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host h9n1c1o994.bredband.skanova.com. (81.225.40.9) Time: Sat Feb 7 15:55:01 2004 Input: CoveringRadius(BCHCode(GF(5),0,3)); Output: Magma V2.10-6 Sat Feb 7 2004 15:54:58 on modular [Seed = 1627681180] ------------------------------------- >> CoveringRadius(BCHCode(GF(5),0,3));; ^ Runtime error in 'BCHCode': Argument 2 (0) should be >= 2 Total time: 3.109 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host h113n3c1o994.bredband.skanova.com. (81.225.42.113) Time: Sat Feb 7 15:57:24 2004 Input: CoveringRadius(BCHCode(5,0,3)); Output: Magma V2.10-6 Sat Feb 7 2004 15:57:21 on modular [Seed = 309789564] ------------------------------------- >> CoveringRadius(BCHCode(5,0,3));; ^ Runtime error in 'BCHCode': Bad argument types Argument types given: RngIntElt, RngIntElt, RngIntElt Total time: 2.979 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host h4n3c1o994.bredband.skanova.com. (81.225.42.4) Time: Sat Feb 7 16:05:08 2004 Input: CoveringRadius(BCHCode(GF(5),21,4,0)); Output: Magma V2.10-6 Sat Feb 7 2004 16:05:05 on modular [Seed = 676150134] ------------------------------------- >> CoveringRadius(BCHCode(GF(5),21,4,0));; ^ Runtime error in 'CoveringRadius': Arguments too large Total time: 3.039 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host h234n2c1o994.bredband.skanova.com. (81.225.41.234) Time: Sat Feb 7 16:06:13 2004 Input: MinimumDistance(BCHCode(GF(5),21,4,0)); Output: Magma V2.10-6 Sat Feb 7 2004 16:06:09 on modular [Seed = 541406014] ------------------------------------- 6 Total time: 2.959 seconds, Total memory usage: 1.99MB ************** MAGMA ***************** Host h234n2c1o994.bredband.skanova.com. (81.225.41.234) Time: Sat Feb 7 16:06:38 2004 Input: CoveringRadius(BCHCode(GF(5),21,4,0)); Output: Magma V2.10-6 Sat Feb 7 2004 16:06:34 on modular [Seed = 3636317149] ------------------------------------- >> CoveringRadius(BCHCode(GF(5),21,4,0));; ^ Runtime error in 'CoveringRadius': Arguments too large Total time: 3.019 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host h234n2c1o994.bredband.skanova.com. (81.225.41.234) Time: Sat Feb 7 16:07:19 2004 Input: CosetLeaders(BCHCode(GF(5),21,4,0)); Output: Magma V2.10-6 Sat Feb 7 2004 16:07:16 on modular [Seed = 3484081172] ------------------------------------- >> CosetLeaders(BCHCode(GF(5),21,4,0));; ^ Runtime error in 'CosetLeaders': Code has too many cosets Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host c-180-200-120.n.dial.de.ignite.net. (62.180.200.120) Time: Sun Feb 8 01:41:02 2004 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: Magma V2.10-6 Sun Feb 8 2004 01:40:59 on modular [Seed = 2814524980] ------------------------------------- Replace this by some code, then click [PARI] or [MAGMA]! Total time: 3.119 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 2(SERVFAIL) (203.91.149.163) Time: Sun Feb 8 03:15:05 2004 Input: k := GF(2); P:=PolynomialRing(K); AllIrreduciblePolynomials(K,8); Output: Magma V2.10-6 Sun Feb 8 2004 03:15:02 on modular [Seed = 326542204] ------------------------------------- >> P:=PolynomialRing(K); ^ User error: Identifier 'K' has not been declared or assigned >> AllIrreduciblePolynomials(K,8); ^ User error: Identifier 'K' has not been declared or assigned Total time: 3.019 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 2(SERVFAIL) (203.91.149.163) Time: Sun Feb 8 03:16:35 2004 Input: K := GF(2); P:=PolynomialRing(K); AllIrreduciblePolynomials(K,8); Output: Magma V2.10-6 Sun Feb 8 2004 03:16:32 on modular [Seed = 3935263459] ------------------------------------- { x^8 + x^7 + x^6 + x^5 + x^4 + x + 1, x^8 + x^6 + x^3 + x^2 + 1, x^8 + x^6 + x^5 + x^3 + 1, x^8 + x^7 + x^4 + x^3 + x^2 + x + 1, x^8 + x^6 + x^5 + x^4 + 1, x^8 + x^7 + x^3 + x^2 + 1, x^8 + x^4 + x^3 + x^2 + 1, x^8 + x^7 + x^5 + x^3 + 1, x^8 + x^7 + x^6 + x + 1, x^8 + x^5 + x^4 + x^3 + 1, x^8 + x^7 + x^6 + x^4 + x^3 + x^2 + 1, x^8 + x^7 + x^5 + x^4 + 1, x^8 + x^7 + x^6 + x^5 + x^4 + x^3 + 1, x^8 + x^7 + x^3 + x + 1, x^8 + x^4 + x^3 + x + 1, x^8 + x^7 + x^6 + x^5 + x^2 + x + 1, x^8 + x^6 + x^5 + x^4 + x^2 + x + 1, x^8 + x^6 + x^5 + x^2 + 1, x^8 + x^5 + x^4 + x^3 + x^2 + x + 1, x^8 + x^5 + x^3 + x^2 + 1, x^8 + x^6 + x^5 + x + 1, x^8 + x^7 + x^6 + x^5 + x^4 + x^2 + 1, x^8 + x^7 + x^2 + x + 1, x^8 + x^5 + x^3 + x + 1, x^8 + x^7 + x^6 + x^3 + x^2 + x + 1, x^8 + x^7 + x^5 + x + 1, x^8 + x^6 + x^4 + x^3 + x^2 + x + 1, x^8 + x^7 + x^5 + x^4 + x^3 + x^2 + 1, x^8 + x^7 + x^6 + x^4 + x^2 + x + 1, x^8 + x^6 + x^5 + x^4 + x^3 + x + 1 } Total time: 2.929 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 2(SERVFAIL) (203.91.149.163) Time: Sun Feb 8 03:17:04 2004 Input: K := GF(2); P:=PolynomialRing(K); AllIrreduciblePolynomials(K,1279); Output: ** WARNING: Computation used more memory than allowed. ** Magma V2.10-6 Sun Feb 8 2004 03:17:01 on modular [Seed = 3850393073] ------------------------------------- Current total memory usage: 1.7MB, failed memory request: 1024.0MB System Error: User memory limit has been reached Total time: 2.919 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host p50861DDB.dip.t-dialin.net. (80.134.29.219) Time: Sun Feb 8 11:51:06 2004 Input: solve(y=x^3-3*x^2-9*x+30,x); Output: Magma V2.10-6 Sun Feb 8 2004 11:51:02 on modular [Seed = 1076258961] ------------------------------------- >> solve(y=x^3-3*x^2-9*x+30,x);; ^ User error: Identifier 'x' has not been declared or assigned Total time: 3.039 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host SAINS.sapmed.ac.jp. (163.130.26.159) Time: Mon Feb 9 01:11:29 2004 Input: g:=PermutationGroup<4,Rationals()|(1,2,3,4),(1,2)>; Order(g); Output: Magma V2.10-6 Mon Feb 9 2004 01:11:25 on modular [Seed = 276264109] ------------------------------------- >> g:=PermutationGroup<4,Rationals()|(1,2,3,4),(1,2)>; ^ User error: bad syntax >> Order(g);; ^ User error: Identifier 'g' has not been declared or assigned Total time: 3.049 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host SAINS.sapmed.ac.jp. (163.130.26.159) Time: Mon Feb 9 01:12:04 2004 Input: 1+3; Output: Magma V2.10-6 Mon Feb 9 2004 01:12:01 on modular [Seed = 427720088] ------------------------------------- 4 Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host c-b41f72d5.07-114-6c6b701.cust.bredbandsbolaget.se. (213.114.31.180) Time: Mon Feb 9 08:27:17 2004 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: Magma V2.10-6 Mon Feb 9 2004 08:27:14 on modular [Seed = 1795989999] ------------------------------------- Replace this by some code, then click [PARI] or [MAGMA]! Total time: 2.939 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host c-b41f72d5.07-114-6c6b701.cust.bredbandsbolaget.se. (213.114.31.180) Time: Mon Feb 9 08:28:06 2004 Input: a := 2+3; print a; Output: Magma V2.10-6 Mon Feb 9 2004 08:28:03 on modular [Seed = 1176603795] ------------------------------------- 5 Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host c-b41f72d5.07-114-6c6b701.cust.bredbandsbolaget.se. (213.114.31.180) Time: Mon Feb 9 08:30:12 2004 Input: GF(8) Output: Magma V2.10-6 Mon Feb 9 2004 08:30:09 on modular [Seed = 3083893984] ------------------------------------- Finite field of size 2^3 Total time: 2.929 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host c-b41f72d5.07-114-6c6b701.cust.bredbandsbolaget.se. (213.114.31.180) Time: Mon Feb 9 08:31:30 2004 Input: F := GF(7); C := AlternantCode([F|1,2,3,4,5,6],[F|1,1,1,1,1,1],4,F); C; Output: Magma V2.10-6 Mon Feb 9 2004 08:31:27 on modular [Seed = 3135074595] ------------------------------------- [6, 2, 5] Alternant code over GF(7) Generator matrix: [1 0 4 6 6 4] [0 1 3 6 3 1] Total time: 2.919 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host c-b41f72d5.07-114-6c6b701.cust.bredbandsbolaget.se. (213.114.31.180) Time: Mon Feb 9 08:31:52 2004 Input: F := GF(7); C := AlternantCode([F|1,2,3,4,5,6],[F|1,1,1,1,1,1],4,F); H := ParityCheckMatrix(C); H; Output: Magma V2.10-6 Mon Feb 9 2004 08:31:49 on modular [Seed = 2747557968] ------------------------------------- [1 0 0 0 6 3] [0 1 0 0 4 1] [0 0 1 0 1 1] [0 0 0 1 4 3] Total time: 3.009 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host c-b41f72d5.07-114-6c6b701.cust.bredbandsbolaget.se. (213.114.31.180) Time: Mon Feb 9 10:21:10 2004 Input: F := GF(7); C := AlternantCode([F|1,2,3,4,5,6],[F|1,1,1,1,1,1],4,F); H := ParityCheckMatrix(C); H; F; Output: Magma V2.10-6 Mon Feb 9 2004 10:21:00 on modular [Seed = 2714125509] ------------------------------------- [1 0 0 0 6 3] [0 1 0 0 4 1] [0 0 1 0 1 1] [0 0 0 1 4 3] Finite field of size 7 Total time: 3.049 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host c-b41f72d5.07-114-6c6b701.cust.bredbandsbolaget.se. (213.114.31.180) Time: Mon Feb 9 10:21:24 2004 Input: F := GF(7); C := AlternantCode([F|1,2,3,4,5,6],[F|1,1,1,1,1,1],4,F); H := ParityCheckMatrix(C); F; Output: Magma V2.10-6 Mon Feb 9 2004 10:21:21 on modular [Seed = 2617016018] ------------------------------------- Finite field of size 7 Total time: 2.999 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host mathdhcp41.ces.clemson.edu. (130.127.112.170) Time: Tue Feb 10 10:20:53 2004 Input: k1:=CompleteGraph(2); k2:=CartesianProduct(k1,k1); k2; G:=SquareLatticeGraph(2); IsIsomorphic(G,k2); Output: Magma V2.10-6 Tue Feb 10 2004 10:20:50 on modular [Seed = 3034317365] ------------------------------------- Graph Vertex Neighbours 1 2 3 ; 2 1 4 ; 3 1 4 ; 4 2 3 ; true Mapping from: Vertex-set of G to Vertex-set of k2 Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host mathdhcp41.ces.clemson.edu. (130.127.112.170) Time: Tue Feb 10 10:21:28 2004 Input: k1:=CompleteGraph(2); k2:=CartesianProduct(k1,k1); k2; G:=SquareLatticeGraph(2); G; IsIsomorphic(G,k2); Output: Magma V2.10-6 Tue Feb 10 2004 10:21:25 on modular [Seed = 2747995397] ------------------------------------- Graph Vertex Neighbours 1 2 3 ; 2 1 4 ; 3 1 4 ; 4 2 3 ; Graph Vertex Neighbours 1 2 3 ; 2 1 4 ; 3 1 4 ; 4 2 3 ; true Mapping from: Vertex-set of G to Vertex-set of k2 Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host mathdhcp41.ces.clemson.edu. (130.127.112.170) Time: Tue Feb 10 10:23:20 2004 Input: k1:=CompleteGraph(2); k2:=CartesianProduct(k1,k1); G:=SquareLatticeGraph(2); H:=KCubeGraph(3); H; Output: Magma V2.10-6 Tue Feb 10 2004 10:23:17 on modular [Seed = 2864848284] ------------------------------------- Graph Vertex Neighbours 1 2 3 5 ; 2 1 4 6 ; 3 1 4 7 ; 4 2 3 8 ; 5 1 6 7 ; 6 2 5 8 ; 7 3 5 8 ; 8 4 6 7 ; Total time: 2.929 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host mathdhcp41.ces.clemson.edu. (130.127.112.170) Time: Tue Feb 10 10:25:05 2004 Input: k1:=CompleteGraph(2); k2:=CartesianProduct(k1,k1); G:=SquareLatticeGraph(2); H:=KCubeGraph(4); H; Output: Magma V2.10-6 Tue Feb 10 2004 10:25:02 on modular [Seed = 1396434121] ------------------------------------- Graph Vertex Neighbours 1 2 3 5 9 ; 2 1 4 6 10 ; 3 1 4 7 11 ; 4 2 3 8 12 ; 5 1 6 7 13 ; 6 2 5 8 14 ; 7 3 5 8 15 ; 8 4 6 7 16 ; 9 1 10 11 13 ; 10 2 9 12 14 ; 11 3 9 12 15 ; 12 4 10 11 16 ; 13 5 9 14 15 ; 14 6 10 13 16 ; 15 7 11 13 16 ; 16 8 12 14 15 ; Total time: 3.049 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host mathdhcp41.ces.clemson.edu. (130.127.112.170) Time: Tue Feb 10 10:26:56 2004 Input: k1:=CompleteGraph(2); k2:=CartesianProduct(k1,k1); k3:CartesianProduct(k1,k2); k3; Output: Magma V2.10-6 Tue Feb 10 2004 10:26:53 on modular [Seed = 1143798829] ------------------------------------- >> k3:CartesianProduct(k1,k2); ^ User error: bad syntax >> k3; ^ User error: Identifier 'k3' has not been declared or assigned Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host mathdhcp41.ces.clemson.edu. (130.127.112.170) Time: Tue Feb 10 10:27:06 2004 Input: k1:=CompleteGraph(2); k2:=CartesianProduct(k1,k1); k3:=CartesianProduct(k1,k2); k3; Output: Magma V2.10-6 Tue Feb 10 2004 10:27:03 on modular [Seed = 1294333278] ------------------------------------- Graph Vertex Neighbours 1 2 3 5 ; 2 1 4 6 ; 3 1 4 7 ; 4 2 3 8 ; 5 1 6 7 ; 6 2 5 8 ; 7 3 5 8 ; 8 4 6 7 ; Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host mathdhcp41.ces.clemson.edu. (130.127.112.170) Time: Tue Feb 10 10:28:36 2004 Input: k1:=CompleteGraph(2); k2:=CartesianProduct(k1,k1); k3:=CartesianProduct(k1,k2); k4:=CartesianProduct(k1,k3); k4; Output: Magma V2.10-6 Tue Feb 10 2004 10:28:33 on modular [Seed = 1981730435] ------------------------------------- Graph Vertex Neighbours 1 2 3 5 9 ; 2 1 4 6 10 ; 3 1 4 7 11 ; 4 2 3 8 12 ; 5 1 6 7 13 ; 6 2 5 8 14 ; 7 3 5 8 15 ; 8 4 6 7 16 ; 9 1 10 11 13 ; 10 2 9 12 14 ; 11 3 9 12 15 ; 12 4 10 11 16 ; 13 5 9 14 15 ; 14 6 10 13 16 ; 15 7 11 13 16 ; 16 8 12 14 15 ; Total time: 2.939 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host mather.maths.liv.ac.uk. (138.253.39.15) Time: Tue Feb 10 11:05:19 2004 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: Magma V2.10-6 Tue Feb 10 2004 11:05:16 on modular [Seed = 3652229297] ------------------------------------- Replace this by some code, then click [PARI] or [MAGMA]! Total time: 2.889 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host mather.maths.liv.ac.uk. (138.253.39.15) Time: Tue Feb 10 11:10:54 2004 Input: P := PolynomialRing(Rationals()); C1 := x*(x+2)*(x+4)*(x^2-8); Jac1 := Jacobian(HyperellipticCurve(C1)); RationalPoints(Jac1 : Bound := 1000); ReducedBasis(RationalPoints(Jac1 : Bound := 1000)); SetVerbose("JacHypSelmer",3); TwoSelmerGroupData(Jac1); Output: Magma V2.10-6 Tue Feb 10 2004 11:10:48 on modular [Seed = 4103976488] ------------------------------------- {@ (1, 0, 0), (x + 4, 0, 1), (x + 2, 0, 1), (x, 0, 1), (x^2 + 6*x + 8, 0, 2), (x^2 + 4*x, 0, 2), (x^2 + 2*x, 0, 2), (x^2 - 8, 0, 2) @} [] Matrix with 0 rows and 0 columns TwoSelmerGroupData of Jacobian of Hyperelliptic Curve defined by y^2 = x^5 + 6*x^4 - 48*x^2 - 64*x over Rational Field m= Mapping from: CrvHyp: C to CrvHyp: C1 with equations : $.1 $.2 $.3 and inverse $.1 $.2 $.3 Bad primes = [ 2 ] f factors as (x) (x + 2) (x + 4) (x^2 - 8). For factor x, use field defined by x - 1 and theta = 0 For factor x + 2, use field defined by x - 1 and theta = -2 For factor x + 4, use field defined by x - 1 and theta = -4 For factor x^2 - 8, use field defined by x^2 - 2 and theta = -2*K.1 The 2-torsion group has dimension 3. Determining local images... p = 2 L_2 decomposes into 4 local fields with invariants (e = 1, f = 1) (e = 1, f = 1) (e = 1, f = 1) (e = 2, f = 1) 2-torsion subgroup has dimension 3. Image of 2-torsion: (1 0 0 1 0 0 1 0 0 1 0 0 0) (0 1 1 1 0 0 0 0 0 1 1 0 1) (0 0 0 0 1 1 0 0 0 0 1 1 1) Dimension of local image = 5. ImageOfDelta: f = x^5 + 6*x^4 - 48*x^2 - 64*x p = 2 DeltaRec(0, 1/4) DeltaRec(0, 1/2) DeltaRec(0, 1) DeltaRec(1/2, 1) DeltaRec(0, 2) DeltaRec(1, 2) DeltaRec(0, 4) DeltaRec(2, 4) DeltaRec(1, 4) DeltaRec(3, 4) DeltaRec(0, 8) DeltaRec(4, 8) DeltaRec(2, 8) DeltaRec(6, 8) DeltaRec(1, 8) DeltaRec(5, 8) DeltaRec(3, 8) x = 3 --> new generator (0 1 0 0 0 1 0 1 1 0 0 0 0) DeltaRec(7, 8) DeltaRec(0, 16) DeltaRec(8, 16) DeltaRec(4, 16) DeltaRec(12, 16) DeltaRec(2, 16) DeltaRec(10, 16) DeltaRec(6, 16) DeltaRec(14, 16) DeltaRec(0, 32) DeltaRec(16, 32) DeltaRec(8, 32) DeltaRec(24, 32) DeltaRec(4, 32) DeltaRec(20, 32) DeltaRec(12, 32) DeltaRec(28, 32) DeltaRec(2, 32) DeltaRec(18, 32) DeltaRec(10, 32) DeltaRec(26, 32) DeltaRec(6, 32) DeltaRec(22, 32) DeltaRec(14, 32) DeltaRec(30, 32) DeltaRec(0, 64) DeltaRec(32, 64) DeltaRec(16, 64) DeltaRec(48, 64) DeltaRec(8, 64) DeltaRec(40, 64) DeltaRec(24, 64) DeltaRec(56, 64) DeltaRec(4, 64) DeltaRec(36, 64) DeltaRec(20, 64) DeltaRec(52, 64) DeltaRec(12, 64) DeltaRec(44, 64) DeltaRec(28, 64) DeltaRec(60, 64) DeltaRec(2, 64) DeltaRec(34, 64) DeltaRec(18, 64) x = 18 --> new generator (1 0 0 0 0 1 1 1 0 0 1 0 1) Local basis: (1 0 0 0 0 1 1 1 0 0 1 0 1) (0 1 0 0 0 1 0 1 1 0 0 0 0) (0 0 1 0 0 0 0 0 1 0 0 0 0) (0 0 0 1 0 1 0 1 0 1 1 0 1) (0 0 0 0 1 1 0 0 0 0 1 1 1) Basis of image under valuation map: (1 0 1 0) (0 1 0 1) p = infinity Real roots: -4.0000000000000000000 -2.8284271247461900976 -2.0000000000000000000 0.E-279 2.8284271247461900976 Local basis: (0 1 1 0 0) (0 0 0 1 1) Computing class groups... Class group data of the fields: Field given by x: [] Field given by x + 2: [] Field given by x + 4: [] Field given by x^2 - 8: [] Dimension of Cl[2] = 0. Signatures: [ 1, 0 ] [ 1, 0 ] [ 1, 0 ] [ 2, 0 ] Dimension of units mod squares = 5. Upper bound for Selmer group dimension: 6. ==> Upper bound for rank = 3. Computing unit groups... Class group and unit data of the fields: Field given by x: Class group = [], units = [ 2 ] Field given by x + 2: Class group = [], units = [ 2 ] Field given by x + 4: Class group = [], units = [ 2 ] Field given by x^2 - 8: Class group = [], units = [ 2, 0 ] Kernel of valuation map has basis 1/32*x^4 + 3/16*x^3 - 3/2*x - 1 -1/8*x^4 - 1/2*x^3 + x^2 + 4*x + 1 -1/32*x^4 - 1/16*x^3 + 1/4*x^2 + 1/2*x + 1 1/8*x^4 + 3/8*x^3 - 5/4*x^2 - 3*x + 1 3/32*x^4 + 5/16*x^3 - 3/4*x^2 - 2*x + 1 Additional generators of bounding group: -1/16*x^3 - 1/8*x^2 + 1/2*x + 2 1/32*x^4 + 1/8*x^3 - 3/8*x^2 - 3/2*x + 1 Images of generators of bounding group: (0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0) (0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 1 0 0) (0 0 0 0 0 0 0 1 1 0 0 0 0 1 0 0 0 0) (0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 0 1) (0 0 0 0 0 0 0 0 0 0 1 1 1 0 1 0 0 0) (1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0) (0 0 0 1 0 0 0 0 0 1 1 0 1 0 0 0 0 1) Time for local computations: 799 ms. Time for class groups: 151 ms. Time for unit groups: 19 ms. Selmer group dimension = 3, Dimension of 2-torsion = 3, ==> Bound for the MW-rank = 0. Basis of Selmer group: 1/16*$.1^4 + 5/16*$.1^3 - 3/8*$.1^2 - 3*$.1 - 1 -1/32*$.1^4 - 3/16*$.1^3 + 1/4*$.1^2 + 2*$.1 + 1 3/32*$.1^4 + 5/16*$.1^3 - 3/4*$.1^2 - 2*$.1 + 2 Total time: 1169 ms. 0 3 <[ 1/16*$.1^4 + 5/16*$.1^3 - 3/8*$.1^2 - 3*$.1 - 1, -1/32*$.1^4 - 3/16*$.1^3 + 1/4*$.1^2 + 2*$.1 + 1, 3/32*$.1^4 + 5/16*$.1^3 - 3/4*$.1^2 - 2*$.1 + 2 ], [], []> { Number Field with defining polynomial x^2 - 2 over the Rational Field } Total time: 5.819 seconds, Total memory usage: 20.10MB ************** MAGMA ***************** Host pD9E78C10.dip0.t-ipconnect.de. (217.231.140.16) Time: Wed Feb 11 08:22:58 2004 Input: 3+4 ; Output: Magma V2.10-6 Wed Feb 11 2004 08:22:54 on modular [Seed = 3168194683] ------------------------------------- 7 Total time: 3.009 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pD9E78C10.dip0.t-ipconnect.de. (217.231.140.16) Time: Wed Feb 11 08:23:42 2004 Input: f(x):=a*x*x*x+b*x*x+c*x+d; Output: Magma V2.10-6 Wed Feb 11 2004 08:23:38 on modular [Seed = 3084770052] ------------------------------------- >> f(x):=a*x*x*x+b*x*x+c*x+d;; ^ User error: Identifier 'a' has not been declared or assigned Total time: 3.129 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pD9E78C10.dip0.t-ipconnect.de. (217.231.140.16) Time: Wed Feb 11 08:24:22 2004 Input: f(x):=3*x*x*x+2*x*x+7*x+21; Output: Magma V2.10-6 Wed Feb 11 2004 08:24:19 on modular [Seed = 2397365220] ------------------------------------- >> f(x):=3*x*x*x+2*x*x+7*x+21;; ^ User error: Identifier 'x' has not been declared or assigned Total time: 3.049 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pD9E78C10.dip0.t-ipconnect.de. (217.231.140.16) Time: Wed Feb 11 08:24:46 2004 Input: solve(3*x*x*x+2*x*x+7*x+21=0,x); Output: Magma V2.10-6 Wed Feb 11 2004 08:24:43 on modular [Seed = 2616325865] ------------------------------------- >> solve(3*x*x*x+2*x*x+7*x+21=0,x); ^ User error: Identifier 'x' has not been declared or assigned Total time: 3.009 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host qn-212-127-199-12.quicknet.nl. (212.127.199.12) Time: Wed Feb 11 13:32:54 2004 Input: 2+3 Output: Magma V2.10-6 Wed Feb 11 2004 13:32:51 on modular [Seed = 3366125032] ------------------------------------- 5 Total time: 2.989 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host qn-212-127-199-12.quicknet.nl. (212.127.199.12) Time: Wed Feb 11 13:33:57 2004 Input: 2+3 log1000+log10= Output: Magma V2.10-6 Wed Feb 11 2004 13:33:54 on modular [Seed = 2781843524] ------------------------------------- >> log1000+log10=; ^ User error: bad syntax Total time: 2.979 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pc56.math.umbc.edu. (130.85.145.214) Time: Wed Feb 11 13:35:11 2004 Input: V := KMatrixSpace(RealField(), 7, 1); Output: Magma V2.10-6 Wed Feb 11 2004 13:35:08 on modular [Seed = 2549981752] ------------------------------------- Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pc56.math.umbc.edu. (130.85.145.214) Time: Wed Feb 11 13:35:25 2004 Input: V := KMatrixSpace(RealField(), 7, 1); print V; Output: Magma V2.10-6 Wed Feb 11 2004 13:35:22 on modular [Seed = 2666834695] ------------------------------------- Full KMatrixSpace of 7 by 1 matrices over Real Field Total time: 3.049 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host gw1.btc.transwitch.com. (63.149.68.2) Time: Wed Feb 11 17:49:30 2004 Input: R := PolynomialRing(RationalField());TransitiveGroupIdentification(GaloisGroup(x^16-6*x^12+6*x^8-6*x^4+1)); Output: Magma V2.10-6 Wed Feb 11 2004 17:49:20 on modular [Seed = 140704001] ------------------------------------- 130 16 Total time: 7.459 seconds, Total memory usage: 6.69MB ************** MAGMA ***************** Host gw1.btc.transwitch.com. (63.149.68.2) Time: Wed Feb 11 17:50:36 2004 Input: R := PolynomialRing(RationalField());TransitiveGroupIdentification(GaloisGroup(x^16 - 48*x^14 + 936*x^12 - 9504*x^10 + 53460*x^8 - 163296*x^6 + 244944*x^4 - 139968*x^2 + 1944)); Output: Magma V2.10-6 Wed Feb 11 2004 17:50:25 on modular [Seed = 4070048570] ------------------------------------- 136 16 Total time: 10.269 seconds, Total memory usage: 6.19MB ************** MAGMA ***************** Host gw1.btc.transwitch.com. (63.149.68.2) Time: Wed Feb 11 17:54:29 2004 Input: R := PolynomialRing(RationalField());TransitiveGroupIdentification(GaloisGroup(x^16-x^12+5*x^8-x^4+1)); Output: Magma V2.10-6 Wed Feb 11 2004 17:54:21 on modular [Seed = 3968212488] ------------------------------------- 149 16 Total time: 7.750 seconds, Total memory usage: 8.72MB ************** MAGMA ***************** Host gw1.btc.transwitch.com. (63.149.68.2) Time: Wed Feb 11 17:57:40 2004 Input: R := PolynomialRing(RationalField());TransitiveGroupIdentification(GaloisGroup(x^16-6*x^12+18*x^8-6*x^4+1)); Output: Magma V2.10-6 Wed Feb 11 2004 17:57:34 on modular [Seed = 3719769850] ------------------------------------- 111 16 Total time: 5.949 seconds, Total memory usage: 4.00MB ************** MAGMA ***************** Host gw1.btc.transwitch.com. (63.149.68.2) Time: Wed Feb 11 17:58:39 2004 Input: R := PolynomialRing(RationalField());TransitiveGroupIdentification(GaloisGroup(x^16-6*x^12+19*x^8-6*x^4+1)); Output: Magma V2.10-6 Wed Feb 11 2004 17:58:28 on modular [Seed = 3619497018] ------------------------------------- 105 16 Total time: 10.289 seconds, Total memory usage: 12.00MB ************** MAGMA ***************** Host gw1.btc.transwitch.com. (63.149.68.2) Time: Wed Feb 11 18:03:13 2004 Input: R := PolynomialRing(RationalField());TransitiveGroupIdentification(GaloisGroup(x^16 - 40*x^14 + 440*x^12 - 2000*x^10 + 4136*x^8 - 4000*x^6 + 1760*x^4 - 320*x^2 + 16)); Output: Magma V2.10-6 Wed Feb 11 2004 18:03:04 on modular [Seed = 2881576826] ------------------------------------- 43 16 Total time: 8.279 seconds, Total memory usage: 6.62MB ************** MAGMA ***************** Host gw1.btc.transwitch.com. (63.149.68.2) Time: Wed Feb 11 18:04:13 2004 Input: R := PolynomialRing(RationalField());TransitiveGroupIdentification(GaloisGroup(x^16 - 123*x^12 - 2900*x^10 - 10152*x^8 - 14750*x^6 + 358857*x^4 - 595650*x^2 + 130321)); Output: Magma V2.10-6 Wed Feb 11 2004 18:04:03 on modular [Seed = 2781827391] ------------------------------------- 105 16 Total time: 10.419 seconds, Total memory usage: 13.82MB ************** MAGMA ***************** Host gw1.btc.transwitch.com. (63.149.68.2) Time: Wed Feb 11 18:05:41 2004 Input: R := PolynomialRing(RationalField());TransitiveGroupIdentification(GaloisGroup(x^16 - 40*x^14 - 32*x^13 + 572*x^12 + 880*x^11 - 3184*x^10 - 7712*x^9 + 2948*x^8 + 21440*x^7 + 18296*x^6 + 688*x^5 - 4064*x^4 - 384*x^3 + 336*x^2 - 16*x - 2)); Output: Magma V2.10-6 Wed Feb 11 2004 18:05:33 on modular [Seed = 2482595543] ------------------------------------- 153 16 Total time: 7.659 seconds, Total memory usage: 9.24MB ************** MAGMA ***************** Host gw1.btc.transwitch.com. (63.149.68.2) Time: Wed Feb 11 18:08:03 2004 Input: R := PolynomialRing(RationalField());TransitiveGroupIdentification(GaloisGroup(x^16 - 100*x^12 - 148*x^8 + 100*x^4 + 1)); Output: Magma V2.10-6 Wed Feb 11 2004 18:07:54 on modular [Seed = 2380757054] ------------------------------------- 132 16 Total time: 9.510 seconds, Total memory usage: 5.27MB ************** MAGMA ***************** Host gw1.btc.transwitch.com. (63.149.68.2) Time: Wed Feb 11 18:08:46 2004 Input: R := PolynomialRing(RationalField());TransitiveGroupIdentification(GaloisGroup(x^16 - 40*x^14 + 440*x^12 - 2000*x^10 + 4136*x^8 - 4000*x^6 + 1760*x^4 - 320*x^2 + 16)); Output: Magma V2.10-6 Wed Feb 11 2004 18:08:37 on modular [Seed = 2230219016] ------------------------------------- 43 16 Total time: 8.340 seconds, Total memory usage: 6.62MB ************** MAGMA ***************** Host gw1.btc.transwitch.com. (63.149.68.2) Time: Wed Feb 11 18:09:48 2004 Input: R := PolynomialRing(RationalField());TransitiveGroupIdentification(GaloisGroup(x^16 - 112*x^14 + 4592*x^12 - 87808*x^10 + 883722*x^8 - 4835712*x^6 + 13655712*x^4 - 15893248*x^2 + 1223236)); Output: Magma V2.10-6 Wed Feb 11 2004 18:09:39 on modular [Seed = 2081851957] ------------------------------------- 132 16 Total time: 9.039 seconds, Total memory usage: 3.59MB ************** MAGMA ***************** Host gw1.btc.transwitch.com. (63.149.68.2) Time: Wed Feb 11 18:12:15 2004 Input: R := PolynomialRing(RationalField());TransitiveGroupIdentification(GaloisGroup(x^16 - 100*x^12 - 148*x^8 + 100*x^4 + 1)); Output: Magma V2.10-6 Wed Feb 11 2004 18:12:06 on modular [Seed = 1611306716] ------------------------------------- 132 16 Total time: 9.419 seconds, Total memory usage: 5.27MB ************** MAGMA ***************** Host gw1.btc.transwitch.com. (63.149.68.2) Time: Wed Feb 11 18:13:38 2004 Input: R := PolynomialRing(RationalField());TransitiveGroupIdentification(GaloisGroup(x^16-40*x^14+440*x^12-2000*x^10+4136*x^8-4000*x^6+1760*x^4-320*x^2+16)); Output: Magma V2.10-6 Wed Feb 11 2004 18:13:29 on modular [Seed = 1580509501] ------------------------------------- 43 16 Total time: 8.289 seconds, Total memory usage: 6.64MB ************** MAGMA ***************** Host cae168-252-126.sc.rr.com. (24.168.252.126) Time: Wed Feb 11 23:33:43 2004 Input: 9+6+6 Output: Magma V2.10-6 Wed Feb 11 2004 23:33:40 on modular [Seed = 995129697] ------------------------------------- 21 Total time: 3.019 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (82.100.96.47) Time: Thu Feb 12 00:47:02 2004 Input: GF(2); C := PrimitivePolynomial(k,9); C; G := 0; for j in [24..31] do for k in [20..23] do for m in [14..19] do for n in [8..13] do C := ((1 + X^13)^n)*((1 + X^17)^m)*((1 + X^19)^k)*((1 + X^23)^j) + X^1279; if IsPrimitive(C) then C; n; m; k; j; G := j+k+m+n; G; end if; end for; end for; end for; end for; Output: Magma V2.10-6 Thu Feb 12 2004 00:46:58 on modular [Seed = 3767251890] ------------------------------------- Finite field of size 2 >> C := PrimitivePolynomial(k,9); ^ User error: Identifier 'k' has not been declared or assigned >> C; ^ User error: Identifier 'C' has not been declared or assigned >> C := ((1 + X^13)^n)*((1 + X^17)^m)*((1 + X^19)^k)*((1 + X^2 ^ User error: Identifier 'X' has not been declared or assigned Total time: 2.909 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (82.100.96.47) Time: Thu Feb 12 00:48:01 2004 Input: C := GF(2); C := PrimitivePolynomial(k,9); C; G := 0; for j in [24..31] do for k in [20..23] do for m in [14..19] do for n in [8..13] do C := ((1 + X^13)^n)*((1 + X^17)^m)*((1 + X^19)^k)*((1 + X^23)^j) + X^1279; if IsPrimitive(C) then C; n; m; k; j; G := j+k+m+n; G; end if; end for; end for; end for; end for; Output: Magma V2.10-6 Thu Feb 12 2004 00:47:58 on modular [Seed = 4070154620] ------------------------------------- >> C := PrimitivePolynomial(k,9); ^ User error: Identifier 'k' has not been declared or assigned Finite field of size 2 1 8 14 20 24 66 1 9 14 20 24 67 1 10 14 20 24 68 1 11 14 20 24 69 1 12 14 20 24 70 1 13 14 20 24 71 1 8 15 20 24 67 1 9 15 20 24 68 1 10 15 20 24 69 1 11 15 20 24 70 1 12 15 20 24 71 1 13 15 20 24 72 1 8 16 20 24 68 1 9 16 20 24 69 1 10 16 20 24 70 1 11 16 20 24 71 1 12 16 20 24 72 1 13 16 20 24 73 1 8 17 20 24 69 1 9 17 20 24 70 1 10 17 20 24 71 1 11 17 20 24 72 1 12 17 20 24 73 1 13 17 20 24 74 1 8 18 20 24 70 1 9 18 20 24 71 1 10 18 20 24 72 1 11 18 20 24 73 1 12 18 20 24 74 1 13 18 20 24 75 1 8 19 20 24 71 1 9 19 20 24 72 1 10 19 20 24 73 1 11 19 20 24 74 1 12 19 20 24 75 1 13 19 20 24 76 1 8 14 21 24 67 1 9 14 21 24 68 1 10 14 21 24 69 1 11 14 21 24 70 1 12 14 21 24 71 1 13 14 21 24 72 1 8 15 21 24 68 1 9 15 21 24 69 1 10 15 21 24 70 1 11 15 21 24 71 1 12 15 21 24 72 1 13 15 21 24 73 1 8 16 21 24 69 1 9 16 21 24 70 1 10 16 21 24 71 1 11 16 21 24 72 1 12 16 21 24 73 1 13 16 21 24 74 1 8 17 21 24 70 1 9 17 21 24 71 1 10 17 21 24 72 1 11 17 21 24 73 1 12 17 21 24 74 1 13 17 21 24 75 1 8 18 21 24 71 1 9 18 21 24 72 1 10 18 21 24 73 1 11 18 21 24 74 1 12 18 21 24 75 1 13 18 21 24 76 1 8 19 21 24 72 1 9 19 21 24 73 1 10 19 21 24 74 1 11 19 21 24 75 1 12 19 21 24 76 1 13 19 21 24 77 1 8 14 22 24 68 1 9 14 22 24 69 1 10 14 22 24 70 1 11 14 22 24 71 1 12 14 22 24 72 1 13 14 22 24 73 1 8 15 22 24 69 1 9 15 22 24 70 1 10 15 22 24 71 1 11 15 22 24 72 1 12 15 22 24 73 1 13 15 22 24 74 1 8 16 22 24 70 1 9 16 22 24 71 1 10 16 22 24 72 1 11 16 22 24 73 1 12 16 22 24 74 1 13 16 22 24 75 1 8 17 22 24 71 1 9 17 22 24 72 1 10 17 22 24 73 1 11 17 22 24 74 1 12 17 22 24 75 1 13 17 22 24 76 1 8 18 22 24 72 1 9 18 22 24 73 1 10 18 22 24 74 1 11 18 22 24 75 1 12 18 22 24 76 1 13 18 22 24 77 1 8 19 22 24 73 1 9 19 22 24 74 1 10 19 22 24 75 1 11 19 22 24 76 1 12 19 22 24 77 1 13 19 22 24 78 1 8 14 23 24 69 1 9 14 23 24 70 1 10 14 23 24 71 1 11 14 23 24 72 1 12 14 23 24 73 1 13 14 23 24 74 1 8 15 23 24 70 1 9 15 23 24 71 1 10 15 23 24 72 1 11 15 23 24 73 1 12 15 23 24 74 1 13 15 23 24 75 1 8 16 23 24 71 1 9 16 23 24 72 1 10 16 23 24 73 1 11 16 23 24 74 1 12 16 23 24 75 1 13 16 23 24 76 1 8 17 23 24 72 1 9 17 23 24 73 1 10 17 23 24 74 1 11 17 23 24 75 1 12 17 23 24 76 1 13 17 23 24 77 1 8 18 23 24 73 1 9 18 23 24 74 1 10 18 23 24 75 1 11 18 23 24 76 1 12 18 23 24 77 1 13 18 23 24 78 1 8 19 23 24 74 1 9 19 23 24 75 1 10 19 23 24 76 1 11 19 23 24 77 1 12 19 23 24 78 1 13 19 23 24 79 1 8 14 20 25 67 1 9 14 20 25 68 1 10 14 20 25 69 1 11 14 20 25 70 1 12 14 20 25 71 1 13 14 20 25 72 1 8 15 20 25 68 1 9 15 20 25 69 1 10 15 20 25 70 1 11 15 20 25 71 1 12 15 20 25 72 1 13 15 20 25 73 1 8 16 20 25 69 1 9 16 20 25 70 1 10 16 20 25 71 1 11 16 20 25 72 1 12 16 20 25 73 1 13 16 20 25 74 1 8 17 20 25 70 1 9 17 20 25 71 1 10 17 20 25 72 1 11 17 20 25 73 1 12 17 20 25 74 1 13 17 20 25 75 1 8 18 20 25 71 1 9 18 20 25 72 1 10 18 20 25 73 1 11 18 20 25 74 1 12 18 20 25 75 1 13 18 20 25 76 1 8 19 20 25 72 1 9 19 20 25 73 1 10 19 20 25 74 1 11 19 20 25 75 1 12 19 20 25 76 1 13 19 20 25 77 1 8 14 21 25 68 1 9 14 21 25 69 1 10 14 21 25 70 1 11 14 21 25 71 1 12 14 21 25 72 1 13 14 21 25 73 1 8 15 21 25 69 1 9 15 21 25 70 1 10 15 21 25 71 1 11 15 21 25 72 1 12 15 21 25 73 1 13 15 21 25 74 1 8 16 21 25 70 1 9 16 21 25 71 1 10 16 21 25 72 1 11 16 21 25 73 1 12 16 21 25 74 1 13 16 21 25 75 1 8 17 21 25 71 1 9 17 21 25 72 1 10 17 21 25 73 1 11 17 21 25 74 1 12 17 21 25 75 1 13 17 21 25 76 1 8 18 21 25 72 1 9 18 21 25 73 1 10 18 21 25 74 1 11 18 21 25 75 1 12 18 21 25 76 1 13 18 21 25 77 1 8 19 21 25 73 1 9 19 21 25 74 1 10 19 21 25 75 1 11 19 21 25 76 1 12 19 21 25 77 1 13 19 21 25 78 1 8 14 22 25 69 1 9 14 22 25 70 1 10 14 22 25 71 1 11 14 22 25 72 1 12 14 22 25 73 1 13 14 22 25 74 1 8 15 22 25 70 1 9 15 22 25 71 1 10 15 22 25 72 1 11 15 22 25 73 1 12 15 22 25 74 1 13 15 22 25 75 1 8 16 22 25 71 1 9 16 22 25 72 1 10 16 22 25 73 1 11 16 22 25 74 1 12 16 22 25 75 1 13 16 22 25 76 1 8 17 22 25 72 1 9 17 22 25 73 1 10 17 22 25 74 1 11 17 22 25 75 1 12 17 22 25 76 1 13 17 22 25 77 1 8 18 22 25 73 1 9 18 22 25 74 1 10 18 22 25 75 1 11 18 22 25 76 1 12 18 22 25 77 1 13 18 22 25 78 1 8 19 22 25 74 1 9 19 22 25 75 1 10 19 22 25 76 1 11 19 22 25 77 1 12 19 22 25 78 1 13 19 22 25 79 1 8 14 23 25 70 1 9 14 23 25 71 1 10 14 23 25 72 1 11 14 23 25 73 1 12 14 23 25 74 1 13 14 23 25 75 1 8 15 23 25 71 1 9 15 23 25 72 1 10 15 23 25 73 1 11 15 23 25 74 1 12 15 23 25 75 1 13 15 23 25 76 1 8 16 23 25 72 1 9 16 23 25 73 1 10 16 23 25 74 1 11 16 23 25 75 1 12 16 23 25 76 1 13 16 23 25 77 1 8 17 23 25 73 1 9 17 23 25 74 1 10 17 23 25 75 1 11 17 23 25 76 1 12 17 23 25 77 1 13 17 23 25 78 1 8 18 23 25 74 1 9 18 23 25 75 1 10 18 23 25 76 1 11 18 23 25 77 1 12 18 23 25 78 1 13 18 23 25 79 1 8 19 23 25 75 1 9 19 23 25 76 1 10 19 23 25 77 1 11 19 23 25 78 1 12 19 23 25 79 1 13 19 23 25 80 1 8 14 20 26 68 1 9 14 20 26 69 1 10 14 20 26 70 1 11 14 20 26 71 1 12 14 20 26 72 1 13 14 20 26 73 1 8 15 20 26 69 1 9 15 20 26 70 1 10 15 20 26 71 1 11 15 20 26 72 1 12 15 20 26 73 1 13 15 20 26 74 1 8 16 20 26 70 1 9 16 20 26 71 1 10 16 20 26 72 1 11 16 20 26 73 1 12 16 20 26 74 1 13 16 20 26 75 1 8 17 20 26 71 1 9 17 20 26 72 1 10 17 20 26 73 1 11 17 20 26 74 1 12 17 20 26 75 1 13 17 20 26 76 1 8 18 20 26 72 1 9 18 20 26 73 1 10 18 20 26 74 1 11 18 20 26 75 1 12 18 20 26 76 1 13 18 20 26 77 1 8 19 20 26 73 1 9 19 20 26 74 1 10 19 20 26 75 1 11 19 20 26 76 1 12 19 20 26 77 1 13 19 20 26 78 1 8 14 21 26 69 1 9 14 21 26 70 1 10 14 21 26 71 1 11 14 21 26 72 1 12 14 21 26 73 1 13 14 21 26 74 1 8 15 21 26 70 1 9 15 21 26 71 1 10 15 21 26 72 1 11 15 21 26 73 1 12 15 21 26 74 1 13 15 21 26 75 1 8 16 21 26 71 1 9 16 21 26 72 1 10 16 21 26 73 1 11 16 21 26 74 1 12 16 21 26 75 1 13 16 21 26 76 1 8 17 21 26 72 1 9 17 21 26 73 1 10 17 21 26 74 1 11 17 21 26 75 1 12 17 21 26 76 1 13 17 21 26 77 1 8 18 21 26 73 1 9 18 21 26 74 1 10 18 21 26 75 1 11 18 21 26 76 1 12 18 21 26 77 1 13 18 21 26 78 1 8 19 21 26 74 1 9 19 21 26 75 1 10 19 21 26 76 1 11 19 21 26 77 1 12 19 21 26 78 1 13 19 21 26 79 1 8 14 22 26 70 1 9 14 22 26 71 1 10 14 22 26 72 1 11 14 22 26 73 1 12 14 22 26 74 1 13 14 22 26 75 1 8 15 22 26 71 1 9 15 22 26 72 1 10 15 22 26 73 1 11 15 22 26 74 1 12 15 22 26 75 1 13 15 22 26 76 1 8 16 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20 27 69 1 9 14 20 27 70 1 10 14 20 27 71 1 11 14 20 27 72 1 12 14 20 27 73 1 13 14 20 27 74 1 8 15 20 27 70 1 9 15 20 27 71 1 10 15 20 27 72 1 11 15 20 27 73 1 12 15 20 27 74 1 13 15 20 27 75 1 8 16 20 27 71 1 9 16 20 27 72 1 10 16 20 27 73 1 11 16 20 27 74 1 12 16 20 27 75 1 13 16 20 27 76 1 8 17 20 27 72 1 9 17 20 27 73 1 10 17 20 27 74 1 11 17 20 27 75 1 12 17 20 27 76 1 13 17 20 27 77 1 8 18 20 27 73 1 9 18 20 27 74 1 10 18 20 27 75 1 11 18 20 27 76 1 12 18 20 27 77 1 13 18 20 27 78 1 8 19 20 27 74 1 9 19 20 27 75 1 10 19 20 27 76 1 11 19 20 27 77 1 12 19 20 27 78 1 13 19 20 27 79 1 8 14 21 27 70 1 9 14 21 27 71 1 10 14 21 27 72 1 11 14 21 27 73 1 12 14 21 27 74 1 13 14 21 27 75 1 8 15 21 27 71 1 9 15 21 27 72 1 10 15 21 27 73 1 11 15 21 27 74 1 12 15 21 27 75 1 13 15 21 27 76 1 8 16 21 27 72 1 9 16 21 27 73 1 10 16 21 27 74 1 11 16 21 27 75 1 12 16 21 27 76 1 13 16 21 27 77 1 8 17 21 27 73 1 9 17 21 27 74 1 10 17 21 27 75 1 11 17 21 27 76 1 12 17 21 27 77 1 13 17 21 27 78 1 8 18 21 27 74 1 9 18 21 27 75 1 10 18 21 27 76 1 11 18 21 27 77 1 12 18 21 27 78 1 13 18 21 27 79 1 8 19 21 27 75 1 9 