CoCalc Shared Fileswww / calc / calc / logfile_gp.txtOpen in CoCalc with one click!
Author: William A. Stein
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'72.30.1'
************** PARI *****************
Host 72.30.129.106 (72.30.129.106)
Time: Wed Aug 23 14:46:53 2006

Input: y=210; for(x=1,8,y=sumdiv(y,x,x)-y;print1(y,","))

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? 366,378,582,594,846,1026,1374,1386,
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.056s
user	0m0.007s
sys	0m0.009s


'69.125.'
************** PARI *****************
Host 69.125.40.37 (69.125.40.37)
Time: Wed Aug 23 13:30:35 2006

Input: 9*10^9

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = 9000000000
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.015s
user	0m0.008s
sys	0m0.009s


'69.125.'
************** PARI *****************
Host 69.125.40.37 (69.125.40.37)
Time: Wed Aug 23 13:30:18 2006

Input: 9*10^9

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = 9000000000
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.287s
user	0m0.005s
sys	0m0.012s


'67.182.'
************** PARI *****************
Host 67.182.44.233 (67.182.44.233)
Time: Tue Aug 22 18:02:14 2006

Input: -2.4 + 0.11 - 3

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = -5.2900000000000000000000000000000000000
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.014s
user	0m0.005s
sys	0m0.009s


'69.208.'
************** PARI *****************
Host 69.208.163.19 (69.208.163.19)
Time: Tue Aug 22 17:57:06 2006

Input: 2^4*4-2/8

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = 255/4
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.015s
user	0m0.009s
sys	0m0.006s


'69.208.'
************** PARI *****************
Host 69.208.163.19 (69.208.163.19)
Time: Tue Aug 22 17:56:14 2006

Input: 6+4

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = 10
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.014s
user	0m0.005s
sys	0m0.009s


'69.208.'
************** PARI *****************
Host 69.208.163.19 (69.208.163.19)
Time: Tue Aug 22 17:55:49 2006

Input: "Replace this by some code, then click [SAGE] or [PARI]!"

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = "Replace this by some code, then click [SAGE] or [PARI]!"
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.014s
user	0m0.005s
sys	0m0.010s


'68.225.'
************** PARI *****************
Host 68.225.63.159 (68.225.63.159)
Time: Tue Aug 22 17:42:20 2006

Input: 16.5*6

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = 99.000000000000000000000000000000000000
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.015s
user	0m0.006s
sys	0m0.008s


'24.252.'
************** PARI *****************
Host 24.252.118.249 (24.252.118.249)
Time: Tue Aug 22 17:27:16 2006

Input: "Replace this by some code, then click [SAGE] or [PARI]!"

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = "Replace this by some code, then click [SAGE] or [PARI]!"
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.015s
user	0m0.006s
sys	0m0.009s


'131.111'
************** PARI *****************
Host 131.111.200.200 (131.111.200.200)
Time: Tue Aug 22 17:07:25 2006

Input: sqrt(2*3.99E+14*(1/6678000-1/6678001)/(1-6678000^2/6678001^2))

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = 7729.7110001915802113615387877878229188
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.016s
user	0m0.011s
sys	0m0.006s


'131.111'
************** PARI *****************
Host 131.111.200.200 (131.111.200.200)
Time: Tue Aug 22 17:07:16 2006

Input: sqrt(2*3.99E+14*(1/6678000-1/6678000)/(1-6678000^2/6678000^2))

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? ? 
Goodbye!

Errors/timing (if any):

  ***   division by zero

Timing:
real	0m0.015s
user	0m0.008s
sys	0m0.006s


'131.111'
************** PARI *****************
Host 131.111.200.200 (131.111.200.200)
Time: Tue Aug 22 17:06:57 2006

Input: sqrt(2*3.99E+14*(1/6678000-1/6778000)/(1-6678000^2/6778000^2))

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = 7758.3797162510811541316832269815493887
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.092s
user	0m0.008s
sys	0m0.009s


'69.238.'
************** PARI *****************
Host 69.238.128.170 (69.238.128.170)
Time: Tue Aug 22 16:46:25 2006

Input: 3x-4(x+11)=-2(x+8)-43

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? ? 
Goodbye!

Errors/timing (if any):

  ***   Warning: unused characters: x-4(x+11)=-2(x+8)-43.
  ***   unexpected character: 3x-4(x+11)=-2(x+8)-43
                                        ^-----------

Timing:
real	0m0.038s
user	0m0.008s
sys	0m0.007s


'66.27.2'
************** PARI *****************
Host 66.27.234.197 (66.27.234.197)
Time: Tue Aug 22 16:24:51 2006

Input: -3*3=

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? ? 
Goodbye!

Errors/timing (if any):

  ***   unexpected character: -3*3=
                                  ^-

Timing:
real	0m0.014s
user	0m0.006s
sys	0m0.007s


'72.30.9'
************** PARI *****************
Host 72.30.98.136 (72.30.98.136)
Time: Tue Aug 22 05:47:23 2006

Input: factor(2^(2^5)+1)

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = 
[641 1]

[6700417 1]

? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.014s
user	0m0.005s
sys	0m0.009s


'71.65.2'
************** PARI *****************
Host 71.65.241.42 (71.65.241.42)
Time: Mon Aug 21 20:24:17 2006

Input: collatzlength(x0)=
{
   local(x,i);
   x=x0;  i=0;   
   while(x-1,
      x=if(Mod(x,2)==Mod(0,2), x/2, (3*x+1)/2);i=i++ );
   i
}
collatzlength(299)

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? ? %1 = 75
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.048s
user	0m0.006s
sys	0m0.012s


'72.30.1'
************** PARI *****************
Host 72.30.111.31 (72.30.111.31)
Time: Mon Aug 21 19:25:39 2006

Input: factor(x^6-1)

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = 
[x - 1 1]

[x + 1 1]

[x^2 - x + 1 1]

[x^2 + x + 1 1]

? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.182s
user	0m0.006s
sys	0m0.011s


'69.154.'
************** PARI *****************
Host 69.154.89.104 (69.154.89.104)
Time: Mon Aug 21 18:15:53 2006

Input: t-(-16)=9

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? ? 
Goodbye!

Errors/timing (if any):

  ***   unexpected character: t-(-16)=9
                                     ^--

Timing:
real	0m0.014s
user	0m0.008s
sys	0m0.006s


'69.154.'
************** PARI *****************
Host 69.154.89.104 (69.154.89.104)
Time: Mon Aug 21 18:08:00 2006

Input: "Replace this by some code, then click [SAGE] or [PARI]!"

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = "Replace this by some code, then click [SAGE] or [PARI]!"
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.014s
user	0m0.008s
sys	0m0.007s


'68.88.2'
************** PARI *****************
Host 68.88.200.203 (68.88.200.203)
Time: Mon Aug 21 16:58:11 2006

Input: 99

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = 99
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.014s
user	0m0.004s
sys	0m0.010s


'24.110.'
************** PARI *****************
Host 24.110.168.190 (24.110.168.190)
Time: Mon Aug 21 15:24:21 2006

Input: 3y/x-2cx/3y

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = y
? 
Goodbye!

Errors/timing (if any):

  ***   Warning: unused characters: y/x-2cx/3y.

Timing:
real	0m0.062s
user	0m0.006s
sys	0m0.011s


'24.45.7'
************** PARI *****************
Host 24.45.76.206 (24.45.76.206)
Time: Mon Aug 21 14:07:55 2006

Input: 5=5

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? ? 
Goodbye!

Errors/timing (if any):

  ***   unexpected character: 5=5
                               ^--

Timing:
real	0m0.015s
user	0m0.006s
sys	0m0.009s


'24.21.1'
************** PARI *****************
Host 24.21.126.54 (24.21.126.54)
Time: Mon Aug 21 13:16:03 2006

Input: 2000000000 x .01


Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? ? 
Goodbye!

Errors/timing (if any):

  ***   Warning: unused characters: x.01.
  ***   unknown member function: 2000000000x.01
                                             ^--

Timing:
real	0m0.023s
user	0m0.008s
sys	0m0.008s


'24.21.1'
************** PARI *****************
Host 24.21.126.54 (24.21.126.54)
Time: Mon Aug 21 13:15:46 2006

Input: 2000000000 x .01%

Output: WARNING: PARI command contains unsafe command '%', so it will not be executed.

'209.99.'
************** PARI *****************
Host 209.99.19.8 (209.99.19.8)
Time: Mon Aug 21 12:42:23 2006

Input: for(n=1,7, print1(n,": ",sum(x=1,n,1/x),",  ") )

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? 1: 1,  2: 3/2,  3: 11/6,  4: 25/12,  5: 137/60,  6: 49/20,  7: 363/140,  
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.016s
user	0m0.006s
sys	0m0.009s


'128.112'
************** PARI *****************
Host 128.112.33.159 (128.112.33.159)
Time: Mon Aug 21 12:38:51 2006

Input: (1+x)^20

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = x^20 + 20*x^19 + 190*x^18 + 1140*x^17 + 4845*x^16 + 15504*x^15 + 38760*x^14 + 77520*x^13 + 125970*x^12 + 167960*x^11 + 184756*x^10 + 167960*x^9 + 125970*x^8 + 77520*x^7 + 38760*x^6 + 15504*x^5 + 4845*x^4 + 1140*x^3 + 190*x^2 + 20*x + 1
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.015s
user	0m0.006s
sys	0m0.010s


'199.172'
************** PARI *****************
Host 199.172.169.21 (199.172.169.21)
Time: Mon Aug 21 10:47:03 2006

Input: a=(x^2+y^2+z^2)^15

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = x^30 + (15*y^2 + 15*z^2)*x^28 + (105*y^4 + 210*z^2*y^2 + 105*z^4)*x^26 + (455*y^6 + 1365*z^2*y^4 + 1365*z^4*y^2 + 455*z^6)*x^24 + (1365*y^8 + 5460*z^2*y^6 + 8190*z^4*y^4 + 5460*z^6*y^2 + 1365*z^8)*x^22 + (3003*y^10 + 15015*z^2*y^8 + 30030*z^4*y^6 + 30030*z^6*y^4 + 15015*z^8*y^2 + 3003*z^10)*x^20 + (5005*y^12 + 30030*z^2*y^10 + 75075*z^4*y^8 + 100100*z^6*y^6 + 75075*z^8*y^4 + 30030*z^10*y^2 + 5005*z^12)*x^18 + (6435*y^14 + 45045*z^2*y^12 + 135135*z^4*y^10 + 225225*z^6*y^8 + 225225*z^8*y^6 + 135135*z^10*y^4 + 45045*z^12*y^2 + 6435*z^14)*x^16 + (6435*y^16 + 51480*z^2*y^14 + 180180*z^4*y^12 + 360360*z^6*y^10 + 450450*z^8*y^8 + 360360*z^10*y^6 + 180180*z^12*y^4 + 51480*z^14*y^2 + 6435*z^16)*x^14 + (5005*y^18 + 45045*z^2*y^16 + 180180*z^4*y^14 + 420420*z^6*y^12 + 630630*z^8*y^10 + 630630*z^10*y^8 + 420420*z^12*y^6 + 180180*z^14*y^4 + 45045*z^16*y^2 + 5005*z^18)*x^12 + (3003*y^20 + 30030*z^2*y^18 + 135135*z^4*y^16 + 360360*z^6*y^14 + 630630*z^8*y^12 + 756756*z^10*y^10 + 630630*z^12*y^8 + 360360*z^14*y^6 + 135135*z^16*y^4 + 30030*z^18*y^2 + 3003*z^20)*x^10 + (1365*y^22 + 15015*z^2*y^20 + 75075*z^4*y^18 + 225225*z^6*y^16 + 450450*z^8*y^14 + 630630*z^10*y^12 + 630630*z^12*y^10 + 450450*z^14*y^8 + 225225*z^16*y^6 + 75075*z^18*y^4 + 15015*z^20*y^2 + 1365*z^22)*x^8 + (455*y^24 + 5460*z^2*y^22 + 30030*z^4*y^20 + 100100*z^6*y^18 + 225225*z^8*y^16 + 360360*z^10*y^14 + 420420*z^12*y^12 + 360360*z^14*y^10 + 225225*z^16*y^8 + 100100*z^18*y^6 + 30030*z^20*y^4 + 5460*z^22*y^2 + 455*z^24)*x^6 + (105*y^26 + 1365*z^2*y^24 + 8190*z^4*y^22 + 30030*z^6*y^20 + 75075*z^8*y^18 + 135135*z^10*y^16 + 180180*z^12*y^14 + 180180*z^14*y^12 + 135135*z^16*y^10 + 75075*z^18*y^8 + 30030*z^20*y^6 + 8190*z^22*y^4 + 1365*z^24*y^2 + 105*z^26)*x^4 + (15*y^28 + 210*z^2*y^26 + 1365*z^4*y^24 + 5460*z^6*y^22 + 15015*z^8*y^20 + 30030*z^10*y^18 + 45045*z^12*y^16 + 51480*z^14*y^14 + 45045*z^16*y^12 + 30030*z^18*y^10 + 15015*z^20*y^8 + 5460*z^22*y^6 + 1365*z^24*y^4 + 210*z^26*y^2 + 15*z^28)*x^2 + (y^30 + 15*z^2*y^28 + 105*z^4*y^26 + 455*z^6*y^24 + 1365*z^8*y^22 + 3003*z^10*y^20 + 5005*z^12*y^18 + 6435*z^14*y^16 + 6435*z^16*y^14 + 5005*z^18*y^12 + 3003*z^20*y^10 + 1365*z^22*y^8 + 455*z^24*y^6 + 105*z^26*y^4 + 15*z^28*y^2 + z^30)
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.036s
user	0m0.010s
sys	0m0.006s


'199.172'
************** PARI *****************
Host 199.172.169.21 (199.172.169.21)
Time: Mon Aug 21 10:46:32 2006

Input: mathilbert(10)^6

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = 
[263861986074337682866598658066009962404513/18649941184431547105657600263389184000000 13916370422793057333854366486049233/1615247488573530944210078128128000 1132808775826053882967916900817043/176710836356762359708452991795200 24306250143189146865512352124950371843/4703600686726122109539747509108736000 780103421152595930763738081883394069/179184788065757032744371333680332800 63384164058838773376695119747773621031/16798573881164721819784812532531200000 134484051734565974845476800893928668937/40316577314795332367483550078074880000 16751637651306080958810077336996036063503/5597284817204085310352299535839395840000 52124191622632203761874981966328598359259/19190690801842578206922169837163642880000 3061393286661591565778580253259078356057763/1230603047668155327518884140808118599680000]

[13916370422793057333854366486049233/1615247488573530944210078128128000 11840379415335103201377327521948705289858073/2256642883316217199784569631870091264000000 55035378377643639919549615899225827/14096705354823542785833409118208000 158324062652739908328394405227714059/50305889697605584059248636461056000 161971341824575226703589824385007579/61085723204235352071944772845568000 8422710658006760389428689385022798463/3665143392254121124316686370734080000 6205166512214915030771199527921026267/3054286160211767603597238642278400000 265006409219960616588529810873289648591/145384021226080137931228559372451840000 7575974009714317550266532292857727630707/4579596668621524344833699620232232960000 150674131239185450763823212432663729243433/99442670518638814344960334610757058560000]

[1132808775826053882967916900817043/176710836356762359708452991795200 55035378377643639919549615899225827/14096705354823542785833409118208000 1638916057345975270846712552176757609602237/564160720829054299946142407967522816000000 93879719799953779837361780013085211/40087505852779449797213757179904000 1291337285445316726449750534452741/654489891473950200770836851916800 5995675212562349517590607409299157/3506195847181876075558054563840000 11081736910412758574165904753340618801/7330286784508242248633372741468160000 1478980742917064920881610957377939577319/1090380159195601034484214195293388800000 4832123093840029670999888975777570318207/3925368573104163724143171103056199680000 98105701915581517196594234375593138105933/87012336703808962551840292784412426240000]

[24306250143189146865512352124950371843/4703600686726122109539747509108736000 158324062652739908328394405227714059/50305889697605584059248636461056000 93879719799953779837361780013085211/40087505852779449797213757179904000 179996672339190542936701642710042941995274053/95343161820110176690898066946511355904000000 3269833830457647737239392928750157/2055769530911766656267372163072000 85018584791429059906299888426749777/61673085927352999688021164892160000 4008657153739045932[+++]
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.022s
user	0m0.016s
sys	0m0.006s


'149.169'
************** PARI *****************
Host 149.169.59.48 (149.169.59.48)
Time: Mon Aug 21 10:11:37 2006

Input: log(x) + log(10^ x) - x 

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? ? 
Goodbye!

Errors/timing (if any):

  *** log: log is not meromorphic at 0.

Timing:
real	0m0.014s
user	0m0.005s
sys	0m0.010s


'88.70.5'
************** PARI *****************
Host 88.70.5.73 (88.70.5.73)
Time: Mon Aug 21 09:58:36 2006

Input: print gap('SubgroupsSolvableGroup(SymmetricGroup(5));') 

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? ? 
Goodbye!

Errors/timing (if any):

  ***   expected character: ',' instead of: ...p('SubgroupsSolvableGroup
  ***   (SymmetricGroup(5));
        ^--------------------

Timing:
real	0m0.014s
user	0m0.004s
sys	0m0.011s


'72.30.1'
************** PARI *****************
Host 72.30.129.106 (72.30.129.106)
Time: Mon Aug 21 09:53:31 2006

Input: y=210; for(x=1,8,y=sumdiv(y,x,x)-y;print1(y,","))

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? 366,378,582,594,846,1026,1374,1386,
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.015s
user	0m0.008s
sys	0m0.007s


'132.227'
************** PARI *****************
Host 132.227.205.230 (132.227.205.230)
Time: Mon Aug 21 09:48:49 2006

Input: factor(1543542)

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = 
[2 1]

[3 1]

[7 1]

[11 1]

[13 1]

[257 1]

? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.053s
user	0m0.006s
sys	0m0.007s


'141.20.'
************** PARI *****************
Host 141.20.50.154 (141.20.50.154)
Time: Mon Aug 21 05:19:01 2006

Input: E = ellinit([0,0,0,5,10]);
ellidentify(E)

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? ? ? 
Goodbye!

Errors/timing (if any):

  *** ellidentify: Elliptic curves files not available for conductor 400
[missing /home/was/sage/sage-0.7.5-2005-09-29/source/../local/share/pari/elldata/ell0].

Timing:
real	0m0.101s
user	0m0.008s
sys	0m0.010s


'141.20.'
************** PARI *****************
Host 141.20.50.154 (141.20.50.154)
Time: Mon Aug 21 05:04:34 2006

Input: E = ellinit([0,0,0,5,10]);
H1 = ellheight(E,[1,4])
H2 = ellheight(E,[6,-16])
ellheight(E, [1,-4])
P = [1,4];
P2 = elladd(E,P,P)
P3 = elladd(E,P2,P)
P4 = elladd(E,P2,P2)
P1 = [6,16];
ellbil(E,P1,P1) 
ellbil(E, P,P1)
e1 = exp(H1)
e2 = exp(H2)
e2/e1

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? ? %2 = 0.12837506294605086906217592378339269243
? %3 = 2.0540010071368139049948147805342830833
? %4 = 0.12837506294605086906217592378339269243
? ? %6 = [-1, -2]
? %7 = [9, -28]
? %8 = [6, 16]
? ? %10 = 2.0540010071368139049948147805342830835
? %11 = 0.51350025178420347624870369513357077103
? %12 = 1.1369793615653033564803326240516575848
? %13 = 7.7990427915805383425320575762755536977
? %14 = 6.8594409496082957922222546031236954267
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.017s
user	0m0.007s
sys	0m0.010s


'141.20.'
************** PARI *****************
Host 141.20.50.154 (141.20.50.154)
Time: Mon Aug 21 05:03:27 2006

Input: E = ellinit([0,0,0,5,10]);
H1 = ellheight(E,[1,4])
H2 = ellheight(E,[6,-16])
ellheight(E, [1,-4])
P = [1,4];
P2 = elladd(E,P,P)
P3 = elladd(E,P2,P)
P4 = elladd(E,P2,P2)
P1 = [6,16];
ellbil(E,P1,P1) 
ellbil(E, P,P1)
exp(H1)
exp(H2)

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? ? %2 = 0.12837506294605086906217592378339269243
? %3 = 2.0540010071368139049948147805342830833
? %4 = 0.12837506294605086906217592378339269243
? ? %6 = [-1, -2]
? %7 = [9, -28]
? %8 = [6, 16]
? ? %10 = 2.0540010071368139049948147805342830835
? %11 = 0.51350025178420347624870369513357077103
? %12 = 1.1369793615653033564803326240516575848
? %13 = 7.7990427915805383425320575762755536977
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.017s
user	0m0.009s
sys	0m0.008s


'141.20.'
************** PARI *****************
Host 141.20.50.154 (141.20.50.154)
Time: Mon Aug 21 04:18:58 2006

Input: E = ellinit([0,0,0,5,10]);
H1 = ellheight(E,[1,4])
H2 = ellheight(E,[6,-16])
ellheight(E, [1,-4])
P = [1,4];
P2 = elladd(E,P,P)
P3 = elladd(E,P2,P)
P4 = elladd(E,P2,P2)
P1 = [6,16];
ellbil(E,P1,P1) 
ellbil(E, P,P1)

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? ? %2 = 0.12837506294605086906217592378339269243
? %3 = 2.0540010071368139049948147805342830833
? %4 = 0.12837506294605086906217592378339269243
? ? %6 = [-1, -2]
? %7 = [9, -28]
? %8 = [6, 16]
? ? %10 = 2.0540010071368139049948147805342830835
? %11 = 0.51350025178420347624870369513357077103
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.017s
user	0m0.010s
sys	0m0.006s


'141.20.'
************** PARI *****************
Host 141.20.50.154 (141.20.50.154)
Time: Mon Aug 21 04:14:10 2006

Input: E = ellinit([0,0,0,5,10]);
H1 = ellheight(E,[1,4])
H2 = ellheight(E,[6,-16])
ellheight(E, [1,-4])
P = [1,4];
P2 = elladd(E,P,P)
P3 = elladd(E,P2,P)
P4 = elladd(E,P2,P2)
P1 = [6,16];
ellbil(E,P1,P1) 
ellbil[E, P,P1)

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? ? %2 = 0.12837506294605086906217592378339269243
? %3 = 2.0540010071368139049948147805342830833
? %4 = 0.12837506294605086906217592378339269243
? ? %6 = [-1, -2]
? %7 = [9, -28]
? %8 = [6, 16]
? ? %10 = 2.0540010071368139049948147805342830835
? ? 
Goodbye!

Errors/timing (if any):

  ***   expected character: ']' instead of: ellbil[E,P,P1)
                                                      ^----

Timing:
real	0m0.017s
user	0m0.006s
sys	0m0.011s


'141.20.'
************** PARI *****************
Host 141.20.50.154 (141.20.50.154)
Time: Mon Aug 21 04:13:04 2006

Input: E = ellinit([0,0,0,5,10]);
H1 = ellheight(E,[1,4])
H2 = ellheight(E,[6,-16])
ellheight(E, [1,-4])
P = [1,4];
P2 = elladd(E,P,P)
P3 = elladd(E,P2,P)
P4 = elladd(E,P2,P2)
ellheight(E, P2)
ellheight(E,P3)
ellheight(E, P4)
P1 = [6,16];
ellbil(E,P1,P1) 

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? ? %2 = 0.12837506294605086906217592378339269243
? %3 = 2.0540010071368139049948147805342830833
? %4 = 0.12837506294605086906217592378339269243
? ? %6 = [-1, -2]
? %7 = [9, -28]
? %8 = [6, 16]
? %9 = 0.51350025178420347624870369513357077067
? %10 = 1.1553755665144578215595833140505342343
? %11 = 2.0540010071368139049948147805342830833
? ? %13 = 2.0540010071368139049948147805342830835
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.017s
user	0m0.009s
sys	0m0.009s


'141.20.'
************** PARI *****************
Host 141.20.50.154 (141.20.50.154)
Time: Mon Aug 21 04:11:53 2006

Input: E = ellinit([0,0,0,5,10]);
H1 = ellheight(E,[1,4])
H2 = ellheight(E,[6,-16])
ellheight(E, [1,-4])
P = [1,4];
P2 = elladd(E,P,P)
P3 = elladd(E,P2,P)
P4 = elladd(E,P2,P2)
ellheight(E, P2)
ellheight(E,P3)
ellheight(E, P4)

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? ? %2 = 0.12837506294605086906217592378339269243
? %3 = 2.0540010071368139049948147805342830833
? %4 = 0.12837506294605086906217592378339269243
? ? %6 = [-1, -2]
? %7 = [9, -28]
? %8 = [6, 16]
? %9 = 0.51350025178420347624870369513357077067
? %10 = 1.1553755665144578215595833140505342343
? %11 = 2.0540010071368139049948147805342830833
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.016s
user	0m0.008s
sys	0m0.009s


'141.20.'
************** PARI *****************
Host 141.20.50.154 (141.20.50.154)
Time: Mon Aug 21 04:10:50 2006

Input: E = ellinit([0,0,0,5,10]);
H1 = ellheight(E,[1,4])
H2 = ellheight(E,[6,-16])
ellheight(E, [1,-4])
P = [1,4];
P2 = elladd(E,P,P)
elladd(E,P2,P)
elladd(E,P2,P2)

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? ? %2 = 0.12837506294605086906217592378339269243
? %3 = 2.0540010071368139049948147805342830833
? %4 = 0.12837506294605086906217592378339269243
? ? %6 = [-1, -2]
? %7 = [9, -28]
? %8 = [6, 16]
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.016s
user	0m0.005s
sys	0m0.011s


'141.20.'
************** PARI *****************
Host 141.20.50.154 (141.20.50.154)
Time: Mon Aug 21 04:10:17 2006

Input: E = ellinit([0,0,0,5,10]);
H1 = ellheight(E,[1,4])
H2 = ellheight(E,[6,-16])
ellheight(E, [1,-4])
P = [1,4];
elladd(E,P,P)

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? ? %2 = 0.12837506294605086906217592378339269243
? %3 = 2.0540010071368139049948147805342830833
? %4 = 0.12837506294605086906217592378339269243
? ? %6 = [-1, -2]
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.016s
user	0m0.007s
sys	0m0.008s


'141.20.'
************** PARI *****************
Host 141.20.50.154 (141.20.50.154)
Time: Mon Aug 21 04:09:52 2006

Input: E = ellinit([0,0,0,5,10]);
H1 = ellheight(E,[1,4])
H2 = ellheight(E,[6,-16])
ellheight(E, [1,-4])
P = [1,4];
P*P

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? ? %2 = 0.12837506294605086906217592378339269243
? %3 = 2.0540010071368139049948147805342830833
? %4 = 0.12837506294605086906217592378339269243
? ? ? 
Goodbye!

Errors/timing (if any):

  ***   forbidden multiplication t_VEC * t_VEC.

Timing:
real	0m0.017s
user	0m0.008s
sys	0m0.009s


'141.20.'
************** PARI *****************
Host 141.20.50.154 (141.20.50.154)
Time: Mon Aug 21 04:09:15 2006

Input: E = ellinit([0,0,0,5,10]);
H1 = ellheight(E,[1,4])
H2 = ellheight(E,[6,-16])
ellheight(E, [1,-4])


Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? ? %2 = 0.12837506294605086906217592378339269243
? %3 = 2.0540010071368139049948147805342830833
? %4 = 0.12837506294605086906217592378339269243
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.016s
user	0m0.007s
sys	0m0.010s


'141.20.'
************** PARI *****************
Host 141.20.50.154 (141.20.50.154)
Time: Mon Aug 21 04:08:49 2006

Input: E = ellinit([0,0,0,5,10]);
H1 = ellheight(E,[1,4])
H2 = ellheight(E,[6,-16])
ellbill(E,[1,4], [6,-16])
ellheight(E, [1,-4])


Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? ? %2 = 0.12837506294605086906217592378339269243
? %3 = 2.0540010071368139049948147805342830833
? ? %4 = 0.12837506294605086906217592378339269243
? 
Goodbye!

Errors/timing (if any):

  ***   unknown function or error in formal parameters: ellbill(E,[1,4],[6,-
                                                        ^--------------------

Timing:
real	0m0.017s
user	0m0.010s
sys	0m0.006s


'141.20.'
************** PARI *****************
Host 141.20.50.154 (141.20.50.154)
Time: Mon Aug 21 04:07:20 2006

Input: E = ellinit([0,0,0,5,10]);
H1 = ellheight(E,[1,4])
H2 = ellheight(E,[6,-16])



Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? ? %2 = 0.12837506294605086906217592378339269243
? %3 = 2.0540010071368139049948147805342830833
? ? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.036s
user	0m0.007s
sys	0m0.011s


'141.20.'
************** PARI *****************
Host 141.20.50.154 (141.20.50.154)
Time: Mon Aug 21 04:06:49 2006

Input: E = ellinit([0,0,0,0,5]);
E.a6


Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? ? %2 = 5
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.015s
user	0m0.006s
sys	0m0.011s


'141.20.'
************** PARI *****************
Host 141.20.50.154 (141.20.50.154)
Time: Mon Aug 21 04:06:18 2006

Input: E = ellinit([0,0,0,0,5]);
E.a6;

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? ? ? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.015s
user	0m0.010s
sys	0m0.006s


'141.20.'
************** PARI *****************
Host 141.20.50.154 (141.20.50.154)
Time: Mon Aug 21 04:06:05 2006

Input: E = ellinit([0,0,0,0,5]);
E.a6;

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? ? ? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.016s
user	0m0.009s
sys	0m0.007s


'141.20.'
************** PARI *****************
Host 141.20.50.154 (141.20.50.154)
Time: Mon Aug 21 04:05:18 2006

Input: 3+4;

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? ? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.015s
user	0m0.009s
sys	0m0.007s


'141.20.'
************** PARI *****************
Host 141.20.50.154 (141.20.50.154)
Time: Mon Aug 21 04:04:53 2006

Input: E = ellinit([0,0,0,5,10]);
E;
3+4;

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? ? ? ? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.016s
user	0m0.008s
sys	0m0.008s


'141.20.'
************** PARI *****************
Host 141.20.50.154 (141.20.50.154)
Time: Mon Aug 21 04:04:24 2006

Input: E = ellinit([0,0,0,5,10]);
E;


Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? ? ? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.016s
user	0m0.008s
sys	0m0.007s


'141.20.'
************** PARI *****************
Host 141.20.50.154 (141.20.50.154)
Time: Mon Aug 21 04:03:58 2006

Input: E = ellinit([0,0,0,5,10]);
E;
H1 = ellheight(E,[1,4]);
H2 = ellheight(E,[6,-16]);
H1;
H2;

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? ? ? ? ? ? ? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.016s
user	0m0.006s
sys	0m0.009s


'141.20.'
************** PARI *****************
Host 141.20.50.154 (141.20.50.154)
Time: Mon Aug 21 04:03:22 2006

Input: E = ellinit([0,0,0,5,10]);


Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? ? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.016s
user	0m0.008s
sys	0m0.008s


'141.20.'
************** PARI *****************
Host 141.20.50.154 (141.20.50.154)
Time: Mon Aug 21 04:02:29 2006

Input: E = ellinit([0,0,0,5,10]);
ellheight(E,[1,4]);
ellheight(E,[6,-16]);

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? ? ? ? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.016s
user	0m0.007s
sys	0m0.009s


'141.20.'
************** PARI *****************
Host 141.20.50.154 (141.20.50.154)
Time: Mon Aug 21 04:02:07 2006

Input: E = ellinit([0,0,0,5,10]);
P = [1,4];
ellheight(E,P);
ellheight(E,[6,-16]);

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? ? ? ? ? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.139s
user	0m0.006s
sys	0m0.014s


'129.26.'
************** PARI *****************
Host 129.26.133.101 (129.26.133.101)
Time: Mon Aug 21 02:34:30 2006

Input: (x+4)^3

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = x^3 + 12*x^2 + 48*x + 64
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.076s
user	0m0.006s
sys	0m0.009s


'24.166.'
************** PARI *****************
Host 24.166.28.255 (24.166.28.255)
Time: Sun Aug 20 20:24:44 2006

Input: log 15

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = log15
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.014s
user	0m0.006s
sys	0m0.007s


'69.27.6'
************** PARI *****************
Host 69.27.68.214 (69.27.68.214)
Time: Sun Aug 20 18:54:18 2006

Input: for(n=1,1000,if(isprime(n^2+n+1712329866165608771),print1(n",")))









Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? 3,14,19,21,27,38,39,57,59,63,64,69,70,82,86,88,93,96,102,103,110,115,119,120,124,130,138,140,146,148,152,155,158,159,160,161,163,167,168,175,177,178,179,187,193,195,196,197,198,202,213,215,217,229,230,234,235,240,245,248,253,254,263,265,267,275,280,282,283,285,292,294,297,302,305,307,311,312,315,317,321,324,325,329,333,335,338,340,341,342,345,358,362,363,365,378,381,383,393,410,412,413,421,423,428,430,434,436,437,443,450,455,457,458,459,470,473,477,478,479,483,485,490,492,494,498,500,510,518,519,522,524,528,535,543,549,553,564,567,569,572,577,578,581,582,584,590,598,609,615,616,617,621,624,628,630,636,637,638,640,643,645,647,653,657,658,660,662,665,677,679,686,694,696,700,705,707,713,714,716,721,723,726,732,733,738,741,742,750,752,755,756,761,770,776,777,783,789,794,796,797,808,813,815,819,821,828,833,840,845,849,852,854,856,864,866,869,874,882,885,886,889,892,897,899,901,902,904,907,910,914,920,924,927,928,931,933,940,942,945,957,960,963,967,970,979,984,988,993,994,998,1000,
? ? ? ? ? ? ? ? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.023s
user	0m0.016s
sys	0m0.007s


'69.27.6'
************** PARI *****************
Host 69.27.68.214 (69.27.68.214)
Time: Sun Aug 20 18:54:03 2006

Input: for(n=1,700,if(isprime(n^2+n+1712329866165608771),print1(n",")))









Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? 3,14,19,21,27,38,39,57,59,63,64,69,70,82,86,88,93,96,102,103,110,115,119,120,124,130,138,140,146,148,152,155,158,159,160,161,163,167,168,175,177,178,179,187,193,195,196,197,198,202,213,215,217,229,230,234,235,240,245,248,253,254,263,265,267,275,280,282,283,285,292,294,297,302,305,307,311,312,315,317,321,324,325,329,333,335,338,340,341,342,345,358,362,363,365,378,381,383,393,410,412,413,421,423,428,430,434,436,437,443,450,455,457,458,459,470,473,477,478,479,483,485,490,492,494,498,500,510,518,519,522,524,528,535,543,549,553,564,567,569,572,577,578,581,582,584,590,598,609,615,616,617,621,624,628,630,636,637,638,640,643,645,647,653,657,658,660,662,665,677,679,686,694,696,700,
? ? ? ? ? ? ? ? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.022s
user	0m0.016s
sys	0m0.007s


'69.27.6'
************** PARI *****************
Host 69.27.68.214 (69.27.68.214)
Time: Sun Aug 20 18:53:47 2006

Input: for(n=1,500,if(isprime(n^2+n+1712329866165608771),print1(n",")))









Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? 3,14,19,21,27,38,39,57,59,63,64,69,70,82,86,88,93,96,102,103,110,115,119,120,124,130,138,140,146,148,152,155,158,159,160,161,163,167,168,175,177,178,179,187,193,195,196,197,198,202,213,215,217,229,230,234,235,240,245,248,253,254,263,265,267,275,280,282,283,285,292,294,297,302,305,307,311,312,315,317,321,324,325,329,333,335,338,340,341,342,345,358,362,363,365,378,381,383,393,410,412,413,421,423,428,430,434,436,437,443,450,455,457,458,459,470,473,477,478,479,483,485,490,492,494,498,500,
? ? ? ? ? ? ? ? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.019s
user	0m0.008s
sys	0m0.010s


'69.27.6'
************** PARI *****************
Host 69.27.68.214 (69.27.68.214)
Time: Sun Aug 20 18:53:27 2006

Input: for(n=1,400,if(isprime(n^2+n+1712329866165608771),print1(n",")))









Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? 3,14,19,21,27,38,39,57,59,63,64,69,70,82,86,88,93,96,102,103,110,115,119,120,124,130,138,140,146,148,152,155,158,159,160,161,163,167,168,175,177,178,179,187,193,195,196,197,198,202,213,215,217,229,230,234,235,240,245,248,253,254,263,265,267,275,280,282,283,285,292,294,297,302,305,307,311,312,315,317,321,324,325,329,333,335,338,340,341,342,345,358,362,363,365,378,381,383,393,
? ? ? ? ? ? ? ? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.018s
user	0m0.013s
sys	0m0.005s


'69.27.6'
************** PARI *****************
Host 69.27.68.214 (69.27.68.214)
Time: Sun Aug 20 18:51:58 2006

Input: for(n=1,300,if(isprime(n^2+n+1712329866165608771),print1(n",")))









Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? 3,14,19,21,27,38,39,57,59,63,64,69,70,82,86,88,93,96,102,103,110,115,119,120,124,130,138,140,146,148,152,155,158,159,160,161,163,167,168,175,177,178,179,187,193,195,196,197,198,202,213,215,217,229,230,234,235,240,245,248,253,254,263,265,267,275,280,282,283,285,292,294,297,
? ? ? ? ? ? ? ? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.017s
user	0m0.010s
sys	0m0.006s


'69.27.6'
************** PARI *****************
Host 69.27.68.214 (69.27.68.214)
Time: Sun Aug 20 18:51:31 2006

Input: for(n=1,200,if(isprime(n^2+n+1712329866165608771),print1(n",")))









Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? 3,14,19,21,27,38,39,57,59,63,64,69,70,82,86,88,93,96,102,103,110,115,119,120,124,130,138,140,146,148,152,155,158,159,160,161,163,167,168,175,177,178,179,187,193,195,196,197,198,
? ? ? ? ? ? ? ? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.016s
user	0m0.009s
sys	0m0.007s


'69.27.6'
************** PARI *****************
Host 69.27.68.214 (69.27.68.214)
Time: Sun Aug 20 18:46:16 2006

Input: for(n=1,100,if(isprime(n^2+n+1712329866165608771),print1(n",")))









Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? 3,14,19,21,27,38,39,57,59,63,64,69,70,82,86,88,93,96,
? ? ? ? ? ? ? ? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.016s
user	0m0.009s
sys	0m0.007s


'69.27.6'
************** PARI *****************
Host 69.27.68.214 (69.27.68.214)
Time: Sun Aug 20 18:45:30 2006

Input: for(n=1,50,if(isprime(n^2+n+1712329866165608771),print1(n",")))









Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? 3,14,19,21,27,38,39,
? ? ? ? ? ? ? ? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.092s
user	0m0.008s
sys	0m0.007s


'72.30.9'
************** PARI *****************
Host 72.30.98.145 (72.30.98.145)
Time: Sun Aug 20 16:02:25 2006

Input: for(n=1,20, print1(n,": ",valuation(n!,2),", ") )

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? 1: 0, 2: 1, 3: 1, 4: 3, 5: 3, 6: 4, 7: 4, 8: 7, 9: 7, 10: 8, 11: 8, 12: 10, 13: 10, 14: 11, 15: 11, 16: 15, 17: 15, 18: 16, 19: 16, 20: 18, 
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.024s
user	0m0.006s
sys	0m0.008s


'72.30.2'
************** PARI *****************
Host 72.30.226.160 (72.30.226.160)
Time: Sun Aug 20 15:36:49 2006

Input: for(n=1,7, print1(n,": ",sum(x=1,n,1/x),",  ") )

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? 1: 1,  2: 3/2,  3: 11/6,  4: 25/12,  5: 137/60,  6: 49/20,  7: 363/140,  
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.015s
user	0m0.006s
sys	0m0.009s


'68.40.2'
************** PARI *****************
Host 68.40.228.245 (68.40.228.245)
Time: Sun Aug 20 15:10:29 2006

Input: "Replace this by some code, then click [SAGE] or [PARI]!"

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = "Replace this by some code, then click [SAGE] or [PARI]!"
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.014s
user	0m0.007s
sys	0m0.008s


'72.30.2'
************** PARI *****************
Host 72.30.226.223 (72.30.226.223)
Time: Sun Aug 20 15:08:25 2006

Input: for(n=1,7, print1(n,": ",sum(x=1,n,1/x),",  ") )

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? 1: 1,  2: 3/2,  3: 11/6,  4: 25/12,  5: 137/60,  6: 49/20,  7: 363/140,  
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.021s
user	0m0.005s
sys	0m0.011s


'72.30.9'
************** PARI *****************
Host 72.30.98.35 (72.30.98.35)
Time: Sun Aug 20 11:29:05 2006

Input: for(b=1,100, for(a=1,b, if( frac((a^2+b^2+1)/(a*b))==0 , print(a,",",b), ) ) )

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? 1,1
1,2
2,5
5,13
13,34
34,89
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.355s
user	0m0.024s
sys	0m0.011s


'86.194.'
************** PARI *****************
Host 86.194.40.94 (86.194.40.94)
Time: Sun Aug 20 00:09:14 2006

Input: 45!


Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = 119622220865480194561963161495657715064383733760000000000
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.079s
user	0m0.007s
sys	0m0.008s


'207.111'
************** PARI *****************
Host 207.111.73.50 (207.111.73.50)
Time: Sat Aug 19 23:34:00 2006

Input: "Replace this by some code, then click [SAGE] or [PARI]!"

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = "Replace this by some code, then click [SAGE] or [PARI]!"
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.073s
user	0m0.011s
sys	0m0.005s


'69.154.'
************** PARI *****************
Host 69.154.191.237 (69.154.191.237)
Time: Sat Aug 19 22:11:45 2006

Input: 15+5[5+3(8/4+2)]

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? ? 
Goodbye!

Errors/timing (if any):

  ***   expected character: ']' instead of: 15+5[5+3(8/4+2)]
                                                    ^--------

Timing:
real	0m0.014s
user	0m0.006s
sys	0m0.008s


'83.129.'
************** PARI *****************
Host 83.129.176.28 (83.129.176.28)
Time: Sat Aug 19 08:02:43 2006

Input: nfroots(x*x*x+4*x*x-35,)



Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? ? ? 
Goodbye!

Errors/timing (if any):

  ***   unexpected character: nfroots(x*x*x+4*x*x-35,)
                                                     ^-

Timing:
real	0m0.048s
user	0m0.005s
sys	0m0.009s


'83.129.'
************** PARI *****************
Host 83.129.176.28 (83.129.176.28)
Time: Sat Aug 19 08:02:24 2006

Input: nfroots(x*x*x+4*x*x-35)


Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? ? 
Goodbye!

Errors/timing (if any):

  ***   expected character: ',' instead of: nfroots(x*x*x+4*x*x-35)
                                                                  ^-

Timing:
real	0m0.014s
user	0m0.006s
sys	0m0.008s


'83.129.'
************** PARI *****************
Host 83.129.176.28 (83.129.176.28)
Time: Sat Aug 19 08:02:06 2006

Input: nfroots(x*x*x+4*x*x-35);


Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? ? 
Goodbye!

Errors/timing (if any):

  ***   expected character: ',' instead of: nfroots(x*x*x+4*x*x-35);
                                                                  ^--

Timing:
real	0m0.071s
user	0m0.007s
sys	0m0.008s


'130.161'
************** PARI *****************
Host 130.161.135.32 (130.161.135.32)
Time: Sat Aug 19 05:54:03 2006

Input: sin(3.1415)


Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = 0.000092653589660671440566174108604596853276
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.014s
user	0m0.007s
sys	0m0.007s


'130.161'
************** PARI *****************
Host 130.161.135.32 (130.161.135.32)
Time: Sat Aug 19 05:53:50 2006

Input: tan(3.1415)


Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = -0.000092653590058372507822043460533803485629
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.059s
user	0m0.005s
sys	0m0.010s


'72.30.1'
************** PARI *****************
Host 72.30.107.151 (72.30.107.151)
Time: Sat Aug 19 00:52:33 2006

Input: vector(20,x,floor((x+1)*sqrt(2))-floor(x*sqrt(2)))

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = [1, 2, 1, 2, 1, 1, 2, 1, 2, 1, 1, 2, 1, 2, 1, 2, 1, 1, 2, 1]
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.074s
user	0m0.007s
sys	0m0.008s


'72.30.1'
************** PARI *****************
Host 72.30.129.106 (72.30.129.106)
Time: Fri Aug 18 23:36:56 2006

Input: y=210; for(x=1,8,y=sumdiv(y,x,x)-y;print1(y,","))

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? 366,378,582,594,846,1026,1374,1386,
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.015s
user	0m0.008s
sys	0m0.008s


'169.231'
************** PARI *****************
Host 169.231.33.177 (169.231.33.177)
Time: Fri Aug 18 20:39:59 2006

Input: [0,1,1;1,1,0;1,0,1]^4

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = 
[6 5 5]

[5 6 5]

[5 5 6]

? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.014s
user	0m0.007s
sys	0m0.007s


'169.231'
************** PARI *****************
Host 169.231.33.177 (169.231.33.177)
Time: Fri Aug 18 20:39:05 2006

Input: [0,1,1;1,1,0;1,0,1]^3

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = 
[2 3 3]

[3 3 2]

[3 2 3]

? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.014s
user	0m0.007s
sys	0m0.006s


'169.231'
************** PARI *****************
Host 169.231.33.177 (169.231.33.177)
Time: Fri Aug 18 20:38:00 2006

Input: [0,1,1;1,1,0;1,0,1]^2

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = 
[2 1 1]

[1 2 1]

[1 1 2]

? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.014s
user	0m0.006s
sys	0m0.008s


'169.231'
************** PARI *****************
Host 169.231.33.177 (169.231.33.177)
Time: Fri Aug 18 20:37:51 2006

Input: [0,1,1;1,1,0;1,0,1]

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = 
[0 1 1]

[1 1 0]

[1 0 1]

? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.014s
user	0m0.007s
sys	0m0.007s


'169.231'
************** PARI *****************
Host 169.231.33.177 (169.231.33.177)
Time: Fri Aug 18 20:37:00 2006

Input: [1,0,1;1,1,0;0,1,1]^6

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = 
[22 21 21]

[21 22 21]

[21 21 22]

? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.014s
user	0m0.005s
sys	0m0.010s


'169.231'
************** PARI *****************
Host 169.231.33.177 (169.231.33.177)
Time: Fri Aug 18 20:35:42 2006

Input: [1,0,1;1,1,0;0,1,1]^5

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = 
[11 11 10]

[10 11 11]

[11 10 11]

? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.014s
user	0m0.008s
sys	0m0.007s


'169.231'
************** PARI *****************
Host 169.231.33.177 (169.231.33.177)
Time: Fri Aug 18 20:35:28 2006

Input: [1,0,1;1,1,0;0,1,1]^4

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = 
[5 6 5]

[5 5 6]

[6 5 5]

? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.014s
user	0m0.007s
sys	0m0.008s


'169.231'
************** PARI *****************
Host 169.231.33.177 (169.231.33.177)
Time: Fri Aug 18 20:35:18 2006

Input: [1,0,1;1,1,0;0,1,1]^3

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = 
[2 3 3]

[3 2 3]

[3 3 2]

? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.014s
user	0m0.006s
sys	0m0.008s


'169.231'
************** PARI *****************
Host 169.231.33.177 (169.231.33.177)
Time: Fri Aug 18 20:34:53 2006

Input: [1,0,1;1,1,0;0,1,1]^4

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = 
[5 6 5]

[5 5 6]

[6 5 5]

? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.014s
user	0m0.006s
sys	0m0.008s


'169.231'
************** PARI *****************
Host 169.231.33.177 (169.231.33.177)
Time: Fri Aug 18 20:34:20 2006

Input: [1,0,1;1,1,0;0,1,1]^3


Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = 
[2 3 3]

[3 2 3]

[3 3 2]

? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.014s
user	0m0.006s
sys	0m0.009s


'169.231'
************** PARI *****************
Host 169.231.33.177 (169.231.33.177)
Time: Fri Aug 18 20:33:48 2006

Input: [1,0,1;1,1,0;0,1,1]^2


Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = 
[1 1 2]

[2 1 1]

[1 2 1]

? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.014s
user	0m0.008s
sys	0m0.005s


'169.231'
************** PARI *****************
Host 169.231.33.177 (169.231.33.177)
Time: Fri Aug 18 20:33:03 2006

Input: [1,0,1;1,1,0;0,1,1]


Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = 
[1 0 1]

[1 1 0]

[0 1 1]

? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.014s
user	0m0.007s
sys	0m0.007s


'169.231'
************** PARI *****************
Host 169.231.33.177 (169.231.33.177)
Time: Fri Aug 18 20:32:46 2006

Input: [1,0,1;1,1,0;0,1,1]^2


Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = 
[1 1 2]

[2 1 1]

[1 2 1]

? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.015s
user	0m0.004s
sys	0m0.011s


'169.231'
************** PARI *****************
Host 169.231.33.177 (169.231.33.177)
Time: Fri Aug 18 20:31:56 2006

Input: [1,0,0;0,1,0;0,0,1]^2



Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = 
[1 0 0]

[0 1 0]

[0 0 1]

? ? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.014s
user	0m0.006s
sys	0m0.008s


'169.231'
************** PARI *****************
Host 169.231.33.177 (169.231.33.177)
Time: Fri Aug 18 20:31:39 2006

Input: [1,0,0;0,1,0;0,0,1]^m


Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? ? 
Goodbye!

Errors/timing (if any):

  ***   gpow: 0 to a forbidden power.

Timing:
real	0m0.014s
user	0m0.006s
sys	0m0.008s


'169.231'
************** PARI *****************
Host 169.231.33.177 (169.231.33.177)
Time: Fri Aug 18 20:31:27 2006

Input: [1,0,0;0,1,0;0,0,1]

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = 
[1 0 0]

[0 1 0]

[0 0 1]

? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.014s
user	0m0.003s
sys	0m0.011s


'169.231'
************** PARI *****************
Host 169.231.33.177 (169.231.33.177)
Time: Fri Aug 18 20:31:13 2006

Input: [1,0,0;0,1,0;0,0,1]^m

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? ? 
Goodbye!

Errors/timing (if any):

  ***   gpow: 0 to a forbidden power.

Timing:
real	0m0.014s
user	0m0.006s
sys	0m0.009s


'72.30.9'
************** PARI *****************
Host 72.30.98.26 (72.30.98.26)
Time: Fri Aug 18 19:37:26 2006

Input: factor(2^(2^5)+1)

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = 
[641 1]

[6700417 1]

? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.014s
user	0m0.007s
sys	0m0.007s


'72.30.1'
************** PARI *****************
Host 72.30.131.199 (72.30.131.199)
Time: Fri Aug 18 18:24:00 2006

Input: {ss(n)=sum(x=1,n,n/gcd(n,x))}
ss(60)

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? ? %1 = 1617
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.015s
user	0m0.006s
sys	0m0.009s


'72.30.9'
************** PARI *****************
Host 72.30.99.77 (72.30.99.77)
Time: Fri Aug 18 17:10:16 2006

Input: factor(x^6-1)

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = 
[x - 1 1]

[x + 1 1]

[x^2 - x + 1 1]

[x^2 + x + 1 1]

? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.091s
user	0m0.007s
sys	0m0.008s


'70.126.'
************** PARI *****************
Host 70.126.58.233 (70.126.58.233)
Time: Fri Aug 18 16:39:16 2006

Input: "Replace this by some code, then click [SAGE] or [PARI]!"

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = "Replace this by some code, then click [SAGE] or [PARI]!"
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.014s
user	0m0.006s
sys	0m0.008s


'70.229.'
************** PARI *****************
Host 70.229.26.148 (70.229.26.148)
Time: Fri Aug 18 15:50:18 2006

Input: 1.609344

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = 1.6093440000000000000000000000000000000
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.014s
user	0m0.008s
sys	0m0.006s


'69.213.'
************** PARI *****************
Host 69.213.205.32 (69.213.205.32)
Time: Fri Aug 18 14:48:29 2006

Input: 21.60/5%


Output: WARNING: PARI command contains unsafe command '%', so it will not be executed.

'66.91.5'
************** PARI *****************
Host 66.91.53.79 (66.91.53.79)
Time: Fri Aug 18 14:24:32 2006

Input: 820.26-11.33


Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = 808.93000000000000000000000000000000000
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.365s
user	0m0.006s
sys	0m0.011s


'65.54.1'
************** PARI *****************
Host 65.54.188.53 (65.54.188.53)
Time: Fri Aug 18 04:40:39 2006

Input: {ss(n)=sum(x=1,n,n/gcd(n,x))}
ss(60)

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? ? %1 = 1617
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.014s
user	0m0.005s
sys	0m0.009s


'72.30.9'
************** PARI *****************
Host 72.30.97.221 (72.30.97.221)
Time: Fri Aug 18 02:29:18 2006

Input: for(n=1,20, print1(n,": ",valuation(n!,2),", ") )

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? 1: 0, 2: 1, 3: 1, 4: 3, 5: 3, 6: 4, 7: 4, 8: 7, 9: 7, 10: 8, 11: 8, 12: 10, 13: 10, 14: 11, 15: 11, 16: 15, 17: 15, 18: 16, 19: 16, 20: 18, 
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.069s
user	0m0.008s
sys	0m0.007s


'72.30.1'
************** PARI *****************
Host 72.30.102.206 (72.30.102.206)
Time: Thu Aug 17 23:13:49 2006

Input: vector(20,x,floor((x+1)*sqrt(2))-floor(x*sqrt(2)))

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = [1, 2, 1, 2, 1, 1, 2, 1, 2, 1, 1, 2, 1, 2, 1, 2, 1, 1, 2, 1]
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.064s
user	0m0.009s
sys	0m0.007s


'66.249.'
************** PARI *****************
Host 66.249.65.113 (66.249.65.113)
Time: Thu Aug 17 21:31:47 2006

Input: {ss(n)=sum(x=1,n,n/gcd(n,x))}
ss(60)

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? ? %1 = 1617
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.107s
user	0m0.005s
sys	0m0.011s


'71.93.1'
************** PARI *****************
Host 71.93.172.203 (71.93.172.203)
Time: Thu Aug 17 18:47:00 2006

Input: 6<2x<8


Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? ? 
Goodbye!

Errors/timing (if any):

  ***   Warning: unused characters: x<8.
  ***   incorrect type in comparison.

Timing:
real	0m0.014s
user	0m0.007s
sys	0m0.006s


'66.68.1'
************** PARI *****************
Host 66.68.12.46 (66.68.12.46)
Time: Thu Aug 17 18:30:19 2006

Input: 3+5


Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = 8
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.014s
user	0m0.007s
sys	0m0.007s


'71.154.'
************** PARI *****************
Host 71.154.245.24 (71.154.245.24)
Time: Thu Aug 17 17:28:25 2006

Input: "Replace this by some code, then click [SAGE] or [PARI]!"

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = "Replace this by some code, then click [SAGE] or [PARI]!"
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.019s
user	0m0.005s
sys	0m0.009s


'24.116.'
************** PARI *****************
Host 24.116.250.166 (24.116.250.166)
Time: Thu Aug 17 16:54:11 2006

Input: "Replace this by some code, then click [SAGE] or [PARI]!"

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = "Replace this by some code, then click [SAGE] or [PARI]!"
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.014s
user	0m0.003s
sys	0m0.011s


'24.116.'
************** PARI *****************
Host 24.116.250.166 (24.116.250.166)
Time: Thu Aug 17 16:54:10 2006

Input: "Replace this by some code, then click [SAGE] or [PARI]!"

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = "Replace this by some code, then click [SAGE] or [PARI]!"
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.014s
user	0m0.005s
sys	0m0.009s


'83.92.5'
************** PARI *****************
Host 83.92.51.114 (83.92.51.114)
Time: Thu Aug 17 16:22:55 2006

Input: print kash(256^512)

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? ? 
Goodbye!

Errors/timing (if any):

  ***   unknown function or error in formal parameters: printkash(256^512)
                                                        ^------------------

Timing:
real	0m0.033s
user	0m0.009s
sys	0m0.005s


'70.180.'
************** PARI *****************
Host 70.180.62.77 (70.180.62.77)
Time: Thu Aug 17 15:26:46 2006

Input: 2.5(x-3)+17x=10.8(x+15)

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = 25.800000000000000000000000000000000000
? 
Goodbye!

Errors/timing (if any):

  ***   Warning: unused characters: (x-3)+17x=10.8(x+15).

Timing:
real	0m0.014s
user	0m0.008s
sys	0m0.007s


'85.182.'
************** PARI *****************
Host 85.182.66.38 (85.182.66.38)
Time: Thu Aug 17 11:32:28 2006

Input: print(gap('LatticeSubgroups(SymmetricGroup(4));')


Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? ? 
Goodbye!

Errors/timing (if any):

  ***   expected character: ',' instead of: ...int(gap('LatticeSubgroups
  ***   (SymmetricGroup(4));
        ^--------------------

Timing:
real	0m0.015s
user	0m0.007s
sys	0m0.007s


'85.182.'
************** PARI *****************
Host 85.182.66.38 (85.182.66.38)
Time: Thu Aug 17 11:31:40 2006

Input: print(gap('SubgroupsSolvableGroup(S4)')


Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? ? 
Goodbye!

Errors/timing (if any):

  ***   expected character: ',' instead of: ...p('SubgroupsSolvableGroup(S4)')
                                                                        ^------

Timing:
real	0m0.014s
user	0m0.005s
sys	0m0.008s


'85.182.'
************** PARI *****************
Host 85.182.66.38 (85.182.66.38)
Time: Thu Aug 17 11:31:24 2006

Input: print(gap('SubgroupsSolvableGroup(SymmetricGroup(4))')


Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? ? 
Goodbye!

Errors/timing (if any):

  ***   expected character: ',' instead of: ...p('SubgroupsSolvableGroup
  ***   (SymmetricGroup(4))'
        ^--------------------

Timing:
real	0m0.014s
user	0m0.007s
sys	0m0.007s


'69.236.'
************** PARI *****************
Host 69.236.179.102 (69.236.179.102)
Time: Thu Aug 17 11:29:45 2006

Input: 4x^3+8x^2>0

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? ? 
Goodbye!

Errors/timing (if any):

  ***   Warning: unused characters: x^3+8x^2>0.
  ***   incorrect type in comparison.

Timing:
real	0m0.299s
user	0m0.005s
sys	0m0.011s


'72.30.2'
************** PARI *****************
Host 72.30.226.160 (72.30.226.160)
Time: Thu Aug 17 06:27:31 2006

Input: for(n=1,7, print1(n,": ",sum(x=1,n,1/x),",  ") )

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? 1: 1,  2: 3/2,  3: 11/6,  4: 25/12,  5: 137/60,  6: 49/20,  7: 363/140,  
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.014s
user	0m0.006s
sys	0m0.008s


'75.4.16'
************** PARI *****************
Host 75.4.167.188 (75.4.167.188)
Time: Thu Aug 17 02:10:42 2006

Input: 5%/1,897


Output: WARNING: PARI command contains unsafe command '%', so it will not be executed.

'75.4.16'
************** PARI *****************
Host 75.4.167.188 (75.4.167.188)
Time: Thu Aug 17 02:10:16 2006

Input: 5% of 1,897


Output: WARNING: PARI command contains unsafe command '%', so it will not be executed.

'218.45.'
************** PARI *****************
Host 218.45.172.241 (218.45.172.241)
Time: Thu Aug 17 01:48:07 2006

Input: (1.01)^35

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = 1.4166027560312678260004629407847590686
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.014s
user	0m0.007s
sys	0m0.008s


'218.45.'
************** PARI *****************
Host 218.45.172.241 (218.45.172.241)
Time: Thu Aug 17 01:47:58 2006

Input: (1.1)^35

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = 28.102436848064247850612139033534048511
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.065s
user	0m0.008s
sys	0m0.007s


'72.30.2'
************** PARI *****************
Host 72.30.226.223 (72.30.226.223)
Time: Thu Aug 17 01:43:14 2006

Input: for(n=1,7, print1(n,": ",sum(x=1,n,1/x),",  ") )

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? 1: 1,  2: 3/2,  3: 11/6,  4: 25/12,  5: 137/60,  6: 49/20,  7: 363/140,  
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.067s
user	0m0.008s
sys	0m0.006s


'219.95.'
************** PARI *****************
Host 219.95.235.147 (219.95.235.147)
Time: Thu Aug 17 01:24:56 2006

Input: for( k=1, 12, print(k,": ",Mod(2^k,13)) )

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? 1: Mod(2, 13)
2: Mod(4, 13)
3: Mod(8, 13)
4: Mod(3, 13)
5: Mod(6, 13)
6: Mod(12, 13)
7: Mod(11, 13)
8: Mod(9, 13)
9: Mod(5, 13)
10: Mod(10, 13)
11: Mod(7, 13)
12: Mod(1, 13)
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.057s
user	0m0.008s
sys	0m0.008s


'72.30.1'
************** PARI *****************
Host 72.30.129.106 (72.30.129.106)
Time: Wed Aug 16 22:59:55 2006

Input: y=210; for(x=1,8,y=sumdiv(y,x,x)-y;print1(y,","))

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? 366,378,582,594,846,1026,1374,1386,
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.109s
user	0m0.009s
sys	0m0.005s


'59.140.'
************** PARI *****************
Host 59.140.3.12 (59.140.3.12)
Time: Wed Aug 16 20:51:28 2006

Input: "Replace this by some code, then click [SAGE] or [PARI]!"

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = "Replace this by some code, then click [SAGE] or [PARI]!"
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.027s
user	0m0.005s
sys	0m0.009s


'213.114'
************** PARI *****************
Host 213.114.87.142 (213.114.87.142)
Time: Wed Aug 16 15:41:29 2006

Input: "Replace this by some code, then click [SAGE] or [PARI]!"

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = "Replace this by some code, then click [SAGE] or [PARI]!"
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.545s
user	0m0.007s
sys	0m0.009s


'65.188.'
************** PARI *****************
Host 65.188.208.165 (65.188.208.165)
Time: Wed Aug 16 05:03:46 2006

Input: factor(2^(2^5)+1)

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = 
[641 1]

[6700417 1]

? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.014s
user	0m0.007s
sys	0m0.007s


'72.30.1'
************** PARI *****************
Host 72.30.103.19 (72.30.103.19)
Time: Wed Aug 16 01:34:00 2006

Input: y=210; for(x=1,8,y=sumdiv(y,x,x)-y;print1(y,","))

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? 366,378,582,594,846,1026,1374,1386,
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.014s
user	0m0.008s
sys	0m0.005s


'71.141.'
************** PARI *****************
Host 71.141.253.153 (71.141.253.153)
Time: Tue Aug 15 23:42:30 2006

Input: for(n=1,7, print1(n,": ",sum(x=1,n,1/x),",  ") )

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? 1: 1,  2: 3/2,  3: 11/6,  4: 25/12,  5: 137/60,  6: 49/20,  7: 363/140,  
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.014s
user	0m0.008s
sys	0m0.006s


'72.30.1'
************** PARI *****************
Host 72.30.129.106 (72.30.129.106)
Time: Tue Aug 15 22:13:02 2006

Input: y=210; for(x=1,8,y=sumdiv(y,x,x)-y;print1(y,","))

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? 366,378,582,594,846,1026,1374,1386,
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.015s
user	0m0.008s
sys	0m0.007s


'24.64.2'
************** PARI *****************
Host 24.64.223.203 (24.64.223.203)
Time: Tue Aug 15 17:22:28 2006

Input: factor(597543644043339483)

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = 
[3 1]

[7 1]

[1019 1]

[1736939 1]

[16076503 1]

? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.115s
user	0m0.007s
sys	0m0.008s


'24.64.2'
************** PARI *****************
Host 24.64.223.203 (24.64.223.203)
Time: Tue Aug 15 17:18:59 2006

Input: 52

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = 52
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.014s
user	0m0.005s
sys	0m0.009s


'24.64.2'
************** PARI *****************
Host 24.64.223.203 (24.64.223.203)
Time: Tue Aug 15 17:18:42 2006

Input: 57

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = 57
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.014s
user	0m0.006s
sys	0m0.008s


'72.128.'
************** PARI *****************
Host 72.128.44.217 (72.128.44.217)
Time: Tue Aug 15 16:24:48 2006

Input: (1/3)(9)�=


Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? ? 
Goodbye!

Errors/timing (if any):

  ***   Warning: unused characters: (9)===.
  ***   unexpected character: (1/3)(9)===
                                        ^-

Timing:
real	0m0.014s
user	0m0.004s
sys	0m0.010s


'72.128.'
************** PARI *****************
Host 72.128.44.217 (72.128.44.217)
Time: Tue Aug 15 16:24:13 2006

Input: (1/3)(9)�=


Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? ? 
Goodbye!

Errors/timing (if any):

  ***   Warning: unused characters: (9)===.
  ***   unexpected character: (1/3)(9)===
                                        ^-

Timing:
real	0m0.028s
user	0m0.007s
sys	0m0.008s


'70.247.'
************** PARI *****************
Host 70.247.113.187 (70.247.113.187)
Time: Tue Aug 15 15:15:36 2006

Input: "Replace this by some code, then click [SAGE] or [PARI]!"

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = "Replace this by some code, then click [SAGE] or [PARI]!"
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.015s
user	0m0.005s
sys	0m0.010s


'84.107.'
************** PARI *****************
Host 84.107.150.174 (84.107.150.174)
Time: Tue Aug 15 11:55:56 2006

Input: Mod(7,30)^(7^7^7)

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = Mod(13, 30)
? 
Goodbye!

Errors/timing (if any):

  ***   Warning: multiword exponent in Fl_pow.

Timing:
real	0m0.268s
user	0m0.215s
sys	0m0.013s


'72.30.1'
************** PARI *****************
Host 72.30.129.138 (72.30.129.138)
Time: Tue Aug 15 11:21:13 2006

Input: for( k=1, 12, print(k,": ",Mod(2^k,13)) )

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? 1: Mod(2, 13)
2: Mod(4, 13)
3: Mod(8, 13)
4: Mod(3, 13)
5: Mod(6, 13)
6: Mod(12, 13)
7: Mod(11, 13)
8: Mod(9, 13)
9: Mod(5, 13)
10: Mod(10, 13)
11: Mod(7, 13)
12: Mod(1, 13)
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.014s
user	0m0.006s
sys	0m0.008s


'84.107.'
************** PARI *****************
Host 84.107.150.174 (84.107.150.174)
Time: Tue Aug 15 11:19:38 2006

Input: Mod(3,1000)^(83)

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = Mod(227, 1000)
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.014s
user	0m0.006s
sys	0m0.008s


'84.107.'
************** PARI *****************
Host 84.107.150.174 (84.107.150.174)
Time: Tue Aug 15 11:12:55 2006

Input: Mod(3,400)^(2003)

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = Mod(27, 400)
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.014s
user	0m0.006s
sys	0m0.008s


'84.107.'
************** PARI *****************
Host 84.107.150.174 (84.107.150.174)
Time: Tue Aug 15 10:55:13 2006

Input: Mod(3,400)^(83)

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = Mod(27, 400)
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.014s
user	0m0.005s
sys	0m0.008s


'84.107.'
************** PARI *****************
Host 84.107.150.174 (84.107.150.174)
Time: Tue Aug 15 10:28:54 2006

Input: 3^83

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = 3990838394187339929534246675572349035227
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.014s
user	0m0.005s
sys	0m0.009s


'84.107.'
************** PARI *****************
Host 84.107.150.174 (84.107.150.174)
Time: Tue Aug 15 10:28:33 2006

Input: 3^20

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = 3486784401
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.014s
user	0m0.005s
sys	0m0.010s


'84.107.'
************** PARI *****************
Host 84.107.150.174 (84.107.150.174)
Time: Tue Aug 15 10:19:00 2006

Input: 3^83

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = 3990838394187339929534246675572349035227
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.014s
user	0m0.007s
sys	0m0.007s


'84.107.'
************** PARI *****************
Host 84.107.150.174 (84.107.150.174)
Time: Tue Aug 15 10:18:46 2006

Input: 3^400

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = 70550791086553325712464271575934796216507949612787315762871223209262085551582934156579298529447134158154952334825355911866929793071824566694145084454535257027960285323760313192443283334088001
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.014s
user	0m0.008s
sys	0m0.006s


'84.107.'
************** PARI *****************
Host 84.107.150.174 (84.107.150.174)
Time: Tue Aug 15 10:13:15 2006

Input: Mod(3,1000)^(2003^2003)

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = Mod(987, 1000)
? 
Goodbye!

Errors/timing (if any):

  ***   Warning: multiword exponent in Fl_pow.

Timing:
real	0m0.016s
user	0m0.008s
sys	0m0.009s


'84.107.'
************** PARI *****************
Host 84.107.150.174 (84.107.150.174)
Time: Tue Aug 15 09:48:20 2006

Input: Mod(3,100)^(2003^2003)

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = Mod(87, 100)
? 
Goodbye!

Errors/timing (if any):

  ***   Warning: multiword exponent in Fl_pow.

Timing:
real	0m0.049s
user	0m0.008s
sys	0m0.009s


'84.107.'
************** PARI *****************
Host 84.107.150.174 (84.107.150.174)
Time: Tue Aug 15 09:45:41 2006

Input: 3^(2003^2003)

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? ? 
Goodbye!

Errors/timing (if any):

  ***   length (lg) overflow

Timing:
real	0m0.015s
user	0m0.005s
sys	0m0.010s


'84.107.'
************** PARI *****************
Host 84.107.150.174 (84.107.150.174)
Time: Tue Aug 15 09:45:01 2006

Input: 3^2003

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = 47192523796511593460819314717445835404284687160750089980920976318888529188136438210870134686346389999041441668795922467896826947768638733482889183456528239010568634262429383843301299968914654135021616852400619449604094035791513517490976267110993951445870348070649724838442950877697281464105603387943746139280208780890973452976589061955333899720134617153262713286486800459846999808593157946089834398450393914138264834193475885957005425265572728480321922372718342943042880916739731170887479399462363014861982530234203725804474544039577325916627591757941754987079099118539866954821154972250974284998342253129564298697533991303605099243743998763493165069920824491545486353467536460616499651953399236100304728302468297087043095519255193036095675710613231999201256180837163220902716746235182201529062324435884453986670695008281249641444785221286768136955402601273270121405513124724415388652516643729635832196015310268380966177525262817036149775193114460981880027
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.015s
user	0m0.007s
sys	0m0.009s


'84.107.'
************** PARI *****************
Host 84.107.150.174 (84.107.150.174)
Time: Tue Aug 15 09:44:39 2006

Input: 2003^2003

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = 1849019260402709591286946172272940395303112445168867902383112555669571680764331263129330914652274495344312361794223854136737235628975718111135048790603351966051089751801492286418588902467028553504583229077928836304421158684528741674751413584648058844055647193516177071717162896188397649366593550136210318645392352569990645096972351505408767255782003625775433472017371179730547137478287893507333560277638389093691937015829221890068050469248634486703551127690968842230454015685132969837483003553059495828232089447828335373623978090541832251404561839854204124893294475642540010052397603804262506936563543122526936967047474058883448638286320846501903634081589405217621172604680678266257943264554652140453584775304923366347265361889863651409967357350610120370545343116444163083489140070777265080161473074590584338930415700500346333630578065794337339456800772435468402349571596298898714975383243864935535636134581337583186012822632640943109188841366090566003571671616355255066629545340775357546670343012710596231482375467743311249226696302796942829058327257509806942696109036650762242172624273154718478553514815075003175820338775199237589617467645726633551827062674809808821496907148128685454048876323643882165409382905436659884016880864706115534311275854858879482590439605638014513404114965161328132476890310946700527095556057226375889945939398114414530519086388011842145370813116466116933677781283418754185176308541744851367722022538010448557111987710967293795913750778380493693364942128158609647913299867196028991715761098664736737689726033022049768616498578659743306410989634574595752793197774095598026370816536578149768457163093990891659686173217641139200667442352618661018059985367747557369405138674119976901185838232734027098311705631317918930369382581576149049468721347552491182500222194663605206043936720336781866516862682519809693874713689647661086241945324543523536693944148087374805375384267176609436513867966084736897671968946642626981894686304621598541991524231414384141282558288006355975293005476137974561143445115105779797830936073546368454667098115241359316617104258762436468188728754333143356008113347748174553932050079642183234048683147769732123261465567836710684328110031873160964530586628853340849483016910719803320336003623157812793587485942907628960069171712069941546144521254605696368192772610846565381585445513891947386210269254508355475189422639476055636015982352067475607003031996183489799837437930982672410956753059148884164506367316219442600996483386809306833003557091114903316063583559200044640197860848036956391379905814413562503411001844090155223225441144384859621030897061479811658231861008612105849597548707170382390239878149382462392451454760982084364281414125014558498298153586644143512342948560725715692468080071277962250555090930040064361149899149864222030853686276876495951900958363725547749789103291905846544642388789885806597704471784458460481220648107198384132908599908344227320292109752815908406413867624583806294047610747554301474744086100782707611290662006703157494157162044337566623400061356300491066346464547827504101349366387203053910739342132649163101380906928003626736950801017814100310095468922280959188145785275380839397906917702194975501151197[+++]
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.017s
user	0m0.005s
sys	0m0.013s


'84.107.'
************** PARI *****************
Host 84.107.150.174 (84.107.150.174)
Time: Tue Aug 15 09:44:14 2006

Input: 3^20

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = 3486784401
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.015s
user	0m0.007s
sys	0m0.008s


'84.107.'
************** PARI *****************
Host 84.107.150.174 (84.107.150.174)
Time: Tue Aug 15 09:42:08 2006

Input: 3^1024

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = 373391848741020043532959754184866588225409776783734007750636931722079040617265251229993688938803977220468765065431475158108727054592160858581351336982809187314191748594262580938807019951956404285571818041046681288797402925517668012340617298396574731619152386723046235125934896058590588284654793540505936202376547807442730582144527058988756251452817793413352141920744623027518729185432862375737063985485319476416926263819972887006907013899256524297198527698749274196276811060702333710356481
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.014s
user	0m0.006s
sys	0m0.007s


'84.107.'
************** PARI *****************
Host 84.107.150.174 (84.107.150.174)
Time: Tue Aug 15 09:35:44 2006

Input: 2003^2003

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = 1849019260402709591286946172272940395303112445168867902383112555669571680764331263129330914652274495344312361794223854136737235628975718111135048790603351966051089751801492286418588902467028553504583229077928836304421158684528741674751413584648058844055647193516177071717162896188397649366593550136210318645392352569990645096972351505408767255782003625775433472017371179730547137478287893507333560277638389093691937015829221890068050469248634486703551127690968842230454015685132969837483003553059495828232089447828335373623978090541832251404561839854204124893294475642540010052397603804262506936563543122526936967047474058883448638286320846501903634081589405217621172604680678266257943264554652140453584775304923366347265361889863651409967357350610120370545343116444163083489140070777265080161473074590584338930415700500346333630578065794337339456800772435468402349571596298898714975383243864935535636134581337583186012822632640943109188841366090566003571671616355255066629545340775357546670343012710596231482375467743311249226696302796942829058327257509806942696109036650762242172624273154718478553514815075003175820338775199237589617467645726633551827062674809808821496907148128685454048876323643882165409382905436659884016880864706115534311275854858879482590439605638014513404114965161328132476890310946700527095556057226375889945939398114414530519086388011842145370813116466116933677781283418754185176308541744851367722022538010448557111987710967293795913750778380493693364942128158609647913299867196028991715761098664736737689726033022049768616498578659743306410989634574595752793197774095598026370816536578149768457163093990891659686173217641139200667442352618661018059985367747557369405138674119976901185838232734027098311705631317918930369382581576149049468721347552491182500222194663605206043936720336781866516862682519809693874713689647661086241945324543523536693944148087374805375384267176609436513867966084736897671968946642626981894686304621598541991524231414384141282558288006355975293005476137974561143445115105779797830936073546368454667098115241359316617104258762436468188728754333143356008113347748174553932050079642183234048683147769732123261465567836710684328110031873160964530586628853340849483016910719803320336003623157812793587485942907628960069171712069941546144521254605696368192772610846565381585445513891947386210269254508355475189422639476055636015982352067475607003031996183489799837437930982672410956753059148884164506367316219442600996483386809306833003557091114903316063583559200044640197860848036956391379905814413562503411001844090155223225441144384859621030897061479811658231861008612105849597548707170382390239878149382462392451454760982084364281414125014558498298153586644143512342948560725715692468080071277962250555090930040064361149899149864222030853686276876495951900958363725547749789103291905846544642388789885806597704471784458460481220648107198384132908599908344227320292109752815908406413867624583806294047610747554301474744086100782707611290662006703157494157162044337566623400061356300491066346464547827504101349366387203053910739342132649163101380906928003626736950801017814100310095468922280959188145785275380839397906917702194975501151197[+++]
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.017s
user	0m0.008s
sys	0m0.010s


'84.107.'
************** PARI *****************
Host 84.107.150.174 (84.107.150.174)
Time: Tue Aug 15 09:35:30 2006

Input: 3^3

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = 27
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.014s
user	0m0.008s
sys	0m0.006s


'84.107.'
************** PARI *****************
Host 84.107.150.174 (84.107.150.174)
Time: Tue Aug 15 09:29:37 2006

Input: 2003^2003

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = 1849019260402709591286946172272940395303112445168867902383112555669571680764331263129330914652274495344312361794223854136737235628975718111135048790603351966051089751801492286418588902467028553504583229077928836304421158684528741674751413584648058844055647193516177071717162896188397649366593550136210318645392352569990645096972351505408767255782003625775433472017371179730547137478287893507333560277638389093691937015829221890068050469248634486703551127690968842230454015685132969837483003553059495828232089447828335373623978090541832251404561839854204124893294475642540010052397603804262506936563543122526936967047474058883448638286320846501903634081589405217621172604680678266257943264554652140453584775304923366347265361889863651409967357350610120370545343116444163083489140070777265080161473074590584338930415700500346333630578065794337339456800772435468402349571596298898714975383243864935535636134581337583186012822632640943109188841366090566003571671616355255066629545340775357546670343012710596231482375467743311249226696302796942829058327257509806942696109036650762242172624273154718478553514815075003175820338775199237589617467645726633551827062674809808821496907148128685454048876323643882165409382905436659884016880864706115534311275854858879482590439605638014513404114965161328132476890310946700527095556057226375889945939398114414530519086388011842145370813116466116933677781283418754185176308541744851367722022538010448557111987710967293795913750778380493693364942128158609647913299867196028991715761098664736737689726033022049768616498578659743306410989634574595752793197774095598026370816536578149768457163093990891659686173217641139200667442352618661018059985367747557369405138674119976901185838232734027098311705631317918930369382581576149049468721347552491182500222194663605206043936720336781866516862682519809693874713689647661086241945324543523536693944148087374805375384267176609436513867966084736897671968946642626981894686304621598541991524231414384141282558288006355975293005476137974561143445115105779797830936073546368454667098115241359316617104258762436468188728754333143356008113347748174553932050079642183234048683147769732123261465567836710684328110031873160964530586628853340849483016910719803320336003623157812793587485942907628960069171712069941546144521254605696368192772610846565381585445513891947386210269254508355475189422639476055636015982352067475607003031996183489799837437930982672410956753059148884164506367316219442600996483386809306833003557091114903316063583559200044640197860848036956391379905814413562503411001844090155223225441144384859621030897061479811658231861008612105849597548707170382390239878149382462392451454760982084364281414125014558498298153586644143512342948560725715692468080071277962250555090930040064361149899149864222030853686276876495951900958363725547749789103291905846544642388789885806597704471784458460481220648107198384132908599908344227320292109752815908406413867624583806294047610747554301474744086100782707611290662006703157494157162044337566623400061356300491066346464547827504101349366387203053910739342132649163101380906928003626736950801017814100310095468922280959188145785275380839397906917702194975501151197[+++]
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.084s
user	0m0.010s
sys	0m0.010s


'72.30.1'
************** PARI *****************
Host 72.30.110.15 (72.30.110.15)
Time: Tue Aug 15 08:13:30 2006

Input: for(x=1,50,print1("d(",x,")=",numdiv(x),", "))

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? d(1)=1, d(2)=2, d(3)=2, d(4)=3, d(5)=2, d(6)=4, d(7)=2, d(8)=4, d(9)=3, d(10)=4, d(11)=2, d(12)=6, d(13)=2, d(14)=4, d(15)=4, d(16)=5, d(17)=2, d(18)=6, d(19)=2, d(20)=6, d(21)=4, d(22)=4, d(23)=2, d(24)=8, d(25)=3, d(26)=4, d(27)=4, d(28)=6, d(29)=2, d(30)=8, d(31)=2, d(32)=6, d(33)=4, d(34)=4, d(35)=4, d(36)=9, d(37)=2, d(38)=4, d(39)=4, d(40)=8, d(41)=2, d(42)=8, d(43)=2, d(44)=6, d(45)=6, d(46)=4, d(47)=2, d(48)=10, d(49)=3, d(50)=6, 
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.255s
user	0m0.009s
sys	0m0.008s


'72.30.2'
************** PARI *****************
Host 72.30.226.160 (72.30.226.160)
Time: Tue Aug 15 03:09:45 2006

Input: for(n=1,7, print1(n,": ",sum(x=1,n,1/x),",  ") )

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? 1: 1,  2: 3/2,  3: 11/6,  4: 25/12,  5: 137/60,  6: 49/20,  7: 363/140,  
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.014s
user	0m0.006s
sys	0m0.009s


'72.30.2'
************** PARI *****************
Host 72.30.226.223 (72.30.226.223)
Time: Tue Aug 15 02:42:02 2006

Input: for(n=1,7, print1(n,": ",sum(x=1,n,1/x),",  ") )

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? 1: 1,  2: 3/2,  3: 11/6,  4: 25/12,  5: 137/60,  6: 49/20,  7: 363/140,  
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.021s
user	0m0.006s
sys	0m0.010s


'169.231'
************** PARI *****************
Host 169.231.33.177 (169.231.33.177)
Time: Mon Aug 14 23:56:53 2006

Input: [1,0,1,0;0,1,0,1;1,1,0,0;0,0,1,1]^3

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = 
[3 2 2 1]

[1 2 2 3]

[2 2 2 2]

[2 2 2 2]

? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.014s
user	0m0.007s
sys	0m0.007s


'169.231'
************** PARI *****************
Host 169.231.33.177 (169.231.33.177)
Time: Mon Aug 14 23:56:45 2006

Input: [1,0,1,0;0,1,0,1;1,1,0,0;0,0,1,1]^2

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = 
[2 1 1 0]

[0 1 1 2]

[1 1 1 1]

[1 1 1 1]

? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.015s
user	0m0.008s
sys	0m0.006s


'169.231'
************** PARI *****************
Host 169.231.33.177 (169.231.33.177)
Time: Mon Aug 14 23:56:30 2006

Input: [1,0,1,0;0,1,0,1;1,1,0,0;0,0,1,1]

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = 
[1 0 1 0]

[0 1 0 1]

[1 1 0 0]

[0 0 1 1]

? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.014s
user	0m0.007s
sys	0m0.007s


'169.231'
************** PARI *****************
Host 169.231.33.177 (169.231.33.177)
Time: Mon Aug 14 23:55:38 2006

Input: [1,1,1,0;0,1,1,1;1,1,0,1;1,0,1,1]^2

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = 
[2 3 2 2]

[2 2 2 3]

[2 2 3 2]

[3 2 2 2]

? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.014s
user	0m0.006s
sys	0m0.008s


'169.231'
************** PARI *****************
Host 169.231.33.177 (169.231.33.177)
Time: Mon Aug 14 23:55:18 2006

Input: [1,1,1,0;0,1,1,1;1,1,0,1;1,0,1,1]

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = 
[1 1 1 0]

[0 1 1 1]

[1 1 0 1]

[1 0 1 1]

? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.014s
user	0m0.007s
sys	0m0.008s


'203.5.3'
************** PARI *****************
Host 203.5.3.200 (203.5.3.200)
Time: Mon Aug 14 23:04:49 2006

Input: "Replace this by some code, then click [SAGE] or [PARI]!"

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = "Replace this by some code, then click [SAGE] or [PARI]!"
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.015s
user	0m0.007s
sys	0m0.007s


'169.231'
************** PARI *****************
Host 169.231.33.177 (169.231.33.177)
Time: Mon Aug 14 22:47:40 2006

Input: [0,1,0;1,0,0;0,0,1]^3





Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = 
[0 1 0]

[1 0 0]

[0 0 1]

? ? ? ? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.014s
user	0m0.005s
sys	0m0.008s


'169.231'
************** PARI *****************
Host 169.231.33.177 (169.231.33.177)
Time: Mon Aug 14 22:46:31 2006

Input: [0,1,0;1,0,0;0,0,1]^2





Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = 
[1 0 0]

[0 1 0]

[0 0 1]

? ? ? ? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.014s
user	0m0.008s
sys	0m0.006s


'169.231'
************** PARI *****************
Host 169.231.33.177 (169.231.33.177)
Time: Mon Aug 14 22:46:18 2006

Input: [0,1,0;1,0,0;0,0,1]^3





Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = 
[0 1 0]

[1 0 0]

[0 0 1]

? ? ? ? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.014s
user	0m0.005s
sys	0m0.008s


'169.231'
************** PARI *****************
Host 169.231.33.177 (169.231.33.177)
Time: Mon Aug 14 22:46:02 2006

Input: [0,1,0;1,0,0;0,0,1]^2





Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = 
[1 0 0]

[0 1 0]

[0 0 1]

? ? ? ? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.014s
user	0m0.008s
sys	0m0.006s


'169.231'
************** PARI *****************
Host 169.231.33.177 (169.231.33.177)
Time: Mon Aug 14 22:42:57 2006

Input: [0,1,0;1,0,0;0,0,1]^3





Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = 
[0 1 0]

[1 0 0]

[0 0 1]

? ? ? ? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.014s
user	0m0.005s
sys	0m0.008s


'169.231'
************** PARI *****************
Host 169.231.33.177 (169.231.33.177)
Time: Mon Aug 14 22:42:46 2006

Input: [0,1,0;1,0,0;0,0,1]^2





Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = 
[1 0 0]

[0 1 0]

[0 0 1]

? ? ? ? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.014s
user	0m0.004s
sys	0m0.011s


'169.231'
************** PARI *****************
Host 169.231.33.177 (169.231.33.177)
Time: Mon Aug 14 22:42:37 2006

Input: [0,1,0;1,0,0;0,0,1]





Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = 
[0 1 0]

[1 0 0]

[0 0 1]

? ? ? ? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.015s
user	0m0.007s
sys	0m0.008s


'169.231'
************** PARI *****************
Host 169.231.33.177 (169.231.33.177)
Time: Mon Aug 14 22:41:36 2006

Input: [1,1,0;1,0,1;0,1,1]^2





Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = 
[2 1 1]

[1 2 1]

[1 1 2]

? ? ? ? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.014s
user	0m0.007s
sys	0m0.007s


'169.231'
************** PARI *****************
Host 169.231.33.177 (169.231.33.177)
Time: Mon Aug 14 22:41:00 2006

Input: [1,1,0;1,0,1;0,1,1]




Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = 
[1 1 0]

[1 0 1]

[0 1 1]

? ? ? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.014s
user	0m0.007s
sys	0m0.007s


'169.231'
************** PARI *****************
Host 169.231.33.177 (169.231.33.177)
Time: Mon Aug 14 22:33:08 2006

Input: [0,1,1;1,0,1;1,1,0]^2




Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = 
[2 1 1]

[1 2 1]

[1 1 2]

? ? ? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.014s
user	0m0.007s
sys	0m0.007s


'169.231'
************** PARI *****************
Host 169.231.33.177 (169.231.33.177)
Time: Mon Aug 14 22:32:53 2006

Input: [0,1,1;1,0,1;1,1,0]



Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = 
[0 1 1]

[1 0 1]

[1 1 0]

? ? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.014s
user	0m0.005s
sys	0m0.009s


'169.231'
************** PARI *****************
Host 169.231.33.177 (169.231.33.177)
Time: Mon Aug 14 22:32:38 2006

Input: [0,1,;1,0,1;1,1,0]



Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? ? ? 
Goodbye!

Errors/timing (if any):

  ***   unexpected character: [0,1,;1,0,1;1,1,0]
                                   ^-------------

Timing:
real	0m0.014s
user	0m0.009s
sys	0m0.007s


'169.231'
************** PARI *****************
Host 169.231.33.177 (169.231.33.177)
Time: Mon Aug 14 22:30:21 2006

Input: [1,1,0;0,1,1;1,0,1]^2



Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = 
[1 2 1]

[1 1 2]

[2 1 1]

? ? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.015s
user	0m0.006s
sys	0m0.007s


'169.231'
************** PARI *****************
Host 169.231.33.177 (169.231.33.177)
Time: Mon Aug 14 22:30:09 2006

Input: [1,1,0;0,1,1;1,0,1]


Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = 
[1 1 0]

[0 1 1]

[1 0 1]

? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.014s
user	0m0.006s
sys	0m0.009s


'72.30.1'
************** PARI *****************
Host 72.30.111.28 (72.30.111.28)
Time: Mon Aug 14 22:18:27 2006

Input: for( k=1, 12, print(k,": ",Mod(2^k,13)) )

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? 1: Mod(2, 13)
2: Mod(4, 13)
3: Mod(8, 13)
4: Mod(3, 13)
5: Mod(6, 13)
6: Mod(12, 13)
7: Mod(11, 13)
8: Mod(9, 13)
9: Mod(5, 13)
10: Mod(10, 13)
11: Mod(7, 13)
12: Mod(1, 13)
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.014s
user	0m0.006s
sys	0m0.008s


'72.30.1'
************** PARI *****************
Host 72.30.129.106 (72.30.129.106)
Time: Mon Aug 14 20:42:02 2006

Input: y=210; for(x=1,8,y=sumdiv(y,x,x)-y;print1(y,","))

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? 366,378,582,594,846,1026,1374,1386,
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.014s
user	0m0.005s
sys	0m0.010s


'203.57.'
************** PARI *****************
Host 203.57.240.95 (203.57.240.95)
Time: Mon Aug 14 20:11:05 2006

Input: "Replace this by some code, then click [SAGE] or [PARI]!"

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = "Replace this by some code, then click [SAGE] or [PARI]!"
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.014s
user	0m0.006s
sys	0m0.007s


'72.30.1'
************** PARI *****************
Host 72.30.107.8 (72.30.107.8)
Time: Mon Aug 14 19:27:20 2006

Input: for(b=1,100, for(a=1,b, if( frac((a^2+b^2)/(a*b))==0 , print(a,",",b), ) ) )

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? 1,1
2,2
3,3
4,4
5,5
6,6
7,7
8,8
9,9
10,10
11,11
12,12
13,13
14,14
15,15
16,16
17,17
18,18
19,19
20,20
21,21
22,22
23,23
24,24
25,25
26,26
27,27
28,28
29,29
30,30
31,31
32,32
33,33
34,34
35,35
36,36
37,37
38,38
39,39
40,40
41,41
42,42
43,43
44,44
45,45
46,46
47,47
48,48
49,49
50,50
51,51
52,52
53,53
54,54
55,55
56,56
57,57
58,58
59,59
60,60
61,61
62,62
63,63
64,64
65,65
66,66
67,67
68,68
69,69
70,70
71,71
72,72
73,73
74,74
75,75
76,76
77,77
78,78
79,79
80,80
81,81
82,82
83,83
84,84
85,85
86,86
87,87
88,88
89,89
90,90
91,91
92,92
93,93
94,94
95,95
96,96
97,97
98,98
99,99
100,100
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.078s
user	0m0.027s
sys	0m0.006s


'69.230.'
************** PARI *****************
Host 69.230.18.219 (69.230.18.219)
Time: Mon Aug 14 19:02:14 2006

Input: (4-3)(x+1)

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = x + 1
? 
Goodbye!

Errors/timing (if any):

  ***   Warning: unused characters: (x+1).

Timing:
real	0m0.014s
user	0m0.007s
sys	0m0.007s


'69.208.'
************** PARI *****************
Host 69.208.186.15 (69.208.186.15)
Time: Mon Aug 14 18:56:45 2006

Input: 9.72+14.88+10.88+10.88+14.88+10.88


Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = 72.119999999999999999999999999999999999
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.056s
user	0m0.005s
sys	0m0.009s


'208.19.'
************** PARI *****************
Host 208.19.62.11 (208.19.62.11)
Time: Mon Aug 14 16:27:35 2006

Input: "Replace this by some code, then click [SAGE] or [PARI]!"

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = "Replace this by some code, then click [SAGE] or [PARI]!"
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.015s
user	0m0.006s
sys	0m0.009s


'80.55.1'
************** PARI *****************
Host 80.55.14.2 (80.55.14.2)
Time: Mon Aug 14 15:30:17 2006

Input: a(n)=2*n-n^2

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? ? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.014s
user	0m0.006s
sys	0m0.007s


'80.55.1'
************** PARI *****************
Host 80.55.14.2 (80.55.14.2)
Time: Mon Aug 14 15:30:02 2006

Input: a(n)=2*n-n%2

Output: WARNING: PARI command contains unsafe command '%', so it will not be executed.

'80.55.1'
************** PARI *****************
Host 80.55.14.2 (80.55.14.2)
Time: Mon Aug 14 15:17:49 2006

Input: print kash('NumberField(X^3 + 15*X^2 - 15*X + 15)')



Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? ? ? 
Goodbye!

Errors/timing (if any):

  ***   expected character: ',' instead of: printkash('NumberField
  ***   (X^3+15*X^2-15*X+15)
        ^--------------------

Timing:
real	0m0.014s
user	0m0.006s
sys	0m0.008s


'80.55.1'
************** PARI *****************
Host 80.55.14.2 (80.55.14.2)
Time: Mon Aug 14 15:09:10 2006

Input: f=x^5-x^4-x^3-x^2-x-1;
Galois(f);


Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? ? ? 
Goodbye!

Errors/timing (if any):

  ***   expected character: '=' instead of: Galois(f);
                                                     ^-

Timing:
real	0m0.068s
user	0m0.010s
sys	0m0.005s


'80.55.1'
************** PARI *****************
Host 80.55.14.2 (80.55.14.2)
Time: Mon Aug 14 15:07:33 2006

Input: Zx<x>:=PolynomialRing(Integers());
f:=x^5-x^4-x^3-x^2-x-1;
G:=GaloisGroup(f);
a,b:=TransitiveGroupIdentification(G);
"Number of group is", a;
TransitiveGroupDescription(a,b);

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? ? ? ? ? ? ? 
Goodbye!

Errors/timing (if any):

  ***   unexpected character: Zx<x>:=PolynomialRing(Int
                                   ^--------------------
  ***   Warning: unused characters: :=x^5-x^4-x^3-x^2-x-1;.
  ***   unexpected character: f:=x^5-x^4-x^3-x^2-x-
                               ^--------------------
  ***   Warning: unused characters: :=GaloisGroup(f);.
  ***   unexpected character: G:=GaloisGroup(f);
                               ^-----------------
  ***   Warning: unused characters: ,b:=TransitiveGroupIdentification(G);.
  ***   Warning: unused characters: ,a;.
  ***   expected character: '=' instead of: ...tiveGroupDescription(a,b);
                                                                        ^-

Timing:
real	0m0.284s
user	0m0.006s
sys	0m0.010s


'72.30.1'
************** PARI *****************
Host 72.30.132.102 (72.30.132.102)
Time: Mon Aug 14 02:33:30 2006

Input: for( k=1, 12, print(k,": ",Mod(2^k,13)) )

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? 1: Mod(2, 13)
2: Mod(4, 13)
3: Mod(8, 13)
4: Mod(3, 13)
5: Mod(6, 13)
6: Mod(12, 13)
7: Mod(11, 13)
8: Mod(9, 13)
9: Mod(5, 13)
10: Mod(10, 13)
11: Mod(7, 13)
12: Mod(1, 13)
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.014s
user	0m0.006s
sys	0m0.008s


'71.105.'
************** PARI *****************
Host 71.105.149.13 (71.105.149.13)
Time: Sun Aug 13 22:07:23 2006

Input: x+7=15

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? ? 
Goodbye!

Errors/timing (if any):

  ***   unexpected character: x+7=15
                                 ^---

Timing:
real	0m0.015s
user	0m0.007s
sys	0m0.009s


'72.30.1'
************** PARI *****************
Host 72.30.129.123 (72.30.129.123)
Time: Sun Aug 13 20:32:01 2006

Input: collatzlength(x0)=
{
   local(x,i);
   x=x0;  i=0;   
   while(x-1,
      x=if(Mod(x,2)==Mod(0,2), x/2, (3*x+1)/2);i=i++ );
   i
}
collatzlength(299)

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? ? %1 = 75
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.072s
user	0m0.007s
sys	0m0.008s


'68.47.1'
************** PARI *****************
Host 68.47.182.155 (68.47.182.155)
Time: Sun Aug 13 14:59:35 2006

Input: print kash('NumberField(X^3 + 15*X^2 - 15*X + 15)')


Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? ? 
Goodbye!

Errors/timing (if any):

  ***   expected character: ',' instead of: printkash('NumberField
  ***   (X^3+15*X^2-15*X+15)
        ^--------------------

Timing:
real	0m0.021s
user	0m0.007s
sys	0m0.009s


'169.231'
************** PARI *****************
Host 169.231.33.177 (169.231.33.177)
Time: Sun Aug 13 14:08:46 2006

Input: [0,1,1,1;1,0,1,1;1,1,0,1;1,1,1,0]^2


Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = 
[3 2 2 2]

[2 3 2 2]

[2 2 3 2]

[2 2 2 3]

? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.014s
user	0m0.005s
sys	0m0.009s


'169.231'
************** PARI *****************
Host 169.231.33.177 (169.231.33.177)
Time: Sun Aug 13 14:08:36 2006

Input: [0,1,1,1;1,0,1,1;1,1,0,1;1,1,1,0]


Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = 
[0 1 1 1]

[1 0 1 1]

[1 1 0 1]

[1 1 1 0]

? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.014s
user	0m0.008s
sys	0m0.006s


'169.231'
************** PARI *****************
Host 169.231.33.177 (169.231.33.177)
Time: Sun Aug 13 14:07:58 2006

Input: [1,1,0,0;1,1,0,0;0,0,1,1;0,0,1,1]^12



Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = 
[2048 2048 0 0]

[2048 2048 0 0]

[0 0 2048 2048]

[0 0 2048 2048]

? ? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.014s
user	0m0.008s
sys	0m0.006s


'169.231'
************** PARI *****************
Host 169.231.33.177 (169.231.33.177)
Time: Sun Aug 13 14:07:04 2006

Input: [1,1,0,0;1,1,0,0;0,0,1,1;0,0,1,1]^4



Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = 
[8 8 0 0]

[8 8 0 0]

[0 0 8 8]

[0 0 8 8]

? ? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.014s
user	0m0.008s
sys	0m0.007s


'169.231'
************** PARI *****************
Host 169.231.33.177 (169.231.33.177)
Time: Sun Aug 13 14:06:59 2006

Input: [1,1,0,0;1,1,0,0;0,0,1,1;0,0,1,1]^3



Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = 
[4 4 0 0]

[4 4 0 0]

[0 0 4 4]

[0 0 4 4]

? ? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.015s
user	0m0.010s
sys	0m0.005s


'169.231'
************** PARI *****************
Host 169.231.33.177 (169.231.33.177)
Time: Sun Aug 13 14:06:52 2006

Input: [1,1,0,0;1,1,0,0;0,0,1,1;0,0,1,1]^2



Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = 
[2 2 0 0]

[2 2 0 0]

[0 0 2 2]

[0 0 2 2]

? ? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.014s
user	0m0.009s
sys	0m0.005s


'169.231'
************** PARI *****************
Host 169.231.33.177 (169.231.33.177)
Time: Sun Aug 13 14:06:43 2006

Input: [1,1,0,0;1,1,0,0;0,0,1,1;0,0,1,1]



Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = 
[1 1 0 0]

[1 1 0 0]

[0 0 1 1]

[0 0 1 1]

? ? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.015s
user	0m0.008s
sys	0m0.006s


'169.231'
************** PARI *****************
Host 169.231.33.177 (169.231.33.177)
Time: Sun Aug 13 14:06:02 2006

Input: [0,1,0,1;0,0,1,1;1,1,0,0;1,0,1,0]^3



Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = 
[3 3 1 1]

[1 3 1 3]

[3 1 3 1]

[1 1 3 3]

? ? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.014s
user	0m0.006s
sys	0m0.007s


'169.231'
************** PARI *****************
Host 169.231.33.177 (169.231.33.177)
Time: Sun Aug 13 14:05:49 2006

Input: [0,1,0,1;0,0,1,1;1,1,0,0;1,0,1,0]^3



Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = 
[3 3 1 1]

[1 3 1 3]

[3 1 3 1]

[1 1 3 3]

? ? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.014s
user	0m0.006s
sys	0m0.008s


'169.231'
************** PARI *****************
Host 169.231.33.177 (169.231.33.177)
Time: Sun Aug 13 14:05:42 2006

Input: [0,1,0,1;0,0,1,1;1,1,0,0;1,0,1,0]^4



Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = 
[2 4 4 6]

[4 2 6 4]

[4 6 2 4]

[6 4 4 2]

? ? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.014s
user	0m0.008s
sys	0m0.006s


'169.231'
************** PARI *****************
Host 169.231.33.177 (169.231.33.177)
Time: Sun Aug 13 14:05:35 2006

Input: [0,1,0,1;0,0,1,1;1,1,0,0;1,0,1,0]^3



Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = 
[3 3 1 1]

[1 3 1 3]

[3 1 3 1]

[1 1 3 3]

? ? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.014s
user	0m0.006s
sys	0m0.009s


'169.231'
************** PARI *****************
Host 169.231.33.177 (169.231.33.177)
Time: Sun Aug 13 14:05:24 2006

Input: [0,1,0,1;0,0,1,1;1,1,0,0;1,0,1,0]^2


Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = 
[1 0 2 1]

[2 1 1 0]

[0 1 1 2]

[1 2 0 1]

? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.014s
user	0m0.007s
sys	0m0.007s


'169.231'
************** PARI *****************
Host 169.231.33.177 (169.231.33.177)
Time: Sun Aug 13 14:05:11 2006

Input: [0,1,0,1;0,0,1,1;1,1,0,0;1,0,1,0]


Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = 
[0 1 0 1]

[0 0 1 1]

[1 1 0 0]

[1 0 1 0]

? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.014s
user	0m0.007s
sys	0m0.007s


'169.231'
************** PARI *****************
Host 169.231.33.177 (169.231.33.177)
Time: Sun Aug 13 14:04:27 2006

Input: [1,0,0,1;1,1,0,0;0,1,1,0;0,0,1,1]^3


Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = 
[1 1 3 3]

[3 1 1 3]

[3 3 1 1]

[1 3 3 1]

? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.014s
user	0m0.005s
sys	0m0.009s


'169.231'
************** PARI *****************
Host 169.231.33.177 (169.231.33.177)
Time: Sun Aug 13 14:04:22 2006

Input: [1,0,0,1;1,1,0,0;0,1,1,0;0,0,1,1]^2


Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = 
[1 0 1 2]

[2 1 0 1]

[1 2 1 0]

[0 1 2 1]

? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.014s
user	0m0.005s
sys	0m0.010s


'169.231'
************** PARI *****************
Host 169.231.33.177 (169.231.33.177)
Time: Sun Aug 13 14:04:11 2006

Input: [1,0,0,1;1,1,0,0;0,1,1,0;0,0,1,1]

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = 
[1 0 0 1]

[1 1 0 0]

[0 1 1 0]

[0 0 1 1]

? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.014s
user	0m0.007s
sys	0m0.007s


'169.231'
************** PARI *****************
Host 169.231.33.177 (169.231.33.177)
Time: Sun Aug 13 13:58:40 2006

Input: [0,1,1,1;1,0,1,1;1,1,1,0;1,1,0,1]^2

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = 
[3 2 2 2]

[2 3 2 2]

[2 2 3 2]

[2 2 2 3]

? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.014s
user	0m0.007s
sys	0m0.007s


'169.231'
************** PARI *****************
Host 169.231.33.177 (169.231.33.177)
Time: Sun Aug 13 13:58:40 2006

Input: [0,1,1,1;1,0,1,1;1,1,1,0;1,1,0,1]^2

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = 
[3 2 2 2]

[2 3 2 2]

[2 2 3 2]

[2 2 2 3]

? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.014s
user	0m0.007s
sys	0m0.005s


'169.231'
************** PARI *****************
Host 169.231.33.177 (169.231.33.177)
Time: Sun Aug 13 13:53:53 2006

Input: [0,1,1,0;1,1,0,0;1,0,0,1;0,0,1,1]^3

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = 
[1 3 3 1]

[3 3 1 1]

[3 1 1 3]

[1 1 3 3]

? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.014s
user	0m0.005s
sys	0m0.010s


'169.231'
************** PARI *****************
Host 169.231.33.177 (169.231.33.177)
Time: Sun Aug 13 13:53:14 2006

Input: [0,1,1,0;1,1,0,0;1,0,0,1;0,0,1,1]^2

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = 
[2 1 0 1]

[1 2 1 0]

[0 1 2 1]

[1 0 1 2]

? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.014s
user	0m0.005s
sys	0m0.009s


'67.10.1'
************** PARI *****************
Host 67.10.132.208 (67.10.132.208)
Time: Sun Aug 13 13:52:08 2006

Input: 2^85


Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = 38685626227668133590597632
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.014s
user	0m0.007s
sys	0m0.007s


'68.199.'
************** PARI *****************
Host 68.199.60.254 (68.199.60.254)
Time: Sun Aug 13 13:36:13 2006

Input: "Replace this by some code, then click [SAGE] or [PARI]!"

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = "Replace this by some code, then click [SAGE] or [PARI]!"
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.014s
user	0m0.007s
sys	0m0.008s


'194.165'
************** PARI *****************
Host 194.165.182.38 (194.165.182.38)
Time: Sun Aug 13 13:17:25 2006

Input: 47/3000.001

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = 0.015666661444446185184604938465020511660
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.052s
user	0m0.005s
sys	0m0.009s


'72.30.1'
************** PARI *****************
Host 72.30.111.93 (72.30.111.93)
Time: Sun Aug 13 12:26:48 2006

Input: {ss(n)=sum(x=1,n,n/gcd(n,x))}
ss(60)

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? ? %1 = 1617
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.080s
user	0m0.008s
sys	0m0.008s


'72.30.1'
************** PARI *****************
Host 72.30.129.106 (72.30.129.106)
Time: Sun Aug 13 10:46:05 2006

Input: y=210; for(x=1,8,y=sumdiv(y,x,x)-y;print1(y,","))

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? 366,378,582,594,846,1026,1374,1386,
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.266s
user	0m0.007s
sys	0m0.010s


'193.171'
************** PARI *****************
Host 193.171.131.247 (193.171.131.247)
Time: Sat Aug 12 04:07:02 2006

Input: 1/2

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = 1/2
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.013s
user	0m0.008s
sys	0m0.006s


'72.30.1'
************** PARI *****************
Host 72.30.129.106 (72.30.129.106)
Time: Sat Aug 12 00:17:00 2006

Input: y=210; for(x=1,8,y=sumdiv(y,x,x)-y;print1(y,","))

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? 366,378,582,594,846,1026,1374,1386,
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.013s
user	0m0.006s
sys	0m0.007s


'72.30.2'
************** PARI *****************
Host 72.30.226.223 (72.30.226.223)
Time: Fri Aug 11 17:41:28 2006

Input: for(n=1,7, print1(n,": ",sum(x=1,n,1/x),",  ") )

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? 1: 1,  2: 3/2,  3: 11/6,  4: 25/12,  5: 137/60,  6: 49/20,  7: 363/140,  
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.115s
user	0m0.006s
sys	0m0.009s


'220.239'
************** PARI *****************
Host 220.239.147.13 (220.239.147.13)
Time: Fri Aug 11 03:04:58 2006

Input: "Replace this by some code, then click [SAGE] or [PARI]!"

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = "Replace this by some code, then click [SAGE] or [PARI]!"
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.015s
user	0m0.006s
sys	0m0.006s


'220.239'
************** PARI *****************
Host 220.239.147.13 (220.239.147.13)
Time: Fri Aug 11 03:02:22 2006

Input: collatz(x0,n)=
{
   local(x,i,ans);
   x=x0;
   ans=[x];
   for(i=1,n,
      x=if(Mod(x,2)==Mod(0,2), x/2, (3*x+1)/2);
      ans =concat(ans,x) );
   ans
}
collatz(19,16)

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? ? %1 = [19, 29, 44, 22, 11, 17, 26, 13, 20, 10, 5, 8, 4, 2, 1, 2, 1]
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.089s
user	0m0.005s
sys	0m0.007s


'169.231'
************** PARI *****************
Host 169.231.35.225 (169.231.35.225)
Time: Fri Aug 11 01:28:29 2006

Input: [1,1,0;0,1,1;1,0,1]^2


Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = 
[1 2 1]

[1 1 2]

[2 1 1]

? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.069s
user	0m0.006s
sys	0m0.009s


'66.249.'
************** PARI *****************
Host 66.249.66.144 (66.249.66.144)
Time: Thu Aug 10 21:18:19 2006

Input: vector(20,x,floor((x+1)*sqrt(2))-floor(x*sqrt(2)))

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = [1, 2, 1, 2, 1, 1, 2, 1, 2, 1, 1, 2, 1, 2, 1, 2, 1, 1, 2, 1]
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.101s
user	0m0.007s
sys	0m0.008s


'66.249.'
************** PARI *****************
Host 66.249.66.144 (66.249.66.144)
Time: Thu Aug 10 19:43:53 2006

Input: for(n=1,7, print1(n,": ",sum(x=1,n,1/x),",  ") )

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? 1: 1,  2: 3/2,  3: 11/6,  4: 25/12,  5: 137/60,  6: 49/20,  7: 363/140,  
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.013s
user	0m0.004s
sys	0m0.009s


'66.249.'
************** PARI *****************
Host 66.249.66.144 (66.249.66.144)
Time: Thu Aug 10 19:43:51 2006

Input: for(x=1,50,print1("d(",x,")=",numdiv(x),", "))

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? d(1)=1, d(2)=2, d(3)=2, d(4)=3, d(5)=2, d(6)=4, d(7)=2, d(8)=4, d(9)=3, d(10)=4, d(11)=2, d(12)=6, d(13)=2, d(14)=4, d(15)=4, d(16)=5, d(17)=2, d(18)=6, d(19)=2, d(20)=6, d(21)=4, d(22)=4, d(23)=2, d(24)=8, d(25)=3, d(26)=4, d(27)=4, d(28)=6, d(29)=2, d(30)=8, d(31)=2, d(32)=6, d(33)=4, d(34)=4, d(35)=4, d(36)=9, d(37)=2, d(38)=4, d(39)=4, d(40)=8, d(41)=2, d(42)=8, d(43)=2, d(44)=6, d(45)=6, d(46)=4, d(47)=2, d(48)=10, d(49)=3, d(50)=6, 
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.020s
user	0m0.005s
sys	0m0.011s


'68.13.2'
************** PARI *****************
Host 68.13.201.86 (68.13.201.86)
Time: Thu Aug 10 19:29:54 2006

Input: 3.35 x 10 - 3 + 4.5 x 10 - 4

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = x10 - 4
? 
Goodbye!

Errors/timing (if any):

  ***   Warning: unused characters: x10-3+4.5x10-4.

Timing:
real	0m0.013s
user	0m0.006s
sys	0m0.008s


'68.13.2'
************** PARI *****************
Host 68.13.201.86 (68.13.201.86)
Time: Thu Aug 10 19:29:30 2006

Input: 3.35x10-3 + 4.5x10-4

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = x10 - 4
? 
Goodbye!

Errors/timing (if any):

  ***   Warning: unused characters: x10-3+4.5x10-4.

Timing:
real	0m0.216s
user	0m0.004s
sys	0m0.010s


'66.249.'
************** PARI *****************
Host 66.249.72.66 (66.249.72.66)
Time: Thu Aug 10 17:59:00 2006

Input: for(n=1,20, print1(n,": ",valuation(n!,2),", ") )

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? 1: 0, 2: 1, 3: 1, 4: 3, 5: 3, 6: 4, 7: 4, 8: 7, 9: 7, 10: 8, 11: 8, 12: 10, 13: 10, 14: 11, 15: 11, 16: 15, 17: 15, 18: 16, 19: 16, 20: 18, 
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.014s
user	0m0.005s
sys	0m0.010s


'68.207.'
************** PARI *****************
Host 68.207.106.75 (68.207.106.75)
Time: Thu Aug 10 16:06:26 2006

Input: 3x5-2x3+5x2-2x+7, if x=-2

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = x + 7
? 
Goodbye!

Errors/timing (if any):

  ***   Warning: unused characters: x5-2x3+5x2-2x+7,ifx=-2.

Timing:
real	0m0.014s
user	0m0.005s
sys	0m0.007s


'68.207.'
************** PARI *****************
Host 68.207.106.75 (68.207.106.75)
Time: Thu Aug 10 16:06:09 2006

Input: 3x5-2x3+5x2-2x+7, if x=-2

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = x + 7
? 
Goodbye!

Errors/timing (if any):

  ***   Warning: unused characters: x5-2x3+5x2-2x+7,ifx=-2.

Timing:
real	0m0.068s
user	0m0.007s
sys	0m0.006s


'72.30.1'
************** PARI *****************
Host 72.30.129.106 (72.30.129.106)
Time: Thu Aug 10 13:08:03 2006

Input: y=210; for(x=1,8,y=sumdiv(y,x,x)-y;print1(y,","))

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? 366,378,582,594,846,1026,1374,1386,
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.072s
user	0m0.008s
sys	0m0.007s


'60.49.1'
************** PARI *****************
Host 60.49.128.6 (60.49.128.6)
Time: Thu Aug 10 13:07:03 2006

Input: 328310094-10%

Output: WARNING: PARI command contains unsafe command '%', so it will not be executed.

'199.9.6'
************** PARI *****************
Host 199.9.64.2 (199.9.64.2)
Time: Thu Aug 10 09:24:43 2006

Input: (-1/2)(-6/7)

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = -6/7
? 
Goodbye!

Errors/timing (if any):

  ***   Warning: unused characters: (-6/7).

Timing:
real	0m0.283s
user	0m0.005s
sys	0m0.008s


'72.30.2'
************** PARI *****************
Host 72.30.252.149 (72.30.252.149)
Time: Thu Aug 10 05:41:19 2006

Input: y=210; for(x=1,8,y=sumdiv(y,x,x)-y;print1(y,","))

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? 366,378,582,594,846,1026,1374,1386,
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.013s
user	0m0.007s
sys	0m0.006s


'193.171'
************** PARI *****************
Host 193.171.131.248 (193.171.131.248)
Time: Thu Aug 10 05:03:02 2006

Input: matrix(3,4,X,Y,-X+Y^20)
a = exp(x)
a

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = 
[0 1048575 3486784400 1099511627775]

[-1 1048574 3486784399 1099511627774]

[-2 1048573 3486784398 1099511627773]

? %2 = 1 + x + 1/2*x^2 + 1/6*x^3 + 1/24*x^4 + 1/120*x^5 + 1/720*x^6 + 1/5040*x^7 + 1/40320*x^8 + 1/362880*x^9 + 1/3628800*x^10 + 1/39916800*x^11 + 1/479001600*x^12 + 1/6227020800*x^13 + 1/87178291200*x^14 + 1/1307674368000*x^15 + 1/20922789888000*x^16 + O(x^17)
? %3 = 1 + x + 1/2*x^2 + 1/6*x^3 + 1/24*x^4 + 1/120*x^5 + 1/720*x^6 + 1/5040*x^7 + 1/40320*x^8 + 1/362880*x^9 + 1/3628800*x^10 + 1/39916800*x^11 + 1/479001600*x^12 + 1/6227020800*x^13 + 1/87178291200*x^14 + 1/1307674368000*x^15 + 1/20922789888000*x^16 + O(x^17)
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.013s
user	0m0.008s
sys	0m0.005s


'193.171'
************** PARI *****************
Host 193.171.131.248 (193.171.131.248)
Time: Thu Aug 10 04:58:32 2006

Input: matrix(3,4,X,Y,X-Y^20)
a = exp(x)
a

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = 
[0 -1048575 -3486784400 -1099511627775]

[1 -1048574 -3486784399 -1099511627774]

[2 -1048573 -3486784398 -1099511627773]

? %2 = 1 + x + 1/2*x^2 + 1/6*x^3 + 1/24*x^4 + 1/120*x^5 + 1/720*x^6 + 1/5040*x^7 + 1/40320*x^8 + 1/362880*x^9 + 1/3628800*x^10 + 1/39916800*x^11 + 1/479001600*x^12 + 1/6227020800*x^13 + 1/87178291200*x^14 + 1/1307674368000*x^15 + 1/20922789888000*x^16 + O(x^17)
? %3 = 1 + x + 1/2*x^2 + 1/6*x^3 + 1/24*x^4 + 1/120*x^5 + 1/720*x^6 + 1/5040*x^7 + 1/40320*x^8 + 1/362880*x^9 + 1/3628800*x^10 + 1/39916800*x^11 + 1/479001600*x^12 + 1/6227020800*x^13 + 1/87178291200*x^14 + 1/1307674368000*x^15 + 1/20922789888000*x^16 + O(x^17)
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.014s
user	0m0.008s
sys	0m0.007s


'193.171'
************** PARI *****************
Host 193.171.131.248 (193.171.131.248)
Time: Thu Aug 10 04:58:15 2006

Input: matrix(3,4,X,Y,X-Y^3)
a = exp(x)
a

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = 
[0 -7 -26 -63]

[1 -6 -25 -62]

[2 -5 -24 -61]

? %2 = 1 + x + 1/2*x^2 + 1/6*x^3 + 1/24*x^4 + 1/120*x^5 + 1/720*x^6 + 1/5040*x^7 + 1/40320*x^8 + 1/362880*x^9 + 1/3628800*x^10 + 1/39916800*x^11 + 1/479001600*x^12 + 1/6227020800*x^13 + 1/87178291200*x^14 + 1/1307674368000*x^15 + 1/20922789888000*x^16 + O(x^17)
? %3 = 1 + x + 1/2*x^2 + 1/6*x^3 + 1/24*x^4 + 1/120*x^5 + 1/720*x^6 + 1/5040*x^7 + 1/40320*x^8 + 1/362880*x^9 + 1/3628800*x^10 + 1/39916800*x^11 + 1/479001600*x^12 + 1/6227020800*x^13 + 1/87178291200*x^14 + 1/1307674368000*x^15 + 1/20922789888000*x^16 + O(x^17)
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.013s
user	0m0.007s
sys	0m0.006s


'193.171'
************** PARI *****************
Host 193.171.131.248 (193.171.131.248)
Time: Thu Aug 10 04:57:04 2006

Input: matrix(3,4,X,Y,X+Y)
a = exp(x)
a

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = 
[2 3 4 5]

[3 4 5 6]

[4 5 6 7]

? %2 = 1 + x + 1/2*x^2 + 1/6*x^3 + 1/24*x^4 + 1/120*x^5 + 1/720*x^6 + 1/5040*x^7 + 1/40320*x^8 + 1/362880*x^9 + 1/3628800*x^10 + 1/39916800*x^11 + 1/479001600*x^12 + 1/6227020800*x^13 + 1/87178291200*x^14 + 1/1307674368000*x^15 + 1/20922789888000*x^16 + O(x^17)
? %3 = 1 + x + 1/2*x^2 + 1/6*x^3 + 1/24*x^4 + 1/120*x^5 + 1/720*x^6 + 1/5040*x^7 + 1/40320*x^8 + 1/362880*x^9 + 1/3628800*x^10 + 1/39916800*x^11 + 1/479001600*x^12 + 1/6227020800*x^13 + 1/87178291200*x^14 + 1/1307674368000*x^15 + 1/20922789888000*x^16 + O(x^17)
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.013s
user	0m0.006s
sys	0m0.007s


'193.171'
************** PARI *****************
Host 193.171.131.248 (193.171.131.248)
Time: Thu Aug 10 04:56:55 2006

Input: matrix(3,4,X,Y,X+Y)
a = exp(x)

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = 
[2 3 4 5]

[3 4 5 6]

[4 5 6 7]

? %2 = 1 + x + 1/2*x^2 + 1/6*x^3 + 1/24*x^4 + 1/120*x^5 + 1/720*x^6 + 1/5040*x^7 + 1/40320*x^8 + 1/362880*x^9 + 1/3628800*x^10 + 1/39916800*x^11 + 1/479001600*x^12 + 1/6227020800*x^13 + 1/87178291200*x^14 + 1/1307674368000*x^15 + 1/20922789888000*x^16 + O(x^17)
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.013s
user	0m0.006s
sys	0m0.007s


'193.171'
************** PARI *****************
Host 193.171.131.248 (193.171.131.248)
Time: Thu Aug 10 04:55:56 2006

Input: matrix(3,4,X,Y,X+Y)
exp(x)

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = 
[2 3 4 5]

[3 4 5 6]

[4 5 6 7]

? %2 = 1 + x + 1/2*x^2 + 1/6*x^3 + 1/24*x^4 + 1/120*x^5 + 1/720*x^6 + 1/5040*x^7 + 1/40320*x^8 + 1/362880*x^9 + 1/3628800*x^10 + 1/39916800*x^11 + 1/479001600*x^12 + 1/6227020800*x^13 + 1/87178291200*x^14 + 1/1307674368000*x^15 + 1/20922789888000*x^16 + O(x^17)
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.082s
user	0m0.007s
sys	0m0.007s


'193.171'
************** PARI *****************
Host 193.171.131.248 (193.171.131.248)
Time: Thu Aug 10 04:54:53 2006

Input: matrix(3,4,X,Y,X+Y)

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = 
[2 3 4 5]

[3 4 5 6]

[4 5 6 7]

? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.014s
user	0m0.006s
sys	0m0.008s


'193.171'
************** PARI *****************
Host 193.171.131.248 (193.171.131.248)
Time: Thu Aug 10 04:40:54 2006

Input: matrix(3,4,X,Y,X+Y)


Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = 
[2 3 4 5]

[3 4 5 6]

[4 5 6 7]

? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.056s
user	0m0.005s
sys	0m0.009s


'193.171'
************** PARI *****************
Host 193.171.131.248 (193.171.131.248)
Time: Thu Aug 10 04:39:08 2006

Input: 
gp('ellinit([1,2,3,4,5])').j

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? ? ? 
Goodbye!

