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Author: William A. Stein
Compute Environment: Ubuntu 18.04 (Deprecated)
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#
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# magma.py -- compute things using system calls to MAGMA
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#
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# William Stein, 10/30/2000
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#
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import os, string
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import misc, constants
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MAGMA='%s/gomagma'%constants.bin
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def magma(cmd, gocmd=MAGMA):
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cmd=cmd+";"
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file = misc.newtempfile()
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outname = misc.newtempfilename()
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cmd = 'Attach("/var/www/%s/magma.m");\n'%constants.CGIROOT + cmd
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cmd = cmd + 'if not assigned ans then ans := $1; end if; \n fprintf Open(\"' + outname + '\","w"), \"%o\", ans;'
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file.write(cmd)
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file.close()
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os.system(MAGMA + ' < ' + file.name + ' > %s/magma.errors'%constants.home )
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if not os.path.exists(outname):
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return "An error occured while running the computation. "+\
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"Please carefully check that your input is valid. "+\
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"If you're sure that it is valid but the computation still "+\
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"won't run, you may want to email "+\
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"William Stein at <a href=\"mailto:[email protected]\">"+\
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"[email protected]</a>.";
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ansfile = open(outname,'r')
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ans = ansfile.read()
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ansfile.close()
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os.remove(file.name)
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os.remove(ansfile.name)
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return ans
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def genusX0(N):
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cmd = "ans := DimensionCuspFormsGamma0(" + str(N) + ",2);ans;";
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return magma(cmd)
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def dimension_cuspforms_gamma0(N,k):
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cmd = "ans := DimensionCuspFormsGamma0(%s, %s);ans;"%(N,k);
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return magma(cmd)
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def dimension_new_cuspforms_gamma0(N,k):
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cmd = "ans := DimensionNewCuspFormsGamma0(%s, %s);ans;"%(N,k);
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return magma(cmd)
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def dimension_cuspforms(N,k,eps):
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if eps == "1":
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return dimension_cuspforms_gamma0(N,k)
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cmd = "eps := DirichletGroup(%s,CyclotomicField(EulerPhi(%s)))!%s; "%(N,N,eps) + \
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"ans := DimensionCuspForms(eps, %s);ans;"%k;
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return magma(cmd)
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def dimension_new_cuspforms(N,k,eps):
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if eps == "1":
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return dimension_new_cuspforms_gamma0(N,k)
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cmd = "eps := DirichletGroup(%s,CyclotomicField(EulerPhi(%s)))!%s; "%(N,N,eps) + \
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"ans := DimensionNewCuspForms(eps, %s);ans;"%k;
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return magma(cmd)
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def charpoly_gamma0(N,k,p):
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cmd = "N := " + str(N) + "; k := " + str(k) + "; p := " + str(p) + ";" +\
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"""R<x> := PolynomialRing(Rationals());
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M := ModularSymbols(N,k,+1);
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S := CuspidalSubspace(M);
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ans := CharacteristicPolynomialOfHeckeOperator(S,p :
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Proof := false);
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"""
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return magma(cmd)
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def character_data(N):
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cmd = 'N := '+str(N)+';\n'+\
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'G := DirichletGroup(N, CyclotomicField(EulerPhi(N)));\n'+\
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'C := GaloisConjugacyRepresentatives(G);\n'+\
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'ans := [<N, Eltseq(e), Order(e), Conductor(e), '+\
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' IsEven(e) select 1 else -1> : e in C];';
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out = magma(cmd)
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out = string.replace(out,'\n','')
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out = string.replace(out,'[<','')
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out = string.replace(out,'>]','')
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out = string.replace(out,' ','')
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dat = string.split(out,'>,<')
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ans = []
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for d in dat:
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eps = [str(N)]
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dd = d[string.find(d,'['):]
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s = string.find(dd,']')+1
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eps.append(dd[:s])
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dd = dd[s+1:]
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for r in string.split(dd,','):
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eps.append(r)
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ans.append(eps)
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ans[0][1] = '1'
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return ans
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def aplist_to_qexpansion(aplist, N, k, eps, prec):
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cmd = 'R<x> := PolynomialRing(RationalField());\n' + \
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'ans := aplist_to_qexpansion(%s,%s,%s,%s,%s);\n'%(aplist,N,k,eps,prec)
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return magma(cmd)
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# an eight tuple: [order_of_root, num_twists, generators, fixed_field, fixed_degree, hilbert_sym, endo_alg, has_cm]
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def inner_twists_data(N, aplist):
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cmd = 'a := %s; ans := inner_twists_data(%s,a[1],a[3],a[2]);\n'%(aplist,N)
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data = magma(cmd)
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data = string.replace(data,'\n','')
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data = string.split(data,'|')
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data[2] = string.replace(data[2],' ','')
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data[6] = string.replace(data[6],' ','')
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return data
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def aplist_to_q_integral_basis(aplist, N, k, eps, prec):
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cmd = 'R<x> := PolynomialRing(RationalField());\n' + \
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'ans := aplist_to_q_integral_basis(%s,%s,%s,%s,%s);\n'%(aplist,N,k,eps,prec)
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data = magma(cmd)
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data = data[:-1]
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data = string.replace(data,'\n','')
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data = string.replace(data,'[','')
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data = string.replace(data,']','')
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data = string.split(data,'|')
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return data
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def index_in_saturation(N1, N2, B):
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BB = '['
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for i in range(len(B)):
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BB = BB + str(B[i])
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if i < len(B)-1:
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BB = BB + ', '
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BB = BB + ']'
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cmd = 'R<q> := PowerSeriesRing(Integers()); \n' + \
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'ans := Invariants(IndexGroupInSaturation(%s*%s,%s) );\n'%(N1,N2,BB)
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return magma(cmd)
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def congruence_group(N1, N2, B1, B2):
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return index_in_saturation(N1, N2, B1+B2)
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def torsion_upper_bound(aplist, N, prec):
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cmd = 'R<x> := PolynomialRing(RationalField());\n' + \
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'ans := torsion_upper_bound(%s,%s,%s);\n'%(aplist,N,prec) + \
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'print "ans = ", ans;\n'
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return magma(cmd)
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