19 21 27 76 1 10 19 21 27 77 1 11 19 21 27 78 1 12 19 21 27 79 1 13 19 21 27 80 1 8 14 22 27 71 1 9 14 22 27 72 1 10 14 22 27 73 1 11 14 22 27 74 1 12 14 22 27 75 1 13 14 22 27 76 1 8 15 22 27 72 1 9 15 22 27 73 1 10 15 22 27 74 1 11 15 22 27 75 1 12 15 22 27 76 1 13 15 22 27 77 1 8 16 22 27 73 1 9 16 22 27 74 1 10 16 22 27 75 1 11 16 22 27 76 1 12 16 22 27 77 1 13 16 22 27 78 1 8 17 22 27 74 1 9 17 22 27 75 1 10 17 22 27 76 1 11 17 22 27 77 1 12 17 22 27 78 1 13 17 22 27 79 1 8 18 22 27 75 1 9 18 22 27 76 1 10 18 22 27 77 1 11 18 22 27 78 1 12 18 22 27 79 1 13 18 22 27 80 1 8 19 22 27 76 1 9 19 22 27 77 1 10 19 22 27 78 1 11 19 22 27 79 1 12 19 22 27 80 1 13 19 22 27 81 1 8 14 23 27 72 1 9 14 23 27 73 1 10 14 23 27 74 1 11 14 23 27 75 1 12 14 23 27 76 1 13 14 23 27 77 1 8 15 23 27 73 1 9 15 23 27 74 1 10 15 23 27 75 1 11 15 23 27 76 1 12 15 23 27 77 1 13 15 23 27 78 1 8 16 23 27 74 1 9 16 23 27 75 1 10 16 23 27 76 1 11 16 23 27 77 1 12 16 23 27 78 1 13 16 23 27 79 1 8 17 23 27 75 1 9 17 23 27 76 1 10 17 23 27 77 1 11 17 23 27 78 1 12 17 23 27 79 1 13 17 23 27 80 1 8 18 23 27 76 1 9 18 23 27 77 1 10 18 23 27 78 1 11 18 23 27 79 1 12 18 23 27 80 1 13 18 23 27 81 1 8 19 23 27 77 1 9 19 23 27 78 1 10 19 23 27 79 1 11 19 23 27 80 1 12 19 23 27 81 1 13 19 23 27 82 1 8 14 20 28 70 1 9 14 20 28 71 1 10 14 20 28 72 1 11 14 20 28 73 1 12 14 20 28 74 1 13 14 20 28 75 1 8 15 20 28 71 1 9 15 20 28 ** WARNING: Output too long, hence truncated. ************** MAGMA ***************** Host 3(NXDOMAIN) (82.100.96.47) Time: Thu Feb 12 00:48:59 2004 Input: k := GF(2); C := PrimitivePolynomial(k,9); C; G := 0; for j in [24..31] do for k in [20..23] do for m in [14..19] do for n in [8..13] do C := ((1 + X^13)^n)*((1 + X^17)^m)*((1 + X^19)^k)*((1 + X^23)^j) + X^1279; if IsPrimitive(C) then C; n; m; k; j; G := j+k+m+n; G; end if; end for; end for; end for; end for; Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Thu Feb 12 2004 00:48:36 on modular [Seed = 91117232] ------------------------------------- X^9 + X^4 + 1 X^1404 + X^1391 + X^1385 + X^1378 + X^1372 + X^1366 + X^1365 + X^1359 + X^1353 + X^1347 + X^1346 + X^1340 + X^1334 + X^1328 + X^1327 + X^1321 + X^1315 + X^1309 + X^1308 + X^1302 + X^1300 + X^1296 + X^1290 + X^1289 + X^1287 + X^1283 + X^1281 + X^1279 + X^1277 + X^1274 + X^1271 + X^1270 + X^1268 + X^1264 + X^1262 + X^1261 + X^1258 + X^1255 + X^1251 + X^1249 + X^1245 + X^1243 + X^1242 + X^1236 + X^1232 + X^1230 + X^1224 + X^1223 + X^1220 + X^1217 + X^1211 + X^1207 + X^1205 + X^1204 + X^1201 + X^1198 + X^1194 + X^1192 + X^1188 + X^1186 + X^1185 + X^1182 + X^1181 + X^1179 + X^1175 + X^1173 + X^1169 + X^1167 + X^1166 + X^1163 + X^1162 + X^1160 + X^1156 + X^1154 + X^1150 + X^1147 + X^1144 + X^1143 + X^1141 + X^1137 + X^1132 + X^1131 + X^1128 + X^1125 + X^1124 + X^1119 + X^1118 + X^1116 + X^1113 + X^1112 + X^1105 + X^1103 + X^1099 + X^1097 + X^1094 + X^1090 + X^1087 + X^1086 + X^1084 + X^1080 + X^1078 + X^1077 + X^1075 + X^1074 + X^1071 + X^1067 + X^1065 + X^1059 + X^1058 + X^1056 + X^1052 + X^1048 + X^1046 + X^1042 + X^1040 + X^1039 + X^1037 + X^1036 + X^1033 + X^1028 + X^1027 + X^1021 + X^1020 + X^1018 + X^1017 + X^1015 + X^1014 + X^1010 + X^1009 + X^1008 + X^1001 + X^999 + X^998 + X^997 + X^995 + X^991 + X^990 + X^983 + X^982 + X^979 + X^978 + X^976 + X^972 + X^971 + X^970 + X^967 + X^963 + X^960 + X^959 + X^954 + X^953 + X^952 + X^948 + X^944 + X^940 + X^938 + X^935 + X^934 + X^933 + X^932 + X^929 + X^921 + X^915 + X^914 + X^913 + X^910 + X^906 + X^903 + X^902 + X^896 + X^895 + X^894 + X^893 + X^891 + X^890 + X^887 + X^883 + X^875 + X^874 + X^872 + X^868 + X^864 + X^863 + X^858 + X^856 + X^855 + X^853 + X^852 + X^850 + X^849 + X^844 + X^836 + X^834 + X^833 + X^831 + X^830 + X^828 + X^826 + X^825 + X^817 + X^814 + X^813 + X^811 + X^809 + X^807 + X^806 + X^802 + X^799 + X^798 + X^796 + X^795 + X^794 + X^792 + X^790 + X^789 + X^788 + X^787 + X^786 + X^779 + X^777 + X^776 + X^775 + X^771 + X^769 + X^768 + X^760 + X^758 + X^756 + X^754 + X^752 + X^750 + X^749 + X^748 + X^739 + X^737 + X^733 + X^732 + X^731 + X^730 + X^729 + X^724 + X^722 + X^720 + X^719 + X^718 + X^714 + X^713 + X^712 + X^710 + X^709 + X^706 + X^705 + X^703 + X^701 + X^699 + X^698 + X^695 + X^694 + X^692 + X^691 + X^690 + X^686 + X^685 + X^684 + X^682 + X^680 + X^675 + X^674 + X^673 + X^672 + X^671 + X^667 + X^665 + X^656 + X^655 + X^654 + X^652 + X^650 + X^648 + X^646 + X^644 + X^636 + X^635 + X^633 + X^629 + X^628 + X^627 + X^625 + X^618 + X^617 + X^616 + X^615 + X^614 + X^612 + X^610 + X^609 + X^608 + X^606 + X^605 + X^602 + X^598 + X^597 + X^595 + X^593 + X^591 + X^590 + X^587 + X^579 + X^578 + X^576 + X^574 + X^573 + X^571 + X^570 + X^568 + X^560 + X^555 + X^554 + X^552 + X^551 + X^549 + X^548 + X^546 + X^541 + X^540 + X^536 + X^532 + X^530 + X^529 + X^521 + X^517 + X^514 + X^513 + X^511 + X^510 + X^509 + X^508 + X^502 + X^501 + X^498 + X^494 + X^491 + X^490 + X^489 + X^483 + X^475 + X^472 + X^471 + X^470 + X^469 + X^466 + X^464 + X^460 + X^456 + X^452 + X^451 + X^450 + X^445 + X^444 + X^441 + X^437 + X^434 + X^433 + X^432 + X^428 + X^426 + X^425 + X^422 + X^421 + X^414 + X^413 + X^409 + X^407 + X^406 + X^405 + X^403 + X^396 + X^395 + X^394 + X^390 + X^389 + X^387 + X^386 + X^384 + X^383 + X^377 + X^376 + X^371 + X^368 + X^367 + X^365 + X^364 + X^362 + X^358 + X^356 + X^352 + X^348 + X^346 + X^345 + X^339 + X^337 + X^333 + X^330 + X^329 + X^327 + X^326 + X^324 + X^320 + X^318 + X^317 + X^314 + X^310 + X^307 + X^305 + X^301 + X^299 + X^292 + X^291 + X^288 + X^286 + X^285 + X^280 + X^279 + X^276 + X^273 + X^272 + X^267 + X^263 + X^261 + X^260 + X^257 + X^254 + X^250 + X^248 + X^244 + X^242 + X^241 + X^238 + X^237 + X^235 + X^231 + X^229 + X^225 + X^223 + X^222 + X^219 + X^218 + X^216 + X^212 + X^210 + X^206 + X^203 + X^200 + X^199 + X^197 + X^193 + X^187 + X^184 + X^181 + X^180 + X^174 + X^172 + X^168 + X^162 + X^161 + X^159 + X^155 + X^153 + X^149 + X^146 + X^143 + X^142 + X^140 + X^136 + X^134 + X^133 + X^130 + X^127 + X^123 + X^121 + X^117 + X^115 + X^114 + X^108 + X^104 + X^102 + X^96 + X^95 + X^89 + X^83 + X^77 + X^76 + X^70 + X^64 + X^58 + X^57 + X^51 + X^45 + X^39 + X^38 + X^32 + X^26 + X^19 + X^13 + 1 11 16 23 24 74 X^1404 + X^1391 + X^1381 + X^1378 + X^1370 + X^1368 + X^1365 + X^1357 + X^1355 + X^1347 + X^1344 + X^1342 + X^1334 + X^1331 + X^1328 + X^1321 + X^1315 + X^1308 + X^1305 + X^1302 + X^1300 + X^1294 + X^1292 + X^1289 + X^1287 + X^1281 + X^1277 + X^1274 + X^1271 + X^1268 + X^1264 + X^1261 + X^1258 + X^1255 + X^1253 + X^1251 + X^1245 + X^1243 + X^1240 + X^1238 + X^1232 + X^1230 + X^1227 + X^1224 + X^1220 + X^1217 + X^1211 + X^1207 + X^1204 + X^1201 + X^1198 + X^1197 + X^1194 + X^1190 + X^1188 + X^1186 + X^1185 + X^1184 + X^1181 + X^1177 + X^1175 + X^1173 + X^1171 + X^1167 + X^1164 + X^1163 + X^1162 + X^1160 + X^1158 + X^1154 + X^1151 + X^1150 + X^1147 + X^1144 + X^1141 + X^1137 + X^1132 + X^1131 + X^1128 + X^1124 + X^1121 + X^1119 + X^1118 + X^1116 + X^1110 + X^1109 + X^1108 + X^1106 + X^1105 + X^1103 + X^1100 + X^1098 + X^1097 + X^1096 + X^1095 + X^1090 + X^1085 + X^1084 + X^1083 + X^1080 + X^1075 + X^1072 + X^1071 + X^1070 + X^1069 + X^1067 + X^1066 + X^1064 + X^1062 + X^1054 + X^1053 + X^1051 + X^1049 + X^1048 + X^1046 + X^1043 + X^1038 + X^1028 + X^1024 + X^1023 + X^1022 + X^1017 + X^1015 + X^1014 + X^1013 + X^1011 + X^1010 + X^1009 + X^1007 + X^1006 + X^1005 + X^1000 + X^999 + X^998 + X^997 + X^993 + X^992 + X^991 + X^990 + X^988 + X^987 + X^986 + X^985 + X^983 + X^981 + X^980 + X^978 + X^977 + X^976 + X^975 + X^974 + X^971 + X^968 + X^964 + X^963 + X^960 + X^958 + X^955 + X^954 + X^953 + X^952 + X^951 + X^949 + X^948 + X^945 + X^944 + X^941 + X^940 + X^937 + X^936 + X^935 + X^929 + X^928 + X^926 + X^925 + X^924 + X^923 + X^922 + X^921 + X^920 + X^919 + X^918 + X^914 + X^913 + X^912 + X^911 + X^907 + X^906 + X^905 + X^903 + X^901 + X^899 + X^897 + X^896 + X^895 + X^894 + X^892 + X^891 + X^890 + X^888 + X^887 + X^885 + X^884 + X^883 + X^881 + X^880 + X^879 + X^878 + X^873 + X^871 + X^870 + X^867 + X^865 + X^864 + X^863 + X^862 + X^860 + X^859 + X^858 + X^856 + X^854 + X^850 + X^847 + X^844 + X^840 + X^839 + X^838 + X^837 + X^833 + X^831 + X^830 + X^829 + X^828 + X^827 + X^826 + X^825 + X^824 + X^823 + X^822 + X^821 + X^816 + X^814 + X^813 + X^809 + X^808 + X^807 + X^806 + X^805 + X^804 + X^803 + X^801 + X^799 + X^797 + X^796 + X^793 + X^791 + X^790 + X^789 + X^787 + X^784 + X^781 + X^780 + X^776 + X^774 + X^770 + X^769 + X^767 + X^766 + X^765 + X^764 + X^761 + X^760 + X^758 + X^757 + X^756 + X^755 + X^753 + X^751 + X^744 + X^742 + X^741 + X^740 + X^738 + X^737 + X^736 + X^735 + X^734 + X^732 + X^730 + X^728 + X^727 + X^726 + X^724 + X^723 + X^722 + X^721 + X^719 + X^718 + X^717 + X^716 + X^715 + X^712 + X^710 + X^708 + X^707 + X^706 + X^705 + X^704 + X^700 + X^699 + X^698 + X^697 + X^696 + X^694 + X^692 + X^689 + X^688 + X^687 + X^686 + X^685 + X^683 + X^682 + X^681 + X^680 + X^678 + X^677 + X^676 + X^674 + X^672 + X^670 + X^669 + X^668 + X^667 + X^666 + X^664 + X^663 + X^662 + X^660 + X^653 + X^651 + X^649 + X^648 + X^647 + X^646 + X^644 + X^643 + X^640 + X^639 + X^638 + X^637 + X^635 + X^634 + X^630 + X^628 + X^624 + X^623 + X^620 + X^617 + X^615 + X^614 + X^613 + X^611 + X^608 + X^607 + X^605 + X^603 + X^601 + X^600 + X^599 + X^598 + X^597 + X^596 + X^595 + X^591 + X^590 + X^588 + X^583 + X^582 + X^581 + X^580 + X^579 + X^578 + X^577 + X^576 + X^575 + X^574 + X^573 + X^571 + X^567 + X^566 + X^565 + X^564 + X^560 + X^557 + X^554 + X^550 + X^548 + X^546 + X^545 + X^544 + X^542 + X^541 + X^540 + X^539 + X^537 + X^534 + X^533 + X^531 + X^526 + X^525 + X^524 + X^523 + X^521 + X^520 + X^519 + X^517 + X^516 + X^514 + X^513 + X^512 + X^510 + X^509 + X^508 + X^507 + X^505 + X^503 + X^501 + X^499 + X^498 + X^497 + X^493 + X^492 + X^491 + X^490 + X^486 + X^485 + X^484 + X^483 + X^482 + X^481 + X^480 + X^479 + X^478 + X^476 + X^475 + X^469 + X^468 + X^467 + X^464 + X^463 + X^460 + X^459 + X^456 + X^455 + X^453 + X^452 + X^451 + X^450 + X^449 + X^446 + X^444 + X^441 + X^440 + X^436 + X^433 + X^430 + X^429 + X^428 + X^427 + X^426 + X^424 + X^423 + X^421 + X^419 + X^418 + X^417 + X^416 + X^414 + X^413 + X^412 + X^411 + X^407 + X^406 + X^405 + X^404 + X^399 + X^398 + X^397 + X^395 + X^394 + X^393 + X^391 + X^390 + X^389 + X^387 + X^382 + X^381 + X^380 + X^376 + X^366 + X^361 + X^358 + X^356 + X^355 + X^353 + X^351 + X^350 + X^342 + X^340 + X^338 + X^337 + X^335 + X^334 + X^333 + X^332 + X^329 + X^324 + X^321 + X^320 + X^319 + X^314 + X^309 + X^308 + X^307 + X^306 + X^304 + X^301 + X^299 + X^298 + X^296 + X^295 + X^294 + X^288 + X^286 + X^285 + X^283 + X^280 + X^276 + X^273 + X^272 + X^267 + X^263 + X^260 + X^257 + X^254 + X^253 + X^250 + X^246 + X^244 + X^242 + X^241 + X^240 + X^237 + X^233 + X^231 + X^229 + X^227 + X^223 + X^220 + X^219 + X^218 + X^216 + X^214 + X^210 + X^207 + X^206 + X^203 + X^200 + X^197 + X^193 + X^187 + X^184 + X^180 + X^177 + X^174 + X^172 + X^166 + X^164 + X^161 + X^159 + X^153 + X^151 + X^149 + X^146 + X^143 + X^140 + X^136 + X^133 + X^130 + X^127 + X^125 + X^123 + X^117 + X^115 + X^112 + X^110 + X^104 + X^102 + X^99 + X^96 + X^89 + X^83 + X^76 + X^73 + X^70 + X^62 + X^60 + X^57 + X^49 + X^47 + X^39 + X^36 + X^34 + X^26 + X^23 + X^13 + 1 11 18 20 25 74 X^1350 + X^1337 + X^133 ** WARNING: Output too long, hence truncated. Errors: /home/mfd/gomagma: line 2: 16644 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host 3(NXDOMAIN) (82.100.96.47) Time: Thu Feb 12 00:50:34 2004 Input: k := GF(2); C := PrimitivePolynomial(k,9); C; G := 0; for j in [21..31] do for k in [19..20] do for m in [13..18] do for n in [8..12] do C := ((1 + X^13)^n)*((1 + X^17)^m)*((1 + X^19)^k)*((1 + X^23)^j) + X^1279; if IsPrimitive(C) then C; n; m; k; j; G := j+k+m+n; G; end if; end for; end for; end for; end for; Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Thu Feb 12 2004 00:50:11 on modular [Seed = 609185846] ------------------------------------- X^9 + X^4 + 1 Errors: /home/mfd/gomagma: line 2: 16677 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host 3(NXDOMAIN) (82.100.96.47) Time: Thu Feb 12 00:51:17 2004 Input: k := GF(2); C := PrimitivePolynomial(k,9); C; G := 0; for j in [21..31] do for k in [19..20] do for m in [13..18] do for n in [8..12] do C := ((1 + X^13)^n)*((1 + X^17)^m)*((1 + X^19)^k)*((1 + X^22)^j) + X^1279; if IsPrimitive(C) then C; n; m; k; j; G := j+k+m+n; G; end if; end for; end for; end for; end for; Output: Magma V2.10-6 Thu Feb 12 2004 00:51:06 on modular [Seed = 811295867] ------------------------------------- X^9 + X^4 + 1 X^1354 + X^1341 + X^1335 + X^1332 + X^1322 + X^1320 + X^1319 + X^1316 + X^1313 + X^1307 + X^1303 + X^1301 + X^1300 + X^1298 + X^1297 + X^1294 + X^1288 + X^1286 + X^1285 + X^1284 + X^1282 + X^1281 + X^1275 + X^1273 + X^1269 + X^1267 + X^1264 + X^1263 + X^1262 + X^1260 + X^1254 + X^1253 + X^1252 + X^1251 + X^1248 + X^1245 + X^1244 + X^1241 + X^1239 + X^1237 + X^1235 + X^1234 + X^1233 + X^1230 + X^1229 + X^1228 + X^1226 + X^1225 + X^1220 + X^1219 + X^1217 + X^1214 + X^1211 + X^1210 + X^1207 + X^1206 + X^1205 + X^1203 + X^1201 + X^1200 + X^1196 + X^1195 + X^1194 + X^1192 + X^1191 + X^1190 + X^1187 + X^1186 + X^1185 + X^1183 + X^1178 + X^1176 + X^1174 + X^1173 + X^1172 + X^1169 + X^1167 + X^1166 + X^1165 + X^1161 + X^1160 + X^1159 + X^1157 + X^1153 + X^1152 + X^1151 + X^1146 + X^1144 + X^1142 + X^1140 + X^1139 + X^1138 + X^1137 + X^1135 + X^1133 + X^1132 + X^1131 + X^1130 + X^1127 + X^1126 + X^1125 + X^1123 + X^1119 + X^1117 + X^1112 + X^1111 + X^1110 + X^1108 + X^1106 + X^1105 + X^1104 + X^1103 + X^1102 + X^1101 + X^1098 + X^1097 + X^1096 + X^1093 + X^1091 + X^1090 + X^1086 + X^1085 + X^1082 + X^1078 + X^1076 + X^1072 + X^1067 + X^1064 + X^1062 + X^1061 + X^1060 + X^1059 + X^1058 + X^1057 + X^1056 + X^1052 + X^1051 + X^1049 + X^1048 + X^1047 + X^1041 + X^1038 + X^1037 + X^1033 + X^1028 + X^1027 + X^1026 + X^1024 + X^1017 + X^1013 + X^1011 + X^1007 + X^1002 + X^1001 + X^998 + X^996 + X^995 + X^992 + X^990 + X^989 + X^986 + X^982 + X^981 + X^979 + X^978 + X^975 + X^972 + X^971 + X^970 + X^968 + X^967 + X^965 + X^964 + X^962 + X^956 + X^955 + X^954 + X^953 + X^952 + X^949 + X^948 + X^947 + X^945 + X^944 + X^943 + X^942 + X^941 + X^940 + X^938 + X^937 + X^936 + X^935 + X^931 + X^928 + X^927 + X^926 + X^923 + X^922 + X^920 + X^919 + X^916 + X^914 + X^911 + X^909 + X^905 + X^904 + X^903 + X^902 + X^899 + X^898 + X^897 + X^890 + X^889 + X^888 + X^887 + X^886 + X^884 + X^883 + X^880 + X^876 + X^875 + X^871 + X^869 + X^868 + X^867 + X^866 + X^864 + X^863 + X^861 + X^856 + X^854 + X^853 + X^850 + X^849 + X^847 + X^845 + X^841 + X^839 + X^838 + X^837 + X^834 + X^832 + X^829 + X^828 + X^825 + X^818 + X^817 + X^816 + X^815 + X^810 + X^807 + X^806 + X^803 + X^802 + X^800 + X^799 + X^798 + X^797 + X^796 + X^791 + X^789 + X^788 + X^784 + X^783 + X^781 + X^779 + X^777 + X^776 + X^772 + X^769 + X^768 + X^767 + X^766 + X^763 + X^762 + X^758 + X^756 + X^755 + X^751 + X^749 + X^746 + X^739 + X^738 + X^735 + X^733 + X^731 + X^730 + X^728 + X^727 + X^725 + X^723 + X^716 + X^715 + X^714 + X^712 + X^711 + X^709 + X^707 + X^706 + X^704 + X^700 + X^697 + X^696 + X^693 + X^686 + X^685 + X^682 + X^681 + X^680 + X^679 + X^678 + X^676 + X^675 + X^674 + X^673 + X^672 + X^669 + X^668 + X^661 + X^658 + X^657 + X^654 + X^650 + X^648 + X^647 + X^645 + X^643 + X^642 + X^640 + X^639 + X^638 + X^631 + X^629 + X^627 + X^626 + X^624 + X^623 + X^621 + X^619 + X^616 + X^615 + X^608 + X^605 + X^603 + X^599 + X^598 + X^596 + X^592 + X^591 + X^588 + X^587 + X^586 + X^585 + X^582 + X^578 + X^577 + X^575 + X^573 + X^571 + X^570 + X^566 + X^565 + X^563 + X^558 + X^557 + X^556 + X^555 + X^554 + X^552 + X^551 + X^548 + X^547 + X^544 + X^539 + X^538 + X^537 + X^536 + X^529 + X^526 + X^525 + X^522 + X^520 + X^517 + X^516 + X^515 + X^513 + X^509 + X^507 + X^505 + X^504 + X^501 + X^500 + X^498 + X^493 + X^491 + X^490 + X^488 + X^487 + X^486 + X^485 + X^483 + X^479 + X^478 + X^474 + X^471 + X^470 + X^468 + X^467 + X^466 + X^465 + X^464 + X^457 + X^456 + X^455 + X^452 + X^451 + X^450 + X^449 + X^445 + X^443 + X^440 + X^438 + X^435 + X^434 + X^432 + X^431 + X^428 + X^427 + X^426 + X^423 + X^419 + X^418 + X^417 + X^416 + X^414 + X^413 + X^412 + X^411 + X^410 + X^409 + X^407 + X^406 + X^405 + X^402 + X^401 + X^400 + X^399 + X^398 + X^392 + X^390 + X^389 + X^387 + X^386 + X^384 + X^383 + X^382 + X^379 + X^376 + X^375 + X^373 + X^372 + X^368 + X^365 + X^364 + X^362 + X^359 + X^358 + X^356 + X^353 + X^352 + X^347 + X^343 + X^341 + X^337 + X^330 + X^328 + X^327 + X^326 + X^321 + X^317 + X^316 + X^313 + X^307 + X^306 + X^305 + X^303 + X^302 + X^298 + X^297 + X^296 + X^295 + X^294 + X^293 + X^292 + X^290 + X^287 + X^282 + X^278 + X^276 + X^272 + X^269 + X^268 + X^264 + X^263 + X^261 + X^258 + X^257 + X^256 + X^253 + X^252 + X^251 + X^250 + X^249 + X^248 + X^246 + X^244 + X^243 + X^242 + X^237 + X^235 + X^231 + X^229 + X^228 + X^227 + X^224 + X^223 + X^222 + X^221 + X^219 + X^217 + X^216 + X^215 + X^214 + X^212 + X^210 + X^208 + X^203 + X^202 + X^201 + X^197 + X^195 + X^194 + X^193 + X^189 + X^188 + X^187 + X^185 + X^182 + X^181 + X^180 + X^178 + X^176 + X^171 + X^169 + X^168 + X^167 + X^164 + X^163 + X^162 + X^160 + X^159 + X^158 + X^154 + X^153 + X^151 + X^149 + X^148 + X^147 + X^144 + X^143 + X^140 + X^137 + X^135 + X^134 + X^129 + X^128 + X^126 + X^125 + X^124 + X^121 + X^120 + X^119 + X^117 + X^115 + X^113 + X^110 + X^109 + X^106 + X^103 + X^102 + X^101 + X^100 + X^94 + X^92 + X^91 + X^90 + X^87 + X^85 + X^81 + X^79 + X^75 + X^73 + X^72 + X^70 + X^69 + X^68 + X^66 + X^60 + X^57 + X^56 + X^54 + X^53 + X^51 + X^47 + X^41 + X^38 + X^35 + X^34 + X^32 + X^22 + X^19 + X^13 + 1 9 14 19 29 71 Total time: 10.019 seconds, Total memory usage: 2.30MB ************** MAGMA ***************** Host 3(NXDOMAIN) (82.100.96.47) Time: Thu Feb 12 00:52:10 2004 Input: k := GF(2); C := PrimitivePolynomial(k,9); C; G := 0; for j in [21..31] do for k in [19..20] do for m in [13..18] do for n in [8..12] do C := ((1 + X^11)^n)*((1 + X^13)^m)*((1 + X^17)^k)*((1 + X^19)^j) + X^1279; if IsPrimitive(C) then C; n; m; k; j; G := j+k+m+n; G; end if; end for; end for; end for; end for; Output: Magma V2.10-6 Thu Feb 12 2004 00:52:01 on modular [Seed = 978415290] ------------------------------------- X^9 + X^4 + 1 X^1279 + X^1129 + X^1116 + X^1112 + X^1110 + X^1107 + X^1099 + X^1097 + X^1095 + X^1094 + X^1093 + X^1090 + X^1088 + X^1082 + X^1080 + X^1078 + X^1077 + X^1076 + X^1075 + X^1073 + X^1071 + X^1065 + X^1063 + X^1060 + X^1059 + X^1058 + X^1056 + X^1054 + X^1046 + X^1043 + X^1037 + X^1028 + X^1022 + X^1019 + X^1011 + X^1009 + X^1007 + X^1006 + X^1005 + X^1002 + X^1000 + X^994 + X^992 + X^990 + X^989 + X^988 + X^987 + X^985 + X^983 + X^975 + X^972 + X^971 + X^970 + X^968 + X^966 + X^964 + X^960 + X^953 + X^949 + X^947 + X^945 + X^943 + X^942 + X^941 + X^938 + X^930 + X^928 + X^926 + X^925 + X^924 + X^923 + X^919 + X^913 + X^911 + X^907 + X^906 + X^899 + X^894 + X^889 + X^887 + X^886 + X^882 + X^880 + X^876 + X^874 + X^872 + X^869 + X^868 + X^865 + X^863 + X^859 + X^857 + X^854 + X^853 + X^852 + X^851 + X^846 + X^844 + X^842 + X^838 + X^837 + X^836 + X^835 + X^833 + X^831 + X^829 + X^827 + X^825 + X^822 + X^821 + X^819 + X^812 + X^811 + X^810 + X^806 + X^805 + X^804 + X^801 + X^798 + X^795 + X^794 + X^792 + X^790 + X^789 + X^788 + X^787 + X^786 + X^781 + X^780 + X^779 + X^778 + X^777 + X^776 + X^775 + X^773 + X^772 + X^769 + X^765 + X^764 + X^763 + X^762 + X^761 + X^760 + X^759 + X^758 + X^756 + X^755 + X^754 + X^747 + X^745 + X^742 + X^741 + X^739 + X^733 + X^728 + X^724 + X^718 + X^715 + X^707 + X^703 + X^702 + X^701 + X^698 + X^696 + X^692 + X^690 + X^685 + X^684 + X^679 + X^675 + X^673 + X^670 + X^669 + X^667 + X^664 + X^660 + X^659 + X^658 + X^654 + X^653 + X^652 + X^646 + X^643 + X^642 + X^640 + X^638 + X^637 + X^635 + X^634 + X^632 + X^630 + X^629 + X^628 + X^626 + X^625 + X^624 + X^623 + X^621 + X^620 + X^619 + X^615 + X^614 + X^612 + X^611 + X^609 + X^607 + X^606 + X^604 + X^603 + X^600 + X^598 + X^597 + X^596 + X^591 + X^590 + X^589 + X^587 + X^585 + X^583 + X^581 + X^580 + X^579 + X^578 + X^574 + X^572 + X^557 + X^555 + X^551 + X^550 + X^549 + X^548 + X^546 + X^544 + X^542 + X^540 + X^539 + X^538 + X^533 + X^532 + X^531 + X^529 + X^526 + X^525 + X^523 + X^522 + X^520 + X^518 + X^517 + X^515 + X^514 + X^510 + X^509 + X^508 + X^506 + X^505 + X^504 + X^503 + X^501 + X^500 + X^499 + X^497 + X^495 + X^494 + X^492 + X^491 + X^489 + X^487 + X^486 + X^483 + X^477 + X^476 + X^475 + X^471 + X^470 + X^469 + X^465 + X^462 + X^460 + X^459 + X^456 + X^454 + X^450 + X^445 + X^444 + X^439 + X^437 + X^433 + X^431 + X^428 + X^427 + X^426 + X^422 + X^414 + X^411 + X^405 + X^401 + X^396 + X^390 + X^388 + X^387 + X^384 + X^382 + X^375 + X^374 + X^373 + X^371 + X^370 + X^369 + X^368 + X^367 + X^366 + X^365 + X^364 + X^360 + X^357 + X^356 + X^354 + X^353 + X^352 + X^351 + X^350 + X^349 + X^348 + X^343 + X^342 + X^341 + X^340 + X^339 + X^337 + X^335 + X^334 + X^331 + X^328 + X^325 + X^324 + X^323 + X^319 + X^318 + X^317 + X^310 + X^308 + X^307 + X^304 + X^302 + X^300 + X^298 + X^296 + X^294 + X^293 + X^292 + X^291 + X^287 + X^285 + X^283 + X^278 + X^277 + X^276 + X^275 + X^272 + X^270 + X^266 + X^264 + X^261 + X^260 + X^257 + X^255 + X^253 + X^249 + X^247 + X^243 + X^242 + X^240 + X^235 + X^230 + X^223 + X^222 + X^218 + X^216 + X^210 + X^206 + X^205 + X^204 + X^203 + X^201 + X^199 + X^191 + X^188 + X^187 + X^186 + X^184 + X^182 + X^180 + X^176 + X^169 + X^165 + X^163 + X^161 + X^159 + X^158 + X^157 + X^154 + X^146 + X^144 + X^142 + X^141 + X^140 + X^139 + X^137 + X^135 + X^129 + X^127 + X^124 + X^123 + X^122 + X^120 + X^118 + X^110 + X^107 + X^101 + X^92 + X^86 + X^83 + X^75 + X^73 + X^71 + X^70 + X^69 + X^66 + X^64 + X^58 + X^56 + X^54 + X^53 + X^52 + X^51 + X^49 + X^47 + X^41 + X^39 + X^36 + X^35 + X^34 + X^32 + X^30 + X^22 + X^19 + X^17 + X^13 + 1 10 17 19 25 71 X^1279 + X^1257 + X^1238 + X^1231 + X^1213 + X^1212 + X^1194 + X^1189 + X^1187 + X^1181 + X^1170 + X^1169 + X^1168 + X^1163 + X^1162 + X^1155 + X^1150 + X^1145 + X^1144 + X^1143 + X^1137 + X^1136 + X^1126 + X^1125 + X^1124 + X^1119 + X^1118 + X^1113 + X^1111 + X^1106 + X^1105 + X^1101 + X^1100 + X^1099 + X^1094 + X^1093 + X^1092 + X^1087 + X^1086 + X^1082 + X^1080 + X^1079 + X^1075 + X^1074 + X^1069 + X^1068 + X^1067 + X^1061 + X^1060 + X^1057 + X^1056 + X^1050 + X^1048 + X^1043 + X^1042 + X^1038 + X^1037 + X^1035 + X^1031 + X^1029 + X^1025 + X^1024 + X^1018 + X^1017 + X^1016 + X^1012 + X^1011 + X^1010 + X^1006 + X^1005 + X^1003 + X^999 + X^998 + X^993 + X^992 + X^991 + X^986 + X^984 + X^980 + X^979 + X^974 + X^972 + X^967 + X^960 + X^953 + X^949 + X^948 + X^937 + X^934 + X^930 + X^929 + X^927 + X^923 + X^918 + X^917 + X^911 + X^910 + X^908 + X^904 + X^903 + X^898 + X^897 + X^893 + X^892 + X^891 + X^884 + X^878 + X^877 + X^874 + X^872 + X^871 + X^867 + X^861 + X^858 + X^852 + X^851 + X^849 + X^848 + X^842 + X^841 + X^835 + X^832 + X^830 + X^829 + X^823 + X^822 + X^821 + X^817 + X^816 + X^815 + X^810 + X^804 + X^803 + X^802 + X^801 + X^798 + X^796 + X^795 + X^791 + X^784 + X^782 + X^777 + X^776 + X^775 + X^773 + X^772 + X^765 + X^758 + X^756 + X^754 + X^753 + X^751 + X^747 + X^746 + X^745 + X^741 + X^739 + X^734 + X^733 + X^732 + X^728 + X^727 + X^726 + X^725 + X^722 + X^720 + X^719 + X^715 + X^714 + X^709 + X^708 + X^707 + X^706 + X^701 + X^700 + X^699 + X^697 + X^696 + X^690 + X^688 + X^683 + X^682 + X^680 + X^678 + X^677 + X^675 + X^671 + X^669 + X^664 + X^658 + X^657 + X^656 + X^652 + X^651 + X^650 + X^645 + X^643 + X^638 + X^633 + X^632 + X^631 + X^626 + X^625 + X^624 + X^619 + X^614 + X^612 + X^607 + X^606 + X^605 + X^601 + X^600 + X^599 + X^593 + X^588 + X^586 + X^582 + X^580 + X^579 + X^577 + X^575 + X^574 + X^569 + X^567 + X^561 + X^560 + X^558 + X^557 + X^556 + X^551 + X^550 + X^549 + X^548 + X^543 + X^542 + X^538 + X^537 + X^535 + X^532 + X^531 + X^530 + X^529 + X^525 + X^524 + X^523 + X^518 + X^516 + X^512 + X^511 + X^510 + X^506 + X^504 + X^503 + X^501 + X^499 + X^492 + X^485 + X^484 + X^482 + X^481 + X^480 + X^475 + X^473 + X^466 + X^462 + X^461 + X^459 + X^456 + X^455 + X^454 + X^453 + X^447 + X^442 + X^441 + X^440 + X^436 + X^435 + X^434 + X^428 + X^427 + X^425 + X^422 + X^416 + X^415 + X^409 + X^408 + X^406 + X^405 + X^399 + X^396 + X^390 + X^386 + X^385 + X^383 + X^380 + X^379 + X^373 + X^366 + X^365 + X^364 + X^360 + X^359 + X^354 + X^353 + X^349 + X^347 + X^346 + X^340 + X^339 + X^334 + X^330 + X^328 + X^327 + X^323 + X^320 + X^309 + X^308 + X^304 + X^297 + X^290 + X^285 + X^283 + X^278 + X^277 + X^273 + X^271 + X^266 + X^265 + X^264 + X^259 + X^258 + X^254 + X^252 + X^251 + X^247 + X^246 + X^245 + X^241 + X^240 + X^239 + X^233 + X^232 + X^228 + X^226 + X^222 + X^220 + X^219 + X^215 + X^214 + X^209 + X^207 + X^201 + X^200 + X^197 + X^196 + X^190 + X^189 + X^188 + X^183 + X^182 + X^178 + X^177 + X^175 + X^171 + X^170 + X^165 + X^164 + X^163 + X^158 + X^157 + X^156 + X^152 + X^151 + X^146 + X^144 + X^139 + X^138 + X^133 + X^132 + X^131 + X^121 + X^120 + X^114 + X^113 + X^112 + X^107 + X^102 + X^95 + X^94 + X^89 + X^88 + X^87 + X^76 + X^70 + X^68 + X^63 + X^45 + X^44 + X^26 + X^19 + 1 12 18 20 29 79 X^1279 + X^1221 + X^1208 + X^1204 + X^1202 + X^1191 + X^1189 + X^1187 + X^1185 + X^1183 + X^1174 + X^1172 + X^1168 + X^1166 + X^1164 + X^1157 + X^1155 + X^1153 + X^1149 + X^1147 + X^1145 + X^1138 + X^1136 + X^1134 + X^1133 + X^1130 + X^1128 + X^1126 + X^1120 + X^1119 + X^1117 + X^1116 + X^1115 + X^1114 + X^1111 + X^1109 + X^1107 + X^1103 + X^1101 + X^1100 + X^1099 + X^1098 + X^1097 + X^1096 + X^1095 + X^1092 + X^1090 + X^1088 + X^1086 + X^1084 + X^1081 + X^1080 + X^1079 + X^1078 + X^1077 + X^1076 + X^1073 + X^1071 + X^1067 + X^1065 + X^1062 + X^1061 + X^1060 + X^1059 + X^1058 + X^1057 + X^1054 + X^1052 + X^1048 + X^1046 + X^1043 + X^1042 + X^1041 + X^1040 + X^1039 + X^1038 + X^1035 + X^1033 + X^1029 + X^1027 + X^1024 + X^1023 + X^1022 + X^1021 + X^1020 + X^1019 + X^1016 + X^1014 + X^1013 + X^1010 + X^1008 + X^1005 + X^1004 + X^1003 + X^1002 + X^1001 + X^997 + X^996 + X^995 + X^994 + X^991 + X^989 + X^986 + X^985 + X^984 + X^982 + X^979 + X^978 + X^977 + X^976 + X^975 + X^972 + X^970 + X^967 + X^965 + X^963 + X^962 + X^960 + X^959 + X^958 + X^957 + X^956 + X^953 + X^951 + X^948 + X^946 + X^944 + X^943 + X^941 + X^940 + X^939 + X^938 + X^937 + X^936 + X^934 + X^929 + X^927 + X^924 + X^922 + X^921 + X^920 + X^918 + X^917 + X^912 + X^910 + X^905 + X^903 + X^901 + X^899 + X^895 + X^893 + X^886 + X^885 + X^884 + X^882 + X^880 + X^878 + X^876 + X^867 + X^866 + X^865 + X^863 + X^861 + X^859 + X^857 + X^847 + X^846 + X^842 + X^840 + X^838 + X^831 + X^828 + X^823 + X^821 + X^819 + X^814 + X^812 + X^810 + X^809 + X^804 + X^802 + X^800 + X^797 + X^795 + X^793 + X^791 + X^790 + X^785 + X^783 + X^781 + X^778 + X^776 + X^774 + X^772 + X^771 + X^766 + X^764 + X^762 + X^759 + X^757 + X^755 + X^753 + X^752 + X^747 + X^745 + X^743 + X^741 + X^740 + X^738 + X^736 + X^734 + X^733 + X^726 + X^722 + X^721 + X^719 + X^717 + X^715 + X^714 + X^711 + X^703 + X^702 + X^700 + X^698 + X^696 + X^695 + X^694 + X^692 + X^690 + X^684 + X^683 + X^681 + X^679 + X^676 + X^675 + X^673 + X^671 + X^665 + X^664 + X^662 + X^660 + X^657 + X^656 + X^654 + X^653 + X^652 + X^646 + X^645 + X^643 + X^641 + X^640 + X^638 + X^637 + X^636 + X^635 + X^634 + X^633 + X^627 + X^626 + X^624 + X^623 + X^622 + X^621 + X^618 + X^617 + X^616 + X^615 + X^614 + X^613 + X^608 + X^607 + X^606 + X^605 + X^604 + X^603 + X^600 + X^599 + X^598 + X^597 + X^595 + X^594 + X^588 + X^587 + X^586 ** WARNING: Output too long, hence truncated. ************** MAGMA ***************** Host 3(NXDOMAIN) (82.100.96.47) Time: Thu Feb 12 00:53:01 2004 Input: k := GF(2); C := PrimitivePolynomial(k,9); C; G := 0; for j in [21..31] do for k in [19..20] do for m in [13..18] do for n in [8..12] do C := ((1 + X^11)^n)*((1 + X^13)^m)*((1 + X^17)^k)*((1 + X^19)^j) + X^1279; if IsPrimitive(C) then n; m; k; j; G := j+k+m+n; G; end if; end for; end for; end for; end for; Output: Magma V2.10-6 Thu Feb 12 2004 00:52:52 on modular [Seed = 1160647152] ------------------------------------- X^9 + X^4 + 1 10 17 19 25 71 12 18 20 29 79 8 17 19 31 75 11 17 19 31 78 Total time: 9.319 seconds, Total memory usage: 2.29MB ************** MAGMA ***************** Host 3(NXDOMAIN) (82.100.96.47) Time: Thu Feb 12 00:54:05 2004 Input: k := GF(2); C := PrimitivePolynomial(k,9); C; G := 0; for j in [21..31] do for k in [19..20] do for m in [13..18] do for n in [8..12] do C := ((1 + X^11)^n)*((1 + X^13)^m)*((1 + X^17)^k)*((1 + X^21)^j) + X^1279; if IsPrimitive(C) then n; m; k; j; G := j+k+m+n; G; end if; end for; end for; end for; end for; Output: Magma V2.10-6 Thu Feb 12 2004 00:53:48 on modular [Seed = 1362757052] ------------------------------------- X^9 + X^4 + 1 12 18 19 21 70 12 17 20 22 71 12 13 20 23 68 12 13 19 24 68 10 17 19 25 71 11 16 20 26 73 9 18 20 26 73 Total time: 16.779 seconds, Total memory usage: 2.25MB ************** MAGMA ***************** Host 3(NXDOMAIN) (82.100.96.47) Time: Thu Feb 12 00:55:32 2004 Input: k := GF(2); C := PrimitivePolynomial(k,9); C; G := 0; for j in [31..41] do for k in [19..20] do for m in [13..18] do for n in [8..12] do C := ((1 + X^11)^n)*((1 + X^13)^m)*((1 + X^17)^k)*((1 + X^21)^j) + X^1279; if IsPrimitive(C) then n; m; k; j; G := j+k+m+n; G; end if; end for; end for; end for; end for; Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Thu Feb 12 2004 00:55:09 on modular [Seed = 1862548051] ------------------------------------- X^9 + X^4 + 1 8 15 20 32 75 Errors: /home/mfd/gomagma: line 2: 16750 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host 3(NXDOMAIN) (82.100.96.47) Time: Thu Feb 12 00:57:24 2004 Input: k := GF(2); C := PrimitivePolynomial(k,9); C; G := 0; for j in [31..41] do for k in [23..30] do for m in [13..18] do for n in [8..12] do C := ((1 + X^9)^n)*((1 + X^11)^m)*((1 + X^13)^k)*((1 + X^19)^j) + X^1279; if IsPrimitive(C) then n; m; k; j; G := j+k+m+n; G; end if; end for; end for; end for; end for; Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Thu Feb 12 2004 00:57:01 on modular [Seed = 2179650605] ------------------------------------- X^9 + X^4 + 1 10 13 23 31 77 11 14 26 31 82 10 18 27 31 86 12 15 30 31 88 12 13 30 32 87 12 18 25 33 88 8 15 30 33 86 9 14 24 35 82 Errors: /home/mfd/gomagma: line 2: 16768 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host 3(NXDOMAIN) (82.100.96.47) Time: Thu Feb 12 00:58:37 2004 Input: k := GF(2); C := PrimitivePolynomial(k,9); C; G := 0; for j in [31..41] do for k in [23..30] do for m in [13..18] do for n in [8..12] do C := ((1 + X^9)^n)*((1 + X^11)^m)*((1 + X^13)^k)*((1 + X^19)^j) + X^1279; if IsPrimitive(C) then C; n; m; k; j; G := j+k+m+n; G; end if; end for; end for; end for; end for; Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Thu Feb 12 2004 00:58:14 on modular [Seed = 2549924448] ------------------------------------- X^9 + X^4 + 1 X^1279 + X^1121 + X^1110 + X^1108 + X^1103 + X^1102 + X^1097 + X^1095 + X^1092 + X^1091 + X^1090 + X^1089 + X^1083 + X^1082 + X^1079 + X^1078 + X^1076 + X^1073 + X^1072 + X^1070 + X^1069 + X^1064 + X^1063 + X^1060 + X^1058 + X^1057 + X^1056 + X^1054 + X^1053 + X^1051 + X^1050 + X^1049 + X^1048 + X^1046 + X^1044 + X^1043 + X^1041 + X^1039 + X^1037 + X^1036 + X^1034 + X^1029 + X^1027 + X^1024 + X^1023 + X^1022 + X^1019 + X^1017 + X^1012 + X^1008 + X^1007 + X^1005 + X^1003 + X^1002 + X^1000 + X^998 + X^997 + X^993 + X^991 + X^989 + X^987 + X^986 + X^983 + X^981 + X^979 + X^978 + X^976 + X^975 + X^973 + X^972 + X^970 + X^968 + X^967 + X^964 + X^963 + X^962 + X^960 + X^959 + X^957 + X^956 + X^955 + X^954 + X^953 + X^951 + X^949 + X^948 + X^942 + X^941 + X^940 + X^938 + X^937 + X^936 + X^935 + X^932 + X^931 + X^929 + X^927 + X^923 + X^922 + X^919 + X^918 + X^917 + X^914 + X^912 + X^911 + X^910 + X^906 + X^904 + X^902 + X^900 + X^895 + X^892 + X^891 + X^889 + X^888 + X^887 + X^886 + X^885 + X^884 + X^881 + X^880 + 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X^162 + X^161 + X^159 + X^158 + X^157 + X^154 + X^153 + X^151 + X^149 + X^148 + X^146 + X^145 + X^143 + X^142 + X^140 + X^138 + X^135 + X^134 + X^132 + X^130 + X^128 + X^124 + X^123 + X^121 + X^119 + X^118 + X^116 + X^114 + X^113 + X^109 + X^104 + X^102 + X^99 + X^98 + X^97 + X^94 + X^92 + X^87 + X^85 + X^84 + X^82 + X^80 + X^78 + X^77 + X^75 + X^73 + X^72 + X^71 + X^70 + X^68 + X^67 + X^65 + X^64 + X^63 + X^61 + X^58 + X^57 + X^52 + X^51 + X^49 + X^48 + X^45 + X^43 + X^42 + X^39 + X^38 + X^32 + X^31 + X^30 + X^29 + X^26 + X^24 + X^19 + X^18 + X^13 + X^11 + 1 10 13 23 31 77 X^1279 + X^1180 + X^1171 + X^1162 + X^1161 + X^1158 + X^1154 + X^1153 + X^1152 + X^1149 + X^1145 + X^1143 + X^1142 + X^1140 + X^1139 + X^1135 + X^1134 + X^1133 + X^1132 + X^1131 + X^1130 + X^1126 + X^1124 + X^1121 + X^1120 + X^1118 + X^1116 + X^1115 + X^1114 + X^1113 + X^1112 + X^1111 + X^1110 + X^1109 + X^1108 + X^1107 + X^1105 + X^1102 + X^1097 + X^1095 + X^1094 + X^1093 + X^1092 + X^1091 + X^1089 + X^1087 + 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X^545 + X^543 + X^542 + X^535 + X^534 + X^532 + X^531 + X^529 + X^527 + X^526 + X^516 + X^513 + X^512 + X^508 + X^507 + X^502 + X^501 + X^500 + X^497 + X^494 + X^491 + X^489 + X^483 + X^481 + X^480 + X^479 + X^475 + X^474 + X^473 + X^472 + X^471 + X^470 + X^469 + X^468 + X^466 + X^465 + X^464 + X^462 + X^461 + X^459 + X^458 + X^457 + X^456 + X^455 + X^454 + X^453 + X^447 + X^445 + X^444 + X^441 + X^440 + X^439 + X^434 + X^433 + X^430 + X^429 + X^427 + X^426 + X^425 + X^419 + X^416 + X^415 + X^413 + X^410 + X^405 + X^399 + X^398 + X^396 + X^392 + X^389 + X^385 + X^384 + X^383 + X^380 + X^379 + X^378 + X^376 + X^375 + X^373 + X^372 + X^369 + X^367 + X^366 + X^365 + X^364 + X^363 + X^362 + X^360 + X^359 + X^357 + X^344 + X^343 + X^339 + X^337 + X^334 + X^332 + X^331 + X^329 + X^328 + X^326 + X^324 + X^323 + X^319 + X^317 + X^316 + X^315 + X^313 + X^311 + X^305 + X^303 + X^301 + X^300 + X^298 + X^297 + X^295 + X^292 + X^290 + X^288 + X^287 + X^286 + X^285 + X^284 + X^280 + X^278 + X^276 + X^274 + X^272 + X^269 + X^267 + X^263 + X^261 + X^258 + X^255 + X^253 + X^252 + X^249 + X^248 + X^246 + X^243 + X^241 + X^239 + X^237 + X^235 + X^229 + X^228 + X^225 + X^221 + X^220 + X^219 + X^218 + X^215 + X^214 + X^213 + X^212 + X^210 + X^209 + X^208 + X^207 + X^205 + X^203 + X^202 + X^201 + X^197 + X^196 + X^195 + X^194 + X^193 + X^192 + X^189 + X^188 + X^182 + X^181 + X^174 + X^173 + X^168 + X^167 + X^164 + X^163 + X^161 + X^159 + X^156 + X^153 + X^149 + X^147 + X^146 + X^144 + X^139 + X^133 + X^132 + X^131 + X^130 + X^128 + X^127 + X^126 + X^124 + X^123 + X^118 + X^117 + X^116 + X^115 + X^114 + X^113 + X^110 + X^108 + X^105 + X^103 + X^102 + X^101 + X^99 + X^98 + X^97 + X^93 + X^91 + X^89 + X^88 + X^87 + X^86 + X^85 + X^83 + X^78 + X^75 + X^73 + X^72 + X^71 + X^70 + X^69 + X^68 + X^67 + X^66 + X^65 + X^64 + X^62 + X^60 + X^59 + X^56 + X^54 + X^50 + X^49 + X^48 + X^47 + X^46 + X^45 + X^41 + X^40 + X^38 + X^37 + X^35 + X^31 + X^28 + X^27 + X^26 + X^22 + X^19 + X^18 + X^9 + 1 11 14 26 31 82 X^1279 + X^1228 + X^1215 + X^1210 + X^1209 + X^1206 + X^1202 + X^1197 + X^1196 + X^1193 + X^1191 + X^1190 + X^1189 + X^1188 + X^1187 + X^1184 + X^1183 + X^1180 + X^1178 + X^1177 + X^1175 + X^1174 + X^1172 + X^1170 + X^1169 + ** WARNING: Output too long, hence truncated. Errors: /home/mfd/gomagma: line 2: 16790 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host 3(NXDOMAIN) (82.100.96.47) Time: Thu Feb 12 00:59:36 2004 Input: k := GF(2); C := PrimitivePolynomial(k,9); C; G := 0; for j in [31..41] do for k in [23..30] do for m in [13..18] do for n in [8..12] do C := ((1 + X^9)^n)*((1 + X^11)^m)*((1 + X^13)^k)*((1 + X^19)^j) + X^1279; if IsPrimitive(C) then n; m; k; j; G := j+k+m+n; G; end if; end for; end for; end for; end for; Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Thu