Errors/timing (if any):

  ***   expected character: ',' instead of: gp('ellinit([1,2,3,4,5])').j
                                                       ^-----------------

Timing:
real	0m0.013s
user	0m0.004s
sys	0m0.009s


'193.171'
************** PARI *****************
Host 193.171.131.248 (193.171.131.248)
Time: Thu Aug 10 04:38:59 2006

Input: print gp('ellinit([1,2,3,4,5])').j

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? ? 
Goodbye!

Errors/timing (if any):

  ***   expected character: ',' instead of: printgp('ellinit([1,2,3,4,5])').j
                                                            ^-----------------

Timing:
real	0m0.019s
user	0m0.008s
sys	0m0.006s


'24.196.'
************** PARI *****************
Host 24.196.114.198 (24.196.114.198)
Time: Wed Aug  9 16:19:36 2006

Input: (x-9) + (x2 - x + 17)

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = x2 + 8
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.013s
user	0m0.006s
sys	0m0.008s


'69.130.'
************** PARI *****************
Host 69.130.157.157 (69.130.157.157)
Time: Wed Aug  9 15:02:28 2006

Input: "Replace this by some code, then click [SAGE] or [PARI]!"

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = "Replace this by some code, then click [SAGE] or [PARI]!"
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.013s
user	0m0.006s
sys	0m0.009s


'192.25.'
************** PARI *****************
Host 192.25.240.225 (192.25.240.225)
Time: Wed Aug  9 14:24:32 2006

Input: 10 log 20

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = log20
? 
Goodbye!

Errors/timing (if any):

  ***   Warning: unused characters: log20.

Timing:
real	0m0.013s
user	0m0.006s
sys	0m0.009s


'192.25.'
************** PARI *****************
Host 192.25.240.225 (192.25.240.225)
Time: Wed Aug  9 14:24:19 2006

Input: 10 log 1

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = log1
? 
Goodbye!

Errors/timing (if any):

  ***   Warning: unused characters: log1.

Timing:
real	0m0.014s
user	0m0.006s
sys	0m0.009s


'75.2.16'
************** PARI *****************
Host 75.2.165.226 (75.2.165.226)
Time: Wed Aug  9 14:02:59 2006

Input: (4.09*10^6)(5.87*10^-7) 

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = 0.00000058700000000000000000000000000000000000
? 
Goodbye!

Errors/timing (if any):

  ***   Warning: unused characters: (5.87*10^-7).

Timing:
real	0m0.013s
user	0m0.007s
sys	0m0.006s


'75.2.16'
************** PARI *****************
Host 75.2.165.226 (75.2.165.226)
Time: Wed Aug  9 14:02:21 2006

Input: (4.09*10^6)(5.87*10^-7) 

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = 0.00000058700000000000000000000000000000000000
? 
Goodbye!

Errors/timing (if any):

  ***   Warning: unused characters: (5.87*10^-7).

Timing:
real	0m0.145s
user	0m0.008s
sys	0m0.007s


'134.219'
************** PARI *****************
Host 134.219.148.42 (134.219.148.42)
Time: Wed Aug  9 08:25:11 2006

Input: ? free group

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? freegroup: unknown identifier

? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.014s
user	0m0.005s
sys	0m0.008s


'134.219'
************** PARI *****************
Host 134.219.148.42 (134.219.148.42)
Time: Wed Aug  9 07:58:33 2006

Input: ? free group

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? freegroup: unknown identifier

? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.014s
user	0m0.004s
sys	0m0.009s


'134.219'
************** PARI *****************
Host 134.219.148.42 (134.219.148.42)
Time: Wed Aug  9 07:58:16 2006

Input: free group

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = freegroup
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.013s
user	0m0.008s
sys	0m0.004s


'72.30.1'
************** PARI *****************
Host 72.30.129.106 (72.30.129.106)
Time: Wed Aug  9 06:45:40 2006

Input: y=210; for(x=1,8,y=sumdiv(y,x,x)-y;print1(y,","))

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? 366,378,582,594,846,1026,1374,1386,
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.283s
user	0m0.008s
sys	0m0.011s


'82.182.'
************** PARI *****************
Host 82.182.86.196 (82.182.86.196)
Time: Wed Aug  9 04:01:21 2006

Input: factor((10^67-1)/9)

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? 
Errors/timing (if any):

/var/www/cgi-bin/calc/gp: line 1:  1207 Killed                  ./gp-2.2.11 -s 256000000 -emacs

Timing:
real	0m21.004s
user	0m20.965s
sys	0m0.037s


'82.182.'
************** PARI *****************
Host 82.182.86.196 (82.182.86.196)
Time: Wed Aug  9 03:59:40 2006

Input: factor((10^43-1)/9)

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = 
[173 1]

[1527791 1]

[1963506722254397 1]

[2140992015395526641 1]

? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.219s
user	0m0.070s
sys	0m0.023s


'66.169.'
************** PARI *****************
Host 66.169.108.181 (66.169.108.181)
Time: Tue Aug  8 19:03:52 2006

Input: 3x+2y=3
-y+4x=1

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = 3
? %2 = 1
? 
Goodbye!

Errors/timing (if any):

  ***   Warning: unused characters: x+2y=3.
  ***   Warning: unused characters: x=1.

Timing:
real	0m0.013s
user	0m0.006s
sys	0m0.007s


'82.45.2'
************** PARI *****************
Host 82.45.250.169 (82.45.250.169)
Time: Tue Aug  8 17:37:55 2006

Input: 19-5+4+3*2+6-5

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = 25
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.013s
user	0m0.006s
sys	0m0.007s


'82.45.2'
************** PARI *****************
Host 82.45.250.169 (82.45.250.169)
Time: Tue Aug  8 17:36:28 2006

Input: Nineteen,Minus,Five
4+3*2
6-5

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = Nineteen
? %2 = 10
? %3 = 1
? 
Goodbye!

Errors/timing (if any):

  ***   Warning: unused characters: ,Minus,Five.

Timing:
real	0m0.075s
user	0m0.006s
sys	0m0.008s


'82.45.2'
************** PARI *****************
Host 82.45.250.169 (82.45.250.169)
Time: Tue Aug  8 17:35:01 2006

Input: Add the numbers

Nineteen Minus Five=
4+3*2=
6-5=

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = Addthenumbers
? ? ? 
Goodbye!

Errors/timing (if any):

  ***   unexpected character: NineteenMinusFive=4+3*2=6-5=
                                                     ^-----

Timing:
real	0m0.013s
user	0m0.006s
sys	0m0.007s


'72.229.'
************** PARI *****************
Host 72.229.120.226 (72.229.120.226)
Time: Tue Aug  8 16:52:18 2006

Input: 5%

Output: WARNING: PARI command contains unsafe command '%', so it will not be executed.

'200.185'
************** PARI *****************
Host 200.185.104.245 (200.185.104.245)
Time: Tue Aug  8 13:36:23 2006

Input: factor(19631212)


Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = 
[2 2]

[251 1]

[19553 1]

? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.185s
user	0m0.006s
sys	0m0.006s


'63.193.'
************** PARI *****************
Host 63.193.144.46 (63.193.144.46)
Time: Tue Aug  8 10:31:42 2006

Input: 4/5

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = 4/5
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.054s
user	0m0.006s
sys	0m0.008s


'63.193.'
************** PARI *****************
Host 63.193.144.46 (63.193.144.46)
Time: Tue Aug  8 10:20:12 2006

Input: 1250x4

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = x4
? 
Goodbye!

Errors/timing (if any):

  ***   Warning: unused characters: x4.

Timing:
real	0m0.299s
user	0m0.007s
sys	0m0.012s


'24.59.1'
************** PARI *****************
Host 24.59.161.234 (24.59.161.234)
Time: Mon Aug  7 22:58:47 2006

Input: 761855+19875


Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = 781730
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.013s
user	0m0.008s
sys	0m0.004s


'146.151'
************** PARI *****************
Host 146.151.49.239 (146.151.49.239)
Time: Mon Aug  7 18:40:40 2006

Input: 42+45


Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = 87
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.013s
user	0m0.006s
sys	0m0.007s


'68.121.'
************** PARI *****************
Host 68.121.22.156 (68.121.22.156)
Time: Mon Aug  7 16:45:11 2006

Input: "Replace this by some code, then click [SAGE] or [PARI]!"

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = "Replace this by some code, then click [SAGE] or [PARI]!"
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.013s
user	0m0.009s
sys	0m0.004s


'72.30.1'
************** PARI *****************
Host 72.30.107.151 (72.30.107.151)
Time: Mon Aug  7 15:50:17 2006

Input: vector(20,x,floor((x+1)*sqrt(2))-floor(x*sqrt(2)))

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = [1, 2, 1, 2, 1, 1, 2, 1, 2, 1, 1, 2, 1, 2, 1, 2, 1, 1, 2, 1]
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.076s
user	0m0.003s
sys	0m0.011s


'72.40.2'
************** PARI *****************
Host 72.40.25.145 (72.40.25.145)
Time: Mon Aug  7 14:15:45 2006

Input: 187416 x 187416

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = x187416
? 
Goodbye!

Errors/timing (if any):

  ***   Warning: unused characters: x187416.

Timing:
real	0m0.030s
user	0m0.009s
sys	0m0.004s


'72.75.2'
************** PARI *****************
Host 72.75.2.9 (72.75.2.9)
Time: Mon Aug  7 14:02:37 2006

Input: ?

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? Help topics: for a list of relevant subtopics, type ?n for n in
  0: user-defined identifiers (variable, alias, function)
  1: Standard monadic or dyadic OPERATORS
  2: CONVERSIONS and similar elementary functions
  3: TRANSCENDENTAL functions
  4: NUMBER THEORETICAL functions
  5: Functions related to ELLIPTIC CURVES
  6: Functions related to general NUMBER FIELDS
  7: POLYNOMIALS and power series
  8: Vectors, matrices, LINEAR ALGEBRA and sets
  9: SUMS, products, integrals and similar functions
 10: GRAPHIC functions
 11: PROGRAMMING under GP
 12: The PARI community

Also:
  ? functionname (short on-line help)
  ?\             (keyboard shortcuts)
  ?.             (member functions)

? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.013s
user	0m0.008s
sys	0m0.007s


'72.75.2'
************** PARI *****************
Host 72.75.2.9 (72.75.2.9)
Time: Mon Aug  7 14:01:49 2006

Input: ?5

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? 
elladd          ellak           ellan           ellap
ellbil          ellchangecurve  ellchangepoint  elleisnum
elleta          ellglobalred    ellheight       ellheightmatrix
ellidentify     ellinit         ellisoncurve    ellj
elllocalred     elllseries      ellminimalmodel ellorder
ellordinate     ellpointtoz     ellpow          ellrootno
ellsearch       ellsigma        ellsub          elltaniyama
elltors         ellwp           ellzeta         ellztopoint

? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.013s
user	0m0.002s
sys	0m0.011s


'72.75.2'
************** PARI *****************
Host 72.75.2.9 (72.75.2.9)
Time: Mon Aug  7 14:01:38 2006

Input: ?

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? Help topics: for a list of relevant subtopics, type ?n for n in
  0: user-defined identifiers (variable, alias, function)
  1: Standard monadic or dyadic OPERATORS
  2: CONVERSIONS and similar elementary functions
  3: TRANSCENDENTAL functions
  4: NUMBER THEORETICAL functions
  5: Functions related to ELLIPTIC CURVES
  6: Functions related to general NUMBER FIELDS
  7: POLYNOMIALS and power series
  8: Vectors, matrices, LINEAR ALGEBRA and sets
  9: SUMS, products, integrals and similar functions
 10: GRAPHIC functions
 11: PROGRAMMING under GP
 12: The PARI community

Also:
  ? functionname (short on-line help)
  ?\             (keyboard shortcuts)
  ?.             (member functions)

? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.308s
user	0m0.005s
sys	0m0.010s


'72.30.1'
************** PARI *****************
Host 72.30.129.106 (72.30.129.106)
Time: Mon Aug  7 06:12:35 2006

Input: y=210; for(x=1,8,y=sumdiv(y,x,x)-y;print1(y,","))

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? 366,378,582,594,846,1026,1374,1386,
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.013s
user	0m0.007s
sys	0m0.007s


'216.184'
************** PARI *****************
Host 216.184.80.146 (216.184.80.146)
Time: Mon Aug  7 05:27:30 2006

Input: for(n=1,1000,if(isprime(2^(2^n-1)-1),print1(n",")))

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? 2,3,5,7,
Errors/timing (if any):

/var/www/cgi-bin/calc/gp: line 1: 22874 Killed                  ./gp-2.2.11 -s 256000000 -emacs

Timing:
real	0m21.093s
user	0m20.844s
sys	0m0.174s


'216.184'
************** PARI *****************
Host 216.184.80.146 (216.184.80.146)
Time: Mon Aug  7 05:26:49 2006

Input: for(n=1,1000,if(isprime(2*(2^n-1)-1),print1(n",")))

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? 2,3,4,5,8,9,11,13,19,21,23,28,93,115,121,149,173,212,220,232,265,335,451,544,688,693,849,
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m15.616s
user	0m15.592s
sys	0m0.014s


'216.184'
************** PARI *****************
Host 216.184.80.146 (216.184.80.146)
Time: Mon Aug  7 05:26:18 2006

Input: for(n=1,1000,if(isprime(2*(2^n-1)),print1(n",")))

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? 1,
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.016s
user	0m0.010s
sys	0m0.006s


'216.184'
************** PARI *****************
Host 216.184.80.146 (216.184.80.146)
Time: Mon Aug  7 05:25:28 2006

Input: for(n=1,1000,if(isprime((2^n-1)-(n^2+1)),print1(n",")))

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? 5,215,253,323,
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.446s
user	0m0.438s
sys	0m0.008s


'216.184'
************** PARI *****************
Host 216.184.80.146 (216.184.80.146)
Time: Mon Aug  7 05:24:35 2006

Input: for(n=1,1000,if(isprime((2^n-1)-(n^2-1)),print1(n",")))

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? 5,7,9,17,19,51,53,81,83,119,189,219,227,301,455,461,623,
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m4.340s
user	0m4.317s
sys	0m0.020s


'216.184'
************** PARI *****************
Host 216.184.80.146 (216.184.80.146)
Time: Mon Aug  7 05:24:10 2006

Input: for(n=1,1000,if(isprime((2^n-1)-(n^2)),print1(n",")))

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? 8,14,26,70,112,122,178,352,
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.801s
user	0m0.551s
sys	0m0.009s


'216.184'
************** PARI *****************
Host 216.184.80.146 (216.184.80.146)
Time: Mon Aug  7 05:23:03 2006

Input: for(n=1,500,if(isprime(613*10^n+1),print1(n",")))

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? 1,6,9,10,18,75,122,165,402,
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m1.002s
user	0m0.988s
sys	0m0.010s


'69.27.6'
************** PARI *****************
Host 69.27.68.214 (69.27.68.214)
Time: Mon Aug  7 04:32:16 2006

Input: for(n=1,1000,if(isprime((2^n-1)+2),print1(n",")))


Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? 1,2,4,8,16,
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.073s
user	0m0.068s
sys	0m0.006s


'69.27.6'
************** PARI *****************
Host 69.27.68.214 (69.27.68.214)
Time: Mon Aug  7 04:31:51 2006

Input: for(n=1,500,if(isprime((2^n-1)+2),print1(n",")))


Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? 1,2,4,8,16,
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.021s
user	0m0.015s
sys	0m0.005s


'85.89.1'
************** PARI *****************
Host 85.89.168.182 (85.89.168.182)
Time: Mon Aug  7 04:20:51 2006

Input: factor(2^31-1)




Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = 
[2147483647 1]

? ? ? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.013s
user	0m0.007s
sys	0m0.007s


'85.89.1'
************** PARI *****************
Host 85.89.168.182 (85.89.168.182)
Time: Mon Aug  7 04:20:10 2006

Input: factor(123)



Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = 
[3 1]

[41 1]

? ? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.014s
user	0m0.008s
sys	0m0.005s


'85.89.1'
************** PARI *****************
Host 85.89.168.182 (85.89.168.182)
Time: Mon Aug  7 04:13:02 2006

Input: factor(2^31-1)



Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = 
[2147483647 1]

? ? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.013s
user	0m0.008s
sys	0m0.006s


'85.89.1'
************** PARI *****************
Host 85.89.168.182 (85.89.168.182)
Time: Mon Aug  7 04:12:15 2006

Input: factor(2^31-1)



Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = 
[2147483647 1]

? ? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.013s
user	0m0.007s
sys	0m0.005s


'85.89.1'
************** PARI *****************
Host 85.89.168.182 (85.89.168.182)
Time: Mon Aug  7 04:10:50 2006

Input: 2^31-1


Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = 2147483647
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.029s
user	0m0.002s
sys	0m0.010s


'164.107'
************** PARI *****************
Host 164.107.204.151 (164.107.204.151)
Time: Sun Aug  6 21:39:30 2006

Input: contfrac(sqrt(61))

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = [7, 1, 4, 3, 1, 2, 2, 1, 3, 4, 1, 14, 1, 4, 3, 1, 2, 2, 1, 3, 4, 1, 14, 1, 4, 3, 1, 2, 2, 1, 3, 4, 1, 14, 1, 4, 3, 1, 2, 2, 1, 3, 5]
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.013s
user	0m0.005s
sys	0m0.007s


'164.107'
************** PARI *****************
Host 164.107.204.151 (164.107.204.151)
Time: Sun Aug  6 21:38:06 2006

Input: contfrac(sqrt(41))

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = [6, 2, 2, 12, 2, 2, 12, 2, 2, 12, 2, 2, 12, 2, 2, 12, 2, 2, 12, 2, 2, 12, 2, 2, 12, 2, 2, 12, 2, 2, 12, 2, 2]
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.085s
user	0m0.010s
sys	0m0.003s


'69.27.6'
************** PARI *****************
Host 69.27.68.214 (69.27.68.214)
Time: Sun Aug  6 20:57:18 2006

Input: for(n=1,1000,if(isprime(n!+1),print1(n",")))
 


Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? 1,2,3,11,27,37,41,73,77,116,154,320,
Errors/timing (if any):

/var/www/cgi-bin/calc/gp: line 1: 18102 Killed                  ./gp-2.2.11 -s 256000000 -emacs

Timing:
real	0m24.558s
user	0m20.962s
sys	0m0.039s


'69.27.6'
************** PARI *****************
Host 69.27.68.214 (69.27.68.214)
Time: Sun Aug  6 20:56:34 2006

Input: for(n=1,100,if(isprime(n!+1),print1(n",")))
 


Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? 1,2,3,11,27,37,41,73,77,
? ? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.198s
user	0m0.090s
sys	0m0.009s


'69.27.6'
************** PARI *****************
Host 69.27.68.214 (69.27.68.214)
Time: Sun Aug  6 20:56:14 2006

Input: for(n=1,100,if(isprime(n),print1(n",")))
 


Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? 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,
? ? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.013s
user	0m0.006s
sys	0m0.007s


'69.27.6'
************** PARI *****************
Host 69.27.68.214 (69.27.68.214)
Time: Sun Aug  6 19:54:18 2006

Input: for(n=1,42,if(isprime(n^2+n+41),print1(n",")))
 


Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? 1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,42,
? ? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.013s
user	0m0.007s
sys	0m0.006s


'69.27.6'
************** PARI *****************
Host 69.27.68.214 (69.27.68.214)
Time: Sun Aug  6 19:54:02 2006

Input: for(n=1,48,if(isprime(n^2+n+41),print1(n",")))
 


Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? 1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,42,43,45,46,47,48,
? ? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.013s
user	0m0.007s
sys	0m0.007s


'69.27.6'
************** PARI *****************
Host 69.27.68.214 (69.27.68.214)
Time: Sun Aug  6 19:53:31 2006

Input: for(n=1,41,if(isprime(n^2+n+41),print1(n",")))
 


Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? 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,
? ? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.014s
user	0m0.008s
sys	0m0.006s


'69.27.6'
************** PARI *****************
Host 69.27.68.214 (69.27.68.214)
Time: Sun Aug  6 19:53:14 2006

Input: for(n=1,40,if(isprime(n^2+n+41),print1(n",")))
 


Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? 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,
? ? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.013s
user	0m0.006s
sys	0m0.007s


'69.27.6'
************** PARI *****************
Host 69.27.68.214 (69.27.68.214)
Time: Sun Aug  6 19:52:49 2006

Input: for(n=1,42,if(isprime(n^2+n+41),print1(n",")))
 


Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? 1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,42,
? ? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.013s
user	0m0.007s
sys	0m0.006s


'69.27.6'
************** PARI *****************
Host 69.27.68.214 (69.27.68.214)
Time: Sun Aug  6 19:51:45 2006

Input: for(n=1,6521,if(isprime(n),print1(n",")))
 


Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? 2,3,5,7,11,13,17,19,23,29,31,37,41,43,47,53,59,61,67,71,73,79,83,89,97,101,103,107,109,113,127,131,137,139,149,151,157,163,167,173,179,181,191,193,197,199,211,223,227,229,233,239,241,251,257,263,269,271,277,281,283,293,307,311,313,317,331,337,347,349,353,359,367,373,379,383,389,397,401,409,419,421,431,433,439,443,449,457,461,463,467,479,487,491,499,503,509,521,523,541,547,557,563,569,571,577,587,593,599,601,607,613,617,619,631,641,643,647,653,659,661,673,677,683,691,701,709,719,727,733,739,743,751,757,761,769,773,787,797,809,811,821,823,827,829,839,853,857,859,863,877,881,883,887,907,911,919,929,937,941,947,953,967,971,977,983,991,997,1009,1013,1019,1021,1031,1033,1039,1049,1051,1061,1063,1069,1087,1091,1093,1097,1103,1109,1117,1123,1129,1151,1153,1163,1171,1181,1187,1193,1201,1213,1217,1223,1229,1231,1237,1249,1259,1277,1279,1283,1289,1291,1297,1301,1303,1307,1319,1321,1327,1361,1367,1373,1381,1399,1409,1423,1427,1429,1433,1439,1447,1451,1453,1459,1471,1481,1483,1487,1489,1493,1499,1511,1523,1531,1543,1549,1553,1559,1567,1571,1579,1583,1597,1601,1607,1609,1613,1619,1621,1627,1637,1657,1663,1667,1669,1693,1697,1699,1709,1721,1723,1733,1741,1747,1753,1759,1777,1783,1787,1789,1801,1811,1823,1831,1847,1861,1867,1871,1873,1877,1879,1889,1901,1907,1913,1931,1933,1949,1951,1973,1979,1987,1993,1997,1999,2003,2011,2017,2027,2029,2039,2053,2063,2069,2081,2083,2087,2089,2099,2111,2113,2129,2131,2137,2141,2143,2153,2161,2179,2203,2207,2213,2221,2237,2239,2243,2251,2267,2269,2273,2281,2287,2293,2297,2309,2311,2333,2339,2341,2347,2351,2357,2371,2377,2381,2383,2389,2393,2399,2411,2417,2423,2437,2441,2447,2459,2467,2473,2477,2503,2521,2531,2539,2543,2549,2551,2557,2579,2591,2593,2609,2617,2621,2633,2647,2657,2659,2663,2671,2677,2683,2687,2689,2693,2699,2707,2711,2713,2719,2729,2731,2741,2749,2753,2767,2777,2789,2791,2797,2801,2803,2819,2833,2837,2843,2851,2857,2861,2879,2887,2897,2903,2909,2917,2927,2939,2953,2957,2963,2969,2971,2999,3001,3011,3019,3023,3037,3041,3049,3061,3067,3079,3083,3089,3109,3119,3121,3137,3163,3167,3169,3181,3187,3191,3203,3209,3217,3221,3229,3251,3253,3257,3259,3271,3299,3301,3307,3313,3319,3323,3329,3331,3343,3347,3359,3361,3371,3373,3389,3391,3407,3413,3433,3449,3457,3461,3463,3467,3469,3491,3499,3511,3517,3527,3529,3533,3539,3541,3547,3557,3559,3571,3581,3583,3593,3607,3613,3617,3623,3631,3637,3643,3659,3671,3673,3677,3691,3697,3701,3709,3719,3727,3733,3739,3761,3767,3769,3779,3793,3797,3803,3821,3823,3833,3847,3851,3853,3863,3877,3881,3889,3907,3911,3917,3919,3923,3929,3931,3943,3947,3967,3989,4001,4003,4007,4013,4019,4021,4027,4049,4051,4057,4073,4079,4091,4093,4099,4111,4127,4129,4133,4139,4153,4157,4159,4177,4201,4211,4217,4219,4229,4231,4241,4243,4253,4259,4261,4271,4273,4283,4289,4297,4327,4337,4339,4349,4357,4363,4373,4391,4397,4409,4421,4423,4441,4447,4451,4457,4463,4481,4483,4493,4507,4513,4517,4519,4523,4547,4549,4561,4567,4583,4591,4597,4603,4621,4637,4639,4643,4649,4651,4657,4663,4673,4679,4691,4703,4721,4723,4729,4733,4751,4759,4783,4787,4789,4793,4799,4801,4813,4817,4831,4861,4871,4877,4889,4903,4909,4919,4931,4933,4937,4943,4951,4957,4967,4969,4973,4987,4993,4999,5003,5009,5011,5021,5023,5039,5051,5059,5077,5081,5087,5099,5101,5107,5113,5119,5147,5153,5167,5171,5179,5189,5197,5209,5227,5231,5233,5237,5261,5273,5279,5281,5297,5303,5309,5323,5333,5347,5351,5381,5387,5393,5399,5407,5413,5417,5419,5431,5437,5441,5443,5449,5471,5477,5479,5483,5501,5503,5507,5519,5521,5527,5531,5557,5563,5569,5573,5581,5591,5623,5639,5641,5647,5651,5653,5657,5659,5669,5683,5689,5693,5701,5711,5717,5737,5741,5743,5749,5779,5783,5791,5801,5807,5813,5821,5827,5839,5843,5849,5851,5857,5861,5867,5869,5879,5881,5897,5903,5923,5927,5939,5953,5981,5987,6007,6011,6029,6037,6043,6047,6053,6067,6073,6079,6089,6091,6101,6113,6121,6131,6133,6143,6151,6163,6173,6197,6199,6203,6211,6217,6221,6229,6247,6257,6263,6269,6271,6277,6287,6299,6301,6311,6317,6323,6329,6337,6343,6353,6359,6361,6367,6373,6379,6389,6397,6421,6427,6449,6451,6469,6473,6481,6491,6521,
? ? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.026s
user	0m0.020s
sys	0m0.007s


'69.27.6'
************** PARI *****************
Host 69.27.68.214 (69.27.68.214)
Time: Sun Aug  6 19:49:35 2006

Input: for(n=1,1000,if(isprime(n),print1(n",")))
 


Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? 2,3,5,7,11,13,17,19,23,29,31,37,41,43,47,53,59,61,67,71,73,79,83,89,97,101,103,107,109,113,127,131,137,139,149,151,157,163,167,173,179,181,191,193,197,199,211,223,227,229,233,239,241,251,257,263,269,271,277,281,283,293,307,311,313,317,331,337,347,349,353,359,367,373,379,383,389,397,401,409,419,421,431,433,439,443,449,457,461,463,467,479,487,491,499,503,509,521,523,541,547,557,563,569,571,577,587,593,599,601,607,613,617,619,631,641,643,647,653,659,661,673,677,683,691,701,709,719,727,733,739,743,751,757,761,769,773,787,797,809,811,821,823,827,829,839,853,857,859,863,877,881,883,887,907,911,919,929,937,941,947,953,967,971,977,983,991,997,
? ? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.017s
user	0m0.010s
sys	0m0.005s


'69.121.'
************** PARI *****************
Host 69.121.152.231 (69.121.152.231)
Time: Sun Aug  6 17:16:38 2006

Input: vector(20,x,floor((x+1)*sqrt(2))-floor(x*sqrt(2)))

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = [1, 2, 1, 2, 1, 1, 2, 1, 2, 1, 1, 2, 1, 2, 1, 2, 1, 1, 2, 1]
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.039s
user	0m0.006s
sys	0m0.010s


'69.27.6'
************** PARI *****************
Host 69.27.68.214 (69.27.68.214)
Time: Sun Aug  6 17:11:05 2006

Input: for(n=0,1000,if(isprime(n^2-n+27941),print1(n",")))


Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? 0,1,2,3,4,5,7,8,10,11,13,14,15,16,19,22,23,24,25,26,27,28,29,31,32,34,35,36,38,39,40,41,42,44,45,46,47,48,49,50,51,52,53,54,55,58,60,61,62,63,64,67,68,69,70,71,72,74,76,80,81,82,83,84,85,86,87,88,90,91,92,93,94,95,96,97,98,99,103,104,105,111,113,114,115,116,117,119,120,121,122,125,126,127,129,130,131,132,133,134,136,137,139,141,142,143,144,145,148,149,150,151,152,153,154,156,157,158,160,163,164,165,166,167,168,169,170,173,174,175,176,177,178,180,181,184,185,186,187,188,189,191,192,193,196,197,198,199,200,201,202,203,205,207,208,209,211,212,214,215,216,219,221,222,223,224,225,226,228,229,230,231,232,234,236,237,238,241,242,245,246,250,252,254,261,262,263,264,267,268,271,272,273,275,276,277,278,279,281,282,283,285,286,287,288,290,291,292,293,294,295,297,298,299,302,303,305,306,307,308,309,310,311,313,314,315,316,317,318,320,322,323,325,328,330,333,335,341,342,344,346,349,350,351,353,355,356,358,360,361,363,364,366,367,368,369,370,371,374,377,378,379,381,382,384,385,386,387,389,390,392,393,395,397,398,399,403,404,405,407,409,412,413,415,417,420,422,423,424,425,426,430,432,434,435,440,442,443,444,447,448,449,451,455,457,459,460,463,464,465,467,468,469,470,471,472,473,474,476,477,478,479,480,482,483,484,485,486,490,491,492,494,497,498,499,502,505,507,508,509,511,512,513,516,521,522,524,526,527,529,530,531,532,534,538,539,540,541,542,543,544,550,553,555,556,557,558,559,561,563,564,565,566,569,570,571,572,573,577,578,580,581,585,590,591,593,595,597,599,600,601,602,604,605,606,608,609,611,613,614,620,622,623,624,625,626,628,631,633,636,637,638,639,642,644,648,652,654,656,658,660,661,662,664,665,666,667,668,671,672,677,678,679,683,684,685,686,690,692,693,695,697,699,700,702,703,704,705,706,710,711,712,714,716,718,719,720,721,722,725,727,728,733,737,738,740,744,745,752,754,756,757,758,760,761,762,765,768,771,775,776,777,778,779,783,784,786,787,788,790,791,792,794,795,797,800,801,802,803,804,805,806,807,809,810,812,813,814,820,822,823,828,832,833,834,835,837,841,842,843,844,845,847,848,851,852,854,855,856,857,861,862,866,867,875,877,878,880,882,885,886,892,893,894,895,897,902,903,904,905,906,910,914,915,916,917,918,920,921,924,926,929,932,933,938,939,941,942,945,946,948,952,953,955,956,959,960,961,962,964,966,967,972,974,975,976,977,978,979,980,981,983,987,988,989,992,993,995,999,1000,
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.092s
user	0m0.010s
sys	0m0.008s


'69.230.'
************** PARI *****************
Host 69.230.18.219 (69.230.18.219)
Time: Sun Aug  6 16:12:30 2006

Input: 1700 = 8000c - 77800/6

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? ? 
Goodbye!

Errors/timing (if any):

  ***   unexpected character: 1700=8000c-77800/6
                                  ^--------------

Timing:
real	0m0.013s
user	0m0.005s
sys	0m0.008s


'72.30.2'
************** PARI *****************
Host 72.30.226.160 (72.30.226.160)
Time: Sun Aug  6 15:18:08 2006

Input: for(n=1,7, print1(n,": ",sum(x=1,n,1/x),",  ") )

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? 1: 1,  2: 3/2,  3: 11/6,  4: 25/12,  5: 137/60,  6: 49/20,  7: 363/140,  
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.253s
user	0m0.007s
sys	0m0.012s


'24.255.'
************** PARI *****************
Host 24.255.160.206 (24.255.160.206)
Time: Sun Aug  6 09:36:37 2006

Input: v-4(4-v)=-2(2v-1)


Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? ? 
Goodbye!

Errors/timing (if any):

  ***   Warning: unused characters: (4-v)=-2(2v-1).
  ***   unexpected character: v-4(4-v)=-2(2v-1)
                                      ^---------

Timing:
real	0m0.013s
user	0m0.006s
sys	0m0.008s


'129.67.'
************** PARI *****************
Host 129.67.126.38 (129.67.126.38)
Time: Sun Aug  6 07:28:52 2006

Input: polrootspadic(162*x^2 + 7164*x + 19177,7,12)

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = [2 + 2*7 + 5*7^2 + 5*7^3 + 4*7^4 + 3*7^5 + 4*7^6 + 3*7^7 + 3*7^8 + 2*7^9 + 2*7^11 + O(7^12), 2 + 2*7 + 2*7^2 + 6*7^4 + 4*7^5 + 7^6 + 5*7^8 + 3*7^9 + 3*7^10 + 6*7^11 + O(7^12), 2 + 2*7 + 5*7^2 + 5*7^3 + 4*7^4 + 3*7^5 + 4*7^6 + 3*7^7 + 3*7^8 + 2*7^9 + 2*7^11 + O(7^12), 2 + 2*7 + 2*7^2 + 6*7^4 + 4*7^5 + 7^6 + 5*7^8 + 3*7^9 + 3*7^10 + 6*7^11 + O(7^12), 4 + 5*7 + 3*7^3 + 5*7^4 + 3*7^6 + 5*7^7 + 3*7^9 + 5*7^10 + O(7^12)]~
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.095s
user	0m0.011s
sys	0m0.006s


'61.5.4.'
************** PARI *****************
Host 61.5.4.144 (61.5.4.144)
Time: Sun Aug  6 05:17:30 2006

Input: 2^32 mod 47

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = mod47
? 
Goodbye!

Errors/timing (if any):

  ***   Warning: unused characters: mod47.

Timing:
real	0m0.013s
user	0m0.009s
sys	0m0.004s


'69.92.1'
************** PARI *****************
Host 69.92.12.82 (69.92.12.82)
Time: Sun Aug  6 02:46:58 2006

Input: for(n=1,500,if(isprime(613*10^n+1),print1(n",")))

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? 1,6,9,10,18,75,122,165,402,
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m2.253s
user	0m0.986s
sys	0m0.013s


'164.107'
************** PARI *****************
Host 164.107.186.40 (164.107.186.40)
Time: Sat Aug  5 23:44:43 2006

Input: primepi(500000)

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = 41538
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.013s
user	0m0.007s
sys	0m0.007s


'164.107'
************** PARI *****************
Host 164.107.186.40 (164.107.186.40)
Time: Sat Aug  5 23:44:25 2006

Input: primepi(1000)

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = 168
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.013s
user	0m0.006s
sys	0m0.006s


'69.27.6'
************** PARI *****************
Host 69.27.68.214 (69.27.68.214)
Time: Sat Aug  5 20:56:11 2006

Input: Do[ If[ PrimeQ[ FromDigits[ RealDigits[ N[ P, n+10], 10, n] [ [1] ] ] ], Print[n] ], {n, 1, 9016} ] 


Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? ? 
Goodbye!

Errors/timing (if any):

  ***   expected character: ']' instead of: ...s[RealDigits[N[P,n+10],10
  ***   ,n][[1]]]],Print[n]]
        ^--------------------

Timing:
real	0m0.013s
user	0m0.006s
sys	0m0.006s


'208.191'
************** PARI *****************
Host 208.191.162.223 (208.191.162.223)
Time: Sat Aug  5 20:42:27 2006

Input: what is 20% of 1250.00

Output: WARNING: PARI command contains unsafe command '%', so it will not be executed.

'24.247.'
************** PARI *****************
Host 24.247.238.196 (24.247.238.196)
Time: Sat Aug  5 19:32:03 2006

Input: 9.95+9.95+7.95+7.95

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = 35.800000000000000000000000000000000000
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.030s
user	0m0.008s
sys	0m0.005s


'69.27.6'
************** PARI *****************
Host 69.27.68.214 (69.27.68.214)
Time: Sat Aug  5 15:46:01 2006

Input: for(n=0,2000,if(isprime(2^n-1),print1(n",")))


Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? 2,3,5,7,13,17,19,31,61,89,107,127,521,607,
Errors/timing (if any):

/var/www/cgi-bin/calc/gp: line 1: 12443 Killed                  ./gp-2.2.11 -s 256000000 -emacs

Timing:
real	0m21.011s
user	0m20.987s
sys	0m0.013s


'69.27.6'
************** PARI *****************
Host 69.27.68.214 (69.27.68.214)
Time: Sat Aug  5 15:45:06 2006

Input: for(n=0,1000,if(isprime(2^n-1),print1(n",")))


Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? 2,3,5,7,13,17,19,31,61,89,107,127,521,607,
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m3.059s
user	0m3.047s
sys	0m0.011s


'69.27.6'
************** PARI *****************
Host 69.27.68.214 (69.27.68.214)
Time: Sat Aug  5 15:44:34 2006

Input: for(n=0,1000,if(isprime(n^2-n+27941),print1(n",")))


Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? 0,1,2,3,4,5,7,8,10,11,13,14,15,16,19,22,23,24,25,26,27,28,29,31,32,34,35,36,38,39,40,41,42,44,45,46,47,48,49,50,51,52,53,54,55,58,60,61,62,63,64,67,68,69,70,71,72,74,76,80,81,82,83,84,85,86,87,88,90,91,92,93,94,95,96,97,98,99,103,104,105,111,113,114,115,116,117,119,120,121,122,125,126,127,129,130,131,132,133,134,136,137,139,141,142,143,144,145,148,149,150,151,152,153,154,156,157,158,160,163,164,165,166,167,168,169,170,173,174,175,176,177,178,180,181,184,185,186,187,188,189,191,192,193,196,197,198,199,200,201,202,203,205,207,208,209,211,212,214,215,216,219,221,222,223,224,225,226,228,229,230,231,232,234,236,237,238,241,242,245,246,250,252,254,261,262,263,264,267,268,271,272,273,275,276,277,278,279,281,282,283,285,286,287,288,290,291,292,293,294,295,297,298,299,302,303,305,306,307,308,309,310,311,313,314,315,316,317,318,320,322,323,325,328,330,333,335,341,342,344,346,349,350,351,353,355,356,358,360,361,363,364,366,367,368,369,370,371,374,377,378,379,381,382,384,385,386,387,389,390,392,393,395,397,398,399,403,404,405,407,409,412,413,415,417,420,422,423,424,425,426,430,432,434,435,440,442,443,444,447,448,449,451,455,457,459,460,463,464,465,467,468,469,470,471,472,473,474,476,477,478,479,480,482,483,484,485,486,490,491,492,494,497,498,499,502,505,507,508,509,511,512,513,516,521,522,524,526,527,529,530,531,532,534,538,539,540,541,542,543,544,550,553,555,556,557,558,559,561,563,564,565,566,569,570,571,572,573,577,578,580,581,585,590,591,593,595,597,599,600,601,602,604,605,606,608,609,611,613,614,620,622,623,624,625,626,628,631,633,636,637,638,639,642,644,648,652,654,656,658,660,661,662,664,665,666,667,668,671,672,677,678,679,683,684,685,686,690,692,693,695,697,699,700,702,703,704,705,706,710,711,712,714,716,718,719,720,721,722,725,727,728,733,737,738,740,744,745,752,754,756,757,758,760,761,762,765,768,771,775,776,777,778,779,783,784,786,787,788,790,791,792,794,795,797,800,801,802,803,804,805,806,807,809,810,812,813,814,820,822,823,828,832,833,834,835,837,841,842,843,844,845,847,848,851,852,854,855,856,857,861,862,866,867,875,877,878,880,882,885,886,892,893,894,895,897,902,903,904,905,906,910,914,915,916,917,918,920,921,924,926,929,932,933,938,939,941,942,945,946,948,952,953,955,956,959,960,961,962,964,966,967,972,974,975,976,977,978,979,980,981,983,987,988,989,992,993,995,999,1000,
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.019s
user	0m0.007s
sys	0m0.013s


'68.93.1'
************** PARI *****************
Host 68.93.143.153 (68.93.143.153)
Time: Sat Aug  5 15:38:03 2006

Input: what is grams


Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = whatisgrams
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.013s
user	0m0.004s
sys	0m0.009s


'69.27.6'
************** PARI *****************
Host 69.27.68.214 (69.27.68.214)
Time: Sat Aug  5 14:25:54 2006

Input: for(n=0,1000,if(isprime(n^2-n+27941),print1(n",")))


Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? 0,1,2,3,4,5,7,8,10,11,13,14,15,16,19,22,23,24,25,26,27,28,29,31,32,34,35,36,38,39,40,41,42,44,45,46,47,48,49,50,51,52,53,54,55,58,60,61,62,63,64,67,68,69,70,71,72,74,76,80,81,82,83,84,85,86,87,88,90,91,92,93,94,95,96,97,98,99,103,104,105,111,113,114,115,116,117,119,120,121,122,125,126,127,129,130,131,132,133,134,136,137,139,141,142,143,144,145,148,149,150,151,152,153,154,156,157,158,160,163,164,165,166,167,168,169,170,173,174,175,176,177,178,180,181,184,185,186,187,188,189,191,192,193,196,197,198,199,200,201,202,203,205,207,208,209,211,212,214,215,216,219,221,222,223,224,225,226,228,229,230,231,232,234,236,237,238,241,242,245,246,250,252,254,261,262,263,264,267,268,271,272,273,275,276,277,278,279,281,282,283,285,286,287,288,290,291,292,293,294,295,297,298,299,302,303,305,306,307,308,309,310,311,313,314,315,316,317,318,320,322,323,325,328,330,333,335,341,342,344,346,349,350,351,353,355,356,358,360,361,363,364,366,367,368,369,370,371,374,377,378,379,381,382,384,385,386,387,389,390,392,393,395,397,398,399,403,404,405,407,409,412,413,415,417,420,422,423,424,425,426,430,432,434,435,440,442,443,444,447,448,449,451,455,457,459,460,463,464,465,467,468,469,470,471,472,473,474,476,477,478,479,480,482,483,484,485,486,490,491,492,494,497,498,499,502,505,507,508,509,511,512,513,516,521,522,524,526,527,529,530,531,532,534,538,539,540,541,542,543,544,550,553,555,556,557,558,559,561,563,564,565,566,569,570,571,572,573,577,578,580,581,585,590,591,593,595,597,599,600,601,602,604,605,606,608,609,611,613,614,620,622,623,624,625,626,628,631,633,636,637,638,639,642,644,648,652,654,656,658,660,661,662,664,665,666,667,668,671,672,677,678,679,683,684,685,686,690,692,693,695,697,699,700,702,703,704,705,706,710,711,712,714,716,718,719,720,721,722,725,727,728,733,737,738,740,744,745,752,754,756,757,758,760,761,762,765,768,771,775,776,777,778,779,783,784,786,787,788,790,791,792,794,795,797,800,801,802,803,804,805,806,807,809,810,812,813,814,820,822,823,828,832,833,834,835,837,841,842,843,844,845,847,848,851,852,854,855,856,857,861,862,866,867,875,877,878,880,882,885,886,892,893,894,895,897,902,903,904,905,906,910,914,915,916,917,918,920,921,924,926,929,932,933,938,939,941,942,945,946,948,952,953,955,956,959,960,961,962,964,966,967,972,974,975,976,977,978,979,980,981,983,987,988,989,992,993,995,999,1000,
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.019s
user	0m0.013s
sys	0m0.007s


'69.27.6'
************** PARI *****************
Host 69.27.68.214 (69.27.68.214)
Time: Sat Aug  5 14:09:49 2006

Input: for(n=0,1000,if(isprime(n^2-n+27941),print1(n",")))
 


Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? 0,1,2,3,4,5,7,8,10,11,13,14,15,16,19,22,23,24,25,26,27,28,29,31,32,34,35,36,38,39,40,41,42,44,45,46,47,48,49,50,51,52,53,54,55,58,60,61,62,63,64,67,68,69,70,71,72,74,76,80,81,82,83,84,85,86,87,88,90,91,92,93,94,95,96,97,98,99,103,104,105,111,113,114,115,116,117,119,120,121,122,125,126,127,129,130,131,132,133,134,136,137,139,141,142,143,144,145,148,149,150,151,152,153,154,156,157,158,160,163,164,165,166,167,168,169,170,173,174,175,176,177,178,180,181,184,185,186,187,188,189,191,192,193,196,197,198,199,200,201,202,203,205,207,208,209,211,212,214,215,216,219,221,222,223,224,225,226,228,229,230,231,232,234,236,237,238,241,242,245,246,250,252,254,261,262,263,264,267,268,271,272,273,275,276,277,278,279,281,282,283,285,286,287,288,290,291,292,293,294,295,297,298,299,302,303,305,306,307,308,309,310,311,313,314,315,316,317,318,320,322,323,325,328,330,333,335,341,342,344,346,349,350,351,353,355,356,358,360,361,363,364,366,367,368,369,370,371,374,377,378,379,381,382,384,385,386,387,389,390,392,393,395,397,398,399,403,404,405,407,409,412,413,415,417,420,422,423,424,425,426,430,432,434,435,440,442,443,444,447,448,449,451,455,457,459,460,463,464,465,467,468,469,470,471,472,473,474,476,477,478,479,480,482,483,484,485,486,490,491,492,494,497,498,499,502,505,507,508,509,511,512,513,516,521,522,524,526,527,529,530,531,532,534,538,539,540,541,542,543,544,550,553,555,556,557,558,559,561,563,564,565,566,569,570,571,572,573,577,578,580,581,585,590,591,593,595,597,599,600,601,602,604,605,606,608,609,611,613,614,620,622,623,624,625,626,628,631,633,636,637,638,639,642,644,648,652,654,656,658,660,661,662,664,665,666,667,668,671,672,677,678,679,683,684,685,686,690,692,693,695,697,699,700,702,703,704,705,706,710,711,712,714,716,718,719,720,721,722,725,727,728,733,737,738,740,744,745,752,754,756,757,758,760,761,762,765,768,771,775,776,777,778,779,783,784,786,787,788,790,791,792,794,795,797,800,801,802,803,804,805,806,807,809,810,812,813,814,820,822,823,828,832,833,834,835,837,841,842,843,844,845,847,848,851,852,854,855,856,857,861,862,866,867,875,877,878,880,882,885,886,892,893,894,895,897,902,903,904,905,906,910,914,915,916,917,918,920,921,924,926,929,932,933,938,939,941,942,945,946,948,952,953,955,956,959,960,961,962,964,966,967,972,974,975,976,977,978,979,980,981,983,987,988,989,992,993,995,999,1000,
? ? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.021s
user	0m0.012s
sys	0m0.006s


'69.27.6'
************** PARI *****************
Host 69.27.68.214 (69.27.68.214)
Time: Sat Aug  5 14:09:01 2006

Input: for(n=1,1000,if(isprime(n^2-n+27941),print1(n",")))
 


Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? 1,2,3,4,5,7,8,10,11,13,14,15,16,19,22,23,24,25,26,27,28,29,31,32,34,35,36,38,39,40,41,42,44,45,46,47,48,49,50,51,52,53,54,55,58,60,61,62,63,64,67,68,69,70,71,72,74,76,80,81,82,83,84,85,86,87,88,90,91,92,93,94,95,96,97,98,99,103,104,105,111,113,114,115,116,117,119,120,121,122,125,126,127,129,130,131,132,133,134,136,137,139,141,142,143,144,145,148,149,150,151,152,153,154,156,157,158,160,163,164,165,166,167,168,169,170,173,174,175,176,177,178,180,181,184,185,186,187,188,189,191,192,193,196,197,198,199,200,201,202,203,205,207,208,209,211,212,214,215,216,219,221,222,223,224,225,226,228,229,230,231,232,234,236,237,238,241,242,245,246,250,252,254,261,262,263,264,267,268,271,272,273,275,276,277,278,279,281,282,283,285,286,287,288,290,291,292,293,294,295,297,298,299,302,303,305,306,307,308,309,310,311,313,314,315,316,317,318,320,322,323,325,328,330,333,335,341,342,344,346,349,350,351,353,355,356,358,360,361,363,364,366,367,368,369,370,371,374,377,378,379,381,382,384,385,386,387,389,390,392,393,395,397,398,399,403,404,405,407,409,412,413,415,417,420,422,423,424,425,426,430,432,434,435,440,442,443,444,447,448,449,451,455,457,459,460,463,464,465,467,468,469,470,471,472,473,474,476,477,478,479,480,482,483,484,485,486,490,491,492,494,497,498,499,502,505,507,508,509,511,512,513,516,521,522,524,526,527,529,530,531,532,534,538,539,540,541,542,543,544,550,553,555,556,557,558,559,561,563,564,565,566,569,570,571,572,573,577,578,580,581,585,590,591,593,595,597,599,600,601,602,604,605,606,608,609,611,613,614,620,622,623,624,625,626,628,631,633,636,637,638,639,642,644,648,652,654,656,658,660,661,662,664,665,666,667,668,671,672,677,678,679,683,684,685,686,690,692,693,695,697,699,700,702,703,704,705,706,710,711,712,714,716,718,719,720,721,722,725,727,728,733,737,738,740,744,745,752,754,756,757,758,760,761,762,765,768,771,775,776,777,778,779,783,784,786,787,788,790,791,792,794,795,797,800,801,802,803,804,805,806,807,809,810,812,813,814,820,822,823,828,832,833,834,835,837,841,842,843,844,845,847,848,851,852,854,855,856,857,861,862,866,867,875,877,878,880,882,885,886,892,893,894,895,897,902,903,904,905,906,910,914,915,916,917,918,920,921,924,926,929,932,933,938,939,941,942,945,946,948,952,953,955,956,959,960,961,962,964,966,967,972,974,975,976,977,978,979,980,981,983,987,988,989,992,993,995,999,1000,
? ? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.022s
user	0m0.017s
sys	0m0.004s


'69.27.6'
************** PARI *****************
Host 69.27.68.214 (69.27.68.214)
Time: Sat Aug  5 14:07:05 2006

Input: for(n=1,1000,if(isprime(2^n-1),print1(n",")))
 


Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? 2,3,5,7,13,17,19,31,61,89,107,127,521,607,
? ? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m3.071s
user	0m3.045s
sys	0m0.008s


'69.27.6'
************** PARI *****************
Host 69.27.68.214 (69.27.68.214)
Time: Sat Aug  5 14:06:51 2006

Input: for(n=1,500,if(isprime(2^n-1),print1(n",")))
 


Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? 2,3,5,7,13,17,19,31,61,89,107,127,
? ? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.060s
user	0m0.052s
sys	0m0.008s


'69.27.6'
************** PARI *****************
Host 69.27.68.214 (69.27.68.214)
Time: Sat Aug  5 14:06:09 2006

Input: for(n=1,500,if(isprime(2^n-1),print1(n",")))
 


Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? 2,3,5,7,13,17,19,31,61,89,107,127,
? ? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.177s
user	0m0.055s
sys	0m0.003s


'69.27.6'
************** PARI *****************
Host 69.27.68.214 (69.27.68.214)
Time: Sat Aug  5 14:04:51 2006

Input: for(n=1,42,if(isprime(n^2+x+41),print1(n",")))


Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? ? 
Goodbye!

Errors/timing (if any):

  *** isprime: not an integer argument in an arithmetic function

Timing:
real	0m0.035s
user	0m0.006s
sys	0m0.010s


'69.27.6'
************** PARI *****************
Host 69.27.68.214 (69.27.68.214)
Time: Sat Aug  5 14:02:21 2006

Input: for(n=1,500,if(isprime(613*10^n+1),print1(n",")))


Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? 1,6,9,10,18,75,122,165,402,
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m1.127s
user	0m0.980s
sys	0m0.011s


'69.92.1'
************** PARI *****************
Host 69.92.12.82 (69.92.12.82)
Time: Sat Aug  5 12:43:48 2006

Input: for(n=1,500,if(isprime(613*10^n+1),print1(n",")))

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? 1,6,9,10,18,75,122,165,402,
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.999s
user	0m0.992s
sys	0m0.007s


'69.92.1'
************** PARI *****************
Host 69.92.12.82 (69.92.12.82)
Time: Sat Aug  5 12:32:50 2006

Input: for(n=1,500,if(isprime(613*10^n+1),print1(n",")))


Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? 1,6,9,10,18,75,122,165,402,
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m1.093s
user	0m0.982s
sys	0m0.009s


'69.92.1'
************** PARI *****************
Host 69.92.12.82 (69.92.12.82)
Time: Sat Aug  5 12:32:28 2006

Input: ? for(n=1,500,if(isprime(613*10^n+1),print1(n",")))


Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? for(X=a,b,seq): the sequence is evaluated, X going from a up to b.

? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.048s
user	0m0.007s
sys	0m0.007s


'24.131.'
************** PARI *****************
Host 24.131.127.122 (24.131.127.122)
Time: Sat Aug  5 10:35:47 2006

Input: print kash('NumberField(X^3 + 15*X^2 - 15*X + 15)')


Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? ? 
Goodbye!

Errors/timing (if any):

  ***   expected character: ',' instead of: printkash('NumberField
  ***   (X^3+15*X^2-15*X+15)
        ^--------------------

Timing:
real	0m0.273s
user	0m0.003s
sys	0m0.015s


'72.30.1'
************** PARI *****************
Host 72.30.129.106 (72.30.129.106)
Time: Sat Aug  5 05:52:11 2006

Input: y=210; for(x=1,8,y=sumdiv(y,x,x)-y;print1(y,","))

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? 366,378,582,594,846,1026,1374,1386,
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.101s
user	0m0.004s
sys	0m0.014s


'75.6.14'
************** PARI *****************
Host 75.6.149.232 (75.6.149.232)
Time: Fri Aug  4 20:54:39 2006

Input: 56124+546523567

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = 546579691
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.059s
user	0m0.004s
sys	0m0.008s


'75.6.14'
************** PARI *****************
Host 75.6.149.232 (75.6.149.232)
Time: Fri Aug  4 20:54:28 2006

Input: "Replace this by some code, then click [SAGE] or [PARI]!"

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = "Replace this by some code, then click [SAGE] or [PARI]!"
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.012s
user	0m0.003s
sys	0m0.010s


'24.161.'
************** PARI *****************
Host 24.161.97.99 (24.161.97.99)
Time: Fri Aug  4 18:35:34 2006

Input: 2700 divided by 27

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = dividedby27
? 
Goodbye!

Errors/timing (if any):

  ***   Warning: unused characters: dividedby27.

Timing:
real	0m0.013s
user	0m0.006s
sys	0m0.007s


'128.208'
************** PARI *****************
Host 128.208.47.43 (128.208.47.43)
Time: Fri Aug  4 10:40:26 2006

Input: 2^15

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = 32768
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.014s
user	0m0.007s
sys	0m0.007s


'212.158'
************** PARI *****************
Host 212.158.224.83 (212.158.224.83)
Time: Fri Aug  4 06:58:58 2006

Input: "Replace this by some code, then click [SAGE] or [PARI]!"

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = "Replace this by some code, then click [SAGE] or [PARI]!"
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.285s
user	0m0.006s
sys	0m0.009s


'81.190.'
************** PARI *****************
Host 81.190.2.171 (81.190.2.171)
Time: Thu Aug  3 17:15:35 2006

Input: E = EllipticCurve([10,20,30,49,50]);
E
E.anlist(10)

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? ? %1 = E
? ? 
Goodbye!

Errors/timing (if any):

  ***   unknown function or error in formal parameters: E=EllipticCurve([10,20
                                                          ^--------------------
  ***   Warning: unused characters: (10).
  ***   unknown member function: E.anlist(10)
                                   ^----------

Timing:
real	0m0.013s
user	0m0.006s
sys	0m0.007s


'81.190.'
************** PARI *****************
Host 81.190.2.171 (81.190.2.171)
Time: Thu Aug  3 16:54:22 2006

Input: def h1(x): return sqrt(x)
def h2(x): return -sqrt(x)
plot([h1, h2], 0,4).show(dpi=70)

Output: WARNING: PARI command contains unsafe command 'plot', so it will not be executed.

'159.242'
************** PARI *****************
Host 159.242.10.178 (159.242.10.178)
Time: Thu Aug  3 16:20:19 2006

Input: 2660999956459044462496559697895207916164979^2484967380701451508112337181106320041688653

3391644668254683815130414077708852650402483

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? ? ? %1 = 3391644668254683815130414077708852650402483
? 
Goodbye!

Errors/timing (if any):

  ***   length (lg) overflow

Timing:
real	0m0.049s
user	0m0.004s
sys	0m0.010s


'65.31.3'
************** PARI *****************
Host 65.31.34.63 (65.31.34.63)
Time: Thu Aug  3 13:03:52 2006

Input: 19.99+7.99=


Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? ? 
Goodbye!

Errors/timing (if any):

  ***   unexpected character: 19.99+7.99=
                                        ^-

Timing:
real	0m0.012s
user	0m0.004s
sys	0m0.009s


'128.244'
************** PARI *****************
Host 128.244.70.112 (128.244.70.112)
Time: Thu Aug  3 08:55:23 2006

Input: 2^312413

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = 4830981466364580262319339049818562968558761028106272923126514918538223897345359936316446318720231182550935815005772315073996555250585693298540893393869965893092771427023973324398278248218175680359827444393509313174684525735678463663338125756964551115437342798314289976505148315466828279216135786601845924061519374988636778812138166301482869293619842397899083644391558537625975319346404544929515996170044151227529786416523393368140240692057558960136886977969459360853671139303206053306955723152430599303215851072815557007673966645878385823632646218356155873846606739507321092585440396351621511927850798205826923798017416153927206387891124567627792684687510179774180313271224111160927439702146890826412635562210651443065158752867553952036555744295988140356916766792733492711250785640478897306333920929841764065832622350747877946551823482187314115902814391938118045061893243257030360736440272387702746257151958562194110609391650030004236271161198917478149407972601791080340416289522217831842149279835538796034145741705373260384364903648065949011881512804322037289046950099011614522708194273468684859406801874157091529832148222328299288313083228093653170268904942449665323783818837931336547816485989215516595643436703960125472804421950729227643775424995665390226098088488420100130103202545344023974701370579360668132145456011523239722123972684999166344157597865557207037334973510208063181572044506866127826166579937040799836980091022005227178463709705067496410505882900234294540070905246120172453872075795510741926131987494670876917571998688053327730386004753469605546394017699620434253124319245235951810127531919801525874034179211514938805278780987944202820044826836109855430759065424813753651861469841704258187919970528928014675879351276720340559579087972476623295822223256347083299401660105337688691448979289075269637164710330897111913041037586535860271603582020639730941234472075388266368302732481390873310271931083219652448099445946604508098857863980957866978377596203570650593766139429847724575195075838452342188246180245513226058215761886236117380443043123188663192557854403152613949044031622909678213681857845610600954804960235913101079902222795134480736652982982306766632503957094862757822086275527390021267896804427483984420687621291870473384994140112770042378319084403156285698992746136555119097875362718125399775260346689252902321886998054019345588595360882048534031439836686597038653268510372778634363156608776954240697148964494042709310374969327886434368252414271912929608815903278270130329523383727733574741070197722548872017944205273685505986533424364627848013888396034174195379168695180492227053312063678932172222808341805857627358459578999746596179020196440429462841970944863716607653637977238621947036196999534721518103803089055338642715622544832669893314068824953086229567991687773603189917159336397138091179415373638117214282655295695467216071610962126082335992862627083119989314386660945600212361119249805546888549357680640983743435475894367263052538391431935336285944258022846877654513700214633120016244441249251826123582445040257840215040969299396786619548604192248415312061624538590283139363792089759812403413123484683794638570913639713120216938900897808778338252786564[+++]
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.542s
user	0m0.416s
sys	0m0.117s


'128.244'
************** PARI *****************
Host 128.244.70.112 (128.244.70.112)
Time: Thu Aug  3 08:55:08 2006

Input: 2^312413

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = 4830981466364580262319339049818562968558761028106272923126514918538223897345359936316446318720231182550935815005772315073996555250585693298540893393869965893092771427023973324398278248218175680359827444393509313174684525735678463663338125756964551115437342798314289976505148315466828279216135786601845924061519374988636778812138166301482869293619842397899083644391558537625975319346404544929515996170044151227529786416523393368140240692057558960136886977969459360853671139303206053306955723152430599303215851072815557007673966645878385823632646218356155873846606739507321092585440396351621511927850798205826923798017416153927206387891124567627792684687510179774180313271224111160927439702146890826412635562210651443065158752867553952036555744295988140356916766792733492711250785640478897306333920929841764065832622350747877946551823482187314115902814391938118045061893243257030360736440272387702746257151958562194110609391650030004236271161198917478149407972601791080340416289522217831842149279835538796034145741705373260384364903648065949011881512804322037289046950099011614522708194273468684859406801874157091529832148222328299288313083228093653170268904942449665323783818837931336547816485989215516595643436703960125472804421950729227643775424995665390226098088488420100130103202545344023974701370579360668132145456011523239722123972684999166344157597865557207037334973510208063181572044506866127826166579937040799836980091022005227178463709705067496410505882900234294540070905246120172453872075795510741926131987494670876917571998688053327730386004753469605546394017699620434253124319245235951810127531919801525874034179211514938805278780987944202820044826836109855430759065424813753651861469841704258187919970528928014675879351276720340559579087972476623295822223256347083299401660105337688691448979289075269637164710330897111913041037586535860271603582020639730941234472075388266368302732481390873310271931083219652448099445946604508098857863980957866978377596203570650593766139429847724575195075838452342188246180245513226058215761886236117380443043123188663192557854403152613949044031622909678213681857845610600954804960235913101079902222795134480736652982982306766632503957094862757822086275527390021267896804427483984420687621291870473384994140112770042378319084403156285698992746136555119097875362718125399775260346689252902321886998054019345588595360882048534031439836686597038653268510372778634363156608776954240697148964494042709310374969327886434368252414271912929608815903278270130329523383727733574741070197722548872017944205273685505986533424364627848013888396034174195379168695180492227053312063678932172222808341805857627358459578999746596179020196440429462841970944863716607653637977238621947036196999534721518103803089055338642715622544832669893314068824953086229567991687773603189917159336397138091179415373638117214282655295695467216071610962126082335992862627083119989314386660945600212361119249805546888549357680640983743435475894367263052538391431935336285944258022846877654513700214633120016244441249251826123582445040257840215040969299396786619548604192248415312061624538590283139363792089759812403413123484683794638570913639713120216938900897808778338252786564[+++]
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.731s
user	0m0.414s
sys	0m0.195s


'84.163.'
************** PARI *****************
Host 84.163.68.223 (84.163.68.223)
Time: Thu Aug  3 08:29:46 2006

Input: integrate(3^x,x);

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? ? 
Goodbye!

Errors/timing (if any):

  ***   unknown function or error in formal parameters: integrate(3^x,x);
                                                        ^-----------------

Timing:
real	0m0.100s
user	0m0.010s
sys	0m0.004s


'72.30.1'
************** PARI *****************
Host 72.30.129.106 (72.30.129.106)
Time: Thu Aug  3 05:23:34 2006

Input: y=210; for(x=1,8,y=sumdiv(y,x,x)-y;print1(y,","))

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? 366,378,582,594,846,1026,1374,1386,
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.107s
user	0m0.009s
sys	0m0.006s


'62.104.'
************** PARI *****************
Host 62.104.129.89 (62.104.129.89)
Time: Wed Aug  2 22:03:34 2006

Input: 2+2;

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? ? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.013s
user	0m0.005s
sys	0m0.009s


'66.69.2'
************** PARI *****************
Host 66.69.229.35 (66.69.229.35)
Time: Wed Aug  2 20:12:55 2006

Input: 35.10 X 7

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = X7
? 
Goodbye!

Errors/timing (if any):

  ***   Warning: unused characters: X7.

Timing:
real	0m0.067s
user	0m0.004s
sys	0m0.008s


'146.186'
************** PARI *****************
Host 146.186.134.174 (146.186.134.174)
Time: Wed Aug  2 10:49:31 2006

Input: sum(n=1,20,1/(1-q^n));


Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? ? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.091s
user	0m0.007s
sys	0m0.009s


'146.186'
************** PARI *****************
Host 146.186.134.174 (146.186.134.174)
Time: Wed Aug  2 10:43:15 2006

Input: sum(n*q^n/(1-q^n), n=1..20);


Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? ? 
Goodbye!

Errors/timing (if any):

  ***   expected character: '=' instead of: sum(n*q^n/(1-q^n),n=1..20
                                                 ^--------------------

Timing:
real	0m0.013s
user	0m0.006s
sys	0m0.008s


'71.111.'
************** PARI *****************
Host 71.111.254.139 (71.111.254.139)
Time: Wed Aug  2 07:37:05 2006

Input: 1057.33-3448.41

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = -2391.0800000000000000000000000000000000
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.119s
user	0m0.009s
sys	0m0.003s


'140.105'
************** PARI *****************
Host 140.105.63.31 (140.105.63.31)
Time: Wed Aug  2 04:25:35 2006

Input: "Replace this by some code, then click [SAGE] or [PARI]!"

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = "Replace this by some code, then click [SAGE] or [PARI]!"
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.013s
user	0m0.006s
sys	0m0.008s


'72.30.9'
************** PARI *****************
Host 72.30.97.221 (72.30.97.221)
Time: Tue Aug  1 22:06:17 2006

Input: for(n=1,20, print1(n,": ",valuation(n!,2),", ") )

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? 1: 0, 2: 1, 3: 1, 4: 3, 5: 3, 6: 4, 7: 4, 8: 7, 9: 7, 10: 8, 11: 8, 12: 10, 13: 10, 14: 11, 15: 11, 16: 15, 17: 15, 18: 16, 19: 16, 20: 18, 
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.013s
user	0m0.006s
sys	0m0.006s


'68.126.'
************** PARI *****************
Host 68.126.176.117 (68.126.176.117)
Time: Tue Aug  1 21:30:17 2006

Input: "Replace this by some code, then click [SAGE] or [PARI]!"

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = "Replace this by some code, then click [SAGE] or [PARI]!"
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.013s
user	0m0.006s
sys	0m0.006s


'72.30.9'
************** PARI *****************
Host 72.30.98.145 (72.30.98.145)
Time: Tue Aug  1 18:17:45 2006

Input: for(n=1,20, print1(n,": ",valuation(n!,2),", ") )

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? 1: 0, 2: 1, 3: 1, 4: 3, 5: 3, 6: 4, 7: 4, 8: 7, 9: 7, 10: 8, 11: 8, 12: 10, 13: 10, 14: 11, 15: 11, 16: 15, 17: 15, 18: 16, 19: 16, 20: 18, 
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.456s
user	0m0.005s
sys	0m0.014s


'12.34.2'
************** PARI *****************
Host 12.34.246.7 (12.34.246.7)
Time: Tue Aug  1 13:25:12 2006

Input: 200.00 x 8.25%

Output: WARNING: PARI command contains unsafe command '%', so it will not be executed.

'71.121.'
************** PARI *****************
Host 71.121.101.100 (71.121.101.100)
Time: Tue Aug  1 09:38:42 2006

Input: "Replace this by some code, then click [SAGE] or [PARI]!"

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = "Replace this by some code, then click [SAGE] or [PARI]!"
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.014s
user	0m0.004s
sys	0m0.008s


'134.76.'
************** PARI *****************
Host 134.76.82.189 (134.76.82.189)
Time: Tue Aug  1 09:19:15 2006

Input: solve(x*x+x=2)


Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? ? 
Goodbye!

Errors/timing (if any):

  ***   expected character: '=' instead of: solve(x*x+x=2)
                                                   ^-------

Timing:
real	0m0.109s
user	0m0.008s
sys	0m0.006s


'134.76.'
************** PARI *****************
Host 134.76.82.190 (134.76.82.190)
Time: Tue Aug  1 02:22:39 2006

Input: algdep(sqrt(2)+sqrt(3),6)
algdep(1.4142135,40)


Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = x^4 - 10*x^2 + 1
? %2 = x^2 - 2
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.014s
user	0m0.008s
sys	0m0.005s


'134.76.'
************** PARI *****************
Host 134.76.82.190 (134.76.82.190)
Time: Tue Aug  1 02:22:31 2006

Input: algdep(sqrt(2)+sqrt(3),6)
algdep(1.414213,40)


Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = x^4 - 10*x^2 + 1
? %2 = 0.5854497518247262726
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.022s
user	0m0.013s
sys	0m0.008s


'134.76.'
************** PARI *****************
Host 134.76.82.190 (134.76.82.190)
Time: Tue Aug  1 02:22:25 2006

Input: algdep(sqrt(2)+sqrt(3),6)
algdep(1.414213,4)


Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = x^4 - 10*x^2 + 1
? %2 = 11995.101306366822445
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.071s
user	0m0.009s
sys	0m0.007s


'134.76.'
************** PARI *****************
Host 134.76.82.190 (134.76.82.190)
Time: Tue Aug  1 02:22:14 2006

Input: algdep(sqrt(2)+sqrt(3),6)
algdep(1.414213562,4)


Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = x^4 - 10*x^2 + 1
? %2 = x^4 - 4*x^2 + 4
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.027s
user	0m0.005s
sys	0m0.009s


'134.76.'
************** PARI *****************
Host 134.76.82.190 (134.76.82.190)
Time: Tue Aug  1 02:22:05 2006

Input: algdep(sqrt(2)+sqrt(3),6)
algdep(1.414213562373,4)


Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = x^4 - 10*x^2 + 1
? %2 = x^4 - 4*x^2 + 4
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.044s
user	0m0.008s
sys	0m0.007s


'134.76.'
************** PARI *****************
Host 134.76.82.190 (134.76.82.190)
Time: Tue Aug  1 02:21:53 2006

Input: algdep(sqrt(2)+sqrt(3),6)
algdep(1.414213562373095,4)


Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = x^4 - 10*x^2 + 1
? %2 = x^3 - x^2 - 2*x + 2
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.015s
user	0m0.009s
sys	0m0.006s


'134.76.'
************** PARI *****************
Host 134.76.82.190 (134.76.82.190)
Time: Tue Aug  1 02:21:36 2006

Input: algdep(sqrt(2)+sqrt(3),6)
algdep(1.41421356237309503,4)


Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = x^4 - 10*x^2 + 1
? %2 = x^2 - 2
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.031s
user	0m0.010s
sys	0m0.004s


'134.76.'
************** PARI *****************
Host 134.76.82.190 (134.76.82.190)
Time: Tue Aug  1 02:21:30 2006

Input: algdep(sqrt(2)+sqrt(3),6)
algdep(1.4142135623730950,4)


Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = x^4 - 10*x^2 + 1
? %2 = x^3 - x^2 - 2*x + 2
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.032s
user	0m0.008s
sys	0m0.005s


'134.76.'
************** PARI *****************
Host 134.76.82.190 (134.76.82.190)
Time: Tue Aug  1 02:21:23 2006

Input: algdep(sqrt(2)+sqrt(3),6)
algdep(1.41421356237309504,4)


Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = x^4 - 10*x^2 + 1
? %2 = x^2 - 2
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.013s
user	0m0.009s
sys	0m0.005s


'134.76.'
************** PARI *****************
Host 134.76.82.190 (134.76.82.190)
Time: Tue Aug  1 02:21:13 2006

Input: algdep(sqrt(2)+sqrt(3),6)
algdep(1.41421356237309504,4)


Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = x^4 - 10*x^2 + 1
? %2 = x^2 - 2
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.063s
user	0m0.005s
sys	0m0.008s


'134.76.'
************** PARI *****************
Host 134.76.82.190 (134.76.82.190)
Time: Tue Aug  1 02:21:06 2006

Input: algdep(sqrt(2)+sqrt(3),6)
algdep(1.4142135623730950,4)


Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = x^4 - 10*x^2 + 1
? %2 = x^3 - x^2 - 2*x + 2
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.096s
user	0m0.007s
sys	0m0.006s


'134.76.'
************** PARI *****************
Host 134.76.82.190 (134.76.82.190)
Time: Tue Aug  1 02:20:55 2006

Input: algdep(sqrt(2)+sqrt(3),6)
algdep(1.414213562373095,4)


Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = x^4 - 10*x^2 + 1
? %2 = x^3 - x^2 - 2*x + 2
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.013s
user	0m0.008s
sys	0m0.005s


'134.76.'
************** PARI *****************
Host 134.76.82.190 (134.76.82.190)
Time: Tue Aug  1 02:20:46 2006

Input: algdep(sqrt(2)+sqrt(3),6)
algdep(1.4142135623730950488,4)


Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = x^4 - 10*x^2 + 1
? %2 = x^2 - 2
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.013s
user	0m0.009s
sys	0m0.004s


'134.76.'
************** PARI *****************
Host 134.76.82.190 (134.76.82.190)
Time: Tue Aug  1 02:20:38 2006

Input: algdep(sqrt(2)+sqrt(3),6)
algdep(1.41421356237309504880168,4)


Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = x^4 - 10*x^2 + 1
? %2 = x^2 - 2
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.066s
user	0m0.007s
sys	0m0.006s


'134.76.'
************** PARI *****************
Host 134.76.82.190 (134.76.82.190)
Time: Tue Aug  1 02:20:29 2006

Input: algdep(sqrt(2)+sqrt(3),6)
algdep(1.414213562373095048801688724,4)


Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = x^4 - 10*x^2 + 1
? %2 = x^2 - 2
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.099s
user	0m0.006s
sys	0m0.007s


'134.76.'
************** PARI *****************
Host 134.76.82.190 (134.76.82.190)
Time: Tue Aug  1 02:20:21 2006

Input: algdep(sqrt(2)+sqrt(3),6)
algdep(1.4142135623730950488016887242096,4)


Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = x^4 - 10*x^2 + 1
? %2 = x^2 - 2
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.013s
user	0m0.006s
sys	0m0.008s


'134.76.'
************** PARI *****************
Host 134.76.82.190 (134.76.82.190)
Time: Tue Aug  1 02:20:11 2006

Input: algdep(sqrt(2)+sqrt(3),6)
algdep(1.4142135623730950488016887242096980,4)


Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = x^4 - 10*x^2 + 1
? %2 = x^2 - 2
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.046s
user	0m0.009s
sys	0m0.004s


'134.76.'
************** PARI *****************
Host 134.76.82.190 (134.76.82.190)
Time: Tue Aug  1 02:20:01 2006

Input: algdep(sqrt(2)+sqrt(3),6)
algdep(1.4142135623730950488016887242096980786,4)


Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = x^4 - 10*x^2 + 1
? %2 = x^2 - 2
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.135s
user	0m0.007s
sys	0m0.007s


'134.76.'
************** PARI *****************
Host 134.76.82.190 (134.76.82.190)
Time: Tue Aug  1 02:19:34 2006

Input: algdep(sqrt(2)+sqrt(3),6)
x=sqrt(2)



Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = x^4 - 10*x^2 + 1
? %2 = 1.4142135623730950488016887242096980786
? ? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.111s
user	0m0.006s
sys	0m0.009s


'134.76.'
************** PARI *****************
Host 134.76.82.190 (134.76.82.190)
Time: Tue Aug  1 02:19:17 2006

Input: algdep(sqrt(2)+sqrt(3),6)
algdep(3.1622776,4)


Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = x^4 - 10*x^2 + 1
? %2 = 8553.919552935008545
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.014s
user	0m0.005s
sys	0m0.010s


'134.76.'
************** PARI *****************
Host 134.76.82.190 (134.76.82.190)
Time: Tue Aug  1 02:18:52 2006

Input: algdep(sqrt(2)+sqrt(3),6)
algdep(67.68755647,10)


Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = x^4 - 10*x^2 + 1
? %2 = 1
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.013s
user	0m0.004s
sys	0m0.008s


'134.76.'
************** PARI *****************
Host 134.76.82.190 (134.76.82.190)
Time: Tue Aug  1 02:18:32 2006

Input: algdep(sqrt(2)+sqrt(3),6)


Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = x^4 - 10*x^2 + 1
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.124s
user	0m0.006s
sys	0m0.008s


'134.76.'
************** PARI *****************
Host 134.76.82.190 (134.76.82.190)
Time: Tue Aug  1 02:17:45 2006

Input: ?algdep
?


Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? algdep(x,n,{flag=0}): algebraic relations up to degree n of x, using 
lindep([1,x,...,x^(n-1)], flag). 

? Help topics: for a list of relevant subtopics, type ?n for n in
  0: user-defined identifiers (variable, alias, function)
  1: Standard monadic or dyadic OPERATORS
  2: CONVERSIONS and similar elementary functions
  3: TRANSCENDENTAL functions
  4: NUMBER THEORETICAL functions
  5: Functions related to ELLIPTIC CURVES
  6: Functions related to general NUMBER FIELDS
  7: POLYNOMIALS and power series
  8: Vectors, matrices, LINEAR ALGEBRA and sets
  9: SUMS, products, integrals and similar functions
 10: GRAPHIC functions
 11: PROGRAMMING under GP
 12: The PARI community

Also:
  ? functionname (short on-line help)
  ?\             (keyboard shortcuts)
  ?.             (member functions)

? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.013s
user	0m0.006s
sys	0m0.008s


'134.76.'
************** PARI *****************
Host 134.76.82.190 (134.76.82.190)
Time: Tue Aug  1 02:17:27 2006

Input: ?algdep


Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? algdep(x,n,{flag=0}): algebraic relations up to degree n of x, using 
lindep([1,x,...,x^(n-1)], flag). 

? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.033s
user	0m0.007s
sys	0m0.005s


'134.76.'
************** PARI *****************
Host 134.76.82.190 (134.76.82.190)
Time: Tue Aug  1 02:17:15 2006

Input: ?8

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? 
algdep           charpoly         concat           lindep
listcreate       listinsert       listkill         listput
listsort         matadjoint       matcompanion     matdet
matdetint        matdiagonal      mateigen         matfrobenius
mathess          mathilbert       mathnf           mathnfmod
mathnfmodid      matid            matimage         matimagecompl
matindexrank     matintersect     matinverseimage  matisdiagonal
matker           matkerint        matmuldiagonal   matmultodiagonal
matpascal        matrank          matrix           matrixqz
matsize          matsnf           matsolve         matsolvemod
matsupplement    mattranspose     qfgaussred       qfjacobi
qflll            qflllgram        qfminim          qfperfection
qfrep            qfsign           setintersect     setisset
setminus         setsearch        setunion         trace
vecextract       vecsort          vector           vectorsmall
vectorv          

? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.013s
user	0m0.007s
sys	0m0.005s


'134.76.'
************** PARI *****************
Host 134.76.82.190 (134.76.82.190)
Time: Tue Aug  1 02:17:06 2006

Input: ?7

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? 
O                  deriv              eval               factorpadic
intformal          padicappr          polcoeff           polcyclo
poldegree          poldisc            poldiscreduced     polhensellift
polinterpolate     polisirreducible   pollead            pollegendre
polrecip           polresultant       polroots           polrootsmod
polrootspadic      polsturm           polsubcyclo        polsylvestermatrix
polsym             poltchebi          polzagier          serconvol
serlaplace         serreverse         subst              substpol
taylor             thue               thueinit           

? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.013s
user	0m0.007s
sys	0m0.007s


'134.76.'
************** PARI *****************
Host 134.76.82.190 (134.76.82.190)
Time: Tue Aug  1 02:17:00 2006

Input: ?6

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? 
bnfcertify         bnfclassunit       bnfclgp            bnfdecodemodule
bnfinit            bnfisintnorm       bnfisnorm          bnfisprincipal
bnfissunit         bnfisunit          bnfmake            bnfnarrow
bnfreg             bnfsignunit        bnfsunit           bnfunit
bnrL1              bnrclass           bnrclassno         bnrclassnolist
bnrconductor       bnrconductorofchar bnrdisc            bnrdisclist
bnrinit            bnrisconductor     bnrisprincipal     bnrrootnumber
bnrstark           dirzetak           factornf           galoisexport
galoisfixedfield   galoisidentify     galoisinit         galoisisabelian
galoispermtopol    galoissubcyclo     galoissubfields    galoissubgroups
idealadd           idealaddtoone      idealappr          idealchinese
idealcoprime       idealdiv           idealfactor        idealhnf
idealintersect     idealinv           ideallist          ideallistarch
ideallog           idealmin           idealmul           idealnorm
idealpow           idealprimedec      idealprincipal     idealred
idealstar          idealtwoelt        idealval           ideleprincipal
matalgtobasis      matbasistoalg      modreverse         newtonpoly
nfalgtobasis       nfbasis            nfbasistoalg       nfdetint
nfdisc             nfeltdiv           nfeltdiveuc        nfeltdivmodpr
nfeltdivrem        nfeltmod           nfeltmul           nfeltmulmodpr
nfeltpow           nfeltpowmodpr      nfeltreduce        nfeltreducemodpr
nfeltval           nffactor           nffactormod        nfgaloisapply
nfgaloisconj       nfhilbert          nfhnf              nfhnfmod
nfinit             nfisideal          nfisincl           nfisisom
nfkermodpr         nfmodprinit        nfnewprec          nfroots
nfrootsof1         nfsnf              nfsolvemodpr       nfsubfields
polcompositum      polgalois          polred             polredabs
polredord          poltschirnhaus     rnfalgtobasis      rnfbasis
rnfbasistoalg      rnfcharpoly        rnfconductor       rnfdedekind
rnfdet             rnfdisc            rnfeltabstorel     rnfeltdown
rnfeltreltoabs     rnfeltup           rnfequation        rnfhnfbasis
rnfidealabstorel   rnfidealdown       rnfidealhnf        rnfidealmul
rnfidealnormabs    rnfidealnormrel    rnfidealreltoabs   rnfidealtwoelt
rnfidealup         rnfinit            rnfisfree          rnfisnorm
rnfisnorminit      rnfkummer          rnflllgram         rnfnormgroup
rnfpolred          rnfpolredabs       rnfpseudobasis     rnfsteinitz
subgrouplist       zetak              zetakinit          

? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.013s
user	0m0.004s
sys	0m0.009s


'134.76.'
************** PARI *****************
Host 134.76.82.190 (134.76.82.190)
Time: Tue Aug  1 02:16:45 2006

Input: ?

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? Help topics: for a list of relevant subtopics, type ?n for n in
  0: user-defined identifiers (variable, alias, function)
  1: Standard monadic or dyadic OPERATORS
  2: CONVERSIONS and similar elementary functions
  3: TRANSCENDENTAL functions
  4: NUMBER THEORETICAL functions
  5: Functions related to ELLIPTIC CURVES
  6: Functions related to general NUMBER FIELDS
  7: POLYNOMIALS and power series
  8: Vectors, matrices, LINEAR ALGEBRA and sets
  9: SUMS, products, integrals and similar functions
 10: GRAPHIC functions
 11: PROGRAMMING under GP
 12: The PARI community

Also:
  ? functionname (short on-line help)
  ?\             (keyboard shortcuts)
  ?.             (member functions)

? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.012s
user	0m0.007s
sys	0m0.005s


'134.76.'
************** PARI *****************
Host 134.76.82.190 (134.76.82.190)
Time: Tue Aug  1 02:16:34 2006

Input: ?algred

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? algred: unknown identifier

? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.105s
user	0m0.005s
sys	0m0.009s


'72.30.1'
************** PARI *****************
Host 72.30.129.106 (72.30.129.106)
Time: Tue Aug  1 01:34:39 2006

Input: y=210; for(x=1,8,y=sumdiv(y,x,x)-y;print1(y,","))

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? 366,378,582,594,846,1026,1374,1386,
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.012s
user	0m0.006s
sys	0m0.006s


'67.42.1'
************** PARI *****************
Host 67.42.147.15 (67.42.147.15)
Time: Mon Jul 31 22:58:30 2006

Input: 4(-2)� + 8(-2) + 3(-2) + 6 

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = 4
? 
Goodbye!

Errors/timing (if any):

  ***   Warning: unused characters: (-2)+8(-2)+3(-2)+6.

Timing:
real	0m0.012s
user	0m0.006s
sys	0m0.006s


'67.42.1'
************** PARI *****************
Host 67.42.147.15 (67.42.147.15)
Time: Mon Jul 31 22:58:04 2006

Input: 4(-2)� + 8(-2) + 3(-2) + 6 

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = 4
? 
Goodbye!

Errors/timing (if any):

  ***   Warning: unused characters: (-2)+8(-2)+3(-2)+6.

Timing:
real	0m0.032s
user	0m0.006s
sys	0m0.006s


'68.39.8'
************** PARI *****************
Host 68.39.84.231 (68.39.84.231)
Time: Mon Jul 31 18:59:13 2006

Input: (x/2)=(3x/4)+5

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? ? 
Goodbye!

Errors/timing (if any):

  ***   unexpected character: (x/2)=(3x/4)+5
                                   ^---------

Timing:
real	0m0.012s
user	0m0.006s
sys	0m0.007s


'68.39.8'
************** PARI *****************
Host 68.39.84.231 (68.39.84.231)
Time: Mon Jul 31 18:58:22 2006

Input: x/2=3x/4+5

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? ? 
Goodbye!

Errors/timing (if any):

  ***   unexpected character: x/2=3x/4+5
                                 ^-------

Timing:
real	0m0.012s
user	0m0.004s
sys	0m0.007s


'131.172'
************** PARI *****************
Host 131.172.42.15 (131.172.42.15)
Time: Mon Jul 31 18:09:53 2006

Input: default(realprecision,100)
Pi

Output: WARNING: PARI command contains unsafe command 'default', so it will not be executed.

'131.172'
************** PARI *****************
Host 131.172.42.15 (131.172.42.15)
Time: Mon Jul 31 18:08:46 2006

Input: Pi

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = 3.1415926535897932384626433832795028842
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.086s
user	0m0.006s
sys	0m0.006s


'65.64.1'
************** PARI *****************
Host 65.64.101.176 (65.64.101.176)
Time: Mon Jul 31 18:04:55 2006

Input: 163 divided by 7


Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = dividedby7
? 
Goodbye!

Errors/timing (if any):

  ***   Warning: unused characters: dividedby7.

Timing:
real	0m0.013s
user	0m0.008s
sys	0m0.004s


'164.107'
************** PARI *****************
Host 164.107.204.151 (164.107.204.151)
Time: Mon Jul 31 18:04:27 2006

Input: znorder(Mod(17, 7))

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = 6
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.047s
user	0m0.006s
sys	0m0.006s


'164.107'
************** PARI *****************
Host 164.107.204.151 (164.107.204.151)
Time: Mon Jul 31 18:00:27 2006

Input: Mod(17, 7)

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = Mod(3, 7)
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.064s
user	0m0.009s
sys	0m0.006s


'83.130.'
************** PARI *****************
Host 83.130.58.173 (83.130.58.173)
Time: Mon Jul 31 13:55:31 2006

Input: c100 = 1522605027922533360535618378132637429718068114961380688657908494580122963258952897654000350692006139;
factor(c100);

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? ? 
Errors/timing (if any):

/var/www/cgi-bin/calc/gp: line 1:  5488 Killed                  ./gp-2.2.11 -s 256000000 -emacs

Timing:
real	0m21.011s
user	0m20.991s
sys	0m0.008s


'83.130.'
************** PARI *****************
Host 83.130.58.173 (83.130.58.173)
Time: Mon Jul 31 13:53:05 2006

Input: print("***",factor(129));


Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? ***[3, 1; 43, 1]
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.012s
user	0m0.005s
sys	0m0.007s


'83.130.'
************** PARI *****************
Host 83.130.58.173 (83.130.58.173)
Time: Mon Jul 31 13:51:51 2006

Input: factor(129^20+1)
/ra
?0
r=123456;
print(factor(r));
print("Hullo");

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = 
[2 1]

[41 1]

[281 1]

[5486561 1]

[138461441 1]

[93034702779013170299681 1]

? ? 
x 

? ? [2, 6; 3, 1; 643, 1]
? Hullo
? 
Goodbye!

Errors/timing (if any):

  ***   unexpected character: /ra
                              ^---

Timing:
real	0m0.049s
user	0m0.036s
sys	0m0.014s


'83.130.'
************** PARI *****************
Host 83.130.58.173 (83.130.58.173)
Time: Mon Jul 31 13:51:19 2006

Input: factor(129^20+1)
/ra
?0
r=123456;
print(factor(r));


Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = 
[2 1]

[41 1]

[281 1]

[5486561 1]

[138461441 1]

[93034702779013170299681 1]

? ? 
x 

? ? [2, 6; 3, 1; 643, 1]
? 
Goodbye!

Errors/timing (if any):

  ***   unexpected character: /ra
                              ^---

Timing:
real	0m0.051s
user	0m0.039s
sys	0m0.012s


'83.130.'
************** PARI *****************
Host 83.130.58.173 (83.130.58.173)
Time: Mon Jul 31 13:50:49 2006

Input: factor(129^20+1)
/ra
?0
r=123456;
print(factor(r));


Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = 
[2 1]

[41 1]

[281 1]

[5486561 1]

[138461441 1]

[93034702779013170299681 1]

? ? 
x 

? ? [2, 6; 3, 1; 643, 1]
? 
Goodbye!

Errors/timing (if any):

  ***   unexpected character: /ra
                              ^---

Timing:
real	0m0.049s
user	0m0.038s
sys	0m0.011s


'83.130.'
************** PARI *****************
Host 83.130.58.173 (83.130.58.173)
Time: Mon Jul 31 13:49:48 2006

Input: factor(129^20+1)
/ra
?0
r=123456;
factor(r);

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = 
[2 1]

[41 1]

[281 1]

[5486561 1]

[138461441 1]

[93034702779013170299681 1]

? ? 
x 

? ? ? 
Goodbye!

Errors/timing (if any):

  ***   unexpected character: /ra
                              ^---

Timing:
real	0m0.094s
user	0m0.042s
sys	0m0.009s


'83.130.'
************** PARI *****************
Host 83.130.58.173 (83.130.58.173)
Time: Mon Jul 31 11:52:18 2006

Input: factor(129)


Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = 
[3 1]

[43 1]

? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.012s
user	0m0.005s
sys	0m0.009s


'128.111'
************** PARI *****************
Host 128.111.88.139 (128.111.88.139)
Time: Mon Jul 31 09:35:01 2006

Input: qfbclassno(-1234567)


Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = 496
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.178s
user	0m0.007s
sys	0m0.008s


'72.30.1'
************** PARI *****************
Host 72.30.103.96 (72.30.103.96)
Time: Mon Jul 31 09:25:47 2006

Input: vector(20,x,floor((x+1)*sqrt(2))-floor(x*sqrt(2)))

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = [1, 2, 1, 2, 1, 1, 2, 1, 2, 1, 1, 2, 1, 2, 1, 2, 1, 1, 2, 1]
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.080s
user	0m0.006s
sys	0m0.007s


'193.170'
************** PARI *****************
Host 193.170.37.83 (193.170.37.83)
Time: Mon Jul 31 02:39:35 2006

Input: f=x^4+2*x^2+7
polred(f)
nf=nfinit(f);
factor(nf.disc);
forstep (A=2, 2000, 2, g1=x^4+A*x^2+A^2/2; g2=x^4-A*x^2-A^2/2; g3=x^4+A*x^2-A^2/2; g4=x^4-A*x^2+A^2/2; nf1=nfinit(g1); nf2=nfinit(g2); nf3=nfinit(g3); nf4=nfinit(g4);factor(nf1.disc);factor(nf2.disc);factor(nf3.disc);factor(nf4.disc);nfisisom(f,g1); print(A,"---",nfisisom(f,g1), nfisisom(f,g2),nfisisom(f,g3),nfisisom(f,g4)))
             

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = x^4 + 2*x^2 + 7
? %2 = [x - 1, x^2 + 6, x^4 - 12*x^2 + 252, x^4 + 2*x^2 + 7]
? ? ? 2---0000
4---0000
6---0000
8---0000
10---0000
12---0000
14---0000
16---0000
18---0000
20---0000
22---0000
24---0000
26---0000
28---0000
30---0000
32---0000
34---0000
36---0000
38---0000
40---0000
42---0000
44---0000
46---0000
48---0000
50---0000
52---0000
54---0000
56---0000
58---0000
60---0000
62---0000
64---0000
66---0000
68---0000
70---0000
72---0000
74---0000
76---0000
78---0000
80---0000
82---0000
84---0000
86---0000
88---0000
90---0000
92---0000
94---0000
96---0000
98---0000
100---0000
102---0000
104---0000
106---0000
108---0000
110---0000
112---0000
114---0000
116---0000
118---0000
120---0000
122---0000
124---0000
126---0000
128---0000
130---0000
132---0000
134---0000
136---0000
138---0000
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142---0000
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148---0000
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158---0000
160---0000
162---0000
164---0000
166---0000
168---0000
170---0000
172---0000
174---0000
176---0000
178---0000
180---0000
182---0000
184---0000
186---0000
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222---0000
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226---0000
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256---0000
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272---0000
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318---0000
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326---0000
328---0000
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430---0000
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436---0000
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458---0000
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466---0000
468---0000
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472---0000
474---0000
476---0000
478---0000
480---0000
482---0000
484---0000
486---0000
488---0000
490---0000
492---0000
494---0000
496---0000
498---0000
500---0000
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504---0000
506---0000
508---0000
510---0000
512---0000
514---0000
516---0000
518---0000
520---0000
522---0000
524---0000
526---0000
528---0000
530---0000
532---0000
534---0000
536---0000
538---0000
540---0000
542---0000
544---0000
546---0000
548---0000
550---0000
552---0000
554---0000
556---0000
558---0000
560---0000
562---0000
564---0000
566---0000
568---0000
570---0000
572---0000
574---0000
576---0000
578---0000
580---0000
582---0000
584---0000
586---0000
588---0000
590---0000
592---0000
594---0000
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598---0000
600---0000
602---0000
604---0000
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608---0000
610---0000
612---0000
614---0000
616---0000
618---0000
620---0000
622---0000
624---0000
626---0000
628---0000
630---0000
632---0000
634---0000
636---0000
638---0000
640---0000
642---0000
644---0000
646---0000
648---0000
650---0000
652---0000
654---0000
656---0000
658---0000
660---0000
662---0000
664---0000
666---0000
668---0000
670---0000
672---0000
674---0000
676---0000
678---0000
680---0000
682---0000
684---0000
686---0000
688---0000
690---0000
692---0000
694---0000
696---0000
698---0000
700---0000
702---0000
704---0000
706---0000
708---0000
710---0000
712---0000
714---0000
716---0000
718---0000
720---0000
722---0000
724---0000
726---0000
728---0000
730---0000
732---0000
734---0000
736---0000
738---0000
740---0000
742---0000
744---0000
746---0000
748---0000
750---0000
752---0000
754---0000
756---0000
758---0000
760---0000
762---0000
764---0000
766---0000
768---0000
770---0000
772---0000
774---0000
776---0000
778---0000
780---0000
782---0000
784---0000
786---0000
788---0000
790---0000
792---0000
794---0000
796---0000
798---0000
800---0000
802---0000
804---0000
806---0000
808---0000
810---0000
812---0000
814---0000
816---0000
818---0000
820---0000
822---0000
824---0000
826---0000
828---0000
830---0000
832---0000
834---0000
836---0000
838---0000
840---0000
842---0000
844---0000
846---0000
848---0000
850---0000
852---0000
854---0000
856---0000
858---0000
860---0000
862---0000
864---0000
866---0000
868---0000
870---0000
872---0000
874---0000
876---0000
878---0000
880---0000
882---0000
884---0000
886---0000
888---0000
890---0000
892---0000
894---0000
896---0000
898---0000
900---0000
902---0000
904---0000
906---0000
908---0000
910---0000
912---0000
914---0000
916---0000
918---0000
920---0000
922---0000
924---0000
926---0000
928---0000
930---0000
932---0000
934---0000
936---0000
938---0000
940---0000
942---0000
944---0000
946---0000
948---0000
950---0000
952---0000
954---0000
956---0000
958---0000
960---0000
962---0000
964---0000
966---0000
968---0000
970---0000
972---0000
974---0000
976---0000
978---0000
980---0000
982---0000
984---0000
986---0000
988---0000
990---0000
992---0000
994---0000
996---0000
998---0000
1000---0000
1002---0000
1004---0000
1006---0000
1008---0000
1010---0000
1012---0000
1014---0000
1016---0000
1018---0000
1020---0000
1022---0000
1024---0000
1026---0000
1028---0000
1030---0000
1032---0000
1034---0000
1036---0000
1038---0000
1040---0000
1042---0000
1044---0000
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1048---0000
1050---0000
1052---0000
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1056---0000
1058---0000
1060---0000
1062---0000
1064---0000
1066---0000
1068---0000
1070---0000
1072---0000
1074---0000
1076---0000
1078---0000
1080---0000
1082---0000
1084---0000
1086---0000
1088---0000
1090---0000
1092---0000
1094---0000
1096---0000
1098---0000
1100---0000
1102---0000
1104---0000
1106---0000
1108---0000
1110---0000
1112---0000
1114---0000
1116---0000
1118---0000
1120---0000
1122---0000
1124---0000
1126---0000
1128---0000
1130---0000
1132---0000
1134---0000
1136---0000
1138---0000
1140---0000
1142---0000
1144---0000
1146---0000
1148---0000
1150---0000
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1154---0000
1156---0000
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1160---0000
1162---0000
1164---0000
1166---0000
1168---0000
1170---0000
1172---0000
1174---0000
1176---0000
1178---0000
1180---0000
1182---0000
1184---0000
1186---0000
1188---0000
1190---0000
1192---0000
1194---0000
1196---0000
1198---0000
1200---0000
1202---0000
1204---0000
1206---0000
1208---0000
1210---0000
1212---0000
1214---0000
1216---0000
1218---0000
1220---0000
1222---0000
1224---0000
1226---0000
1228---0000
1230---0000
1232---0000
1234---0000
1236---0000
1238---0000
1240---0000
1242---0000
1244---0000
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1248---0000
1250---0000
1252---0000
1254---0000
1256---0000
1258---0000
1260---0000
1262---0000
1264---0000
1266---0000
1268---0000
1270---0000
1272---0000
1274---0000
1276---0000
1278---0000
1280---0000
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1284---0000
1286---0000
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1300---0000
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1312---0000
1314---0000
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1326---0000
1328---0000
1330---0000
1332---0000
1334---0000
1336---0000
1338---0000
1340---0000
1342---0000
1344---0000
1346---0000
1348---0000
1350---0000
1352---0000
1354---0000
1356---0000
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1360---0000
1362---0000
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1366---0000
1368---0000
1370---0000
1372---0000
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1376---0000
1378---0000
1380---0000
1382---0000
1384---0000
1386---0000
1388---0000
1390---0000
1392---0000
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1398---0000
1400---0000
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1430---0000
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1434---0000
1436---0000
1438---0000
1440---0000
1442---0000
1444---0000
1446---0000
1448---0000
1450---0000
1452---0000
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1456---0000
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1460---0000
1462---0000
1464---0000
1466---0000
1468---0000
1470---0000
1472---0000
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1476---0000
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1484---0000
1486---0000
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1490---0000
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1500---0000
1502---0000
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1522---0000
1524---0000
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1528---0000
1530---0000
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1546---0000
1548---0000
1550---0000
1552---0000
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1556---0000
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1562---0000
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1650---0000
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1656---0000
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1660---0000
1662---0000
1664---0000
1666---0000
1668---0000
1670---0000
1672---0000
1674---0000
1676---0000
1678---0000
1680---0000
1682---0000
1684---0000
1686---0000
1688---0000
1690---0000
1692---0000
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1696---0000
1698---0000
1700---0000
1702---0000
1704---0000
1706---0000
1708---0000
1710---0000
1712---0000
1714---0000
1716---0000
1718---0000
1720---0000
1722---0000
1724---0000
1726
 ** WARNING: Output too long, hence truncated.
Errors/timing (if any):


Timing:
real	0m7.495s
user	0m3.858s
sys	0m0.015s


'193.170'
************** PARI *****************
Host 193.170.37.83 (193.170.37.83)
Time: Mon Jul 31 01:56:58 2006

Input: f=x^4+2*x^2+7
polred(f)
nf=nfinit(f);
factor(nf.disc);
forstep (A=2, 1000, 2, g1=x^4+A*x^2+A^2/2; g2=x^4-A*x^2-A^2/2; g3=x^4+A*x^2-A^2/2; g4=x^4-A*x^2+A^2/2; nf1=nfinit(g1); nf2=nfinit(g2); nf3=nfinit(g3); nf4=nfinit(g4);factor(nf1.disc);factor(nf2.disc);factor(nf3.disc);factor(nf4.disc);nfisisom(f,g1); print(A,"---",nfisisom(f,g1), nfisisom(f,g2),nfisisom(f,g3),nfisisom(f,g4)))
             

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = x^4 + 2*x^2 + 7
? %2 = [x - 1, x^2 + 6, x^4 - 12*x^2 + 252, x^4 + 2*x^2 + 7]
? ? ? 2---0000
4---0000
6---0000
8---0000
10---0000
12---0000
14---0000
16---0000
18---0000
20---0000
22---0000
24---0000
26---0000
28---0000
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790---0000
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822---0000
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830---0000
832---0000
834---0000
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840---0000
842---0000
844---0000
846---0000
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850---0000
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854---0000
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858---0000
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866---0000
868---0000
870---0000
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890---0000
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914---0000
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922---0000
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926---0000
928---0000
930---0000
932---0000
934---0000
936---0000
938---0000
940---0000
942---0000
944---0000
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948---0000
950---0000
952---0000
954---0000
956---0000
958---0000
960---0000
962---0000
964---0000
966---0000
968---0000
970---0000
972---0000
974---0000
976---0000
978---0000
980---0000
982---0000
984---0000
986---0000
988---0000
990---0000
992---0000
994---0000
996---0000
998---0000
1000---0000
? ? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m3.692s
user	0m1.864s
sys	0m0.012s


'193.170'
************** PARI *****************
Host 193.170.37.83 (193.170.37.83)
Time: Mon Jul 31 01:56:47 2006

Input: f=x^4+2*x^2+7
polred(f)
nf=nfinit(f);
factor(nf.disc);
forstep (A=0, 1000, 2, g1=x^4+A*x^2+A^2/2; g2=x^4-A*x^2-A^2/2; g3=x^4+A*x^2-A^2/2; g4=x^4-A*x^2+A^2/2; nf1=nfinit(g1); nf2=nfinit(g2); nf3=nfinit(g3); nf4=nfinit(g4);factor(nf1.disc);factor(nf2.disc);factor(nf3.disc);factor(nf4.disc);nfisisom(f,g1); print(A,"---",nfisisom(f,g1), nfisisom(f,g2),nfisisom(f,g3),nfisisom(f,g4)))
             

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = x^4 + 2*x^2 + 7
? %2 = [x - 1, x^2 + 6, x^4 - 12*x^2 + 252, x^4 + 2*x^2 + 7]
? ? ? ? ? 
Goodbye!

Errors/timing (if any):

  *** nfinit: reducible polynomial in nfinit.

Timing:
real	0m0.015s
user	0m0.009s
sys	0m0.007s


'193.170'
************** PARI *****************
Host 193.170.37.83 (193.170.37.83)
Time: Mon Jul 31 01:56:37 2006

Input: f=x^4+2*x^2+7
polred(f)
nf=nfinit(f);
factor(nf.disc);
forstep (A=1, 1000, 2, g1=x^4+A*x^2+A^2/2; g2=x^4-A*x^2-A^2/2; g3=x^4+A*x^2-A^2/2; g4=x^4-A*x^2+A^2/2; nf1=nfinit(g1); nf2=nfinit(g2); nf3=nfinit(g3); nf4=nfinit(g4);factor(nf1.disc);factor(nf2.disc);factor(nf3.disc);factor(nf4.disc);nfisisom(f,g1); print(A,"---",nfisisom(f,g1), nfisisom(f,g2),nfisisom(f,g3),nfisisom(f,g4)))
             

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = x^4 + 2*x^2 + 7
? %2 = [x - 1, x^2 + 6, x^4 - 12*x^2 + 252, x^4 + 2*x^2 + 7]
? ? ? ? ? 
Goodbye!

Errors/timing (if any):

  *** nfinit: polynomial not in Z[X] in nfinit.

Timing:
real	0m0.109s
user	0m0.009s
sys	0m0.006s


'193.170'
************** PARI *****************
Host 193.170.37.83 (193.170.37.83)
Time: Mon Jul 31 01:56:10 2006

Input: f=x^4+2*x^2+7
polred(f)
nf=nfinit(f);
factor(nf.disc);
forstep (A=1300, 3300, 2, g1=x^4+A*x^2+A^2/2; g2=x^4-A*x^2-A^2/2; g3=x^4+A*x^2-A^2/2; g4=x^4-A*x^2+A^2/2; nf1=nfinit(g1); nf2=nfinit(g2); nf3=nfinit(g3); nf4=nfinit(g4);factor(nf1.disc);factor(nf2.disc);factor(nf3.disc);factor(nf4.disc);nfisisom(f,g1); print(A,"---",nfisisom(f,g1), nfisisom(f,g2),nfisisom(f,g3),nfisisom(f,g4)))
             

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = x^4 + 2*x^2 + 7
? %2 = [x - 1, x^2 + 6, x^4 - 12*x^2 + 252, x^4 + 2*x^2 + 7]
? ? ? 1300---0000
1302---0000
1304---0000
1306---0000
1308---0000
1310---0000
1312---0000
1314---0000
1316---0000
1318---0000
1320---0000
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2378---0000
2380---0000
2382---0000
2384---0000
2386---0000
2388---0000
2390---0000
2392---0000
2394---0000
2396---0000
2398---0000
2400---0000
2402---0000
2404---0000
2406---0000
2408---0000
2410---0000
2412---0000
2414---0000
2416---0000
2418---0000
2420---0000
2422---0000
2424---0000
2426---0000
2428---0000
2430---0000
2432---0000
2434---0000
2436---0000
2438---0000
2440---0000
2442---0000
2444---0000
2446---0000
2448---0000
2450---0000
2452---0000
2454---0000
2456---0000
2458---0000
2460---0000
2462---0000
2464---0000
2466---0000
2468---0000
2470---0000
2472---0000
2474---0000
2476---0000
2478---0000
2480---0000
2482---0000
2484---0000
2486---0000
2488---0000
2490---0000
2492---0000
2494---0000
2496---0000
2498---0000
2500---0000
2502---0000
2504---0000
2506---0000
2508---0000
2510---0000
2512---0000
2514---0000
2516---0000
2518---0000
2520---0000
2522---0000
2524---0000
2526---0000
2528---0000
2530---0000
2532---0000
2534---0000
2536---0000
2538---0000
2540---0000
2542---0000
2544---0000
2546---0000
2548---0000
2550---0000
2552---0000
2554---0000
2556---0000
2558---0000
2560---0000
2562---0000
2564---0000
2566---0000
2568---0000
2570---0000
2572---0000
2574---0000
2576---0000
2578---0000
2580---0000
2582---0000
2584---0000
2586---0000
2588---0000
2590---0000
2592---0000
2594---0000
2596---0000
2598---0000
2600---0000
2602---0000
2604---0000
2606---0000
2608---0000
2610---0000
2612---0000
2614---0000
2616---0000
2618---0000
2620---0000
2622---0000
2624---0000
2626---0000
2628---0000
2630---0000
2632---0000
2634---0000
2636---0000
2638---0000
2640---0000
2642---0000
2644---0000
2646---0000
2648---0000
2650---0000
2652---0000
2654---0000
2656---0000
2658---0000
2660---0000
2662---0000
2664---0000
2666---0000
2668---0000
2670---0000
2672---0000
2674---0000
2676---0000
2678---0000
2680---0000
2682---0000
2684---0000
2686---0000
2688---0000
2690---0000
2692---0000
2694---0000
2696---0000
2698---0000
2700---0000
2702---0000
2704---0000
2706---0000
2708---0000
2710---0000
2712---0000
2714---0000
2716---0000
2718---0000
2720---0000
2722---0000
2724---0000
2726---0000
2728---0000
2730---0000
2732---0000
2734---0000
2736---0000
2738---0000
2740---0000
2742---0000
2744---0000
2746---0000
2748---0000
2750---0000
2752---0000
2754---0000
2756---0000
2758---0000
2760---0000
2762---0000
2764---0000
2766---0000
2768---0000
2770---0000
2772---0000
2774---0000
2776---0000
2778---0000
2780---0000
2782---0000
2784---0000
2786---0000
2788---0000
2790---0000
2792---0000
2794---0000
2796---0000
2798---0000
2800---0000
2802---0000
2804---0000
2806---0000
2808---0000
2810---0000
2812---0000
2814---0000
2816---0000
2818---0000
2820---0000
2822---0000
2824---0000
2826---0000
2828---0000
2830---0000
2832---0000
2834---0000
2836---0000
2838---0000
2840---0000
2842---0000
2844---0000
2846---0000
2848---0000
2850---0000
2852---0000
2854---0000
2856---0000
2858---0000
2860---0000
2862---0000
2864---0000
2866---0000
2868---0000
2870---0000
2872---0000
2874---0000
2876---0000
2878---0000
2880---0000
2882---0000
2884---0000
2886---0000
2888---0000
2890---0000
2892---0000
2894---0000
2896---0000
2898---0000
2900---0000
2902---0000
2904---0000
2906---0000
2908---0000
2910---0000
2912---0000
2914---0000
2916---0000
2918---0000
2920---0000
2922---0000
2924---0000
2926---0000
2928---0000
2930---0000
2932
 ** WARNING: Output too long, hence truncated.
Errors/timing (if any):


Timing:
real	0m8.388s
user	0m4.103s
sys	0m0.022s


'24.155.'
************** PARI *****************
Host 24.155.217.187 (24.155.217.187)
Time: Sun Jul 30 15:21:46 2006

Input: what is 39.59 + 16.75% of tax


Output: WARNING: PARI command contains unsafe command '%', so it will not be executed.

'72.30.1'
************** PARI *****************
Host 72.30.102.206 (72.30.102.206)
Time: Sun Jul 30 04:46:27 2006

Input: vector(20,x,floor((x+1)*sqrt(2))-floor(x*sqrt(2)))

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = [1, 2, 1, 2, 1, 1, 2, 1, 2, 1, 1, 2, 1, 2, 1, 2, 1, 1, 2, 1]
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.066s
user	0m0.006s
sys	0m0.007s


'72.30.1'
************** PARI *****************
Host 72.30.129.106 (72.30.129.106)
Time: Sun Jul 30 00:49:59 2006

Input: y=210; for(x=1,8,y=sumdiv(y,x,x)-y;print1(y,","))

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? 366,378,582,594,846,1026,1374,1386,
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.023s
user	0m0.007s
sys	0m0.007s


'169.231'
************** PARI *****************
Host 169.231.35.225 (169.231.35.225)
Time: Sat Jul 29 23:45:58 2006

Input: [1+0+1+1]


Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = [3]
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.011s
user	0m0.003s
sys	0m0.008s


'169.231'
************** PARI *****************
Host 169.231.35.225 (169.231.35.225)
Time: Sat Jul 29 23:16:46 2006

Input: [1,1,0,1;1,0,1,1;0,1,1,1;1,1,1,0]^2

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = 
[3 2 2 2]

[2 3 2 2]

[2 2 3 2]

[2 2 2 3]

? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.011s
user	0m0.007s
sys	0m0.005s


'169.231'
************** PARI *****************
Host 169.231.35.225 (169.231.35.225)
Time: Sat Jul 29 23:16:31 2006

Input: [1,1,0,1;1,0,1,1;0,1,1,1;1,1,1,0]

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = 
[1 1 0 1]

[1 0 1 1]

[0 1 1 1]

[1 1 1 0]

? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.011s
user	0m0.006s
sys	0m0.005s


'169.231'
************** PARI *****************
Host 169.231.35.225 (169.231.35.225)
Time: Sat Jul 29 23:11:46 2006

Input: [1,0,0,0;1,1,0,0;0,1,1,0;0,0,1,1]^6

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = 
[1 0 0 0]

[6 1 0 0]

[15 6 1 0]

[20 15 6 1]

? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.012s
user	0m0.006s
sys	0m0.007s


'169.231'
************** PARI *****************
Host 169.231.35.225 (169.231.35.225)
Time: Sat Jul 29 23:11:35 2006

Input: [1,0,0,0;1,1,0,0;0,1,1,0;0,0,1,1]^2

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = 
[1 0 0 0]

[2 1 0 0]

[1 2 1 0]

[0 1 2 1]

? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.012s
user	0m0.009s
sys	0m0.002s


'169.231'
************** PARI *****************
Host 169.231.35.225 (169.231.35.225)
Time: Sat Jul 29 23:11:21 2006

Input: [1,0,0,0;1,1,0,0;0,1,1,0;0,0,1,1]^3

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = 
[1 0 0 0]

[3 1 0 0]

[3 3 1 0]

[1 3 3 1]

? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.012s
user	0m0.007s
sys	0m0.005s


'169.231'
************** PARI *****************
Host 169.231.35.225 (169.231.35.225)
Time: Sat Jul 29 23:08:08 2006

Input: [1,1,0,0;0,1,1,0;0,0,1,1;1,0,0,1]^3

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = 
[1 3 3 1]

[1 1 3 3]

[3 1 1 3]

[3 3 1 1]

? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.012s
user	0m0.006s
sys	0m0.005s


'169.231'
************** PARI *****************
Host 169.231.35.225 (169.231.35.225)
Time: Sat Jul 29 23:07:51 2006

Input: [1,1,0,0;0,1,1,0;0,0,1,1;1,0,0,1]^2

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = 
[1 2 1 0]

[0 1 2 1]

[1 0 1 2]

[2 1 0 1]

? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.102s
user	0m0.003s
sys	0m0.010s


'169.231'
************** PARI *****************
Host 169.231.35.225 (169.231.35.225)
Time: Sat Jul 29 23:07:41 2006

Input: [1,1,0,0;0,1,1,0;0,0,1,1;1,0,0,1]

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = 
[1 1 0 0]

[0 1 1 0]

[0 0 1 1]

[1 0 0 1]

? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.012s
user	0m0.008s
sys	0m0.004s


'169.231'
************** PARI *****************
Host 169.231.35.225 (169.231.35.225)
Time: Sat Jul 29 23:03:07 2006

Input: [0,1,1,1;1,1,0,1;1,0,1,1;1,1,1,0]^2

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = 
[3 2 2 2]

[2 3 2 2]

[2 2 3 2]

[2 2 2 3]

? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.012s
user	0m0.009s
sys	0m0.003s


'169.231'
************** PARI *****************
Host 169.231.35.225 (169.231.35.225)
Time: Sat Jul 29 23:02:53 2006

Input: [0,1,1,1;1,1,0,1;1,0,1,1;1,1,1,0]

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = 
[0 1 1 1]

[1 1 0 1]

[1 0 1 1]

[1 1 1 0]

? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.012s
user	0m0.006s
sys	0m0.006s


'169.231'
************** PARI *****************
Host 169.231.35.225 (169.231.35.225)
Time: Sat Jul 29 22:58:38 2006

Input: [0,1,1,0;0,1,1,0;1,0,0,1;1,0,0,1]^2

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = 
[1 1 1 1]

[1 1 1 1]

[1 1 1 1]

[1 1 1 1]

? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.011s
user	0m0.005s
sys	0m0.006s


'169.231'
************** PARI *****************
Host 169.231.35.225 (169.231.35.225)
Time: Sat Jul 29 22:58:23 2006

Input: [0,1,1,0;0,1,1,0;1,0,0,1;1,0,0,1]

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = 
[0 1 1 0]

[0 1 1 0]

[1 0 0 1]

[1 0 0 1]

? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.012s
user	0m0.005s
sys	0m0.006s


'169.231'
************** PARI *****************
Host 169.231.35.225 (169.231.35.225)
Time: Sat Jul 29 22:55:54 2006

Input: [1,0,0,1;1,0,1,0;0,1,1,0;0,1,0,1]^3

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = 
[2 2 1 3]

[2 2 2 2]

[2 2 3 1]

[2 2 2 2]

? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.012s
user	0m0.007s
sys	0m0.005s


'169.231'
************** PARI *****************
Host 169.231.35.225 (169.231.35.225)
Time: Sat Jul 29 22:55:23 2006

Input: [1,0,0,1;1,0,1,0;0,1,1,0;0,1,0,1]^2

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = 
[1 1 0 2]

[1 1 1 1]

[1 1 2 0]

[1 1 1 1]

? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.030s
user	0m0.007s
sys	0m0.004s


'169.231'
************** PARI *****************
Host 169.231.35.225 (169.231.35.225)
Time: Sat Jul 29 22:55:08 2006

Input: [1,0,0,1;1,0,1,0;0,1,1,0;0,1,0,1]

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = 
[1 0 0 1]

[1 0 1 0]

[0 1 1 0]

[0 1 0 1]

? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.011s
user	0m0.006s
sys	0m0.005s


'169.231'
************** PARI *****************
Host 169.231.35.225 (169.231.35.225)
Time: Sat Jul 29 22:47:23 2006

Input: [1,1,1,0;1,1,0,1;0,1,1,1;1,0,1,1]^2

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = 
[2 3 2 2]

[3 2 2 2]

[2 2 2 3]

[2 2 3 2]

? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.012s
user	0m0.007s
sys	0m0.005s


'169.231'
************** PARI *****************
Host 169.231.35.225 (169.231.35.225)
Time: Sat Jul 29 22:47:04 2006

Input: [1,1,1,0;1,1,0,1;0,1,1,1;1,0,1,1]

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = 
[1 1 1 0]

[1 1 0 1]

[0 1 1 1]

[1 0 1 1]

? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.012s
user	0m0.004s
sys	0m0.009s


'169.231'
************** PARI *****************
Host 169.231.35.225 (169.231.35.225)
Time: Sat Jul 29 22:45:02 2006

Input: [1,0,1,0;1,0,1,0;0,1,0,1;0,1,0,1]^2

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = 
[1 1 1 1]

[1 1 1 1]

[1 1 1 1]

[1 1 1 1]

? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.012s
user	0m0.006s
sys	0m0.005s


'169.231'
************** PARI *****************
Host 169.231.35.225 (169.231.35.225)
Time: Sat Jul 29 22:43:38 2006

Input: [1,0,1,0;1,0,1,0;0,1,0,1;0,1,0,1]

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = 
[1 0 1 0]

[1 0 1 0]

[0 1 0 1]

[0 1 0 1]

? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.011s
user	0m0.009s
sys	0m0.004s


'169.231'
************** PARI *****************
Host 169.231.35.225 (169.231.35.225)
Time: Sat Jul 29 22:40:20 2006

Input: [0,1,1,1;1,0,1,1;1,1,0,1;1,1,1,0]^2

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = 
[3 2 2 2]

[2 3 2 2]

[2 2 3 2]

[2 2 2 3]

? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.012s
user	0m0.005s
sys	0m0.006s


'169.231'
************** PARI *****************
Host 169.231.35.225 (169.231.35.225)
Time: Sat Jul 29 22:40:06 2006

Input: [0,1,1,1;1,0,1,1;1,1,0,1;1,1,1,0]

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = 
[0 1 1 1]

[1 0 1 1]

[1 1 0 1]

[1 1 1 0]

? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.011s
user	0m0.009s
sys	0m0.003s


'169.231'
************** PARI *****************
Host 169.231.35.225 (169.231.35.225)
Time: Sat Jul 29 22:35:46 2006

Input: [1,0,0,1;1,0,0,1;0,1,1,0;0,1,1,0]^2

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = 
[1 1 1 1]

[1 1 1 1]

[1 1 1 1]

[1 1 1 1]

? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.032s
user	0m0.007s
sys	0m0.006s


'169.231'
************** PARI *****************
Host 169.231.35.225 (169.231.35.225)
Time: Sat Jul 29 22:35:24 2006

Input: [1,0,0,1;1,0,0,1;0,1,1,0;0,1,1,0]

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = 
[1 0 0 1]

[1 0 0 1]

[0 1 1 0]

[0 1 1 0]

? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.190s
user	0m0.007s
sys	0m0.004s


'164.107'
************** PARI *****************
Host 164.107.205.56 (164.107.205.56)
Time: Sat Jul 29 20:23:17 2006

Input: contfrac(4*sqrt(11)/15)

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = [0, 1, 7, 1, 1, 1, 7, 2, 7, 1, 1, 1, 7, 2, 7, 1, 1, 1, 7, 2, 7, 1, 1, 1, 7, 2, 7, 1, 1, 1, 7, 2, 7, 1, 1, 1, 7, 2, 7, 1, 1, 1, 7, 2, 7]
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.012s
user	0m0.005s
sys	0m0.008s


'164.107'
************** PARI *****************
Host 164.107.205.56 (164.107.205.56)
Time: Sat Jul 29 20:23:00 2006

Input: contfrac(3*sqrt(11)/15)

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = [0, 1, 1, 1, 32, 1, 1, 2, 1, 1, 32, 1, 1, 2, 1, 1, 32, 1, 1, 2, 1, 1, 32, 1, 1, 2, 1, 1, 32, 1, 1, 2, 1, 1, 32, 1, 1, 2, 1, 1, 32, 1, 1, 3]
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.012s
user	0m0.007s
sys	0m0.006s


'164.107'
************** PARI *****************
Host 164.107.205.56 (164.107.205.56)
Time: Sat Jul 29 20:22:53 2006

Input: contfrac(2*sqrt(11)/15)

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = [0, 2, 3, 1, 4, 1, 3, 4, 3, 1, 4, 1, 3, 4, 3, 1, 4, 1, 3, 4, 3, 1, 4, 1, 3, 4, 3, 1, 4, 1, 3, 4, 3, 1, 4, 1, 3, 4, 3, 1, 4, 1, 3, 4, 3]
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.056s
user	0m0.007s
sys	0m0.005s


'164.107'
************** PARI *****************
Host 164.107.205.56 (164.107.205.56)
Time: Sat Jul 29 20:22:28 2006

Input: contfrac(sqrt(11)/15)

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = [0, 4, 1, 1, 10, 1, 1, 8, 1, 1, 10, 1, 1, 8, 1, 1, 10, 1, 1, 8, 1, 1, 10, 1, 1, 8, 1, 1, 10, 1, 1, 8, 1, 1, 10, 1, 1, 8, 1, 1, 10, 1, 1, 9]
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.071s
user	0m0.007s
sys	0m0.004s


'164.107'
************** PARI *****************
Host 164.107.205.56 (164.107.205.56)
Time: Sat Jul 29 20:22:07 2006

Input: contfrac(2*sqrt(11)/15)

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = [0, 2, 3, 1, 4, 1, 3, 4, 3, 1, 4, 1, 3, 4, 3, 1, 4, 1, 3, 4, 3, 1, 4, 1, 3, 4, 3, 1, 4, 1, 3, 4, 3, 1, 4, 1, 3, 4, 3, 1, 4, 1, 3, 4, 3]
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.072s
user	0m0.007s
sys	0m0.006s


'164.107'
************** PARI *****************
Host 164.107.205.56 (164.107.205.56)
Time: Sat Jul 29 20:19:14 2006

Input: contfrac(3/5+2*sqrt(11)/15)

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = [1, 23, 1, 2, 5, 24, 1, 2, 5, 24, 1, 2, 5, 24, 1, 2, 5, 24, 1, 2, 5, 24, 1, 2, 5, 24, 1, 2, 5]
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.012s
user	0m0.005s
sys	0m0.007s


'164.107'
************** PARI *****************
Host 164.107.205.56 (164.107.205.56)
Time: Sat Jul 29 20:18:14 2006

Input: contfrac(3/5+2*sqrt(5)/15)

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = [0, 1, 8, 1, 4, 2, 14, 2, 4, 1, 7, 1, 1, 3, 5, 12, 134, 12, 5, 3, 1, 1, 7, 1, 4, 2, 14, 2, 4, 1, 7, 1, 1, 3, 4]
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.012s
user	0m0.009s
sys	0m0.003s


'164.107'
************** PARI *****************
Host 164.107.205.56 (164.107.205.56)
Time: Sat Jul 29 20:17:27 2006

Input: contfrac(3/5+2*sqrt(7)/15)

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = [0, 1, 20, 5, 1, 4, 1, 5, 19, 1, 2, 22, 2, 1, 19, 5, 1, 4, 1, 5, 19, 1, 2, 22, 2, 1, 19, 5, 1, 4, 1, 5]
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.012s
user	0m0.006s
sys	0m0.007s


'164.107'
************** PARI *****************
Host 164.107.205.56 (164.107.205.56)
Time: Sat Jul 29 20:17:14 2006

Input: contfrac(3/5+2*sqrt(39)/15)

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = [1, 2, 3, 4, 1, 2, 3, 4, 1, 2, 3, 4, 1, 2, 3, 4, 1, 2, 3, 4, 1, 2, 3, 4, 1, 2, 3, 4, 1, 2, 3, 4, 1, 2, 3, 4, 1, 2, 3, 4, 1, 2, 3, 4, 1, 2]
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.012s
user	0m0.006s
sys	0m0.006s


'164.107'
************** PARI *****************
Host 164.107.204.151 (164.107.204.151)
Time: Sat Jul 29 18:45:45 2006

Input: contfrac(3/5+2*sqrt(13)/15)

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = [1, 12, 2, 1, 1, 2, 7, 13, 2, 1, 1, 2, 7, 13, 2, 1, 1, 2, 7, 13, 2, 1, 1, 2, 7, 13, 2, 1, 1, 2, 7, 13, 2, 1, 1, 2, 7]
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.012s
user	0m0.008s
sys	0m0.004s


'164.107'
************** PARI *****************
Host 164.107.204.151 (164.107.204.151)
Time: Sat Jul 29 18:45:28 2006

Input: contfrac(3/5+2*sqrt(11)/15)

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = [1, 23, 1, 2, 5, 24, 1, 2, 5, 24, 1, 2, 5, 24, 1, 2, 5, 24, 1, 2, 5, 24, 1, 2, 5, 24, 1, 2, 5]
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.012s
user	0m0.007s
sys	0m0.005s


'164.107'
************** PARI *****************
Host 164.107.204.151 (164.107.204.151)
Time: Sat Jul 29 18:45:16 2006

Input: contfrac(3/5+2*sqrt(10)/15)

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = [1, 46, 4, 1, 1, 1, 1, 5, 1, 1, 20, 1, 1, 5, 1, 1, 1, 1, 4, 47, 4, 1, 1, 1, 1, 5, 1, 1, 20, 1, 1, 5, 1, 1, 1, 1, 4, 47, 4, 1, 1, 2]
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.012s
user	0m0.006s
sys	0m0.006s


'164.107'
************** PARI *****************
Host 164.107.204.151 (164.107.204.151)
Time: Sat Jul 29 18:44:48 2006

Input: contfrac(3/5+2*sqrt(7)/15)

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = [0, 1, 20, 5, 1, 4, 1, 5, 19, 1, 2, 22, 2, 1, 19, 5, 1, 4, 1, 5, 19, 1, 2, 22, 2, 1, 19, 5, 1, 4, 1, 5]
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.014s
user	0m0.005s
sys	0m0.007s


'164.107'
************** PARI *****************
Host 164.107.204.151 (164.107.204.151)
Time: Sat Jul 29 18:44:09 2006

Input: contfrac(3/5+2*sqrt(5)/15)

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = [0, 1, 8, 1, 4, 2, 14, 2, 4, 1, 7, 1, 1, 3, 5, 12, 134, 12, 5, 3, 1, 1, 7, 1, 4, 2, 14, 2, 4, 1, 7, 1, 1, 3, 4]
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.012s
user	0m0.007s
sys	0m0.005s


'164.107'
************** PARI *****************
Host 164.107.204.151 (164.107.204.151)
Time: Sat Jul 29 18:43:58 2006

Input: contfrac(3/5+2*sqrt(3)/15)

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = [0, 1, 4, 1, 10, 1, 3, 2, 2, 2, 3, 1, 10, 1, 3, 2, 2, 2, 3, 1, 10, 1, 3, 2, 2, 2, 3, 1, 10, 1, 3, 2, 2, 2, 3, 1, 10, 1, 3, 2, 2, 2, 3, 1, 10, 2]
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.054s
user	0m0.008s
sys	0m0.005s


'164.107'
************** PARI *****************
Host 164.107.204.151 (164.107.204.151)
Time: Sat Jul 29 18:43:30 2006

Input: contfrac(3/5+2*sqrt(2)/15)

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = [0, 1, 3, 1, 2, 1, 2, 3, 3, 10, 3, 3, 2, 1, 2, 1, 2, 3, 3, 10, 3, 3, 2, 1, 2, 1, 2, 3, 3, 10, 3, 3, 2, 1, 2, 1, 2, 3, 3, 10, 3, 3, 2]
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.012s
user	0m0.008s
sys	0m0.004s


'164.107'
************** PARI *****************
Host 164.107.204.151 (164.107.204.151)
Time: Sat Jul 29 18:42:19 2006

Input: contfrac(3/5+2*sqrt(39)/15)

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = [1, 2, 3, 4, 1, 2, 3, 4, 1, 2, 3, 4, 1, 2, 3, 4, 1, 2, 3, 4, 1, 2, 3, 4, 1, 2, 3, 4, 1, 2, 3, 4, 1, 2, 3, 4, 1, 2, 3, 4, 1, 2, 3, 4, 1, 2]
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.031s
user	0m0.007s
sys	0m0.006s


'164.107'
************** PARI *****************
Host 164.107.204.151 (164.107.204.151)
Time: Sat Jul 29 18:42:01 2006

Input: contfrac(2*sqrt(39)/15)

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = [0, 1, 4, 1, 40, 1, 4, 2, 4, 1, 40, 1, 4, 2, 4, 1, 40, 1, 4, 2, 4, 1, 40, 1, 4, 2, 4, 1, 40, 1, 4, 2, 5]
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.047s
user	0m0.005s
sys	0m0.009s


'164.107'
************** PARI *****************
Host 164.107.204.151 (164.107.204.151)
Time: Sat Jul 29 18:41:45 2006

Input: contfrac(sqrt(39)/15)

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = [0, 2, 2, 2, 20, 2, 2, 4, 2, 2, 20, 2, 2, 4, 2, 2, 20, 2, 2, 4, 2, 2, 20, 2, 2, 4, 2, 2, 20, 2, 2, 4, 2, 2, 20]
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.011s
user	0m0.009s
sys	0m0.004s


'164.107'
************** PARI *****************
Host 164.107.204.151 (164.107.204.151)
Time: Sat Jul 29 18:41:31 2006

Input: contfrac(sqrt(39))

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = [6, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 2]
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.047s
user	0m0.005s
sys	0m0.008s


'164.107'
************** PARI *****************
Host 164.107.204.151 (164.107.204.151)
Time: Sat Jul 29 18:30:24 2006

Input: contfrac(sqrt(7)/17)

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = [0, 6, 2, 2, 1, 5, 1, 2, 2, 12, 2, 2, 1, 5, 1, 2, 2, 12, 2, 2, 1, 5, 1, 2, 2, 12, 2, 2, 1, 5, 1, 2, 2, 12, 2, 2, 1, 5, 1, 2, 2, 12, 2]
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.012s
user	0m0.006s
sys	0m0.006s


'164.107'
************** PARI *****************
Host 164.107.204.151 (164.107.204.151)
Time: Sat Jul 29 18:30:15 2006

Input: contfrac(sqrt(7)/16)

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = [0, 6, 21, 12, 21, 12, 21, 12, 21, 12, 21, 12, 21, 12, 21, 12, 21]
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.011s
user	0m0.007s
sys	0m0.004s


'164.107'
************** PARI *****************
Host 164.107.204.151 (164.107.204.151)
Time: Sat Jul 29 18:30:08 2006

Input: contfrac(sqrt(7)/7)

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = [0, 2, 1, 1, 1, 4, 1, 1, 1, 4, 1, 1, 1, 4, 1, 1, 1, 4, 1, 1, 1, 4, 1, 1, 1, 4, 1, 1, 1, 4, 1, 1, 1, 4, 1, 1, 1, 4, 1, 1, 1, 4, 1, 1, 1, 4, 1, 1, 1, 4, 1, 1, 1, 4, 1, 1, 1, 4, 1, 1, 1, 4, 1, 2]
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.012s
user	0m0.005s
sys	0m0.008s


'164.107'
************** PARI *****************
Host 164.107.204.151 (164.107.204.151)
Time: Sat Jul 29 18:29:54 2006

Input: contfrac(sqrt(7)/5)

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = [0, 1, 1, 8, 13, 8, 1, 2, 1, 8, 13, 8, 1, 2, 1, 8, 13, 8, 1, 2, 1, 8, 13, 8, 1, 2, 1, 8, 13, 8, 1, 2, 1, 7]
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.041s
user	0m0.009s
sys	0m0.003s


'164.107'
************** PARI *****************
Host 164.107.204.151 (164.107.204.151)
Time: Sat Jul 29 18:29:19 2006

Input: contfrac((2+sqrt(7))/5)

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = [0, 1, 13, 8, 1, 2, 1, 8, 13, 8, 1, 2, 1, 8, 13, 8, 1, 2, 1, 8, 13, 8, 1, 2, 1, 8, 13, 8, 1, 2, 1, 8, 12]
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.011s
user	0m0.006s
sys	0m0.005s


'164.107'
************** PARI *****************
Host 164.107.204.151 (164.107.204.151)
Time: Sat Jul 29 18:29:11 2006

Input: contfrac((2+sqrt(7))/3)

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = [1, 1, 1, 4, 1, 1, 1, 4, 1, 1, 1, 4, 1, 1, 1, 4, 1, 1, 1, 4, 1, 1, 1, 4, 1, 1, 1, 4, 1, 1, 1, 4, 1, 1, 1, 4, 1, 1, 1, 4, 1, 1, 1, 4, 1, 1, 1, 4, 1, 1, 1, 4, 1, 1, 1, 4, 1, 1, 1, 4, 1, 1, 1, 5]
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.127s
user	0m0.007s
sys	0m0.006s


'24.118.'
************** PARI *****************
Host 24.118.196.126 (24.118.196.126)
Time: Sat Jul 29 16:11:30 2006

Input: "Replace this by some code, then click [SAGE] or [PARI]!"

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = "Replace this by some code, then click [SAGE] or [PARI]!"
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.014s
user	0m0.008s
sys	0m0.004s


'72.30.9'
************** PARI *****************
Host 72.30.98.136 (72.30.98.136)
Time: Sat Jul 29 14:56:22 2006

Input: factor(2^(2^5)+1)

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = 
[641 1]

[6700417 1]

? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.086s
user	0m0.007s
sys	0m0.009s


'67.182.'
************** PARI *****************
Host 67.182.66.86 (67.182.66.86)
Time: Sat Jul 29 10:35:47 2006

Input: "Replace this by some code, then click [SAGE] or [PARI]!"

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = "Replace this by some code, then click [SAGE] or [PARI]!"
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.250s
user	0m0.006s
sys	0m0.008s


'65.54.1'
************** PARI *****************
Host 65.54.188.53 (65.54.188.53)
Time: Fri Jul 28 22:13:16 2006

Input: for(n=1,20, print1(n,": ",valuation(n!,2),", ") )

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? 1: 0, 2: 1, 3: 1, 4: 3, 5: 3, 6: 4, 7: 4, 8: 7, 9: 7, 10: 8, 11: 8, 12: 10, 13: 10, 14: 11, 15: 11, 16: 15, 17: 15, 18: 16, 19: 16, 20: 18, 
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.012s
user	0m0.008s
sys	0m0.005s


'66.142.'
************** PARI *****************
Host 66.142.153.233 (66.142.153.233)
Time: Fri Jul 28 21:37:08 2006

Input: 500000000*0.016


Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = 7999999.9999999999999999999999999999999
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.011s
user	0m0.006s
sys	0m0.005s


'164.107'
************** PARI *****************
Host 164.107.205.56 (164.107.205.56)
Time: Fri Jul 28 20:52:06 2006

Input: contfrac(43^(1/2))

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = [6, 1, 1, 3, 1, 5, 1, 3, 1, 1, 12, 1, 1, 3, 1, 5, 1, 3, 1, 1, 12, 1, 1, 3, 1, 5, 1, 3, 1, 1, 12, 1, 1, 3, 1, 5, 1, 3, 1, 1, 12, 1, 1, 3, 1, 5, 1, 3, 2]
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.012s
user	0m0.009s
sys	0m0.004s


'164.107'
************** PARI *****************
Host 164.107.205.56 (164.107.205.56)
Time: Fri Jul 28 20:51:59 2006

Input: contfrac(42^(1/2))

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = [6, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2]
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.011s
user	0m0.007s
sys	0m0.004s


'164.107'
************** PARI *****************
Host 164.107.205.56 (164.107.205.56)
Time: Fri Jul 28 20:51:56 2006

Input: contfrac(42^(1/2))

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = [6, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2]
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.012s
user	0m0.007s
sys	0m0.005s


'164.107'
************** PARI *****************
Host 164.107.205.56 (164.107.205.56)
Time: Fri Jul 28 20:51:47 2006

Input: contfrac(41^(1/2))

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = [6, 2, 2, 12, 2, 2, 12, 2, 2, 12, 2, 2, 12, 2, 2, 12, 2, 2, 12, 2, 2, 12, 2, 2, 12, 2, 2, 12, 2, 2, 12, 2]
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.011s
user	0m0.008s
sys	0m0.003s


'164.107'
************** PARI *****************
Host 164.107.205.56 (164.107.205.56)
Time: Fri Jul 28 20:51:39 2006

Input: contfrac(40^(1/2))

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = [6, 3, 12, 3, 12, 3, 12, 3, 12, 3, 12, 3, 12, 3, 12, 3, 12, 3, 12, 3, 12, 3, 12, 3]
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.012s
user	0m0.005s
sys	0m0.006s


'164.107'
************** PARI *****************
Host 164.107.205.56 (164.107.205.56)
Time: Fri Jul 28 20:51:28 2006

Input: contfrac(38^(1/2))

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = [6, 6, 12, 6, 12, 6, 12, 6, 12, 6, 12, 6, 12, 6, 12, 6, 12, 6, 12, 6, 11]
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.012s
user	0m0.008s
sys	0m0.003s


'164.107'
************** PARI *****************
Host 164.107.205.56 (164.107.205.56)
Time: Fri Jul 28 20:51:21 2006

Input: contfrac(37^(1/2))

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = [6, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12]
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.011s
user	0m0.005s
sys	0m0.007s


'164.107'
************** PARI *****************
Host 164.107.205.56 (164.107.205.56)
Time: Fri Jul 28 20:51:14 2006

Input: contfrac(35^(1/2))

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = [5, 1, 10, 1, 10, 1, 10, 1, 10, 1, 10, 1, 10, 1, 10, 1, 10, 1, 10, 1, 10, 1, 10, 1, 10, 1, 10, 1, 10, 1, 10, 1, 10, 1, 10]
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.011s
user	0m0.006s
sys	0m0.007s


'164.107'
************** PARI *****************
Host 164.107.205.56 (164.107.205.56)
Time: Fri Jul 28 20:51:07 2006

Input: contfrac(34^(1/2))

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = [5, 1, 4, 1, 10, 1, 4, 1, 10, 1, 4, 1, 10, 1, 4, 1, 10, 1, 4, 1, 10, 1, 4, 1, 10, 1, 4, 1, 10, 1, 4, 1, 10, 1, 4, 1, 10, 1, 4, 1, 11]
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.012s
user	0m0.007s
sys	0m0.005s


'164.107'
************** PARI *****************
Host 164.107.205.56 (164.107.205.56)
Time: Fri Jul 28 20:50:59 2006

Input: contfrac(33^(1/2))

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = [5, 1, 2, 1, 10, 1, 2, 1, 10, 1, 2, 1, 10, 1, 2, 1, 10, 1, 2, 1, 10, 1, 2, 1, 10, 1, 2, 1, 10, 1, 2, 1, 10, 1, 2, 1, 10, 1, 2, 1, 10, 1, 2, 1, 11]
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.011s
user	0m0.008s
sys	0m0.003s


'164.107'
************** PARI *****************
Host 164.107.205.56 (164.107.205.56)
Time: Fri Jul 28 20:50:19 2006

Input: contfrac(31^(1/2))

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = [5, 1, 1, 3, 5, 3, 1, 1, 10, 1, 1, 3, 5, 3, 1, 1, 10, 1, 1, 3, 5, 3, 1, 1, 10, 1, 1, 3, 5, 3, 1, 1, 10, 1, 1, 3, 5, 3, 1, 1, 10, 1, 1, 3]
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.012s
user	0m0.008s
sys	0m0.005s


'164.107'
************** PARI *****************
Host 164.107.205.56 (164.107.205.56)
Time: Fri Jul 28 20:50:08 2006

Input: contfrac(30^(1/2))

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = [5, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 9]
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.012s
user	0m0.005s
sys	0m0.008s


'164.107'
************** PARI *****************
Host 164.107.205.56 (164.107.205.56)
Time: Fri Jul 28 20:49:56 2006

Input: contfrac(29^(1/2))

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = [5, 2, 1, 1, 2, 10, 2, 1, 1, 2, 10, 2, 1, 1, 2, 10, 2, 1, 1, 2, 10, 2, 1, 1, 2, 10, 2, 1, 1, 2, 10, 2, 1, 1, 2, 10, 2, 1, 1, 2, 10, 2, 1, 1, 2]
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.012s
user	0m0.006s
sys	0m0.005s


'164.107'
************** PARI *****************
Host 164.107.205.56 (164.107.205.56)
Time: Fri Jul 28 20:49:45 2006

Input: contfrac(26^(1/2))

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = [5, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10]
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.011s
user	0m0.005s
sys	0m0.006s


'164.107'
************** PARI *****************
Host 164.107.205.56 (164.107.205.56)
Time: Fri Jul 28 20:48:32 2006

Input: contfrac(23^(1/2))

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = [4, 1, 3, 1, 8, 1, 3, 1, 8, 1, 3, 1, 8, 1, 3, 1, 8, 1, 3, 1, 8, 1, 3, 1, 8, 1, 3, 1, 8, 1, 3, 1, 8, 1, 3, 1, 8, 1, 3, 1, 8, 1, 3, 1, 9]
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.011s
user	0m0.008s
sys	0m0.005s


'164.107'
************** PARI *****************
Host 164.107.205.56 (164.107.205.56)
Time: Fri Jul 28 20:48:13 2006

Input: contfrac(22^(1/2))

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = [4, 1, 2, 4, 2, 1, 8, 1, 2, 4, 2, 1, 8, 1, 2, 4, 2, 1, 8, 1, 2, 4, 2, 1, 8, 1, 2, 4, 2, 1, 8, 1, 2, 4, 2, 1, 8, 1, 2, 4, 2, 1, 8, 1, 2]
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.011s
user	0m0.006s
sys	0m0.005s


'164.107'
************** PARI *****************
Host 164.107.205.56 (164.107.205.56)
Time: Fri Jul 28 20:47:56 2006

Input: contfrac(21^(1/2))

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = [4, 1, 1, 2, 1, 1, 8, 1, 1, 2, 1, 1, 8, 1, 1, 2, 1, 1, 8, 1, 1, 2, 1, 1, 8, 1, 1, 2, 1, 1, 8, 1, 1, 2, 1, 1, 8, 1, 1, 2, 1, 1, 8, 1, 1, 2, 1, 1, 8, 1, 1, 2, 1, 1, 8, 2]
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.012s
user	0m0.006s
sys	0m0.007s


'164.107'
************** PARI *****************
Host 164.107.205.56 (164.107.205.56)
Time: Fri Jul 28 20:47:37 2006

Input: contfrac(15^(1/2))

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = [3, 1, 6, 1, 6, 1, 6, 1, 6, 1, 6, 1, 6, 1, 6, 1, 6, 1, 6, 1, 6, 1, 6, 1, 6, 1, 6, 1, 6, 1, 6, 1, 6, 1, 6, 1, 6, 1, 6, 1, 6, 1, 7]
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.011s
user	0m0.006s
sys	0m0.005s


'164.107'
************** PARI *****************
Host 164.107.205.56 (164.107.205.56)
Time: Fri Jul 28 20:47:27 2006

Input: contfrac(14^(1/2))

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = [3, 1, 2, 1, 6, 1, 2, 1, 6, 1, 2, 1, 6, 1, 2, 1, 6, 1, 2, 1, 6, 1, 2, 1, 6, 1, 2, 1, 6, 1, 2, 1, 6, 1, 2, 1, 6, 1, 2, 1, 6, 1, 2, 1, 6, 1, 2, 1, 6, 1, 3]
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.012s
user	0m0.006s
sys	0m0.005s


'164.107'
************** PARI *****************
Host 164.107.205.56 (164.107.205.56)
Time: Fri Jul 28 20:47:10 2006

Input: contfrac(13^(1/2))

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = [3, 1, 1, 1, 1, 6, 1, 1, 1, 1, 6, 1, 1, 1, 1, 6, 1, 1, 1, 1, 6, 1, 1, 1, 1, 6, 1, 1, 1, 1, 6, 1, 1, 1, 1, 6, 1, 1, 1, 1, 6, 1, 1, 1, 1, 6, 1, 1, 1, 1, 6, 1, 1, 1, 1, 6, 1, 1, 1, 1, 7]
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.012s
user	0m0.006s
sys	0m0.005s


'164.107'
************** PARI *****************
Host 164.107.205.56 (164.107.205.56)
Time: Fri Jul 28 20:46:53 2006

Input: contfrac(11^(1/2))

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = [3, 3, 6, 3, 6, 3, 6, 3, 6, 3, 6, 3, 6, 3, 6, 3, 6, 3, 6, 3, 6, 3, 6, 3, 6, 3, 6, 3, 6, 3]
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.011s
user	0m0.007s
sys	0m0.005s


'164.107'
************** PARI *****************
Host 164.107.205.56 (164.107.205.56)
Time: Fri Jul 28 20:45:25 2006

Input: contfrac(259^(1/2))

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = [16, 10, 1, 2, 3, 4, 3, 2, 1, 10, 32, 10, 1, 2, 3, 4, 3, 2, 1, 10, 32, 10, 1, 2, 3, 4, 3, 2, 1, 10]
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.012s
user	0m0.006s
sys	0m0.007s


'164.107'
************** PARI *****************
Host 164.107.205.56 (164.107.205.56)
Time: Fri Jul 28 20:42:43 2006

Input: contfrac(199^(1/2))

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = [14, 9, 2, 1, 2, 2, 5, 4, 1, 1, 13, 1, 1, 4, 5, 2, 2, 1, 2, 9, 28, 9, 2, 1, 2, 2, 5, 4, 1, 1, 13, 1, 1, 4, 5, 2, 2, 1, 2]
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.012s
user	0m0.008s
sys	0m0.003s


'164.107'
************** PARI *****************
Host 164.107.205.56 (164.107.205.56)
Time: Fri Jul 28 20:41:51 2006

Input: contfrac(172^(1/2))

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = [13, 8, 1, 2, 2, 1, 1, 3, 6, 3, 1, 1, 2, 2, 1, 8, 26, 8, 1, 2, 2, 1, 1, 3, 6, 3, 1, 1, 2, 2, 1, 8, 26, 8, 1, 2, 2, 1, 1, 3]
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.011s
user	0m0.008s
sys	0m0.003s


'164.107'
************** PARI *****************
Host 164.107.205.56 (164.107.205.56)
Time: Fri Jul 28 20:41:24 2006

Input: contfrac(147^(1/2))

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = [12, 8, 24, 8, 24, 8, 24, 8, 24, 8, 24, 8, 24, 8, 24, 8, 23]
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.014s
user	0m0.006s
sys	0m0.005s


'164.107'
************** PARI *****************
Host 164.107.205.56 (164.107.205.56)
Time: Fri Jul 28 20:38:28 2006

Input: contfrac(84^(1/2))

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = [9, 6, 18, 6, 18, 6, 18, 6, 18, 6, 18, 6, 18, 6, 18, 6, 18, 6, 17]
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.012s
user	0m0.005s
sys	0m0.008s


'164.107'
************** PARI *****************
Host 164.107.205.56 (164.107.205.56)
Time: Fri Jul 28 20:37:46 2006

Input: contfrac(124^(1/2))

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = [11, 7, 2, 1, 1, 1, 3, 1, 4, 1, 3, 1, 1, 1, 2, 7, 22, 7, 2, 1, 1, 1, 3, 1, 4, 1, 3, 1, 1, 1, 2, 7, 22, 7, 2, 1, 1, 1, 3, 1, 4, 1, 3, 1, 1, 2]
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.012s
user	0m0.006s
sys	0m0.006s


'164.107'
************** PARI *****************
Host 164.107.205.56 (164.107.205.56)
Time: Fri Jul 28 20:37:32 2006

Input: contfrac(28^(1/2))

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = [5, 3, 2, 3, 10, 3, 2, 3, 10, 3, 2, 3, 10, 3, 2, 3, 10, 3, 2, 3, 10, 3, 2, 3, 10, 3, 2, 3, 10, 3, 2, 3]
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.012s
user	0m0.008s
sys	0m0.004s


'164.107'
************** PARI *****************
Host 164.107.205.56 (164.107.205.56)
Time: Fri Jul 28 20:37:11 2006

Input: contfrac(28^(1/2))
contfracpnqn(%)

Output: WARNING: PARI command contains unsafe command '%', so it will not be executed.

'164.107'
************** PARI *****************
Host 164.107.205.56 (164.107.205.56)
Time: Fri Jul 28 20:35:14 2006

Input: contfrac(28^(1/2))

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = [5, 3, 2, 3, 10, 3, 2, 3, 10, 3, 2, 3, 10, 3, 2, 3, 10, 3, 2, 3, 10, 3, 2, 3, 10, 3, 2, 3, 10, 3, 2, 3]
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.012s
user	0m0.006s
sys	0m0.007s


'164.107'
************** PARI *****************
Host 164.107.205.56 (164.107.205.56)
Time: Fri Jul 28 20:29:49 2006

Input: contfrac(103^(1/2))

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = [10, 6, 1, 2, 1, 1, 9, 1, 1, 2, 1, 6, 20, 6, 1, 2, 1, 1, 9, 1, 1, 2, 1, 6, 20, 6, 1, 2, 1, 1, 9, 1, 1, 2, 1, 6, 20, 6, 1, 3]
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.011s
user	0m0.006s
sys	0m0.005s


'164.107'
************** PARI *****************
Host 164.107.205.56 (164.107.205.56)
Time: Fri Jul 28 20:28:54 2006

Input: contfrac(2^(1/2), 10, 90)

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = [1, 2, 2, 2, 2, 2, 2, 2, 2, 2]
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.012s
user	0m0.007s
sys	0m0.004s


'164.107'
************** PARI *****************
Host 164.107.205.56 (164.107.205.56)
Time: Fri Jul 28 20:28:39 2006

Input: contfrac(2^(1/2))

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = [1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2]
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.011s
user	0m0.007s
sys	0m0.005s


'164.107'
************** PARI *****************
Host 164.107.205.56 (164.107.205.56)
Time: Fri Jul 28 20:27:49 2006

Input: contfrac(sqrt(67))

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = [8, 5, 2, 1, 1, 7, 1, 1, 2, 5, 16, 5, 2, 1, 1, 7, 1, 1, 2, 5, 16, 5, 2, 1, 1, 7, 1, 1, 2, 5, 16, 5, 2, 1, 1, 7, 1, 1, 2, 4]
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.012s
user	0m0.007s
sys	0m0.005s


'164.107'
************** PARI *****************
Host 164.107.205.56 (164.107.205.56)
Time: Fri Jul 28 20:27:20 2006

Input: contfrac(39^(1/2))

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = [6, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 11]
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.011s
user	0m0.005s
sys	0m0.006s


'164.107'
************** PARI *****************
Host 164.107.205.56 (164.107.205.56)
Time: Fri Jul 28 20:27:05 2006

Input: contfrac(19^(1/2))

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = [4, 2, 1, 3, 1, 2, 8, 2, 1, 3, 1, 2, 8, 2, 1, 3, 1, 2, 8, 2, 1, 3, 1, 2, 8, 2, 1, 3, 1, 2, 8, 2, 1, 3, 1, 2, 8, 2, 1, 3, 1, 2, 8, 2, 1, 4]
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.012s
user	0m0.006s
sys	0m0.005s


'164.107'
************** PARI *****************
Host 164.107.205.56 (164.107.205.56)
Time: Fri Jul 28 20:26:58 2006

Input: contfrac(7^(1/2))

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = [2, 1, 1, 1, 4, 1, 1, 1, 4, 1, 1, 1, 4, 1, 1, 1, 4, 1, 1, 1, 4, 1, 1, 1, 4, 1, 1, 1, 4, 1, 1, 1, 4, 1, 1, 1, 4, 1, 1, 1, 4, 1, 1, 1, 4, 1, 1, 1, 4, 1, 1, 1, 4, 1, 1, 1, 4, 1, 1, 1, 4, 1, 2]
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.012s
user	0m0.008s
sys	0m0.004s


'164.107'
************** PARI *****************
Host 164.107.205.56 (164.107.205.56)
Time: Fri Jul 28 20:26:12 2006

Input: contfrac(2^(1/3))

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = [1, 3, 1, 5, 1, 1, 4, 1, 1, 8, 1, 14, 1, 10, 2, 1, 4, 12, 2, 3, 2, 1, 3, 4, 1, 1, 2, 14, 3, 12, 1, 15, 3, 1, 4]
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.011s
user	0m0.006s
sys	0m0.005s


'164.107'
************** PARI *****************
Host 164.107.205.56 (164.107.205.56)
Time: Fri Jul 28 20:26:00 2006

Input: contfrac(2^(1/2))

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = [1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2]
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.011s
user	0m0.007s
sys	0m0.004s


'164.107'
************** PARI *****************
Host 164.107.205.56 (164.107.205.56)
Time: Fri Jul 28 20:24:54 2006

Input: contfrac(2^{1/2},5,5)

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = [1]
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.011s
user	0m0.007s
sys	0m0.004s


'164.107'
************** PARI *****************
Host 164.107.205.56 (164.107.205.56)
Time: Fri Jul 28 20:24:22 2006

Input: contfrac(2^{1/2})

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = [1]
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.012s
user	0m0.010s
sys	0m0.001s


'164.107'
************** PARI *****************
Host 164.107.205.56 (164.107.205.56)
Time: Fri Jul 28 20:23:54 2006

Input: contfrac(7/5)

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = [1, 2, 2]
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.011s
user	0m0.006s
sys	0m0.005s


'164.107'
************** PARI *****************
Host 164.107.205.56 (164.107.205.56)
Time: Fri Jul 28 20:22:53 2006

Input: contfrac(2^{1/3})

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = [0, 1, 2]
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.011s
user	0m0.007s
sys	0m0.004s


'207.38.'
************** PARI *****************
Host 207.38.199.36 (207.38.199.36)
Time: Fri Jul 28 18:27:56 2006

Input: for(x=1,50,print1("d(",x,")=",numdiv(x),", "))

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? d(1)=1, d(2)=2, d(3)=2, d(4)=3, d(5)=2, d(6)=4, d(7)=2, d(8)=4, d(9)=3, d(10)=4, d(11)=2, d(12)=6, d(13)=2, d(14)=4, d(15)=4, d(16)=5, d(17)=2, d(18)=6, d(19)=2, d(20)=6, d(21)=4, d(22)=4, d(23)=2, d(24)=8, d(25)=3, d(26)=4, d(27)=4, d(28)=6, d(29)=2, d(30)=8, d(31)=2, d(32)=6, d(33)=4, d(34)=4, d(35)=4, d(36)=9, d(37)=2, d(38)=4, d(39)=4, d(40)=8, d(41)=2, d(42)=8, d(43)=2, d(44)=6, d(45)=6, d(46)=4, d(47)=2, d(48)=10, d(49)=3, d(50)=6, 
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.012s
user	0m0.006s
sys	0m0.006s


'69.118.'
************** PARI *****************
Host 69.118.114.229 (69.118.114.229)
Time: Fri Jul 28 15:34:34 2006

Input: 25x20

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = x20
? 
Goodbye!

Errors/timing (if any):

  ***   Warning: unused characters: x20.

Timing:
real	0m0.012s
user	0m0.004s
sys	0m0.009s


'69.152.'
************** PARI *****************
Host 69.152.202.120 (69.152.202.120)
Time: Fri Jul 28 15:10:08 2006

Input: 1.8643 x 12


Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = x12
? 
Goodbye!

Errors/timing (if any):

  ***   Warning: unused characters: x12.

Timing:
real	0m0.077s
user	0m0.007s
sys	0m0.005s


'70.20.1'
************** PARI *****************
Host 70.20.177.202 (70.20.177.202)
Time: Fri Jul 28 14:34:26 2006

Input: for(x=1,50,print1("d(",x,")=",numdiv(x),", "))

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? d(1)=1, d(2)=2, d(3)=2, d(4)=3, d(5)=2, d(6)=4, d(7)=2, d(8)=4, d(9)=3, d(10)=4, d(11)=2, d(12)=6, d(13)=2, d(14)=4, d(15)=4, d(16)=5, d(17)=2, d(18)=6, d(19)=2, d(20)=6, d(21)=4, d(22)=4, d(23)=2, d(24)=8, d(25)=3, d(26)=4, d(27)=4, d(28)=6, d(29)=2, d(30)=8, d(31)=2, d(32)=6, d(33)=4, d(34)=4, d(35)=4, d(36)=9, d(37)=2, d(38)=4, d(39)=4, d(40)=8, d(41)=2, d(42)=8, d(43)=2, d(44)=6, d(45)=6, d(46)=4, d(47)=2, d(48)=10, d(49)=3, d(50)=6, 
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.012s
user	0m0.009s
sys	0m0.003s


'70.20.1'
************** PARI *****************
Host 70.20.177.202 (70.20.177.202)
Time: Fri Jul 28 14:34:21 2006

Input: vector(20,x,floor((x+1)*sqrt(2))-floor(x*sqrt(2)))

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = [1, 2, 1, 2, 1, 1, 2, 1, 2, 1, 1, 2, 1, 2, 1, 2, 1, 1, 2, 1]
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.038s
user	0m0.004s
sys	0m0.008s


'70.20.1'
************** PARI *****************
Host 70.20.177.202 (70.20.177.202)
Time: Fri Jul 28 14:33:21 2006

Input: for(x=1,50,print1("d(",x,")=",numdiv(x),", "))

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? d(1)=1, d(2)=2, d(3)=2, d(4)=3, d(5)=2, d(6)=4, d(7)=2, d(8)=4, d(9)=3, d(10)=4, d(11)=2, d(12)=6, d(13)=2, d(14)=4, d(15)=4, d(16)=5, d(17)=2, d(18)=6, d(19)=2, d(20)=6, d(21)=4, d(22)=4, d(23)=2, d(24)=8, d(25)=3, d(26)=4, d(27)=4, d(28)=6, d(29)=2, d(30)=8, d(31)=2, d(32)=6, d(33)=4, d(34)=4, d(35)=4, d(36)=9, d(37)=2, d(38)=4, d(39)=4, d(40)=8, d(41)=2, d(42)=8, d(43)=2, d(44)=6, d(45)=6, d(46)=4, d(47)=2, d(48)=10, d(49)=3, d(50)=6, 
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.096s
user	0m0.007s
sys	0m0.005s


'72.30.1'
************** PARI *****************
Host 72.30.132.102 (72.30.132.102)
Time: Fri Jul 28 10:07:05 2006

Input: for( k=1, 12, print(k,": ",Mod(2^k,13)) )

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? 1: Mod(2, 13)
2: Mod(4, 13)
3: Mod(8, 13)
4: Mod(3, 13)
5: Mod(6, 13)
6: Mod(12, 13)
7: Mod(11, 13)
8: Mod(9, 13)
9: Mod(5, 13)
10: Mod(10, 13)
11: Mod(7, 13)
12: Mod(1, 13)
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.088s
user	0m0.008s
sys	0m0.005s


'72.30.2'
************** PARI *****************
Host 72.30.226.223 (72.30.226.223)
Time: Fri Jul 28 07:02:39 2006

Input: for(n=1,7, print1(n,": ",sum(x=1,n,1/x),",  ") )

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? 1: 1,  2: 3/2,  3: 11/6,  4: 25/12,  5: 137/60,  6: 49/20,  7: 363/140,  
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m1.161s
user	0m0.003s
sys	0m0.012s


'81.69.2'
************** PARI *****************
Host 81.69.212.71 (81.69.212.71)
Time: Fri Jul 28 02:43:42 2006

Input: print gap('SymmetricGroup(7)')
   print kash('NumberField(X^3 + 15*X^2 - 15*X + 15)')
   print maxima('tan(x)').integrate('x')
   print singular.ring(0, '(x,y,z)', 'dp')
   print gp('ellinit([1,2,3,4,5])').j


Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? ? ? ? ? ? 
Goodbye!

Errors/timing (if any):

  ***   expected character: ',' instead of: printgap('SymmetricGroup(7)')
                                                                    ^-----
  ***   expected character: ',' instead of: printkash('NumberField
  ***   (X^3+15*X^2-15*X+15)
        ^--------------------
  ***   expected character: ',' instead of: printmaxima('tan
  ***   (x)').integrate('x')
        ^--------------------
  ***   Warning: unused characters: (0,'(x,y,z)','dp').
  ***   unknown member function: printsingular.ring(0,'(x,y,z)','dp
                                               ^--------------------
  ***   expected character: ',' instead of: printgp('ellinit([1,2,3,4,5])').j
                                                            ^-----------------

Timing:
real	0m0.168s
user	0m0.008s
sys	0m0.005s


'72.30.9'
************** PARI *****************
Host 72.30.98.35 (72.30.98.35)
Time: Thu Jul 27 23:35:33 2006

Input: for(b=1,100, for(a=1,b, if( frac((a^2+b^2+1)/(a*b))==0 , print(a,",",b), ) ) )

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? 1,1
1,2
2,5
5,13
13,34
34,89
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.313s
user	0m0.024s
sys	0m0.010s


'160.39.'
************** PARI *****************
Host 160.39.34.2 (160.39.34.2)
Time: Thu Jul 27 19:45:36 2006

Input: "Replace this by some code, then click [SAGE] or [PARI]!"

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = "Replace this by some code, then click [SAGE] or [PARI]!"
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.011s
user	0m0.005s
sys	0m0.006s


'72.30.1'
************** PARI *****************
Host 72.30.107.8 (72.30.107.8)
Time: Thu Jul 27 19:35:17 2006

Input: for(b=1,100, for(a=1,b, if( frac((a^2+b^2)/(a*b))==0 , print(a,",",b), ) ) )

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? 1,1
2,2
3,3
4,4
5,5
6,6
7,7
8,8
9,9
10,10
11,11
12,12
13,13
14,14
15,15
16,16
17,17
18,18
19,19
20,20
21,21
22,22
23,23
24,24
25,25
26,26
27,27
28,28
29,29
30,30
31,31
32,32
33,33
34,34
35,35
36,36
37,37
38,38
39,39
40,40
41,41
42,42
43,43
44,44
45,45
46,46
47,47
48,48
49,49
50,50
51,51
52,52
53,53
54,54
55,55
56,56
57,57
58,58
59,59
60,60
61,61
62,62
63,63
64,64
65,65
66,66
67,67
68,68
69,69
70,70
71,71
72,72
73,73
74,74
75,75
76,76
77,77
78,78
79,79
80,80
81,81
82,82
83,83
84,84
85,85
86,86
87,87
88,88
89,89
90,90
91,91
92,92
93,93
94,94
95,95
96,96
97,97
98,98
99,99
100,100
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.144s
user	0m0.024s
sys	0m0.006s


'72.30.1'
************** PARI *****************
Host 72.30.111.31 (72.30.111.31)
Time: Thu Jul 27 17:01:35 2006

Input: factor(x^6-1)

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = 
[x - 1 1]

[x + 1 1]

[x^2 - x + 1 1]

[x^2 + x + 1 1]

? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.288s
user	0m0.009s
sys	0m0.009s


'141.209'
************** PARI *****************
Host 141.209.171.175 (141.209.171.175)
Time: Thu Jul 27 12:28:42 2006

Input: factor(2^256+1)

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = 
[1238926361552897 1]

[93461639715357977769163558199606896584051237541638188580280321 1]

? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m17.638s
user	0m3.120s
sys	0m0.012s


'141.209'
************** PARI *****************
Host 141.209.171.175 (141.209.171.175)
Time: Thu Jul 27 12:28:04 2006

Input: factor(2^256-1)

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = 
[3 1]

[5 1]

[17 1]

[257 1]

[641 1]

[65537 1]

[274177 1]

[6700417 1]

[67280421310721 1]

[59649589127497217 1]

[5704689200685129054721 1]

? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m26.683s
user	0m4.662s
sys	0m0.076s


'141.209'
************** PARI *****************
Host 141.209.171.175 (141.209.171.175)
Time: Thu Jul 27 12:27:09 2006

Input: 200!

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = 788657867364790503552363213932185062295135977687173263294742533244359449963403342920304284011984623904177212138919638830257642790242637105061926624952829931113462857270763317237396988943922445621451664240254033291864131227428294853277524242407573903240321257405579568660226031904170324062351700858796178922222789623703897374720000000000000000000000000000000000000000000000000
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.066s
user	0m0.005s
sys	0m0.007s


'141.158'
************** PARI *****************
Host 141.158.63.163 (141.158.63.163)
Time: Thu Jul 27 09:02:26 2006

Input: 66% of 480$

Output: WARNING: PARI command contains unsafe command '%', so it will not be executed.

'72.30.9'
************** PARI *****************
Host 72.30.98.26 (72.30.98.26)
Time: Thu Jul 27 08:25:08 2006

Input: factor(2^(2^5)+1)

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = 
[641 1]

[6700417 1]

? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.261s
user	0m0.003s
sys	0m0.011s


'193.170'
************** PARI *****************
Host 193.170.37.83 (193.170.37.83)
Time: Thu Jul 27 03:48:39 2006

Input: f=x^4-6
polred(f)
nf=nfinit(f);
factor(nf.disc)
forstep (A=11504, 13000, 2, g1=x^4+A*x^2+A^2/2; g2=x^4-A*x^2-A^2/2; g3=x^4+A*x^2-A^2/2; g4=x^4-A*x^2+A^2/2; nf1=nfinit(g1); nf2=nfinit(g2); nf3=nfinit(g3); nf4=nfinit(g4);factor(nf1.disc);factor(nf2.disc);factor(nf3.disc);factor(nf4.disc);nfisisom(f,g1); print(A,"---",nfisisom(f,g1), nfisisom(f,g2),nfisisom(f,g3),nfisisom(f,g4)))

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = x^4 - 6
? %2 = [x - 1, x^2 - 6, x^4 - 216, x^4 - 6]
? ? %4 = 
[-1 1]

[2 11]

[3 3]

? 11504---0000
11506---0000
11508---0000
11510---0000
11512---0000
11514---0000
11516---0000
11518---0000
11520---0000
11522---0000
11524---0000
11526---0000
11528---0000
11530---0000
11532---0000
11534---0000
11536---0000
11538---0000
11540---0000
11542---0000
11544---0000
11546---0000
11548---0000
11550---0000
11552---0000
11554---0000
11556---0000
11558---0000
11560---0000
11562---0000
11564---0000
11566---0000
11568---0000
11570---0000
11572---0000
11574---0000
11576---0000
11578---0000
11580---0000
11582---0000
11584---0000
11586---0000
11588---0000
11590---0000
11592---0000
11594---0000
11596---0000
11598---0000
11600---0000
11602---0000
11604---0000
11606---0000
11608---0000
11610---0000
11612---0000
11614---0000
11616---0000
11618---0000
11620---0000
11622---0000
11624---0000
11626---0000
11628---0000
11630---0000
11632---0000
11634---0000
11636---0000
11638---0000
11640---0000
11642---0000
11644---0000
11646---0000
11648---0000
11650---0000
11652---0000
11654---0000
11656---0000
11658---0000
11660---0000
11662---0000
11664---0000
11666---0000
11668---0000
11670---0000
11672---0000
11674---0000
11676---0000
11678---0000
11680---0000
11682---0000
11684---0000
11686---0000
11688---0000
11690---0000
11692---0000
11694---0000
11696---0000
11698---0000
11700---0000
11702---0000
11704---0000
11706---0000
11708---0000
11710---0000
11712---0000
11714---0000
11716---0000
11718---0000
11720---0000
11722---0000
11724---0000
11726---0000
11728---0000
11730---0000
11732---0000
11734---0000
11736---0000
11738---0000
11740---0000
11742---0000
11744---0000
11746---0000
11748---0000
11750---0000
11752---0000
11754---0000
11756---0000
11758---0000
11760---0000
11762---0000
11764---0000
11766---0000
11768---0000
11770---0000
11772---0000
11774---0000
11776---0000
11778---0000
11780---0000
11782---0000
11784---0000
11786---0000
11788---0000
11790---0000
11792---0000
11794---0000
11796---0000
11798---0000
11800---0000
11802---0000
11804---0000
11806---0000
11808---0000
11810---0000
11812---0000
11814---0000
11816---0000
11818---0000
11820---0000
11822---0000
11824---0000
11826---0000
11828---0000
11830---0000
11832---0000
11834---0000
11836---0000
11838---0000
11840---0000
11842---0000
11844---0000
11846---0000
11848---0000
11850---0000
11852---0000
11854---0000
11856---0000
11858---0000
11860---0000
11862---0000
11864---0000
11866---0000
11868---0000
11870---0000
11872---0000
11874---0000
11876---0000
11878---0000
11880---0000
11882---0000
11884---0000
11886---0000
11888---0000
11890---0000
11892---0000
11894---0000
11896---0000
11898---0000
11900---0000
11902---0000
11904---0000
11906---0000
11908---0000
11910---0000
11912---0000
11914---0000
11916---0000
11918---0000
11920---0000
11922---0000
11924---0000
11926---0000
11928---0000
11930---0000
11932---0000
11934---0000
11936---0000
11938---0000
11940---0000
11942---0000
11944---0000
11946---0000
11948---0000
11950---0000
11952---0000
11954---0000
11956---0000
11958---0000
11960---0000
11962---0000
11964---0000
11966---0000
11968---0000
11970---0000
11972---0000
11974---0000
11976---0000
11978---0000
11980---0000
11982---0000
11984---0000
11986---0000
11988---0000
11990---0000
11992---0000
11994---0000
11996---0000
11998---0000
12000---0000
12002---0000
12004---0000
12006---0000
12008---0000
12010---0000
12012---0000
12014---0000
12016---0000
12018---0000
12020---0000
12022---0000
12024---0000
12026---0000
12028---0000
12030---0000
12032---0000
12034---0000
12036---0000
12038---0000
12040---0000
12042---0000
12044---0000
12046---0000
12048---0000
12050---0000
12052---0000
12054---0000
12056---0000
12058---0000
12060---0000
12062---0000
12064---0000
12066---0000
12068---0000
12070---0000
12072---0000
12074---0000
12076---0000
12078---0000
12080---0000
12082---0000
12084---0000
12086---0000
12088---0000
12090---0000
12092---0000
12094---0000
12096---0000
12098---0000
12100---0000
12102---0000
12104---0000
12106---0000
12108---0000
12110---0000
12112---0000
12114---0000
12116---0000
12118---0000
12120---0000
12122---0000
12124---0000
12126---0000
12128---0000
12130---0000
12132---0000
12134---0000
12136---0000
12138---0000
12140---0000
12142---0000
12144---0000
12146---0000
12148---0000
12150---0000
12152---0000
12154---0000
12156---0000
12158---0000
12160---0000
12162---0000
12164---0000
12166---0000
12168---0000
12170---0000
12172---0000
12174---0000
12176---0000
12178---0000
12180---0000
12182---0000
12184---0000
12186---0000
12188---0000
12190---0000
12192---0000
12194---0000
12196---0000
12198---0000
12200---0000
12202---0000
12204---0000
12206---0000
12208---0000
12210---0000
12212---0000
12214---0000
12216---0000
12218---0000
12220---0000
12222---0000
12224---0000
12226---0000
12228---0000
12230---0000
12232---0000
12234---0000
12236---0000
12238---0000
12240---0000
12242---0000
12244---0000
12246---0000
12248---0000
12250---0000
12252---0000
12254---0000
12256---0000
12258---0000
12260---0000
12262---0000
12264---0000
12266---0000
12268---0000
12270---0000
12272---0000
12274---0000
12276---0000
12278---0000
12280---0000
12282---0000
12284---0000
12286---0000
12288---0000
12290---0000
12292---0000
12294---0000
12296---0000
12298---0000
12300---0000
12302---0000
12304---0000
12306---0000
12308---0000
12310---0000
12312---0000
12314---0000
12316---0000
12318---0000
12320---0000
12322---0000
12324---0000
12326---0000
12328---0000
12330---0000
12332---0000
12334---0000
12336---0000
12338---0000
12340---0000
12342---0000
12344---0000
12346---0000
12348---0000
12350---0000
12352---0000
12354---0000
12356---0000
12358---0000
12360---0000
12362---0000
12364---0000
12366---0000
12368---0000
12370---0000
12372---0000
12374---0000
12376---0000
12378---0000
12380---0000
12382---0000
12384---0000
12386---0000
12388---0000
12390---0000
12392---0000
12394---0000
12396---0000
12398---0000
12400---0000
12402---0000
12404---0000
12406---0000
12408---0000
12410---0000
12412---0000
12414---0000
12416---0000
12418---0000
12420---0000
12422---0000
12424---0000
12426---0000
12428---0000
12430---0000
12432---0000
12434---0000
12436---0000
12438---0000
12440---0000
12442---0000
12444---0000
12446---0000
12448---0000
12450---0000
12452---0000
12454---0000
12456---0000
12458---0000
12460---0000
12462---0000
12464---0000
12466---0000
12468---0000
12470---0000
12472---0000
12474---0000
12476---0000
12478---0000
12480---0000
12482---0000
12484---0000
12486---0000
12488---0000
12490---0000
12492---0000
12494---0000
12496---0000
12498---0000
12500---0000
12502---0000
12504---0000
12506---0000
12508---0000
12510---0000
12512---0000
12514---0000
12516---0000
12518---0000
12520---0000
12522---0000
12524---0000
12526---0000
12528---0000
12530---0000
12532---0000
12534---0000
12536---0000
12538---0000
12540---0000
12542---0000
12544---0000
12546---0000
12548---0000
12550---0000
12552---0000
12554---0000
12556---0000
12558---0000
12560---0000
12562---0000
12564---0000
12566---0000
12568---0000
12570---0000
12572---0000
12574---0000
12576---0000
12578---0000
12580---0000
12582---0000
12584---0000
12586---0000
12588---0000
12590---0000
12592---0000
12594---0000
12596---0000
12598---0000
12600---0000
12602---0000
12604---0000
12606---0000
12608---0000
12610---0000
12612---0000
12614---0000
12616---0000
12618---0000
12620---0000
12622---0000
12624---0000
12626---0000
12628---0000
12630---0000
12632---0000
12634---0000
12636---0000
12638---0000
12640---0000
12642---0000
12644---0000
12646---0000
12648---0000
12650---0000
12652---0000
12654---0000
12656---0000
12658---0000
12660---0000
12662---0000
12664---0000
12666---0000
12668---0000
12670---0000
12672---0000
12674---0000
12676---0000
12678---0000
12680---0000
12682---0000
12684---0000
12686---0000
12688---0000
12690---0000
12692---0000
12694---0000
12696---0000
12698---0000
12700---0000
12702---0000
12704---0000
12706---0000
12708---0000
12710---0000
12712---0000
12714---0000
12716---0000
12718---0000
12720---0000
12722---0000
12724---0000
12726---0000
12728---0000
12730---0000
12732---0000
12734---0000
12736---0000
12738---0000
12740---0000
12742---0000
12744---0000
12746---0000
12748---0000
12750---0000
12752---0000
12754---0000
12756---0000
12758---0000
12760---0000
12762---0000
12764---0000
12766---0000
12768---0000
12770---0000
12772---0000
12774---0000
12776---0000
12778---0000
12780---0000
12782---0000
12784---0000
12786---0000
12788---0000
12790---0000
12792---0000
12794---0000
12796---0000
12798---0000
12800---0000
12802---0000
12804---0000
12806---0000
12808---0000
12810---0000
12812---0000
12814---0000
12816---0000
12818---0000
12820---0000
12822---0000
12824---0000
12826---0000
12828---0000
12830---0000
12832---0000
12834---0000
12836---0000
12838---0000
12840---0000
12842---0000
12844---0000
12846---0000
12848---0000
12850---0000
12852---0000
12854---0000
12856---0000
12858---0000
12860---0000
12862---0000
12864---0000
12866---0000
12868---0000
12870---0000
12872---0000
12874---0000
12876---0000
12878---0000
12880---0000
12882---0000
12884---0000
12886---0000
12888---0000
12890---0000
12892---0000
12894---0000
12896---0000
12898---0000
12900---0000
12902---0000
12904---0000
12906---0000
12908---0000
12910---0000
12912---0000
12914---0000
12916---0000
12918---0000
12920---0000
12922---0000
12924---0000
12926---0000
12928---0000
12930---0000
12932---0000
12934---0000
12936---0000
12938---0000
12940---0000
12942---0000
12944---0000
12946---0000
12948---0000
12950---0000
12952---0000
12954---0000
12956---0000
12958---0000
12960---0000
12962---0000
12964---0000
12966---0000
12968---0000
12970---0000
12972---0000
12974---0000
12976---0000
12978---0000
12980---0000
12982---0000
12984---0000
12986---0000
12988---0000
12990---0000
12992---0000
12994---0000
12996---0000
12998---0000
13000---0000
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m19.086s
user	0m3.372s
sys	0m0.013s


'193.170'
************** PARI *****************
Host 193.170.37.83 (193.170.37.83)
Time: Thu Jul 27 03:47:41 2006

Input: f=x^4-6
polred(f)
nf=nfinit(f);
factor(nf.disc)
forstep (A=10000, 12000, 2, g1=x^4+A*x^2+A^2/2; g2=x^4-A*x^2-A^2/2; g3=x^4+A*x^2-A^2/2; g4=x^4-A*x^2+A^2/2; nf1=nfinit(g1); nf2=nfinit(g2); nf3=nfinit(g3); nf4=nfinit(g4);factor(nf1.disc);factor(nf2.disc);factor(nf3.disc);factor(nf4.disc);nfisisom(f,g1); print(A,"---",nfisisom(f,g1), nfisisom(f,g2),nfisisom(f,g3),nfisisom(f,g4)))

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = x^4 - 6
? %2 = [x - 1, x^2 - 6, x^4 - 216, x^4 - 6]
? ? %4 = 
[-1 1]

[2 11]

[3 3]

? 10000---0000
10002---0000
10004---0000
10006---0000
10008---0000
10010---0000
10012---0000
10014---0000
10016---0000
10018---0000
10020---0000
10022---0000
10024---0000
10026---0000
10028---0000
10030---0000
10032---0000
10034---0000
10036---0000
10038---0000
10040---0000
10042---0000
10044---0000
10046---0000
10048---0000
10050---0000
10052---0000
10054---0000
10056---0000
10058---0000
10060---0000
10062---0000
10064---0000
10066---0000
10068---0000
10070---0000
10072---0000
10074---0000
10076---0000
10078---0000
10080---0000
10082---0000
10084---0000
10086---0000
10088---0000
10090---0000
10092---0000
10094---0000
10096---0000
10098---0000
10100---0000
10102---0000
10104---0000
10106---0000
10108---0000
10110---0000
10112---0000
10114---0000
10116---0000
10118---0000
10120---0000
10122---0000
10124---0000
10126---0000
10128---0000
10130---0000
10132---0000
10134---0000
10136---0000
10138---0000
10140---0000
10142---0000
10144---0000
10146---0000
10148---0000
10150---0000
10152---0000
10154---0000
10156---0000
10158---0000
10160---0000
10162---0000
10164---0000
10166---0000
10168---0000
10170---0000
10172---0000
10174---0000
10176---0000
10178---0000
10180---0000
10182---0000
10184---0000
10186---0000
10188---0000
10190---0000
10192---0000
10194---0000
10196---0000
10198---0000
10200---0000
10202---0000
10204---0000
10206---0000
10208---0000
10210---0000
10212---0000
10214---0000
10216---0000
10218---0000
10220---0000
10222---0000
10224---0000
10226---0000
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10230---0000
10232---0000
10234---0000
10236---0000
10238---0000
10240---0000
10242---0000
10244---0000
10246---0000
10248---0000
10250---0000
10252---0000
10254---0000
10256---0000
10258---0000
10260---0000
10262---0000
10264---0000
10266---0000
10268---0000
10270---0000
10272---0000
10274---0000
10276---0000
10278---0000
10280---0000
10282---0000
10284---0000
10286---0000
10288---0000
10290---0000
10292---0000
10294---0000
10296---0000
10298---0000
10300---0000
10302---0000
10304---0000
10306---0000
10308---0000
10310---0000
10312---0000
10314---0000
10316---0000
10318---0000
10320---0000
10322---0000
10324---0000
10326---0000
10328---0000
10330---0000
10332---0000
10334---0000
10336---0000
10338---0000
10340---0000
10342---0000
10344---0000
10346---0000
10348---0000
10350---0000
10352---0000
10354---0000
10356---0000
10358---0000
10360---0000
10362---0000
10364---0000
10366---0000
10368---0000
10370---0000
10372---0000
10374---0000
10376---0000
10378---0000
10380---0000
10382---0000
10384---0000
10386---0000
10388---0000
10390---0000
10392---0000
10394---0000
10396---0000
10398---0000
10400---0000
10402---0000
10404---0000
10406---0000
10408---0000
10410---0000
10412---0000
10414---0000
10416---0000
10418---0000
10420---0000
10422---0000
10424---0000
10426---0000
10428---0000
10430---0000
10432---0000
10434---0000
10436---0000
10438---0000
10440---0000
10442---0000
10444---0000
10446---0000
10448---0000
10450---0000
10452---0000
10454---0000
10456---0000
10458---0000
10460---0000
10462---0000
10464---0000
10466---0000
10468---0000
10470---0000
10472---0000
10474---0000
10476---0000
10478---0000
10480---0000
10482---0000
10484---0000
10486---0000
10488---0000
10490---0000
10492---0000
10494---0000
10496---0000
10498---0000
10500---0000
10502---0000
10504---0000
10506---0000
10508---0000
10510---0000
10512---0000
10514---0000
10516---0000
10518---0000
10520---0000
10522---0000
10524---0000
10526---0000
10528---0000
10530---0000
10532---0000
10534---0000
10536---0000
10538---0000
10540---0000
10542---0000
10544---0000
10546---0000
10548---0000
10550---0000
10552---0000
10554---0000
10556---0000
10558---0000
10560---0000
10562---0000
10564---0000
10566---0000
10568---0000
10570---0000
10572---0000
10574---0000
10576---0000
10578---0000
10580---0000
10582---0000
10584---0000
10586---0000
10588---0000
10590---0000
10592---0000
10594---0000
10596---0000
10598---0000
10600---0000
10602---0000
10604---0000
10606---0000
10608---0000
10610---0000
10612---0000
10614---0000
10616---0000
10618---0000
10620---0000
10622---0000
10624---0000
10626---0000
10628---0000
10630---0000
10632---0000
10634---0000
10636---0000
10638---0000
10640---0000
10642---0000
10644---0000
10646---0000
10648---0000
10650---0000
10652---0000
10654---0000
10656---0000
10658---0000
10660---0000
10662---0000
10664---0000
10666---0000
10668---0000
10670---0000
10672---0000
10674---0000
10676---0000
10678---0000
10680---0000
10682---0000
10684---0000
10686---0000
10688---0000
10690---0000
10692---0000
10694---0000
10696---0000
10698---0000
10700---0000
10702---0000
10704---0000
10706---0000
10708---0000
10710---0000
10712---0000
10714---0000
10716---0000
10718---0000
10720---0000
10722---0000
10724---0000
10726---0000
10728---0000
10730---0000
10732---0000
10734---0000
10736---0000
10738---0000
10740---0000
10742---0000
10744---0000
10746---0000
10748---0000
10750---0000
10752---0000
10754---0000
10756---0000
10758---0000
10760---0000
10762---0000
10764---0000
10766---0000
10768---0000
10770---0000
10772---0000
10774---0000
10776---0000
10778---0000
10780---0000
10782---0000
10784---0000
10786---0000
10788---0000
10790---0000
10792---0000
10794---0000
10796---0000
10798---0000
10800---0000
10802---0000
10804---0000
10806---0000
10808---0000
10810---0000
10812---0000
10814---0000
10816---0000
10818---0000
10820---0000
10822---0000
10824---0000
10826---0000
10828---0000
10830---0000
10832---0000
10834---0000
10836---0000
10838---0000
10840---0000
10842---0000
10844---0000
10846---0000
10848---0000
10850---0000
10852---0000
10854---0000
10856---0000
10858---0000
10860---0000
10862---0000
10864---0000
10866---0000
10868---0000
10870---0000
10872---0000
10874---0000
10876---0000
10878---0000
10880---0000
10882---0000
10884---0000
10886---0000
10888---0000
10890---0000
10892---0000
10894---0000
10896---0000
10898---0000
10900---0000
10902---0000
10904---0000
10906---0000
10908---0000
10910---0000
10912---0000
10914---0000
10916---0000
10918---0000
10920---0000
10922---0000
10924---0000
10926---0000
10928---0000
10930---0000
10932---0000
10934---0000
10936---0000
10938---0000
10940---0000
10942---0000
10944---0000
10946---0000
10948---0000
10950---0000
10952---0000
10954---0000
10956---0000
10958---0000
10960---0000
10962---0000
10964---0000
10966---0000
10968---0000
10970---0000
10972---0000
10974---0000
10976---0000
10978---0000
10980---0000
10982---0000
10984---0000
10986---0000
10988---0000
10990---0000
10992---0000
10994---0000
10996---0000
10998---0000
11000---0000
11002---0000
11004---0000
11006---0000
11008---0000
11010---0000
11012---0000
11014---0000
11016---0000
11018---0000
11020---0000
11022---0000
11024---0000
11026---0000
11028---0000
11030---0000
11032---0000
11034---0000
11036---0000
11038---0000
11040---0000
11042---0000
11044---0000
11046---0000
11048---0000
11050---0000
11052---0000
11054---0000
11056---0000
11058---0000
11060---0000
11062---0000
11064---0000
11066---0000
11068---0000
11070---0000
11072---0000
11074---0000
11076---0000
11078---0000
11080---0000
11082---0000
11084---0000
11086---0000
11088---0000
11090---0000
11092---0000
11094---0000
11096---0000
11098---0000
11100---0000
11102---0000
11104---0000
11106---0000
11108---0000
11110---0000
11112---0000
11114---0000
11116---0000
11118---0000
11120---0000
11122---0000
11124---0000
11126---0000
11128---0000
11130---0000
11132---0000
11134---0000
11136---0000
11138---0000
11140---0000
11142---0000
11144---0000
11146---0000
11148---0000
11150---0000
11152---0000
11154---0000
11156---0000
11158---0000
11160---0000
11162---0000
11164---0000
11166---0000
11168---0000
11170---0000
11172---0000
11174---0000
11176---0000
11178---0000
11180---0000
11182---0000
11184---0000
11186---0000
11188---0000
11190---0000
11192---0000
11194---0000
11196---0000
11198---0000
11200---0000
11202---0000
11204---0000
11206---0000
11208---0000
11210---0000
11212---0000
11214---0000
11216---0000
11218---0000
11220---0000
11222---0000
11224---0000
11226---0000
11228---0000
11230---0000
11232---0000
11234---0000
11236---0000
11238---0000
11240---0000
11242---0000
11244---0000
11246---0000
11248---0000
11250---0000
11252---0000
11254---0000
11256---0000
11258---0000
11260---0000
11262---0000
11264---0000
11266---0000
11268---0000
11270---0000
11272---0000
11274---0000
11276---0000
11278---0000
11280---0000
11282---0000
11284---0000
11286---0000
11288---0000
11290---0000
11292---0000
11294---0000
11296---0000
11298---0000
11300---0000
11302---0000
11304---0000
11306---0000
11308---0000
11310---0000
11312---0000
11314---0000
11316---0000
11318---0000
11320---0000
11322---0000
11324---0000
11326---0000
11328---0000
11330---0000
11332---0000
11334---0000
11336---0000
11338---0000
11340---0000
11342---0000
11344---0000
11346---0000
11348---0000
11350---0000
11352---0000
11354---0000
11356---0000
11358---0000
11360---0000
11362---0000
11364---0000
11366---0000
11368---0000
11370---0000
11372---0000
11374---0000
11376---0000
11378---0000
11380---0000
11382---0000
11384---0000
11386---0000
11388---0000
11390---0000
11392---0000
11394---0000
11396---0000
11398---0000
11400---0000
11402---0000
11404---0000
11406---0000
11408---0000
11410---0000
11412---0000
11414---0000
11416---0000
11418---0000
11420---0000
11422---0000
11424---0000
11426---0000
11428---0000
11430---0000
11432---0000
11434---0000
11436---0000
11438---0000
11440---0000
11442---0000
11444---0000
11446---0000
11448---0000
11450---0000
11452---0000
11454---0000
11456---0000
11458---0000
11460---0000
11462---0000
11464---0000
11466---0000
11468---0000
11470---0000
11472---0000
11474---0000
11476---0000
11478---0000
11480---0000
11482---0000
11484---0000
11486---0000
11488---0000
11490---0000
11492---0000
11494---0000
11496---0000
11498---0000
11500---0000
11502---0000
11504---0000
115
 ** WARNING: Output too long, hence truncated.
Errors/timing (if any):


Timing:
real	0m25.679s
user	0m4.522s
sys	0m0.013s


'193.170'
************** PARI *****************
Host 193.170.37.83 (193.170.37.83)
Time: Thu Jul 27 03:46:54 2006

Input: f=x^4-6
polred(f)
nf=nfinit(f);
factor(nf.disc)
forstep (A=8630, 10000, 2, g1=x^4+A*x^2+A^2/2; g2=x^4-A*x^2-A^2/2; g3=x^4+A*x^2-A^2/2; g4=x^4-A*x^2+A^2/2; nf1=nfinit(g1); nf2=nfinit(g2); nf3=nfinit(g3); nf4=nfinit(g4);factor(nf1.disc);factor(nf2.disc);factor(nf3.disc);factor(nf4.disc);nfisisom(f,g1); print(A,"---",nfisisom(f,g1), nfisisom(f,g2),nfisisom(f,g3),nfisisom(f,g4)))

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = x^4 - 6
? %2 = [x - 1, x^2 - 6, x^4 - 216, x^4 - 6]
? ? %4 = 
[-1 1]

[2 11]

[3 3]

? 8630---0000
8632---0000
8634---0000
8636---0000
8638---0000
8640---0000
8642---0000
8644---0000
8646---0000
8648---0000
8650---0000
8652---0000
8654---0000
8656---0000
8658---0000
8660---0000
8662---0000
8664---0000
8666---0000
8668---0000
8670---0000
8672---0000
8674---0000
8676---0000
8678---0000
8680---0000
8682---0000
8684---0000
8686---0000
8688---0000
8690---0000
8692---0000
8694---0000
8696---0000
8698---0000
8700---0000
8702---0000
8704---0000
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? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m17.858s
user	0m3.059s
sys	0m0.017s


'193.170'
************** PARI *****************
Host 193.170.37.83 (193.170.37.83)
Time: Thu Jul 27 03:46:15 2006

Input: f=x^4-6
polred(f)
nf=nfinit(f);
factor(nf.disc)
forstep (A=7000, 9000, 2, g1=x^4+A*x^2+A^2/2; g2=x^4-A*x^2-A^2/2; g3=x^4+A*x^2-A^2/2; g4=x^4-A*x^2+A^2/2; nf1=nfinit(g1); nf2=nfinit(g2); nf3=nfinit(g3); nf4=nfinit(g4);factor(nf1.disc);factor(nf2.disc);factor(nf3.disc);factor(nf4.disc);nfisisom(f,g1); print(A,"---",nfisisom(f,g1), nfisisom(f,g2),nfisisom(f,g3),nfisisom(f,g4)))

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = x^4 - 6
? %2 = [x - 1, x^2 - 6, x^4 - 216, x^4 - 6]
? ? %4 = 
[-1 1]

[2 11]

[3 3]

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8280---0000
8282---0000
8284---0000
8286---0000
8288---0000
8290---0000
8292---0000
8294---0000
8296---0000
8298---0000
8300---0000
8302---0000
8304---0000
8306---0000
8308---0000
8310---0000
8312---0000
8314---0000
8316---0000
8318---0000
8320---0000
8322---0000
8324---0000
8326---0000
8328---0000
8330---0000
8332---0000
8334---0000
8336---0000
8338---0000
8340---0000
8342---0000
8344---0000
8346---0000
8348---0000
8350---0000
8352---0000
8354---0000
8356---0000
8358---0000
8360---0000
8362---0000
8364---0000
8366---0000
8368---0000
8370---0000
8372---0000
8374---0000
8376---0000
8378---0000
8380---0000
8382---0000
8384---0000
8386---0000
8388---0000
8390---0000
8392---0000
8394---0000
8396---0000
8398---0000
8400---0000
8402---0000
8404---0000
8406---0000
8408---0000
8410---0000
8412---0000
8414---0000
8416---0000
8418---0000
8420---0000
8422---0000
8424---0000
8426---0000
8428---0000
8430---0000
8432---0000
8434---0000
8436---0000
8438---0000
8440---0000
8442---0000
8444---0000
8446---0000
8448---0000
8450---0000
8452---0000
8454---0000
8456---0000
8458---0000
8460---0000
8462---0000
8464---0000
8466---0000
8468---0000
8470---0000
8472---0000
8474---0000
8476---0000
8478---0000
8480---0000
8482---0000
8484---0000
8486---0000
8488---0000
8490---0000
8492---0000
8494---0000
8496---0000
8498---0000
8500---0000
8502---0000
8504---0000
8506---0000
8508---0000
8510---0000
8512---0000
8514---0000
8516---0000
8518---0000
8520---0000
8522---0000
8524---0000
8526---0000
8528---0000
8530---0000
8532---0000
8534---0000
8536---0000
8538---0000
8540---0000
8542---0000
8544---0000
8546---0000
8548---0000
8550---0000
8552---0000
8554---0000
8556---0000
8558---0000
8560---0000
8562---0000
8564---0000
8566---0000
8568---0000
8570---0000
8572---0000
8574---0000
8576---0000
8578---0000
8580---0000
8582---0000
8584---0000
8586---0000
8588---0000
8590---0000
8592---0000
8594---0000
8596---0000
8598---0000
8600---0000
8602---0000
8604---0000
8606---0000
8608---0000
8610---0000
8612---0000
8614---0000
8616---0000
8618---0000
8620---0000
8622---0000
8624---0000
8626---0000
8628---0000
8630---0000

 ** WARNING: Output too long, hence truncated.
Errors/timing (if any):


Timing:
real	0m24.849s
user	0m4.415s
sys	0m0.017s


'193.170'
************** PARI *****************
Host 193.170.37.83 (193.170.37.83)
Time: Thu Jul 27 03:45:33 2006

Input: f=x^4-6
polred(f)
nf=nfinit(f);
factor(nf.disc)
forstep (A=5630, 7000, 2, g1=x^4+A*x^2+A^2/2; g2=x^4-A*x^2-A^2/2; g3=x^4+A*x^2-A^2/2; g4=x^4-A*x^2+A^2/2; nf1=nfinit(g1); nf2=nfinit(g2); nf3=nfinit(g3); nf4=nfinit(g4);factor(nf1.disc);factor(nf2.disc);factor(nf3.disc);factor(nf4.disc);nfisisom(f,g1); print(A,"---",nfisisom(f,g1), nfisisom(f,g2),nfisisom(f,g3),nfisisom(f,g4)))

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = x^4 - 6
? %2 = [x - 1, x^2 - 6, x^4 - 216, x^4 - 6]
? ? %4 = 
[-1 1]

[2 11]

[3 3]

? 5630---0000
5632---0000
5634---0000
5636---0000
5638---0000
5640---0000
5642---0000
5644---0000
5646---0000
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5652---0000
5654---0000
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5660---0000
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5668---0000
5670---0000
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6340---0000
6342---0000
6344---0000
6346---0000
6348---0000
6350---0000
6352---0000
6354---0000
6356---0000
6358---0000
6360---0000
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6364---0000
6366---0000
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6370---0000
6372---0000
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6380---0000
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6384---0000
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6400---0000
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6540---0000
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6700---0000
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6704---0000
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6708---0000
6710---0000
6712---0000
6714---0000
6716---0000
6718---0000
6720---0000
6722---0000
6724---0000
6726---0000
6728---0000
6730---0000
6732---0000
6734---0000
6736---0000
6738---0000
6740---0000
6742---0000
6744---0000
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6748---0000
6750---0000
6752---0000
6754---0000
6756---0000
6758---0000
6760---0000
6762---0000
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6766---0000
6768---0000
6770---0000
6772---0000
6774---0000
6776---0000
6778---0000
6780---0000
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6784---0000
6786---0000
6788---0000
6790---0000
6792---0000
6794---0000
6796---0000
6798---0000
6800---0000
6802---0000
6804---0000
6806---0000
6808---0000
6810---0000
6812---0000
6814---0000
6816---0000
6818---0000
6820---0000
6822---0000
6824---0000
6826---0000
6828---0000
6830---0000
6832---0000
6834---0000
6836---0000
6838---0000
6840---0000
6842---0000
6844---0000
6846---0000
6848---0000
6850---0000
6852---0000
6854---0000
6856---0000
6858---0000
6860---0000
6862---0000
6864---0000
6866---0000
6868---0000
6870---0000
6872---0000
6874---0000
6876---0000
6878---0000
6880---0000
6882---0000
6884---0000
6886---0000
6888---0000
6890---0000
6892---0000
6894---0000
6896---0000
6898---0000
6900---0000
6902---0000
6904---0000
6906---0000
6908---0000
6910---0000
6912---0000
6914---0000
6916---0000
6918---0000
6920---0000
6922---0000
6924---0000
6926---0000
6928---0000
6930---0000
6932---0000
6934---0000
6936---0000
6938---0000
6940---0000
6942---0000
6944---0000
6946---0000
6948---0000
6950---0000
6952---0000
6954---0000
6956---0000
6958---0000
6960---0000
6962---0000
6964---0000
6966---0000
6968---0000
6970---0000
6972---0000
6974---0000
6976---0000
6978---0000
6980---0000
6982---0000
6984---0000
6986---0000
6988---0000
6990---0000
6992---0000
6994---0000
6996---0000
6998---0000
7000---0000
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m16.644s
user	0m2.973s
sys	0m0.016s


'193.170'
************** PARI *****************
Host 193.170.37.83 (193.170.37.83)
Time: Thu Jul 27 03:44:57 2006

Input: f=x^4-6
polred(f)
nf=nfinit(f);
factor(nf.disc)
forstep (A=4000, 6000, 2, g1=x^4+A*x^2+A^2/2; g2=x^4-A*x^2-A^2/2; g3=x^4+A*x^2-A^2/2; g4=x^4-A*x^2+A^2/2; nf1=nfinit(g1); nf2=nfinit(g2); nf3=nfinit(g3); nf4=nfinit(g4);factor(nf1.disc);factor(nf2.disc);factor(nf3.disc);factor(nf4.disc);nfisisom(f,g1); print(A,"---",nfisisom(f,g1), nfisisom(f,g2),nfisisom(f,g3),nfisisom(f,g4)))

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = x^4 - 6
? %2 = [x - 1, x^2 - 6, x^4 - 216, x^4 - 6]
? ? %4 = 
[-1 1]

[2 11]

[3 3]

? 4000---0000
4002---0000
4004---0000
4006---0000
4008---0000
4010---0000
4012---0000
4014---0000
4016---0000
4018---0000
4020---0000
4022---0000
4024---0000
4026---0000
4028---0000
4030---0000
4032---0000
4034---0000
4036---0000
4038---0000
4040---0000
4042---0000
4044---0000
4046---0000
4048---0000
4050---0000
4052---0000
4054---0000
4056---0000
4058---0000
4060---0000
4062---0000
4064---0000
4066---0000
4068---0000
4070---0000
4072---0000
4074---0000
4076---0000
4078---0000
4080---0000
4082---0000
4084---0000
4086---0000
4088---0000
4090---0000
4092---0000
4094---0000
4096---0000
4098---0000
4100---0000
4102---0000
4104---0000
4106---0000
4108---0000
4110---0000
4112---0000
4114---0000
4116---0000
4118---0000
4120---0000
4122---0000
4124---0000
4126---0000
4128---0000
4130---0000
4132---0000
4134---0000
4136---0000
4138---0000
4140---0000
4142---0000
4144---0000
4146---0000
4148---0000
4150---0000
4152---0000
4154---0000
4156---0000
4158---0000
4160---0000
4162---0000
4164---0000
4166---0000
4168---0000
4170---0000
4172---0000
4174---0000
4176---0000
4178---0000
4180---0000
4182---0000
4184---0000
4186---0000
4188---0000
4190---0000
4192---0000
4194---0000
4196---0000
4198---0000
4200---0000
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4204---0000
4206---0000
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4210---0000
4212---0000
4214---0000
4216---0000
4218---0000
4220---0000
4222---0000
4224---0000
4226---0000
4228---0000
4230---0000
4232---0000
4234---0000
4236---0000
4238---0000
4240---0000
4242---0000
4244---0000
4246---0000
4248---0000
4250---0000
4252---0000
4254---0000
4256---0000
4258---0000
4260---0000
4262---0000
4264---0000
4266---0000
4268---0000
4270---0000
4272---0000
4274---0000
4276---0000
4278---0000
4280---0000
4282---0000
4284---0000
4286---0000
4288---0000
4290---0000
4292---0000
4294---0000
4296---0000
4298---0000
4300---0000
4302---0000
4304---0000
4306---0000
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4310---0000
4312---0000
4314---0000
4316---0000
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4320---0000
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4332---0000
4334---0000
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4340---0000
4342---0000
4344---0000
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4350---0000
4352---0000
4354---0000
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4360---0000
4362---0000
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4370---0000
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4410---0000
4412---0000
4414---0000
4416---0000
4418---0000
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4426---0000
4428---0000
4430---0000
4432---0000
4434---0000
4436---0000
4438---0000
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4444---0000
4446---0000
4448---0000
4450---0000
4452---0000
4454---0000
4456---0000
4458---0000
4460---0000
4462---0000
4464---0000
4466---0000
4468---0000
4470---0000
4472---0000
4474---0000
4476---0000
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4480---0000
4482---0000
4484---0000
4486---0000
4488---0000
4490---0000
4492---0000
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4502---0000
4504---0000
4506---0000
4508---0000
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4520---0000
4522---0000
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4528---0000
4530---0000
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4540---0000
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4548---0000
4550---0000
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4628---0000
4630---0000
4632---0000
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4642---0000
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4646---0000
4648---0000
4650---0000
4652---0000
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4656---0000
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4660---0000
4662---0000
4664---0000
4666---0000
4668---0000
4670---0000
4672---0000
4674---0000
4676---0000
4678---0000
4680---0000
4682---0000
4684---0000
4686---0000
4688---0000
4690---0000
4692---0000
4694---0000
4696---0000
4698---0000
4700---0000
4702---0000
4704---0000
4706---0000
4708---0000
4710---0000
4712---0000
4714---0000
4716---0000
4718---0000
4720---0000
4722---0000
4724---0000
4726---0000
4728---0000
4730---0000
4732---0000
4734---0000
4736---0000
4738---0000
4740---0000
4742---0000
4744---0000
4746---0000
4748---0000
4750---0000
4752---0000
4754---0000
4756---0000
4758---0000
4760---0000
4762---0000
4764---0000
4766---0000
4768---0000
4770---0000
4772---0000
4774---0000
4776---0000
4778---0000
4780---0000
4782---0000
4784---0000
4786---0000
4788---0000
4790---0000
4792---0000
4794---0000
4796---0000
4798---0000
4800---0000
4802---0000
4804---0000
4806---0000
4808---0000
4810---0000
4812---0000
4814---0000
4816---0000
4818---0000
4820---0000
4822---0000
4824---0000
4826---0000
4828---0000
4830---0000
4832---0000
4834---0000
4836---0000
4838---0000
4840---0000
4842---0000
4844---0000
4846---0000
4848---0000
4850---0000
4852---0000
4854---0000
4856---0000
4858---0000
4860---0000
4862---0000
4864---0000
4866---0000
4868---0000
4870---0000
4872---0000
4874---0000
4876---0000
4878---0000
4880---0000
4882---0000
4884---0000
4886---0000
4888---0000
4890---0000
4892---0000
4894---0000
4896---0000
4898---0000
4900---0000
4902---0000
4904---0000
4906---0000
4908---0000
4910---0000
4912---0000
4914---0000
4916---0000
4918---0000
4920---0000
4922---0000
4924---0000
4926---0000
4928---0000
4930---0000
4932---0000
4934---0000
4936---0000
4938---0000
4940---0000
4942---0000
4944---0000
4946---0000
4948---0000
4950---0000
4952---0000
4954---0000
4956---0000
4958---0000
4960---0000
4962---0000
4964---0000
4966---0000
4968---0000
4970---0000
4972---0000
4974---0000
4976---0000
4978---0000
4980---0000
4982---0000
4984---0000
4986---0000
4988---0000
4990---0000
4992---0000
4994---0000
4996---0000
4998---0000
5000---0000
5002---0000
5004---0000
5006---0000
5008---0000
5010---0000
5012---0000
5014---0000
5016---0000
5018---0000
5020---0000
5022---0000
5024---0000
5026---0000
5028---0000
5030---0000
5032---0000
5034---0000
5036---0000
5038---0000
5040---0000
5042---0000
5044---0000
5046---0000
5048---0000
5050---0000
5052---0000
5054---0000
5056---0000
5058---0000
5060---0000
5062---0000
5064---0000
5066---0000
5068---0000
5070---0000
5072---0000
5074---0000
5076---0000
5078---0000
5080---0000
5082---0000
5084---0000
5086---0000
5088---0000
5090---0000
5092---0000
5094---0000
5096---0000
5098---0000
5100---0000
5102---0000
5104---0000
5106---0000
5108---0000
5110---0000
5112---0000
5114---0000
5116---0000
5118---0000
5120---0000
5122---0000
5124---0000
5126---0000
5128---0000
5130---0000
5132---0000
5134---0000
5136---0000
5138---0000
5140---0000
5142---0000
5144---0000
5146---0000
5148---0000
5150---0000
5152---0000
5154---0000
5156---0000
5158---0000
5160---0000
5162---0000
5164---0000
5166---0000
5168---0000
5170---0000
5172---0000
5174---0000
5176---0000
5178---0000
5180---0000
5182---0000
5184---0000
5186---0000
5188---0000
5190---0000
5192---0000
5194---0000
5196---0000
5198---0000
5200---0000
5202---0000
5204---0000
5206---0000
5208---0000
5210---0000
5212---0000
5214---0000
5216---0000
5218---0000
5220---0000
5222---0000
5224---0000
5226---0000
5228---0000
5230---0000
5232---0000
5234---0000
5236---0000
5238---0000
5240---0000
5242---0000
5244---0000
5246---0000
5248---0000
5250---0000
5252---0000
5254---0000
5256---0000
5258---0000
5260---0000
5262---0000
5264---0000
5266---0000
5268---0000
5270---0000
5272---0000
5274---0000
5276---0000
5278---0000
5280---0000
5282---0000
5284---0000
5286---0000
5288---0000
5290---0000
5292---0000
5294---0000
5296---0000
5298---0000
5300---0000
5302---0000
5304---0000
5306---0000
5308---0000
5310---0000
5312---0000
5314---0000
5316---0000
5318---0000
5320---0000
5322---0000
5324---0000
5326---0000
5328---0000
5330---0000
5332---0000
5334---0000
5336---0000
5338---0000
5340---0000
5342---0000
5344---0000
5346---0000
5348---0000
5350---0000
5352---0000
5354---0000
5356---0000
5358---0000
5360---0000
5362---0000
5364---0000
5366---0000
5368---0000
5370---0000
5372---0000
5374---0000
5376---0000
5378---0000
5380---0000
5382---0000
5384---0000
5386---0000
5388---0000
5390---0000
5392---0000
5394---0000
5396---0000
5398---0000
5400---0000
5402---0000
5404---0000
5406---0000
5408---0000
5410---0000
5412---0000
5414---0000
5416---0000
5418---0000
5420---0000
5422---0000
5424---0000
5426---0000
5428---0000
5430---0000
5432---0000
5434---0000
5436---0000
5438---0000
5440---0000
5442---0000
5444---0000
5446---0000
5448---0000
5450---0000
5452---0000
5454---0000
5456---0000
5458---0000
5460---0000
5462---0000
5464---0000
5466---0000
5468---0000
5470---0000
5472---0000
5474---0000
5476---0000
5478---0000
5480---0000
5482---0000
5484---0000
5486---0000
5488---0000
5490---0000
5492---0000
5494---0000
5496---0000
5498---0000
5500---0000
5502---0000
5504---0000
5506---0000
5508---0000
5510---0000
5512---0000
5514---0000
5516---0000
5518---0000
5520---0000
5522---0000
5524---0000
5526---0000
5528---0000
5530---0000
5532---0000
5534---0000
5536---0000
5538---0000
5540---0000
5542---0000
5544---0000
5546---0000
5548---0000
5550---0000
5552---0000
5554---0000
5556---0000
5558---0000
5560---0000
5562---0000
5564---0000
5566---0000
5568---0000
5570---0000
5572---0000
5574---0000
5576---0000
5578---0000
5580---0000
5582---0000
5584---0000
5586---0000
5588---0000
5590---0000
5592---0000
5594---0000
5596---0000
5598---0000
5600---0000
5602---0000
5604---0000
5606---0000
5608---0000
5610---0000
5612---0000
5614---0000
5616---0000
5618---0000
5620---0000
5622---0000
5624---0000
5626---0000
5628---0000
5630---0000

 ** WARNING: Output too long, hence truncated.
Errors/timing (if any):


Timing:
real	0m8.480s
user	0m4.227s
sys	0m0.011s


'193.170'
************** PARI *****************
Host 193.170.37.83 (193.170.37.83)
Time: Thu Jul 27 03:44:28 2006

Input: f=x^4-6
polred(f)
nf=nfinit(f);
factor(nf.disc)
forstep (A=2630, 4000, 2, g1=x^4+A*x^2+A^2/2; g2=x^4-A*x^2-A^2/2; g3=x^4+A*x^2-A^2/2; g4=x^4-A*x^2+A^2/2; nf1=nfinit(g1); nf2=nfinit(g2); nf3=nfinit(g3); nf4=nfinit(g4);factor(nf1.disc);factor(nf2.disc);factor(nf3.disc);factor(nf4.disc);nfisisom(f,g1); print(A,"---",nfisisom(f,g1), nfisisom(f,g2),nfisisom(f,g3),nfisisom(f,g4)))

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = x^4 - 6
? %2 = [x - 1, x^2 - 6, x^4 - 216, x^4 - 6]
? ? %4 = 
[-1 1]

[2 11]

[3 3]

? 2630---0000
2632---0000
2634---0000
2636---0000
2638---0000
2640---0000
2642---0000
2644---0000
2646---0000
2648---0000
2650---0000
2652---0000
2654---0000
2656---0000
2658---0000
2660---0000
2662---0000
2664---0000
2666---0000
2668---0000
2670---0000
2672---0000
2674---0000
2676---0000
2678---0000
2680---0000
2682---0000
2684---0000
2686---0000
2688---0000
2690---0000
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2738---0000
2740---0000
2742---0000
2744---0000
2746---0000
2748---0000
2750---0000
2752---0000
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2756---0000
2758---0000
2760---0000
2762---0000
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2766---0000
2768---0000
2770---0000
2772---0000
2774---0000
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2782---0000
2784---0000
2786---0000
2788---0000
2790---0000
2792---0000
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2796---0000
2798---0000
2800---0000
2802---0000
2804---0000
2806---0000
2808---0000
2810---0000
2812---0000
2814---0000
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2818---0000
2820---0000
2822---0000
2824---0000
2826---0000
2828---0000
2830---0000
2832---0000
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2838---0000
2840---0000
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2990---0000
2992---0000
2994---0000
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3000---0000
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3108---0000
3110---0000
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3114---0000
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3300---0000
3302---0000
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3306---0000
3308---0000
3310---0000
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3322---0000
3324---0000
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3334---0000
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3338---0000
3340---0000
3342---0000
3344---0000
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3348---0000
3350---0000
3352---0000
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3356---0000
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3360---0000
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3380---0000
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3400---0000
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3404---0000
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3478---0000
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3502---0000
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3514---0000
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3518---0000
3520---0000
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3528---0000
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3538---0000
3540---0000
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3556---0000
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3560---0000
3562---0000
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3638---0000
3640---0000
3642---0000
3644---0000
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3656---0000
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3660---0000
3662---0000
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3668---0000
3670---0000
3672---0000
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3676---0000
3678---0000
3680---0000
3682---0000
3684---0000
3686---0000
3688---0000
3690---0000
3692---0000
3694---0000
3696---0000
3698---0000
3700---0000
3702---0000
3704---0000
3706---0000
3708---0000
3710---0000
3712---0000
3714---0000
3716---0000
3718---0000
3720---0000
3722---0000
3724---0000
3726---0000
3728---0000
3730---0000
3732---0000
3734---0000
3736---0000
3738---0000
3740---0000
3742---0000
3744---0000
3746---0000
3748---0000
3750---0000
3752---0000
3754---0000
3756---0000
3758---0000
3760---0000
3762---0000
3764---0000
3766---0000
3768---0000
3770---0000
3772---0000
3774---0000
3776---0000
3778---0000
3780---0000
3782---0000
3784---0000
3786---0000
3788---0000
3790---0000
3792---0000
3794---0000
3796---0000
3798---0000
3800---0000
3802---0000
3804---0000
3806---0000
3808---0000
3810---0000
3812---0000
3814---0000
3816---0000
3818---0000
3820---0000
3822---0000
3824---0000
3826---0000
3828---0000
3830---0000
3832---0000
3834---0000
3836---0000
3838---0000
3840---0000
3842---0000
3844---0000
3846---0000
3848---0000
3850---0000
3852---0000
3854---0000
3856---0000
3858---0000
3860---0000
3862---0000
3864---0000
3866---0000
3868---0000
3870---0000
3872---0000
3874---0000
3876---0000
3878---0000
3880---0000
3882---0000
3884---0000
3886---0000
3888---0000
3890---0000
3892---0000
3894---0000
3896---0000
3898---0000
3900---0000
3902---0000
3904---0000
3906---0000
3908---0000
3910---0000
3912---0000
3914---0000
3916---0000
3918---0000
3920---0000
3922---0000
3924---0000
3926---0000
3928---0000
3930---0000
3932---0000
3934---0000
3936---0000
3938---0000
3940---0000
3942---0000
3944---0000
3946---0000
3948---0000
3950---0000
3952---0000
3954---0000
3956---0000
3958---0000
3960---0000
3962---0000
3964---0000
3966---0000
3968---0000
3970---0000
3972---0000
3974---0000
3976---0000
3978---0000
3980---0000
3982---0000
3984---0000
3986---0000
3988---0000
3990---0000
3992---0000
3994---0000
3996---0000
3998---0000
4000---0000
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m16.353s
user	0m2.881s
sys	0m0.015s


'193.170'
************** PARI *****************
Host 193.170.37.83 (193.170.37.83)
Time: Thu Jul 27 03:43:37 2006

Input: f=x^4-6
polred(f)
nf=nfinit(f);
factor(nf.disc)
forstep (A=1000, 3000, 2, g1=x^4+A*x^2+A^2/2; g2=x^4-A*x^2-A^2/2; g3=x^4+A*x^2-A^2/2; g4=x^4-A*x^2+A^2/2; nf1=nfinit(g1); nf2=nfinit(g2); nf3=nfinit(g3); nf4=nfinit(g4);factor(nf1.disc);factor(nf2.disc);factor(nf3.disc);factor(nf4.disc);nfisisom(f,g1); print(A,"---",nfisisom(f,g1), nfisisom(f,g2),nfisisom(f,g3),nfisisom(f,g4)))

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = x^4 - 6
? %2 = [x - 1, x^2 - 6, x^4 - 216, x^4 - 6]
? ? %4 = 
[-1 1]

[2 11]

[3 3]

? 1000---0000
1002---0000
1004---0000
1006---0000
1008---0000
1010---0000
1012---0000
1014---0000
1016---0000
1018---0000
1020---0000
1022---0000
1024---0000
1026---0000
1028---0000
1030---0000
1032---0000
1034---0000
1036---0000
1038---0000
1040---0000
1042---0000
1044---0000
1046---0000
1048---0000
1050---0000
1052---0000
1054---0000
1056---0000
1058---0000
1060---0000
1062---0000
1064---0000
1066---0000
1068---0000
1070---0000
1072---0000
1074---0000
1076---0000
1078---0000
1080---0000
1082---0000
1084---0000
1086---0000
1088---0000
1090---0000
1092---0000
1094---0000
1096---0000
1098---0000
1100---0000
1102---0000
1104---0000
1106---0000
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2624---0000
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2628---0000
2630---0000

 ** WARNING: Output too long, hence truncated.
Errors/timing (if any):


Timing:
real	0m7.931s
user	0m4.057s
sys	0m0.015s


'193.170'
************** PARI *****************
Host 193.170.37.83 (193.170.37.83)
Time: Thu Jul 27 03:42:58 2006

Input: f=x^4-6
polred(f)
nf=nfinit(f);
factor(nf.disc)
forstep (A=2, 1000, 2, g1=x^4+A*x^2+A^2/2; g2=x^4-A*x^2-A^2/2; g3=x^4+A*x^2-A^2/2; g4=x^4-A*x^2+A^2/2; nf1=nfinit(g1); nf2=nfinit(g2); nf3=nfinit(g3); nf4=nfinit(g4);factor(nf1.disc);factor(nf2.disc);factor(nf3.disc);factor(nf4.disc);nfisisom(f,g1); print(A,"---",nfisisom(f,g1), nfisisom(f,g2),nfisisom(f,g3),nfisisom(f,g4)))

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = x^4 - 6
? %2 = [x - 1, x^2 - 6, x^4 - 216, x^4 - 6]
? ? %4 = 
[-1 1]

[2 11]

[3 3]

? 2---0000
4---0000
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1000---0000
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m9.921s
user	0m1.881s
sys	0m0.008s


'193.170'
************** PARI *****************
Host 193.170.37.83 (193.170.37.83)
Time: Thu Jul 27 03:42:45 2006

Input: f=x^4+2*x^2-11
polred(f)
nf=nfinit(f);
factor(nf.disc)
forstep (A=2, 1000, 2, g1=x^4+A*x^2+A^2/2; g2=x^4-A*x^2-A^2/2; g3=x^4+A*x^2-A^2/2; g4=x^4-A*x^2+A^2/2; nf1=nfinit(g1); nf2=nfinit(g2); nf3=nfinit(g3); nf4=nfinit(g4);factor(nf1.disc);factor(nf2.disc);factor(nf3.disc);factor(nf4.disc);nfisisom(f,g1); print(A,"---",nfisisom(f,g1), nfisisom(f,g2),nfisisom(f,g3),nfisisom(f,g4)))

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = x^4 + 2*x^2 - 11
? %2 = [x - 1, x^2 - 3, x^4 - 2*x^3 - 4*x^2 + 14*x - 11, x^4 + 2*x^2 - 11]
? ? %4 = 
[-1 1]

[2 6]

[3 2]

[11 1]

? 2---0000
4---0000
6---0000
8---0000
10---0000
12---0000
14---0000
16---0000
18---0000
20---0000
22---0000
24---0000
26---0000
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1000---0000
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m10.100s
user	0m1.876s
sys	0m0.015s


'193.170'
************** PARI *****************
Host 193.170.37.83 (193.170.37.83)
Time: Thu Jul 27 03:20:14 2006

Input: f=x^4+2*x^2-11
polred(f)
nf=nfinit(f);
factor(nf.disc)
forstep (A=2, 1000, 2, g1=x^4+A*x^2+A^2/2; g2=x^4-A*x^2-A^2/2; g3=x^4+A*x^2-A^2/2; g4=x^4-A*x^2+A^2/2; nf1=nfinit(g1); nf2=nfinit(g2); nf3=nfinit(g3); nf4=nfinit(g4);factor(nf1.disc);factor(nf2.disc);factor(nf3.disc);factor(nf4.disc);nfisisom(f,g1); print(A,"---",nfisisom(f,g1), nfisisom(f,g2),nfisisom(f,g3),nfisisom(f,g4)))

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = x^4 + 2*x^2 - 11
? %2 = [x - 1, x^2 - 3, x^4 - 2*x^3 - 4*x^2 + 14*x - 11, x^4 + 2*x^2 - 11]
? ? %4 = 
[-1 1]

[2 6]

[3 2]

[11 1]

? 2---0000
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968---0000
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978---0000
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982---0000
984---0000
986---0000
988---0000
990---0000
992---0000
994---0000
996---0000
998---0000
1000---0000
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m10.009s
user	0m1.877s
sys	0m0.013s


'193.170'
************** PARI *****************
Host 193.170.37.83 (193.170.37.83)
Time: Thu Jul 27 03:19:49 2006

Input: f=x^4+2*x^2+11
polred(f)
nf=nfinit(f);
factor(nf.disc)
forstep (A=2, 1000, 2, g1=x^4+A*x^2+A^2/2; g2=x^4-A*x^2-A^2/2; g3=x^4+A*x^2-A^2/2; g4=x^4-A*x^2+A^2/2; nf1=nfinit(g1); nf2=nfinit(g2); nf3=nfinit(g3); nf4=nfinit(g4);factor(nf1.disc);factor(nf2.disc);factor(nf3.disc);factor(nf4.disc);nfisisom(f,g1); print(A,"---",nfisisom(f,g1), nfisisom(f,g2),nfisisom(f,g3),nfisisom(f,g4)))

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = x^4 + 2*x^2 + 11
? %2 = [x - 1, x^2 + 10, x^4 - 20*x^2 + 1100, x^4 + 2*x^2 + 11]
? ? %4 = 
[2 10]

[5 2]

[11 1]

? 2---0000
4---0000
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996---0000
998---0000
1000---0000
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m10.999s
user	0m1.880s
sys	0m0.016s


'193.170'
************** PARI *****************
Host 193.170.37.83 (193.170.37.83)
Time: Thu Jul 27 03:19:11 2006

Input: f=x^4+2*x^2+11
polred(f)
nf=nfinit(f);
factor(nf.disc);
forstep (A=2, 1000, 2, g1=x^4+A*x^2+A^2/2; g2=x^4-A*x^2-A^2/2; g3=x^4+A*x^2-A^2/2; g4=x^4-A*x^2+A^2/2; nf1=nfinit(g1); nf2=nfinit(g2); nf3=nfinit(g3); nf4=nfinit(g4);factor(nf1.disc);factor(nf2.disc);factor(nf3.disc);factor(nf4.disc);nfisisom(f,g1); print(A,"---",nfisisom(f,g1), nfisisom(f,g2),nfisisom(f,g3),nfisisom(f,g4)))

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = x^4 + 2*x^2 + 11
? %2 = [x - 1, x^2 + 10, x^4 - 20*x^2 + 1100, x^4 + 2*x^2 + 11]
? ? ? 2---0000
4---0000
6---0000
8---0000
10---0000
12---0000
14---0000
16---0000
18---0000
20---0000
22---0000
24---0000
26---0000
28---0000
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952---0000
954---0000
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960---0000
962---0000
964---0000
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968---0000
970---0000
972---0000
974---0000
976---0000
978---0000
980---0000
982---0000
984---0000
986---0000
988---0000
990---0000
992---0000
994---0000
996---0000
998---0000
1000---0000
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m10.187s
user	0m1.878s
sys	0m0.015s


'193.170'
************** PARI *****************
Host 193.170.37.83 (193.170.37.83)
Time: Thu Jul 27 03:04:23 2006

Input: f=x^4+2*x^2+7
polred(f)
nf=nfinit(f);
factor(nf.disc);
forstep (A=5000, 6000, 2, g1=x^4+A*x^2+A^2/2; g2=x^4-A*x^2-A^2/2; g3=x^4+A*x^2-A^2/2; g4=x^4-A*x^2+A^2/2; nf1=nfinit(g1); nf2=nfinit(g2); nf3=nfinit(g3); nf4=nfinit(g4);factor(nf1.disc);factor(nf2.disc);factor(nf3.disc);factor(nf4.disc);nfisisom(f,g1); print(A,"---",nfisisom(f,g1), nfisisom(f,g2),nfisisom(f,g3),nfisisom(f,g4)))

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = x^4 + 2*x^2 + 7
? %2 = [x - 1, x^2 + 6, x^4 - 12*x^2 + 252, x^4 + 2*x^2 + 7]
? ? ? 5000---0000
5002---0000
5004---0000
5006---0000
5008---0000
5010---0000
5012---0000
5014---0000
5016---0000
5018---0000
5020---0000
5022---0000
5024---0000
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5990---0000
5992---0000
5994---0000
5996---0000
5998---0000
6000---0000
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m11.364s
user	0m2.140s
sys	0m0.014s


'193.170'
************** PARI *****************
Host 193.170.37.83 (193.170.37.83)
Time: Thu Jul 27 03:03:51 2006

Input: f=x^4+2*x^2+7
polred(f)
nf=nfinit(f);
factor(nf.disc);
forstep (A=4000, 5000, 2, g1=x^4+A*x^2+A^2/2; g2=x^4-A*x^2-A^2/2; g3=x^4+A*x^2-A^2/2; g4=x^4-A*x^2+A^2/2; nf1=nfinit(g1); nf2=nfinit(g2); nf3=nfinit(g3); nf4=nfinit(g4);factor(nf1.disc);factor(nf2.disc);factor(nf3.disc);factor(nf4.disc);nfisisom(f,g1); print(A,"---",nfisisom(f,g1), nfisisom(f,g2),nfisisom(f,g3),nfisisom(f,g4)))

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = x^4 + 2*x^2 + 7
? %2 = [x - 1, x^2 + 6, x^4 - 12*x^2 + 252, x^4 + 2*x^2 + 7]
? ? ? 4000---0000
4002---0000
4004---0000
4006---0000
4008---0000
4010---0000
4012---0000
4014---0000
4016---0000
4018---0000
4020---0000
4022---0000
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5000---0000
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m4.262s
user	0m2.114s
sys	0m0.014s


'193.170'
************** PARI *****************
Host 193.170.37.83 (193.170.37.83)
Time: Thu Jul 27 03:02:25 2006

Input: f=x^4+2*x^2+7
polred(f)
nf=nfinit(f);
factor(nf.disc);
forstep (A=3000, 4000, 2, g1=x^4+A*x^2+A^2/2; g2=x^4-A*x^2-A^2/2; g3=x^4+A*x^2-A^2/2; g4=x^4-A*x^2+A^2/2; nf1=nfinit(g1); nf2=nfinit(g2); nf3=nfinit(g3); nf4=nfinit(g4);factor(nf1.disc);factor(nf2.disc);factor(nf3.disc);factor(nf4.disc);nfisisom(f,g1); print(A,"---",nfisisom(f,g1), nfisisom(f,g2),nfisisom(f,g3),nfisisom(f,g4)))

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = x^4 + 2*x^2 + 7
? %2 = [x - 1, x^2 + 6, x^4 - 12*x^2 + 252, x^4 + 2*x^2 + 7]
? ? ? 3000---0000
3002---0000
3004---0000
3006---0000
3008---0000
3010---0000
3012---0000
3014---0000
3016---0000
3018---0000
3020---0000
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3984---0000
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3988---0000
3990---0000
3992---0000
3994---0000
3996---0000
3998---0000
4000---0000
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m4.178s
user	0m2.098s
sys	0m0.008s


'193.170'
************** PARI *****************
Host 193.170.37.83 (193.170.37.83)
Time: Thu Jul 27 03:01:59 2006

Input: f=x^4+2*x^2+7
polred(f)
nf=nfinit(f);
factor(nf.disc);
forstep (A=2, 200, 2, g1=x^4+A*x^2+A^2/2; g2=x^4-A*x^2-A^2/2; g3=x^4+A*x^2-A^2/2; g4=x^4-A*x^2+A^2/2; nf1=nfinit(g1); nf2=nfinit(g2); nf3=nfinit(g3); nf4=nfinit(g4);factor(nf1.disc);factor(nf2.disc);factor(nf3.disc);factor(nf4.disc);nfisisom(f,g1); print(A,"---",nfisisom(f,g1), nfisisom(f,g2),nfisisom(f,g3),nfisisom(f,g4)))

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = x^4 + 2*x^2 + 7
? %2 = [x - 1, x^2 + 6, x^4 - 12*x^2 + 252, x^4 + 2*x^2 + 7]
? ? ? 2---0000
4---0000
6---0000
8---0000
10---0000
12---0000
14---0000
16---0000
18---0000
20---0000
22---0000
24---0000
26---0000
28---0000
30---0000
32---0000
34---0000
36---0000
38---0000
40---0000
42---0000
44---0000
46---0000
48---0000
50---0000
52---0000
54---0000
56---0000
58---0000
60---0000
62---0000
64---0000
66---0000
68---0000
70---0000
72---0000
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76---0000
78---0000
80---0000
82---0000
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88---0000
90---0000
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170---0000
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174---0000
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178---0000
180---0000
182---0000
184---0000
186---0000
188---0000
190---0000
192---0000
194---0000
196---0000
198---0000
200---0000
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.461s
user	0m0.346s
sys	0m0.007s


'193.170'
************** PARI *****************
Host 193.170.37.83 (193.170.37.83)
Time: Thu Jul 27 03:01:40 2006

Input: f=x^4+2*x^2+7
polred(f)
nf=nfinit(f);
factor(nf.disc);
for (A=2, 2, g1=x^4+A*x^2+A^2/2; g2=x^4-A*x^2-A^2/2; g3=x^4+A*x^2-A^2/2; g4=x^4-A*x^2+A^2/2; nf1=nfinit(g1); nf2=nfinit(g2); nf3=nfinit(g3); nf4=nfinit(g4);factor(nf1.disc);factor(nf2.disc);factor(nf3.disc);factor(nf4.disc);nfisisom(f,g1); print(A,"---",nfisisom(f,g1), nfisisom(f,g2),nfisisom(f,g3),nfisisom(f,g4)))

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = x^4 + 2*x^2 + 7
? %2 = [x - 1, x^2 + 6, x^4 - 12*x^2 + 252, x^4 + 2*x^2 + 7]
? ? ? 2---0000
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.021s
user	0m0.009s
sys	0m0.007s


'193.170'
************** PARI *****************
Host 193.170.37.83 (193.170.37.83)
Time: Thu Jul 27 03:01:18 2006

Input: f=x^4+2*x^2+7
polred(f)
nf=nfinit(f);
factor(nf.disc);
forstep (A=2, 500, 0, g1=x^4+A*x^2+A^2/2; g2=x^4-A*x^2-A^2/2; g3=x^4+A*x^2-A^2/2; g4=x^4-A*x^2+A^2/2; nf1=nfinit(g1); nf2=nfinit(g2); nf3=nfinit(g3); nf4=nfinit(g4);factor(nf1.disc);factor(nf2.disc);factor(nf3.disc);factor(nf4.disc);nfisisom(f,g1); print(A,"---",nfisisom(f,g1), nfisisom(f,g2),nfisisom(f,g3),nfisisom(f,g4)))

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = x^4 + 2*x^2 + 7
? %2 = [x - 1, x^2 + 6, x^4 - 12*x^2 + 252, x^4 + 2*x^2 + 7]
? ? ? ? 
Goodbye!

Errors/timing (if any):

  *** forstep: step equal to zero in forstep.

Timing:
real	0m0.040s
user	0m0.008s
sys	0m0.007s


'193.170'
************** PARI *****************
Host 193.170.37.83 (193.170.37.83)
Time: Thu Jul 27 03:00:36 2006

Input: f=x^4+2*x^2+7
polred(f)
nf=nfinit(f);
factor(nf.disc);
forstep (A=-1000, 500, 2, g1=x^4+A*x^2+A^2/2; g2=x^4-A*x^2-A^2/2; g3=x^4+A*x^2-A^2/2; g4=x^4-A*x^2+A^2/2; nf1=nfinit(g1); nf2=nfinit(g2); nf3=nfinit(g3); nf4=nfinit(g4);factor(nf1.disc);factor(nf2.disc);factor(nf3.disc);factor(nf4.disc);nfisisom(f,g1); print(A,"---",nfisisom(f,g1), nfisisom(f,g2),nfisisom(f,g3),nfisisom(f,g4)))

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = x^4 + 2*x^2 + 7
? %2 = [x - 1, x^2 + 6, x^4 - 12*x^2 + 252, x^4 + 2*x^2 + 7]
? ? ? -1000---0000
-998---0000
-996---0000
-994---0000
-992---0000
-990---0000
-988---0000
-986---0000
-984---0000
-982---0000
-980---0000
-978---0000
-976---0000
-974---0000
-972---0000
-970---0000
-968---0000
-966---0000
-964---0000
-962---0000
-960---0000
-958---0000
-956---0000
-954---0000
-952---0000
-950---0000
-948---0000
-946---0000
-944---0000
-942---0000
-940---0000
-938---0000
-936---0000
-934---0000
-932---0000
-930---0000
-928---0000
-926---0000
-924---0000
-922---0000
-920---0000
-918---0000
-916---0000
-914---0000
-912---0000
-910---0000
-908---0000
-906---0000
-904---0000
-902---0000
-900---0000
-898---0000
-896---0000
-894---0000
-892---0000
-890---0000
-888---0000
-886---0000
-884---0000
-882---0000
-880---0000
-878---0000
-876---0000
-874---0000
-872---0000
-870---0000
-868---0000
-866---0000
-864---0000
-862---0000
-860---0000
-858---0000
-856---0000
-854---0000
-852---0000
-850---0000
-848---0000
-846---0000
-844---0000
-842---0000
-840---0000
-838---0000
-836---0000
-834---0000
-832---0000
-830---0000
-828---0000
-826---0000
-824---0000
-822---0000
-820---0000
-818---0000
-816---0000
-814---0000
-812---0000
-810---0000
-808---0000
-806---0000
-804---0000
-802---0000
-800---0000
-798---0000
-796---0000
-794---0000
-792---0000
-790---0000
-788---0000
-786---0000
-784---0000
-782---0000
-780---0000
-778---0000
-776---0000
-774---0000
-772---0000
-770---0000
-768---0000
-766---0000
-764---0000
-762---0000
-760---0000
-758---0000
-756---0000
-754---0000
-752---0000
-750---0000
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-746---0000
-744---0000
-742---0000
-740---0000
-738---0000
-736---0000
-734---0000
-732---0000
-730---0000
-728---0000
-726---0000
-724---0000
-722---0000
-720---0000
-718---0000
-716---0000
-714---0000
-712---0000
-710---0000
-708---0000
-706---0000
-704---0000
-702---0000
-700---0000
-698---0000
-696---0000
-694---0000
-692---0000
-690---0000
-688---0000
-686---0000
-684---0000
-682---0000
-680---0000
-678---0000
-676---0000
-674---0000
-672---0000
-670---0000
-668---0000
-666---0000
-664---0000
-662---0000
-660---0000
-658---0000
-656---0000
-654---0000
-652---0000
-650---0000
-648---0000
-646---0000
-644---0000
-642---0000
-640---0000
-638---0000
-636---0000
-634---0000
-632---0000
-630---0000
-628---0000
-626---0000
-624---0000
-622---0000
-620---0000
-618---0000
-616---0000
-614---0000
-612---0000
-610---0000
-608---0000
-606---0000
-604---0000
-602---0000
-600---0000
-598---0000
-596---0000
-594---0000
-592---0000
-590---0000
-588---0000
-586---0000
-584---0000
-582---0000
-580---0000
-578---0000
-576---0000
-574---0000
-572---0000
-570---0000
-568---0000
-566---0000
-564---0000
-562---0000
-560---0000
-558---0000
-556---0000
-554---0000
-552---0000
-550---0000
-548---0000
-546---0000
-544---0000
-542---0000
-540---0000
-538---0000
-536---0000
-534---0000
-532---0000
-530---0000
-528---0000
-526---0000
-524---0000
-522---0000
-520---0000
-518---0000
-516---0000
-514---0000
-512---0000
-510---0000
-508---0000
-506---0000
-504---0000
-502---0000
-500---0000
-498---0000
-496---0000
-494---0000
-492---0000
-490---0000
-488---0000
-486---0000
-484---0000
-482---0000
-480---0000
-478---0000
-476---0000
-474---0000
-472---0000
-470---0000
-468---0000
-466---0000
-464---0000
-462---0000
-460---0000
-458---0000
-456---0000
-454---0000
-452---0000
-450---0000
-448---0000
-446---0000
-444---0000
-442---0000
-440---0000
-438---0000
-436---0000
-434---0000
-432---0000
-430---0000
-428---0000
-426---0000
-424---0000
-422---0000
-420---0000
-418---0000
-416---0000
-414---0000
-412---0000
-410---0000
-408---0000
-406---0000
-404---0000
-402---0000
-400---0000
-398---0000
-396---0000
-394---0000
-392---0000
-390---0000
-388---0000
-386---0000
-384---0000
-382---0000
-380---0000
-378---0000
-376---0000
-374---0000
-372---0000
-370---0000
-368---0000
-366---0000
-364---0000
-362---0000
-360---0000
-358---0000
-356---0000
-354---0000
-352---0000
-350---0000
-348---0000
-346---0000
-344---0000
-342---0000
-340---0000
-338---0000
-336---0000
-334---0000
-332---0000
-330---0000
-328---0000
-326---0000
-324---0000
-322---0000
-320---0000
-318---0000
-316---0000
-314---0000
-312---0000
-310---0000
-308---0000
-306---0000
-304---0000
-302---0000
-300---0000
-298---0000
-296---0000
-294---0000
-292---0000
-290---0000
-288---0000
-286---0000
-284---0000
-282---0000
-280---0000
-278---0000
-276---0000
-274---0000
-272---0000
-270---0000
-268---0000
-266---0000
-264---0000
-262---0000
-260---0000
-258---0000
-256---0000
-254---0000
-252---0000
-250---0000
-248---0000
-246---0000
-244---0000
-242---0000
-240---0000
-238---0000
-236---0000
-234---0000
-232---0000
-230---0000
-228---0000
-226---0000
-224---0000
-222---0000
-220---0000
-218---0000
-216---0000
-214---0000
-212---0000
-210---0000
-208---0000
-206---0000
-204---0000
-202---0000
-200---0000
-198---0000
-196---0000
-194---0000
-192---0000
-190---0000
-188---0000
-186---0000
-184---0000
-182---0000
-180---0000
-178---0000
-176---0000
-174---0000
-172---0000
-170---0000
-168---0000
-166---0000
-164---0000
-162---0000
-160---0000
-158---0000
-156---0000
-154---0000
-152---0000
-150---0000
-148---0000
-146---0000
-144---0000
-142---0000
-140---0000
-138---0000
-136---0000
-134---0000
-132---0000
-130---0000
-128---0000
-126---0000
-124---0000
-122---0000
-120---0000
-118---0000
-116---0000
-114---0000
-112---0000
-110---0000
-108---0000
-106---0000
-104---0000
-102---0000
-100---0000
-98---0000
-96---0000
-94---0000
-92---0000
-90---0000
-88---0000
-86---0000
-84---0000
-82---0000
-80---0000
-78---0000
-76---0000
-74---0000
-72---0000
-70---0000
-68---0000
-66---0000
-64---0000
-62---0000
-60---0000
-58---0000
-56---0000
-54---0000
-52---0000
-50---0000
-48---0000
-46---0000
-44---0000
-42---0000
-40---0000
-38---0000
-36---0000
-34---0000
-32---0000
-30---0000
-28---0000
-26---0000
-24---0000
-22---0000
-20---0000
-18---0000
-16---0000
-14---0000
-12---0000
-10---0000
-8---0000
-6---0000
-4---0000
-2---0000
? 
Goodbye!

Errors/timing (if any):

  *** nfinit: reducible polynomial in nfinit.

Timing:
real	0m11.060s
user	0m1.878s
sys	0m0.012s


'193.170'
************** PARI *****************
Host 193.170.37.83 (193.170.37.83)
Time: Thu Jul 27 02:59:15 2006

Input: f=x^4+2*x^2+7
polred(f)
nf=nfinit(f);
factor(nf.disc);
forstep (A=-1000, 0, 2, g1=x^4+A*x^2+A^2/2; g2=x^4-A*x^2-A^2/2; g3=x^4+A*x^2-A^2/2; g4=x^4-A*x^2+A^2/2; nf1=nfinit(g1); nf2=nfinit(g2); nf3=nfinit(g3); nf4=nfinit(g4);factor(nf1.disc);factor(nf2.disc);factor(nf3.disc);factor(nf4.disc);nfisisom(f,g1); print(A,"---",nfisisom(f,g1), nfisisom(f,g2),nfisisom(f,g3),nfisisom(f,g4)))

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = x^4 + 2*x^2 + 7
? %2 = [x - 1, x^2 + 6, x^4 - 12*x^2 + 252, x^4 + 2*x^2 + 7]
? ? ? -1000---0000
-998---0000
-996---0000
-994---0000
-992---0000
-990---0000
-988---0000
-986---0000
-984---0000
-982---0000
-980---0000
-978---0000
-976---0000
-974---0000
-972---0000
-970---0000
-968---0000
-966---0000
-964---0000
-962---0000
-960---0000
-958---0000
-956---0000
-954---0000
-952---0000
-950---0000
-948---0000
-946---0000
-944---0000
-942---0000
-940---0000
-938---0000
-936---0000
-934---0000
-932---0000
-930---0000
-928---0000
-926---0000
-924---0000
-922---0000
-920---0000
-918---0000
-916---0000
-914---0000
-912---0000
-910---0000
-908---0000
-906---0000
-904---0000
-902---0000
-900---0000
-898---0000
-896---0000
-894---0000
-892---0000
-890---0000
-888---0000
-886---0000
-884---0000
-882---0000
-880---0000
-878---0000
-876---0000
-874---0000
-872---0000
-870---0000
-868---0000
-866---0000
-864---0000
-862---0000
-860---0000
-858---0000
-856---0000
-854---0000
-852---0000
-850---0000
-848---0000
-846---0000
-844---0000
-842---0000
-840---0000
-838---0000
-836---0000
-834---0000
-832---0000
-830---0000
-828---0000
-826---0000
-824---0000
-822---0000
-820---0000
-818---0000
-816---0000
-814---0000
-812---0000
-810---0000
-808---0000
-806---0000
-804---0000
-802---0000
-800---0000
-798---0000
-796---0000
-794---0000
-792---0000
-790---0000
-788---0000
-786---0000
-784---0000
-782---0000
-780---0000
-778---0000
-776---0000
-774---0000
-772---0000
-770---0000
-768---0000
-766---0000
-764---0000
-762---0000
-760---0000
-758---0000
-756---0000
-754---0000
-752---0000
-750---0000
-748---0000
-746---0000
-744---0000
-742---0000
-740---0000
-738---0000
-736---0000
-734---0000
-732---0000
-730---0000
-728---0000
-726---0000
-724---0000
-722---0000
-720---0000
-718---0000
-716---0000
-714---0000
-712---0000
-710---0000
-708---0000
-706---0000
-704---0000
-702---0000
-700---0000
-698---0000
-696---0000
-694---0000
-692---0000
-690---0000
-688---0000
-686---0000
-684---0000
-682---0000
-680---0000
-678---0000
-676---0000
-674---0000
-672---0000
-670---0000
-668---0000
-666---0000
-664---0000
-662---0000
-660---0000
-658---0000
-656---0000
-654---0000
-652---0000
-650---0000
-648---0000
-646---0000
-644---0000
-642---0000
-640---0000
-638---0000
-636---0000
-634---0000
-632---0000
-630---0000
-628---0000
-626---0000
-624---0000
-622---0000
-620---0000
-618---0000
-616---0000
-614---0000
-612---0000
-610---0000
-608---0000
-606---0000
-604---0000
-602---0000
-600---0000
-598---0000
-596---0000
-594---0000
-592---0000
-590---0000
-588---0000
-586---0000
-584---0000
-582---0000
-580---0000
-578---0000
-576---0000
-574---0000
-572---0000
-570---0000
-568---0000
-566---0000
-564---0000
-562---0000
-560---0000
-558---0000
-556---0000
-554---0000
-552---0000
-550---0000
-548---0000
-546---0000
-544---0000
-542---0000
-540---0000
-538---0000
-536---0000
-534---0000
-532---0000
-530---0000
-528---0000
-526---0000
-524---0000
-522---0000
-520---0000
-518---0000
-516---0000
-514---0000
-512---0000
-510---0000
-508---0000
-506---0000
-504---0000
-502---0000
-500---0000
-498---0000
-496---0000
-494---0000
-492---0000
-490---0000
-488---0000
-486---0000
-484---0000
-482---0000
-480---0000
-478---0000
-476---0000
-474---0000
-472---0000
-470---0000
-468---0000
-466---0000
-464---0000
-462---0000
-460---0000
-458---0000
-456---0000
-454---0000
-452---0000
-450---0000
-448---0000
-446---0000
-444---0000
-442---0000
-440---0000
-438---0000
-436---0000
-434---0000
-432---0000
-430---0000
-428---0000
-426---0000
-424---0000
-422---0000
-420---0000
-418---0000
-416---0000
-414---0000
-412---0000
-410---0000
-408---0000
-406---0000
-404---0000
-402---0000
-400---0000
-398---0000
-396---0000
-394---0000
-392---0000
-390---0000
-388---0000
-386---0000
-384---0000
-382---0000
-380---0000
-378---0000
-376---0000
-374---0000
-372---0000
-370---0000
-368---0000
-366---0000
-364---0000
-362---0000
-360---0000
-358---0000
-356---0000
-354---0000
-352---0000
-350---0000
-348---0000
-346---0000
-344---0000
-342---0000
-340---0000
-338---0000
-336---0000
-334---0000
-332---0000
-330---0000
-328---0000
-326---0000
-324---0000
-322---0000
-320---0000
-318---0000
-316---0000
-314---0000
-312---0000
-310---0000
-308---0000
-306---0000
-304---0000
-302---0000
-300---0000
-298---0000
-296---0000
-294---0000
-292---0000
-290---0000
-288---0000
-286---0000
-284---0000
-282---0000
-280---0000
-278---0000
-276---0000
-274---0000
-272---0000
-270---0000
-268---0000
-266---0000
-264---0000
-262---0000
-260---0000
-258---0000
-256---0000
-254---0000
-252---0000
-250---0000
-248---0000
-246---0000
-244---0000
-242---0000
-240---0000
-238---0000
-236---0000
-234---0000
-232---0000
-230---0000
-228---0000
-226---0000
-224---0000
-222---0000
-220---0000
-218---0000
-216---0000
-214---0000
-212---0000
-210---0000
-208---0000
-206---0000
-204---0000
-202---0000
-200---0000
-198---0000
-196---0000
-194---0000
-192---0000
-190---0000
-188---0000
-186---0000
-184---0000
-182---0000
-180---0000
-178---0000
-176---0000
-174---0000
-172---0000
-170---0000
-168---0000
-166---0000
-164---0000
-162---0000
-160---0000
-158---0000
-156---0000
-154---0000
-152---0000
-150---0000
-148---0000
-146---0000
-144---0000
-142---0000
-140---0000
-138---0000
-136---0000
-134---0000
-132---0000
-130---0000
-128---0000
-126---0000
-124---0000
-122---0000
-120---0000
-118---0000
-116---0000
-114---0000
-112---0000
-110---0000
-108---0000
-106---0000
-104---0000
-102---0000
-100---0000
-98---0000
-96---0000
-94---0000
-92---0000
-90---0000
-88---0000
-86---0000
-84---0000
-82---0000
-80---0000
-78---0000
-76---0000
-74---0000
-72---0000
-70---0000
-68---0000
-66---0000
-64---0000
-62---0000
-60---0000
-58---0000
-56---0000
-54---0000
-52---0000
-50---0000
-48---0000
-46---0000
-44---0000
-42---0000
-40---0000
-38---0000
-36---0000
-34---0000
-32---0000
-30---0000
-28---0000
-26---0000
-24---0000
-22---0000
-20---0000
-18---0000
-16---0000
-14---0000
-12---0000
-10---0000
-8---0000
-6---0000
-4---0000
-2---0000
? 
Goodbye!