Feb 12 2004 00:59:13 on modular [Seed = 2747856275] ------------------------------------- X^9 + X^4 + 1 10 13 23 31 77 11 14 26 31 82 10 18 27 31 86 12 15 30 31 88 12 13 30 32 87 12 18 25 33 88 8 15 30 33 86 9 14 24 35 82 Errors: /home/mfd/gomagma: line 2: 16802 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host 3(NXDOMAIN) (82.100.96.47) Time: Thu Feb 12 01:03:01 2004 Input: k := GF(2); C := PrimitivePolynomial(k,9); C; G := 0; C := ((1 + X^9)^12)*((1 + X^11)^18)*((1 + X^13)^25)*((1 + X^19)^33) + X^1279; for j in [31..41] do for k in [23..30] do for m in [13..18] do for n in [8..12] do C := ((1 + X^9)^n)*((1 + X^11)^m)*((1 + X^13)^k)*((1 + X^19)^j) + X^1279; if IsPrimitive(C) then n; m; k; j; G := j+k+m+n; G; end if; end for; end for; end for; end for; Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Thu Feb 12 2004 01:02:38 on modular [Seed = 3619455272] ------------------------------------- X^9 + X^4 + 1 10 13 23 31 77 11 14 26 31 82 10 18 27 31 86 12 15 30 31 88 12 13 30 32 87 12 18 25 33 88 8 15 30 33 86 9 14 24 35 82 Errors: /home/mfd/gomagma: line 2: 16854 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host 3(NXDOMAIN) (82.100.96.47) Time: Thu Feb 12 01:05:03 2004 Input: k := GF(2); C := PrimitivePolynomial(k,9); C; G := 0; C := ((1 + X^9)^12)*((1 + X^11)^18)*((1 + X^13)^25)*((1 + X^19)^33) + X^1279; C; for j in [31..41] do for k in [23..30] do for m in [13..18] do for n in [8..12] do C := ((1 + X^9)^n)*((1 + X^11)^m)*((1 + X^13)^k)*((1 + X^19)^j) + X^1279; if IsPrimitive(C) then n; m; k; j; G := j+k+m+n; G; end if; end for; end for; end for; end for; Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Thu Feb 12 2004 01:04:40 on modular [Seed = 3783964312] ------------------------------------- X^9 + X^4 + 1 X^1279 + X^1258 + X^1245 + X^1239 + X^1236 + X^1226 + X^1223 + X^1222 + X^1217 + X^1209 + X^1204 + X^1203 + X^1200 + X^1190 + X^1187 + X^1186 + X^1181 + X^1173 + X^1168 + X^1167 + X^1164 + X^1151 + X^1150 + X^1145 + X^1141 + X^1137 + X^1135 + X^1131 + X^1128 + X^1122 + X^1119 + X^1115 + X^1113 + X^1109 + X^1105 + X^1100 + X^1099 + X^1086 + X^1083 + X^1077 + X^1064 + X^1050 + X^1037 + X^1031 + X^1028 + X^1018 + X^1015 + X^1014 + X^1010 + X^1009 + X^1001 + X^997 + X^996 + X^995 + X^992 + X^991 + X^988 + X^982 + X^979 + X^978 + X^975 + X^974 + X^973 + X^969 + X^961 + X^960 + X^956 + X^955 + X^952 + X^946 + X^942 + X^939 + X^927 + X^924 + X^920 + X^914 + X^911 + X^910 + X^906 + X^905 + X^897 + X^893 + X^892 + X^891 + X^888 + X^887 + X^884 + X^878 + X^875 + X^874 + X^871 + X^870 + X^869 + X^865 + X^857 + X^856 + X^852 + X^851 + X^848 + X^838 + X^835 + X^829 + X^816 + X^802 + X^789 + X^783 + X^780 + X^767 + X^766 + X^761 + X^757 + X^753 + X^751 + X^747 + X^744 + X^738 + X^735 + X^731 + X^729 + X^725 + X^721 + X^716 + X^715 + X^702 + X^699 + X^698 + X^693 + X^685 + X^680 + X^679 + X^676 + X^666 + X^663 + X^662 + X^657 + X^650 + X^649 + X^644 + X^643 + X^640 + X^637 + X^631 + X^630 + X^628 + X^627 + X^621 + X^618 + X^615 + X^614 + X^609 + X^608 + X^601 + X^596 + X^595 + X^592 + X^582 + X^579 + X^578 + X^573 + X^565 + X^560 + X^559 + X^556 + X^543 + X^542 + X^537 + X^533 + X^529 + X^527 + X^523 + X^520 + X^514 + X^511 + X^507 + X^505 + X^501 + X^497 + X^492 + X^491 + X^478 + X^475 + X^469 + X^456 + X^442 + X^429 + X^423 + X^420 + X^410 + X^407 + X^406 + X^402 + X^401 + X^393 + X^389 + X^388 + X^387 + X^384 + X^383 + X^380 + X^374 + X^371 + X^370 + X^367 + X^366 + X^365 + X^361 + X^353 + X^352 + X^348 + X^347 + X^344 + X^338 + X^334 + X^331 + X^319 + X^316 + X^312 + X^306 + X^303 + X^302 + X^298 + X^297 + X^289 + X^285 + X^284 + X^283 + X^280 + X^279 + X^276 + X^270 + X^267 + X^266 + X^263 + X^262 + X^261 + X^257 + X^249 + X^248 + X^244 + X^243 + X^240 + X^230 + X^227 + X^221 + X^208 + X^194 + X^181 + X^175 + X^172 + X^159 + X^158 + X^153 + X^149 + X^145 + X^143 + X^139 + X^136 + X^130 + X^127 + X^123 + X^121 + X^117 + X^113 + X^108 + X^107 + X^94 + X^91 + X^90 + X^85 + X^77 + X^72 + X^71 + X^68 + X^58 + X^55 + X^54 + X^49 + X^41 + X^36 + X^35 + X^32 + X^22 + X^19 + X^13 + 1 10 13 23 31 77 11 14 26 31 82 10 18 27 31 86 12 15 30 31 88 12 13 30 32 87 12 18 25 33 88 8 15 30 33 86 9 14 24 35 82 Errors: /home/mfd/gomagma: line 2: 16864 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host 3(NXDOMAIN) (82.100.96.47) Time: Thu Feb 12 01:08:08 2004 Input: k := GF(2); C := PrimitivePolynomial(k,9); C; G := 0; C := ((1 + X^9)^12)*((1 + X^11)^18)*((1 + X^13)^25)*((1 + X^19)^33) + X^1279; if IsPrimitive(C) then C; end if; Output: Magma V2.10-6 Thu Feb 12 2004 01:08:04 on modular [Seed = 4001740459] ------------------------------------- X^9 + X^4 + 1 X^1279 + X^1258 + X^1245 + X^1239 + X^1236 + X^1226 + X^1223 + X^1222 + X^1217 + X^1209 + X^1204 + X^1203 + X^1200 + X^1190 + X^1187 + X^1186 + X^1181 + X^1173 + X^1168 + X^1167 + X^1164 + X^1151 + X^1150 + X^1145 + X^1141 + X^1137 + X^1135 + X^1131 + X^1128 + X^1122 + X^1119 + X^1115 + X^1113 + X^1109 + X^1105 + X^1100 + X^1099 + X^1086 + X^1083 + X^1077 + X^1064 + X^1050 + X^1037 + X^1031 + X^1028 + X^1018 + X^1015 + X^1014 + X^1010 + X^1009 + X^1001 + X^997 + X^996 + X^995 + X^992 + X^991 + X^988 + X^982 + X^979 + X^978 + X^975 + X^974 + X^973 + X^969 + X^961 + X^960 + X^956 + X^955 + X^952 + X^946 + X^942 + X^939 + X^927 + X^924 + X^920 + X^914 + X^911 + X^910 + X^906 + X^905 + X^897 + X^893 + X^892 + X^891 + X^888 + X^887 + X^884 + X^878 + X^875 + X^874 + X^871 + X^870 + X^869 + X^865 + X^857 + X^856 + X^852 + X^851 + X^848 + X^838 + X^835 + X^829 + X^816 + X^802 + X^789 + X^783 + X^780 + X^767 + X^766 + X^761 + X^757 + X^753 + X^751 + X^747 + X^744 + X^738 + X^735 + X^731 + X^729 + X^725 + X^721 + X^716 + X^715 + X^702 + X^699 + X^698 + X^693 + X^685 + X^680 + X^679 + X^676 + X^666 + X^663 + X^662 + X^657 + X^650 + X^649 + X^644 + X^643 + X^640 + X^637 + X^631 + X^630 + X^628 + X^627 + X^621 + X^618 + X^615 + X^614 + X^609 + X^608 + X^601 + X^596 + X^595 + X^592 + X^582 + X^579 + X^578 + X^573 + X^565 + X^560 + X^559 + X^556 + X^543 + X^542 + X^537 + X^533 + X^529 + X^527 + X^523 + X^520 + X^514 + X^511 + X^507 + X^505 + X^501 + X^497 + X^492 + X^491 + X^478 + X^475 + X^469 + X^456 + X^442 + X^429 + X^423 + X^420 + X^410 + X^407 + X^406 + X^402 + X^401 + X^393 + X^389 + X^388 + X^387 + X^384 + X^383 + X^380 + X^374 + X^371 + X^370 + X^367 + X^366 + X^365 + X^361 + X^353 + X^352 + X^348 + X^347 + X^344 + X^338 + X^334 + X^331 + X^319 + X^316 + X^312 + X^306 + X^303 + X^302 + X^298 + X^297 + X^289 + X^285 + X^284 + X^283 + X^280 + X^279 + X^276 + X^270 + X^267 + X^266 + X^263 + X^262 + X^261 + X^257 + X^249 + X^248 + X^244 + X^243 + X^240 + X^230 + X^227 + X^221 + X^208 + X^194 + X^181 + X^175 + X^172 + X^159 + X^158 + X^153 + X^149 + X^145 + X^143 + X^139 + X^136 + X^130 + X^127 + X^123 + X^121 + X^117 + X^113 + X^108 + X^107 + X^94 + X^91 + X^90 + X^85 + X^77 + X^72 + X^71 + X^68 + X^58 + X^55 + X^54 + X^49 + X^41 + X^36 + X^35 + X^32 + X^22 + X^19 + X^13 + 1 Total time: 4.109 seconds, Total memory usage: 2.15MB ************** MAGMA ***************** Host 3(NXDOMAIN) (82.100.96.47) Time: Thu Feb 12 01:09:25 2004 Input: k := GF(2); C := PrimitivePolynomial(k,9); C; C := ((1 + X^9)^12)*((1 + X^11)^15)*((1 + X^13)^30)*((1 + X^19)^31) + X^1279; if IsPrimitive(C) then C; end if; Output: Magma V2.10-6 Thu Feb 12 2004 01:09:20 on modular [Seed = 4187136360] ------------------------------------- X^9 + X^4 + 1 X^1279 + X^1252 + X^1241 + X^1233 + X^1230 + X^1226 + X^1222 + X^1219 + X^1216 + X^1215 + X^1214 + X^1211 + X^1208 + X^1207 + X^1205 + X^1204 + X^1203 + X^1196 + X^1195 + X^1194 + X^1193 + X^1192 + X^1190 + X^1188 + X^1185 + X^1184 + X^1183 + X^1182 + X^1180 + X^1179 + X^1178 + X^1177 + X^1176 + X^1173 + X^1172 + X^1168 + X^1167 + X^1166 + X^1165 + X^1164 + X^1159 + X^1156 + X^1153 + X^1152 + X^1150 + X^1144 + X^1143 + X^1141 + X^1140 + X^1139 + X^1136 + X^1135 + X^1132 + X^1131 + X^1130 + X^1126 + X^1123 + X^1122 + X^1120 + X^1119 + X^1118 + X^1117 + X^1116 + X^1115 + X^1114 + X^1112 + X^1111 + X^1110 + X^1108 + X^1101 + X^1100 + X^1098 + X^1096 + X^1095 + X^1092 + X^1091 + X^1089 + X^1088 + X^1081 + X^1079 + X^1076 + X^1073 + X^1072 + X^1071 + X^1069 + X^1062 + X^1060 + X^1059 + X^1057 + X^1054 + X^1053 + X^1052 + X^1050 + X^1048 + X^1044 + X^1043 + X^1041 + X^1040 + X^1038 + X^1037 + X^1035 + X^1031 + X^1029 + X^1026 + X^1025 + X^1024 + X^1023 + X^1021 + X^1019 + X^1016 + X^1015 + X^1011 + X^1010 + X^1008 + X^1006 + X^1005 + X^1004 + X^1002 + X^1001 + X^991 + X^990 + X^987 + X^983 + X^981 + X^979 + X^975 + X^974 + X^972 + X^970 + X^968 + X^966 + X^963 + X^962 + X^959 + X^951 + X^948 + X^947 + X^945 + X^943 + X^938 + X^937 + X^934 + X^933 + X^932 + X^930 + X^928 + X^927 + X^926 + X^924 + X^923 + X^922 + X^915 + X^913 + X^912 + X^909 + X^905 + X^901 + X^897 + X^894 + X^892 + X^890 + X^888 + X^885 + X^881 + X^877 + X^873 + X^870 + X^869 + X^867 + X^860 + X^859 + X^858 + X^856 + X^855 + X^854 + X^852 + X^850 + X^849 + X^848 + X^845 + X^844 + X^839 + X^837 + X^836 + X^835 + X^834 + X^831 + X^825 + X^823 + X^820 + X^819 + X^817 + X^816 + X^812 + X^808 + X^807 + X^806 + X^801 + X^800 + X^798 + X^789 + X^788 + X^787 + X^781 + X^779 + X^771 + X^769 + X^768 + X^764 + X^762 + X^760 + X^759 + X^753 + X^752 + X^750 + X^749 + X^748 + X^745 + X^744 + X^743 + X^742 + X^741 + X^740 + X^738 + X^737 + X^730 + X^729 + X^728 + X^727 + X^725 + X^724 + X^721 + X^720 + X^719 + X^717 + X^716 + X^715 + X^710 + X^707 + X^704 + X^701 + X^695 + X^694 + X^693 + X^692 + X^689 + X^688 + X^687 + X^684 + X^683 + X^682 + X^681 + X^680 + X^678 + X^676 + X^675 + X^672 + X^668 + X^667 + X^666 + X^665 + X^664 + X^658 + X^657 + X^656 + X^655 + X^653 + X^652 + X^651 + X^649 + X^646 + X^645 + X^641 + X^639 + X^638 + X^634 + X^633 + X^632 + X^630 + X^627 + X^625 + X^622 + X^620 + X^619 + X^618 + X^614 + X^613 + X^611 + X^607 + X^606 + X^603 + X^601 + X^600 + X^599 + X^597 + X^596 + X^595 + X^594 + X^588 + X^587 + X^586 + X^585 + X^584 + X^580 + X^577 + X^576 + X^574 + X^572 + X^571 + X^570 + X^569 + X^568 + X^565 + X^564 + X^563 + X^560 + X^559 + X^558 + X^557 + X^551 + X^548 + X^545 + X^542 + X^537 + X^536 + X^535 + X^533 + X^532 + X^531 + X^528 + X^527 + X^525 + X^524 + X^523 + X^522 + X^515 + X^514 + X^512 + X^511 + X^510 + X^509 + X^508 + X^507 + X^504 + X^503 + X^502 + X^500 + X^499 + X^493 + X^492 + X^490 + X^488 + X^484 + X^483 + X^481 + X^473 + X^471 + X^465 + X^464 + X^463 + X^454 + X^452 + X^451 + X^446 + X^445 + X^444 + X^440 + X^436 + X^435 + X^433 + X^432 + X^429 + X^427 + X^421 + X^418 + X^417 + X^416 + X^415 + X^413 + X^408 + X^407 + X^404 + X^403 + X^402 + X^400 + X^398 + X^397 + X^396 + X^394 + X^393 + X^392 + X^385 + X^383 + X^382 + X^379 + X^375 + X^371 + X^367 + X^364 + X^362 + X^360 + X^358 + X^355 + X^351 + X^347 + X^343 + X^340 + X^339 + X^337 + X^330 + X^329 + X^328 + X^326 + X^325 + X^324 + X^322 + X^320 + X^319 + X^318 + X^315 + X^314 + X^309 + X^307 + X^305 + X^304 + X^301 + X^293 + X^290 + X^289 + X^286 + X^284 + X^282 + X^280 + X^278 + X^277 + X^273 + X^271 + X^269 + X^265 + X^262 + X^261 + X^251 + X^250 + X^248 + X^247 + X^246 + X^244 + X^242 + X^241 + X^237 + X^236 + X^233 + X^231 + X^229 + X^228 + X^227 + X^226 + X^223 + X^221 + X^217 + X^215 + X^214 + X^212 + X^211 + X^209 + X^208 + X^204 + X^202 + X^200 + X^199 + X^198 + X^195 + X^193 + X^192 + X^190 + X^183 + X^181 + X^180 + X^179 + X^176 + X^173 + X^171 + X^164 + X^163 + X^161 + X^160 + X^157 + X^156 + X^154 + X^152 + X^151 + X^144 + X^142 + X^141 + X^140 + X^138 + X^137 + X^136 + X^135 + X^134 + X^133 + X^132 + X^130 + X^129 + X^126 + X^122 + X^121 + X^120 + X^117 + X^116 + X^113 + X^112 + X^111 + X^109 + X^108 + X^102 + X^100 + X^99 + X^96 + X^93 + X^88 + X^87 + X^86 + X^85 + X^84 + X^80 + X^79 + X^76 + X^75 + X^74 + X^73 + X^72 + X^70 + X^69 + X^68 + X^67 + X^64 + X^62 + X^60 + X^59 + X^58 + X^57 + X^56 + X^49 + X^48 + X^47 + X^45 + X^44 + X^41 + X^38 + X^37 + X^36 + X^33 + X^30 + X^26 + X^22 + X^19 + X^11 + 1 Total time: 4.109 seconds, Total memory usage: 2.26MB ************** MAGMA ***************** Host 3(NXDOMAIN) (82.100.96.47) Time: Thu Feb 12 01:11:10 2004 Input: k := GF(2); C := PrimitivePolynomial(k,9); C; C := ((1 + X^9)^12)*((1 + X^11)^13)*((1 + X^13)^30)*((1 + X^19)^32) + X^1279; if IsPrimitive(C) then C; end if; Output: Magma V2.10-6 Thu Feb 12 2004 01:11:06 on modular [Seed = 241522422] ------------------------------------- X^9 + X^4 + 1 X^1279 + X^1249 + X^1238 + X^1223 + X^1213 + X^1212 + X^1205 + X^1202 + X^1197 + X^1194 + X^1187 + X^1186 + X^1179 + X^1177 + X^1176 + X^1171 + X^1169 + X^1168 + X^1166 + X^1160 + X^1158 + X^1153 + X^1151 + X^1145 + X^1143 + X^1142 + X^1141 + X^1140 + X^1134 + X^1133 + X^1132 + X^1130 + X^1127 + X^1122 + X^1119 + X^1116 + X^1115 + X^1108 + X^1107 + X^1104 + X^1101 + X^1097 + X^1096 + X^1093 + X^1090 + X^1086 + X^1082 + X^1075 + X^1071 + X^1067 + X^1064 + X^1060 + X^1056 + X^1053 + X^1049 + X^1042 + X^1041 + X^1038 + X^1030 + X^1027 + X^1023 + X^1016 + X^1015 + X^1012 + X^1009 + X^1004 + X^1001 + X^998 + X^997 + X^990 + X^989 + X^986 + X^983 + X^978 + X^975 + X^972 + X^971 + X^964 + X^963 + X^960 + X^957 + X^952 + X^949 + X^946 + X^945 + X^938 + X^937 + X^934 + X^931 + X^926 + X^923 + X^920 + X^919 + X^912 + X^911 + X^908 + X^905 + X^900 + X^897 + X^894 + X^893 + X^886 + X^885 + X^882 + X^879 + X^874 + X^871 + X^868 + X^867 + X^860 + X^859 + X^856 + X^853 + X^848 + X^845 + X^842 + X^841 + X^834 + X^830 + X^827 + X^819 + X^816 + X^815 + X^808 + X^804 + X^801 + X^797 + X^793 + X^790 + X^786 + X^782 + X^775 + X^771 + X^767 + X^764 + X^761 + X^760 + X^756 + X^753 + X^750 + X^749 + X^742 + X^741 + X^738 + X^735 + X^730 + X^727 + X^725 + X^724 + X^723 + X^717 + X^716 + X^715 + X^714 + X^712 + X^706 + X^704 + X^699 + X^697 + X^691 + X^689 + X^688 + X^686 + X^681 + X^680 + X^678 + X^671 + X^670 + X^663 + X^660 + X^655 + X^652 + X^645 + X^644 + X^641 + X^634 + X^630 + X^619 + X^615 + X^608 + X^605 + X^604 + X^597 + X^594 + X^589 + X^586 + X^579 + X^578 + X^571 + X^569 + X^568 + X^563 + X^561 + X^560 + X^558 + X^552 + X^550 + X^545 + X^543 + X^537 + X^535 + X^534 + X^533 + X^532 + X^526 + X^525 + X^524 + X^522 + X^519 + X^514 + X^511 + X^508 + X^507 + X^500 + X^499 + X^496 + X^493 + X^489 + X^488 + X^485 + X^482 + X^478 + X^474 + X^467 + X^463 + X^459 + X^456 + X^452 + X^448 + X^445 + X^441 + X^434 + X^433 + X^430 + X^422 + X^419 + X^415 + X^408 + X^407 + X^404 + X^401 + X^396 + X^393 + X^390 + X^389 + X^382 + X^381 + X^378 + X^375 + X^370 + X^367 + X^364 + X^363 + X^356 + X^355 + X^352 + X^349 + X^344 + X^341 + X^338 + X^337 + X^330 + X^329 + X^326 + X^323 + X^318 + X^315 + X^312 + X^311 + X^304 + X^303 + X^300 + X^297 + X^292 + X^289 + X^286 + X^285 + X^278 + X^277 + X^274 + X^271 + X^266 + X^263 + X^260 + X^259 + X^252 + X^251 + X^248 + X^245 + X^240 + X^237 + X^234 + X^233 + X^226 + X^222 + X^219 + X^211 + X^208 + X^207 + X^200 + X^196 + X^193 + X^189 + X^185 + X^182 + X^178 + X^174 + X^167 + X^163 + X^159 + X^156 + X^153 + X^152 + X^148 + X^145 + X^142 + X^141 + X^134 + X^133 + X^130 + X^127 + X^122 + X^119 + X^117 + X^116 + X^115 + X^109 + X^108 + X^107 + X^106 + X^104 + X^98 + X^96 + X^91 + X^89 + X^83 + X^81 + X^80 + X^78 + X^73 + X^72 + X^70 + X^63 + X^62 + X^55 + X^52 + X^47 + X^44 + X^37 + X^36 + X^26 + X^11 + 1 Total time: 4.269 seconds, Total memory usage: 2.23MB ************** MAGMA ***************** Host host81-152-19-158.range81-152.btcentralplus.com. (81.152.19.158) Time: Thu Feb 12 05:21:48 2004 Input: 219x + 285y = 3 Output: Magma V2.10-6 Thu Feb 12 2004 05:21:44 on modular [Seed = 1327783152] ------------------------------------- >> 219x + 285y = 3; ^ User error: bad syntax Total time: 3.059 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host host81-152-19-158.range81-152.btcentralplus.com. (81.152.19.158) Time: Thu Feb 12 05:22:31 2004 Input: (219*x)+ (285*y) = 3 Output: Magma V2.10-6 Thu Feb 12 2004 05:22:28 on modular [Seed = 1446856117] ------------------------------------- >> (219*x)+ (285*y) = 3; ^ User error: Identifier 'x' has not been declared or assigned Total time: 2.939 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 84e5e4e4.math.leidenuniv.nl. (132.229.228.228) Time: Thu Feb 12 10:52:29 2004 Input: ?better Output: Magma V2.10-6 Thu Feb 12 2004 10:52:26 on modular [Seed = 4287897295] ------------------------------------- No references for word "better" Total time: 2.989 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 84e5e4e4.math.leidenuniv.nl. (132.229.228.228) Time: Thu Feb 12 10:52:43 2004 Input: ?betterpolynomial Output: Magma V2.10-6 Thu Feb 12 2004 10:52:40 on modular [Seed = 4104066486] ------------------------------------- No references for word "betterpolynomial" Total time: 2.929 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 84e5e4e4.math.leidenuniv.nl. (132.229.228.228) Time: Thu Feb 12 10:52:56 2004 Input: ?BetterPolynomial Output: Magma V2.10-6 Thu Feb 12 2004 10:52:53 on modular [Seed = 208137554] ------------------------------------- No references for word "BetterPolynomial" Total time: 2.939 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host heidelberg.bund.de. (194.95.179.177) Time: Thu Feb 12 11:07:47 2004 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: Magma V2.10-6 Thu Feb 12 2004 11:07:44 on modular [Seed = 1294379414] ------------------------------------- Replace this by some code, then click [PARI] or [MAGMA]! Total time: 2.989 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host cache1.nottingham.ac.uk. (128.243.220.21) Time: Thu Feb 12 11:35:21 2004 Input: F:=FiniteField(8); Output: Magma V2.10-6 Thu Feb 12 2004 11:35:17 on modular [Seed = 2414109889] ------------------------------------- Total time: 3.079 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host cache1.nottingham.ac.uk. (128.243.220.21) Time: Thu Feb 12 11:35:30 2004 Input: F:=FiniteField(8); F; Output: Magma V2.10-6 Thu Feb 12 2004 11:35:27 on modular [Seed = 2246995649] ------------------------------------- Finite field of size 2^3 Total time: 3.029 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host cache1.nottingham.ac.uk. (128.243.220.21) Time: Thu Feb 12 11:36:50 2004 Input: F:=FiniteField(8); F; E:=EllipticCurve([F|0,0,0,F.1^3,1]); E; Output: Magma V2.10-6 Thu Feb 12 2004 11:36:47 on modular [Seed = 2633463560] ------------------------------------- Finite field of size 2^3 >> E:=EllipticCurve([F|0,0,0,F.1^3,1]); ^ Runtime error in 'EllipticCurve': Curve is singular >> E; ^ User error: Identifier 'E' has not been declared or assigned Total time: 3.029 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host cache1.nottingham.ac.uk. (128.243.220.21) Time: Thu Feb 12 11:37:06 2004 Input: F:=FiniteField(8); F; E:=EllipticCurve([F|0,0,1,F.1^3,1]); E; Output: Magma V2.10-6 Thu Feb 12 2004 11:37:03 on modular [Seed = 2881503247] ------------------------------------- Finite field of size 2^3 Elliptic Curve defined by y^2 + y = x^3 + F.1^3*x + 1 over GF(2^3) Total time: 3.029 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host cache1.nottingham.ac.uk. (128.243.220.21) Time: Thu Feb 12 11:37:25 2004 Input: F:=FiniteField(8); F; E:=EllipticCurve([F|0,0,1,F.1^3,1]); E; Points(E); Output: Magma V2.10-6 Thu Feb 12 2004 11:37:21 on modular [Seed = 2714389099] ------------------------------------- Finite field of size 2^3 Elliptic Curve defined by y^2 + y = x^3 + F.1^3*x + 1 over GF(2^3) {@ (0 : 1 : 0), (F.1 : F.1^4 : 1), (F.1 : F.1^5 : 1), (F.1^3 : 0 : 1), (F.1^3 : 1 : 1) @} Total time: 2.999 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host cache1.nottingham.ac.uk. (128.243.220.21) Time: Thu Feb 12 11:38:08 2004 Input: F:=FiniteField(8); F; E:=EllipticCurve([F|0,0,1,F.1^3,1]); E; Points(E); V:=ProjectiveLine(F); Output: Magma V2.10-6 Thu Feb 12 2004 11:38:05 on modular [Seed = 3218363481] ------------------------------------- Finite field of size 2^3 Elliptic Curve defined by y^2 + y = x^3 + F.1^3*x + 1 over GF(2^3) {@ (0 : 1 : 0), (F.1 : F.1^4 : 1), (F.1 : F.1^5 : 1), (F.1^3 : 0 : 1), (F.1^3 : 1 : 1) @} >> V:=ProjectiveLine(F); ^ User error: Identifier 'ProjectiveLine' has not been declared or assigned Total time: 2.999 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host cache1.nottingham.ac.uk. (128.243.220.21) Time: Thu Feb 12 11:38:37 2004 Input: F:=FiniteField(8); F; E:=EllipticCurve([F|0,0,1,F.1^3,1]); E; Points(E); V:=ProjectiveSpace(F,1); Output: Magma V2.10-6 Thu Feb 12 2004 11:38:33 on modular [Seed = 3067959988] ------------------------------------- Finite field of size 2^3 Elliptic Curve defined by y^2 + y = x^3 + F.1^3*x + 1 over GF(2^3) {@ (0 : 1 : 0), (F.1 : F.1^4 : 1), (F.1 : F.1^5 : 1), (F.1^3 : 0 : 1), (F.1^3 : 1 : 1) @} Total time: 3.009 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host cache1.nottingham.ac.uk. (128.243.220.21) Time: Thu Feb 12 11:38:45 2004 Input: F:=FiniteField(8); F; E:=EllipticCurve([F|0,0,1,F.1^3,1]); E; Points(E); V:=ProjectiveSpace(F,1); V; Output: Magma V2.10-6 Thu Feb 12 2004 11:38:42 on modular [Seed = 3450216916] ------------------------------------- Finite field of size 2^3 Elliptic Curve defined by y^2 + y = x^3 + F.1^3*x + 1 over GF(2^3) {@ (0 : 1 : 0), (F.1 : F.1^4 : 1), (F.1 : F.1^5 : 1), (F.1^3 : 0 : 1), (F.1^3 : 1 : 1) @} Projective Space of dimension 1 Variables : $.1, $.2 Total time: 2.929 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host cache1.nottingham.ac.uk. (128.243.220.21) Time: Thu Feb 12 11:39:06 2004 Input: F:=FiniteField(8); F; E:=EllipticCurve([F|0,0,1,F.1^3,1]); E; Points(E); V:=ProjectiveSpace(F,1); V; Points(V); Output: Magma V2.10-6 Thu Feb 12 2004 11:39:03 on modular [Seed = 3299813608] ------------------------------------- Finite field of size 2^3 Elliptic Curve defined by y^2 + y = x^3 + F.1^3*x + 1 over GF(2^3) {@ (0 : 1 : 0), (F.1 : F.1^4 : 1), (F.1 : F.1^5 : 1), (F.1^3 : 0 : 1), (F.1^3 : 1 : 1) @} Projective Space of dimension 1 Variables : $.1, $.2 {@ (1 : 1), (F.1 : 1), (F.1^2 : 1), (F.1^3 : 1), (F.1^4 : 1), (F.1^5 : 1), (F.1^6 : 1), (0 : 1), (1 : 0) @} Total time: 2.979 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host cache1.nottingham.ac.uk. (128.243.220.21) Time: Thu Feb 12 11:42:42 2004 Input: F:=FiniteField(8); F; E:=EllipticCurve([F|0,0,1,F.1^3,1]); E; Points(E); V:=ProjectiveSpace(F,1); V; Points(V); Output: Magma V2.10-6 Thu Feb 12 2004 11:42:39 on modular [Seed = 3868002834] ------------------------------------- Finite field of size 2^3 Elliptic Curve defined by y^2 + y = x^3 + F.1^3*x + 1 over GF(2^3) {@ (0 : 1 : 0), (F.1 : F.1^4 : 1), (F.1 : F.1^5 : 1), (F.1^3 : 0 : 1), (F.1^3 : 1 : 1) @} Projective Space of dimension 1 Variables : $.1, $.2 {@ (1 : 1), (F.1 : 1), (F.1^2 : 1), (F.1^3 : 1), (F.1^4 : 1), (F.1^5 : 1), (F.1^6 : 1), (0 : 1), (1 : 0) @} Total time: 3.059 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host resnet-248-150.resnet.umbc.edu. (130.85.248.150) Time: Thu Feb 12 23:31:52 2004 Input: // Magma Example 1 // --------------- // This is supposed to be a tutorial on some of the basic stuff Magma can do. I'm sure that Magma has functions that do exactly what our code is going to do, but // a) I'm feeling lazy right now; // b) It can be (read is) a pain in the ass to look stuff up in the Magma introduction and handbook just because they are so extensive; and // c) Starting from scratch will help us get acquainted with tools that we'll have to use on a fairly regular basis, anyway. // Well, first things first, you can comment out a whole line after a certain position using // and you can also comment out blocks of code in Magma by putting them between /* and */. Just like C++. /* Okay, with that out of the way, you might find yourself thinking, "What the hell is the example going to be?" Well, I figure since this is the first example, we should do something simple, like finding all the irreducible representations of an arbitrary finite group G. So, on we go... */ // Just kidding! :) /* What we're REALLY going to do is write a function that takes a matrix A with entries in GF(2) and parameters v, k, and l which returns 1 if A is an incidence matrix for a nontrivial design with parameters (v,k,l). */ /* So, how do we go about doing this. First, we have to pick a good name for our function. isIncidenceMatrix sounds nice and impressive, doesn't it? Let's use that. In general, it is considered good form (I guess) to begin user-defined function names in Magma with a lower-case letter because the system functions all begin with an upper-case letter. */ // Time to define the function... // BEGIN FUNCTION isIncidenceMatrix isIncidenceMatrix := function(A,v,k,l) // We have a lemma which says that A is an incidence matrix for a nontrivial 2-(v,k,l) design (Assmus and Key notation) if and only if it satisfies the following conditions: // 1) A*Transpose(j_v) = kj_b; // 2) j_b*A = r*j_v; // 3) Transpose(A)*A = nI_v + lJ_v. /* First things first, we need to worry about errors. And what's everybody's favourite error? You got it -- dividing by 0. r is defined to be ((v-1)/(k-1))l and we don't want k to be 1, otherwise we'll be dividing by 0. I'm not going to worry about checking that v, k, and l are natural numbers. We're not stupid enough to give the isIncidenceMatrix function any negative/nonintegral arguments and we're going to make damn sure that our program doesn't do it either. Anyway, let's write the error case. */ if k le 1 then // This is how if statements work if we're only checking for one condition. return false; // If there are more conditions, we have to parenthesize everything so that the 'if' receives only one true or false end if; // Let's give Magma some definitions: r := IntegerRing()!(((v-1)/(k-1))*l); // I'll explain the whole 'IntegerRing()!' thing in a few lines. b := IntegerRing()!((v/k)*r); // Suppose A is an m x n matrix. We want to have m = b and n = v, otherwise A cannot be an incidence matrix for a design with the given parameters. // Magma has functions NumberOfRows() and NumberOfColumns() that will do the job for us. // Alternatively, you could use the functions Nrows() and Ncolumns(). if ((b ne NumberOfRows(A)) or (v ne NumberOfColumns(A))) then // See what I mean about the parentheses? return false; end if; // Note that in the lemma, we are doing the arithmetic over the integers. However, our matrix A is a matrix over GF(2). We want to force A to be a matrix over Z. // There are a lot of ways in which we can do it. We're going to be hardcore and write a couple while loops. // A more elegant solution would be to do the following: // M := MatrixRing(IntegerRing(),b,v); // A := M!A; // The reason that we're not using the above solution, though, is that doing it the crude way give us an opportunity to learn about while loops. Yay! // It involves creating a matris space over the real numbers and create a matrix in that space that has the same entries as A. Unfortunately, Magma doesn't seem to realize that the // integers live in R, though, so you can't coerce the matrix A to be a matrix over R like we did with Z above. Anyway, enough talk, let's do something. C := KMatrixSpace(RealField(), b, v)!0; // Magma uses an exclamation mark to denote what the universe of an object is. // For example, the 0 in R and the 0 in GF(2) are different things. Trying to check if they are //// equal using the command "RealField()!0 eq GF(2)!0;" will give you an error because they live in different aggregate structures. // The reason I forced r and b to be integers above is that KMatrixSpace NEEDS arguments in the form Field, Integer, Integer (these are not the actual names of the aggregate structures, // but you get the idea). Otherwise, Bad things happen (yes, capital B). // Now we will to go through B, entry by entry, and set it equal to A. We'll need some counters to do this. Let i count the rows and j count the columns. i := 1; // Unlike C and C++, Magma begins indexing arrays, matrices, sequences, etc. with a 1, not a 0. Keep this in mind, otherwise Magma will hate you. j := 1; while i le b do while j le v do if A[i][j] eq GF(2)!1 then C[i][j] := 1; else C[i][j] := 0; end if; j := j + 1; end while; j := 1; i := i + 1; end while; // Now we want to give j_v and j_b some homes. They are really vectors, but in my experience, it's a whole lot easier to just let them live in KMatrixSpace's. V := KMatrixSpace(RealField(), v, 1); B := KMatrixSpace(RealField(), 1, b); // Let's see if A fulfils the conditions in the lemma. Although Magma could probably just figure out conditiong 3) for us, we're going to write some more while loops, just for shits and giggles. :) jv := V!0; jb := B!0; // We want to set jv and jb as the all 1 vectors. Let's just go all out brute force and use some while loops. i := 1; while i le v do jv[i][1] := 1; i := i + 1; end while; i := 1; while i le b do jb[1][i] := 1; i := i + 1; end while; // Let's create the matrices that we're going to use to check the conditions: C1 := C*jv; C2 := jb*C; C3 := Transpose(C)*C; if (not (C1 eq k*Transpose(jb))) then return false; end if; // print "Pass1"; if (not (C2 eq r*Transpose(jv))) then return false; end if; // print "Pass2"; i := 1; j := 1; while i le b do while j le v do if i eq j then if C3[i][j] ne r then return false; end if; else if C3[i][j] ne l then return false; end if; end if; j := j + 1; end while; j := 1; i := i + 1; end while; return true; // Every function in Magma must end with a return statement, otherwise it should just be a procedure, which we shall discuss in a later example. end function; // So now we have our beautiful little (laugh!) isIncidenceMatrix() function. We want to write some code to make use of the bloody thing. // I'm going to create the matrix generated by the primitive 3-sequence that we had on the second homework. // This is kind of hacked together from the code for my homework, so don't pay too much attention to it. :) m := 3; c := 2^m-1; S := [n eq 1 select GF(2)!1 else n in {2..m} select GF(2)!0 else Self(n-m) + Self(n-m+1) : n in [1..c]]; // Create the sequence using recursion. Z := IntegerRing(); // Everyone's favourite ring! R := ResidueClassRing(2^m-1); // Creates the integers modulo 2^m - 1. A := KMatrixSpace(GF(2),2^m-1,2^m-1)!0; i := 1; j := 1; while i le c do while j le c do A[i][j] := S[Z!(R!(j-i))+1]; j := j + 1; end while; j := 1; i := i + 1; end while; // Output if isIncidenceMatrix(A, c, 2^(m-1), 2^(m-2)) then print "A is the incidence matrix for a design with parameters (", c, ",", 2^(m-1), ",", 2^(m-2), ")n"; else print "A is not an incidence matrix for a design with the specified parameters.n"; end if; Output: WARNING: MAGMA command contains unsafe command 'system', so it will not be executed. ************** MAGMA ***************** Host janssons.medic.chalmers.se. (129.16.32.56) Time: Fri Feb 13 08:50:09 2004 Input: 1+2 Output: Magma V2.10-6 Fri Feb 13 2004 08:50:04 on modular [Seed = 1845688440] ------------------------------------- 3 Total time: 3.059 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host janssons.medic.chalmers.se. (129.16.32.56) Time: Fri Feb 13 08:50:39 2004 Input: 1+2 Output: Magma V2.10-6 Fri Feb 13 2004 08:50:36 on modular [Seed = 2632977066] ------------------------------------- 3 Total time: 2.999 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host mathl30.sogang.ac.kr. (163.239.42.230) Time: Fri Feb 13 20:36:47 2004 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: Magma V2.10-6 Fri Feb 13 2004 20:36:44 on modular [Seed = 3316186696] ------------------------------------- Replace this by some code, then click [PARI] or [MAGMA]! Total time: 3.059 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (218.79.220.21) Time: Mon Feb 16 00:18:41 2004 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: Magma V2.10-6 Mon Feb 16 2004 00:18:37 on modular [Seed = 3049629541] ------------------------------------- Replace this by some code, then click [PARI] or [MAGMA]! Total time: 3.099 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host classic.univ-ab.pt. (193.136.111.1) Time: Mon Feb 16 07:29:48 2004 Input: (a+b)+c=a+(b+c). a+a=a. (a+b)+(a+d)!=(a+b)+d. Output: Magma V2.10-6 Mon Feb 16 2004 07:29:44 on modular [Seed = 4119134799] ------------------------------------- >> (a+b)+(a+d)!=(a+b)+d.; ^ User error: bad syntax Total time: 3.119 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host classic.univ-ab.pt. (193.136.111.1) Time: Mon Feb 16 07:32:06 2004 Input: (a+b)+c=a+(b+c). a+a=a. (a+b)+(a+d)>(a+b)+d. Output: Magma V2.10-6 Mon Feb 16 2004 07:32:03 on modular [Seed = 74775620] ------------------------------------- >> (a+b)+(a+d)>(a+b)+d.; ^ User error: bad syntax Total time: 2.999 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host classic.univ-ab.pt. (193.136.111.1) Time: Mon Feb 16 07:37:36 2004 Input: (a+b)+c=a+(b+c) & a+a=a -> (a+b)+(a+d)(a+b)+d. Output: Magma V2.10-6 Mon Feb 16 2004 07:37:33 on modular [Seed = 359001243] ------------------------------------- >> (a+b)+c=a+(b+c) & a+a=a -> (a+b)+(a+d)(a+b)+d.; ^ User error: Bad reduction operator Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host classic.univ-ab.pt. (193.136.111.1) Time: Mon Feb 16 07:52:55 2004 Input: (a+b)+c=a+(b+c) and a+a=a and (a+b)+(a+d) ne (a+b)+d. Output: Magma V2.10-6 Mon Feb 16 2004 07:52:52 on modular [Seed = 927451664] ------------------------------------- >> (a+b)+c=a+(b+c) and a+a=a and (a+b)+(a+d) ne (a+b)+d.; ^ User error: bad syntax Total time: 3.099 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host classic.univ-ab.pt. (193.136.111.1) Time: Mon Feb 16 07:54:21 2004 Input: (a+b)+c=a+(b+c) and a+a=a and (a+b)+(a+d) ne (a+b)+d Output: Magma V2.10-6 Mon Feb 16 2004 07:54:18 on modular [Seed = 1045349191] ------------------------------------- >> (a+b)+c=a+(b+c) and a+a=a and (a+b)+(a+d) ne (a+b)+d; ^ User error: Identifier 'a' has not been declared or assigned Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host classic.univ-ab.pt. (193.136.111.1) Time: Mon Feb 16 08:00:10 2004 Input: (a+b)+c=a+(b+c) a+a=a (a+b)+(a+d) ne (a+b)+d Output: Magma V2.10-6 Mon Feb 16 2004 08:00:07 on modular [Seed = 1580114058] ------------------------------------- >> a+a=a ^ User error: bad syntax >> (a+b)+(a+d) ne (a+b)+d; ^ User error: Identifier 'a' has not been declared or assigned Total time: 3.079 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 2(SERVFAIL) (12.104.244.38) Time: Mon Feb 16 12:01:13 2004 Input: GetSeed(); Output: Magma V2.10-6 Mon Feb 16 2004 12:01:09 on modular [Seed = 2314813145] ------------------------------------- 2314813145 0 Total time: 3.009 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 2(SERVFAIL) (12.104.244.38) Time: Mon Feb 16 12:02:01 2004 Input: K := GF(RandomPrime(40)); E := EllipticCurve([Random(K), Random(K)]); E; Output: Magma V2.10-6 Mon Feb 16 2004 12:01:56 on modular [Seed = 2481136658] ------------------------------------- Elliptic Curve defined by y^2 = x^3 + 95578316362*x + 101604805736 over GF(430691276293) Total time: 2.989 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 2(SERVFAIL) (12.104.244.38) Time: Mon Feb 16 12:03:48 2004 Input: GetSeed(); K := GF(RandomPrime(40)); E := EllipticCurve([Random(K), Random(K)]); E; Q := Random(E); Q; FactoredOrder(Q); P := Random(Order(Q))*Q; P; m := Log(Q, P); m; m*Q - P; Output: Magma V2.10-6 Mon Feb 16 2004 12:03:44 on modular [Seed = 2782204496] ------------------------------------- 2782204496 0 Elliptic Curve defined by y^2 = x^3 + 39359586944*x + 190995520634 over GF(957632693371) (613100332250 : 469510526239 : 1) [ <2, 4>, <2621, 1>, <22835569, 1> ] (160753340997 : 392177928413 : 1) 829514499424 (0 : 1 : 0) Total time: 3.369 seconds, Total memory usage: 2.85MB ************** MAGMA ***************** Host m157.tnt04-bp.pool.eol.hu. (212.108.246.157) Time: Mon Feb 16 14:30:57 2004 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: Magma V2.10-6 Mon Feb 16 2004 14:30:54 on modular [Seed = 910650463] ------------------------------------- Replace this by some code, then click [PARI] or [MAGMA]! Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 2(SERVFAIL) (140.115.25.8) Time: Mon Feb 16 20:07:17 2004 Input: 1 Output: Magma V2.10-6 Mon Feb 16 2004 20:07:14 on modular [Seed = 3818048171] ------------------------------------- 1 Total time: 3.109 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 2(SERVFAIL) (140.115.25.8) Time: Mon Feb 16 20:07:32 2004 Input: 1 + 1 Output: Magma V2.10-6 Mon Feb 16 2004 20:07:29 on modular [Seed = 4186493090] ------------------------------------- 2 Total time: 2.939 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 2(SERVFAIL) (140.115.25.8) Time: Mon Feb 16 20:07:47 2004 Input: 1/2 * 2 Output: Magma V2.10-6 Mon Feb 16 2004 20:07:44 on modular [Seed = 4136099740] ------------------------------------- 1 Total time: 2.939 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 2(SERVFAIL) (140.115.25.8) Time: Mon Feb 16 20:08:00 2004 Input: 1/123456789 * 2 Output: Magma V2.10-6 Mon Feb 16 2004 20:07:57 on modular [Seed = 243214184] ------------------------------------- 2/123456789 Total time: 2.939 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 2(SERVFAIL) (140.115.25.8) Time: Mon Feb 16 20:08:12 2004 Input: 2**2 * 2 Output: Magma V2.10-6 Mon Feb 16 2004 20:08:09 on modular [Seed = 91499639] ------------------------------------- >> 2**2 * 2; ^ User error: bad syntax Total time: 2.919 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 2(SERVFAIL) (140.115.25.8) Time: Mon Feb 16 20:08:22 2004 Input: 2^2 * 2 Output: Magma V2.10-6 Mon Feb 16 2004 20:08:19 on modular [Seed = 476919188] ------------------------------------- 8 Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 2(SERVFAIL) (140.115.25.8) Time: Mon Feb 16 20:08:32 2004 Input: 2^2048 * 2 Output: Magma V2.10-6 Mon Feb 16 2004 20:08:29 on modular [Seed = 727319213] ------------------------------------- 6463401214262201460142975337733990392088820533943096806426069085504931027773578\ 1786394402823045826927377435921843796038988239118300981842190176304772896566241\ 2617547346019921835003955007793042135921152767681351365535844372852395123236761\ 8867695234094116329170407261008577515178308213161721510479824786077104382866677\ 9336684841369949573129138989712352070652644116155611318662052385416920628300517\ 1857283542334518872074369237147151967023046032918088073952264665744624542513694\ 2164041945031420345386264693935708516131339587009199453670599727643105033277887\ 4671087204270866459209290636957209904296387111707222119192461312 Total time: 2.989 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 2(SERVFAIL) (140.115.25.8) Time: Mon Feb 16 20:08:51 2004 Input: atan(1) Output: Magma V2.10-6 Mon Feb 16 2004 20:08:48 on modular [Seed = 575867785] ------------------------------------- >> atan(1); ^ User error: Identifier 'atan' has not been declared or assigned Total time: 3.059 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 2(SERVFAIL) (140.115.25.8) Time: Mon Feb 16 20:09:04 2004 Input: tan(1) Output: Magma V2.10-6 Mon Feb 16 2004 20:09:01 on modular [Seed = 961024159] ------------------------------------- >> tan(1); ^ User error: Identifier 'tan' has not been declared or assigned Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 2(SERVFAIL) (140.115.25.8) Time: Mon Feb 16 20:09:27 2004 Input: 2^(-100) Output: Magma V2.10-6 Mon Feb 16 2004 20:09:24 on modular [Seed = 809572863] ------------------------------------- 1/1267650600228229401496703205376 Total time: 2.979 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam145-177.student.harvard.edu. (140.247.145.177) Time: Mon Feb 16 23:26:18 2004 Input: Factorial(10000) Output: Magma V2.10-6 Mon Feb 16 2004 23:26:14 on modular [Seed = 4152762397] ------------------------------------- 2846259680917054518906413212119868890148051401702799230794179994274411340003764\ 4437729907867577847758158840621423175288300423399401535187390524211613827161748\ 1982419982759241828925978789812425312059465996259867065601615720360323979263287\ 3671705574197596209947972034615369811989709261127750048419884541047554464244213\ 6573303076703628825803548967461117097369578603670191071512730587281041158640561\ 2811653853259684258259955846881464304255898366493170592517172042765974074461334\ 0005419405246230343686915405940406622782824837151203832217864462718382292389963\ 8992827221879702459387693803094627332292570555459690027875282242544348021127559\ 0191694254290289169072190970836905398737474524833728995218023632827412170402680\ 8676921045155584056717255537201585213282903427998981844931361064038148930449962\ 1599999359670892980190336998484404665419236258424947163178961192041233108268651\ 0713545168455409360330096072103469443779823494307806260694223026818852275920570\ 2923084312618849760656074258627944882715595683153344053442544664841689458042570\ 9461673613187605234982286326452921529423479870603344290737158688499178932580691\ 4831688542519560061723726363239744207869246429560123062887201226529529640915083\ 0133663098273380635397290150658182257429547589439976511386554120812578868370423\ 9208764484761569001264889271590706306409661628038784044485191643790807186112370\ 6221334154150659918438759610239267132765469861636577066264386380298480519527695\ 3619525924093090861447190739076858575593478698172073437209310482547562856777769\ 4081564074962275254993384112809289637516990219870492405617531786346939798024619\ 7370790418683299310165541507423083931768783669236948490259996077296842939774275\ 3626311982541668153189176323483919082100014717893218422780513518173492190114624\ 6875769835373441456013122615221391178759688367364087207937002992038279198038702\ 3720780391403123689976081528403060511167094847222248703891999934420713958369830\ 6396223207911562404425080891991431983712044559834404755675948921210149815245454\ 3594285414390843564419984224855478532163624030098442855331829253154206551237079\ 7058163934602962476970103887422064415366267337154287007891227493406843364428898\ 4710084064160009362393526124803797529334392876439831639031277645072247926785170\ 0826669598389526150759007349215197592659192708873202594066382118801988854748266\ 0483422564577057439731222597006719360617635135795298217942907977053272832675014\ 8802444352868164502616566283754651900617187344226043891929850607151539003110668\ 4727360135816706437861756757439184376479658136100599638689552334648781746143243\ 5732248643267984819814584327030358955084205347884933645824825920332880890257823\ 8823326577020524897093704721021424841334246526820680673231421448385407418213962\ 1846870108359582946965235632764870475718351616879235068366271743711915723361143\ 0701211207676086978515597218464859859186436417168508996255168209107935702311185\ 1817477501080462258552131476489749066075287708289766751495100968232968973200062\ 2392888056658036140311285465929084078033974900664953205873164948093883816198658\ 8508273824680348978647571166798904235680183035041338757319726308979094357106877\ 9730163391808786847494363353389337358690640584841782806519627582643442925805842\ 2212947649402948622670761832988229004072390403733168207417413251656688443079339\ 4470192089056207883875853425128209573593070181977083401638176382785625395168254\ 2664461494104471157953326237281546879408042371858742302620026422182269418862621\ 2107297776657401018376182280136857586442185863011539843712299107010094061929413\ 2232027731939594670067136953770978977781182882424429208648161341795620174718316\ 0968766104314049795819823644580736820940402221118153005143338707660706314961610\ 7771117448059552764348333385744040212757031851527298377435921878558552795591028\ 6644579173620072218581433099772947789237207179428577562713009239823979219575811\ 9726474264287826668235391568785727162014619224426626670840076566562580710947439\ 8740110772811669918806268726626565583345665007890309050656074633078027158530817\ 6912237728135105845273265916262196476205714348802156308152590053437211410003030\ 3924286645720732847348171203416818632896886504828736793339844397123673508452734\ 0196309427697652684170174990756947982757825835229994315633322107439131550124459\ 0053247026803129123922979790304175878233986223735350546426469135025039510092392\ 8658510868208807066273473320035499572039708648806604092985460700633940988583634\ 9865466136727880748764700702458790118046518296111277090609016152022111461543158\ 3176699570609746180853593904000678928785488278509386373537039040494126846189912\ 7287156265500127083303995025787993170543188275265922581494895074663997600731692\ 7310831735883056612614782997663188070063044632429112260691931278881566221591523\ 2704576958675128219909389426866019639044897189185974729253103224802105438410443\ 2582847283058429780416240510811032691400190056878439634150269652104892027214023\ 2160234898588827371428695339681755106287470907473718188014223487248498558198439\ 0946517083643689943061896502432883532796671901845276205510857076262042445096233\ 2320474470783119043449935144262550170177101737955112474615947173186270156557126\ 6295855125077711738338208419705893367323724453280456537178514960308802580284067\ 8478094146418386592266528068679788432506605379430462502871051049293472674712674\ 9989263462735816714693506049511034075540465817039348104675848562596776795976829\ 9409334026387269378365320912287718077451152622642548771835461108886360843272806\ 2277766430972838790567286180360486334648933714394152502594596525015209595361579\ 7713559579496572977565090269442808847976127666484700361964890604376193469427044\ 4070215317943583831051404915462608728486678750541674146731648999356381312866931\ 4276168635373056345866269578945682750658102359508148887789550739393653419373657\ 0084831850447568221544406759920313807707353997803633926733454954929666875992253\ 0893898086430606532961793164029612492673080638031873912596151131890359351266480\ 8185683667702865377423907465823909109555171797705807977892897524902307378017531\ 4268036391424472025772889178495007811788933662975043680421466819782427298069757\ 9391742229456683185815676816288797870624531246651727622758295493421483658868919\ 2995874020956960002435603052898298663868920769928340305497102665143223061252319\ 1513184387690382370620539920693394371688046642971147674356448637502684769814885\ 3105354063328845062012173302630676481322931561043551941761050712449024873277273\ 1120919458651374931909651624976916575538121985664322079786663003989386602386073\ 5785811439471587280089337416503379296583261843607313332752602360511552422722844\ 7251463863269369763762510196714380125691227784428426999440829152215904694437282\ 4986580852051865762929927755088331286726384187132777808744466438753526447335624\ 4113944762878097465068395298210817496795883645227334469487379347179071006497823\ 6466016680572034297929207446822322848665839522211446859572858403863377278030227\ 5915304978658739195136502462741958990883743873315942873720297706202071202130385\ 7217593321116241333042277374241635355358797706530964768588607730143277829032889\ 4795818404378858567772932094476778669357537460048142376741194182671636870481056\ 9111562156143575162905273512243500806046536689174581965494826086122607502930627\ 6147881326895528073614902252581968281505103331813212965966495815903042123877564\ 5990973296728066683849166257949747922905361845563741034791430771561168650484292\ 4902811029925296787352987678292690407887784802624792227507359484058174390862518\ 7794689004594206016860514277224448627246991114620014988066272353883780938062854\ 4384763053235070132028029488392008132135446450056134987017834271106158177289819\ 2906564986880810455622337030672542512772773302834984335957725759562247037077933\ 8714659303308862969944031833266579751467650271734629888377739784821870071802674\ 1265997158728035440478432478674907127921672898523588486943546692255101337606377\ 9151645972542571169684773399511589983490818882812639844005055462100669887926145\ 5821456531969690982725393451576040861347625877816586729441077535882416231577908\ 2538054746933540582469717674324523451498483027170396543887737637358191736582454\ 2733474904242629460112998819165637138471118491569150547681404117498014542657123\ 9420442544102807580600138819865061375928853903892264432294799028648284009959867\ 5963580999112695367601527173086852756572147583507122298296529564917835071750835\ 7413622825450556202709694174767992592297748886274113145876761475314568953280931\ 1705269648641018740767329698664923643738256547502281647192681555988319662984830\ 7776666840622314315884384910519058281816740764463033300119710293036455866594651\ 8690744752508378419876229904159117936827997606541860887216266548864923443910309\ 2325691063377596973905178112276466848679173604940439370333935190060938726839729\ 9246478483727274770977466693599784857120156789000241947269220974984127323147401\ 5499809203814598214164811763571478015542315996678385348544864069364105569135313\ 3523118405358134894093819182189869482538396098994282202759933963520621770534357\ 2073396250574216769465101608495601439303244304271576099527308684609204422226103\ 1542299844448021100981613338248273752189987382053151649271344981059501599748005\ 7159191220215448774875010347324619063394130303089239941198500622590218416440998\ 8173214324422108554248620896250260604398180189026317781146617454999771440665232\ 8638463638470016556181538610981881111817341913055050248603458567555856375117297\ 7429932907494423657966833270091836733897734790175924888566037995277154056908301\ 7311723894140326159612292912225191095948743805673381278538616491842786938417556\ 8980471008598683720336151751580970225662752001609561922299254017598785220385459\ 1377178397638981119848580329104875166692119510451489667776159824946872742066343\ 7593207852618922687285527671324883267794152912839165407968344190239094803676688\ 7 ** WARNING: Output too long, hence truncated. ************** MAGMA ***************** Host roam145-177.student.harvard.edu. (140.247.145.177) Time: Mon Feb 16 23:26:22 2004 Input: Factorial(10000) Output: Magma V2.10-6 Mon Feb 16 2004 23:26:19 on modular [Seed = 158916335] ------------------------------------- 2846259680917054518906413212119868890148051401702799230794179994274411340003764\ 4437729907867577847758158840621423175288300423399401535187390524211613827161748\ 1982419982759241828925978789812425312059465996259867065601615720360323979263287\ 3671705574197596209947972034615369811989709261127750048419884541047554464244213\ 6573303076703628825803548967461117097369578603670191071512730587281041158640561\ 2811653853259684258259955846881464304255898366493170592517172042765974074461334\ 0005419405246230343686915405940406622782824837151203832217864462718382292389963\ 8992827221879702459387693803094627332292570555459690027875282242544348021127559\ 0191694254290289169072190970836905398737474524833728995218023632827412170402680\ 8676921045155584056717255537201585213282903427998981844931361064038148930449962\ 1599999359670892980190336998484404665419236258424947163178961192041233108268651\ 0713545168455409360330096072103469443779823494307806260694223026818852275920570\ 2923084312618849760656074258627944882715595683153344053442544664841689458042570\ 9461673613187605234982286326452921529423479870603344290737158688499178932580691\ 4831688542519560061723726363239744207869246429560123062887201226529529640915083\ 0133663098273380635397290150658182257429547589439976511386554120812578868370423\ 9208764484761569001264889271590706306409661628038784044485191643790807186112370\ 6221334154150659918438759610239267132765469861636577066264386380298480519527695\ 3619525924093090861447190739076858575593478698172073437209310482547562856777769\ 4081564074962275254993384112809289637516990219870492405617531786346939798024619\ 7370790418683299310165541507423083931768783669236948490259996077296842939774275\ 3626311982541668153189176323483919082100014717893218422780513518173492190114624\ 6875769835373441456013122615221391178759688367364087207937002992038279198038702\ 3720780391403123689976081528403060511167094847222248703891999934420713958369830\ 6396223207911562404425080891991431983712044559834404755675948921210149815245454\ 3594285414390843564419984224855478532163624030098442855331829253154206551237079\ 7058163934602962476970103887422064415366267337154287007891227493406843364428898\ 4710084064160009362393526124803797529334392876439831639031277645072247926785170\ 0826669598389526150759007349215197592659192708873202594066382118801988854748266\ 0483422564577057439731222597006719360617635135795298217942907977053272832675014\ 8802444352868164502616566283754651900617187344226043891929850607151539003110668\ 4727360135816706437861756757439184376479658136100599638689552334648781746143243\ 5732248643267984819814584327030358955084205347884933645824825920332880890257823\ 8823326577020524897093704721021424841334246526820680673231421448385407418213962\ 1846870108359582946965235632764870475718351616879235068366271743711915723361143\ 0701211207676086978515597218464859859186436417168508996255168209107935702311185\ 1817477501080462258552131476489749066075287708289766751495100968232968973200062\ 2392888056658036140311285465929084078033974900664953205873164948093883816198658\ 8508273824680348978647571166798904235680183035041338757319726308979094357106877\ 9730163391808786847494363353389337358690640584841782806519627582643442925805842\ 2212947649402948622670761832988229004072390403733168207417413251656688443079339\ 4470192089056207883875853425128209573593070181977083401638176382785625395168254\ 2664461494104471157953326237281546879408042371858742302620026422182269418862621\ 2107297776657401018376182280136857586442185863011539843712299107010094061929413\ 2232027731939594670067136953770978977781182882424429208648161341795620174718316\ 0968766104314049795819823644580736820940402221118153005143338707660706314961610\ 7771117448059552764348333385744040212757031851527298377435921878558552795591028\ 6644579173620072218581433099772947789237207179428577562713009239823979219575811\ 9726474264287826668235391568785727162014619224426626670840076566562580710947439\ 8740110772811669918806268726626565583345665007890309050656074633078027158530817\ 6912237728135105845273265916262196476205714348802156308152590053437211410003030\ 3924286645720732847348171203416818632896886504828736793339844397123673508452734\ 0196309427697652684170174990756947982757825835229994315633322107439131550124459\ 0053247026803129123922979790304175878233986223735350546426469135025039510092392\ 8658510868208807066273473320035499572039708648806604092985460700633940988583634\ 9865466136727880748764700702458790118046518296111277090609016152022111461543158\ 3176699570609746180853593904000678928785488278509386373537039040494126846189912\ 7287156265500127083303995025787993170543188275265922581494895074663997600731692\ 7310831735883056612614782997663188070063044632429112260691931278881566221591523\ 2704576958675128219909389426866019639044897189185974729253103224802105438410443\ 2582847283058429780416240510811032691400190056878439634150269652104892027214023\ 2160234898588827371428695339681755106287470907473718188014223487248498558198439\ 0946517083643689943061896502432883532796671901845276205510857076262042445096233\ 2320474470783119043449935144262550170177101737955112474615947173186270156557126\ 6295855125077711738338208419705893367323724453280456537178514960308802580284067\ 8478094146418386592266528068679788432506605379430462502871051049293472674712674\ 9989263462735816714693506049511034075540465817039348104675848562596776795976829\ 9409334026387269378365320912287718077451152622642548771835461108886360843272806\ 2277766430972838790567286180360486334648933714394152502594596525015209595361579\ 7713559579496572977565090269442808847976127666484700361964890604376193469427044\ 4070215317943583831051404915462608728486678750541674146731648999356381312866931\ 4276168635373056345866269578945682750658102359508148887789550739393653419373657\ 0084831850447568221544406759920313807707353997803633926733454954929666875992253\ 0893898086430606532961793164029612492673080638031873912596151131890359351266480\ 8185683667702865377423907465823909109555171797705807977892897524902307378017531\ 4268036391424472025772889178495007811788933662975043680421466819782427298069757\ 9391742229456683185815676816288797870624531246651727622758295493421483658868919\ 2995874020956960002435603052898298663868920769928340305497102665143223061252319\ 1513184387690382370620539920693394371688046642971147674356448637502684769814885\ 3105354063328845062012173302630676481322931561043551941761050712449024873277273\ 1120919458651374931909651624976916575538121985664322079786663003989386602386073\ 5785811439471587280089337416503379296583261843607313332752602360511552422722844\ 7251463863269369763762510196714380125691227784428426999440829152215904694437282\ 4986580852051865762929927755088331286726384187132777808744466438753526447335624\ 4113944762878097465068395298210817496795883645227334469487379347179071006497823\ 6466016680572034297929207446822322848665839522211446859572858403863377278030227\ 5915304978658739195136502462741958990883743873315942873720297706202071202130385\ 7217593321116241333042277374241635355358797706530964768588607730143277829032889\ 4795818404378858567772932094476778669357537460048142376741194182671636870481056\ 9111562156143575162905273512243500806046536689174581965494826086122607502930627\ 6147881326895528073614902252581968281505103331813212965966495815903042123877564\ 5990973296728066683849166257949747922905361845563741034791430771561168650484292\ 4902811029925296787352987678292690407887784802624792227507359484058174390862518\ 7794689004594206016860514277224448627246991114620014988066272353883780938062854\ 4384763053235070132028029488392008132135446450056134987017834271106158177289819\ 2906564986880810455622337030672542512772773302834984335957725759562247037077933\ 8714659303308862969944031833266579751467650271734629888377739784821870071802674\ 1265997158728035440478432478674907127921672898523588486943546692255101337606377\ 9151645972542571169684773399511589983490818882812639844005055462100669887926145\ 5821456531969690982725393451576040861347625877816586729441077535882416231577908\ 2538054746933540582469717674324523451498483027170396543887737637358191736582454\ 2733474904242629460112998819165637138471118491569150547681404117498014542657123\ 9420442544102807580600138819865061375928853903892264432294799028648284009959867\ 5963580999112695367601527173086852756572147583507122298296529564917835071750835\ 7413622825450556202709694174767992592297748886274113145876761475314568953280931\ 1705269648641018740767329698664923643738256547502281647192681555988319662984830\ 7776666840622314315884384910519058281816740764463033300119710293036455866594651\ 8690744752508378419876229904159117936827997606541860887216266548864923443910309\ 2325691063377596973905178112276466848679173604940439370333935190060938726839729\ 9246478483727274770977466693599784857120156789000241947269220974984127323147401\ 5499809203814598214164811763571478015542315996678385348544864069364105569135313\ 3523118405358134894093819182189869482538396098994282202759933963520621770534357\ 2073396250574216769465101608495601439303244304271576099527308684609204422226103\ 1542299844448021100981613338248273752189987382053151649271344981059501599748005\ 7159191220215448774875010347324619063394130303089239941198500622590218416440998\ 8173214324422108554248620896250260604398180189026317781146617454999771440665232\ 8638463638470016556181538610981881111817341913055050248603458567555856375117297\ 7429932907494423657966833270091836733897734790175924888566037995277154056908301\ 7311723894140326159612292912225191095948743805673381278538616491842786938417556\ 8980471008598683720336151751580970225662752001609561922299254017598785220385459\ 1377178397638981119848580329104875166692119510451489667776159824946872742066343\ 7593207852618922687285527671324883267794152912839165407968344190239094803676688\ 70 ** WARNING: Output too long, hence truncated. ************** MAGMA ***************** Host 218-164-123-55.HINET-IP.hinet.net. (218.164.123.55) Time: Tue Feb 17 00:36:46 2004 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: Magma V2.10-6 Tue Feb 17 2004 00:36:42 on modular [Seed = 3500226743] ------------------------------------- Replace this by some code, then click [PARI] or [MAGMA]! Total time: 2.979 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host 3(NXDOMAIN) (81.6.87.13) Time: Tue Feb 17 05:22:49 2004 Input: ? hadamard Output: Magma V2.10-6 Tue Feb 17 2004 05:22:45 on modular [Seed = 1062114392] ------------------------------------- 9 matches: 1 S /magma/combinatorial-geometrical-incidence/\ incidence-structure-design/operation/hadamard 2 I /magma/combinatorial-geometrical-incidence/graph/\ group-code-design/code-design/HadamardGraph 3 I /magma/combinatorial-geometrical-incidence/\ incidence-structure-design/operation/hadamard/\ HadamardAutomorphismGroup 4 I /magma/combinatorial-geometrical-incidence/\ incidence-structure-design/operation/hadamard/HadamardColumnDesign 5 I /magma/combinatorial-geometrical-incidence/\ incidence-structure-design/operation/hadamard/HadamardNormalize 6 I /magma/combinatorial-geometrical-incidence/\ incidence-structure-design/operation/hadamard/HadamardRowDesign 7 I /magma/combinatorial-geometrical-incidence/\ incidence-structure-design/operation/hadamard/IsHadamard 8 I /magma/combinatorial-geometrical-incidence/\ incidence-structure-design/operation/hadamard/IsHadamardEquivalent 9 E /magma/combinatorial-geometrical-incidence/\ incidence-structure-design/operation/hadamard/Example-hadamard To view an entry, type ? followed by the number next to it Total time: 3.159 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host irmasrv3.u-strasbg.fr. (130.79.4.200) Time: Tue Feb 17 07:06:25 2004 Input: P:=PolynomialRing(IntegerRing(),2); f0:=2*(x^2+y^2)+x-y-16; f1:=6*(x^4+y^4)+2*(x^3-y^3)+x-y-192; f2:=40*(x^6+y^6)+11*(x^5-y^5)+5*(x^3-y^3)+4*(x-y)-5120; f3:=630*x^8+630*y^8-322560+151*x^7-151*y^7+70*x^5-70*y^5+49*x^3-49*y^3+45*x-45*y; I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Output: Magma V2.10-6 Tue Feb 17 2004 07:06:21 on modular [Seed = 192497829] ------------------------------------- [ x^2 + 8*x + 31*y^2 - 8*y - 128, x*y + 2*x + 4*y^3 + 111*y^2 - 18*y - 448, 15*x + 60*y^2 - 15*y - 240, 4*y^4 + 20*y^2 - 144, 8*y^3 + 72*y^2 - 32*y - 288, 120*y^2 - 480 ] Total time: 3.089 seconds, Total memory usage: 1.93MB ************** MAGMA ***************** Host irmasrv3.u-strasbg.fr. (130.79.4.200) Time: Tue Feb 17 07:07:29 2004 Input: P:=PolynomialRing(IntegerRing(),2); f0:=2*(x^2+y^2)+x-y-16; Output: Magma V2.10-6 Tue Feb 17 2004 07:07:26 on modular [Seed = 910456283] ------------------------------------- Total time: 3.059 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host ZWLEE.ECE.CMU.EDU. (128.2.132.182) Time: Tue Feb 17 10:35:47 2004 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: Magma V2.10-6 Tue Feb 17 2004 10:35:44 on modular [Seed = 3817969447] ------------------------------------- Replace this by some code, then click [PARI] or [MAGMA]! Total time: 3.039 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pD9E0C8D5.dip.t-dialin.net. (217.224.200.213) Time: Tue Feb 17 12:14:47 2004 Input: > x := 1; > S := { }; > for i := 1 to 10 do > S join:= { x }; > x *:= 2; > end for; > S; Output: Magma V2.10-6 Tue Feb 17 2004 12:14:43 on modular [Seed = 4287493097] ------------------------------------- { 1, 2, 4, 8, 16, 32, 64, 128, 256, 512 } Total time: 2.979 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pD9E0C8D5.dip.t-dialin.net. (217.224.200.213) Time: Tue Feb 17 12:15:25 2004 Input: x := 1; S := { }; for i := 1 to 10 do S join:= { x }; x *:= 2; end for; S; Output: Magma V2.10-6 Tue Feb 17 2004 12:15:22 on modular [Seed = 3801149149] ------------------------------------- { 1, 2, 4, 8, 16, 32, 64, 128, 256, 512 } Total time: 2.979 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pD9E0C8D5.dip.t-dialin.net. (217.224.200.213) Time: Tue Feb 17 12:21:09 2004 Input: primeDivisors(120) Output: Magma V2.10-6 Tue Feb 17 2004 12:21:06 on modular [Seed = 510399370] ------------------------------------- >> primeDivisors(120); ^ User error: Identifier 'primeDivisors' has not been declared or assigned Total time: 2.979 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pD9E0C8D5.dip.t-dialin.net. (217.224.200.213) Time: Tue Feb 17 12:22:22 2004 Input: > primeDivisors := function(n) > if isPrime(n) then > return { n }; > else > return func< d | primeDivisors(d) join primeDivisors(n div d) > > ( rep{ d : d in [2..Isqrt(n)] | n mod d eq 0 }); > end if; > end function; > isPrime(1087); true; primeDivisors(120) Output: Magma V2.10-6 Tue Feb 17 2004 12:22:19 on modular [Seed = 125111002] ------------------------------------- >> if isPrime(n) then ^ User error: Identifier 'isPrime' has not been declared or assigned >> isPrime(1087); ^ User error: Identifier 'isPrime' has not been declared or assigned true >> primeDivisors(120); ^ User error: Identifier 'primeDivisors' has not been declared or assigned Total time: 2.919 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pD9E0C8D5.dip.t-dialin.net. (217.224.200.213) Time: Tue Feb 17 12:26:18 2004 Input: PrimeDivisors(120) Output: Magma V2.10-6 Tue Feb 17 2004 12:26:15 on modular [Seed = 159057832] ------------------------------------- [ 2, 3, 5 ] Total time: 2.929 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pD9E0C8D5.dip.t-dialin.net. (217.224.200.213) Time: Tue Feb 17 12:26:37 2004 Input: PrimeDivisors(123456789) Output: Magma V2.10-6 Tue Feb 17 2004 12:26:34 on modular [Seed = 1045180642] ------------------------------------- [ 3, 3607, 3803 ] Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pD9E0C8D5.dip.t-dialin.net. (217.224.200.213) Time: Tue Feb 17 12:27:54 2004 Input: PrimeBasis(123456789) Output: Magma V2.10-6 Tue Feb 17 2004 12:27:51 on modular [Seed = 609626917] ------------------------------------- [ 3, 3607, 3803 ] Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pD9E0C8D5.dip.t-dialin.net. (217.224.200.213) Time: Tue Feb 17 12:30:18 2004 Input: SquarefreeFactorization(123456789) Output: Magma V2.10-6 Tue Feb 17 2004 12:30:15 on modular [Seed = 1411800037] ------------------------------------- 13717421 3 Total time: 3.039 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pD9E0C8D5.dip.t-dialin.net. (217.224.200.213) Time: Tue Feb 17 12:34:38 2004 Input: Facint(12) Output: Magma V2.10-6 Tue Feb 17 2004 12:34:35 on modular [Seed = 1512590055] ------------------------------------- >> Facint(12); ^ Runtime error in 'Facint': Bad argument types Argument types given: RngIntElt Total time: 3.019 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pD9E0C8D5.dip.t-dialin.net. (217.224.200.213) Time: Tue Feb 17 12:35:44 2004 Input: Divisors(12) Output: Magma V2.10-6 Tue Feb 17 2004 12:35:41 on modular [Seed = 1329422260] ------------------------------------- [ 1, 2, 3, 4, 6, 12 ] Total time: 2.999 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam149-32.student.harvard.edu. (140.247.149.32) Time: Tue Feb 17 18:56:13 2004 Input: F := NumberField(x^3-2) Output: Magma V2.10-6 Tue Feb 17 2004 18:56:10 on modular [Seed = 2649716636] ------------------------------------- >> F := NumberField(x^3-2) ^ User error: Identifier 'x' has not been declared or assigned Total time: 3.069 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam149-32.student.harvard.edu. (140.247.149.32) Time: Tue Feb 17 18:56:38 2004 Input: F := NumberField(x^3-2) R := RingOfIntegers(F) Output: Magma V2.10-6 Tue Feb 17 2004 18:56:35 on modular [Seed = 2498133692] ------------------------------------- >> R := RingOfIntegers(F); ^ User error: bad syntax Total time: 2.929 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam149-32.student.harvard.edu. (140.247.149.32) Time: Tue Feb 17 18:56:49 2004 Input: F := NumberField(x^3-2); R := RingOfIntegers(F); Output: Magma V2.10-6 Tue Feb 17 2004 18:56:46 on modular [Seed = 2213636518] ------------------------------------- >> F := NumberField(x^3-2); ^ User error: Identifier 'x' has not been declared or assigned >> R := RingOfIntegers(F);; ^ User error: Identifier 'F' has not been declared or assigned Total time: 2.999 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam149-32.student.harvard.edu. (140.247.149.32) Time: Tue Feb 17 18:59:03 2004 Input: Q := PolynomialRing(Rationals()); F := NumberField(x^3-2); R := RingOfIntegers(F); Output: Magma V2.10-6 Tue Feb 17 2004 18:58:59 on modular [Seed = 3184482149] ------------------------------------- Total time: 3.009 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam149-32.student.harvard.edu. (140.247.149.32) Time: Tue Feb 17 18:59:14 2004 Input: Q := PolynomialRing(Rationals()); F := NumberField(x^3-2); R := RingOfIntegers(F); Output: Magma V2.10-6 Tue Feb 17 2004 18:59:11 on modular [Seed = 3032899168] ------------------------------------- Total time: 2.999 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam149-32.student.harvard.edu. (140.247.149.32) Time: Tue Feb 17 19:02:11 2004 Input: Q := PolynomialRing(Rationals()); F := NumberField(x^3-2); R := RingOfIntegers(F); Integers(K) : FldNum -> RngOrd; Output: Magma V2.10-6 Tue Feb 17 2004 19:02:08 on modular [Seed = 3384484434] ------------------------------------- >> Integers(K) : FldNum -> RngOrd;; ^ User error: bad syntax Total time: 2.939 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam149-32.student.harvard.edu. (140.247.149.32) Time: Tue Feb 17 19:02:20 2004 Input: Q := PolynomialRing(Rationals()); F := NumberField(x^3-2); R := RingOfIntegers(F); Integers(K) : FldNum -> RngOrd Output: Magma V2.10-6 Tue Feb 17 2004 19:02:17 on modular [Seed = 3232901970] ------------------------------------- >> Integers(K) : FldNum -> RngOrd; ^ User error: bad syntax Total time: 2.919 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam149-32.student.harvard.edu. (140.247.149.32) Time: Tue Feb 17 19:02:32 2004 Input: Q := PolynomialRing(Rationals()) F := NumberField(x^3-2) R := RingOfIntegers(F) Output: Magma V2.10-6 Tue Feb 17 2004 19:02:29 on modular [Seed = 4287435889] ------------------------------------- >> F := NumberField(x^3-2) ^ User error: bad syntax >> R := RingOfIntegers(F) ^ User error: Identifier 'F' has not been declared or assigned Total time: 2.989 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam149-32.student.harvard.edu. (140.247.149.32) Time: Tue Feb 17 19:02:43 2004 Input: Q := PolynomialRing(Rationals()); F := NumberField(x^3-2); R := RingOfIntegers(F); Output: Magma V2.10-6 Tue Feb 17 2004 19:02:40 on modular [Seed = 4135853389] ------------------------------------- Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam149-32.student.harvard.edu. (140.247.149.32) Time: Tue Feb 17 19:28:16 2004 Input: Q := PolynomialRing(Rationals()); F := NumberField(x^3-2); R := RingOfIntegers(F); Basis(R); Output: Magma V2.10-6 Tue Feb 17 2004 19:28:13 on modular [Seed = 74904965] ------------------------------------- [ R.1, R.2, R.3 ] Total time: 2.979 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam149-32.student.harvard.edu. (140.247.149.32) Time: Tue Feb 17 19:30:18 2004 Input: Q := PolynomialRing(Rationals()); F := NumberField(x^3-2); R := RingOfIntegers(F); Basis(R); R.1; Output: Magma V2.10-6 Tue Feb 17 2004 19:30:15 on modular [Seed = 877053503] ------------------------------------- [ R.1, R.2, R.3 ] R.1 Total time: 3.029 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam149-32.student.harvard.edu. (140.247.149.32) Time: Tue Feb 17 19:30:41 2004 Input: Q := PolynomialRing(Rationals()); F := NumberField(x^3-2); R := RingOfIntegers(F); Basis(R); R.1 =1; Output: Magma V2.10-6 Tue Feb 17 2004 19:30:37 on modular [Seed = 