Errors/timing (if any):

  *** nfinit: reducible polynomial in nfinit.

Timing:
real	0m10.470s
user	0m1.879s
sys	0m0.012s


'193.170'
************** PARI *****************
Host 193.170.37.83 (193.170.37.83)
Time: Thu Jul 27 02:58:28 2006

Input: f=x^4+2*x^2+7
polred(f)
nf=nfinit(f);
factor(nf.disc);
forstep (A=1300, 3300, 2, g1=x^4+A*x^2+A^2/2; g2=x^4-A*x^2-A^2/2; g3=x^4+A*x^2-A^2/2; g4=x^4-A*x^2+A^2/2; nf1=nfinit(g1); nf2=nfinit(g2); nf3=nfinit(g3); nf4=nfinit(g4);factor(nf1.disc);factor(nf2.disc);factor(nf3.disc);factor(nf4.disc);nfisisom(f,g1); print(A,"---",nfisisom(f,g1), nfisisom(f,g2),nfisisom(f,g3),nfisisom(f,g4)))

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = x^4 + 2*x^2 + 7
? %2 = [x - 1, x^2 + 6, x^4 - 12*x^2 + 252, x^4 + 2*x^2 + 7]
? ? ? 1300---0000
1302---0000
1304---0000
1306---0000
1308---0000
1310---0000
1312---0000
1314---0000
1316---0000
1318---0000
1320---0000
1322---0000
1324---0000
1326---0000
1328---0000
1330---0000
1332---0000
1334---0000
1336---0000
1338---0000
1340---0000
1342---0000
1344---0000
1346---0000
1348---0000
1350---0000
1352---0000
1354---0000
1356---0000
1358---0000
1360---0000
1362---0000
1364---0000
1366---0000
1368---0000
1370---0000
1372---0000
1374---0000
1376---0000
1378---0000
1380---0000
1382---0000
1384---0000
1386---0000
1388---0000
1390---0000
1392---0000
1394---0000
1396---0000
1398---0000
1400---0000
1402---0000
1404---0000
1406---0000
1408---0000
1410---0000
1412---0000
1414---0000
1416---0000
1418---0000
1420---0000
1422---0000
1424---0000
1426---0000
1428---0000
1430---0000
1432---0000
1434---0000
1436---0000
1438---0000
1440---0000
1442---0000
1444---0000
1446---0000
1448---0000
1450---0000
1452---0000
1454---0000
1456---0000
1458---0000
1460---0000
1462---0000
1464---0000
1466---0000
1468---0000
1470---0000
1472---0000
1474---0000
1476---0000
1478---0000
1480---0000
1482---0000
1484---0000
1486---0000
1488---0000
1490---0000
1492---0000
1494---0000
1496---0000
1498---0000
1500---0000
1502---0000
1504---0000
1506---0000
1508---0000
1510---0000
1512---0000
1514---0000
1516---0000
1518---0000
1520---0000
1522---0000
1524---0000
1526---0000
1528---0000
1530---0000
1532---0000
1534---0000
1536---0000
1538---0000
1540---0000
1542---0000
1544---0000
1546---0000
1548---0000
1550---0000
1552---0000
1554---0000
1556---0000
1558---0000
1560---0000
1562---0000
1564---0000
1566---0000
1568---0000
1570---0000
1572---0000
1574---0000
1576---0000
1578---0000
1580---0000
1582---0000
1584---0000
1586---0000
1588---0000
1590---0000
1592---0000
1594---0000
1596---0000
1598---0000
1600---0000
1602---0000
1604---0000
1606---0000
1608---0000
1610---0000
1612---0000
1614---0000
1616---0000
1618---0000
1620---0000
1622---0000
1624---0000
1626---0000
1628---0000
1630---0000
1632---0000
1634---0000
1636---0000
1638---0000
1640---0000
1642---0000
1644---0000
1646---0000
1648---0000
1650---0000
1652---0000
1654---0000
1656---0000
1658---0000
1660---0000
1662---0000
1664---0000
1666---0000
1668---0000
1670---0000
1672---0000
1674---0000
1676---0000
1678---0000
1680---0000
1682---0000
1684---0000
1686---0000
1688---0000
1690---0000
1692---0000
1694---0000
1696---0000
1698---0000
1700---0000
1702---0000
1704---0000
1706---0000
1708---0000
1710---0000
1712---0000
1714---0000
1716---0000
1718---0000
1720---0000
1722---0000
1724---0000
1726---0000
1728---0000
1730---0000
1732---0000
1734---0000
1736---0000
1738---0000
1740---0000
1742---0000
1744---0000
1746---0000
1748---0000
1750---0000
1752---0000
1754---0000
1756---0000
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2930---0000
2932
 ** WARNING: Output too long, hence truncated.
Errors/timing (if any):


Timing:
real	0m8.261s
user	0m4.092s
sys	0m0.017s


'72.30.1'
************** PARI *****************
Host 72.30.129.123 (72.30.129.123)
Time: Thu Jul 27 00:08:50 2006

Input: collatzlength(x0)=
{
   local(x,i);
   x=x0;  i=0;   
   while(x-1,
      x=if(Mod(x,2)==Mod(0,2), x/2, (3*x+1)/2);i=i++ );
   i
}
collatzlength(299)

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? ? %1 = 75
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.241s
user	0m0.008s
sys	0m0.004s


'72.30.2'
************** PARI *****************
Host 72.30.226.160 (72.30.226.160)
Time: Wed Jul 26 22:52:15 2006

Input: for(n=1,7, print1(n,": ",sum(x=1,n,1/x),",  ") )

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? 1: 1,  2: 3/2,  3: 11/6,  4: 25/12,  5: 137/60,  6: 49/20,  7: 363/140,  
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.421s
user	0m0.008s
sys	0m0.008s


'72.177.'
************** PARI *****************
Host 72.177.144.182 (72.177.144.182)
Time: Wed Jul 26 10:23:50 2006

Input: vector(20,x,floor((x+1)*sqrt(2))-floor(x*sqrt(2)))

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = [1, 2, 1, 2, 1, 1, 2, 1, 2, 1, 1, 2, 1, 2, 1, 2, 1, 1, 2, 1]
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.011s
user	0m0.008s
sys	0m0.004s


'72.177.'
************** PARI *****************
Host 72.177.144.182 (72.177.144.182)
Time: Wed Jul 26 10:23:10 2006

Input: vector(20,x,floor((x+1)*sqrt(2))-floor(x*sqrt(2)))

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = [1, 2, 1, 2, 1, 1, 2, 1, 2, 1, 1, 2, 1, 2, 1, 2, 1, 1, 2, 1]
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.043s
user	0m0.005s
sys	0m0.006s


'193.170'
************** PARI *****************
Host 193.170.37.83 (193.170.37.83)
Time: Wed Jul 26 08:45:41 2006

Input: f=x^4+2*x^2+13
polred(f)
nf=nfinit(f);
factor(nf.disc);
forstep (A=220, 1220, 2, g1=x^4+A*x^2+A^2/2; g2=x^4-A*x^2-A^2/2; g3=x^4+A*x^2-A^2/2; g4=x^4-A*x^2+A^2/2; nf1=nfinit(g1); nf2=nfinit(g2); nf3=nfinit(g3); nf4=nfinit(g4);factor(nf1.disc);factor(nf2.disc);factor(nf3.disc);factor(nf4.disc);nfisisom(f,g1); print(A,"---",nfisisom(f,g1), nfisisom(f,g2),nfisisom(f,g3),nfisisom(f,g4)))
             



Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = x^4 + 2*x^2 + 13
? %2 = [x - 1, x^2 - x + 1, x^4 - 2*x^3 + 2*x^2 - x + 1, x^4 - x^3 - x^2 + x + 1]
? ? ? 220---0000
222---0000
224---0000
226---0000
228---0000
230---0000
232---0000
234---0000
236---0000
238---0000
240---0000
242---0000
244---0000
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1188---0000
1190---0000
1192---0000
1194---0000
1196---0000
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1202---0000
1204---0000
1206---0000
1208---0000
1210---0000
1212---0000
1214---0000
1216---0000
1218---0000
1220---0000
? ? ? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m11.329s
user	0m1.940s
sys	0m0.011s


'193.170'
************** PARI *****************
Host 193.170.37.83 (193.170.37.83)
Time: Wed Jul 26 08:45:09 2006

Input: f=x^4+2*x^2+13
polred(f)
nf=nfinit(f);
factor(nf.disc);
forstep (A=2, 220, 2, g1=x^4+A*x^2+A^2/2; g2=x^4-A*x^2-A^2/2; g3=x^4+A*x^2-A^2/2; g4=x^4-A*x^2+A^2/2; nf1=nfinit(g1); nf2=nfinit(g2); nf3=nfinit(g3); nf4=nfinit(g4);factor(nf1.disc);factor(nf2.disc);factor(nf3.disc);factor(nf4.disc);nfisisom(f,g1); print(A,"---",nfisisom(f,g1), nfisisom(f,g2),nfisisom(f,g3),nfisisom(f,g4)))
             



Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = x^4 + 2*x^2 + 13
? %2 = [x - 1, x^2 - x + 1, x^4 - 2*x^3 + 2*x^2 - x + 1, x^4 - x^3 - x^2 + x + 1]
? ? ? 2---0000
4---0000
6---0000
8---0000
10---0000
12---0000
14---0000
16---0000
18---0000
20---0000
22---0000
24---0000
26---0000
28---0000
30---0000
32---0000
34---0000
36---0000
38---0000
40---0000
42---0000
44---0000
46---0000
48---0000
50---0000
52---0000
54---0000
56---0000
58---0000
60---0000
62---0000
64---0000
66---0000
68---0000
70---0000
72---0000
74---0000
76---0000
78---0000
80---0000
82---0000
84---0000
86---0000
88---0000
90---0000
92---0000
94---0000
96---0000
98---0000
100---0000
102---0000
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106---0000
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112---0000
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120---0000
122---0000
124---0000
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128---0000
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132---0000
134---0000
136---0000
138---0000
140---0000
142---0000
144---0000
146---0000
148---0000
150---0000
152---0000
154---0000
156---0000
158---0000
160---0000
162---0000
164---0000
166---0000
168---0000
170---0000
172---0000
174---0000
176---0000
178---0000
180---0000
182---0000
184---0000
186---0000
188---0000
190---0000
192---0000
194---0000
196---0000
198---0000
200---0000
202---0000
204---0000
206---0000
208---0000
210---0000
212---0000
214---0000
216---0000
218---0000
220---0000
? ? ? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m2.299s
user	0m0.384s
sys	0m0.007s


'193.170'
************** PARI *****************
Host 193.170.37.83 (193.170.37.83)
Time: Wed Jul 26 08:44:40 2006

Input: f=x^4+2*x^2+7
polred(f)
nf=nfinit(f);
factor(nf.disc);
forstep (A=4932, 5300, 2, g1=x^4+A*x^2+A^2/2; g2=x^4-A*x^2-A^2/2; g3=x^4+A*x^2-A^2/2; g4=x^4-A*x^2+A^2/2; nf1=nfinit(g1); nf2=nfinit(g2); nf3=nfinit(g3); nf4=nfinit(g4);factor(nf1.disc);factor(nf2.disc);factor(nf3.disc);factor(nf4.disc);nfisisom(f,g1); print(A,"---",nfisisom(f,g1), nfisisom(f,g2),nfisisom(f,g3),nfisisom(f,g4)))
             



Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = x^4 + 2*x^2 + 7
? %2 = [x - 1, x^2 + 6, x^4 - 12*x^2 + 252, x^4 + 2*x^2 + 7]
? ? ? 4932---0000
4934---0000
4936---0000
4938---0000
4940---0000
4942---0000
4944---0000
4946---0000
4948---0000
4950---0000
4952---0000
4954---0000
4956---0000
4958---0000
4960---0000
4962---0000
4964---0000
4966---0000
4968---0000
4970---0000
4972---0000
4974---0000
4976---0000
4978---0000
4980---0000
4982---0000
4984---0000
4986---0000
4988---0000
4990---0000
4992---0000
4994---0000
4996---0000
4998---0000
5000---0000
5002---0000
5004---0000
5006---0000
5008---0000
5010---0000
5012---0000
5014---0000
5016---0000
5018---0000
5020---0000
5022---0000
5024---0000
5026---0000
5028---0000
5030---0000
5032---0000
5034---0000
5036---0000
5038---0000
5040---0000
5042---0000
5044---0000
5046---0000
5048---0000
5050---0000
5052---0000
5054---0000
5056---0000
5058---0000
5060---0000
5062---0000
5064---0000
5066---0000
5068---0000
5070---0000
5072---0000
5074---0000
5076---0000
5078---0000
5080---0000
5082---0000
5084---0000
5086---0000
5088---0000
5090---0000
5092---0000
5094---0000
5096---0000
5098---0000
5100---0000
5102---0000
5104---0000
5106---0000
5108---0000
5110---0000
5112---0000
5114---0000
5116---0000
5118---0000
5120---0000
5122---0000
5124---0000
5126---0000
5128---0000
5130---0000
5132---0000
5134---0000
5136---0000
5138---0000
5140---0000
5142---0000
5144---0000
5146---0000
5148---0000
5150---0000
5152---0000
5154---0000
5156---0000
5158---0000
5160---0000
5162---0000
5164---0000
5166---0000
5168---0000
5170---0000
5172---0000
5174---0000
5176---0000
5178---0000
5180---0000
5182---0000
5184---0000
5186---0000
5188---0000
5190---0000
5192---0000
5194---0000
5196---0000
5198---0000
5200---0000
5202---0000
5204---0000
5206---0000
5208---0000
5210---0000
5212---0000
5214---0000
5216---0000
5218---0000
5220---0000
5222---0000
5224---0000
5226---0000
5228---0000
5230---0000
5232---0000
5234---0000
5236---0000
5238---0000
5240---0000
5242---0000
5244---0000
5246---0000
5248---0000
5250---0000
5252---0000
5254---0000
5256---0000
5258---0000
5260---0000
5262---0000
5264---0000
5266---0000
5268---0000
5270---0000
5272---0000
5274---0000
5276---0000
5278---0000
5280---0000
5282---0000
5284---0000
5286---0000
5288---0000
5290---0000
5292---0000
5294---0000
5296---0000
5298---0000
5300---0000
? ? ? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m1.603s
user	0m0.783s
sys	0m0.010s


'193.170'
************** PARI *****************
Host 193.170.37.83 (193.170.37.83)
Time: Wed Jul 26 08:43:47 2006

Input: f=x^4+2*x^2+7
polred(f)
nf=nfinit(f);
factor(nf.disc);
forstep (A=3300, 5300, 2, g1=x^4+A*x^2+A^2/2; g2=x^4-A*x^2-A^2/2; g3=x^4+A*x^2-A^2/2; g4=x^4-A*x^2+A^2/2; nf1=nfinit(g1); nf2=nfinit(g2); nf3=nfinit(g3); nf4=nfinit(g4);factor(nf1.disc);factor(nf2.disc);factor(nf3.disc);factor(nf4.disc);nfisisom(f,g1); print(A,"---",nfisisom(f,g1), nfisisom(f,g2),nfisisom(f,g3),nfisisom(f,g4)))
             



Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = x^4 + 2*x^2 + 7
? %2 = [x - 1, x^2 + 6, x^4 - 12*x^2 + 252, x^4 + 2*x^2 + 7]
? ? ? 3300---0000
3302---0000
3304---0000
3306---0000
3308---0000
3310---0000
3312---0000
3314---0000
3316---0000
3318---0000
3320---0000
3322---0000
3324---0000
3326---0000
3328---0000
3330---0000
3332---0000
3334---0000
3336---0000
3338---0000
3340---0000
3342---0000
3344---0000
3346---0000
3348---0000
3350---0000
3352---0000
3354---0000
3356---0000
3358---0000
3360---0000
3362---0000
3364---0000
3366---0000
3368---0000
3370---0000
3372---0000
3374---0000
3376---0000
3378---0000
3380---0000
3382---0000
3384---0000
3386---0000
3388---0000
3390---0000
3392---0000
3394---0000
3396---0000
3398---0000
3400---0000
3402---0000
3404---0000
3406---0000
3408---0000
3410---0000
3412---0000
3414---0000
3416---0000
3418---0000
3420---0000
3422---0000
3424---0000
3426---0000
3428---0000
3430---0000
3432---0000
3434---0000
3436---0000
3438---0000
3440---0000
3442---0000
3444---0000
3446---0000
3448---0000
3450---0000
3452---0000
3454---0000
3456---0000
3458---0000
3460---0000
3462---0000
3464---0000
3466---0000
3468---0000
3470---0000
3472---0000
3474---0000
3476---0000
3478---0000
3480---0000
3482---0000
3484---0000
3486---0000
3488---0000
3490---0000
3492---0000
3494---0000
3496---0000
3498---0000
3500---0000
3502---0000
3504---0000
3506---0000
3508---0000
3510---0000
3512---0000
3514---0000
3516---0000
3518---0000
3520---0000
3522---0000
3524---0000
3526---0000
3528---0000
3530---0000
3532---0000
3534---0000
3536---0000
3538---0000
3540---0000
3542---0000
3544---0000
3546---0000
3548---0000
3550---0000
3552---0000
3554---0000
3556---0000
3558---0000
3560---0000
3562---0000
3564---0000
3566---0000
3568---0000
3570---0000
3572---0000
3574---0000
3576---0000
3578---0000
3580---0000
3582---0000
3584---0000
3586---0000
3588---0000
3590---0000
3592---0000
3594---0000
3596---0000
3598---0000
3600---0000
3602---0000
3604---0000
3606---0000
3608---0000
3610---0000
3612---0000
3614---0000
3616---0000
3618---0000
3620---0000
3622---0000
3624---0000
3626---0000
3628---0000
3630---0000
3632---0000
3634---0000
3636---0000
3638---0000
3640---0000
3642---0000
3644---0000
3646---0000
3648---0000
3650---0000
3652---0000
3654---0000
3656---0000
3658---0000
3660---0000
3662---0000
3664---0000
3666---0000
3668---0000
3670---0000
3672---0000
3674---0000
3676---0000
3678---0000
3680---0000
3682---0000
3684---0000
3686---0000
3688---0000
3690---0000
3692---0000
3694---0000
3696---0000
3698---0000
3700---0000
3702---0000
3704---0000
3706---0000
3708---0000
3710---0000
3712---0000
3714---0000
3716---0000
3718---0000
3720---0000
3722---0000
3724---0000
3726---0000
3728---0000
3730---0000
3732---0000
3734---0000
3736---0000
3738---0000
3740---0000
3742---0000
3744---0000
3746---0000
3748---0000
3750---0000
3752---0000
3754---0000
3756---0000
3758---0000
3760---0000
3762---0000
3764---0000
3766---0000
3768---0000
3770---0000
3772---0000
3774---0000
3776---0000
3778---0000
3780---0000
3782---0000
3784---0000
3786---0000
3788---0000
3790---0000
3792---0000
3794---0000
3796---0000
3798---0000
3800---0000
3802---0000
3804---0000
3806---0000
3808---0000
3810---0000
3812---0000
3814---0000
3816---0000
3818---0000
3820---0000
3822---0000
3824---0000
3826---0000
3828---0000
3830---0000
3832---0000
3834---0000
3836---0000
3838---0000
3840---0000
3842---0000
3844---0000
3846---0000
3848---0000
3850---0000
3852---0000
3854---0000
3856---0000
3858---0000
3860---0000
3862---0000
3864---0000
3866---0000
3868---0000
3870---0000
3872---0000
3874---0000
3876---0000
3878---0000
3880---0000
3882---0000
3884---0000
3886---0000
3888---0000
3890---0000
3892---0000
3894---0000
3896---0000
3898---0000
3900---0000
3902---0000
3904---0000
3906---0000
3908---0000
3910---0000
3912---0000
3914---0000
3916---0000
3918---0000
3920---0000
3922---0000
3924---0000
3926---0000
3928---0000
3930---0000
3932---0000
3934---0000
3936---0000
3938---0000
3940---0000
3942---0000
3944---0000
3946---0000
3948---0000
3950---0000
3952---0000
3954---0000
3956---0000
3958---0000
3960---0000
3962---0000
3964---0000
3966---0000
3968---0000
3970---0000
3972---0000
3974---0000
3976---0000
3978---0000
3980---0000
3982---0000
3984---0000
3986---0000
3988---0000
3990---0000
3992---0000
3994---0000
3996---0000
3998---0000
4000---0000
4002---0000
4004---0000
4006---0000
4008---0000
4010---0000
4012---0000
4014---0000
4016---0000
4018---0000
4020---0000
4022---0000
4024---0000
4026---0000
4028---0000
4030---0000
4032---0000
4034---0000
4036---0000
4038---0000
4040---0000
4042---0000
4044---0000
4046---0000
4048---0000
4050---0000
4052---0000
4054---0000
4056---0000
4058---0000
4060---0000
4062---0000
4064---0000
4066---0000
4068---0000
4070---0000
4072---0000
4074---0000
4076---0000
4078---0000
4080---0000
4082---0000
4084---0000
4086---0000
4088---0000
4090---0000
4092---0000
4094---0000
4096---0000
4098---0000
4100---0000
4102---0000
4104---0000
4106---0000
4108---0000
4110---0000
4112---0000
4114---0000
4116---0000
4118---0000
4120---0000
4122---0000
4124---0000
4126---0000
4128---0000
4130---0000
4132---0000
4134---0000
4136---0000
4138---0000
4140---0000
4142---0000
4144---0000
4146---0000
4148---0000
4150---0000
4152---0000
4154---0000
4156---0000
4158---0000
4160---0000
4162---0000
4164---0000
4166---0000
4168---0000
4170---0000
4172---0000
4174---0000
4176---0000
4178---0000
4180---0000
4182---0000
4184---0000
4186---0000
4188---0000
4190---0000
4192---0000
4194---0000
4196---0000
4198---0000
4200---0000
4202---0000
4204---0000
4206---0000
4208---0000
4210---0000
4212---0000
4214---0000
4216---0000
4218---0000
4220---0000
4222---0000
4224---0000
4226---0000
4228---0000
4230---0000
4232---0000
4234---0000
4236---0000
4238---0000
4240---0000
4242---0000
4244---0000
4246---0000
4248---0000
4250---0000
4252---0000
4254---0000
4256---0000
4258---0000
4260---0000
4262---0000
4264---0000
4266---0000
4268---0000
4270---0000
4272---0000
4274---0000
4276---0000
4278---0000
4280---0000
4282---0000
4284---0000
4286---0000
4288---0000
4290---0000
4292---0000
4294---0000
4296---0000
4298---0000
4300---0000
4302---0000
4304---0000
4306---0000
4308---0000
4310---0000
4312---0000
4314---0000
4316---0000
4318---0000
4320---0000
4322---0000
4324---0000
4326---0000
4328---0000
4330---0000
4332---0000
4334---0000
4336---0000
4338---0000
4340---0000
4342---0000
4344---0000
4346---0000
4348---0000
4350---0000
4352---0000
4354---0000
4356---0000
4358---0000
4360---0000
4362---0000
4364---0000
4366---0000
4368---0000
4370---0000
4372---0000
4374---0000
4376---0000
4378---0000
4380---0000
4382---0000
4384---0000
4386---0000
4388---0000
4390---0000
4392---0000
4394---0000
4396---0000
4398---0000
4400---0000
4402---0000
4404---0000
4406---0000
4408---0000
4410---0000
4412---0000
4414---0000
4416---0000
4418---0000
4420---0000
4422---0000
4424---0000
4426---0000
4428---0000
4430---0000
4432---0000
4434---0000
4436---0000
4438---0000
4440---0000
4442---0000
4444---0000
4446---0000
4448---0000
4450---0000
4452---0000
4454---0000
4456---0000
4458---0000
4460---0000
4462---0000
4464---0000
4466---0000
4468---0000
4470---0000
4472---0000
4474---0000
4476---0000
4478---0000
4480---0000
4482---0000
4484---0000
4486---0000
4488---0000
4490---0000
4492---0000
4494---0000
4496---0000
4498---0000
4500---0000
4502---0000
4504---0000
4506---0000
4508---0000
4510---0000
4512---0000
4514---0000
4516---0000
4518---0000
4520---0000
4522---0000
4524---0000
4526---0000
4528---0000
4530---0000
4532---0000
4534---0000
4536---0000
4538---0000
4540---0000
4542---0000
4544---0000
4546---0000
4548---0000
4550---0000
4552---0000
4554---0000
4556---0000
4558---0000
4560---0000
4562---0000
4564---0000
4566---0000
4568---0000
4570---0000
4572---0000
4574---0000
4576---0000
4578---0000
4580---0000
4582---0000
4584---0000
4586---0000
4588---0000
4590---0000
4592---0000
4594---0000
4596---0000
4598---0000
4600---0000
4602---0000
4604---0000
4606---0000
4608---0000
4610---0000
4612---0000
4614---0000
4616---0000
4618---0000
4620---0000
4622---0000
4624---0000
4626---0000
4628---0000
4630---0000
4632---0000
4634---0000
4636---0000
4638---0000
4640---0000
4642---0000
4644---0000
4646---0000
4648---0000
4650---0000
4652---0000
4654---0000
4656---0000
4658---0000
4660---0000
4662---0000
4664---0000
4666---0000
4668---0000
4670---0000
4672---0000
4674---0000
4676---0000
4678---0000
4680---0000
4682---0000
4684---0000
4686---0000
4688---0000
4690---0000
4692---0000
4694---0000
4696---0000
4698---0000
4700---0000
4702---0000
4704---0000
4706---0000
4708---0000
4710---0000
4712---0000
4714---0000
4716---0000
4718---0000
4720---0000
4722---0000
4724---0000
4726---0000
4728---0000
4730---0000
4732---0000
4734---0000
4736---0000
4738---0000
4740---0000
4742---0000
4744---0000
4746---0000
4748---0000
4750---0000
4752---0000
4754---0000
4756---0000
4758---0000
4760---0000
4762---0000
4764---0000
4766---0000
4768---0000
4770---0000
4772---0000
4774---0000
4776---0000
4778---0000
4780---0000
4782---0000
4784---0000
4786---0000
4788---0000
4790---0000
4792---0000
4794---0000
4796---0000
4798---0000
4800---0000
4802---0000
4804---0000
4806---0000
4808---0000
4810---0000
4812---0000
4814---0000
4816---0000
4818---0000
4820---0000
4822---0000
4824---0000
4826---0000
4828---0000
4830---0000
4832---0000
4834---0000
4836---0000
4838---0000
4840---0000
4842---0000
4844---0000
4846---0000
4848---0000
4850---0000
4852---0000
4854---0000
4856---0000
4858---0000
4860---0000
4862---0000
4864---0000
4866---0000
4868---0000
4870---0000
4872---0000
4874---0000
4876---0000
4878---0000
4880---0000
4882---0000
4884---0000
4886---0000
4888---0000
4890---0000
4892---0000
4894---0000
4896---0000
4898---0000
4900---0000
4902---0000
4904---0000
4906---0000
4908---0000
4910---0000
4912---0000
4914---0000
4916---0000
4918---0000
4920---0000
4922---0000
4924---0000
4926---0000
4928---0000
4930---0000
4932
 ** WARNING: Output too long, hence truncated.
Errors/timing (if any):


Timing:
real	0m8.477s
user	0m4.207s
sys	0m0.017s


'193.170'
************** PARI *****************
Host 193.170.37.83 (193.170.37.83)
Time: Wed Jul 26 08:42:29 2006

Input: f=x^4+2*x^2+7
polred(f)
nf=nfinit(f);
factor(nf.disc);
forstep (A=1300, 3300, 2, g1=x^4+A*x^2+A^2/2; g2=x^4-A*x^2-A^2/2; g3=x^4+A*x^2-A^2/2; g4=x^4-A*x^2+A^2/2; nf1=nfinit(g1); nf2=nfinit(g2); nf3=nfinit(g3); nf4=nfinit(g4);factor(nf1.disc);factor(nf2.disc);factor(nf3.disc);factor(nf4.disc);nfisisom(f,g1); print(A,"---",nfisisom(f,g1), nfisisom(f,g2),nfisisom(f,g3),nfisisom(f,g4)))
             



Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = x^4 + 2*x^2 + 7
? %2 = [x - 1, x^2 + 6, x^4 - 12*x^2 + 252, x^4 + 2*x^2 + 7]
? ? ? 1300---0000
1302---0000
1304---0000
1306---0000
1308---0000
1310---0000
1312---0000
1314---0000
1316---0000
1318---0000
1320---0000
1322---0000
1324---0000
1326---0000
1328---0000
1330---0000
1332---0000
1334---0000
1336---0000
1338---0000
1340---0000
1342---0000
1344---0000
1346---0000
1348---0000
1350---0000
1352---0000
1354---0000
1356---0000
1358---0000
1360---0000
1362---0000
1364---0000
1366---0000
1368---0000
1370---0000
1372---0000
1374---0000
1376---0000
1378---0000
1380---0000
1382---0000
1384---0000
1386---0000
1388---0000
1390---0000
1392---0000
1394---0000
1396---0000
1398---0000
1400---0000
1402---0000
1404---0000
1406---0000
1408---0000
1410---0000
1412---0000
1414---0000
1416---0000
1418---0000
1420---0000
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2922---0000
2924---0000
2926---0000
2928---0000
2930---0000
2932
 ** WARNING: Output too long, hence truncated.
Errors/timing (if any):


Timing:
real	0m23.839s
user	0m4.133s
sys	0m0.029s


'193.170'
************** PARI *****************
Host 193.170.37.83 (193.170.37.83)
Time: Wed Jul 26 08:41:42 2006

Input: f=x^4+2*x^2+7
polred(f)
nf=nfinit(f);
factor(nf.disc);
forstep (A=300, 1300, 2, g1=x^4+A*x^2+A^2/2; g2=x^4-A*x^2-A^2/2; g3=x^4+A*x^2-A^2/2; g4=x^4-A*x^2+A^2/2; nf1=nfinit(g1); nf2=nfinit(g2); nf3=nfinit(g3); nf4=nfinit(g4);factor(nf1.disc);factor(nf2.disc);factor(nf3.disc);factor(nf4.disc);nfisisom(f,g1); print(A,"---",nfisisom(f,g1), nfisisom(f,g2),nfisisom(f,g3),nfisisom(f,g4)))
             



Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = x^4 + 2*x^2 + 7
? %2 = [x - 1, x^2 + 6, x^4 - 12*x^2 + 252, x^4 + 2*x^2 + 7]
? ? ? 300---0000
302---0000
304---0000
306---0000
308---0000
310---0000
312---0000
314---0000
316---0000
318---0000
320---0000
322---0000
324---0000
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1294---0000
1296---0000
1298---0000
1300---0000
? ? ? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m8.800s
user	0m1.952s
sys	0m0.011s


'193.170'
************** PARI *****************
Host 193.170.37.83 (193.170.37.83)
Time: Wed Jul 26 08:41:07 2006

Input: f=x^4+2*x^2+7
polred(f)
nf=nfinit(f);
factor(nf.disc);
forstep (A=2, 300, 2, g1=x^4+A*x^2+A^2/2; g2=x^4-A*x^2-A^2/2; g3=x^4+A*x^2-A^2/2; g4=x^4-A*x^2+A^2/2; nf1=nfinit(g1); nf2=nfinit(g2); nf3=nfinit(g3); nf4=nfinit(g4);factor(nf1.disc);factor(nf2.disc);factor(nf3.disc);factor(nf4.disc);nfisisom(f,g1); print(A,"---",nfisisom(f,g1), nfisisom(f,g2),nfisisom(f,g3),nfisisom(f,g4)))
             



Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = x^4 + 2*x^2 + 7
? %2 = [x - 1, x^2 + 6, x^4 - 12*x^2 + 252, x^4 + 2*x^2 + 7]
? ? ? 2---0000
4---0000
6---0000
8---0000
10---0000
12---0000
14---0000
16---0000
18---0000
20---0000
22---0000
24---0000
26---0000
28---0000
30---0000
32---0000
34---0000
36---0000
38---0000
40---0000
42---0000
44---0000
46---0000
48---0000
50---0000
52---0000
54---0000
56---0000
58---0000
60---0000
62---0000
64---0000
66---0000
68---0000
70---0000
72---0000
74---0000
76---0000
78---0000
80---0000
82---0000
84---0000
86---0000
88---0000
90---0000
92---0000
94---0000
96---0000
98---0000
100---0000
102---0000
104---0000
106---0000
108---0000
110---0000
112---0000
114---0000
116---0000
118---0000
120---0000
122---0000
124---0000
126---0000
128---0000
130---0000
132---0000
134---0000
136---0000
138---0000
140---0000
142---0000
144---0000
146---0000
148---0000
150---0000
152---0000
154---0000
156---0000
158---0000
160---0000
162---0000
164---0000
166---0000
168---0000
170---0000
172---0000
174---0000
176---0000
178---0000
180---0000
182---0000
184---0000
186---0000
188---0000
190---0000
192---0000
194---0000
196---0000
198---0000
200---0000
202---0000
204---0000
206---0000
208---0000
210---0000
212---0000
214---0000
216---0000
218---0000
220---0000
222---0000
224---0000
226---0000
228---0000
230---0000
232---0000
234---0000
236---0000
238---0000
240---0000
242---0000
244---0000
246---0000
248---0000
250---0000
252---0000
254---0000
256---0000
258---0000
260---0000
262---0000
264---0000
266---0000
268---0000
270---0000
272---0000
274---0000
276---0000
278---0000
280---0000
282---0000
284---0000
286---0000
288---0000
290---0000
292---0000
294---0000
296---0000
298---0000
300---0000
? ? ? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m2.148s
user	0m0.532s
sys	0m0.005s


'193.170'
************** PARI *****************
Host 193.170.37.83 (193.170.37.83)
Time: Wed Jul 26 08:40:24 2006

Input: f=x^4+2*x^2+1
polred(f)
nf=nfinit(f);
factor(nf.disc);
forstep (A=2, 2000, 2, g1=x^4+A*x^2+A^2/2; g2=x^4-A*x^2-A^2/2; g3=x^4+A*x^2-A^2/2; g4=x^4-A*x^2+A^2/2; nf1=nfinit(g1); nf2=nfinit(g2); nf3=nfinit(g3); nf4=nfinit(g4);factor(nf1.disc);factor(nf2.disc);factor(nf3.disc);factor(nf4.disc);nfisisom(f,g1); print(A,"---",nfisisom(f,g1), nfisisom(f,g2),nfisisom(f,g3),nfisisom(f,g4)))
             



Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = x^4 + 2*x^2 + 1
? ? ? ? 2---[-x^2 - 1, x^2 + 1]00[-x^2 + 1, x^2 - 1]
4---[-1/2*x^2 - 1, 1/2*x^2 + 1]00[-1/2*x^2 + 1, 1/2*x^2 - 1]
6---[-1/3*x^2 - 1, 1/3*x^2 + 1]00[-1/3*x^2 + 1, 1/3*x^2 - 1]
8---[-1/4*x^2 - 1, 1/4*x^2 + 1]00[-1/4*x^2 + 1, 1/4*x^2 - 1]
10---[-1/5*x^2 - 1, 1/5*x^2 + 1]00[-1/5*x^2 + 1, 1/5*x^2 - 1]
12---[-1/6*x^2 - 1, 1/6*x^2 + 1]00[-1/6*x^2 + 1, 1/6*x^2 - 1]
14---[-1/7*x^2 - 1, 1/7*x^2 + 1]00[-1/7*x^2 + 1, 1/7*x^2 - 1]
16---[-1/8*x^2 - 1, 1/8*x^2 + 1]00[-1/8*x^2 + 1, 1/8*x^2 - 1]
18---[-1/9*x^2 - 1, 1/9*x^2 + 1]00[-1/9*x^2 + 1, 1/9*x^2 - 1]
20---[-1/10*x^2 - 1, 1/10*x^2 + 1]00[-1/10*x^2 + 1, 1/10*x^2 - 1]
22---[-1/11*x^2 - 1, 1/11*x^2 + 1]00[-1/11*x^2 + 1, 1/11*x^2 - 1]
24---[-1/12*x^2 - 1, 1/12*x^2 + 1]00[-1/12*x^2 + 1, 1/12*x^2 - 1]
26---[-1/13*x^2 - 1, 1/13*x^2 + 1]00[-1/13*x^2 + 1, 1/13*x^2 - 1]
28---[-1/14*x^2 - 1, 1/14*x^2 + 1]00[-1/14*x^2 + 1, 1/14*x^2 - 1]
30---[-1/15*x^2 - 1, 1/15*x^2 + 1]00[-1/15*x^2 + 1, 1/15*x^2 - 1]
32---[-1/16*x^2 - 1, 1/16*x^2 + 1]00[-1/16*x^2 + 1, 1/16*x^2 - 1]
34---[-1/17*x^2 - 1, 1/17*x^2 + 1]00[-1/17*x^2 + 1, 1/17*x^2 - 1]
36---[-1/18*x^2 - 1, 1/18*x^2 + 1]00[-1/18*x^2 + 1, 1/18*x^2 - 1]
38---[-1/19*x^2 - 1, 1/19*x^2 + 1]00[-1/19*x^2 + 1, 1/19*x^2 - 1]
40---[-1/20*x^2 - 1, 1/20*x^2 + 1]00[-1/20*x^2 + 1, 1/20*x^2 - 1]
42---[-1/21*x^2 - 1, 1/21*x^2 + 1]00[-1/21*x^2 + 1, 1/21*x^2 - 1]
44---[-1/22*x^2 - 1, 1/22*x^2 + 1]00[-1/22*x^2 + 1, 1/22*x^2 - 1]
46---[-1/23*x^2 - 1, 1/23*x^2 + 1]00[-1/23*x^2 + 1, 1/23*x^2 - 1]
48---[-1/24*x^2 - 1, 1/24*x^2 + 1]00[-1/24*x^2 + 1, 1/24*x^2 - 1]
50---[-1/25*x^2 - 1, 1/25*x^2 + 1]00[-1/25*x^2 + 1, 1/25*x^2 - 1]
52---[-1/26*x^2 - 1, 1/26*x^2 + 1]00[-1/26*x^2 + 1, 1/26*x^2 - 1]
54---[-1/27*x^2 - 1, 1/27*x^2 + 1]00[-1/27*x^2 + 1, 1/27*x^2 - 1]
56---[-1/28*x^2 - 1, 1/28*x^2 + 1]00[-1/28*x^2 + 1, 1/28*x^2 - 1]
58---[-1/29*x^2 - 1, 1/29*x^2 + 1]00[-1/29*x^2 + 1, 1/29*x^2 - 1]
60---[-1/30*x^2 - 1, 1/30*x^2 + 1]00[-1/30*x^2 + 1, 1/30*x^2 - 1]
62---[-1/31*x^2 - 1, 1/31*x^2 + 1]00[-1/31*x^2 + 1, 1/31*x^2 - 1]
64---[-1/32*x^2 - 1, 1/32*x^2 + 1]00[-1/32*x^2 + 1, 1/32*x^2 - 1]
66---[-1/33*x^2 - 1, 1/33*x^2 + 1]00[-1/33*x^2 + 1, 1/33*x^2 - 1]
68---[-1/34*x^2 - 1, 1/34*x^2 + 1]00[-1/34*x^2 + 1, 1/34*x^2 - 1]
70---[-1/35*x^2 - 1, 1/35*x^2 + 1]00[-1/35*x^2 + 1, 1/35*x^2 - 1]
72---[-1/36*x^2 - 1, 1/36*x^2 + 1]00[-1/36*x^2 + 1, 1/36*x^2 - 1]
74---[-1/37*x^2 - 1, 1/37*x^2 + 1]00[-1/37*x^2 + 1, 1/37*x^2 - 1]
76---[-1/38*x^2 - 1, 1/38*x^2 + 1]00[-1/38*x^2 + 1, 1/38*x^2 - 1]
78---[-1/39*x^2 - 1, 1/39*x^2 + 1]00[-1/39*x^2 + 1, 1/39*x^2 - 1]
80---[-1/40*x^2 - 1, 1/40*x^2 + 1]00[-1/40*x^2 + 1, 1/40*x^2 - 1]
82---[-1/41*x^2 - 1, 1/41*x^2 + 1]00[-1/41*x^2 + 1, 1/41*x^2 - 1]
84---[-1/42*x^2 - 1, 1/42*x^2 + 1]00[-1/42*x^2 + 1, 1/42*x^2 - 1]
86---[-1/43*x^2 - 1, 1/43*x^2 + 1]00[-1/43*x^2 + 1, 1/43*x^2 - 1]
88---[-1/44*x^2 - 1, 1/44*x^2 + 1]00[-1/44*x^2 + 1, 1/44*x^2 - 1]
90---[-1/45*x^2 - 1, 1/45*x^2 + 1]00[-1/45*x^2 + 1, 1/45*x^2 - 1]
92---[-1/46*x^2 - 1, 1/46*x^2 + 1]00[-1/46*x^2 + 1, 1/46*x^2 - 1]
94---[-1/47*x^2 - 1, 1/47*x^2 + 1]00[-1/47*x^2 + 1, 1/47*x^2 - 1]
96---[-1/48*x^2 - 1, 1/48*x^2 + 1]00[-1/48*x^2 + 1, 1/48*x^2 - 1]
98---[-1/49*x^2 - 1, 1/49*x^2 + 1]00[-1/49*x^2 + 1, 1/49*x^2 - 1]
100---[-1/50*x^2 - 1, 1/50*x^2 + 1]00[-1/50*x^2 + 1, 1/50*x^2 - 1]
102---[-1/51*x^2 - 1, 1/51*x^2 + 1]00[-1/51*x^2 + 1, 1/51*x^2 - 1]
104---[-1/52*x^2 - 1, 1/52*x^2 + 1]00[-1/52*x^2 + 1, 1/52*x^2 - 1]
106---[-1/53*x^2 - 1, 1/53*x^2 + 1]00[-1/53*x^2 + 1, 1/53*x^2 - 1]
108---[-1/54*x^2 - 1, 1/54*x^2 + 1]00[-1/54*x^2 + 1, 1/54*x^2 - 1]
110---[-1/55*x^2 - 1, 1/55*x^2 + 1]00[-1/55*x^2 + 1, 1/55*x^2 - 1]
112---[-1/56*x^2 - 1, 1/56*x^2 + 1]00[-1/56*x^2 + 1, 1/56*x^2 - 1]
114---[-1/57*x^2 - 1, 1/57*x^2 + 1]00[-1/57*x^2 + 1, 1/57*x^2 - 1]
116---[-1/58*x^2 - 1, 1/58*x^2 + 1]00[-1/58*x^2 + 1, 1/58*x^2 - 1]
118---[-1/59*x^2 - 1, 1/59*x^2 + 1]00[-1/59*x^2 + 1, 1/59*x^2 - 1]
120---[-1/60*x^2 - 1, 1/60*x^2 + 1]00[-1/60*x^2 + 1, 1/60*x^2 - 1]
122---[-1/61*x^2 - 1, 1/61*x^2 + 1]00[-1/61*x^2 + 1, 1/61*x^2 - 1]
124---[-1/62*x^2 - 1, 1/62*x^2 + 1]00[-1/62*x^2 + 1, 1/62*x^2 - 1]
126---[-1/63*x^2 - 1, 1/63*x^2 + 1]00[-1/63*x^2 + 1, 1/63*x^2 - 1]
128---[-1/64*x^2 - 1, 1/64*x^2 + 1]00[-1/64*x^2 + 1, 1/64*x^2 - 1]
130---[-1/65*x^2 - 1, 1/65*x^2 + 1]00[-1/65*x^2 + 1, 1/65*x^2 - 1]
132---[-1/66*x^2 - 1, 1/66*x^2 + 1]00[-1/66*x^2 + 1, 1/66*x^2 - 1]
134---[-1/67*x^2 - 1, 1/67*x^2 + 1]00[-1/67*x^2 + 1, 1/67*x^2 - 1]
136---[-1/68*x^2 - 1, 1/68*x^2 + 1]00[-1/68*x^2 + 1, 1/68*x^2 - 1]
138---[-1/69*x^2 - 1, 1/69*x^2 + 1]00[-1/69*x^2 + 1, 1/69*x^2 - 1]
140---[-1/70*x^2 - 1, 1/70*x^2 + 1]00[-1/70*x^2 + 1, 1/70*x^2 - 1]
142---[-1/71*x^2 - 1, 1/71*x^2 + 1]00[-1/71*x^2 + 1, 1/71*x^2 - 1]
144---[-1/72*x^2 - 1, 1/72*x^2 + 1]00[-1/72*x^2 + 1, 1/72*x^2 - 1]
146---[-1/73*x^2 - 1, 1/73*x^2 + 1]00[-1/73*x^2 + 1, 1/73*x^2 - 1]
148---[-1/74*x^2 - 1, 1/74*x^2 + 1]00[-1/74*x^2 + 1, 1/74*x^2 - 1]
150---[-1/75*x^2 - 1, 1/75*x^2 + 1]00[-1/75*x^2 + 1, 1/75*x^2 - 1]
152---[-1/76*x^2 - 1, 1/76*x^2 + 1]00[-1/76*x^2 + 1, 1/76*x^2 - 1]
154---[-1/77*x^2 - 1, 1/77*x^2 + 1]00[-1/77*x^2 + 1, 1/77*x^2 - 1]
156---[-1/78*x^2 - 1, 1/78*x^2 + 1]00[-1/78*x^2 + 1, 1/78*x^2 - 1]
158---[-1/79*x^2 - 1, 1/79*x^2 + 1]00[-1/79*x^2 + 1, 1/79*x^2 - 1]
160---[-1/80*x^2 - 1, 1/80*x^2 + 1]00[-1/80*x^2 + 1, 1/80*x^2 - 1]
162---[-1/81*x^2 - 1, 1/81*x^2 + 1]00[-1/81*x^2 + 1, 1/81*x^2 - 1]
164---[-1/82*x^2 - 1, 1/82*x^2 + 1]00[-1/82*x^2 + 1, 1/82*x^2 - 1]
166---[-1/83*x^2 - 1, 1/83*x^2 + 1]00[-1/83*x^2 + 1, 1/83*x^2 - 1]
168---[-1/84*x^2 - 1, 1/84*x^2 + 1]00[-1/84*x^2 + 1, 1/84*x^2 - 1]
170---[-1/85*x^2 - 1, 1/85*x^2 + 1]00[-1/85*x^2 + 1, 1/85*x^2 - 1]
172---[-1/86*x^2 - 1, 1/86*x^2 + 1]00[-1/86*x^2 + 1, 1/86*x^2 - 1]
174---[-1/87*x^2 - 1, 1/87*x^2 + 1]00[-1/87*x^2 + 1, 1/87*x^2 - 1]
176---[-1/88*x^2 - 1, 1/88*x^2 + 1]00[-1/88*x^2 + 1, 1/88*x^2 - 1]
178---[-1/89*x^2 - 1, 1/89*x^2 + 1]00[-1/89*x^2 + 1, 1/89*x^2 - 1]
180---[-1/90*x^2 - 1, 1/90*x^2 + 1]00[-1/90*x^2 + 1, 1/90*x^2 - 1]
182---[-1/91*x^2 - 1, 1/91*x^2 + 1]00[-1/91*x^2 + 1, 1/91*x^2 - 1]
184---[-1/92*x^2 - 1, 1/92*x^2 + 1]00[-1/92*x^2 + 1, 1/92*x^2 - 1]
186---[-1/93*x^2 - 1, 1/93*x^2 + 1]00[-1/93*x^2 + 1, 1/93*x^2 - 1]
188---[-1/94*x^2 - 1, 1/94*x^2 + 1]00[-1/94*x^2 + 1, 1/94*x^2 - 1]
190---[-1/95*x^2 - 1, 1/95*x^2 + 1]00[-1/95*x^2 + 1, 1/95*x^2 - 1]
192---[-1/96*x^2 - 1, 1/96*x^2 + 1]00[-1/96*x^2 + 1, 1/96*x^2 - 1]
194---[-1/97*x^2 - 1, 1/97*x^2 + 1]00[-1/97*x^2 + 1, 1/97*x^2 - 1]
196---[-1/98*x^2 - 1, 1/98*x^2 + 1]00[-1/98*x^2 + 1, 1/98*x^2 - 1]
198---[-1/99*x^2 - 1, 1/99*x^2 + 1]00[-1/99*x^2 + 1, 1/99*x^2 - 1]
200---[-1/100*x^2 - 1, 1/100*x^2 + 1]00[-1/100*x^2 + 1, 1/100*x^2 - 1]
202---[-1/101*x^2 - 1, 1/101*x^2 + 1]00[-1/101*x^2 + 1, 1/101*x^2 - 1]
204---[-1/102*x^2 - 1, 1/102*x^2 + 1]00[-1/102*x^2 + 1, 1/102*x^2 - 1]
206---[-1/103*x^2 - 1, 1/103*x^2 + 1]00[-1/103*x^2 + 1, 1/103*x^2 - 1]
208---[-1/104*x^2 - 1, 1/104*x^2 + 1]00[-1/104*x^2 + 1, 1/104*x^2 - 1]
210---[-1/105*x^2 - 1, 1/105*x^2 + 1]00[-1/105*x^2 + 1, 1/105*x^2 - 1]
212---[-1/106*x^2 - 1, 1/106*x^2 + 1]00[-1/106*x^2 + 1, 1/106*x^2 - 1]
214---[-1/107*x^2 - 1, 1/107*x^2 + 1]00[-1/107*x^2 + 1, 1/107*x^2 - 1]
216---[-1/108*x^2 - 1, 1/108*x^2 + 1]00[-1/108*x^2 + 1, 1/108*x^2 - 1]
218---[-1/109*x^2 - 1, 1/109*x^2 + 1]00[-1/109*x^2 + 1, 1/109*x^2 - 1]
220---[-1/110*x^2 - 1, 1/110*x^2 + 1]00[-1/110*x^2 + 1, 1/110*x^2 - 1]
222---[-1/111*x^2 - 1, 1/111*x^2 + 1]00[-1/111*x^2 + 1, 1/111*x^2 - 1]
224---[-1/112*x^2 - 1, 1/112*x^2 + 1]00[-1/112*x^2 + 1, 1/112*x^2 - 1]
226---[-1/113*x^2 - 1, 1/113*x^2 + 1]00[-1/113*x^2 + 1, 1/113*x^2 - 1]
228---[-1/114*x^2 - 1, 1/114*x^2 + 1]00[-1/114*x^2 + 1, 1/114*x^2 - 1]
230---[-1/115*x^2 - 1, 1/115*x^2 + 1]00[-1/115*x^2 + 1, 1/115*x^2 - 1]
232---[-1/116*x^2 - 1, 1/116*x^2 + 1]00[-1/116*x^2 + 1, 1/116*x^2 - 1]
234---[-1/117*x^2 - 1, 1/117*x^2 + 1]00[-1/117*x^2 + 1, 1/117*x^2 - 1]
236---[-1/118*x^2 - 1, 1/118*x^2 + 1]00[-1/118*x^2 + 1, 1/118*x^2 - 1]
238---[-1/119*x^2 - 1, 1/119*x^2 + 1]00[-1/119*x^2 + 1, 1/119*x^2 - 1]
240---[-1/120*x^2 - 1, 1/120*x^2 + 1]00[-1/120*x^2 + 1, 1/120*x^2 - 1]
242---[-1/121*x^2 - 1, 1/121*x^2 + 1]00[-1/121*x^2 + 1, 1/121*x^2 - 1]
244---[-1/122*x^2 - 1, 1/122*x^2 + 1]00[-1/122*x^2 + 1, 1/122*x^2 - 1]
246---[-1/123*x^2 - 1, 1/123*x^2 + 1]00[-1/123*x^2 + 1, 1/123*x^2 - 1]
248---[-1/124*x^2 - 1, 1/124*x^2 + 1]00[-1/124*x^2 + 1, 1/124*x^2 - 1]
250---[-1/125*x^2 - 1, 1/125*x^2 + 1]00[-1/125*x^2 + 1, 1/125*x^2 - 1]
252---[-1/126*x^2 - 1, 1/126*x^2 + 1]00[-1/126*x^2 + 1, 1/126*x^2 - 1]
254---[-1/127*x^2 - 1, 1/127*x^2 + 1]00[-1/127*x^2 + 1, 1/127*x^2 - 1]
256---[-1/128*x^2 - 1, 1/128*x^2 + 1]00[-1/128*x^2 + 1, 1/128*x^2 - 1]
258---[-1/129*x^2 - 1, 1/129*x^2 + 1]00[-1/129*x^2 + 1, 1/129*x^2 - 1]
260---[-1/130*x^2 - 1, 1/130*x^2 + 1]00[-1/130*x^2 + 1, 1/130*x^2 - 1]
262---[-1/131*x^2 - 1, 1/131*x^2 + 1]00[-1/131*x^2 + 1, 1/131*x^2 - 1]
264---[-1/132*x^2 - 1, 1/132*x^2 + 1]00[-1/132*x^2 + 1, 1/132*x^2 - 1]
266---[-1/133*x^2 - 1, 1/133*x^2 + 1]00[-1/133*x^2 + 1, 1/133*x^2 - 1]
268---[-1/134*x^2 - 1, 1/134*x^2 + 1]00[-1/134*x^2 + 1, 1/134*x^2 - 1]
270---[-1/135*x^2 - 1, 1/135*x^2 + 1]00[-1/135*x^2 + 1, 1/135*x^2 - 1]
272---[-1/136*x^2 - 1, 1/136*x^2 + 1]00[-1/136*x^2 + 1, 1/136*x^2 - 1]
274---[-1/137*x^2 - 1, 1/137*x^2 + 1]00[-1/137*x^2 + 1, 1/137*x^2 - 1]
276---[-1/138*x^2 - 1, 1/138*x^2 + 1]00[-1/138*x^2 + 1, 1/138*x^2 - 1]
278---[-1/139*x^2 - 1, 1/139*x^2 + 1]00[-1/139*x^2 + 1, 1/139*x^2 - 1]
280---[-1/140*x^2 - 1, 1/140*x^2 + 1]00[-1/140*x^2 + 1, 1/140*x^2 - 1]
282---[-1/141*x^2 - 1, 1/141*x^2 + 1]00[-1/141*x^2 + 1, 1/141*x^2 - 1]
284---[-1/142*x^2 - 1, 1/142*x^2 + 1]00[-1/142*x^2 + 1, 1/142*x^2 - 1]
286---[-1/143*x^2 - 1, 1/143*x^2 + 1]00[-1/143*x^2 + 1, 1/143*x^2 - 1]
288---[-1/144*x^2 - 1, 1/144*x^2 + 1]00[-1/144*x^2 + 1, 1/144*x^2 - 1]
290---[-1/145*x^2 - 1, 1/145*x^2 + 1]00[-1/145*x^2 + 1, 1/145*x^2 - 1]
292---[-1/146*x^2 - 1, 1/146*x^2 + 1]00[-1/146*x^2 + 1, 1/146
 ** WARNING: Output too long, hence truncated.
Errors/timing (if any):

  *** polred: reducible polynomial in nfinit.
  *** nfinit: reducible polynomial in nfinit.
  ***   incorrect type in disc: factor(nf.disc);
                                          ^------

Timing:
real	0m43.529s
user	0m7.442s
sys	0m0.025s


'193.170'
************** PARI *****************
Host 193.170.37.83 (193.170.37.83)
Time: Wed Jul 26 08:40:19 2006

Input: f=x^4+2*x^2+1
polred(f)
nf=nfinit(f);
factor(nf.disc);
forstep (A=2, 300, 2, g1=x^4+A*x^2+A^2/2; g2=x^4-A*x^2-A^2/2; g3=x^4+A*x^2-A^2/2; g4=x^4-A*x^2+A^2/2; nf1=nfinit(g1); nf2=nfinit(g2); nf3=nfinit(g3); nf4=nfinit(g4);factor(nf1.disc);factor(nf2.disc);factor(nf3.disc);factor(nf4.disc);nfisisom(f,g1); print(A,"---",nfisisom(f,g1), nfisisom(f,g2),nfisisom(f,g3),nfisisom(f,g4)))
             



Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = x^4 + 2*x^2 + 1
? ? ? ? 2---[-x^2 - 1, x^2 + 1]00[-x^2 + 1, x^2 - 1]
4---[-1/2*x^2 - 1, 1/2*x^2 + 1]00[-1/2*x^2 + 1, 1/2*x^2 - 1]
6---[-1/3*x^2 - 1, 1/3*x^2 + 1]00[-1/3*x^2 + 1, 1/3*x^2 - 1]
8---[-1/4*x^2 - 1, 1/4*x^2 + 1]00[-1/4*x^2 + 1, 1/4*x^2 - 1]
10---[-1/5*x^2 - 1, 1/5*x^2 + 1]00[-1/5*x^2 + 1, 1/5*x^2 - 1]
12---[-1/6*x^2 - 1, 1/6*x^2 + 1]00[-1/6*x^2 + 1, 1/6*x^2 - 1]
14---[-1/7*x^2 - 1, 1/7*x^2 + 1]00[-1/7*x^2 + 1, 1/7*x^2 - 1]
16---[-1/8*x^2 - 1, 1/8*x^2 + 1]00[-1/8*x^2 + 1, 1/8*x^2 - 1]
18---[-1/9*x^2 - 1, 1/9*x^2 + 1]00[-1/9*x^2 + 1, 1/9*x^2 - 1]
20---[-1/10*x^2 - 1, 1/10*x^2 + 1]00[-1/10*x^2 + 1, 1/10*x^2 - 1]
22---[-1/11*x^2 - 1, 1/11*x^2 + 1]00[-1/11*x^2 + 1, 1/11*x^2 - 1]
24---[-1/12*x^2 - 1, 1/12*x^2 + 1]00[-1/12*x^2 + 1, 1/12*x^2 - 1]
26---[-1/13*x^2 - 1, 1/13*x^2 + 1]00[-1/13*x^2 + 1, 1/13*x^2 - 1]
28---[-1/14*x^2 - 1, 1/14*x^2 + 1]00[-1/14*x^2 + 1, 1/14*x^2 - 1]
30---[-1/15*x^2 - 1, 1/15*x^2 + 1]00[-1/15*x^2 + 1, 1/15*x^2 - 1]
32---[-1/16*x^2 - 1, 1/16*x^2 + 1]00[-1/16*x^2 + 1, 1/16*x^2 - 1]
34---[-1/17*x^2 - 1, 1/17*x^2 + 1]00[-1/17*x^2 + 1, 1/17*x^2 - 1]
36---[-1/18*x^2 - 1, 1/18*x^2 + 1]00[-1/18*x^2 + 1, 1/18*x^2 - 1]
38---[-1/19*x^2 - 1, 1/19*x^2 + 1]00[-1/19*x^2 + 1, 1/19*x^2 - 1]
40---[-1/20*x^2 - 1, 1/20*x^2 + 1]00[-1/20*x^2 + 1, 1/20*x^2 - 1]
42---[-1/21*x^2 - 1, 1/21*x^2 + 1]00[-1/21*x^2 + 1, 1/21*x^2 - 1]
44---[-1/22*x^2 - 1, 1/22*x^2 + 1]00[-1/22*x^2 + 1, 1/22*x^2 - 1]
46---[-1/23*x^2 - 1, 1/23*x^2 + 1]00[-1/23*x^2 + 1, 1/23*x^2 - 1]
48---[-1/24*x^2 - 1, 1/24*x^2 + 1]00[-1/24*x^2 + 1, 1/24*x^2 - 1]
50---[-1/25*x^2 - 1, 1/25*x^2 + 1]00[-1/25*x^2 + 1, 1/25*x^2 - 1]
52---[-1/26*x^2 - 1, 1/26*x^2 + 1]00[-1/26*x^2 + 1, 1/26*x^2 - 1]
54---[-1/27*x^2 - 1, 1/27*x^2 + 1]00[-1/27*x^2 + 1, 1/27*x^2 - 1]
56---[-1/28*x^2 - 1, 1/28*x^2 + 1]00[-1/28*x^2 + 1, 1/28*x^2 - 1]
58---[-1/29*x^2 - 1, 1/29*x^2 + 1]00[-1/29*x^2 + 1, 1/29*x^2 - 1]
60---[-1/30*x^2 - 1, 1/30*x^2 + 1]00[-1/30*x^2 + 1, 1/30*x^2 - 1]
62---[-1/31*x^2 - 1, 1/31*x^2 + 1]00[-1/31*x^2 + 1, 1/31*x^2 - 1]
64---[-1/32*x^2 - 1, 1/32*x^2 + 1]00[-1/32*x^2 + 1, 1/32*x^2 - 1]
66---[-1/33*x^2 - 1, 1/33*x^2 + 1]00[-1/33*x^2 + 1, 1/33*x^2 - 1]
68---[-1/34*x^2 - 1, 1/34*x^2 + 1]00[-1/34*x^2 + 1, 1/34*x^2 - 1]
70---[-1/35*x^2 - 1, 1/35*x^2 + 1]00[-1/35*x^2 + 1, 1/35*x^2 - 1]
72---[-1/36*x^2 - 1, 1/36*x^2 + 1]00[-1/36*x^2 + 1, 1/36*x^2 - 1]
74---[-1/37*x^2 - 1, 1/37*x^2 + 1]00[-1/37*x^2 + 1, 1/37*x^2 - 1]
76---[-1/38*x^2 - 1, 1/38*x^2 + 1]00[-1/38*x^2 + 1, 1/38*x^2 - 1]
78---[-1/39*x^2 - 1, 1/39*x^2 + 1]00[-1/39*x^2 + 1, 1/39*x^2 - 1]
80---[-1/40*x^2 - 1, 1/40*x^2 + 1]00[-1/40*x^2 + 1, 1/40*x^2 - 1]
82---[-1/41*x^2 - 1, 1/41*x^2 + 1]00[-1/41*x^2 + 1, 1/41*x^2 - 1]
84---[-1/42*x^2 - 1, 1/42*x^2 + 1]00[-1/42*x^2 + 1, 1/42*x^2 - 1]
86---[-1/43*x^2 - 1, 1/43*x^2 + 1]00[-1/43*x^2 + 1, 1/43*x^2 - 1]
88---[-1/44*x^2 - 1, 1/44*x^2 + 1]00[-1/44*x^2 + 1, 1/44*x^2 - 1]
90---[-1/45*x^2 - 1, 1/45*x^2 + 1]00[-1/45*x^2 + 1, 1/45*x^2 - 1]
92---[-1/46*x^2 - 1, 1/46*x^2 + 1]00[-1/46*x^2 + 1, 1/46*x^2 - 1]
94---[-1/47*x^2 - 1, 1/47*x^2 + 1]00[-1/47*x^2 + 1, 1/47*x^2 - 1]
96---[-1/48*x^2 - 1, 1/48*x^2 + 1]00[-1/48*x^2 + 1, 1/48*x^2 - 1]
98---[-1/49*x^2 - 1, 1/49*x^2 + 1]00[-1/49*x^2 + 1, 1/49*x^2 - 1]
100---[-1/50*x^2 - 1, 1/50*x^2 + 1]00[-1/50*x^2 + 1, 1/50*x^2 - 1]
102---[-1/51*x^2 - 1, 1/51*x^2 + 1]00[-1/51*x^2 + 1, 1/51*x^2 - 1]
104---[-1/52*x^2 - 1, 1/52*x^2 + 1]00[-1/52*x^2 + 1, 1/52*x^2 - 1]
106---[-1/53*x^2 - 1, 1/53*x^2 + 1]00[-1/53*x^2 + 1, 1/53*x^2 - 1]
108---[-1/54*x^2 - 1, 1/54*x^2 + 1]00[-1/54*x^2 + 1, 1/54*x^2 - 1]
110---[-1/55*x^2 - 1, 1/55*x^2 + 1]00[-1/55*x^2 + 1, 1/55*x^2 - 1]
112---[-1/56*x^2 - 1, 1/56*x^2 + 1]00[-1/56*x^2 + 1, 1/56*x^2 - 1]
114---[-1/57*x^2 - 1, 1/57*x^2 + 1]00[-1/57*x^2 + 1, 1/57*x^2 - 1]
116---[-1/58*x^2 - 1, 1/58*x^2 + 1]00[-1/58*x^2 + 1, 1/58*x^2 - 1]
118---[-1/59*x^2 - 1, 1/59*x^2 + 1]00[-1/59*x^2 + 1, 1/59*x^2 - 1]
120---[-1/60*x^2 - 1, 1/60*x^2 + 1]00[-1/60*x^2 + 1, 1/60*x^2 - 1]
122---[-1/61*x^2 - 1, 1/61*x^2 + 1]00[-1/61*x^2 + 1, 1/61*x^2 - 1]
124---[-1/62*x^2 - 1, 1/62*x^2 + 1]00[-1/62*x^2 + 1, 1/62*x^2 - 1]
126---[-1/63*x^2 - 1, 1/63*x^2 + 1]00[-1/63*x^2 + 1, 1/63*x^2 - 1]
128---[-1/64*x^2 - 1, 1/64*x^2 + 1]00[-1/64*x^2 + 1, 1/64*x^2 - 1]
130---[-1/65*x^2 - 1, 1/65*x^2 + 1]00[-1/65*x^2 + 1, 1/65*x^2 - 1]
132---[-1/66*x^2 - 1, 1/66*x^2 + 1]00[-1/66*x^2 + 1, 1/66*x^2 - 1]
134---[-1/67*x^2 - 1, 1/67*x^2 + 1]00[-1/67*x^2 + 1, 1/67*x^2 - 1]
136---[-1/68*x^2 - 1, 1/68*x^2 + 1]00[-1/68*x^2 + 1, 1/68*x^2 - 1]
138---[-1/69*x^2 - 1, 1/69*x^2 + 1]00[-1/69*x^2 + 1, 1/69*x^2 - 1]
140---[-1/70*x^2 - 1, 1/70*x^2 + 1]00[-1/70*x^2 + 1, 1/70*x^2 - 1]
142---[-1/71*x^2 - 1, 1/71*x^2 + 1]00[-1/71*x^2 + 1, 1/71*x^2 - 1]
144---[-1/72*x^2 - 1, 1/72*x^2 + 1]00[-1/72*x^2 + 1, 1/72*x^2 - 1]
146---[-1/73*x^2 - 1, 1/73*x^2 + 1]00[-1/73*x^2 + 1, 1/73*x^2 - 1]
148---[-1/74*x^2 - 1, 1/74*x^2 + 1]00[-1/74*x^2 + 1, 1/74*x^2 - 1]
150---[-1/75*x^2 - 1, 1/75*x^2 + 1]00[-1/75*x^2 + 1, 1/75*x^2 - 1]
152---[-1/76*x^2 - 1, 1/76*x^2 + 1]00[-1/76*x^2 + 1, 1/76*x^2 - 1]
154---[-1/77*x^2 - 1, 1/77*x^2 + 1]00[-1/77*x^2 + 1, 1/77*x^2 - 1]
156---[-1/78*x^2 - 1, 1/78*x^2 + 1]00[-1/78*x^2 + 1, 1/78*x^2 - 1]
158---[-1/79*x^2 - 1, 1/79*x^2 + 1]00[-1/79*x^2 + 1, 1/79*x^2 - 1]
160---[-1/80*x^2 - 1, 1/80*x^2 + 1]00[-1/80*x^2 + 1, 1/80*x^2 - 1]
162---[-1/81*x^2 - 1, 1/81*x^2 + 1]00[-1/81*x^2 + 1, 1/81*x^2 - 1]
164---[-1/82*x^2 - 1, 1/82*x^2 + 1]00[-1/82*x^2 + 1, 1/82*x^2 - 1]
166---[-1/83*x^2 - 1, 1/83*x^2 + 1]00[-1/83*x^2 + 1, 1/83*x^2 - 1]
168---[-1/84*x^2 - 1, 1/84*x^2 + 1]00[-1/84*x^2 + 1, 1/84*x^2 - 1]
170---[-1/85*x^2 - 1, 1/85*x^2 + 1]00[-1/85*x^2 + 1, 1/85*x^2 - 1]
172---[-1/86*x^2 - 1, 1/86*x^2 + 1]00[-1/86*x^2 + 1, 1/86*x^2 - 1]
174---[-1/87*x^2 - 1, 1/87*x^2 + 1]00[-1/87*x^2 + 1, 1/87*x^2 - 1]
176---[-1/88*x^2 - 1, 1/88*x^2 + 1]00[-1/88*x^2 + 1, 1/88*x^2 - 1]
178---[-1/89*x^2 - 1, 1/89*x^2 + 1]00[-1/89*x^2 + 1, 1/89*x^2 - 1]
180---[-1/90*x^2 - 1, 1/90*x^2 + 1]00[-1/90*x^2 + 1, 1/90*x^2 - 1]
182---[-1/91*x^2 - 1, 1/91*x^2 + 1]00[-1/91*x^2 + 1, 1/91*x^2 - 1]
184---[-1/92*x^2 - 1, 1/92*x^2 + 1]00[-1/92*x^2 + 1, 1/92*x^2 - 1]
186---[-1/93*x^2 - 1, 1/93*x^2 + 1]00[-1/93*x^2 + 1, 1/93*x^2 - 1]
188---[-1/94*x^2 - 1, 1/94*x^2 + 1]00[-1/94*x^2 + 1, 1/94*x^2 - 1]
190---[-1/95*x^2 - 1, 1/95*x^2 + 1]00[-1/95*x^2 + 1, 1/95*x^2 - 1]
192---[-1/96*x^2 - 1, 1/96*x^2 + 1]00[-1/96*x^2 + 1, 1/96*x^2 - 1]
194---[-1/97*x^2 - 1, 1/97*x^2 + 1]00[-1/97*x^2 + 1, 1/97*x^2 - 1]
196---[-1/98*x^2 - 1, 1/98*x^2 + 1]00[-1/98*x^2 + 1, 1/98*x^2 - 1]
198---[-1/99*x^2 - 1, 1/99*x^2 + 1]00[-1/99*x^2 + 1, 1/99*x^2 - 1]
200---[-1/100*x^2 - 1, 1/100*x^2 + 1]00[-1/100*x^2 + 1, 1/100*x^2 - 1]
202---[-1/101*x^2 - 1, 1/101*x^2 + 1]00[-1/101*x^2 + 1, 1/101*x^2 - 1]
204---[-1/102*x^2 - 1, 1/102*x^2 + 1]00[-1/102*x^2 + 1, 1/102*x^2 - 1]
206---[-1/103*x^2 - 1, 1/103*x^2 + 1]00[-1/103*x^2 + 1, 1/103*x^2 - 1]
208---[-1/104*x^2 - 1, 1/104*x^2 + 1]00[-1/104*x^2 + 1, 1/104*x^2 - 1]
210---[-1/105*x^2 - 1, 1/105*x^2 + 1]00[-1/105*x^2 + 1, 1/105*x^2 - 1]
212---[-1/106*x^2 - 1, 1/106*x^2 + 1]00[-1/106*x^2 + 1, 1/106*x^2 - 1]
214---[-1/107*x^2 - 1, 1/107*x^2 + 1]00[-1/107*x^2 + 1, 1/107*x^2 - 1]
216---[-1/108*x^2 - 1, 1/108*x^2 + 1]00[-1/108*x^2 + 1, 1/108*x^2 - 1]
218---[-1/109*x^2 - 1, 1/109*x^2 + 1]00[-1/109*x^2 + 1, 1/109*x^2 - 1]
220---[-1/110*x^2 - 1, 1/110*x^2 + 1]00[-1/110*x^2 + 1, 1/110*x^2 - 1]
222---[-1/111*x^2 - 1, 1/111*x^2 + 1]00[-1/111*x^2 + 1, 1/111*x^2 - 1]
224---[-1/112*x^2 - 1, 1/112*x^2 + 1]00[-1/112*x^2 + 1, 1/112*x^2 - 1]
226---[-1/113*x^2 - 1, 1/113*x^2 + 1]00[-1/113*x^2 + 1, 1/113*x^2 - 1]
228---[-1/114*x^2 - 1, 1/114*x^2 + 1]00[-1/114*x^2 + 1, 1/114*x^2 - 1]
230---[-1/115*x^2 - 1, 1/115*x^2 + 1]00[-1/115*x^2 + 1, 1/115*x^2 - 1]
232---[-1/116*x^2 - 1, 1/116*x^2 + 1]00[-1/116*x^2 + 1, 1/116*x^2 - 1]
234---[-1/117*x^2 - 1, 1/117*x^2 + 1]00[-1/117*x^2 + 1, 1/117*x^2 - 1]
236---[-1/118*x^2 - 1, 1/118*x^2 + 1]00[-1/118*x^2 + 1, 1/118*x^2 - 1]
238---[-1/119*x^2 - 1, 1/119*x^2 + 1]00[-1/119*x^2 + 1, 1/119*x^2 - 1]
240---[-1/120*x^2 - 1, 1/120*x^2 + 1]00[-1/120*x^2 + 1, 1/120*x^2 - 1]
242---[-1/121*x^2 - 1, 1/121*x^2 + 1]00[-1/121*x^2 + 1, 1/121*x^2 - 1]
244---[-1/122*x^2 - 1, 1/122*x^2 + 1]00[-1/122*x^2 + 1, 1/122*x^2 - 1]
246---[-1/123*x^2 - 1, 1/123*x^2 + 1]00[-1/123*x^2 + 1, 1/123*x^2 - 1]
248---[-1/124*x^2 - 1, 1/124*x^2 + 1]00[-1/124*x^2 + 1, 1/124*x^2 - 1]
250---[-1/125*x^2 - 1, 1/125*x^2 + 1]00[-1/125*x^2 + 1, 1/125*x^2 - 1]
252---[-1/126*x^2 - 1, 1/126*x^2 + 1]00[-1/126*x^2 + 1, 1/126*x^2 - 1]
254---[-1/127*x^2 - 1, 1/127*x^2 + 1]00[-1/127*x^2 + 1, 1/127*x^2 - 1]
256---[-1/128*x^2 - 1, 1/128*x^2 + 1]00[-1/128*x^2 + 1, 1/128*x^2 - 1]
258---[-1/129*x^2 - 1, 1/129*x^2 + 1]00[-1/129*x^2 + 1, 1/129*x^2 - 1]
260---[-1/130*x^2 - 1, 1/130*x^2 + 1]00[-1/130*x^2 + 1, 1/130*x^2 - 1]
262---[-1/131*x^2 - 1, 1/131*x^2 + 1]00[-1/131*x^2 + 1, 1/131*x^2 - 1]
264---[-1/132*x^2 - 1, 1/132*x^2 + 1]00[-1/132*x^2 + 1, 1/132*x^2 - 1]
266---[-1/133*x^2 - 1, 1/133*x^2 + 1]00[-1/133*x^2 + 1, 1/133*x^2 - 1]
268---[-1/134*x^2 - 1, 1/134*x^2 + 1]00[-1/134*x^2 + 1, 1/134*x^2 - 1]
270---[-1/135*x^2 - 1, 1/135*x^2 + 1]00[-1/135*x^2 + 1, 1/135*x^2 - 1]
272---[-1/136*x^2 - 1, 1/136*x^2 + 1]00[-1/136*x^2 + 1, 1/136*x^2 - 1]
274---[-1/137*x^2 - 1, 1/137*x^2 + 1]00[-1/137*x^2 + 1, 1/137*x^2 - 1]
276---[-1/138*x^2 - 1, 1/138*x^2 + 1]00[-1/138*x^2 + 1, 1/138*x^2 - 1]
278---[-1/139*x^2 - 1, 1/139*x^2 + 1]00[-1/139*x^2 + 1, 1/139*x^2 - 1]
280---[-1/140*x^2 - 1, 1/140*x^2 + 1]00[-1/140*x^2 + 1, 1/140*x^2 - 1]
282---[-1/141*x^2 - 1, 1/141*x^2 + 1]00[-1/141*x^2 + 1, 1/141*x^2 - 1]
284---[-1/142*x^2 - 1, 1/142*x^2 + 1]00[-1/142*x^2 + 1, 1/142*x^2 - 1]
286---[-1/143*x^2 - 1, 1/143*x^2 + 1]00[-1/143*x^2 + 1, 1/143*x^2 - 1]
288---[-1/144*x^2 - 1, 1/144*x^2 + 1]00[-1/144*x^2 + 1, 1/144*x^2 - 1]
290---[-1/145*x^2 - 1, 1/145*x^2 + 1]00[-1/145*x^2 + 1, 1/145*x^2 - 1]
292---[-1/146*x^2 - 1, 1/146*x^2 + 1]00[-1/146*x^2 + 1, 1/146
 ** WARNING: Output too long, hence truncated.
Errors/timing (if any):

  *** polred: reducible polynomial in nfinit.
  *** nfinit: reducible polynomial in nfinit.
  ***   incorrect type in disc: factor(nf.disc);
                                          ^------

Timing:
real	0m2.068s
user	0m1.024s
sys	0m0.012s


'193.170'
************** PARI *****************
Host 193.170.37.83 (193.170.37.83)
Time: Wed Jul 26 08:38:40 2006

Input: f=x^4-6
polred(f)
nf=nfinit(f);
factor(nf.disc);
forstep (A=2, 5000, 2, g1=x^4+A*x^2+A^2/2; g2=x^4-A*x^2-A^2/2; g3=x^4+A*x^2-A^2/2; g4=x^4-A*x^2+A^2/2; nf1=nfinit(g1); nf2=nfinit(g2); nf3=nfinit(g3); nf4=nfinit(g4);factor(nf1.disc);factor(nf2.disc);factor(nf3.disc);factor(nf4.disc);nfisisom(f,g1); print(A,"---",nfisisom(f,g1), nfisisom(f,g2),nfisisom(f,g3),nfisisom(f,g4)))
             



Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = x^4 - 6
? %2 = [x - 1, x^2 - 6, x^4 - 216, x^4 - 6]
? ? ? 2---0000
4---0000
6---0000
8---0000
10---0000
12---0000
14---0000
16---0000
18---0000
20---0000
22---0000
24---0000
26---0000
28---0000
30---0000
32---0000
34---0000
36---0000
38---0000
40---0000
42---0000
44---0000
46---0000
48---0000
50---0000
52---0000
54---0000
56---0000
58---0000
60---0000
62---0000
64---0000
66---0000
68---0000
70---0000
72---0000
74---0000
76---0000
78---0000
80---0000
82---0000
84---0000
86---0000
88---0000
90---0000
92---0000
94---0000
96---0000
98---0000
100---0000
102---0000
104---0000
106---0000
108---0000
110---0000
112---0000
114---0000
116---0000
118---0000
120---0000
122---0000
124---0000
126---0000
128---0000
130---0000
132---0000
134---0000
136---0000
138---0000
140---0000
142---0000
144---0000
146---0000
148---0000
150---0000
152---0000
154---0000
156---0000
158---0000
160---0000
162---0000
164---0000
166---0000
168---0000
170---0000
172---0000
174---0000
176---0000
178---0000
180---0000
182---0000
184---0000
186---0000
188---0000
190---0000
192---0000
194---0000
196---0000
198---0000
200---0000
202---0000
204---0000
206---0000
208---0000
210---0000
212---0000
214---0000
216---0000
218---0000
220---0000
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1730-
 ** WARNING: Output too long, hence truncated.
Errors/timing (if any):


Timing:
real	0m58.259s
user	0m10.161s
sys	0m0.038s


'193.170'
************** PARI *****************
Host 193.170.37.83 (193.170.37.83)
Time: Wed Jul 26 08:38:39 2006

Input: f=x^4-6
polred(f)
nf=nfinit(f);
factor(nf.disc);
forstep (A=2, 2000, 2, g1=x^4+A*x^2+A^2/2; g2=x^4-A*x^2-A^2/2; g3=x^4+A*x^2-A^2/2; g4=x^4-A*x^2+A^2/2; nf1=nfinit(g1); nf2=nfinit(g2); nf3=nfinit(g3); nf4=nfinit(g4);factor(nf1.disc);factor(nf2.disc);factor(nf3.disc);factor(nf4.disc);nfisisom(f,g1); print(A,"---",nfisisom(f,g1), nfisisom(f,g2),nfisisom(f,g3),nfisisom(f,g4)))
             



Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = x^4 - 6
? %2 = [x - 1, x^2 - 6, x^4 - 216, x^4 - 6]
? ? ? 2---0000
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1340---0000
1342---0000
1344---0000
1346---0000
1348---0000
1350---0000
1352---0000
1354---0000
1356---0000
1358---0000
1360---0000
1362---0000
1364---0000
1366---0000
1368---0000
1370---0000
1372---0000
1374---0000
1376---0000
1378---0000
1380---0000
1382---0000
1384---0000
1386---0000
1388---0000
1390---0000
1392---0000
1394---0000
1396---0000
1398---0000
1400---0000
1402---0000
1404---0000
1406---0000
1408---0000
1410---0000
1412---0000
1414---0000
1416---0000
1418---0000
1420---0000
1422---0000
1424---0000
1426---0000
1428---0000
1430---0000
1432---0000
1434---0000
1436---0000
1438---0000
1440---0000
1442---0000
1444---0000
1446---0000
1448---0000
1450---0000
1452---0000
1454---0000
1456---0000
1458---0000
1460---0000
1462---0000
1464---0000
1466---0000
1468---0000
1470---0000
1472---0000
1474---0000
1476---0000
1478---0000
1480---0000
1482---0000
1484---0000
1486---0000
1488---0000
1490---0000
1492---0000
1494---0000
1496---0000
1498---0000
1500---0000
1502---0000
1504---0000
1506---0000
1508---0000
1510---0000
1512---0000
1514---0000
1516---0000
1518---0000
1520---0000
1522---0000
1524---0000
1526---0000
1528---0000
1530---0000
1532---0000
1534---0000
1536---0000
1538---0000
1540---0000
1542---0000
1544---0000
1546---0000
1548---0000
1550---0000
1552---0000
1554---0000
1556---0000
1558---0000
1560---0000
1562---0000
1564---0000
1566---0000
1568---0000
1570---0000
1572---0000
1574---0000
1576---0000
1578---0000
1580---0000
1582---0000
1584---0000
1586---0000
1588---0000
1590---0000
1592---0000
1594---0000
1596---0000
1598---0000
1600---0000
1602---0000
1604---0000
1606---0000
1608---0000
1610---0000
1612---0000
1614---0000
1616---0000
1618---0000
1620---0000
1622---0000
1624---0000
1626---0000
1628---0000
1630---0000
1632---0000
1634---0000
1636---0000
1638---0000
1640---0000
1642---0000
1644---0000
1646---0000
1648---0000
1650---0000
1652---0000
1654---0000
1656---0000
1658---0000
1660---0000
1662---0000
1664---0000
1666---0000
1668---0000
1670---0000
1672---0000
1674---0000
1676---0000
1678---0000
1680---0000
1682---0000
1684---0000
1686---0000
1688---0000
1690---0000
1692---0000
1694---0000
1696---0000
1698---0000
1700---0000
1702---0000
1704---0000
1706---0000
1708---0000
1710---0000
1712---0000
1714---0000
1716---0000
1718---0000
1720---0000
1722---0000
1724---0000
1726---0000
1728---0000
1730-
 ** WARNING: Output too long, hence truncated.
Errors/timing (if any):


Timing:
real	0m7.730s
user	0m3.852s
sys	0m0.011s


'193.170'
************** PARI *****************
Host 193.170.37.83 (193.170.37.83)
Time: Wed Jul 26 08:37:22 2006

Input: f=x^4-6
polred(f)
nf=nfinit(f);
factor(nf.disc);
forstep (A=0, 1000, 2, g1=x^4+A*x^2+A^2/2; g2=x^4-A*x^2-A^2/2; g3=x^4+A*x^2-A^2/2; g4=x^4-A*x^2+A^2/2; nf1=nfinit(g1); nf2=nfinit(g2); nf3=nfinit(g3); nf4=nfinit(g4);factor(nf1.disc);factor(nf2.disc);factor(nf3.disc);factor(nf4.disc);nfisisom(f,g1); print(A,"---",nfisisom(f,g1), nfisisom(f,g2),nfisisom(f,g3),nfisisom(f,g4)))
             



Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = x^4 - 6
? %2 = [x - 1, x^2 - 6, x^4 - 216, x^4 - 6]
? ? ? ? ? ? 
Goodbye!

Errors/timing (if any):

  *** nfinit: reducible polynomial in nfinit.

Timing:
real	0m0.016s
user	0m0.007s
sys	0m0.008s


'193.170'
************** PARI *****************
Host 193.170.37.83 (193.170.37.83)
Time: Wed Jul 26 08:36:48 2006

Input: f=x^4-6
polred(f)
nf=nfinit(f);
factor(nf.disc);
forstep (A=2, 1000, 2, g1=x^4+A*x^2+A^2/2; g2=x^4-A*x^2-A^2/2; g3=x^4+A*x^2-A^2/2; g4=x^4-A*x^2+A^2/2; nf1=nfinit(g1); nf2=nfinit(g2); nf3=nfinit(g3); nf4=nfinit(g4);factor(nf1.disc);factor(nf2.disc);factor(nf3.disc);factor(nf4.disc);nfisisom(f,g1); print(A,"---",nfisisom(f,g1), nfisisom(f,g2),nfisisom(f,g3),nfisisom(f,g4)))
             



Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = x^4 - 6
? %2 = [x - 1, x^2 - 6, x^4 - 216, x^4 - 6]
? ? ? 2---0000
4---0000
6---0000
8---0000
10---0000
12---0000
14---0000
16---0000
18---0000
20---0000
22---0000
24---0000
26---0000
28---0000
30---0000
32---0000
34---0000
36---0000
38---0000
40---0000
42---0000
44---0000
46---0000
48---0000
50---0000
52---0000
54---0000
56---0000
58---0000
60---0000
62---0000
64---0000
66---0000
68---0000
70---0000
72---0000
74---0000
76---0000
78---0000
80---0000
82---0000
84---0000
86---0000
88---0000
90---0000
92---0000
94---0000
96---0000
98---0000
100---0000
102---0000
104---0000
106---0000
108---0000
110---0000
112---0000
114---0000
116---0000
118---0000
120---0000
122---0000
124---0000
126---0000
128---0000
130---0000
132---0000
134---0000
136---0000
138---0000
140---0000
142---0000
144---0000
146---0000
148---0000
150---0000
152---0000
154---0000
156---0000
158---0000
160---0000
162---0000
164---0000
166---0000
168---0000
170---0000
172---0000
174---0000
176---0000
178---0000
180---0000
182---0000
184---0000
186---0000
188---0000
190---0000
192---0000
194---0000
196---0000
198---0000
200---0000
202---0000
204---0000
206---0000
208---0000
210---0000
212---0000
214---0000
216---0000
218---0000
220---0000
222---0000
224---0000
226---0000
228---0000
230---0000
232---0000
234---0000
236---0000
238---0000
240---0000
242---0000
244---0000
246---0000
248---0000
250---0000
252---0000
254---0000
256---0000
258---0000
260---0000
262---0000
264---0000
266---0000
268---0000
270---0000
272---0000
274---0000
276---0000
278---0000
280---0000
282---0000
284---0000
286---0000
288---0000
290---0000
292---0000
294---0000
296---0000
298---0000
300---0000
302---0000
304---0000
306---0000
308---0000
310---0000
312---0000
314---0000
316---0000
318---0000
320---0000
322---0000
324---0000
326---0000
328---0000
330---0000
332---0000
334---0000
336---0000
338---0000
340---0000
342---0000
344---0000
346---0000
348---0000
350---0000
352---0000
354---0000
356---0000
358---0000
360---0000
362---0000
364---0000
366---0000
368---0000
370---0000
372---0000
374---0000
376---0000
378---0000
380---0000
382---0000
384---0000
386---0000
388---0000
390---0000
392---0000
394---0000
396---0000
398---0000
400---0000
402---0000
404---0000
406---0000
408---0000
410---0000
412---0000
414---0000
416---0000
418---0000
420---0000
422---0000
424---0000
426---0000
428---0000
430---0000
432---0000
434---0000
436---0000
438---0000
440---0000
442---0000
444---0000
446---0000
448---0000
450---0000
452---0000
454---0000
456---0000
458---0000
460---0000
462---0000
464---0000
466---0000
468---0000
470---0000
472---0000
474---0000
476---0000
478---0000
480---0000
482---0000
484---0000
486---0000
488---0000
490---0000
492---0000
494---0000
496---0000
498---0000
500---0000
502---0000
504---0000
506---0000
508---0000
510---0000
512---0000
514---0000
516---0000
518---0000
520---0000
522---0000
524---0000
526---0000
528---0000
530---0000
532---0000
534---0000
536---0000
538---0000
540---0000
542---0000
544---0000
546---0000
548---0000
550---0000
552---0000
554---0000
556---0000
558---0000
560---0000
562---0000
564---0000
566---0000
568---0000
570---0000
572---0000
574---0000
576---0000
578---0000
580---0000
582---0000
584---0000
586---0000
588---0000
590---0000
592---0000
594---0000
596---0000
598---0000
600---0000
602---0000
604---0000
606---0000
608---0000
610---0000
612---0000
614---0000
616---0000
618---0000
620---0000
622---0000
624---0000
626---0000
628---0000
630---0000
632---0000
634---0000
636---0000
638---0000
640---0000
642---0000
644---0000
646---0000
648---0000
650---0000
652---0000
654---0000
656---0000
658---0000
660---0000
662---0000
664---0000
666---0000
668---0000
670---0000
672---0000
674---0000
676---0000
678---0000
680---0000
682---0000
684---0000
686---0000
688---0000
690---0000
692---0000
694---0000
696---0000
698---0000
700---0000
702---0000
704---0000
706---0000
708---0000
710---0000
712---0000
714---0000
716---0000
718---0000
720---0000
722---0000
724---0000
726---0000
728---0000
730---0000
732---0000
734---0000
736---0000
738---0000
740---0000
742---0000
744---0000
746---0000
748---0000
750---0000
752---0000
754---0000
756---0000
758---0000
760---0000
762---0000
764---0000
766---0000
768---0000
770---0000
772---0000
774---0000
776---0000
778---0000
780---0000
782---0000
784---0000
786---0000
788---0000
790---0000
792---0000
794---0000
796---0000
798---0000
800---0000
802---0000
804---0000
806---0000
808---0000
810---0000
812---0000
814---0000
816---0000
818---0000
820---0000
822---0000
824---0000
826---0000
828---0000
830---0000
832---0000
834---0000
836---0000
838---0000
840---0000
842---0000
844---0000
846---0000
848---0000
850---0000
852---0000
854---0000
856---0000
858---0000
860---0000
862---0000
864---0000
866---0000
868---0000
870---0000
872---0000
874---0000
876---0000
878---0000
880---0000
882---0000
884---0000
886---0000
888---0000
890---0000
892---0000
894---0000
896---0000
898---0000
900---0000
902---0000
904---0000
906---0000
908---0000
910---0000
912---0000
914---0000
916---0000
918---0000
920---0000
922---0000
924---0000
926---0000
928---0000
930---0000
932---0000
934---0000
936---0000
938---0000
940---0000
942---0000
944---0000
946---0000
948---0000
950---0000
952---0000
954---0000
956---0000
958---0000
960---0000
962---0000
964---0000
966---0000
968---0000
970---0000
972---0000
974---0000
976---0000
978---0000
980---0000
982---0000
984---0000
986---0000
988---0000
990---0000
992---0000
994---0000
996---0000
998---0000
1000---0000
? ? ? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m9.311s
user	0m1.881s
sys	0m0.011s


'193.170'
************** PARI *****************
Host 193.170.37.83 (193.170.37.83)
Time: Wed Jul 26 08:36:27 2006

Input: f=x^4-6
polred(f)
nf=nfinit(f);
factor(nf.disc);
forstep (A=2, 100, 2, g1=x^4+A*x^2+A^2/2; g2=x^4-A*x^2-A^2/2; g3=x^4+A*x^2-A^2/2; g4=x^4-A*x^2+A^2/2; nf1=nfinit(g1); nf2=nfinit(g2); nf3=nfinit(g3); nf4=nfinit(g4);factor(nf1.disc);factor(nf2.disc);factor(nf3.disc);factor(nf4.disc);nfisisom(f,g1); print(A,"---",nfisisom(f,g1), nfisisom(f,g2),nfisisom(f,g3),nfisisom(f,g4)))
             



Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = x^4 - 6
? %2 = [x - 1, x^2 - 6, x^4 - 216, x^4 - 6]
? ? ? 2---0000
4---0000
6---0000
8---0000
10---0000
12---0000
14---0000
16---0000
18---0000
20---0000
22---0000
24---0000
26---0000
28---0000
30---0000
32---0000
34---0000
36---0000
38---0000
40---0000
42---0000
44---0000
46---0000
48---0000
50---0000
52---0000
54---0000
56---0000
58---0000
60---0000
62---0000
64---0000
66---0000
68---0000
70---0000
72---0000
74---0000
76---0000
78---0000
80---0000
82---0000
84---0000
86---0000
88---0000
90---0000
92---0000
94---0000
96---0000
98---0000
100---0000
? ? ? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.174s
user	0m0.171s
sys	0m0.003s


'193.170'
************** PARI *****************
Host 193.170.37.83 (193.170.37.83)
Time: Wed Jul 26 08:36:18 2006

Input: f=x^4-6
polred(f)
nf=nfinit(f);
factor(nf.disc);
forstep (A=2, 100, 2, g1=x^4+A*x^2+A^2/2; g2=x^4-A*x^2-A^2/2; g3=x^4+A*x^2-A^2/2; g4=x^4-A*x^2+A^2/2; nf1=nfinit(g1); nf2=nfinit(g2); nf3=nfinit(g3); nf4=nfinit(g4);factor(nf1.disc);factor(nf2.disc);factor(nf3.disc);factor(nf4.disc);nfisisom(f,g1); print(A,---,nfisisom(f,g1), nfisisom(f,g2),nfisisom(f,g3),nfisisom(f,g4)))
             



Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = x^4 - 6
? %2 = [x - 1, x^2 - 6, x^4 - 216, x^4 - 6]
? ? ? ? ? ? 
Goodbye!

Errors/timing (if any):

  ***   unexpected character: ...;nfisisom(f,g1);print(A,---,nfisisom(f,g1),nf
                                                          ^--------------------

Timing:
real	0m0.014s
user	0m0.008s
sys	0m0.006s


'193.170'
************** PARI *****************
Host 193.170.37.83 (193.170.37.83)
Time: Wed Jul 26 08:36:06 2006

Input: f=x^4-6
polred(f)
nf=nfinit(f);
factor(nf.disc);
forstep (A=2, 100, 2, g1=x^4+A*x^2+A^2/2; g2=x^4-A*x^2-A^2/2; g3=x^4+A*x^2-A^2/2; g4=x^4-A*x^2+A^2/2; nf1=nfinit(g1); nf2=nfinit(g2); nf3=nfinit(g3); nf4=nfinit(g4);factor(nf1.disc);factor(nf2.disc);factor(nf3.disc);factor(nf4.disc);nfisisom(f,g1); print(A,/t,nfisisom(f,g1), nfisisom(f,g2),nfisisom(f,g3),nfisisom(f,g4)))
             



Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = x^4 - 6
? %2 = [x - 1, x^2 - 6, x^4 - 216, x^4 - 6]
? ? ? ? ? ? 
Goodbye!

Errors/timing (if any):

  ***   unexpected character: ...);nfisisom(f,g1);print(A,/t,nfisisom(f,g1),nf
                                                          ^--------------------

Timing:
real	0m0.014s
user	0m0.008s
sys	0m0.006s


'193.170'
************** PARI *****************
Host 193.170.37.83 (193.170.37.83)
Time: Wed Jul 26 08:35:59 2006

Input: f=x^4-6
polred(f)
nf=nfinit(f);
factor(nf.disc);
forstep (A=2, 100, 2, g1=x^4+A*x^2+A^2/2; g2=x^4-A*x^2-A^2/2; g3=x^4+A*x^2-A^2/2; g4=x^4-A*x^2+A^2/2; nf1=nfinit(g1); nf2=nfinit(g2); nf3=nfinit(g3); nf4=nfinit(g4);factor(nf1.disc);factor(nf2.disc);factor(nf3.disc);factor(nf4.disc);nfisisom(f,g1); print(A,t,nfisisom(f,g1), nfisisom(f,g2),nfisisom(f,g3),nfisisom(f,g4)))
             



Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = x^4 - 6
? %2 = [x - 1, x^2 - 6, x^4 - 216, x^4 - 6]
? ? ? 2t0000
4t0000
6t0000
8t0000
10t0000
12t0000
14t0000
16t0000
18t0000
20t0000
22t0000
24t0000
26t0000
28t0000
30t0000
32t0000
34t0000
36t0000
38t0000
40t0000
42t0000
44t0000
46t0000
48t0000
50t0000
52t0000
54t0000
56t0000
58t0000
60t0000
62t0000
64t0000
66t0000
68t0000
70t0000
72t0000
74t0000
76t0000
78t0000
80t0000
82t0000
84t0000
86t0000
88t0000
90t0000
92t0000
94t0000
96t0000
98t0000
100t0000
? ? ? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.174s
user	0m0.168s
sys	0m0.007s


'193.170'
************** PARI *****************
Host 193.170.37.83 (193.170.37.83)
Time: Wed Jul 26 08:35:50 2006

Input: f=x^4-6
polred(f)
nf=nfinit(f);
factor(nf.disc);
forstep (A=2, 100, 2, g1=x^4+A*x^2+A^2/2; g2=x^4-A*x^2-A^2/2; g3=x^4+A*x^2-A^2/2; g4=x^4-A*x^2+A^2/2; nf1=nfinit(g1); nf2=nfinit(g2); nf3=nfinit(g3); nf4=nfinit(g4);factor(nf1.disc);factor(nf2.disc);factor(nf3.disc);factor(nf4.disc);nfisisom(f,g1); print(A,t,nfisisom(f,g1), nfisisom(f,g2),nfisisom(f,g3),nfisisom(f,g4)))
             



Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = x^4 - 6
? %2 = [x - 1, x^2 - 6, x^4 - 216, x^4 - 6]
? ? ? 2t0000
4t0000
6t0000
8t0000
10t0000
12t0000
14t0000
16t0000
18t0000
20t0000
22t0000
24t0000
26t0000
28t0000
30t0000
32t0000
34t0000
36t0000
38t0000
40t0000
42t0000
44t0000
46t0000
48t0000
50t0000
52t0000
54t0000
56t0000
58t0000
60t0000
62t0000
64t0000
66t0000
68t0000
70t0000
72t0000
74t0000
76t0000
78t0000
80t0000
82t0000
84t0000
86t0000
88t0000
90t0000
92t0000
94t0000
96t0000
98t0000
100t0000
? ? ? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.900s
user	0m0.171s
sys	0m0.003s


'193.170'
************** PARI *****************
Host 193.170.37.83 (193.170.37.83)
Time: Wed Jul 26 08:35:36 2006

Input: f=x^4-6
polred(f)
nf=nfinit(f);
factor(nf.disc);
forstep (A=2, 100, 2, g1=x^4+A*x^2+A^2/2; g2=x^4-A*x^2-A^2/2; g3=x^4+A*x^2-A^2/2; g4=x^4-A*x^2+A^2/2; nf1=nfinit(g1); nf2=nfinit(g2); nf3=nfinit(g3); nf4=nfinit(g4);factor(nf1.disc);factor(nf2.disc);factor(nf3.disc);factor(nf4.disc);nfisisom(f,g1); print(A,nfisisom(f,g1), nfisisom(f,g2),nfisisom(f,g3),nfisisom(f,g4)))
             



Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = x^4 - 6
? %2 = [x - 1, x^2 - 6, x^4 - 216, x^4 - 6]
? ? ? 20000
40000
60000
80000
100000
120000
140000
160000
180000
200000
220000
240000
260000
280000
300000
320000
340000
360000
380000
400000
420000
440000
460000
480000
500000
520000
540000
560000
580000
600000
620000
640000
660000
680000
700000
720000
740000
760000
780000
800000
820000
840000
860000
880000
900000
920000
940000
960000
980000
1000000
? ? ? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.174s
user	0m0.169s
sys	0m0.006s


'193.170'
************** PARI *****************
Host 193.170.37.83 (193.170.37.83)
Time: Wed Jul 26 08:35:23 2006

Input: f=x^4-6
polred(f)
nf=nfinit(f);
factor(nf.disc);
forstep (A=2, 100, 2, g1=x^4+A*x^2+A^2/2; g2=x^4-A*x^2-A^2/2; g3=x^4+A*x^2-A^2/2; g4=x^4-A*x^2+A^2/2; nf1=nfinit(g1); nf2=nfinit(g2); nf3=nfinit(g3); nf4=nfinit(g4);factor(nf1.disc);factor(nf2.disc);factor(nf3.disc);factor(nf4.disc);nfisisom(f,g1); print(nfisisom(f,g1), nfisisom(f,g2),nfisisom(f,g3),nfisisom(f,g4)))
             



Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = x^4 - 6
? %2 = [x - 1, x^2 - 6, x^4 - 216, x^4 - 6]
? ? ? 0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
0000
? ? ? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.177s
user	0m0.166s
sys	0m0.008s


'193.170'
************** PARI *****************
Host 193.170.37.83 (193.170.37.83)
Time: Wed Jul 26 08:34:59 2006

Input: f=x^4-6
polred(f)
nf=nfinit(f);
factor(nf.disc);
for (i=1, 19, print(i); g1=x^4+A*x^2+A^2/2);
forstep (A=2, 100, 2, g1=x^4+A*x^2+A^2/2; g2=x^4-A*x^2-A^2/2; g3=x^4+A*x^2-A^2/2; g4=x^4-A*x^2+A^2/2; nf1=nfinit(g1); nf2=nfinit(g2); nf3=nfinit(g3); nf4=nfinit(g4);factor(nf1.disc);factor(nf2.disc);factor(nf3.disc);factor(nf4.disc);nfisisom(f,g1); print(nfisisom(f,g2),nfisisom(f,g3),nfisisom(f,g4)))
             



Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = x^4 - 6
? %2 = [x - 1, x^2 - 6, x^4 - 216, x^4 - 6]
? ? ? 1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
? 000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
? ? ? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.273s
user	0m0.165s
sys	0m0.008s


'193.170'
************** PARI *****************
Host 193.170.37.83 (193.170.37.83)
Time: Wed Jul 26 08:34:10 2006

Input: f=x^4-6
polred(f)
nf=nfinit(f);
factor(nf.disc);
for (i=1, 19, print(i); g1=x^4+A*x^2+A^2/2);
forstep (A=2, 100, 2, g1=x^4+A*x^2+A^2/2; g2=x^4-A*x^2-A^2/2; g3=x^4+A*x^2-A^2/2; g4=x^4-A*x^2+A^2/2; nf1=nfinit(g1); nf2=nfinit(g2); nf3=nfinit(g3); nf4=nfinit(g4);factor(nf1.disc);factor(nf2.disc);factor(nf3.disc);factor(nf4.disc);nfisisom(f,g1); nfisisom(f,g2);nfisisom(f,g3);nfisisom(f,g4))              



Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = x^4 - 6
? %2 = [x - 1, x^2 - 6, x^4 - 216, x^4 - 6]
? ? ? 1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
? ? ? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.173s
user	0m0.167s
sys	0m0.005s


'193.170'
************** PARI *****************
Host 193.170.37.83 (193.170.37.83)
Time: Wed Jul 26 08:33:51 2006

Input: f=x^4-6
polred(f)
nf=nfinit(f);
factor(nf.disc);
for (i=1, 19, print(i); g1=x^4+A*x^2+A^2/2);
forstep (A=0, 100, 2, g1=x^4+A*x^2+A^2/2; g2=x^4-A*x^2-A^2/2; g3=x^4+A*x^2-A^2/2; g4=x^4-A*x^2+A^2/2; nf1=nfinit(g1); nf2=nfinit(g2); nf3=nfinit(g3); nf4=nfinit(g4);factor(nf1.disc);factor(nf2.disc);factor(nf3.disc);factor(nf4.disc);nfisisom(f,g1); nfisisom(f,g2);nfisisom(f,g3);nfisisom(f,g4))              



Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = x^4 - 6
? %2 = [x - 1, x^2 - 6, x^4 - 216, x^4 - 6]
? ? ? 1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
? ? ? 
Goodbye!

Errors/timing (if any):

  *** nfinit: reducible polynomial in nfinit.

Timing:
real	0m0.013s
user	0m0.010s
sys	0m0.003s


'193.170'
************** PARI *****************
Host 193.170.37.83 (193.170.37.83)
Time: Wed Jul 26 08:33:37 2006

Input: f=x^4-6
polred(f)
nf=nfinit(f);
factor(nf.disc);
for (i=1, 19, print(i); g1=x^4+A*x^2+A^2/2);
forstep (A=1, 100, 2, g1=x^4+A*x^2+A^2/2; g2=x^4-A*x^2-A^2/2; g3=x^4+A*x^2-A^2/2; g4=x^4-A*x^2+A^2/2; nf1=nfinit(g1); nf2=nfinit(g2); nf3=nfinit(g3); nf4=nfinit(g4);factor(nf1.disc);factor(nf2.disc);factor(nf3.disc);factor(nf4.disc);nfisisom(f,g1); nfisisom(f,g2);nfisisom(f,g3);nfisisom(f,g4))              



Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = x^4 - 6
? %2 = [x - 1, x^2 - 6, x^4 - 216, x^4 - 6]
? ? ? 1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
? ? ? 
Goodbye!

Errors/timing (if any):

  *** nfinit: polynomial not in Z[X] in nfinit.

Timing:
real	0m0.057s
user	0m0.010s
sys	0m0.005s


'193.170'
************** PARI *****************
Host 193.170.37.83 (193.170.37.83)
Time: Wed Jul 26 08:13:56 2006

Input: f=x^4-6
polred(f)
nf=nfinit(f);
factor(nf.disc);
for (i=1, 19, print(i); g1=x^4+A*x^2+A^2/2);
for (A=1, 5, g1=x^4+A*x^2+A^2/2; g2=x^4-A*x^2-A^2/2; g3=x^4+A*x^2-A^2/2; g4=x^4-A*x^2+A^2/2; nf1=nfinit(g1); nf2=nfinit(g2); nf3=nfinit(g3); nf4=nfinit(g4);factor(nf1.disc);factor(nf2.disc);factor(nf3.disc);factor(nf4.disc);nfisisom(f,g1); nfisisom(f,g2);nfisisom(f,g3);nfisisom(f,g4))              



Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = x^4 - 6
? %2 = [x - 1, x^2 - 6, x^4 - 216, x^4 - 6]
? ? ? 1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
? ? ? 
Goodbye!

Errors/timing (if any):

  *** nfinit: polynomial not in Z[X] in nfinit.

Timing:
real	0m0.013s
user	0m0.010s
sys	0m0.003s


'193.170'
************** PARI *****************
Host 193.170.37.83 (193.170.37.83)
Time: Wed Jul 26 08:13:44 2006

Input: f=x^4-6
polred(f)
nf=nfinit(f);
factor(nf.disc);
for (i=1, 19, print(i); g1=x^4+A*x^2+A^2/2);
for (A=1, 5, g1=x^4+A*x^2+A^2/2; g2=x^4-A*x^2-A^2/2; g3=x^4+A*x^2-A^2/2; g4=x^4-A*x^2+A^2/2; nf1=nfinit(g1); nf2=nfinit(g2); nf3=nfinit(g3); nf4=nfinit(g4);factor(nf1.disc);factor(nf2.disc);factor(nf3.disc);factor(nf4.disc);nfisisom(f,g1); nfisisom(f,g2);nfisisom(f,g3);nfisisom(f,g4));              



Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = x^4 - 6
? %2 = [x - 1, x^2 - 6, x^4 - 216, x^4 - 6]
? ? ? 1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
? ? ? 
Goodbye!

Errors/timing (if any):

  *** nfinit: polynomial not in Z[X] in nfinit.

Timing:
real	0m0.022s
user	0m0.009s
sys	0m0.007s


'193.170'
************** PARI *****************
Host 193.170.37.83 (193.170.37.83)
Time: Wed Jul 26 08:12:53 2006

Input: f=x^4-6
polred(f)
nf=nfinit(f);
factor(nf.disc);
for (i=1, 19, print(i); g1=x^4+A*x^2+A^2/2);
for (A=1, 5, g1=x^4+A*x^2+A^2/2, g2=x^4-A*x^2-A^2/2, g3=x^4+A*x^2-A^2/2, g4=x^4-A*x^2+A^2/2, nf1=nfinit(g1), nf2=nfinit(g2), nf3=nfinit(g3), nf4=nfinit(g4),factor(nf1.disc),factor(nf2.disc),factor(nf3.disc),factor(nf4.disc),nfisisom(f,g1), nfisisom(f,g2)nfisisom(f,g3),nfisisom(f,g4))              



Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = x^4 - 6
? %2 = [x - 1, x^2 - 6, x^4 - 216, x^4 - 6]
? ? ? 1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
? ? ? 
Goodbye!

Errors/timing (if any):

  ***   expected character: ')' instead of: ...(A=1,5,g1=x^4+A*x^2+A^2/2
  ***   ,g2=x^4-A*x^2-A^2/2,
        ^--------------------

Timing:
real	0m0.016s
user	0m0.007s
sys	0m0.007s


'193.170'
************** PARI *****************
Host 193.170.37.83 (193.170.37.83)
Time: Wed Jul 26 08:12:14 2006

Input: f=x^4-6
polred(f)
nf=nfinit(f);
factor(nf.disc);
for (i=1, 19, (print(i), g1=x^4+A*x^2+A^2/2));
for (A=1, 5, g1=x^4+A*x^2+A^2/2, g2=x^4-A*x^2-A^2/2, g3=x^4+A*x^2-A^2/2, g4=x^4-A*x^2+A^2/2, nf1=nfinit(g1), nf2=nfinit(g2), nf3=nfinit(g3), nf4=nfinit(g4),factor(nf1.disc),factor(nf2.disc),factor(nf3.disc),factor(nf4.disc),nfisisom(f,g1), nfisisom(f,g2)nfisisom(f,g3),nfisisom(f,g4))              



Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = x^4 - 6
? %2 = [x - 1, x^2 - 6, x^4 - 216, x^4 - 6]
? ? ? ? ? ? 
Goodbye!

Errors/timing (if any):

  ***   expected character: ')' instead of: for(i=1,19,(print(i)
  ***   ,g1=x^4+A*x^2+A^2/2)
        ^--------------------
  ***   expected character: ')' instead of: ...(A=1,5,g1=x^4+A*x^2+A^2/2
  ***   ,g2=x^4-A*x^2-A^2/2,
        ^--------------------

Timing:
real	0m0.013s
user	0m0.008s
sys	0m0.005s


'193.170'
************** PARI *****************
Host 193.170.37.83 (193.170.37.83)
Time: Wed Jul 26 08:11:46 2006

Input: f=x^4-6
polred(f)
nf=nfinit(f);
factor(nf.disc);
for (i=1, 19, print(i), g1=x^4+A*x^2+A^2/2);
for (A=1, 5, g1=x^4+A*x^2+A^2/2, g2=x^4-A*x^2-A^2/2, g3=x^4+A*x^2-A^2/2, g4=x^4-A*x^2+A^2/2, nf1=nfinit(g1), nf2=nfinit(g2), nf3=nfinit(g3), nf4=nfinit(g4),factor(nf1.disc),factor(nf2.disc),factor(nf3.disc),factor(nf4.disc),nfisisom(f,g1), nfisisom(f,g2)nfisisom(f,g3),nfisisom(f,g4))              



Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = x^4 - 6
? %2 = [x - 1, x^2 - 6, x^4 - 216, x^4 - 6]
? ? ? ? ? ? 
Goodbye!

Errors/timing (if any):

  ***   expected character: ')' instead of: for(i=1,19,print(i)
  ***   ,g1=x^4+A*x^2+A^2/2)
        ^--------------------
  ***   expected character: ')' instead of: ...(A=1,5,g1=x^4+A*x^2+A^2/2
  ***   ,g2=x^4-A*x^2-A^2/2,
        ^--------------------

Timing:
real	0m0.098s
user	0m0.009s
sys	0m0.006s


'193.170'
************** PARI *****************
Host 193.170.37.83 (193.170.37.83)
Time: Wed Jul 26 08:11:40 2006

Input: f=x^4-6
polred(f)
nf=nfinit(f);
factor(nf.disc);
for (i=1, 19, print(i), g1=x^4+A*x^2+A^2/2);
for (A=1, 5, g1=x^4+A*x^2+A^2/2, g2=x^4-A*x^2-A^2/2, g3=x^4+A*x^2-A^2/2, g4=x^4-A*x^2+A^2/2, nf1=nfinit(g1), nf2=nfinit(g2), nf3=nfinit(g3), nf4=nfinit(g4),factor(nf1.disc),factor(nf2.disc),factor(nf3.disc),factor(nf4.disc),nfisisom(f,g1), nfisisom(f,g2)nfisisom(f,g3),nfisisom(f,g4))              



Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = x^4 - 6
? %2 = [x - 1, x^2 - 6, x^4 - 216, x^4 - 6]
? ? ? ? ? ? 
Goodbye!

Errors/timing (if any):

  ***   expected character: ')' instead of: for(i=1,19,print(i)
  ***   ,g1=x^4+A*x^2+A^2/2)
        ^--------------------
  ***   expected character: ')' instead of: ...(A=1,5,g1=x^4+A*x^2+A^2/2
  ***   ,g2=x^4-A*x^2-A^2/2,
        ^--------------------

Timing:
real	0m0.013s
user	0m0.007s
sys	0m0.006s


'193.170'
************** PARI *****************
Host 193.170.37.83 (193.170.37.83)
Time: Wed Jul 26 08:11:34 2006

Input: f=x^4-6
polred(f)
nf=nfinit(f);
factor(nf.disc);
for (i=1, 19, print(i), g1=x^4+A*x^2+A^2/2,);
for (A=1, 5, g1=x^4+A*x^2+A^2/2, g2=x^4-A*x^2-A^2/2, g3=x^4+A*x^2-A^2/2, g4=x^4-A*x^2+A^2/2, nf1=nfinit(g1), nf2=nfinit(g2), nf3=nfinit(g3), nf4=nfinit(g4),factor(nf1.disc),factor(nf2.disc),factor(nf3.disc),factor(nf4.disc),nfisisom(f,g1), nfisisom(f,g2)nfisisom(f,g3),nfisisom(f,g4))              



Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = x^4 - 6
? %2 = [x - 1, x^2 - 6, x^4 - 216, x^4 - 6]
? ? ? ? ? ? 
Goodbye!

Errors/timing (if any):

  ***   expected character: ')' instead of: for(i=1,19,print(i)
  ***   ,g1=x^4+A*x^2+A^2/2,
        ^--------------------
  ***   expected character: ')' instead of: ...(A=1,5,g1=x^4+A*x^2+A^2/2
  ***   ,g2=x^4-A*x^2-A^2/2,
        ^--------------------

Timing:
real	0m0.039s
user	0m0.007s
sys	0m0.007s


'193.170'
************** PARI *****************
Host 193.170.37.83 (193.170.37.83)
Time: Wed Jul 26 08:11:16 2006

Input: f=x^4-6
polred(f)
nf=nfinit(f);
factor(nf.disc);
for (i=1, 19, print(i));
for (A=1, 5, g1=x^4+A*x^2+A^2/2, g2=x^4-A*x^2-A^2/2, g3=x^4+A*x^2-A^2/2, g4=x^4-A*x^2+A^2/2, nf1=nfinit(g1), nf2=nfinit(g2), nf3=nfinit(g3), nf4=nfinit(g4),factor(nf1.disc),factor(nf2.disc),factor(nf3.disc),factor(nf4.disc),nfisisom(f,g1), nfisisom(f,g2)nfisisom(f,g3),nfisisom(f,g4))              



Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = x^4 - 6
? %2 = [x - 1, x^2 - 6, x^4 - 216, x^4 - 6]
? ? ? 1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
? ? ? 
Goodbye!

Errors/timing (if any):

  ***   expected character: ')' instead of: ...(A=1,5,g1=x^4+A*x^2+A^2/2
  ***   ,g2=x^4-A*x^2-A^2/2,
        ^--------------------

Timing:
real	0m0.015s
user	0m0.008s
sys	0m0.005s


'193.170'
************** PARI *****************
Host 193.170.37.83 (193.170.37.83)
Time: Wed Jul 26 08:10:25 2006

Input: f=x^4-6
polred(f)
nf=nfinit(f);
factor(nf.disc);
for (A=1, 5, g1=x^4+A*x^2+A^2/2, g2=x^4-A*x^2-A^2/2, g3=x^4+A*x^2-A^2/2, g4=x^4-A*x^2+A^2/2, nf1=nfinit(g1), nf2=nfinit(g2), nf3=nfinit(g3), nf4=nfinit(g4),factor(nf1.disc),factor(nf2.disc),factor(nf3.disc),factor(nf4.disc),nfisisom(f,g1), nfisisom(f,g2)nfisisom(f,g3),nfisisom(f,g4))              



Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = x^4 - 6
? %2 = [x - 1, x^2 - 6, x^4 - 216, x^4 - 6]
? ? ? ? ? 
Goodbye!

Errors/timing (if any):

  ***   expected character: ')' instead of: ...(A=1,5,g1=x^4+A*x^2+A^2/2
  ***   ,g2=x^4-A*x^2-A^2/2,
        ^--------------------

Timing:
real	0m0.013s
user	0m0.006s
sys	0m0.008s


'193.170'
************** PARI *****************
Host 193.170.37.83 (193.170.37.83)
Time: Wed Jul 26 08:09:50 2006

Input: f=x^4-6
polred(f)
nf=nfinit(f);
factor(nf.disc);
for (A=1, 5, g1=x^4+A*x^2+A^2/2, g2=x^4-A*x^2-A^2/2,g3=x^4+A*x^2-A^2/2, g4=x^4-A*x^2+A^2/2, nf1=nfinit(g1), nf2=nfinit(g2), nf3=nfinit(g3), nf4=nfinit(g4),factor(nf1.disc),factor(nf2.disc),factor(nf3.disc),factor(nf4.disc),nfisisom(f,g1)nfisisom(f,g2)nfisisom(f,g3),nfisisom(f,g4))              



Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = x^4 - 6
? %2 = [x - 1, x^2 - 6, x^4 - 216, x^4 - 6]
? ? ? ? ? 
Goodbye!

Errors/timing (if any):

  ***   expected character: ')' instead of: ...(A=1,5,g1=x^4+A*x^2+A^2/2
  ***   ,g2=x^4-A*x^2-A^2/2,
        ^--------------------

Timing:
real	0m0.014s
user	0m0.009s
sys	0m0.006s


'193.170'
************** PARI *****************
Host 193.170.37.83 (193.170.37.83)
Time: Wed Jul 26 08:09:17 2006

Input: f=x^4-6
polred(f)
nf=nfinit(f);
factor(nf.disc);
for (A=1, 5, g1=x^4+A*x^2+A^2/2, g2=x^4-A*x^2-A^2/2,g3=x^4+A*x^2-A^2/2, g4=x^4-A*x^2+A^2/2,nf1=nfinit(g1),nf2=nfinit(g2),nf3=nfinit(g3),nf4=nfinit(g4),factor(nf1.disc),factor(nf2.disc),factor(nf3.disc),factor(nf4.disc),nfisisom(f,g1)nfisisom(f,g2)nfisisom(f,g3),nfisisom(f,g4))              



Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = x^4 - 6
? %2 = [x - 1, x^2 - 6, x^4 - 216, x^4 - 6]
? ? ? ? ? 
Goodbye!

Errors/timing (if any):

  ***   expected character: ')' instead of: ...(A=1,5,g1=x^4+A*x^2+A^2/2
  ***   ,g2=x^4-A*x^2-A^2/2,
        ^--------------------

Timing:
real	0m0.016s
user	0m0.008s
sys	0m0.005s


'193.170'
************** PARI *****************
Host 193.170.37.83 (193.170.37.83)
Time: Wed Jul 26 08:07:49 2006

Input: f=x^4-6
polred(f)
nf=nfinit(f);
factor(nf.disc);
{for (A=1, 5 ,g1=x^4+A*x^2+A^2/2,g2=x^4-A*x^2-A^2/2,g3=x^4+A*x^2-A^2/2,g4=x^4-A*x^2+A^2/2,nf1=nfinit(g1),nf2=nfinit(g2),nf3=nfinit(g3),nf4=nfinit(g4),factor(nf1.disc),factor(nf2.disc),factor(nf3.disc),factor(nf4.disc),nfisisom(f,g1)nfisisom(f,g2)nfisisom(f,g3),nfisisom(f,g4))              
}


Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = x^4 - 6
? %2 = [x - 1, x^2 - 6, x^4 - 216, x^4 - 6]
? ? ? ? 
Goodbye!

Errors/timing (if any):

  ***   expected character: ')' instead of: ...(A=1,5,g1=x^4+A*x^2+A^2/2
  ***   ,g2=x^4-A*x^2-A^2/2,
        ^--------------------

Timing:
real	0m0.077s
user	0m0.009s
sys	0m0.005s


'193.170'
************** PARI *****************
Host 193.170.37.83 (193.170.37.83)
Time: Wed Jul 26 08:07:29 2006

Input: f=x^4-6
polred(f)
nf=nfinit(f);
factor(nf.disc);
{for (A=1, 5 ,g1=x^4+A*x^2+A^2/2,g2=x^4-A*x^2-A^2/2,g3=x^4+A*x^2-A^2/2,g4=x^4-A*x^2+A^2/2,nf1=nfinit(g1),nf2=nfinit(g2),nf3=nfinit(g3),nf4=nfinit(g4),factor(nf1.disc),factor(nf2.disc),factor(nf3.disc),factor(nf4.disc),nfisisom(f,g1)nfisisom(f,g2)nfisisom(f,g3)nfisisom(f,g4))              
}


Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = x^4 - 6
? %2 = [x - 1, x^2 - 6, x^4 - 216, x^4 - 6]
? ? ? ? 
Goodbye!

Errors/timing (if any):

  ***   expected character: ')' instead of: ...(A=1,5,g1=x^4+A*x^2+A^2/2
  ***   ,g2=x^4-A*x^2-A^2/2,
        ^--------------------

Timing:
real	0m0.052s
user	0m0.007s
sys	0m0.005s


'193.170'
************** PARI *****************
Host 193.170.37.83 (193.170.37.83)
Time: Wed Jul 26 08:03:22 2006

Input: for (i=1, 19, print(i));

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? 1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.055s
user	0m0.007s
sys	0m0.005s


'193.170'
************** PARI *****************
Host 193.170.37.83 (193.170.37.83)
Time: Wed Jul 26 08:03:08 2006

Input: for (i=1, 19, 2, print(i));

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? ? 
Goodbye!

Errors/timing (if any):

  ***   expected character: ')' instead of: for(i=1,19,2,print(i));
                                                        ^-----------

Timing:
real	0m0.011s
user	0m0.007s
sys	0m0.004s


'193.170'
************** PARI *****************
Host 193.170.37.83 (193.170.37.83)
Time: Wed Jul 26 08:03:00 2006

Input: for (i=1, 19, print(i));

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? 1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.011s
user	0m0.007s
sys	0m0.004s


'193.170'
************** PARI *****************
Host 193.170.37.83 (193.170.37.83)
Time: Wed Jul 26 08:02:55 2006

Input: for (i=1, 19, print(i));

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? 1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.011s
user	0m0.007s
sys	0m0.004s


'193.170'
************** PARI *****************
Host 193.170.37.83 (193.170.37.83)
Time: Wed Jul 26 08:02:48 2006

Input: for (i=1, 19, print(i))

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? 1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.098s
user	0m0.010s
sys	0m0.003s


'193.170'
************** PARI *****************
Host 193.170.37.83 (193.170.37.83)
Time: Wed Jul 26 08:01:37 2006

Input: f=x^4-6
polred(f)
nf=nfinit(f);
factor(nf.disc);
{for (A=1, 5 ,g1=x^4+A*x^2+A^2/2,
g2=x^4-A*x^2-A^2/2,
g3=x^4+A*x^2-A^2/2,
g4=x^4-A*x^2+A^2/2,
nf1=nfinit(g1),
nf2=nfinit(g2),
nf3=nfinit(g3),
nf4=nfinit(g4),
factor(nf1.disc),
factor(nf2.disc),
factor(nf3.disc),
factor(nf4.disc),
nfisisom(f,g1)
nfisisom(f,g2)
nfisisom(f,g3)
nfisisom(f,g4))                
}


Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = x^4 - 6
? %2 = [x - 1, x^2 - 6, x^4 - 216, x^4 - 6]
? ? ? ? 
Goodbye!

Errors/timing (if any):

  ***   expected character: ')' instead of: ...(A=1,5,g1=x^4+A*x^2+A^2/2
  ***   ,g2=x^4-A*x^2-A^2/2,
        ^--------------------

Timing:
real	0m0.099s
user	0m0.009s
sys	0m0.006s


'193.170'
************** PARI *****************
Host 193.170.37.83 (193.170.37.83)
Time: Wed Jul 26 08:01:31 2006

Input: f=x^4-6
polred(f)
nf=nfinit(f);
factor(nf.disc);
{for (A=1, 5 ,
g1=x^4+A*x^2+A^2/2,
g2=x^4-A*x^2-A^2/2,
g3=x^4+A*x^2-A^2/2,
g4=x^4-A*x^2+A^2/2,
nf1=nfinit(g1),
nf2=nfinit(g2),
nf3=nfinit(g3),
nf4=nfinit(g4),
factor(nf1.disc),
factor(nf2.disc),
factor(nf3.disc),
factor(nf4.disc),
nfisisom(f,g1)
nfisisom(f,g2)
nfisisom(f,g3)
nfisisom(f,g4))                
}


Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = x^4 - 6
? %2 = [x - 1, x^2 - 6, x^4 - 216, x^4 - 6]
? ? ? ? 
Goodbye!

Errors/timing (if any):

  ***   expected character: ')' instead of: ...(A=1,5,g1=x^4+A*x^2+A^2/2
  ***   ,g2=x^4-A*x^2-A^2/2,
        ^--------------------

Timing:
real	0m0.014s
user	0m0.008s
sys	0m0.006s


'193.170'
************** PARI *****************
Host 193.170.37.83 (193.170.37.83)
Time: Wed Jul 26 08:01:27 2006

Input: f=x^4-6
polred(f)
nf=nfinit(f);
factor(nf.disc);
{for (A=1, 5 ,
g1=x^4+A*x^2+A^2/2,
g2=x^4-A*x^2-A^2/2,
g3=x^4+A*x^2-A^2/2,
g4=x^4-A*x^2+A^2/2,
nf1=nfinit(g1),
nf2=nfinit(g2),
nf3=nfinit(g3),
nf4=nfinit(g4),
factor(nf1.disc),
factor(nf2.disc),
factor(nf3.disc),
factor(nf4.disc),
nfisisom(f,g1)
nfisisom(f,g2)
nfisisom(f,g3)
nfisisom(f,g4))                
}


Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = x^4 - 6
? %2 = [x - 1, x^2 - 6, x^4 - 216, x^4 - 6]
? ? ? ? 
Goodbye!

Errors/timing (if any):

  ***   expected character: ')' instead of: ...(A=1,5,g1=x^4+A*x^2+A^2/2
  ***   ,g2=x^4-A*x^2-A^2/2,
        ^--------------------

Timing:
real	0m0.013s
user	0m0.010s
sys	0m0.004s


'193.170'
************** PARI *****************
Host 193.170.37.83 (193.170.37.83)
Time: Wed Jul 26 08:01:14 2006

Input: f=x^4-6
polred(f)
nf=nfinit(f);
factor(nf.disc);
{for 
(A=1, 5 ,
g1=x^4+A*x^2+A^2/2,
g2=x^4-A*x^2-A^2/2,
g3=x^4+A*x^2-A^2/2,
g4=x^4-A*x^2+A^2/2,
nf1=nfinit(g1),
nf2=nfinit(g2),
nf3=nfinit(g3),
nf4=nfinit(g4),
factor(nf1.disc),
factor(nf2.disc),
factor(nf3.disc),
factor(nf4.disc),
nfisisom(f,g1)
nfisisom(f,g2)
nfisisom(f,g3)
nfisisom(f,g4))                
}


Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = x^4 - 6
? %2 = [x - 1, x^2 - 6, x^4 - 216, x^4 - 6]
? ? ? ? 
Goodbye!

Errors/timing (if any):

  ***   expected character: ')' instead of: ...(A=1,5,g1=x^4+A*x^2+A^2/2
  ***   ,g2=x^4-A*x^2-A^2/2,
        ^--------------------

Timing:
real	0m0.016s
user	0m0.008s
sys	0m0.006s


'193.170'
************** PARI *****************
Host 193.170.37.83 (193.170.37.83)
Time: Wed Jul 26 08:00:39 2006

Input: f=x^4-6
polred(f)
nf=nfinit(f);
factor(nf.disc);
{for 
(A=1, 5 ,
g1=x^4+A*x^2+A^2/2;
g2=x^4-A*x^2-A^2/2;
g3=x^4+A*x^2-A^2/2;
g4=x^4-A*x^2+A^2/2;
nf1=nfinit(g1);
nf2=nfinit(g2);
nf3=nfinit(g3);
nf4=nfinit(g4);
factor(nf1.disc);
factor(nf2.disc);
factor(nf3.disc);
factor(nf4.disc);
nfisisom(f,g1)
nfisisom(f,g2)
nfisisom(f,g3)
nfisisom(f,g4))                
}


Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = x^4 - 6
? %2 = [x - 1, x^2 - 6, x^4 - 216, x^4 - 6]
? ? ? ? 
Goodbye!

Errors/timing (if any):

  ***   expected character: ')' instead of: ...(nf4.disc);nfisisom(f,g1)
  ***   nfisisom(f,g2)nfisis
        ^--------------------

Timing:
real	0m0.013s
user	0m0.007s
sys	0m0.006s


'193.170'
************** PARI *****************
Host 193.170.37.83 (193.170.37.83)
Time: Wed Jul 26 08:00:21 2006

Input: f=x^4-6
polred(f)
nf=nfinit(f);
factor(nf.disc);
{for 
(A=1, 5 ,
g1=x^4+A*x^2+A^2/2;
g2=x^4-A*x^2-A^2/2;
g3=x^4+A*x^2-A^2/2;
g4=x^4-A*x^2+A^2/2;
nf1=nfinit(g1);
nf2=nfinit(g2);
nf3=nfinit(g3);
nf4=nfinit(g4);
factor(nf1.disc);
factor(nf2.disc);
factor(nf3.disc);
factor(nf4.disc);
nfisisom(f,g1)
nfisisom(f,g2)
nfisisom(f,g3)
nfisisom(f,g4)

)                  /*1*/
}


Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = x^4 - 6
? %2 = [x - 1, x^2 - 6, x^4 - 216, x^4 - 6]
? ? ? ? 
Goodbye!

Errors/timing (if any):

  ***   expected character: ')' instead of: ...(nf4.disc);nfisisom(f,g1)
  ***   nfisisom(f,g2)nfisis
        ^--------------------

Timing:
real	0m0.038s
user	0m0.007s
sys	0m0.008s


'193.170'
************** PARI *****************
Host 193.170.37.83 (193.170.37.83)
Time: Wed Jul 26 07:57:53 2006

Input: f=x^4-6
polred(f)
nf=nfinit(f);
factor(nf.disc);
{for 
(                     /*1*/
A=1, 5 ,

g1=x^4+A*x^2+A^2/2;
g2=x^4-A*x^2-A^2/2;
g3=x^4+A*x^2-A^2/2;
g4=x^4-A*x^2+A^2/2;
nf1=nfinit(g1);
nf2=nfinit(g2);
nf3=nfinit(g3);
nf4=nfinit(g4);
factor(nf1.disc);
factor(nf2.disc);
factor(nf3.disc);
factor(nf4.disc);
nfisisom(f,g1)
nfisisom(f,g2)
nfisisom(f,g3)
nfisisom(f,g4)

)                  /*1*/
}


Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = x^4 - 6
? %2 = [x - 1, x^2 - 6, x^4 - 216, x^4 - 6]
? ? ? ? 
Goodbye!

Errors/timing (if any):

  ***   expected character: ')' instead of: ...(nf4.disc);nfisisom(f,g1)
  ***   nfisisom(f,g2)nfisis
        ^--------------------

Timing:
real	0m0.014s
user	0m0.005s
sys	0m0.009s


'193.170'
************** PARI *****************
Host 193.170.37.83 (193.170.37.83)
Time: Wed Jul 26 07:57:24 2006

Input: f=x^4-6
polred(f)
nf=nfinit(f);
factor(nf.disc);
{for 
(                     /*1*/
A=1, 5 ,
(                    /*2*/


g1=x^4+A*x^2+A^2/2;
g2=x^4-A*x^2-A^2/2;
g3=x^4+A*x^2-A^2/2;
g4=x^4-A*x^2+A^2/2;
nf1=nfinit(g1);
nf2=nfinit(g2);
nf3=nfinit(g3);
nf4=nfinit(g4);
factor(nf1.disc);
factor(nf2.disc);
factor(nf3.disc);
factor(nf4.disc);
nfisisom(f,g1)
nfisisom(f,g2)
nfisisom(f,g3)
nfisisom(f,g4)

)                   /*2*/
)                  /*1*/
}


Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = x^4 - 6
? %2 = [x - 1, x^2 - 6, x^4 - 216, x^4 - 6]
? ? ? ? 
Goodbye!

Errors/timing (if any):

  ***   expected character: ')' instead of: ...A=1,5,(g1=x^4+A*x^2+A^2/2
  ***   ;g2=x^4-A*x^2-A^2/2;
        ^--------------------

Timing:
real	0m0.014s
user	0m0.009s
sys	0m0.005s


'193.170'
************** PARI *****************
Host 193.170.37.83 (193.170.37.83)
Time: Wed Jul 26 07:57:14 2006

Input: f=x^4-6
polred(f)
nf=nfinit(f);
factor(nf.disc);
{for 
(                     /*1*/
A=1, n ,
(                    /*2*/


g1=x^4+A*x^2+A^2/2;
g2=x^4-A*x^2-A^2/2;
g3=x^4+A*x^2-A^2/2;
g4=x^4-A*x^2+A^2/2;
nf1=nfinit(g1);
nf2=nfinit(g2);
nf3=nfinit(g3);
nf4=nfinit(g4);
factor(nf1.disc);
factor(nf2.disc);
factor(nf3.disc);
factor(nf4.disc);
nfisisom(f,g1)
nfisisom(f,g2)
nfisisom(f,g3)
nfisisom(f,g4)

)                   /*2*/
)                  /*1*/
}


Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = x^4 - 6
? %2 = [x - 1, x^2 - 6, x^4 - 216, x^4 - 6]
? ? ? ? 
Goodbye!

Errors/timing (if any):

  ***   expected character: ')' instead of: ...A=1,n,(g1=x^4+A*x^2+A^2/2
  ***   ;g2=x^4-A*x^2-A^2/2;
        ^--------------------

Timing:
real	0m0.016s
user	0m0.009s
sys	0m0.007s


'193.170'
************** PARI *****************
Host 193.170.37.83 (193.170.37.83)
Time: Wed Jul 26 07:56:50 2006

Input: f=x^4-6
polred(f)
nf=nfinit(f);
factor(nf.disc);
{for 
(                     /*1*/
A=1, n ,if 
(                    /*2*/
k[count],a1 = length(k[count]);nf=nfinit(k[count][a1]);print(factor(nf.disc))

g1=x^4+A*x^2+A^2/2;
g2=x^4-A*x^2-A^2/2;
g3=x^4+A*x^2-A^2/2;
g4=x^4-A*x^2+A^2/2;
nf1=nfinit(g1);
nf2=nfinit(g2);
nf3=nfinit(g3);
nf4=nfinit(g4);
factor(nf1.disc);
factor(nf2.disc);
factor(nf3.disc);
factor(nf4.disc);
nfisisom(f,g1)
nfisisom(f,g2)
nfisisom(f,g3)
nfisisom(f,g4)

)                   /*2*/
)                  /*1*/
}


Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = x^4 - 6
? %2 = [x - 1, x^2 - 6, x^4 - 216, x^4 - 6]
? ? ? ? 
Goodbye!

Errors/timing (if any):

  ***   expected character: ',' instead of: ...]);print(factor(nf.disc))
  ***   g1=x^4+A*x^2+A^2/2;g
        ^--------------------

Timing:
real	0m0.015s
user	0m0.010s
sys	0m0.004s


'193.170'
************** PARI *****************
Host 193.170.37.83 (193.170.37.83)
Time: Wed Jul 26 07:41:24 2006

Input: f=x^4-6
polred(f)
nf=nfinit(f);
factor(nf.disc);
A=212;
g1=x^4+A*x^2+A^2/2;
g2=x^4-A*x^2-A^2/2;
g3=x^4+A*x^2-A^2/2;
g4=x^4-A*x^2+A^2/2;
nf1=nfinit(g1);
nf2=nfinit(g2);
nf3=nfinit(g3);
nf4=nfinit(g4);
factor(nf1.disc);
factor(nf2.disc);
factor(nf3.disc);
factor(nf4.disc);
nfisisom(f,g1)
nfisisom(f,g2)
nfisisom(f,g3)
nfisisom(f,g4)

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = x^4 - 6
? %2 = [x - 1, x^2 - 6, x^4 - 216, x^4 - 6]
? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? %18 = 0
? %19 = 0
? %20 = 0
? %21 = 0
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.038s
user	0m0.015s
sys	0m0.003s


'193.170'
************** PARI *****************
Host 193.170.37.83 (193.170.37.83)
Time: Wed Jul 26 07:41:02 2006

Input: f=x^4-6
polred(f);
nf=nfinit(f);
factor(nf.disc);
A=212;
g1=x^4+A*x^2+A^2/2;
g2=x^4-A*x^2-A^2/2;
g3=x^4+A*x^2-A^2/2;
g4=x^4-A*x^2+A^2/2;
nf1=nfinit(g1);
nf2=nfinit(g2);
nf3=nfinit(g3);
nf4=nfinit(g4);
factor(nf1.disc);
factor(nf2.disc);
factor(nf3.disc);
factor(nf4.disc);
nfisisom(f,g1)
nfisisom(f,g2)
nfisisom(f,g3)
nfisisom(f,g4)

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = x^4 - 6
? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? %18 = 0
? %19 = 0
? %20 = 0
? %21 = 0
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.017s
user	0m0.012s
sys	0m0.005s


'193.170'
************** PARI *****************
Host 193.170.37.83 (193.170.37.83)
Time: Wed Jul 26 07:40:56 2006

Input: f=x^4-6
polred(f);
nf=nfinit(f);
factor(nf.disc);
A=210;
g1=x^4+A*x^2+A^2/2;
g2=x^4-A*x^2-A^2/2;
g3=x^4+A*x^2-A^2/2;
g4=x^4-A*x^2+A^2/2;
nf1=nfinit(g1);
nf2=nfinit(g2);
nf3=nfinit(g3);
nf4=nfinit(g4);
factor(nf1.disc);
factor(nf2.disc);
factor(nf3.disc);
factor(nf4.disc);
nfisisom(f,g1)
nfisisom(f,g2)
nfisisom(f,g3)
nfisisom(f,g4)

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = x^4 - 6
? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? %18 = 0
? %19 = 0
? %20 = 0
? %21 = 0
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.019s
user	0m0.012s
sys	0m0.007s


'193.170'
************** PARI *****************
Host 193.170.37.83 (193.170.37.83)
Time: Wed Jul 26 07:40:47 2006

Input: f=x^4-6
polred(f);
nf=nfinit(f);
factor(nf.disc);
A=208;
g1=x^4+A*x^2+A^2/2;
g2=x^4-A*x^2-A^2/2;
g3=x^4+A*x^2-A^2/2;
g4=x^4-A*x^2+A^2/2;
nf1=nfinit(g1);
nf2=nfinit(g2);
nf3=nfinit(g3);
nf4=nfinit(g4);
factor(nf1.disc);
factor(nf2.disc);
factor(nf3.disc);
factor(nf4.disc);
nfisisom(f,g1)
nfisisom(f,g2)
nfisisom(f,g3)
nfisisom(f,g4)

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = x^4 - 6
? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? %18 = 0
? %19 = 0
? %20 = 0
? %21 = 0
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.017s
user	0m0.011s
sys	0m0.007s


'193.170'
************** PARI *****************
Host 193.170.37.83 (193.170.37.83)
Time: Wed Jul 26 07:27:43 2006

Input: f=x^4-6
polred(f);
nf=nfinit(f);
factor(nf.disc);
A=206;
g1=x^4+A*x^2+A^2/2;
g2=x^4-A*x^2-A^2/2;
g3=x^4+A*x^2-A^2/2;
g4=x^4-A*x^2+A^2/2;
nf1=nfinit(g1);
nf2=nfinit(g2);
nf3=nfinit(g3);
nf4=nfinit(g4);
factor(nf1.disc);
factor(nf2.disc);
factor(nf3.disc);
factor(nf4.disc);
nfisisom(f,g1)
nfisisom(f,g2)
nfisisom(f,g3)
nfisisom(f,g4)

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = x^4 - 6
? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? %18 = 0
? %19 = 0
? %20 = 0
? %21 = 0
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.018s
user	0m0.008s
sys	0m0.010s


'193.170'
************** PARI *****************
Host 193.170.37.83 (193.170.37.83)
Time: Wed Jul 26 07:27:31 2006

Input: f=x^4-6
polred(f);
nf=nfinit(f);
factor(nf.disc);
A=204;
g1=x^4+A*x^2+A^2/2;
g2=x^4-A*x^2-A^2/2;
g3=x^4+A*x^2-A^2/2;
g4=x^4-A*x^2+A^2/2;
nf1=nfinit(g1);
nf2=nfinit(g2);
nf3=nfinit(g3);
nf4=nfinit(g4);
factor(nf1.disc);
factor(nf2.disc);
factor(nf3.disc);
factor(nf4.disc);
nfisisom(f,g1)
nfisisom(f,g2)
nfisisom(f,g3)
nfisisom(f,g4)

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = x^4 - 6
? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? %18 = 0
? %19 = 0
? %20 = 0
? %21 = 0
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.019s
user	0m0.014s
sys	0m0.004s


'193.170'
************** PARI *****************
Host 193.170.37.83 (193.170.37.83)
Time: Wed Jul 26 07:27:24 2006

Input: f=x^4-6
polred(f);
nf=nfinit(f);
factor(nf.disc);
A=202;
g1=x^4+A*x^2+A^2/2;
g2=x^4-A*x^2-A^2/2;
g3=x^4+A*x^2-A^2/2;
g4=x^4-A*x^2+A^2/2;
nf1=nfinit(g1);
nf2=nfinit(g2);
nf3=nfinit(g3);
nf4=nfinit(g4);
factor(nf1.disc);
factor(nf2.disc);
factor(nf3.disc);
factor(nf4.disc);
nfisisom(f,g1)
nfisisom(f,g2)
nfisisom(f,g3)
nfisisom(f,g4)

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = x^4 - 6
? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? %18 = 0
? %19 = 0
? %20 = 0
? %21 = 0
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.018s
user	0m0.012s
sys	0m0.006s


'193.170'
************** PARI *****************
Host 193.170.37.83 (193.170.37.83)
Time: Wed Jul 26 07:27:17 2006

Input: f=x^4-6
polred(f);
nf=nfinit(f);
factor(nf.disc);
A=200;
g1=x^4+A*x^2+A^2/2;
g2=x^4-A*x^2-A^2/2;
g3=x^4+A*x^2-A^2/2;
g4=x^4-A*x^2+A^2/2;
nf1=nfinit(g1);
nf2=nfinit(g2);
nf3=nfinit(g3);
nf4=nfinit(g4);
factor(nf1.disc);
factor(nf2.disc);
factor(nf3.disc);
factor(nf4.disc);
nfisisom(f,g1)
nfisisom(f,g2)
nfisisom(f,g3)
nfisisom(f,g4)

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = x^4 - 6
? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? %18 = 0
? %19 = 0
? %20 = 0
? %21 = 0
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.017s
user	0m0.011s
sys	0m0.006s


'193.170'
************** PARI *****************
Host 193.170.37.83 (193.170.37.83)
Time: Wed Jul 26 07:27:09 2006

Input: f=x^4-6
polred(f);
nf=nfinit(f);
factor(nf.disc);
A=198;
g1=x^4+A*x^2+A^2/2;
g2=x^4-A*x^2-A^2/2;
g3=x^4+A*x^2-A^2/2;
g4=x^4-A*x^2+A^2/2;
nf1=nfinit(g1);
nf2=nfinit(g2);
nf3=nfinit(g3);
nf4=nfinit(g4);
factor(nf1.disc);
factor(nf2.disc);
factor(nf3.disc);
factor(nf4.disc);
nfisisom(f,g1)
nfisisom(f,g2)
nfisisom(f,g3)
nfisisom(f,g4)

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = x^4 - 6
? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? %18 = 0
? %19 = 0
? %20 = 0
? %21 = 0
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.018s
user	0m0.015s
sys	0m0.003s


'193.170'
************** PARI *****************
Host 193.170.37.83 (193.170.37.83)
Time: Wed Jul 26 07:27:02 2006

Input: f=x^4-6
polred(f);
nf=nfinit(f);
factor(nf.disc);
A=196;
g1=x^4+A*x^2+A^2/2;
g2=x^4-A*x^2-A^2/2;
g3=x^4+A*x^2-A^2/2;
g4=x^4-A*x^2+A^2/2;
nf1=nfinit(g1);
nf2=nfinit(g2);
nf3=nfinit(g3);
nf4=nfinit(g4);
factor(nf1.disc);
factor(nf2.disc);
factor(nf3.disc);
factor(nf4.disc);
nfisisom(f,g1)
nfisisom(f,g2)
nfisisom(f,g3)
nfisisom(f,g4)

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = x^4 - 6
? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? %18 = 0
? %19 = 0
? %20 = 0
? %21 = 0
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.104s
user	0m0.012s
sys	0m0.005s


'193.170'
************** PARI *****************
Host 193.170.37.83 (193.170.37.83)
Time: Wed Jul 26 07:26:56 2006

Input: f=x^4-6
polred(f);
nf=nfinit(f);
factor(nf.disc);
A=194;
g1=x^4+A*x^2+A^2/2;
g2=x^4-A*x^2-A^2/2;
g3=x^4+A*x^2-A^2/2;
g4=x^4-A*x^2+A^2/2;
nf1=nfinit(g1);
nf2=nfinit(g2);
nf3=nfinit(g3);
nf4=nfinit(g4);
factor(nf1.disc);
factor(nf2.disc);
factor(nf3.disc);
factor(nf4.disc);
nfisisom(f,g1)
nfisisom(f,g2)
nfisisom(f,g3)
nfisisom(f,g4)

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = x^4 - 6
? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? %18 = 0
? %19 = 0
? %20 = 0
? %21 = 0
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.017s
user	0m0.009s
sys	0m0.008s


'193.170'
************** PARI *****************
Host 193.170.37.83 (193.170.37.83)
Time: Wed Jul 26 07:26:47 2006

Input: f=x^4-6
polred(f);
nf=nfinit(f);
factor(nf.disc);
A=192;
g1=x^4+A*x^2+A^2/2;
g2=x^4-A*x^2-A^2/2;
g3=x^4+A*x^2-A^2/2;
g4=x^4-A*x^2+A^2/2;
nf1=nfinit(g1);
nf2=nfinit(g2);
nf3=nfinit(g3);
nf4=nfinit(g4);
factor(nf1.disc);
factor(nf2.disc);
factor(nf3.disc);
factor(nf4.disc);
nfisisom(f,g1)
nfisisom(f,g2)
nfisisom(f,g3)
nfisisom(f,g4)

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = x^4 - 6
? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? %18 = 0
? %19 = 0
? %20 = 0
? %21 = 0
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.020s
user	0m0.013s
sys	0m0.005s


'193.170'
************** PARI *****************
Host 193.170.37.83 (193.170.37.83)
Time: Wed Jul 26 07:26:39 2006

Input: f=x^4-6
polred(f);
nf=nfinit(f);
factor(nf.disc);
A=190;
g1=x^4+A*x^2+A^2/2;
g2=x^4-A*x^2-A^2/2;
g3=x^4+A*x^2-A^2/2;
g4=x^4-A*x^2+A^2/2;
nf1=nfinit(g1);
nf2=nfinit(g2);
nf3=nfinit(g3);
nf4=nfinit(g4);
factor(nf1.disc);
factor(nf2.disc);
factor(nf3.disc);
factor(nf4.disc);
nfisisom(f,g1)
nfisisom(f,g2)
nfisisom(f,g3)
nfisisom(f,g4)

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = x^4 - 6
? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? %18 = 0
? %19 = 0
? %20 = 0
? %21 = 0
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.019s
user	0m0.012s
sys	0m0.007s


'193.170'
************** PARI *****************
Host 193.170.37.83 (193.170.37.83)
Time: Wed Jul 26 07:26:28 2006

Input: f=x^4-6
polred(f);
nf=nfinit(f);
factor(nf.disc);
A=188;
g1=x^4+A*x^2+A^2/2;
g2=x^4-A*x^2-A^2/2;
g3=x^4+A*x^2-A^2/2;
g4=x^4-A*x^2+A^2/2;
nf1=nfinit(g1);
nf2=nfinit(g2);
nf3=nfinit(g3);
nf4=nfinit(g4);
factor(nf1.disc);
factor(nf2.disc);
factor(nf3.disc);
factor(nf4.disc);
nfisisom(f,g1)
nfisisom(f,g2)
nfisisom(f,g3)
nfisisom(f,g4)

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = x^4 - 6
? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? %18 = 0
? %19 = 0
? %20 = 0
? %21 = 0
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.020s
user	0m0.012s
sys	0m0.006s


'193.170'
************** PARI *****************
Host 193.170.37.83 (193.170.37.83)
Time: Wed Jul 26 07:26:03 2006

Input: f=x^4-6
polred(f);
nf=nfinit(f);
factor(nf.disc);
A=186;
g1=x^4+A*x^2+A^2/2
g2=x^4-A*x^2-A^2/2;
g3=x^4+A*x^2-A^2/2;
g4=x^4-A*x^2+A^2/2;
nf1=nfinit(g1);
nf2=nfinit(g2);
nf3=nfinit(g3);
nf4=nfinit(g4);
factor(nf1.disc);
factor(nf2.disc);
factor(nf3.disc);
factor(nf4.disc);
nfisisom(f,g1)
nfisisom(f,g2)
nfisisom(f,g3)
nfisisom(f,g4)

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = x^4 - 6
? ? ? ? ? %6 = x^4 + 186*x^2 + 17298
? ? ? ? ? ? ? ? ? ? ? ? %18 = 0
? %19 = 0
? %20 = 0
? %21 = 0
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.018s
user	0m0.012s
sys	0m0.006s


'193.170'
************** PARI *****************
Host 193.170.37.83 (193.170.37.83)
Time: Wed Jul 26 07:25:52 2006

Input: f=x^4-6
polred(f);
nf=nfinit(f);
factor(nf.disc);
A=184;
g1=x^4+A*x^2+A^2/2
g2=x^4-A*x^2-A^2/2;
g3=x^4+A*x^2-A^2/2;
g4=x^4-A*x^2+A^2/2;
nf1=nfinit(g1);
nf2=nfinit(g2);
nf3=nfinit(g3);
nf4=nfinit(g4);
factor(nf1.disc);
factor(nf2.disc);
factor(nf3.disc);
factor(nf4.disc);
nfisisom(f,g1)
nfisisom(f,g2)
nfisisom(f,g3)
nfisisom(f,g4)

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = x^4 - 6
? ? ? ? ? %6 = x^4 + 184*x^2 + 16928
? ? ? ? ? ? ? ? ? ? ? ? %18 = 0
? %19 = 0
? %20 = 0
? %21 = 0
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.017s
user	0m0.010s
sys	0m0.008s


'193.170'
************** PARI *****************
Host 193.170.37.83 (193.170.37.83)
Time: Wed Jul 26 07:25:44 2006

Input: f=x^4-6
polred(f);
nf=nfinit(f);
factor(nf.disc);
A=182;
g1=x^4+A*x^2+A^2/2
g2=x^4-A*x^2-A^2/2;
g3=x^4+A*x^2-A^2/2;
g4=x^4-A*x^2+A^2/2;
nf1=nfinit(g1);
nf2=nfinit(g2);
nf3=nfinit(g3);
nf4=nfinit(g4);
factor(nf1.disc);
factor(nf2.disc);
factor(nf3.disc);
factor(nf4.disc);
nfisisom(f,g1)
nfisisom(f,g2)
nfisisom(f,g3)
nfisisom(f,g4)

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = x^4 - 6
? ? ? ? ? %6 = x^4 + 182*x^2 + 16562
? ? ? ? ? ? ? ? ? ? ? ? %18 = 0
? %19 = 0
? %20 = 0
? %21 = 0
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.018s
user	0m0.011s
sys	0m0.006s


'193.170'
************** PARI *****************
Host 193.170.37.83 (193.170.37.83)
Time: Wed Jul 26 07:25:37 2006

Input: f=x^4-6
polred(f);
nf=nfinit(f);
factor(nf.disc);
A=180;
g1=x^4+A*x^2+A^2/2
g2=x^4-A*x^2-A^2/2;
g3=x^4+A*x^2-A^2/2;
g4=x^4-A*x^2+A^2/2;
nf1=nfinit(g1);
nf2=nfinit(g2);
nf3=nfinit(g3);
nf4=nfinit(g4);
factor(nf1.disc);
factor(nf2.disc);
factor(nf3.disc);
factor(nf4.disc);
nfisisom(f,g1)
nfisisom(f,g2)
nfisisom(f,g3)
nfisisom(f,g4)

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = x^4 - 6
? ? ? ? ? %6 = x^4 + 180*x^2 + 16200
? ? ? ? ? ? ? ? ? ? ? ? %18 = 0
? %19 = 0
? %20 = 0
? %21 = 0
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.069s
user	0m0.013s
sys	0m0.005s


'193.170'
************** PARI *****************
Host 193.170.37.83 (193.170.37.83)
Time: Wed Jul 26 07:25:27 2006

Input: f=x^4-6
polred(f);
nf=nfinit(f);
factor(nf.disc);
A=178;
g1=x^4+A*x^2+A^2/2
g2=x^4-A*x^2-A^2/2;
g3=x^4+A*x^2-A^2/2;
g4=x^4-A*x^2+A^2/2;
nf1=nfinit(g1);
nf2=nfinit(g2);
nf3=nfinit(g3);
nf4=nfinit(g4);
factor(nf1.disc);
factor(nf2.disc);
factor(nf3.disc);
factor(nf4.disc);
nfisisom(f,g1)
nfisisom(f,g2)
nfisisom(f,g3)
nfisisom(f,g4)

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = x^4 - 6
? ? ? ? ? %6 = x^4 + 178*x^2 + 15842
? ? ? ? ? ? ? ? ? ? ? ? %18 = 0
? %19 = 0
? %20 = 0
? %21 = 0
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.017s
user	0m0.012s
sys	0m0.005s


'193.170'
************** PARI *****************
Host 193.170.37.83 (193.170.37.83)
Time: Wed Jul 26 07:24:43 2006

Input: f=x^4-6
polred(f);
nf=nfinit(f);
factor(nf.disc);
A=176;
g1=x^4+A*x^2+A^2/2
g2=x^4-A*x^2-A^2/2;
g3=x^4+A*x^2-A^2/2;
g4=x^4-A*x^2+A^2/2;
nf1=nfinit(g1);
nf2=nfinit(g2);
nf3=nfinit(g3);
nf4=nfinit(g4);
factor(nf1.disc);
factor(nf2.disc);
factor(nf3.disc);
factor(nf4.disc);
nfisisom(f,g1)
nfisisom(f,g2)
nfisisom(f,g3)
nfisisom(f,g4)

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = x^4 - 6
? ? ? ? ? %6 = x^4 + 176*x^2 + 15488
? ? ? ? ? ? ? ? ? ? ? ? %18 = 0
? %19 = 0
? %20 = 0
? %21 = 0
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.018s
user	0m0.012s
sys	0m0.005s


'193.170'
************** PARI *****************
Host 193.170.37.83 (193.170.37.83)
Time: Wed Jul 26 07:24:35 2006

Input: f=x^4-6
polred(f);
nf=nfinit(f);
factor(nf.disc);
A=174;
g1=x^4+A*x^2+A^2/2
g2=x^4-A*x^2-A^2/2;
g3=x^4+A*x^2-A^2/2;
g4=x^4-A*x^2+A^2/2;
nf1=nfinit(g1);
nf2=nfinit(g2);
nf3=nfinit(g3);
nf4=nfinit(g4);
factor(nf1.disc);
factor(nf2.disc);
factor(nf3.disc);
factor(nf4.disc);
nfisisom(f,g1)
nfisisom(f,g2)
nfisisom(f,g3)
nfisisom(f,g4)

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = x^4 - 6
? ? ? ? ? %6 = x^4 + 174*x^2 + 15138
? ? ? ? ? ? ? ? ? ? ? ? %18 = 0
? %19 = 0
? %20 = 0
? %21 = 0
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.019s
user	0m0.012s
sys	0m0.007s


'193.170'
************** PARI *****************
Host 193.170.37.83 (193.170.37.83)
Time: Wed Jul 26 07:24:27 2006

Input: f=x^4-6
polred(f);
nf=nfinit(f);
factor(nf.disc);
A=172;
g1=x^4+A*x^2+A^2/2
g2=x^4-A*x^2-A^2/2;
g3=x^4+A*x^2-A^2/2;
g4=x^4-A*x^2+A^2/2;
nf1=nfinit(g1);
nf2=nfinit(g2);
nf3=nfinit(g3);
nf4=nfinit(g4);
factor(nf1.disc);
factor(nf2.disc);
factor(nf3.disc);
factor(nf4.disc);
nfisisom(f,g1)
nfisisom(f,g2)
nfisisom(f,g3)
nfisisom(f,g4)

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = x^4 - 6
? ? ? ? ? %6 = x^4 + 172*x^2 + 14792
? ? ? ? ? ? ? ? ? ? ? ? %18 = 0
? %19 = 0
? %20 = 0
? %21 = 0
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.046s
user	0m0.013s
sys	0m0.005s


'193.170'
************** PARI *****************
Host 193.170.37.83 (193.170.37.83)
Time: Wed Jul 26 07:24:19 2006

Input: f=x^4-6
polred(f);
nf=nfinit(f);
factor(nf.disc);
A=170;
g1=x^4+A*x^2+A^2/2
g2=x^4-A*x^2-A^2/2;
g3=x^4+A*x^2-A^2/2;
g4=x^4-A*x^2+A^2/2;
nf1=nfinit(g1);
nf2=nfinit(g2);
nf3=nfinit(g3);
nf4=nfinit(g4);
factor(nf1.disc);
factor(nf2.disc);
factor(nf3.disc);
factor(nf4.disc);
nfisisom(f,g1)
nfisisom(f,g2)
nfisisom(f,g3)
nfisisom(f,g4)

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = x^4 - 6
? ? ? ? ? %6 = x^4 + 170*x^2 + 14450
? ? ? ? ? ? ? ? ? ? ? ? %18 = 0
? %19 = 0
? %20 = 0
? %21 = 0
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.102s
user	0m0.012s
sys	0m0.006s


'193.170'
************** PARI *****************
Host 193.170.37.83 (193.170.37.83)
Time: Wed Jul 26 07:24:11 2006

Input: f=x^4-6
polred(f);
nf=nfinit(f);
factor(nf.disc);
A=168;
g1=x^4+A*x^2+A^2/2
g2=x^4-A*x^2-A^2/2;
g3=x^4+A*x^2-A^2/2;
g4=x^4-A*x^2+A^2/2;
nf1=nfinit(g1);
nf2=nfinit(g2);
nf3=nfinit(g3);
nf4=nfinit(g4);
factor(nf1.disc);
factor(nf2.disc);
factor(nf3.disc);
factor(nf4.disc);
nfisisom(f,g1)
nfisisom(f,g2)
nfisisom(f,g3)
nfisisom(f,g4)

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = x^4 - 6
? ? ? ? ? %6 = x^4 + 168*x^2 + 14112
? ? ? ? ? ? ? ? ? ? ? ? %18 = 0
? %19 = 0
? %20 = 0
? %21 = 0
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.019s
user	0m0.009s
sys	0m0.011s


'193.170'
************** PARI *****************
Host 193.170.37.83 (193.170.37.83)
Time: Wed Jul 26 07:24:02 2006

Input: f=x^4-6
polred(f);
nf=nfinit(f);
factor(nf.disc);
A=166;
g1=x^4+A*x^2+A^2/2
g2=x^4-A*x^2-A^2/2;
g3=x^4+A*x^2-A^2/2;
g4=x^4-A*x^2+A^2/2;
nf1=nfinit(g1);
nf2=nfinit(g2);
nf3=nfinit(g3);
nf4=nfinit(g4);
factor(nf1.disc);
factor(nf2.disc);
factor(nf3.disc);
factor(nf4.disc);
nfisisom(f,g1)
nfisisom(f,g2)
nfisisom(f,g3)
nfisisom(f,g4)

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = x^4 - 6
? ? ? ? ? %6 = x^4 + 166*x^2 + 13778
? ? ? ? ? ? ? ? ? ? ? ? %18 = 0
? %19 = 0
? %20 = 0
? %21 = 0
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.018s
user	0m0.013s
sys	0m0.005s


'193.170'
************** PARI *****************
Host 193.170.37.83 (193.170.37.83)
Time: Wed Jul 26 07:23:53 2006

Input: f=x^4-6
polred(f);
nf=nfinit(f);
factor(nf.disc);
A=164;
g1=x^4+A*x^2+A^2/2
g2=x^4-A*x^2-A^2/2;
g3=x^4+A*x^2-A^2/2;
g4=x^4-A*x^2+A^2/2;
nf1=nfinit(g1);
nf2=nfinit(g2);
nf3=nfinit(g3);
nf4=nfinit(g4);
factor(nf1.disc);
factor(nf2.disc);
factor(nf3.disc);
factor(nf4.disc);
nfisisom(f,g1)
nfisisom(f,g2)
nfisisom(f,g3)
nfisisom(f,g4)

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = x^4 - 6
? ? ? ? ? %6 = x^4 + 164*x^2 + 13448
? ? ? ? ? ? ? ? ? ? ? ? %18 = 0
? %19 = 0
? %20 = 0
? %21 = 0
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.074s
user	0m0.014s
sys	0m0.004s


'193.170'
************** PARI *****************
Host 193.170.37.83 (193.170.37.83)
Time: Wed Jul 26 07:23:45 2006

Input: f=x^4-6
polred(f);
nf=nfinit(f);
factor(nf.disc);
A=162;
g1=x^4+A*x^2+A^2/2
g2=x^4-A*x^2-A^2/2;
g3=x^4+A*x^2-A^2/2;
g4=x^4-A*x^2+A^2/2;
nf1=nfinit(g1);
nf2=nfinit(g2);
nf3=nfinit(g3);
nf4=nfinit(g4);
factor(nf1.disc);
factor(nf2.disc);
factor(nf3.disc);
factor(nf4.disc);
nfisisom(f,g1)
nfisisom(f,g2)
nfisisom(f,g3)
nfisisom(f,g4)

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = x^4 - 6
? ? ? ? ? %6 = x^4 + 162*x^2 + 13122
? ? ? ? ? ? ? ? ? ? ? ? %18 = 0
? %19 = 0
? %20 = 0
? %21 = 0
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.094s
user	0m0.014s
sys	0m0.004s


'193.170'
************** PARI *****************
Host 193.170.37.83 (193.170.37.83)
Time: Wed Jul 26 07:23:35 2006

Input: f=x^4-6
polred(f);
nf=nfinit(f);
factor(nf.disc);
A=160;
g1=x^4+A*x^2+A^2/2
g2=x^4-A*x^2-A^2/2;
g3=x^4+A*x^2-A^2/2;
g4=x^4-A*x^2+A^2/2;
nf1=nfinit(g1);
nf2=nfinit(g2);
nf3=nfinit(g3);
nf4=nfinit(g4);
factor(nf1.disc);
factor(nf2.disc);
factor(nf3.disc);
factor(nf4.disc);
nfisisom(f,g1)
nfisisom(f,g2)
nfisisom(f,g3)
nfisisom(f,g4)

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = x^4 - 6
? ? ? ? ? %6 = x^4 + 160*x^2 + 12800
? ? ? ? ? ? ? ? ? ? ? ? %18 = 0
? %19 = 0
? %20 = 0
? %21 = 0
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.017s
user	0m0.013s
sys	0m0.004s


'193.170'
************** PARI *****************
Host 193.170.37.83 (193.170.37.83)
Time: Wed Jul 26 07:23:28 2006

Input: f=x^4-6
polred(f);
nf=nfinit(f);
factor(nf.disc);
A=158;
g1=x^4+A*x^2+A^2/2
g2=x^4-A*x^2-A^2/2;
g3=x^4+A*x^2-A^2/2;
g4=x^4-A*x^2+A^2/2;
nf1=nfinit(g1);
nf2=nfinit(g2);
nf3=nfinit(g3);
nf4=nfinit(g4);
factor(nf1.disc);
factor(nf2.disc);
factor(nf3.disc);
factor(nf4.disc);
nfisisom(f,g1)
nfisisom(f,g2)
nfisisom(f,g3)
nfisisom(f,g4)

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = x^4 - 6
? ? ? ? ? %6 = x^4 + 158*x^2 + 12482
? ? ? ? ? ? ? ? ? ? ? ? %18 = 0
? %19 = 0
? %20 = 0
? %21 = 0
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.018s
user	0m0.012s
sys	0m0.006s


'193.170'
************** PARI *****************
Host 193.170.37.83 (193.170.37.83)
Time: Wed Jul 26 07:23:19 2006

Input: f=x^4-6
polred(f);
nf=nfinit(f);
factor(nf.disc);
A=156;
g1=x^4+A*x^2+A^2/2
g2=x^4-A*x^2-A^2/2;
g3=x^4+A*x^2-A^2/2;
g4=x^4-A*x^2+A^2/2;
nf1=nfinit(g1);
nf2=nfinit(g2);
nf3=nfinit(g3);
nf4=nfinit(g4);
factor(nf1.disc);
factor(nf2.disc);
factor(nf3.disc);
factor(nf4.disc);
nfisisom(f,g1)
nfisisom(f,g2)
nfisisom(f,g3)
nfisisom(f,g4)

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = x^4 - 6
? ? ? ? ? %6 = x^4 + 156*x^2 + 12168
? ? ? ? ? ? ? ? ? ? ? ? %18 = 0
? %19 = 0
? %20 = 0
? %21 = 0
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.050s
user	0m0.013s
sys	0m0.005s


'193.170'
************** PARI *****************
Host 193.170.37.83 (193.170.37.83)
Time: Wed Jul 26 07:23:11 2006

Input: f=x^4-6
polred(f);
nf=nfinit(f);
factor(nf.disc);
A=154;
g1=x^4+A*x^2+A^2/2
g2=x^4-A*x^2-A^2/2;
g3=x^4+A*x^2-A^2/2;
g4=x^4-A*x^2+A^2/2;
nf1=nfinit(g1);
nf2=nfinit(g2);
nf3=nfinit(g3);
nf4=nfinit(g4);
factor(nf1.disc);
factor(nf2.disc);
factor(nf3.disc);
factor(nf4.disc);
nfisisom(f,g1)
nfisisom(f,g2)
nfisisom(f,g3)
nfisisom(f,g4)

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = x^4 - 6
? ? ? ? ? %6 = x^4 + 154*x^2 + 11858
? ? ? ? ? ? ? ? ? ? ? ? %18 = 0
? %19 = 0
? %20 = 0
? %21 = 0
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.393s
user	0m0.013s
sys	0m0.006s


'193.170'
************** PARI *****************
Host 193.170.37.83 (193.170.37.83)
Time: Wed Jul 26 07:22:40 2006

Input: f=x^4-6
polred(f);
nf=nfinit(f);
factor(nf.disc);
A=152;
g1=x^4+A*x^2+A^2/2
g2=x^4-A*x^2-A^2/2;
g3=x^4+A*x^2-A^2/2;
g4=x^4-A*x^2+A^2/2;
nf1=nfinit(g1);
nf2=nfinit(g2);
nf3=nfinit(g3);
nf4=nfinit(g4);
factor(nf1.disc);
factor(nf2.disc);
factor(nf3.disc);
factor(nf4.disc);
nfisisom(f,g1)
nfisisom(f,g2)
nfisisom(f,g3)
nfisisom(f,g4)

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = x^4 - 6
? ? ? ? ? %6 = x^4 + 152*x^2 + 11552
? ? ? ? ? ? ? ? ? ? ? ? %18 = 0
? %19 = 0
? %20 = 0
? %21 = 0
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.018s
user	0m0.012s
sys	0m0.005s


'193.170'
************** PARI *****************
Host 193.170.37.83 (193.170.37.83)
Time: Wed Jul 26 07:22:32 2006

Input: f=x^4-6
polred(f);
nf=nfinit(f);
factor(nf.disc);
A=150;
g1=x^4+A*x^2+A^2/2
g2=x^4-A*x^2-A^2/2;
g3=x^4+A*x^2-A^2/2;
g4=x^4-A*x^2+A^2/2;
nf1=nfinit(g1);
nf2=nfinit(g2);
nf3=nfinit(g3);
nf4=nfinit(g4);
factor(nf1.disc);
factor(nf2.disc);
factor(nf3.disc);
factor(nf4.disc);
nfisisom(f,g1)
nfisisom(f,g2)
nfisisom(f,g3)
nfisisom(f,g4)

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = x^4 - 6
? ? ? ? ? %6 = x^4 + 150*x^2 + 11250
? ? ? ? ? ? ? ? ? ? ? ? %18 = 0
? %19 = 0
? %20 = 0
? %21 = 0
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.052s
user	0m0.012s
sys	0m0.007s


'193.170'
************** PARI *****************
Host 193.170.37.83 (193.170.37.83)
Time: Wed Jul 26 07:22:21 2006

Input: f=x^4-6
polred(f);
nf=nfinit(f);
factor(nf.disc);
A=148;
g1=x^4+A*x^2+A^2/2
g2=x^4-A*x^2-A^2/2;
g3=x^4+A*x^2-A^2/2;
g4=x^4-A*x^2+A^2/2;
nf1=nfinit(g1);
nf2=nfinit(g2);
nf3=nfinit(g3);
nf4=nfinit(g4);
factor(nf1.disc);
factor(nf2.disc);
factor(nf3.disc);
factor(nf4.disc);
nfisisom(f,g1)
nfisisom(f,g2)
nfisisom(f,g3)
nfisisom(f,g4)

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = x^4 - 6
? ? ? ? ? %6 = x^4 + 148*x^2 + 10952
? ? ? ? ? ? ? ? ? ? ? ? %18 = 0
? %19 = 0
? %20 = 0
? %21 = 0
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.017s
user	0m0.009s
sys	0m0.008s


'193.170'
************** PARI *****************
Host 193.170.37.83 (193.170.37.83)
Time: Wed Jul 26 07:22:13 2006

Input: f=x^4-6
polred(f);
nf=nfinit(f);
factor(nf.disc);
A=146;
g1=x^4+A*x^2+A^2/2
g2=x^4-A*x^2-A^2/2;
g3=x^4+A*x^2-A^2/2;
g4=x^4-A*x^2+A^2/2;
nf1=nfinit(g1);
nf2=nfinit(g2);
nf3=nfinit(g3);
nf4=nfinit(g4);
factor(nf1.disc);
factor(nf2.disc);
factor(nf3.disc);
factor(nf4.disc);
nfisisom(f,g1)
nfisisom(f,g2)
nfisisom(f,g3)
nfisisom(f,g4)

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = x^4 - 6
? ? ? ? ? %6 = x^4 + 146*x^2 + 10658
? ? ? ? ? ? ? ? ? ? ? ? %18 = 0
? %19 = 0
? %20 = 0
? %21 = 0
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.018s
user	0m0.010s
sys	0m0.007s


'193.170'
************** PARI *****************
Host 193.170.37.83 (193.170.37.83)
Time: Wed Jul 26 07:22:02 2006

Input: f=x^4-6
polred(f);
nf=nfinit(f);
factor(nf.disc);
A=144;
g1=x^4+A*x^2+A^2/2
g2=x^4-A*x^2-A^2/2;
g3=x^4+A*x^2-A^2/2;
g4=x^4-A*x^2+A^2/2;
nf1=nfinit(g1);
nf2=nfinit(g2);
nf3=nfinit(g3);
nf4=nfinit(g4);
factor(nf1.disc);
factor(nf2.disc);
factor(nf3.disc);
factor(nf4.disc);
nfisisom(f,g1)
nfisisom(f,g2)
nfisisom(f,g3)
nfisisom(f,g4)

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = x^4 - 6
? ? ? ? ? %6 = x^4 + 144*x^2 + 10368
? ? ? ? ? ? ? ? ? ? ? ? %18 = 0
? %19 = 0
? %20 = 0
? %21 = 0
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.030s
user	0m0.011s
sys	0m0.006s


'193.170'
************** PARI *****************
Host 193.170.37.83 (193.170.37.83)
Time: Wed Jul 26 07:21:55 2006

Input: f=x^4-6
polred(f);
nf=nfinit(f);
factor(nf.disc);
A=142;
g1=x^4+A*x^2+A^2/2
g2=x^4-A*x^2-A^2/2;
g3=x^4+A*x^2-A^2/2;
g4=x^4-A*x^2+A^2/2;
nf1=nfinit(g1);
nf2=nfinit(g2);
nf3=nfinit(g3);
nf4=nfinit(g4);
factor(nf1.disc);
factor(nf2.disc);
factor(nf3.disc);
factor(nf4.disc);
nfisisom(f,g1)
nfisisom(f,g2)
nfisisom(f,g3)
nfisisom(f,g4)

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = x^4 - 6
? ? ? ? ? %6 = x^4 + 142*x^2 + 10082
? ? ? ? ? ? ? ? ? ? ? ? %18 = 0
? %19 = 0
? %20 = 0
? %21 = 0
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.017s
user	0m0.014s
sys	0m0.003s


'193.170'
************** PARI *****************
Host 193.170.37.83 (193.170.37.83)
Time: Wed Jul 26 07:21:48 2006

Input: f=x^4-6
polred(f);
nf=nfinit(f);
factor(nf.disc);
A=140;
g1=x^4+A*x^2+A^2/2
g2=x^4-A*x^2-A^2/2;
g3=x^4+A*x^2-A^2/2;
g4=x^4-A*x^2+A^2/2;
nf1=nfinit(g1);
nf2=nfinit(g2);
nf3=nfinit(g3);
nf4=nfinit(g4);
factor(nf1.disc);
factor(nf2.disc);
factor(nf3.disc);
factor(nf4.disc);
nfisisom(f,g1)
nfisisom(f,g2)
nfisisom(f,g3)
nfisisom(f,g4)

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = x^4 - 6
? ? ? ? ? %6 = x^4 + 140*x^2 + 9800
? ? ? ? ? ? ? ? ? ? ? ? %18 = 0
? %19 = 0
? %20 = 0
? %21 = 0
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.018s
user	0m0.012s
sys	0m0.006s


'193.170'
************** PARI *****************
Host 193.170.37.83 (193.170.37.83)
Time: Wed Jul 26 07:21:38 2006

Input: f=x^4-6
polred(f);
nf=nfinit(f);
factor(nf.disc);
A=138;
g1=x^4+A*x^2+A^2/2
g2=x^4-A*x^2-A^2/2;
g3=x^4+A*x^2-A^2/2;
g4=x^4-A*x^2+A^2/2;
nf1=nfinit(g1);
nf2=nfinit(g2);
nf3=nfinit(g3);
nf4=nfinit(g4);
factor(nf1.disc);
factor(nf2.disc);
factor(nf3.disc);
factor(nf4.disc);
nfisisom(f,g1)
nfisisom(f,g2)
nfisisom(f,g3)
nfisisom(f,g4)

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = x^4 - 6
? ? ? ? ? %6 = x^4 + 138*x^2 + 9522
? ? ? ? ? ? ? ? ? ? ? ? %18 = 0
? %19 = 0
? %20 = 0
? %21 = 0
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.018s
user	0m0.010s
sys	0m0.008s


'193.170'
************** PARI *****************
Host 193.170.37.83 (193.170.37.83)
Time: Wed Jul 26 07:21:29 2006

Input: f=x^4-6
polred(f);
nf=nfinit(f);
factor(nf.disc);
A=136;
g1=x^4+A*x^2+A^2/2
g2=x^4-A*x^2-A^2/2;
g3=x^4+A*x^2-A^2/2;
g4=x^4-A*x^2+A^2/2;
nf1=nfinit(g1);
nf2=nfinit(g2);
nf3=nfinit(g3);
nf4=nfinit(g4);
factor(nf1.disc);
factor(nf2.disc);
factor(nf3.disc);
factor(nf4.disc);
nfisisom(f,g1)
nfisisom(f,g2)
nfisisom(f,g3)
nfisisom(f,g4)

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = x^4 - 6
? ? ? ? ? %6 = x^4 + 136*x^2 + 9248
? ? ? ? ? ? ? ? ? ? ? ? %18 = 0
? %19 = 0
? %20 = 0
? %21 = 0
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.017s
user	0m0.013s
sys	0m0.004s


'193.170'
************** PARI *****************
Host 193.170.37.83 (193.170.37.83)
Time: Wed Jul 26 07:21:22 2006

Input: f=x^4-6
polred(f);
nf=nfinit(f);
factor(nf.disc);
A=134;
g1=x^4+A*x^2+A^2/2
g2=x^4-A*x^2-A^2/2;
g3=x^4+A*x^2-A^2/2;
g4=x^4-A*x^2+A^2/2;
nf1=nfinit(g1);
nf2=nfinit(g2);
nf3=nfinit(g3);
nf4=nfinit(g4);
factor(nf1.disc);
factor(nf2.disc);
factor(nf3.disc);
factor(nf4.disc);
nfisisom(f,g1)
nfisisom(f,g2)
nfisisom(f,g3)
nfisisom(f,g4)

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = x^4 - 6
? ? ? ? ? %6 = x^4 + 134*x^2 + 8978
? ? ? ? ? ? ? ? ? ? ? ? %18 = 0
? %19 = 0
? %20 = 0
? %21 = 0
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.094s
user	0m0.012s
sys	0m0.006s


'193.170'
************** PARI *****************
Host 193.170.37.83 (193.170.37.83)
Time: Wed Jul 26 07:20:57 2006

Input: f=x^4-6
polred(f);
nf=nfinit(f);
factor(nf.disc);
A=132;
g1=x^4+A*x^2+A^2/2
g2=x^4-A*x^2-A^2/2;
g3=x^4+A*x^2-A^2/2;
g4=x^4-A*x^2+A^2/2;
nf1=nfinit(g1);
nf2=nfinit(g2);
nf3=nfinit(g3);
nf4=nfinit(g4);
factor(nf1.disc);
factor(nf2.disc);
factor(nf3.disc);
factor(nf4.disc);
nfisisom(f,g1)
nfisisom(f,g2)
nfisisom(f,g3)
nfisisom(f,g4)

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = x^4 - 6
? ? ? ? ? %6 = x^4 + 132*x^2 + 8712
? ? ? ? ? ? ? ? ? ? ? ? %18 = 0
? %19 = 0
? %20 = 0
? %21 = 0
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.100s
user	0m0.014s
sys	0m0.005s


'193.170'
************** PARI *****************
Host 193.170.37.83 (193.170.37.83)
Time: Wed Jul 26 07:20:45 2006

Input: f=x^4-6
polred(f);
nf=nfinit(f);
factor(nf.disc);
A=130;
g1=x^4+A*x^2+A^2/2
g2=x^4-A*x^2-A^2/2;
g3=x^4+A*x^2-A^2/2;
g4=x^4-A*x^2+A^2/2;
nf1=nfinit(g1);
nf2=nfinit(g2);
nf3=nfinit(g3);
nf4=nfinit(g4);
factor(nf1.disc);
factor(nf2.disc);
factor(nf3.disc);
factor(nf4.disc);
nfisisom(f,g1)
nfisisom(f,g2)
nfisisom(f,g3)
nfisisom(f,g4)

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = x^4 - 6
? ? ? ? ? %6 = x^4 + 130*x^2 + 8450
? ? ? ? ? ? ? ? ? ? ? ? %18 = 0
? %19 = 0
? %20 = 0
? %21 = 0
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.018s
user	0m0.014s
sys	0m0.004s


'193.170'
************** PARI *****************
Host 193.170.37.83 (193.170.37.83)
Time: Wed Jul 26 07:20:38 2006

Input: f=x^4-6
polred(f);
nf=nfinit(f);
factor(nf.disc);
A=128;
g1=x^4+A*x^2+A^2/2
g2=x^4-A*x^2-A^2/2;
g3=x^4+A*x^2-A^2/2;
g4=x^4-A*x^2+A^2/2;
nf1=nfinit(g1);
nf2=nfinit(g2);
nf3=nfinit(g3);
nf4=nfinit(g4);
factor(nf1.disc);
factor(nf2.disc);
factor(nf3.disc);
factor(nf4.disc);
nfisisom(f,g1)
nfisisom(f,g2)
nfisisom(f,g3)
nfisisom(f,g4)

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = x^4 - 6
? ? ? ? ? %6 = x^4 + 128*x^2 + 8192
? ? ? ? ? ? ? ? ? ? ? ? %18 = 0
? %19 = 0
? %20 = 0
? %21 = 0
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.017s
user	0m0.011s
sys	0m0.005s


'193.170'
************** PARI *****************
Host 193.170.37.83 (193.170.37.83)
Time: Wed Jul 26 07:20:26 2006

Input: f=x^4-6
polred(f);
nf=nfinit(f);
factor(nf.disc);
A=124;
g1=x^4+A*x^2+A^2/2
g2=x^4-A*x^2-A^2/2;
g3=x^4+A*x^2-A^2/2;
g4=x^4-A*x^2+A^2/2;
nf1=nfinit(g1);
nf2=nfinit(g2);
nf3=nfinit(g3);
nf4=nfinit(g4);
factor(nf1.disc);
factor(nf2.disc);
factor(nf3.disc);
factor(nf4.disc);
nfisisom(f,g1)
nfisisom(f,g2)
nfisisom(f,g3)
nfisisom(f,g4)

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = x^4 - 6
? ? ? ? ? %6 = x^4 + 124*x^2 + 7688
? ? ? ? ? ? ? ? ? ? ? ? %18 = 0
? %19 = 0
? %20 = 0
? %21 = 0
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.082s
user	0m0.012s
sys	0m0.008s


'193.170'
************** PARI *****************
Host 193.170.37.83 (193.170.37.83)
Time: Wed Jul 26 07:20:19 2006

Input: f=x^4-6
polred(f);
nf=nfinit(f);
factor(nf.disc);
A=122;
g1=x^4+A*x^2+A^2/2
g2=x^4-A*x^2-A^2/2;
g3=x^4+A*x^2-A^2/2;
g4=x^4-A*x^2+A^2/2;
nf1=nfinit(g1);
nf2=nfinit(g2);
nf3=nfinit(g3);
nf4=nfinit(g4);
factor(nf1.disc);
factor(nf2.disc);
factor(nf3.disc);
factor(nf4.disc);
nfisisom(f,g1)
nfisisom(f,g2)
nfisisom(f,g3)
nfisisom(f,g4)

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = x^4 - 6
? ? ? ? ? %6 = x^4 + 122*x^2 + 7442
? ? ? ? ? ? ? ? ? ? ? ? %18 = 0
? %19 = 0
? %20 = 0
? %21 = 0
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.017s
user	0m0.009s
sys	0m0.008s


'193.170'
************** PARI *****************
Host 193.170.37.83 (193.170.37.83)
Time: Wed Jul 26 07:20:11 2006

Input: f=x^4-6
polred(f);
nf=nfinit(f);
factor(nf.disc);
A=120;
g1=x^4+A*x^2+A^2/2
g2=x^4-A*x^2-A^2/2;
g3=x^4+A*x^2-A^2/2;
g4=x^4-A*x^2+A^2/2;
nf1=nfinit(g1);
nf2=nfinit(g2);
nf3=nfinit(g3);
nf4=nfinit(g4);
factor(nf1.disc);
factor(nf2.disc);
factor(nf3.disc);
factor(nf4.disc);
nfisisom(f,g1)
nfisisom(f,g2)
nfisisom(f,g3)
nfisisom(f,g4)

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = x^4 - 6
? ? ? ? ? %6 = x^4 + 120*x^2 + 7200
? ? ? ? ? ? ? ? ? ? ? ? %18 = 0
? %19 = 0
? %20 = 0
? %21 = 0
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.098s
user	0m0.014s
sys	0m0.005s


'193.170'
************** PARI *****************
Host 193.170.37.83 (193.170.37.83)
Time: Wed Jul 26 07:20:03 2006

Input: f=x^4-6
polred(f);
nf=nfinit(f);
factor(nf.disc);
A=118;
g1=x^4+A*x^2+A^2/2
g2=x^4-A*x^2-A^2/2;
g3=x^4+A*x^2-A^2/2;
g4=x^4-A*x^2+A^2/2;
nf1=nfinit(g1);
nf2=nfinit(g2);
nf3=nfinit(g3);
nf4=nfinit(g4);
factor(nf1.disc);
factor(nf2.disc);
factor(nf3.disc);
factor(nf4.disc);
nfisisom(f,g1)
nfisisom(f,g2)
nfisisom(f,g3)
nfisisom(f,g4)

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = x^4 - 6
? ? ? ? ? %6 = x^4 + 118*x^2 + 6962
? ? ? ? ? ? ? ? ? ? ? ? %18 = 0
? %19 = 0
? %20 = 0
? %21 = 0
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.017s
user	0m0.013s
sys	0m0.005s


'193.170'
************** PARI *****************
Host 193.170.37.83 (193.170.37.83)
Time: Wed Jul 26 07:19:55 2006

Input: f=x^4-6
polred(f);
nf=nfinit(f);
factor(nf.disc);
A=116;
g1=x^4+A*x^2+A^2/2
g2=x^4-A*x^2-A^2/2;
g3=x^4+A*x^2-A^2/2;
g4=x^4-A*x^2+A^2/2;
nf1=nfinit(g1);
nf2=nfinit(g2);
nf3=nfinit(g3);
nf4=nfinit(g4);
factor(nf1.disc);
factor(nf2.disc);
factor(nf3.disc);
factor(nf4.disc);
nfisisom(f,g1)
nfisisom(f,g2)
nfisisom(f,g3)
nfisisom(f,g4)

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = x^4 - 6
? ? ? ? ? %6 = x^4 + 116*x^2 + 6728
? ? ? ? ? ? ? ? ? ? ? ? %18 = 0
? %19 = 0
? %20 = 0
? %21 = 0
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.017s
user	0m0.015s
sys	0m0.004s


'193.170'
************** PARI *****************
Host 193.170.37.83 (193.170.37.83)
Time: Wed Jul 26 07:19:48 2006

Input: f=x^4-6
polred(f);
nf=nfinit(f);
factor(nf.disc);
A=115;
g1=x^4+A*x^2+A^2/2
g2=x^4-A*x^2-A^2/2;
g3=x^4+A*x^2-A^2/2;
g4=x^4-A*x^2+A^2/2;
nf1=nfinit(g1);
nf2=nfinit(g2);
nf3=nfinit(g3);
nf4=nfinit(g4);
factor(nf1.disc);
factor(nf2.disc);
factor(nf3.disc);
factor(nf4.disc);
nfisisom(f,g1)
nfisisom(f,g2)
nfisisom(f,g3)
nfisisom(f,g4)

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = x^4 - 6
? ? ? ? ? %6 = x^4 + 115*x^2 + 13225/2
? ? ? ? ? ? ? ? ? ? ? ? %10 = 0
? %11 = 0
? %12 = 0
? %13 = 0
? 
Goodbye!

Errors/timing (if any):

  *** nfinit: polynomial not in Z[X] in nfinit.
  *** nfinit: polynomial not in Z[X] in nfinit.
  *** nfinit: polynomial not in Z[X] in nfinit.
  *** nfinit: polynomial not in Z[X] in nfinit.
  ***   incorrect type in disc: factor(nf1.disc);
                                           ^------
  ***   incorrect type in disc: factor(nf2.disc);
                                           ^------
  ***   incorrect type in disc: factor(nf3.disc);
                                           ^------
  ***   incorrect type in disc: factor(nf4.disc);
                                           ^------

Timing:
real	0m0.015s
user	0m0.008s
sys	0m0.006s


'193.170'
************** PARI *****************
Host 193.170.37.83 (193.170.37.83)
Time: Wed Jul 26 07:19:40 2006

Input: f=x^4-6
polred(f);
nf=nfinit(f);
factor(nf.disc);
A=114;
g1=x^4+A*x^2+A^2/2
g2=x^4-A*x^2-A^2/2;
g3=x^4+A*x^2-A^2/2;
g4=x^4-A*x^2+A^2/2;
nf1=nfinit(g1);
nf2=nfinit(g2);
nf3=nfinit(g3);
nf4=nfinit(g4);
factor(nf1.disc);
factor(nf2.disc);
factor(nf3.disc);
factor(nf4.disc);
nfisisom(f,g1)
nfisisom(f,g2)
nfisisom(f,g3)
nfisisom(f,g4)

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = x^4 - 6
? ? ? ? ? %6 = x^4 + 114*x^2 + 6498
? ? ? ? ? ? ? ? ? ? ? ? %18 = 0
? %19 = 0
? %20 = 0
? %21 = 0
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.019s
user	0m0.011s
sys	0m0.007s


'193.170'
************** PARI *****************
Host 193.170.37.83 (193.170.37.83)
Time: Wed Jul 26 07:19:32 2006

Input: f=x^4-6
polred(f);
nf=nfinit(f);
factor(nf.disc);
A=112;
g1=x^4+A*x^2+A^2/2
g2=x^4-A*x^2-A^2/2;
g3=x^4+A*x^2-A^2/2;
g4=x^4-A*x^2+A^2/2;
nf1=nfinit(g1);
nf2=nfinit(g2);
nf3=nfinit(g3);
nf4=nfinit(g4);
factor(nf1.disc);
factor(nf2.disc);
factor(nf3.disc);
factor(nf4.disc);
nfisisom(f,g1)
nfisisom(f,g2)
nfisisom(f,g3)
nfisisom(f,g4)

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = x^4 - 6
? ? ? ? ? %6 = x^4 + 112*x^2 + 6272
? ? ? ? ? ? ? ? ? ? ? ? %18 = 0
? %19 = 0
? %20 = 0
? %21 = 0
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.018s
user	0m0.012s
sys	0m0.006s


'193.170'
************** PARI *****************
Host 193.170.37.83 (193.170.37.83)
Time: Wed Jul 26 07:19:24 2006

Input: f=x^4-6
polred(f);
nf=nfinit(f);
factor(nf.disc);
A=110;
g1=x^4+A*x^2+A^2/2
g2=x^4-A*x^2-A^2/2;
g3=x^4+A*x^2-A^2/2;
g4=x^4-A*x^2+A^2/2;
nf1=nfinit(g1);
nf2=nfinit(g2);
nf3=nfinit(g3);
nf4=nfinit(g4);
factor(nf1.disc);
factor(nf2.disc);
factor(nf3.disc);
factor(nf4.disc);
nfisisom(f,g1)
nfisisom(f,g2)
nfisisom(f,g3)
nfisisom(f,g4)

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = x^4 - 6
? ? ? ? ? %6 = x^4 + 110*x^2 + 6050
? ? ? ? ? ? ? ? ? ? ? ? %18 = 0
? %19 = 0
? %20 = 0
? %21 = 0
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.018s
user	0m0.011s
sys	0m0.007s


'193.170'
************** PARI *****************
Host 193.170.37.83 (193.170.37.83)
Time: Wed Jul 26 07:19:15 2006

Input: f=x^4-6
polred(f);
nf=nfinit(f);
factor(nf.disc);
A=108;
g1=x^4+A*x^2+A^2/2
g2=x^4-A*x^2-A^2/2;
g3=x^4+A*x^2-A^2/2;
g4=x^4-A*x^2+A^2/2;
nf1=nfinit(g1);
nf2=nfinit(g2);
nf3=nfinit(g3);
nf4=nfinit(g4);
factor(nf1.disc);
factor(nf2.disc);
factor(nf3.disc);
factor(nf4.disc);
nfisisom(f,g1)
nfisisom(f,g2)
nfisisom(f,g3)
nfisisom(f,g4)

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = x^4 - 6
? ? ? ? ? %6 = x^4 + 108*x^2 + 5832
? ? ? ? ? ? ? ? ? ? ? ? %18 = 0
? %19 = 0
? %20 = 0
? %21 = 0
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.062s
user	0m0.011s
sys	0m0.007s


'193.170'
************** PARI *****************
Host 193.170.37.83 (193.170.37.83)
Time: Wed Jul 26 07:19:07 2006

Input: f=x^4-6
polred(f);
nf=nfinit(f);
factor(nf.disc);
A=106;
g1=x^4+A*x^2+A^2/2
g2=x^4-A*x^2-A^2/2;
g3=x^4+A*x^2-A^2/2;
g4=x^4-A*x^2+A^2/2;
nf1=nfinit(g1);
nf2=nfinit(g2);
nf3=nfinit(g3);
nf4=nfinit(g4);
factor(nf1.disc);
factor(nf2.disc);
factor(nf3.disc);
factor(nf4.disc);
nfisisom(f,g1)
nfisisom(f,g2)
nfisisom(f,g3)
nfisisom(f,g4)

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = x^4 - 6
? ? ? ? ? %6 = x^4 + 106*x^2 + 5618
? ? ? ? ? ? ? ? ? ? ? ? %18 = 0
? %19 = 0
? %20 = 0
? %21 = 0
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.018s
user	0m0.013s
sys	0m0.006s


'193.170'
************** PARI *****************
Host 193.170.37.83 (193.170.37.83)
Time: Wed Jul 26 07:18:59 2006

Input: f=x^4-6
polred(f);
nf=nfinit(f);
factor(nf.disc);
A=104;
g1=x^4+A*x^2+A^2/2
g2=x^4-A*x^2-A^2/2;
g3=x^4+A*x^2-A^2/2;
g4=x^4-A*x^2+A^2/2;
nf1=nfinit(g1);
nf2=nfinit(g2);
nf3=nfinit(g3);
nf4=nfinit(g4);
factor(nf1.disc);
factor(nf2.disc);
factor(nf3.disc);
factor(nf4.disc);
nfisisom(f,g1)
nfisisom(f,g2)
nfisisom(f,g3)
nfisisom(f,g4)

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = x^4 - 6
? ? ? ? ? %6 = x^4 + 104*x^2 + 5408
? ? ? ? ? ? ? ? ? ? ? ? %18 = 0
? %19 = 0
? %20 = 0
? %21 = 0
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.018s
user	0m0.011s
sys	0m0.006s


'193.170'
************** PARI *****************
Host 193.170.37.83 (193.170.37.83)
Time: Wed Jul 26 07:18:47 2006

Input: f=x^4-6
polred(f);
nf=nfinit(f);
factor(nf.disc);
A=102;
g1=x^4+A*x^2+A^2/2
g2=x^4-A*x^2-A^2/2;
g3=x^4+A*x^2-A^2/2;
g4=x^4-A*x^2+A^2/2;
nf1=nfinit(g1);
nf2=nfinit(g2);
nf3=nfinit(g3);
nf4=nfinit(g4);
factor(nf1.disc);
factor(nf2.disc);
factor(nf3.disc);
factor(nf4.disc);
nfisisom(f,g1)
nfisisom(f,g2)
nfisisom(f,g3)
nfisisom(f,g4)

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = x^4 - 6
? ? ? ? ? %6 = x^4 + 102*x^2 + 5202
? ? ? ? ? ? ? ? ? ? ? ? %18 = 0
? %19 = 0
? %20 = 0
? %21 = 0
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.018s
user	0m0.013s
sys	0m0.005s


'193.170'
************** PARI *****************
Host 193.170.37.83 (193.170.37.83)
Time: Wed Jul 26 07:18:38 2006

Input: f=x^4-6
polred(f);
nf=nfinit(f);
factor(nf.disc);
A=102;
g1=x^4+A*x^2+A^2/2
g2=x^4-A*x^2-A^2/2;
g3=x^4+A*x^2-A^2/2;
g4=x^4-A*x^2+A^2/2;
nf1=nfinit(g1);
nf2=nfinit(g2);
nf3=nfinit(g3);
nf4=nfinit(g4);
factor(nf1.disc);
factor(nf2.disc);
factor(nf3.disc);
factor(nf4.disc)
nfisisom(f,g1)
nfisisom(f,g2)
nfisisom(f,g3)
nfisisom(f,g4)

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = x^4 - 6
? ? ? ? ? %6 = x^4 + 102*x^2 + 5202
? ? ? ? ? ? ? ? ? ? ? %17 = 
[2 9]

[3 2]

[17 2]

? %18 = 0
? %19 = 0
? %20 = 0
? %21 = 0
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.018s
user	0m0.012s
sys	0m0.006s


'193.170'
************** PARI *****************
Host 193.170.37.83 (193.170.37.83)
Time: Wed Jul 26 07:18:27 2006

Input: f=x^4-6
polred(f);
nf=nfinit(f);
factor(nf.disc)
A=102;
g1=x^4+A*x^2+A^2/2
g2=x^4-A*x^2-A^2/2;
g3=x^4+A*x^2-A^2/2;
g4=x^4-A*x^2+A^2/2;
nf1=nfinit(g1);
nf2=nfinit(g2);
nf3=nfinit(g3);
nf4=nfinit(g4);
factor(nf1.disc);
factor(nf2.disc);
factor(nf3.disc);
factor(nf4.disc)
nfisisom(f,g1)
nfisisom(f,g2)
nfisisom(f,g3)
nfisisom(f,g4)

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = x^4 - 6
? ? ? %4 = 
[-1 1]

[2 11]

[3 3]

? ? %6 = x^4 + 102*x^2 + 5202
? ? ? ? ? ? ? ? ? ? ? %17 = 
[2 9]

[3 2]

[17 2]

? %18 = 0
? %19 = 0
? %20 = 0
? %21 = 0
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.018s
user	0m0.015s
sys	0m0.003s


'193.170'
************** PARI *****************
Host 193.170.37.83 (193.170.37.83)
Time: Wed Jul 26 07:18:09 2006

Input: f=x^4-6
polred(f);
nf=nfinit(f);
factor(nf.disc)
A=100;
g1=x^4+A*x^2+A^2/2
g2=x^4-A*x^2-A^2/2;
g3=x^4+A*x^2-A^2/2;
g4=x^4-A*x^2+A^2/2;
nf1=nfinit(g1);
nf2=nfinit(g2);
nf3=nfinit(g3);
nf4=nfinit(g4);
factor(nf1.disc);
factor(nf2.disc);
factor(nf3.disc);
factor(nf4.disc)
nfisisom(f,g1)
nfisisom(f,g2)
nfisisom(f,g3)
nfisisom(f,g4)

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = x^4 - 6
? ? ? %4 = 
[-1 1]

[2 11]

[3 3]

? ? %6 = x^4 + 100*x^2 + 5000
? ? ? ? ? ? ? ? ? ? ? %17 = 
[2 9]

? %18 = 0
? %19 = 0
? %20 = 0
? %21 = 0
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.019s
user	0m0.011s
sys	0m0.006s


'193.170'
************** PARI *****************
Host 193.170.37.83 (193.170.37.83)
Time: Wed Jul 26 07:17:31 2006

Input: f=x^4-6
polred(f);
nf=nfinit(f);
factor(nf.disc);
A=100;
g1=x^4+A*x^2+A^2/2
g2=x^4-A*x^2-A^2/2;
g3=x^4+A*x^2-A^2/2;
g4=x^4-A*x^2+A^2/2;
nf1=nfinit(g1);
nf2=nfinit(g2);
nf3=nfinit(g3);
nf4=nfinit(g4);
factor(nf1.disc);
factor(nf2.disc);
factor(nf3.disc);
factor(nf4.disc)
nfisisom(f,g1)
nfisisom(f,g2)
nfisisom(f,g3)
nfisisom(f,g4)

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = x^4 - 6
? ? ? ? ? %6 = x^4 + 100*x^2 + 5000
? ? ? ? ? ? ? ? ? ? ? %17 = 
[2 9]

? %18 = 0
? %19 = 0
? %20 = 0
? %21 = 0
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.018s
user	0m0.012s
sys	0m0.006s


'193.170'
************** PARI *****************
Host 193.170.37.83 (193.170.37.83)
Time: Wed Jul 26 07:17:20 2006

Input: f=x^4-6
polred(f);
nf=nfinit(f);
factor(nf.disc);
A=100;
g1=x^4+A*x^2+A^2/2
g2=x^4-A*x^2-A^2/2;
g3=x^4+A*x^2-A^2/2;
g4=x^4-A*x^2+A^2/2;
nf1=nfinit(g1)
nf2=nfinit(g2);
nf3=nfinit(g3);
nf4=nfinit(g4);
factor(nf1.disc);
factor(nf2.disc);
factor(nf3.disc);
factor(nf4.disc);
nfisisom(f,g1)
nfisisom(f,g2)
nfisisom(f,g3)
nfisisom(f,g4)

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = x^4 - 6
? ? ? ? ? %6 = x^4 + 100*x^2 + 5000
? ? ? ? %10 = [x^4 + 100*x^2 + 5000, [0, 2], 512, 125000, [[1, 3.761581922631320025 E-39 + 1.0000000000000000000000000000000000000*I, -1.0986841134678099660398011952406783785 - 0.45508986056222734130435775782246856961*I, -0.45508986056222734130435775782246856961 + 1.0986841134678099660398011952406783785*I; 1, 3.761581922631320025 E-39 + 1.0000000000000000000000000000000000000*I, 1.0986841134678099660398011952406783785 + 0.45508986056222734130435775782246856961*I, 0.45508986056222734130435775782246856961 - 1.0986841134678099660398011952406783785*I], [1, 1.0000000000000000000000000000000000000, -1.5537739740300373073441589530631469482, 0.64359425290558262473544343741820980893; 1, -1.0000000000000000000000000000000000000, -0.64359425290558262473544343741820980892, -1.5537739740300373073441589530631469482; 1, 1.0000000000000000000000000000000000000, 1.5537739740300373073441589530631469482, -0.64359425290558262473544343741820980893; 1, -1.0000000000000000000000000000000000000, 0.64359425290558262473544343741820980892, 1.5537739740300373073441589530631469482], 0, [4, 0, 0, 0; 0, -4, 0, 0; 0, 0, 4, 4; 0, 0, 4, -4], [8, 4, 0, 0; 0, 4, 0, 0; 0, 0, 4, 0; 0, 0, 0, 4], [2, 0, 0, 0; 0, -2, 0, 0; 0, 0, 1, 1; 0, 0, 1, -1], [2, [0, 0, 2, 0; 0, 0, 0, -2; 1, 1, 0, 0; 1, -1, 0, 0]]], [3.2179712645279131236772171870910490446 + 7.7688698701501865367207947653157347408*I, -3.2179712645279131236772171870910490446 - 7.7688698701501865367207947653157347408*I], [1, 1/50*x^2 + 1, 1/500*x^3, 1/500*x^3 + 1/5*x], [1, 0, -50, 0; 0, 0, 50, 0; 0, -5, 0, 500; 0, 5, 0, 0], [1, 0, 0, 0, 0, -1, 0, 0, 0, 0, 1, 1, 0, 0, 1, -1; 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 1, -1, 0, 0, -1, -1; 0, 0, 1, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 1, 0, 0; 0, 0, 0, 1, 0, 0, -1, 0, 0, -1, 0, 0, 1, 0, 0, 0]]
? ? ? ? ? ? ? ? %18 = 0
? %19 = 0
? %20 = 0
? %21 = 0
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.018s
user	0m0.011s
sys	0m0.006s


'193.170'
************** PARI *****************
Host 193.170.37.83 (193.170.37.83)
Time: Wed Jul 26 07:17:12 2006

Input: f=x^4-6
polred(f);
nf=nfinit(f);
factor(nf.disc);
A=100;
g1=x^4+A*x^2+A^2/2
g2=x^4-A*x^2-A^2/2;
g3=x^4+A*x^2-A^2/2;
g4=x^4-A*x^2+A^2/2;
nf1=nfinit(g1);
nf2=nfinit(g2);
nf3=nfinit(g3);
nf4=nfinit(g4);
factor(nf1.disc);
factor(nf2.disc);
factor(nf3.disc);
factor(nf4.disc);
nfisisom(f,g1)
nfisisom(f,g2)
nfisisom(f,g3)
nfisisom(f,g4)

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = x^4 - 6
? ? ? ? ? %6 = x^4 + 100*x^2 + 5000
? ? ? ? ? ? ? ? ? ? ? ? %18 = 0
? %19 = 0
? %20 = 0
? %21 = 0
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.018s
user	0m0.011s
sys	0m0.006s


'193.170'
************** PARI *****************
Host 193.170.37.83 (193.170.37.83)
Time: Wed Jul 26 07:17:02 2006

Input: f=x^4-6
polred(f);
nf=nfinit(f);
factor(nf.disc);
A=98;
g1=x^4+A*x^2+A^2/2
g2=x^4-A*x^2-A^2/2;
g3=x^4+A*x^2-A^2/2;
g4=x^4-A*x^2+A^2/2;
nf1=nfinit(g1);
nf2=nfinit(g2);
nf3=nfinit(g3);
nf4=nfinit(g4);
factor(nf1.disc);
factor(nf2.disc);
factor(nf3.disc);
factor(nf4.disc);
nfisisom(f,g1)
nfisisom(f,g2)
nfisisom(f,g3)
nfisisom(f,g4)

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = x^4 - 6
? ? ? ? ? %6 = x^4 + 98*x^2 + 4802
? ? ? ? ? ? ? ? ? ? ? ? %18 = 0
? %19 = 0
? %20 = 0
? %21 = 0
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.017s
user	0m0.010s
sys	0m0.007s


'193.170'
************** PARI *****************
Host 193.170.37.83 (193.170.37.83)
Time: Wed Jul 26 07:16:52 2006

Input: f=x^4-6
polred(f);
nf=nfinit(f);
factor(nf.disc);
A=96;
g1=x^4+A*x^2+A^2/2
g2=x^4-A*x^2-A^2/2;
g3=x^4+A*x^2-A^2/2;
g4=x^4-A*x^2+A^2/2;
nf1=nfinit(g1);
nf2=nfinit(g2);
nf3=nfinit(g3);
nf4=nfinit(g4);
factor(nf1.disc);
factor(nf2.disc);
factor(nf3.disc);
factor(nf4.disc);
nfisisom(f,g1)
nfisisom(f,g2)
nfisisom(f,g3)
nfisisom(f,g4)

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = x^4 - 6
? ? ? ? ? %6 = x^4 + 96*x^2 + 4608
? ? ? ? ? ? ? ? ? ? ? ? %18 = 0
? %19 = 0
? %20 = 0
? %21 = 0
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.090s
user	0m0.013s
sys	0m0.005s


'193.170'
************** PARI *****************
Host 193.170.37.83 (193.170.37.83)
Time: Wed Jul 26 07:16:45 2006

Input: f=x^4-6
polred(f);
nf=nfinit(f);
factor(nf.disc);
A=94;
g1=x^4+A*x^2+A^2/2
g2=x^4-A*x^2-A^2/2;
g3=x^4+A*x^2-A^2/2;
g4=x^4-A*x^2+A^2/2;
nf1=nfinit(g1);
nf2=nfinit(g2);
nf3=nfinit(g3);
nf4=nfinit(g4);
factor(nf1.disc);
factor(nf2.disc);
factor(nf3.disc);
factor(nf4.disc);
nfisisom(f,g1)
nfisisom(f,g2)
nfisisom(f,g3)
nfisisom(f,g4)

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = x^4 - 6
? ? ? ? ? %6 = x^4 + 94*x^2 + 4418
? ? ? ? ? ? ? ? ? ? ? ? %18 = 0
? %19 = 0
? %20 = 0
? %21 = 0
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.018s
user	0m0.012s
sys	0m0.005s


'193.170'
************** PARI *****************
Host 193.170.37.83 (193.170.37.83)
Time: Wed Jul 26 07:16:37 2006

Input: f=x^4-6
polred(f);
nf=nfinit(f);
factor(nf.disc);
A=92;
g1=x^4+A*x^2+A^2/2
g2=x^4-A*x^2-A^2/2;
g3=x^4+A*x^2-A^2/2;
g4=x^4-A*x^2+A^2/2;
nf1=nfinit(g1);
nf2=nfinit(g2);
nf3=nfinit(g3);
nf4=nfinit(g4);
factor(nf1.disc);
factor(nf2.disc);
factor(nf3.disc);
factor(nf4.disc);
nfisisom(f,g1)
nfisisom(f,g2)
nfisisom(f,g3)
nfisisom(f,g4)

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = x^4 - 6
? ? ? ? ? %6 = x^4 + 92*x^2 + 4232
? ? ? ? ? ? ? ? ? ? ? ? %18 = 0
? %19 = 0
? %20 = 0
? %21 = 0
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.068s
user	0m0.012s
sys	0m0.006s


'193.170'
************** PARI *****************
Host 193.170.37.83 (193.170.37.83)
Time: Wed Jul 26 07:16:29 2006

Input: f=x^4-6
polred(f);
nf=nfinit(f);
factor(nf.disc);
A=90;
g1=x^4+A*x^2+A^2/2
g2=x^4-A*x^2-A^2/2;
g3=x^4+A*x^2-A^2/2;
g4=x^4-A*x^2+A^2/2;
nf1=nfinit(g1);
nf2=nfinit(g2);
nf3=nfinit(g3);
nf4=nfinit(g4);
factor(nf1.disc);
factor(nf2.disc);
factor(nf3.disc);
factor(nf4.disc);
nfisisom(f,g1)
nfisisom(f,g2)
nfisisom(f,g3)
nfisisom(f,g4)

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = x^4 - 6
? ? ? ? ? %6 = x^4 + 90*x^2 + 4050
? ? ? ? ? ? ? ? ? ? ? ? %18 = 0
? %19 = 0
? %20 = 0
? %21 = 0
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.018s
user	0m0.011s
sys	0m0.006s


'193.170'
************** PARI *****************
Host 193.170.37.83 (193.170.37.83)
Time: Wed Jul 26 07:16:21 2006

Input: f=x^4-6
polred(f);
nf=nfinit(f);
factor(nf.disc);
A=88;
g1=x^4+A*x^2+A^2/2
g2=x^4-A*x^2-A^2/2;
g3=x^4+A*x^2-A^2/2;
g4=x^4-A*x^2+A^2/2;
nf1=nfinit(g1);
nf2=nfinit(g2);
nf3=nfinit(g3);
nf4=nfinit(g4);
factor(nf1.disc);
factor(nf2.disc);
factor(nf3.disc);
factor(nf4.disc);
nfisisom(f,g1)
nfisisom(f,g2)
nfisisom(f,g3)
nfisisom(f,g4)

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = x^4 - 6
? ? ? ? ? %6 = x^4 + 88*x^2 + 3872
? ? ? ? ? ? ? ? ? ? ? ? %18 = 0
? %19 = 0
? %20 = 0
? %21 = 0
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.018s
user	0m0.011s
sys	0m0.006s


'193.170'
************** PARI *****************
Host 193.170.37.83 (193.170.37.83)
Time: Wed Jul 26 07:16:08 2006

Input: f=x^4-6
polred(f);
nf=nfinit(f);
factor(nf.disc);
A=86;
g1=x^4+A*x^2+A^2/2
g2=x^4-A*x^2-A^2/2;
g3=x^4+A*x^2-A^2/2;
g4=x^4-A*x^2+A^2/2;
nf1=nfinit(g1);
nf2=nfinit(g2);
nf3=nfinit(g3);
nf4=nfinit(g4);
factor(nf1.disc);
factor(nf2.disc);
factor(nf3.disc);
factor(nf4.disc);
nfisisom(f,g1)
nfisisom(f,g2)
nfisisom(f,g3)
nfisisom(f,g4)

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = x^4 - 6
? ? ? ? ? %6 = x^4 + 86*x^2 + 3698
? ? ? ? ? ? ? ? ? ? ? ? %18 = 0
? %19 = 0
? %20 = 0
? %21 = 0
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.018s
user	0m0.009s
sys	0m0.008s


'193.170'
************** PARI *****************
Host 193.170.37.83 (193.170.37.83)
Time: Wed Jul 26 07:15:58 2006

Input: f=x^4-6
polred(f);
nf=nfinit(f);
factor(nf.disc);
A=84;
g1=x^4+A*x^2+A^2/2;
g2=x^4-A*x^2-A^2/2;
g3=x^4+A*x^2-A^2/2;
g4=x^4-A*x^2+A^2/2;
nf1=nfinit(g1);
nf2=nfinit(g2);
nf3=nfinit(g3);
nf4=nfinit(g4);
factor(nf1.disc);
factor(nf2.disc);
factor(nf3.disc);
factor(nf4.disc);
nfisisom(f,g1)
nfisisom(f,g2)
nfisisom(f,g3)
nfisisom(f,g4)

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = x^4 - 6
? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? %18 = 0
? %19 = 0
? %20 = 0
? %21 = 0
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.020s
user	0m0.012s
sys	0m0.009s


'193.170'
************** PARI *****************
Host 193.170.37.83 (193.170.37.83)
Time: Wed Jul 26 07:15:49 2006

Input: f=x^4-6
polred(f);
nf=nfinit(f);
factor(nf.disc);
A=82;
g1=x^4+A*x^2+A^2/2;
g2=x^4-A*x^2-A^2/2;
g3=x^4+A*x^2-A^2/2;
g4=x^4-A*x^2+A^2/2;
nf1=nfinit(g1);
nf2=nfinit(g2);
nf3=nfinit(g3);
nf4=nfinit(g4);
factor(nf1.disc);
factor(nf2.disc);
factor(nf3.disc);
factor(nf4.disc);
nfisisom(f,g1)
nfisisom(f,g2)
nfisisom(f,g3)
nfisisom(f,g4)

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = x^4 - 6
? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? %18 = 0
? %19 = 0
? %20 = 0
? %21 = 0
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.018s
user	0m0.012s
sys	0m0.005s


'193.170'
************** PARI *****************
Host 193.170.37.83 (193.170.37.83)
Time: Wed Jul 26 07:15:39 2006

Input: f=x^4-6
polred(f);
nf=nfinit(f);
factor(nf.disc);
A=80;
g1=x^4+A*x^2+A^2/2;
g2=x^4-A*x^2-A^2/2;
g3=x^4+A*x^2-A^2/2;
g4=x^4-A*x^2+A^2/2;
nf1=nfinit(g1);
nf2=nfinit(g2);
nf3=nfinit(g3);
nf4=nfinit(g4);
factor(nf1.disc);
factor(nf2.disc);
factor(nf3.disc);
factor(nf4.disc);
nfisisom(f,g1)
nfisisom(f,g2)
nfisisom(f,g3)
nfisisom(f,g4)

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = x^4 - 6
? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? %18 = 0
? %19 = 0
? %20 = 0
? %21 = 0
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.018s
user	0m0.011s
sys	0m0.007s


'193.170'
************** PARI *****************
Host 193.170.37.83 (193.170.37.83)
Time: Wed Jul 26 07:15:33 2006

Input: f=x^4-6
polred(f);
nf=nfinit(f);
factor(nf.disc);
A=78;
g1=x^4+A*x^2+A^2/2;
g2=x^4-A*x^2-A^2/2;
g3=x^4+A*x^2-A^2/2;
g4=x^4-A*x^2+A^2/2;
nf1=nfinit(g1);
nf2=nfinit(g2);
nf3=nfinit(g3);
nf4=nfinit(g4);
factor(nf1.disc);
factor(nf2.disc);
factor(nf3.disc);
factor(nf4.disc);
nfisisom(f,g1)
nfisisom(f,g2)
nfisisom(f,g3)
nfisisom(f,g4)

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = x^4 - 6
? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? %18 = 0
? %19 = 0
? %20 = 0
? %21 = 0
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.094s
user	0m0.009s
sys	0m0.009s


'193.170'
************** PARI *****************
Host 193.170.37.83 (193.170.37.83)
Time: Wed Jul 26 07:15:25 2006

Input: f=x^4-6
polred(f);
nf=nfinit(f);
factor(nf.disc);
A=76;
g1=x^4+A*x^2+A^2/2;
g2=x^4-A*x^2-A^2/2;
g3=x^4+A*x^2-A^2/2;
g4=x^4-A*x^2+A^2/2;
nf1=nfinit(g1);
nf2=nfinit(g2);
nf3=nfinit(g3);
nf4=nfinit(g4);
factor(nf1.disc);
factor(nf2.disc);
factor(nf3.disc);
factor(nf4.disc);
nfisisom(f,g1)
nfisisom(f,g2)
nfisisom(f,g3)
nfisisom(f,g4)

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = x^4 - 6
? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? %18 = 0
? %19 = 0
? %20 = 0
? %21 = 0
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.017s
user	0m0.012s
sys	0m0.007s


'193.170'
************** PARI *****************
Host 193.170.37.83 (193.170.37.83)
Time: Wed Jul 26 07:15:16 2006

Input: f=x^4-6
polred(f);
nf=nfinit(f);
factor(nf.disc);
A=74;
g1=x^4+A*x^2+A^2/2;
g2=x^4-A*x^2-A^2/2;
g3=x^4+A*x^2-A^2/2;
g4=x^4-A*x^2+A^2/2;
nf1=nfinit(g1);
nf2=nfinit(g2);
nf3=nfinit(g3);
nf4=nfinit(g4);
factor(nf1.disc);
factor(nf2.disc);
factor(nf3.disc);
factor(nf4.disc);
nfisisom(f,g1)
nfisisom(f,g2)
nfisisom(f,g3)
nfisisom(f,g4)

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = x^4 - 6
? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? %18 = 0
? %19 = 0
? %20 = 0
? %21 = 0
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.017s
user	0m0.012s
sys	0m0.005s


'193.170'
************** PARI *****************
Host 193.170.37.83 (193.170.37.83)
Time: Wed Jul 26 07:15:09 2006

Input: f=x^4-6
polred(f);
nf=nfinit(f);
factor(nf.disc);
A=72;
g1=x^4+A*x^2+A^2/2;
g2=x^4-A*x^2-A^2/2;
g3=x^4+A*x^2-A^2/2;
g4=x^4-A*x^2+A^2/2;
nf1=nfinit(g1);
nf2=nfinit(g2);
nf3=nfinit(g3);
nf4=nfinit(g4);
factor(nf1.disc);
factor(nf2.disc);
factor(nf3.disc);
factor(nf4.disc);
nfisisom(f,g1)
nfisisom(f,g2)
nfisisom(f,g3)
nfisisom(f,g4)

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = x^4 - 6
? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? %18 = 0
? %19 = 0
? %20 = 0
? %21 = 0
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.018s
user	0m0.011s
sys	0m0.007s


'193.170'
************** PARI *****************
Host 193.170.37.83 (193.170.37.83)
Time: Wed Jul 26 07:15:02 2006

Input: f=x^4-6
polred(f);
nf=nfinit(f);
factor(nf.disc);
A=70;
g1=x^4+A*x^2+A^2/2;
g2=x^4-A*x^2-A^2/2;
g3=x^4+A*x^2-A^2/2;
g4=x^4-A*x^2+A^2/2;
nf1=nfinit(g1);
nf2=nfinit(g2);
nf3=nfinit(g3);
nf4=nfinit(g4);
factor(nf1.disc);
factor(nf2.disc);
factor(nf3.disc);
factor(nf4.disc);
nfisisom(f,g1)
nfisisom(f,g2)
nfisisom(f,g3)
nfisisom(f,g4)

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = x^4 - 6
? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? %18 = 0
? %19 = 0
? %20 = 0
? %21 = 0
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.019s
user	0m0.012s
sys	0m0.006s


'193.170'
************** PARI *****************
Host 193.170.37.83 (193.170.37.83)
Time: Wed Jul 26 07:14:54 2006

Input: f=x^4-6
polred(f);
nf=nfinit(f);
factor(nf.disc);
A=68;
g1=x^4+A*x^2+A^2/2;
g2=x^4-A*x^2-A^2/2;
g3=x^4+A*x^2-A^2/2;
g4=x^4-A*x^2+A^2/2;
nf1=nfinit(g1);
nf2=nfinit(g2);
nf3=nfinit(g3);
nf4=nfinit(g4);
factor(nf1.disc);
factor(nf2.disc);
factor(nf3.disc);
factor(nf4.disc);
nfisisom(f,g1)
nfisisom(f,g2)
nfisisom(f,g3)
nfisisom(f,g4)

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = x^4 - 6
? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? %18 = 0
? %19 = 0
? %20 = 0
? %21 = 0
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.020s
user	0m0.013s
sys	0m0.005s


'193.170'
************** PARI *****************
Host 193.170.37.83 (193.170.37.83)
Time: Wed Jul 26 07:14:47 2006

Input: f=x^4-6
polred(f);
nf=nfinit(f);
factor(nf.disc);
A=66;
g1=x^4+A*x^2+A^2/2;
g2=x^4-A*x^2-A^2/2;
g3=x^4+A*x^2-A^2/2;
g4=x^4-A*x^2+A^2/2;
nf1=nfinit(g1);
nf2=nfinit(g2);
nf3=nfinit(g3);
nf4=nfinit(g4);
factor(nf1.disc);
factor(nf2.disc);
factor(nf3.disc);
factor(nf4.disc);
nfisisom(f,g1)
nfisisom(f,g2)
nfisisom(f,g3)
nfisisom(f,g4)

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = x^4 - 6
? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? %18 = 0
? %19 = 0
? %20 = 0
? %21 = 0
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.019s
user	0m0.014s
sys	0m0.005s


'193.170'
************** PARI *****************
Host 193.170.37.83 (193.170.37.83)
Time: Wed Jul 26 07:14:40 2006

Input: f=x^4-6
polred(f);
nf=nfinit(f);
factor(nf.disc);
A=64;
g1=x^4+A*x^2+A^2/2;
g2=x^4-A*x^2-A^2/2;
g3=x^4+A*x^2-A^2/2;
g4=x^4-A*x^2+A^2/2;
nf1=nfinit(g1);
nf2=nfinit(g2);
nf3=nfinit(g3);
nf4=nfinit(g4);
factor(nf1.disc);
factor(nf2.disc);
factor(nf3.disc);
factor(nf4.disc);
nfisisom(f,g1)
nfisisom(f,g2)
nfisisom(f,g3)
nfisisom(f,g4)

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = x^4 - 6
? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? %18 = 0
? %19 = 0
? %20 = 0
? %21 = 0
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.018s
user	0m0.012s
sys	0m0.005s


'193.170'
************** PARI *****************
Host 193.170.37.83 (193.170.37.83)
Time: Wed Jul 26 07:14:33 2006

Input: f=x^4-6
polred(f);
nf=nfinit(f);
factor(nf.disc);
A=62;
g1=x^4+A*x^2+A^2/2;
g2=x^4-A*x^2-A^2/2;
g3=x^4+A*x^2-A^2/2;
g4=x^4-A*x^2+A^2/2;
nf1=nfinit(g1);
nf2=nfinit(g2);
nf3=nfinit(g3);
nf4=nfinit(g4);
factor(nf1.disc);
factor(nf2.disc);
factor(nf3.disc);
factor(nf4.disc);
nfisisom(f,g1)
nfisisom(f,g2)
nfisisom(f,g3)
nfisisom(f,g4)

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = x^4 - 6
? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? %18 = 0
? %19 = 0
? %20 = 0
? %21 = 0
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.018s
user	0m0.014s
sys	0m0.004s


'193.170'
************** PARI *****************
Host 193.170.37.83 (193.170.37.83)
Time: Wed Jul 26 07:14:24 2006

Input: f=x^4-6
polred(f);
nf=nfinit(f);
factor(nf.disc);
A=60;
g1=x^4+A*x^2+A^2/2;
g2=x^4-A*x^2-A^2/2;
g3=x^4+A*x^2-A^2/2;
g4=x^4-A*x^2+A^2/2;
nf1=nfinit(g1);
nf2=nfinit(g2);
nf3=nfinit(g3);
nf4=nfinit(g4);
factor(nf1.disc);
factor(nf2.disc);
factor(nf3.disc);
factor(nf4.disc);
nfisisom(f,g1)
nfisisom(f,g2)
nfisisom(f,g3)
nfisisom(f,g4)

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = x^4 - 6
? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? %18 = 0
? %19 = 0
? %20 = 0
? %21 = 0
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.018s
user	0m0.012s
sys	0m0.006s


'193.170'
************** PARI *****************
Host 193.170.37.83 (193.170.37.83)
Time: Wed Jul 26 07:14:16 2006

Input: f=x^4-6
polred(f);
nf=nfinit(f);
factor(nf.disc);
A=58;
g1=x^4+A*x^2+A^2/2;
g2=x^4-A*x^2-A^2/2;
g3=x^4+A*x^2-A^2/2;
g4=x^4-A*x^2+A^2/2;
nf1=nfinit(g1);
nf2=nfinit(g2);
nf3=nfinit(g3);
nf4=nfinit(g4);
factor(nf1.disc);
factor(nf2.disc);
factor(nf3.disc);
factor(nf4.disc);
nfisisom(f,g1)
nfisisom(f,g2)
nfisisom(f,g3)
nfisisom(f,g4)

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = x^4 - 6
? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? %18 = 0
? %19 = 0
? %20 = 0
? %21 = 0
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.040s
user	0m0.012s
sys	0m0.006s


'193.170'
************** PARI *****************
Host 193.170.37.83 (193.170.37.83)
Time: Wed Jul 26 07:14:07 2006

Input: f=x^4-6
polred(f);
nf=nfinit(f);
factor(nf.disc);
A=56;
g1=x^4+A*x^2+A^2/2;
g2=x^4-A*x^2-A^2/2;
g3=x^4+A*x^2-A^2/2;
g4=x^4-A*x^2+A^2/2;
nf1=nfinit(g1);
nf2=nfinit(g2);
nf3=nfinit(g3);
nf4=nfinit(g4);
factor(nf1.disc);
factor(nf2.disc);
factor(nf3.disc);
factor(nf4.disc);
nfisisom(f,g1)
nfisisom(f,g2)
nfisisom(f,g3)
nfisisom(f,g4)

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = x^4 - 6
? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? %18 = 0
? %19 = 0
? %20 = 0
? %21 = 0
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.018s
user	0m0.012s
sys	0m0.005s


'193.170'
************** PARI *****************
Host 193.170.37.83 (193.170.37.83)
Time: Wed Jul 26 07:13:58 2006

Input: f=x^4-6
polred(f);
nf=nfinit(f);
factor(nf.disc);
A=54;
g1=x^4+A*x^2+A^2/2;
g2=x^4-A*x^2-A^2/2;
g3=x^4+A*x^2-A^2/2;
g4=x^4-A*x^2+A^2/2;
nf1=nfinit(g1);
nf2=nfinit(g2);
nf3=nfinit(g3);
nf4=nfinit(g4);
factor(nf1.disc);
factor(nf2.disc);
factor(nf3.disc);
factor(nf4.disc);
nfisisom(f,g1)
nfisisom(f,g2)
nfisisom(f,g3)
nfisisom(f,g4)

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = x^4 - 6
? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? %18 = 0
? %19 = 0
? %20 = 0
? %21 = 0
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.018s
user	0m0.012s
sys	0m0.005s


'193.170'
************** PARI *****************
Host 193.170.37.83 (193.170.37.83)
Time: Wed Jul 26 07:13:52 2006

Input: f=x^4-6
polred(f);
nf=nfinit(f);
factor(nf.disc);
A=52;
g1=x^4+A*x^2+A^2/2;
g2=x^4-A*x^2-A^2/2;
g3=x^4+A*x^2-A^2/2;
g4=x^4-A*x^2+A^2/2;
nf1=nfinit(g1);
nf2=nfinit(g2);
nf3=nfinit(g3);
nf4=nfinit(g4);
factor(nf1.disc);
factor(nf2.disc);
factor(nf3.disc);
factor(nf4.disc);
nfisisom(f,g1)
nfisisom(f,g2)
nfisisom(f,g3)
nfisisom(f,g4)

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = x^4 - 6
? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? %18 = 0
? %19 = 0
? %20 = 0
? %21 = 0
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.017s
user	0m0.007s
sys	0m0.010s


'193.170'
************** PARI *****************
Host 193.170.37.83 (193.170.37.83)
Time: Wed Jul 26 07:13:44 2006

Input: f=x^4-6
polred(f);
nf=nfinit(f);
factor(nf.disc);
A=50;
g1=x^4+A*x^2+A^2/2;
g2=x^4-A*x^2-A^2/2;
g3=x^4+A*x^2-A^2/2;
g4=x^4-A*x^2+A^2/2;
nf1=nfinit(g1);
nf2=nfinit(g2);
nf3=nfinit(g3);
nf4=nfinit(g4);
factor(nf1.disc);
factor(nf2.disc);
factor(nf3.disc);
factor(nf4.disc);
nfisisom(f,g1)
nfisisom(f,g2)
nfisisom(f,g3)
nfisisom(f,g4)

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = x^4 - 6
? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? %18 = 0
? %19 = 0
? %20 = 0
? %21 = 0
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.017s
user	0m0.013s
sys	0m0.005s


'193.170'
************** PARI *****************
Host 193.170.37.83 (193.170.37.83)
Time: Wed Jul 26 07:13:35 2006

Input: f=x^4-6
polred(f);
nf=nfinit(f);
factor(nf.disc);
A=48;
g1=x^4+A*x^2+A^2/2;
g2=x^4-A*x^2-A^2/2;
g3=x^4+A*x^2-A^2/2;
g4=x^4-A*x^2+A^2/2;
nf1=nfinit(g1);
nf2=nfinit(g2);
nf3=nfinit(g3);
nf4=nfinit(g4);
factor(nf1.disc);
factor(nf2.disc);
factor(nf3.disc);
factor(nf4.disc);
nfisisom(f,g1)
nfisisom(f,g2)
nfisisom(f,g3)
nfisisom(f,g4)

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = x^4 - 6
? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? %18 = 0
? %19 = 0
? %20 = 0
? %21 = 0
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.018s
user	0m0.012s
sys	0m0.006s


'193.170'
************** PARI *****************
Host 193.170.37.83 (193.170.37.83)
Time: Wed Jul 26 07:13:28 2006

Input: f=x^4-6
polred(f);
nf=nfinit(f);
factor(nf.disc);
A=46;
g1=x^4+A*x^2+A^2/2;
g2=x^4-A*x^2-A^2/2;
g3=x^4+A*x^2-A^2/2;
g4=x^4-A*x^2+A^2/2;
nf1=nfinit(g1);
nf2=nfinit(g2);
nf3=nfinit(g3);
nf4=nfinit(g4);
factor(nf1.disc);
factor(nf2.disc);
factor(nf3.disc);
factor(nf4.disc);
nfisisom(f,g1)
nfisisom(f,g2)
nfisisom(f,g3)
nfisisom(f,g4)

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = x^4 - 6
? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? %18 = 0
? %19 = 0
? %20 = 0
? %21 = 0
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.017s
user	0m0.008s
sys	0m0.008s


'193.170'
************** PARI *****************
Host 193.170.37.83 (193.170.37.83)
Time: Wed Jul 26 07:13:20 2006

Input: f=x^4-6
polred(f);
nf=nfinit(f);
factor(nf.disc);
A=44;
g1=x^4+A*x^2+A^2/2;
g2=x^4-A*x^2-A^2/2;
g3=x^4+A*x^2-A^2/2;
g4=x^4-A*x^2+A^2/2;
nf1=nfinit(g1);
nf2=nfinit(g2);
nf3=nfinit(g3);
nf4=nfinit(g4);
factor(nf1.disc);
factor(nf2.disc);
factor(nf3.disc);
factor(nf4.disc);
nfisisom(f,g1)
nfisisom(f,g2)
nfisisom(f,g3)
nfisisom(f,g4)

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = x^4 - 6
? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? %18 = 0
? %19 = 0
? %20 = 0
? %21 = 0
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.018s
user	0m0.014s
sys	0m0.003s


'193.170'
************** PARI *****************
Host 193.170.37.83 (193.170.37.83)
Time: Wed Jul 26 07:13:14 2006

Input: f=x^4-6
polred(f);
nf=nfinit(f);
factor(nf.disc);
A=42;
g1=x^4+A*x^2+A^2/2;
g2=x^4-A*x^2-A^2/2;
g3=x^4+A*x^2-A^2/2;
g4=x^4-A*x^2+A^2/2;
nf1=nfinit(g1);
nf2=nfinit(g2);
nf3=nfinit(g3);
nf4=nfinit(g4);
factor(nf1.disc);
factor(nf2.disc);
factor(nf3.disc);
factor(nf4.disc);
nfisisom(f,g1)
nfisisom(f,g2)
nfisisom(f,g3)
nfisisom(f,g4)

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = x^4 - 6
? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? %18 = 0
? %19 = 0
? %20 = 0
? %21 = 0
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.018s
user	0m0.013s
sys	0m0.005s


'193.170'
************** PARI *****************
Host 193.170.37.83 (193.170.37.83)
Time: Wed Jul 26 07:13:06 2006

Input: f=x^4-6
polred(f);
nf=nfinit(f);
factor(nf.disc);
A=40;
g1=x^4+A*x^2+A^2/2;
g2=x^4-A*x^2-A^2/2;
g3=x^4+A*x^2-A^2/2;
g4=x^4-A*x^2+A^2/2;
nf1=nfinit(g1);
nf2=nfinit(g2);
nf3=nfinit(g3);
nf4=nfinit(g4);
factor(nf1.disc);
factor(nf2.disc);
factor(nf3.disc);
factor(nf4.disc);
nfisisom(f,g1)
nfisisom(f,g2)
nfisisom(f,g3)
nfisisom(f,g4)

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = x^4 - 6
? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? %18 = 0
? %19 = 0
? %20 = 0
? %21 = 0
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.017s
user	0m0.013s
sys	0m0.004s


'193.170'
************** PARI *****************
Host 193.170.37.83 (193.170.37.83)
Time: Wed Jul 26 07:12:54 2006

Input: f=x^4-6
polred(f);
nf=nfinit(f);
factor(nf.disc);
A=38;
g1=x^4+A*x^2+A^2/2;
g2=x^4-A*x^2-A^2/2;
g3=x^4+A*x^2-A^2/2;
g4=x^4-A*x^2+A^2/2;
nf1=nfinit(g1);
nf2=nfinit(g2);
nf3=nfinit(g3);
nf4=nfinit(g4);
factor(nf1.disc);
factor(nf2.disc);
factor(nf3.disc);
factor(nf4.disc);
nfisisom(f,g1)
nfisisom(f,g2)
nfisisom(f,g3)
nfisisom(f,g4)

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = x^4 - 6
? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? %18 = 0
? %19 = 0
? %20 = 0
? %21 = 0
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.112s
user	0m0.012s
sys	0m0.005s


'193.170'
************** PARI *****************
Host 193.170.37.83 (193.170.37.83)
Time: Wed Jul 26 07:12:47 2006

Input: f=x^4-6
polred(f);
nf=nfinit(f);
factor(nf.disc);
A=36;
g1=x^4+A*x^2+A^2/2;
g2=x^4-A*x^2-A^2/2;
g3=x^4+A*x^2-A^2/2;
g4=x^4-A*x^2+A^2/2;
nf1=nfinit(g1);
nf2=nfinit(g2);
nf3=nfinit(g3);
nf4=nfinit(g4);
factor(nf1.disc);
factor(nf2.disc);
factor(nf3.disc);
factor(nf4.disc);
nfisisom(f,g1)
nfisisom(f,g2)
nfisisom(f,g3)
nfisisom(f,g4)

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = x^4 - 6
? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? %18 = 0
? %19 = 0
? %20 = 0
? %21 = 0
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.017s
user	0m0.010s
sys	0m0.007s


'193.170'
************** PARI *****************
Host 193.170.37.83 (193.170.37.83)
Time: Wed Jul 26 07:12:40 2006

Input: f=x^4-6
polred(f);
nf=nfinit(f);
factor(nf.disc);
A=34;
g1=x^4+A*x^2+A^2/2;
g2=x^4-A*x^2-A^2/2;
g3=x^4+A*x^2-A^2/2;
g4=x^4-A*x^2+A^2/2;
nf1=nfinit(g1);
nf2=nfinit(g2);
nf3=nfinit(g3);
nf4=nfinit(g4);
factor(nf1.disc);
factor(nf2.disc);
factor(nf3.disc);
factor(nf4.disc);
nfisisom(f,g1)
nfisisom(f,g2)
nfisisom(f,g3)
nfisisom(f,g4)

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = x^4 - 6
? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? %18 = 0
? %19 = 0
? %20 = 0
? %21 = 0
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.017s
user	0m0.009s
sys	0m0.007s


'193.170'
************** PARI *****************
Host 193.170.37.83 (193.170.37.83)
Time: Wed Jul 26 07:12:34 2006

Input: f=x^4-6
polred(f);
nf=nfinit(f);
factor(nf.disc);
A=32;
g1=x^4+A*x^2+A^2/2;
g2=x^4-A*x^2-A^2/2;
g3=x^4+A*x^2-A^2/2;
g4=x^4-A*x^2+A^2/2;
nf1=nfinit(g1);
nf2=nfinit(g2);
nf3=nfinit(g3);
nf4=nfinit(g4);
factor(nf1.disc);
factor(nf2.disc);
factor(nf3.disc);
factor(nf4.disc);
nfisisom(f,g1)
nfisisom(f,g2)
nfisisom(f,g3)
nfisisom(f,g4)

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = x^4 - 6
? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? %18 = 0
? %19 = 0
? %20 = 0
? %21 = 0
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.017s
user	0m0.009s
sys	0m0.007s


'193.170'
************** PARI *****************
Host 193.170.37.83 (193.170.37.83)
Time: Wed Jul 26 07:12:24 2006

Input: f=x^4-6
polred(f);
nf=nfinit(f);
factor(nf.disc);
A=30;
g1=x^4+A*x^2+A^2/2;
g2=x^4-A*x^2-A^2/2;
g3=x^4+A*x^2-A^2/2;
g4=x^4-A*x^2+A^2/2;
nf1=nfinit(g1);
nf2=nfinit(g2);
nf3=nfinit(g3);
nf4=nfinit(g4);
factor(nf1.disc);
factor(nf2.disc);
factor(nf3.disc);
factor(nf4.disc);
nfisisom(f,g1)
nfisisom(f,g2)
nfisisom(f,g3)
nfisisom(f,g4)

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = x^4 - 6
? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? %18 = 0
? %19 = 0
? %20 = 0
? %21 = 0
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.081s
user	0m0.013s
sys	0m0.005s


'193.170'
************** PARI *****************
Host 193.170.37.83 (193.170.37.83)
Time: Wed Jul 26 07:12:15 2006

Input: f=x^4-6
polred(f);
nf=nfinit(f);
factor(nf.disc);
A-30;
g1=x^4+A*x^2+A^2/2;
g2=x^4-A*x^2-A^2/2;
g3=x^4+A*x^2-A^2/2;
g4=x^4-A*x^2+A^2/2;
nf1=nfinit(g1);
nf2=nfinit(g2);
nf3=nfinit(g3);
nf4=nfinit(g4);
factor(nf1.disc);
factor(nf2.disc);
factor(nf3.disc);
factor(nf4.disc);
nfisisom(f,g1)
nfisisom(f,g2)
nfisisom(f,g3)
nfisisom(f,g4)

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = x^4 - 6
? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? 
Goodbye!

Errors/timing (if any):

  *** nfinit: polynomial not in Z[X] in nfinit.
  *** nfinit: polynomial not in Z[X] in nfinit.
  *** nfinit: polynomial not in Z[X] in nfinit.
  *** nfinit: polynomial not in Z[X] in nfinit.
  ***   incorrect type in disc: factor(nf1.disc);
                                           ^------
  ***   incorrect type in disc: factor(nf2.disc);
                                           ^------
  ***   incorrect type in disc: factor(nf3.disc);
                                           ^------
  ***   incorrect type in disc: factor(nf4.disc);
                                           ^------
  *** nfisisom: polynomial not in Z[X] in nsiso0.
  *** nfisisom: polynomial not in Z[X] in nsiso0.
  *** nfisisom: polynomial not in Z[X] in nsiso0.
  *** nfisisom: polynomial not in Z[X] in nsiso0.