761257756] ------------------------------------- [ R.1, R.2, R.3 ] R.1 = R.1 Total time: 3.029 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam149-32.student.harvard.edu. (140.247.149.32) Time: Tue Feb 17 19:36:08 2004 Input: Q := PolynomialRing(Rationals()); F := NumberField(x^3-2); R := RingOfIntegers(F); MaximalOrder(F) Output: Magma V2.10-6 Tue Feb 17 2004 19:36:05 on modular [Seed = 592564298] ------------------------------------- Maximal Equation Order with defining polynomial x^3 - 2 over its ground order Total time: 2.919 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam149-32.student.harvard.edu. (140.247.149.32) Time: Tue Feb 17 19:39:14 2004 Input: Q := PolynomialRing(Rationals()); K := AdjoinRoot(Q, 2^(1/3); R := RingOfIntegers(K); MaximalOrder(K) Output: Magma V2.10-6 Tue Feb 17 2004 19:39:10 on modular [Seed = 1428660582] ------------------------------------- >> K := AdjoinRoot(Q, 2^(1/3); ^ User error: bad syntax >> R := RingOfIntegers(K); ^ User error: Identifier 'K' has not been declared or assigned >> MaximalOrder(K); ^ User error: Identifier 'K' has not been declared or assigned Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam149-32.student.harvard.edu. (140.247.149.32) Time: Tue Feb 17 19:42:06 2004 Input: Q := PolynomialRing(Rationals()); K := NumberField(x^3-2); E := EquationOrder(K); O := MaximalOrder(K); Index(O, E); Output: Magma V2.10-6 Tue Feb 17 2004 19:42:03 on modular [Seed = 1194701696] ------------------------------------- 1 Total time: 2.909 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam149-32.student.harvard.edu. (140.247.149.32) Time: Tue Feb 17 19:42:16 2004 Input: Q := PolynomialRing(Rationals()); K := NumberField(x^3-2); E := EquationOrder(K); O := MaximalOrder(K); Output: Magma V2.10-6 Tue Feb 17 2004 19:42:13 on modular [Seed = 2013957249] ------------------------------------- Total time: 2.939 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam149-32.student.harvard.edu. (140.247.149.32) Time: Tue Feb 17 19:42:26 2004 Input: Q := PolynomialRing(Rationals()); K := NumberField(x^3-2); E := EquationOrder(K); O := MaximalOrder(K); O Output: Magma V2.10-6 Tue Feb 17 2004 19:42:23 on modular [Seed = 1896056194] ------------------------------------- Maximal Equation Order with defining polynomial x^3 - 2 over its ground order Total time: 2.939 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam149-32.student.harvard.edu. (140.247.149.32) Time: Tue Feb 17 19:54:44 2004 Input: Q := PolynomialRing(Rationals()); K := NumberField(x^3-2); E := EquationOrder(K); O := MaximalOrder(K); IntegralBasis(K); Output: Magma V2.10-6 Tue Feb 17 2004 19:54:41 on modular [Seed = 2565500757] ------------------------------------- [ 1, K.1, K.1^2 ] Total time: 2.919 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam149-32.student.harvard.edu. (140.247.149.32) Time: Tue Feb 17 20:05:34 2004 Input: Q := PolynomialRing(Rationals()); K := NumberField(x^3-2); E := EquationOrder(K); O := MaximalOrder(K); IntegralBasis(K); Output: Magma V2.10-6 Tue Feb 17 2004 20:05:30 on modular [Seed = 2900252395] ------------------------------------- >> E := EquationOrder(K); ^ User error: bad syntax >> O := MaximalOrder(K); ^ User error: bad syntax [ 1, y, y^2 ] Total time: 3.009 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam149-32.student.harvard.edu. (140.247.149.32) Time: Tue Feb 17 20:06:27 2004 Input: Q := PolynomialRing(Rationals()); K := NumberField(x^3-2); E := EquationOrder(K); O := MaximalOrder(K); IntegralBasis(K); Output: Magma V2.10-6 Tue Feb 17 2004 20:06:24 on modular [Seed = 2798935082] ------------------------------------- >> E := EquationOrder(K); ^ User error: bad syntax >> O := MaximalOrder(K); ^ User error: bad syntax [ 1, x, x^2 ] Total time: 2.939 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam149-32.student.harvard.edu. (140.247.149.32) Time: Tue Feb 17 20:10:32 2004 Input: Q := PolynomialRing(Rationals()); K := NumberField(x^3-2); print IntegralBasis(K); Output: Magma V2.10-6 Tue Feb 17 2004 20:10:29 on modular [Seed = 4102426477] ------------------------------------- [ 1, y, y^2 ] Total time: 2.909 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam183-108.student.harvard.edu. (140.247.183.108) Time: Tue Feb 17 21:02:38 2004 Input: d := 2 ; Output: Magma V2.10-6 Tue Feb 17 2004 21:02:34 on modular [Seed = 1980035537] ------------------------------------- Total time: 3.109 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam183-108.student.harvard.edu. (140.247.183.108) Time: Tue Feb 17 21:03:03 2004 Input: d := 2; Q(Sqrt(d)); Q; Output: Magma V2.10-6 Tue Feb 17 2004 21:03:00 on modular [Seed = 1696064172] ------------------------------------- >> Q(Sqrt(d)); ^ User error: Identifier 'Q' has not been declared or assigned >> Q; ^ User error: Identifier 'Q' has not been declared or assigned Total time: 2.979 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam183-108.student.harvard.edu. (140.247.183.108) Time: Tue Feb 17 21:06:44 2004 Input: d := 2; Q := RationalField(); F := Q(Sqrt(d)); Q; IntegerRing(F); Output: Magma V2.10-6 Tue Feb 17 2004 21:06:41 on modular [Seed = 2514951481] ------------------------------------- >> F := Q(Sqrt(d)); ^ Runtime error: Bad argument types Argument types given: FldPrElt, FldRat Rational Field >> IntegerRing(F);; ^ User error: Identifier 'F' has not been declared or assigned Total time: 3.029 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam183-108.student.harvard.edu. (140.247.183.108) Time: Tue Feb 17 21:10:23 2004 Input: d := 2; Q := RationalField(); R := QuadraticField(d); Q; IntegerRing(F); Output: Magma V2.10-6 Tue Feb 17 2004 21:10:20 on modular [Seed = 2280984086] ------------------------------------- Rational Field >> IntegerRing(F);; ^ User error: Identifier 'F' has not been declared or assigned Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam183-108.student.harvard.edu. (140.247.183.108) Time: Tue Feb 17 21:10:32 2004 Input: d := 2; Q := RationalField(); R := QuadraticField(d); Q; IntegerRing(R); Output: Magma V2.10-6 Tue Feb 17 2004 21:10:29 on modular [Seed = 3100258608] ------------------------------------- Rational Field Maximal Equation Order of R Total time: 2.929 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam183-108.student.harvard.edu. (140.247.183.108) Time: Tue Feb 17 21:11:16 2004 Input: d := 2; Q := RationalField(); R := QuadraticField(d); Q; IntegerRing(R); RingOfIntegers(R); Output: Magma V2.10-6 Tue Feb 17 2004 21:11:13 on modular [Seed = 3015785071] ------------------------------------- Rational Field Maximal Equation Order of R Maximal Equation Order of R Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam183-108.student.harvard.edu. (140.247.183.108) Time: Tue Feb 17 21:11:34 2004 Input: d := 2; Q := RationalField(); R := QuadraticField(d); Q; IntegerRing(R); RingOfIntegers(R); Output: Magma V2.10-6 Tue Feb 17 2004 21:11:31 on modular [Seed = 2866291556] ------------------------------------- Rational Field Maximal Equation Order of R >> RingOfIntegers(R);; ^ User error: bad syntax Total time: 3.019 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam183-108.student.harvard.edu. (140.247.183.108) Time: Tue Feb 17 21:11:49 2004 Input: d := 2; Q := RationalField(); R := QuadraticField(d); Q; IntegerRing(R); RingOfIntegers(R); Output: Magma V2.10-6 Tue Feb 17 2004 21:11:46 on modular [Seed = 3719255074] ------------------------------------- Rational Field Maximal Equation Order of R Maximal Equation Order of R Total time: 2.919 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host d66-222-151-70.abhsia.telus.net. (66.222.151.70) Time: Tue Feb 17 21:22:04 2004 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: Magma V2.10-6 Tue Feb 17 2004 21:22:01 on modular [Seed = 4270617258] ------------------------------------- Replace this by some code, then click [PARI] or [MAGMA]! Total time: 3.049 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam183-108.student.harvard.edu. (140.247.183.108) Time: Tue Feb 17 21:40:36 2004 Input: N := NumberField(x^3 -2); Output: Magma V2.10-6 Tue Feb 17 2004 21:40:33 on modular [Seed = 2548369192] ------------------------------------- >> N := NumberField(x^3 -2);; ^ User error: Identifier 'x' has not been declared or assigned Total time: 3.019 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam183-108.student.harvard.edu. (140.247.183.108) Time: Tue Feb 17 21:41:32 2004 Input: N := NumberField(x^3 -2); Output: Magma V2.10-6 Tue Feb 17 2004 21:41:29 on modular [Seed = 2365463627] ------------------------------------- >> N := NumberField(x^3 -2);; ^ User error: Identifier 'x' has not been declared or assigned Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam183-108.student.harvard.edu. (140.247.183.108) Time: Tue Feb 17 21:43:01 2004 Input: PQ := PlynomialRing(RationalField()); N := NumberField(x^3 -2); Output: Magma V2.10-6 Tue Feb 17 2004 21:42:58 on modular [Seed = 2247562409] ------------------------------------- >> PQ := PlynomialRing(RationalField()); ^ User error: Identifier 'PlynomialRing' has not been declared or assigned >> N := NumberField(x^3 -2);; ^ User error: Identifier 'x' has not been declared or assigned Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam183-108.student.harvard.edu. (140.247.183.108) Time: Tue Feb 17 21:43:11 2004 Input: PQ := PolynomialRing(RationalField()); N := NumberField(x^3 -2); Output: Magma V2.10-6 Tue Feb 17 2004 21:43:08 on modular [Seed = 3150523033] ------------------------------------- Total time: 2.909 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam183-108.student.harvard.edu. (140.247.183.108) Time: Tue Feb 17 21:43:30 2004 Input: PQ := PolynomialRing(RationalField()); N := NumberField(x^3 -2); RingOfIntegers(N); Output: Magma V2.10-6 Tue Feb 17 2004 21:43:27 on modular [Seed = 2982355168] ------------------------------------- Maximal Equation Order with defining polynomial x^3 - 2 over its ground order Total time: 2.929 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam183-108.student.harvard.edu. (140.247.183.108) Time: Tue Feb 17 21:44:03 2004 Input: PQ := PolynomialRing(RationalField()); N := NumberField(x^3 -2); print RingOfIntegers(N); Output: Magma V2.10-6 Tue Feb 17 2004 21:44:00 on modular [Seed = 2798925768] ------------------------------------- Maximal Equation Order with defining polynomial x^3 - 2 over its ground order Total time: 2.929 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam183-108.student.harvard.edu. (140.247.183.108) Time: Tue Feb 17 21:44:27 2004 Input: PQ := PolynomialRing(RationalField()); N := NumberField(x^3 -2); P := RingOfIntegers(N); Output: Magma V2.10-6 Tue Feb 17 2004 21:44:24 on modular [Seed = 3752676937] ------------------------------------- >> P := RingOfIntegers(N);; ^ Runtime error in 'Name': Bad argument types Total time: 2.919 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam183-108.student.harvard.edu. (140.247.183.108) Time: Tue Feb 17 21:44:40 2004 Input: PQ := PolynomialRing(RationalField()); N := NumberField(x^3 -2); P := RingOfIntegers(N); Output: Magma V2.10-6 Tue Feb 17 2004 21:44:37 on modular [Seed = 3567666527] ------------------------------------- Total time: 2.919 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam183-108.student.harvard.edu. (140.247.183.108) Time: Tue Feb 17 21:44:54 2004 Input: PQ := PolynomialRing(RationalField()); N := NumberField(x^3 -2); P := RingOfIntegers(N); print P; Output: Magma V2.10-6 Tue Feb 17 2004 21:44:50 on modular [Seed = 3451870321] ------------------------------------- Maximal Equation Order with defining polynomial x^3 - 2 over its ground order Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam183-108.student.harvard.edu. (140.247.183.108) Time: Tue Feb 17 21:45:38 2004 Input: PQ := RationalField(); N := NumberField(x^3 -2); P := RingOfIntegers(N); print P; Output: Magma V2.10-6 Tue Feb 17 2004 21:45:35 on modular [Seed = 4270616367] ------------------------------------- >> PQ := RationalField(); ^ Runtime error in 'Name': Bad argument types >> N := NumberField(x^3 -2); ^ User error: Identifier 'x' has not been declared or assigned >> P := RingOfIntegers(N); ^ User error: Identifier 'N' has not been declared or assigned >> print P;; ^ User error: Identifier 'P' has not been declared or assigned Total time: 2.939 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam183-108.student.harvard.edu. (140.247.183.108) Time: Tue Feb 17 21:46:40 2004 Input: PQ := PolynomialRing(RationalField()); N := NumberField(x^2 - 3); P := RingOfIntegers(N); print P; Output: Magma V2.10-6 Tue Feb 17 2004 21:46:37 on modular [Seed = 4102448871] ------------------------------------- Maximal Equation Order with defining polynomial x^2 - 3 over its ground order Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam183-108.student.harvard.edu. (140.247.183.108) Time: Tue Feb 17 21:47:01 2004 Input: PQ := PolynomialRing(RationalField()); N := NumberField(x^2 + 3); P := RingOfIntegers(N); print P; Output: Magma V2.10-6 Tue Feb 17 2004 21:46:58 on modular [Seed = 3986653137] ------------------------------------- Maximal Order of Equation Order with defining polynomial x^2 + 3 over its ground order Total time: 2.929 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host roam183-108.student.harvard.edu. (140.247.183.108) Time: Tue Feb 17 21:47:35 2004 Input: PQ := PolynomialRing(RationalField()); N := NumberField(x^3 - 2); P := RingOfIntegers(N); print P; Output: Magma V2.10-6 Tue Feb 17 2004 21:47:32 on modular [Seed = 3817959865] ------------------------------------- Maximal Equation Order with defining polynomial x^3 - 2 over its ground order Total time: 2.919 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam183-108.student.harvard.edu. (140.247.183.108) Time: Tue Feb 17 21:56:13 2004 Input: PQ := PolynomialRing(RationalField()); N := NumberField(x^3 - 2); w; P := RingOfIntegers(N); print P; Output: Magma V2.10-6 Tue Feb 17 2004 21:56:10 on modular [Seed = 159096156] ------------------------------------- w Maximal Equation Order with defining polynomial x^3 - 2 over its ground order Total time: 2.979 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam183-108.student.harvard.edu. (140.247.183.108) Time: Tue Feb 17 21:56:29 2004 Input: PQ := PolynomialRing(RationalField()); N := NumberField(x^3 - 2); print w; P := RingOfIntegers(N); print P; Output: Magma V2.10-6 Tue Feb 17 2004 21:56:26 on modular [Seed = 7509061] ------------------------------------- w Maximal Equation Order with defining polynomial x^3 - 2 over its ground order Total time: 2.979 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam183-108.student.harvard.edu. (140.247.183.108) Time: Tue Feb 17 22:01:49 2004 Input: PQ := PolynomialRing(RationalField()); N := NumberField(x^3 - 2); print w^3; P := RingOfIntegers(N); print P; Output: Magma V2.10-6 Tue Feb 17 2004 22:01:46 on modular [Seed = 1512624095] ------------------------------------- 2 Maximal Equation Order with defining polynomial x^3 - 2 over its ground order Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam183-108.student.harvard.edu. (140.247.183.108) Time: Tue Feb 17 22:02:43 2004 Input: PQ := PolynomialRing(RationalField()); N := NumberField(x^3 - 2); print w^2; P := RingOfIntegers(N); print P; Output: Magma V2.10-6 Tue Feb 17 2004 22:02:40 on modular [Seed = 1344456095] ------------------------------------- w^2 Maximal Equation Order with defining polynomial x^3 - 2 over its ground order Total time: 2.929 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam183-108.student.harvard.edu. (140.247.183.108) Time: Tue Feb 17 22:06:42 2004 Input: PQ := PolynomialRing(RationalField()); N := NumberField(x^3 - 2); print w^2; P := MaximalOrder(N); print P; Output: Magma V2.10-6 Tue Feb 17 2004 22:06:39 on modular [Seed = 2098195421] ------------------------------------- w^2 Maximal Equation Order with defining polynomial x^3 - 2 over its ground order Total time: 2.929 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam183-108.student.harvard.edu. (140.247.183.108) Time: Tue Feb 17 22:07:18 2004 Input: PQ := PolynomialRing(RationalField()); N := NumberField(x^2 + 3); print w^2; P := MaximalOrder(N); print P; Output: Magma V2.10-6 Tue Feb 17 2004 22:07:15 on modular [Seed = 1946608264] ------------------------------------- -3 Maximal Order of Equation Order with defining polynomial x^2 + 3 over its ground order Total time: 2.919 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host roam183-108.student.harvard.edu. (140.247.183.108) Time: Tue Feb 17 22:07:47 2004 Input: PQ := PolynomialRing(RationalField()); N := NumberField(x^2 - 3); print w^2; P := MaximalOrder(N); print P; Output: Magma V2.10-6 Tue Feb 17 2004 22:07:44 on modular [Seed = 1780022645] ------------------------------------- 3 Maximal Equation Order with defining polynomial x^2 - 3 over its ground order Total time: 2.939 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam183-108.student.harvard.edu. (140.247.183.108) Time: Tue Feb 17 22:08:36 2004 Input: PQ := PolynomialRing(RationalField()); N := NumberField(x^2 - 3); print w^2; P := IntegerRing(N); print P; Output: Magma V2.10-6 Tue Feb 17 2004 22:08:33 on modular [Seed = 1611855694] ------------------------------------- 3 Maximal Equation Order with defining polynomial x^2 - 3 over its ground order Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam183-108.student.harvard.edu. (140.247.183.108) Time: Tue Feb 17 22:09:07 2004 Input: PQ := PolynomialRing(RationalField()); N := NumberField(x^2 - 3); print w^2; P := IntegerRing(N); print P;print P;print P;print P;print P;print P; Output: Magma V2.10-6 Tue Feb 17 2004 22:09:04 on modular [Seed = 2548367576] ------------------------------------- 3 Maximal Equation Order with defining polynomial x^2 - 3 over its ground order Maximal Equation Order with defining polynomial x^2 - 3 over its ground order Maximal Equation Order with defining polynomial x^2 - 3 over its ground order Maximal Equation Order with defining polynomial x^2 - 3 over its ground order Maximal Equation Order with defining polynomial x^2 - 3 over its ground order Maximal Equation Order with defining polynomial x^2 - 3 over its ground order Total time: 2.939 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam183-108.student.harvard.edu. (140.247.183.108) Time: Tue Feb 17 22:12:27 2004 Input: PQ := PolynomialRing(RationalField()); N := NumberField(x^2 - 3); print w^2; P := IntegerRing(N); IsIntegral(N, w); print P;print P;print P;print P;print P;print P; Output: Magma V2.10-6 Tue Feb 17 2004 22:12:24 on modular [Seed = 2230721667] ------------------------------------- 3 >> IsIntegral(N, w); ^ Runtime error in 'IsIntegral': Bad argument types Argument types given: FldNum, FldNumElt Maximal Equation Order with defining polynomial x^2 - 3 over its ground order Maximal Equation Order with defining polynomial x^2 - 3 over its ground order Maximal Equation Order with defining polynomial x^2 - 3 over its ground order Maximal Equation Order with defining polynomial x^2 - 3 over its ground order Maximal Equation Order with defining polynomial x^2 - 3 over its ground order Maximal Equation Order with defining polynomial x^2 - 3 over its ground order Total time: 2.929 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam183-108.student.harvard.edu. (140.247.183.108) Time: Tue Feb 17 22:12:47 2004 Input: PQ := PolynomialRing(RationalField()); N := NumberField(x^2 - 3); print w^2; P := IntegerRing(N); IsIntegral(w); print P;print P;print P;print P;print P;print P; Output: Magma V2.10-6 Tue Feb 17 2004 22:12:43 on modular [Seed = 3150521231] ------------------------------------- 3 true Maximal Equation Order with defining polynomial x^2 - 3 over its ground order Maximal Equation Order with defining polynomial x^2 - 3 over its ground order Maximal Equation Order with defining polynomial x^2 - 3 over its ground order Maximal Equation Order with defining polynomial x^2 - 3 over its ground order Maximal Equation Order with defining polynomial x^2 - 3 over its ground order Maximal Equation Order with defining polynomial x^2 - 3 over its ground order Total time: 2.979 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam183-108.student.harvard.edu. (140.247.183.108) Time: Tue Feb 17 22:13:16 2004 Input: PQ := PolynomialRing(RationalField()); N := NumberField(x^2 - 3); print w^2; P := IntegerRing(N); IsIntegral(w); IsIntegral(w/2); print P;print P;print P;print P;print P;print P; Output: Magma V2.10-6 Tue Feb 17 2004 22:13:13 on modular [Seed = 2982357479] ------------------------------------- 3 true false Maximal Equation Order with defining polynomial x^2 - 3 over its ground order Maximal Equation Order with defining polynomial x^2 - 3 over its ground order Maximal Equation Order with defining polynomial x^2 - 3 over its ground order Maximal Equation Order with defining polynomial x^2 - 3 over its ground order Maximal Equation Order with defining polynomial x^2 - 3 over its ground order Maximal Equation Order with defining polynomial x^2 - 3 over its ground order Total time: 2.929 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam183-108.student.harvard.edu. (140.247.183.108) Time: Tue Feb 17 22:13:41 2004 Input: PQ := PolynomialRing(RationalField()); N := NumberField(x^2 - 3); print w^2; P := IntegerRing(N); IsIntegral(w); IsIntegral(w/3); print P;print P;print P;print P;print P;print P; Output: Magma V2.10-6 Tue Feb 17 2004 22:13:38 on modular [Seed = 2832871637] ------------------------------------- 3 true false Maximal Equation Order with defining polynomial x^2 - 3 over its ground order Maximal Equation Order with defining polynomial x^2 - 3 over its ground order Maximal Equation Order with defining polynomial x^2 - 3 over its ground order Maximal Equation Order with defining polynomial x^2 - 3 over its ground order Maximal Equation Order with defining polynomial x^2 - 3 over its ground order Maximal Equation Order with defining polynomial x^2 - 3 over its ground order Total time: 2.939 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam183-108.student.harvard.edu. (140.247.183.108) Time: Tue Feb 17 22:14:02 2004 Input: PQ := PolynomialRing(RationalField()); N := NumberField(x^2 - 3); print w^2; P := IntegerRing(N); IsIntegral(w); IsIntegral(2w); IsIntegral(w + 2); IsIntegral(w + 3); IsIntegral(w/3); print P;print P;print P;print P;print P;print P; Output: Magma V2.10-6 Tue Feb 17 2004 22:13:59 on modular [Seed = 3735832246] ------------------------------------- 3 true >> IsIntegral(2w); ^ User error: bad syntax true true false Maximal Equation Order with defining polynomial x^2 - 3 over its ground order Maximal Equation Order with defining polynomial x^2 - 3 over its ground order Maximal Equation Order with defining polynomial x^2 - 3 over its ground order Maximal Equation Order with defining polynomial x^2 - 3 over its ground order Maximal Equation Order with defining polynomial x^2 - 3 over its ground order Maximal Equation Order with defining polynomial x^2 - 3 over its ground order Total time: 2.889 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam183-108.student.harvard.edu. (140.247.183.108) Time: Tue Feb 17 22:14:13 2004 Input: PQ := PolynomialRing(RationalField()); N := NumberField(x^2 - 3); print w^2; P := IntegerRing(N); IsIntegral(w); IsIntegral(2*w); IsIntegral(w + 2); IsIntegral(w + 3); IsIntegral(w/3); print P;print P;print P;print P;print P;print P; Output: Magma V2.10-6 Tue Feb 17 2004 22:14:09 on modular [Seed = 3584511304] ------------------------------------- 3 true true true true false Maximal Equation Order with defining polynomial x^2 - 3 over its ground order Maximal Equation Order with defining polynomial x^2 - 3 over its ground order Maximal Equation Order with defining polynomial x^2 - 3 over its ground order Maximal Equation Order with defining polynomial x^2 - 3 over its ground order Maximal Equation Order with defining polynomial x^2 - 3 over its ground order Maximal Equation Order with defining polynomial x^2 - 3 over its ground order Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam183-108.student.harvard.edu. (140.247.183.108) Time: Tue Feb 17 22:14:35 2004 Input: PQ := PolynomialRing(RationalField()); N := NumberField(x^2 - 3); print w^2; P := IntegerRing(N); IsIntegral(w); IsIntegral(2*w); IsIntegral(w + 2); IsIntegral(w + 3); IsIntegral(w div 3); print P;print P;print P;print P;print P;print P; Output: Magma V2.10-6 Tue Feb 17 2004 22:14:32 on modular [Seed = 3435025483] ------------------------------------- 3 true true true true >> IsIntegral(w div 3); ^ Runtime error in 'div': Bad argument types Argument types given: FldNumElt, FldNumElt Maximal Equation Order with defining polynomial x^2 - 3 over its ground order Maximal Equation Order with defining polynomial x^2 - 3 over its ground order Maximal Equation Order with defining polynomial x^2 - 3 over its ground order Maximal Equation Order with defining polynomial x^2 - 3 over its ground order Maximal Equation Order with defining polynomial x^2 - 3 over its ground order Maximal Equation Order with defining polynomial x^2 - 3 over its ground order Total time: 2.939 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam183-108.student.harvard.edu. (140.247.183.108) Time: Tue Feb 17 22:14:56 2004 Input: PQ := PolynomialRing(RationalField()); N := NumberField(x^2 - 3); print w^2; P := IntegerRing(N); IsIntegral(w); IsIntegral(2*w); IsIntegral(w + 2); IsIntegral(w + 3); IsIntegral(w div 2); IsIntegral(w div 3); print P;print P;print P;print P;print P;print P; Output: Magma V2.10-6 Tue Feb 17 2004 22:14:53 on modular [Seed = 3283180401] ------------------------------------- 3 true true true true >> IsIntegral(w div 2); ^ Runtime error in 'div': Bad argument types Argument types given: FldNumElt, FldNumElt >> IsIntegral(w div 3); ^ Runtime error in 'div': Bad argument types Argument types given: FldNumElt, FldNumElt Maximal Equation Order with defining polynomial x^2 - 3 over its ground order Maximal Equation Order with defining polynomial x^2 - 3 over its ground order Maximal Equation Order with defining polynomial x^2 - 3 over its ground order Maximal Equation Order with defining polynomial x^2 - 3 over its ground order Maximal Equation Order with defining polynomial x^2 - 3 over its ground order Maximal Equation Order with defining polynomial x^2 - 3 over its ground order Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam183-108.student.harvard.edu. (140.247.183.108) Time: Tue Feb 17 22:15:11 2004 Input: PQ := PolynomialRing(RationalField()); N := NumberField(x^2 - 3); print w^2; P := IntegerRing(N); IsIntegral(w); IsIntegral(2*w); IsIntegral(w + 2); IsIntegral(w + 3); IsIntegral(w / 2); IsIntegral(w div 3); print P;print P;print P;print P;print P;print P; Output: Magma V2.10-6 Tue Feb 17 2004 22:15:08 on modular [Seed = 4135874133] ------------------------------------- 3 true true true true false >> IsIntegral(w div 3); ^ Runtime error in 'div': Bad argument types Argument types given: FldNumElt, FldNumElt Maximal Equation Order with defining polynomial x^2 - 3 over its ground order Maximal Equation Order with defining polynomial x^2 - 3 over its ground order Maximal Equation Order with defining polynomial x^2 - 3 over its ground order Maximal Equation Order with defining polynomial x^2 - 3 over its ground order Maximal Equation Order with defining polynomial x^2 - 3 over its ground order Maximal Equation Order with defining polynomial x^2 - 3 over its ground order Total time: 2.939 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam183-108.student.harvard.edu. (140.247.183.108) Time: Tue Feb 17 22:17:23 2004 Input: PQ := PolynomialRing(RationalField()); N := NumberField(x^2 - 3); print w^2; P := IntegerRing(N); IsIntegral(w); IsIntegral(2*w); IsIntegral(w + 1/2); IsIntegral(w + 3); IsIntegral(w / 2); IsIntegral(w div 3); print P;print P;print P;print P;print P;print P; Output: Magma V2.10-6 Tue Feb 17 2004 22:17:20 on modular [Seed = 3969807795] ------------------------------------- 3 true true false true false >> IsIntegral(w div 3); ^ Runtime error in 'div': Bad argument types Argument types given: FldNumElt, FldNumElt Maximal Equation Order with defining polynomial x^2 - 3 over its ground order Maximal Equation Order with defining polynomial x^2 - 3 over its ground order Maximal Equation Order with defining polynomial x^2 - 3 over its ground order Maximal Equation Order with defining polynomial x^2 - 3 over its ground order Maximal Equation Order with defining polynomial x^2 - 3 over its ground order Maximal Equation Order with defining polynomial x^2 - 3 over its ground order Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam183-108.student.harvard.edu. (140.247.183.108) Time: Tue Feb 17 22:17:41 2004 Input: PQ := PolynomialRing(RationalField()); N := NumberField(x^2 - 3); print w^2; P := IntegerRing(N); IsIntegral(w^2); IsIntegral(2*w); IsIntegral(w + 1/2); IsIntegral(w + 3); IsIntegral(w / 2); IsIntegral(w div 3); print P;print P;print P;print P;print P;print P; Output: Magma V2.10-6 Tue Feb 17 2004 22:17:38 on modular [Seed = 3817962158] ------------------------------------- 3 true true false true false >> IsIntegral(w div 3); ^ Runtime error in 'div': Bad argument types Argument types given: FldNumElt, FldNumElt Maximal Equation Order with defining polynomial x^2 - 3 over its ground order Maximal Equation Order with defining polynomial x^2 - 3 over its ground order Maximal Equation Order with defining polynomial x^2 - 3 over its ground order Maximal Equation Order with defining polynomial x^2 - 3 over its ground order Maximal Equation Order with defining polynomial x^2 - 3 over its ground order Maximal Equation Order with defining polynomial x^2 - 3 over its ground order Total time: 2.909 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam183-108.student.harvard.edu. (140.247.183.108) Time: Tue Feb 17 22:21:16 2004 Input: PQ := PolynomialRing(RationalField()); N := NumberField(x^2 - 3); print w^2; P := IntegerRing(N); Trace(1 + w + w^2); IsIntegral(w^2); IsIntegral(2*w); IsIntegral(w + 1/2); IsIntegral(w + 3); IsIntegral(w / 2); IsIntegral(w div 3); print P;print P;print P;print P;print P;print P; Output: Magma V2.10-6 Tue Feb 17 2004 22:21:13 on modular [Seed = 777827367] ------------------------------------- 3 8 true true false true false >> IsIntegral(w div 3); ^ Runtime error in 'div': Bad argument types Argument types given: FldNumElt, FldNumElt Maximal Equation Order with defining polynomial x^2 - 3 over its ground order Maximal Equation Order with defining polynomial x^2 - 3 over its ground order Maximal Equation Order with defining polynomial x^2 - 3 over its ground order Maximal Equation Order with defining polynomial x^2 - 3 over its ground order Maximal Equation Order with defining polynomial x^2 - 3 over its ground order Maximal Equation Order with defining polynomial x^2 - 3 over its ground order Total time: 2.999 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam183-108.student.harvard.edu. (140.247.183.108) Time: Tue Feb 17 22:21:52 2004 Input: PQ := PolynomialRing(RationalField()); N := NumberField(x^2 - 3); print w^2; P := IntegerRing(N); Trace(1 + w + w^2); Trace(1); Trace(w); Trace(w^2); IsIntegral(w^2); IsIntegral(2*w); IsIntegral(w + 1/2); IsIntegral(w + 3); IsIntegral(w / 2); IsIntegral(w div 3); print P;print P;print P;print P;print P;print P; Output: Magma V2.10-6 Tue Feb 17 2004 22:21:49 on modular [Seed = 927313242] ------------------------------------- 3 8 1 0 6 true true false true false >> IsIntegral(w div 3); ^ Runtime error in 'div': Bad argument types Argument types given: FldNumElt, FldNumElt Maximal Equation Order with defining polynomial x^2 - 3 over its ground order Maximal Equation Order with defining polynomial x^2 - 3 over its ground order Maximal Equation Order with defining polynomial x^2 - 3 over its ground order Maximal Equation Order with defining polynomial x^2 - 3 over its ground order Maximal Equation Order with defining polynomial x^2 - 3 over its ground order Maximal Equation Order with defining polynomial x^2 - 3 over its ground order Total time: 3.029 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam183-108.student.harvard.edu. (140.247.183.108) Time: Tue Feb 17 22:29:30 2004 Input: PQ := PolynomialRing(RationalField()); N := NumberField(x^2 - 3); print w^2; P := IntegerRing(N); Basis(P); Output: Magma V2.10-6 Tue Feb 17 2004 22:29:27 on modular [Seed = 226464058] ------------------------------------- 3 [ P.1, P.2 ] Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam183-108.student.harvard.edu. (140.247.183.108) Time: Tue Feb 17 22:30:09 2004 Input: PQ := PolynomialRing(RationalField()); N := NumberField(x^2 + 3); print w^2; P := IntegerRing(N); Basis(P); Output: Magma V2.10-6 Tue Feb 17 2004 22:30:06 on modular [Seed = 493846787] ------------------------------------- -3 [ P.1, P.2 ] Total time: 3.019 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host roam183-108.student.harvard.edu. (140.247.183.108) Time: Tue Feb 17 22:30:26 2004 Input: PQ := PolynomialRing(RationalField()); N := NumberField(x^3 + 2); print w^2; P := IntegerRing(N); Basis(P); Output: Magma V2.10-6 Tue Feb 17 2004 22:30:23 on modular [Seed = 1712650761] ------------------------------------- w^2 [ P.1, P.2, P.3 ] Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam183-108.student.harvard.edu. (140.247.183.108) Time: Tue Feb 17 22:30:45 2004 Input: PQ := PolynomialRing(RationalField()); N := NumberField(x^3 + 2); print w^2; P := IntegerRing(N); Basis(P); P.1; P.2; Output: Magma V2.10-6 Tue Feb 17 2004 22:30:43 on modular [Seed = 1864233772] ------------------------------------- w^2 [ P.1, P.2, P.3 ] P.1 P.2 Total time: 2.909 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam183-108.student.harvard.edu. (140.247.183.108) Time: Tue Feb 17 22:31:39 2004 Input: PQ := PolynomialRing(RationalField()); N := NumberField(x^3 + 2); print w^2; P := IntegerRing(N); Basis(P); IntegralBasis(N); Output: Magma V2.10-6 Tue Feb 17 2004 22:31:36 on modular [Seed = 2013979840] ------------------------------------- w^2 [ P.1, P.2, P.3 ] [ 1, w, w^2 ] Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam183-108.student.harvard.edu. (140.247.183.108) Time: Tue Feb 17 22:31:58 2004 Input: PQ := PolynomialRing(RationalField()); N := NumberField(x^3 + 2); print w^2; P := IntegerRing(N); Basis(P); print w^2; IntegralBasis(N); Output: Magma V2.10-6 Tue Feb 17 2004 22:31:55 on modular [Seed = 1110499017] ------------------------------------- w^2 [ P.1, P.2, P.3 ] w^2 [ 1, w, w^2 ] Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam183-108.student.harvard.edu. (140.247.183.108) Time: Tue Feb 17 22:32:25 2004 Input: PQ := PolynomialRing(RationalField()); N := NumberField(x^3 - 2); print w^2; P := IntegerRing(N); Basis(P); print w^2; IntegralBasis(N); Output: Magma V2.10-6 Tue Feb 17 2004 22:32:22 on modular [Seed = 1329451945] ------------------------------------- w^2 [ P.1, P.2, P.3 ] w^2 [ 1, w, w^2 ] Total time: 2.929 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam183-108.student.harvard.edu. (140.247.183.108) Time: Tue Feb 17 22:32:42 2004 Input: PQ := PolynomialRing(RationalField()); N := NumberField(x^2 - 3); print w^2; P := IntegerRing(N); Basis(P); print w^2; IntegralBasis(N); Output: Magma V2.10-6 Tue Feb 17 2004 22:32:39 on modular [Seed = 1479197871] ------------------------------------- 3 [ P.1, P.2 ] 3 [ 1, w ] Total time: 2.929 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam183-108.student.harvard.edu. (140.247.183.108) Time: Tue Feb 17 22:32:58 2004 Input: PQ := PolynomialRing(RationalField()); N := NumberField(x^2 + 3); print w^2; P := IntegerRing(N); Basis(P); print w^2; IntegralBasis(N); Output: Magma V2.10-6 Tue Feb 17 2004 22:32:55 on modular [Seed = 2714975590] ------------------------------------- -3 [ P.1, P.2 ] -3 [ 1, 1/2*(w + 1) ] Total time: 2.959 seconds, Total memory usage: 1.89MB ************** MAGMA ***************** Host roam183-108.student.harvard.edu. (140.247.183.108) Time: Tue Feb 17 22:33:48 2004 Input: PQ := PolynomialRing(RationalField()); N := NumberField(x^2 + 2); IntegralBasis(N); Output: Magma V2.10-6 Tue Feb 17 2004 22:33:45 on modular [Seed = 2883139218] ------------------------------------- [ 1, w ] Total time: 2.909 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host roam183-108.student.harvard.edu. (140.247.183.108) Time: Tue Feb 17 22:34:01 2004 Input: PQ := PolynomialRing(RationalField()); N := NumberField(x^3 + 2); IntegralBasis(N); Output: Magma V2.10-6 Tue Feb 17 2004 22:33:58 on modular [Seed = 3032885682] ------------------------------------- [ 1, w, w^2 ] Total time: 2.979 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host h24-81-108-53.vc.shawcable.net. (24.81.108.53) Time: Wed Feb 18 02:50:41 2004 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: Magma V2.10-6 Wed Feb 18 2004 02:50:37 on modular [Seed = 826435679] ------------------------------------- Replace this by some code, then click [PARI] or [MAGMA]! Total time: 2.929 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host h24-81-108-53.vc.shawcable.net. (24.81.108.53) Time: Wed Feb 18 02:53:01 2004 Input: E=EllipticCurve([1,2]); E=BaseChange(E, GF(17)); Order(E); Output: Magma V2.10-6 Wed Feb 18 2004 02:52:58 on modular [Seed = 1061971654] ------------------------------------- >> E=EllipticCurve([1,2]); ^ User error: Identifier 'E' has not been declared or assigned >> E=BaseChange(E, GF(17)); ^ User error: Identifier 'E' has not been declared or assigned >> Order(E);; ^ User error: Identifier 'E' has not been declared or assigned Total time: 3.059 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host h24-81-108-53.vc.shawcable.net. (24.81.108.53) Time: Wed Feb 18 02:53:19 2004 Input: E:=EllipticCurve([1,2]); E:=BaseChange(E, GF(17)); Order(E); Output: Magma V2.10-6 Wed Feb 18 2004 02:53:16 on modular [Seed = 108355529] ------------------------------------- >> E:=BaseChange(E, GF(17)); ^ Runtime error in 'BaseChange': Coercion of equations is not possible >> Order(E);; ^ Runtime error in 'Order': Algorithm does not work for this ring Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host h24-81-108-53.vc.shawcable.net. (24.81.108.53) Time: Wed Feb 18 02:53:46 2004 Input: E:=EllipticCurve([1,2]); E:=ChangeRing(E, GF(17)); Order(E); Output: Magma V2.10-6 Wed Feb 18 2004 02:53:43 on modular [Seed = 274942516] ------------------------------------- 24 Total time: 3.029 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host h24-81-108-53.vc.shawcable.net. (24.81.108.53) Time: Wed Feb 18 02:54:21 2004 Input: E:=EllipticCurve([1,2]); E:=ChangeRing(E, GF(19)); Order(E); Output: Magma V2.10-6 Wed Feb 18 2004 02:54:18 on modular [Seed = 527189270] ------------------------------------- 12 Total time: 2.899 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host irmasrv3.u-strasbg.fr. (130.79.4.200) Time: Wed Feb 18 03:42:46 2004 Input: P:=PolynomialRing(IntegerRing(),2); f0:=2*(x^2+y^2)+x-y-16; f1:=6*(x^4+y^4)+2*(x^3-y^3)+x-y-192; f2:=40*(x^6+y^6)+11*(x^5-y^5)+5*(x^3-y^3)+4*(x-y)-5120; I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Output: Magma V2.10-6 Wed Feb 18 2004 03:42:43 on modular [Seed = 2314923049] ------------------------------------- [ x^2 + 8*x + 232315781992*y^3 + 5693103461359*y^2 - 929263127976*y - 22772413845440, x*y + 2*x + 65228091924*y^3 + 4892924850951*y^2 - 260912367698*y - 19571699403808, 15*x + 75708865464*y^3 + 2052062158236*y^2 - 302835461871*y - 8208248632944, 4*y^4 + 30002386104*y^3 + 1969993642436*y^2 - 120009544416*y - 7879974569808, 388922698520*y^3 + 3500304286680*y^2 - 1555690794080*y - 14001217146720, 5833840477800*y^2 - 23335361911200 ] Total time: 3.039 seconds, Total memory usage: 1.93MB ************** MAGMA ***************** Host unallocated.star.net.uk. (62.173.118.42) Time: Wed Feb 18 04:48:44 2004 Input: integrate( x ) Output: Magma V2.10-6 Wed Feb 18 2004 04:48:40 on modular [Seed = 1796743093] ------------------------------------- >> integrate( x ); ^ User error: Identifier 'x' has not been declared or assigned Total time: 3.059 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host irmasrv3.u-strasbg.fr. (130.79.4.200) Time: Wed Feb 18 05:26:52 2004 Input: P:=PolynomialRing(IntegerRing(),2); f0:=2*(x^2+y^2)+x-y-16; f1:=6*(x^4+y^4)+2*(x^3-y^3)+x-y-192; f2:=40*(x^6+y^6)+11*(x^5-y^5)+5*(x^3-y^3)+4*(x-y)-5120; f3:=630*x^8+630*y^8-322560+151*x^7-151*y^7+70*x^5-70*y^5+49*x^3-49*y^3+45*x-45*y; I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Output: Magma V2.10-6 Wed Feb 18 2004 05:26:49 on modular [Seed = 2498226523] ------------------------------------- [ x^2 + 8*x + 31*y^2 - 8*y - 128, x*y + 2*x + 4*y^3 + 111*y^2 - 18*y - 448, 15*x + 60*y^2 - 15*y - 240, 4*y^4 + 20*y^2 - 144, 8*y^3 + 72*y^2 - 32*y - 288, 120*y^2 - 480 ] Total time: 2.979 seconds, Total memory usage: 1.93MB ************** MAGMA ***************** Host aula-a-siee03.uab.es. (158.109.66.3) Time: Wed Feb 18 06:02:30 2004 Input: Floor(3.141592); Output: Magma V2.10-6 Wed Feb 18 2004 06:02:27 on modular [Seed = 843134038] ------------------------------------- 3 Total time: 3.029 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-a-siee03.uab.es. (158.109.66.3) Time: Wed Feb 18 06:04:37 2004 Input: x:=2; y:=3; assigned x; assigned y; Output: Magma V2.10-6 Wed Feb 18 2004 06:04:33 on modular [Seed = 125043169] ------------------------------------- true true Total time: 3.409 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-a-siee03.uab.es. (158.109.66.3) Time: Wed Feb 18 06:05:04 2004 Input: x:=2; y:=3; assigned x; assigned y; delete x; assigned x; assigned y; Output: Magma V2.10-6 Wed Feb 18 2004 06:05:01 on modular [Seed = 158994419] ------------------------------------- true true false true Total time: 3.179 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-a-siee03.uab.es. (158.109.66.3) Time: Wed Feb 18 06:05:17 2004 Input: x:=2; y:=3; assigned x; assigned y; x; delete x; assigned x; assigned y; Output: Magma V2.10-6 Wed Feb 18 2004 06:05:14 on modular [Seed = 274929373] ------------------------------------- true true 2 false true Total time: 3.189 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-a-siee03.uab.es. (158.109.66.3) Time: Wed Feb 18 06:07:25 2004 Input: x:=2; y:=3; assigned x; assigned y; x; print y; delete x; assigned x; assigned y; Output: Magma V2.10-6 Wed Feb 18 2004 06:07:22 on modular [Seed = 1662018606] ------------------------------------- true true 2 3 false true Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host irmasrv3.u-strasbg.fr. (130.79.4.200) Time: Wed Feb 18 06:07:40 2004 Input: P:=PolynomialRing(IntegerRing(),2); f0:=2*(x^2+y^2)+x-y-16; f1:=6*(x^4+y^4)+2*(x^3-y^3)+x-y-192; f2:=40*(x^6+y^6)+11*(x^5-y^5)+5*(x^3-y^3)+4*(x-y)-5120; f3:=630*x^8+630*y^8-322560+151*x^7-151*y^7+70*x^5-70*y^5+49*x^3-49*y^3+45*x-45*y; I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Output: Magma V2.10-6 Wed Feb 18 2004 06:07:37 on modular [Seed = 1780051252] ------------------------------------- [ x^2 + 8*x + 31*y^2 - 8*y - 128, x*y + 2*x + 4*y^3 + 111*y^2 - 18*y - 448, 15*x + 60*y^2 - 15*y - 240, 4*y^4 + 20*y^2 - 144, 8*y^3 + 72*y^2 - 32*y - 288, 120*y^2 - 480 ] Total time: 2.959 seconds, Total memory usage: 1.93MB ************** MAGMA ***************** Host irmasrv3.u-strasbg.fr. (130.79.4.200) Time: Wed Feb 18 06:08:22 2004 Input: P:=PolynomialRing(IntegerRing(),2); f0:=2*(x^2+y^2)+x-y-16; f1:=6*(x^4+y^4)+2*(x^3-y^3)+x-y-192; f2:=40*(x^6+y^6)+11*(x^5-y^5)+5*(x^3-y^3)+4*(x-y)-5120; f3:=645120*x^8+645120*y^8-330303015+2251776*x^7-154624*y^7-1075200*x^5-71680*y^5+ 182784*x^3-50176*y^3+44280*x-46080*y+1835008*x^6-1003520*x^4+116032*x^2; I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Output: Magma V2.10-6 Wed Feb 18 2004 06:08:19 on modular [Seed = 1895986933] ------------------------------------- [ x^2 + 8*x + y^2 + 14549527*y + 2648015362, x*y + 2*x + 14549533*y + 14695030346, 15*x + 14549520*y + 14695030350, y^3 + 9*y^2 + 14549531*y + 11683276569, 15*y^2 + 3011753685, 14549535*y + 5659769115, 15058768725 ] Total time: 2.969 seconds, Total memory usage: 1.93MB ************** MAGMA ***************** Host aula-a-siee03.uab.es. (158.109.66.3) Time: Wed Feb 18 06:08:35 2004 Input: x:=2; y:=3; assigned x; assigned y; x; print y; x and y; Output: Magma V2.10-6 Wed Feb 18 2004 06:08:32 on modular [Seed = 2014019567] ------------------------------------- true true 2 3 >> x and y;; ^ Runtime error: Expected a logical for the 'and' operator Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-a-siee03.uab.es. (158.109.66.3) Time: Wed Feb 18 06:09:01 2004 Input: x:=true; y:=false; assigned x; assigned y; x; print y; x and y; Output: Magma V2.10-6 Wed Feb 18 2004 06:08:58 on modular [Seed = 1312639395] ------------------------------------- true true true false false Total time: 2.939 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-a-siee03.uab.es. (158.109.66.3) Time: Wed Feb 18 06:09:12 2004 Input: x:=true; y:=false; assigned x; assigned y; x; print y; x or y; Output: Magma V2.10-6 Wed Feb 18 2004 06:09:09 on modular [Seed = 1428574887] ------------------------------------- true true true false true Total time: 3.039 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-a-siee03.uab.es. (158.109.66.3) Time: Wed Feb 18 06:09:57 2004 Input: GCD(12,4); Output: Magma V2.10-6 Wed Feb 18 2004 06:09:54 on modular [Seed = 1529369470] ------------------------------------- 4 Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-a-siee03.uab.es. (158.109.66.3) Time: Wed Feb 18 06:10:12 2004 Input: GCD(12,4); GCD(120,2); Output: Magma V2.10-6 Wed Feb 18 2004 06:10:09 on modular [Seed = 2883101597] ------------------------------------- 4 2 Total time: 3.029 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-a-siee03.uab.es. (158.109.66.3) Time: Wed Feb 18 06:10:40 2004 Input: GCD(12,4); GCD(120,2); x:=[1,2,3,6,3]; Output: Magma V2.10-6 Wed Feb 18 2004 06:10:37 on modular [Seed = 2965616826] ------------------------------------- 4 2 Total time: 3.019 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-a-siee03.uab.es. (158.109.66.3) Time: Wed Feb 18 06:10:50 2004 Input: GCD(12,4); GCD(120,2); x:=[1,2,3,6,3]; x; Output: Magma V2.10-6 Wed Feb 18 2004 06:10:47 on modular [Seed = 2280951703] ------------------------------------- 4 2 [ 1, 2, 3, 6, 3 ] Total time: 2.999 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-a-siee03.uab.es. (158.109.66.3) Time: Wed Feb 18 06:11:48 2004 Input: GCD(12,4); GCD(120,2); x:=[1,2,3,6,3]; x; Sort x; Output: Magma V2.10-6 Wed Feb 18 2004 06:11:45 on modular [Seed = 2398979800] ------------------------------------- 4 2 [ 1, 2, 3, 6, 3 ] >> Sort x;; ^ User error: bad syntax Total time: 2.989 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-a-siee03.uab.es. (158.109.66.3) Time: Wed Feb 18 06:12:02 2004 Input: GCD(12,4); GCD(120,2); x:=[1,2,3,6,3]; x; Sort (x); Output: Magma V2.10-6 Wed Feb 18 2004 06:11:59 on modular [Seed = 2514918861] ------------------------------------- 4 2 [ 1, 2, 3, 6, 3 ] [ 1, 2, 3, 3, 6 ] Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-a-siee03.uab.es. (158.109.66.3) Time: Wed Feb 18 06:12:23 2004 Input: GCD(12,4); GCD(120,2); x:=[1,2,3,6,3]; x; Sort (x); Min (x); Output: Magma V2.10-6 Wed Feb 18 2004 06:12:20 on modular [Seed = 2615710504] ------------------------------------- 4 2 [ 1, 2, 3, 6, 3 ] [ 1, 2, 3, 3, 6 ] 1 1 Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-a-siee03.uab.es. (158.109.66.3) Time: Wed Feb 18 06:12:51 2004 Input: GCD(12,4); GCD(120,2); x:=[1,2,3,6,3,6]; x; Sort (x); Min (x); Max (x); Output: Magma V2.10-6 Wed Feb 18 2004 06:12:48 on modular [Seed = 3801213557] ------------------------------------- 4 2 [ 1, 2, 3, 6, 3, 6 ] [ 1, 2, 3, 3, 6, 6 ] 1 1 6 4 Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host irmasrv3.u-strasbg.fr. (130.79.4.200) Time: Wed Feb 18 06:13:23 2004 Input: P:=PolynomialRing(IntegerRing(),2); f0:=2*(x^2+y^2)+x-y-16; f1:=6*(x^4+y^4)+2*(x^3-y^3)+x-y-192; f2:=40*(x^6+y^6)+11*(x^5-y^5)+5*(x^3-y^3)+4*(x-y)-5120; f3:=630*x^8+630*y^8-322560+151*x^7-151*y^7+70*x^5-70*y^5+49*x^3-49*y^3+45*x-45*y; I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Output: Magma V2.10-6 Wed Feb 18 2004 06:13:20 on modular [Seed = 3919241502] ------------------------------------- [ x^2 + 8*x + 31*y^2 - 8*y - 128, x*y + 2*x + 4*y^3 + 111*y^2 - 18*y - 448, 15*x + 60*y^2 - 15*y - 240, 4*y^4 + 20*y^2 - 144, 8*y^3 + 72*y^2 - 32*y - 288, 120*y^2 - 480 ] Total time: 3.009 seconds, Total memory usage: 1.93MB ************** MAGMA ***************** Host irmasrv3.u-strasbg.fr. (130.79.4.200) Time: Wed Feb 18 06:13:49 2004 Input: P:=PolynomialRing(IntegerRing(),2); f0:=2*(x^2+y^2)+x-y-16; f1:=6*(x^4+y^4)+2*(x^3-y^3)+x-y-192; f2:=40*(x^6+y^6)+11*(x^5-y^5)+5*(x^3-y^3)+4*(x-y)-5120; f3:=645120*x^8+645120*y^8-330303015+2251776*x^7-154624*y^7-1075200*x^5-71680*y^5+ 182784*x^3-50176*y^3+44280*x-46080*y+1835008*x^6-1003520*x^4+116032*x^2; I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Output: Magma V2.10-6 Wed Feb 18 2004 06:13:46 on modular [Seed = 4035180605] ------------------------------------- [ x^2 + 8*x + y^2 + 14549527*y + 2648015362, x*y + 2*x + 14549533*y + 14695030346, 15*x + 14549520*y + 14695030350, y^3 + 9*y^2 + 14549531*y + 11683276569, 15*y^2 + 3011753685, 14549535*y + 5659769115, 15058768725 ] Total time: 2.999 seconds, Total memory usage: 1.93MB ************** MAGMA ***************** Host irmasrv3.u-strasbg.fr. (130.79.4.200) Time: Wed Feb 18 06:15:21 2004 Input: P:=PolynomialRing(IntegerRing(),2); f0:=2*(x^2+y^2)+x-y-16; f1:=6*(x^4+y^4)+2*(x^3-y^3)+x-y-192; f2:=40*(x^6+y^6)+11*(x^5-y^5)+5*(x^3-y^3)+4*(x-y)-5120; f3:=645120*x^8+645120*y^8-330303015+2251776*x^7-154624*y^7-1075200*x^5-71680*y^5+ 182784*x^3-50176*y^3+44280*x-46080*y+1835008*x^6-1003520*x^4+116032*x^2; I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Factorization(14549535); Factorization(15058768725); Output: Magma V2.10-6 Wed Feb 18 2004 06:15:18 on modular [Seed = 3249719456] ------------------------------------- [ x^2 + 8*x + y^2 + 14549527*y + 2648015362, x*y + 2*x + 14549533*y + 14695030346, 15*x + 14549520*y + 14695030350, y^3 + 9*y^2 + 14549531*y + 11683276569, 15*y^2 + 3011753685, 14549535*y + 5659769115, 15058768725 ] [ <3, 2>, <5, 1>, <7, 1>, <11, 1>, <13, 1>, <17, 1>, <19, 1> ] [ <3, 4>, <5, 2>, <7, 1>, <11, 1>, <13, 1>, <17, 1>, <19, 1>, <23, 1> ] Total time: 3.039 seconds, Total memory usage: 1.93MB ************** MAGMA ***************** Host aula-a-siee03.uab.es. (158.109.66.3) Time: Wed Feb 18 06:15:39 2004 Input: GCD(12,4); GCD(120,2); x:=[1,2,3,6,3,6]; x; Sort (x); min,pos:=Min (x); Max (x); Output: Magma V2.10-6 Wed Feb 18 2004 06:15:36 on modular [Seed = 3367748023] ------------------------------------- 4 2 [ 1, 2, 3, 6, 3, 6 ] [ 1, 2, 3, 3, 6, 6 ] 6 4 Total time: 2.939 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-a-siee03.uab.es. (158.109.66.3) Time: Wed Feb 18 06:15:51 2004 Input: GCD(12,4); GCD(120,2); x:=[1,2,3,6,3,6]; x; Sort (x); min,pos:=Min (x); min; pos; Max (x); Output: Magma V2.10-6 Wed Feb 18 2004 06:15:48 on modular [Seed = 3752646300] ------------------------------------- 4 2 [ 1, 2, 3, 6, 3, 6 ] [ 1, 2, 3, 3, 6, 6 ] 1 1 6 4 Total time: 3.029 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host irmasrv3.u-strasbg.fr. (130.79.4.200) Time: Wed Feb 18 06:17:16 2004 Input: P:=PolynomialRing(IntegerRing(),2); f0:=2*(x^2+y^2)+x-y-16; f1:=6*(x^4+y^4)+2*(x^3-y^3)+x-y-192; f2:=40*(x^6+y^6)+11*(x^5-y^5)+5*(x^3-y^3)+4*(x-y)-5120; f3:=645120*x^8+645120*y^8-330303015+2251776*x^7-154624*y^7-1075200*x^5-71680*y^5+ 182784*x^3-50176*y^3+44280*x-46080*y+1835008*x^6-1003520*x^4+116032*x^2; I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Factorization(14549535); Factorization(15058768725); Bn:=GroebnerBasis(ChangeRing(I,GF(11))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(11^2))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(13))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(13^2))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(17))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(17^2))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(19))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(19^2))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(23))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(23^2))); Bn; Output: Magma V2.10-6 Wed Feb 18 2004 06:17:13 on modular [Seed = 693772472] ------------------------------------- [ x^2 + 8*x + y^2 + 14549527*y + 2648015362, x*y + 2*x + 14549533*y + 14695030346, 15*x + 14549520*y + 14695030350, y^3 + 9*y^2 + 14549531*y + 11683276569, 15*y^2 + 3011753685, 14549535*y + 5659769115, 15058768725 ] [ <3, 2>, <5, 1>, <7, 1>, <11, 1>, <13, 1>, <17, 1>, <19, 1> ] [ <3, 4>, <5, 2>, <7, 1>, <11, 1>, <13, 1>, <17, 1>, <19, 1>, <23, 1> ] [ x + 10*y, y^2 + 7 ] [ x + 10*y, y^2 + 7 ] [ x + 12*y, y^2 + 9 ] [ x + 12*y, y^2 + 9 ] [ x + 16*y, y^2 + 13 ] [ x + 16*y, y^2 + 13 ] [ x + 18*y, y^2 + 15 ] [ x + 18*y, y^2 + 15 ] [ x + 21, y + 21 ] [ x + 21, y + 21 ] Total time: 3.129 seconds, Total memory usage: 2.23MB ************** MAGMA ***************** Host aula-a-siee03.uab.es. (158.109.66.3) Time: Wed Feb 18 06:17:32 2004 Input: x:=[1,2,3,6,3,6]; x; min,pos:=Min (x); min; pos; print "hola"; Output: Magma V2.10-6 Wed Feb 18 2004 06:17:29 on modular [Seed = 575744963] ------------------------------------- [ 1, 2, 3, 6, 3, 6 ] 1 1 hola Total time: 3.049 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-a-siee03.uab.es. (158.109.66.3) Time: Wed Feb 18 06:18:54 2004 Input: x:=[1,2,3,6,3,6]; x; y:=true; min,pos:=Min (x); min; pos; print "hola"; if y then print x+2; Output: Magma V2.10-6 Wed Feb 18 2004 06:18:51 on modular [Seed = 1028536078] ------------------------------------- [ 1, 2, 3, 6, 3, 6 ] 1 1 hola User error: syntax error at end of input Total time: 3.049 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-a-siee03.uab.es. (158.109.66.3) Time: Wed Feb 18 06:19:07 2004 Input: x:=[1,2,3,6,3,6]; x; y:=true; min,pos:=Min (x); min; pos; print "hola"; if y then print (x+2); Output: Magma V2.10-6 Wed Feb 18 2004 06:19:04 on modular [Seed = 910507062] ------------------------------------- [ 1, 2, 3, 6, 3, 6 ] 1 1 hola User error: syntax error at end of input Total time: 2.999 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host irmasrv3.u-strasbg.fr. (130.79.4.200) Time: Wed Feb 18 06:19:27 2004 Input: P:=PolynomialRing(IntegerRing(),2); f0:=2*(x^2+y^2)+x-y-16; f1:=6*(x^4+y^4)+2*(x^3-y^3)+x-y-192; f2:=1280*x^6+1280*y^6+2944*x^5-352*y^5-560*x^3-160*y^3+146*x-128*y+2160*x^4-600*x^2 -163825; f3:=645120*x^8+645120*y^8-330303015+2251776*x^7-154624*y^7-1075200*x^5-71680*y^5+ 182784*x^3-50176*y^3+44280*x-46080*y+1835008*x^6-1003520*x^4+116032*x^2; I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Output: Magma V2.10-6 Wed Feb 18 2004 06:19:24 on modular [Seed = 259786011] ------------------------------------- [ x^2 + 23*x + y^2 + 6412*y + 643492, x*y + 2*x + 6433*y + 643496, 45*x + 6390*y + 643500, y^3 + 9*y^2 + 6431*y + 643464, 15*y^2 + 765705, 6435*y + 643500, 765765 ] Total time: 3.049 seconds, Total memory usage: 1.93MB ************** MAGMA ***************** Host irmasrv3.u-strasbg.fr. (130.79.4.200) Time: Wed Feb 18 06:20:33 2004 Input: P:=PolynomialRing(IntegerRing(),2); f0:=2*(x^2+y^2)+x-y-16; f1:=6*(x^4+y^4)+2*(x^3-y^3)+x-y-192; f2:=1280*x^6+1280*y^6+2944*x^5-352*y^5-560*x^3-160*y^3+146*x-128*y+2160*x^4-600*x^2 -163825; f3:=645120*x^8+645120*y^8-330303015+2251776*x^7-154624*y^7-1075200*x^5-71680*y^5+ 182784*x^3-50176*y^3+44280*x-46080*y+1835008*x^6-1003520*x^4+116032*x^2; I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Factorization(6435); Factorization(765765); Output: Magma V2.10-6 Wed Feb 18 2004 06:20:30 on modular [Seed = 527177033] ------------------------------------- [ x^2 + 23*x + y^2 + 6412*y + 643492, x*y + 2*x + 6433*y + 643496, 45*x + 6390*y + 643500, y^3 + 9*y^2 + 6431*y + 643464, 15*y^2 + 765705, 6435*y + 643500, 765765 ] [ <3, 2>, <5, 1>, <11, 1>, <13, 1> ] [ <3, 2>, <5, 1>, <7, 1>, <11, 1>, <13, 1>, <17, 1> ] Total time: 3.159 seconds, Total memory usage: 1.93MB ************** MAGMA ***************** Host irmasrv3.u-strasbg.fr. (130.79.4.200) Time: Wed Feb 18 06:21:09 2004 Input: P:=PolynomialRing(IntegerRing(),2); f0:=2*(x^2+y^2)+x-y-16; f1:=6*(x^4+y^4)+2*(x^3-y^3)+x-y-192; f2:=1280*x^6+1280*y^6+2944*x^5-352*y^5-560*x^3-160*y^3+146*x-128*y+2160*x^4-600*x^2 -163825; f3:=645120*x^8+645120*y^8-330303015+2251776*x^7-154624*y^7-1075200*x^5-71680*y^5+ 182784*x^3-50176*y^3+44280*x-46080*y+1835008*x^6-1003520*x^4+116032*x^2; I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Factorization(6435); Factorization(765765); Bn:=GroebnerBasis(ChangeRing(I,GF(11))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(11^2))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(13))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(13^2))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(17))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(17^2))); Bn; Output: Magma V2.10-6 Wed Feb 18 2004 06:21:05 on modular [Seed = 1746625249] ------------------------------------- [ x^2 + 23*x + y^2 + 6412*y + 643492, x*y + 2*x + 6433*y + 643496, 45*x + 6390*y + 643500, y^3 + 9*y^2 + 6431*y + 643464, 15*y^2 + 765705, 6435*y + 643500, 765765 ] [ <3, 2>, <5, 1>, <11, 1>, <13, 1> ] [ <3, 2>, <5, 1>, <7, 1>, <11, 1>, <13, 1>, <17, 1> ] [ x + 10*y, y^2 + 7 ] [ x + 10*y, y^2 + 7 ] [ x + 12*y, y^2 + 9 ] [ x + 12*y, y^2 + 9 ] [ x + 15, y + 15 ] [ x + 15, y + 15 ] Total time: 3.049 seconds, Total memory usage: 2.23MB ************** MAGMA ***************** Host irmasrv3.u-strasbg.fr. (130.79.4.200) Time: Wed Feb 18 06:22:03 2004 Input: P:=PolynomialRing(IntegerRing(),2); f0:=2*(x^2+y^2)+x-y-16; f1:=6*(x^4+y^4)+2*(x^3-y^3)+x-y-192; f2:=1280*x^6+1280*y^6+2944*x^5-352*y^5-560*x^3-160*y^3+146*x-128*y+2160*x^4-600*x^2 -163825; f3:=645120*x^8+645120*y^8-330290415+12288*x^7-154624*y^7+1102080*x^5-71680*y^5- 264768*x^3-50176*y^3+55080*x-46080*y-777728*x^6+1536640*x^4-406112*x^2; I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Output: Magma V2.10-6 Wed Feb 18 2004 06:22:00 on modular [Seed = 1645308050] ------------------------------------- [ x^2 + 248*x + y^2 + 6187*y + 643492, x*y + 317*x + 6118*y + 2175026, 495*x + 5940*y + 1409265, y^3 + 9*y^2 + 6431*y + 643464, 15*y^2 + 2297235, 6435*y + 2175030, 2297295 ] Total time: 3.019 seconds, Total memory usage: 1.93MB ************** MAGMA ***************** Host irmasrv3.u-strasbg.fr. (130.79.4.200) Time: Wed Feb 18 06:24:03 2004 Input: P:=PolynomialRing(IntegerRing(),2); f0:=2*(x^2+y^2)+x-y-16; f1:=6*(x^4+y^4)+2*(x^3-y^3)+x-y-192; f2:=1280*x^6+1280*y^6+2944*x^5-352*y^5-560*x^3-160*y^3+146*x-128*y+2160*x^4-600*x^2 -163825; f3:=645120*x^8+645120*y^8-330290415+12288*x^7-154624*y^7+1102080*x^5-71680*y^5- 264768*x^3-50176*y^3+55080*x-46080*y-777728*x^6+1536640*x^4-406112*x^2; I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Factorization(6435); Factorization(2297295); Output: Magma V2.10-6 Wed Feb 18 2004 06:24:00 on modular [Seed = 2081388292] ------------------------------------- [ x^2 + 248*x + y^2 + 6187*y + 643492, x*y + 317*x + 6118*y + 2175026, 495*x + 5940*y + 1409265, y^3 + 9*y^2 + 6431*y + 643464, 15*y^2 + 2297235, 6435*y + 2175030, 2297295 ] [ <3, 2>, <5, 1>, <11, 1>, <13, 1> ] [ <3, 3>, <5, 1>, <7, 1>, <11, 1>, <13, 1>, <17, 1> ] Total time: 2.929 seconds, Total memory usage: 1.93MB ************** MAGMA ***************** Host irmasrv3.u-strasbg.fr. (130.79.4.200) Time: Wed Feb 18 06:24:39 2004 Input: P:=PolynomialRing(IntegerRing(),2); f0:=2*(x^2+y^2)+x-y-16; f1:=6*(x^4+y^4)+2*(x^3-y^3)+x-y-192; f2:=1280*x^6+1280*y^6+2944*x^5-352*y^5-560*x^3-160*y^3+146*x-128*y+2160*x^4-600*x^2 -163825; f3:=645120*x^8+645120*y^8-330290415+12288*x^7-154624*y^7+1102080*x^5-71680*y^5- 264768*x^3-50176*y^3+55080*x-46080*y-777728*x^6+1536640*x^4-406112*x^2; I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Factorization(6435); Factorization(2297295); Bn:=GroebnerBasis(ChangeRing(I,GF(11))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(11^2))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(13))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(13^2))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(17))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(17^2))); Bn; Output: Magma V2.10-6 Wed Feb 18 2004 06:24:35 on modular [Seed = 1980071213] ------------------------------------- [ x^2 + 248*x + y^2 + 6187*y + 643492, x*y + 317*x + 6118*y + 2175026, 495*x + 5940*y + 1409265, y^3 + 9*y^2 + 6431*y + 643464, 15*y^2 + 2297235, 6435*y + 2175030, 2297295 ] [ <3, 2>, <5, 1>, <11, 1>, <13, 1> ] [ <3, 3>, <5, 1>, <7, 1>, <11, 1>, <13, 1>, <17, 1> ] [ x^2 + 6*x + 5*y + 7, x*y + 9*x + 2*y + 7, y^2 + 7 ] [ x^2 + 6*x + 5*y + 7, x*y + 9*x + 2*y + 7, y^2 + 7 ] [ x + 12*y, y^2 + 9 ] [ x + 12*y, y^2 + 9 ] [ x + 15, y + 15 ] [ x + 15, y + 15 ] Total time: 3.069 seconds, Total memory usage: 2.23MB ************** MAGMA ***************** Host irmasrv3.u-strasbg.fr. (130.79.4.200) Time: Wed Feb 18 06:26:58 2004 Input: P:=PolynomialRing(IntegerRing(),2); f0:=2*(x^2+y^2)+x-y-16; f1:=6*(x^4+y^4)+2*(x^3-y^3)+x-y-192; f2:=40*(x^6+y^6)+11*(x^5-y^5)+5*(x^3-y^3)+4*(x-y)-5120; f3:=645120*x^8+645120*y^8-330303015+154624*x^7-2251776*y^7+71680*x^5+1075200*y^5+ 50176*x^3-182784*y^3+46080*x-44280*y+1835008*y^6-1003520*y^4+116032*y^2; I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Output: Magma V2.10-6 Wed Feb 18 2004 06:26:55 on modular [Seed = 1127237780] ------------------------------------- [ x^2 + 8*x + y^2 + 14549527*y + 363738367, x*y + 2*x + 14549533*y + 12410753351, 15*x + 14549520*y + 12410753355, y^3 + 9*y^2 + 14549531*y + 12410753319, 15*y^2 + 15058768665, 14549535*y + 3375492120, 15058768725 ] Total time: 2.959 seconds, Total memory usage: 1.93MB ************** MAGMA ***************** Host irmasrv3.u-strasbg.fr. (130.79.4.200) Time: Wed Feb 18 06:27:42 2004 Input: P:=PolynomialRing(IntegerRing(),2); f0:=2*(x^2+y^2)+x-y-16; f1:=6*(x^4+y^4)+2*(x^3-y^3)+x-y-192; f2:=40*(x^6+y^6)+11*(x^5-y^5)+5*(x^3-y^3)+4*(x-y)-5120; f3:=645120*x^8+645120*y^8-330303015+154624*x^7-2251776*y^7+71680*x^5+1075200*y^5+ 50176*x^3-182784*y^3+46080*x-44280*y+1835008*y^6-1003520*y^4+116032*y^2; I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Factorization(14549535); Factorization(15058768725); Output: Magma V2.10-6 Wed Feb 18 2004 06:27:38 on modular [Seed = 1563316575] ------------------------------------- [ x^2 + 8*x + y^2 + 14549527*y + 363738367, x*y + 2*x + 14549533*y + 12410753351, 15*x + 14549520*y + 12410753355, y^3 + 9*y^2 + 14549531*y + 12410753319, 15*y^2 + 15058768665, 14549535*y + 3375492120, 15058768725 ] [ <3, 2>, <5, 1>, <7, 1>, <11, 1>, <13, 1>, <17, 1>, <19, 1> ] [ <3, 4>, <5, 2>, <7, 1>, <11, 1>, <13, 1>, <17, 1>, <19, 1>, <23, 1> ] Total time: 3.099 seconds, Total memory usage: 1.93MB ************** MAGMA ***************** Host irmasrv3.u-strasbg.fr. (130.79.4.200) Time: Wed Feb 18 06:28:38 2004 Input: P:=PolynomialRing(IntegerRing(),2); f0:=2*(x^2+y^2)+x-y-16; f1:=6*(x^4+y^4)+2*(x^3-y^3)+x-y-192; f2:=40*(x^6+y^6)+11*(x^5-y^5)+5*(x^3-y^3)+4*(x-y)-5120; f3:=645120*x^8+645120*y^8-330303015+154624*x^7-2251776*y^7+71680*x^5+1075200*y^5+ 50176*x^3-182784*y^3+46080*x-44280*y+1835008*y^6-1003520*y^4+116032*y^2; I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Factorization(14549535); Factorization(15058768725); Bn:=GroebnerBasis(ChangeRing(I,GF(11))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(11^2))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(13))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(13^2))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(17))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(17^2))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(19))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(19^2))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(23))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(23^2))); Bn; Output: Magma V2.10-6 Wed Feb 18 2004 06:28:35 on modular [Seed = 1445288477] ------------------------------------- [ x^2 + 8*x + y^2 + 14549527*y + 363738367, x*y + 2*x + 14549533*y + 12410753351, 15*x + 14549520*y + 12410753355, y^3 + 9*y^2 + 14549531*y + 12410753319, 15*y^2 + 15058768665, 14549535*y + 3375492120, 15058768725 ] [ <3, 2>, <5, 1>, <7, 1>, <11, 1>, <13, 1>, <17, 1>, <19, 1> ] [ <3, 4>, <5, 2>, <7, 1>, <11, 1>, <13, 1>, <17, 1>, <19, 1>, <23, 1> ] [ x + 10*y, y^2 + 7 ] [ x + 10*y, y^2 + 7 ] [ x + 12*y, y^2 + 9 ] [ x + 12*y, y^2 + 9 ] [ x + 16*y, y^2 + 13 ] [ x + 16*y, y^2 + 13 ] [ x + 18*y, y^2 + 15 ] [ x + 18*y, y^2 + 15 ] [ x + 2, y + 2 ] [ x + 2, y + 2 ] Total time: 2.999 seconds, Total memory usage: 2.23MB ************** MAGMA ***************** Host irmasrv3.u-strasbg.fr. (130.79.4.200) Time: Wed Feb 18 06:29:33 2004 Input: P:=PolynomialRing(IntegerRing(),2); f0:=2*(x^2+y^2)+x-y-16; f1:=6*(x^4+y^4)+2*(x^3-y^3)+x-y-192; f2:=40*(x^6+y^6)+11*(x^5-y^5)+5*(x^3-y^3)+4*(x-y)-5120; f3:=322560*x^8+322560*y^8-165152295+1125888*x^7-1125888*y^7-537600*x^5+537600*y^5+ 91392*x^3-91392*y^3+22140*x-22140*y+917504*y^6-501760*y^4+58016*y^2+917504*x^6- 501760*x^4+58016*x^2; I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Output: Magma V2.10-6 Wed Feb 18 2004 06:29:30 on modular [Seed = 2698226706] ------------------------------------- [ x^2 + 8*x + y^2 + 101846737*y + 101846737, x*y + 2*x + 101846743*y + 101846741, 15*x + 101846730*y, y^3 + 9*y^2 + 101846741*y + 101846709, 15*y^2 + 101846685, 101846745 ] Total time: 2.969 seconds, Total memory usage: 1.93MB ************** MAGMA ***************** Host irmasrv3.u-strasbg.fr. (130.79.4.200) Time: Wed Feb 18 06:29:59 2004 Input: P:=PolynomialRing(IntegerRing(),2); f0:=2*(x^2+y^2)+x-y-16; f1:=6*(x^4+y^4)+2*(x^3-y^3)+x-y-192; f2:=40*(x^6+y^6)+11*(x^5-y^5)+5*(x^3-y^3)+4*(x-y)-5120; f3:=322560*x^8+322560*y^8-165152295+1125888*x^7-1125888*y^7-537600*x^5+537600*y^5+ 91392*x^3-91392*y^3+22140*x-22140*y+917504*y^6-501760*y^4+58016*y^2+917504*x^6- 501760*x^4+58016*x^2; I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Factorization(101846745); Output: Magma V2.10-6 Wed Feb 18 2004 06:29:55 on modular [Seed = 3117069602] ------------------------------------- [ x^2 + 8*x + y^2 + 101846737*y + 101846737, x*y + 2*x + 101846743*y + 101846741, 15*x + 101846730*y, y^3 + 9*y^2 + 101846741*y + 101846709, 15*y^2 + 101846685, 101846745 ] [ <3, 2>, <5, 1>, <7, 2>, <11, 1>, <13, 1>, <17, 1>, <19, 1> ] Total time: 3.069 seconds, Total memory usage: 1.93MB ************** MAGMA ***************** Host irmasrv3.u-strasbg.fr. (130.79.4.200) Time: Wed Feb 18 06:30:54 2004 Input: P:=PolynomialRing(IntegerRing(),2); f0:=2*(x^2+y^2)+x-y-16; f1:=6*(x^4+y^4)+2*(x^3-y^3)+x-y-192; f2:=40*(x^6+y^6)+11*(x^5-y^5)+5*(x^3-y^3)+4*(x-y)-5120; f3:=322560*x^8+322560*y^8-165152295+1125888*x^7-1125888*y^7-537600*x^5+537600*y^5+ 91392*x^3-91392*y^3+22140*x-22140*y+917504*y^6-501760*y^4+58016*y^2+917504*x^6- 501760*x^4+58016*x^2; I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Factorization(101846745); Bn:=GroebnerBasis(ChangeRing(I,GF(11))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(11^2))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(13))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(13^2))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(17))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(17^2))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(19))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(19^2))); Bn; Output: Magma V2.10-6 Wed Feb 18 2004 06:30:51 on modular [Seed = 2331608649] ------------------------------------- [ x^2 + 8*x + y^2 + 101846737*y + 101846737, x*y + 2*x + 101846743*y + 101846741, 15*x + 101846730*y, y^3 + 9*y^2 + 101846741*y + 101846709, 15*y^2 + 101846685, 101846745 ] [ <3, 2>, <5, 1>, <7, 2>, <11, 1>, <13, 1>, <17, 1>, <19, 1> ] [ x + 10*y, y^2 + 7 ] [ x + 10*y, y^2 + 7 ] [ x + 12*y, y^2 + 9 ] [ x + 12*y, y^2 + 9 ] [ x + 16*y, y^2 + 13 ] [ x + 16*y, y^2 + 13 ] [ x + 18*y, y^2 + 15 ] [ x + 18*y, y^2 + 15 ] Total time: 3.069 seconds, Total memory usage: 2.23MB ************** MAGMA ***************** Host irmasrv3.u-strasbg.fr. (130.79.4.200) Time: Wed Feb 18 06:31:35 2004 Input: P:=PolynomialRing(IntegerRing(),2); f0:=2*(x^2+y^2)+x-y-16; f1:=6*(x^4+y^4)+2*(x^3-y^3)+x-y-192; f2:=1280*x^6+1280*y^6+2944*x^5-352*y^5-560*x^3-160*y^3+146*x-128*y+2160*x^4-600*x^2 -163825; f3:=322560*x^8+322560*y^8-165152295+1125888*x^7-1125888*y^7-537600*x^5+537600*y^5+ 91392*x^3-91392*y^3+22140*x-22140*y+917504*y^6-501760*y^4+58016*y^2+917504*x^6- 501760*x^4+58016*x^2; I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Output: Magma V2.10-6 Wed Feb 18 2004 06:31:32 on modular [Seed = 2213580479] ------------------------------------- [ x^2 + 23*x + y^2 + 6412*y + 643492, x*y + 2*x + 6433*y + 643496, 45*x + 6390*y + 643500, y^3 + 9*y^2 + 6431*y + 643464, 15*y^2 + 765705, 6435*y + 643500, 765765 ] Total time: 2.969 seconds, Total memory usage: 1.93MB ************** MAGMA ***************** Host irmasrv3.u-strasbg.fr. (130.79.4.200) Time: Wed Feb 18 06:32:04 2004 Input: P:=PolynomialRing(IntegerRing(),2); f0:=2*(x^2+y^2)+x-y-16; f1:=6*(x^4+y^4)+2*(x^3-y^3)+x-y-192; f2:=1280*x^6+1280*y^6+2944*x^5-352*y^5-560*x^3-160*y^3+146*x-128*y+2160*x^4-600*x^2 -163825; f3:=322560*x^8+322560*y^8-165152295+1125888*x^7-1125888*y^7-537600*x^5+537600*y^5+ 91392*x^3-91392*y^3+22140*x-22140*y+917504*y^6-501760*y^4+58016*y^2+917504*x^6- 501760*x^4+58016*x^2; I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Factorization(6435); Factorization(765765); Output: Magma V2.10-6 Wed Feb 18 2004 06:32:01 on modular [Seed = 2632946053] ------------------------------------- [ x^2 + 23*x + y^2 + 6412*y + 643492, x*y + 2*x + 6433*y + 643496, 45*x + 6390*y + 643500, y^3 + 9*y^2 + 6431*y + 643464, 15*y^2 + 765705, 6435*y + 643500, 765765 ] [ <3, 2>, <5, 1>, <11, 1>, <13, 1> ] [ <3, 2>, <5, 1>, <7, 1>, <11, 1>, <13, 1>, <17, 1> ] Total time: 3.059 seconds, Total memory usage: 1.93MB ************** MAGMA ***************** Host irmasrv3.u-strasbg.fr. (130.79.4.200) Time: Wed Feb 18 06:32:29 2004 Input: P:=PolynomialRing(IntegerRing(),2); f0:=2*(x^2+y^2)+x-y-16; f1:=6*(x^4+y^4)+2*(x^3-y^3)+x-y-192; f2:=1280*x^6+1280*y^6+2944*x^5-352*y^5-560*x^3-160*y^3+146*x-128*y+2160*x^4-600*x^2 -163825; f3:=322560*x^8+322560*y^8-165152295+1125888*x^7-1125888*y^7-537600*x^5+537600*y^5+ 91392*x^3-91392*y^3+22140*x-22140*y+917504*y^6-501760*y^4+58016*y^2+917504*x^6- 501760*x^4+58016*x^2; I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Factorization(6435); Factorization(765765); Bn:=GroebnerBasis(ChangeRing(I,GF(11))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(11^2))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(13))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(13^2))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(17))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(17^2))); Bn; Output: Magma V2.10-6 Wed Feb 18 2004 06:32:26 on modular [Seed = 2514917623] ------------------------------------- [ x^2 + 23*x + y^2 + 6412*y + 643492, x*y + 2*x + 6433*y + 643496, 45*x + 6390*y + 643500, y^3 + 9*y^2 + 6431*y + 643464, 15*y^2 + 765705, 6435*y + 643500, 765765 ] [ <3, 2>, <5, 1>, <11, 1>, <13, 1> ] [ <3, 2>, <5, 1>, <7, 1>, <11, 1>, <13, 1>, <17, 1> ] [ x + 10*y, y^2 + 7 ] [ x + 10*y, y^2 + 7 ] [ x + 12*y, y^2 + 9 ] [ x + 12*y, y^2 + 9 ] [ x + 15, y + 15 ] [ x + 15, y + 15 ] Total time: 3.119 seconds, Total memory usage: 2.23MB ************** MAGMA ***************** Host irmasrv3.u-strasbg.fr. (130.79.4.200) Time: Wed Feb 18 06:33:28 2004 Input: P:=PolynomialRing(IntegerRing(),2); f0:=2*(x^2+y^2)+x-y-16; f1:=6*(x^4+y^4)+2*(x^3-y^3)+x-y-192; f2:=1280*x^6+1280*y^6+2944*x^5-352*y^5-560*x^3-160*y^3+146*x-128*y+2160*x^4-600*x^2 -163825; f3:=322560*x^8+322560*y^8-165145995+6144*x^7-1125888*y^7+551040*x^5+537600*y^5- 132384*x^3-91392*y^3+27540*x-22140*y+917504*y^6-501760*y^4+58016*y^2-388864*x^6 +768320*x^4-203056*x^2; I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Output: Magma V2.10-6 Wed Feb 18 2004 06:33:25 on modular [Seed = 4020036162] ------------------------------------- [ x^2 + 248*x + y^2 + 6187*y + 643492, x*y + 317*x + 6118*y + 643496, 495*x + 5940*y + 643500, y^3 + 9*y^2 + 6431*y + 643464, 15*y^2 + 765705, 6435*y + 643500, 765765 ] Total time: 3.009 seconds, Total memory usage: 1.93MB ************** MAGMA ***************** Host irmasrv3.u-strasbg.fr. (130.79.4.200) Time: Wed Feb 18 06:34:07 2004 Input: P:=PolynomialRing(IntegerRing(),2); f0:=2*(x^2+y^2)+x-y-16; f1:=6*(x^4+y^4)+2*(x^3-y^3)+x-y-192; f2:=1280*x^6+1280*y^6+2944*x^5-352*y^5-560*x^3-160*y^3+146*x-128*y+2160*x^4-600*x^2 -163825; f3:=322560*x^8+322560*y^8-165145995+6144*x^7-1125888*y^7+551040*x^5+537600*y^5- 132384*x^3-91392*y^3+27540*x-22140*y+917504*y^6-501760*y^4+58016*y^2-388864*x^6 +768320*x^4-203056*x^2; I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Factorization(6435); Factorization(765765); Bn:=GroebnerBasis(ChangeRing(I,GF(11))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(11^2))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(13))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(13^2))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(17))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(17^2))); Bn; Output: Magma V2.10-6 Wed Feb 18 2004 06:34:04 on modular [Seed = 4186633341] ------------------------------------- [ x^2 + 248*x + y^2 + 6187*y + 643492, x*y + 317*x + 6118*y + 643496, 495*x + 5940*y + 643500, y^3 + 9*y^2 + 6431*y + 643464, 15*y^2 + 765705, 6435*y + 643500, 765765 ] [ <3, 2>, <5, 1>, <11, 1>, <13, 1> ] [ <3, 2>, <5, 1>, <7, 1>, <11, 1>, <13, 1>, <17, 1> ] [ x^2 + 6*x + 5*y + 7, x*y + 9*x + 2*y + 7, y^2 + 7 ] [ x^2 + 6*x + 5*y + 7, x*y + 9*x + 2*y + 7, y^2 + 7 ] [ x + 12*y, y^2 + 9 ] [ x + 12*y, y^2 + 9 ] [ x + 15, y + 15 ] [ x + 15, y + 15 ] Total time: 3.049 seconds, Total memory usage: 2.23MB ************** MAGMA ***************** Host irmasrv3.u-strasbg.fr. (130.79.4.200) Time: Wed Feb 18 06:34:53 2004 Input: P:=PolynomialRing(IntegerRing(),2); f0:=2*(x^2+y^2)+x-y-16; f1:=6*(x^4+y^4)+2*(x^3-y^3)+x-y-192; f2:=1280*x^6+1280*y^6+352*x^5-2944*y^5+160*x^3+560*y^3+128*x-146*y+2160*y^4+600*y^2 -163825; f3:=645120*x^8+645120*y^8-330303015+154624*x^7-2251776*y^7+71680*x^5+1075200*y^5+ 50176*x^3-182784*y^3+46080*x-44280*y+1835008*y^6-1003520*y^4+116032*y^2; I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Output: Magma V2.10-6 Wed Feb 18 2004 06:34:50 on modular [Seed = 4068605696] ------------------------------------- [ x^2 + 8*x + y^2 + 7*y + 22, x*y + 2*x + 13*y + 716, 15*x + 375, y^3 + 9*y^2 + 11*y + 1029, 15*y + 720, 1035 ] Total time: 3.039 seconds, Total memory usage: 1.93MB ************** MAGMA ***************** Host irmasrv3.u-strasbg.fr. (130.79.4.200) Time: Wed Feb 18 06:35:19 2004 Input: P:=PolynomialRing(IntegerRing(),2); f0:=2*(x^2+y^2)+x-y-16; f1:=6*(x^4+y^4)+2*(x^3-y^3)+x-y-192; f2:=1280*x^6+1280*y^6+352*x^5-2944*y^5+160*x^3+560*y^3+128*x-146*y+2160*y^4+600*y^2 -163825; f3:=645120*x^8+645120*y^8-330303015+154624*x^7-2251776*y^7+71680*x^5+1075200*y^5+ 50176*x^3-182784*y^3+46080*x-44280*y+1835008*y^6-1003520*y^4+116032*y^2; I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Factorization(1035); Output: Magma V2.10-6 Wed Feb 18 2004 06:35:15 on modular [Seed = 3485254164] ------------------------------------- [ x^2 + 8*x + y^2 + 7*y + 22, x*y + 2*x + 13*y + 716, 15*x + 375, y^3 + 9*y^2 + 11*y + 1029, 15*y + 720, 1035 ] [ <3, 2>, <5, 1>, <23, 1> ] Total time: 2.969 seconds, Total memory usage: 1.93MB ************** MAGMA ***************** Host irmasrv3.u-strasbg.fr. (130.79.4.200) Time: Wed Feb 18 06:36:27 2004 Input: P:=PolynomialRing(IntegerRing(),2); f0:=2*(x^2+y^2)+x-y-16; f1:=6*(x^4+y^4)+2*(x^3-y^3)+x-y-192; f2:=1280*x^6+1280*y^6+352*x^5-2944*y^5+160*x^3+560*y^3+128*x-146*y+2160*y^4+600*y^2 -163825; f3:=645120*x^8+645120*y^8-330303015+154624*x^7-2251776*y^7+71680*x^5+1075200*y^5+ 50176*x^3-182784*y^3+46080*x-44280*y+1835008*y^6-1003520*y^4+116032*y^2; I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Factorization(1035); Bn:=GroebnerBasis(ChangeRing(I,GF(23))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(23^2))); Bn; Output: Magma V2.10-6 Wed Feb 18 2004 06:36:24 on modular [Seed = 3651852233] ------------------------------------- [ x^2 + 8*x + y^2 + 7*y + 22, x*y + 2*x + 13*y + 716, 15*x + 375, y^3 + 9*y^2 + 11*y + 1029, 15*y + 720, 1035 ] [ <3, 2>, <5, 1>, <23, 1> ] [ x + 2, y + 2 ] [ x + 2, y + 2 ] Total time: 3.119 seconds, Total memory usage: 1.93MB ************** MAGMA ***************** Host irmasrv3.u-strasbg.fr. (130.79.4.200) Time: Wed Feb 18 06:37:20 2004 Input: P:=PolynomialRing(IntegerRing(),2); f0:=2*(x^2+y^2)+x-y-16; f1:=6*(x^4+y^4)+2*(x^3-y^3)+x-y-192; f2:=1280*x^6+1280*y^6+352*x^5-2944*y^5+160*x^3+560*y^3+128*x-146*y+2160*y^4+600*y^2 -163825; f3:=322560*x^8+322560*y^8-165152295+1125888*x^7-1125888*y^7-537600*x^5+537600*y^5+ 91392*x^3-91392*y^3+22140*x-22140*y+917504*y^6-501760*y^4+58016*y^2+917504*x^6- 501760*x^4+58016*x^2; I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Output: Magma V2.10-6 Wed Feb 18 2004 06:37:17 on modular [Seed = 3533823127] ------------------------------------- [ x^2 + 8*x + y^2 + 7*y + 22, x*y + 2*x + 13*y + 41, 15*x + 15, y^3 + 9*y^2 + 11*y + 39, 15*y, 45 ] Total time: 3.089 seconds, Total memory usage: 1.93MB ************** MAGMA ***************** Host irmasrv3.u-strasbg.fr. (130.79.4.200) Time: Wed Feb 18 06:38:14 2004 Input: P:=PolynomialRing(IntegerRing(),2); f0:=2*(x^2+y^2)+x-y-16; f1:=6*(x^4+y^4)+2*(x^3-y^3)+x-y-192; f2:=640*x^6+640*y^6+1472*x^5-1472*y^5+1080*x^4+1080*y^4-280*x^3+280*y^3; f3:=322560*x^8+322560*y^8-165152295+1125888*x^7-1125888*y^7-537600*x^5+537600*y^5+ 91392*x^3-91392*y^3+22140*x-22140*y+917504*y^6-501760*y^4+58016*y^2+917504*x^6- 501760*x^4+58016*x^2; I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Output: Magma V2.10-6 Wed Feb 18 2004 06:38:11 on modular [Seed = 710485152] ------------------------------------- [ x + 4094*y + 910, y^2 + 3185*y + 2271, 4095 ] Total time: 3.059 seconds, Total memory usage: 1.93MB ************** MAGMA ***************** Host irmasrv3.u-strasbg.fr. (130.79.4.200) Time: Wed Feb 18 06:38:51 2004 Input: P:=PolynomialRing(IntegerRing(),2); f0:=2*(x^2+y^2)+x-y-16; f1:=6*(x^4+y^4)+2*(x^3-y^3)+x-y-192; f2:=640*x^6+640*y^6+1472*x^5-1472*y^5+1080*x^4+1080*y^4-280*x^3+280*y^3; f3:=322560*x^8+322560*y^8-165152295+1125888*x^7-1125888*y^7-537600*x^5+537600*y^5+ 91392*x^3-91392*y^3+22140*x-22140*y+917504*y^6-501760*y^4+58016*y^2+917504*x^6- 501760*x^4+58016*x^2; I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Factorization(4095); Output: Magma V2.10-6 Wed Feb 18 2004 06:38:48 on modular [Seed = 609692357] ------------------------------------- [ x + 4094*y + 910, y^2 + 3185*y + 2271, 4095 ] [ <3, 2>, <5, 1>, <7, 1>, <13, 1> ] Total time: 3.099 seconds, Total memory usage: 1.93MB ************** MAGMA ***************** Host irmasrv3.u-strasbg.fr. (130.79.4.200) Time: Wed Feb 18 06:39:20 2004 Input: P:=PolynomialRing(IntegerRing(),2); f0:=2*(x^2+y^2)+x-y-16; f1:=6*(x^4+y^4)+2*(x^3-y^3)+x-y-192; f2:=640*x^6+640*y^6+1472*x^5-1472*y^5+1080*x^4+1080*y^4-280*x^3+280*y^3; f3:=322560*x^8+322560*y^8-165152295+1125888*x^7-1125888*y^7-537600*x^5+537600*y^5+ 91392*x^3-91392*y^3+22140*x-22140*y+917504*y^6-501760*y^4+58016*y^2+917504*x^6- 501760*x^4+58016*x^2; I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Factorization(4095); Bn:=GroebnerBasis(ChangeRing(I,GF(13))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(13^2))); Bn; Output: Magma V2.10-6 Wed Feb 18 2004 06:39:17 on modular [Seed = 1045246194] ------------------------------------- [ x + 4094*y + 910, y^2 + 3185*y + 2271, 4095 ] [ <3, 2>, <5, 1>, <7, 1>, <13, 1> ] [ x + 12*y, y^2 + 9 ] [ x + 12*y, y^2 + 9 ] Total time: 2.989 seconds, Total memory usage: 2.13MB ************** MAGMA ***************** Host irmasrv3.u-strasbg.fr. (130.79.4.200) Time: Wed Feb 18 06:40:00 2004 Input: P:=PolynomialRing(IntegerRing(),2); f0:=2*(x^2+y^2)+x-y-16; f1:=6*(x^4+y^4)+2*(x^3-y^3)+x-y-192; f2:=640*x^6+640*y^6+1472*x^5-1472*y^5+1080*x^4+1080*y^4-280*x^3+280*y^3; f3:=322560*x^8+322560*y^8-165145995+6144*x^7-1125888*y^7+551040*x^5+537600*y^5- 132384*x^3-91392*y^3+27540*x-22140*y+917504*y^6-501760*y^4+58016*y^2-388864*x^6 +768320*x^4-203056*x^2; I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Output: Magma V2.10-6 Wed Feb 18 2004 06:39:57 on modular [Seed = 158991917] ------------------------------------- [ x + 4094*y + 910, y^2 + 3185*y + 2271, 4095 ] Total time: 2.989 seconds, Total memory usage: 1.93MB ************** MAGMA ***************** Host irmasrv3.u-strasbg.fr. (130.79.4.200) Time: Wed Feb 18 06:40:28 2004 Input: P:=PolynomialRing(IntegerRing(),2); f0:=2*(x^2+y^2)+x-y-16; f1:=6*(x^4+y^4)+2*(x^3-y^3)+x-y-192; f2:=640*x^6+640*y^6+1472*x^5-1472*y^5+1080*x^4+1080*y^4-280*x^3+280*y^3; f3:=322560*x^8+322560*y^8-165145995+6144*x^7-1125888*y^7+551040*x^5+537600*y^5- 132384*x^3-91392*y^3+27540*x-22140*y+917504*y^6-501760*y^4+58016*y^2-388864*x^6 +768320*x^4-203056*x^2; I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Factorization(4095); Bn:=GroebnerBasis(ChangeRing(I,GF(13))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(13^2))); Bn; Output: Magma V2.10-6 Wed Feb 18 2004 06:40:25 on modular [Seed = 426382873] ------------------------------------- [ x + 4094*y + 910, y^2 + 3185*y + 2271, 4095 ] [ <3, 2>, <5, 1>, <7, 1>, <13, 1> ] [ x + 12*y, y^2 + 9 ] [ x + 12*y, y^2 + 9 ] Total time: 2.949 seconds, Total memory usage: 2.13MB ************** MAGMA ***************** Host irmasrv3.u-strasbg.fr. (130.79.4.200) Time: Wed Feb 18 06:41:26 2004 Input: P:=PolynomialRing(IntegerRing(),2); f0:=2*(x^2+y^2)+x-y-16; f1:=6*(x^4+y^4)+2*(x^3-y^3)+x-y-192; f2:=1280*x^6+1280*y^6+352*x^5-2944*y^5+160*x^3+560*y^3+128*x-146*y+2160*y^4+600*y^2 -163825; f3:=645120*x^8+645120*y^8-330290415+154624*x^7-12288*y^7+71680*x^5-1102080*y^5+ 50176*x^3+264768*y^3+46080*x-55080*y-777728*y^6+1536640*y^4-406112*y^2; I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Output: Magma V2.10-6 Wed Feb 18 2004 06:41:23 on modular [Seed = 274931546] ------------------------------------- [ x^2 + 8*x + y^2 + 7*y + 22, x*y + 2*x + 13*y + 176, 15*x + 240, y^3 + 9*y^2 + 11*y + 354, 15*y + 225, 405 ] Total time: 3.059 seconds, Total memory usage: 1.93MB ************** MAGMA ***************** Host irmasrv3.u-strasbg.fr. (130.79.4.200) Time: Wed Feb 18 06:41:54 2004 Input: P:=PolynomialRing(IntegerRing(),2); f0:=2*(x^2+y^2)+x-y-16; f1:=6*(x^4+y^4)+2*(x^3-y^3)+x-y-192; f2:=1280*x^6+1280*y^6+352*x^5-2944*y^5+160*x^3+560*y^3+128*x-146*y+2160*y^4+600*y^2 -163825; f3:=645120*x^8+645120*y^8-330290415+154624*x^7-12288*y^7+71680*x^5-1102080*y^5+ 50176*x^3+264768*y^3+46080*x-55080*y-777728*y^6+1536640*y^4-406112*y^2; I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Factorization(405); Output: Magma V2.10-6 Wed Feb 18 2004 06:41:51 on modular [Seed = 1796760637] ------------------------------------- [ x^2 + 8*x + y^2 + 7*y + 22, x*y + 2*x + 13*y + 176, 15*x + 240, y^3 + 9*y^2 + 11*y + 354, 15*y + 225, 405 ] [ <3, 4>, <5, 1> ] Total time: 2.919 seconds, Total memory usage: 1.93MB ************** MAGMA ***************** Host irmasrv3.u-strasbg.fr. (130.79.4.200) Time: Wed Feb 18 06:42:19 2004 Input: P:=PolynomialRing(IntegerRing(),2); f0:=2*(x^2+y^2)+x-y-16; f1:=6*(x^4+y^4)+2*(x^3-y^3)+x-y-192; f2:=1280*x^6+1280*y^6+352*x^5-2944*y^5+160*x^3+560*y^3+128*x-146*y+2160*y^4+600*y^2 -163825; f3:=645120*x^8+645120*y^8-330290415+154624*x^7-12288*y^7+71680*x^5-1102080*y^5+ 50176*x^3+264768*y^3+46080*x-55080*y-777728*y^6+1536640*y^4-406112*y^2; I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Output: Magma V2.10-6 Wed Feb 18 2004 06:42:16 on modular [Seed = 1695967956] ------------------------------------- [ x^2 + 8*x + y^2 + 7*y + 22, x*y + 2*x + 13*y + 176, 15*x + 240, y^3 + 9*y^2 + 11*y + 354, 15*y + 225, 405 ] Total time: 3.089 seconds, Total memory usage: 1.93MB ************** MAGMA ***************** Host aula-a-siee03.uab.es. (158.109.66.3) Time: Wed Feb 18 06:42:23 2004 Input: x:=[1,2,3,6,3,6]; x; y:=true; min,pos:=Min (x); min; pos; print "hola"; if y then print (x+2); Output: Magma V2.10-6 Wed Feb 18 2004 06:42:20 on modular [Seed = 2081387465] ------------------------------------- [ 1, 2, 3, 6, 3, 6 ] 1 1 hola User error: syntax error at end of input Total time: 2.999 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-a-siee03.uab.es. (158.109.66.3) Time: Wed Feb 18 06:42:35 2004 Input: x:=[1,2,3,6,3,6]; x; y:=true; min,pos:=Min (x); min; pos; print "hola"; if y then print x; Output: Magma V2.10-6 Wed Feb 18 2004 06:42:32 on modular [Seed = 1996781814] ------------------------------------- [ 1, 2, 3, 6, 3, 6 ] 1 1 hola User error: syntax error at end of input Total time: 2.979 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-a-siee03.uab.es. (158.109.66.3) Time: Wed Feb 18 06:42:53 2004 Input: x:=[1,2,3,6,3,6]; x; y:=true; min,pos:=Min (x); min; pos; print "hola"; if (y) then (print x); Output: Magma V2.10-6 Wed Feb 18 2004 06:42:50 on modular [Seed = 1312637405] ------------------------------------- [ 1, 2, 3, 6, 3, 6 ] 1 1 hola >> if (y) then (print x);; ^ User error: bad syntax Total time: 3.019 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host irmasrv3.u-strasbg.fr. (130.79.4.200) Time: Wed Feb 18 06:42:58 2004 Input: P:=PolynomialRing(IntegerRing(),2); f0:=2*(x^2+y^2)+x-y-16; f1:=6*(x^4+y^4)+2*(x^3-y^3)+x-y-192; f2:=1280*x^6+1280*y^6+352*x^5-2944*y^5+160*x^3+560*y^3+128*x-146*y+2160*y^4+600*y^2 -163825; f3:=322560*x^8+322560*y^8-165145995+1125888*x^7-6144*y^7-537600*x^5-551040*y^5+ 91392*x^3+132384*y^3+22140*x-27540*y+917504*x^6-501760*x^4+58016*x^2-388864*y^6 +768320*y^4-203056*y^2; I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Output: Magma V2.10-6 Wed Feb 18 2004 06:42:55 on modular [Seed = 1495946959] ------------------------------------- [ x^2 + 8*x + y^2 + 7*y + 22, x*y + 2*x + 13*y + 41, 15*x + 15, y^3 + 9*y^2 + 11*y + 39, 15*y, 45 ] Total time: 3.049 seconds, Total memory usage: 1.93MB ************** MAGMA ***************** Host aula-a-siee03.uab.es. (158.109.66.3) Time: Wed Feb 18 06:43:27 2004 Input: x:=[1,2,3,6,3,6]; x; y:=true; min,pos:=Min (x); min; pos; print "hola"; if (y) then (print x) end if; Output: Magma V2.10-6 Wed Feb 18 2004 06:43:24 on modular [Seed = 1344495525] ------------------------------------- [ 1, 2, 3, 6, 3, 6 ] 1 1 hola >> if (y) then (print x) end if;; ^ User error: bad syntax Total time: 3.009 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host irmasrv3.u-strasbg.fr. (130.79.4.200) Time: Wed Feb 18 06:43:36 2004 Input: P:=PolynomialRing(IntegerRing(),2); f0:=2*(x^2+y^2)+x-y-16; f1:=6*(x^4+y^4)+2*(x^3-y^3)+x-y-192; f2:=640*x^6+640*y^6+1472*x^5-1472*y^5+1080*x^4+1080*y^4-280*x^3+280*y^3; f3:=322560*x^8+322560*y^8-165145995+1125888*x^7-6144*y^7-537600*x^5-551040*y^5+ 91392*x^3+132384*y^3+22140*x-27540*y+917504*x^6-501760*x^4+58016*x^2-388864*y^6 +768320*y^4-203056*y^2; I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Output: Magma V2.10-6 Wed Feb 18 2004 06:43:32 on modular [Seed = 2883101798] ------------------------------------- [ x + 4094*y + 910, y^2 + 3185*y + 2271, 4095 ] Total time: 3.049 seconds, Total memory usage: 1.93MB ************** MAGMA ***************** Host irmasrv3.u-strasbg.fr. (130.79.4.200) Time: Wed Feb 18 06:44:16 2004 Input: P:=PolynomialRing(IntegerRing(),2); f0:=2*(x^2+y^2)+x-y-16; f1:=6*(x^4+y^4)+2*(x^3-y^3)+x-y-192; f2:=640*x^6+640*y^6+1472*x^5-1472*y^5+1080*x^4+1080*y^4-280*x^3+280*y^3; f3:=322560*x^8+322560*y^8-165145995+1125888*x^7-6144*y^7-537600*x^5-551040*y^5+ 91392*x^3+132384*y^3+22140*x-27540*y+917504*x^6-501760*x^4+58016*x^2-388864*y^6 +768320*y^4-203056*y^2; I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Factorization(4095); Bn:=GroebnerBasis(ChangeRing(I,GF(13))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(13^2))); Bn; Output: Magma V2.10-6 Wed Feb 18 2004 06:44:13 on modular [Seed = 2782311809] ------------------------------------- [ x + 4094*y + 910, y^2 + 3185*y + 2271, 4095 ] [ <3, 2>, <5, 1>, <7, 1>, <13, 1> ] [ x + 12*y, y^2 + 9 ] [ x + 12*y, y^2 + 9 ] Total time: 3.039 seconds, Total memory usage: 2.13MB ************** MAGMA ***************** Host aula-a-siee03.uab.es. (158.109.66.3) Time: Wed Feb 18 06:44:48 2004 Input: x:=[1,2,3,6,3,6]; x; y:=true; min,pos:=Min (x); min; pos; print "hola"; IsPrime(2); if (y) then (print x) end if; Output: Magma V2.10-6 Wed Feb 18 2004 06:44:45 on modular [Seed = 3167726776] ------------------------------------- [ 1, 2, 3, 6, 3, 6 ] 1 1 hola true >> if (y) then (print x) end if;; ^ User error: bad syntax Total time: 3.029 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host irmasrv3.u-strasbg.fr. (130.79.4.200) Time: Wed Feb 18 06:44:52 2004 Input: P:=PolynomialRing(IntegerRing(),2); f0:=2*(x^2+y^2)+x-y-16; f1:=6*(x^4+y^4)+2*(x^3-y^3)+x-y-192; f2:=640*x^6+640*y^6+1472*x^5-1472*y^5+1080*x^4+1080*y^4-280*x^3+280*y^3; f3:=322560*x^8+322560*y^8-165139695+6144*x^7-6144*y^7+551040*x^5-551040*y^5-132384* x^3+132384*y^3+27540*x-27540*y-388864*x^6+768320*x^4-203056*x^2-388864*y^6+ 768320*y^4-203056*y^2; I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Output: Magma V2.10-6 Wed Feb 18 2004 06:44:49 on modular [Seed = 3083118511] ------------------------------------- [ x + 4094*y + 910, y^2 + 3185*y + 2271, 4095 ] Total time: 2.949 seconds, Total memory usage: 1.94MB ************** MAGMA ***************** Host aula-a-siee03.uab.es. (158.109.66.3) Time: Wed Feb 18 06:44:56 2004 Input: x:=[1,2,3,6,3,6]; x; y:=true; min,pos:=Min (x); min; pos; print "hola"; IsPrime(20); if (y) then (print x) end if; Output: Magma V2.10-6 Wed Feb 18 2004 06:44:53 on modular [Seed = 2398985874] ------------------------------------- [ 1, 2, 3, 6, 3, 6 ] 1 1 hola false >> if (y) then (print x) end if;; ^ User error: bad syntax Total time: 2.939 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-a-siee03.uab.es. (158.109.66.3) Time: Wed Feb 18 06:45:04 2004 Input: x:=[1,2,3,6,3,6]; x; y:=true; min,pos:=Min (x); min; pos; print "hola"; IsPrime(1); if (y) then (print x) end if; Output: Magma V2.10-6 Wed Feb 18 2004 06:45:01 on modular [Seed = 2649656713] ------------------------------------- [ 1, 2, 3, 6, 3, 6 ] 1 1 hola false >> if (y) then (print x) end if;; ^ User error: bad syntax Total time: 3.099 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-a-siee03.uab.es. (158.109.66.3) Time: Wed Feb 18 06:45:13 2004 Input: x:=[1,2,3,6,3,6]; x; y:=true; min,pos:=Min (x); min; pos; print "hola"; IsPrime(0); if (y) then (print x) end if; Output: Magma V2.10-6 Wed Feb 18 2004 06:45:10 on modular [Seed = 2498200827] ------------------------------------- [ 1, 2, 3, 6, 3, 6 ] 1 1 hola false >> if (y) then (print x) end if;; ^ User error: bad syntax Total time: 3.029 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-a-siee03.uab.es. (158.109.66.3) Time: Wed Feb 18 06:45:21 2004 Input: x:=[1,2,3,6,3,6]; x; y:=true; min,pos:=Min (x); min; pos; print "hola"; IsPrime(5); if (y) then (print x) end if; Output: Magma V2.10-6 Wed Feb 18 2004 06:45:18 on modular [Seed = 4003331721] ------------------------------------- [ 1, 2, 3, 6, 3, 6 ] 1 1 hola true >> if (y) then (print x) end if;; ^ User error: bad syntax Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host irmasrv3.u-strasbg.fr. (130.79.4.200) Time: Wed Feb 18 06:45:31 2004 Input: P:=PolynomialRing(IntegerRing(),2); f0:=2*(x^2+y^2)+x-y-16; f1:=6*(x^4+y^4)+2*(x^3-y^3)+x-y-192; f2:=640*x^6+640*y^6+1472*x^5-1472*y^5+1080*x^4+1080*y^4-280*x^3+280*y^3; f3:=322560*x^8+322560*y^8-165139695+6144*x^7-6144*y^7+551040*x^5-551040*y^5-132384* x^3+132384*y^3+27540*x-27540*y-388864*x^6+768320*x^4-203056*x^2-388864*y^6+ 768320*y^4-203056*y^2; I:=ideal; B:=GroebnerBasis(I:Al:="Direct"); B; Factorization(4095); Bn:=GroebnerBasis(ChangeRing(I,GF(13))); Bn; Bn:=GroebnerBasis(ChangeRing(I,GF(13^2))); Bn; Output: Magma V2.10-6 Wed Feb 18 2004 06:45:28 on modular [Seed = 4186630536] ------------------------------------- [ x + 4094*y + 910, y^2 + 3185*y + 2271, 4095 ] [ <3, 2>, <5, 1>, <7, 1>, <13, 1> ] [ x + 12*y, y^2 + 9 ] [ x + 12*y, y^2 + 9 ] Total time: 3.039 seconds, Total memory usage: 2.14MB ************** MAGMA ***************** Host aula-a-siee03.uab.es. (158.109.66.3) Time: Wed Feb 18 06:45:42 2004 Input: x:=[1,2,3,6,3,6]; x; y:=true; min,pos:=Min (x); min; pos; print "hola"; IsPrime(5); if (min==1) then (print x) end if; Output: Magma V2.10-6 Wed Feb 18 2004 06:45:39 on modular [Seed = 4035174586] ------------------------------------- [ 1, 2, 3, 6, 3, 6 ] 1 1 hola true >> if (min==1) then (print x) end if;; ^ User error: bad syntax Total time: 3.009 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-a-siee03.uab.es. (158.109.66.3) Time: Wed Feb 18 06:48:12 2004 Input: x:=[1,2,3,6,3,6]; x; y:=true; min,pos:=Min (x); min; pos; print "hola"; IsPrime(5); if (min==1) then x; Output: Magma V2.10-6 Wed Feb 18 2004 06:48:09 on modular [Seed = 3417889563] ------------------------------------- [ 1, 2, 3, 6, 3, 6 ] 1 1 hola true >> if (min==1) then x;; ^ User error: bad syntax Total time: 2.999 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-a-siee03.uab.es. (158.109.66.3) Time: Wed Feb 18 06:49:56 2004 Input: x:=[1,2,3,6,3,6]; x; y:=true; min,pos:=Min (x); min; pos; print "hola"; IsPrime(5); if (min==1) then x; Output: Magma V2.10-6 Wed Feb 18 2004 06:49:53 on modular [Seed = 3317093517] ------------------------------------- [ 1, 2, 3, 6, 3, 6 ] 1 1 hola true >> if (min==1) then x;; ^ User error: bad syntax Total time: 3.039 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-a-siee03.uab.es. (158.109.66.3) Time: Wed Feb 18 06:57:08 2004 Input: Z4:=Integers(4); Output: Magma V2.10-6 Wed Feb 18 2004 06:57:05 on modular [Seed = 24252986] ------------------------------------- Total time: 3.049 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-a-siee03.uab.es. (158.109.66.3) Time: Wed Feb 18 06:57:21 2004 Input: Z4:=Integers(4); Z4; Output: Magma V2.10-6 Wed Feb 18 2004 06:57:18 on modular [Seed = 510463274] ------------------------------------- Residue class ring of integers modulo 4 Total time: 3.059 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-a-siee03.uab.es. (158.109.66.3) Time: Wed Feb 18 06:57:37 2004 Input: Z4:=Integers(4); Z4; Print(Z4); Output: Magma V2.10-6 Wed Feb 18 2004 06:57:34 on modular [Seed = 392430611] ------------------------------------- Residue class ring of integers modulo 4 >> Print(Z4);; ^ User error: Identifier 'Print' has not been declared or assigned Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-a-siee03.uab.es. (158.109.66.3) Time: Wed Feb 18 06:57:55 2004 Input: Z4:=Integers(4); Z4; Print Z4; Output: Magma V2.10-6 Wed Feb 18 2004 06:57:52 on modular [Seed = 1814003462] ------------------------------------- Residue class ring of integers modulo 4 >> Print Z4;; ^ User error: bad syntax Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-a-siee03.uab.es. (158.109.66.3) Time: Wed Feb 18 06:59:09 2004 Input: Z4:=Integers(4); Z4; IsField (Z4); Output: Magma V2.10-6 Wed Feb 18 2004 06:59:06 on modular [Seed = 2064148699] ------------------------------------- Residue class ring of integers modulo 4 false Total time: 3.069 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-a-siee03.uab.es. (158.109.66.3) Time: Wed Feb 18 06:59:38 2004 Input: Z4:=Integers(4); Z4; IsField (Z4); IsInvertible (Z4); Output: Magma V2.10-6 Wed Feb 18 2004 06:59:35 on modular [Seed = 1879270397] ------------------------------------- Residue class ring of integers modulo 4 false >> IsInvertible (Z4);; ^ Runtime error in 'IsInvertible': Bad argument types Argument types given: RngIntRes Total time: 2.999 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-a-siee03.uab.es. (158.109.66.3) Time: Wed Feb 18 07:00:26 2004 Input: Z4:=Integers(4); Z4; IsField (Z4); Z4!2; Output: Magma V2.10-6 Wed Feb 18 2004 07:00:22 on modular [Seed = 1093817021] ------------------------------------- Residue class ring of integers modulo 4 false 2 Total time: 3.059 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-a-siee03.uab.es. (158.109.66.3) Time: Wed Feb 18 07:00:50 2004 Input: Z4:=Integers(4); Z4; IsField (Z4); Z4!2; IsInvertible (Z4!2); Output: Magma V2.10-6 Wed Feb 18 2004 07:00:47 on modular [Seed = 1580027291] ------------------------------------- Residue class ring of integers modulo 4 false 2 false Total time: 3.009 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-a-siee03.uab.es. (158.109.66.3) Time: Wed Feb 18 07:01:00 2004 Input: Z4:=Integers(4); Z4; IsField (Z4); Z4!2; IsInvertible (Z4); Output: Magma V2.10-6 Wed Feb 18 2004 07:00:57 on modular [Seed = 1461994628] ------------------------------------- Residue class ring of integers modulo 4 false 2 >> IsInvertible (Z4); ^ Runtime error in 'IsInvertible': Bad argument types Argument types given: RngIntRes Total time: 2.889 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-a-siee03.uab.es. (158.109.66.3) Time: Wed Feb 18 07:01:09 2004 Input: Z4:=Integers(4); Z4; IsField (Z4); Z4!2; IsInvertible (Z4!2); Output: Magma V2.10-6 Wed Feb 18 2004 07:01:06 on modular [Seed = 2999035546] ------------------------------------- Residue class ring of integers modulo 4 false 2 false Total time: 3.009 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-a-siee03.uab.es. (158.109.66.3) Time: Wed Feb 18 07:01:41 2004 Input: Z4:=Integers(4); Z4; IsField (Z4); Z4!2; IsInvertible (Z4!2); IsInvertible (Z4!3); Output: Magma V2.10-6 Wed Feb 18 2004 07:01:38 on modular [Seed = 2298190976] ------------------------------------- Residue class ring of integers modulo 4 false 2 false true 3 Total time: 2.939 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host aula-a-siee03.uab.es. (158.109.66.3) Time: Wed Feb 18 07:02:06 2004 Input: Z4:=Integers(4); Z4; IsField (Z4); Z4!2; IsInvertible (Z4!2); IsInvertible (Z4!3); Z5:=Integers(41); Output: Magma V2.10-6 Wed Feb 18 2004 07:02:03 on modular [Seed = 2180158864] ------------------------------------- Residue class ring of integers modulo 4 false 2 false true 3 Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pxy-2b.kyoto-u.ac.jp. (130.54.130.228) Time: Wed Feb 18 07:08:45 2004 Input: Sqrt(2); Output: Magma V2.10-6 Wed Feb 18 2004 07:08:42 on modular [Seed = 3902536968] ------------------------------------- 1.414213562373095048801688724198 Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pxy-2b.kyoto-u.ac.jp. (130.54.130.228) Time: Wed Feb 18 07:08:48 2004 Input: Sqrt(2); Output: Magma V2.10-6 Wed Feb 18 2004 07:08:45 on modular [Seed = 3767792903] ------------------------------------- 1.414213562373095048801688724198 Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pxy-2b.kyoto-u.ac.jp. (130.54.130.228) Time: Wed Feb 18 07:09:36 2004 Input: Sqrt(2); Sqrt(100); Output: Magma V2.10-6 Wed Feb 18 2004 07:09:33 on modular [Seed = 4270713641] ------------------------------------- 1.414213562373095048801688724198 10.00000000000000000000000000 Total time: 3.019 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pxy-2b.kyoto-u.ac.jp. (130.54.130.228) Time: Wed Feb 18 07:10:26 2004 Input: Ceiling(Sqrt(100)); Floor(Sqrt(999)); Output: Magma V2.10-6 Wed Feb 18 2004 07:10:23 on modular [Seed = 3435125449] ------------------------------------- 10 31 Total time: 2.979 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pxy-2b.kyoto-u.ac.jp. (130.54.130.228) Time: Wed Feb 18 07:18:40 2004 Input: print 2+4; 2+4; Output: Magma V2.10-6 Wed Feb 18 2004 07:18:37 on modular [Seed = 3533818597] ------------------------------------- 6 6 Total time: 3.079 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pxy-2b.kyoto-u.ac.jp. (130.54.130.228) Time: Wed Feb 18 07:23:49 2004 Input: P:=PolynomialRing(IntegerRing()); P; Output: Magma V2.10-6 Wed Feb 18 2004 07:23:46 on modular [Seed = 643120991] ------------------------------------- Univariate Polynomial Ring in x over Integer Ring Total time: 2.939 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pxy-2b.kyoto-u.ac.jp. (130.54.130.228) Time: Wed Feb 18 07:27:00 2004 Input: (x^6-5*x^2+2)*(17*x^3-1); Output: Magma V2.10-6 Wed Feb 18 2004 07:26:57 on modular [Seed = 809708042] ------------------------------------- >> (x^6-5*x^2+2)*(17*x^3-1); ^ User error: Identifier 'x' has not been declared or assigned Total time: 2.939 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pxy-2b.kyoto-u.ac.jp. (130.54.130.228) Time: Wed Feb 18 07:27:39 2004 Input: P:=PolynomialRing(IntegerRing()); (x^6-5*x^2+2)*(17*x^3-1); Output: Magma V2.10-6 Wed Feb 18 2004 07:27:36 on modular [Seed = 259790108] ------------------------------------- 17*x^9 - x^6 - 85*x^5 + 34*x^3 + 5*x^2 - 2 Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pxy-2b.kyoto-u.ac.jp. (130.54.130.228) Time: Wed Feb 18 07:28:12 2004 Input: P:=PolynomialRing(IntegerRing()); (x^6-5*x^2+2)*(17*x^3-1); Factorization(x^8-1); Output: Magma V2.10-6 Wed Feb 18 2004 07:28:09 on modular [Seed = 108338292] ------------------------------------- 17*x^9 - x^6 - 85*x^5 + 34*x^3 + 5*x^2 - 2 [ , , , ] Total time: 2.979 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pxy-2b.kyoto-u.ac.jp. (130.54.130.228) Time: Wed Feb 18 07:29:06 2004 Input: ?div Output: Magma V2.10-6 Wed Feb 18 2004 07:29:03 on modular [Seed = 477038264] ------------------------------------- 16 matches: 1 O /magma/ring-field-algebra 2 S /magma/ring-field-algebra/algebraic-field/divisors/div-arith 3 S /magma/ring-field-algebra/algebraic-field/divisors/div-create-e 4 S /magma/ring-field-algebra/algebraic-field/divisors/div-create-s 5 S /magma/ring-field-algebra/algebraic-field/divisors/div-other 6 I /magma/geometry/algebraic-curve/divisors/divisor-arithmetic/\ divisors-coeff-arith/+ 7 I /magma/group/braid/braid-groups-elements/braid-groups-arithmetic/\ LeftDiv 8 I /magma/group/braid/braid-groups-elements/braid-groups-arithmetic/\ LeftDiv 9 I /magma/module-lattice/lattice/element/operation/div 10 I /magma/module-lattice/modules-affine-algebras/element-access/\ arithmetic/div 11 I /magma/ring-field-algebra/algebraic-field/operation-element/\ field-element/div 12 I /magma/ring-field-algebra/distributive-multivariate-polynomial/\ operation-element/division/div 13 I /magma/ring-field-algebra/integer/operation-element/arithmetic/div 14 I /magma/ring-field-algebra/local/operation-element/arithmetic/div 15 I /magma/ring-field-algebra/univariate-polynomial/\ operation-element/division/div 16 I /magma/ring-field-algebra/valuation/element/arithmetic/div To view an entry, type ? followed by the number next to it Total time: 3.019 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pxy-2b.kyoto-u.ac.jp. (130.54.130.228) Time: Wed Feb 18 07:31:37 2004 Input: ?div ?15 Output: Magma V2.10-6 Wed Feb 18 2004 07:31:34 on modular [Seed = 1814001505] ------------------------------------- 16 matches: 1 O /magma/ring-field-algebra 2 S /magma/ring-field-algebra/algebraic-field/divisors/div-arith 3 S /magma/ring-field-algebra/algebraic-field/divisors/div-create-e 4 S /magma/ring-field-algebra/algebraic-field/divisors/div-create-s 5 S /magma/ring-field-algebra/algebraic-field/divisors/div-other 6 I /magma/geometry/algebraic-curve/divisors/divisor-arithmetic/\ divisors-coeff-arith/+ 7 I /magma/group/braid/braid-groups-elements/braid-groups-arithmetic/\ LeftDiv 8 I /magma/group/braid/braid-groups-elements/braid-groups-arithmetic/\ LeftDiv 9 I /magma/module-lattice/lattice/element/operation/div 10 I /magma/module-lattice/modules-affine-algebras/element-access/\ arithmetic/div 11 I /magma/ring-field-algebra/algebraic-field/operation-element/\ field-element/div 12 I /magma/ring-field-algebra/distributive-multivariate-polynomial/\ operation-element/division/div 13 I /magma/ring-field-algebra/integer/operation-element/arithmetic/div 14 I /magma/ring-field-algebra/local/operation-element/arithmetic/div 15 I /magma/ring-field-algebra/univariate-polynomial/\ operation-element/division/div 16 I /magma/ring-field-algebra/valuation/element/arithmetic/div To view an entry, type ? followed by the number next to it =============================================================================== PATH: /magma/ring-field-algebra/univariate-polynomial/operation-element/\ division/div KIND: Intrinsic =============================================================================== f div g : RngUPolElt, RngUPolElt -> RngUPolElt The quotient q of f by g, where f and g are in the polynomial ring P=R[x]. Magma calculates the polynomials q (quotient) and r (remainder) in P such that f = q * g + r, and the degree of r is minimal. The leading coefficient of g has to be a unit. If the leading coefficient of g is a unit in R, then the degree of r will be strictly less than that of g (taking the degree of 0 to be -1). Over the integers (R=Z) this will be true in general when the leading coefficient of g divides that of f. To find r, use mod, and to find both q and r, use Quotrem. =============================================================================== Total time: 3.079 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pxy-2b.kyoto-u.ac.jp. (130.54.130.228) Time: Wed Feb 18 07:33:04 2004 Input: ?Quotrem Output: Magma V2.10-6 Wed Feb 18 2004 07:33:00 on modular [Seed = 2064146477] ------------------------------------- 5 matches: 1 I /magma/ring-field-algebra/function-field/Divisors/\ operation-element/arithmetic/Quotrem 2 I /magma/ring-field-algebra/function-field/Places/\ operation-element/arithmetic/Quotrem 3 I /magma/ring-field-algebra/integer/operation-element/simple/Quotrem 4 I /magma/ring-field-algebra/univariate-polynomial/\ operation-element/division/Quotrem 5 I /magma/ring-field-algebra/valuation/element/other/Quotrem To view an entry, type ? followed by the number next to it Total time: 3.009 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pxy-2b.kyoto-u.ac.jp. (130.54.130.228) Time: Wed Feb 18 07:33:21 2004 Input: ?Quotrem ?4 Output: Magma V2.10-6 Wed Feb 18 2004 07:33:18 on modular [Seed = 1912695255] ------------------------------------- 5 matches: 1 I /magma/ring-field-algebra/function-field/Divisors/\ operation-element/arithmetic/Quotrem 2 I /magma/ring-field-algebra/function-field/Places/\ operation-element/arithmetic/Quotrem 3 I /magma/ring-field-algebra/integer/operation-element/simple/Quotrem 4 I /magma/ring-field-algebra/univariate-polynomial/\ operation-element/division/Quotrem 5 I /magma/ring-field-algebra/valuation/element/other/Quotrem To view an entry, type ? followed by the number next to it =============================================================================== PATH: /magma/ring-field-algebra/univariate-polynomial/operation-element/\ division/Quotrem KIND: Intrinsic =============================================================================== Quotrem(f, g) : RngUPolElt, RngUPolElt -> RngUPolElt, RngUPolElt Given elements f and g of the polynomial ring P=R[x], this function returns polynomials q (quotient) and r (remainder) in P such that f = q.g + r, and the degree of r is minimal. The leading coefficient of g has to be a non-zero divisor in R. If the leading coefficient of g is a unit, then the degree of r will be strictly less than that of g (taking the degree of 0 to be -1). Over the integers (R=Z) this will be true in general when the leading coefficient of g divides that of f. =============================================================================== Total time: 3.069 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pxy-2b.kyoto-u.ac.jp. (130.54.130.228) Time: Wed Feb 18 07:34:08 2004 Input: ? Output: Magma V2.10-6 Wed Feb 18 2004 07:34:04 on modular [Seed = 1211847647] ------------------------------------- =============================================================================== PATH: /language/statement KIND: Overview =============================================================================== A statement is a complete command to Magma. Every statement must end with a semicolon ( ; ). If you press the key before typing ; then Magma may give you a special prompt symbol such as print> or if> to remind you that the statement is not yet finished. EXAMPLE: > print 5+8; > DivBy3 := func< n | IsZero(n mod 3) >; =============================================================================== Total time: 3.069 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pxy-2b.kyoto-u.ac.jp. (130.54.130.228) Time: Wed Feb 18 07:36:27 2004 Input: 23 div 4; 23 mod 4; Output: Magma V2.10-6 Wed Feb 18 2004 07:36:24 on modular [Seed = 1529366328] ------------------------------------- 5 3 Total time: 2.939 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pxy-2b.kyoto-u.ac.jp. (130.54.130.228) Time: Wed Feb 18 07:36:47 2004 Input: 23 div 4, 23 mod 4; Output: Magma V2.10-6 Wed Feb 18 2004 07:36:44 on modular [Seed = 1377914405] ------------------------------------- 5 3 Total time: 2.989 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pxy-2b.kyoto-u.ac.jp. (130.54.130.228) Time: Wed Feb 18 07:38:28 2004 Input: (2/3)/(4+7/9); 4.7/2.6; Output: Magma V2.10-6 Wed Feb 18 2004 07:38:25 on modular [Seed = 2849682755] ------------------------------------- 6/43 1.80769230769230769230769230768 Total time: 2.999 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pxy-2b.kyoto-u.ac.jp. (130.54.130.228) Time: Wed Feb 18 07:39:51 2004 Input: 2+4*9; (2+4)*9; 3^3^3; Output: Magma V2.10-6 Wed Feb 18 2004 07:39:48 on modular [Seed = 2815736472] ------------------------------------- 38 54 7625597484987 Total time: 2.889 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pxy-2b.kyoto-u.ac.jp. (130.54.130.228) Time: Wed Feb 18 07:40:15 2004 Input: 2^2; 2^2^2; 2^2^2^2; 2^2^2^2^2; Output: Magma V2.10-6 Wed Feb 18 2004 07:40:11 on modular [Seed = 3083119287] ------------------------------------- 4 16 65536 2003529930406846464979072351560255750447825475569751419265016973710894059556311\ 4530895061308809333481010382343429072631818229493821188126688695063647615470291\ 6504187191635158796634721944293092798208430910485599057015931895963952486337236\ 7203002916969592156108764948889254090805911457037675208500206671563702366126359\ 7471448071117748158809141357427209671901518362825606180914588526998261414250301\ 2339110827360384376787644904320596037912449090570756031403507616256247603186379\ 3126484703743782954975613770981604614413308692118102485959152380195331030292162\ 8001605686701056516467505680387415294638422448452925373614425336143737290883037\ 9460127472495841486491593064725201515569392262818069165079638106413227530726714\ 3998158508811292628901134237782705567421080070065283963322155077831214288551675\ 5540733451072131124273995629827197691500548839052238043570458481979563931578535\ 1001899200002414196370681355984046403947219401606951769015611972698233789001764\ 1517190051133466306898140219383481435426387306539552969691388024158161859561100\ 6403621197961018595348027871672001226046424923851113934004643516238675670787452\ 5946467090388654774348321789701276445552940909202195958575162297333357615955239\ 4885297579954028471943529913543763705986928913757153740001986394332464890052543\ 1066296691652434191746913896324765602894151997754777031380647813423095961909606\ 5459130089018888758808473362595606544488850144733570605881709016210849971452956\ 8344061979690565469813631162053579369791403236328496233046421066136200220175787\ 8518574091620504897117818204001872829399434461862243280098373237649318147898481\ 1945271300744022076568091037620399920349202390662626449190916798546151577883906\ 0397720759279378852241294301017458086862263369284725851403039615558564330385450\ 6886522131148136384083847782637904596071868767285097634712719888906804782432303\ 9471865052566097815072986114143030581692792497140916105941718535227588750447759\ 2218301158780701975535722241400019548102005661773589781499532325208589753463547\ 0077866904064290167638081617405504051176700936732028045493390279924918673065399\ 3164072049223847481528061916690093380573212081635070763435166986962502096902316\ 2859350071874190579161241536897514808261904847946571736601005892476655445840838\ 3347905441448176842553272073155863493476051374197795251903650321980201087647383\ 6868253102518337753390886142618480037400808223810407646887847164755294532694766\ 1700424461063311238021134588694532200116564076327023074292426051582811070387018\ 3453245676356259514300320374327407808790562836634069650308442258559670392718694\ 6115851379338647569974856867007982396060439347885086164926030494506174341236582\ 8352144806726676841807083754862211408236579802961200027441324438432402331257403\ 5450193524287764308802328508558860899627744581646808578751158070147437638679769\ 5504999164399828435729041537814343884730348426190338884149403136613985425763557\ 7105335580206622185577060082551288893332226436281984838613239570676191409638533\ 8323743437588308592337222846442879962456054769324289984326526773783731732880632\ 1075321123868060467470842805116648870908477029120816110491255559832236624486855\ 6651402684641209694982590565519216188104341226838996283071654868525536914850299\ 5396755039549383718534059000961874894739928804324963731657538036735867101757839\ 9481847179849824694806053208199606618343401247609663951977802144119975254670408\ 0608499344178256285092726523709898651539462193004607364507926212975917698293892\ 3670151709920915315678144397912484757062378046000099182933213068805700465914583\ 8720808801688744583555792625846512476308714856631352893416611749061752667149267\ 2176128330845273936469244582892571388877839056300482483799839692029222215486145\ 9023734782226825216399574408017271441461795592261750838890200741699262383002822\ 8624928418267124340575142418856999427233160699871298688277182061721445314257494\ 4015066139463169197629181506579745526236191224848063890033669074365989226349564\ 1146655030629659601997206362026035219177767406687774635493753188995878662821254\ 6979710206574723272137291814466665942187200347450894283091153518927111428710837\ 6159222380276605327823351661555149369375778466670145717971901227117812780450240\ 0263847587883393968179629506907988171216906869295382485298300234760684541141781\ 3911064856023654975422749723100761513187002405391051091381784372179142252858743\ 2098524957878034683703337818421444017138688124249984418618129271198533315382567\ 3218704215306311977485352146709553346263366108646673322924098798492566911095161\ 4361860154890974024191350962304361219612816595051866602203071561368473236466086\ 8905014263913906515063908199378852318365059897299125404479443425166774299659811\ 8492331515552728832740283526884424087528112832899806259126736995462473415433335\ 0014723143061275039030739713525206933817384332295070104906186753943313078479801\ 5655130384758155685236218010419650255596181934986315913233036096461905990236112\ 6811960234418433633345949276319461017166529138237171823942992162725384617760656\ 9454229787707138319881703696458868981186321097690035573588462446483570629145305\ 2757101278872027965364479724025405448132748391794128826423835171949197209797145\ 9368875371987291308317380339110161285474153773777159517280841116275971863849242\ 2280237344192546999198367219213128703558530796694271341639103388275431861364349\ 0100943197409047331014476299861725424423355612237435715825933382804986243892498\ 2227807159517627578471094751190334822414120251826887137281931042534781961284401\ 7647953150505711072297431456991522345164312184865757578652819756484350895838472\ 2923534559464521215831657751471298708225909292655638836651120681943836904116252\ 6687100445602437042006637090019411855571604720446436969328500600469281405071190\ 6926139399390273553454556747031490388602202463994826050176243196930564066636662\ 6090207048887438898907498152865444381862917382901051820869936382661868303915273\ 2645812867828066013375000965933646251460917231803129303478774212346791184547913\ 1110989779464821692250562939995679348380169915743970053754213448587458685604728\ 6751065423341893839099110586465595113646061055156838541217459801807133163612573\ 0796111683438637676673073545834947897883163301292408008363568259391571131309780\ 3051644171668251834657367593419808495894794098329250008638977856349469321247342\ 6103062713745077286156922596628573857905533240641849018451328284632709269753830\ 8673084091422476594744399733481308109863994173797896570106870267341619671965915\ 9958853783482298827012560584236558953969030647496558414798131099715754204325639\ 5776070485100881578291408250777738559790129129407309462785944505859412273194812\ 7532251523248015034665190482289614066468903051025109162377704484862302294889667\ 1138055560795662073244937337402783676730020301161522700892184351565212137921574\ 8206859356920790214502277133099987729459596952817044582181956080965811702798062\ 6698912050615607423256868422713062950098644218534708104071289176469065508361299\ 1669477802382250278966784348919940965736170458678624255400694251669397929262471\ 4524945408858422726153755260071904336329196375777502176005195800693847635789586\ 8784895368721228985578068265181927036320994801558744555751753127364714212955364\ 9408438558661520801211507907506855334448925869328385965301327204697069457154695\ 9353658571788894862333292465202735853188533370948455403336565356988172582528918\ 0566354883637437933484118455801683318276768346462919956055134700391478768086403\ 2262961664156066750815371064672310846196424753749055374480531822600271021640098\ 0584497526023035640038083472053149941172965736785066421400842696497103241919182\ 1212132069397691439233683747092282677387081322366800869247034915868409911530983\ 1541206356612318750430546753698323082796645741762080659317726568584168183796610\ 6144963432544111706941700222657817358351259821080769101961052229263879745049019\ 2543119006205619065774524161919131875339840493439768233102984658933183730158095\ 9252282920682086223033258528011926649631444131644277300323779227471233069641714\ 9945532261035475145631290668854345426869788447742981777493710117614651624183616\ 6802548152963353084908499430067636548061029400946937506098455885580439704859144\ 4958444507997849704558355068540874516331646411808312307970438984919050658758642\ 5810738422420591191941674182490452700288263983057950057341711487031187142834184\ 4991534567029152801044851451760553069714417613685823841027876593246626899784183\ 1962031226242117739147720800488357833356920453393595325456489702855858973550575\ 1235129536540502842081022785248776603574246366673148680279486052445782673626230\ 8529782650571146248465959142102781227889414481639949738818846227682448516220518\ 1707672216986326570165431691974265123004175732990447353767253684579275436541282\ 6553581858046840069367718605020070547247548400805530424951854495267247261347318\ 1747421800785746934654471360369758841180294080396167469462885406791721386012254\ 1950381970453841726800639882065632879283958270851091995883944829777564715202613\ 2871089526163417707151642899487953564854553553148754978134009964854498635824847\ 6905900331169613037661279234643231297066284113074270462020320133683503854253603\ 1363676357521260470742531120923340283748294945310472741896928727557202761527226\ 8283376741393425652653283068469997597097750005560889932685025049212884068274139\ 8816315404564903507758716800740556857240217586854390532281337707074158307562696\ 2831695568742406052772648585305061135638485196591896864959633556821697543762143\ 0778665934730450164822432964891270709898076676625671517269062058815549666382573\ 8292741820822789606844882229833948166709840390242835143068137672534601260072692\ 6296946867275079434619043999661897961192875051944235640264430327173734159128149\ 6056168353988188569484045342311424613559925272330064881627466723523751234311893\ 44211888508507935816384899448754475633168921386967557430273795378526254 ** WARNING: Output too long, hence truncated. ************** MAGMA ***************** Host pxy-2b.kyoto-u.ac.jp. (130.54.130.228) Time: Wed Feb 18 07:41:17 2004 Input: 3^3^3; 4^4^4; 5^5^5; 6^6^6; 7^7^7; Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Wed Feb 18 2004 07:40:54 on modular [Seed = 2398983155] ------------------------------------- 7625597484987 1340780792994259709957402499820584612747936582059239337772356144372176403007354\ 6976801874298166903427690031858186486050853753882811946569946433649006084096 1911012597945477520356404559703964599198081048990094337139512789246520530242615\ 8030120593865197398502655864401557944622353592127886738069722884101469159866020\ 8796189675719570183928166033804761122597553362610100148265112341314776825241149\ 3094447176965282756285196737514395357542479093219206641883011787169122552421070\ 0507090646743828708514499502565861944615431835113798491336917799281274338404315\ 4923685552678359637410210533154603135372532574863690915977869032826645918298381\ 5230286936572873691422648131291743762136325730321645282979486862576245362218017\ 6732249405676428193600787207138370723553054463561539464011853484937927195145945\ 0550823274922160584891291094518995994868619954314766693801303717616359259447974\ 6164220050885079469804487133205133160739134230540198872570038329801246050197013\ 4673971759090273894939238173157869968458997947810680428224360937839463352654228\ 1570430283244238551508231649096728571217170812323279048181726832751011274678231\ 7410985888683708522000711733492253913322300756147180429007527677793352306200618\ 2860124552542430610068948054465847048206509826643193609603887362585107470743406\ 3628697657670269925864995355797631817390255089133122329474393034395616132833407\ 2831663498258145226862004307799084688103804187368324800903873596212919633602583\ 1207816736737425333228792969072054905956214068888259912445818423795978634764843\ 1567376092362509037151179894142426227022006628648686786871018298087280256069310\ 1949280830825044198424796792058908817112327192301455582916746795197430548026404\ 6468540027339938607985944659615017525869658114475685100415686877309037124825353\ 4383928539759874945849705003822501248928400182659005625128618762993804440734014\ 2347062055785305325034918189589707199305662188512963187501743535960282201038211\ 6160485451210393133122563322607664362366882968502088394961428304847391139916696\ 2264994856368523471287329479668088450940589395110465094413790950227654565313301\ 8670633521323028460519434381399810561400652595300731790772711065783494174642684\ 7209561346473277485842382748996687550525043942182321913572230540667153733742485\ 4364566378204570165459321815405354839361425066449858540330746646854189014813434\ 7714650315037954175778622811776585876941680908203125 2659119772153226779682489404387918594905342200269924300660432789497073559873882\ 9091213422929061755830324406828265067234256016357755902793896426126110930203989\ 3034777446061389442537960087466214788422902213385381919290542791575075927495293\ 5109319020362271989830578539328807633196834507090639946131138999460277671978289\ 4125322123292520329605118204879136400838954904436579209562671262919222892246094\ 4103484957826646121969087967503992005139138817452525944319386504163034800032329\ 5729231692725808120388628956451330203199414186213654593812478970390749485268614\ 9719642484285627826487208185484939372990256931327191655440604310691360290106405\ 5895953421212374607966076698330673506053248292555308212118869609719907808556324\ 6046013216102655431476452400396602364732664246252767374593256582134654265209220\ 0423701432404566464797038786340284767995163013023205896206379946238959999623765\ 3062587414899860913010693318793720947688749687131107213871394369489435728806106\ 1557708461902289692063089736008186036231141171109877425423962410946849388972369\ 2229868569843429449642470140802948317293238661862906599604019822684282364653842\ 2586113704883857989007702229553937496834838684871215875596667442178077474619334\ 1210284889327660838136389953101390774574758301775513253381447321315090878342620\ 2141074589657337735067867485009838541438860204109111373970447647124896178134657\ 6074509649789560993834854196961759483379704895730837108476073243820752302407048\ 5676366743247949452619568563043097519281279901865567251422836828609153126216460\ 7345315800880321538864368261641121986701237220967952805350151681595261506024638\ 5651031976562807101388014614012727625982704958770707410574826165853317280489979\ 6647665799512016121857794554314732807944463937679710202841966709590373326913064\ 8509487971165760759273875265486950175533115298307542310219922387378915117039469\ 8211199449920074131308554214681213100553681303428933484193987068952218348302678\ 8318279211074015593520658290920832202358534204685761697532570041173608482405870\ 8316251068319872736680439547350926932156113607132883103875634505032211015537060\ 5205773322174682858545420089112607776943756235718685791083329489150388849193534\ 3685602140772592750173300818010227855065558133740979531794020135520818832606782\ 0100816398249113946898528658683952592451639902206088916703402630725949553703103\ 6865710606177193275628159515876151135875206383384565803345010001967990900297897\ 7210476250415036861890539382236467101342139404047198098937821736422631345084415\ 5084928788944718684436772321138168459653343097848549218348328628086605976293753\ 3235790152346913482052907574065476985428074987463200630523320192960729488033220\ 1004717281324198437509334189946518277661952803985354578792105909387255417312074\ 7621525117838001854428727026143848075169886235092312850223508774079275269944791\ 6376634508067462510897466136541982989588498885556218913512465902304156653376336\ 8715666883872519670361529007800640686028880699319352079993106891407764243519484\ 1873000496551583222171096899743145933378494129522944030965551185586702844503519\ 8762119848288829295380202219936661078120427828843001276230841951275304807279299\ 9430981041279846531138489663915470801660511525166958395469518574113425090292056\ 5803702371824003777483260335454309351150011847970153429740074513674484611585461\ 8011592988204941297108616076522379205004659217817374565514468243397003282844487\ 4727091779059199199358992754255739644938275793654460000274764771917984145132545\ 8165027536733301982127884317270946575069275217180859490121750950120741742161758\ 6944497161282705033574579740947969818330006129341292987484417693746915156267819\ 6944190690705517408341270110116530574809547623023762237215060111172786568367816\ 8746764256566024505419592238301506354098330297656458503223221234832849268443851\ 7686135813543777864727386998363224693825363151801851106716453198841449354389812\ 1913341135214098433302365245387920761986009692225770264786814922275015405662983\ 5170763956641633686286846795059729747683692320947290092229370228618694089033287\ 8669151652070026861441427046793265655884082960714097320267268049408177667445088\ 4965348180178536723618226884857339133854002554565679342826314848719771140478757\ 0805868543619247666329872476144815634284283040260250502157420429656415893036607\ 8365481437442997463536675091000411699963360673064732160583745460680016965456758\ 5660962905152709201645875359613001828866538307844122009421906770504442910472440\ 0338945610254181442573942904470433088000869614865383635497648482086438633359077\ 2821957611006776947872616515008395331769033371947624815253698065061836502368055\ 4431459093152034405561484568860650743316691318968247599582565088000180171489431\ 1432338616140040591744676003585928270381442887477162496213203619776525245493346\ 7861555487197397619695431510692383342974202667545414955466938030160673169706724\ 4626258551370851645391322577304348105969848017839230034831055415640301000157431\ 8363088271619670316655426565096307103879220539680315920477904433236931651777785\ 9190655421620788215534975404890121605354486244302325493234970592691383707828560\ 1349377225336743205365375169877349183777799512554222275972716118029303245222040\ 2175805775241249712745521825292094227842847947169853969781345269676790717922850\ 8491839775153628228243052306992659549440199892772061036616473355839050070498310\ 4734871820642675450015770792062615402032657173010642210191250683502667912493991\ 7960929109036707635684925844071845295552207259748158406331181740311377161873180\ 1958998128677729597378367094064062033675539166479397859978760723803175210934594\ 3211213245184776643282291717067329390590611377334237254454253333764205685000119\ 3700991122080485436988881739995354037296008464004215102803014253112283196161957\ 1524522422266809290751616197961883530242609434051902857830543763397061153243582\ 4942105030926815212418399836123882923621685584810804537249260089845227867729237\ 3925746477183290922071023540633431838930936317317923907752973092138140886569986\ 9199075222777463146266117543342519940204770331943339078678783474761260772613750\ 6165832564303984452942500391460991393998606523780004197450420782411818751232638\ 0718368393963815092903223756458204021992572554406619436546545607277504604301995\ 3993748322983683489516208150738424224196778813811196748091317343045579356718550\ 3253077370951114339420093226364558981503238107164979185429453859587491416458261\ 1340382160163904914690554622878987393587127110178251704306000449333379035230261\ 3291297240328564529779500158901992057657168980489272863072158461749965174823389\ 9013735670497661974774566958118340094026521126535891155535929942925658149730479\ 9536927229726101711111934451119961877285162664439375171281088704824407739875503\ 2272241691310649437516764253759232572706022781934855221122174485770810461351760\ 7227866285161431584555506426114705436926937102207295289591203404452105297886929\ 0369227711092923808319201305155269917739063897908527599113641594775880324806565\ 8708433324533317375936823619422963019751271123958949266745154287327508514137369\ 6736275088647141468241347762353946251726651995399677652856675923289105145097886\ 7257444586595186908132381256973600847975826933474902529005843319787694328408058\ 0745193611989429990468280533178199550083230163227944716082271056280731820677005\ 3559618683620245098910221398201256238417876905853099286122673035956258245084360\ 1854424142186404275027338471616760698128093125032964959943475205297146297336367\ 2222035938392416581 ** WARNING: Output too long, hence truncated. Errors: /home/mfd/gomagma: line 2: 27557 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host pxy-2b.kyoto-u.ac.jp. (130.54.130.228) Time: Wed Feb 18 07:42:52 2004 Input: Factorial(18); GCD(15130,3162); Output: Magma V2.10-6 Wed Feb 18 2004 07:42:49 on modular [Seed = 2247530599] ------------------------------------- 6402373705728000 34 Total time: 3.009 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pxy-2b.kyoto-u.ac.jp. (130.54.130.228) Time: Wed Feb 18 07:46:31 2004 Input: "Number of permutations of five objects is",Factorial(5); Output: Magma V2.10-6 Wed Feb 18 2004 07:46:27 on modular [Seed = 2548336920] ------------------------------------- Number of permutations of five objects is 120 Total time: 3.019 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pxy-2b.kyoto-u.ac.jp. (130.54.130.228) Time: Wed Feb 18 07:49:29 2004 Input: rqA5:=1492478; rqA5*10; rqA5:=rqA5+1; ShowIdentifiers(); ShowValues(); Output: Magma V2.10-6 Wed Feb 18 2004 07:49:26 on modular [Seed = 3986616976] ------------------------------------- 14924780 rqA5 rqA5: 1492479 Total time: 2.939 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pxy-2b.kyoto-u.ac.jp. (130.54.130.228) Time: Wed Feb 18 07:57:09 2004 Input: IsPrime(257); IsPrime(2^59-1); IsPrime(2^61-1); IsPrime(2^67-1); Output: Magma V2.10-6 Wed Feb 18 2004 07:57:06 on modular [Seed = 4102542845] ------------------------------------- true false true false Total time: 3.019 seconds, Total memory usage: 2.99MB ************** MAGMA ***************** Host pxy-2b.kyoto-u.ac.jp. (130.54.130.228) Time: Wed Feb 18 07:57:34 2004 Input: IsPrime(2^521-1); Output: Magma V2.10-6 Wed Feb 18 2004 07:57:31 on modular [Seed = 3283149523] ------------------------------------- true Total time: 3.689 seconds, Total memory usage: 2.99MB ************** MAGMA ***************** Host pxy-2b.kyoto-u.ac.jp. (130.54.130.228) Time: Wed Feb 18 07:58:11 2004 Input: IsPrime(2^2281-1); Output: Magma V2.10-6 Wed Feb 18 2004 07:57:48 on modular [Seed = 3668573117] ------------------------------------- true Total time: 22.250 seconds, Total memory usage: 3.00MB ************** MAGMA ***************** Host 3(NXDOMAIN) (159.226.47.109) Time: Wed Feb 18 08:01:02 2004 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: Magma V2.10-6 Wed Feb 18 2004 08:00:59 on modular [Seed = 1045240857] ------------------------------------- Replace this by some code, then click [PARI] or [MAGMA]! Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pxy-2b.kyoto-u.ac.jp. (130.54.130.228) Time: Wed Feb 18 08:01:12 2004 Input: a:=6; b:=8; c:=10; if (a gt (b+c)) and (b gt (c+a)) and (c gt (a+b)) then s:=(a+b+c)/2; "Area is", Sqrt(s*(s-a)*(s-b)*(s-c)), "square units."; else "Triangle is degenerate."; endif; Output: Magma V2.10-6 Wed Feb 18 2004 08:01:08 on modular [Seed = 24257337] ------------------------------------- User error: syntax error at end of input Total time: 3.009 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pxy-2b.kyoto-u.ac.jp. (130.54.130.228) Time: Wed Feb 18 08:01:24 2004 Input: a:=6; b:=8; c:=10; if (a gt (b+c)) and (b gt (c+a)) and (c gt (a+b)) then s:=(a+b+c)/2; "Area is", Sqrt(s*(s-a)*(s-b)*(s-c)), "square units."; else "Triangle is degenerate."; endif Output: Magma V2.10-6 Wed Feb 18 2004 08:01:21 on modular [Seed = 443103255] ------------------------------------- User error: syntax error at end of input Total time: 2.939 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pxy-2b.kyoto-u.ac.jp. (130.54.130.228) Time: Wed Feb 18 08:01:34 2004 Input: a:=6; b:=8; c:=10; if (a gt (b+c)) and (b gt (c+a)) and (c gt (a+b)) then s:=(a+b+c)/2; "Area is", Sqrt(s*(s-a)*(s-b)*(s-c)), "square units."; else "Triangle is degenerate."; end if Output: Magma V2.10-6 Wed Feb 18 2004 08:01:31 on modular [Seed = 1813991019] ------------------------------------- Triangle is degenerate. Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pxy-2b.kyoto-u.ac.jp. (130.54.130.228) Time: Wed Feb 18 08:03:27 2004 Input: a:=6; b:=8; c:=10; if ((a+b) gt c) and ((b+c) gt a) and ((c+a) gt b) then s:=(a+b+c)/2; "Area is", Sqrt(s*(s-a)*(s-b)*(s-c)), "square units."; else "Triangle is degenerate."; end if Output: Magma V2.10-6 Wed Feb 18 2004 08:03:24 on modular [Seed = 1712669910] ------------------------------------- Area is 24.00000000000000000000000000 square units. Total time: 3.029 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pxy-2b.kyoto-u.ac.jp. (130.54.130.228) Time: Wed Feb 18 08:03:46 2004 Input: a:=6; b:=8; c:=15; if ((a+b) gt c) and ((b+c) gt a) and ((c+a) gt b) then s:=(a+b+c)/2; "Area is", Sqrt(s*(s-a)*(s-b)*(s-c)), "square units."; else "Triangle is degenerate."; end if Output: Magma V2.10-6 Wed Feb 18 2004 08:03:43 on modular [Seed = 2131516924] ------------------------------------- Triangle is degenerate. Total time: 3.019 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host scylla.inria.fr. (138.96.81.2) Time: Wed Feb 18 08:18:03 2004 Input: 2+2; Output: Magma V2.10-6 Wed Feb 18 2004 08:18:00 on modular [Seed = 1462006131] ------------------------------------- 4 Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host host250-185.pool81115.interbusiness.it. (81.115.185.250) Time: Wed Feb 18 09:47:30 2004 Input: a=1:100 Output: Magma V2.10-6 Wed Feb 18 2004 09:47:27 on modular [Seed = 7551698] ------------------------------------- >> a=1:100; ^ User error: bad syntax Total time: 2.949 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host host250-185.pool81115.interbusiness.it. (81.115.185.250) Time: Wed Feb 18 09:47:47 2004 Input: a:=1 Output: Magma V2.10-6 Wed Feb 18 2004 09:47:44 on modular [Seed = 459808806] ------------------------------------- Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pD95438A3.dip.t-dialin.net. (217.84.56.163) Time: Wed Feb 18 14:07:20 2004 Input: > t := { n^2 : n in [-11..11 by 2] | IsPrime(n) }; Output: Magma V2.10-6 Wed Feb 18 2004 14:07:17 on modular [Seed = 927252706] ------------------------------------- Total time: 3.089 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pD95438A3.dip.t-dialin.net. (217.84.56.163) Time: Wed Feb 18 14:07:43 2004 Input: > t := { n^2 : n in [-11..11 by 2] | IsPrime(n) }; t Output: Magma V2.10-6 Wed Feb 18 2004 14:07:40 on modular [Seed = 542365676] ------------------------------------- { 9, 25, 49, 121 } Total time: 3.059 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pD95438A3.dip.t-dialin.net. (217.84.56.163) Time: Wed Feb 18 14:08:17 2004 Input: t := { n^2 : n in [-11..11 by 2] | IsPrime(n) } t Output: Magma V2.10-6 Wed Feb 18 2004 14:08:14 on modular [Seed = 693817607] ------------------------------------- >> t; ^ User error: bad syntax Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pD95438A3.dip.t-dialin.net. (217.84.56.163) Time: Wed Feb 18 14:08:29 2004 Input: t := { n^2 : n in [-11..11 by 2] | IsPrime(n) }; t Output: Magma V2.10-6 Wed Feb 18 2004 14:08:26 on modular [Seed = 308406792] ------------------------------------- { 9, 25, 49, 121 } Total time: 2.969 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pD95438A3.dip.t-dialin.net. (217.84.56.163) Time: Wed Feb 18 14:11:28 2004 Input: XGCD(21, 27) Output: Magma V2.10-6 Wed Feb 18 2004 14:11:25 on modular [Seed = 91684328] ------------------------------------- 3 4 -3 Total time: 2.999 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pD95438A3.dip.t-dialin.net. (217.84.56.163) Time: Wed Feb 18 14:12:33 2004 Input: d, p, q := XGCD(21, 27); d, p, q; Output: Magma V2.10-6 Wed Feb 18 2004 14:12:30 on modular [Seed = 243136288] ------------------------------------- 3 4 -3 Total time: 2.999 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pD95438A3.dip.t-dialin.net. (217.84.56.163) Time: Wed Feb 18 14:13:02 2004 Input: d, p, q := XGCD(a, b); d, p, q; Output: Magma V2.10-6 Wed Feb 18 2004 14:12:59 on modular [Seed = 1996787324] ------------------------------------- >> d, p, q := XGCD(a, b); ^ User error: Identifier 'a' has not been declared or assigned >> d, p, q; ^ User error: Identifier 'd' has not been declared or assigned Total time: 2.999 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pD95438A3.dip.t-dialin.net. (217.84.56.163) Time: Wed Feb 18 14:13:44 2004 Input: a, b := 12, 8; d, p, q := XGCD(a, b); d, p, q; Output: Magma V2.10-6 Wed Feb 18 2004 14:13:41 on modular [Seed = 1611897141] ------------------------------------- >> a, b := 12, 8; ^ User error: bad syntax >> d, p, q := XGCD(a, b); ^ User error: Identifier 'a' has not been declared or assigned >> d, p, q; ^ User error: Identifier 'd' has not been declared or assigned Total time: 2.919 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pD95438A3.dip.t-dialin.net. (217.84.56.163) Time: Wed Feb 18 14:15:31 2004 Input: a := 12; b := 8; d, p, q := XGCD(a, b); d, p, q; Output: Magma V2.10-6 Wed Feb 18 2004 14:15:28 on modular [Seed = 1847433102] ------------------------------------- 4 1 -1 Total time: 2.929 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pD95438A3.dip.t-dialin.net. (217.84.56.163) Time: Wed Feb 18 14:27:22 2004 Input: // Cartesian product of all combinations > firstnames := {"Margie", "Marion", "Myrtle", "Martha", "Mary"}; > surnames := {"Brown", "Green", "Grey", "Black", "White"}; > dogbreeds := {"terrier", "poodle", "great dane", "basset", "setter"}; > dognames := {"Loopsie", "Mooksie", "Smooksie", "Woopsie", "Poopsie"}; > C := car; > // Some useful functions are defined: > iff := 'eq'; // the '...' treats this operator as a function > implies := func< A, B | B or not A >; > S := { a : a in C | > implies(sn eq "Brown", (dn in {"Loopsie","Mooksie"})) and > implies(sn eq "Brown", (db ne "terrier")) and > iff(dn eq "Woopsie", db eq "poodle") and > implies(dn eq "Woopsie", fn ne "Mary") and > iff(fn eq "Marion", db eq "setter") and > implies(fn eq "Marion", dn ne "Loopsie") and > iff(fn eq "Margie", db eq "basset") and > implies(fn eq "Margie", (dn in {"Smooksie","Mooksie"})) and > implies(fn eq "Myrtle", sn ne "Grey") and > implies(fn eq "Myrtle", (dn in {"Poopsie","Smooksie"})) and > iff(fn eq "Martha", sn eq "Black") and > implies(fn eq "Martha", db ne "great dane") and > implies(sn eq "Grey", dn ne "Poopsie") and > iff(dn eq "Mooksie", sn eq "White") and > implies(sn eq "White", fn ne "Marion") > where fn, sn, db, dn is Explode(a) }; > findsoln := function(S, n) > if n eq 1 then > return {S}; > end if; > soln := {}; > T := S; > while #T ge n do > ExtractRep(~T, ~x); > sol:=$$({a : a in T | forall{i : i in [1..4] | a[i] ne x[i] }}, n-1); > soln join:= { Include(U, x) : U in sol | #U eq n-1 }; > end while; > return soln; > end function; > findsoln(S, 5); Output: Magma V2.10-6 Wed Feb 18 2004 14:27:18 on modular [Seed = 1211872494] ------------------------------------- { { , , , , } } Total time: 3.119 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pD95438A3.dip.t-dialin.net. (217.84.56.163) Time: Wed Feb 18 14:33:20 2004 Input: > PartitionWithSeq:=function(set) > > function partnsq(seq) //returns sequence of sets of sets > if #seq le 1 then > return [{Seqset(seq)}]; > else > x := seq[#seq]; > p := partnsq(Prune(seq)); > return [Include(y, {x}) : y in p] > cat [ {Include(z, x)} join Exclude(y, z) : z in y, y in p ]; > end if; > end function; > > return Seqset(partnsq(Setseq(set))); > > end function; > > PartitionWithSeq( {1..2} ); Output: Magma V2.10-6 Wed Feb 18 2004 14:33:17 on modular [Seed = 3117040756] ------------------------------------- >> > ^ User error: bad syntax >> > ^ User error: bad syntax >> return Seqset(partnsq(Setseq(set))); ^ User error: A 'return' can only be used inside a procedure or function >> > ^ User error: bad syntax >> end function; ^ User error: bad syntax >> > ^ User error: bad syntax >> PartitionWithSeq( {1..2} );; ^ User error: Identifier 'PartitionWithSeq' has not been declared or assigned Total time: 3.099 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host pD95438A3.dip.t-dialin.net. (217.84.56.163) Time: Wed Feb 18 14:34:31 2004 Input: > function PartitionSet(s) > if #s le 1 then > return {{s}}; > else > x := Rep(s); > p := PartitionSet(Exclude(s, x)); > return {Include(y, {x}) : y in p} > join { {Include(z, x)} join Exclude(y, z) : z in y, y in p }; > end if; > end function; > PartitionWithSeq:=function(set) > > function partnsq(seq) //returns sequence of sets of sets > if #seq le 1 then > return [{Seqset(seq)}]; > else > x := seq[#seq]; > p := partnsq(Prune(seq)); > return [Include(y, {x}) : y in p] > cat [ {Include(z, x)} join Exclude(y, z) : z in y, y in p ]; > end if; > end function; > > return Seqset(partnsq(Setseq(set))); > > end function; > > PartitionWithSeq( {1..2} ); Output: Magma V2.10-6 Wed Feb 18 2004 14:34:28 on modular [Seed = 2748341719] ------------------------------------- >> > ^ User error: bad syntax >> > ^ User error: bad syntax >> return Seqset(partnsq(Setseq(set))); ^ User error: A 'return' can only be used inside a procedure or function >> > ^ User error: bad syntax >> end function; ^ User error: bad syntax >> > ^ User error: bad syntax >> PartitionWithSeq( {1..2} );; ^ User error: Identifier 'PartitionWithSeq' has not been declared or assigned Total time: 3.019 seconds, Total memory usage: 1.80MB