Timing:
real	0m0.014s
user	0m0.010s
sys	0m0.004s


'193.170'
************** PARI *****************
Host 193.170.37.83 (193.170.37.83)
Time: Wed Jul 26 07:12:04 2006

Input: f=x^4-6
polred(f);
nf=nfinit(f);
factor(nf.disc);
A=28;
g1=x^4+A*x^2+A^2/2;
g2=x^4-A*x^2-A^2/2;
g3=x^4+A*x^2-A^2/2;
g4=x^4-A*x^2+A^2/2;
nf1=nfinit(g1);
nf2=nfinit(g2);
nf3=nfinit(g3);
nf4=nfinit(g4);
factor(nf1.disc);
factor(nf2.disc);
factor(nf3.disc);
factor(nf4.disc);
nfisisom(f,g1)
nfisisom(f,g2)
nfisisom(f,g3)
nfisisom(f,g4)

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = x^4 - 6
? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? %18 = 0
? %19 = 0
? %20 = 0
? %21 = 0
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.018s
user	0m0.012s
sys	0m0.006s


'193.170'
************** PARI *****************
Host 193.170.37.83 (193.170.37.83)
Time: Wed Jul 26 07:11:56 2006

Input: f=x^4-6
polred(f);
nf=nfinit(f);
factor(nf.disc);
A=26;
g1=x^4+A*x^2+A^2/2;
g2=x^4-A*x^2-A^2/2;
g3=x^4+A*x^2-A^2/2;
g4=x^4-A*x^2+A^2/2;
nf1=nfinit(g1);
nf2=nfinit(g2);
nf3=nfinit(g3);
nf4=nfinit(g4);
factor(nf1.disc);
factor(nf2.disc);
factor(nf3.disc);
factor(nf4.disc);
nfisisom(f,g1)
nfisisom(f,g2)
nfisisom(f,g3)
nfisisom(f,g4)

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = x^4 - 6
? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? %18 = 0
? %19 = 0
? %20 = 0
? %21 = 0
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.038s
user	0m0.011s
sys	0m0.006s


'193.170'
************** PARI *****************
Host 193.170.37.83 (193.170.37.83)
Time: Wed Jul 26 07:11:49 2006

Input: f=x^4-6
polred(f);
nf=nfinit(f);
factor(nf.disc);
A=24;
g1=x^4+A*x^2+A^2/2;
g2=x^4-A*x^2-A^2/2;
g3=x^4+A*x^2-A^2/2;
g4=x^4-A*x^2+A^2/2;
nf1=nfinit(g1);
nf2=nfinit(g2);
nf3=nfinit(g3);
nf4=nfinit(g4);
factor(nf1.disc);
factor(nf2.disc);
factor(nf3.disc);
factor(nf4.disc);
nfisisom(f,g1)
nfisisom(f,g2)
nfisisom(f,g3)
nfisisom(f,g4)

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = x^4 - 6
? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? %18 = 0
? %19 = 0
? %20 = 0
? %21 = 0
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.017s
user	0m0.012s
sys	0m0.004s


'193.170'
************** PARI *****************
Host 193.170.37.83 (193.170.37.83)
Time: Wed Jul 26 07:11:39 2006

Input: f=x^4-6
polred(f);
nf=nfinit(f);
factor(nf.disc);
A=22;
g1=x^4+A*x^2+A^2/2;
g2=x^4-A*x^2-A^2/2;
g3=x^4+A*x^2-A^2/2;
g4=x^4-A*x^2+A^2/2;
nf1=nfinit(g1);
nf2=nfinit(g2);
nf3=nfinit(g3);
nf4=nfinit(g4);
factor(nf1.disc);
factor(nf2.disc);
factor(nf3.disc);
factor(nf4.disc);
nfisisom(f,g1)
nfisisom(f,g2)
nfisisom(f,g3)
nfisisom(f,g4)

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = x^4 - 6
? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? %18 = 0
? %19 = 0
? %20 = 0
? %21 = 0
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.331s
user	0m0.016s
sys	0m0.002s


'193.170'
************** PARI *****************
Host 193.170.37.83 (193.170.37.83)
Time: Wed Jul 26 07:11:33 2006

Input: f=x^4-6
polred(f);
nf=nfinit(f);
factor(nf.disc);
A=21;
g1=x^4+A*x^2+A^2/2;
g2=x^4-A*x^2-A^2/2;
g3=x^4+A*x^2-A^2/2;
g4=x^4-A*x^2+A^2/2;
nf1=nfinit(g1);
nf2=nfinit(g2);
nf3=nfinit(g3);
nf4=nfinit(g4);
factor(nf1.disc);
factor(nf2.disc);
factor(nf3.disc);
factor(nf4.disc);
nfisisom(f,g1)
nfisisom(f,g2)
nfisisom(f,g3)
nfisisom(f,g4)

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = x^4 - 6
? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? %10 = 0
? %11 = 0
? %12 = 0
? %13 = 0
? 
Goodbye!

Errors/timing (if any):

  *** nfinit: polynomial not in Z[X] in nfinit.
  *** nfinit: polynomial not in Z[X] in nfinit.
  *** nfinit: polynomial not in Z[X] in nfinit.
  *** nfinit: polynomial not in Z[X] in nfinit.
  ***   incorrect type in disc: factor(nf1.disc);
                                           ^------
  ***   incorrect type in disc: factor(nf2.disc);
                                           ^------
  ***   incorrect type in disc: factor(nf3.disc);
                                           ^------
  ***   incorrect type in disc: factor(nf4.disc);
                                           ^------

Timing:
real	0m0.014s
user	0m0.008s
sys	0m0.006s


'193.170'
************** PARI *****************
Host 193.170.37.83 (193.170.37.83)
Time: Wed Jul 26 07:11:24 2006

Input: f=x^4-6
polred(f);
nf=nfinit(f);
factor(nf.disc);
A=20;
g1=x^4+A*x^2+A^2/2;
g2=x^4-A*x^2-A^2/2;
g3=x^4+A*x^2-A^2/2;
g4=x^4-A*x^2+A^2/2;
nf1=nfinit(g1);
nf2=nfinit(g2);
nf3=nfinit(g3);
nf4=nfinit(g4);
factor(nf1.disc);
factor(nf2.disc);
factor(nf3.disc);
factor(nf4.disc);
nfisisom(f,g1)
nfisisom(f,g2)
nfisisom(f,g3)
nfisisom(f,g4)

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = x^4 - 6
? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? %18 = 0
? %19 = 0
? %20 = 0
? %21 = 0
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.018s
user	0m0.010s
sys	0m0.008s


'193.170'
************** PARI *****************
Host 193.170.37.83 (193.170.37.83)
Time: Wed Jul 26 07:11:14 2006

Input: f=x^4-6
polred(f);
nf=nfinit(f);
factor(nf.disc);
A=18;
g1=x^4+A*x^2+A^2/2;
g2=x^4-A*x^2-A^2/2;
g3=x^4+A*x^2-A^2/2;
g4=x^4-A*x^2+A^2/2;
nf1=nfinit(g1);
nf2=nfinit(g2);
nf3=nfinit(g3);
nf4=nfinit(g4);
factor(nf1.disc);
factor(nf2.disc);
factor(nf3.disc);
factor(nf4.disc);
nfisisom(f,g1)
nfisisom(f,g2)
nfisisom(f,g3)
nfisisom(f,g4)

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = x^4 - 6
? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? %18 = 0
? %19 = 0
? %20 = 0
? %21 = 0
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.020s
user	0m0.010s
sys	0m0.009s


'193.170'
************** PARI *****************
Host 193.170.37.83 (193.170.37.83)
Time: Wed Jul 26 07:11:05 2006

Input: f=x^4-6
polred(f);
nf=nfinit(f);
factor(nf.disc);
A=16;
g1=x^4+A*x^2+A^2/2;
g2=x^4-A*x^2-A^2/2;
g3=x^4+A*x^2-A^2/2;
g4=x^4-A*x^2+A^2/2;
nf1=nfinit(g1);
nf2=nfinit(g2);
nf3=nfinit(g3);
nf4=nfinit(g4);
factor(nf1.disc);
factor(nf2.disc);
factor(nf3.disc);
factor(nf4.disc);
nfisisom(f,g1)
nfisisom(f,g2)
nfisisom(f,g3)
nfisisom(f,g4)

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = x^4 - 6
? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? %18 = 0
? %19 = 0
? %20 = 0
? %21 = 0
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.017s
user	0m0.008s
sys	0m0.008s


'193.170'
************** PARI *****************
Host 193.170.37.83 (193.170.37.83)
Time: Wed Jul 26 07:10:56 2006

Input: f=x^4-6
polred(f);
nf=nfinit(f);
factor(nf.disc);
A=14;
g1=x^4+A*x^2+A^2/2;
g2=x^4-A*x^2-A^2/2;
g3=x^4+A*x^2-A^2/2;
g4=x^4-A*x^2+A^2/2;
nf1=nfinit(g1);
nf2=nfinit(g2);
nf3=nfinit(g3);
nf4=nfinit(g4);
factor(nf1.disc);
factor(nf2.disc);
factor(nf3.disc);
factor(nf4.disc);
nfisisom(f,g1)
nfisisom(f,g2)
nfisisom(f,g3)
nfisisom(f,g4)

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = x^4 - 6
? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? %18 = 0
? %19 = 0
? %20 = 0
? %21 = 0
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.111s
user	0m0.013s
sys	0m0.006s


'193.170'
************** PARI *****************
Host 193.170.37.83 (193.170.37.83)
Time: Wed Jul 26 07:10:28 2006

Input: f=x^4-6
polred(f);
nf=nfinit(f);
factor(nf.disc);
A=14;
g1=x^4+A*x^2+A^2/2;
g2=x^4-A*x^2-A^2/2;
g3=x^4+A*x^2-A^2/2;
g4=x^4-A*x^2+A^2/2;
nf1=nfinit(g1);
nf2=nfinit(g2);
nf3=nfinit(g3);
nf4=nfinit(g4);
factor(nf1.disc)
factor(nf2.disc)
factor(nf3.disc)
factor(nf4.disc)
nfisisom(f,g1);
nfisisom(f,g2);
nfisisom(f,g3);
nfisisom(f,g4);

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = x^4 - 6
? ? ? ? ? ? ? ? ? ? ? ? ? %14 = 
[2 9]

[7 2]

? %15 = 
[-1 1]

[2 9]

[3 2]

[7 2]

? %16 = 
[-1 1]

[2 9]

[3 2]

[7 2]

? %17 = 
[2 9]

[7 2]

? ? ? ? ? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.017s
user	0m0.014s
sys	0m0.003s


'193.170'
************** PARI *****************
Host 193.170.37.83 (193.170.37.83)
Time: Wed Jul 26 07:10:03 2006

Input: f=x^4-6
polred(f);
nf=nfinit(f);
factor(nf.disc);
A=14;
g1=x^4+A*x^2+A^2/2;
g2=x^4-A*x^2-A^2/2;
g3=x^4+A*x^2-A^2/2;
g4=x^4-A*x^2+A^2/2;
nf1=nfinit(g1);
nf2=nfinit(g2);
nf3=nfinit(g3);
nf4=nfinit(g4);
factor(nf1.disc)
factor(nf2.disc)
factor(nf3.disc)
factor(nf4.disc)
nfisisom(f,g1)
nfisisom(f,g2)
nfisisom(f,g3)
nfisisom(f,g4)

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = x^4 - 6
? ? ? ? ? ? ? ? ? ? ? ? ? %14 = 
[2 9]

[7 2]

? %15 = 
[-1 1]

[2 9]

[3 2]

[7 2]

? %16 = 
[-1 1]

[2 9]

[3 2]

[7 2]

? %17 = 
[2 9]

[7 2]

? %18 = 0
? %19 = 0
? %20 = 0
? %21 = 0
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.020s
user	0m0.011s
sys	0m0.008s


'193.170'
************** PARI *****************
Host 193.170.37.83 (193.170.37.83)
Time: Wed Jul 26 07:09:49 2006

Input: f=x^4-6
polred(f);
nf=nfinit(f);
factor(nf.disc);
A=12;
g1=x^4+A*x^2+A^2/2;
g2=x^4-A*x^2-A^2/2;
g3=x^4+A*x^2-A^2/2;
g4=x^4-A*x^2+A^2/2;
nf1=nfinit(g1);
nf2=nfinit(g2);
nf3=nfinit(g3);
nf4=nfinit(g4);
factor(nf1.disc)
factor(nf2.disc)
factor(nf3.disc)
factor(nf4.disc)
nfisisom(f,g1)
nfisisom(f,g2)
nfisisom(f,g3)
nfisisom(f,g4)

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = x^4 - 6
? ? ? ? ? ? ? ? ? ? ? ? ? %14 = 
[2 9]

[3 2]

? %15 = 
[-1 1]

[2 9]

[3 2]

? %16 = 
[-1 1]

[2 9]

[3 2]

? %17 = 
[2 9]

[3 2]

? %18 = 0
? %19 = 0
? %20 = 0
? %21 = 0
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.035s
user	0m0.009s
sys	0m0.010s


'193.170'
************** PARI *****************
Host 193.170.37.83 (193.170.37.83)
Time: Wed Jul 26 07:09:29 2006

Input: f=x^4-6
polred(f);
nf=nfinit(f);
factor(nf.disc);
A=12;
g1=x^4+A*x^2+A^2/2;
g2=x^4-A*x^2-A^2/2;
g3=x^4+A*x^2-A^2/2;
g4=x^4-A*x^2+A^2/2;
nf1=nfinit(g1);
nf2=nfinit(g2);
nf3=nfinit(g3);
nf4=nfinit(g4);
factor(nf1.disc);
factor(nf2.disc)
factor(nf3.disc);
factor(nf4.disc)
nfisisom(f,g1)
nfisisom(f,g2)
nfisisom(f,g3)
nfisisom(f,g4)

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = x^4 - 6
? ? ? ? ? ? ? ? ? ? ? ? ? ? %15 = 
[-1 1]

[2 9]

[3 2]

? ? %17 = 
[2 9]

[3 2]

? %18 = 0
? %19 = 0
? %20 = 0
? %21 = 0
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.058s
user	0m0.013s
sys	0m0.006s


'193.170'
************** PARI *****************
Host 193.170.37.83 (193.170.37.83)
Time: Wed Jul 26 07:09:18 2006

Input: f=x^4-6
polred(f);
nf=nfinit(f);
factor(nf.disc);
A=12;
g1=x^4+A*x^2+A^2/2;
g2=x^4-A*x^2-A^2/2;
g3=x^4+A*x^2-A^2/2;
g4=x^4-A*x^2+A^2/2;
nf1=nfinit(g1);
nf2=nfinit(g2);
nf3=nfinit(g3);
nf4=nfinit(g4);
factor(nf1.disc);
factor(nf2.disc);
factor(nf3.disc);
factor(nf4.disc);
nfisisom(f,g1)
nfisisom(f,g2)
nfisisom(f,g3)
nfisisom(f,g4)

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = x^4 - 6
? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? %18 = 0
? %19 = 0
? %20 = 0
? %21 = 0
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.018s
user	0m0.010s
sys	0m0.008s


'193.170'
************** PARI *****************
Host 193.170.37.83 (193.170.37.83)
Time: Wed Jul 26 07:09:09 2006

Input: f=x^4-6
polred(f);
nf=nfinit(f);
factor(nf.disc);
A=10;
g1=x^4+A*x^2+A^2/2;
g2=x^4-A*x^2-A^2/2;
g3=x^4+A*x^2-A^2/2;
g4=x^4-A*x^2+A^2/2;
nf1=nfinit(g1);
nf2=nfinit(g2);
nf3=nfinit(g3);
nf4=nfinit(g4);
factor(nf1.disc);
factor(nf2.disc);
factor(nf3.disc);
factor(nf4.disc);
nfisisom(f,g1)
nfisisom(f,g2)
nfisisom(f,g3)
nfisisom(f,g4)

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = x^4 - 6
? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? %18 = 0
? %19 = 0
? %20 = 0
? %21 = 0
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.017s
user	0m0.011s
sys	0m0.005s


'193.170'
************** PARI *****************
Host 193.170.37.83 (193.170.37.83)
Time: Wed Jul 26 07:09:01 2006

Input: f=x^4-6
polred(f);
nf=nfinit(f);
factor(nf.disc);
A=8;
g1=x^4+A*x^2+A^2/2;
g2=x^4-A*x^2-A^2/2;
g3=x^4+A*x^2-A^2/2;
g4=x^4-A*x^2+A^2/2;
nf1=nfinit(g1);
nf2=nfinit(g2);
nf3=nfinit(g3);
nf4=nfinit(g4);
factor(nf1.disc);
factor(nf2.disc);
factor(nf3.disc);
factor(nf4.disc);
nfisisom(f,g1)
nfisisom(f,g2)
nfisisom(f,g3)
nfisisom(f,g4)

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = x^4 - 6
? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? %18 = 0
? %19 = 0
? %20 = 0
? %21 = 0
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.017s
user	0m0.011s
sys	0m0.005s


'193.170'
************** PARI *****************
Host 193.170.37.83 (193.170.37.83)
Time: Wed Jul 26 07:08:51 2006

Input: f=x^4-6
polred(f);
nf=nfinit(f);
factor(nf.disc);
A=6;
g1=x^4+A*x^2+A^2/2;
g2=x^4-A*x^2-A^2/2;
g3=x^4+A*x^2-A^2/2;
g4=x^4-A*x^2+A^2/2;
nf1=nfinit(g1);
nf2=nfinit(g2);
nf3=nfinit(g3);
nf4=nfinit(g4);
factor(nf1.disc);
factor(nf2.disc);
factor(nf3.disc);
factor(nf4.disc);
nfisisom(f,g1)
nfisisom(f,g2)
nfisisom(f,g3)
nfisisom(f,g4)

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = x^4 - 6
? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? %18 = 0
? %19 = 0
? %20 = 0
? %21 = 0
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.018s
user	0m0.013s
sys	0m0.006s


'193.170'
************** PARI *****************
Host 193.170.37.83 (193.170.37.83)
Time: Wed Jul 26 07:08:44 2006

Input: f=x^4-6
polred(f);
nf=nfinit(f);
factor(nf.disc);
A=-6;
g1=x^4+A*x^2+A^2/2;
g2=x^4-A*x^2-A^2/2;
g3=x^4+A*x^2-A^2/2;
g4=x^4-A*x^2+A^2/2;
nf1=nfinit(g1);
nf2=nfinit(g2);
nf3=nfinit(g3);
nf4=nfinit(g4);
factor(nf1.disc);
factor(nf2.disc);
factor(nf3.disc);
factor(nf4.disc);
nfisisom(f,g1)
nfisisom(f,g2)
nfisisom(f,g3)
nfisisom(f,g4)

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = x^4 - 6
? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? %18 = 0
? %19 = 0
? %20 = 0
? %21 = 0
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.273s
user	0m0.013s
sys	0m0.005s


'193.170'
************** PARI *****************
Host 193.170.37.83 (193.170.37.83)
Time: Wed Jul 26 07:08:34 2006

Input: f=x^4-6
polred(f);
nf=nfinit(f);
factor(nf.disc);
A=-4;
g1=x^4+A*x^2+A^2/2;
g2=x^4-A*x^2-A^2/2;
g3=x^4+A*x^2-A^2/2;
g4=x^4-A*x^2+A^2/2;
nf1=nfinit(g1);
nf2=nfinit(g2);
nf3=nfinit(g3);
nf4=nfinit(g4);
factor(nf1.disc);
factor(nf2.disc);
factor(nf3.disc);
factor(nf4.disc);
nfisisom(f,g1)
nfisisom(f,g2)
nfisisom(f,g3)
nfisisom(f,g4)

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = x^4 - 6
? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? %18 = 0
? %19 = 0
? %20 = 0
? %21 = 0
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.016s
user	0m0.011s
sys	0m0.005s


'193.170'
************** PARI *****************
Host 193.170.37.83 (193.170.37.83)
Time: Wed Jul 26 07:08:27 2006

Input: f=x^4-6
polred(f);
nf=nfinit(f);
factor(nf.disc);
A=-2;
g1=x^4+A*x^2+A^2/2;
g2=x^4-A*x^2-A^2/2;
g3=x^4+A*x^2-A^2/2;
g4=x^4-A*x^2+A^2/2;
nf1=nfinit(g1);
nf2=nfinit(g2);
nf3=nfinit(g3);
nf4=nfinit(g4);
factor(nf1.disc);
factor(nf2.disc);
factor(nf3.disc);
factor(nf4.disc);
nfisisom(f,g1)
nfisisom(f,g2)
nfisisom(f,g3)
nfisisom(f,g4)

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = x^4 - 6
? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? %18 = 0
? %19 = 0
? %20 = 0
? %21 = 0
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.064s
user	0m0.011s
sys	0m0.005s


'193.170'
************** PARI *****************
Host 193.170.37.83 (193.170.37.83)
Time: Wed Jul 26 07:08:08 2006

Input: f=x^4-6
polred(f);
nf=nfinit(f);
factor(nf.disc);
A=-44;
g1=x^4+A*x^2+A^2/2;
g2=x^4-A*x^2-A^2/2;
g3=x^4+A*x^2-A^2/2;
g4=x^4-A*x^2+A^2/2;
nf1=nfinit(g1);
nf2=nfinit(g2)
nf3=nfinit(g3);
nf4=nfinit(g4)
factor(nf1.disc);
factor(nf2.disc);
factor(nf3.disc);
factor(nf4.disc);
nfisisom(f,g1)
nfisisom(f,g2)
nfisisom(f,g3)
nfisisom(f,g4)

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = x^4 - 6
? ? ? ? ? ? ? ? ? ? %11 = [x^4 + 44*x^2 - 968, [2, 1], -557568, 968, [[1, 1.7320508075688772935274463415058723669, -5.4820214230936429485194608254230802233, -4.0131182098855872672625221821856992525; 1, 1.7320508075688772935274463415058723669, 5.4820214230936429485194608254230802233, 4.0131182098855872672625221821856992525; 1, -1.7320508075688772935274463415058723669 + 0.E-39*I, 0.E-38 + 2.8377030999133172580306931790731170238*I, 0.E-38 - 7.7527490457588849041629151053839403122*I], [1, 1.7320508075688772935274463415058723669, -5.4820214230936429485194608254230802233, -4.0131182098855872672625221821856992525; 1, 1.7320508075688772935274463415058723669, 5.4820214230936429485194608254230802233, 4.0131182098855872672625221821856992525; 1, -1.7320508075688772935274463415058723669, 2.8377030999133172580306931790731170238, -7.7527490457588849041629151053839403122; 1, -1.7320508075688772935274463415058723669, -2.8377030999133172580306931790731170238, 7.7527490457588849041629151053839403122], 0, [4, 0, 0, 0; 0, 12, 0, 0; 0, 0, 44, 88; 0, 0, 88, -88], [-264, -132, 0, 0; 0, -44, 0, 0; 0, 0, -12, -4; 0, 0, 0, -4], [-66, 0, 0, 0; 0, -22, 0, 0; 0, 0, -2, -2; 0, 0, -2, 1], [66, [0, 0, 66, 66; 0, 0, 44, 22; 4, 6, 0, 0; 1, 3, 0, 0]]], [-4.0131182098855872672625221821856992525, 4.0131182098855872672625221821856992525, 0.E-38 - 7.7527490457588849041629151053839403122*I], [1, 1/22*x^2 + 1, 1/44*x^3 + x, x], [1, 0, -22, 0; 0, 0, 22, 0; 0, 0, 0, 44; 0, 1, 0, -44], [1, 0, 0, 0, 0, 3, 0, 0, 0, 0, 11, 22, 0, 0, 22, -22; 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 11, 0, 0, 0, 0, 22; 0, 0, 1, 0, 0, 0, 1, 2, 1, 1, 0, 0, 0, 2, 0, 0; 0, 0, 0, 1, 0, 0, 1, -1, 0, 1, 0, 0, 1, -1, 0, 0]]
? ? %13 = [x^4 + 44*x^2 + 968, [0, 2], 61952, 968, [[1, 0.E-39 + 1.0000000000000000000000000000000000000*I, -1.5093623133800654055633752499315538832 + 3.6439229674969835685280960709955670516*I, 3.6439229674969835685280960709955670515 + 1.5093623133800654055633752499315538832*I; 1, 0.E-39 + 1.0000000000000000000000000000000000000*I, 1.5093623133800654055633752499315538832 - 3.6439229674969835685280960709955670516*I, -3.6439229674969835685280960709955670515 - 1.5093623133800654055633752499315538832*I], [1, 1.0000000000000000000000000000000000000, 2.1345606541169181629647208210640131683, 5.1532852808770489740914713209271209347; 1, -1.0000000000000000000000000000000000000, -5.1532852808770489740914713209271209347, 2.1345606541169181629647208210640131683; 1, 1.0000000000000000000000000000000000000, -2.1345606541169181629647208210640131683, -5.1532852808770489740914713209271209347; 1, -1.0000000000000000000000000000000000000, 5.1532852808770489740914713209271209347, -2.1345606541169181629647208210640131683], 0, [4, 0, 0, 0; 0, -4, 0, 0; 0, 0, -44, -44; 0, 0, -44, 44], [88, 44, 0, 0; 0, 44, 0, 0; 0, 0, 4, 0; 0, 0, 0, 4], [22, 0, 0, 0; 0, -22, 0, 0; 0, 0, -1, -1; 0, 0, -1, 1], [22, [0, 0, -22, 0; 0, 0, 0, 22; 1, 1, 0, 0; 1, -1, 0, 0]]], [2.1345606541169181629647208210640131683 + 5.1532852808770489740914713209271209347*I, -2.1345606541169181629647208210640131683 - 5.1532852808770489740914713209271209347*I], [1, 1/22*x^2 + 1, 1/44*x^3 + x, -1/44*x^3], [1, 0, -22, 0; 0, 0, 22, 0; 0, 1, 0, 0; 0, 1, 0, -44], [1, 0, 0, 0, 0, -1, 0, 0, 0, 0, -11, -11, 0, 0, -11, 11; 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, -11, 11, 0, 0, 11, 11; 0, 0, 1, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 1, 0, 0; 0, 0, 0, 1, 0, 0, -1, 0, 0, -1, 0, 0, 1, 0, 0, 0]]
? ? ? ? ? %18 = 0
? %19 = 0
? %20 = 0
? %21 = 0
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.061s
user	0m0.012s
sys	0m0.007s


'193.170'
************** PARI *****************
Host 193.170.37.83 (193.170.37.83)
Time: Wed Jul 26 07:07:56 2006

Input: f=x^4-6
polred(f);
nf=nfinit(f);
factor(nf.disc);
A=-44;
g1=x^4+A*x^2+A^2/2;
g2=x^4-A*x^2-A^2/2;
g3=x^4+A*x^2-A^2/2;
g4=x^4-A*x^2+A^2/2;
nf1=nfinit(g1);
nf2=nfinit(g2);
nf3=nfinit(g1);
nf4=nfinit(g2);
factor(nf1.disc);
factor(nf2.disc);
factor(nf3.disc);
factor(nf4.disc);
nfisisom(f,g1)
nfisisom(f,g2)
nfisisom(f,g3)
nfisisom(f,g4)

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = x^4 - 6
? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? %18 = 0
? %19 = 0
? %20 = 0
? %21 = 0
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.363s
user	0m0.013s
sys	0m0.005s


'193.170'
************** PARI *****************
Host 193.170.37.83 (193.170.37.83)
Time: Wed Jul 26 07:07:48 2006

Input: f=x^4-6
polred(f);
nf=nfinit(f);
factor(nf.disc);
A=-14;
g1=x^4+A*x^2+A^2/2;
g2=x^4-A*x^2-A^2/2;
g3=x^4+A*x^2-A^2/2;
g4=x^4-A*x^2+A^2/2;
nf1=nfinit(g1);
nf2=nfinit(g2);
nf3=nfinit(g1);
nf4=nfinit(g2);
factor(nf1.disc);
factor(nf2.disc);
factor(nf3.disc);
factor(nf4.disc);
nfisisom(f,g1)
nfisisom(f,g2)
nfisisom(f,g3)
nfisisom(f,g4)

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = x^4 - 6
? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? %18 = 0
? %19 = 0
? %20 = 0
? %21 = 0
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.018s
user	0m0.012s
sys	0m0.004s


'193.170'
************** PARI *****************
Host 193.170.37.83 (193.170.37.83)
Time: Wed Jul 26 07:07:40 2006

Input: f=x^4-6
polred(f);
nf=nfinit(f);
factor(nf.disc);
A=-12;
g1=x^4+A*x^2+A^2/2;
g2=x^4-A*x^2-A^2/2;
g3=x^4+A*x^2-A^2/2;
g4=x^4-A*x^2+A^2/2;
nf1=nfinit(g1);
nf2=nfinit(g2);
nf3=nfinit(g1);
nf4=nfinit(g2);
factor(nf1.disc);
factor(nf2.disc);
factor(nf3.disc);
factor(nf4.disc);
nfisisom(f,g1)
nfisisom(f,g2)
nfisisom(f,g3)
nfisisom(f,g4)

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = x^4 - 6
? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? %18 = 0
? %19 = 0
? %20 = 0
? %21 = 0
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.042s
user	0m0.014s
sys	0m0.004s


'193.170'
************** PARI *****************
Host 193.170.37.83 (193.170.37.83)
Time: Wed Jul 26 07:07:34 2006

Input: f=x^4-6
polred(f);
nf=nfinit(f);
factor(nf.disc);
A=-10;
g1=x^4+A*x^2+A^2/2;
g2=x^4-A*x^2-A^2/2;
g3=x^4+A*x^2-A^2/2;
g4=x^4-A*x^2+A^2/2;
nf1=nfinit(g1);
nf2=nfinit(g2);
nf3=nfinit(g1);
nf4=nfinit(g2);
factor(nf1.disc);
factor(nf2.disc);
factor(nf3.disc);
factor(nf4.disc);
nfisisom(f,g1)
nfisisom(f,g2)
nfisisom(f,g3)
nfisisom(f,g4)

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = x^4 - 6
? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? %18 = 0
? %19 = 0
? %20 = 0
? %21 = 0
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.018s
user	0m0.012s
sys	0m0.005s


'193.170'
************** PARI *****************
Host 193.170.37.83 (193.170.37.83)
Time: Wed Jul 26 07:07:25 2006

Input: f=x^4-6
polred(f);
nf=nfinit(f);
factor(nf.disc);
A=-8;
g1=x^4+A*x^2+A^2/2;
g2=x^4-A*x^2-A^2/2;
g3=x^4+A*x^2-A^2/2;
g4=x^4-A*x^2+A^2/2;
nf1=nfinit(g1);
nf2=nfinit(g2);
nf3=nfinit(g1);
nf4=nfinit(g2);
factor(nf1.disc);
factor(nf2.disc);
factor(nf3.disc);
factor(nf4.disc);
nfisisom(f,g1)
nfisisom(f,g2)
nfisisom(f,g3)
nfisisom(f,g4)

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = x^4 - 6
? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? %18 = 0
? %19 = 0
? %20 = 0
? %21 = 0
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.017s
user	0m0.008s
sys	0m0.010s


'193.170'
************** PARI *****************
Host 193.170.37.83 (193.170.37.83)
Time: Wed Jul 26 07:07:17 2006

Input: f=x^4-6
polred(f);
nf=nfinit(f);
factor(nf.disc);
A=-6;
g1=x^4+A*x^2+A^2/2;
g2=x^4-A*x^2-A^2/2;
g3=x^4+A*x^2-A^2/2;
g4=x^4-A*x^2+A^2/2;
nf1=nfinit(g1);
nf2=nfinit(g2);
nf3=nfinit(g1);
nf4=nfinit(g2);
factor(nf1.disc);
factor(nf2.disc);
factor(nf3.disc);
factor(nf4.disc);
nfisisom(f,g1)
nfisisom(f,g2)
nfisisom(f,g3)
nfisisom(f,g4)

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = x^4 - 6
? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? %18 = 0
? %19 = 0
? %20 = 0
? %21 = 0
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.035s
user	0m0.011s
sys	0m0.006s


'193.170'
************** PARI *****************
Host 193.170.37.83 (193.170.37.83)
Time: Wed Jul 26 07:07:11 2006

Input: f=x^4-6
polred(f);
nf=nfinit(f);
factor(nf.disc);
A=-4;
g1=x^4+A*x^2+A^2/2;
g2=x^4-A*x^2-A^2/2;
g3=x^4+A*x^2-A^2/2;
g4=x^4-A*x^2+A^2/2;
nf1=nfinit(g1);
nf2=nfinit(g2);
nf3=nfinit(g1);
nf4=nfinit(g2);
factor(nf1.disc);
factor(nf2.disc);
factor(nf3.disc);
factor(nf4.disc);
nfisisom(f,g1)
nfisisom(f,g2)
nfisisom(f,g3)
nfisisom(f,g4)

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = x^4 - 6
? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? %18 = 0
? %19 = 0
? %20 = 0
? %21 = 0
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.020s
user	0m0.012s
sys	0m0.005s


'193.170'
************** PARI *****************
Host 193.170.37.83 (193.170.37.83)
Time: Wed Jul 26 07:07:05 2006

Input: f=x^4-6
polred(f);
nf=nfinit(f);
factor(nf.disc);
A=-2;
g1=x^4+A*x^2+A^2/2;
g2=x^4-A*x^2-A^2/2;
g3=x^4+A*x^2-A^2/2;
g4=x^4-A*x^2+A^2/2;
nf1=nfinit(g1);
nf2=nfinit(g2);
nf3=nfinit(g1);
nf4=nfinit(g2);
factor(nf1.disc);
factor(nf2.disc);
factor(nf3.disc);
factor(nf4.disc);
nfisisom(f,g1)
nfisisom(f,g2)
nfisisom(f,g3)
nfisisom(f,g4)

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = x^4 - 6
? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? %18 = 0
? %19 = 0
? %20 = 0
? %21 = 0
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.016s
user	0m0.011s
sys	0m0.005s


'193.170'
************** PARI *****************
Host 193.170.37.83 (193.170.37.83)
Time: Wed Jul 26 07:06:57 2006

Input: f=x^4-6
polred(f);
nf=nfinit(f);
factor(nf.disc)
A=-2;
g1=x^4+A*x^2+A^2/2;
g2=x^4-A*x^2-A^2/2;
g3=x^4+A*x^2-A^2/2;
g4=x^4-A*x^2+A^2/2;
nf1=nfinit(g1);
nf2=nfinit(g2);
nf3=nfinit(g1);
nf4=nfinit(g2);
factor(nf1.disc);
factor(nf2.disc);
factor(nf3.disc);
factor(nf4.disc);
nfisisom(f,g1)
nfisisom(f,g2)
nfisisom(f,g3)
nfisisom(f,g4)

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = x^4 - 6
? ? ? %4 = 
[-1 1]

[2 11]

[3 3]

? ? ? ? ? ? ? ? ? ? ? ? ? ? %18 = 0
? %19 = 0
? %20 = 0
? %21 = 0
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.016s
user	0m0.010s
sys	0m0.006s


'193.170'
************** PARI *****************
Host 193.170.37.83 (193.170.37.83)
Time: Wed Jul 26 07:06:45 2006

Input: f=x^4-6
polred(f);
nf=nfinit(f);
factor(nf.disc)
A=44;
g1=x^4+A*x^2+A^2/2;
g2=x^4-A*x^2-A^2/2;
g3=x^4+A*x^2-A^2/2;
g4=x^4-A*x^2+A^2/2;
nf1=nfinit(g1);
nf2=nfinit(g2);
nf3=nfinit(g1);
nf4=nfinit(g2);
factor(nf1.disc);
factor(nf2.disc);
factor(nf3.disc);
factor(nf4.disc);
nfisisom(f,g1)
nfisisom(f,g2)
nfisisom(f,g3)
nfisisom(f,g4)

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = x^4 - 6
? ? ? %4 = 
[-1 1]

[2 11]

[3 3]

? ? ? ? ? ? ? ? ? ? ? ? ? ? %18 = 0
? %19 = 0
? %20 = 0
? %21 = 0
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.064s
user	0m0.014s
sys	0m0.006s


'193.170'
************** PARI *****************
Host 193.170.37.83 (193.170.37.83)
Time: Wed Jul 26 07:06:26 2006

Input: f=x^4-6
polred(f);
nf=nfinit(f);
fact6r(nf.disc);
A=42;
g1=x^4+A*x^2+A^2/2;
g2=x^4-A*x^2-A^2/2;
g3=x^4+A*x^2-A^2/2;
g4=x^4-A*x^2+A^2/2;
nf1=nfinit(g1);
nf2=nfinit(g2);
nf3=nfinit(g1);
nf4=nfinit(g2);
factor(nf1.disc);
factor(nf2.disc);
factor(nf3.disc);
factor(nf4.disc);
nfisisom(f,g1)
nfisisom(f,g2)
nfisisom(f,g3)
nfisisom(f,g4)

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = x^4 - 6
? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? %17 = 0
? %18 = 0
? %19 = 0
? %20 = 0
? 
Goodbye!

Errors/timing (if any):

  ***   expected character: ',' instead of: fact6r(nf.disc);
                                                     ^-------

Timing:
real	0m0.018s
user	0m0.009s
sys	0m0.009s


'193.170'
************** PARI *****************
Host 193.170.37.83 (193.170.37.83)
Time: Wed Jul 26 07:06:18 2006

Input: f=x^4-6
polred(f);
nf=nfinit(f);
fact6r(nf.disc);
A=40;
g1=x^4+A*x^2+A^2/2;
g2=x^4-A*x^2-A^2/2;
g3=x^4+A*x^2-A^2/2;
g4=x^4-A*x^2+A^2/2;
nf1=nfinit(g1);
nf2=nfinit(g2);
nf3=nfinit(g1);
nf4=nfinit(g2);
factor(nf1.disc);
factor(nf2.disc);
factor(nf3.disc);
factor(nf4.disc);
nfisisom(f,g1)
nfisisom(f,g2)
nfisisom(f,g3)
nfisisom(f,g4)

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = x^4 - 6
? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? %17 = 0
? %18 = 0
? %19 = 0
? %20 = 0
? 
Goodbye!

Errors/timing (if any):

  ***   expected character: ',' instead of: fact6r(nf.disc);
                                                     ^-------

Timing:
real	0m0.018s
user	0m0.011s
sys	0m0.007s


'193.170'
************** PARI *****************
Host 193.170.37.83 (193.170.37.83)
Time: Wed Jul 26 07:06:10 2006

Input: f=x^4-6
polred(f);
nf=nfinit(f);
fact6r(nf.disc);
A=38;
g1=x^4+A*x^2+A^2/2;
g2=x^4-A*x^2-A^2/2;
g3=x^4+A*x^2-A^2/2;
g4=x^4-A*x^2+A^2/2;
nf1=nfinit(g1);
nf2=nfinit(g2);
nf3=nfinit(g1);
nf4=nfinit(g2);
factor(nf1.disc);
factor(nf2.disc);
factor(nf3.disc);
factor(nf4.disc);
nfisisom(f,g1)
nfisisom(f,g2)
nfisisom(f,g3)
nfisisom(f,g4)

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = x^4 - 6
? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? %17 = 0
? %18 = 0
? %19 = 0
? %20 = 0
? 
Goodbye!

Errors/timing (if any):

  ***   expected character: ',' instead of: fact6r(nf.disc);
                                                     ^-------

Timing:
real	0m0.097s
user	0m0.014s
sys	0m0.005s


'193.170'
************** PARI *****************
Host 193.170.37.83 (193.170.37.83)
Time: Wed Jul 26 07:06:01 2006

Input: f=x^4-6
polred(f);
nf=nfinit(f);
fact6r(nf.disc);
A=36;
g1=x^4+A*x^2+A^2/2;
g2=x^4-A*x^2-A^2/2;
g3=x^4+A*x^2-A^2/2;
g4=x^4-A*x^2+A^2/2;
nf1=nfinit(g1);
nf2=nfinit(g2);
nf3=nfinit(g1);
nf4=nfinit(g2);
factor(nf1.disc);
factor(nf2.disc);
factor(nf3.disc);
factor(nf4.disc);
nfisisom(f,g1)
nfisisom(f,g2)
nfisisom(f,g3)
nfisisom(f,g4)

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = x^4 - 6
? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? %17 = 0
? %18 = 0
? %19 = 0
? %20 = 0
? 
Goodbye!

Errors/timing (if any):

  ***   expected character: ',' instead of: fact6r(nf.disc);
                                                     ^-------

Timing:
real	0m0.018s
user	0m0.013s
sys	0m0.005s


'193.170'
************** PARI *****************
Host 193.170.37.83 (193.170.37.83)
Time: Wed Jul 26 07:05:53 2006

Input: f=x^4-6
polred(f);
nf=nfinit(f);
fact6r(nf.disc);
A=34;
g1=x^4+A*x^2+A^2/2;
g2=x^4-A*x^2-A^2/2;
g3=x^4+A*x^2-A^2/2;
g4=x^4-A*x^2+A^2/2;
nf1=nfinit(g1);
nf2=nfinit(g2);
nf3=nfinit(g1);
nf4=nfinit(g2);
factor(nf1.disc);
factor(nf2.disc);
factor(nf3.disc);
factor(nf4.disc);
nfisisom(f,g1)
nfisisom(f,g2)
nfisisom(f,g3)
nfisisom(f,g4)

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = x^4 - 6
? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? %17 = 0
? %18 = 0
? %19 = 0
? %20 = 0
? 
Goodbye!

Errors/timing (if any):

  ***   expected character: ',' instead of: fact6r(nf.disc);
                                                     ^-------

Timing:
real	0m0.107s
user	0m0.014s
sys	0m0.004s


'193.170'
************** PARI *****************
Host 193.170.37.83 (193.170.37.83)
Time: Wed Jul 26 07:05:47 2006

Input: f=x^4-6
polred(f);
nf=nfinit(f);
fact6r(nf.disc);
A=32;
g1=x^4+A*x^2+A^2/2;
g2=x^4-A*x^2-A^2/2;
g3=x^4+A*x^2-A^2/2;
g4=x^4-A*x^2+A^2/2;
nf1=nfinit(g1);
nf2=nfinit(g2);
nf3=nfinit(g1);
nf4=nfinit(g2);
factor(nf1.disc);
factor(nf2.disc);
factor(nf3.disc);
factor(nf4.disc);
nfisisom(f,g1)
nfisisom(f,g2)
nfisisom(f,g3)
nfisisom(f,g4)

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = x^4 - 6
? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? %17 = 0
? %18 = 0
? %19 = 0
? %20 = 0
? 
Goodbye!

Errors/timing (if any):

  ***   expected character: ',' instead of: fact6r(nf.disc);
                                                     ^-------

Timing:
real	0m0.017s
user	0m0.009s
sys	0m0.009s


'193.170'
************** PARI *****************
Host 193.170.37.83 (193.170.37.83)
Time: Wed Jul 26 07:05:40 2006

Input: f=x^4-6
polred(f);
nf=nfinit(f);
fact6r(nf.disc);
A=30;
g1=x^4+A*x^2+A^2/2;
g2=x^4-A*x^2-A^2/2;
g3=x^4+A*x^2-A^2/2;
g4=x^4-A*x^2+A^2/2;
nf1=nfinit(g1);
nf2=nfinit(g2);
nf3=nfinit(g1);
nf4=nfinit(g2);
factor(nf1.disc);
factor(nf2.disc);
factor(nf3.disc);
factor(nf4.disc);
nfisisom(f,g1)
nfisisom(f,g2)
nfisisom(f,g3)
nfisisom(f,g4)

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = x^4 - 6
? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? %17 = 0
? %18 = 0
? %19 = 0
? %20 = 0
? 
Goodbye!

Errors/timing (if any):

  ***   expected character: ',' instead of: fact6r(nf.disc);
                                                     ^-------

Timing:
real	0m0.037s
user	0m0.013s
sys	0m0.005s


'193.170'
************** PARI *****************
Host 193.170.37.83 (193.170.37.83)
Time: Wed Jul 26 07:05:32 2006

Input: f=x^4-6
polred(f);
nf=nfinit(f);
fact6r(nf.disc);
A=28;
g1=x^4+A*x^2+A^2/2;
g2=x^4-A*x^2-A^2/2;
g3=x^4+A*x^2-A^2/2;
g4=x^4-A*x^2+A^2/2;
nf1=nfinit(g1);
nf2=nfinit(g2);
nf3=nfinit(g1);
nf4=nfinit(g2);
factor(nf1.disc);
factor(nf2.disc);
factor(nf3.disc);
factor(nf4.disc);
nfisisom(f,g1)
nfisisom(f,g2)
nfisisom(f,g3)
nfisisom(f,g4)

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = x^4 - 6
? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? %17 = 0
? %18 = 0
? %19 = 0
? %20 = 0
? 
Goodbye!

Errors/timing (if any):

  ***   expected character: ',' instead of: fact6r(nf.disc);
                                                     ^-------

Timing:
real	0m0.018s
user	0m0.011s
sys	0m0.007s


'193.170'
************** PARI *****************
Host 193.170.37.83 (193.170.37.83)
Time: Wed Jul 26 07:05:24 2006

Input: f=x^4-6
polred(f);
nf=nfinit(f);
fact6r(nf.disc);
A=26;
g1=x^4+A*x^2+A^2/2;
g2=x^4-A*x^2-A^2/2;
g3=x^4+A*x^2-A^2/2;
g4=x^4-A*x^2+A^2/2;
nf1=nfinit(g1);
nf2=nfinit(g2);
nf3=nfinit(g1);
nf4=nfinit(g2);
factor(nf1.disc);
factor(nf2.disc);
factor(nf3.disc);
factor(nf4.disc);
nfisisom(f,g1)
nfisisom(f,g2)
nfisisom(f,g3)
nfisisom(f,g4)

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = x^4 - 6
? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? %17 = 0
? %18 = 0
? %19 = 0
? %20 = 0
? 
Goodbye!

Errors/timing (if any):

  ***   expected character: ',' instead of: fact6r(nf.disc);
                                                     ^-------

Timing:
real	0m0.075s
user	0m0.015s
sys	0m0.004s


'193.170'
************** PARI *****************
Host 193.170.37.83 (193.170.37.83)
Time: Wed Jul 26 07:05:16 2006

Input: f=x^4-6
polred(f);
nf=nfinit(f);
fact6r(nf.disc);
A=24;
g1=x^4+A*x^2+A^2/2;
g2=x^4-A*x^2-A^2/2;
g3=x^4+A*x^2-A^2/2;
g4=x^4-A*x^2+A^2/2;
nf1=nfinit(g1);
nf2=nfinit(g2);
nf3=nfinit(g1);
nf4=nfinit(g2);
factor(nf1.disc);
factor(nf2.disc);
factor(nf3.disc);
factor(nf4.disc);
nfisisom(f,g1)
nfisisom(f,g2)
nfisisom(f,g3)
nfisisom(f,g4)

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = x^4 - 6
? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? %17 = 0
? %18 = 0
? %19 = 0
? %20 = 0
? 
Goodbye!

Errors/timing (if any):

  ***   expected character: ',' instead of: fact6r(nf.disc);
                                                     ^-------

Timing:
real	0m0.017s
user	0m0.011s
sys	0m0.006s


'193.170'
************** PARI *****************
Host 193.170.37.83 (193.170.37.83)
Time: Wed Jul 26 07:05:10 2006

Input: f=x^4-6
polred(f);
nf=nfinit(f);
fact6r(nf.disc);
A=22;
g1=x^4+A*x^2+A^2/2;
g2=x^4-A*x^2-A^2/2;
g3=x^4+A*x^2-A^2/2;
g4=x^4-A*x^2+A^2/2;
nf1=nfinit(g1);
nf2=nfinit(g2);
nf3=nfinit(g1);
nf4=nfinit(g2);
factor(nf1.disc);
factor(nf2.disc);
factor(nf3.disc);
factor(nf4.disc);
nfisisom(f,g1)
nfisisom(f,g2)
nfisisom(f,g3)
nfisisom(f,g4)

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = x^4 - 6
? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? %17 = 0
? %18 = 0
? %19 = 0
? %20 = 0
? 
Goodbye!

Errors/timing (if any):

  ***   expected character: ',' instead of: fact6r(nf.disc);
                                                     ^-------

Timing:
real	0m0.017s
user	0m0.012s
sys	0m0.006s


'193.170'
************** PARI *****************
Host 193.170.37.83 (193.170.37.83)
Time: Wed Jul 26 07:05:02 2006

Input: f=x^4-6
polred(f);
nf=nfinit(f);
fact6r(nf.disc);
A=20;
g1=x^4+A*x^2+A^2/2;
g2=x^4-A*x^2-A^2/2;
g3=x^4+A*x^2-A^2/2;
g4=x^4-A*x^2+A^2/2;
nf1=nfinit(g1);
nf2=nfinit(g2);
nf3=nfinit(g1);
nf4=nfinit(g2);
factor(nf1.disc);
factor(nf2.disc);
factor(nf3.disc);
factor(nf4.disc);
nfisisom(f,g1)
nfisisom(f,g2)
nfisisom(f,g3)
nfisisom(f,g4)

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = x^4 - 6
? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? %17 = 0
? %18 = 0
? %19 = 0
? %20 = 0
? 
Goodbye!

Errors/timing (if any):

  ***   expected character: ',' instead of: fact6r(nf.disc);
                                                     ^-------

Timing:
real	0m0.018s
user	0m0.012s
sys	0m0.005s


'193.170'
************** PARI *****************
Host 193.170.37.83 (193.170.37.83)
Time: Wed Jul 26 07:04:52 2006

Input: f=x^4-6
polred(f);
nf=nfinit(f);
fact6r(nf.disc);
A=18;
g1=x^4+A*x^2+A^2/2;
g2=x^4-A*x^2-A^2/2;
g3=x^4+A*x^2-A^2/2;
g4=x^4-A*x^2+A^2/2;
nf1=nfinit(g1);
nf2=nfinit(g2);
nf3=nfinit(g1);
nf4=nfinit(g2);
factor(nf1.disc);
factor(nf2.disc);
factor(nf3.disc);
factor(nf4.disc);
nfisisom(f,g1)
nfisisom(f,g2)
nfisisom(f,g3)
nfisisom(f,g4)

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = x^4 - 6
? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? %17 = 0
? %18 = 0
? %19 = 0
? %20 = 0
? 
Goodbye!

Errors/timing (if any):

  ***   expected character: ',' instead of: fact6r(nf.disc);
                                                     ^-------

Timing:
real	0m0.093s
user	0m0.010s
sys	0m0.007s


'193.170'
************** PARI *****************
Host 193.170.37.83 (193.170.37.83)
Time: Wed Jul 26 07:04:44 2006

Input: f=x^4-6
polred(f);
nf=nfinit(f);
fact6r(nf.disc);
A=16;
g1=x^4+A*x^2+A^2/2;
g2=x^4-A*x^2-A^2/2;
g3=x^4+A*x^2-A^2/2;
g4=x^4-A*x^2+A^2/2;
nf1=nfinit(g1);
nf2=nfinit(g2);
nf3=nfinit(g1);
nf4=nfinit(g2);
factor(nf1.disc);
factor(nf2.disc);
factor(nf3.disc);
factor(nf4.disc);
nfisisom(f,g1)
nfisisom(f,g2)
nfisisom(f,g3)
nfisisom(f,g4)

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = x^4 - 6
? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? %17 = 0
? %18 = 0
? %19 = 0
? %20 = 0
? 
Goodbye!

Errors/timing (if any):

  ***   expected character: ',' instead of: fact6r(nf.disc);
                                                     ^-------

Timing:
real	0m0.016s
user	0m0.011s
sys	0m0.005s


'193.170'
************** PARI *****************
Host 193.170.37.83 (193.170.37.83)
Time: Wed Jul 26 07:04:35 2006

Input: f=x^4-6
polred(f);
nf=nfinit(f);
fact6r(nf.disc);
A=14;
g1=x^4+A*x^2+A^2/2;
g2=x^4-A*x^2-A^2/2;
g3=x^4+A*x^2-A^2/2;
g4=x^4-A*x^2+A^2/2;
nf1=nfinit(g1);
nf2=nfinit(g2);
nf3=nfinit(g1);
nf4=nfinit(g2);
factor(nf1.disc);
factor(nf2.disc);
factor(nf3.disc);
factor(nf4.disc);
nfisisom(f,g1)
nfisisom(f,g2)
nfisisom(f,g3)
nfisisom(f,g4)

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = x^4 - 6
? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? %17 = 0
? %18 = 0
? %19 = 0
? %20 = 0
? 
Goodbye!

Errors/timing (if any):

  ***   expected character: ',' instead of: fact6r(nf.disc);
                                                     ^-------

Timing:
real	0m0.017s
user	0m0.009s
sys	0m0.008s


'193.170'
************** PARI *****************
Host 193.170.37.83 (193.170.37.83)
Time: Wed Jul 26 07:04:28 2006

Input: f=x^4-6
polred(f);
nf=nfinit(f);
fact6r(nf.disc);
A=12;
g1=x^4+A*x^2+A^2/2;
g2=x^4-A*x^2-A^2/2;
g3=x^4+A*x^2-A^2/2;
g4=x^4-A*x^2+A^2/2;
nf1=nfinit(g1);
nf2=nfinit(g2);
nf3=nfinit(g1);
nf4=nfinit(g2);
factor(nf1.disc);
factor(nf2.disc);
factor(nf3.disc);
factor(nf4.disc);
nfisisom(f,g1)
nfisisom(f,g2)
nfisisom(f,g3)
nfisisom(f,g4)

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = x^4 - 6
? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? %17 = 0
? %18 = 0
? %19 = 0
? %20 = 0
? 
Goodbye!

Errors/timing (if any):

  ***   expected character: ',' instead of: fact6r(nf.disc);
                                                     ^-------

Timing:
real	0m0.018s
user	0m0.011s
sys	0m0.006s


'193.170'
************** PARI *****************
Host 193.170.37.83 (193.170.37.83)
Time: Wed Jul 26 07:04:18 2006

Input: f=x^4-6
polred(f);
nf=nfinit(f);
fact6r(nf.disc);
A=10;
g1=x^4+A*x^2+A^2/2;
g2=x^4-A*x^2-A^2/2;
g3=x^4+A*x^2-A^2/2;
g4=x^4-A*x^2+A^2/2;
nf1=nfinit(g1);
nf2=nfinit(g2);
nf3=nfinit(g1);
nf4=nfinit(g2);
factor(nf1.disc);
factor(nf2.disc);
factor(nf3.disc);
factor(nf4.disc);
nfisisom(f,g1)
nfisisom(f,g2)
nfisisom(f,g3)
nfisisom(f,g4)

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = x^4 - 6
? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? %17 = 0
? %18 = 0
? %19 = 0
? %20 = 0
? 
Goodbye!

Errors/timing (if any):

  ***   expected character: ',' instead of: fact6r(nf.disc);
                                                     ^-------

Timing:
real	0m0.032s
user	0m0.013s
sys	0m0.004s


'193.170'
************** PARI *****************
Host 193.170.37.83 (193.170.37.83)
Time: Wed Jul 26 07:04:09 2006

Input: f=x^4-6
polred(f);
nf=nfinit(f);
fact6r(nf.disc);
A=8;
g1=x^4+A*x^2+A^2/2;
g2=x^4-A*x^2-A^2/2;
g3=x^4+A*x^2-A^2/2;
g4=x^4-A*x^2+A^2/2;
nf1=nfinit(g1);
nf2=nfinit(g2);
nf3=nfinit(g1);
nf4=nfinit(g2);
factor(nf1.disc);
factor(nf2.disc);
factor(nf3.disc);
factor(nf4.disc);
nfisisom(f,g1)
nfisisom(f,g2)
nfisisom(f,g3)
nfisisom(f,g4)

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = x^4 - 6
? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? %17 = 0
? %18 = 0
? %19 = 0
? %20 = 0
? 
Goodbye!

Errors/timing (if any):

  ***   expected character: ',' instead of: fact6r(nf.disc);
                                                     ^-------

Timing:
real	0m0.047s
user	0m0.009s
sys	0m0.009s


'193.170'
************** PARI *****************
Host 193.170.37.83 (193.170.37.83)
Time: Wed Jul 26 07:04:02 2006

Input: f=x^4-6
polred(f);
nf=nfinit(f);
fact6r(nf.disc);
A=6;
g1=x^4+A*x^2+A^2/2;
g2=x^4-A*x^2-A^2/2;
g3=x^4+A*x^2-A^2/2;
g4=x^4-A*x^2+A^2/2;
nf1=nfinit(g1);
nf2=nfinit(g2);
nf3=nfinit(g1);
nf4=nfinit(g2);
factor(nf1.disc);
factor(nf2.disc);
factor(nf3.disc);
factor(nf4.disc);
nfisisom(f,g1)
nfisisom(f,g2)
nfisisom(f,g3)
nfisisom(f,g4)

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = x^4 - 6
? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? %17 = 0
? %18 = 0
? %19 = 0
? %20 = 0
? 
Goodbye!

Errors/timing (if any):

  ***   expected character: ',' instead of: fact6r(nf.disc);
                                                     ^-------

Timing:
real	0m0.295s
user	0m0.015s
sys	0m0.003s


'193.170'
************** PARI *****************
Host 193.170.37.83 (193.170.37.83)
Time: Wed Jul 26 07:03:54 2006

Input: f=x^4-6
polred(f);
nf=nfinit(f);
fact6r(nf.disc);
A=4;
g1=x^4+A*x^2+A^2/2;
g2=x^4-A*x^2-A^2/2;
g3=x^4+A*x^2-A^2/2;
g4=x^4-A*x^2+A^2/2;
nf1=nfinit(g1);
nf2=nfinit(g2);
nf3=nfinit(g1);
nf4=nfinit(g2);
factor(nf1.disc);
factor(nf2.disc);
factor(nf3.disc);
factor(nf4.disc);
nfisisom(f,g1)
nfisisom(f,g2)
nfisisom(f,g3)
nfisisom(f,g4)

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = x^4 - 6
? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? %17 = 0
? %18 = 0
? %19 = 0
? %20 = 0
? 
Goodbye!

Errors/timing (if any):

  ***   expected character: ',' instead of: fact6r(nf.disc);
                                                     ^-------

Timing:
real	0m0.019s
user	0m0.012s
sys	0m0.005s


'193.170'
************** PARI *****************
Host 193.170.37.83 (193.170.37.83)
Time: Wed Jul 26 07:03:23 2006

Input: f=x^4-6
polred(f);
nf=nfinit(f);
fact6r(nf.disc);
A=2;
g1=x^4+A*x^2+A^2/2;
g2=x^4-A*x^2-A^2/2;
g3=x^4+A*x^2-A^2/2;
g4=x^4-A*x^2+A^2/2;
nf1=nfinit(g1);
nf2=nfinit(g2);
nf3=nfinit(g1);
nf4=nfinit(g2);
factor(nf1.disc);
factor(nf2.disc);
factor(nf3.disc);
factor(nf4.disc);
nfisisom(f,g1)
nfisisom(f,g2)
nfisisom(f,g3)
nfisisom(f,g4)

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = x^4 - 6
? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? %17 = 0
? %18 = 0
? %19 = 0
? %20 = 0
? 
Goodbye!

Errors/timing (if any):

  ***   expected character: ',' instead of: fact6r(nf.disc);
                                                     ^-------

Timing:
real	0m0.154s
user	0m0.011s
sys	0m0.007s


'193.170'
************** PARI *****************
Host 193.170.37.83 (193.170.37.83)
Time: Wed Jul 26 07:02:48 2006

Input: f=x^4-6
polred(f);
nf=nfinit(f);
fact6r(nf.disc);
A=20;
g1=x^4+A*x^2+A^2/2
g2=x^4-A*x^2-A^2/2
g3=x^4+A*x^2-A^2/2
g4=x^4-A*x^2+A^2/2
nf1=nfinit(g1);
nf2=nfinit(g2);
nf3=nfinit(g1);
nf4=nfinit(g2);
factor(nf1.disc)
factor(nf2.disc)
factor(nf3.disc)
factor(nf4.disc)
nfisisom(f,g1)
nfisisom(f,g2)
nfisisom(f,g3)
nfisisom(f,g4)

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = x^4 - 6
? ? ? ? ? %5 = x^4 + 20*x^2 + 200
? %6 = x^4 - 20*x^2 - 200
? %7 = x^4 + 20*x^2 - 200
? %8 = x^4 - 20*x^2 + 200
? ? ? ? ? %13 = 
[2 9]

[5 2]

? %14 = 
[-1 1]

[2 9]

[3 2]

[5 2]

? %15 = 
[2 9]

[5 2]

? %16 = 
[-1 1]

[2 9]

[3 2]

[5 2]

? %17 = 0
? %18 = 0
? %19 = 0
? %20 = 0
? 
Goodbye!

Errors/timing (if any):

  ***   expected character: ',' instead of: fact6r(nf.disc);
                                                     ^-------

Timing:
real	0m0.044s
user	0m0.013s
sys	0m0.006s


'193.170'
************** PARI *****************
Host 193.170.37.83 (193.170.37.83)
Time: Wed Jul 26 07:00:15 2006

Input: f=x^4-6
polred(f);
nf=nfinit(f);
fact6r(nf.disc);
A=20;
g1=x^4+A*x^2+A^2/2
g2=x^4-A*x^2+A^2/2
nf1=nfinit(g1);
nf2=nfinit(g2);
factor(nf1.disc)
factor(nf2.disc)
nfisisom(f,g1)
nfisisom(f,g2)

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = x^4 - 6
? ? ? ? ? %5 = x^4 + 20*x^2 + 200
? %6 = x^4 - 20*x^2 + 200
? ? ? %9 = 
[2 9]

[5 2]

? %10 = 
[2 9]

[5 2]

? %11 = 0
? %12 = 0
? 
Goodbye!

Errors/timing (if any):

  ***   expected character: ',' instead of: fact6r(nf.disc);
                                                     ^-------

Timing:
real	0m0.099s
user	0m0.013s
sys	0m0.005s


'193.170'
************** PARI *****************
Host 193.170.37.83 (193.170.37.83)
Time: Wed Jul 26 06:59:58 2006

Input: f=x^4-6
polred(f);
nf=nfinit(f);
fact6r(nf.disc);
A=20;
g1=x^4+A*x^2+A^2/2
g2=x^4+A*x^2+A^2/2
nf1=nfinit(g1);
nf2=nfinit(g2);
factor(nf1.disc)
factor(nf2.disc)
nfisisom(f,g1)
nfisisom(f,g2)

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = x^4 - 6
? ? ? ? ? %5 = x^4 + 20*x^2 + 200
? %6 = x^4 + 20*x^2 + 200
? ? ? %9 = 
[2 9]

[5 2]

? %10 = 
[2 9]

[5 2]

? %11 = 0
? %12 = 0
? 
Goodbye!

Errors/timing (if any):

  ***   expected character: ',' instead of: fact6r(nf.disc);
                                                     ^-------

Timing:
real	0m0.089s
user	0m0.009s
sys	0m0.007s


'193.170'
************** PARI *****************
Host 193.170.37.83 (193.170.37.83)
Time: Wed Jul 26 06:59:43 2006

Input: f=x^4-6
polred(f);
nf=nfinit(f);
fact6r(nf.disc);
A=20;
g1=x^4+A*x^2+A^2/2
g2=x^4=A*x^2+A^2/2
nf1=nfinit(g1);
nf2=nfinit(g2);
factor(nf1.disc)
factor(nf2.disc)
nfisisom(f,g1)
nfisisom(f,g2)

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = x^4 - 6
? ? ? ? ? %5 = x^4 + 20*x^2 + 200
? ? ? ? %8 = 
[2 9]

[5 2]

? %9 = [;]

? %10 = 0
? %11 = 0
? 
Goodbye!

Errors/timing (if any):

  ***   expected character: ',' instead of: fact6r(nf.disc);
                                                     ^-------
  ***   unexpected character: g2=x^4=A*x^2+A^2/2
                                    ^------------

Timing:
real	0m0.019s
user	0m0.009s
sys	0m0.006s


'193.170'
************** PARI *****************
Host 193.170.37.83 (193.170.37.83)
Time: Wed Jul 26 06:58:59 2006

Input: f=x^4-6
polred(f);
nf=nfinit(f);
fact6r(nf.disc);
A=20;
g1=x^4+A*x^2+A^2/2
g2=x^4+A*x^2-A^2/2
nf1=nfinit(g1);
nf2=nfinit(g2);
factor(nf1.disc)
factor(nf2.disc)
nfisisom(f,g1)
nfisisom(f,g2)

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = x^4 - 6
? ? ? ? ? %5 = x^4 + 20*x^2 + 200
? %6 = x^4 + 20*x^2 - 200
? ? ? %9 = 
[2 9]

[5 2]

? %10 = 
[-1 1]

[2 9]

[3 2]

[5 2]

? %11 = 0
? %12 = 0
? 
Goodbye!

Errors/timing (if any):

  ***   expected character: ',' instead of: fact6r(nf.disc);
                                                     ^-------

Timing:
real	0m0.083s
user	0m0.012s
sys	0m0.006s


'193.170'
************** PARI *****************
Host 193.170.37.83 (193.170.37.83)
Time: Wed Jul 26 06:58:45 2006

Input: f=x^4-6
polred(f);
nf=nfinit(f);
fact6r(nf.disc);
A=18;
g1=x^4+A*x^2+A^2/2
g2=x^4+A*x^2-A^2/2
nf1=nfinit(g1);
nf2=nfinit(g2);
factor(nf1.disc)
factor(nf2.disc)
nfisisom(f,g1)
nfisisom(f,g2)

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = x^4 - 6
? ? ? ? ? %5 = x^4 + 18*x^2 + 162
? %6 = x^4 + 18*x^2 - 162
? ? ? %9 = 
[2 9]

? %10 = 
[-1 1]

[2 9]

[3 2]

? %11 = 0
? %12 = 0
? 
Goodbye!

Errors/timing (if any):

  ***   expected character: ',' instead of: fact6r(nf.disc);
                                                     ^-------

Timing:
real	0m0.039s
user	0m0.010s
sys	0m0.005s


'193.170'
************** PARI *****************
Host 193.170.37.83 (193.170.37.83)
Time: Wed Jul 26 06:58:37 2006

Input: f=x^4-6
polred(f);
nf=nfinit(f);
fact6r(nf.disc);
A=16;
g1=x^4+A*x^2+A^2/2
g2=x^4+A*x^2-A^2/2
nf1=nfinit(g1);
nf2=nfinit(g2);
factor(nf1.disc)
factor(nf2.disc)
nfisisom(f,g1)
nfisisom(f,g2)

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = x^4 - 6
? ? ? ? ? %5 = x^4 + 16*x^2 + 128
? %6 = x^4 + 16*x^2 - 128
? ? ? %9 = 
[2 9]

? %10 = 
[-1 1]

[2 9]

[3 2]

? %11 = 0
? %12 = 0
? 
Goodbye!

Errors/timing (if any):

  ***   expected character: ',' instead of: fact6r(nf.disc);
                                                     ^-------

Timing:
real	0m0.053s
user	0m0.007s
sys	0m0.008s


'193.170'
************** PARI *****************
Host 193.170.37.83 (193.170.37.83)
Time: Wed Jul 26 06:58:27 2006

Input: f=x^4-6
polred(f);
nf=nfinit(f);
fact6r(nf.disc);
A=14;
g1=x^4+A*x^2+A^2/2
g2=x^4+A*x^2-A^2/2
nf1=nfinit(g1);
nf2=nfinit(g2);
factor(nf1.disc)
factor(nf2.disc)
nfisisom(f,g1)
nfisisom(f,g2)

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = x^4 - 6
? ? ? ? ? %5 = x^4 + 14*x^2 + 98
? %6 = x^4 + 14*x^2 - 98
? ? ? %9 = 
[2 9]

[7 2]

? %10 = 
[-1 1]

[2 9]

[3 2]

[7 2]

? %11 = 0
? %12 = 0
? 
Goodbye!

Errors/timing (if any):

  ***   expected character: ',' instead of: fact6r(nf.disc);
                                                     ^-------

Timing:
real	0m0.068s
user	0m0.011s
sys	0m0.005s


'193.170'
************** PARI *****************
Host 193.170.37.83 (193.170.37.83)
Time: Wed Jul 26 06:58:19 2006

Input: f=x^4-6
polred(f);
nf=nfinit(f);
fact6r(nf.disc);
A=12;
g1=x^4+A*x^2+A^2/2
g2=x^4+A*x^2-A^2/2
nf1=nfinit(g1);
nf2=nfinit(g2);
factor(nf1.disc)
factor(nf2.disc)
nfisisom(f,g1)
nfisisom(f,g2)

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = x^4 - 6
? ? ? ? ? %5 = x^4 + 12*x^2 + 72
? %6 = x^4 + 12*x^2 - 72
? ? ? %9 = 
[2 9]

[3 2]

? %10 = 
[-1 1]

[2 9]

[3 2]

? %11 = 0
? %12 = 0
? 
Goodbye!

Errors/timing (if any):

  ***   expected character: ',' instead of: fact6r(nf.disc);
                                                     ^-------

Timing:
real	0m0.065s
user	0m0.008s
sys	0m0.008s


'193.170'
************** PARI *****************
Host 193.170.37.83 (193.170.37.83)
Time: Wed Jul 26 06:58:10 2006

Input: f=x^4-6
polred(f);
nf=nfinit(f);
fact6r(nf.disc);
A=10;
g1=x^4+A*x^2+A^2/2
g2=x^4+A*x^2-A^2/2
nf1=nfinit(g1);
nf2=nfinit(g2);
factor(nf1.disc)
factor(nf2.disc)
nfisisom(f,g1)
nfisisom(f,g2)

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = x^4 - 6
? ? ? ? ? %5 = x^4 + 10*x^2 + 50
? %6 = x^4 + 10*x^2 - 50
? ? ? %9 = 
[2 9]

[5 2]

? %10 = 
[-1 1]

[2 9]

[3 2]

[5 2]

? %11 = 0
? %12 = 0
? 
Goodbye!

Errors/timing (if any):

  ***   expected character: ',' instead of: fact6r(nf.disc);
                                                     ^-------

Timing:
real	0m0.248s
user	0m0.008s
sys	0m0.008s


'193.170'
************** PARI *****************
Host 193.170.37.83 (193.170.37.83)
Time: Wed Jul 26 06:58:01 2006

Input: f=x^4-6
polred(f);
nf=nfinit(f);
fact6r(nf.disc);
A=8;
g1=x^4+A*x^2+A^2/2
g2=x^4+A*x^2-A^2/2
nf1=nfinit(g1);
nf2=nfinit(g2);
factor(nf1.disc)
factor(nf2.disc)
nfisisom(f,g1)
nfisisom(f,g2)

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = x^4 - 6
? ? ? ? ? %5 = x^4 + 8*x^2 + 32
? %6 = x^4 + 8*x^2 - 32
? ? ? %9 = 
[2 9]

? %10 = 
[-1 1]

[2 9]

[3 2]

? %11 = 0
? %12 = 0
? 
Goodbye!

Errors/timing (if any):

  ***   expected character: ',' instead of: fact6r(nf.disc);
                                                     ^-------

Timing:
real	0m0.045s
user	0m0.009s
sys	0m0.005s


'193.170'
************** PARI *****************
Host 193.170.37.83 (193.170.37.83)
Time: Wed Jul 26 06:57:51 2006

Input: f=x^4-6
polred(f);
nf=nfinit(f);
fact6r(nf.disc);
A=6;
g1=x^4+A*x^2+A^2/2
g2=x^4+A*x^2-A^2/2
nf1=nfinit(g1);
nf2=nfinit(g2);
factor(nf1.disc)
factor(nf2.disc)
nfisisom(f,g1)
nfisisom(f,g2)

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = x^4 - 6
? ? ? ? ? %5 = x^4 + 6*x^2 + 18
? %6 = x^4 + 6*x^2 - 18
? ? ? %9 = 
[2 9]

[3 2]

? %10 = 
[-1 1]

[2 9]

[3 2]

? %11 = 0
? %12 = 0
? 
Goodbye!

Errors/timing (if any):

  ***   expected character: ',' instead of: fact6r(nf.disc);
                                                     ^-------

Timing:
real	0m0.041s
user	0m0.007s
sys	0m0.009s


'193.170'
************** PARI *****************
Host 193.170.37.83 (193.170.37.83)
Time: Wed Jul 26 06:57:40 2006

Input: f=x^4-6
polred(f);
nf=nfinit(f);
fact6r(nf.disc);
A=4;
g1=x^4+A*x^2+A^2/2
g2=x^4+A*x^2-A^2/2
nf1=nfinit(g1);
nf2=nfinit(g2);
factor(nf1.disc)
factor(nf2.disc)
nfisisom(f,g1)
nfisisom(f,g2)

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = x^4 - 6
? ? ? ? ? %5 = x^4 + 4*x^2 + 8
? %6 = x^4 + 4*x^2 - 8
? ? ? %9 = 
[2 9]

? %10 = 
[-1 1]

[2 9]

[3 2]

? %11 = 0
? %12 = 0
? 
Goodbye!

Errors/timing (if any):

  ***   expected character: ',' instead of: fact6r(nf.disc);
                                                     ^-------

Timing:
real	0m0.055s
user	0m0.009s
sys	0m0.007s


'193.170'
************** PARI *****************
Host 193.170.37.83 (193.170.37.83)
Time: Wed Jul 26 06:57:25 2006

Input: f=x^4-6
polred(f);
nf=nfinit(f);
fact6r(nf.disc);
A=2;
g1=x^4+A*x^2+A^2/2
g2=x^4+A*x^2-A^2/2
nf1=nfinit(g1);
nf2=nfinit(g2);
factor(nf1.disc)
factor(nf2.disc)
nfisisom(f,g1)
nfisisom(f,g2)

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = x^4 - 6
? ? ? ? ? %5 = x^4 + 2*x^2 + 2
? %6 = x^4 + 2*x^2 - 2
? ? ? %9 = 
[2 9]

? %10 = 
[-1 1]

[2 9]

[3 2]

? %11 = 0
? %12 = 0
? 
Goodbye!

Errors/timing (if any):

  ***   expected character: ',' instead of: fact6r(nf.disc);
                                                     ^-------

Timing:
real	0m0.017s
user	0m0.011s
sys	0m0.005s


'193.170'
************** PARI *****************
Host 193.170.37.83 (193.170.37.83)
Time: Wed Jul 26 06:57:05 2006

Input: f=x^4-6
polred(f);
nf=nfinit(f);
fact6r(nf.disc);
A=2;
g1=x^4+A*x^2+A^2/2
g2=x^4+A*x^2-A^2/2
nf1=nfinit(g1);
n2=nfinit(g2);
factor(nf1.disc)
factor(nf2.disc)
nfisisom(f,g1)
nfisisom(f,g2)

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = x^4 - 6
? ? ? ? ? %5 = x^4 + 2*x^2 + 2
? %6 = x^4 + 2*x^2 - 2
? ? ? %9 = 
[2 9]

? ? %10 = 0
? %11 = 0
? 
Goodbye!

Errors/timing (if any):

  ***   expected character: ',' instead of: fact6r(nf.disc);
                                                     ^-------
  ***   incorrect type in disc: factor(nf2.disc)
                                           ^-----

Timing:
real	0m0.386s
user	0m0.009s
sys	0m0.006s


'193.170'
************** PARI *****************
Host 193.170.37.83 (193.170.37.83)
Time: Wed Jul 26 06:56:23 2006

Input: f=x^4-6
polred(f);
nf=nfinit(f);
fact6r(nf.disc);
A=2;
g1=x^4+A*x^2+A^2/2
g2=x^4+A*x^2-A^2/2
nf1=nfinit(g);
factor(nf1.disc)
nfisisom(f,g1)
nfisisom(f,g2)

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = x^4 - 6
? ? ? ? ? %5 = x^4 + 2*x^2 + 2
? %6 = x^4 + 2*x^2 - 2
? ? %8 = [;]

? %9 = 0
? %10 = 0
? 
Goodbye!

Errors/timing (if any):

  ***   expected character: ',' instead of: fact6r(nf.disc);
                                                     ^-------

Timing:
real	0m0.087s
user	0m0.010s
sys	0m0.005s


'193.170'
************** PARI *****************
Host 193.170.37.83 (193.170.37.83)
Time: Wed Jul 26 06:56:06 2006

Input: f=x^4-6
polred(f);
nf=nfinit(f);
fact6r(nf.disc);
A=2;
g1=x^4+A*x^2+A^2/2
g2=x^4+A*x^2-A^2/2
nf1=nfinit(g);
factor(nf1.disc)
nfisisom(f,g)

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = x^4 - 6
? ? ? ? ? %5 = x^4 + 2*x^2 + 2
? %6 = x^4 + 2*x^2 - 2
? ? %8 = [;]

? %9 = 0
? 
Goodbye!

Errors/timing (if any):

  ***   expected character: ',' instead of: fact6r(nf.disc);
                                                     ^-------

Timing:
real	0m0.014s
user	0m0.011s
sys	0m0.004s


'193.170'
************** PARI *****************
Host 193.170.37.83 (193.170.37.83)
Time: Wed Jul 26 06:55:01 2006

Input: f=x^4-6
polred(f);
nf=nfinit(f);
fact6r(nf.disc);
A=2;
g=x^4+A*x^2+A^2/2
nf1=nfinit(g);
factor(nf1.disc)
nfisisom(f,g)

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = x^4 - 6
? ? ? ? ? %5 = x^4 + 2*x^2 + 2
? ? %7 = 
[2 9]

? %8 = 0
? 
Goodbye!

Errors/timing (if any):

  ***   expected character: ',' instead of: fact6r(nf.disc);
                                                     ^-------

Timing:
real	0m0.051s
user	0m0.013s
sys	0m0.002s


'193.170'
************** PARI *****************
Host 193.170.37.83 (193.170.37.83)
Time: Wed Jul 26 06:54:52 2006

Input: f=x^4-6
polred(f);
nf=nfinit(f);
fact6r(nf.disc);
A=-2;
g=x^4+A*x^2+A^2/2
nf1=nfinit(g);
factor(nf1.disc)
nfisisom(f,g)

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = x^4 - 6
? ? ? ? ? %5 = x^4 - 2*x^2 + 2
? ? %7 = 
[2 9]

? %8 = 0
? 
Goodbye!

Errors/timing (if any):

  ***   expected character: ',' instead of: fact6r(nf.disc);
                                                     ^-------

Timing:
real	0m0.443s
user	0m0.006s
sys	0m0.009s


'193.170'
************** PARI *****************
Host 193.170.37.83 (193.170.37.83)
Time: Wed Jul 26 06:54:45 2006

Input: f=x^4-6
polred(f);
nf=nfinit(f);
fact6r(nf.disc);
A=-24;
g=x^4+A*x^2+A^2/2
nf1=nfinit(g);
factor(nf1.disc)
nfisisom(f,g)

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = x^4 - 6
? ? ? ? ? %5 = x^4 - 24*x^2 + 288
? ? %7 = 
[2 9]

[3 2]

? %8 = 0
? 
Goodbye!

Errors/timing (if any):

  ***   expected character: ',' instead of: fact6r(nf.disc);
                                                     ^-------

Timing:
real	0m0.208s
user	0m0.009s
sys	0m0.006s


'193.170'
************** PARI *****************
Host 193.170.37.83 (193.170.37.83)
Time: Wed Jul 26 06:54:37 2006

Input: f=x^4-6
polred(f);
nf=nfinit(f);
fact6r(nf.disc);
A=-24;
g=x^4+A*x^2+A^2/2
nf1=nfinit(g);
factor(nf1.disc)
nfisisom(f,g)

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = x^4 - 6
? ? ? ? ? %5 = x^4 - 24*x^2 + 288
? ? %7 = 
[2 9]

[3 2]

? %8 = 0
? 
Goodbye!

Errors/timing (if any):

  ***   expected character: ',' instead of: fact6r(nf.disc);
                                                     ^-------

Timing:
real	0m0.234s
user	0m0.011s
sys	0m0.004s


'193.170'
************** PARI *****************
Host 193.170.37.83 (193.170.37.83)
Time: Wed Jul 26 06:54:27 2006

Input: f=x^4-6
polred(f);
nf=nfinit(f);
fact6r(nf.disc);
A=24;
g=x^4+A*x^2+A^2/2
nf1=nfinit(g);
factor(nf1.disc)
nfisisom(f,g)

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = x^4 - 6
? ? ? ? ? %5 = x^4 + 24*x^2 + 288
? ? %7 = 
[2 9]

[3 2]

? %8 = 0
? 
Goodbye!

Errors/timing (if any):

  ***   expected character: ',' instead of: fact6r(nf.disc);
                                                     ^-------

Timing:
real	0m0.014s
user	0m0.009s
sys	0m0.005s


'193.170'
************** PARI *****************
Host 193.170.37.83 (193.170.37.83)
Time: Wed Jul 26 06:54:08 2006

Input: f=x^4-6
polred(f);
nf=nfinit(f);
fact6r(nf.disc);
A=24;
g=x^4+x^2+A^2/2
nf1=nfinit(g);
factor(nf1.disc)
nfisisom(f,g)

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = x^4 - 6
? ? ? ? ? %5 = x^4 + x^2 + 288
? ? %7 = 
[2 5]

[1151 2]

? %8 = 0
? 
Goodbye!

Errors/timing (if any):

  ***   expected character: ',' instead of: fact6r(nf.disc);
                                                     ^-------

Timing:
real	0m0.015s
user	0m0.010s
sys	0m0.005s


'193.170'
************** PARI *****************
Host 193.170.37.83 (193.170.37.83)
Time: Wed Jul 26 06:54:01 2006

Input: f=x^4-6
polred(f);
nf=nfinit(f);
fact6r(nf.disc);
A=-24;
g=x^4+x^2+A^2/2
nf1=nfinit(g);
factor(nf1.disc)
nfisisom(f,g)

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = x^4 - 6
? ? ? ? ? %5 = x^4 + x^2 + 288
? ? %7 = 
[2 5]

[1151 2]

? %8 = 0
? 
Goodbye!

Errors/timing (if any):

  ***   expected character: ',' instead of: fact6r(nf.disc);
                                                     ^-------

Timing:
real	0m0.016s
user	0m0.007s
sys	0m0.009s


'193.170'
************** PARI *****************
Host 193.170.37.83 (193.170.37.83)
Time: Wed Jul 26 06:53:53 2006

Input: f=x^4-6
polred(f);
nf=nfinit(f);
fact6r(nf.disc);
A=-22;
g=x^4+x^2+A^2/2
nf1=nfinit(g);
factor(nf1.disc)
nfisisom(f,g)

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = x^4 - 6
? ? ? ? ? %5 = x^4 + x^2 + 242
? ? %7 = 
[2 3]

[967 2]

? %8 = 0
? 
Goodbye!

Errors/timing (if any):

  ***   expected character: ',' instead of: fact6r(nf.disc);
                                                     ^-------

Timing:
real	0m0.278s
user	0m0.010s
sys	0m0.005s


'193.170'
************** PARI *****************
Host 193.170.37.83 (193.170.37.83)
Time: Wed Jul 26 06:53:44 2006

Input: f=x^4-6
polred(f);
nf=nfinit(f);
fact6r(nf.disc);
A=22;
g=x^4+x^2+A^2/2
nf1=nfinit(g);
factor(nf1.disc)
nfisisom(f,g)

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = x^4 - 6
? ? ? ? ? %5 = x^4 + x^2 + 242
? ? %7 = 
[2 3]

[967 2]

? %8 = 0
? 
Goodbye!

Errors/timing (if any):

  ***   expected character: ',' instead of: fact6r(nf.disc);
                                                     ^-------

Timing:
real	0m0.123s
user	0m0.005s
sys	0m0.009s


'193.170'
************** PARI *****************
Host 193.170.37.83 (193.170.37.83)
Time: Wed Jul 26 06:53:39 2006

Input: f=x^4-6
polred(f);
nf=nfinit(f);
fact6r(nf.disc);
A=22;
g=x^4+x^2+A^2/2
nf1=nfinit(g);
factor(nf1.disc)
nfisisom(f,g)

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = x^4 - 6
? ? ? ? ? %5 = x^4 + x^2 + 242
? ? %7 = 
[2 3]

[967 2]

? %8 = 0
? 
Goodbye!

Errors/timing (if any):

  ***   expected character: ',' instead of: fact6r(nf.disc);
                                                     ^-------

Timing:
real	0m0.015s
user	0m0.008s
sys	0m0.008s


'193.170'
************** PARI *****************
Host 193.170.37.83 (193.170.37.83)
Time: Wed Jul 26 06:53:28 2006

Input: f=x^4-6
polred(f);
nf=nfinit(f);
fact6r(nf.disc);
A=-22;
g=x^4+x^2+A^2/2
nf1=nfinit(g);
factor(nf1.disc)
nfisisom(f,g)

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = x^4 - 6
? ? ? ? ? %5 = x^4 + x^2 + 242
? ? %7 = 
[2 3]

[967 2]

? %8 = 0
? 
Goodbye!

Errors/timing (if any):

  ***   expected character: ',' instead of: fact6r(nf.disc);
                                                     ^-------

Timing:
real	0m0.107s
user	0m0.011s
sys	0m0.005s


'193.170'
************** PARI *****************
Host 193.170.37.83 (193.170.37.83)
Time: Wed Jul 26 06:53:16 2006

Input: f=x^4-6
polred(f);
nf=nfinit(f);
fact6r(nf.disc);
A=-22;
g=x^4+x^2+A^2/2
nf1=nfinit(g);
factor(nf1.disc);
nfisisom(f,g)

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = x^4 - 6
? ? ? ? ? %5 = x^4 + x^2 + 242
? ? ? %8 = 0
? 
Goodbye!

Errors/timing (if any):

  ***   expected character: ',' instead of: fact6r(nf.disc);
                                                     ^-------

Timing:
real	0m0.015s
user	0m0.011s
sys	0m0.005s


'193.170'
************** PARI *****************
Host 193.170.37.83 (193.170.37.83)
Time: Wed Jul 26 06:53:08 2006

Input: f=x^4-6
polred(f);
nf=nfinit(f);
fact6r(nf.disc);
A=-2;
g=x^4+x^2+A^2/2
nf1=nfinit(g);
factor(nf1.disc);
nfisisom(f,g)

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = x^4 - 6
? ? ? ? ? %5 = x^4 + x^2 + 2
? ? ? %8 = 0
? 
Goodbye!

Errors/timing (if any):

  ***   expected character: ',' instead of: fact6r(nf.disc);
                                                     ^-------

Timing:
real	0m0.060s
user	0m0.009s
sys	0m0.006s


'193.170'
************** PARI *****************
Host 193.170.37.83 (193.170.37.83)
Time: Wed Jul 26 06:52:57 2006

Input: f=x^4-6
polred(f);
nf=nfinit(f);
fact6r(nf.disc);
A=-4;
g=x^4+x^2+A^2/2
nf1=nfinit(g);
factor(nf1.disc);
nfisisom(f,g)

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = x^4 - 6
? ? ? ? ? %5 = x^4 + x^2 + 8
? ? ? %8 = 0
? 
Goodbye!

Errors/timing (if any):

  ***   expected character: ',' instead of: fact6r(nf.disc);
                                                     ^-------

Timing:
real	0m0.015s
user	0m0.009s
sys	0m0.007s


'193.170'
************** PARI *****************
Host 193.170.37.83 (193.170.37.83)
Time: Wed Jul 26 06:52:44 2006

Input: f=x^4-6
polred(f);
nf=nfinit(f);
fact6r(nf.disc);
A=-6;
g=x^4+x^2+A^2/2;;
nf1=nfinit(g);
factor(nf1.disc);
nfisisom(f,g)

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = x^4 - 6
? ? ? ? ? ? ? ? %8 = 0
? 
Goodbye!

Errors/timing (if any):

  ***   expected character: ',' instead of: fact6r(nf.disc);
                                                     ^-------

Timing:
real	0m0.015s
user	0m0.009s
sys	0m0.005s


'193.170'
************** PARI *****************
Host 193.170.37.83 (193.170.37.83)
Time: Wed Jul 26 06:52:36 2006

Input: f=x^4-6
polred(f);
nf=nfinit(f);
fact6r(nf.disc);
A=-8;
g=x^4+x^2+A^2/2;;
nf1=nfinit(g);
factor(nf1.disc);
nfisisom(f,g)

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = x^4 - 6
? ? ? ? ? ? ? ? %8 = 0
? 
Goodbye!

Errors/timing (if any):

  ***   expected character: ',' instead of: fact6r(nf.disc);
                                                     ^-------

Timing:
real	0m0.014s
user	0m0.011s
sys	0m0.005s


'193.170'
************** PARI *****************
Host 193.170.37.83 (193.170.37.83)
Time: Wed Jul 26 06:52:29 2006

Input: f=x^4-6
polred(f);
nf=nfinit(f);
fact6r(nf.disc);
A=-10;
g=x^4+x^2+A^2/2;;
nf1=nfinit(g);
factor(nf1.disc);
nfisisom(f,g)

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = x^4 - 6
? ? ? ? ? ? ? ? %8 = 0
? 
Goodbye!

Errors/timing (if any):

  ***   expected character: ',' instead of: fact6r(nf.disc);
                                                     ^-------

Timing:
real	0m0.015s
user	0m0.010s
sys	0m0.006s


'193.170'
************** PARI *****************
Host 193.170.37.83 (193.170.37.83)
Time: Wed Jul 26 06:52:22 2006

Input: f=x^4-6
polred(f);
nf=nfinit(f);
fact6r(nf.disc);
A=-12;
g=x^4+x^2+A^2/2;;
nf1=nfinit(g);
factor(nf1.disc);
nfisisom(f,g)

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = x^4 - 6
? ? ? ? ? ? ? ? %8 = 0
? 
Goodbye!

Errors/timing (if any):

  ***   expected character: ',' instead of: fact6r(nf.disc);
                                                     ^-------

Timing:
real	0m0.354s
user	0m0.009s
sys	0m0.007s


'193.170'
************** PARI *****************
Host 193.170.37.83 (193.170.37.83)
Time: Wed Jul 26 06:52:16 2006

Input: f=x^4-6
polred(f);
nf=nfinit(f);
fact6r(nf.disc);
A=-14;
g=x^4+x^2+A^2/2;;
nf1=nfinit(g);
factor(nf1.disc);
nfisisom(f,g)

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = x^4 - 6
? ? ? ? ? ? ? ? %8 = 0
? 
Goodbye!

Errors/timing (if any):

  ***   expected character: ',' instead of: fact6r(nf.disc);
                                                     ^-------

Timing:
real	0m0.102s
user	0m0.008s
sys	0m0.006s


'193.170'
************** PARI *****************
Host 193.170.37.83 (193.170.37.83)
Time: Wed Jul 26 06:52:09 2006

Input: f=x^4-6
polred(f);
nf=nfinit(f);
fact6r(nf.disc);
A=-16;
g=x^4+x^2+A^2/2;;
nf1=nfinit(g);
factor(nf1.disc);
nfisisom(f,g)

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = x^4 - 6
? ? ? ? ? ? ? ? %8 = 0
? 
Goodbye!

Errors/timing (if any):

  ***   expected character: ',' instead of: fact6r(nf.disc);
                                                     ^-------

Timing:
real	0m0.014s
user	0m0.008s
sys	0m0.006s


'193.170'
************** PARI *****************
Host 193.170.37.83 (193.170.37.83)
Time: Wed Jul 26 06:52:02 2006

Input: f=x^4-6
polred(f);
nf=nfinit(f);
fact6r(nf.disc);
A=-18;
g=x^4+x^2+A^2/2;;
nf1=nfinit(g);
factor(nf1.disc);
nfisisom(f,g)

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = x^4 - 6
? ? ? ? ? ? ? ? %8 = 0
? 
Goodbye!

Errors/timing (if any):

  ***   expected character: ',' instead of: fact6r(nf.disc);
                                                     ^-------

Timing:
real	0m0.015s
user	0m0.008s
sys	0m0.006s


'193.170'
************** PARI *****************
Host 193.170.37.83 (193.170.37.83)
Time: Wed Jul 26 06:51:53 2006

Input: f=x^4-6
polred(f);
nf=nfinit(f);
factor(nf.disc);
A=-18;
g=x^4+x^2+A^2/2;;
nf1=nfinit(g);
factor(nf1.disc);
nfisisom(f,g)

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = x^4 - 6
? ? ? ? ? ? ? ? %9 = 0
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.015s
user	0m0.007s
sys	0m0.008s


'193.170'
************** PARI *****************
Host 193.170.37.83 (193.170.37.83)
Time: Wed Jul 26 06:51:45 2006

Input: f=x^4-6
polred(f);
nf=nfinit(f);
factor(nf.disc);
A=-20;
g=x^4+x^2+A^2/2;;
nf1=nfinit(g);
factor(nf1.disc);
nfisisom(f,g)

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = x^4 - 6
? ? ? ? ? ? ? ? %9 = 0
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.087s
user	0m0.011s
sys	0m0.004s


'193.170'
************** PARI *****************
Host 193.170.37.83 (193.170.37.83)
Time: Wed Jul 26 06:51:32 2006

Input: f=x^4-6
polred(f);
nf=nfinit(f);
factor(nf.disc);
A=20;
g=x^4+x^2+A^2/2;;
nf1=nfinit(g);
factor(nf1.disc);
nfisisom(f,g)

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = x^4 - 6
? ? ? ? ? ? ? ? %9 = 0
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.015s
user	0m0.009s
sys	0m0.006s


'193.170'
************** PARI *****************
Host 193.170.37.83 (193.170.37.83)
Time: Wed Jul 26 06:51:25 2006

Input: f=x^4-6
polred(f);
nf=nfinit(f);
factor(nf.disc);
A=18;
g=x^4+x^2+A^2/2;;
nf1=nfinit(g);
factor(nf1.disc);
nfisisom(f,g)

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = x^4 - 6
? ? ? ? ? ? ? ? %9 = 0
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.040s
user	0m0.007s
sys	0m0.009s


'193.170'
************** PARI *****************
Host 193.170.37.83 (193.170.37.83)
Time: Wed Jul 26 06:51:16 2006

Input: f=x^4-6
polred(f);
nf=nfinit(f);
factor(nf.disc);
A=16;
g=x^4+x^2+A^2/2;;
nf1=nfinit(g);
factor(nf1.disc);
nfisisom(f,g)

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = x^4 - 6
? ? ? ? ? ? ? ? %9 = 0
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.075s
user	0m0.010s
sys	0m0.005s


'193.170'
************** PARI *****************
Host 193.170.37.83 (193.170.37.83)
Time: Wed Jul 26 06:51:08 2006

Input: f=x^4-6
polred(f);
nf=nfinit(f);
factor(nf.disc);
A=14;
g=x^4+x^2+A^2/2;;
nf1=nfinit(g);
factor(nf1.disc);
nfisisom(f,g)

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = x^4 - 6
? ? ? ? ? ? ? ? %9 = 0
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.092s
user	0m0.011s
sys	0m0.004s


'193.170'
************** PARI *****************
Host 193.170.37.83 (193.170.37.83)
Time: Wed Jul 26 06:51:01 2006

Input: f=x^4-6
polred(f);
nf=nfinit(f);
factor(nf.disc);
A=12;
g=x^4+x^2+A^2/2;;
nf1=nfinit(g);
factor(nf1.disc);
nfisisom(f,g)

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = x^4 - 6
? ? ? ? ? ? ? ? %9 = 0
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.014s
user	0m0.009s
sys	0m0.005s


'193.170'
************** PARI *****************
Host 193.170.37.83 (193.170.37.83)
Time: Wed Jul 26 06:50:51 2006

Input: f=x^4-6
polred(f);
nf=nfinit(f);
factor(nf.disc);
A=10;
g=x^4+x^2+A^2/2;;
nf1=nfinit(g);
factor(nf1.disc);
nfisisom(f,g)

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = x^4 - 6
? ? ? ? ? ? ? ? %9 = 0
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.014s
user	0m0.008s
sys	0m0.005s


'193.170'
************** PARI *****************
Host 193.170.37.83 (193.170.37.83)
Time: Wed Jul 26 06:50:41 2006

Input: f=x^4-6
polred(f);
nf=nfinit(f);
factor(nf.disc);
A=8;
g=x^4+x^2+A^2/2;;
nf1=nfinit(g);
factor(nf1.disc);
nfisisom(f,g)

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = x^4 - 6
? ? ? ? ? ? ? ? %9 = 0
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.423s
user	0m0.007s
sys	0m0.007s


'193.170'
************** PARI *****************
Host 193.170.37.83 (193.170.37.83)
Time: Wed Jul 26 06:50:27 2006

Input: f=x^4-6
polred(f);
nf=nfinit(f);
factor(nf.disc);
A=8;
g=x^4-6;
nf1=nfinit(g);
factor(nf1.disc);
nfisisom(f,g)

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = x^4 - 6
? ? ? ? ? ? ? ? %9 = [-x, x]
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.015s
user	0m0.009s
sys	0m0.006s


'193.170'
************** PARI *****************
Host 193.170.37.83 (193.170.37.83)
Time: Wed Jul 26 06:50:01 2006

Input: f=x^4-6
polred(f);
nf=nfinit(f);
factor(nf.disc);
A=8;
g=x^4+A*x^2+A^2/2;
nf1=nfinit(g);
factor(nf1.disc);
nfisisom(f,g)

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = x^4 - 6
? ? ? ? ? ? ? ? %9 = 0
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.056s
user	0m0.012s
sys	0m0.004s


'193.170'
************** PARI *****************
Host 193.170.37.83 (193.170.37.83)
Time: Wed Jul 26 06:49:44 2006

Input: f=x^4-6
polred(f);
nf=nfinit(f);
factor(nf.disc)
A=8
g=x^4+A*x^2+A^2/2
nf1=nfinit(g);
factor(nf1.disc)
nfisisom(f,g)

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = x^4 - 6
? ? ? %4 = 
[-1 1]

[2 11]

[3 3]

? %5 = 8
? %6 = x^4 + 8*x^2 + 32
? ? %8 = 
[2 9]

? %9 = 0
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.015s
user	0m0.008s
sys	0m0.007s


'193.170'
************** PARI *****************
Host 193.170.37.83 (193.170.37.83)
Time: Wed Jul 26 06:49:24 2006

Input: f=x^4-6
polred(f);
nf=nfinit(f);
factor(nf.disc)
A=6
g=x^4+A*x^2+A^2/2
nf1=nfinit(g);
factor(nf1.disc)
nfisisom(f,g)

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = x^4 - 6
? ? ? %4 = 
[-1 1]

[2 11]

[3 3]

? %5 = 6
? %6 = x^4 + 6*x^2 + 18
? ? %8 = 
[2 9]

[3 2]

? %9 = 0
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.014s
user	0m0.011s
sys	0m0.004s


'193.170'
************** PARI *****************
Host 193.170.37.83 (193.170.37.83)
Time: Wed Jul 26 06:49:18 2006

Input: f=x^4-6
polred(f);
nf=nfinit(f);
factor(nf.disc)
A=6
g=x^4+A*x^2+A^2/2
nf1=nfinit(g);
factor(nf1.disc)
nfisisom(f,g);

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = x^4 - 6
? ? ? %4 = 
[-1 1]

[2 11]

[3 3]

? %5 = 6
? %6 = x^4 + 6*x^2 + 18
? ? %8 = 
[2 9]

[3 2]

? ? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.015s
user	0m0.006s
sys	0m0.009s


'193.170'
************** PARI *****************
Host 193.170.37.83 (193.170.37.83)
Time: Wed Jul 26 06:49:04 2006

Input: f=x^4-6
polred(f);
nf=nfinit(f);
factor(nf.disc)
A=5
g=x^4+A*x^2+A^2/2
nf1=nfinit(g);
factor(nf1.disc)
nfisisom(f,g);

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = x^4 - 6
? ? ? %4 = 
[-1 1]

[2 11]

[3 3]

? %5 = 5
? %6 = x^4 + 5*x^2 + 25/2
? ? ? ? 
Goodbye!

Errors/timing (if any):

  *** nfinit: polynomial not in Z[X] in nfinit.
  ***   incorrect type in disc: factor(nf1.disc)
                                           ^-----

Timing:
real	0m0.060s
user	0m0.007s
sys	0m0.007s


'193.170'
************** PARI *****************
Host 193.170.37.83 (193.170.37.83)
Time: Wed Jul 26 06:48:51 2006

Input: f=x^4-6
polred(f)
nf=nfinit(f);
factor(nf.disc)
A=5
g=x^4+A*x^2+A^2/2
nf1=nfinit(g);
factor(nf1.disc)
nfisisom(f,g);

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = x^4 - 6
? %2 = [x - 1, x^2 - 6, x^4 - 216, x^4 - 6]
? ? %4 = 
[-1 1]

[2 11]

[3 3]

? %5 = 5
? %6 = x^4 + 5*x^2 + 25/2
? ? ? ? 
Goodbye!

Errors/timing (if any):

  *** nfinit: polynomial not in Z[X] in nfinit.
  ***   incorrect type in disc: factor(nf1.disc)
                                           ^-----

Timing:
real	0m0.016s
user	0m0.008s
sys	0m0.005s


'193.170'
************** PARI *****************
Host 193.170.37.83 (193.170.37.83)
Time: Wed Jul 26 06:48:32 2006

Input: f=x^4-6
polred(f);
nf=nfinit(f);
factor(nf.disc)
A=5
g=x^4+A*x^2+A^2/2
nf1=nfinit(g);
factor(nf1.disc)
nfisisom(f,g);

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = x^4 - 6
? ? ? %4 = 
[-1 1]

[2 11]

[3 3]

? %5 = 5
? %6 = x^4 + 5*x^2 + 25/2
? ? ? ? 
Goodbye!

Errors/timing (if any):

  *** nfinit: polynomial not in Z[X] in nfinit.
  ***   incorrect type in disc: factor(nf1.disc)
                                           ^-----

Timing:
real	0m0.013s
user	0m0.007s
sys	0m0.005s


'193.170'
************** PARI *****************
Host 193.170.37.83 (193.170.37.83)
Time: Wed Jul 26 06:48:16 2006

Input: f=x^4-6
polred(f);
nf=nfinit(f);
factor(nf.disc)
A=4
g=x^4+A*x^2+A^2/2
nf1=nfinit(g);
factor(nf1.disc)
nfisisom(f,g);

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = x^4 - 6
? ? ? %4 = 
[-1 1]

[2 11]

[3 3]

? %5 = 4
? %6 = x^4 + 4*x^2 + 8
? ? %8 = 
[2 9]

? ? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.179s
user	0m0.010s
sys	0m0.006s


'193.170'
************** PARI *****************
Host 193.170.37.83 (193.170.37.83)
Time: Wed Jul 26 06:48:06 2006

Input: f=x^4-6
polred(f);
nf=nfinit(f);
factor(nf.disc)
A=3
g=x^4+A*x^2+A^2/2
nf1=nfinit(g);
factor(nf1.disc)
nfisisom(f,g);

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = x^4 - 6
? ? ? %4 = 
[-1 1]

[2 11]

[3 3]

? %5 = 3
? %6 = x^4 + 3*x^2 + 9/2
? ? ? ? 
Goodbye!

Errors/timing (if any):

  *** nfinit: polynomial not in Z[X] in nfinit.
  ***   incorrect type in disc: factor(nf1.disc)
                                           ^-----

Timing:
real	0m0.013s
user	0m0.008s
sys	0m0.005s


'193.170'
************** PARI *****************
Host 193.170.37.83 (193.170.37.83)
Time: Wed Jul 26 06:47:40 2006

Input: f=x^4-6
polred(f);
nf=nfinit(f);
factor(nf.disc)
A=2
g=x^4+A*x^2+A^2/2
nf1=nfinit(g);
factor(nf1.disc)
nfisisom(f,g);

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = x^4 - 6
? ? ? %4 = 
[-1 1]

[2 11]

[3 3]

? %5 = 2
? %6 = x^4 + 2*x^2 + 2
? ? %8 = 
[2 9]

? ? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.051s
user	0m0.012s
sys	0m0.005s


'193.170'
************** PARI *****************
Host 193.170.37.83 (193.170.37.83)
Time: Wed Jul 26 06:47:18 2006

Input: f=x^4-6
polred(f);
nf=nfinit(f);
factor(nf.disc)
A=2
g=x^4+A*x^2+A^2/2
nf1=nfinit(g);
factor(nf1.disc)
isisom(f,g);

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = x^4 - 6
? ? ? %4 = 
[-1 1]

[2 11]

[3 3]

? %5 = 2
? %6 = x^4 + 2*x^2 + 2
? ? %8 = 
[2 9]

? ? 
Goodbye!

Errors/timing (if any):

  ***   obsolete function: isisom(f,g);
                           ^------------
For full compatibility with GP 1.39.15, type "default(compatible,3)", or set 
"compatible = 3" in your GPRC file.

New syntax: isisom(x,y) ===> nfisisom(x,y)

nfisisom(x,y): as nfisincl but tests whether x is isomorphic to y.



Timing:
real	0m0.117s
user	0m0.009s
sys	0m0.005s


'193.170'
************** PARI *****************
Host 193.170.37.83 (193.170.37.83)
Time: Wed Jul 26 06:47:00 2006

Input: f=x^4-6
polred(f)
nf=nfinit(f);
factor(nf.disc)
A=2
g=x^4+A*x^2+A^2/2
nf1=nfinit(g);
factor(nf1.disc)
isisom(f,g);

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = x^4 - 6
? %2 = [x - 1, x^2 - 6, x^4 - 216, x^4 - 6]
? ? %4 = 
[-1 1]

[2 11]

[3 3]

? %5 = 2
? %6 = x^4 + 2*x^2 + 2
? ? %8 = 
[2 9]

? ? 
Goodbye!

Errors/timing (if any):

  ***   obsolete function: isisom(f,g);
                           ^------------
For full compatibility with GP 1.39.15, type "default(compatible,3)", or set 
"compatible = 3" in your GPRC file.

New syntax: isisom(x,y) ===> nfisisom(x,y)

nfisisom(x,y): as nfisincl but tests whether x is isomorphic to y.



Timing:
real	0m0.015s
user	0m0.009s
sys	0m0.006s


'193.170'
************** PARI *****************
Host 193.170.37.83 (193.170.37.83)
Time: Wed Jul 26 06:46:43 2006

Input: f=x^4-6
polred(f)
nf=nfinit(f);
factor(nf.disc)
A=2
g=x^4+A*x^2+A^2/2
nf1=nfinit(g);
factor(nf1.disc)
isincl(f,g);

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = x^4 - 6
? %2 = [x - 1, x^2 - 6, x^4 - 216, x^4 - 6]
? ? %4 = 
[-1 1]

[2 11]

[3 3]

? %5 = 2
? %6 = x^4 + 2*x^2 + 2
? ? %8 = 
[2 9]

? ? 
Goodbye!

Errors/timing (if any):

  ***   obsolete function: isincl(f,g);
                           ^------------
For full compatibility with GP 1.39.15, type "default(compatible,3)", or set 
"compatible = 3" in your GPRC file.

New syntax: isincl(x,y) ===> nfisincl(x,y)

nfisincl(x,y): tests whether the number field x is isomorphic to a subfield of 
y (where x and y are either polynomials or number fields as output by nfinit). 
Return 0 if not, and otherwise all the isomorphisms. If y is a number field, a 
faster algorithm is used.



Timing:
real	0m0.014s
user	0m0.008s
sys	0m0.005s


'193.170'
************** PARI *****************
Host 193.170.37.83 (193.170.37.83)
Time: Wed Jul 26 06:45:35 2006

Input: f=x^4-6
polred(f)
nf=nfinit(f);
factor(nf.disc)
A=2
g=x^4+A*x^2+A^2/2
isincl(f,g);

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = x^4 - 6
? %2 = [x - 1, x^2 - 6, x^4 - 216, x^4 - 6]
? ? %4 = 
[-1 1]

[2 11]

[3 3]

? %5 = 2
? %6 = x^4 + 2*x^2 + 2
? ? 
Goodbye!

Errors/timing (if any):

  ***   obsolete function: isincl(f,g);
                           ^------------
For full compatibility with GP 1.39.15, type "default(compatible,3)", or set 
"compatible = 3" in your GPRC file.

New syntax: isincl(x,y) ===> nfisincl(x,y)

nfisincl(x,y): tests whether the number field x is isomorphic to a subfield of 
y (where x and y are either polynomials or number fields as output by nfinit). 
Return 0 if not, and otherwise all the isomorphisms. If y is a number field, a 
faster algorithm is used.



Timing:
real	0m0.013s
user	0m0.008s
sys	0m0.005s


'193.170'
************** PARI *****************
Host 193.170.37.83 (193.170.37.83)
Time: Wed Jul 26 06:45:14 2006

Input: f=x^4-6
polred(f)
nf=nfinit(f);
factor(nf.disc)
A=2
g=x^4+A*x^2+A^2/2
isisom(f,g);

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = x^4 - 6
? %2 = [x - 1, x^2 - 6, x^4 - 216, x^4 - 6]
? ? %4 = 
[-1 1]

[2 11]

[3 3]

? %5 = 2
? %6 = x^4 + 2*x^2 + 2
? ? 
Goodbye!

Errors/timing (if any):

  ***   obsolete function: isisom(f,g);
                           ^------------
For full compatibility with GP 1.39.15, type "default(compatible,3)", or set 
"compatible = 3" in your GPRC file.

New syntax: isisom(x,y) ===> nfisisom(x,y)

nfisisom(x,y): as nfisincl but tests whether x is isomorphic to y.



Timing:
real	0m0.079s
user	0m0.010s
sys	0m0.005s


'193.170'
************** PARI *****************
Host 193.170.37.83 (193.170.37.83)
Time: Wed Jul 26 06:45:02 2006

Input: f=x^4-6
polred(f)
nf=nfinit(f);
factor(nf.disc)
A=1
g=x^4+A*x^2+A^2/2
isisom(f,g);

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = x^4 - 6
? %2 = [x - 1, x^2 - 6, x^4 - 216, x^4 - 6]
? ? %4 = 
[-1 1]

[2 11]

[3 3]

? %5 = 1
? %6 = x^4 + x^2 + 1/2
? ? 
Goodbye!

Errors/timing (if any):

  ***   obsolete function: isisom(f,g);
                           ^------------
For full compatibility with GP 1.39.15, type "default(compatible,3)", or set 
"compatible = 3" in your GPRC file.

New syntax: isisom(x,y) ===> nfisisom(x,y)

nfisisom(x,y): as nfisincl but tests whether x is isomorphic to y.



Timing:
real	0m0.067s
user	0m0.006s
sys	0m0.007s


'193.170'
************** PARI *****************
Host 193.170.37.83 (193.170.37.83)
Time: Wed Jul 26 06:42:14 2006

Input: f=x^4-6
polred(f)
nf=nfinit(f);
factor(nf.disc)

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = x^4 - 6
? %2 = [x - 1, x^2 - 6, x^4 - 216, x^4 - 6]
? ? %4 = 
[-1 1]

[2 11]

[3 3]

? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.065s
user	0m0.011s
sys	0m0.005s


'193.170'
************** PARI *****************
Host 193.170.37.83 (193.170.37.83)
Time: Wed Jul 26 06:41:47 2006

Input: f=x^4-6
polred(f)
nf=nfinit(f)
nf.disc

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = x^4 - 6
? %2 = [x - 1, x^2 - 6, x^4 - 216, x^4 - 6]
? %3 = [x^4 - 6, [2, 1], -55296, 1, [[1, -1.5650845800732873165844854991586898098, 2.4494897427831780981972840747058913920, -3.8336586254776348551320958309633386020; 1, 1.5650845800732873165844854991586898098, 2.4494897427831780981972840747058913920, 3.8336586254776348551320958309633386020; 1, 0.E-38 - 1.5650845800732873165844854991586898098*I, -2.4494897427831780981972840747058913920 + 0.E-38*I, 0.E-37 + 3.8336586254776348551320958309633386020*I], [1, -1.5650845800732873165844854991586898098, 2.4494897427831780981972840747058913920, -3.8336586254776348551320958309633386020; 1, 1.5650845800732873165844854991586898098, 2.4494897427831780981972840747058913920, 3.8336586254776348551320958309633386020; 1, -1.5650845800732873165844854991586898098, -2.4494897427831780981972840747058913920, 3.8336586254776348551320958309633386020; 1, 1.5650845800732873165844854991586898098, -2.4494897427831780981972840747058913920, -3.8336586254776348551320958309633386020], 0, [4, 0, 0, 0; 0, 0, 0, 24; 0, 0, 24, 0; 0, 24, 0, 0], [24, 0, 0, 0; 0, 24, 0, 0; 0, 0, 24, 0; 0, 0, 0, 4], [-6, 0, 0, 0; 0, 0, 0, -1; 0, 0, -1, 0; 0, -1, 0, 0], [6, [0, 0, 0, 6; 1, 0, 0, 0; 0, 1, 0, 0; 0, 0, 1, 0]]], [-1.5650845800732873165844854991586898098, 1.5650845800732873165844854991586898098, 0.E-38 - 1.5650845800732873165844854991586898098*I], [1, x, x^2, x^3], [1, 0, 0, 0; 0, 1, 0, 0; 0, 0, 1, 0; 0, 0, 0, 1], [1, 0, 0, 0, 0, 0, 0, 6, 0, 0, 6, 0, 0, 6, 0, 0; 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 6, 0, 0, 6, 0; 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 6; 0, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 0]]
? %4 = -55296
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.017s
user	0m0.005s
sys	0m0.008s


'193.170'
************** PARI *****************
Host 193.170.37.83 (193.170.37.83)
Time: Wed Jul 26 06:38:55 2006

Input: f=x^4-6
polred(f)

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = x^4 - 6
? %2 = [x - 1, x^2 - 6, x^4 - 216, x^4 - 6]
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.142s
user	0m0.009s
sys	0m0.009s


'72.30.1'
************** PARI *****************
Host 72.30.131.199 (72.30.131.199)
Time: Wed Jul 26 05:14:49 2006

Input: {ss(n)=sum(x=1,n,n/gcd(n,x))}
ss(60)

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? ? %1 = 1617
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.103s
user	0m0.004s
sys	0m0.007s


'80.36.9'
************** PARI *****************
Host 80.36.96.104 (80.36.96.104)
Time: Wed Jul 26 04:36:04 2006

Input: "Replace this by some code, then click [SAGE] or [PARI]!"

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = "Replace this by some code, then click [SAGE] or [PARI]!"
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.042s
user	0m0.010s
sys	0m0.003s


'72.30.1'
************** PARI *****************
Host 72.30.129.106 (72.30.129.106)
Time: Wed Jul 26 03:54:54 2006

Input: y=210; for(x=1,8,y=sumdiv(y,x,x)-y;print1(y,","))

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? 366,378,582,594,846,1026,1374,1386,
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.207s
user	0m0.007s
sys	0m0.005s


'61.246.'
************** PARI *****************
Host 61.246.151.223 (61.246.151.223)
Time: Tue Jul 25 23:13:51 2006

Input: for(n=1,20, print1(n,": ",valuation(n!,2),", ") )

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? 1: 0, 2: 1, 3: 1, 4: 3, 5: 3, 6: 4, 7: 4, 8: 7, 9: 7, 10: 8, 11: 8, 12: 10, 13: 10, 14: 11, 15: 11, 16: 15, 17: 15, 18: 16, 19: 16, 20: 18, 
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.707s
user	0m0.007s
sys	0m0.008s


'68.42.0'
************** PARI *****************
Host 68.42.0.194 (68.42.0.194)
Time: Tue Jul 25 19:06:38 2006

Input: 163.205 x log10(36.5 + 46.5 � 15.5) � 97.684 x log10(60) � 78.387=



Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? ? 
Goodbye!

Errors/timing (if any):

  ***   Warning: unused characters: xlog10(36.5+46.515.5)97.684xlog10(60)78.387=.
  ***   unknown function or error in formal parameters: 163.205
  ***   xlog10(36.5+46.515.5
        ^--------------------

Timing:
real	0m0.110s
user	0m0.006s
sys	0m0.006s


'68.238.'
************** PARI *****************
Host 68.238.95.250 (68.238.95.250)
Time: Tue Jul 25 18:57:33 2006

Input: "Replace this by some code, then click [SAGE] or [PARI]!"

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = "Replace this by some code, then click [SAGE] or [PARI]!"
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.012s
user	0m0.009s
sys	0m0.004s


'68.238.'
************** PARI *****************
Host 68.238.95.250 (68.238.95.250)
Time: Tue Jul 25 18:57:26 2006

Input: "Replace this by some code, then click [SAGE] or [PARI]!"

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = "Replace this by some code, then click [SAGE] or [PARI]!"
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.011s
user	0m0.009s
sys	0m0.003s


'71.107.'
************** PARI *****************
Host 71.107.11.162 (71.107.11.162)
Time: Tue Jul 25 11:39:56 2006

Input: 13divided by 211


Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = dividedby211
? 
Goodbye!

Errors/timing (if any):

  ***   Warning: unused characters: dividedby211.

Timing:
real	0m0.011s
user	0m0.008s
sys	0m0.005s


'68.3.25'
************** PARI *****************
Host 68.3.255.90 (68.3.255.90)
Time: Tue Jul 25 09:37:47 2006

Input: 355/40

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = 71/8
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.012s
user	0m0.007s
sys	0m0.004s


'82.3.11'
************** PARI *****************
Host 82.3.119.241 (82.3.119.241)
Time: Tue Jul 25 05:54:42 2006

Input: "Replace this by some code, then click [SAGE] or [PARI]!"

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = "Replace this by some code, then click [SAGE] or [PARI]!"
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.011s
user	0m0.006s
sys	0m0.005s


'134.76.'
************** PARI *****************
Host 134.76.82.180 (134.76.82.180)
Time: Tue Jul 25 03:22:03 2006

Input: e=ellinit([0,0,0,0,-11^17]);
factor(ellglobalred(e)[1])
factor(e.disc)

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? ? %2 = 
[2 2]

[3 3]

[11 2]

? %3 = 
[-1 1]

[2 4]

[3 3]

[11 34]

? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.012s
user	0m0.008s
sys	0m0.004s


'134.76.'
************** PARI *****************
Host 134.76.82.180 (134.76.82.180)
Time: Tue Jul 25 03:21:51 2006

Input: e=ellinit([0,0,0,0,-11^17]);
factor(ellglobalred(e)[1])
e.disc

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? ? %2 = 
[2 2]

[3 3]

[11 2]

? %3 = -110365933803306864286040400568060990512
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.013s
user	0m0.007s
sys	0m0.006s


'134.76.'
************** PARI *****************
Host 134.76.82.180 (134.76.82.180)
Time: Tue Jul 25 03:19:59 2006

Input: e=ellinit([0,0,0,0,-11^17]);
factor(ellglobalred(e)[1])


Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? ? %2 = 
[2 2]

[3 3]

[11 2]

? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.013s
user	0m0.006s
sys	0m0.005s


'134.76.'
************** PARI *****************
Host 134.76.82.180 (134.76.82.180)
Time: Tue Jul 25 03:17:23 2006

Input: e=ellinit([0,0,0,-889,11^7]);
factor(ellglobalred(e)[1])
e.c4
e.j
e

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? ? %2 = 
[2 4]

[29 1]

[84017 1]

[4208197067 1]

? %3 = 42672
? %4 = -4856339190528/10253242696366031
? %5 = [0, 0, 0, -889, 19487171, 0, -1778, 77948684, -790321, 42672, -16836915744, -164051883141856496, -4856339190528/10253242696366031, [-270.20277986293979247624839699180734070, 135.10138993146989623812419849590367035 - 232.09514575760783533338793980997212795*I, 135.10138993146989623812419849590367035 + 232.09514575760783533338793980997212795*I]~, 0.25675192542122520606233702175134539177, -0.12837596271061260303116851087567269588 + 0.073931596105245620496114662347600232939*I, -21.219736618399018488603469510838682856, 10.609868309199509244301734755419341428 - 18.346120065090502369024160253262708027*I, 0.018982079649486167464146454267069478279]
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.018s
user	0m0.012s
sys	0m0.002s


'134.76.'
************** PARI *****************
Host 134.76.82.180 (134.76.82.180)
Time: Tue Jul 25 03:17:08 2006

Input: e=ellinit([0,0,0,0,11^7]);
factor(ellglobalred(e)[1])
e.c4
e.j
e

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? ? %2 = 
[2 4]

[3 3]

[11 2]

? %3 = 0
? %4 = 0
? %5 = [0, 0, 0, 0, 19487171, 0, 0, 77948684, 0, 0, -16836915744, -164051928107960112, 0, [-269.10159095888717806100896858338102078, 134.55079547944358903050448429169051039 + 233.04881396920511266557247053075664850*I, 134.55079547944358903050448429169051039 - 233.04881396920511266557247053075664850*I]~, 0.25642923832450672651956603972861282501, -0.12821461916225336325978301986430641250 + 0.074024744887372329104082094358979742342*I, -21.219881665041094945371208085615038980, 10.609940832520547472685604042807519490 - 18.376956587225220519437540828473337000*I, 0.018982108948634809819292170949530388106]
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.013s
user	0m0.005s
sys	0m0.008s


'134.76.'
************** PARI *****************
Host 134.76.82.180 (134.76.82.180)
Time: Tue Jul 25 03:16:22 2006

Input: e=ellinit([0,0,0,0,11^7]);
factor(ellglobalred(e)[1])
e.c4
e.j

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? ? %2 = 
[2 4]

[3 3]

[11 2]

? %3 = 0
? %4 = 0
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.013s
user	0m0.008s
sys	0m0.005s


'134.76.'
************** PARI *****************
Host 134.76.82.180 (134.76.82.180)
Time: Tue Jul 25 03:14:30 2006

Input: e=ellinit([0,0,0,0,11^7]);
factor(ellglobalred(e)[1])

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? ? %2 = 
[2 4]

[3 3]

[11 2]

? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.096s
user	0m0.005s
sys	0m0.009s


'137.193'
************** PARI *****************
Host 137.193.61.27 (137.193.61.27)
Time: Tue Jul 25 03:10:34 2006

Input: 8+5

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = 13
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.012s
user	0m0.006s
sys	0m0.005s


'63.241.'
************** PARI *****************
Host 63.241.61.7 (63.241.61.7)
Time: Mon Jul 24 22:40:08 2006

Input: {ss(n)=sum(x=1,n,n/gcd(n,x))}ss(60)

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = 1617
? 
Goodbye!

Errors/timing (if any):

  ***   Warning: unused characters: ss(60).

Timing:
real	0m0.024s
user	0m0.007s
sys	0m0.007s


'72.30.2'
************** PARI *****************
Host 72.30.226.223 (72.30.226.223)
Time: Mon Jul 24 20:38:42 2006

Input: for(n=1,7, print1(n,": ",sum(x=1,n,1/x),",  ") )

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? 1: 1,  2: 3/2,  3: 11/6,  4: 25/12,  5: 137/60,  6: 49/20,  7: 363/140,  
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.012s
user	0m0.008s
sys	0m0.004s


'69.153.'
************** PARI *****************
Host 69.153.68.164 (69.153.68.164)
Time: Mon Jul 24 18:40:05 2006

Input: -3

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = -3
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.012s
user	0m0.006s
sys	0m0.006s


'75.3.15'
************** PARI *****************
Host 75.3.153.31 (75.3.153.31)
Time: Mon Jul 24 18:33:37 2006

Input: -1/6+5/6


Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = 2/3
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.047s
user	0m0.005s
sys	0m0.007s


'199.91.'
************** PARI *****************
Host 199.91.33.254 (199.91.33.254)
Time: Mon Jul 24 14:28:37 2006

Input: "Replace this by some code, then click [SAGE] or [PARI]!"

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = "Replace this by some code, then click [SAGE] or [PARI]!"
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.011s
user	0m0.005s
sys	0m0.006s


'199.91.'
************** PARI *****************
Host 199.91.33.254 (199.91.33.254)
Time: Mon Jul 24 14:28:28 2006

Input: "Replace this by some code, then click [SAGE] or [PARI]!"

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = "Replace this by some code, then click [SAGE] or [PARI]!"
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.011s
user	0m0.005s
sys	0m0.006s


'71.39.1'
************** PARI *****************
Host 71.39.185.145 (71.39.185.145)
Time: Mon Jul 24 12:13:50 2006

Input: p=43
q=79
n=p*q
e=p+q
h=q-p
a=2
x=(a^(h*h)) / n
g=Mod((a^(h*h)), n)
Mod(p*x, n)
Mod(-1*(g-1), p)

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = 43
? %2 = 79
? %3 = 3397
? %4 = 122
? %5 = 36
? %6 = 2
? %7 = 1364188488619052116466105100188265419717379653273741532242786693992101715597506680981060248106739195555665885784215520253232226795300253192439713838619337787037991503054663889161182688006843079127591737170026798935139113651083474222050508981461091652957942433095504472118187338632823518614811421165606509195698926020610034372011417336379206274761103883598061489450479872973957125731659022336/3397
? %8 = Mod(1460, 3397)
? %9 = Mod(0, 3397)
? %10 = Mod(3, 43)
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.012s
user	0m0.006s
sys	0m0.005s


'71.39.1'
************** PARI *****************
Host 71.39.185.145 (71.39.185.145)
Time: Mon Jul 24 12:13:32 2006

Input: p=43
q=79
n=p*q
e=p+q
h=q-p
a=17
x=(a^(h*h)) / n
g=Mod((a^(h*h)), n)
Mod(p*x, n)
Mod(-1*(g-1), p)

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = 43
? %2 = 79
? %3 = 3397
? %4 = 122
? %5 = 36
? %6 = 17
? %7 = 45898881902230086977008023085916961541815117623689130740904824776533559669194060851416144585018762202477517028290707846663584926325663405357533068224069461994481866198087722267263547713252969528336288682644846039976108304777267408108919737394031674717215599101643532476586721703718659903733211550424739299016656840392339854866942146104015514234730950387483253604366918343888794721553105602112012886818089195059935334735406110472510759971984334640176462525387539456719696024474770282733758923194387905544871614348609927825150234892973603182406795191294207509448549395834252963575522943864736878805925993888165756092444451635073670473562866201092130186340627849882024910598620588365169942575069502169854669277645588419550795349617154674172435761920523437820854684825668256644709722514058493852530675307845834464449988160922693197629230312660149307097509901338261705858084130332051634496451896344752591272453693118427665363868618629423815734263425228535406641068782589246414713897670527226029828635200211843872351475618555679376428476061300534550845571242514199756464411458862263778642740302375725365466183738523469357827777448414600784466724300748777290989194243974939747913178191631114146194846879904250322713542108792780545658883326584240159827102242354180809264261395666216265527978227408879577449029429561901620458138683359486376273198964247785750187165433821888065346088886816373224148567324758675307712551978391988792095159092037763693917870269814697330854299143367146839752649854934716353195472499687855010271328291637764835054222384207209021913398471282371367195124689775931327316806682881/3397
? %8 = Mod(575, 3397)
? %9 = Mod(0, 3397)
? %10 = Mod(28, 43)
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.029s
user	0m0.009s
sys	0m0.003s


'71.39.1'
************** PARI *****************
Host 71.39.185.145 (71.39.185.145)
Time: Mon Jul 24 12:12:39 2006

Input: p=43
q=251
n=p*q
e=p+q
h=q-p
a=17
x=(a^(h*h)) / n
g=Mod((a^(h*h)), n)
Mod(p*x, n)
Mod(-1*(g-1), p)

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = 43
? %2 = 251
? %3 = 10793
? %4 = 294
? %5 = 208
? %6 = 17
? %7 = 1387185401267822509924759255297292885804433274300386345030683365755856554164294480232262571778968780024860079407669388921233980137027507877839700198748264927484292334741828053300815150976158655656213571613796604392820704096821678169572747819286632039828436103256749601201006269095900339995836605336691896532928488558382080623833584701636960250656591737267560929788654008664946714908777700777223068816400042896391063669331801065990788824063604937495039495637818134908746258562161235362047486721679013422572314918970917210961277956232017738891205581920314496300269413322120618284929589780007311518776567394209668191180641985096128927135849953974812947151489884084719586623158191775760536806858042885375033670728202881232392872240600994041238501542345238032568866447257084663755986727629612522001095617502334947739021516140716834105291657513885311131364860490068841001636219374618521893173392620227773980811536735805642602844355109845673075616432584935272255987757443154878200356088006004263237794075696571636001133113175334131701489431433009495454457592964007257381372302678475496639202198036713246981352332852264845066617308226786879397377267263226702870836729116952885398065575325182324365882886855284213971535926515087376457532860647517570498763369635115889300140712120239630505957561387748872291667831800031569383349545939109505985606205489756617552288995710202414329155875435428966280007896974426700259946674766598952101813672378324255642119879626986100348692373281137555902818698601473534260237683313511446283584806873989020892629521306199650462150824395045212181528713011014420340528846159967895529466158939355400303688155536441463459610340808384852885448423916030847852447053417076986657543691779334587771148881759227403563232340372537652579683881122519296450500062094997304816854092348814225263417023537076435204165278111073660828555638194107100432010597326625044795956850215905560749288616141972649127075864504359032024812131595647856185286420829471735119240617488153588560327748851278210373327370435211270490272702456881185800153161605963046634004056722853297976159850995758621443183440260868659428304623206127339816288159688063106076116831464594847795565974873849704703482040307548511851772052757993548485254454335662229527876005052780746694290753882519829371430172554347641415620601518244902223053653222609006252931285367362823945711411593475561222443269226181803384881654890419331904943298592060996494231252182177887360616211711606449308990501196764535708893730777601850342991553868296923840044231207282693145413297336574367919316501111113362810417691559169108887716584494861539845439716655409199546982875342603217858281201008176020548486874994064803236341135876682323017101871265138955385320502874356600951497854078658027851666798939001368302299322727411050776201778661691958852910661568072958766717339211700337500640224421492285573861028100165056209705372564956546625196900524912389637716708247744870070788356444727578957644667729616312667500572898057387183185073603478883880484902219126174324610215605389481762057058100716218186902800759032661461209063426007794341853123551563297941611240986092285816266532160604003132605368808840327632308138810724810327318787311146661263677[+++]
? %8 = Mod(6895, 10793)
? %9 = Mod(0, 10793)
? %10 = Mod(29, 43)
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.211s
user	0m0.151s
sys	0m0.060s


'71.39.1'
************** PARI *****************
Host 71.39.185.145 (71.39.185.145)
Time: Mon Jul 24 12:12:31 2006

Input: p=43
q=251
n=p*q
e=p+q
h=q-p
a=17
x=(a^(h*h)) / n
g=Mod((a^(h*h)), n)
Mod(p*x, n)
Mod((g-1), p)

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = 43
? %2 = 251
? %3 = 10793
? %4 = 294
? %5 = 208
? %6 = 17
? %7 = 1387185401267822509924759255297292885804433274300386345030683365755856554164294480232262571778968780024860079407669388921233980137027507877839700198748264927484292334741828053300815150976158655656213571613796604392820704096821678169572747819286632039828436103256749601201006269095900339995836605336691896532928488558382080623833584701636960250656591737267560929788654008664946714908777700777223068816400042896391063669331801065990788824063604937495039495637818134908746258562161235362047486721679013422572314918970917210961277956232017738891205581920314496300269413322120618284929589780007311518776567394209668191180641985096128927135849953974812947151489884084719586623158191775760536806858042885375033670728202881232392872240600994041238501542345238032568866447257084663755986727629612522001095617502334947739021516140716834105291657513885311131364860490068841001636219374618521893173392620227773980811536735805642602844355109845673075616432584935272255987757443154878200356088006004263237794075696571636001133113175334131701489431433009495454457592964007257381372302678475496639202198036713246981352332852264845066617308226786879397377267263226702870836729116952885398065575325182324365882886855284213971535926515087376457532860647517570498763369635115889300140712120239630505957561387748872291667831800031569383349545939109505985606205489756617552288995710202414329155875435428966280007896974426700259946674766598952101813672378324255642119879626986100348692373281137555902818698601473534260237683313511446283584806873989020892629521306199650462150824395045212181528713011014420340528846159967895529466158939355400303688155536441463459610340808384852885448423916030847852447053417076986657543691779334587771148881759227403563232340372537652579683881122519296450500062094997304816854092348814225263417023537076435204165278111073660828555638194107100432010597326625044795956850215905560749288616141972649127075864504359032024812131595647856185286420829471735119240617488153588560327748851278210373327370435211270490272702456881185800153161605963046634004056722853297976159850995758621443183440260868659428304623206127339816288159688063106076116831464594847795565974873849704703482040307548511851772052757993548485254454335662229527876005052780746694290753882519829371430172554347641415620601518244902223053653222609006252931285367362823945711411593475561222443269226181803384881654890419331904943298592060996494231252182177887360616211711606449308990501196764535708893730777601850342991553868296923840044231207282693145413297336574367919316501111113362810417691559169108887716584494861539845439716655409199546982875342603217858281201008176020548486874994064803236341135876682323017101871265138955385320502874356600951497854078658027851666798939001368302299322727411050776201778661691958852910661568072958766717339211700337500640224421492285573861028100165056209705372564956546625196900524912389637716708247744870070788356444727578957644667729616312667500572898057387183185073603478883880484902219126174324610215605389481762057058100716218186902800759032661461209063426007794341853123551563297941611240986092285816266532160604003132605368808840327632308138810724810327318787311146661263677[+++]
? %8 = Mod(6895, 10793)
? %9 = Mod(0, 10793)
? %10 = Mod(14, 43)
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.205s
user	0m0.147s
sys	0m0.059s


'71.39.1'
************** PARI *****************
Host 71.39.185.145 (71.39.185.145)
Time: Mon Jul 24 12:12:15 2006

Input: p=43
q=251
n=p*q
e=p+q
h=q-p
a=17
x=(a^(h*h)) / n
g=Mod((a^(h*h)), n)
Mod(p*x, n)
Mod(-1*(g-1), p)

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = 43
? %2 = 251
? %3 = 10793
? %4 = 294
? %5 = 208
? %6 = 17
? %7 = 1387185401267822509924759255297292885804433274300386345030683365755856554164294480232262571778968780024860079407669388921233980137027507877839700198748264927484292334741828053300815150976158655656213571613796604392820704096821678169572747819286632039828436103256749601201006269095900339995836605336691896532928488558382080623833584701636960250656591737267560929788654008664946714908777700777223068816400042896391063669331801065990788824063604937495039495637818134908746258562161235362047486721679013422572314918970917210961277956232017738891205581920314496300269413322120618284929589780007311518776567394209668191180641985096128927135849953974812947151489884084719586623158191775760536806858042885375033670728202881232392872240600994041238501542345238032568866447257084663755986727629612522001095617502334947739021516140716834105291657513885311131364860490068841001636219374618521893173392620227773980811536735805642602844355109845673075616432584935272255987757443154878200356088006004263237794075696571636001133113175334131701489431433009495454457592964007257381372302678475496639202198036713246981352332852264845066617308226786879397377267263226702870836729116952885398065575325182324365882886855284213971535926515087376457532860647517570498763369635115889300140712120239630505957561387748872291667831800031569383349545939109505985606205489756617552288995710202414329155875435428966280007896974426700259946674766598952101813672378324255642119879626986100348692373281137555902818698601473534260237683313511446283584806873989020892629521306199650462150824395045212181528713011014420340528846159967895529466158939355400303688155536441463459610340808384852885448423916030847852447053417076986657543691779334587771148881759227403563232340372537652579683881122519296450500062094997304816854092348814225263417023537076435204165278111073660828555638194107100432010597326625044795956850215905560749288616141972649127075864504359032024812131595647856185286420829471735119240617488153588560327748851278210373327370435211270490272702456881185800153161605963046634004056722853297976159850995758621443183440260868659428304623206127339816288159688063106076116831464594847795565974873849704703482040307548511851772052757993548485254454335662229527876005052780746694290753882519829371430172554347641415620601518244902223053653222609006252931285367362823945711411593475561222443269226181803384881654890419331904943298592060996494231252182177887360616211711606449308990501196764535708893730777601850342991553868296923840044231207282693145413297336574367919316501111113362810417691559169108887716584494861539845439716655409199546982875342603217858281201008176020548486874994064803236341135876682323017101871265138955385320502874356600951497854078658027851666798939001368302299322727411050776201778661691958852910661568072958766717339211700337500640224421492285573861028100165056209705372564956546625196900524912389637716708247744870070788356444727578957644667729616312667500572898057387183185073603478883880484902219126174324610215605389481762057058100716218186902800759032661461209063426007794341853123551563297941611240986092285816266532160604003132605368808840327632308138810724810327318787311146661263677[+++]
? %8 = Mod(6895, 10793)
? %9 = Mod(0, 10793)
? %10 = Mod(29, 43)
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.205s
user	0m0.132s
sys	0m0.073s


'71.39.1'
************** PARI *****************
Host 71.39.185.145 (71.39.185.145)
Time: Mon Jul 24 12:12:06 2006

Input: p=43
q=251
n=p*q
e=p+q
h=q-p
a=17
x=(a^(h*h)) / n
g=Mod((a^(h*h)), n)
Mod(p*x, n)
Mod(-1*(g-1), n)

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = 43
? %2 = 251
? %3 = 10793
? %4 = 294
? %5 = 208
? %6 = 17
? %7 = 1387185401267822509924759255297292885804433274300386345030683365755856554164294480232262571778968780024860079407669388921233980137027507877839700198748264927484292334741828053300815150976158655656213571613796604392820704096821678169572747819286632039828436103256749601201006269095900339995836605336691896532928488558382080623833584701636960250656591737267560929788654008664946714908777700777223068816400042896391063669331801065990788824063604937495039495637818134908746258562161235362047486721679013422572314918970917210961277956232017738891205581920314496300269413322120618284929589780007311518776567394209668191180641985096128927135849953974812947151489884084719586623158191775760536806858042885375033670728202881232392872240600994041238501542345238032568866447257084663755986727629612522001095617502334947739021516140716834105291657513885311131364860490068841001636219374618521893173392620227773980811536735805642602844355109845673075616432584935272255987757443154878200356088006004263237794075696571636001133113175334131701489431433009495454457592964007257381372302678475496639202198036713246981352332852264845066617308226786879397377267263226702870836729116952885398065575325182324365882886855284213971535926515087376457532860647517570498763369635115889300140712120239630505957561387748872291667831800031569383349545939109505985606205489756617552288995710202414329155875435428966280007896974426700259946674766598952101813672378324255642119879626986100348692373281137555902818698601473534260237683313511446283584806873989020892629521306199650462150824395045212181528713011014420340528846159967895529466158939355400303688155536441463459610340808384852885448423916030847852447053417076986657543691779334587771148881759227403563232340372537652579683881122519296450500062094997304816854092348814225263417023537076435204165278111073660828555638194107100432010597326625044795956850215905560749288616141972649127075864504359032024812131595647856185286420829471735119240617488153588560327748851278210373327370435211270490272702456881185800153161605963046634004056722853297976159850995758621443183440260868659428304623206127339816288159688063106076116831464594847795565974873849704703482040307548511851772052757993548485254454335662229527876005052780746694290753882519829371430172554347641415620601518244902223053653222609006252931285367362823945711411593475561222443269226181803384881654890419331904943298592060996494231252182177887360616211711606449308990501196764535708893730777601850342991553868296923840044231207282693145413297336574367919316501111113362810417691559169108887716584494861539845439716655409199546982875342603217858281201008176020548486874994064803236341135876682323017101871265138955385320502874356600951497854078658027851666798939001368302299322727411050776201778661691958852910661568072958766717339211700337500640224421492285573861028100165056209705372564956546625196900524912389637716708247744870070788356444727578957644667729616312667500572898057387183185073603478883880484902219126174324610215605389481762057058100716218186902800759032661461209063426007794341853123551563297941611240986092285816266532160604003132605368808840327632308138810724810327318787311146661263677[+++]
? %8 = Mod(6895, 10793)
? %9 = Mod(0, 10793)
? %10 = Mod(3899, 10793)
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.205s
user	0m0.145s
sys	0m0.060s


'71.39.1'
************** PARI *****************
Host 71.39.185.145 (71.39.185.145)
Time: Mon Jul 24 12:11:37 2006

Input: p=43
q=251
n=p*q
e=p+q
h=q-p
a=17
x=(a^(h*h)) / n
g=Mod((a^(h*h)), n)
Mod(p*x, n)
Mod((g-1), n)

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = 43
? %2 = 251
? %3 = 10793
? %4 = 294
? %5 = 208
? %6 = 17
? %7 = 1387185401267822509924759255297292885804433274300386345030683365755856554164294480232262571778968780024860079407669388921233980137027507877839700198748264927484292334741828053300815150976158655656213571613796604392820704096821678169572747819286632039828436103256749601201006269095900339995836605336691896532928488558382080623833584701636960250656591737267560929788654008664946714908777700777223068816400042896391063669331801065990788824063604937495039495637818134908746258562161235362047486721679013422572314918970917210961277956232017738891205581920314496300269413322120618284929589780007311518776567394209668191180641985096128927135849953974812947151489884084719586623158191775760536806858042885375033670728202881232392872240600994041238501542345238032568866447257084663755986727629612522001095617502334947739021516140716834105291657513885311131364860490068841001636219374618521893173392620227773980811536735805642602844355109845673075616432584935272255987757443154878200356088006004263237794075696571636001133113175334131701489431433009495454457592964007257381372302678475496639202198036713246981352332852264845066617308226786879397377267263226702870836729116952885398065575325182324365882886855284213971535926515087376457532860647517570498763369635115889300140712120239630505957561387748872291667831800031569383349545939109505985606205489756617552288995710202414329155875435428966280007896974426700259946674766598952101813672378324255642119879626986100348692373281137555902818698601473534260237683313511446283584806873989020892629521306199650462150824395045212181528713011014420340528846159967895529466158939355400303688155536441463459610340808384852885448423916030847852447053417076986657543691779334587771148881759227403563232340372537652579683881122519296450500062094997304816854092348814225263417023537076435204165278111073660828555638194107100432010597326625044795956850215905560749288616141972649127075864504359032024812131595647856185286420829471735119240617488153588560327748851278210373327370435211270490272702456881185800153161605963046634004056722853297976159850995758621443183440260868659428304623206127339816288159688063106076116831464594847795565974873849704703482040307548511851772052757993548485254454335662229527876005052780746694290753882519829371430172554347641415620601518244902223053653222609006252931285367362823945711411593475561222443269226181803384881654890419331904943298592060996494231252182177887360616211711606449308990501196764535708893730777601850342991553868296923840044231207282693145413297336574367919316501111113362810417691559169108887716584494861539845439716655409199546982875342603217858281201008176020548486874994064803236341135876682323017101871265138955385320502874356600951497854078658027851666798939001368302299322727411050776201778661691958852910661568072958766717339211700337500640224421492285573861028100165056209705372564956546625196900524912389637716708247744870070788356444727578957644667729616312667500572898057387183185073603478883880484902219126174324610215605389481762057058100716218186902800759032661461209063426007794341853123551563297941611240986092285816266532160604003132605368808840327632308138810724810327318787311146661263677[+++]
? %8 = Mod(6895, 10793)
? %9 = Mod(0, 10793)
? %10 = Mod(6894, 10793)
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.210s
user	0m0.143s
sys	0m0.068s


'71.39.1'
************** PARI *****************
Host 71.39.185.145 (71.39.185.145)
Time: Mon Jul 24 12:11:11 2006

Input: p=43
q=251
n=p*q
e=p+q
h=q-p
a=17
x=(a^(h*h)) / n
g=Mod((a^(h*h)), n)
Mod(p*x, n)
Mod(-1*(g-1), n)

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = 43
? %2 = 251
? %3 = 10793
? %4 = 294
? %5 = 208
? %6 = 17
? %7 = 1387185401267822509924759255297292885804433274300386345030683365755856554164294480232262571778968780024860079407669388921233980137027507877839700198748264927484292334741828053300815150976158655656213571613796604392820704096821678169572747819286632039828436103256749601201006269095900339995836605336691896532928488558382080623833584701636960250656591737267560929788654008664946714908777700777223068816400042896391063669331801065990788824063604937495039495637818134908746258562161235362047486721679013422572314918970917210961277956232017738891205581920314496300269413322120618284929589780007311518776567394209668191180641985096128927135849953974812947151489884084719586623158191775760536806858042885375033670728202881232392872240600994041238501542345238032568866447257084663755986727629612522001095617502334947739021516140716834105291657513885311131364860490068841001636219374618521893173392620227773980811536735805642602844355109845673075616432584935272255987757443154878200356088006004263237794075696571636001133113175334131701489431433009495454457592964007257381372302678475496639202198036713246981352332852264845066617308226786879397377267263226702870836729116952885398065575325182324365882886855284213971535926515087376457532860647517570498763369635115889300140712120239630505957561387748872291667831800031569383349545939109505985606205489756617552288995710202414329155875435428966280007896974426700259946674766598952101813672378324255642119879626986100348692373281137555902818698601473534260237683313511446283584806873989020892629521306199650462150824395045212181528713011014420340528846159967895529466158939355400303688155536441463459610340808384852885448423916030847852447053417076986657543691779334587771148881759227403563232340372537652579683881122519296450500062094997304816854092348814225263417023537076435204165278111073660828555638194107100432010597326625044795956850215905560749288616141972649127075864504359032024812131595647856185286420829471735119240617488153588560327748851278210373327370435211270490272702456881185800153161605963046634004056722853297976159850995758621443183440260868659428304623206127339816288159688063106076116831464594847795565974873849704703482040307548511851772052757993548485254454335662229527876005052780746694290753882519829371430172554347641415620601518244902223053653222609006252931285367362823945711411593475561222443269226181803384881654890419331904943298592060996494231252182177887360616211711606449308990501196764535708893730777601850342991553868296923840044231207282693145413297336574367919316501111113362810417691559169108887716584494861539845439716655409199546982875342603217858281201008176020548486874994064803236341135876682323017101871265138955385320502874356600951497854078658027851666798939001368302299322727411050776201778661691958852910661568072958766717339211700337500640224421492285573861028100165056209705372564956546625196900524912389637716708247744870070788356444727578957644667729616312667500572898057387183185073603478883880484902219126174324610215605389481762057058100716218186902800759032661461209063426007794341853123551563297941611240986092285816266532160604003132605368808840327632308138810724810327318787311146661263677[+++]
? %8 = Mod(6895, 10793)
? %9 = Mod(0, 10793)
? %10 = Mod(3899, 10793)
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.223s
user	0m0.147s
sys	0m0.060s


'71.39.1'
************** PARI *****************
Host 71.39.185.145 (71.39.185.145)
Time: Mon Jul 24 12:10:50 2006

Input: p=43
q=251
n=p*q
e=p+q
h=q-p
a=17
x=(a^(h*h)) / n
g=Mod((a^(h*h)), n)
Mod(p*x, n)

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = 43
? %2 = 251
? %3 = 10793
? %4 = 294
? %5 = 208
? %6 = 17
? %7 = 1387185401267822509924759255297292885804433274300386345030683365755856554164294480232262571778968780024860079407669388921233980137027507877839700198748264927484292334741828053300815150976158655656213571613796604392820704096821678169572747819286632039828436103256749601201006269095900339995836605336691896532928488558382080623833584701636960250656591737267560929788654008664946714908777700777223068816400042896391063669331801065990788824063604937495039495637818134908746258562161235362047486721679013422572314918970917210961277956232017738891205581920314496300269413322120618284929589780007311518776567394209668191180641985096128927135849953974812947151489884084719586623158191775760536806858042885375033670728202881232392872240600994041238501542345238032568866447257084663755986727629612522001095617502334947739021516140716834105291657513885311131364860490068841001636219374618521893173392620227773980811536735805642602844355109845673075616432584935272255987757443154878200356088006004263237794075696571636001133113175334131701489431433009495454457592964007257381372302678475496639202198036713246981352332852264845066617308226786879397377267263226702870836729116952885398065575325182324365882886855284213971535926515087376457532860647517570498763369635115889300140712120239630505957561387748872291667831800031569383349545939109505985606205489756617552288995710202414329155875435428966280007896974426700259946674766598952101813672378324255642119879626986100348692373281137555902818698601473534260237683313511446283584806873989020892629521306199650462150824395045212181528713011014420340528846159967895529466158939355400303688155536441463459610340808384852885448423916030847852447053417076986657543691779334587771148881759227403563232340372537652579683881122519296450500062094997304816854092348814225263417023537076435204165278111073660828555638194107100432010597326625044795956850215905560749288616141972649127075864504359032024812131595647856185286420829471735119240617488153588560327748851278210373327370435211270490272702456881185800153161605963046634004056722853297976159850995758621443183440260868659428304623206127339816288159688063106076116831464594847795565974873849704703482040307548511851772052757993548485254454335662229527876005052780746694290753882519829371430172554347641415620601518244902223053653222609006252931285367362823945711411593475561222443269226181803384881654890419331904943298592060996494231252182177887360616211711606449308990501196764535708893730777601850342991553868296923840044231207282693145413297336574367919316501111113362810417691559169108887716584494861539845439716655409199546982875342603217858281201008176020548486874994064803236341135876682323017101871265138955385320502874356600951497854078658027851666798939001368302299322727411050776201778661691958852910661568072958766717339211700337500640224421492285573861028100165056209705372564956546625196900524912389637716708247744870070788356444727578957644667729616312667500572898057387183185073603478883880484902219126174324610215605389481762057058100716218186902800759032661461209063426007794341853123551563297941611240986092285816266532160604003132605368808840327632308138810724810327318787311146661263677[+++]
? %8 = Mod(6895, 10793)
? %9 = Mod(0, 10793)
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.211s
user	0m0.144s
sys	0m0.068s


'71.39.1'
************** PARI *****************
Host 71.39.185.145 (71.39.185.145)
Time: Mon Jul 24 12:09:55 2006

Input: p=43
q=251
n=p*q
e=p+q
h=q-p
a=17
x=(a^(h*h)) / n
g=Mod((a^(h*h)), n)


Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = 43
? %2 = 251
? %3 = 10793
? %4 = 294
? %5 = 208
? %6 = 17
? %7 = 1387185401267822509924759255297292885804433274300386345030683365755856554164294480232262571778968780024860079407669388921233980137027507877839700198748264927484292334741828053300815150976158655656213571613796604392820704096821678169572747819286632039828436103256749601201006269095900339995836605336691896532928488558382080623833584701636960250656591737267560929788654008664946714908777700777223068816400042896391063669331801065990788824063604937495039495637818134908746258562161235362047486721679013422572314918970917210961277956232017738891205581920314496300269413322120618284929589780007311518776567394209668191180641985096128927135849953974812947151489884084719586623158191775760536806858042885375033670728202881232392872240600994041238501542345238032568866447257084663755986727629612522001095617502334947739021516140716834105291657513885311131364860490068841001636219374618521893173392620227773980811536735805642602844355109845673075616432584935272255987757443154878200356088006004263237794075696571636001133113175334131701489431433009495454457592964007257381372302678475496639202198036713246981352332852264845066617308226786879397377267263226702870836729116952885398065575325182324365882886855284213971535926515087376457532860647517570498763369635115889300140712120239630505957561387748872291667831800031569383349545939109505985606205489756617552288995710202414329155875435428966280007896974426700259946674766598952101813672378324255642119879626986100348692373281137555902818698601473534260237683313511446283584806873989020892629521306199650462150824395045212181528713011014420340528846159967895529466158939355400303688155536441463459610340808384852885448423916030847852447053417076986657543691779334587771148881759227403563232340372537652579683881122519296450500062094997304816854092348814225263417023537076435204165278111073660828555638194107100432010597326625044795956850215905560749288616141972649127075864504359032024812131595647856185286420829471735119240617488153588560327748851278210373327370435211270490272702456881185800153161605963046634004056722853297976159850995758621443183440260868659428304623206127339816288159688063106076116831464594847795565974873849704703482040307548511851772052757993548485254454335662229527876005052780746694290753882519829371430172554347641415620601518244902223053653222609006252931285367362823945711411593475561222443269226181803384881654890419331904943298592060996494231252182177887360616211711606449308990501196764535708893730777601850342991553868296923840044231207282693145413297336574367919316501111113362810417691559169108887716584494861539845439716655409199546982875342603217858281201008176020548486874994064803236341135876682323017101871265138955385320502874356600951497854078658027851666798939001368302299322727411050776201778661691958852910661568072958766717339211700337500640224421492285573861028100165056209705372564956546625196900524912389637716708247744870070788356444727578957644667729616312667500572898057387183185073603478883880484902219126174324610215605389481762057058100716218186902800759032661461209063426007794341853123551563297941611240986092285816266532160604003132605368808840327632308138810724810327318787311146661263677[+++]
? %8 = Mod(6895, 10793)
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.210s
user	0m0.156s
sys	0m0.053s


'71.39.1'
************** PARI *****************
Host 71.39.185.145 (71.39.185.145)
Time: Mon Jul 24 12:09:29 2006

Input: p=43
q=251
n=p*q
e=p+q
h=q-p
a=17
x=(a^(h*h)) / n
g=Mod((a^(h*h)) / n, n)


Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = 43
? %2 = 251
? %3 = 10793
? %4 = 294
? %5 = 208
? %6 = 17
? %7 = 1387185401267822509924759255297292885804433274300386345030683365755856554164294480232262571778968780024860079407669388921233980137027507877839700198748264927484292334741828053300815150976158655656213571613796604392820704096821678169572747819286632039828436103256749601201006269095900339995836605336691896532928488558382080623833584701636960250656591737267560929788654008664946714908777700777223068816400042896391063669331801065990788824063604937495039495637818134908746258562161235362047486721679013422572314918970917210961277956232017738891205581920314496300269413322120618284929589780007311518776567394209668191180641985096128927135849953974812947151489884084719586623158191775760536806858042885375033670728202881232392872240600994041238501542345238032568866447257084663755986727629612522001095617502334947739021516140716834105291657513885311131364860490068841001636219374618521893173392620227773980811536735805642602844355109845673075616432584935272255987757443154878200356088006004263237794075696571636001133113175334131701489431433009495454457592964007257381372302678475496639202198036713246981352332852264845066617308226786879397377267263226702870836729116952885398065575325182324365882886855284213971535926515087376457532860647517570498763369635115889300140712120239630505957561387748872291667831800031569383349545939109505985606205489756617552288995710202414329155875435428966280007896974426700259946674766598952101813672378324255642119879626986100348692373281137555902818698601473534260237683313511446283584806873989020892629521306199650462150824395045212181528713011014420340528846159967895529466158939355400303688155536441463459610340808384852885448423916030847852447053417076986657543691779334587771148881759227403563232340372537652579683881122519296450500062094997304816854092348814225263417023537076435204165278111073660828555638194107100432010597326625044795956850215905560749288616141972649127075864504359032024812131595647856185286420829471735119240617488153588560327748851278210373327370435211270490272702456881185800153161605963046634004056722853297976159850995758621443183440260868659428304623206127339816288159688063106076116831464594847795565974873849704703482040307548511851772052757993548485254454335662229527876005052780746694290753882519829371430172554347641415620601518244902223053653222609006252931285367362823945711411593475561222443269226181803384881654890419331904943298592060996494231252182177887360616211711606449308990501196764535708893730777601850342991553868296923840044231207282693145413297336574367919316501111113362810417691559169108887716584494861539845439716655409199546982875342603217858281201008176020548486874994064803236341135876682323017101871265138955385320502874356600951497854078658027851666798939001368302299322727411050776201778661691958852910661568072958766717339211700337500640224421492285573861028100165056209705372564956546625196900524912389637716708247744870070788356444727578957644667729616312667500572898057387183185073603478883880484902219126174324610215605389481762057058100716218186902800759032661461209063426007794341853123551563297941611240986092285816266532160604003132605368808840327632308138810724810327318787311146661263677[+++]
? %8 = Mod(0, 10793)
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.211s
user	0m0.138s
sys	0m0.074s


'71.39.1'
************** PARI *****************
Host 71.39.185.145 (71.39.185.145)
Time: Mon Jul 24 12:08:44 2006

Input: p=43
q=251
n=p*q
e=p+q
h=q-p
a=17
x=(a^((h)*(h))) / n
g=Mod((a^((h)*(h))) / n, n)


Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = 43
? %2 = 251
? %3 = 10793
? %4 = 294
? %5 = 208
? %6 = 17
? %7 = 1387185401267822509924759255297292885804433274300386345030683365755856554164294480232262571778968780024860079407669388921233980137027507877839700198748264927484292334741828053300815150976158655656213571613796604392820704096821678169572747819286632039828436103256749601201006269095900339995836605336691896532928488558382080623833584701636960250656591737267560929788654008664946714908777700777223068816400042896391063669331801065990788824063604937495039495637818134908746258562161235362047486721679013422572314918970917210961277956232017738891205581920314496300269413322120618284929589780007311518776567394209668191180641985096128927135849953974812947151489884084719586623158191775760536806858042885375033670728202881232392872240600994041238501542345238032568866447257084663755986727629612522001095617502334947739021516140716834105291657513885311131364860490068841001636219374618521893173392620227773980811536735805642602844355109845673075616432584935272255987757443154878200356088006004263237794075696571636001133113175334131701489431433009495454457592964007257381372302678475496639202198036713246981352332852264845066617308226786879397377267263226702870836729116952885398065575325182324365882886855284213971535926515087376457532860647517570498763369635115889300140712120239630505957561387748872291667831800031569383349545939109505985606205489756617552288995710202414329155875435428966280007896974426700259946674766598952101813672378324255642119879626986100348692373281137555902818698601473534260237683313511446283584806873989020892629521306199650462150824395045212181528713011014420340528846159967895529466158939355400303688155536441463459610340808384852885448423916030847852447053417076986657543691779334587771148881759227403563232340372537652579683881122519296450500062094997304816854092348814225263417023537076435204165278111073660828555638194107100432010597326625044795956850215905560749288616141972649127075864504359032024812131595647856185286420829471735119240617488153588560327748851278210373327370435211270490272702456881185800153161605963046634004056722853297976159850995758621443183440260868659428304623206127339816288159688063106076116831464594847795565974873849704703482040307548511851772052757993548485254454335662229527876005052780746694290753882519829371430172554347641415620601518244902223053653222609006252931285367362823945711411593475561222443269226181803384881654890419331904943298592060996494231252182177887360616211711606449308990501196764535708893730777601850342991553868296923840044231207282693145413297336574367919316501111113362810417691559169108887716584494861539845439716655409199546982875342603217858281201008176020548486874994064803236341135876682323017101871265138955385320502874356600951497854078658027851666798939001368302299322727411050776201778661691958852910661568072958766717339211700337500640224421492285573861028100165056209705372564956546625196900524912389637716708247744870070788356444727578957644667729616312667500572898057387183185073603478883880484902219126174324610215605389481762057058100716218186902800759032661461209063426007794341853123551563297941611240986092285816266532160604003132605368808840327632308138810724810327318787311146661263677[+++]
? %8 = Mod(0, 10793)
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.264s
user	0m0.131s
sys	0m0.081s


'71.39.1'
************** PARI *****************
Host 71.39.185.145 (71.39.185.145)
Time: Mon Jul 24 12:07:23 2006

Input: p=43
q=251
n=p*q
e=p+q
h=q-p
a=17
x=(a^((h)*(h))) / n

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = 43
? %2 = 251
? %3 = 10793
? %4 = 294
? %5 = 208
? %6 = 17
? %7 = 1387185401267822509924759255297292885804433274300386345030683365755856554164294480232262571778968780024860079407669388921233980137027507877839700198748264927484292334741828053300815150976158655656213571613796604392820704096821678169572747819286632039828436103256749601201006269095900339995836605336691896532928488558382080623833584701636960250656591737267560929788654008664946714908777700777223068816400042896391063669331801065990788824063604937495039495637818134908746258562161235362047486721679013422572314918970917210961277956232017738891205581920314496300269413322120618284929589780007311518776567394209668191180641985096128927135849953974812947151489884084719586623158191775760536806858042885375033670728202881232392872240600994041238501542345238032568866447257084663755986727629612522001095617502334947739021516140716834105291657513885311131364860490068841001636219374618521893173392620227773980811536735805642602844355109845673075616432584935272255987757443154878200356088006004263237794075696571636001133113175334131701489431433009495454457592964007257381372302678475496639202198036713246981352332852264845066617308226786879397377267263226702870836729116952885398065575325182324365882886855284213971535926515087376457532860647517570498763369635115889300140712120239630505957561387748872291667831800031569383349545939109505985606205489756617552288995710202414329155875435428966280007896974426700259946674766598952101813672378324255642119879626986100348692373281137555902818698601473534260237683313511446283584806873989020892629521306199650462150824395045212181528713011014420340528846159967895529466158939355400303688155536441463459610340808384852885448423916030847852447053417076986657543691779334587771148881759227403563232340372537652579683881122519296450500062094997304816854092348814225263417023537076435204165278111073660828555638194107100432010597326625044795956850215905560749288616141972649127075864504359032024812131595647856185286420829471735119240617488153588560327748851278210373327370435211270490272702456881185800153161605963046634004056722853297976159850995758621443183440260868659428304623206127339816288159688063106076116831464594847795565974873849704703482040307548511851772052757993548485254454335662229527876005052780746694290753882519829371430172554347641415620601518244902223053653222609006252931285367362823945711411593475561222443269226181803384881654890419331904943298592060996494231252182177887360616211711606449308990501196764535708893730777601850342991553868296923840044231207282693145413297336574367919316501111113362810417691559169108887716584494861539845439716655409199546982875342603217858281201008176020548486874994064803236341135876682323017101871265138955385320502874356600951497854078658027851666798939001368302299322727411050776201778661691958852910661568072958766717339211700337500640224421492285573861028100165056209705372564956546625196900524912389637716708247744870070788356444727578957644667729616312667500572898057387183185073603478883880484902219126174324610215605389481762057058100716218186902800759032661461209063426007794341853123551563297941611240986092285816266532160604003132605368808840327632308138810724810327318787311146661263677[+++]
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.202s
user	0m0.132s
sys	0m0.071s


'71.39.1'
************** PARI *****************
Host 71.39.185.145 (71.39.185.145)
Time: Mon Jul 24 12:07:10 2006

Input: p=43
q=251
n=p*q
e=p+q
h=q-p
a=17
x=(a^((n-1)*(n-1))) / n

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = 43
? %2 = 251
? %3 = 10793
? %4 = 294
? %5 = 208
? %6 = 17
? 
Errors/timing (if any):

/var/www/cgi-bin/calc/gp: line 1: 20364 Killed                  ./gp-2.2.11 -s 256000000 -emacs

Timing:
real	0m21.103s
user	0m20.600s
sys	0m0.431s


'71.39.1'
************** PARI *****************
Host 71.39.185.145 (71.39.185.145)
Time: Mon Jul 24 12:06:40 2006

Input: p=43
q=251
n=p*q
e=p+q
h=q-p
a=17
x=(a^((n-1)*(n-1))) / p

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = 43
? %2 = 251
? %3 = 10793
? %4 = 294
? %5 = 208
? %6 = 17
? 
Errors/timing (if any):

/var/www/cgi-bin/calc/gp: line 1: 20355 Killed                  ./gp-2.2.11 -s 256000000 -emacs

Timing:
real	0m21.123s
user	0m20.584s
sys	0m0.445s


'71.39.1'
************** PARI *****************
Host 71.39.185.145 (71.39.185.145)
Time: Mon Jul 24 12:06:15 2006

Input: p=43
q=251
n=p*q
e=p+q
h=q-p
a=17
x=(a^((n-1)*(n-1))) / p

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = 43
? %2 = 251
? %3 = 10793
? %4 = 294
? %5 = 208
? %6 = 17
? 
Errors/timing (if any):

/var/www/cgi-bin/calc/gp: line 1: 20344 Killed                  ./gp-2.2.11 -s 256000000 -emacs

Timing:
real	0m21.345s
user	0m20.468s
sys	0m0.562s


'71.39.1'
************** PARI *****************
Host 71.39.185.145 (71.39.185.145)
Time: Mon Jul 24 12:06:15 2006

Input: p=43
q=251
n=p*q
e=p+q
h=q-p
a=17


Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = 43
? %2 = 251
? %3 = 10793
? %4 = 294
? %5 = 208
? %6 = 17
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.012s
user	0m0.007s
sys	0m0.004s


'71.39.1'
************** PARI *****************
Host 71.39.185.145 (71.39.185.145)
Time: Mon Jul 24 12:05:45 2006

Input: P=43
q=251
n=p*q


Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = 43
? %2 = 251
? %3 = 251*p
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.013s
user	0m0.007s
sys	0m0.005s


'71.39.1'
************** PARI *****************
Host 71.39.185.145 (71.39.185.145)
Time: Mon Jul 24 12:05:37 2006

Input: P=43;
q=251;
n=p*q;


Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? ? ? ? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.011s
user	0m0.006s
sys	0m0.005s


'71.39.1'
************** PARI *****************
Host 71.39.185.145 (71.39.185.145)
Time: Mon Jul 24 12:05:31 2006

Input: P=43
q=251
n=p*q;


Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = 43
? %2 = 251
? ? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.011s
user	0m0.007s
sys	0m0.004s


'71.39.1'
************** PARI *****************
Host 71.39.185.145 (71.39.185.145)
Time: Mon Jul 24 12:05:25 2006

Input: P=43
q=251
n=p*q


Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = 43
? %2 = 251
? %3 = 251*p
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.011s
user	0m0.003s
sys	0m0.009s


'71.39.1'
************** PARI *****************
Host 71.39.185.145 (71.39.185.145)
Time: Mon Jul 24 12:04:58 2006

Input: P=43
q=251
n=p*q
e=p+q
h=q-p
a=17
x=(a^((n-1)*(n-1))) / p

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = 43
? %2 = 251
? %3 = 251*p
? %4 = p + 251
? %5 = -p + 251
? %6 = 17
? %7 = 17.000000000000000000000000000000000000*p^-1 - 24178.642678175748028849528428929261854 + 20228736.178431694885440087994107421648*p - 12467444727.271974325493802370832327495*p^2 + 6238394713630.1666842720705640085846837*p^3 - 2664692180589515.0220741632053507666505*p^4 + 1002827991814119709.3237607641069529220*p^5 - 339652170943518224477.07253192773747608*p^6 + 105134782472266759163697.31051215304037*p^7 - 30086998600969158543176295.881292507845*p^8 + 8032405231654233844599969060.2770886535*p^9 - 2015004362774387974242834215406.1100560*p^10 + 477781603549259438278453683177587.10415*p^11 - 107605648694695217196207934613330594.67*p^12 + 23114866841254664064004610624222882372.*p^13 - 4.7526568506817171410932884741988588531 E39*p^14 + O(p^15)
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.013s
user	0m0.004s
sys	0m0.009s


'71.39.1'
************** PARI *****************
Host 71.39.185.145 (71.39.185.145)
Time: Mon Jul 24 12:04:38 2006

Input: P=43
q=251
n=p*q
e=p+q
h=q-p
a=17
x=a^((n-1)*(n-1)) / p

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = 43
? %2 = 251
? %3 = 251*p
? %4 = p + 251
? %5 = -p + 251
? %6 = 17
? %7 = 17.000000000000000000000000000000000000*p^-1 - 24178.642678175748028849528428929261854 + 20228736.178431694885440087994107421648*p - 12467444727.271974325493802370832327495*p^2 + 6238394713630.1666842720705640085846837*p^3 - 2664692180589515.0220741632053507666505*p^4 + 1002827991814119709.3237607641069529220*p^5 - 339652170943518224477.07253192773747608*p^6 + 105134782472266759163697.31051215304037*p^7 - 30086998600969158543176295.881292507845*p^8 + 8032405231654233844599969060.2770886535*p^9 - 2015004362774387974242834215406.1100560*p^10 + 477781603549259438278453683177587.10415*p^11 - 107605648694695217196207934613330594.67*p^12 + 23114866841254664064004610624222882372.*p^13 - 4.7526568506817171410932884741988588531 E39*p^14 + O(p^15)
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.024s
user	0m0.009s
sys	0m0.004s


'169.229'
************** PARI *****************
Host 169.229.137.154 (169.229.137.154)
Time: Mon Jul 24 11:45:31 2006

Input: f1 = 'alt=sin(t)'
f2 = 'azm=sin(t)*cos(p)'
eqn=maxima([f1,f2])
s = eqn.solve('[p,t]'); s



Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? ? ? ? ? ? 
Goodbye!

Errors/timing (if any):

  ***   unexpected character: f1='alt=sin(t)'
                                     ^--------
  ***   unexpected character: f2='azm=sin(t)*cos(p)'
                                     ^---------------
  ***   unknown function or error in formal parameters: eqn=maxima([f1,f2])
                                                            ^---------------
  ***   Warning: unused characters: ('[p,t]');s.
  ***   unknown member function: s=eqn.solve('[p,t]');s
                                       ^----------------

Timing:
real	0m0.012s
user	0m0.005s
sys	0m0.006s


'67.11.2'
************** PARI *****************
Host 67.11.212.178 (67.11.212.178)
Time: Mon Jul 24 09:26:22 2006

Input: 20 * .30


Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = 6.0000000000000000000000000000000000000
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.011s
user	0m0.005s
sys	0m0.007s


'67.11.2'
************** PARI *****************
Host 67.11.212.178 (67.11.212.178)
Time: Mon Jul 24 09:26:11 2006

Input: 20 x .30


Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? ? 
Goodbye!

Errors/timing (if any):

  ***   Warning: unused characters: x.30.
  ***   unknown member function: 20x.30
                                     ^--

Timing:
real	0m0.011s
user	0m0.007s
sys	0m0.004s


'72.30.1'
************** PARI *****************
Host 72.30.129.106 (72.30.129.106)
Time: Mon Jul 24 09:11:54 2006

Input: y=210; for(x=1,8,y=sumdiv(y,x,x)-y;print1(y,","))

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? 366,378,582,594,846,1026,1374,1386,
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.012s
user	0m0.004s
sys	0m0.007s


'169.237'
************** PARI *****************
Host 169.237.30.114 (169.237.30.114)
Time: Mon Jul 24 09:07:17 2006

Input: "Replace this by some code, then click [SAGE] or [PARI]!"

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = "Replace this by some code, then click [SAGE] or [PARI]!"
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.011s
user	0m0.006s
sys	0m0.005s


'70.31.1'
************** PARI *****************
Host 70.31.199.89 (70.31.199.89)
Time: Mon Jul 24 06:37:32 2006

Input: (4m + 5)2

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? ? 
Goodbye!

Errors/timing (if any):

  ***   expected character: ')' instead of: (4m+5)2
                                              ^-----

Timing:
real	0m0.011s
user	0m0.007s
sys	0m0.005s


'134.76.'
************** PARI *****************
Host 134.76.82.172 (134.76.82.172)
Time: Mon Jul 24 05:28:36 2006

Input: q(d)=quadclassunit(nfinit(x^2-d).disc);
q(3)
q(5)
q(15)
q(19)
?quadclassunit
?4
?qfbclassno
?qfbhclassno



Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? ? %1 = [1, [], [], 1.3169578969248167086250463473079684440]
? %2 = [1, [], [], 0.48121182505960344749775891342436842314]
? %3 = [2, [2], [Qfb(2, 6, -3, 0.E-57)], 2.0634370688955605467272811726201318715]
? %4 = [1, [], [], 5.8289369669789265547345668575229095390]
? quadclassunit(D,{flag=0},{tech=[]}): compute the structure of the class group 
and the regulator of the quadratic field of discriminant D. If flag is 
non-null (and D>0), compute the narrow class group. See manual for the 
optional technical parameters.

? 
addprimes     bestappr      bezout        bezoutres     bigomega
binomial      chinese       content       contfrac      contfracpnqn
core          coredisc      dirdiv        direuler      dirmul
divisors      eulerphi      factor        factorback    factorcantor
factorff      factorial     factorint     factormod     ffinit
fibonacci     gcd           hilbert       isfundamental ispower
isprime       ispseudoprime issquare      issquarefree  kronecker
lcm           moebius       nextprime     numbpart      numdiv
omega         precprime     prime         primepi       primes
qfbclassno    qfbcompraw    qfbhclassno   qfbnucomp     qfbnupow
qfbpowraw     qfbprimeform  qfbred        qfbsolve      quadclassunit
quaddisc      quadgen       quadhilbert   quadpoly      quadray
quadregulator quadunit      removeprimes  sigma         sqrtint
zncoppersmith znlog         znorder       znprimroot    znstar

? qfbclassno(x,{flag=0}): class number of discriminant x using Shanks's method 
by default. If (optional) flag is set to 1, use Euler products.

? qfbhclassno(x): Hurwitz-Kronecker class number of x>0.

? ? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.016s
user	0m0.009s
sys	0m0.007s


'134.76.'
************** PARI *****************
Host 134.76.82.172 (134.76.82.172)
Time: Mon Jul 24 05:27:19 2006

Input: q(d)=quadclassunit(nfinit(x^2-d).disc);
q(3)
q(5)
q(15)
q(19)
?quadclassunit
?4




Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? ? %1 = [1, [], [], 1.3169578969248167086250463473079684440]
? %2 = [1, [], [], 0.48121182505960344749775891342436842314]
? %3 = [2, [2], [Qfb(2, 6, -3, 0.E-57)], 2.0634370688955605467272811726201318715]
? %4 = [1, [], [], 5.8289369669789265547345668575229095390]
? quadclassunit(D,{flag=0},{tech=[]}): compute the structure of the class group 
and the regulator of the quadratic field of discriminant D. If flag is 
non-null (and D>0), compute the narrow class group. See manual for the 
optional technical parameters.

? 
addprimes     bestappr      bezout        bezoutres     bigomega
binomial      chinese       content       contfrac      contfracpnqn
core          coredisc      dirdiv        direuler      dirmul
divisors      eulerphi      factor        factorback    factorcantor
factorff      factorial     factorint     factormod     ffinit
fibonacci     gcd           hilbert       isfundamental ispower
isprime       ispseudoprime issquare      issquarefree  kronecker
lcm           moebius       nextprime     numbpart      numdiv
omega         precprime     prime         primepi       primes
qfbclassno    qfbcompraw    qfbhclassno   qfbnucomp     qfbnupow
qfbpowraw     qfbprimeform  qfbred        qfbsolve      quadclassunit
quaddisc      quadgen       quadhilbert   quadpoly      quadray
quadregulator quadunit      removeprimes  sigma         sqrtint
zncoppersmith znlog         znorder       znprimroot    znstar

? ? ? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.015s
user	0m0.008s
sys	0m0.008s


'134.76.'
************** PARI *****************
Host 134.76.82.172 (134.76.82.172)
Time: Mon Jul 24 05:26:37 2006

Input: q(d)=quadclassunit(nfinit(x^2-d).disc);
q(3)
q(5)
q(15)
q(19)
?quadclassunit




Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? ? %1 = [1, [], [], 1.3169578969248167086250463473079684440]
? %2 = [1, [], [], 0.48121182505960344749775891342436842314]
? %3 = [2, [2], [Qfb(2, 6, -3, 0.E-57)], 2.0634370688955605467272811726201318715]
? %4 = [1, [], [], 5.8289369669789265547345668575229095390]
? quadclassunit(D,{flag=0},{tech=[]}): compute the structure of the class group 
and the regulator of the quadratic field of discriminant D. If flag is 
non-null (and D>0), compute the narrow class group. See manual for the 
optional technical parameters.

? ? ? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.015s
user	0m0.009s
sys	0m0.007s


'134.76.'
************** PARI *****************
Host 134.76.82.172 (134.76.82.172)
Time: Mon Jul 24 05:26:17 2006

Input: q(d)=quadclassunit(nfinit(x^2-d).disc);
q(3)
q(5)
q(15)
q(19)



Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? ? %1 = [1, [], [], 1.3169578969248167086250463473079684440]
? %2 = [1, [], [], 0.48121182505960344749775891342436842314]
? %3 = [2, [2], [Qfb(2, 6, -3, 0.E-57)], 2.0634370688955605467272811726201318715]
? %4 = [1, [], [], 5.8289369669789265547345668575229095390]
? ? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.016s
user	0m0.010s
sys	0m0.005s


'134.76.'
************** PARI *****************
Host 134.76.82.172 (134.76.82.172)
Time: Mon Jul 24 05:25:38 2006

Input: q(d)=quadclassunit(nfinit(x^2-d).disc);
q(5)
q(-5)
q(-163)
q(-167)
q(11)
q(12)
q(13)
q(14)
q(15)
q(16)
q(17)
q(18)
q(19)



Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? ? %1 = [1, [], [], 0.48121182505960344749775891342436842314]
? %2 = [2, [2], [Qfb(3, -2, 2)], 1]
? %3 = [1, [], [], 1]
? %4 = [11, [11], [Qfb(2, 1, 21)], 1]
? %5 = [1, [], [], 2.9932228461263808979126677137741829131]
? %6 = [1, [], [], 1.3169578969248167086250463473079684440]
? %7 = [1, [], [], 1.1947632172871093041119308285190905235]
? %8 = [1, [], [], 3.4000844141133395007001872142448670645]
? %9 = [2, [2], [Qfb(2, 6, -3, 0.E-57)], 2.0634370688955605467272811726201318715]
? ? %10 = [1, [], [], 2.0947125472611012942448228460655286535]
? %11 = [1, [], [], 0.88137358701954302523260932497979230902]
? %12 = [1, [], [], 5.8289369669789265547345668575229095390]
? ? 
Goodbye!

Errors/timing (if any):

  *** nfinit: reducible polynomial in nfinit.

Timing:
real	0m0.020s
user	0m0.014s
sys	0m0.006s


'134.76.'
************** PARI *****************
Host 134.76.82.172 (134.76.82.172)
Time: Mon Jul 24 05:24:53 2006

Input: q(d)=quadclassunit(nfinit(x^2-d).disc);
q(5)
q(-5)
q(-163)
q(-167)
q(11)
q(12)
q(13)


Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? ? %1 = [1, [], [], 0.48121182505960344749775891342436842314]
? %2 = [2, [2], [Qfb(3, -2, 2)], 1]
? %3 = [1, [], [], 1]
? %4 = [11, [11], [Qfb(2, 1, 21)], 1]
? %5 = [1, [], [], 2.9932228461263808979126677137741829131]
? %6 = [1, [], [], 1.3169578969248167086250463473079684440]
? %7 = [1, [], [], 1.1947632172871093041119308285190905235]
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.018s
user	0m0.011s
sys	0m0.007s


'134.76.'
************** PARI *****************
Host 134.76.82.172 (134.76.82.172)
Time: Mon Jul 24 05:24:10 2006

Input: q(d)=quadclassunit(nfinit(x^2-d).disc);
q(13)


Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? ? %1 = [1, [], [], 1.1947632172871093041119308285190905235]
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.013s
user	0m0.005s
sys	0m0.008s


'134.76.'
************** PARI *****************
Host 134.76.82.172 (134.76.82.172)
Time: Mon Jul 24 05:22:37 2006

Input: p=x^2-13;
nf=nfinit(p);
factor(nf.disc);
?4
?quadclassunit
quadclassunit(13)


Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? ? ? ? 
addprimes     bestappr      bezout        bezoutres     bigomega
binomial      chinese       content       contfrac      contfracpnqn
core          coredisc      dirdiv        direuler      dirmul
divisors      eulerphi      factor        factorback    factorcantor
factorff      factorial     factorint     factormod     ffinit
fibonacci     gcd           hilbert       isfundamental ispower
isprime       ispseudoprime issquare      issquarefree  kronecker
lcm           moebius       nextprime     numbpart      numdiv
omega         precprime     prime         primepi       primes
qfbclassno    qfbcompraw    qfbhclassno   qfbnucomp     qfbnupow
qfbpowraw     qfbprimeform  qfbred        qfbsolve      quadclassunit
quaddisc      quadgen       quadhilbert   quadpoly      quadray
quadregulator quadunit      removeprimes  sigma         sqrtint
zncoppersmith znlog         znorder       znprimroot    znstar

? quadclassunit(D,{flag=0},{tech=[]}): compute the structure of the class group 
and the regulator of the quadratic field of discriminant D. If flag is 
non-null (and D>0), compute the narrow class group. See manual for the 
optional technical parameters.

? %4 = [1, [], [], 1.1947632172871093041119308285190905235]
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.013s
user	0m0.009s
sys	0m0.004s


'134.76.'
************** PARI *****************
Host 134.76.82.172 (134.76.82.172)
Time: Mon Jul 24 05:21:55 2006

Input: p=x^2-13;
nf=nfinit(p);
factor(nf.disc);
?4
?quadclassunit


Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? ? ? ? 
addprimes     bestappr      bezout        bezoutres     bigomega
binomial      chinese       content       contfrac      contfracpnqn
core          coredisc      dirdiv        direuler      dirmul
divisors      eulerphi      factor        factorback    factorcantor
factorff      factorial     factorint     factormod     ffinit
fibonacci     gcd           hilbert       isfundamental ispower
isprime       ispseudoprime issquare      issquarefree  kronecker
lcm           moebius       nextprime     numbpart      numdiv
omega         precprime     prime         primepi       primes
qfbclassno    qfbcompraw    qfbhclassno   qfbnucomp     qfbnupow
qfbpowraw     qfbprimeform  qfbred        qfbsolve      quadclassunit
quaddisc      quadgen       quadhilbert   quadpoly      quadray
quadregulator quadunit      removeprimes  sigma         sqrtint
zncoppersmith znlog         znorder       znprimroot    znstar

? quadclassunit(D,{flag=0},{tech=[]}): compute the structure of the class group 
and the regulator of the quadratic field of discriminant D. If flag is 
non-null (and D>0), compute the narrow class group. See manual for the 
optional technical parameters.

? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.014s
user	0m0.009s
sys	0m0.004s


'134.76.'
************** PARI *****************
Host 134.76.82.172 (134.76.82.172)
Time: Mon Jul 24 05:20:15 2006

Input: p=x^2-13;
nf=nfinit(p);
factor(nf.disc);
?4



Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? ? ? ? 
addprimes     bestappr      bezout        bezoutres     bigomega
binomial      chinese       content       contfrac      contfracpnqn
core          coredisc      dirdiv        direuler      dirmul
divisors      eulerphi      factor        factorback    factorcantor
factorff      factorial     factorint     factormod     ffinit
fibonacci     gcd           hilbert       isfundamental ispower
isprime       ispseudoprime issquare      issquarefree  kronecker
lcm           moebius       nextprime     numbpart      numdiv
omega         precprime     prime         primepi       primes
qfbclassno    qfbcompraw    qfbhclassno   qfbnucomp     qfbnupow
qfbpowraw     qfbprimeform  qfbred        qfbsolve      quadclassunit
quaddisc      quadgen       quadhilbert   quadpoly      quadray
quadregulator quadunit      removeprimes  sigma         sqrtint
zncoppersmith znlog         znorder       znprimroot    znstar

? ? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.013s
user	0m0.008s
sys	0m0.005s


'134.76.'
************** PARI *****************
Host 134.76.82.172 (134.76.82.172)
Time: Mon Jul 24 05:19:54 2006

Input: p=x^2-13;
nf=nfinit(p);
factor(nf.disc);
?



Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? ? ? ? Help topics: for a list of relevant subtopics, type ?n for n in
  0: user-defined identifiers (variable, alias, function)
  1: Standard monadic or dyadic OPERATORS
  2: CONVERSIONS and similar elementary functions
  3: TRANSCENDENTAL functions
  4: NUMBER THEORETICAL functions
  5: Functions related to ELLIPTIC CURVES
  6: Functions related to general NUMBER FIELDS
  7: POLYNOMIALS and power series
  8: Vectors, matrices, LINEAR ALGEBRA and sets
  9: SUMS, products, integrals and similar functions
 10: GRAPHIC functions
 11: PROGRAMMING under GP
 12: The PARI community

Also:
  ? functionname (short on-line help)
  ?\             (keyboard shortcuts)
  ?.             (member functions)

? ? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.012s
user	0m0.007s
sys	0m0.007s


'134.76.'
************** PARI *****************
Host 134.76.82.172 (134.76.82.172)
Time: Mon Jul 24 05:17:26 2006

Input: p=x^2-13;
nf=nfinit(p);
factor(nf.disc);
?6


Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? ? ? ? 
bnfcertify         bnfclassunit       bnfclgp            bnfdecodemodule
bnfinit            bnfisintnorm       bnfisnorm          bnfisprincipal
bnfissunit         bnfisunit          bnfmake            bnfnarrow
bnfreg             bnfsignunit        bnfsunit           bnfunit
bnrL1              bnrclass           bnrclassno         bnrclassnolist
bnrconductor       bnrconductorofchar bnrdisc            bnrdisclist
bnrinit            bnrisconductor     bnrisprincipal     bnrrootnumber
bnrstark           dirzetak           factornf           galoisexport
galoisfixedfield   galoisidentify     galoisinit         galoisisabelian
galoispermtopol    galoissubcyclo     galoissubfields    galoissubgroups
idealadd           idealaddtoone      idealappr          idealchinese
idealcoprime       idealdiv           idealfactor        idealhnf
idealintersect     idealinv           ideallist          ideallistarch
ideallog           idealmin           idealmul           idealnorm
idealpow           idealprimedec      idealprincipal     idealred
idealstar          idealtwoelt        idealval           ideleprincipal
matalgtobasis      matbasistoalg      modreverse         newtonpoly
nfalgtobasis       nfbasis            nfbasistoalg       nfdetint
nfdisc             nfeltdiv           nfeltdiveuc        nfeltdivmodpr
nfeltdivrem        nfeltmod           nfeltmul           nfeltmulmodpr
nfeltpow           nfeltpowmodpr      nfeltreduce        nfeltreducemodpr
nfeltval           nffactor           nffactormod        nfgaloisapply
nfgaloisconj       nfhilbert          nfhnf              nfhnfmod
nfinit             nfisideal          nfisincl           nfisisom
nfkermodpr         nfmodprinit        nfnewprec          nfroots
nfrootsof1         nfsnf              nfsolvemodpr       nfsubfields
polcompositum      polgalois          polred             polredabs
polredord          poltschirnhaus     rnfalgtobasis      rnfbasis
rnfbasistoalg      rnfcharpoly        rnfconductor       rnfdedekind
rnfdet             rnfdisc            rnfeltabstorel     rnfeltdown
rnfeltreltoabs     rnfeltup           rnfequation        rnfhnfbasis
rnfidealabstorel   rnfidealdown       rnfidealhnf        rnfidealmul
rnfidealnormabs    rnfidealnormrel    rnfidealreltoabs   rnfidealtwoelt
rnfidealup         rnfinit            rnfisfree          rnfisnorm
rnfisnorminit      rnfkummer          rnflllgram         rnfnormgroup
rnfpolred          rnfpolredabs       rnfpseudobasis     rnfsteinitz
subgrouplist       zetak              zetakinit          

? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.013s
user	0m0.008s
sys	0m0.005s


'134.76.'
************** PARI *****************
Host 134.76.82.172 (134.76.82.172)
Time: Mon Jul 24 05:16:50 2006

Input: p=x^2-13;
nf=nfinit(p);
factor(nf.disc)
?


Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? ? ? %3 = 
[13 1]

? Help topics: for a list of relevant subtopics, type ?n for n in
  0: user-defined identifiers (variable, alias, function)
  1: Standard monadic or dyadic OPERATORS
  2: CONVERSIONS and similar elementary functions
  3: TRANSCENDENTAL functions
  4: NUMBER THEORETICAL functions
  5: Functions related to ELLIPTIC CURVES
  6: Functions related to general NUMBER FIELDS
  7: POLYNOMIALS and power series
  8: Vectors, matrices, LINEAR ALGEBRA and sets
  9: SUMS, products, integrals and similar functions
 10: GRAPHIC functions
 11: PROGRAMMING under GP
 12: The PARI community

Also:
  ? functionname (short on-line help)
  ?\             (keyboard shortcuts)
  ?.             (member functions)

? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.013s
user	0m0.009s
sys	0m0.004s


'134.76.'
************** PARI *****************
Host 134.76.82.172 (134.76.82.172)
Time: Mon Jul 24 05:16:25 2006

Input: p=x^2-13;
nf=nfinit(p);
factor(nf.disc)

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? ? ? %3 = 
[13 1]

? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.123s
user	0m0.010s
sys	0m0.006s


'72.30.1'
************** PARI *****************
Host 72.30.110.15 (72.30.110.15)
Time: Sun Jul 23 21:06:21 2006

Input: for(x=1,50,print1("d(",x,")=",numdiv(x),", "))

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? d(1)=1, d(2)=2, d(3)=2, d(4)=3, d(5)=2, d(6)=4, d(7)=2, d(8)=4, d(9)=3, d(10)=4, d(11)=2, d(12)=6, d(13)=2, d(14)=4, d(15)=4, d(16)=5, d(17)=2, d(18)=6, d(19)=2, d(20)=6, d(21)=4, d(22)=4, d(23)=2, d(24)=8, d(25)=3, d(26)=4, d(27)=4, d(28)=6, d(29)=2, d(30)=8, d(31)=2, d(32)=6, d(33)=4, d(34)=4, d(35)=4, d(36)=9, d(37)=2, d(38)=4, d(39)=4, d(40)=8, d(41)=2, d(42)=8, d(43)=2, d(44)=6, d(45)=6, d(46)=4, d(47)=2, d(48)=10, d(49)=3, d(50)=6, 
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.053s
user	0m0.008s
sys	0m0.003s


'69.199.'
************** PARI *****************
Host 69.199.89.124 (69.199.89.124)
Time: Sun Jul 23 18:55:26 2006

Input: log(0.7, 0.028)=


Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? ? 
Goodbye!

Errors/timing (if any):

  ***   expected character: ')' instead of: log(0.7,0.028)=
                                                   ^--------

Timing:
real	0m0.011s
user	0m0.006s
sys	0m0.005s


'68.65.1'
************** PARI *****************
Host 68.65.144.232 (68.65.144.232)
Time: Sun Jul 23 17:18:48 2006

Input: 2052/160

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = 513/40
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.012s
user	0m0.005s
sys	0m0.007s


'130.13.'
************** PARI *****************
Host 130.13.101.118 (130.13.101.118)
Time: Sun Jul 23 12:18:36 2006

Input: p=282174488599599500573849980909
q=671998030559713968361666935769
phi=p*q
p1=sqrt(phi)
r=phi-p1*p1

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = 282174488599599500573849980909
? %2 = 671998030559713968361666935769
? %3 = 189620700613125325959116839007395234454467716598457179234021
? %4 = 435454590759042665485476994260.29417462
? %5 = 0.E21
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.012s
user	0m0.008s
sys	0m0.004s


'72.30.9'
************** PARI *****************
Host 72.30.98.145 (72.30.98.145)
Time: Sun Jul 23 12:07:03 2006

Input: for(n=1,20, print1(n,": ",valuation(n!,2),", ") )

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? 1: 0, 2: 1, 3: 1, 4: 3, 5: 3, 6: 4, 7: 4, 8: 7, 9: 7, 10: 8, 11: 8, 12: 10, 13: 10, 14: 11, 15: 11, 16: 15, 17: 15, 18: 16, 19: 16, 20: 18, 
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.027s
user	0m0.007s
sys	0m0.004s


'65.54.1'
************** PARI *****************
Host 65.54.188.53 (65.54.188.53)
Time: Sun Jul 23 11:07:14 2006

Input: {ss(n)=sum(x=1,n,n/gcd(n,x))}
ss(60)

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? ? %1 = 1617
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.012s
user	0m0.008s
sys	0m0.003s


'74.129.'
************** PARI *****************
Host 74.129.80.7 (74.129.80.7)
Time: Sun Jul 23 10:32:31 2006

Input: 251 - 121 + 441 - 340 + 130 - 113 + 409 - 253 + 130 - 181 + 297 - 149 + 081 - 088 + 467 - 059 + 306 - 229 + 345 - 351 + 117 - 047 + 353 - 216 + 401 - 147

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = 1434
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.012s
user	0m0.007s
sys	0m0.005s


'74.129.'
************** PARI *****************
Host 74.129.80.7 (74.129.80.7)
Time: Sun Jul 23 10:32:18 2006

Input: 251 - 121 + 441 - 340 + 130 - 113 + 409 - 253 + 130 - 181 + 297 - 149 + 081 - 088 + 467 - 059 + 306 - 229 + 345 - 351 + 117 - 047 + 353 - 216 + 401 - 147

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = 1434
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.011s
user	0m0.006s
sys	0m0.005s


'169.231'
************** PARI *****************
Host 169.231.35.225 (169.231.35.225)
Time: Sun Jul 23 09:46:24 2006

Input: [1,0;1,1]^2

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = 
[1 0]

[2 1]

? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.011s
user	0m0.006s
sys	0m0.005s


'169.231'
************** PARI *****************
Host 169.231.35.225 (169.231.35.225)
Time: Sun Jul 23 09:46:11 2006

Input: [1,1;0,1]^2

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = 
[1 2]

[0 1]

? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.011s
user	0m0.006s
sys	0m0.005s


'169.231'
************** PARI *****************
Host 169.231.35.225 (169.231.35.225)
Time: Sun Jul 23 09:45:52 2006

Input: [1,0;0,0]^2

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = 
[1 0]

[0 0]

? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.011s
user	0m0.007s
sys	0m0.005s


'169.231'
************** PARI *****************
Host 169.231.35.225 (169.231.35.225)
Time: Sun Jul 23 09:45:38 2006

Input: [1,1;0,0]^2

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = 
[1 1]

[0 0]

? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.011s
user	0m0.006s
sys	0m0.006s


'169.231'
************** PARI *****************
Host 169.231.35.225 (169.231.35.225)
Time: Sun Jul 23 09:44:22 2006

Input: [1,1,0;0,1,1;1,0,1]^5

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = 
[11 10 11]

[11 11 10]

[10 11 11]

? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.011s
user	0m0.006s
sys	0m0.006s


'169.231'
************** PARI *****************
Host 169.231.35.225 (169.231.35.225)
Time: Sun Jul 23 09:43:48 2006

Input: [1,1,0;0,1,1;1,0,1]^4

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = 
[5 5 6]

[6 5 5]

[5 6 5]

? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.011s
user	0m0.004s
sys	0m0.007s


'169.231'
************** PARI *****************
Host 169.231.35.225 (169.231.35.225)
Time: Sun Jul 23 09:42:51 2006

Input: [1,1,0;0,1,1;1,0,1]^3

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = 
[2 3 3]

[3 2 3]

[3 3 2]

? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.012s
user	0m0.005s
sys	0m0.006s


'169.231'
************** PARI *****************
Host 169.231.35.225 (169.231.35.225)
Time: Sun Jul 23 09:42:42 2006

Input: [1,1,0;0,1,1;1,0,1]^2

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = 
[1 2 1]

[1 1 2]

[2 1 1]

? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.011s
user	0m0.005s
sys	0m0.006s


'210.56.'
************** PARI *****************
Host 210.56.15.19 (210.56.15.19)
Time: Sun Jul 23 09:42:24 2006

Input: "Replace this by some code, then click [SAGE] or [PARI]!"

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = "Replace this by some code, then click [SAGE] or [PARI]!"
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.012s
user	0m0.007s
sys	0m0.005s


'169.231'
************** PARI *****************
Host 169.231.35.225 (169.231.35.225)
Time: Sun Jul 23 09:40:56 2006

Input: [1,0,1;0,1,1;1,1,0]^7

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = 
[43 42 43]

[42 43 43]

[43 43 42]

? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.012s
user	0m0.008s
sys	0m0.005s


'169.231'
************** PARI *****************
Host 169.231.35.225 (169.231.35.225)
Time: Sun Jul 23 09:40:19 2006

Input: [1,0,1;0,1,1;1,1,0]^6

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = 
[22 21 21]

[21 22 21]

[21 21 22]

? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.012s
user	0m0.007s
sys	0m0.006s


'169.231'
************** PARI *****************
Host 169.231.35.225 (169.231.35.225)
Time: Sun Jul 23 09:39:29 2006

Input: [1,0,1;0,1,1;1,1,0]^5

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = 
[11 10 11]

[10 11 11]

[11 11 10]

? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.032s
user	0m0.006s
sys	0m0.006s


'169.231'
************** PARI *****************
Host 169.231.35.225 (169.231.35.225)
Time: Sun Jul 23 09:38:16 2006

Input: [1,0,1;0,1,1;1,1,0]*[1,0,1;0,1,1;1,1,0]*[1,0,1;0,1,1;1,1,0]*[1,0,1;0,1,1;1,1,0]

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = 
[6 5 5]

[5 6 5]

[5 5 6]

? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.012s
user	0m0.005s
sys	0m0.007s


'169.231'
************** PARI *****************
Host 169.231.35.225 (169.231.35.225)
Time: Sun Jul 23 09:36:38 2006

Input: [1,0,1;0,1,1;1,1,0]*[1,0,1;0,1,1;1,1,0]*[1,0,1;0,1,1;1,1,0]

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = 
[3 2 3]

[2 3 3]

[3 3 2]

? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.012s
user	0m0.007s
sys	0m0.005s


'169.231'
************** PARI *****************
Host 169.231.35.225 (169.231.35.225)
Time: Sun Jul 23 09:34:04 2006

Input: [1,1,1,1;0,2,1,0;1,0,1,2;1,1,1,1]*[1,0,0,1;0,0,1,1;1,1,0,0;0,1,1,0]

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = 
[2 2 2 2]

[1 1 2 2]

[2 3 2 1]

[2 2 2 2]

? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.025s
user	0m0.006s
sys	0m0.006s


'67.33.2'
************** PARI *****************
Host 67.33.205.137 (67.33.205.137)
Time: Sun Jul 23 09:11:54 2006

Input: 39.54+10.00+3.74+1.69+1.29+3.36+8.51+5.31+39.88+20.00+6.72+4.49+4.12+6.40+3.18+1.67+10.00+7.89+5.00+3.45+10.03+3.74+8.92-5.55


Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = 203.38000000000000000000000000000000000
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.284s
user	0m0.008s
sys	0m0.005s


'72.30.1'
************** PARI *****************
Host 72.30.129.106 (72.30.129.106)
Time: Sun Jul 23 07:21:12 2006

Input: y=210; for(x=1,8,y=sumdiv(y,x,x)-y;print1(y,","))

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? 366,378,582,594,846,1026,1374,1386,
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.106s
user	0m0.009s
sys	0m0.003s


'72.30.1'
************** PARI *****************
Host 72.30.102.206 (72.30.102.206)
Time: Sun Jul 23 01:55:51 2006

Input: vector(20,x,floor((x+1)*sqrt(2))-floor(x*sqrt(2)))

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = [1, 2, 1, 2, 1, 1, 2, 1, 2, 1, 1, 2, 1, 2, 1, 2, 1, 1, 2, 1]
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.120s
user	0m0.003s
sys	0m0.010s


'72.30.1'
************** PARI *****************
Host 72.30.129.123 (72.30.129.123)
Time: Sat Jul 22 20:48:42 2006

Input: collatzlength(x0)=
{
   local(x,i);
   x=x0;  i=0;   
   while(x-1,
      x=if(Mod(x,2)==Mod(0,2), x/2, (3*x+1)/2);i=i++ );
   i
}
collatzlength(299)

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? ? %1 = 75
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.051s
user	0m0.006s
sys	0m0.011s


'72.30.2'
************** PARI *****************
Host 72.30.226.223 (72.30.226.223)
Time: Sat Jul 22 14:44:05 2006

Input: for(n=1,7, print1(n,": ",sum(x=1,n,1/x),",  ") )

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? 1: 1,  2: 3/2,  3: 11/6,  4: 25/12,  5: 137/60,  6: 49/20,  7: 363/140,  
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.011s
user	0m0.006s
sys	0m0.006s


'169.231'
************** PARI *****************
Host 169.231.35.225 (169.231.35.225)
Time: Sat Jul 22 10:30:12 2006

Input: [1,0,0;1,1,0;1,1,1]*[1,0,0;1,1,0;1,1,1]

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = 
[1 0 0]

[2 1 0]

[3 2 1]

? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.012s
user	0m0.004s
sys	0m0.007s


'169.231'
************** PARI *****************
Host 169.231.35.225 (169.231.35.225)
Time: Sat Jul 22 09:49:46 2006

Input: [1,0,0;1,1,0;1,1,1]*[1,0,0;1,1,0;1,1,1]*[1,0,0;1,1,0;1,1,1]


Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = 
[1 0 0]

[3 1 0]

[6 3 1]

? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.011s
user	0m0.006s
sys	0m0.006s


'169.231'
************** PARI *****************
Host 169.231.35.225 (169.231.35.225)
Time: Sat Jul 22 09:47:52 2006

Input: [1,0,0;1,1,0;1,1,1]*[1,0,0;1,1,0;1,1,1]

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = 
[1 0 0]

[2 1 0]

[3 2 1]

? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.011s
user	0m0.006s
sys	0m0.005s


'169.231'
************** PARI *****************
Host 169.231.35.225 (169.231.35.225)
Time: Sat Jul 22 09:47:34 2006

Input: [1,0,0;1,1,0;1,1,1]*[1,0,0;1,1,;1,1,1]

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? ? 
Goodbye!

Errors/timing (if any):

  ***   unexpected character: ...;1,1,0;1,1,1]*[1,0,0;1,1,;1,1,1]
                                                          ^-------

Timing:
real	0m0.011s
user	0m0.005s
sys	0m0.006s


'169.231'
************** PARI *****************
Host 169.231.35.225 (169.231.35.225)
Time: Sat Jul 22 09:46:44 2006

Input: [1,0,0;1,1,1;1,1,1]*[1,0,0;1,1,1;1,1,1]

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = 
[1 0 0]

[3 2 2]

[3 2 2]

? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.011s
user	0m0.006s
sys	0m0.005s


'169.231'
************** PARI *****************
Host 169.231.35.225 (169.231.35.225)
Time: Sat Jul 22 09:46:29 2006

Input: [1,0,0;1,1,1,;1,1,1]*[1,0,0;1,1,1;1,1,1]

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? ? 
Goodbye!

Errors/timing (if any):

  ***   expected character: ';' instead of: [1,0,0;1,1,1,;1,1,1]*[1,0,0;1,1,
                                                        ^--------------------

Timing:
real	0m0.014s
user	0m0.009s
sys	0m0.004s


'72.30.1'
************** PARI *****************
Host 72.30.129.106 (72.30.129.106)
Time: Sat Jul 22 06:10:38 2006

Input: y=210; for(x=1,8,y=sumdiv(y,x,x)-y;print1(y,","))

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? 366,378,582,594,846,1026,1374,1386,
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.011s
user	0m0.003s
sys	0m0.008s


'72.30.9'
************** PARI *****************
Host 72.30.98.26 (72.30.98.26)
Time: Sat Jul 22 03:24:42 2006

Input: factor(2^(2^5)+1)

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = 
[641 1]

[6700417 1]

? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.012s
user	0m0.006s
sys	0m0.005s


'169.231'
************** PARI *****************
Host 169.231.35.225 (169.231.35.225)
Time: Fri Jul 21 20:25:34 2006

Input: [1, 0, 1;1, 1,0;0, 1, 1]*[1, 0, 1;1, 1,0;0, 1, 1]


Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = 
[1 1 2]

[2 1 1]

[1 2 1]

? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.012s
user	0m0.004s
sys	0m0.008s


'169.231'
************** PARI *****************
Host 169.231.35.225 (169.231.35.225)
Time: Fri Jul 21 20:25:17 2006

Input: {[1, 0, 1;1, 1,0;0, 1, 1]}*{[1, 0, 1;1, 1,0;0, 1, 1]}


Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? ? 
Goodbye!

Errors/timing (if any):

  ***   sorry, embedded braces (in parser) is not yet implemented.

Timing:
real	0m0.012s
user	0m0.006s
sys	0m0.005s


'169.231'
************** PARI *****************
Host 169.231.35.225 (169.231.35.225)
Time: Fri Jul 21 20:24:32 2006

Input: [1, 0, 1;1, 1,0;0, 1, 1]


Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = 
[1 0 1]

[1 1 0]

[0 1 1]

? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.012s
user	0m0.006s
sys	0m0.005s


'169.231'
************** PARI *****************
Host 169.231.35.225 (169.231.35.225)
Time: Fri Jul 21 20:19:39 2006

Input: [2,2;3,4;6,5]


Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = 
[2 2]

[3 4]

[6 5]

? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.012s
user	0m0.008s
sys	0m0.004s


'169.231'
************** PARI *****************
Host 169.231.35.225 (169.231.35.225)
Time: Fri Jul 21 20:18:55 2006

Input: [2,1]*[2,1]


Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? ? 
Goodbye!

Errors/timing (if any):

  ***   forbidden multiplication t_VEC * t_VEC.

Timing:
real	0m0.012s
user	0m0.007s
sys	0m0.005s


'169.231'
************** PARI *****************
Host 169.231.35.225 (169.231.35.225)
Time: Fri Jul 21 20:18:34 2006

Input: [2,1]


Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = [2, 1]
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.012s
user	0m0.008s
sys	0m0.005s


'72.30.1'
************** PARI *****************
Host 72.30.107.8 (72.30.107.8)
Time: Fri Jul 21 20:00:55 2006

Input: for(b=1,100, for(a=1,b, if( frac((a^2+b^2)/(a*b))==0 , print(a,",",b), ) ) )

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? 1,1
2,2
3,3
4,4
5,5
6,6
7,7
8,8
9,9
10,10
11,11
12,12
13,13
14,14
15,15
16,16
17,17
18,18
19,19
20,20
21,21
22,22
23,23
24,24
25,25
26,26
27,27
28,28
29,29
30,30
31,31
32,32
33,33
34,34
35,35
36,36
37,37
38,38
39,39
40,40
41,41
42,42
43,43
44,44
45,45
46,46
47,47
48,48
49,49
50,50
51,51
52,52
53,53
54,54
55,55
56,56
57,57
58,58
59,59
60,60
61,61
62,62
63,63
64,64
65,65
66,66
67,67
68,68
69,69
70,70
71,71
72,72
73,73
74,74
75,75
76,76
77,77
78,78
79,79
80,80
81,81
82,82
83,83
84,84
85,85
86,86
87,87
88,88
89,89
90,90
91,91
92,92
93,93
94,94
95,95
96,96
97,97
98,98
99,99
100,100
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.045s
user	0m0.024s
sys	0m0.006s


'24.250.'
************** PARI *****************
Host 24.250.16.34 (24.250.16.34)
Time: Fri Jul 21 17:39:17 2006

Input: "Replace this by some code, then click [SAGE] or [PARI]!"

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = "Replace this by some code, then click [SAGE] or [PARI]!"
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.012s
user	0m0.007s
sys	0m0.005s


'128.193'
************** PARI *****************
Host 128.193.221.253 (128.193.221.253)
Time: Fri Jul 21 17:01:13 2006

Input: log ( 27 * 54 )

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = 7.2848209125686034577887035429933307959
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.011s
user	0m0.005s
sys	0m0.006s


'206.15.'
************** PARI *****************
Host 206.15.72.193 (206.15.72.193)
Time: Fri Jul 21 16:06:17 2006

Input: y= t*(x+2)

(169/220*x^2 + (-104/55*y - 291/220)*x + (64/55*y^2 + 31/110*y - 47/110))/(x+2)


Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = t*x + 2*t
? ? %2 = ((256*t^2 - 416*t + 169)*x^2 + (1024*t^2 - 770*t - 291)*x + (1024*t^2 + 124*t - 94))/(220*x + 440)
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.012s
user	0m0.010s
sys	0m0.002s


'206.15.'
************** PARI *****************
Host 206.15.72.193 (206.15.72.193)
Time: Fri Jul 21 16:05:03 2006

Input: x = t*(y+2)

(169/220*x^2 + (-104/55*y - 291/220)*x + (64/55*y^2 + 31/110*y - 47/110))/(y+2)


Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = (y + 2)*t
? ? %2 = (169/220*y + 169/110)*t^2 + (-104/55*y - 291/220)*t + ((128*y^2 + 31*y - 47)/(110*y + 220))
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.012s
user	0m0.007s
sys	0m0.005s


'206.15.'
************** PARI *****************
Host 206.15.72.193 (206.15.72.193)
Time: Fri Jul 21 16:04:06 2006

Input: x = t*(y+2)

(169/220*x^2 + (-104/55*y - 291/220)*x + (64/55*y^2 + 31/110*y - 47/110))


Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = (y + 2)*t
? ? %2 = (169/220*y^2 + 169/55*y + 169/55)*t^2 + (-104/55*y^2 - 1123/220*y - 291/110)*t + (64/55*y^2 + 31/110*y - 47/110)
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.011s
user	0m0.007s
sys	0m0.004s


'206.15.'
************** PARI *****************
Host 206.15.72.193 (206.15.72.193)
Time: Fri Jul 21 16:03:49 2006

Input: x = t*(y+2)

(169/220*x^2 + (-104/55*y - 291/220)*x + (64/55*y^2 + 31/110*y - 47/110))/(x+1)


Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = (y + 2)*t
? ? %2 = ((169*y^2 + 676*y + 676)*t^2 + (-416*y^2 - 1123*y - 582)*t + (256*y^2 + 62*y - 94))/((220*y + 440)*t + 220)
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.012s
user	0m0.007s
sys	0m0.006s


'206.15.'
************** PARI *****************
Host 206.15.72.193 (206.15.72.193)
Time: Fri Jul 21 15:55:58 2006

Input: y = t*x + t -1

(169/220*x^2 + (-104/55*y - 291/220)*x + (64/55*y^2 + 31/110*y - 47/110))/(x+1)


Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = t*x + (t - 1)
? ? %2 = ((256*t^2 - 416*t + 169)*x^2 + (512*t^2 - 866*t + 125)*x + (256*t^2 - 450*t + 100))/(220*x + 220)
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.012s
user	0m0.009s
sys	0m0.004s


'206.15.'
************** PARI *****************
Host 206.15.72.193 (206.15.72.193)
Time: Fri Jul 21 15:55:41 2006

Input: y = t*x + t -1

169/220*x^2 + (-104/55*y - 291/220)*x + (64/55*y^2 + 31/110*y - 47/110)(x+1)


Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = t*x + (t - 1)
? ? %2 = x + 1
? 
Goodbye!

Errors/timing (if any):

  ***   Warning: unused characters: (x+1).

Timing:
real	0m0.012s
user	0m0.007s
sys	0m0.005s


'206.15.'
************** PARI *****************
Host 206.15.72.193 (206.15.72.193)
Time: Fri Jul 21 15:54:52 2006

Input: y = t*x +t -1

169/220*x^2 + (-104/55*y - 291/220)*x + (64/55*y^2 + 31/110*y - 47/110)


Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = t*x + (t - 1)
? ? %2 = (64/55*t^2 - 104/55*t + 169/220)*x^2 + (128/55*t^2 - 433/110*t + 25/44)*x + (64/55*t^2 - 45/22*t + 5/11)
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.012s
user	0m0.006s
sys	0m0.005s


'206.15.'
************** PARI *****************
Host 206.15.72.193 (206.15.72.193)
Time: Fri Jul 21 15:54:10 2006

Input: c = 1/55

(3/2*x - y + 1/2)*(1/2*x - y -1) + c * (x + 3*y -2)^2 

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = 1/55
? ? %2 = 169/220*x^2 + (-104/55*y - 291/220)*x + (64/55*y^2 + 31/110*y - 47/110)
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.012s
user	0m0.006s
sys	0m0.005s


'70.34.1'
************** PARI *****************
Host 70.34.176.199 (70.34.176.199)
Time: Fri Jul 21 15:29:41 2006

Input: 6892 � 5 


Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = 68925
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.011s
user	0m0.008s
sys	0m0.003s


'71.231.'
************** PARI *****************
Host 71.231.40.180 (71.231.40.180)
Time: Fri Jul 21 15:08:53 2006

Input: c = 1/55

(3/2*x - y + 1/2)*(1/2*x - y -1) + c * (x + 3*y -2)^2 

(6*c-2)^2 - 4*(c+3/4)*(9*c +1)




Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = 1/55
? ? %2 = 169/220*x^2 + (-104/55*y - 291/220)*x + (64/55*y^2 + 31/110*y - 47/110)
? ? %3 = 0
? ? ? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.012s
user	0m0.005s
sys	0m0.007s


'71.231.'
************** PARI *****************
Host 71.231.40.180 (71.231.40.180)
Time: Fri Jul 21 15:08:06 2006

Input: (3/2*x - y + 1/2)*(1/2*x - y -1) + c * (x + 3*y -2)^2 

(6*c-2)^2 - 4*(c+3/4)*(9*c +1)




Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = (c + 3/4)*x^2 + ((6*c - 2)*y + (-4*c - 5/4))*x + ((9*c + 1)*y^2 + (-12*c + 1/2)*y + (4*c - 1/2))
? ? %2 = -55*c + 1
? ? ? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.012s
user	0m0.008s
sys	0m0.004s


'71.231.'
************** PARI *****************
Host 71.231.40.180 (71.231.40.180)
Time: Fri Jul 21 15:04:02 2006

Input: (3/2*x - y + 1/2)*(1/2*x - y -1) + c * (x + 3*y -2)^2 






Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = (c + 3/4)*x^2 + ((6*c - 2)*y + (-4*c - 5/4))*x + ((9*c + 1)*y^2 + (-12*c + 1/2)*y + (4*c - 1/2))
? ? ? ? ? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.012s
user	0m0.002s
sys	0m0.011s


'71.231.'
************** PARI *****************
Host 71.231.40.180 (71.231.40.180)
Time: Fri Jul 21 15:03:09 2006

Input: 
3/2*x - y + 1/2)*(1/2*x - y -1) + c * (x + 3*y -2)^2 






Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? ? %1 = 3/2*x + (-y + 1/2)
? ? ? ? ? 
Goodbye!

Errors/timing (if any):

  ***   Warning: unused characters: )*(1/2*x-y-1)+c*(x+3*y-2)^2.

Timing:
real	0m0.012s
user	0m0.007s
sys	0m0.005s


'71.231.'
************** PARI *****************
Host 71.231.40.180 (71.231.40.180)
Time: Fri Jul 21 14:38:09 2006

Input: 4*(x - 2*y - 2)*( x - y +2) + (y + 2*x +1)*(y+x-2)


t = 9/2
((2*t^2 - 3*t + 3)*(4*t -1)- (4*t - 3)*(2*t^2-t-6) )/(2*t^2 - 3*t + 3)^2









Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = 6*x^2 + (-9*y - 3)*x + (9*y^2 - 9*y - 18)
? ? ? %2 = 9/2
? %3 = 1/15
? ? ? ? ? ? ? ? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.014s
user	0m0.004s
sys	0m0.012s


'71.231.'
************** PARI *****************
Host 71.231.40.180 (71.231.40.180)
Time: Fri Jul 21 14:27:09 2006

Input: 4*(x - 2*y - 2)*( x - y +2) + (y + 2*x +1)*(y+x-2)

y = (6*t^2 - 3*t - 18)/(6*t^2 - 9*t + 9)


x = t*(y+1)






Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = 6*x^2 + (-9*y - 3)*x + (9*y^2 - 9*y - 18)
? ? %2 = (2*t^2 - t - 6)/(2*t^2 - 3*t + 3)
? ? ? %3 = (4*t^3 - 4*t^2 - 3*t)/(2*t^2 - 3*t + 3)
? ? ? ? ? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.012s
user	0m0.006s
sys	0m0.006s


'71.231.'
************** PARI *****************
Host 71.231.40.180 (71.231.40.180)
Time: Fri Jul 21 14:26:32 2006

Input: 4*(x - 2*y - 2)*( x - y +2) + (y + 2*x +1)*(y+x-2)

y = (6*t^2 - 3*t - 18)/(6*t^2 - 9*t + 9)


(6*x^2 - 9*y*x - 3*x + 9*y^2 - 9*y - 18)/(y+1)




Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = 6*x^2 + (-9*y - 3)*x + (9*y^2 - 9*y - 18)
? ? %2 = (2*t^2 - t - 6)/(2*t^2 - 3*t + 3)
? ? ? %3 = ((12*t^2 - 18*t + 18)/(4*t^2 - 4*t - 3))*x^2 + ((-24*t^2 + 18*t + 45)/(4*t^2 - 4*t - 3))*x + ((-18*t^2 + 45*t - 108)/(2*t^2 - 3*t + 3))
? ? ? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.012s
user	0m0.006s
sys	0m0.005s


'71.231.'
************** PARI *****************
Host 71.231.40.180 (71.231.40.180)
Time: Fri Jul 21 14:26:19 2006

Input: 4*(x - 2*y - 2)*( x - y +2) + (y + 2*x +1)*(y+x-2)

y = (6*t^2 - 3*t - 18)/(6*t^2 - 9*t + 9)


x = t*(y+1)

(6*x^2 - 9*y*x - 3*x + 9*y^2 - 9*y - 18)/(y+1)




Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = 6*x^2 + (-9*y - 3)*x + (9*y^2 - 9*y - 18)
? ? %2 = (2*t^2 - t - 6)/(2*t^2 - 3*t + 3)
? ? ? %3 = (4*t^3 - 4*t^2 - 3*t)/(2*t^2 - 3*t + 3)
? ? %4 = 12*t^2 - 6*t - 36
? ? ? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.012s
user	0m0.006s
sys	0m0.006s


'71.231.'
************** PARI *****************
Host 71.231.40.180 (71.231.40.180)
Time: Fri Jul 21 14:17:19 2006

Input: 4*(x - 2*y - 2)*( x - y +2) + (y + 2*x +1)*(y+x-2)


x = t*(y+1)

(6*x^2 - 9*y*x - 3*x + 9*y^2 - 9*y - 18)/(y+1)




Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = 6*x^2 + (-9*y - 3)*x + (9*y^2 - 9*y - 18)
? ? ? %2 = t*y + t
? ? %3 = (6*t^2 - 9*t + 9)*y + (6*t^2 - 3*t - 18)
? ? ? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.012s
user	0m0.005s
sys	0m0.007s


'71.231.'
************** PARI *****************
Host 71.231.40.180 (71.231.40.180)
Time: Fri Jul 21 14:16:15 2006

Input: 4*(x - 2*y - 2)*( x - y +2) + (y + 2*x +1)*(y+x-2)


x = t*(y+1)

(6*x^2 - 9*y*x - 3*x + 9*y^2 - 9*y - 18)




Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = 6*x^2 + (-9*y - 3)*x + (9*y^2 - 9*y - 18)
? ? ? %2 = t*y + t
? ? %3 = (6*t^2 - 9*t + 9)*y^2 + (12*t^2 - 12*t - 9)*y + (6*t^2 - 3*t - 18)
? ? ? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.012s
user	0m0.004s
sys	0m0.007s


'71.231.'
************** PARI *****************
Host 71.231.40.180 (71.231.40.180)
Time: Fri Jul 21 14:16:09 2006

Input: 4*(x - 2*y - 2)*( x - y +2) + (y + 2*x +1)*(y+x-2)


x = t*(y+1)

(6*x^2 - 9*y*x - 3*x + 9*y^2 - 9*y - 18)/(y+1)




Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = 6*x^2 + (-9*y - 3)*x + (9*y^2 - 9*y - 18)
? ? ? %2 = t*y + t
? ? %3 = (6*t^2 - 9*t + 9)*y + (6*t^2 - 3*t - 18)
? ? ? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.012s
user	0m0.007s
sys	0m0.005s


'71.231.'
************** PARI *****************
Host 71.231.40.180 (71.231.40.180)
Time: Fri Jul 21 14:15:29 2006

Input: 4*(x - 2*y - 2)*( x - y +2) + (y + 2*x +1)*(y+x-2)


x = t*(y+1)

6*x^2 - 9*y*x - 3*x + 9*y^2 - 9*y - 18




Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = 6*x^2 + (-9*y - 3)*x + (9*y^2 - 9*y - 18)
? ? ? %2 = t*y + t
? ? %3 = (6*t^2 - 9*t + 9)*y^2 + (12*t^2 - 12*t - 9)*y + (6*t^2 - 3*t - 18)
? ? ? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.012s
user	0m0.006s
sys	0m0.005s


'71.231.'
************** PARI *****************
Host 71.231.40.180 (71.231.40.180)
Time: Fri Jul 21 14:15:22 2006

Input: 4*(x - 2*y - 2)*( x - y +2) + (y + 2*x +1)*(y+x-2)


x = t*(y+x)

6*x^2 - 9*y*x - 3*x + 9*y^2 - 9*y - 18




Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = 6*x^2 + (-9*y - 3)*x + (9*y^2 - 9*y - 18)
? ? ? %2 = t*x + t*y
? ? %3 = 6*t^2*x^2 + ((12*t^2 - 9*t)*y - 3*t)*x + ((6*t^2 - 9*t + 9)*y^2 + (-3*t - 9)*y - 18)
? ? ? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.012s
user	0m0.006s
sys	0m0.006s


'71.231.'
************** PARI *****************
Host 71.231.40.180 (71.231.40.180)
Time: Fri Jul 21 14:09:28 2006

Input: 4*(x - 2*y - 2)*( x - y +2) + (y + 2*x +1)*(y+x-2)


y = (t*x + 1)

6*x^2 + (-9*y - 3)*x + (9*y^2 - 9*y - 18)




Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = 6*x^2 + (-9*y - 3)*x + (9*y^2 - 9*y - 18)
? ? ? %2 = t*x + 1
? ? %3 = (9*t^2 - 9*t + 6)*x^2 + (9*t - 12)*x - 18
? ? ? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.012s
user	0m0.008s
sys	0m0.004s


'71.231.'
************** PARI *****************
Host 71.231.40.180 (71.231.40.180)
Time: Fri Jul 21 14:07:42 2006

Input: 4*(x - 2*y - 2)*( x - y +2) + (y + 2*x +1)*(y+x-2)


y = (t*x + t)/(x+1)

6*x^2 + (-9*y - 3)*x + (9*y^2 - 9*y - 18)


((9*t^2 - 9*t + 6)*x^2 + (18*t^2 - 18*t - 3)*x + (9*t^2 - 9*t - 18))/(x +1)

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = 6*x^2 + (-9*y - 3)*x + (9*y^2 - 9*y - 18)
? ? ? %2 = t
? ? %3 = 6*x^2 + (-9*t - 3)*x + (9*t^2 - 9*t - 18)
? ? ? %4 = ((9*t^2 - 9*t + 6)*x^2 + (18*t^2 - 18*t - 3)*x + (9*t^2 - 9*t - 18))/(x + 1)
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.012s
user	0m0.008s
sys	0m0.005s


'71.231.'
************** PARI *****************
Host 71.231.40.180 (71.231.40.180)
Time: Fri Jul 21 14:07:21 2006

Input: 4*(x - 2*y - 2)*( x - y +2) + (y + 2*x +1)*(y+x-2)


y = (t*x + t)
6*x^2 + (-9*y - 3)*x + (9*y^2 - 9*y - 18)


((9*t^2 - 9*t + 6)*x^2 + (18*t^2 - 18*t - 3)*x + (9*t^2 - 9*t - 18))/(x +1)

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = 6*x^2 + (-9*y - 3)*x + (9*y^2 - 9*y - 18)
? ? ? %2 = t*x + t
? %3 = (9*t^2 - 9*t + 6)*x^2 + (18*t^2 - 18*t - 3)*x + (9*t^2 - 9*t - 18)
? ? ? %4 = ((9*t^2 - 9*t + 6)*x^2 + (18*t^2 - 18*t - 3)*x + (9*t^2 - 9*t - 18))/(x + 1)
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.012s
user	0m0.008s
sys	0m0.005s


'71.231.'
************** PARI *****************
Host 71.231.40.180 (71.231.40.180)
Time: Fri Jul 21 14:05:39 2006

Input: 4*(x - 2*y - 2)*( x - y +2) + (y + 2*x +1)*(y+x-2)


y = (t*x + t)
6*x^2 + (-9*y - 3)*x + (9*y^2 - 9*y - 18)

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = 6*x^2 + (-9*y - 3)*x + (9*y^2 - 9*y - 18)
? ? ? %2 = t*x + t
? %3 = (9*t^2 - 9*t + 6)*x^2 + (18*t^2 - 18*t - 3)*x + (9*t^2 - 9*t - 18)
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.012s
user	0m0.006s
sys	0m0.007s


'71.231.'
************** PARI *****************
Host 71.231.40.180 (71.231.40.180)
Time: Fri Jul 21 14:04:40 2006

Input: 4*(x - 2*y - 2)*( x - y +2) + (y + 2*x +1)*(y+x-2)


y = (t*x - t)
6*x^2 + (-9*y - 3)*x + (9*y^2 - 9*y - 18)


((9*t^2 - 9*t + 6)*x^2 + (-18*t^2 - 3)*x + (9*t^2 + 9*t - 18))/(x +1)

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = 6*x^2 + (-9*y - 3)*x + (9*y^2 - 9*y - 18)
? ? ? %2 = t*x - t
? %3 = (9*t^2 - 9*t + 6)*x^2 + (-18*t^2 - 3)*x + (9*t^2 + 9*t - 18)
? ? ? %4 = ((9*t^2 - 9*t + 6)*x^2 + (-18*t^2 - 3)*x + (9*t^2 + 9*t - 18))/(x + 1)
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.012s
user	0m0.005s
sys	0m0.006s


'71.231.'
************** PARI *****************
Host 71.231.40.180 (71.231.40.180)
Time: Fri Jul 21 14:03:16 2006

Input: 4*(x - 2*y - 2)*( x - y +2) + (y + 2*x +1)*(y+x-2)


y = (t*x - t)
6*x^2 + (-9*y - 3)*x + (9*y^2 - 9*y - 18)

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = 6*x^2 + (-9*y - 3)*x + (9*y^2 - 9*y - 18)
? ? ? %2 = t*x - t
? %3 = (9*t^2 - 9*t + 6)*x^2 + (-18*t^2 - 3)*x + (9*t^2 + 9*t - 18)
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.011s
user	0m0.006s
sys	0m0.005s


'71.231.'
************** PARI *****************
Host 71.231.40.180 (71.231.40.180)
Time: Fri Jul 21 14:02:18 2006

Input: 4*(x - 2*y - 2)*( x - y +2) + (y + 2*x +1)*(y+x-2)


y = (tx - t)
6*x^2 + (-9*y - 3)*x + (9*y^2 - 9*y - 18)

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = 6*x^2 + (-9*y - 3)*x + (9*y^2 - 9*y - 18)
? ? ? %2 = tx - t
? %3 = 6*x^2 + (-9*tx + (9*t - 3))*x + (9*tx^2 + (-18*t - 9)*tx + (9*t^2 + 9*t - 18))
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.012s
user	0m0.007s
sys	0m0.005s


'71.231.'
************** PARI *****************
Host 71.231.40.180 (71.231.40.180)
Time: Fri Jul 21 13:49:26 2006

Input: 4*(x - 2*y - 2)*( x - y +2) + (y + 2*x +1)*(y+x-2)

81 - 4*6*(9)

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = 6*x^2 + (-9*y - 3)*x + (9*y^2 - 9*y - 18)
? ? %2 = -135
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.011s
user	0m0.006s
sys	0m0.005s


'71.231.'
************** PARI *****************
Host 71.231.40.180 (71.231.40.180)
Time: Fri Jul 21 13:48:40 2006

Input: 4*(x - 2*y - 2)*( x - y +2) + (y + 2*x +1)*(y+x-2)

81 - 4*6*(-3)

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = 6*x^2 + (-9*y - 3)*x + (9*y^2 - 9*y - 18)
? ? %2 = 153
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.011s
user	0m0.006s
sys	0m0.005s


'71.231.'
************** PARI *****************
Host 71.231.40.180 (71.231.40.180)
Time: Fri Jul 21 13:47:28 2006

Input: //x = 3
//y = 1

(x - 2*y - 2)*( x - y +2) + (1/4)*( -2*x - y  -1)*(-1*x - y +2)

81 - 4*6*(-3)

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? ? ? ? %1 = 3/2*x^2 + (-9/4*y - 3/4)*x + (9/4*y^2 - 9/4*y - 9/2)
? ? %2 = 153
? 
Goodbye!

Errors/timing (if any):

  ***   unexpected character: //x=3
                              ^-----
  ***   unexpected character: //y=1
                              ^-----

Timing:
real	0m0.012s
user	0m0.007s
sys	0m0.006s


'71.231.'
************** PARI *****************
Host 71.231.40.180 (71.231.40.180)
Time: Fri Jul 21 13:47:12 2006

Input: //x = 3
//y = 1

(x - 2*y - 2)*( x - y +2) + c*( -2*x - y  -1)*(-1*x - y +2)

81 - 4*6*(-3)

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? ? ? ? %1 = (2*c + 1)*x^2 + ((3*c - 3)*y - 3*c)*x + ((c + 2)*y^2 + (-c - 2)*y + (-2*c - 4))
? ? %2 = 153
? 
Goodbye!

Errors/timing (if any):

  ***   unexpected character: //x=3
                              ^-----
  ***   unexpected character: //y=1
                              ^-----

Timing:
real	0m0.012s
user	0m0.008s
sys	0m0.003s


'71.231.'
************** PARI *****************
Host 71.231.40.180 (71.231.40.180)
Time: Fri Jul 21 13:46:35 2006

Input: x = 3
y = 1

(x - 2*y - 2)*( x - y +2) + c*( -2*x - y  -1)*(-1*x - y +2)

81 - 4*6*(-3)

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = 3
? %2 = 1
? ? %3 = 16*c - 4
? ? %4 = 153
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.012s
user	0m0.005s
sys	0m0.006s


'71.231.'
************** PARI *****************
Host 71.231.40.180 (71.231.40.180)
Time: Fri Jul 21 13:43:38 2006

Input: (x - 2*y - 2)*( x - y +2) + 1/4*(y + 2*x +1)*(y+x-2)

81 - 4*6*(-3)

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = 3/2*x^2 + (-9/4*y - 3/4)*x + (9/4*y^2 - 9/4*y - 9/2)
? ? %2 = 153
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.011s
user	0m0.005s
sys	0m0.006s


'71.231.'
************** PARI *****************
Host 71.231.40.180 (71.231.40.180)
Time: Fri Jul 21 13:43:12 2006

Input: 4*(x - 2*y - 2)*( x - y +2) + (y + 2*x +1)*(y+x-2)

81 - 4*6*(-3)

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = 6*x^2 + (-9*y - 3)*x + (9*y^2 - 9*y - 18)
? ? %2 = 153
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.011s
user	0m0.007s
sys	0m0.005s


'71.231.'
************** PARI *****************
Host 71.231.40.180 (71.231.40.180)
Time: Fri Jul 21 13:42:19 2006

Input: 4*(x - 2*y - 2)*( x - y +2) + (y + 2*x +1)*(y+x-2)

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = 6*x^2 + (-9*y - 3)*x + (9*y^2 - 9*y - 18)
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.011s
user	0m0.006s
sys	0m0.005s


'71.231.'
************** PARI *****************
Host 71.231.40.180 (71.231.40.180)
Time: Fri Jul 21 13:42:05 2006

Input: 4*(x - 2*y - 2)( x - y +2) + (y + 2*x +1)(y+x-2)

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = x + (y - 2)
? 
Goodbye!

Errors/timing (if any):

  ***   Warning: unused characters: (x-y+2)+(y+2*x+1)(y+x-2).

Timing:
real	0m0.011s
user	0m0.007s
sys	0m0.004s


'65.64.1'
************** PARI *****************
Host 65.64.103.23 (65.64.103.23)
Time: Fri Jul 21 12:55:57 2006

Input: 6+2+1+9+7=

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? ? 
Goodbye!

Errors/timing (if any):

  ***   unexpected character: 6+2+1+9+7=
                                       ^-

Timing:
real	0m0.011s
user	0m0.005s
sys	0m0.007s


'68.142.'
************** PARI *****************
Host 68.142.249.88 (68.142.249.88)
Time: Fri Jul 21 11:08:16 2006

Input: factor(x^6-1)

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = 
[x - 1 1]

[x + 1 1]

[x^2 - x + 1 1]

[x^2 + x + 1 1]

? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.087s
user	0m0.005s
sys	0m0.010s


'71.231.'
************** PARI *****************
Host 71.231.40.180 (71.231.40.180)
Time: Fri Jul 21 10:58:15 2006

Input: //a3 = 1
36/84
t = 2

a0 = 3/7
a1 = -9/2*a0
a2 = 1 - 27*a0 - 8*(-9/2*a0)
a3 = -29/2*a0 + 8 
a4 = -7
a5 = 0
a6 = 0
a7 = 0

a0*(t+3)^3 + (-9/2*a0)*(t+2)^3 + a2 *(t+1)^3 + a3*(t-0)^3 + a4*(t-1)^3 + a5*(t-2)^3 + a6*(t-3)^3 + a7*(t-4)^3




Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? ? %1 = 3/7
? %2 = 2
? ? %3 = 3/7
? %4 = -27/14
? %5 = 34/7
? %6 = 25/14
? %7 = -7
? %8 = 0
? %9 = 0
? %10 = 0
? ? %11 = 480/7
? ? ? 
Goodbye!

Errors/timing (if any):

  ***   unexpected character: //a3=1
                              ^------

Timing:
real	0m0.012s
user	0m0.008s
sys	0m0.004s


'71.231.'
************** PARI *****************
Host 71.231.40.180 (71.231.40.180)
Time: Fri Jul 21 10:57:35 2006

Input: //a3 = 1
36/84
t = 2

//a0 = 
//a1 = -9/2*a0
a2 = 1 - 27*a0 - 8*(-9/2*a0)
a3 = -29/2*a0 + 8 
a4 = -7
a5 = 0
a6 = 0
a7 = 0

a0*(t+3)^3 + (-9/2*a0)*(t+2)^3 + a2 *(t+1)^3 + a3*(t-0)^3 + a4*(t-1)^3 + a5*(t-2)^3 + a6*(t-3)^3 + a7*(t-4)^3




Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? ? %1 = 3/7
? %2 = 2
? ? ? %3 = 9*a0 + 1
? %4 = -29/2*a0 + 8
? %5 = -7
? %6 = 0
? %7 = 0
? %8 = 0
? ? %9 = -36*a0 + 84
? ? ? 
Goodbye!

Errors/timing (if any):

  ***   unexpected character: //a3=1
                              ^------
  ***   unexpected character: //a0=//a1=-9/2*a0
                              ^-----------------

Timing:
real	0m0.036s
user	0m0.009s
sys	0m0.003s


'71.231.'
************** PARI *****************
Host 71.231.40.180 (71.231.40.180)
Time: Fri Jul 21 10:55:38 2006

Input: //a3 = 1

t = 2

//a0 = 
//a1 = -9/2*a0
a2 = 1 - 27*a0 - 8*(-9/2*a0)
a3 = -29/2*a0 + 8 
a4 = -7
a5 = 0
a6 = 0
a7 = 0

a0*(t+3)^3 + (-9/2*a0)*(t+2)^3 + a2 *(t+1)^3 + a3*(t-0)^3 + a4*(t-1)^3 + a5*(t-2)^3 + a6*(t-3)^3 + a7*(t-4)^3




Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? ? ? %1 = 2
? ? ? %2 = 9*a0 + 1
? %3 = -29/2*a0 + 8
? %4 = -7
? %5 = 0
? %6 = 0
? %7 = 0
? ? %8 = -36*a0 + 84
? ? ? 
Goodbye!

Errors/timing (if any):

  ***   unexpected character: //a3=1
                              ^------
  ***   unexpected character: //a0=//a1=-9/2*a0
                              ^-----------------

Timing:
real	0m0.012s
user	0m0.007s
sys	0m0.005s


'71.231.'
************** PARI *****************
Host 71.231.40.180 (71.231.40.180)
Time: Fri Jul 21 10:41:53 2006

Input: //a3 = 1

t = 1

//a0 = 
//a1 = -9/2*a0
a2 = 1 - 27*a0 - 8*(-9/2*a0)
a3 = -29/2*a0 + 8 
a4 = -7
a5 = 0
a6 = 0
a7 = 0

a0*(t+3)^3 + (-9/2*a0)*(t+2)^3 + a2 *(t+1)^3 + a3*(t-0)^3 + a4*(t-1)^3 + a5*(t-2)^3 + a6*(t-3)^3 + a7*(t-4)^3



3*a0*(t+3)^2 + 3*a1*(t+2)^2 + 3*a2 *(t+1)^2 + a3*(t-0)^3 + 3*a4*(t-1)^2 + 3*a5*(t-2)^2 + 3*a6*(t-3)^2 + 3*a7*(t-4)^2




Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? ? ? %1 = 1
? ? ? %2 = 9*a0 + 1
? %3 = -29/2*a0 + 8
? %4 = -7
? %5 = 0
? %6 = 0
? %7 = 0
? ? %8 = 16
? ? ? ? %9 = 283/2*a0 + (27*a1 + 20)
? ? ? 
Goodbye!

Errors/timing (if any):

  ***   unexpected character: //a3=1
                              ^------
  ***   unexpected character: //a0=//a1=-9/2*a0
                              ^-----------------

Timing:
real	0m0.012s
user	0m0.004s
sys	0m0.008s


'71.231.'
************** PARI *****************
Host 71.231.40.180 (71.231.40.180)
Time: Fri Jul 21 10:36:39 2006

Input: //a3 = 1

t = 1

//a0 = 
//a1 = -9/2*a0
a2 = 1 - 27*a0 - 8*(-9/2*a0)
//a3 = 0 
a4 = -7
a5 = 0
a6 = 0
a7 = 0

a0*(t+3)^3 + (-9/2*a0)*(t+2)^3 + a2 *(t+1)^3 + a3*(t-0)^3 + a4*(t-1)^3 + a5*(t-2)^3 + a6*(t-3)^3 + a7*(t-4)^3



3*a0*(t+3)^2 + 3*a1*(t+2)^2 + 3*a2 *(t+1)^2 + a3*(t-0)^3 + 3*a4*(t-1)^2 + 3*a5*(t-2)^2 + 3*a6*(t-3)^2 + 3*a7*(t-4)^2




Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? ? ? %1 = 1
? ? ? %2 = 9*a0 + 1
? ? %3 = -7
? %4 = 0
? %5 = 0
? %6 = 0
? ? %7 = 29/2*a0 + (a3 + 8)
? ? ? ? %8 = 156*a0 + (a3 + (27*a1 + 12))
? ? ? 
Goodbye!

Errors/timing (if any):

  ***   unexpected character: //a3=1
                              ^------
  ***   unexpected character: //a0=//a1=-9/2*a0
                              ^-----------------
  ***   unexpected character: //a3=0
                              ^------

Timing:
real	0m0.012s
user	0m0.005s
sys	0m0.007s


'71.231.'
************** PARI *****************
Host 71.231.40.180 (71.231.40.180)
Time: Fri Jul 21 10:35:29 2006

Input: //a3 = 1

t = 1

//a0 = 
//a1 = -9/2*a0
a2 = 1 - 27*a0 - 8*(-9/2*a0)
//a3 = 0 
a4 = 0
a5 = 0
a6 = 0
a7 = 0

a0*(t+3)^3 + (-9/2*a0)*(t+2)^3 + a2 *(t+1)^3 + a3*(t-0)^3 + a4*(t-1)^3 + a5*(t-2)^3 + a6*(t-3)^3 + a7*(t-4)^3

3*a0*(t+3)^2 + 3*a1*(t+2)^2 + 3*a2 *(t+1)^2 + a3*(t-0)^3 + 3*a4*(t-1)^2 + 3*a5*(t-2)^2 + 3*a6*(t-3)^2 + 3*a7*(t-4)^2




Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? ? ? %1 = 1
? ? ? %2 = 9*a0 + 1
? ? %3 = 0
? %4 = 0
? %5 = 0
? %6 = 0
? ? %7 = 29/2*a0 + (a3 + 8)
? ? %8 = 156*a0 + (a3 + (27*a1 + 12))
? ? ? 
Goodbye!

Errors/timing (if any):

  ***   unexpected character: //a3=1
                              ^------
  ***   unexpected character: //a0=//a1=-9/2*a0
                              ^-----------------
  ***   unexpected character: //a3=0
                              ^------

Timing:
real	0m0.012s
user	0m0.006s
sys	0m0.005s


'71.231.'
************** PARI *****************
Host 71.231.40.180 (71.231.40.180)
Time: Fri Jul 21 10:35:16 2006

Input: //a3 = 1

t = 1

//a0 = 
a1 = -9/2*a0
a2 = 1 - 27*a0 - 8*(-9/2*a0)
//a3 = 0 
a4 = 0
a5 = 0
a6 = 0
a7 = 0

a0*(t+3)^3 + (-9/2*a0)*(t+2)^3 + a2 *(t+1)^3 + a3*(t-0)^3 + a4*(t-1)^3 + a5*(t-2)^3 + a6*(t-3)^3 + a7*(t-4)^3

3*a0*(t+3)^2 + 3*a1*(t+2)^2 + 3*a2 *(t+1)^2 + a3*(t-0)^3 + 3*a4*(t-1)^2 + 3*a5*(t-2)^2 + 3*a6*(t-3)^2 + 3*a7*(t-4)^2




Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? ? ? %1 = 1
? ? ? %2 = 9*a0 + 1
? ? %3 = 0
? %4 = 0
? %5 = 0
? %6 = 0
? ? %7 = 29/2*a0 + (a3 + 8)
? ? %8 = 156*a0 + (a3 + (27*a1 + 12))
? ? ? 
Goodbye!

Errors/timing (if any):

  ***   unexpected character: //a3=1
                              ^------
  ***   unexpected character: //a0=a1=-9/2*a0
                              ^---------------
  ***   unexpected character: //a3=0
                              ^------

Timing:
real	0m0.013s
user	0m0.007s
sys	0m0.006s


'71.231.'
************** PARI *****************
Host 71.231.40.180 (71.231.40.180)
Time: Fri Jul 21 10:34:42 2006

Input: //a3 = 1

t = 1

//a0 = 
a1 = -9/2*a0
a2 = 1 - 27*a0 - 8*(-9/2*a0)
//a3 = 0 
a4 = 0
a5 = 0
a6 = 0
a7 = 0

a0*(t+3)^3 + a1*(t+2)^3 + a2 *(t+1)^3 + a3*(t-0)^3 + a4*(t-1)^3 + a5*(t-2)^3 + a6*(t-3)^3 + a7*(t-4)^3

3*a0*(t+3)^2 + 3*a1*(t+2)^2 + 3*a2 *(t+1)^2 + a3*(t-0)^3 + 3*a4*(t-1)^2 + 3*a5*(t-2)^2 + 3*a6*(t-3)^2 + 3*a7*(t-4)^2




Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? ? ? %1 = 1
? ? ? %2 = 9*a0 + 1
? ? %3 = 0
? %4 = 0
? %5 = 0
? %6 = 0
? ? %7 = 136*a0 + (27*a1 + (a3 + 8))
? ? %8 = 156*a0 + (27*a1 + (a3 + 12))
? ? ? 
Goodbye!

Errors/timing (if any):

  ***   unexpected character: //a3=1
                              ^------
  ***   unexpected character: //a0=a1=-9/2*a0
                              ^---------------
  ***   unexpected character: //a3=0
                              ^------

Timing:
real	0m0.012s
user	0m0.007s
sys	0m0.005s


'71.231.'
************** PARI *****************
Host 71.231.40.180 (71.231.40.180)
Time: Fri Jul 21 10:33:54 2006

Input: //a3 = 1

t = 1

//a0 = 
a1 = -9/2*a0
a2 = 1 - 27*a0 - 8*a1
//a3 = 0 
a4 = 0
a5 = 0
a6 = 0
a7 = 0

a0*(t+3)^3 + (-9/2*a0)*(t+2)^3 + a2 *(t+1)^3 + a3*(t-0)^3 + a4*(t-1)^3 + a5*(t-2)^3 + a6*(t-3)^3 + a7*(t-4)^3

3*a0*(t+3)^2 + 3*a1*(t+2)^2 + 3*a2 *(t+1)^2 + a3*(t-0)^3 + 3*a4*(t-1)^2 + 3*a5*(t-2)^2 + 3*a6*(t-3)^2 + 3*a7*(t-4)^2




Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? ? ? %1 = 1
? ? ? %2 = -27*a0 + (-8*a1 + 1)
? ? %3 = 0
? %4 = 0
? %5 = 0
? %6 = 0
? ? %7 = -547/2*a0 + (-64*a1 + (a3 + 8))
? ? %8 = -276*a0 + (-69*a1 + (a3 + 12))
? ? ? 
Goodbye!

Errors/timing (if any):

  ***   unexpected character: //a3=1
                              ^------
  ***   unexpected character: //a0=a1=-9/2*a0
                              ^---------------
  ***   unexpected character: //a3=0
                              ^------

Timing:
real	0m0.012s
user	0m0.005s
sys	0m0.007s


'71.231.'
************** PARI *****************
Host 71.231.40.180 (71.231.40.180)
Time: Fri Jul 21 10:32:45 2006

Input: //a3 = 1

t = 1

//a0 = 
a1 = -9/2*a0
a2 = 1 - 27*a0 - 8*a1
//a3 = 0 
a4 = 0
a5 = 0
a6 = 0
a7 = 0

a0*(t+3)^3 + a1*(t+2)^3 + a2 *(t+1)^3 + a3*(t-0)^3 + a4*(t-1)^3 + a5*(t-2)^3 + a6*(t-3)^3 + a7*(t-4)^3

3*a0*(t+3)^2 + 3*a1*(t+2)^2 + 3*a2 *(t+1)^2 + a3*(t-0)^3 + 3*a4*(t-1)^2 + 3*a5*(t-2)^2 + 3*a6*(t-3)^2 + 3*a7*(t-4)^2




Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? ? ? %1 = 1
? ? ? %2 = -27*a0 + (-8*a1 + 1)
? ? %3 = 0
? %4 = 0
? %5 = 0
? %6 = 0
? ? %7 = -152*a0 + (-37*a1 + (a3 + 8))
? ? %8 = -276*a0 + (-69*a1 + (a3 + 12))
? ? ? 
Goodbye!

Errors/timing (if any):

  ***   unexpected character: //a3=1
                              ^------
  ***   unexpected character: //a0=a1=-9/2*a0
                              ^---------------
  ***   unexpected character: //a3=0
                              ^------

Timing:
real	0m0.013s
user	0m0.006s
sys	0m0.006s


'71.231.'
************** PARI *****************
Host 71.231.40.180 (71.231.40.180)
Time: Fri Jul 21 10:32:00 2006

Input: //a3 = 1

t = 1

//a0 = 
a1 = (-9/2)*a0
a2 = 1 - 27*a0 - 8*a1
//a3 = 0 
a4 = 0
a5 = 0
a6 = 0
a7 = 0

a0*(t+3)^3 + a1*(t+2)^3 + a2 *(t+1)^3 + a3*(t-0)^3 + a4*(t-1)^3 + a5*(t-2)^3 + a6*(t-3)^3 + a7*(t-4)^3

3*a0*(t+3)^2 + 3*a1*(t+2)^2 + 3*a2 *(t+1)^2 + a3*(t-0)^3 + 3*a4*(t-1)^2 + 3*a5*(t-2)^2 + 3*a6*(t-3)^2 + 3*a7*(t-4)^2




Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? ? ? %1 = 1
? ? ? %2 = -27*a0 + (-8*a1 + 1)
? ? %3 = 0
? %4 = 0
? %5 = 0
? %6 = 0
? ? %7 = -152*a0 + (-37*a1 + (a3 + 8))
? ? %8 = -276*a0 + (-69*a1 + (a3 + 12))
? ? ? 
Goodbye!

Errors/timing (if any):

  ***   unexpected character: //a3=1
                              ^------
  ***   unexpected character: //a0=a1=(-9/2)*a0
                              ^-----------------
  ***   unexpected character: //a3=0
                              ^------

Timing:
real	0m0.012s
user	0m0.006s
sys	0m0.007s


'71.231.'
************** PARI *****************
Host 71.231.40.180 (71.231.40.180)
Time: Fri Jul 21 10:28:24 2006

Input: //a3 = 1

t = 0

//a0 = 
//a1 = 0
a2 = 1 - 27*a0 - 8*a1
//a3 = 0 
a4 = 0
a5 = 0
a6 = 0
a7 = 0

a0*(t+3)^3 + a1*(t+2)^3 + a2 *(t+1)^3 + a3*(t-0)^3 + a4*(t-1)^3 + a5*(t-2)^3 + a6*(t-3)^3 + a7*(t-4)^3

3*a0*(t+3)^2 + 3*a1*(t+2)^2 + 3*a2 *(t+1)^2 + a3*(t-0)^3 + 3*a4*(t-1)^2 + 3*a5*(t-2)^2 + 3*a6*(t-3)^2 + 3*a7*(t-4)^2


3*(1 - 27*a0 - 8*a1) *(t+1)^2

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? ? ? %1 = 0
? ? ? %2 = -27*a0 + (-8*a1 + 1)
? ? %3 = 0
? %4 = 0
? %5 = 0
? %6 = 0
? ? %7 = 1
? ? %8 = -54*a0 + (-12*a1 + 3)
? ? ? %9 = -81*a0 + (-24*a1 + 3)
? 
Goodbye!

Errors/timing (if any):

  ***   unexpected character: //a3=1
                              ^------
  ***   unexpected character: //a0=//a1=0
                              ^-----------
  ***   unexpected character: //a3=0
                              ^------

Timing:
real	0m0.012s
user	0m0.005s
sys	0m0.007s


'71.231.'
************** PARI *****************
Host 71.231.40.180 (71.231.40.180)
Time: Fri Jul 21 10:28:09 2006

Input: //a3 = 1

t = 0

//a0 = 
//a1 = 0
a2 = 1 - 27*a0 - 8*a1
//a3 = 0 
a4 = 0
a5 = 0
a6 = 0
a7 = 0

a0*(t+3)^3 + a1*(t+2)^3 + a2 *(t+1)^3 + a3*(t-0)^3 + a4*(t-1)^3 + a5*(t-2)^3 + a6*(t-3)^3 + a7*(t-4)^3

3*a0*(t+3)^2 + 3*a1*(t+2)^2 + 3*a2 *(t+1)^2 + a3*(t-0)^3 + 3*a4*(t-1)^2 + 3*a5*(t-2)^2 + 3*a6*(t-3)^2 + 3*a7*(t-4)^2


3*(1 - 27*a0 - 8a1) *(t+1)^2

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? ? ? %1 = 0
? ? ? %2 = -27*a0 + (-8*a1 + 1)
? ? %3 = 0
? %4 = 0
? %5 = 0
? %6 = 0
? ? %7 = 1
? ? %8 = -54*a0 + (-12*a1 + 3)
? ? ? ? 
Goodbye!

Errors/timing (if any):

  ***   unexpected character: //a3=1
                              ^------
  ***   unexpected character: //a0=//a1=0
                              ^-----------
  ***   unexpected character: //a3=0
                              ^------
  ***   expected character: ')' instead of: 3*(1-27*a0-8a1)*(t+1)^2
                                                        ^-----------

Timing:
real	0m0.032s
user	0m0.007s
sys	0m0.006s


'71.231.'
************** PARI *****************
Host 71.231.40.180 (71.231.40.180)
Time: Fri Jul 21 10:27:42 2006

Input: //a3 = 1

t = 0

//a0 = 
//a1 = 0
a2 = 1 - 27a0 - 8a1
//a3 = 0 
a4 = 0
a5 = 0
a6 = 0
a7 = 0

a0*(t+3)^3 + a1*(t+2)^3 + a2 *(t+1)^3 + a3*(t-0)^3 + a4*(t-1)^3 + a5*(t-2)^3 + a6*(t-3)^3 + a7*(t-4)^3

3*a0*(t+3)^2 + 3*a1*(t+2)^2 + 3*a2 *(t+1)^2 + a3*(t-0)^3 + 3*a4*(t-1)^2 + 3*a5*(t-2)^2 + 3*a6*(t-3)^2 + 3*a7*(t-4)^2


3*(1 - 27a0 - 8a1) *(t+1)^2

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? ? ? %1 = 0
? ? ? %2 = a1
? ? %3 = 0
? %4 = 0
? %5 = 0
? %6 = 0
? ? %7 = 27*a0 + (8*a1 - 26)
? ? %8 = 27*a0 + (12*a1 - 78)
? ? ? ? 
Goodbye!

Errors/timing (if any):

  ***   unexpected character: //a3=1
                              ^------
  ***   unexpected character: //a0=//a1=0
                              ^-----------
  ***   Warning: unused characters: a0-8a1.
  ***   unexpected character: //a3=0
                              ^------
  ***   expected character: ')' instead of: 3*(1-27a0-8a1)*(t+1)^2
                                                   ^---------------

Timing:
real	0m0.013s
user	0m0.009s
sys	0m0.004s


'71.231.'
************** PARI *****************
Host 71.231.40.180 (71.231.40.180)
Time: Fri Jul 21 10:26:53 2006

Input: //a3 = 1

t = 0

//a0 = 
//a1 = 0
a2 = 1 - 27a0 - 8a1
//a3 = 0 
a4 = 0
a5 = 0
a6 = 0
a7 = 0

a0*(t+3)^3 + a1*(t+2)^3 + a2 *(t+1)^3 + a3*(t-0)^3 + a4*(t-1)^3 + a5*(t-2)^3 + a6*(t-3)^3 + a7*(t-4)^3

3*a0*(t+3)^2 + 3*a1*(t+2)^2 + 3*a2 *(t+1)^2 + a3*(t-0)^3 + 3*a4*(t-1)^2 + 3*a5*(t-2)^2 + 3*a6*(t-3)^2 + 3*a7*(t-4)^2


3*a2 *(t+1)^2

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? ? ? %1 = 0
? ? ? %2 = a1
? ? %3 = 0
? %4 = 0
? %5 = 0
? %6 = 0
? ? %7 = 27*a0 + (8*a1 - 26)
? ? %8 = 27*a0 + (12*a1 - 78)
? ? ? %9 = -78
? 
Goodbye!

Errors/timing (if any):

  ***   unexpected character: //a3=1
                              ^------
  ***   unexpected character: //a0=//a1=0
                              ^-----------
  ***   Warning: unused characters: a0-8a1.
  ***   unexpected character: //a3=0
                              ^------

Timing:
real	0m0.013s
user	0m0.007s
sys	0m0.005s


'71.231.'
************** PARI *****************
Host 71.231.40.180 (71.231.40.180)
Time: Fri Jul 21 10:24:17 2006

Input: //a3 = 1

t = 0

//a0 = 
//a1 = 0
a2 = 1 - 27a0 - 8a1
//a3 = 0 
a4 = 0
a5 = 0
a6 = 0
a7 = 0

a0*(t+3)^3 + a1*(t+2)^3 + a2 *(t+1)^3 + a3*(t-0)^3 + a4*(t-1)^3 + a5*(t-2)^3 + a6*(t-3)^3 + a7*(t-4)^3

3*a0*(t+3)^2 + 3*a1*(t+2)^2 + 3*a2 *(t+1)^2 + a3*(t-0)^3 + 3*a4*(t-1)^2 + 3*a5*(t-2)^2 + 3*a6*(t-3)^2 + 3*a7*(t-4)^2

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? ? ? %1 = 0
? ? ? %2 = a1
? ? %3 = 0
? %4 = 0
? %5 = 0
? %6 = 0
? ? %7 = 27*a0 + (8*a1 - 26)
? ? %8 = 27*a0 + (12*a1 - 78)
? 
Goodbye!

Errors/timing (if any):

  ***   unexpected character: //a3=1
                              ^------
  ***   unexpected character: //a0=//a1=0
                              ^-----------
  ***   Warning: unused characters: a0-8a1.
  ***   unexpected character: //a3=0
                              ^------

Timing:
real	0m0.012s
user	0m0.007s
sys	0m0.005s


'71.231.'
************** PARI *****************
Host 71.231.40.180 (71.231.40.180)
Time: Fri Jul 21 10:23:32 2006

Input: //a3 = 1

t = 0

//a0 = 
//a1 = 0
//a2 = 0
//a3 = 0 
a4 = 0
a5 = 0
a6 = 0
a7 = 0

a0*(t+3)^3 + a1*(t+2)^3 + a2 *(t+1)^3 + a3*(t-0)^3 + a4*(t-1)^3 + a5*(t-2)^3 + a6*(t-3)^3 + a7*(t-4)^3

3*a0*(t+3)^2 + 3*a1*(t+2)^2 + 3*a2 *(t+1)^2 + a3*(t-0)^3 + 3*a4*(t-1)^2 + 3*a5*(t-2)^2 + 3*a6*(t-3)^2 + 3*a7*(t-4)^2

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? ? ? %1 = 0
? ? ? ? ? %2 = 0
? %3 = 0
? %4 = 0
? %5 = 0
? ? %6 = 27*a0 + (8*a1 + a2)
? ? %7 = 27*a0 + (12*a1 + 3*a2)
? 
Goodbye!

Errors/timing (if any):

  ***   unexpected character: //a3=1
                              ^------
  ***   unexpected character: //a0=//a1=0
                              ^-----------
  ***   unexpected character: //a2=0
                              ^------
  ***   unexpected character: //a3=0
                              ^------

Timing:
real	0m0.012s
user	0m0.007s
sys	0m0.005s


'71.231.'
************** PARI *****************
Host 71.231.40.180 (71.231.40.180)
Time: Fri Jul 21 10:21:53 2006

Input: //a3 = 1

t = 0

//a0 = 
//a1 = 0
//a2 = 0
//a3 = 0 
a4 = 0
a5 = 0
a6 = 0
a7 = 0

a0*(t+3)^3 + a1*(t+2)^3 + a2 *(t+1)^3 + a3*(t-0)^3 + a4*(t-1)^3 + a5*(t-2)^3 + a6*(t-3)^3 + a7*(t-4)^3

 a1 + a2 * 2*t + 3*a3* t^2 + 3*a4*(t-1)^2 + 3*a5*(t-2)^2 + 3*a6*(t-3)^2 + 3*a7*(t-4)^2

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? ? ? %1 = 0
? ? ? ? ? %2 = 0
? %3 = 0
? %4 = 0
? %5 = 0
? ? %6 = 27*a0 + (8*a1 + a2)
? ? %7 = a1
? 
Goodbye!

Errors/timing (if any):

  ***   unexpected character: //a3=1
                              ^------
  ***   unexpected character: //a0=//a1=0
                              ^-----------
  ***   unexpected character: //a2=0
                              ^------
  ***   unexpected character: //a3=0
                              ^------

Timing:
real	0m0.012s
user	0m0.008s
sys	0m0.004s


'71.231.'
************** PARI *****************
Host 71.231.40.180 (71.231.40.180)
Time: Fri Jul 21 10:20:35 2006

Input: a3 = 1


//a0 = 
a1 = 0
a2 = 0
a3 = 0 
a4 = 0
a5 = 0
a6 = 0
a7 = 0

a0*(t+3)^3 + a1*(t+2)^3 + a2 *(t+1)^3 + a3*(t-0)^3 + a4*(t-1)^3 + a5*(t-2)^3 + a6*(t-3)^3 + a7*(t-4)^3

 //a1 + a2 * 2*t + 3*a3* t^2 + 3*a4*(t-1)^2 + 3*a5*(t-2)^2 + 3*a6*(t-3)^2 + 3*a7*(t-4)^2

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = 1
? ? ? ? %2 = 0
? %3 = 0
? %4 = 0
? %5 = 0
? %6 = 0
? %7 = 0
? ? %8 = (t^3 + 9*t^2 + 27*t + 27)*a0 + (a1*t^3 + 6*a1*t^2 + 12*a1*t + 8*a1)
? ? ? 
Goodbye!

Errors/timing (if any):

  ***   unexpected character: //a0=a1=0
                              ^---------
  ***   unexpected character: //a1+a2*2*t+3*a3*t^2
                              ^--------------------

Timing:
real	0m0.012s
user	0m0.005s
sys	0m0.008s


'71.231.'
************** PARI *****************
Host 71.231.40.180 (71.231.40.180)
Time: Fri Jul 21 10:20:18 2006

Input: a3 = 1


a0 = 1
a1 = 0
a2 = 0
a3 = 0 
a4 = 0
a5 = 0
a6 = 0
a7 = 0

a0*(t+3)^3 + a1*(t+2)^3 + a2 *(t+1)^3 + a3*(t-0)^3 + a4*(t-1)^3 + a5*(t-2)^3 + a6*(t-3)^3 + a7*(t-4)^3

 //a1 + a2 * 2*t + 3*a3* t^2 + 3*a4*(t-1)^2 + 3*a5*(t-2)^2 + 3*a6*(t-3)^2 + 3*a7*(t-4)^2

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = 1
? ? ? %2 = 1
? %3 = 0
? %4 = 0
? %5 = 0
? %6 = 0
? %7 = 0
? %8 = 0
? %9 = 0
? ? %10 = t^3 + 9*t^2 + 27*t + 27
? ? ? 
Goodbye!

Errors/timing (if any):

  ***   unexpected character: //a1+a2*2*t+3*a3*t^2
                              ^--------------------

Timing:
real	0m0.071s
user	0m0.005s
sys	0m0.009s


'24.179.'
************** PARI *****************
Host 24.179.14.186 (24.179.14.186)
Time: Fri Jul 21 09:13:10 2006

Input: 21,478,350*33,780


Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = 21
? 
Goodbye!

Errors/timing (if any):

  ***   Warning: unused characters: ,478,350*33,780.

Timing:
real	0m0.053s
user	0m0.005s
sys	0m0.007s


'72.30.1'
************** PARI *****************
Host 72.30.132.102 (72.30.132.102)
Time: Fri Jul 21 08:22:13 2006

Input: for( k=1, 12, print(k,": ",Mod(2^k,13)) )

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? 1: Mod(2, 13)
2: Mod(4, 13)
3: Mod(8, 13)
4: Mod(3, 13)
5: Mod(6, 13)
6: Mod(12, 13)
7: Mod(11, 13)
8: Mod(9, 13)
9: Mod(5, 13)
10: Mod(10, 13)
11: Mod(7, 13)
12: Mod(1, 13)
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.012s
user	0m0.008s
sys	0m0.004s


'63.241.'
************** PARI *****************
Host 63.241.61.7 (63.241.61.7)
Time: Fri Jul 21 05:39:51 2006

Input: for(b=1,100, for(a=1,b, if( frac((a^2+b^2+1)/(a*b))==0 , print(a,",",b), ) ) )

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? 1,1
1,2
2,5
5,13
13,34
34,89
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.029s
user	0m0.023s
sys	0m0.007s


'139.179'
************** PARI *****************
Host 139.179.137.109 (139.179.137.109)
Time: Fri Jul 21 05:23:09 2006

Input: 2+2

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = 4
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.012s
user	0m0.005s
sys	0m0.007s


'72.30.1'
************** PARI *****************
Host 72.30.103.19 (72.30.103.19)
Time: Fri Jul 21 02:23:36 2006

Input: y=210; for(x=1,8,y=sumdiv(y,x,x)-y;print1(y,","))

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? 366,378,582,594,846,1026,1374,1386,
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.012s
user	0m0.004s
sys	0m0.008s


'206.127'
************** PARI *****************
Host 206.127.2.114 (206.127.2.114)
Time: Fri Jul 21 01:41:12 2006

Input: (3x^3)-(x^2)-(15x)+5

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? ? 
Goodbye!

Errors/timing (if any):

  ***   expected character: ')' instead of: (3x^3)-(x^2)-(15x)+5
                                              ^------------------

Timing:
real	0m0.011s
user	0m0.006s
sys	0m0.005s


'206.127'
************** PARI *****************
Host 206.127.2.114 (206.127.2.114)
Time: Fri Jul 21 01:40:50 2006

Input: (3x^3)-(x^2)-(15x)+5=0

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? ? 
Goodbye!

Errors/timing (if any):

  ***   expected character: ')' instead of: (3x^3)-(x^2)-(15x)+5=0
                                              ^--------------------

Timing:
real	0m0.011s
user	0m0.008s
sys	0m0.004s


'68.142.'
************** PARI *****************
Host 68.142.250.91 (68.142.250.91)
Time: Fri Jul 21 01:03:33 2006

Input: for(b=1,100, for(a=1,b, if( frac((a^2+b^2+1)/(a*b))==0 , print(a,",",b), ) ) )

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? 1,1
1,2
2,5
5,13
13,34
34,89
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.030s
user	0m0.024s
sys	0m0.005s


'68.142.'
************** PARI *****************
Host 68.142.249.166 (68.142.249.166)
Time: Fri Jul 21 00:25:34 2006

Input: for(n=1,7, print1(n,": ",sum(x=1,n,1/x),",  ") )

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? 1: 1,  2: 3/2,  3: 11/6,  4: 25/12,  5: 137/60,  6: 49/20,  7: 363/140,  
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.011s
user	0m0.008s
sys	0m0.003s


'72.30.1'
************** PARI *****************
Host 72.30.133.210 (72.30.133.210)
Time: Thu Jul 20 23:26:18 2006

Input: collatzlength(x0)=
{
   local(x,i);
   x=x0;  i=0;   
   while(x-1,
      x=if(Mod(x,2)==Mod(0,2), x/2, (3*x+1)/2);i=i++ );
   i
}
collatzlength(299)

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? ? %1 = 75
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.012s
user	0m0.005s
sys	0m0.007s


'68.142.'
************** PARI *****************
Host 68.142.249.35 (68.142.249.35)
Time: Thu Jul 20 22:35:55 2006

Input: collatzlength(x0)=
{
   local(x,i);
   x=x0;  i=0;   
   while(x-1,
      x=if(Mod(x,2)==Mod(0,2), x/2, (3*x+1)/2);i=i++ );
   i
}
collatzlength(299)

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? ? %1 = 75
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.047s
user	0m0.005s
sys	0m0.006s


'72.30.9'
************** PARI *****************
Host 72.30.99.77 (72.30.99.77)
Time: Thu Jul 20 21:56:02 2006

Input: factor(x^6-1)

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = 
[x - 1 1]

[x + 1 1]

[x^2 - x + 1 1]

[x^2 + x + 1 1]

? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.111s
user	0m0.010s
sys	0m0.008s


'69.231.'
************** PARI *****************
Host 69.231.67.105 (69.231.67.105)
Time: Thu Jul 20 20:26:44 2006

Input: 79

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = 79
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.011s
user	0m0.006s
sys	0m0.005s


'71.39.1'
************** PARI *****************
Host 71.39.185.145 (71.39.185.145)
Time: Thu Jul 20 19:49:12 2006

Input: p=137
q=419
n=p*q
e=p+q
h=q-p
a=41
Mod(a^h,p)
Mod(a^(n-1),p)
que=Mod(a^h,n)
m=Mod(a^(n-1),n)
Mod(que,p)
Mod(m,p)
Mod(a^e,n)
Mod(a^(n+1),n)
l=Mod(a^(h^2),n)
Mod(l^a, n)
Mod(l^a, p)

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = 137
? %2 = 419
? %3 = 57403
? %4 = 556
? %5 = 282
? %6 = 41
? %7 = Mod(37, 137)
? %8 = Mod(37, 137)
? %9 = Mod(28396, 57403)
? %10 = Mod(20998, 57403)
? %11 = Mod(37, 137)
? %12 = Mod(37, 137)
? %13 = Mod(52196, 57403)
? %14 = Mod(52196, 57403)
? %15 = Mod(17124, 57403)
? %16 = Mod(27399, 57403)
? %17 = Mod(136, 137)
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.042s
user	0m0.040s
sys	0m0.002s


'71.39.1'
************** PARI *****************
Host 71.39.185.145 (71.39.185.145)
Time: Thu Jul 20 19:49:00 2006

Input: p=37
q=419
n=p*q
e=p+q
h=q-p
a=41
Mod(a^h,p)
Mod(a^(n-1),p)
que=Mod(a^h,n)
m=Mod(a^(n-1),n)
Mod(que,p)
Mod(m,p)
Mod(a^e,n)
Mod(a^(n+1),n)
l=Mod(a^(h^2),n)
Mod(l^a, n)
Mod(l^a, p)

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = 37
? %2 = 419
? %3 = 15503
? %4 = 456
? %5 = 382
? %6 = 41
? %7 = Mod(34, 37)
? %8 = Mod(34, 37)
? %9 = Mod(2809, 15503)
? %10 = Mod(4511, 15503)
? %11 = Mod(34, 37)
? %12 = Mod(34, 37)
? %13 = Mod(2024, 15503)
? %14 = Mod(2024, 15503)
? %15 = Mod(6186, 15503)
? %16 = Mod(6003, 15503)
? %17 = Mod(9, 37)
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.043s
user	0m0.039s
sys	0m0.005s


'71.39.1'
************** PARI *****************
Host 71.39.185.145 (71.39.185.145)
Time: Thu Jul 20 19:48:16 2006

Input: p=137
q=419
n=p*q
e=p+q
h=q-p
a=41
Mod(a^h,p)
Mod(a^(n-1),p)
que=Mod(a^h,n)
m=Mod(a^(n-1),n)
Mod(que,p)
Mod(m,p)
Mod(a^e,n)
Mod(a^(n+1),n)
l=Mod(a^(h^2),n)
Mod(l^a, n)
Mod(l^a, p)

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = 137
? %2 = 419
? %3 = 57403
? %4 = 556
? %5 = 282
? %6 = 41
? %7 = Mod(37, 137)
? %8 = Mod(37, 137)
? %9 = Mod(28396, 57403)
? %10 = Mod(20998, 57403)
? %11 = Mod(37, 137)
? %12 = Mod(37, 137)
? %13 = Mod(52196, 57403)
? %14 = Mod(52196, 57403)
? %15 = Mod(17124, 57403)
? %16 = Mod(27399, 57403)
? %17 = Mod(136, 137)
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.043s
user	0m0.037s
sys	0m0.006s


'71.39.1'
************** PARI *****************
Host 71.39.185.145 (71.39.185.145)
Time: Thu Jul 20 19:47:37 2006

Input: p=137
q=419
n=p*q
e=p+q
h=q-p
a=41
Mod(a^h,p)
Mod(a^(n-1),p)
que=Mod(a^h,n)
m=Mod(a^(n-1),n)
Mod(que,p)
Mod(m,p)
Mod(a^e,n)
Mod(a^(n+1),n)
l=Mod(a^(h^2),n)
Mod(a^l, n)
Mod(a^l, p)

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = 137
? %2 = 419
? %3 = 57403
? %4 = 556
? %5 = 282
? %6 = 41
? %7 = Mod(37, 137)
? %8 = Mod(37, 137)
? %9 = Mod(28396, 57403)
? %10 = Mod(20998, 57403)
? %11 = Mod(37, 137)
? %12 = Mod(37, 137)
? %13 = Mod(52196, 57403)
? %14 = Mod(52196, 57403)
? %15 = Mod(17124, 57403)
? ? ? 
Goodbye!

Errors/timing (if any):

  ***   forbidden multiplication t_REAL * t_INTMOD.
  ***   forbidden multiplication t_REAL * t_INTMOD.

Timing:
real	0m0.043s
user	0m0.038s
sys	0m0.005s


'71.39.1'
************** PARI *****************
Host 71.39.185.145 (71.39.185.145)
Time: Thu Jul 20 19:22:42 2006

Input: p=137
q=419
n=p*q
e=p+q
h=q-p
a=41
Mod(a^h,p)
Mod(a^(n-1),p)
que=Mod(a^h,n)
m=Mod(a^(n-1),n)
Mod(que,p)
Mod(m,p)

Mod(a^e,n)
Mod(a^(n+1),n)
l=Mod(a^(h^2),n)


Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = 137
? %2 = 419
? %3 = 57403
? %4 = 556
? %5 = 282
? %6 = 41
? %7 = Mod(37, 137)
? %8 = Mod(37, 137)
? %9 = Mod(28396, 57403)
? %10 = Mod(20998, 57403)
? %11 = Mod(37, 137)
? %12 = Mod(37, 137)
? ? %13 = Mod(52196, 57403)
? %14 = Mod(52196, 57403)
? %15 = Mod(17124, 57403)
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.042s
user	0m0.036s
sys	0m0.006s


'71.39.1'
************** PARI *****************
Host 71.39.185.145 (71.39.185.145)
Time: Thu Jul 20 19:22:31 2006

Input: p=137
q=419
n=p*q
e=p+q
h=q-p
a=41
Mod(a^h,p)
Mod(a^(n-1),p)
que=Mod(a^h,n)
m=Mod(a^(n-1),n)
Mod(que,p)
Mod(m,p)

l=Mod(a^e,n)
Mod(a^(n+1),n)
l=Mod(a^(h^2),n)


Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = 137
? %2 = 419
? %3 = 57403
? %4 = 556
? %5 = 282
? %6 = 41
? %7 = Mod(37, 137)
? %8 = Mod(37, 137)
? %9 = Mod(28396, 57403)
? %10 = Mod(20998, 57403)
? %11 = Mod(37, 137)
? %12 = Mod(37, 137)
? ? %13 = Mod(52196, 57403)
? %14 = Mod(52196, 57403)
? %15 = Mod(17124, 57403)
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.043s
user	0m0.036s
sys	0m0.008s


'71.39.1'
************** PARI *****************
Host 71.39.185.145 (71.39.185.145)
Time: Thu Jul 20 19:22:05 2006

Input: p=137
q=419
n=p*q
e=p+q
h=q-p
a=41
Mod(a^h,p)
Mod(a^(n-1),p)
que=Mod(a^h,n)
m=Mod(a^(n-1),n)
Mod(que,p)
Mod(m,p)

l=Mod(a^e,n)
Mod(a^(n+1),n)
Mod(a^((n-1)^2),n)
Mod(a^(h^2),n)


Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = 137
? %2 = 419
? %3 = 57403
? %4 = 556
? %5 = 282
? %6 = 41
? %7 = Mod(37, 137)
? %8 = Mod(37, 137)
? %9 = Mod(28396, 57403)
? %10 = Mod(20998, 57403)
? %11 = Mod(37, 137)
? %12 = Mod(37, 137)
? ? %13 = Mod(52196, 57403)
? %14 = Mod(52196, 57403)
? 
Errors/timing (if any):

/var/www/cgi-bin/calc/gp: line 1: 16123 Killed                  ./gp-2.2.11 -s 256000000 -emacs

Timing:
real	0m28.672s
user	0m20.512s
sys	0m0.522s


'71.39.1'
************** PARI *****************
Host 71.39.185.145 (71.39.185.145)
Time: Thu Jul 20 19:21:52 2006

Input: p=137
q=419
n=p*q
e=p+q
h=q-p
a=41
Mod(a^h,p)
Mod(a^(n-1),p)
que=Mod(a^h,n)
m=Mod(a^(n-1),n)
Mod(que,p)
Mod(m,p)

l=Mod(a^e,n)
Mod(a^(n+1),n)
Mod(a^((n-1)^2),n)
Mod(a^(h^2),n)


Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = 137
? %2 = 419
? %3 = 57403
? %4 = 556
? %5 = 282
? %6 = 41
? %7 = Mod(37, 137)
? %8 = Mod(37, 137)
? %9 = Mod(28396, 57403)
? %10 = Mod(20998, 57403)
? %11 = Mod(37, 137)
? %12 = Mod(37, 137)
? ? %13 = Mod(52196, 57403)
? %14 = Mod(52196, 57403)
? 
Errors/timing (if any):

/var/www/cgi-bin/calc/gp: line 1: 16119 Killed                  ./gp-2.2.11 -s 256000000 -emacs

Timing:
real	0m28.936s
user	0m20.461s
sys	0m0.578s


'71.39.1'
************** PARI *****************
Host 71.39.185.145 (71.39.185.145)
Time: Thu Jul 20 19:19:31 2006

Input: p=137
q=419
n=p*q
e=p+q
h=q-p
a=41
Mod(a^h,p)
Mod(a^(n-1),p)
que=Mod(a^h,n)
m=Mod(a^(n-1),n)
Mod(que,p)
Mod(m,p)

l=Mod(a^e,n)
Mod(a^(n+1),n)
Mod(a^(h^2),n)
Mod(a^(h^2),p)


Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = 137
? %2 = 419
? %3 = 57403
? %4 = 556
? %5 = 282
? %6 = 41
? %7 = Mod(37, 137)
? %8 = Mod(37, 137)
? %9 = Mod(28396, 57403)
? %10 = Mod(20998, 57403)
? %11 = Mod(37, 137)
? %12 = Mod(37, 137)
? ? %13 = Mod(52196, 57403)
? %14 = Mod(52196, 57403)
? %15 = Mod(17124, 57403)
? %16 = Mod(136, 137)
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.053s
user	0m0.046s
sys	0m0.007s


'71.39.1'
************** PARI *****************
Host 71.39.185.145 (71.39.185.145)
Time: Thu Jul 20 19:19:14 2006

Input: p=137
q=419
n=p*q
e=p+q
h=q-p
a=41
Mod(a^h,p)
Mod(a^(n-1),p)
que=Mod(a^h,n)
m=Mod(a^(n-1),n)
Mod(que,p)
Mod(m,p)

l=Mod(a^e,n)
Mod(a^(n+1),n)
Mod(m^(h^2),n)
Mod(m^(h^2),p)


Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = 137
? %2 = 419
? %3 = 57403
? %4 = 556
? %5 = 282
? %6 = 41
? %7 = Mod(37, 137)
? %8 = Mod(37, 137)
? %9 = Mod(28396, 57403)
? %10 = Mod(20998, 57403)
? %11 = Mod(37, 137)
? %12 = Mod(37, 137)
? ? %13 = Mod(52196, 57403)
? %14 = Mod(52196, 57403)
? %15 = Mod(48362, 57403)
? %16 = Mod(1, 137)
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.032s
user	0m0.027s
sys	0m0.005s


'71.39.1'
************** PARI *****************
Host 71.39.185.145 (71.39.185.145)
Time: Thu Jul 20 19:18:18 2006

Input: p=137
q=419
n=p*q
e=p+q
h=q-p
a=41
Mod(a^h,p)
Mod(a^(n-1),p)
que=Mod(a^h,n)
m=Mod(a^(n-1),n)
Mod(que,p)
Mod(m,p)

l=Mod(a^e,n)
Mod(a^(n+1),n)
Mod(m^h,n)
Mod(m^h,p)


Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = 137
? %2 = 419
? %3 = 57403
? %4 = 556
? %5 = 282
? %6 = 41
? %7 = Mod(37, 137)
? %8 = Mod(37, 137)
? %9 = Mod(28396, 57403)
? %10 = Mod(20998, 57403)
? %11 = Mod(37, 137)
? %12 = Mod(37, 137)
? ? %13 = Mod(52196, 57403)
? %14 = Mod(52196, 57403)
? %15 = Mod(15343, 57403)
? %16 = Mod(136, 137)
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.050s
user	0m0.028s
sys	0m0.003s


'71.39.1'
************** PARI *****************
Host 71.39.185.145 (71.39.185.145)
Time: Thu Jul 20 19:15:26 2006

Input: p=137
q=419
n=p*q
e=p+q
h=q-p
a=41
Mod(a^h,p)
Mod(a^(n-1),p)
que=Mod(a^h,n)
m=Mod(a^(n-1),n)
Mod(que,p)
Mod(m,p)


Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = 137
? %2 = 419
? %3 = 57403
? %4 = 556
? %5 = 282
? %6 = 41
? %7 = Mod(37, 137)
? %8 = Mod(37, 137)
? %9 = Mod(28396, 57403)
? %10 = Mod(20998, 57403)
? %11 = Mod(37, 137)
? %12 = Mod(37, 137)
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.025s
user	0m0.020s
sys	0m0.005s


'71.39.1'
************** PARI *****************
Host 71.39.185.145 (71.39.185.145)
Time: Thu Jul 20 19:14:39 2006

Input: p=137
q=419
n=p*q
e=p+q
h=q-p
a=41
Mod(a^h,p)
Mod(a^(n-1),p)
que=Mod(a^h,n)
m=Mod(a^(n-1),n)
Mod(que,p)
Mod(m,p)
Mod(que,n)
Mod(m,n)

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = 137
? %2 = 419
? %3 = 57403
? %4 = 556
? %5 = 282
? %6 = 41
? %7 = Mod(37, 137)
? %8 = Mod(37, 137)
? %9 = Mod(28396, 57403)
? %10 = Mod(20998, 57403)
? %11 = Mod(37, 137)
? %12 = Mod(37, 137)
? %13 = Mod(28396, 57403)
? %14 = Mod(20998, 57403)
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.025s
user	0m0.017s
sys	0m0.009s


'71.39.1'
************** PARI *****************
Host 71.39.185.145 (71.39.185.145)
Time: Thu Jul 20 19:14:17 2006

Input: p=137
q=419
n=p*q
e=p+q
h=q-p
a=41
Mod(a^h,p)
Mod(a^(n-1),p)
que=Mod(a^h,n)
m=Mod(a^(n-1),n)
Mod(que,p)
Mod(m,p)

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = 137
? %2 = 419
? %3 = 57403
? %4 = 556
? %5 = 282
? %6 = 41
? %7 = Mod(37, 137)
? %8 = Mod(37, 137)
? %9 = Mod(28396, 57403)
? %10 = Mod(20998, 57403)
? %11 = Mod(37, 137)
? %12 = Mod(37, 137)
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.025s
user	0m0.019s
sys	0m0.005s


'71.39.1'
************** PARI *****************
Host 71.39.185.145 (71.39.185.145)
Time: Thu Jul 20 19:13:44 2006

Input: p=137
q=419
n=p*q
e=p+q
h=q-p
a=41
Mod(a^h,p)
Mod(a^(n-1),p)
Mod(a^h,n)
Mod(a^(n-1),n)


Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = 137
? %2 = 419
? %3 = 57403
? %4 = 556
? %5 = 282
? %6 = 41
? %7 = Mod(37, 137)
? %8 = Mod(37, 137)
? %9 = Mod(28396, 57403)
? %10 = Mod(20998, 57403)
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.025s
user	0m0.023s
sys	0m0.002s


'71.39.1'
************** PARI *****************
Host 71.39.185.145 (71.39.185.145)
Time: Thu Jul 20 19:13:30 2006

Input: p=137
q=419
n=p*q
e=p+q
h=q-p
a=41
mod(a^h,p)
mod(a^(n-1),p)
mod(a^h,n)
mod(a^(n-1),n)


Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = 137
? %2 = 419
? %3 = 57403
? %4 = 556
? %5 = 282
? %6 = 41
? ? ? ? ? 
Goodbye!

Errors/timing (if any):

  ***   obsolete function: mod(a^h,p)
                           ^----------
For full compatibility with GP 1.39.15, type "default(compatible,3)", or set 
"compatible = 3" in your GPRC file.

New syntax: mod(x,y) ===> Mod(x,y)

Mod(x,y,{flag=0}): creates the object x modulo y. flag is optional, and can be 
0: default, creates on the Pari stack, or 1: creates a permanent object on the 
heap.


  ***   obsolete function: mod(a^(n-1),p)
                           ^--------------
For full compatibility with GP 1.39.15, type "default(compatible,3)", or set 
"compatible = 3" in your GPRC file.

New syntax: mod(x,y) ===> Mod(x,y)

Mod(x,y,{flag=0}): creates the object x modulo y. flag is optional, and can be 
0: default, creates on the Pari stack, or 1: creates a permanent object on the 
heap.


  ***   obsolete function: mod(a^h,n)
                           ^----------
For full compatibility with GP 1.39.15, type "default(compatible,3)", or set 
"compatible = 3" in your GPRC file.

New syntax: mod(x,y) ===> Mod(x,y)

Mod(x,y,{flag=0}): creates the object x modulo y. flag is optional, and can be 
0: default, creates on the Pari stack, or 1: creates a permanent object on the 
heap.


  ***   obsolete function: mod(a^(n-1),n)
                           ^--------------
For full compatibility with GP 1.39.15, type "default(compatible,3)", or set 
"compatible = 3" in your GPRC file.

New syntax: mod(x,y) ===> Mod(x,y)

Mod(x,y,{flag=0}): creates the object x modulo y. flag is optional, and can be 
0: default, creates on the Pari stack, or 1: creates a permanent object on the 
heap.



Timing:
real	0m0.031s
user	0m0.005s
sys	0m0.006s


'63.199.'
************** PARI *****************
Host 63.199.242.110 (63.199.242.110)
Time: Thu Jul 20 17:40:11 2006

Input: 333^(1/6)

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = 2.6327363651586554792281444498210712531
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.012s
user	0m0.008s
sys	0m0.004s


'63.199.'
************** PARI *****************
Host 63.199.242.110 (63.199.242.110)
Time: Thu Jul 20 17:39:46 2006

Input: 1.91293^3

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = 6.9999870156307569999999999999999999999
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.011s
user	0m0.007s
sys	0m0.004s


'63.199.'
************** PARI *****************
Host 63.199.242.110 (63.199.242.110)
Time: Thu Jul 20 17:39:25 2006

Input: 7^(1/3)

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = 1.9129311827723891011991168395487602829
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.087s
user	0m0.005s
sys	0m0.006s


'68.73.1'
************** PARI *****************
Host 68.73.123.250 (68.73.123.250)
Time: Thu Jul 20 15:13:36 2006

Input:  31 * 31

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = 961
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.011s
user	0m0.006s
sys	0m0.005s


'68.142.'
************** PARI *****************
Host 68.142.249.32 (68.142.249.32)
Time: Thu Jul 20 15:04:18 2006

Input: factor(2^(2^5)+1)

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = 
[641 1]

[6700417 1]

? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.038s
user	0m0.006s
sys	0m0.006s


'72.30.9'
************** PARI *****************
Host 72.30.98.35 (72.30.98.35)
Time: Thu Jul 20 14:59:11 2006

Input: for(b=1,100, for(a=1,b, if( frac((a^2+b^2+1)/(a*b))==0 , print(a,",",b), ) ) )

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? 1,1
1,2
2,5
5,13
13,34
34,89
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.148s
user	0m0.025s
sys	0m0.008s


'195.112'
************** PARI *****************
Host 195.112.44.172 (195.112.44.172)
Time: Thu Jul 20 13:08:08 2006

Input: DirichletGroup(20)

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? ? 
Goodbye!

Errors/timing (if any):

  ***   unknown function or error in formal parameters: DirichletGroup(20)
                                                        ^------------------

Timing:
real	0m0.012s
user	0m0.009s
sys	0m0.003s


'138.162'
************** PARI *****************
Host 138.162.5.12 (138.162.5.12)
Time: Thu Jul 20 09:33:53 2006

Input: for(x=1,50,print1("d(",x,")=",numdiv(x),", "))

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? d(1)=1, d(2)=2, d(3)=2, d(4)=3, d(5)=2, d(6)=4, d(7)=2, d(8)=4, d(9)=3, d(10)=4, d(11)=2, d(12)=6, d(13)=2, d(14)=4, d(15)=4, d(16)=5, d(17)=2, d(18)=6, d(19)=2, d(20)=6, d(21)=4, d(22)=4, d(23)=2, d(24)=8, d(25)=3, d(26)=4, d(27)=4, d(28)=6, d(29)=2, d(30)=8, d(31)=2, d(32)=6, d(33)=4, d(34)=4, d(35)=4, d(36)=9, d(37)=2, d(38)=4, d(39)=4, d(40)=8, d(41)=2, d(42)=8, d(43)=2, d(44)=6, d(45)=6, d(46)=4, d(47)=2, d(48)=10, d(49)=3, d(50)=6, 
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.013s
user	0m0.004s
sys	0m0.009s


'208.54.'
************** PARI *****************
Host 208.54.94.73 (208.54.94.73)
Time: Thu Jul 20 08:12:49 2006

Input: for(x=1,50,print1("d(",x,")=",numdiv(x),", "))

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? d(1)=1, d(2)=2, d(3)=2, d(4)=3, d(5)=2, d(6)=4, d(7)=2, d(8)=4, d(9)=3, d(10)=4, d(11)=2, d(12)=6, d(13)=2, d(14)=4, d(15)=4, d(16)=5, d(17)=2, d(18)=6, d(19)=2, d(20)=6, d(21)=4, d(22)=4, d(23)=2, d(24)=8, d(25)=3, d(26)=4, d(27)=4, d(28)=6, d(29)=2, d(30)=8, d(31)=2, d(32)=6, d(33)=4, d(34)=4, d(35)=4, d(36)=9, d(37)=2, d(38)=4, d(39)=4, d(40)=8, d(41)=2, d(42)=8, d(43)=2, d(44)=6, d(45)=6, d(46)=4, d(47)=2, d(48)=10, d(49)=3, d(50)=6, 
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.012s
user	0m0.006s
sys	0m0.005s


'68.142.'
************** PARI *****************
Host 68.142.251.155 (68.142.251.155)
Time: Thu Jul 20 06:24:49 2006

Input: {ss(n)=sum(x=1,n,n/gcd(n,x))}
ss(60)

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? ? %1 = 1617
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.013s
user	0m0.010s
sys	0m0.002s


'72.30.1'
************** PARI *****************
Host 72.30.129.106 (72.30.129.106)
Time: Thu Jul 20 02:55:14 2006

Input: y=210; for(x=1,8,y=sumdiv(y,x,x)-y;print1(y,","))

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? 366,378,582,594,846,1026,1374,1386,
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.066s
user	0m0.006s
sys	0m0.009s


'68.142.'
************** PARI *****************
Host 68.142.250.147 (68.142.250.147)
Time: Thu Jul 20 02:43:21 2006

Input: for(n=1,20, print1(n,": ",valuation(n!,2),", ") )

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? 1: 0, 2: 1, 3: 1, 4: 3, 5: 3, 6: 4, 7: 4, 8: 7, 9: 7, 10: 8, 11: 8, 12: 10, 13: 10, 14: 11, 15: 11, 16: 15, 17: 15, 18: 16, 19: 16, 20: 18, 
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.011s
user	0m0.006s
sys	0m0.005s


'129.217'
************** PARI *****************
Host 129.217.4.64 (129.217.4.64)
Time: Thu Jul 20 02:13:25 2006

Input: 12000!

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = 1201858406751094813215537862229413579273903778819871509781937698530038350660860169670917371878152953448126096270928257528762029090464991491076442906109525418045467519792725373198536354301858453253846165195884935721164436213505153722760122056793086146140905433159473067748531674800236644754708239931069034241296663953338927096775251375029665424008771069634452986894902622957878834581870518862710573293627105221942614088527635926932398344032949842161644969853918449341240708119783886434362219851357290562966666105006287400515466950853748185151637476631407136164092451450025703570632794085427076382136807103101966488567634804715767206079288231734866173361080038077977602168094101167976673856833209964261177857055872793240166881327686111541877999904012889743561036361655983541476096196638459905407459395925871680045369295198360303076468230606297056864947387260231992171519443686692238802735289613296859967770839283263403806385209112168372142293253662281712714495704459907641566305808111352873610453046172363915674399945257285698908699657142585503488495196837565280149793042480811970338804942507273426741834641076044494523665417337436990883431542844969718525209724183471945174759947180279586329694782666848422167638419490229463830545367926262011688150634911635610939838446115823846213359251061555047211817135057012771136047458679916266381752610547815807579377682191473292496800208703700515673596366788785158748151866312551170360471417673866041244849690269491617684455163010206719285101844946768817465854897763361742331376939693720799411394822064175584141397983128027579566456816219796068779500188112072489098109919082756265307945040329208001984233420336499058141509467427088478556323722870712482892044523282899294135422935244125676123349312017047923070858868902817791302059265230569604798628355893345570295954687258691289343421370547561835601212354894510113855172164223742887955106787739330026149589382135847175306705548238306702310024707479558036404066282278669025905150070262103680183123694185414659339459748832669124924280245365198626654805750377769079111161268905199670388519325457357799002112841179008342483409618850135047574281110795388595683003077802351065244551300757071706050356977798620602479359144117344123774225069550262059126922141853452194569248510850905986323885856892760864357500075373968548984931058807388261363117077893331085322598490397497246191300447394799013063388036987931085468278826236511216212942874265386988220673529482541533633235535431545571452620978548092772518060236716644822529963314595647273386361565894921793481157813682928823947226944897617211730724928507616597083945381726055844938261571369510797612966640393069503548216213079022638787122859347632343871969616838286298140195222789325898866514950645873310283352239785750676185784532017718919374610494867137021634811726883381821571548639992187486546956814724833222136466745526632234485914231245030406482619752076076954125629297107274899730116441138406955253196139029162811650331688727340149451116062073149640127650336308177330022521701054222470762226042541696968100263888044022668931744100022913733213976440275222168948266084762525618856825000145165748358360040257782942254414393986427281116537307737738353209993[+++]
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.164s
user	0m0.102s
sys	0m0.054s


'129.217'
************** PARI *****************
Host 129.217.4.64 (129.217.4.64)
Time: Thu Jul 20 02:13:10 2006

Input: 1200!

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = 63507890863456767124026223135865363993920361927048401849732641593094118304334664838518489279761202858110442656198961423888337785958374054395875090008179394602121729048755527506222388620438398012556615061940909904115015164483186340282667999681601237310950712039020066375755766076440811303940538840103890741951917564190561275396873204122937083746098640414588850116107225675520412584415359155103495655208534054658149146203739758027326003354866456731097561086620889903717246818807490131678158299401901235057514328881677204150054888001843870188616756694468379677033228639349974219800691760236674808772459147849761319772233349285258185354881462706759016416844508026593468378544952254302304068325633905800617846092173316334920423976973219453332902616477256306327233355305287468380745909208415980513577159243876582648875144838454034618802839634184994308400967856236366107563273185702779295861081100580569890291839403080692152562549750464518941296615589072961901445867101610266912853288908304184351248084449986727837714164724886934713403840928394071581648559037175552279054765268191336562999918827853842984694855922999162907679561931097787771324637893456823082524179018246504955405803121771121360752264414781039718455098118457351815525441962553663917394824907930942411732997508709279776658345871568600666174624864566227235992187598660130953640936345350873339744682415089563501119516442999676532779307108492176925439731860347372511112433604790992759325197681339726349322054878255119874625965850196940660648685990671210212572225564228346159053754713667934756177880507837712524591347066833930606771513277248914447108453842428044821209156242191481316239948456314071437111282270756494813443336707372525017024678559199590515860360962136467183581351799081925904581530470013515629221769984825958416224944982867113744499809912183809641523923237883957287541972186804232110652653006828947123647231393100716154785438044926596489481061404444949958850342025214038700582411675847296195285368313134928856220726124462351334098415059073275239953735718425086123827271757497468773885713767925771130546617686545287963633612898691413349119011210341661317374809835898724194978360650558823413986166888783608735534361048197825992486540004672367499044204531085976637277941222039312514997381320707709813267213844400528265917241905520030567187527121305903232698469502319828288497642071789544559470672876896682816986176852553613912123976135208540633191577134212923764719883260091745561140753211368159375154389149276613870478944559132118639123292629448861220166692668795869998815536697843168702435154762819119055700781916899847331952260368608062686678197902264191722301178373738543720223581116366378070649868986724225640819288848872888236573440404740650405057575066492961346462735749115329710082527101393654163731209311139319445720303577449977552535888706315264756010489543514382828926003274237925093166062460951592960000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.012s
user	0m0.006s
sys	0m0.008s


'129.217'
************** PARI *****************
Host 129.217.4.64 (129.217.4.64)
Time: Thu Jul 20 02:12:39 2006

Input: 120!

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = 6689502913449127057588118054090372586752746333138029810295671352301633557244962989366874165271984981308157637893214090552534408589408121859898481114389650005964960521256960000000000000000000000000000
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.034s
user	0m0.008s
sys	0m0.003s


'68.142.'
************** PARI *****************
Host 68.142.249.131 (68.142.249.131)
Time: Wed Jul 19 22:37:04 2006

Input: vector(20,x,floor((x+1)*sqrt(2))-floor(x*sqrt(2)))

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = [1, 2, 1, 2, 1, 1, 2, 1, 2, 1, 1, 2, 1, 2, 1, 2, 1, 1, 2, 1]
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.081s
user	0m0.004s
sys	0m0.008s


'68.142.'
************** PARI *****************
Host 68.142.249.100 (68.142.249.100)
Time: Wed Jul 19 21:54:32 2006

Input: for(b=1,100, for(a=1,b, if( frac((a^2+b^2)/(a*b))==0 , print(a,",",b), ) ) )

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? 1,1
2,2
3,3
4,4
5,5
6,6
7,7
8,8
9,9
10,10
11,11
12,12
13,13
14,14
15,15
16,16
17,17
18,18
19,19
20,20
21,21
22,22
23,23
24,24
25,25
26,26
27,27
28,28
29,29
30,30
31,31
32,32
33,33
34,34
35,35
36,36
37,37
38,38
39,39
40,40
41,41
42,42
43,43
44,44
45,45
46,46
47,47
48,48
49,49
50,50
51,51
52,52
53,53
54,54
55,55
56,56
57,57
58,58
59,59
60,60
61,61
62,62
63,63
64,64
65,65
66,66
67,67
68,68
69,69
70,70
71,71
72,72
73,73
74,74
75,75
76,76
77,77
78,78
79,79
80,80
81,81
82,82
83,83
84,84
85,85
86,86
87,87
88,88
89,89
90,90
91,91
92,92
93,93
94,94
95,95
96,96
97,97
98,98
99,99
100,100
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.048s
user	0m0.024s
sys	0m0.006s


'206.15.'
************** PARI *****************
Host 206.15.72.193 (206.15.72.193)
Time: Wed Jul 19 21:02:50 2006

Input: a3 = 1

t = 4

a0 = 1
a1 = -3
a2 = 2 - a3
a3 = 1 
a4 = -4*a3 - 3
a5 = 14*a3 + 14
a6 = -52*a3 - 52
a7 = 194*a3 + 195

a0 + a1*t + a2 * t^2 + a3* t^3 + a4*(t-1)^3 + a5*(t-2)^3 + a6*(t-3)^3 + a7*(t-4)^3

 a1 + a2 * 2*t + 3*a3* t^2 + 3*a4*(t-1)^2 + 3*a5*(t-2)^2 + 3*a6*(t-3)^2 + 3*a7*(t-4)^2




Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = 1
? ? %2 = 4
? ? %3 = 1
? %4 = -3
? %5 = 1
? %6 = 1
? %7 = -7
? %8 = 28
? %9 = -104
? %10 = 389
? ? %11 = 0
? ? %12 = -112
? ? ? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.012s
user	0m0.003s
sys	0m0.008s


'206.15.'
************** PARI *****************
Host 206.15.72.193 (206.15.72.193)
Time: Wed Jul 19 21:02:23 2006

Input: a3 = 1

t = 3

a0 = 1
a1 = -3
a2 = 2 - a3
a3 = 1 
a4 = -4*a3 - 3
a5 = 14*a3 + 14
a6 = -52*a3 - 52
a7 = 0

a0 + a1*t + a2 * t^2 + a3* t^3 + a4*(t-1)^3 + a5*(t-2)^3 + a6*(t-3)^3 + a7*(t-4)^3

 a1 + a2 * 2*t + 3*a3* t^2 + 3*a4*(t-1)^2 + 3*a5*(t-2)^2 + 3*a6*(t-3)^2 + 3*a7*(t-4)^2




Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = 1
? ? %2 = 3
? ? %3 = 1
? %4 = -3
? %5 = 1
? %6 = 1
? %7 = -7
? %8 = 28
? %9 = -104
? %10 = 0
? ? %11 = 0
? ? %12 = 30
? ? ? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.013s
user	0m0.007s
sys	0m0.005s


'206.15.'
************** PARI *****************
Host 206.15.72.193 (206.15.72.193)
Time: Wed Jul 19 21:01:31 2006

Input: a3 = 1

t = 2

a0 = 1
a1 = -3
a2 = 2 - a3
a3 = 1 
a4 = -4*a3 - 3
a5 = 14*a3 + 14
a6 = -52*a3 - 52
a7 = 0

a0 + a1*t + a2 * t^2 + a3* t^3 + a4*(t-1)^3 + a5*(t-2)^3 + a6*(t-3)^3 + a7*(t-4)^3

 a1 + a2 * 2*t + 3*a3* t^2 + 3*a4*(t-1)^2 + 3*a5*(t-2)^2 + 3*a6*(t-3)^2 + 3*a7*(t-4)^2




Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = 1
? ? %2 = 2
? ? %3 = 1
? %4 = -3
? %5 = 1
? %6 = 1
? %7 = -7
? %8 = 28
? %9 = -104
? %10 = 0
? ? %11 = 104
? ? %12 = -320
? ? ? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.012s
user	0m0.006s
sys	0m0.007s


'206.15.'
************** PARI *****************
Host 206.15.72.193 (206.15.72.193)
Time: Wed Jul 19 21:00:12 2006

Input: a3 = 1

t = 2

a0 = 1
a1 = -3
a2 = 2 - a3
a3 = 1 
a4 = -4*a3 - 3
a5 = 14*a3 + 14
a6 = 0
a7 = 0

a0 + a1*t + a2 * t^2 + a3* t^3 + a4*(t-1)^3 + a5*(t-2)^3 + a6*(t-3)^3 + a7*(t-4)^3

 a1 + a2 * 2*t + 3*a3* t^2 + 3*a4*(t-1)^2 + 3*a5*(t-2)^2 + 3*a6*(t-3)^2 + 3*a7*(t-4)^2




Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = 1
? ? %2 = 2
? ? %3 = 1
? %4 = -3
? %5 = 1
? %6 = 1
? %7 = -7
? %8 = 28
? %9 = 0
? %10 = 0
? ? %11 = 0
? ? %12 = -8
? ? ? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.012s
user	0m0.008s
sys	0m0.004s


'206.15.'
************** PARI *****************
Host 206.15.72.193 (206.15.72.193)
Time: Wed Jul 19 20:59:33 2006

Input: a3 = 1

t = 1

a0 = 1
a1 = -3
a2 = 2 - a3
a3 = 1 
a4 = -4*a3 - 3
a5 = 0
a6 = 0
a7 = 0

a0 + a1*t + a2 * t^2 + a3* t^3 + a4*(t-1)^3 + a5*(t-2)^3 + a6*(t-3)^3 + a7*(t-4)^3

 a1 + a2 * 2*t + 3*a3* t^2 + 3*a4*(t-1)^2 + 3*a5*(t-2)^2 + 3*a6*(t-3)^2 + 3*a7*(t-4)^2




Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = 1
? ? %2 = 1
? ? %3 = 1
? %4 = -3
? %5 = 1
? %6 = 1
? %7 = -7
? %8 = 0
? %9 = 0
? %10 = 0
? ? %11 = 0
? ? %12 = 2
? ? ? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.012s
user	0m0.008s
sys	0m0.004s


'206.15.'
************** PARI *****************
Host 206.15.72.193 (206.15.72.193)
Time: Wed Jul 19 20:58:58 2006

Input: a3 = 1

t = 0

a0 = 1
a1 = -3
a2 = 2 - a3
a3 = 1 
a4 = 0
a5 = 0
a6 = 0
a7 = 0

a0 + a1*t + a2 * t^2 + a3* t^3 + a4*(t-1)^3 + a5*(t-2)^3 + a6*(t-3)^3 + a7*(t-4)^3

 a1 + a2 * 2*t + 3*a3* t^2 + 3*a4*(t-1)^2 + 3*a5*(t-2)^2 + 3*a6*(t-3)^2 + 3*a7*(t-4)^2




Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = 1
? ? %2 = 0
? ? %3 = 1
? %4 = -3
? %5 = 1
? %6 = 1
? %7 = 0
? %8 = 0
? %9 = 0
? %10 = 0
? ? %11 = 1
? ? %12 = -3
? ? ? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.019s
user	0m0.009s
sys	0m0.007s


'206.15.'
************** PARI *****************
Host 206.15.72.193 (206.15.72.193)
Time: Wed Jul 19 20:43:17 2006

Input: a3 = 1


a0 = 1
a1 = -3
a2 = 2 - a3
a3 = 1 
a4 = -4*a3 - 3
a5 = 14*a3 + 14
a6 = -52*a3 - 52
a7 = 194*a3 + 195

a0 + a1*t + a2 * t^2 + a3* t^3 + a4*(t-1)^3 + a5*(t-2)^3 + a6*(t-3)^3 + a7*(t-4)^3

 a1 + a2 * 2*t + 3*a3* t^2 + 3*a4*(t-1)^2 + 3*a5*(t-2)^2 + 3*a6*(t-3)^2 + 3*a7*(t-4)^2




Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = 1
? ? ? %2 = 1
? %3 = -3
? %4 = 1
? %5 = 1
? %6 = -7
? %7 = 28
? %8 = -104
? %9 = 389
? ? %10 = 307*t^3 - 3878*t^2 + 16176*t - 22304
? ? %11 = 921*t^2 - 7756*t + 16176
? ? ? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.012s
user	0m0.006s
sys	0m0.007s


'206.15.'
************** PARI *****************
Host 206.15.72.193 (206.15.72.193)
Time: Wed Jul 19 20:42:56 2006

Input: a3 = 1


a0 = 1
a1 = -3
a2 = 2 - a3 
a4 = -4*a3 - 3
a5 = 14*a3 + 14
a6 = -52*a3 - 52
a7 = 194*a3 + 195

a0 + a1*t + a2 * t^2 + a3* t^3 + a4*(t-1)^3 + a5*(t-2)^3 + a6*(t-3)^3 + a7*(t-4)^3

 a1 + a2 * 2*t + 3*a3* t^2 + 3*a4*(t-1)^2 + 3*a5*(t-2)^2 + 3*a6*(t-3)^2 + 3*a7*(t-4)^2




Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = 1
? ? ? %2 = 1
? %3 = -3
? %4 = 1
? %5 = -7
? %6 = 28
? %7 = -104
? %8 = 389
? ? %9 = 307*t^3 - 3878*t^2 + 16176*t - 22304
? ? %10 = 921*t^2 - 7756*t + 16176
? ? ? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.012s
user	0m0.008s
sys	0m0.004s


'206.15.'
************** PARI *****************
Host 206.15.72.193 (206.15.72.193)
Time: Wed Jul 19 20:41:56 2006

Input: //a3 = -206/209

t = 5
a0 = 1
a1 = -3
a2 = 2 - a3 
a4 = -4*a3 - 3
a5 = 14*a3 + 14
a6 = -52*a3 - 52
a7 = 194*a3 + 195

a0 + a1*t + a2 * t^2 + a3* t^3 + a4*(t-1)^3 + a5*(t-2)^3 + a6*(t-3)^3 + a7*(t-4)^3

 a1 + a2 * 2*t + 3*a3* t^2 + 3*a4*(t-1)^2 + 3*a5*(t-2)^2 + 3*a6*(t-3)^2 + 3*a7*(t-4)^2


-3 + (2 - a3) * t^2 + a3* t^3 + (-4*a3-3)*(t-1)^3 + (14*a3+14)*(t-2)^3 +(-52*a3-52)*(t-3)^3 + a7*(t-4)^3

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? ? ? %1 = 5
? %2 = 1
? %3 = -3
? %4 = -a3 + 2
? %5 = -4*a3 - 3
? %6 = 14*a3 + 14
? %7 = -52*a3 - 52
? %8 = 194*a3 + 195
? ? %9 = 1
? ? %10 = 209*a3 + 212
? ? ? %11 = 12
? 
Goodbye!

Errors/timing (if any):

  ***   unexpected character: //a3=-206/209
                              ^-------------

Timing:
real	0m0.012s
user	0m0.004s
sys	0m0.008s


'206.15.'
************** PARI *****************
Host 206.15.72.193 (206.15.72.193)
Time: Wed Jul 19 20:41:30 2006

Input: //a3 = -206/209
a0 = 1
a1 = -3
a2 = 2 - a3 
a4 = -4*a3 - 3
a5 = 14*a3 + 14
a6 = -52*a3 - 52
a7 = 194*a3 + 195

a0 + a1*t + a2 * t^2 + a3* t^3 + a4*(t-1)^3 + a5*(t-2)^3 + a6*(t-3)^3 + a7*(t-4)^3

 a1 + a2 * 2*t + 3*a3* t^2 + 3*a4*(t-1)^2 + 3*a5*(t-2)^2 + 3*a6*(t-3)^2 + 3*a7*(t-4)^2


-3 + (2 - a3) * t^2 + a3* t^3 + (-4*a3-3)*(t-1)^3 + (14*a3+14)*(t-2)^3 +(-52*a3-52)*(t-3)^3 + a7*(t-4)^3

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? ? %1 = 1
? %2 = -3
? %3 = -a3 + 2
? %4 = -4*a3 - 3
? %5 = 14*a3 + 14
? %6 = -52*a3 - 52
? %7 = 194*a3 + 195
? ? %8 = (153*t^3 - 1933*t^2 + 8064*t - 11120)*a3 + (154*t^3 - 1945*t^2 + 8112*t - 11184)
? ? %9 = (459*t^2 - 3866*t + 8064)*a3 + (462*t^2 - 3890*t + 8112)
? ? ? %10 = (153*t^3 - 1933*t^2 + 8064*t - 11120)*a3 + (154*t^3 - 1945*t^2 + 8115*t - 11188)
? 
Goodbye!

Errors/timing (if any):

  ***   unexpected character: //a3=-206/209
                              ^-------------

Timing:
real	0m0.012s
user	0m0.006s
sys	0m0.006s


'206.15.'
************** PARI *****************
Host 206.15.72.193 (206.15.72.193)
Time: Wed Jul 19 20:34:17 2006

Input: a3 = -206/209
- 3 + 2*(2 - a3) * t + 3*a3* t^2 + 3*(-4*a3-3)*(t-1)^2 + 3*(14*a3+14)*(t-2)^2 +3*(-52*a3-52)*(t-3)^2 + 3*(194*a3+194)*(t-4)^2


(3-209)/209


Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = -206/209
? %2 = 1377/209*t^2 - 11598/209*t + 24192/209
? ? ? %3 = -206/209
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.012s
user	0m0.009s
sys	0m0.003s


'206.15.'
************** PARI *****************
Host 206.15.72.193 (206.15.72.193)
Time: Wed Jul 19 20:32:48 2006

Input: t = 5
- 3 + 2*(2 - a3) * t + 3*a3* t^2 + 3*(-4*a3-3)*(t-1)^2 + 3*(14*a3+14)*(t-2)^2 +3*(-52*a3-52)*(t-3)^2 + 3*(194*a3+194)*(t-4)^2


(3-209)/209


Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = 5
? %2 = 209*a3 + 209
? ? ? %3 = -206/209
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.011s
user	0m0.005s
sys	0m0.008s


'206.15.'
************** PARI *****************
Host 206.15.72.193 (206.15.72.193)
Time: Wed Jul 19 20:30:45 2006

Input: t = 5
- 3 + 2*(2 - a3) * t + 3*a3* t^2 + 3*(-4*a3-3)*(t-1)^2 + 3*(14*a3+14)*(t-2)^2 +3*(-52*a3-52)*(t-3)^2 + 3*(194*a3+194)*(t-4)^2


Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = 5
? %2 = 209*a3 + 209
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.012s
user	0m0.008s
sys	0m0.004s


'206.15.'
************** PARI *****************
Host 206.15.72.193 (206.15.72.193)
Time: Wed Jul 19 20:28:31 2006

Input: t = 5
1 - 3*t + (2 - a3) * t^2 + a3* t^3 + (-4*a3-3)*(t-1)^3 + (14*a3+14)*(t-2)^3 +(-52*a3-52)*(t-3)^3 + a7*(t-4)^3


Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = 5
? %2 = -194*a3 + (a7 - 194)
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.012s
user	0m0.006s
sys	0m0.005s


'206.15.'
************** PARI *****************
Host 206.15.72.193 (206.15.72.193)
Time: Wed Jul 19 20:20:36 2006

Input: t = 5
1 - 3*t + (2 - a3) * t^2 + a3* t^3 + (-4*a3-3)*(t-1)^3 + (14*a3+14)*(t-2)^3 +(-51*a3-52)*(t-3)^3 + a7*(t-4)^3


Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = 5
? %2 = -186*a3 + (a7 - 194)
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.011s
user	0m0.006s
sys	0m0.005s


'206.15.'
************** PARI *****************
Host 206.15.72.193 (206.15.72.193)
Time: Wed Jul 19 20:20:14 2006

Input: t = 4
1 - 3*t + (2 - a3) * t^2 + a3* t^3 + (-4*a3-3)*(t-1)^3 + (14*a3+14)*(t-2)^3 +(-51*a3-52)*(t-3)^3 + a7*(t-4)^3


Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = 4
? %2 = a3
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.011s
user	0m0.006s
sys	0m0.005s


'69.180.'
************** PARI *****************
Host 69.180.5.21 (69.180.5.21)
Time: Wed Jul 19 20:20:09 2006

Input: 251 - 121 + 441 - 340 + 130 - 113 + 409 - 253 + 130 - 181 + 297 - 149 + 081 - 088 + 467 - 059 + 306 - 229 + 345 - 351 + 117 - 047 + 353 - 216 + 401 - 147

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = 1434
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.011s
user	0m0.004s
sys	0m0.007s


'206.15.'
************** PARI *****************
Host 206.15.72.193 (206.15.72.193)
Time: Wed Jul 19 20:15:28 2006

Input: t = 4
1 - 3*t + (2 - a3) * t^2 + a3* t^3 + (-4*a3-3)*(t-1)^3 + (14*a3+14)*(t-2)^3 +a6*(t-3)^3 + a7*(t-4)^3


Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = 4
? %2 = 52*a3 + (a6 + 52)
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.012s
user	0m0.009s
sys	0m0.003s


'206.15.'
************** PARI *****************
Host 206.15.72.193 (206.15.72.193)
Time: Wed Jul 19 20:14:36 2006

Input: t = 4
1 - 3*t + (2 - a3) * t^2 + a3* t^3 + (-4*a3-3)*(t-1)^3 + (a5)*(t-2)^3 +a6*(t-3)^3 + a7*(t-4)^3


Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = 4
? %2 = -60*a3 + (8*a5 + (a6 - 60))
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.012s
user	0m0.005s
sys	0m0.008s


'206.15.'
************** PARI *****************
Host 206.15.72.193 (206.15.72.193)
Time: Wed Jul 19 20:07:03 2006

Input: t = 3
1 - 3*t + (2 - a3) * t^2 + a3* t^3 + (-4*a3-3)*(t-1)^3 + (a5)*(t-2)^3 


Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = 3
? %2 = -14*a3 + (a5 - 14)
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.011s
user	0m0.007s
sys	0m0.005s


'206.15.'
************** PARI *****************
Host 206.15.72.193 (206.15.72.193)
Time: Wed Jul 19 20:04:00 2006

Input: t = 4
1 - 3*t + (2 - a3) * t^2 + a3* t^3 + (-4*a3+3)*(t-1)^3 + (14*a3-34)*(t-2)^3 + (-52*a3-170) * (t-3)^3 + a7*(t-4)^3



Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = 4
? %2 = -340
? ? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.011s
user	0m0.007s
sys	0m0.005s


'206.15.'
************** PARI *****************
Host 206.15.72.193 (206.15.72.193)
Time: Wed Jul 19 20:02:36 2006

Input: t = 4
1 - 3*t + (2 - a3) * t^2 + a3* t^3 + (-4*a3+3)*(t-1)^3 + (14*a3-34)*(t-2)^3 + a6 * (t-3)^3



Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = 4
? %2 = 52*a3 + (a6 - 170)
? ? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.011s
user	0m0.007s
sys	0m0.004s


'206.15.'
************** PARI *****************
Host 206.15.72.193 (206.15.72.193)
Time: Wed Jul 19 19:59:25 2006

Input: t = 3
1 - 3*t + (2 - a3) * t^2 + a3* t^3 + (-4*a3+3)*(t-1)^3 + a5*(t-2)^3 + a6 * (t-3)^3



Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = 3
? %2 = -14*a3 + (a5 + 34)
? ? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.011s
user	0m0.006s
sys	0m0.005s


'206.15.'
************** PARI *****************
Host 206.15.72.193 (206.15.72.193)
Time: Wed Jul 19 19:52:07 2006

Input: t = 2
1 - 3*t + (2 - a3) * t^2 + a3* t^3 + a4*(t-1)^3

a3

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = 2
? %2 = 4*a3 + (a4 + 3)
? ? %3 = a3
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.011s
user	0m0.009s
sys	0m0.002s


'206.15.'
************** PARI *****************
Host 206.15.72.193 (206.15.72.193)
Time: Wed Jul 19 19:51:52 2006

Input: t = 2
1 - 3*t + (2 - a3) * t^2 + a3* t^3 + a4*(t-1)^3 + 

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = 2
? ? 
Goodbye!

Errors/timing (if any):

  ***   unexpected character: ...3)*t^2+a3*t^3+a4*(t-1)^3+
                                                          ^

Timing:
real	0m0.011s
user	0m0.007s
sys	0m0.004s


'206.15.'
************** PARI *****************
Host 206.15.72.193 (206.15.72.193)
Time: Wed Jul 19 19:46:22 2006

Input: t = 5
1 - 3*t+ ( -4 - a3) * t^2 + a3* t^3 + (-9-4*a3)*(t-1)^3 + (14*a3 + 116)*(t-2)^3 + (-52*a3 - 610)*(t -3)^3 + a7*(t- 4)^3 

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = 5
? %2 = -194*a3 + (a7 - 2438)
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.012s
user	0m0.008s
sys	0m0.003s


'206.15.'
************** PARI *****************
Host 206.15.72.193 (206.15.72.193)
Time: Wed Jul 19 19:46:13 2006

Input: t = 4
1 - 3*t+ ( -4 - a3) * t^2 + a3* t^3 + (-9-4*a3)*(t-1)^3 + (14*a3 + 116)*(t-2)^3 + (-52*a3 - 610)*(t -3)^3 + a7*(t- 4)^3 

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = 4
? %2 = 0
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.012s
user	0m0.007s
sys	0m0.004s


'206.15.'
************** PARI *****************
Host 206.15.72.193 (206.15.72.193)
Time: Wed Jul 19 19:38:10 2006

Input: t = 4
1 - 3*t+ ( -4 - a3) * t^2 + a3* t^3 + (-9-4*a3)*(t-1)^3 + (14*a3 + 116)*(t-2)^3 + a6*(t -3)^3

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = 4
? %2 = 52*a3 + (a6 + 610)
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.011s
user	0m0.005s
sys	0m0.007s


'206.15.'
************** PARI *****************
Host 206.15.72.193 (206.15.72.193)
Time: Wed Jul 19 19:31:35 2006

Input: t = 3
1 - 3*t+ ( -4 - a3) * t^2 + a3* t^3 + (-9-4*a3)*(t-1)^3 + (a5)*(t-2)^3 

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = 3
? %2 = -14*a3 + (a5 - 116)
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.011s
user	0m0.005s
sys	0m0.006s


'206.15.'
************** PARI *****************
Host 206.15.72.193 (206.15.72.193)
Time: Wed Jul 19 19:31:03 2006

Input: t = 3
1 - 3*t+ ( -4 - a3) * t^2 + a3* t^3 + (-9-4*a3)*(t-1)^3 + (86*a3+44)*(t-2)^3 

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = 3
? %2 = 72*a3 - 72
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.012s
user	0m0.006s
sys	0m0.006s


'206.15.'
************** PARI *****************
Host 206.15.72.193 (206.15.72.193)
Time: Wed Jul 19 19:09:01 2006

Input: t = 3
1 - 3*t+ ( -4 - a3) * t^2 + a3* t^3 + (-9-4)*a3*(t-1)^3 + a5*(t-2)^3 

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = 3
? %2 = -86*a3 + (a5 - 44)
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.011s
user	0m0.007s
sys	0m0.005s


'206.15.'
************** PARI *****************
Host 206.15.72.193 (206.15.72.193)
Time: Wed Jul 19 19:08:43 2006

Input: 1 - 3*t+ ( -4 - a3) * t^2 + a3* t^3 + (-9-4)*a3*(t-1)^3 + a5*(t-2)^3 

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = (-12*a3 + a5)*t^3 + (38*a3 + (-6*a5 - 4))*t^2 + (-39*a3 + (12*a5 - 3))*t + (13*a3 + (-8*a5 + 1))
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.011s
user	0m0.006s
sys	0m0.005s


'206.15.'
************** PARI *****************
Host 206.15.72.193 (206.15.72.193)
Time: Wed Jul 19 18:40:54 2006

Input: (t-1)^3

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = t^3 - 3*t^2 + 3*t - 1
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.051s
user	0m0.005s
sys	0m0.006s


'206.15.'
************** PARI *****************
Host 206.15.72.193 (206.15.72.193)
Time: Wed Jul 19 18:40:46 2006

Input: (t-1)^-1

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = 1/(t - 1)
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.012s
user	0m0.006s
sys	0m0.006s


'206.15.'
************** PARI *****************
Host 206.15.72.193 (206.15.72.193)
Time: Wed Jul 19 18:40:28 2006

Input: "Replace this by some code, then click [SAGE] or [PARI]!"

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = "Replace this by some code, then click [SAGE] or [PARI]!"
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.011s
user	0m0.006s
sys	0m0.006s


'68.142.'
************** PARI *****************
Host 68.142.251.11 (68.142.251.11)
Time: Wed Jul 19 17:53:59 2006

Input: for( k=1, 12, print(k,": ",Mod(2^k,13)) )

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? 1: Mod(2, 13)
2: Mod(4, 13)
3: Mod(8, 13)
4: Mod(3, 13)
5: Mod(6, 13)
6: Mod(12, 13)
7: Mod(11, 13)
8: Mod(9, 13)
9: Mod(5, 13)
10: Mod(10, 13)
11: Mod(7, 13)
12: Mod(1, 13)
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.048s
user	0m0.010s
sys	0m0.002s


'68.142.'
************** PARI *****************
Host 68.142.251.91 (68.142.251.91)
Time: Wed Jul 19 17:45:47 2006

Input: for(x=1,50,print1("d(",x,")=",numdiv(x),", "))

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? d(1)=1, d(2)=2, d(3)=2, d(4)=3, d(5)=2, d(6)=4, d(7)=2, d(8)=4, d(9)=3, d(10)=4, d(11)=2, d(12)=6, d(13)=2, d(14)=4, d(15)=4, d(16)=5, d(17)=2, d(18)=6, d(19)=2, d(20)=6, d(21)=4, d(22)=4, d(23)=2, d(24)=8, d(25)=3, d(26)=4, d(27)=4, d(28)=6, d(29)=2, d(30)=8, d(31)=2, d(32)=6, d(33)=4, d(34)=4, d(35)=4, d(36)=9, d(37)=2, d(38)=4, d(39)=4, d(40)=8, d(41)=2, d(42)=8, d(43)=2, d(44)=6, d(45)=6, d(46)=4, d(47)=2, d(48)=10, d(49)=3, d(50)=6, 
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.011s
user	0m0.006s
sys	0m0.005s


'217.191'
************** PARI *****************
Host 217.191.224.235 (217.191.224.235)
Time: Wed Jul 19 17:17:33 2006

Input: 2+3

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = 5
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.011s
user	0m0.006s
sys	0m0.006s


'217.191'
************** PARI *****************
Host 217.191.224.235 (217.191.224.235)
Time: Wed Jul 19 17:17:23 2006

Input: 2+pi

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = pi + 2
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.012s
user	0m0.006s
sys	0m0.006s


'217.191'
************** PARI *****************
Host 217.191.224.235 (217.191.224.235)
Time: Wed Jul 19 17:17:05 2006

Input: e


Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = e
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.012s
user	0m0.004s
sys	0m0.008s


'217.191'
************** PARI *****************
Host 217.191.224.235 (217.191.224.235)
Time: Wed Jul 19 17:16:47 2006

Input: n 100


Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = n100
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.011s
user	0m0.007s
sys	0m0.004s


'217.191'
************** PARI *****************
Host 217.191.224.235 (217.191.224.235)
Time: Wed Jul 19 17:16:06 2006

Input: "Replace this by some code, then click [SAGE] or [PARI]!"

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = "Replace this by some code, then click [SAGE] or [PARI]!"
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.011s
user	0m0.007s
sys	0m0.005s


'206.15.'
************** PARI *****************
Host 206.15.72.193 (206.15.72.193)
Time: Wed Jul 19 16:20:46 2006

Input: g = [ 1, -1, 0, 3, -2]

m = [ 0, 2, 0, 0, 0;1,-1, 1, 1, 4;2, 0, 0, -1/2, 1;-2, 1,1, 1/4, 1;-28, 0, 2,0, 2 ]

q = m^(-1)

g*q


      

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = [1, -1, 0, 3, -2]
? ? %2 = 
[0 2 0 0 0]

[1 -1 1 1 4]

[2 0 0 -1/2 1]

[-2 1 1 1/4 1]

[-28 0 2 0 2]

? ? %3 = 
[-11/222 -1/111 1/37 10/111 -3/74]

[1/2 0 0 0 0]

[-109/111 -40/111 3/37 178/111 -9/74]

[14/37 16/37 -48/37 -12/37 -2/37]

[32/111 26/111 11/37 -38/111 2/37]

? ? %4 = [1/111, 91/111, -165/37, -22/111, -23/74]
? ? ? ? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.012s
user	0m0.006s
sys	0m0.006s


'206.15.'
************** PARI *****************
Host 206.15.72.193 (206.15.72.193)
Time: Wed Jul 19 16:20:40 2006

Input: g = [ 1, -1, 0, 3, -2]

m = [ 0, 2, 0, 0, 0;1,-1, 1, 1, 4;2, 0, 0, -1/2, 1;-2, 1,1, 1/4, 1;-28, 0, 2,0, 2 ]

q = m^(-1)

g*g


      

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = [1, -1, 0, 3, -2]
? ? %2 = 
[0 2 0 0 0]

[1 -1 1 1 4]

[2 0 0 -1/2 1]

[-2 1 1 1/4 1]

[-28 0 2 0 2]

? ? %3 = 
[-11/222 -1/111 1/37 10/111 -3/74]

[1/2 0 0 0 0]

[-109/111 -40/111 3/37 178/111 -9/74]

[14/37 16/37 -48/37 -12/37 -2/37]

[32/111 26/111 11/37 -38/111 2/37]

? ? ? ? ? ? 
Goodbye!

Errors/timing (if any):

  ***   forbidden multiplication t_VEC * t_VEC.

Timing:
real	0m0.023s
user	0m0.007s
sys	0m0.005s


'206.15.'
************** PARI *****************
Host 206.15.72.193 (206.15.72.193)
Time: Wed Jul 19 16:18:32 2006

Input: g = [ 1, -1, 0, 3, -2]

m = [ 0, 2, 0, 0, 0;1,-1, 1, 1, 4;2, 0, 0, -1/2, 1;-2, 1,1, 1/4, 1;-28, 0, 2,0, 2 ]

m^(-1)*g
      

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = [1, -1, 0, 3, -2]
? ? %2 = 
[0 2 0 0 0]

[1 -1 1 1 4]

[2 0 0 -1/2 1]

[-2 1 1 1/4 1]

[-28 0 2 0 2]

? ? ? ? 
Goodbye!

Errors/timing (if any):

  ***   impossible multiplication t_MAT * t_VEC.

Timing:
real	0m0.012s
user	0m0.005s
sys	0m0.008s


'206.15.'
************** PARI *****************
Host 206.15.72.193 (206.15.72.193)
Time: Wed Jul 19 16:14:35 2006

Input: m = [ 0, 2, 0, 0, 0;1,-1, 1, 1, 4;2, 0, 0, -1/2, 1;-2, 1,1, 1/4, 1;-28, 0, 2,0, 2 ]

m^(-1)
      

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = 
[0 2 0 0 0]

[1 -1 1 1 4]

[2 0 0 -1/2 1]

[-2 1 1 1/4 1]

[-28 0 2 0 2]

? ? %2 = 
[-11/222 -1/111 1/37 10/111 -3/74]

[1/2 0 0 0 0]

[-109/111 -40/111 3/37 178/111 -9/74]

[14/37 16/37 -48/37 -12/37 -2/37]

[32/111 26/111 11/37 -38/111 2/37]

? ? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.049s
user	0m0.007s
sys	0m0.006s


'206.15.'
************** PARI *****************
Host 206.15.72.193 (206.15.72.193)
Time: Wed Jul 19 16:14:18 2006

Input: m = [ 0, 2, 0, 0, 0;1,-1, 1, 1, 4;2, 0, 0, -1/2, 1;-2, 1,1, 1/4, 1;-28 0, 2, 0, 2 ]

m^(-1)
      

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? ? ? %1 = 1/m
? ? 
Goodbye!

Errors/timing (if any):

  ***   expected character: ',' instead of: ...1;-2,1,1,1/4,1;-280,2,0,2]
                                                                        ^-

Timing:
real	0m0.012s
user	0m0.006s
sys	0m0.006s


'206.15.'
************** PARI *****************
Host 206.15.72.193 (206.15.72.193)
Time: Wed Jul 19 16:14:02 2006

Input: m = [ 0, 2, 0, 0, 0;1,-1, 1, 1, 4;2, 0, 0, -1/2, 1;-2, 1,1, 1/4, 1;-28 0, 2, 0, 2]

m^(-1)
      

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? ? ? %1 = 1/m
? ? 
Goodbye!

Errors/timing (if any):

  ***   expected character: ',' instead of: ...1;-2,1,1,1/4,1;-280,2,0,2]
                                                                        ^-

Timing:
real	0m0.012s
user	0m0.007s
sys	0m0.005s


'206.15.'
************** PARI *****************
Host 206.15.72.193 (206.15.72.193)
Time: Wed Jul 19 16:13:24 2006

Input: m = [ 0, 2, 0, 0, 0;  
      1,-1, 1, 1, 4; 
      2, 0, 0, -1/2, 1; 
     -2, 1,1, 1/4, 1; 
     -28 0, 2, 0, 2]

m^(-1)
      

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? ? ? ? ? %4 = -280
? ? %5 = 1/m
? ? 
Goodbye!

Errors/timing (if any):

  ***   unexpected character: m=[0,2,0,0,0;
                                           ^
  ***   Warning: unused characters: ,-1,1,1,4;.
  ***   Warning: unused characters: ,0,0,-1/2,1;.
  ***   Warning: unused characters: ,1,1,1/4,1;.
  ***   Warning: unused characters: ,2,0,2].

Timing:
real	0m0.059s
user	0m0.006s
sys	0m0.007s


'206.15.'
************** PARI *****************
Host 206.15.72.193 (206.15.72.193)
Time: Wed Jul 19 16:09:01 2006

Input: m = [ 0, 2, 0, 0, 0;  1,-1, 1, 1, 4;]
      

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? ? ? 
Goodbye!

Errors/timing (if any):

  ***   unexpected character: m=[0,2,0,0,0;1,-1,1,1,4;]
                                                      ^-

Timing:
real	0m0.012s
user	0m0.008s
sys	0m0.002s


'206.15.'
************** PARI *****************
Host 206.15.72.193 (206.15.72.193)
Time: Wed Jul 19 16:07:47 2006

Input: m = [ 0, 2, 0, 0, 0;
      1,-1, 1, 1, 4]
      

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? ? %1 = 1
? ? 
Goodbye!

Errors/timing (if any):

  ***   unexpected character: m=[0,2,0,0,0;
                                           ^
  ***   Warning: unused characters: ,-1,1,1,4].

Timing:
real	0m0.012s
user	0m0.009s
sys	0m0.003s


'201.34.'
************** PARI *****************
Host 201.34.91.89 (201.34.91.89)
Time: Wed Jul 19 13:08:24 2006

Input: b=1
c=2
a^2=b^2+c^2

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = 1
? %2 = 2
? ? 
Goodbye!

Errors/timing (if any):

  ***   unexpected character: a^2=b^2+c^2
                                 ^--------

Timing:
real	0m0.012s
user	0m0.007s
sys	0m0.004s


'72.30.1'
************** PARI *****************
Host 72.30.110.15 (72.30.110.15)
Time: Wed Jul 19 11:35:23 2006

Input: for(x=1,50,print1("d(",x,")=",numdiv(x),", "))

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? d(1)=1, d(2)=2, d(3)=2, d(4)=3, d(5)=2, d(6)=4, d(7)=2, d(8)=4, d(9)=3, d(10)=4, d(11)=2, d(12)=6, d(13)=2, d(14)=4, d(15)=4, d(16)=5, d(17)=2, d(18)=6, d(19)=2, d(20)=6, d(21)=4, d(22)=4, d(23)=2, d(24)=8, d(25)=3, d(26)=4, d(27)=4, d(28)=6, d(29)=2, d(30)=8, d(31)=2, d(32)=6, d(33)=4, d(34)=4, d(35)=4, d(36)=9, d(37)=2, d(38)=4, d(39)=4, d(40)=8, d(41)=2, d(42)=8, d(43)=2, d(44)=6, d(45)=6, d(46)=4, d(47)=2, d(48)=10, d(49)=3, d(50)=6, 
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.011s
user	0m0.006s
sys	0m0.006s


'212.128'
************** PARI *****************
Host 212.128.170.213 (212.128.170.213)
Time: Wed Jul 19 08:40:59 2006

Input: exp(1)

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = 2.7182818284590452353602874713526624978
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.028s
user	0m0.006s
sys	0m0.007s


'212.117'
************** PARI *****************
Host 212.117.127.210 (212.117.127.210)
Time: Wed Jul 19 06:58:48 2006

Input: for(x=1,50,print1("d(",x,")=",numdiv(x),", "))

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? d(1)=1, d(2)=2, d(3)=2, d(4)=3, d(5)=2, d(6)=4, d(7)=2, d(8)=4, d(9)=3, d(10)=4, d(11)=2, d(12)=6, d(13)=2, d(14)=4, d(15)=4, d(16)=5, d(17)=2, d(18)=6, d(19)=2, d(20)=6, d(21)=4, d(22)=4, d(23)=2, d(24)=8, d(25)=3, d(26)=4, d(27)=4, d(28)=6, d(29)=2, d(30)=8, d(31)=2, d(32)=6, d(33)=4, d(34)=4, d(35)=4, d(36)=9, d(37)=2, d(38)=4, d(39)=4, d(40)=8, d(41)=2, d(42)=8, d(43)=2, d(44)=6, d(45)=6, d(46)=4, d(47)=2, d(48)=10, d(49)=3, d(50)=6, 
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.035s
user	0m0.008s
sys	0m0.005s


'203.160'
************** PARI *****************
Host 203.160.1.47 (203.160.1.47)
Time: Wed Jul 19 06:58:31 2006

Input: "Replace this by some code, then click [SAGE] or [PARI]!"

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = "Replace this by some code, then click [SAGE] or [PARI]!"
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.011s
user	0m0.004s
sys	0m0.007s


'203.160'
************** PARI *****************
Host 203.160.1.47 (203.160.1.47)
Time: Wed Jul 19 06:58:25 2006

Input: "Replace this by some code, then click [SAGE] or [PARI]!"

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = "Replace this by some code, then click [SAGE] or [PARI]!"
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.011s
user	0m0.007s
sys	0m0.004s


'212.117'
************** PARI *****************
Host 212.117.127.210 (212.117.127.210)
Time: Wed Jul 19 06:53:16 2006

Input: 9*(3/2)


Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = 27/2
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.012s
user	0m0.008s
sys	0m0.005s


'68.142.'
************** PARI *****************
Host 68.142.250.91 (68.142.250.91)
Time: Wed Jul 19 04:20:15 2006

Input: for(b=1,100, for(a=1,b, if( frac((a^2+b^2+1)/(a*b))==0 , print(a,",",b), ) ) )

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? 1,1
1,2
2,5
5,13
13,34
34,89
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.029s
user	0m0.024s
sys	0m0.006s


'141.20.'
************** PARI *****************
Host 141.20.50.145 (141.20.50.145)
Time: Wed Jul 19 03:45:33 2006

Input: E = ellinit([0,0,0,5,10]);
E.disc
E.j

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? ? %2 = -51200
? %3 = 270
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.013s
user	0m0.007s
sys	0m0.005s


'141.20.'
************** PARI *****************
Host 141.20.50.145 (141.20.50.145)
Time: Wed Jul 19 03:40:02 2006

Input: E = ellinit([0,0,0,5,10]);
E.disc
E.b2
E.b4
E.b6

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? ? %2 = -51200
? %3 = 0
? %4 = 10
? %5 = 40
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.013s
user	0m0.009s
sys	0m0.003s


'141.20.'
************** PARI *****************
Host 141.20.50.145 (141.20.50.145)
Time: Wed Jul 19 03:30:17 2006

Input: E = ellinit([0,0,0,5,10]);
E.disc

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? ? %2 = -51200
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.029s
user	0m0.006s
sys	0m0.006s


'141.20.'
************** PARI *****************
Host 141.20.50.145 (141.20.50.145)
Time: Wed Jul 19 03:29:51 2006

Input: E = ellinit([0,0,0,5,10]);
E.delta

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? ? ? 
Goodbye!

Errors/timing (if any):

  ***   unknown member function: E.delta
                                   ^-----

Timing:
real	0m0.013s
user	0m0.006s
sys	0m0.006s


'141.20.'
************** PARI *****************
Host 141.20.50.145 (141.20.50.145)
Time: Wed Jul 19 03:20:59 2006

Input: E = ellinit([0,0,0,5,10]);
ellbil(E, [1,4], [1,4])
ellan(E,20)

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? ? %2 = 0.12837506294605086906217592378339269291
? %3 = [1, 0, -3, 0, 0, 0, 2, 0, 6, 0, -1, 0, -4, 0, 0, 0, -5, 0, -1, 0]
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.014s
user	0m0.008s
sys	0m0.005s


'141.20.'
************** PARI *****************
Host 141.20.50.145 (141.20.50.145)
Time: Wed Jul 19 03:16:04 2006

Input: E = ellinit([0,0,0,5,10]);
ellbil(E, [1,4], [1,4])

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? ? %2 = 0.12837506294605086906217592378339269291
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.013s
user	0m0.008s
sys	0m0.005s


'141.20.'
************** PARI *****************
Host 141.20.50.145 (141.20.50.145)
Time: Wed Jul 19 03:15:15 2006

Input: E = ellinit([0,0,0,5,10]);
ellbil(E, (1,4), (1,4))

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? ? ? 
Goodbye!

Errors/timing (if any):

  ***   expected character: ')' instead of: ellbil(E,(1,4),(1,4))
                                                       ^----------

Timing:
real	0m0.014s
user	0m0.010s
sys	0m0.004s


'141.20.'
************** PARI *****************
Host 141.20.50.145 (141.20.50.145)
Time: Wed Jul 19 03:14:13 2006

Input: E = ellinit([0,0,0,5,10]);
P = (1,4);
ellbil(E, P, P)

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? ? ? ? 
Goodbye!

Errors/timing (if any):

  ***   expected character: ')' instead of: P=(1,4);
                                                ^----
  *** ellbil: bad argument for an elliptic curve related function

Timing:
real	0m0.013s
user	0m0.007s
sys	0m0.006s


'141.20.'
************** PARI *****************
Host 141.20.50.145 (141.20.50.145)
Time: Wed Jul 19 03:12:19 2006

Input: E = ellinit([0,0,0,5,10]);
ellminimalmodel(E)

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? ? %2 = [0, 0, 0, 5, 10, 0, 10, 40, -25, -240, -8640, -51200, 270, [-1.4233183447530720839637549246282910396, 0.71165917237653604198187746231414551980 - 2.5533069405935058319433718225821719402*I, 0.71165917237653604198187746231414551980 + 2.5533069405935058319433718225821719402*I]~, 2.5292107620580267572591609417786962829, -1.2646053810290133786295804708893481415 + 0.90405376585134445817384638151563273959*I, -1.8391281983676645395951280657774160868 + 7.792038177385329417 E-39*I, 0.91956409918383226979756403288870804342 - 1.8995109064371664100222636546513616911*I, 2.2865425140703078042026374234384580468]
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.034s
user	0m0.007s
sys	0m0.005s


'141.20.'
************** PARI *****************
Host 141.20.50.145 (141.20.50.145)
Time: Wed Jul 19 03:10:58 2006

Input: E = ellinit([0,0,0,5,10]);
ellgenerators(E);

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? ? ? 
Goodbye!

Errors/timing (if any):

  ***   expected character: '=' instead of: ellgenerators(E);
                                                            ^-

Timing:
real	0m0.013s
user	0m0.008s
sys	0m0.005s


'141.20.'
************** PARI *****************
Host 141.20.50.145 (141.20.50.145)
Time: Wed Jul 19 03:10:47 2006

Input: E = ellinit([0,0,0,5,10]);
ellgenerators(E)

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? ? ? 
Goodbye!

Errors/timing (if any):

  ***   expected character: '=' instead of: ellgenerators(E)
                                                            ^

Timing:
real	0m0.012s
user	0m0.008s
sys	0m0.004s


'141.20.'
************** PARI *****************
Host 141.20.50.145 (141.20.50.145)
Time: Wed Jul 19 03:09:18 2006

Input: E = ellinit([0,0,0,5,10]);
ellan(E,20)
ellgenerators(E)

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? ? %2 = [1, 0, -3, 0, 0, 0, 2, 0, 6, 0, -1, 0, -4, 0, 0, 0, -5, 0, -1, 0]
? ? 
Goodbye!

Errors/timing (if any):

  ***   expected character: '=' instead of: ellgenerators(E)
                                                            ^

Timing:
real	0m0.017s
user	0m0.006s
sys	0m0.006s


'141.20.'
************** PARI *****************
Host 141.20.50.145 (141.20.50.145)
Time: Wed Jul 19 03:03:15 2006

Input: E = ellinit([0,0,0,5,10]);
ellan(E,20)

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? ? %2 = [1, 0, -3, 0, 0, 0, 2, 0, 6, 0, -1, 0, -4, 0, 0, 0, -5, 0, -1, 0]
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.013s
user	0m0.009s
sys	0m0.004s


'141.20.'
************** PARI *****************
Host 141.20.50.145 (141.20.50.145)
Time: Wed Jul 19 03:02:32 2006

Input: E = ellinit([0,0,0,5,10]);
ellak(E,1)

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? ? %2 = 1
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.012s
user	0m0.009s
sys	0m0.003s


'141.20.'
************** PARI *****************
Host 141.20.50.145 (141.20.50.145)
Time: Wed Jul 19 03:02:27 2006

Input: E = ellinit([0,0,0,5,10]);
ellak(E,1);

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? ? ? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.012s
user	0m0.007s
sys	0m0.005s


'141.20.'
************** PARI *****************
Host 141.20.50.145 (141.20.50.145)
Time: Wed Jul 19 03:00:48 2006

Input: E = ellinit([0,0,0,5,10]);
E.a4

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? ? %2 = 5
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.012s
user	0m0.007s
sys	0m0.006s


'141.20.'
************** PARI *****************
Host 141.20.50.145 (141.20.50.145)
Time: Wed Jul 19 03:00:29 2006

Input: E = ellinit([0,0,0,5,10]);
E.a4;

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? ? ? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.013s
user	0m0.005s
sys	0m0.008s


'141.20.'
************** PARI *****************
Host 141.20.50.145 (141.20.50.145)
Time: Wed Jul 19 02:59:58 2006

Input: E = ellinit([0,0,0,5,10]);

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? ? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.073s
user	0m0.009s
sys	0m0.006s


'141.20.'
************** PARI *****************
Host 141.20.50.145 (141.20.50.145)
Time: Wed Jul 19 02:59:46 2006

Input: E = ellinit([0,0,05,10]);

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? ? 
Goodbye!

Errors/timing (if any):

  *** ellinit: bad argument for an elliptic curve related function

Timing:
real	0m0.011s
user	0m0.008s
sys	0m0.003s


'141.20.'
************** PARI *****************
Host 141.20.50.145 (141.20.50.145)
Time: Wed Jul 19 02:59:24 2006

Input: E = ellinit([0,0,05,10]);
E.ellminimalmodel;

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? ? ? 
Goodbye!

Errors/timing (if any):

  *** ellinit: bad argument for an elliptic curve related function
  ***   unknown member function: E.ellminimalmodel;
                                   ^----------------

Timing:
real	0m0.046s
user	0m0.004s
sys	0m0.007s


'72.30.9'
************** PARI *****************
Host 72.30.98.145 (72.30.98.145)
Time: Wed Jul 19 02:54:28 2006

Input: for(n=1,20, print1(n,": ",valuation(n!,2),", ") )

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? 1: 0, 2: 1, 3: 1, 4: 3, 5: 3, 6: 4, 7: 4, 8: 7, 9: 7, 10: 8, 11: 8, 12: 10, 13: 10, 14: 11, 15: 11, 16: 15, 17: 15, 18: 16, 19: 16, 20: 18, 
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.044s
user	0m0.004s
sys	0m0.008s


'68.9.91'
************** PARI *****************
Host 68.9.91.53 (68.9.91.53)
Time: Tue Jul 18 18:48:07 2006

Input: "Replace this by some code, then click [SAGE] or [PARI]!"

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = "Replace this by some code, then click [SAGE] or [PARI]!"
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.011s
user	0m0.007s
sys	0m0.004s


'68.124.'
************** PARI *****************
Host 68.124.160.207 (68.124.160.207)
Time: Tue Jul 18 17:57:09 2006

Input: negative nine minus negative forty eight


Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = negativenineminusnegativefortyeight
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.011s
user	0m0.005s
sys	0m0.006s


'137.30.'
************** PARI *****************
Host 137.30.109.12 (137.30.109.12)
Time: Tue Jul 18 16:01:34 2006

Input: "Replace this by some code, then click [SAGE] or [PARI]!"

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = "Replace this by some code, then click [SAGE] or [PARI]!"
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.011s
user	0m0.006s
sys	0m0.006s


'68.142.'
************** PARI *****************
Host 68.142.249.32 (68.142.249.32)
Time: Tue Jul 18 14:56:35 2006

Input: factor(2^(2^5)+1)

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = 
[641 1]

[6700417 1]

? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.012s
user	0m0.005s
sys	0m0.006s


'67.51.1'
************** PARI *****************
Host 67.51.134.174 (67.51.134.174)
Time: Tue Jul 18 14:31:34 2006

Input: "Replace this by some code, then click [SAGE] or [PARI]!"

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = "Replace this by some code, then click [SAGE] or [PARI]!"
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.011s
user	0m0.007s
sys	0m0.004s


'68.142.'
************** PARI *****************
Host 68.142.249.166 (68.142.249.166)
Time: Tue Jul 18 14:12:40 2006

Input: for(n=1,7, print1(n,": ",sum(x=1,n,1/x),",  ") )

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? 1: 1,  2: 3/2,  3: 11/6,  4: 25/12,  5: 137/60,  6: 49/20,  7: 363/140,  
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.012s
user	0m0.006s
sys	0m0.006s


'68.142.'
************** PARI *****************
Host 68.142.249.35 (68.142.249.35)
Time: Tue Jul 18 14:06:47 2006

Input: collatzlength(x0)=
{
   local(x,i);
   x=x0;  i=0;   
   while(x-1,
      x=if(Mod(x,2)==Mod(0,2), x/2, (3*x+1)/2);i=i++ );
   i
}
collatzlength(299)

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? ? %1 = 75
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.036s
user	0m0.005s
sys	0m0.007s


'155.229'
************** PARI *****************
Host 155.229.77.1 (155.229.77.1)
Time: Tue Jul 18 13:55:44 2006

Input: x+5
____
x+2

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = x + 5
? ? %2 = x + 2
? 
Goodbye!

Errors/timing (if any):

  ***   unexpected character: ____
                              ^----

Timing:
real	0m0.031s
user	0m0.007s
sys	0m0.006s


'68.189.'
************** PARI *****************
Host 68.189.248.100 (68.189.248.100)
Time: Tue Jul 18 12:36:02 2006

Input: leg8

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = leg8
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.011s
user	0m0.008s
sys	0m0.003s


'68.189.'
************** PARI *****************
Host 68.189.248.100 (68.189.248.100)
Time: Tue Jul 18 12:34:35 2006

Input: leg8

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = leg8
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.011s
user	0m0.008s
sys	0m0.003s


'68.189.'
************** PARI *****************
Host 68.189.248.100 (68.189.248.100)
Time: Tue Jul 18 12:33:19 2006

Input: "Replace this by some code, then click [SAGE] or [PARI]!"

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = "Replace this by some code, then click [SAGE] or [PARI]!"
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.012s
user	0m0.006s
sys	0m0.005s


'68.189.'
************** PARI *****************
Host 68.189.248.100 (68.189.248.100)
Time: Tue Jul 18 12:33:16 2006

Input: "Replace this by some code, then click [SAGE] or [PARI]!"

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = "Replace this by some code, then click [SAGE] or [PARI]!"
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.011s
user	0m0.006s
sys	0m0.005s


'68.142.'
************** PARI *****************
Host 68.142.249.88 (68.142.249.88)
Time: Tue Jul 18 11:39:33 2006

Input: factor(x^6-1)

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = 
[x - 1 1]

[x + 1 1]

[x^2 - x + 1 1]

[x^2 + x + 1 1]

? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.143s
user	0m0.005s
sys	0m0.008s


'72.30.2'
************** PARI *****************
Host 72.30.226.223 (72.30.226.223)
Time: Tue Jul 18 11:13:29 2006

Input: for(n=1,7, print1(n,": ",sum(x=1,n,1/x),",  ") )

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? 1: 1,  2: 3/2,  3: 11/6,  4: 25/12,  5: 137/60,  6: 49/20,  7: 363/140,  
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.066s
user	0m0.006s
sys	0m0.006s


'65.106.'
************** PARI *****************
Host 65.106.182.67 (65.106.182.67)
Time: Tue Jul 18 09:37:10 2006

Input: 3+4


Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = 7
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.011s
user	0m0.005s
sys	0m0.006s


'65.106.'
************** PARI *****************
Host 65.106.182.67 (65.106.182.67)
Time: Tue Jul 18 09:37:00 2006

Input: 3+4


Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = 7
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.011s
user	0m0.008s
sys	0m0.003s


'72.30.1'
************** PARI *****************
Host 72.30.129.123 (72.30.129.123)
Time: Tue Jul 18 03:36:50 2006

Input: collatzlength(x0)=
{
   local(x,i);
   x=x0;  i=0;   
   while(x-1,
      x=if(Mod(x,2)==Mod(0,2), x/2, (3*x+1)/2);i=i++ );
   i
}
collatzlength(299)

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? ? %1 = 75
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.021s
user	0m0.008s
sys	0m0.003s


'68.142.'
************** PARI *****************
Host 68.142.251.86 (68.142.251.86)
Time: Tue Jul 18 02:58:38 2006

Input: collatz(x0,n)=
{
   local(x,i,ans);
   x=x0;
   ans=[x];
   for(i=1,n,
      x=if(Mod(x,2)==Mod(0,2), x/2, (3*x+1)/2);
      ans =concat(ans,x) );
   ans
}
collatz(19,16)

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? ? %1 = [19, 29, 44, 22, 11, 17, 26, 13, 20, 10, 5, 8, 4, 2, 1, 2, 1]
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.051s
user	0m0.008s
sys	0m0.005s


'71.132.'
************** PARI *****************
Host 71.132.130.250 (71.132.130.250)
Time: Tue Jul 18 01:03:57 2006

Input: print gap('SymmetricGroup(5)')


Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? ? 
Goodbye!

Errors/timing (if any):

  ***   expected character: ',' instead of: printgap('SymmetricGroup(5)')
                                                                    ^-----

Timing:
real	0m0.011s
user	0m0.007s
sys	0m0.005s


'71.132.'
************** PARI *****************
Host 71.132.130.250 (71.132.130.250)
Time: Tue Jul 18 01:03:37 2006

Input: print gap('SymmetricGroup(7)')


Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? ? 
Goodbye!

Errors/timing (if any):

  ***   expected character: ',' instead of: printgap('SymmetricGroup(7)')
                                                                    ^-----

Timing:
real	0m0.012s
user	0m0.006s
sys	0m0.006s


'72.30.1'
************** PARI *****************
Host 72.30.107.8 (72.30.107.8)
Time: Tue Jul 18 00:10:53 2006

Input: for(b=1,100, for(a=1,b, if( frac((a^2+b^2)/(a*b))==0 , print(a,",",b), ) ) )

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? 1,1
2,2
3,3
4,4
5,5
6,6
7,7
8,8
9,9
10,10
11,11
12,12
13,13
14,14
15,15
16,16
17,17
18,18
19,19
20,20
21,21
22,22
23,23
24,24
25,25
26,26
27,27
28,28
29,29
30,30
31,31
32,32
33,33
34,34
35,35
36,36
37,37
38,38
39,39
40,40
41,41
42,42
43,43
44,44
45,45
46,46
47,47
48,48
49,49
50,50
51,51
52,52
53,53
54,54
55,55
56,56
57,57
58,58
59,59
60,60
61,61
62,62
63,63
64,64
65,65
66,66
67,67
68,68
69,69
70,70
71,71
72,72
73,73
74,74
75,75
76,76
77,77
78,78
79,79
80,80
81,81
82,82
83,83
84,84
85,85
86,86
87,87
88,88
89,89
90,90
91,91
92,92
93,93
94,94
95,95
96,96
97,97
98,98
99,99
100,100
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.030s
user	0m0.024s
sys	0m0.006s


'68.142.'
************** PARI *****************
Host 68.142.250.147 (68.142.250.147)
Time: Mon Jul 17 23:25:54 2006

Input: for(n=1,20, print1(n,": ",valuation(n!,2),", ") )

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? 1: 0, 2: 1, 3: 1, 4: 3, 5: 3, 6: 4, 7: 4, 8: 7, 9: 7, 10: 8, 11: 8, 12: 10, 13: 10, 14: 11, 15: 11, 16: 15, 17: 15, 18: 16, 19: 16, 20: 18, 
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.012s
user	0m0.008s
sys	0m0.005s


'71.131.'
************** PARI *****************
Host 71.131.60.92 (71.131.60.92)
Time: Mon Jul 17 21:49:37 2006

Input: 436/3


Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = 436/3
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.011s
user	0m0.007s
sys	0m0.005s


'152.163'
************** PARI *****************
Host 152.163.100.68 (152.163.100.68)
Time: Mon Jul 17 19:05:54 2006

Input: y=x+3
3x+y=11 

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = x + 3
? %2 = x + 11
? 
Goodbye!

Errors/timing (if any):

  ***   Warning: unused characters: x+y=11.

Timing:
real	0m0.011s
user	0m0.007s
sys	0m0.004s


'152.163'
************** PARI *****************
Host 152.163.100.68 (152.163.100.68)
Time: Mon Jul 17 19:05:38 2006

Input: y=x+3
3x+y=11 solve for x and y

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = x + 3
? %2 = solveforxandy
? 
Goodbye!

Errors/timing (if any):

  ***   Warning: unused characters: x+y=11solveforxandy.

Timing:
real	0m0.021s
user	0m0.003s
sys	0m0.008s


'68.142.'
************** PARI *****************
Host 68.142.249.160 (68.142.249.160)
Time: Mon Jul 17 18:14:39 2006

Input: y=210; for(x=1,8,y=sumdiv(y,x,x)-y;print1(y,","))

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? 366,378,582,594,846,1026,1374,1386,
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.011s
user	0m0.005s
sys	0m0.006s


'68.142.'
************** PARI *****************
Host 68.142.251.155 (68.142.251.155)
Time: Mon Jul 17 17:55:23 2006

Input: {ss(n)=sum(x=1,n,n/gcd(n,x))}
ss(60)

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? ? %1 = 1617
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.011s
user	0m0.007s
sys	0m0.004s


'68.142.'
************** PARI *****************
Host 68.142.249.100 (68.142.249.100)
Time: Mon Jul 17 17:09:06 2006

Input: for(b=1,100, for(a=1,b, if( frac((a^2+b^2)/(a*b))==0 , print(a,",",b), ) ) )

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? 1,1
2,2
3,3
4,4
5,5
6,6
7,7
8,8
9,9
10,10
11,11
12,12
13,13
14,14
15,15
16,16
17,17
18,18
19,19
20,20
21,21
22,22
23,23
24,24
25,25
26,26
27,27
28,28
29,29
30,30
31,31
32,32
33,33
34,34
35,35
36,36
37,37
38,38
39,39
40,40
41,41
42,42
43,43
44,44
45,45
46,46
47,47
48,48
49,49
50,50
51,51
52,52
53,53
54,54
55,55
56,56
57,57
58,58
59,59
60,60
61,61
62,62
63,63
64,64
65,65
66,66
67,67
68,68
69,69
70,70
71,71
72,72
73,73
74,74
75,75
76,76
77,77
78,78
79,79
80,80
81,81
82,82
83,83
84,84
85,85
86,86
87,87
88,88
89,89
90,90
91,91
92,92
93,93
94,94
95,95
96,96
97,97
98,98
99,99
100,100
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.031s
user	0m0.025s
sys	0m0.007s


'72.30.1'
************** PARI *****************
Host 72.30.131.199 (72.30.131.199)
Time: Mon Jul 17 14:46:11 2006

Input: {ss(n)=sum(x=1,n,n/gcd(n,x))}
ss(60)

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? ? %1 = 1617
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.014s
user	0m0.008s
sys	0m0.005s


'195.93.'
************** PARI *****************
Host 195.93.21.40 (195.93.21.40)
Time: Mon Jul 17 14:20:24 2006

Input: 8! + (112 + 1)2 + 53 + 72

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = 127
? 
Goodbye!

Errors/timing (if any):

  ***   Warning: unused characters: 2+53+72.

Timing:
real	0m0.011s
user	0m0.005s
sys	0m0.006s


'68.142.'
************** PARI *****************
Host 68.142.251.91 (68.142.251.91)
Time: Mon Jul 17 14:19:50 2006

Input: for(x=1,50,print1("d(",x,")=",numdiv(x),", "))

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? d(1)=1, d(2)=2, d(3)=2, d(4)=3, d(5)=2, d(6)=4, d(7)=2, d(8)=4, d(9)=3, d(10)=4, d(11)=2, d(12)=6, d(13)=2, d(14)=4, d(15)=4, d(16)=5, d(17)=2, d(18)=6, d(19)=2, d(20)=6, d(21)=4, d(22)=4, d(23)=2, d(24)=8, d(25)=3, d(26)=4, d(27)=4, d(28)=6, d(29)=2, d(30)=8, d(31)=2, d(32)=6, d(33)=4, d(34)=4, d(35)=4, d(36)=9, d(37)=2, d(38)=4, d(39)=4, d(40)=8, d(41)=2, d(42)=8, d(43)=2, d(44)=6, d(45)=6, d(46)=4, d(47)=2, d(48)=10, d(49)=3, d(50)=6, 
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.023s
user	0m0.006s
sys	0m0.011s


'72.30.1'
************** PARI *****************
Host 72.30.129.106 (72.30.129.106)
Time: Mon Jul 17 13:35:45 2006

Input: y=210; for(x=1,8,y=sumdiv(y,x,x)-y;print1(y,","))

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? 366,378,582,594,846,1026,1374,1386,
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.012s
user	0m0.006s
sys	0m0.006s


'129.6.5'
************** PARI *****************
Host 129.6.54.202 (129.6.54.202)
Time: Mon Jul 17 13:30:35 2006

Input: factor(3446457653424234237543333333333333745645645646346456456456534535345)

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? 
Errors/timing (if any):

/var/www/cgi-bin/calc/gp: line 1:  1801 Killed                  ./gp-2.2.11 -s 256000000 -emacs

Timing:
real	0m21.041s
user	0m20.966s
sys	0m0.032s


'129.6.5'
************** PARI *****************
Host 129.6.54.202 (129.6.54.202)
Time: Mon Jul 17 13:30:10 2006

Input: factor(344645765342423423754745645645646346456456456534535345)

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = 
[5 1]

[101 1]

[666637 1]

[86385313930118357381 1]

[11850924690911985200827577 1]

? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m1.207s
user	0m1.169s
sys	0m0.036s


'129.6.5'
************** PARI *****************
Host 129.6.54.202 (129.6.54.202)
Time: Mon Jul 17 13:30:06 2006

Input: factor(344645765754745645645646346456456456534535345)

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = 
[5 1]

[5313541 1]

[16746739 1]

[774619909288243940476642329731 1]

? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.047s
user	0m0.009s
sys	0m0.008s


'129.6.5'
************** PARI *****************
Host 129.6.54.202 (129.6.54.202)
Time: Mon Jul 17 13:30:03 2006

Input: factor(34464576575476346456456456534535345)

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = 
[3 1]

[5 1]

[11 2]

[331 1]

[599 1]

[10155599789 1]

[9430526152364143 1]

? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.027s
user	0m0.016s
sys	0m0.012s


'129.6.5'
************** PARI *****************
Host 129.6.54.202 (129.6.54.202)
Time: Mon Jul 17 13:29:59 2006

Input: factor(344645765754763534535345)

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = 
[5 1]

[839 1]

[2111 1]

[38918200284085861 1]

? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.012s
user	0m0.007s
sys	0m0.006s


'129.6.5'
************** PARI *****************
Host 129.6.54.202 (129.6.54.202)
Time: Mon Jul 17 13:29:53 2006

Input: factor(15)

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = 
[3 1]

[5 1]

? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.012s
user	0m0.004s
sys	0m0.007s


'129.6.5'
************** PARI *****************
Host 129.6.54.202 (129.6.54.202)
Time: Mon Jul 17 13:29:46 2006

Input: factor(9)

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = 
[3 2]

? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.011s
user	0m0.006s
sys	0m0.005s


'129.6.5'
************** PARI *****************
Host 129.6.54.202 (129.6.54.202)
Time: Mon Jul 17 13:29:33 2006

Input: 1000!

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = 402387260077093773543702433923003985719374864210714632543799910429938512398629020592044208486969404800479988610197196058631666872994808558901323829669944590997424504087073759918823627727188732519779505950995276120874975462497043601418278094646496291056393887437886487337119181045825783647849977012476632889835955735432513185323958463075557409114262417474349347553428646576611667797396668820291207379143853719588249808126867838374559731746136085379534524221586593201928090878297308431392844403281231558611036976801357304216168747609675871348312025478589320767169132448426236131412508780208000261683151027341827977704784635868170164365024153691398281264810213092761244896359928705114964975419909342221566832572080821333186116811553615836546984046708975602900950537616475847728421889679646244945160765353408198901385442487984959953319101723355556602139450399736280750137837615307127761926849034352625200015888535147331611702103968175921510907788019393178114194545257223865541461062892187960223838971476088506276862967146674697562911234082439208160153780889893964518263243671616762179168909779911903754031274622289988005195444414282012187361745992642956581746628302955570299024324153181617210465832036786906117260158783520751516284225540265170483304226143974286933061690897968482590125458327168226458066526769958652682272807075781391858178889652208164348344825993266043367660176999612831860788386150279465955131156552036093988180612138558600301435694527224206344631797460594682573103790084024432438465657245014402821885252470935190620929023136493273497565513958720559654228749774011413346962715422845862377387538230483865688976461927383814900140767310446640259899490222221765904339901886018566526485061799702356193897017860040811889729918311021171229845901641921068884387121855646124960798722908519296819372388642614839657382291123125024186649353143970137428531926649875337218940694281434118520158014123344828015051399694290153483077644569099073152433278288269864602789864321139083506217095002597389863554277196742822248757586765752344220207573630569498825087968928162753848863396909959826280956121450994871701244516461260379029309120889086942028510640182154399457156805941872748998094254742173582401063677404595741785160829230135358081840096996372524230560855903700624271243416909004153690105933983835777939410970027753472000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.012s
user	0m0.007s
sys	0m0.004s


'129.6.5'
************** PARI *****************
Host 129.6.54.202 (129.6.54.202)
Time: Mon Jul 17 13:29:29 2006

Input: 100!

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = 93326215443944152681699238856266700490715968264381621468592963895217599993229915608941463976156518286253697920827223758251185210916864000000000000000000000000
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.011s
user	0m0.006s
sys	0m0.005s


'129.6.5'
************** PARI *****************
Host 129.6.54.202 (129.6.54.202)
Time: Mon Jul 17 13:29:21 2006

Input: 5^70

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = 8470329472543003390683225006796419620513916015625
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.012s
user	0m0.006s
sys	0m0.006s


'129.6.5'
************** PARI *****************
Host 129.6.54.202 (129.6.54.202)
Time: Mon Jul 17 13:29:05 2006

Input: 5^7

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = 78125
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.012s
user	0m0.007s
sys	0m0.005s


'129.6.5'
************** PARI *****************
Host 129.6.54.202 (129.6.54.202)
Time: Mon Jul 17 13:29:00 2006

Input: 5**5

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? ? 
Goodbye!

Errors/timing (if any):

  ***   unexpected character: 5**5
                                ^--

Timing:
real	0m0.011s
user	0m0.007s
sys	0m0.004s


'67.11.2'
************** PARI *****************
Host 67.11.212.178 (67.11.212.178)
Time: Mon Jul 17 13:10:41 2006

Input: 24.50 - 7.30



Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = 17.200000000000000000000000000000000000
? ? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.054s
user	0m0.007s
sys	0m0.004s


'68.142.'
************** PARI *****************
Host 68.142.249.131 (68.142.249.131)
Time: Mon Jul 17 12:25:15 2006

Input: vector(20,x,floor((x+1)*sqrt(2))-floor(x*sqrt(2)))

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = [1, 2, 1, 2, 1, 1, 2, 1, 2, 1, 1, 2, 1, 2, 1, 2, 1, 1, 2, 1]
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.162s
user	0m0.004s
sys	0m0.007s


'59.144.'
************** PARI *****************
Host 59.144.61.43 (59.144.61.43)
Time: Mon Jul 17 11:10:45 2006

Input: for(x=1,50,print1("d(",x,")=",numdiv(x),", "))

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? d(1)=1, d(2)=2, d(3)=2, d(4)=3, d(5)=2, d(6)=4, d(7)=2, d(8)=4, d(9)=3, d(10)=4, d(11)=2, d(12)=6, d(13)=2, d(14)=4, d(15)=4, d(16)=5, d(17)=2, d(18)=6, d(19)=2, d(20)=6, d(21)=4, d(22)=4, d(23)=2, d(24)=8, d(25)=3, d(26)=4, d(27)=4, d(28)=6, d(29)=2, d(30)=8, d(31)=2, d(32)=6, d(33)=4, d(34)=4, d(35)=4, d(36)=9, d(37)=2, d(38)=4, d(39)=4, d(40)=8, d(41)=2, d(42)=8, d(43)=2, d(44)=6, d(45)=6, d(46)=4, d(47)=2, d(48)=10, d(49)=3, d(50)=6, 
? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m0.012s
user	0m0.005s
sys	0m0.006s


'66.117.'
************** PARI *****************
Host 66.117.135.200 (66.117.135.200)
Time: Mon Jul 17 10:19:23 2006

Input: factor(2^257-1)

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? 
Errors/timing (if any):

/var/www/cgi-bin/calc/gp: line 1:   447 Killed                  ./gp-2.2.11 -s 256000000 -emacs

Timing:
real	0m21.002s
user	0m20.984s
sys	0m0.015s


'66.117.'
************** PARI *****************
Host 66.117.135.200 (66.117.135.200)
Time: Mon Jul 17 10:16:24 2006

Input: factor(2^256-1)

Output:          GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327)
parisize = 256000000, primelimit = 500000
? %1 = 
[3 1]

[5 1]

[17 1]

[257 1]

[641 1]

[65537 1]

[274177 1]

[6700417 1]

[67280421310721 1]

[59649589127497217 1]

[5704689200685129054721 1]

? 
Goodbye!

Errors/timing (if any):


Timing:
real	0m4.543s
user	0m4.488s
sys	0m0.054s


'66.117.'
************** PARI *****************
Host 66.117.135.200 (66.117.135.200)
Time: Mon Jul 17 10:15:58 2006

Input: