PARI/GP Bug report logs - #1239
./Configure issue with GMP ABI selection on HPux 11iv3(B.11.31) ia64

Package: pari; Maintainer for pari is Aurel Page <aurel.page@normalesup.org>; Source for pari is src:pari.

Reported by: Bill.Glessner@cwu.EDU

Date: Wed, 7 Sep 2011 20:18:02 UTC

Severity: normal

Done: Bill Allombert <Bill.Allombert@math.u-bordeaux1.fr>

Bug is archived. No further changes may be made.

Full log

Message #35 received at 1239@pari.math.u-bordeaux.fr (full text, mbox, reply):

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Date: Thu, 22 Sep 2011 08:18:16 -0700 (PDT)
From: Bill.Glessner@cwu.EDU
Subject: Re: Bug#1239: ./Configure issue with GMP ABI selection on HPux
 11iv3(B.11.31) ia64
To: 1239@pari.math.u-bordeaux.fr
Message-id: <01O6CI4H5KLE8WW2FJ@cluster.cwu.edu>
MIME-version: 1.0
Content-type: text/plain; CHARSET=us-ascii

Package: pari
Version: 2.5.0

>Return-path: <Bill.Allombert@math.u-bordeaux1.fr>
>Date: Thu, 22 Sep 2011 16:40:00 +0200
>From: Bill Allombert <Bill.Allombert@math.u-bordeaux1.fr>
>Subject: Re: Bug#1239: ./Configure issue with GMP ABI selection on HPux
> 11iv3(B.11.31) ia64o
>To: Bill.Glessner@cwu.edu, 1239@pari.math.u-bordeaux.fr
>
>On Thu, Sep 22, 2011 at 07:20:50AM -0700, Bill.Glessner@cwu.EDU wrote:
>> 
 Hi Bill,

>> ...
>> Making dobench in Ohpux-ia64
>> 
>> gmake[1]: Entering directory `/DreamLand/JunqueYard_gccN/pari-2.5.0/Ohpux-ia64'
>> * Testing objets        for gp-dyn..BUG [0]
>> * Testing analyz        for gp-dyn..BUG [0]
>> * Testing number        for gp-dyn..BUG [0]
>> * Testing polyser       for gp-dyn..BUG [0]
>> * Testing linear        for gp-dyn..BUG [0]
>> * Testing elliptic      for gp-dyn..BUG [0]
>> * Testing sumiter       for gp-dyn..BUG [0]
>> * Testing graph         for gp-dyn..BUG [0]
>> * Testing program       for gp-dyn..BUG [0]
>> * Testing trans         for gp-dyn..BUG [0]
>> * Testing nfields       for gp-dyn..BUG [0]
>> +++ [BUG] Total bench for gp-dyn is 0
>> 
>> PROBLEMS WERE NOTED. The following files list them in diff format:
>> Directory: /DreamLand/JunqueYard_gccN/pari-2.5.0/Ohpux-ia64
>>         objets-dyn.dif
>>         analyz-dyn.dif
>>         number-dyn.dif
>>         polyser-dyn.dif
>>         linear-dyn.dif
>>         elliptic-dyn.dif
>>         sumiter-dyn.dif
>>         graph-dyn.dif
>>         program-dyn.dif
>>         trans-dyn.dif
>>         nfields-dyn.dif
>> gmake[1]: *** [dobench] Error 1
>> gmake[1]: Leaving directory `/DreamLand/JunqueYard_gccN/pari-2.5.0/Ohpux-ia64'
>> gmake: *** [dobench] Error 2
>> 
>>...
>> None of the others show anything other than commands followed by results
>> with no error or exception indications. I can send you any or all of the 
>> actual .dif files, if that will help.
>
>Yes please. The error above is intentional (we check the error is reported properly).
>

The individual .dif files are appended with the names of the .dif file
enclosed in < >.

<objets-dyn.dif>:
*** ../src/test/64/objets	Mon May 30 02:28:26 2011
--- gp.out	Wed Sep 21 13:20:17 2011
***************
*** 1,126 ****
-    echo = 1 (on)
- ? gettime;+3
- 3
- ? -5
- -5
- ? 5+3
- 8
- ? 5-3
- 2
- ? 5/3
- 5/3
- ? 5\3
- 1
- ? 5\/3
- 2
- ? 5%3
- 2
- ? 5^3
- 125
- ? binary(65537)
- [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1]
- ? bittest(10^100,100)
- 1
- ? ceil(-2.5)
- -2
- ? centerlift(Mod(456,555))
- -99
- ? component(1+O(7^4),3)
- 1
- ? conj(1+I)
- 1 - I
- ? conjvec(Mod(x^2+x+1,x^3-x-1))
- [4.0795956234914387860104177508366260326, 0.46020218825428060699479112458168
- 698368 + 0.18258225455744299269398828369501930574*I, 0.460202188254280606994
- 79112458168698368 - 0.18258225455744299269398828369501930574*I]~
- ? truncate(1.7,&e)
- 1
- ? e
- -1
- ? denominator(12345/54321)
- 18107
- ? divrem(345,123)
- [2, 99]~
- ? divrem(x^7-1,x^5+1)
- [x^2, -x^2 - 1]~
- ? floor(-1/2)
- -1
- ? floor(-2.5)
- -3
- ? frac(-2.7)
- 0.30000000000000000000000000000000000000
- ? I^2
- -1
- ? imag(2+3*I)
- 3
- ? lex([1,3],[1,3,5])
- -1
- ? max(2,3)
- 3
- ? min(2,3)
- 2
- ? Mod(-12,7)
- Mod(2, 7)
- ? norm(1+I)
- 2
- ? norm(Mod(x+5,x^3+x+1))
- 129
- ? numerator((x+1)/(x-1))
- x + 1
- ? 1/(1+x)+O(x^20)
- 1 - x + x^2 - x^3 + x^4 - x^5 + x^6 - x^7 + x^8 - x^9 + x^10 - x^11 + x^12 -
-  x^13 + x^14 - x^15 + x^16 - x^17 + x^18 - x^19 + O(x^20)
- ? numtoperm(7,1035)
- [4, 7, 1, 6, 3, 5, 2]
- ? permtonum([4,7,1,6,3,5,2])
- 1035
- ? 37.
- 37.000000000000000000000000000000000000
- ? real(5-7*I)
- 5
- ? shift(1,50)
- 1125899906842624
- ? shift([3,4,-11,-12],-2)
- [0, 1, -2, -3]
- ? shiftmul([3,4,-11,-12],-2)
- [3/4, 1, -11/4, -3]
- ? sign(-1)
- -1
- ? sign(0)
- 0
- ? sign(0.)
- 0
- ? simplify(((x+I+1)^2-x^2-2*x*(I+1))^2)
- -4
- ? sizedigit([1.3*10^5,2*I*Pi*exp(4*Pi)])
- 7
- ? truncate(-2.7)
- -2
- ? truncate(sin(x^2))
- -1/5040*x^14 + 1/120*x^10 - 1/6*x^6 + x^2
- ? type(Mod(x,x^2+1))
- "t_POLMOD"
- ? valuation(6^10000-1,5)
- 5
- ? \p57
-    realprecision = 57 significant digits
- ? Pi
- 3.14159265358979323846264338327950288419716939937510582098
- ? \p38
-    realprecision = 38 significant digits
- ? O(x^12)
- O(x^12)
- ? padicno=(5/3)*127+O(127^5)
- 44*127 + 42*127^2 + 42*127^3 + 42*127^4 + O(127^5)
- ? padicprec(padicno,127)
- 5
- ? length(divisors(1000))
- 16
- ? Mod(10873,49649)^-1
-   ***   at top-level: Mod(10873,49649)^-1
-   ***                                 ^---
-   *** _^_: impossible inverse modulo: Mod(131, 49649).
- ? getheap
- [59, 784]
- ? print("Total time spent: ",gettime);
- Total time spent: 0
--- 0 ----

<analyz-dyn.dif>:
*** ../src/test/64/analyz	Mon May 30 02:28:26 2011
--- gp.out	Wed Sep 21 13:20:18 2011
***************
*** 1,9 ****
-    echo = 1 (on)
- ? gettime;sum(x=0,50000,x);
- ? sum(x=1,1000,log(x));
- ? sum(x=1,25,sum(y=1,100,x/y),0.0);
- ? sum(x=1,100,sum(y=1,100,x/y,0.0));
- ? getheap
- [6, 50]
- ? print("Total time spent: ",gettime);
- Total time spent: 16
--- 0 ----

<number-dyn.dif>:
*** ../src/test/64/number	Mon May 30 02:28:26 2011
--- gp.out	Wed Sep 21 13:20:18 2011
***************
*** 1,273 ****
-    echo = 1 (on)
- ? gettime;addprimes([nextprime(10^9),nextprime(10^10)])
- [1000000007, 10000000019]
- ? bestappr(Pi,10000)
- 355/113
- ? bezout(123456789,987654321)
- [-8, 1, 9]
- ? bigomega(12345678987654321)
- 8
- ? binomial(1.1,5)
- -0.0045457500000000000000000000000000000001
- ? chinese(Mod(7,15),Mod(13,21))
- Mod(97, 105)
- ? content([123,456,789,234])
- 3
- ? contfrac(Pi)
- [3, 7, 15, 1, 292, 1, 1, 1, 2, 1, 3, 1, 14, 2, 1, 1, 2, 2, 2, 2, 1, 84, 2, 1
- , 1, 15, 3, 13, 1, 4, 2, 6, 6]
- ? contfrac(Pi,5)
- [3, 7, 15, 1, 292]
- ? contfrac((exp(1)-1)/(exp(1)+1),[1,3,5,7,9])
- [0, 6, 10, 42, 30]
- ? contfracpnqn([2,6,10,14,18,22,26])
- 
- [19318376 741721]
- 
- [8927353 342762]
- 
- ? contfracpnqn([1,1,1,1,1,1,1,1;1,1,1,1,1,1,1,1])
- 
- [34 21]
- 
- [21 13]
- 
- ? core(54713282649239)
- 5471
- ? core(54713282649239,1)
- [5471, 100003]
- ? coredisc(54713282649239)
- 21884
- ? coredisc(54713282649239,1)
- [21884, 100003/2]
- ? divisors(8!)
- [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 14, 15, 16, 18, 20, 21, 24, 28, 30, 32, 
- 35, 36, 40, 42, 45, 48, 56, 60, 63, 64, 70, 72, 80, 84, 90, 96, 105, 112, 12
- 0, 126, 128, 140, 144, 160, 168, 180, 192, 210, 224, 240, 252, 280, 288, 315
- , 320, 336, 360, 384, 420, 448, 480, 504, 560, 576, 630, 640, 672, 720, 840,
-  896, 960, 1008, 1120, 1152, 1260, 1344, 1440, 1680, 1920, 2016, 2240, 2520,
-  2688, 2880, 3360, 4032, 4480, 5040, 5760, 6720, 8064, 10080, 13440, 20160, 
- 40320]
- ? eulerphi(257^2)
- 65792
- ? factor(17!+1)
- 
- [661 1]
- 
- [537913 1]
- 
- [1000357 1]
- 
- ? factor(100!+1,0)
- 
- [101 1]
- 
- [14303 1]
- 
- [149239 1]
- 
- [432885273849892962613071800918658949059679308685024481795740765527568493010
- 727023757461397498800981521440877813288657839195622497225621499427628453 1]
- 
- ? factor(40!+1,100000)
- 
- [41 1]
- 
- [59 1]
- 
- [277 1]
- 
- [1217669507565553887239873369513188900554127 1]
- 
- ? factorback(factor(12354545545))
- 12354545545
- ? factor(230873846780665851254064061325864374115500032^6)
- 
- [2 120]
- 
- [3 6]
- 
- [7 6]
- 
- [23 6]
- 
- [29 6]
- 
- [500501 36]
- 
- ? factorcantor(x^11+1,7)
- 
- [Mod(1, 7)*x + Mod(1, 7) 1]
- 
- [Mod(1, 7)*x^10 + Mod(6, 7)*x^9 + Mod(1, 7)*x^8 + Mod(6, 7)*x^7 + Mod(1, 7)*
- x^6 + Mod(6, 7)*x^5 + Mod(1, 7)*x^4 + Mod(6, 7)*x^3 + Mod(1, 7)*x^2 + Mod(6,
-  7)*x + Mod(1, 7) 1]
- 
- ? centerlift(lift(factorff(x^3+x^2+x-1,3,t^3+t^2+t-1)))
- 
- [x - t 1]
- 
- [x + (t^2 + t - 1) 1]
- 
- [x + (-t^2 - 1) 1]
- 
- ? 10!
- 3628800
- ? factorial(10)
- 3628800.0000000000000000000000000000000
- ? factormod(x^11+1,7)
- 
- [Mod(1, 7)*x + Mod(1, 7) 1]
- 
- [Mod(1, 7)*x^10 + Mod(6, 7)*x^9 + Mod(1, 7)*x^8 + Mod(6, 7)*x^7 + Mod(1, 7)*
- x^6 + Mod(6, 7)*x^5 + Mod(1, 7)*x^4 + Mod(6, 7)*x^3 + Mod(1, 7)*x^2 + Mod(6,
-  7)*x + Mod(1, 7) 1]
- 
- ? factormod(x^11+1,7,1)
- 
- [1 1]
- 
- [10 1]
- 
- ? setrand(1);ffinit(2,11)
- Mod(1, 2)*x^11 + Mod(1, 2)*x^10 + Mod(1, 2)*x^8 + Mod(1, 2)*x^4 + Mod(1, 2)*
- x^3 + Mod(1, 2)*x^2 + Mod(1, 2)
- ? setrand(1);ffinit(7,4)
- Mod(1, 7)*x^4 + Mod(1, 7)*x^3 + Mod(1, 7)*x^2 + Mod(1, 7)*x + Mod(1, 7)
- ? fibonacci(100)
- 354224848179261915075
- ? gcd(12345678,87654321)
- 9
- ? gcd(x^10-1,x^15-1)
- x^5 - 1
- ? hilbert(2/3,3/4,5)
- 1
- ? hilbert(Mod(5,7),Mod(6,7))
- 1
- ? isfundamental(12345)
- 1
- ? isprime(12345678901234567)
- 0
- ? ispseudoprime(73!+1)
- 1
- ? issquare(12345678987654321)
- 1
- ? issquarefree(123456789876543219)
- 0
- ? kronecker(5,7)
- -1
- ? kronecker(3,18)
- 0
- ? lcm(15,-21)
- 105
- ? lift(chinese(Mod(7,15),Mod(4,21)))
- 67
- ? modreverse(Mod(x^2+1,x^3-x-1))
- Mod(x^2 - 3*x + 2, x^3 - 5*x^2 + 8*x - 5)
- ? moebius(3*5*7*11*13)
- -1
- ? nextprime(100000000000000000000000)
- 100000000000000000000117
- ? numdiv(2^99*3^49)
- 5000
- ? omega(100!)
- 25
- ? precprime(100000000000000000000000)
- 99999999999999999999977
- ? prime(100)
- 541
- ? primes(100)
- [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, 2
- 39, 241, 251, 257, 263, 269, 271, 277, 281, 283, 293, 307, 311, 313, 317, 33
- 1, 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]
- ? qfbclassno(-12391)
- 63
- ? qfbclassno(1345)
- 6
- ? qfbclassno(-12391,1)
- 63
- ? qfbclassno(1345,1)
- 6
- ? Qfb(2,1,3)*Qfb(2,1,3)
- Qfb(2, -1, 3)
- ? qfbcompraw(Qfb(5,3,-1,0.),Qfb(7,1,-1,0.))
- Qfb(35, 43, 13, 0.E-38)
- ? qfbhclassno(2000003)
- 357
- ? qfbnucomp(Qfb(2,1,9),Qfb(4,3,5),3)
- Qfb(2, -1, 9)
- ? form=Qfb(2,1,9);qfbnucomp(form,form,3)
- Qfb(4, -3, 5)
- ? qfbnupow(form,111)
- Qfb(2, -1, 9)
- ? qfbpowraw(Qfb(5,3,-1,0.),3)
- Qfb(125, 23, 1, 0.E-38)
- ? qfbprimeform(-44,3)
- Qfb(3, 2, 4)
- ? qfbred(Qfb(3,10,12),,-1)
- Qfb(3, -2, 4)
- ? qfbred(Qfb(3,10,-20,1.5))
- Qfb(3, 16, -7, 1.5000000000000000000000000000000000000)
- ? qfbred(Qfb(3,10,-20,1.5),2,,18)
- Qfb(3, 16, -7, 1.5000000000000000000000000000000000000)
- ? qfbred(Qfb(3,10,-20,1.5),1)
- Qfb(-20, -10, 3, 2.1074451073987839947135880252731470616)
- ? qfbred(Qfb(3,10,-20,1.5),3,,18)
- Qfb(-20, -10, 3, 1.5000000000000000000000000000000000000)
- ? quaddisc(-252)
- -7
- ? quadgen(-11)
- w
- ? quadpoly(-11)
- x^2 - x + 3
- ? quadregulator(17)
- 2.0947125472611012942448228460655286535
- ? quadunit(17)
- 3 + 2*w
- ? sigma(100)
- 217
- ? sigma(100,2)
- 13671
- ? sigma(100,-3)
- 1149823/1000000
- ? sqrtint(10!^2+1)
- 3628800
- ? znorder(Mod(33,2^16+1))
- 2048
- ? forprime(p=2,100,print(p," ",lift(znprimroot(p))))
- 2 1
- 3 2
- 5 2
- 7 3
- 11 2
- 13 2
- 17 3
- 19 2
- 23 5
- 29 2
- 31 3
- 37 2
- 41 6
- 43 3
- 47 5
- 53 2
- 59 2
- 61 2
- 67 2
- 71 7
- 73 5
- 79 3
- 83 2
- 89 3
- 97 5
- ? znstar(3120)
- [768, [12, 4, 4, 2, 2], [Mod(2641, 3120), Mod(2341, 3120), Mod(2497, 3120), 
- Mod(391, 3120), Mod(2081, 3120)]]
- ? getheap
- [87, 2686]
- ? print("Total time spent: ",gettime);
- Total time spent: 20
--- 0 ----

<polyser-dyn.dif>:
*** ../src/test/64/polyser	Mon May 30 02:28:26 2011
--- gp.out	Wed Sep 21 13:20:18 2011
***************
*** 1,161 ****
-    echo = 1 (on)
- ? gettime;apol=x^3+5*x+1
- x^3 + 5*x + 1
- ? deriv((x+y)^5,y)
- 5*x^4 + 20*y*x^3 + 30*y^2*x^2 + 20*y^3*x + 5*y^4
- ? ((x+y)^5)'
- 5*x^4 + 20*y*x^3 + 30*y^2*x^2 + 20*y^3*x + 5*y^4
- ? dz=vector(30,k,1);dd=vector(30,k,k==1);dm=dirdiv(dd,dz)
- [1, -1, -1, 0, -1, 1, -1, 0, 0, 1, -1, 0, -1, 1, 1, 0, -1, 0, -1, 0, 1, 1, -
- 1, 0, 0, 1, 0, 0, -1, -1]
- ? direuler(s=1,40,1+s*X+s^2*X)
- [1, 6, 12, 0, 30, 72, 56, 0, 0, 180, 132, 0, 182, 336, 360, 0, 306, 0, 380, 
- 0, 672, 792, 552, 0, 0, 1092, 0, 0, 870, 2160, 992, 0, 1584, 1836, 1680, 0, 
- 1406, 2280, 2184, 0]
- ? dirmul(abs(dm),dz)
- [1, 2, 2, 2, 2, 4, 2, 2, 2, 4, 2, 4, 2, 4, 4, 2, 2, 4, 2, 4, 4, 4, 2, 4, 2, 
- 4, 2, 4, 2, 8]
- ? zz=yy;yy=xx;eval(zz)
- xx
- ? factorpadic(apol,7,8)
- 
- [(1 + O(7^8))*x + (6 + 2*7^2 + 2*7^3 + 3*7^4 + 2*7^5 + 6*7^6 + O(7^8)) 1]
- 
- [(1 + O(7^8))*x^2 + (1 + 6*7 + 4*7^2 + 4*7^3 + 3*7^4 + 4*7^5 + 6*7^7 + O(7^8
- ))*x + (6 + 5*7 + 3*7^2 + 6*7^3 + 7^4 + 3*7^5 + 2*7^6 + 5*7^7 + O(7^8)) 1]
- 
- ? factorpadic(apol,7,8,1)
- 
- [(1 + O(7^8))*x + (6 + 2*7^2 + 2*7^3 + 3*7^4 + 2*7^5 + 6*7^6 + O(7^8)) 1]
- 
- [(1 + O(7^8))*x^2 + (1 + 6*7 + 4*7^2 + 4*7^3 + 3*7^4 + 4*7^5 + 6*7^7 + O(7^8
- ))*x + (6 + 5*7 + 3*7^2 + 6*7^3 + 7^4 + 3*7^5 + 2*7^6 + 5*7^7 + O(7^8)) 1]
- 
- ? intformal(sin(x))
- 1/2*x^2 - 1/24*x^4 + 1/720*x^6 - 1/40320*x^8 + 1/3628800*x^10 - 1/479001600*
- x^12 + 1/87178291200*x^14 - 1/20922789888000*x^16 + O(x^18)
- ? intformal((-x^2-2*a*x+8*a)/(x^4-14*x^3+(2*a+49)*x^2-14*a*x+a^2))
- (x + a)/(x^2 - 7*x + a)
- ? newtonpoly(x^4+3*x^3+27*x^2+9*x+81,3)
- [2, 2/3, 2/3, 2/3]
- ? padicappr(apol,1+O(7^8))
- [1 + 6*7 + 4*7^2 + 4*7^3 + 3*7^4 + 4*7^5 + 6*7^7 + O(7^8)]~
- ? padicappr(x^3+5*x+1,Mod(x*(1+O(7^8)),x^2+x-1))
- [Mod((1 + 3*7 + 3*7^2 + 4*7^3 + 4*7^4 + 4*7^5 + 2*7^6 + 3*7^7 + O(7^8))*x + 
- (2*7 + 6*7^2 + 6*7^3 + 3*7^4 + 3*7^5 + 4*7^6 + 5*7^7 + O(7^8)), x^2 + x - 1)
- ]~
- ? Pol(sin(x))
- -1/1307674368000*x^15 + 1/6227020800*x^13 - 1/39916800*x^11 + 1/362880*x^9 -
-  1/5040*x^7 + 1/120*x^5 - 1/6*x^3 + x
- ? Pol([1,2,3,4,5])
- x^4 + 2*x^3 + 3*x^2 + 4*x + 5
- ? Polrev([1,2,3,4,5])
- 5*x^4 + 4*x^3 + 3*x^2 + 2*x + 1
- ? polcoeff(sin(x),7)
- -1/5040
- ? polcyclo(105)
- x^48 + x^47 + x^46 - x^43 - x^42 - 2*x^41 - x^40 - x^39 + x^36 + x^35 + x^34
-  + x^33 + x^32 + x^31 - x^28 - x^26 - x^24 - x^22 - x^20 + x^17 + x^16 + x^1
- 5 + x^14 + x^13 + x^12 - x^9 - x^8 - 2*x^7 - x^6 - x^5 + x^2 + x + 1
- ? pcy=polcyclo(405)
- x^216 - x^189 + x^135 - x^108 + x^81 - x^27 + 1
- ? pcy*pcy
- x^432 - 2*x^405 + x^378 + 2*x^351 - 4*x^324 + 4*x^297 - x^270 - 4*x^243 + 7*
- x^216 - 4*x^189 - x^162 + 4*x^135 - 4*x^108 + 2*x^81 + x^54 - 2*x^27 + 1
- ? poldegree(x^3/(x-1))
- 2
- ? poldisc(x^3+4*x+12)
- -4144
- ? poldiscreduced(x^3+4*x+12)
- [1036, 4, 1]
- ? polinterpolate([0,2,3],[0,4,9],5)
- 25
- ? polisirreducible(x^5+3*x^3+5*x^2+15)
- 0
- ? pollegendre(10)
- 46189/256*x^10 - 109395/256*x^8 + 45045/128*x^6 - 15015/128*x^4 + 3465/256*x
- ^2 - 63/256
- ? zpol=0.3+pollegendre(10)
- 46189/256*x^10 - 109395/256*x^8 + 45045/128*x^6 - 15015/128*x^4 + 3465/256*x
- ^2 + 0.053906250000000000000000000000000000001
- ? polrecip(3*x^7-5*x^3+6*x-9)
- -9*x^7 + 6*x^6 - 5*x^4 + 3
- ? polresultant(x^3-1,x^3+1)
- 8
- ? polresultant(x^3-1.,x^3+1.,,1)
- 8.0000000000000000000000000000000000000
- ? polroots(x^5-5*x^2-5*x-5)
- [2.0509134529831982130058170163696514536 + 0.E-38*I, -0.67063790319207539268
- 663382582902335604 + 0.84813118358634026680538906224199030918*I, -0.67063790
- 319207539268663382582902335604 - 0.84813118358634026680538906224199030918*I,
-  -0.35481882329952371381627468235580237078 + 1.39980287391035466982975228340
- 62081965*I, -0.35481882329952371381627468235580237078 - 1.399802873910354669
- 8297522834062081965*I]~
- ? polroots(x^4-1000000000000000000000,1)
- [-177827.94100389228012254211951926848447 + 0.E-38*I, 177827.941003892280122
- 54211951926848447 + 0.E-38*I, 0.E-98 + 177827.941003892280122542119519268484
- 47*I, 0.E-98 - 177827.94100389228012254211951926848447*I]~
- ? polrootsmod(x^16-1,41)
- [Mod(1, 41), Mod(3, 41), Mod(9, 41), Mod(14, 41), Mod(27, 41), Mod(32, 41), 
- Mod(38, 41), Mod(40, 41)]~
- ? polrootspadic(x^4+1,41,6)
- [3 + 22*41 + 27*41^2 + 15*41^3 + 27*41^4 + 33*41^5 + O(41^6), 14 + 20*41 + 2
- 5*41^2 + 24*41^3 + 4*41^4 + 18*41^5 + O(41^6), 27 + 20*41 + 15*41^2 + 16*41^
- 3 + 36*41^4 + 22*41^5 + O(41^6), 38 + 18*41 + 13*41^2 + 25*41^3 + 13*41^4 + 
- 7*41^5 + O(41^6)]~
- ? polsturm(zpol)
- 4
- ? polsturm(zpol,0.91,1)
- 1
- ? polsylvestermatrix(a2*x^2+a1*x+a0,b1*x+b0)
- 
- [a2 b1 0]
- 
- [a1 b0 b1]
- 
- [a0 0 b0]
- 
- ? polsym(x^17-1,17)
- [17, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 17]~
- ? poltchebi(10)
- 512*x^10 - 1280*x^8 + 1120*x^6 - 400*x^4 + 50*x^2 - 1
- ? polzagier(6,3)
- 4608*x^6 - 13824*x^5 + 46144/3*x^4 - 23168/3*x^3 + 5032/3*x^2 - 120*x + 1
- ? serconvol(sin(x),x*cos(x))
- x + 1/12*x^3 + 1/2880*x^5 + 1/3628800*x^7 + 1/14631321600*x^9 + 1/1448500838
- 40000*x^11 + 1/2982752926433280000*x^13 + 1/114000816848279961600000*x^15 + 
- O(x^17)
- ? serlaplace(x*exp(x*y)/(exp(x)-1))
- 1 + (y - 1/2)*x + (y^2 - y + 1/6)*x^2 + (y^3 - 3/2*y^2 + 1/2*y)*x^3 + (y^4 -
-  2*y^3 + y^2 - 1/30)*x^4 + (y^5 - 5/2*y^4 + 5/3*y^3 - 1/6*y)*x^5 + (y^6 - 3*
- y^5 + 5/2*y^4 - 1/2*y^2 + 1/42)*x^6 + (y^7 - 7/2*y^6 + 7/2*y^5 - 7/6*y^3 + 1
- /6*y)*x^7 + (y^8 - 4*y^7 + 14/3*y^6 - 7/3*y^4 + 2/3*y^2 - 1/30)*x^8 + (y^9 -
-  9/2*y^8 + 6*y^7 - 21/5*y^5 + 2*y^3 - 3/10*y)*x^9 + (y^10 - 5*y^9 + 15/2*y^8
-  - 7*y^6 + 5*y^4 - 3/2*y^2 + 5/66)*x^10 + (y^11 - 11/2*y^10 + 55/6*y^9 - 11*
- y^7 + 11*y^5 - 11/2*y^3 + 5/6*y)*x^11 + (y^12 - 6*y^11 + 11*y^10 - 33/2*y^8 
- + 22*y^6 - 33/2*y^4 + 5*y^2 - 691/2730)*x^12 + (y^13 - 13/2*y^12 + 13*y^11 -
-  143/6*y^9 + 286/7*y^7 - 429/10*y^5 + 65/3*y^3 - 691/210*y)*x^13 + (y^14 - 7
- *y^13 + 91/6*y^12 - 1001/30*y^10 + 143/2*y^8 - 1001/10*y^6 + 455/6*y^4 - 691
- /30*y^2 + 7/6)*x^14 + (y^15 - 15/2*y^14 + 35/2*y^13 - 91/2*y^11 + 715/6*y^9 
- - 429/2*y^7 + 455/2*y^5 - 691/6*y^3 + 35/2*y)*x^15 + O(x^16)
- ? serreverse(tan(x))
- x - 1/3*x^3 + 1/5*x^5 - 1/7*x^7 + 1/9*x^9 - 1/11*x^11 + 1/13*x^13 - 1/15*x^1
- 5 + O(x^17)
- ? subst(sin(x),x,y)
- y - 1/6*y^3 + 1/120*y^5 - 1/5040*y^7 + 1/362880*y^9 - 1/39916800*y^11 + 1/62
- 27020800*y^13 - 1/1307674368000*y^15 + O(y^17)
- ? subst(sin(x),x,x+x^2)
- x + x^2 - 1/6*x^3 - 1/2*x^4 - 59/120*x^5 - 1/8*x^6 + 419/5040*x^7 + 59/720*x
- ^8 + 13609/362880*x^9 + 19/13440*x^10 - 273241/39916800*x^11 - 14281/3628800
- *x^12 - 6495059/6227020800*x^13 + 69301/479001600*x^14 + 26537089/1188794880
- 00*x^15 + 1528727/17435658240*x^16 + O(x^17)
- ? taylor(y/(x-y),y)
- (O(y^16)*x^15 + y*x^14 + y^2*x^13 + y^3*x^12 + y^4*x^11 + y^5*x^10 + y^6*x^9
-  + y^7*x^8 + y^8*x^7 + y^9*x^6 + y^10*x^5 + y^11*x^4 + y^12*x^3 + y^13*x^2 +
-  y^14*x + y^15)/x^15
- ? variable(name^4-other)
- name
- ? getheap
- [58, 7149]
- ? print("Total time spent: ",gettime);
- Total time spent: 8
--- 0 ----

<linear-dyn.dif>:
*** ../src/test/64/linear	Mon May 30 02:28:26 2011
--- gp.out	Wed Sep 21 13:20:18 2011
***************
*** 1,696 ****
-    echo = 1 (on)
- ? gettime;algdep(2*cos(2*Pi/13),6)
- x^6 + x^5 - 5*x^4 - 4*x^3 + 6*x^2 + 3*x - 1
- ? algdep(2*cos(2*Pi/13),6,15)
- x^6 + x^5 - 5*x^4 - 4*x^3 + 6*x^2 + 3*x - 1
- ? charpoly([1,2;3,4],z)
- z^2 - 5*z - 2
- ? charpoly(Mod(x^2+x+1,x^3+5*x+1),z)
- z^3 + 7*z^2 + 16*z - 19
- ? charpoly([1,2;3,4],z,1)
- z^2 - 5*z - 2
- ? charpoly(Mod(1,8191)*[1,2;3,4],z,2)
- z^2 + Mod(8186, 8191)*z + Mod(8189, 8191)
- ? lindep(Mod(1,7)*[2,-1;1,3],-2)
- [Mod(6, 7), Mod(5, 7)]~
- ? lindep([(1-3*sqrt(2))/(3-2*sqrt(3)),1,sqrt(2),sqrt(3),sqrt(6)])
- [3, 3, -9, 2, -6]~
- ? lindep([(1-3*sqrt(2))/(3-2*sqrt(3)),1,sqrt(2),sqrt(3),sqrt(6)],14)
- [-3, -3, 9, -2, 6]~
- ? matadjoint([1,2;3,4])
- 
- [4 -2]
- 
- [-3 1]
- 
- ? matcompanion(x^5-12*x^3+0.0005)
- 
- [0 0 0 0 -0.00050000000000000000000000000000000000000]
- 
- [1 0 0 0 0]
- 
- [0 1 0 0 0]
- 
- [0 0 1 0 12]
- 
- [0 0 0 1 0]
- 
- ? matdet([1,2,3;1,5,6;9,8,7])
- -30
- ? matdet([1,2,3;1,5,6;9,8,7],1)
- -30
- ? matdetint([1,2,3;4,5,6])
- 3
- ? matdiagonal([2,4,6])
- 
- [2 0 0]
- 
- [0 4 0]
- 
- [0 0 6]
- 
- ? mateigen([1,2,3;4,5,6;7,8,9])
- 
- [-1.2833494518006402717978106547571267252 1 0.283349451800640271797810654757
- 12672521]
- 
- [-0.14167472590032013589890532737856336261 -2 0.6416747259003201358989053273
- 7856336260]
- 
- [1 1 1]
- 
- ? mathess(mathilbert(7))
- 
- [1 90281/58800 -1919947/4344340 4858466341/1095033030 -77651417539/819678732
- 6 3386888964/106615355 1/2]
- 
- [1/3 43/48 38789/5585580 268214641/109503303 -581330123627/126464718744 4365
- 450643/274153770 1/4]
- 
- [0 217/2880 442223/7447440 53953931/292008808 -32242849453/168619624992 1475
- 457901/1827691800 1/80]
- 
- [0 0 1604444/264539275 24208141/149362505292 847880210129/47916076768560 -45
- 44407141/103873817300 -29/40920]
- 
- [0 0 0 9773092581/35395807550620 -24363634138919/107305824577186620 72118203
- 606917/60481351061158500 55899/3088554700]
- 
- [0 0 0 0 67201501179065/8543442888354179988 -9970556426629/74082861999267660
- 0 -3229/13661312210]
- 
- [0 0 0 0 0 -258198800769/9279048099409000 -13183/38381527800]
- 
- ? mathilbert(5)
- 
- [1 1/2 1/3 1/4 1/5]
- 
- [1/2 1/3 1/4 1/5 1/6]
- 
- [1/3 1/4 1/5 1/6 1/7]
- 
- [1/4 1/5 1/6 1/7 1/8]
- 
- [1/5 1/6 1/7 1/8 1/9]
- 
- ? amat=1/mathilbert(7)
- 
- [49 -1176 8820 -29400 48510 -38808 12012]
- 
- [-1176 37632 -317520 1128960 -1940400 1596672 -504504]
- 
- [8820 -317520 2857680 -10584000 18711000 -15717240 5045040]
- 
- [-29400 1128960 -10584000 40320000 -72765000 62092800 -20180160]
- 
- [48510 -1940400 18711000 -72765000 133402500 -115259760 37837800]
- 
- [-38808 1596672 -15717240 62092800 -115259760 100590336 -33297264]
- 
- [12012 -504504 5045040 -20180160 37837800 -33297264 11099088]
- 
- ? mathnf(amat)
- 
- [420 0 0 0 210 168 175]
- 
- [0 840 0 0 0 0 504]
- 
- [0 0 2520 0 0 0 1260]
- 
- [0 0 0 2520 0 0 840]
- 
- [0 0 0 0 13860 0 6930]
- 
- [0 0 0 0 0 5544 0]
- 
- [0 0 0 0 0 0 12012]
- 
- ? mathnf(amat,1)
- [[420, 0, 0, 0, 210, 168, 175; 0, 840, 0, 0, 0, 0, 504; 0, 0, 2520, 0, 0, 0,
-  1260; 0, 0, 0, 2520, 0, 0, 840; 0, 0, 0, 0, 13860, 0, 6930; 0, 0, 0, 0, 0, 
- 5544, 0; 0, 0, 0, 0, 0, 0, 12012], [420, 420, 840, 630, 2982, 1092, 4159; 21
- 0, 280, 630, 504, 2415, 876, 3395; 140, 210, 504, 420, 2050, 749, 2901; 105,
-  168, 420, 360, 1785, 658, 2542; 84, 140, 360, 315, 1582, 588, 2266; 70, 120
- , 315, 280, 1421, 532, 2046; 60, 105, 280, 252, 1290, 486, 1866]]
- ? mathnf(amat,4)
- [[420, 0, 0, 0, 210, 168, 175; 0, 840, 0, 0, 0, 0, 504; 0, 0, 2520, 0, 0, 0,
-  1260; 0, 0, 0, 2520, 0, 0, 840; 0, 0, 0, 0, 13860, 0, 6930; 0, 0, 0, 0, 0, 
- 5544, 0; 0, 0, 0, 0, 0, 0, 12012], [420, 420, 840, 630, 2982, 1092, 4159; 21
- 0, 280, 630, 504, 2415, 876, 3395; 140, 210, 504, 420, 2050, 749, 2901; 105,
-  168, 420, 360, 1785, 658, 2542; 84, 140, 360, 315, 1582, 588, 2266; 70, 120
- , 315, 280, 1421, 532, 2046; 60, 105, 280, 252, 1290, 486, 1866]]
- ? mathnf(amat,3)
- [[360360, 0, 0, 0, 0, 144144, 300300; 0, 27720, 0, 0, 0, 0, 22176; 0, 0, 277
- 20, 0, 0, 0, 6930; 0, 0, 0, 2520, 0, 0, 840; 0, 0, 0, 0, 2520, 0, 1260; 0, 0
- , 0, 0, 0, 168, 0; 0, 0, 0, 0, 0, 0, 7], [51480, 4620, 5544, 630, 840, 20676
- , 48619; 45045, 3960, 4620, 504, 630, 18074, 42347; 40040, 3465, 3960, 420, 
- 504, 16058, 37523; 36036, 3080, 3465, 360, 420, 14448, 33692; 32760, 2772, 3
- 080, 315, 360, 13132, 30574; 30030, 2520, 2772, 280, 315, 12036, 27986; 2772
- 0, 2310, 2520, 252, 280, 11109, 25803], Vecsmall([7, 6, 5, 4, 3, 2, 1])]
- ? mathnfmod(amat,matdetint(amat))
- 
- [420 0 0 0 210 168 175]
- 
- [0 840 0 0 0 0 504]
- 
- [0 0 2520 0 0 0 1260]
- 
- [0 0 0 2520 0 0 840]
- 
- [0 0 0 0 13860 0 6930]
- 
- [0 0 0 0 0 5544 0]
- 
- [0 0 0 0 0 0 12012]
- 
- ? mathnfmodid(amat,123456789*10^100)
- 
- [60 0 0 0 30 24 35]
- 
- [0 120 0 0 0 0 24]
- 
- [0 0 360 0 0 0 180]
- 
- [0 0 0 360 0 0 240]
- 
- [0 0 0 0 180 0 90]
- 
- [0 0 0 0 0 72 0]
- 
- [0 0 0 0 0 0 12]
- 
- ? matid(5)
- 
- [1 0 0 0 0]
- 
- [0 1 0 0 0]
- 
- [0 0 1 0 0]
- 
- [0 0 0 1 0]
- 
- [0 0 0 0 1]
- 
- ? matimage([1,3,5;2,4,6;3,5,7])
- 
- [1 3]
- 
- [2 4]
- 
- [3 5]
- 
- ? matimage([1,3,5;2,4,6;3,5,7],1)
- 
- [3 5]
- 
- [4 6]
- 
- [5 7]
- 
- ? matimage(Pi*[1,3,5;2,4,6;3,5,7])
- 
- [3.1415926535897932384626433832795028842 9.424777960769379715387930149838508
- 6526]
- 
- [6.2831853071795864769252867665590057684 12.56637061435917295385057353311801
- 1537]
- 
- [9.4247779607693797153879301498385086526 15.70796326794896619231321691639751
- 4421]
- 
- ? matimagecompl([1,3,5;2,4,6;3,5,7])
- [3]
- ? matimagecompl(Pi*[1,3,5;2,4,6;3,5,7])
- [3]
- ? matindexrank([1,1,1;1,1,1;1,1,2])
- [Vecsmall([1, 3]), Vecsmall([1, 3])]
- ? matintersect([1,2;3,4;5,6],[2,3;7,8;8,9])
- 
- [-1]
- 
- [-1]
- 
- [-1]
- 
- ? matinverseimage([1,1;2,3;5,7],[2,2,6]~)
- [4, -2]~
- ? matisdiagonal([1,0,0;0,5,0;0,0,0])
- 1
- ? matker(matrix(4,4,x,y,x/y))
- 
- [-1/2 -1/3 -1/4]
- 
- [1 0 0]
- 
- [0 1 0]
- 
- [0 0 1]
- 
- ? matker(matrix(4,4,x,y,sin(x+y)))
- 
- [1.0000000000000000000000000000000000000 1.080604611736279434801873214885953
- 2075]
- 
- [-1.0806046117362794348018732148859532075 -0.1677063269057152260048635409984
- 7562047]
- 
- [1 0]
- 
- [0 1]
- 
- ? matker(matrix(4,4,x,y,x+y),1)
- 
- [1 2]
- 
- [-2 -3]
- 
- [1 0]
- 
- [0 1]
- 
- ? matkerint(matrix(4,4,x,y,x*y))
- 
- [-1 -1 -1]
- 
- [-1 0 1]
- 
- [1 -1 1]
- 
- [0 1 -1]
- 
- ? matkerint(matrix(4,4,x,y,x*y),1)
- 
- [-1 -1 -1]
- 
- [-1 0 1]
- 
- [1 -1 1]
- 
- [0 1 -1]
- 
- ? matkerint(matrix(4,6,x,y,2520/(x+y)))
- 
- [3 1]
- 
- [-30 -15]
- 
- [70 70]
- 
- [0 -140]
- 
- [-126 126]
- 
- [84 -42]
- 
- ? matmuldiagonal(amat,[1,2,3,4,5,6,7])
- 
- [49 -2352 26460 -117600 242550 -232848 84084]
- 
- [-1176 75264 -952560 4515840 -9702000 9580032 -3531528]
- 
- [8820 -635040 8573040 -42336000 93555000 -94303440 35315280]
- 
- [-29400 2257920 -31752000 161280000 -363825000 372556800 -141261120]
- 
- [48510 -3880800 56133000 -291060000 667012500 -691558560 264864600]
- 
- [-38808 3193344 -47151720 248371200 -576298800 603542016 -233080848]
- 
- [12012 -1009008 15135120 -80720640 189189000 -199783584 77693616]
- 
- ? matmultodiagonal(amat^-1,%)
- 
- [1 0 0 0 0 0 0]
- 
- [0 2 0 0 0 0 0]
- 
- [0 0 3 0 0 0 0]
- 
- [0 0 0 4 0 0 0]
- 
- [0 0 0 0 5 0 0]
- 
- [0 0 0 0 0 6 0]
- 
- [0 0 0 0 0 0 7]
- 
- ? matpascal(8)
- 
- [1 0 0 0 0 0 0 0 0]
- 
- [1 1 0 0 0 0 0 0 0]
- 
- [1 2 1 0 0 0 0 0 0]
- 
- [1 3 3 1 0 0 0 0 0]
- 
- [1 4 6 4 1 0 0 0 0]
- 
- [1 5 10 10 5 1 0 0 0]
- 
- [1 6 15 20 15 6 1 0 0]
- 
- [1 7 21 35 35 21 7 1 0]
- 
- [1 8 28 56 70 56 28 8 1]
- 
- ? matrank(matrix(5,5,x,y,x+y))
- 2
- ? matrix(5,5,x,y,gcd(x,y))
- 
- [1 1 1 1 1]
- 
- [1 2 1 2 1]
- 
- [1 1 3 1 1]
- 
- [1 2 1 4 1]
- 
- [1 1 1 1 5]
- 
- ? matrixqz([1,3;3,5;5,7],0)
- 
- [1 1]
- 
- [3 2]
- 
- [5 3]
- 
- ? matrixqz([1/3,1/4,1/6;1/2,1/4,-1/4;1/3,1,0],-1)
- 
- [19 12 2]
- 
- [0 1 0]
- 
- [0 0 1]
- 
- ? matrixqz([1,3;3,5;5,7],-2)
- 
- [2 -1]
- 
- [1 0]
- 
- [0 1]
- 
- ? matsize([1,2;3,4;5,6])
- [3, 2]
- ? matsnf(1/mathilbert(6))
- [27720, 2520, 2520, 840, 210, 6]
- ? matsnf(x*matid(5)-matrix(5,5,j,k,1),2)
- [x^2 - 5*x, x, x, x, 1]
- ? matsolve(mathilbert(10),[1,2,3,4,5,6,7,8,9,0]~)
- [9236800, -831303990, 18288515520, -170691240720, 832112321040, -23298940665
- 00, 3883123564320, -3803844432960, 2020775945760, -449057772020]~
- ? matsolvemod([2,3;5,4],[7,11]~,[1,4]~)
- [-5, -1]~
- ? matsolvemod([2,3;5,4],[7,11]~,[1,4]~,1)
- [[-5, -1]~, [4, 9; -5, 8]]
- ? matsupplement([1,3;2,4;3,6])
- 
- [1 3 0]
- 
- [2 4 0]
- 
- [3 6 1]
- 
- ? mattranspose(vector(2,x,x))
- [1, 2]~
- ? %*%~
- 
- [1 2]
- 
- [2 4]
- 
- ? norml2(vector(10,x,x))
- 385
- ? qfgaussred(mathilbert(5))
- 
- [1 1/2 1/3 1/4 1/5]
- 
- [0 1/12 1 9/10 4/5]
- 
- [0 0 1/180 3/2 12/7]
- 
- [0 0 0 1/2800 2]
- 
- [0 0 0 0 1/44100]
- 
- ? qfjacobi(mathilbert(6))
- [[1.0827994845655497685388772372251778091 E-7, 1.257075712262519492298239799
- 6498755378 E-5, 0.00061574835418265769764919938428527140434, 0.0163215213198
- 75822124345079564191505890, 0.24236087057520955213572841585070114077, 1.6188
- 998589243390969705881471257800713]~, [-0.00124819408408217511693981630463878
- 36342, 0.011144320930724710530678340374220998345, -0.06222658815019768177515
- 2126611810492941, 0.24032536934252330399154228873240534569, -0.6145448282925
- 8676899320019644273870646, 0.74871921887909485900280109200517845109; 0.03560
- 6642944287635266122848131812051370, -0.1797327572407600375877689780374064077
- 9, 0.49083920971092436297498316169060045043, -0.6976513752773701229620833504
- 6678265583, 0.21108248167867048675227675845247769095, 0.44071750324351206127
- 160083580231701802; -0.24067907958842295837736719558855680218, 0.60421220675
- 295973004426567844103061740, -0.53547692162107486593474491750949545605, -0.2
- 3138937333290388042251363554209048307, 0.36589360730302614149086554211117169
- 623, 0.32069686982225190106359024326699463107; 0.625460386549227244577534410
- 39459331707, -0.44357471627623954554460416705180104473, -0.41703769221897886
- 840494514780771076350, 0.13286315850933553530333839628101576048, 0.394706776
- 09501756783094636145991581709, 0.25431138634047419251788312792590944672; -0.
- 68980719929383668419801738006926828754, -0.441536641012289662221436497529772
- 04448, 0.047034018933115649705614518466541245344, 0.362714921464871475252994
- 57604461742112, 0.38819043387388642863111448825992418974, 0.2115308400789652
- 4664213667673977991960; 0.27160545336631286930015536176213646338, 0.45911481
- 681642960284551392793050867151, 0.54068156310385293880022293448123781988, 0.
- 50276286675751538489260566368647786274, 0.3706959077673628086177550108480739
- 4603, 0.18144297664876947372217005457727093716]]
- ? m=1/mathilbert(7)
- 
- [49 -1176 8820 -29400 48510 -38808 12012]
- 
- [-1176 37632 -317520 1128960 -1940400 1596672 -504504]
- 
- [8820 -317520 2857680 -10584000 18711000 -15717240 5045040]
- 
- [-29400 1128960 -10584000 40320000 -72765000 62092800 -20180160]
- 
- [48510 -1940400 18711000 -72765000 133402500 -115259760 37837800]
- 
- [-38808 1596672 -15717240 62092800 -115259760 100590336 -33297264]
- 
- [12012 -504504 5045040 -20180160 37837800 -33297264 11099088]
- 
- ? mp=concat(m,matid(7))
- 
- [49 -1176 8820 -29400 48510 -38808 12012 1 0 0 0 0 0 0]
- 
- [-1176 37632 -317520 1128960 -1940400 1596672 -504504 0 1 0 0 0 0 0]
- 
- [8820 -317520 2857680 -10584000 18711000 -15717240 5045040 0 0 1 0 0 0 0]
- 
- [-29400 1128960 -10584000 40320000 -72765000 62092800 -20180160 0 0 0 1 0 0 
- 0]
- 
- [48510 -1940400 18711000 -72765000 133402500 -115259760 37837800 0 0 0 0 1 0
-  0]
- 
- [-38808 1596672 -15717240 62092800 -115259760 100590336 -33297264 0 0 0 0 0 
- 1 0]
- 
- [12012 -504504 5045040 -20180160 37837800 -33297264 11099088 0 0 0 0 0 0 1]
- 
- ? qflll(m)
- 
- [-420 -420 840 630 -1092 757 2982]
- 
- [-210 -280 630 504 -876 700 2415]
- 
- [-140 -210 504 420 -749 641 2050]
- 
- [-105 -168 420 360 -658 589 1785]
- 
- [-84 -140 360 315 -588 544 1582]
- 
- [-70 -120 315 280 -532 505 1421]
- 
- [-60 -105 280 252 -486 471 1290]
- 
- ? qflllgram(m)
- 
- [1 1 27 -27 69 0 141]
- 
- [0 1 5 -23 35 -24 50]
- 
- [0 1 4 -22 19 -24 24]
- 
- [0 1 4 -21 11 -19 14]
- 
- [0 1 4 -20 7 -14 9]
- 
- [0 1 4 -19 5 -10 6]
- 
- [0 1 4 -18 4 -7 4]
- 
- ? qflllgram(m,1)
- 
- [1 1 27 -27 69 0 141]
- 
- [0 1 5 -23 35 -24 50]
- 
- [0 1 4 -22 19 -24 24]
- 
- [0 1 4 -21 11 -19 14]
- 
- [0 1 4 -20 7 -14 9]
- 
- [0 1 4 -19 5 -10 6]
- 
- [0 1 4 -18 4 -7 4]
- 
- ? qflllgram(mp~*mp,4)
- [[-420, -420, 840, 630, 2982, -1092, 757; -210, -280, 630, 504, 2415, -876, 
- 700; -140, -210, 504, 420, 2050, -749, 641; -105, -168, 420, 360, 1785, -658
- , 589; -84, -140, 360, 315, 1582, -588, 544; -70, -120, 315, 280, 1421, -532
- , 505; -60, -105, 280, 252, 1290, -486, 471; 420, 0, 0, 0, -210, 168, 35; 0,
-  840, 0, 0, 0, 0, 336; 0, 0, -2520, 0, 0, 0, -1260; 0, 0, 0, -2520, 0, 0, -8
- 40; 0, 0, 0, 0, -13860, 0, 6930; 0, 0, 0, 0, 0, 5544, 0; 0, 0, 0, 0, 0, 0, -
- 12012], [0, 0, 0, 0, 0, 0, 0; 0, 0, 0, 0, 0, 0, 0; 0, 0, 0, 0, 0, 0, 0; 0, 0
- , 0, 0, 0, 0, 0; 0, 0, 0, 0, 0, 0, 0; 0, 0, 0, 0, 0, 0, 0; 0, 0, 0, 0, 0, 0,
-  0; 1, 0, 0, 0, 0, 0, 0; 0, 1, 0, 0, 0, 0, 0; 0, 0, 1, 0, 0, 0, 0; 0, 0, 0, 
- 1, 0, 0, 0; 0, 0, 0, 0, 1, 0, 0; 0, 0, 0, 0, 0, 1, 0; 0, 0, 0, 0, 0, 0, 1]]
- ? qflll(m,1)
- 
- [-420 -420 840 630 -1092 757 2982]
- 
- [-210 -280 630 504 -876 700 2415]
- 
- [-140 -210 504 420 -749 641 2050]
- 
- [-105 -168 420 360 -658 589 1785]
- 
- [-84 -140 360 315 -588 544 1582]
- 
- [-70 -120 315 280 -532 505 1421]
- 
- [-60 -105 280 252 -486 471 1290]
- 
- ? qflll(m,2)
- 
- [-420 -420 -630 840 1092 2982 -83]
- 
- [-210 -280 -504 630 876 2415 70]
- 
- [-140 -210 -420 504 749 2050 137]
- 
- [-105 -168 -360 420 658 1785 169]
- 
- [-84 -140 -315 360 588 1582 184]
- 
- [-70 -120 -280 315 532 1421 190]
- 
- [-60 -105 -252 280 486 1290 191]
- 
- ? qflll(mp,4)
- [[-420, -420, 840, 630, 2982, -1092, 757; -210, -280, 630, 504, 2415, -876, 
- 700; -140, -210, 504, 420, 2050, -749, 641; -105, -168, 420, 360, 1785, -658
- , 589; -84, -140, 360, 315, 1582, -588, 544; -70, -120, 315, 280, 1421, -532
- , 505; -60, -105, 280, 252, 1290, -486, 471; 420, 0, 0, 0, -210, 168, 35; 0,
-  840, 0, 0, 0, 0, 336; 0, 0, -2520, 0, 0, 0, -1260; 0, 0, 0, -2520, 0, 0, -8
- 40; 0, 0, 0, 0, -13860, 0, 6930; 0, 0, 0, 0, 0, 5544, 0; 0, 0, 0, 0, 0, 0, -
- 12012], [0, 0, 0, 0, 0, 0, 0; 0, 0, 0, 0, 0, 0, 0; 0, 0, 0, 0, 0, 0, 0; 0, 0
- , 0, 0, 0, 0, 0; 0, 0, 0, 0, 0, 0, 0; 0, 0, 0, 0, 0, 0, 0; 0, 0, 0, 0, 0, 0,
-  0; 1, 0, 0, 0, 0, 0, 0; 0, 1, 0, 0, 0, 0, 0; 0, 0, 1, 0, 0, 0, 0; 0, 0, 0, 
- 1, 0, 0, 0; 0, 0, 0, 0, 1, 0, 0; 0, 0, 0, 0, 0, 1, 0; 0, 0, 0, 0, 0, 0, 1]]
- ? qfminim([2,1;1,2],4,6)
- [6, 2, [0, -1, 1; 1, 1, 0]]
- ? qfperfection([2,0,1;0,2,1;1,1,2])
- 6
- ? qfsign(mathilbert(5)-0.11*matid(5))
- [2, 3]
- ? aset=Set([5,-2,7,3,5,1])
- ["-2", "1", "3", "5", "7"]
- ? bset=Set([7,5,-5,7,2])
- ["-5", "2", "5", "7"]
- ? setintersect(aset,bset)
- ["5", "7"]
- ? setisset([-3,5,7,7])
- 0
- ? setminus(aset,bset)
- ["-2", "1", "3"]
- ? setsearch(aset,3)
- 3
- ? setsearch(bset,3)
- 0
- ? setunion(aset,bset)
- ["-2", "-5", "1", "2", "3", "5", "7"]
- ? trace(1+I)
- 2
- ? trace(Mod(x+5,x^3+x+1))
- 15
- ? Vec(sin(x))
- [1, 0, -1/6, 0, 1/120, 0, -1/5040, 0, 1/362880, 0, -1/39916800, 0, 1/6227020
- 800, 0, -1/1307674368000, 0]
- ? vecmax([-3,7,-2,11])
- 11
- ? vecmin([-3,7,-2,11])
- -3
- ? concat([1,2],[3,4])
- [1, 2, 3, 4]
- ? concat(Mat(vector(4,x,x)~),vector(4,x,10+x)~)
- 
- [1 11]
- 
- [2 12]
- 
- [3 13]
- 
- [4 14]
- 
- ? vecextract([1,2,3,4,5,6,7,8,9,10],1000)
- [4, 6, 7, 8, 9, 10]
- ? vecextract(matrix(15,15,x,y,x+y),vector(5,x,3*x),vector(3,y,3*y))
- 
- [6 9 12]
- 
- [9 12 15]
- 
- [12 15 18]
- 
- [15 18 21]
- 
- [18 21 24]
- 
- ? round((1.*mathilbert(7))^(-1)<<77)/2^77
- 
- [49 -1176 8820 -29400 48510 -38808 12012]
- 
- [-1176 37632 -317520 1128960 -1940400 1596672 -504504]
- 
- [8820 -317520 2857680 -10584000 18711000 -15717240 5045040]
- 
- [-29400 1128960 -10584000 6092986130857731040519127040001/151115727451828646
- 838272 -10995935908032311487186862080001/151115727451828646838272 9383198641
- 520905802399455641601/151115727451828646838272 -20180160]
- 
- [48510 -1940400 18711000 -10995935908032311487186862080001/15111572745182864
- 6838272 10079607915696285529921290240001/75557863725914323419136 -8708781239
- 161590697851994767361/75557863725914323419136 37837800]
- 
- [-38808 1596672 -15717240 9383198641520905802399455641601/151115727451828646
- 838272 -8708781239161590697851994767361/75557863725914323419136 152007817992
- 63867399887118139393/151115727451828646838272 -33297264]
- 
- [12012 -504504 5045040 -20180160 37837800 -33297264 11099088]
- 
- ? vecsort([8,7,6,5],,1)
- Vecsmall([4, 3, 2, 1])
- ? vecsort([[1,5],[2,4],[1,5,1],[1,4,2]],,2)
- [[1, 4, 2], [1, 5], [1, 5, 1], [2, 4]]
- ? vecsort(vector(17,x,5*x%17))
- [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16]
- ? vecsort([[1,8,5],[2,5,8],[3,6,-6],[4,8,6]],2)
- [[2, 5, 8], [3, 6, -6], [1, 8, 5], [4, 8, 6]]
- ? vecsort([[1,8,5],[2,5,8],[3,6,-6],[4,8,6]],[2,1])
- [[2, 5, 8], [3, 6, -6], [1, 8, 5], [4, 8, 6]]
- ? vector(10,x,1/x)
- [1, 1/2, 1/3, 1/4, 1/5, 1/6, 1/7, 1/8, 1/9, 1/10]
- ? getheap
- [104, 10299]
- ? print("Total time spent: ",gettime);
- Total time spent: 4
--- 0 ----

<elliptic-dyn.dif>:
*** ../src/test/64/elliptic	Mon May 30 02:28:26 2011
--- gp.out	Wed Sep 21 13:20:18 2011
***************
*** 1,160 ****
-    echo = 1 (on)
- ? gettime;ellinit([0,0,0,-1,0])
- [0, 0, 0, -1, 0, 0, -2, 0, -1, 48, 0, 64, 1728, [1.0000000000000000000000000
- 000000000000, 0.E-57, -1.0000000000000000000000000000000000000]~, 2.62205755
- 42921198104648395898911194137, -2.6220575542921198104648395898911194137*I, 1
- .1981402347355922074399224922803238782, 1.1981402347355922074399224922803238
- 782*I, 6.8751858180203728274900957798105571979]
- ? ellinit([0,0,0,-17,0],1)
- [0, 0, 0, -17, 0, 0, -34, 0, -289, 816, 0, 314432, 1728]
- ? ellsub(%,[-1,4],[-4,2])
- [9, -24]
- ? ellj(I)
- 1728.0000000000000000000000000000000000
- ? acurve=ellinit([0,0,1,-1,0])
- [0, 0, 1, -1, 0, 0, -2, 1, -1, 48, -216, 37, 110592/37, [0.83756543528332303
- 544481089907503024040, 0.26959443640544455826293795134926000405, -1.10715987
- 16887675937077488504242902445]~, 2.9934586462319596298320099794525081778, -2
- .4513893819867900608542248318665252254*I, 0.94263855591362295176518779416067
- 539931, 1.3270305788796764757190502098362372906*I, 7.33813274078957673907072
- 10033323055880]
- ? apoint=[2,2]
- [2, 2]
- ? elladd(acurve,apoint,apoint)
- [21/25, -56/125]
- ? ellak(acurve,1000000007)
- 43800
- ? ellan(acurve,100)
- [1, -2, -3, 2, -2, 6, -1, 0, 6, 4, -5, -6, -2, 2, 6, -4, 0, -12, 0, -4, 3, 1
- 0, 2, 0, -1, 4, -9, -2, 6, -12, -4, 8, 15, 0, 2, 12, -1, 0, 6, 0, -9, -6, 2,
-  -10, -12, -4, -9, 12, -6, 2, 0, -4, 1, 18, 10, 0, 0, -12, 8, 12, -8, 8, -6,
-  -8, 4, -30, 8, 0, -6, -4, 9, 0, -1, 2, 3, 0, 5, -12, 4, 8, 9, 18, -15, 6, 0
- , -4, -18, 0, 4, 24, 2, 4, 12, 18, 0, -24, 4, 12, -30, -2]
- ? ellap(acurve,10007)
- 66
- ? deu=direuler(p=2,100,1/(1-ellap(acurve,p)*x+if(acurve[12]%p,p,0)*x^2))
- [1, -2, -3, 2, -2, 6, -1, 0, 6, 4, -5, -6, -2, 2, 6, -4, 0, -12, 0, -4, 3, 1
- 0, 2, 0, -1, 4, -9, -2, 6, -12, -4, 8, 15, 0, 2, 12, -1, 0, 6, 0, -9, -6, 2,
-  -10, -12, -4, -9, 12, -6, 2, 0, -4, 1, 18, 10, 0, 0, -12, 8, 12, -8, 8, -6,
-  -8, 4, -30, 8, 0, -6, -4, 9, 0, -1, 2, 3, 0, 5, -12, 4, 8, 9, 18, -15, 6, 0
- , -4, -18, 0, 4, 24, 2, 4, 12, 18, 0, -24, 4, 12, -30, -2]
- ? ellan(acurve,100)==deu
- 1
- ? ellisoncurve(acurve,apoint)
- 1
- ? acurve=ellchangecurve(acurve,[-1,1,2,3])
- [-4, -1, -7, -12, -12, 12, 4, 1, -1, 48, -216, 37, 110592/37, [-0.1624345647
- 1667696455518910092496975960, -0.73040556359455544173706204865073999595, -2.
- 1071598716887675937077488504242902445]~, -2.99345864623195962983200997945250
- 81778, 2.4513893819867900608542248318665252254*I, -0.94263855591362295176518
- 779416067539931, -1.3270305788796764757190502098362372906*I, 7.3381327407895
- 767390707210033323055880]
- ? apoint=ellchangepoint(apoint,[-1,1,2,3])
- [1, 3]
- ? ellisoncurve(acurve,apoint)
- 1
- ? ellglobalred(acurve)
- [37, [1, -1, 2, 2], 1]
- ? ellheight(acurve,apoint)
- 0.81778253183950144377417759611107234575
- ? ellheight(acurve,apoint,1)
- 0.81778253183950144377417759611107234576
- ? ellordinate(acurve,1)
- [8, 3]
- ? ellpointtoz(acurve,apoint)
- 0.72491221490962306778878739838332384646 + 7.589868072444759051 E-59*I
- ? ellztopoint(acurve,%)
- [0.99999999999999999999999999999999999994 - 3.794934036222379527 E-58*I, 2.9
- 999999999999999999999999999999999998 + 0.E-37*I]
- ? ellpow(acurve,apoint,10)
- [-28919032218753260057646013785951999/292736325329248127651484680640160000, 
- 478051489392386968218136375373985436596569736643531551/158385319626308443937
- 475969221994173751192384064000000]
- ? ellwp(acurve,,,32)
- x^-2 + 1/5*x^2 - 1/28*x^4 + 1/75*x^6 - 3/1540*x^8 + 1943/3822000*x^10 - 1/11
- 550*x^12 + 193/10510500*x^14 - 1269/392392000*x^16 + 21859/34684650000*x^18 
- - 1087/9669660000*x^20 + 22179331/1060517858400000*x^22 - 463/124093970000*x
- ^24 + 47495017/70175140035000000*x^26 - 34997918161/291117454720092000000*x^
- 28 + O(x^30)
- ? q*Ser(ellan(acurve,100),q)
- q - 2*q^2 - 3*q^3 + 2*q^4 - 2*q^5 + 6*q^6 - q^7 + 6*q^9 + 4*q^10 - 5*q^11 - 
- 6*q^12 - 2*q^13 + 2*q^14 + 6*q^15 - 4*q^16 - 12*q^18 - 4*q^20 + 3*q^21 + 10*
- q^22 + 2*q^23 - q^25 + 4*q^26 - 9*q^27 - 2*q^28 + 6*q^29 - 12*q^30 - 4*q^31 
- + 8*q^32 + 15*q^33 + 2*q^35 + 12*q^36 - q^37 + 6*q^39 - 9*q^41 - 6*q^42 + 2*
- q^43 - 10*q^44 - 12*q^45 - 4*q^46 - 9*q^47 + 12*q^48 - 6*q^49 + 2*q^50 - 4*q
- ^52 + q^53 + 18*q^54 + 10*q^55 - 12*q^58 + 8*q^59 + 12*q^60 - 8*q^61 + 8*q^6
- 2 - 6*q^63 - 8*q^64 + 4*q^65 - 30*q^66 + 8*q^67 - 6*q^69 - 4*q^70 + 9*q^71 -
-  q^73 + 2*q^74 + 3*q^75 + 5*q^77 - 12*q^78 + 4*q^79 + 8*q^80 + 9*q^81 + 18*q
- ^82 - 15*q^83 + 6*q^84 - 4*q^86 - 18*q^87 + 4*q^89 + 24*q^90 + 2*q^91 + 4*q^
- 92 + 12*q^93 + 18*q^94 - 24*q^96 + 4*q^97 + 12*q^98 - 30*q^99 - 2*q^100 + O(
- q^101)
- ? bcurve=ellinit([0,0,0,-3,0])
- [0, 0, 0, -3, 0, 0, -6, 0, -9, 144, 0, 1728, 1728, [1.7320508075688772935274
- 463415058723669, 0.E-57, -1.7320508075688772935274463415058723669]~, 1.99233
- 28995834907073368080310227454215, -1.9923328995834907073368080310227454215*I
- , 1.5768412268083121362312158419045774608, 1.5768412268083121362312158419045
- 774608*I, 3.9693903827627596663162680332564652025]
- ? elllocalred(bcurve,2)
- [6, 2, [1, 1, 1, 0], 1]
- ? elltaniyama(bcurve)
- [x^-2 - x^2 + 3*x^6 - 2*x^10 + 7*x^14 + O(x^15), -x^-3 + 3*x - 3*x^5 + 8*x^9
-  - 9*x^13 + O(x^14)]
- ? ccurve=ellinit([0,0,-1,-1,0])
- [0, 0, -1, -1, 0, 0, -2, 1, -1, 48, -216, 37, 110592/37, [0.8375654352833230
- 3544481089907503024040, 0.26959443640544455826293795134926000405, -1.1071598
- 716887675937077488504242902445]~, 2.9934586462319596298320099794525081778, -
- 2.4513893819867900608542248318665252254*I, 0.9426385559136229517651877941606
- 7539931, 1.3270305788796764757190502098362372906*I, 7.3381327407895767390707
- 210033323055880]
- ? l=elllseries(ccurve,2)
- 0.38157540826071121129371040958008663664
- ? elllseries(ccurve,2,1.2)-l
- 2.292213984103460641 E-37
- ? tcurve=ellinit([1,0,1,-19,26]);
- ? ellorder(tcurve,[1,2])
- 6
- ? elltors(tcurve)
- [12, [6, 2], [[-2, 8], [3, -2]]]
- ? mcurve=ellinit([0,0,0,-17,0])
- [0, 0, 0, -17, 0, 0, -34, 0, -289, 816, 0, 314432, 1728, [4.1231056256176605
- 498214098559740770251, 0.E-57, -4.1231056256176605498214098559740770251]~, 1
- .2913084409290072207105564235857096010, -1.291308440929007220710556423585709
- 6010*I, 2.4328754881596176532948539893637583869, 2.4328754881596176532948539
- 893637583869*I, 1.6674774896145033307120230298772362382]
- ? mpoints=[[-1,4],[-4,2]]~
- [[-1, 4], [-4, 2]]~
- ? mhbi=ellbil(mcurve,mpoints,[9,24])
- [-0.72448571035980184146215805860545027441, 1.307328627832055544492943428892
- 1943056]~
- ? ma=ellheightmatrix(mcurve,mpoints)
- 
- [1.1721830987006970106016415566698834135 0.447697388340895169139483498064433
- 13906]
- 
- [0.44769738834089516913948349806443313906 1.75502601617295071363242692695662
- 74446]
- 
- ? matsolve(ma,mhbi)
- [-1.0000000000000000000000000000000000000, 1.0000000000000000000000000000000
- 000000]~
- ? cmcurve=ellinit([0,-3/4,0,-2,-1])
- [0, -3/4, 0, -2, -1, -3, -4, -4, -1, 105, 1323, -343, -3375, [2.000000000000
- 0000000000000000000000000, -0.62500000000000000000000000000000000000 + 0.330
- 71891388307382381270196920490755321*I, -0.6250000000000000000000000000000000
- 0000 - 0.33071891388307382381270196920490755321*I]~, 1.933311705616811546733
- 0768390298137311, -0.96665585280840577336653841951490686553 - 2.557530989916
- 0994790492257969408742850*I, 1.7116972661997117051282981581331545224 - 8.816
- 207631167156310 E-39*I, -0.85584863309985585256414907906657726121 + 0.985597
- 14813873164489992761459498878368*I, 4.9445046002825467364981969681843776445]
- ? ellpow(cmcurve,[x,y],quadgen(-7))
- [((-2 + 3*w)*x^2 + (6 - w))/((-2 - 5*w)*x + (-4 - 2*w)), ((34 - 11*w)*y*x^2 
- + (40 - 28*w)*y*x + (22 + 23*w)*y)/((-90 - w)*x^2 + (-136 + 44*w)*x + (-40 +
-  28*w))]
- ? \p96
-    realprecision = 96 significant digits
- ? precision(cmcurve)
- 38
- ? getheap
- [57, 4395]
- ? print("Total time spent: ",gettime);
- Total time spent: 12
--- 0 ----

<sumiter-dyn.dif>:
*** ../src/test/64/sumiter	Mon May 30 02:28:26 2011
--- gp.out	Wed Sep 21 13:20:18 2011
***************
*** 1,44 ****
     realprecision = 19 significant digits
-    echo = 1 (on)
- ? gettime;intnum(x=0,Pi,sin(x))
- 2.000000000000000000
- ? intnum(x=0,4,exp(-x^2))
- 0.8862269117895689458
- ? intnum(x=1,[1],1/(1+x^2))-Pi/4
- 0.E-19
- ? intnum(x=-0.5,0.5,1/sqrt(1-x^2))-Pi/3
- 0.E-18
- ? intnum(x=0,[[1],-I],sin(x)/x)-Pi/2
- 0.E-18
- ? \p38
-    realprecision = 38 significant digits
- ? prod(k=1,10,1+1/k!)
- 3335784368058308553334783/905932868585678438400000
- ? prod(k=1,10,1+1./k!)
- 3.6821540356142043935732308433185262946
- ? Pi^2/6*prodeuler(p=2,10000,1-p^-2)
- 1.0000098157493066238697591433298145196
- ? prodinf(n=0,(1+2^-n)/(1+2^(-n+1)))
- 0.33333333333333333333333333333333333320
- ? prodinf(n=0,-2^-n/(1+2^(-n+1)),1)
- 0.33333333333333333333333333333333333320
- ? solve(x=1,4,sin(x))
- 3.1415926535897932384626433832795028842
- ? sum(k=1,10,2^-k)
- 1023/1024
- ? sum(k=1,10,2.^-k)
- 0.99902343750000000000000000000000000000
- ? 4*sumalt(n=0,(-1)^n/(2*n+1))
- 3.1415926535897932384626433832795028842
- ? 4*sumalt(n=0,(-1)^n/(2*n+1),1)
- 3.1415926535897932384626433832795028842
- ? sumdiv(8!,x,x)
- 159120
- ? suminf(n=1,2.^-n)
- 1.0000000000000000000000000000000000000
- ? 6/Pi^2*sumpos(n=1,n^-2)
- 1.0000000000000000000000000000000000000
- ? getheap
- [20, 170]
- ? print("Total time spent: ",gettime);
- Total time spent: 24
--- 1 ----

<graph-dyn.dif>:
*** ../src/test/64/graph	Mon May 30 02:28:26 2011
--- gp.out	Wed Sep 21 13:20:18 2011
***************
*** 1,66 ****
-    echo = 1 (on)
- ? gettime;plotinit(0,500,500)
- ? plotmove(0,0,0);plotbox(0,500,500)
- ? plotmove(0,200,150)
- ? plotcursor(0)
- [200, 150]
- ? psdraw([0,0,0])
- ? plotinit(1,700,700)
- ? plotkill(1)
- ? plotmove(0,0,900);plotlines(0,900,0)
- ? plotlines(0,vector(5,k,50*k),vector(5,k,10*k*k))
- ? plotmove(0,243,583);plotcursor(0)
- [243, 583]
- ? plot(x=-5,5,sin(x))
- 
- 0.9995545 x""x_''''''''''''''''''''''''''''''''''_x""x'''''''''''''''''''|
-           |    x                                _     "_                 |
-           |     x                              _        _                |
-           |      x                            _                          |
-           |       _                                      "               |
-           |                                  "            x              |
-           |        x                        _                            |
-           |                                                "             |
-           |         "                      x                _            |
-           |          _                                                   |
-           |                               "                  x           |
-           ````````````x``````````````````_````````````````````````````````
-           |                                                   "          |
-           |            "                x                      _         |
-           |             _                                                |
-           |                            "                        x        |
-           |              x            _                                  |
-           |               _                                      "       |
-           |                          "                            x      |
-           |                "        "                              x     |
-           |                 "_     "                                x    |
- -0.999555 |...................x__x".................................."x__x
-           -5                                                             5
- ? plotpoints(0,225,334)
- ? plotpoints(0,vector(10,k,10*k),vector(10,k,5*k*k))
- ? psdraw([0,20,20])
- ? psploth(x=-5,5,sin(x))
- [-5.000000000000000000, 5.000000000000000000, -0.9999964107564721649, 0.9999
- 964107564721649]
- ? psploth(t=0,2*Pi,[sin(5*t),sin(7*t)],1,100)
- [-0.9998741276738750683, 0.9998741276738750683, -0.9998741276738750683, 0.99
- 98741276738750683]
- ? psplothraw(vector(100,k,k),vector(100,k,k*k/100))
- [1.0000000000000000000, 100.00000000000000000, 0.010000000000000000208, 100.
- 00000000000000000]
- ? plotmove(0,50,50);plotrbox(0,50,50)
- ? plotrline(0,200,150)
- ? plotcursor(0)
- [250, 200]
- ? plotrmove(0,5,5);plotcursor(0)
- [255, 205]
- ? plotrpoint(0,20,20)
- ? plotinit(3,600,600);plotscale(3,-7,7,-2,2);plotcursor(3)
- [-7, 2]
- ? plotmove(0,100,100);plotstring(0,Pi)
- ? plotmove(0,200,200);plotstring(0,"(0,0)")
- ? psdraw([0,10,10])
- ? getheap
- [9, 137]
- ? print("Total time spent: ",gettime);
- Total time spent: 12
--- 0 ----

<program-dyn.dif>:
*** ../src/test/64/program	Mon May 30 02:28:26 2011
--- gp.out	Wed Sep 21 13:20:18 2011
***************
*** 1,135 ****
-    echo = 1 (on)
- ? gettime;alias(ln,log)
- ? ln(2)
- 0.69314718055994530941723212145817656808
- ? for(x=1,5,print(x!))
- 1
- 2
- 6
- 24
- 120
- ? fordiv(10,x,print(x))
- 1
- 2
- 5
- 10
- ? forprime(p=1,30,print(p))
- 2
- 3
- 5
- 7
- 11
- 13
- 17
- 19
- 23
- 29
- ? forstep(x=0,Pi,Pi/12,print(sin(x)))
- 0.E-38
- 0.25881904510252076234889883762404832835
- 0.50000000000000000000000000000000000000
- 0.70710678118654752440084436210484903928
- 0.86602540378443864676372317075293618347
- 0.96592582628906828674974319972889736763
- 1.0000000000000000000000000000000000000
- 0.96592582628906828674974319972889736764
- 0.86602540378443864676372317075293618348
- 0.70710678118654752440084436210484903931
- 0.50000000000000000000000000000000000003
- 0.25881904510252076234889883762404832839
- 4.701977403289150032 E-38
- ? forvec(x=[[1,3],[-2,2]],print1([x[1],x[2]]," "));print(" ");
- [1, -2] [1, -1] [1, 0] [1, 1] [1, 2] [2, -2] [2, -1] [2, 0] [2, 1] [2, 2] [3
- , -2] [3, -1] [3, 0] [3, 1] [3, 2]  
- ? getheap
- [4, 31]
- ? getrand
- Vecsmall([815394335184717944, 4549279032150680234, 6773728374826070157, -237
- 0373754265190617, -7192197643876677099, 3146002372671609152, -37889119021821
- 81465, -3110751447065112512, -7839888805667742928, -1750047523337007702, -48
- 13916526844204946, 2197460154196732106, 2172222412836515817, 750148670758846
- 8027, -2859630236012475958, -7521563591744261058, -5098751749791804186, -493
- 2847221747616924, -83017490560352414, 909833191470153253, -68907000334182407
- 26, -2667729487396035417, 7945873742069551774, -8335875119100634420, -269516
- 2268485432158, 907840774270685481, -2649846143482627435, 4432371968824575795
- , 675084127798063203, 1330710101237874403, -3282824841646116129, 66137656958
- 55811188, -4997019453007867026, -2517134063026061436, 6601608070123470072, 8
- 315730897074524817, 7382824712320294655, 8382147984209176484, 61195565499152
- 33413, -6473138824261887547, 3868662552751602358, -7049890781912985631, 5825
- 089164294808030, -747565901986682173, -3706701696228594999, 8547465356109452
- 89, -2464579454622871361, -6442828218203469284, 7444846227663661231, -159718
- 0339169755613, 1305732653808028370, 4846884492315410984, -592680480505270414
- 1, -5320891424889011357, -7613917326037722204, 4603012696960730681, -4168740
- 837400896895, 8981763047278317166, 7331246918389417837, -4002039446830895798
- , 4582267480000687864, -7629613429408037667, 4813661187837882458, -776313336
- 5088963398, 63, 3001673639903682625])
- ? getstack
- 200
- ? if(3<2,print("bof"),print("ok"));
- ok
- ? kill(y);print(x+y);
- x + y
- ? f(u)=u+1;
- ? print(f(5));kill(f);
- 6
- ? f=12
- 12
- ? g(u)=if(u,,return(17));u+2
- (u)->if(u,,return(17));u+2
- ? g(2)
- 4
- ? g(0)
- 17
- ? setrand(10)
- ? n=33;until(n==1,print1(n," ");if(n%2,n=3*n+1,n=n/2));print(1)
- 33 100 50 25 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1
- ? m=5;while(m<20,print1(m," ");m=m+1);print()
- 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 
- ? default(realprecision,28)
- ? default(seriesprecision,12)
- ? print((x-12*y)/(y+13*x));
- (x - 12*y)/(13*x + y)
- ? print([1,2;3,4])
- [1, 2; 3, 4]
- ? print1(x+y);print(x+y);
- x + yx + y
- ? print((x-12*y)/(y+13*x));
- (x - 12*y)/(13*x + y)
- ? print([1,2;3,4])
- [1, 2; 3, 4]
- ? print1(x+y);print1(" equals ");print(x+y);
- x + y equals x + y
- ? print1("give a value for s? ");s=input();print(1/(s^2+1))
- give a value for s? printtex((x+y)^3/(x-y)^2)
- \frac{x^3
-  + 3 y x^2
-  + 3 y^2 x
-  + y^3}{x^2
-  - 2 y x
-  + y^2}
- 1
- ? for(i=1,100,for(j=1,25,if(i+j==32,break(2)));print(i))
- 1
- 2
- 3
- 4
- 5
- 6
- ? u=v=p=q=1;for(k=1,400,w=u+v;u=v;v=w;p*=w;q=lcm(q,w);if(k%50==0,print(k" "l
- og(p)/log(q))));
- 50 1.561229126903099279206171725
- 100 1.601335375590875348711141031
- 150 1.606915548673659127523394774
- 200 1.618659998991528481508175176
- 250 1.626284706204746765086080988
- 300 1.627822776845103001192024532
- 350 1.632105905172986668189652273
- 400 1.632424285532931448171405619
- ? install(addii,GG)
- ? addii(1,2)
- 3
- ? kill(addii)
- ? getheap
- [23, 1822]
- ? print("Total time spent: ",gettime);
- Total time spent: 8
--- 0 ----

<trans-dyn.dif>:
*** ../src/test/64/trans	Mon May 30 02:28:26 2011
--- gp.out	Wed Sep 21 13:20:18 2011
***************
*** 1,432 ****
     realprecision = 2003 significant digits (2000 digits displayed)
-    echo = 1 (on)
- ? gettime;abs(-0.01)
- 0.01000000000000000000000000000000000000000000000000000000000000000000000000
- 0000000000000000000000000000000000000000000000000000000000000000000000000000
- 0000000000000000000000000000000000000000000000000000000000000000000000000000
- 0000000000000000000000000000000000000000000000000000000000000000000000000000
- 0000000000000000000000000000000000000000000000000000000000000000000000000000
- 0000000000000000000000000000000000000000000000000000000000000000000000000000
- 0000000000000000000000000000000000000000000000000000000000000000000000000000
- 0000000000000000000000000000000000000000000000000000000000000000000000000000
- 0000000000000000000000000000000000000000000000000000000000000000000000000000
- 0000000000000000000000000000000000000000000000000000000000000000000000000000
- 0000000000000000000000000000000000000000000000000000000000000000000000000000
- 0000000000000000000000000000000000000000000000000000000000000000000000000000
- 0000000000000000000000000000000000000000000000000000000000000000000000000000
- 0000000000000000000000000000000000000000000000000000000000000000000000000000
- 0000000000000000000000000000000000000000000000000000000000000000000000000000
- 0000000000000000000000000000000000000000000000000000000000000000000000000000
- 0000000000000000000000000000000000000000000000000000000000000000000000000000
- 0000000000000000000000000000000000000000000000000000000000000000000000000000
- 0000000000000000000000000000000000000000000000000000000000000000000000000000
- 0000000000000000000000000000000000000000000000000000000000000000000000000000
- 0000000000000000000000000000000000000000000000000000000000000000000000000000
- 0000000000000000000000000000000000000000000000000000000000000000000000000000
- 0000000000000000000000000000000000000000000000000000000000000000000000000000
- 0000000000000000000000000000000000000000000000000000000000000000000000000000
- 0000000000000000000000000000000000000000000000000000000000000000000000000000
- 0000000000000000000000000000000000000000000000000000000000000000000000000000
- 000000000000000000000000000
- ? agm(1,2)
- 1.45679103104690686918643238326508197497386394322130559079417238326792645458
- 0250900257473712818448444328189401816036799935576243074340124511691213249952
- 2793768970211976726893728266666782707432902072384564600963133367494416649516
- 4008269322390862633767383824102548872626451365906604088758851004667281309474
- 3978935512911720175447186956416035641113070606125170400972745374521370401420
- 1441576823232389645029091322392292018630204591966775362115295609984320494009
- 6186133886391108403038148862815907317011423554730230353362620898683561308007
- 5985703121250813571733533606272496417145565136129415437696905495272776402217
- 1898328404019382434954163396634111712470749200493994758236553202742331569542
- 1876892595105619103413471250457295583940482770732998417330233202020190654108
- 3764475690954512308594220997449412380273230046465841574004772512701790771147
- 6178286660643441589473410355454995401702603050129297014707762364655074858504
- 2893120294754259839628734570376126531045680923276419320475962493117272367678
- 4849010063883831645335627155765372880260543270126668904548807658246837332956
- 7456063204392060008273159252979241205175727929568980698371820180811180125021
- 3108997246951100317036787543001787446227930192106015685776149083936743191510
- 5478717272782446538831715921363968336746689231345994523668360452657260101103
- 3970534995271323625630073974543738138730451563908543487241207008447748794693
- 7515044344604858428093017239592603673212918887571985640286492629881099516041
- 7385214470404976503137921156910217010840121652176385776278443131535045190731
- 0748437504378670908384466987679450508904899924299954903140622820681590930451
- 6140452345824869722715061998188837843566441517471116059500690242314345907596
- 6810454416997061373268370421830924936517791683419258027937814913005585514983
- 9054216129918366396073532425917284089191304056017436113358867622552811309835
- 6883812066118653768412057434259281956810028485877428124011968982035483804304
- 1113162808407169939503577633814675423251711145297625856010709698328986771681
- 3002707534621244314382491
- ? agm(1+O(7^5),8+O(7^5))
- 1 + 4*7 + 6*7^2 + 5*7^3 + 2*7^4 + O(7^5)
- ? 4*arg(3+3*I)
- 3.14159265358979323846264338327950288419716939937510582097494459230781640628
- 6208998628034825342117067982148086513282306647093844609550582231725359408128
- 4811174502841027019385211055596446229489549303819644288109756659334461284756
- 4823378678316527120190914564856692346034861045432664821339360726024914127372
- 4587006606315588174881520920962829254091715364367892590360011330530548820466
- 5213841469519415116094330572703657595919530921861173819326117931051185480744
- 6237996274956735188575272489122793818301194912983367336244065664308602139494
- 6395224737190702179860943702770539217176293176752384674818467669405132000568
- 1271452635608277857713427577896091736371787214684409012249534301465495853710
- 5079227968925892354201995611212902196086403441815981362977477130996051870721
- 1349999998372978049951059731732816096318595024459455346908302642522308253344
- 6850352619311881710100031378387528865875332083814206171776691473035982534904
- 2875546873115956286388235378759375195778185778053217122680661300192787661119
- 5909216420198938095257201065485863278865936153381827968230301952035301852968
- 9957736225994138912497217752834791315155748572424541506959508295331168617278
- 5588907509838175463746493931925506040092770167113900984882401285836160356370
- 7660104710181942955596198946767837449448255379774726847104047534646208046684
- 2590694912933136770289891521047521620569660240580381501935112533824300355876
- 4024749647326391419927260426992279678235478163600934172164121992458631503028
- 6182974555706749838505494588586926995690927210797509302955321165344987202755
- 9602364806654991198818347977535663698074265425278625518184175746728909777727
- 9380008164706001614524919217321721477235014144197356854816136115735255213347
- 5741849468438523323907394143334547762416862518983569485562099219222184272550
- 2542568876717904946016534668049886272327917860857843838279679766814541009538
- 8378636095068006422512520511739298489608412848862694560424196528502221066118
- 6306744278622039194945047123713786960956364371917287467764657573962413890865
- 8326459958133904780275901
- ? bernreal(12)
- -0.2531135531135531135531135531135531135531135531135531135531135531135531135
- 5311355311355311355311355311355311355311355311355311355311355311355311355311
- 3553113553113553113553113553113553113553113553113553113553113553113553113553
- 1135531135531135531135531135531135531135531135531135531135531135531135531135
- 5311355311355311355311355311355311355311355311355311355311355311355311355311
- 3553113553113553113553113553113553113553113553113553113553113553113553113553
- 1135531135531135531135531135531135531135531135531135531135531135531135531135
- 5311355311355311355311355311355311355311355311355311355311355311355311355311
- 3553113553113553113553113553113553113553113553113553113553113553113553113553
- 1135531135531135531135531135531135531135531135531135531135531135531135531135
- 5311355311355311355311355311355311355311355311355311355311355311355311355311
- 3553113553113553113553113553113553113553113553113553113553113553113553113553
- 1135531135531135531135531135531135531135531135531135531135531135531135531135
- 5311355311355311355311355311355311355311355311355311355311355311355311355311
- 3553113553113553113553113553113553113553113553113553113553113553113553113553
- 1135531135531135531135531135531135531135531135531135531135531135531135531135
- 5311355311355311355311355311355311355311355311355311355311355311355311355311
- 3553113553113553113553113553113553113553113553113553113553113553113553113553
- 1135531135531135531135531135531135531135531135531135531135531135531135531135
- 5311355311355311355311355311355311355311355311355311355311355311355311355311
- 3553113553113553113553113553113553113553113553113553113553113553113553113553
- 1135531135531135531135531135531135531135531135531135531135531135531135531135
- 5311355311355311355311355311355311355311355311355311355311355311355311355311
- 3553113553113553113553113553113553113553113553113553113553113553113553113553
- 1135531135531135531135531135531135531135531135531135531135531135531135531135
- 5311355311355311355311355311355311355311355311355311355311355311355311355311
- 355311355311355311355311355
- ? bernvec(6)
- [1, 1/6, -1/30, 1/42, -1/30, 5/66, -691/2730]
- ? eta(q)
- 1 - q - q^2 + q^5 + q^7 - q^12 - q^15 + O(q^17)
- ? gammah(10)
- 1133278.38894878556733457416558889247556029830827515977660872341452948339005
- 6004153717630538727607290658350271700893237334889580173178076577597995379664
- 6009714415152490764416630481375706606053932396039541459764525989187023837695
- 1671610855238044170151137400635358652611835795089229729903867565432085491785
- 4385740637379886563030379410949122020517030255827739818376409926875136586189
- 2723863412249690833216320407918186480305202146014474770321625907339955121137
- 5592642390902407584016964257200480120814533383602757695668466603948271024098
- 9327940404023866529740516995285324916879158647845355052036653927090566136730
- 0094575478250332011940143726954935586482054200041299507288301750480889450074
- 6343904971296912338686722783533463981407672637863409944118391772608796763236
- 9447079178552767334696553209914181695759970997941993901164691598147347830004
- 4823839605663115658079374350293361148126253885222073444191541294051101114944
- 2148757269775793389728426903218921936202601614618932645339512192242743521391
- 3623655029508006651504215607326378350230912034475135438952688674605137188671
- 8291478726407002040566684129567384943465438236552781293212272474626739330722
- 3823357944724162685811265841905467657996783321819427448381523647154314724898
- 8856361879313902224622692050075011483135711717132961476630033785190129658511
- 7517708668749218485078393526224163290497667641778463362558549256811856160652
- 4106684792418747471383982225174086085681964985490608637796815226536639176681
- 1441751691654768874563756211537865821827254193841183086848150171014212517613
- 4162649414056791266931385305249721381461657257845049119527820872404022311592
- 3493153739717855496390762049815239940623016182617392553134094087438136687759
- 5419535805662758475769269988659439227267578534611414012815013931015921875970
- 6336658641047462598114625941565529553227923237890531007539153745378752638260
- 5084066808355122734552729235496172099847732335381840125710668124155748264901
- 6432532465927671474115401431858884909633728259417038958526362232126251606829
- 1066841997114282966060548
- ? Pi
- 3.14159265358979323846264338327950288419716939937510582097494459230781640628
- 6208998628034825342117067982148086513282306647093844609550582231725359408128
- 4811174502841027019385211055596446229489549303819644288109756659334461284756
- 4823378678316527120190914564856692346034861045432664821339360726024914127372
- 4587006606315588174881520920962829254091715364367892590360011330530548820466
- 5213841469519415116094330572703657595919530921861173819326117931051185480744
- 6237996274956735188575272489122793818301194912983367336244065664308602139494
- 6395224737190702179860943702770539217176293176752384674818467669405132000568
- 1271452635608277857713427577896091736371787214684409012249534301465495853710
- 5079227968925892354201995611212902196086403441815981362977477130996051870721
- 1349999998372978049951059731732816096318595024459455346908302642522308253344
- 6850352619311881710100031378387528865875332083814206171776691473035982534904
- 2875546873115956286388235378759375195778185778053217122680661300192787661119
- 5909216420198938095257201065485863278865936153381827968230301952035301852968
- 9957736225994138912497217752834791315155748572424541506959508295331168617278
- 5588907509838175463746493931925506040092770167113900984882401285836160356370
- 7660104710181942955596198946767837449448255379774726847104047534646208046684
- 2590694912933136770289891521047521620569660240580381501935112533824300355876
- 4024749647326391419927260426992279678235478163600934172164121992458631503028
- 6182974555706749838505494588586926995690927210797509302955321165344987202755
- 9602364806654991198818347977535663698074265425278625518184175746728909777727
- 9380008164706001614524919217321721477235014144197356854816136115735255213347
- 5741849468438523323907394143334547762416862518983569485562099219222184272550
- 2542568876717904946016534668049886272327917860857843838279679766814541009538
- 8378636095068006422512520511739298489608412848862694560424196528502221066118
- 6306744278622039194945047123713786960956364371917287467764657573962413890865
- 8326459958133904780275901
- ? precision(Pi,20)
- 3.14159265358979323846264338327950288420
- ? sqr(1+O(2))
- 1 + O(2^3)
- ? sqrt(13+O(127^12))
- 34 + 125*127 + 83*127^2 + 107*127^3 + 53*127^4 + 42*127^5 + 22*127^6 + 98*12
- 7^7 + 127^8 + 23*127^9 + 122*127^10 + 79*127^11 + O(127^12)
- ? teichmuller(7+O(127^12))
- 7 + 57*127 + 58*127^2 + 83*127^3 + 52*127^4 + 109*127^5 + 74*127^6 + 16*127^
- 7 + 60*127^8 + 47*127^9 + 65*127^10 + 5*127^11 + O(127^12)
- ? \p500
-    realprecision = 500 significant digits
- ? Euler
- 0.57721566490153286060651209008240243104215933593992359880576723488486772677
- 7664670936947063291746749514631447249807082480960504014486542836224173997644
- 9235362535003337429373377376739427925952582470949160087352039481656708532331
- 5177661152862119950150798479374508570574002992135478614669402960432542151905
- 8775535267331399254012967420513754139549111685102807984234877587205038431093
- 9973613725530608893312676001724795378367592713515772261027349291394079843010
- 3417771778088154957066107501016191663340152279
- ? acos(0.5)
- 1.04719755119659774615421446109316762806572313312503527365831486410260546876
- 2069666209344941780705689327382695504427435549031281536516860743908453136042
- 8270391500947009006461737018532148743163183101273214762703252219778153761585
- 4941126226105509040063638188285564115344953681810888273779786908674971375790
- 8195668868771862724960506973654276418030571788122630863453337110176849606822
- 1737947156506471705364776857567885865306510307287057939775372643683728493581
- 541266542498557839619175749637426460610039831
- ? acosh(3)
- 1.76274717403908605046521864995958461805632065652327082150659121730675436844
- 4052175667413783820512085713479632384212984377524145023953183875054510925531
- 5808184431573607257943924806147148192510979557431265247356130135260657908083
- 2711638011905460870335948934683023103172356012785221262668194525145789831496
- 9445764001529311893860982812579887622449034763169345542526389217689105106337
- 1787365189299048490338319777210134365908031791918295896639410019154526845141
- 480345838118685682417318463628901744528191443
- ? 3*asin(sqrt(3)/2)
- 3.14159265358979323846264338327950288419716939937510582097494459230781640628
- 6208998628034825342117067982148086513282306647093844609550582231725359408128
- 4811174502841027019385211055596446229489549303819644288109756659334461284756
- 4823378678316527120190914564856692346034861045432664821339360726024914127372
- 4587006606315588174881520920962829254091715364367892590360011330530548820466
- 5213841469519415116094330572703657595919530921861173819326117931051185480744
- 623799627495673518857527248912279381830119491
- ? asinh(0.5)
- 0.48121182505960344749775891342436842313518433438566051966101816884016386760
- 8221774412009429122723474997231839958293656411272568323726737622753059241864
- 4097541824170072118371502238239374691872752432791930187970790035617267969445
- 4575230534543418876528553256490207399693496618755630102123996367930820635997
- 7988509980156825797852649328666651116241713808272592788479026096533113247227
- 5149314064985088932176366002566661953210679681757661847307351598603984845754
- 5412056323413570047800639487224315261789680045
- ? 3*atan(sqrt(3))
- 3.14159265358979323846264338327950288419716939937510582097494459230781640628
- 6208998628034825342117067982148086513282306647093844609550582231725359408128
- 4811174502841027019385211055596446229489549303819644288109756659334461284756
- 4823378678316527120190914564856692346034861045432664821339360726024914127372
- 4587006606315588174881520920962829254091715364367892590360011330530548820466
- 5213841469519415116094330572703657595919530921861173819326117931051185480744
- 623799627495673518857527248912279381830119491
- ? atanh(0.5)
- 0.54930614433405484569762261846126285232374527891137472586734716681874714660
- 9304483436807877406866044393985014532978932871184002112965259910526400935383
- 6387053015813845916906835896868494221804799518712851583979557605727959588753
- 3567352747008338779011110158512647344878034505326075282143406901815868664928
- 8891183495827396065909074510015051911815061124326374099112995548726245448229
- 0267335044229825428742220595094285438237474335398065429147058010830605920007
- 0491275719597438444683992471511278657676648427
- ? besseljh(1,1)
- 0.24029783912342701089584304474193368045758480608072900860700721913956804181
- 9821642483230581867706826873304134469286897059613333800107373387969440858132
- 2409671228346463513063730101700769785661236389472736777787130860593313537501
- 4950471611773181090861874975058165031596147120593670107339079838226694509538
- 1174862561382806604491442967609698710345402983618630021989455840750069855186
- 9089492304665506543890102558566214670131694260158621630986009048855189842820
- 0103186464147214505293464124112486584095535336
- ? cos(1)
- 0.54030230586813971740093660744297660373231042061792222767009725538110039477
- 4471764517951856087183089343571731160030089097860633760021663456406512265417
- 3185847179711644744794942331179245513932543359435177567028925963757361543275
- 4964175449177511513122273010063135707823223677140151746899593667873067422762
- 0245077637440675874981617842720216455851115632968890571081242729331698685247
- 1456894904342375433094423024093596239583182454728173664078071243433621748100
- 3220271297578822917644683598726994264913443918
- ? cosh(1)
- 1.54308063481524377847790562075706168260152911236586370473740221471076906304
- 9223698964264726435543035587046858604423527565032194694709586290763493942377
- 3472069151633480026408029059364105029494057980033657762593319443209506958499
- 1368981037430548471273929845616039038581747145363600451873630682751434880120
- 2720574972705524471670706447103271142282939448411677273102139632958667273012
- 2826261409857215459162042522453939258584439199475134380734969475319971032521
- 055637731102374474158960765443652715148207669
- ? exp(1)
- 2.71828182845904523536028747135266249775724709369995957496696762772407663035
- 3547594571382178525166427427466391932003059921817413596629043572900334295260
- 5956307381323286279434907632338298807531952510190115738341879307021540891499
- 3488416750924476146066808226480016847741185374234544243710753907774499206955
- 1702761838606261331384583000752044933826560297606737113200709328709127443747
- 0472306969772093101416928368190255151086574637721112523897844250569536967707
- 854499699679468644549059879316368892300987931
- ? exp(1.123)
- 3.07406257154898987680161138009760625104248179708261339399712186197767466996
- 4935625311477807765382361174054209564400933143178772679923822312458571526893
- 0949675915002937652898704613739372482459452568993085662295138072557500421797
- 5971600253639265100975969190654549368799844236165029593059925114588814911583
- 9185488320031389051117206437605098919216790228388886978184284707042848120462
- 1182818728513135542290354814654148922271957843494116542832234810156127014491
- 955053641170027738831683277094167546025000529
- ? incgam(4,1,6)
- 5.88607105874307714552838032258337387913297809650828535212538882715938393191
- 8396853714356389534714299946037204429503923331951612684642064138026457431905
- 5805294751098780374098407782238580023298615198035196589516153270359568407982
- 7992725182985932743696823436032979670756942663882506560584119323653928852565
- 9814209708876601791309278295271957611829097587465878928057118995331313636440
- 2883453599077405070514506827481973857316860179666499801153515201126481557348
- 108412200404484860301786425134984607926838502
- ? incgamc(2,1)
- 0.26424111765711535680895245967707826510837773793646433098432639660507700851
- 0200393285705451308160712506745349446312009583506048414419741982746692821011
- 8024338156112652453237699027220177497087673100245600426310480841205053949002
- 1500909352126758407037897070495877541155382167014686679926985084543258893429
- 2523223786390424776086340213091005298521362801566765133992860125583585795444
- 9639568300115324366185686646564753267835392477541687524855810599859189805331
- 4864484749494393924622766968581269240091451867
- ? log(2)
- 0.69314718055994530941723212145817656807550013436025525412068000949339362196
- 9694715605863326996418687542001481020570685733685520235758130557032670751635
- 0759619307275708283714351903070386238916734711233501153644979552391204751726
- 8157493206515552473413952588295045300709532636664265410423915781495204374043
- 0385500801944170641671518644712839968171784546957026271631064546150257207402
- 4816377733896385506952606683411372738737229289564935470257626520988596932019
- 6505855476470330679365443254763274495125040607
- ? sin(Pi/6)
- 0.50000000000000000000000000000000000000000000000000000000000000000000000000
- 0000000000000000000000000000000000000000000000000000000000000000000000000000
- 0000000000000000000000000000000000000000000000000000000000000000000000000000
- 0000000000000000000000000000000000000000000000000000000000000000000000000000
- 0000000000000000000000000000000000000000000000000000000000000000000000000000
- 0000000000000000000000000000000000000000000000000000000000000000000000000000
- 0000000000000000000000000000000000000000000000
- ? sinh(1)
- 1.17520119364380145688238185059560081515571798133409587022956541301330756730
- 4323895607117452089623391840419533327579532356785218901919457282136840352883
- 2484238229689806253026878572974193778037894530156457975748559863812033933000
- 2119435713493927674792878380863977809159438228870943791837123225023064326834
- 8982186865900736859713876553648773791543620849195059840098569695750460170734
- 7646045559914877642254885845736315892502135438245978143162874775249565935186
- 798861968577094170390099113872716177152780263
- ? sqr(tan(Pi/3))
- 3.00000000000000000000000000000000000000000000000000000000000000000000000000
- 0000000000000000000000000000000000000000000000000000000000000000000000000000
- 0000000000000000000000000000000000000000000000000000000000000000000000000000
- 0000000000000000000000000000000000000000000000000000000000000000000000000000
- 0000000000000000000000000000000000000000000000000000000000000000000000000000
- 0000000000000000000000000000000000000000000000000000000000000000000000000000
- 000000000000000000000000000000000000000000000
- ? tanh(1)
- 0.76159415595576488811945828260479359041276859725793655159681050012195324457
- 6638483458947521673676714421902759701554077532368309114762485413297006669611
- 3211253965101376080877764393409926042066795531174758011305900662577831975245
- 1237997591796119707757354591410814335043351567518059703276048802963895774140
- 4110555282743457474128870116732022433666141820426521385314984008017809424940
- 5971665020197077111278076211510055741702778683601321201082307883017522102475
- 0850545493659202265152413525903793814306804484
- ? thetanullk(0.5,7)
- -804.63037320243369422783730584965684022502842525603918290428537089203649185
- 3005202838354617419978916066838351498344792388634514250685494567531066970308
- 1395985000299687911464724641787835671746030420666636980738176244141521534964
- 5910468287548147547821547802569972386188420035275376210374637455233928908304
- 8519707951113024675783203592515011343853492633432924541927657918744234297707
- 8009339159045897789510058204677594956471190358977738843586880213576194151544
- 6040652826323066997075899093444932117587282486
- ? \p210
-    realprecision = 211 significant digits (210 digits displayed)
- ? dilog(0.5)
- 0.58224052646501250590265632015968010874419847480612642543434704787317104407
- 1683200816840318587915857185644360650489146599186798136823369642378773825725
- 010992996274322284433100379999291599248198351965163954430361
- ? eint1(2)
- 0.04890051070806111956723983522804952231449218496302311632732287371169292871
- 4152191279268961007451641767339733440496339126093474911387068904573480132428
- 0606565260878276314803271231475388617592828799527149833070515
- ? lngamma(10^50*I)
- -157079632679489661923132169163975144209858469968811.93673753887608474948977
- 0941153418951907406847934940095420371647821881900698782085734298414871973667
- 351244826946727013485797329023211606491949054831345082284018 + 1141292546497
- 0228420089957273421821038005507443143864.09476847610738955343272591658130426
- 4976155641647932550343141949832879612722439831043441291767982893579577059574
- 3877177782974245137531522747279687821610884364*I
- ? polylog(5,0.5)
- 0.50840057924226870745910884925858994131954112566482164872449779635262539422
- 8780242619384210049344955062253148566177885373776251290109126927256295587733
- 653575441097747430180753135597085935261518462072899907112039
- ? polylog(-4,t)
- (t^4 + 11*t^3 + 11*t^2 + t)/(-t^5 + 5*t^4 - 10*t^3 + 10*t^2 - 5*t + 1)
- ? polylog(5,0.5,1)
- 1.03379274554168906408344764673478841754654188263517803810922886849674521856
- 8302490767987790059233900087664928281011147504065464055196977752510643903051
- 08453214093020806938180803753912648028281347292317330014656
- ? polylog(5,0.5,2)
- 1.03445942344901048625461825783418822628308099519811715037388226488478462874
- 5613316541842884367897989911634714028478465772399056966065341954518002332809
- 93803867195735501893802985262734041524337126856608372430479
- ? polylog(5,0.5,3)
- 0.94956934899649226018699647701016092398772870595673235481511016276008056001
- 9780143078976018486726179185715990894178927384257428042889858760164776911430
- 334108913396327982261675208743365007260765477862866539420350
- ? psi(1)
- -0.5772156649015328606065120900824024310421593359399235988057672348848677267
- 7766467093694706329174674951463144724980708248096050401448654283622417399764
- 4923536253500333742937337737673942792595258247094916008735204
- ? round(prod(k=1,17,x-exp(2*I*Pi*k/17)),&e)
- x^17 - 1
- ? e
- -693
- ? theta(0.5,3)
- 0.08080641825189469129987168321046629852436630463736585818145355698789812007
- 7007090242373481570553349455066987093523256662570622075796055596272586626054
- 1756288186798491280103427257359418016911094472073083250230198
- ? weber(I)
- 1.18920711500272106671749997056047591529297209246381741301900222471946666822
- 6917159870781344538137673716037394774769213186063726361789847756785360862538
- 01777507015151140355709227316234286888992417544607190871050 - 5.940911144672
- 374449 E-213*I
- ? weber(I,1)
- 1.09050773266525765920701065576070797899270271854006712178566764768330053084
- 8841840338211140494203119891451619262918090010347769026116087255320275930582
- 70136445935603377184958072509793552467405409688916300069889
- ? weber(I,2)
- 1.09050773266525765920701065576070797899270271854006712178566764768330053084
- 8841840338211140494203119891451619262918090010347769026116087255320275930582
- 70136445935603377184958072509793552467405409688916300069889
- ? zeta(3)
- 1.20205690315959428539973816151144999076498629234049888179227155534183820578
- 6313090186455873609335258146199157795260719418491995998673283213776396837207
- 90016145394178294936006671919157552224249424396156390966410
- ? \p38
-    realprecision = 38 significant digits
- ? besselk(1+I,1)
- 0.32545977186584141085464640324923711950 + 0.2894280370259921276345671592415
- 2302743*I
- ? erfc(2)
- 0.0046777349810472658379307436327470713891
- ? gamma(10.5)
- 1133278.3889487855673345741655888924756
- ? hyperu(1,1,1)
- 0.59634736232319407434107849936927937607
- ? incgam(2,1)
- 0.73575888234288464319104754032292173491
- ? zeta(0.5+14.1347251*I)
- 5.2043097453468479398562848599360610966 E-9 - 3.2690639869786982176409251733
- 763732423 E-8*I
- ? getheap
- [60, 3954]
- ? print("Total time spent: ",gettime);
- Total time spent: 32
--- 1 ----

<nfields-dyn.dif>:
*** ../src/test/64/nfields	Mon May 30 02:28:26 2011
--- gp.out	Wed Sep 21 13:20:18 2011
***************
*** 1,1035 ****
-    echo = 1 (on)
- ? gettime;p2=Pol([1,3021,-786303,-6826636057,-546603588746,3853890514072057]
- )
- x^5 + 3021*x^4 - 786303*x^3 - 6826636057*x^2 - 546603588746*x + 385389051407
- 2057
- ? fa=[11699,6;2392997,2;4987333019653,2]
- 
- [11699 6]
- 
- [2392997 2]
- 
- [4987333019653 2]
- 
- ? setrand(1);a=matrix(3,5,j,k,vectorv(5,l,random\10^8));
- ? setrand(1);as=matrix(3,3,j,k,vectorv(5,l,random\10^8));
- ? nfpol=x^5-5*x^3+5*x+25;nf=nfinit(nfpol)
- [x^5 - 5*x^3 + 5*x + 25, [1, 2], 595125, 45, [[1, -1.08911514572050482502495
- 27946671612684, -2.4285174907194186068992069565359418365, 0.7194669112891317
- 8943997506477288225737, -2.5558200350691694950646071159426779972; 1, -0.1383
- 8372073406036365047976417441696637 - 0.4918163765776864349975328551474152510
- 7*I, 1.9647119211288133163138753392090569931 + 0.809714924188978951282940822
- 19556466857*I, -0.072312766896812300380582649294307897075 + 2.19808037538462
- 76641195195160383234878*I, -0.98796319352507039803950539735452837193 + 1.570
- 1452385894131769052374806001981109*I; 1, 1.682941293594312776162956161507997
- 6006 + 2.0500351226010726172974286983598602164*I, -0.75045317576910401286427
- 186094108607489 + 1.3101462685358123283560773619310445916*I, -0.787420688747
- 75359433940488309213323154 + 2.1336633893126618034168454610457936018*I, 1.26
- 58732110596551455718089553258673705 - 2.716479010374315056657802803578983483
- 5*I], [1, -1.0891151457205048250249527946671612684, -2.428517490719418606899
- 2069565359418365, 0.71946691128913178943997506477288225737, -2.5558200350691
- 694950646071159426779972; 1, -0.63020009731174679864801261932183221743, 2.77
- 44268453177922675968161614046216617, 2.1257676084878153637389368667440155907
- , 0.58218204506434277886573208324566973897; 1, 0.353432655843626071347053090
- 97299828470, 1.1549969969398343650309345170134923246, -2.2703931422814399645
- 001021653326313849, -2.5581084321144835749447428779547264828; 1, 3.732976416
- 1953853934603848598678578170, 0.55969309276670831549180550098995851667, 1.34
- 62427005649082090774405779536603703, -1.450605799314659911085993848253116112
- 9; 1, -0.36709382900675984113447253685186261580, -2.060599444304916341220349
- 2228721306665, -2.9210840780604153977562503441379268334, 3.98235222143397020
- 22296117589048508540], [1, -1, -2, 1, -3; 1, -1, 3, 2, 1; 1, 0, 1, -2, -3; 1
- , 4, 1, 1, -1; 1, 0, -2, -3, 4], [5, 2, 0, -1, -2; 2, -2, -5, -10, 20; 0, -5
- , 10, -10, 5; -1, -10, -10, -17, 1; -2, 20, 5, 1, -8], [345, 0, 200, 110, 17
- 7; 0, 345, 95, 1, 145; 0, 0, 5, 4, 3; 0, 0, 0, 1, 0; 0, 0, 0, 0, 1], [63, 3,
-  0, -6, -9; 3, 8, -5, -1, 16; 0, -5, 22, -10, 0; -6, -1, -10, -14, -9; -9, 1
- 6, 0, -9, -2], [345, [138, 117, 330, 288, -636; -172, -88, 65, 118, -116; 53
- , 1, 138, -173, 65; 1, -172, 54, 191, 106; 0, 118, 173, 225, -34]]], [-2.428
- 5174907194186068992069565359418365, 1.9647119211288133163138753392090569931 
- + 0.80971492418897895128294082219556466857*I, -0.750453175769104012864271860
- 94108607489 + 1.3101462685358123283560773619310445916*I], [1, 1/15*x^4 - 2/3
- *x^2 + 1/3*x + 4/3, x, 2/15*x^4 - 1/3*x^2 + 2/3*x - 1/3, -1/15*x^4 + 1/3*x^3
-  + 1/3*x^2 - 4/3*x - 2/3], [1, 0, 3, 1, 10; 0, 0, -2, 1, -5; 0, 1, 0, 3, -5;
-  0, 0, 1, 1, 10; 0, 0, 0, 3, 0], [1, 0, 0, 0, 0, 0, -1, -1, -2, 4, 0, -1, 3,
-  -1, 1, 0, -2, -1, -3, -1, 0, 4, 1, -1, -1; 0, 1, 0, 0, 0, 1, 1, -1, -1, 1, 
- 0, -1, -2, -1, 1, 0, -1, -1, -1, 3, 0, 1, 1, 3, -3; 0, 0, 1, 0, 0, 0, 0, 0, 
- 1, -1, 1, 0, 0, 0, -2, 0, 1, 0, -1, -1, 0, -1, -2, -1, -1; 0, 0, 0, 1, 0, 0,
-  1, 0, 0, 0, 0, 0, 1, 1, 2, 1, 0, 1, 0, 0, 0, 0, 2, 0, -1; 0, 0, 0, 0, 1, 0,
-  -1, -1, -1, 1, 0, -1, 0, 1, 0, 0, -1, 1, 0, 0, 1, 1, 0, 0, -1]]
- ? nfinit(nfpol,2)
- [x^5 - 2*x^4 + 3*x^3 + 8*x^2 + 3*x + 2, [1, 2], 595125, 4, [[1, -1.089115145
- 7205048250249527946671612684, -2.4285174907194186068992069565359418365, 0.71
- 946691128913178943997506477288225735, -2.55582003506916949506460711594267799
- 71; 1, -0.13838372073406036365047976417441696637 + 0.49181637657768643499753
- 285514741525107*I, 1.9647119211288133163138753392090569931 - 0.8097149241889
- 7895128294082219556466857*I, -0.072312766896812300380582649294307897123 - 2.
- 1980803753846276641195195160383234878*I, -0.98796319352507039803950539735452
- 837196 - 1.5701452385894131769052374806001981109*I; 1, 1.6829412935943127761
- 629561615079976006 + 2.0500351226010726172974286983598602164*I, -0.750453175
- 76910401286427186094108607490 + 1.3101462685358123283560773619310445915*I, -
- 0.78742068874775359433940488309213323160 + 2.1336633893126618034168454610457
- 936016*I, 1.2658732110596551455718089553258673705 - 2.7164790103743150566578
- 028035789834836*I], [1, -1.0891151457205048250249527946671612684, -2.4285174
- 907194186068992069565359418365, 0.71946691128913178943997506477288225735, -2
- .5558200350691694950646071159426779971; 1, 0.3534326558436260713470530909729
- 9828470, 1.1549969969398343650309345170134923246, -2.27039314228143996450010
- 21653326313849, -2.5581084321144835749447428779547264828; 1, -0.630200097311
- 74679864801261932183221744, 2.7744268453177922675968161614046216617, 2.12576
- 76084878153637389368667440155906, 0.58218204506434277886573208324566973893; 
- 1, 3.7329764161953853934603848598678578170, 0.559693092766708315491805500989
- 95851657, 1.3462427005649082090774405779536603700, -1.4506057993146599110859
- 938482531161132; 1, -0.36709382900675984113447253685186261580, -2.0605994443
- 049163412203492228721306664, -2.9210840780604153977562503441379268332, 3.982
- 3522214339702022296117589048508541], [1, -1, -2, 1, -3; 1, 0, 1, -2, -3; 1, 
- -1, 3, 2, 1; 1, 4, 1, 1, -1; 1, 0, -2, -3, 4], [5, 2, 0, -1, -2; 2, -2, -5, 
- -10, 20; 0, -5, 10, -10, 5; -1, -10, -10, -17, 1; -2, 20, 5, 1, -8], [345, 0
- , 200, 110, 177; 0, 345, 95, 1, 145; 0, 0, 5, 4, 3; 0, 0, 0, 1, 0; 0, 0, 0, 
- 0, 1], [63, 3, 0, -6, -9; 3, 8, -5, -1, 16; 0, -5, 22, -10, 0; -6, -1, -10, 
- -14, -9; -9, 16, 0, -9, -2], [345, [138, 117, 330, 288, -636; -172, -88, 65,
-  118, -116; 53, 1, 138, -173, 65; 1, -172, 54, 191, 106; 0, 118, 173, 225, -
- 34]]], [-1.0891151457205048250249527946671612684, -0.13838372073406036365047
- 976417441696637 + 0.49181637657768643499753285514741525107*I, 1.682941293594
- 3127761629561615079976006 + 2.0500351226010726172974286983598602164*I], [1, 
- x, -1/2*x^4 + 3/2*x^3 - 5/2*x^2 - 2*x + 1, -1/2*x^4 + x^3 - x^2 - 9/2*x - 1,
-  -1/2*x^4 + x^3 - 2*x^2 - 7/2*x - 2], [1, 0, -1, -7, -14; 0, 1, 1, -2, -15; 
- 0, 0, 0, 2, 4; 0, 0, 1, 1, -2; 0, 0, -1, -3, -4], [1, 0, 0, 0, 0, 0, -1, -1,
-  -2, 4, 0, -1, 3, -1, 1, 0, -2, -1, -3, -1, 0, 4, 1, -1, -1; 0, 1, 0, 0, 0, 
- 1, 1, -1, -1, 1, 0, -1, -2, -1, 1, 0, -1, -1, -1, 3, 0, 1, 1, 3, -3; 0, 0, 1
- , 0, 0, 0, 0, 0, 1, -1, 1, 0, 0, 0, -2, 0, 1, 0, -1, -1, 0, -1, -2, -1, -1; 
- 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 2, 1, 0, 1, 0, 0, 0, 0, 2, 0, -1; 
- 0, 0, 0, 0, 1, 0, -1, -1, -1, 1, 0, -1, 0, 1, 0, 0, -1, 1, 0, 0, 1, 1, 0, 0,
-  -1]]
- ? nfinit(nfpol,3)
- [[x^5 - 2*x^4 + 3*x^3 + 8*x^2 + 3*x + 2, [1, 2], 595125, 4, [[1, -1.08911514
- 57205048250249527946671612684, -2.4285174907194186068992069565359418365, 0.7
- 1946691128913178943997506477288225735, -2.5558200350691694950646071159426779
- 971; 1, -0.13838372073406036365047976417441696637 + 0.4918163765776864349975
- 3285514741525107*I, 1.9647119211288133163138753392090569931 - 0.809714924188
- 97895128294082219556466857*I, -0.072312766896812300380582649294307897123 - 2
- .1980803753846276641195195160383234878*I, -0.9879631935250703980395053973545
- 2837196 - 1.5701452385894131769052374806001981109*I; 1, 1.682941293594312776
- 1629561615079976006 + 2.0500351226010726172974286983598602164*I, -0.75045317
- 576910401286427186094108607490 + 1.3101462685358123283560773619310445915*I, 
- -0.78742068874775359433940488309213323160 + 2.133663389312661803416845461045
- 7936016*I, 1.2658732110596551455718089553258673705 - 2.716479010374315056657
- 8028035789834836*I], [1, -1.0891151457205048250249527946671612684, -2.428517
- 4907194186068992069565359418365, 0.71946691128913178943997506477288225735, -
- 2.5558200350691694950646071159426779971; 1, 0.353432655843626071347053090972
- 99828470, 1.1549969969398343650309345170134923246, -2.2703931422814399645001
- 021653326313849, -2.5581084321144835749447428779547264828; 1, -0.63020009731
- 174679864801261932183221744, 2.7744268453177922675968161614046216617, 2.1257
- 676084878153637389368667440155906, 0.58218204506434277886573208324566973893;
-  1, 3.7329764161953853934603848598678578170, 0.55969309276670831549180550098
- 995851657, 1.3462427005649082090774405779536603700, -1.450605799314659911085
- 9938482531161132; 1, -0.36709382900675984113447253685186261580, -2.060599444
- 3049163412203492228721306664, -2.9210840780604153977562503441379268332, 3.98
- 23522214339702022296117589048508541], [1, -1, -2, 1, -3; 1, 0, 1, -2, -3; 1,
-  -1, 3, 2, 1; 1, 4, 1, 1, -1; 1, 0, -2, -3, 4], [5, 2, 0, -1, -2; 2, -2, -5,
-  -10, 20; 0, -5, 10, -10, 5; -1, -10, -10, -17, 1; -2, 20, 5, 1, -8], [345, 
- 0, 200, 110, 177; 0, 345, 95, 1, 145; 0, 0, 5, 4, 3; 0, 0, 0, 1, 0; 0, 0, 0,
-  0, 1], [63, 3, 0, -6, -9; 3, 8, -5, -1, 16; 0, -5, 22, -10, 0; -6, -1, -10,
-  -14, -9; -9, 16, 0, -9, -2], [345, [138, 117, 330, 288, -636; -172, -88, 65
- , 118, -116; 53, 1, 138, -173, 65; 1, -172, 54, 191, 106; 0, 118, 173, 225, 
- -34]]], [-1.0891151457205048250249527946671612684, -0.1383837207340603636504
- 7976417441696637 + 0.49181637657768643499753285514741525107*I, 1.68294129359
- 43127761629561615079976006 + 2.0500351226010726172974286983598602164*I], [1,
-  x, -1/2*x^4 + 3/2*x^3 - 5/2*x^2 - 2*x + 1, -1/2*x^4 + x^3 - x^2 - 9/2*x - 1
- , -1/2*x^4 + x^3 - 2*x^2 - 7/2*x - 2], [1, 0, -1, -7, -14; 0, 1, 1, -2, -15;
-  0, 0, 0, 2, 4; 0, 0, 1, 1, -2; 0, 0, -1, -3, -4], [1, 0, 0, 0, 0, 0, -1, -1
- , -2, 4, 0, -1, 3, -1, 1, 0, -2, -1, -3, -1, 0, 4, 1, -1, -1; 0, 1, 0, 0, 0,
-  1, 1, -1, -1, 1, 0, -1, -2, -1, 1, 0, -1, -1, -1, 3, 0, 1, 1, 3, -3; 0, 0, 
- 1, 0, 0, 0, 0, 0, 1, -1, 1, 0, 0, 0, -2, 0, 1, 0, -1, -1, 0, -1, -2, -1, -1;
-  0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 2, 1, 0, 1, 0, 0, 0, 0, 2, 0, -1;
-  0, 0, 0, 0, 1, 0, -1, -1, -1, 1, 0, -1, 0, 1, 0, 0, -1, 1, 0, 0, 1, 1, 0, 0
- , -1]], Mod(-1/2*x^4 + 3/2*x^3 - 5/2*x^2 - 2*x + 1, x^5 - 2*x^4 + 3*x^3 + 8*
- x^2 + 3*x + 2)]
- ? nf3=nfinit(x^6+108);
- ? nf4=nfinit(x^3-10*x+8)
- [x^3 - 10*x + 8, [3, 0], 568, 2, [[1, -0.36332823793268357037416860931988791
- 957, -3.1413361156553641347759399165844441384; 1, -1.76155718183189058754537
- 11274124874988, 2.6261980685272936133764995500786243868; 1, 3.12488541976457
- 41579195397367323754184, -0.48486195287192947860055963349418024847], [1, -0.
- 36332823793268357037416860931988791957, -3.141336115655364134775939916584444
- 1384; 1, -1.7615571818318905875453711274124874988, 2.62619806852729361337649
- 95500786243868; 1, 3.1248854197645741579195397367323754184, -0.4848619528719
- 2947860055963349418024847], [1, 0, -3; 1, -2, 3; 1, 3, 0], [3, 1, -1; 1, 13,
-  -5; -1, -5, 17], [284, 76, 46; 0, 2, 0; 0, 0, 1], [98, -6, 4; -6, 25, 7; 4,
-  7, 19], [284, [60, 418, -204; 105, 270, -2; 1, 104, -46]]], [-3.50466435358
- 80477051501085259043320579, 0.86464088669540302583112842266613688801, 2.6400
- 234668926446793189801032381951699], [1, 1/2*x^2 + x - 3, -1/2*x^2 + 3], [1, 
- 0, 6; 0, 1, 0; 0, 1, -2], [1, 0, 0, 0, 4, -2, 0, -2, 6; 0, 1, 0, 1, 2, 0, 0,
-  0, -2; 0, 0, 1, 0, 1, -1, 1, -1, -1]]
- ? setrand(1);bnf2=bnfinit(y^3-y-1);nf2=bnf2[7];
- ? setrand(1);bnf=bnfinit(x^2-x-57,,[0.2,0.2])
- [Mat(3), Mat([1, 2, 1, 2, 1, 2, 1, 1, 2]), [-2.71246530518434397468087951060
- 61300701 - 3.1415926535897932384626433832795028843*I; 2.71246530518434397468
- 08795106061300701 - 6.2831853071795864769252867665590057684*I], [-0.92212354
- 848661459835166758997591019383 + 3.1415926535897932384626433832795028842*I, 
- -1.4227033521190704721778709033666269682, 0.70148550268542821846861610071436
- 900869 + 3.1415926535897932384626433832795028842*I, 0.E-38, 0.50057980363245
- 587382620331339071677438 + 3.1415926535897932384626433832795028842*I, -1.623
- 6090511720428168202836906902792025, -0.5788359042095875039617797232424909750
- 4, -0.34328764427702709438988786673341921877 + 3.141592653589793238462643383
- 2795028842*I, 0.066178301882745732185368492323164193427 + 3.1415926535897932
- 384626433832795028842*I, -0.98830185036936033053703608229907438725; 0.922123
- 54848661459835166758997591019383, 1.4227033521190704721778709033666269682, -
- 0.70148550268542821846861610071436900869 + 3.1415926535897932384626433832795
- 028842*I, 0.E-38, -0.50057980363245587382620331339071677436, 1.6236090511720
- 428168202836906902792025 + 3.1415926535897932384626433832795028842*I, 0.5788
- 3590420958750396177972324249097504, 0.34328764427702709438988786673341921877
- , -0.066178301882745732185368492323164193427, 0.9883018503693603305370360822
- 9907438725], [[3, [-1, 1]~, 1, 1, [0, 57; 1, 1]], [5, [-2, 1]~, 1, 1, [1, 57
- ; 1, 2]], [11, [-2, 1]~, 1, 1, [1, 57; 1, 2]], [3, [0, 1]~, 1, 1, [-1, 57; 1
- , 0]], [5, [1, 1]~, 1, 1, [-2, 57; 1, -1]], [11, [1, 1]~, 1, 1, [-2, 57; 1, 
- -1]], [17, [-3, 1]~, 1, 1, [2, 57; 1, 3]], [17, [2, 1]~, 1, 1, [-3, 57; 1, -
- 2]], [19, [-1, 1]~, 1, 1, [0, 57; 1, 1]], [19, [0, 1]~, 1, 1, [-1, 57; 1, 0]
- ]], 0, [x^2 - x - 57, [2, 0], 229, 1, [[1, -7.066372975210777963595931024670
- 5326059; 1, 8.0663729752107779635959310246705326059], [1, -7.066372975210777
- 9635959310246705326059; 1, 8.0663729752107779635959310246705326059], [1, -7;
-  1, 8], [2, 1; 1, 115], [229, 114; 0, 1], [115, -1; -1, 2], [229, [114, 57; 
- 1, 115]]], [-7.0663729752107779635959310246705326059, 8.06637297521077796359
- 59310246705326059], [1, x], [1, 0; 0, 1], [1, 0, 0, 57; 0, 1, 1, 1]], [[3, [
- 3], [[3, 2; 0, 1]]], 2.7124653051843439746808795106061300701, 1, [2, -1], [x
-  + 7]], [Mat(1), [[0, 0]], [[-0.92212354848661459835166758997591019383 + 3.1
- 415926535897932384626433832795028842*I, 0.9221235484866145983516675899759101
- 9383]]], 0]
- ? setrand(1);bnfinit(x^2-x-100000,1)
- [Mat(5), Mat([3, 2, 1, 2, 0, 3, 2, 3, 3, 2, 0, 0, 4, 1, 3, 2, 2, 3]), [-129.
- 82045011403975460991182396195022419 - 3.624180943686747091 E-113*I; 129.8204
- 5011403975460991182396195022419 + 1.2486673839592994179 E-113*I], [-41.81126
- 4589129943393339502258694361489 + 6.2831853071795864769252867665590057684*I,
-  9.2399004147902289816376260438840931575, -11.874609881075406725097315997431
- 161032 + 3.1415926535897932384626433832795028842*I, 0, 598.05108556627860067
- 458199150717266631 + 2.079081953128979844 E-112*I, -194.73067517105963191486
- 773594292533629 + 3.1415926535897932384626433832795028842*I, -289.5775549361
- 3404588806583418516364884 + 3.1415926535897932384626433832795028842*I, 102.9
- 8937362955842429020308089254908188 + 3.898278662116837207 E-113*I, -404.4415
- 3844676787690336623107514389175 + 3.1415926535897932384626433832795028842*I,
-  484.20828704532476310708802954016117339 + 3.1415926535897932384626433832795
- 028842*I, 123.08269893574406654913158801089558608 + 3.898278662116837207 E-1
- 13*I, -731.25438161267029366213802528899365727 + 6.2831853071795864769252867
- 665590057684*I, 601.43393149863053905222620132704343308 + 2.0790819531289798
- 44 E-112*I, 1093.4420050106303665241166125712749392 + 3.14159265358979323846
- 26433832795028842*I, -745.79191925764104608772064294411862807 + 3.1415926535
- 897932384626433832795028842*I, -671.20676609281265093040971423356733550 + 6.
- 2831853071795864769252867665590057684*I, 239.9341511615634437073347400890223
- 0144 + 3.1415926535897932384626433832795028842*I, 652.9785442166766555563076
- 0228878662857 + 3.1415926535897932384626433832795028842*I, -1733.35340971812
- 46358289416962430827836 + 6.2831853071795864769252867665590057684*I; 41.8112
- 64589129943393339502258694361489 + 8.933555267351085266 E-114*I, -9.23990041
- 47902289816376260438840931575 + 3.1415926535897932384626433832795028842*I, 1
- 1.874609881075406725097315997431161032 + 2.030353469852519379 E-115*I, 0, -5
- 98.05108556627860067458199150717266631 + 3.141592653589793238462643383279502
- 8842*I, 194.73067517105963191486773594292533629 + 3.248565551764031006 E-113
- *I, 289.57755493613404588806583418516364884 + 4.547991772469643408 E-113*I, 
- -102.98937362955842429020308089254908188 + 3.1415926535897932384626433832795
- 028842*I, 404.44153844676787690336623107514389175 + 6.497131103528062012 E-1
- 13*I, -484.20828704532476310708802954016117339 + 6.2831853071795864769252867
- 665590057684*I, -123.08269893574406654913158801089558608 + 3.141592653589793
- 2384626433832795028842*I, 731.25438161267029366213802528899365727 + 1.299426
- 2207056124024 E-112*I, -601.43393149863053905222620132704343308 + 6.28318530
- 71795864769252867665590057684*I, -1093.4420050106303665241166125712749392 + 
- 3.1415926535897932384626433832795028842*I, 745.79191925764104608772064294411
- 862807 + 3.1415926535897932384626433832795028842*I, 671.20676609281265093040
- 971423356733550 + 3.1415926535897932384626433832795028842*I, -239.9341511615
- 6344370733474008902230144 + 6.2831853071795864769252867665590057684*I, -652.
- 97854421667665555630760228878662857 + 3.141592653589793238462643383279502884
- 2*I, 1733.3534097181246358289416962430827836 + 2.598852441411224805 E-112*I]
- , [[2, [1, 1]~, 1, 1, [0, 100000; 1, 1]], [5, [4, 1]~, 1, 1, [0, 100000; 1, 
- 1]], [13, [-6, 1]~, 1, 1, [5, 100000; 1, 6]], [2, [2, 1]~, 1, 1, [1, 100000;
-  1, 2]], [5, [5, 1]~, 1, 1, [-1, 100000; 1, 0]], [7, [3, 1]~, 2, 1, [3, 1000
- 00; 1, 4]], [13, [5, 1]~, 1, 1, [-6, 100000; 1, -5]], [31, [23, 1]~, 1, 1, [
- 7, 100000; 1, 8]], [31, [38, 1]~, 1, 1, [-8, 100000; 1, -7]], [17, [14, 1]~,
-  1, 1, [2, 100000; 1, 3]], [17, [19, 1]~, 1, 1, [-3, 100000; 1, -2]], [23, [
- -7, 1]~, 1, 1, [6, 100000; 1, 7]], [23, [6, 1]~, 1, 1, [-7, 100000; 1, -6]],
-  [29, [-14, 1]~, 1, 1, [13, 100000; 1, 14]], [29, [13, 1]~, 1, 1, [-14, 1000
- 00; 1, -13]], [41, [-7, 1]~, 1, 1, [6, 100000; 1, 7]], [41, [6, 1]~, 1, 1, [
- -7, 100000; 1, -6]], [43, [-16, 1]~, 1, 1, [15, 100000; 1, 16]], [43, [15, 1
- ]~, 1, 1, [-16, 100000; 1, -15]]], 0, [x^2 - x - 100000, [2, 0], 400001, 1, 
- [[1, -315.72816130129840161392089489603747004; 1, 316.7281613012984016139208
- 9489603747004], [1, -315.72816130129840161392089489603747004; 1, 316.7281613
- 0129840161392089489603747004], [1, -316; 1, 317], [2, 1; 1, 200001], [400001
- , 200000; 0, 1], [200001, -1; -1, 2], [400001, [200000, 100000; 1, 200001]]]
- , [-315.72816130129840161392089489603747004, 316.728161301298401613920894896
- 03747004], [1, x], [1, 0; 0, 1], [1, 0, 0, 100000; 0, 1, 1, 1]], [[5, [5], [
- [2, 1; 0, 1]]], 129.82045011403975460991182396195022419, 1, [2, -1], [379554
- 884019013781006303254896369154068336082609238336*x + 11983616564425078999046
- 2835950022871665178127611316131167]], [Mat(1), [[0, 0]], [[-41.8112645891299
- 43393339502258694361489 + 6.2831853071795864769252867665590057684*I, 41.8112
- 64589129943393339502258694361489 + 8.933555267351085266 E-114*I]]], 0]
- ? \p19
-    realprecision = 19 significant digits
- ? setrand(1);sbnf=bnfcompress(bnfinit(x^3-x^2-14*x-1))
- [x^3 - x^2 - 14*x - 1, 3, 10889, [1, x, x^2 - x - 9], [-3.233732695981516673
- , -0.07182350902743636345, 4.305556205008953036], 0, Mat(2), Mat([1, 1, 0, 1
- , 0, 1, 1, 1]), [9, 15, 16, 33, 39, 17, 10, 57, 69], [2, -1], [[0, 1, 0]~, [
- 5, 3, 1]~], [[[4, -1, 0]~, [1, -1, 0]~, [-2, -1, 0]~, [1, 1, 0]~, [10, 5, 1]
- ~, [3, 1, 0]~, [3, 0, 0]~, [7, 2, 0]~, [-2, -1, 1]~], 0]]
- ? \p38
-    realprecision = 38 significant digits
- ? bnr=bnrinit(bnf,[[5,3;0,1],[1,0]],1)
- [[Mat(3), Mat([1, 2, 1, 2, 1, 2, 1, 1, 2]), [-2.7124653051843439746808795106
- 061300701 - 3.1415926535897932384626433832795028843*I; 2.7124653051843439746
- 808795106061300701 - 6.2831853071795864769252867665590057684*I], [-0.9221235
- 4848661459835166758997591019383 + 3.1415926535897932384626433832795028842*I,
-  -1.4227033521190704721778709033666269682, 0.7014855026854282184686161007143
- 6900869 + 3.1415926535897932384626433832795028842*I, 0.E-38, 0.5005798036324
- 5587382620331339071677438 + 3.1415926535897932384626433832795028842*I, -1.62
- 36090511720428168202836906902792025, -0.578835904209587503961779723242490975
- 04, -0.34328764427702709438988786673341921877 + 3.14159265358979323846264338
- 32795028842*I, 0.066178301882745732185368492323164193427 + 3.141592653589793
- 2384626433832795028842*I, -0.98830185036936033053703608229907438725; 0.92212
- 354848661459835166758997591019383, 1.4227033521190704721778709033666269682, 
- -0.70148550268542821846861610071436900869 + 3.141592653589793238462643383279
- 5028842*I, 0.E-38, -0.50057980363245587382620331339071677436, 1.623609051172
- 0428168202836906902792025 + 3.1415926535897932384626433832795028842*I, 0.578
- 83590420958750396177972324249097504, 0.3432876442770270943898878667334192187
- 7, -0.066178301882745732185368492323164193427, 0.988301850369360330537036082
- 29907438725], [[3, [-1, 1]~, 1, 1, [0, 57; 1, 1]], [5, [-2, 1]~, 1, 1, [1, 5
- 7; 1, 2]], [11, [-2, 1]~, 1, 1, [1, 57; 1, 2]], [3, [0, 1]~, 1, 1, [-1, 57; 
- 1, 0]], [5, [1, 1]~, 1, 1, [-2, 57; 1, -1]], [11, [1, 1]~, 1, 1, [-2, 57; 1,
-  -1]], [17, [-3, 1]~, 1, 1, [2, 57; 1, 3]], [17, [2, 1]~, 1, 1, [-3, 57; 1, 
- -2]], [19, [-1, 1]~, 1, 1, [0, 57; 1, 1]], [19, [0, 1]~, 1, 1, [-1, 57; 1, 0
- ]]], 0, [x^2 - x - 57, [2, 0], 229, 1, [[1, -7.06637297521077796359593102467
- 05326059; 1, 8.0663729752107779635959310246705326059], [1, -7.06637297521077
- 79635959310246705326059; 1, 8.0663729752107779635959310246705326059], [1, -7
- ; 1, 8], [2, 1; 1, 115], [229, 114; 0, 1], [115, -1; -1, 2], [229, [114, 57;
-  1, 115]]], [-7.0663729752107779635959310246705326059, 8.0663729752107779635
- 959310246705326059], [1, x], [1, 0; 0, 1], [1, 0, 0, 57; 0, 1, 1, 1]], [[3, 
- [3], [[3, 2; 0, 1]]], 2.7124653051843439746808795106061300701, 1, [2, -1], [
- x + 7]], [Mat(1), [[0, 0]], [[-0.92212354848661459835166758997591019383 + 3.
- 1415926535897932384626433832795028842*I, 0.922123548486614598351667589975910
- 19383]]], [0, [Mat([[5, 1]~, 1])]]], [[[5, 3; 0, 1], [1, 0]], [8, [4, 2], [2
- , [-4, 0]~]], Mat([[5, [-2, 1]~, 1, 1, [1, 1]~], 1]), [[[[4], [[2, 0]~], [[2
- , 0]~], [Vecsmall([0])], 1]], [[2], [-4], [Vecsmall([1])]]], [1, 0; 0, 1]], 
- [1], Mat([1, -3, -6]), [12, [12], [[3, 2; 0, 1]]], [[0, 1; 0, 0], [-1, -1; 1
- , -1], 1]]
- ? rnfinit(nf2,x^5-x-2)
- [x^5 - x - 2, [], [[49744, 0, 0; 0, 49744, 0; 0, 0, 49744], 3109], 1, [], []
- , [[1, x, x^2, x^3, x^4], [1, 1, 1, 1, 1]], [1, 0, 0, 0, 0; 0, 1, 0, 0, 0; 0
- , 0, 1, 0, 0; 0, 0, 0, 1, 0; 0, 0, 0, 0, 1], [], [y^3 - y - 1, [1, 1], -23, 
- 1, [[1, 0.75487766624669276004950889635852869190, 1.324717957244746025960908
- 8544780973407; 1, -0.87743883312334638002475444817926434595 - 0.744861766619
- 74423659317042860439236724*I, -0.66235897862237301298045442723904867037 + 0.
- 56227951206230124389918214490937306150*I], [1, 0.754877666246692760049508896
- 35852869190, 1.3247179572447460259609088544780973407; 1, -1.6223005997430906
- 166179248767836567132, -0.10007946656007176908127228232967560887; 1, -0.1325
- 7706650360214343158401957487197871, -1.2246384906846742568796365721484217319
- ], [1, 1, 1; 1, -2, 0; 1, 0, -1], [3, -1, 0; -1, 1, 3; 0, 3, 2], [23, 16, 13
- ; 0, 1, 0; 0, 0, 1], [7, -2, 3; -2, -6, 9; 3, 9, -2], [23, [10, 1, 8; 7, 3, 
- 1; 1, 7, 10]]], [1.3247179572447460259609088544780973407, -0.662358978622373
- 01298045442723904867037 + 0.56227951206230124389918214490937306150*I], [1, y
- ^2 - 1, y], [1, 0, 1; 0, 0, 1; 0, 1, 0], [1, 0, 0, 0, 0, 1, 0, 1, 1; 0, 1, 0
- , 1, -1, 0, 0, 0, 1; 0, 0, 1, 0, 1, 0, 1, 0, 0]], [x^15 - 5*x^13 + 5*x^12 + 
- 7*x^11 - 26*x^10 - 5*x^9 + 45*x^8 + 158*x^7 - 98*x^6 + 110*x^5 - 190*x^4 + 1
- 89*x^3 + 144*x^2 + 25*x + 1, Mod(39516536165538345/83718587879473471*x^14 - 
- 6500512476832995/83718587879473471*x^13 - 196215472046117185/837185878794734
- 71*x^12 + 229902227480108910/83718587879473471*x^11 + 237380704030959181/837
- 18587879473471*x^10 - 1064931988160773805/83718587879473471*x^9 - 2065708667
- 1714300/83718587879473471*x^8 + 1772885205999206010/83718587879473471*x^7 + 
- 5952033217241102348/83718587879473471*x^6 - 4838840187320655696/837185878794
- 73471*x^5 + 5180390720553188700/83718587879473471*x^4 - 8374015687535120430/
- 83718587879473471*x^3 + 8907744727915040221/83718587879473471*x^2 + 41559766
- 64123434381/83718587879473471*x + 318920215718580450/83718587879473471, x^15
-  - 5*x^13 + 5*x^12 + 7*x^11 - 26*x^10 - 5*x^9 + 45*x^8 + 158*x^7 - 98*x^6 + 
- 110*x^5 - 190*x^4 + 189*x^3 + 144*x^2 + 25*x + 1), -1], 0]
- ? bnfcertify(bnf)
- 1
- ? setrand(1);bnfinit(x^2-x-100000,1).fu
- [Mod(379554884019013781006303254896369154068336082609238336*x + 119836165644
- 250789990462835950022871665178127611316131167, x^2 - x - 100000)]
- ? setrand(1);bnfinit(x^4+24*x^2+585*x+1791,,[0.1,0.1])
- [Mat(4), Mat([1, 3, 2, 2, 1, 2, 2, 3, 1, 3, 1]), [3.794126968821658934140827
- 4220859400302 + 17.051293362170144593106294159002845606*I; -3.79412696882165
- 89341408274220859400302 + 12.270238071334592299211710751605847980*I], [1.931
- 3880959585148864147377738135342090 + 2.6094045420344387591770907735373697726
- *I, -4.701977403289150032 E-38 + 11.899424269855508723178392022414809397*I, 
- -3.9880090562278299060379033618568304190 + 4.8170180346492352747549401763817
- 845238*I, 0.96569404797925744320736888690676710450 + 1.828301046615518252665
- 6526173152687003*I, -0.93136943643157202386304482413620291064 + 10.990051815
- 371901190031232280542867475*I, 2.1252701833646858583118137135844245978 + 0.2
- 5759541125748255276389824853295908861*I, 3.117999308786939916447700453089569
- 1176 + 11.763189456789071757159536232166443442*I, 2.607515755993233904107864
- 7428099051217 + 3.2235904944381500597928062956324708834*I, 0.807090594795827
- 43770186957565773006252 + 8.6810952775533156350341070283687472525*I, 1.12429
- 75011626874487128681981558041465 + 0.69662231985168015178245507209625882934*
- I, 2.1166141872052248127966075549404537821 + 10.0938249624782783222208828410
- 41949946*I, -0.18522609124670992638186978112691957309 + 0.075884278933757561
- 441547351857249422597*I; -1.9313880959585148864147377738135342090 + 7.289180
- 6943100772719847567167678332032*I, 4.701977403289150032 E-38 + 11.8994242698
- 55508723178392022414809397*I, 3.9880090562278299060379033618568304190 + 2.22
- 66696859162182331344124909571522200*I, -0.9656940479792574432073688869067671
- 0449 + 10.451374429932923985994772355489506184*I, 0.931369436431572023863044
- 82413620291066 + 9.4372822297479101164570701892975922345*I, -2.1252701833646
- 858583118137135844245978 + 12.308775203101690401086675284585052448*I, -3.117
- 9993087869399164477004530895691175 + 9.4561362323377796461746343301082095543
- *I, -2.6075157559932339041078647428099051217 + 5.429364580329528389690790733
- 5241705757*I, -0.80709059479582743770186957565773006250 + 8.6527493586654216
- 544393932995672941726*I, -1.1242975011626874487128681981558041465 + 5.404744
- 3910152126451848347441281753397*I, -2.1166141872052248127966075549404537821 
- + 8.0320113177474990640984855793282847659*I, 0.18522609124670992638186978112
- 691957310 + 6.8174740759401753323716105568013780333*I], [[7, [-2, 3, 3, -1]~
- , 1, 1, [3, 1, 56, 11; 4, 6, -7, 45; 4, -1, 7, -4; 1, 5, 0, 6]], [7, [1, -6,
-  -2, 1]~, 1, 1, [3, 1, -12, -35; 0, 0, 35, 21; -2, -3, 1, 0; 3, 1, 2, 0]], [
- 7, [2, -6, -2, 1]~, 1, 1, [2, -1, -1, 30; -1, 4, -31, -29; 1, 3, 3, 1; -3, -
- 2, -2, 4]], [3, [-1, 0, 1, 0]~, 4, 1, [0, 0, 18, -3; 2, 1, 5, 20; 1, -1, 1, 
- -2; 1, 2, 1, 1]], [19, [-5, -6, -2, 1]~, 2, 1, [9, 13, 36, -14; -8, -1, 6, 6
- 1; 3, -2, 12, 8; 2, 5, -11, -1]], [7, [7, -2, -1, 3]~, 1, 1, [2, -1, 32, 3; 
- 4, 5, 1, 27; 2, -1, 4, -4; 1, 3, 2, 5]], [13, [-1, -6, -2, 1]~, 1, 1, [-3, 9
- , 19, -28; -5, -11, 23, 53; 1, -3, -2, 5; 3, 4, -6, -11]], [13, [0, -6, -2, 
- 1]~, 1, 1, [4, 14, 89, -24; -3, -4, 21, 122; 6, -5, 10, 3; 5, 11, -9, -4]], 
- [13, [8, -6, -2, 1]~, 1, 1, [6, 11, 77, 3; -3, 1, -6, 83; 6, -2, 12, 3; 2, 8
- , -9, 1]], [13, [9, -6, -2, 1]~, 1, 1, [-6, 2, -9, 35; -5, -7, -40, -38; 1, 
- 4, -5, 5; -4, -3, -6, -7]], [19, [-4, -6, -2, 1]~, 1, 1, [8, 7, 20, -76; 0, 
- 0, 76, 95; -1, -8, 7, 0; 8, 7, 1, 0]], [19, [11, -6, -2, 1]~, 1, 1, [9, -4, 
- -133, -9; -9, 4, 0, -124; -9, 4, 0, 9; -4, -13, 0, 4]]], 0, [x^4 + 24*x^2 + 
- 585*x + 1791, [0, 2], 18981, 3087, [[1, 0.4999999999999999999999999999999999
- 9995 - 0.86602540378443864676372317075293618353*I, -3.0933488079472828155742
- 243261531931904 - 0.11742462569605115853137757107804136513*I, -2.64836711285
- 63006823406123980207685802 + 2.6202063376006319767212962440086284031*I; 1, 0
- .50000000000000000000000000000000000000 - 0.86602540378443864676372317075293
- 618347*I, 3.5933488079472828155742243261531931904 + 0.9834500294804898052951
- 0074183097754868*I, 1.6483671128563006823406123980207685802 - 2.620206337600
- 6319767212962440086284032*I], [1, -0.36602540378443864676372317075293618358,
-  -3.2107734336433339741056018972312345555, -0.028160775255668705619316154012
- 140177111; 1, 1.3660254037844386467637231707529361835, -2.975924182251231657
- 0428467550751518252, -5.2685734504569326590619086420293969833; 1, -0.3660254
- 0378443864676372317075293618347, 4.5767988374277726208693250679841707391, -0
- .97183922474433129438068384598785982299; 1, 1.366025403784438646763723170752
- 9361835, 2.6098987784667930102791235843222156418, 4.268573450456932659061908
- 6420293969834], [1, 0, -3, 0; 1, 1, -3, -5; 1, 0, 5, -1; 1, 1, 3, 4], [4, 2,
-  1, -2; 2, -2, 2, -1; 1, 2, 43, 34; -2, -1, 34, -8], [2109, 363, 1926, 1236;
-  0, 3, 0, 2; 0, 0, 3, 1; 0, 0, 0, 1], [317, 360, 17, -52; 360, -700, 6, 23; 
- 17, 6, 12, 46; -52, 23, 46, -58], [2109, [-993, -60, 7618, 2957; 642, -352, 
- -2315, 4600; 581, -1, -412, -642; 1, 582, 61, -352]]], [4.538330503038264948
- 8078362542856178008 + 8.0512080116993661743663904106823282345*I, -4.53833050
- 30382649488078362542856178008 + 0.60904602614502029327084129684703360027*I],
-  [1, -10/1029*x^3 + 13/343*x^2 - 165/343*x - 1135/343, 17/1029*x^3 - 32/1029
- *x^2 + 109/343*x + 2444/343, -26/1029*x^3 + 170/1029*x^2 - 429/343*x - 3294/
- 343], [1, 4, 15, -480; 0, -6, -39, 42; 0, -2, 0, 99; 0, 1, 15, 9], [1, 0, 0,
-  0, 0, -1, 1, 1, 0, 1, 12, 4, 0, 1, 4, -9; 0, 1, 0, 0, 1, 1, 0, -1, 0, 0, -4
- , 9, 0, -1, 9, 13; 0, 0, 1, 0, 0, 0, 0, -1, 1, 0, 1, 0, 0, -1, 0, 0; 0, 0, 0
- , 1, 0, 0, 1, 1, 0, 1, -1, 0, 1, 1, 0, -1]], [[4, [4], [[7, 2, 4, 0; 0, 1, 0
- , 0; 0, 0, 1, 0; 0, 0, 0, 1]]], 3.7941269688216589341408274220859400302, 1, 
- [6, 10/1029*x^3 - 13/343*x^2 + 165/343*x + 1478/343], [4/1029*x^3 + 53/1029*
- x^2 + 66/343*x + 111/343]], [Mat(-1), [[1.9459101490553133051053527434431797
- 297 + 3.5218438602827267539446763336694683720*I, 1.9459101490553133051053527
- 434431797296 + 3.5218438602827267539446763336694683721*I]], [[5.852252500262
- 7383340066731999591847100 + 11.477970899096468256601614561140503715*I, 9.715
- 0286921797681068361487475862531275 + 6.7981947468208297437939486179100402854
- *I]]], 0]
- ? bnrconductor(bnf,[[25,13;0,1],[1,1]])
- [[5, 3; 0, 1], [1, 0]]
- ? bnrconductorofchar(bnr,[2])
- [[5, 3; 0, 1], [0, 0]]
- ? bnfisprincipal(bnf,[5,1;0,1],0)
- [1]~
- ? bnfisprincipal(bnf,[5,1;0,1])
- [[1]~, [2, 1/3]~]
- ? bnfisunit(bnf,Mod(3405*x-27466,x^2-x-57))
- [-4, Mod(1, 2)]~
- ? \p19
-    realprecision = 19 significant digits
- ? bnfinit(sbnf)
- [Mat(2), Mat([1, 1, 0, 1, 0, 1, 1, 1]), [1.173637103435061715 + 3.1415926535
- 89793239*I, -4.562279014988837911 + 3.141592653589793239*I; -2.6335434327389
- 76050 + 3.141592653589793239*I, 1.420330600779487358 + 3.141592653589793239*
- I; 1.459906329303914335, 3.141948414209350544], [1.246346989334819161, 0.540
- 4006376129469728, -0.6926391142471042845, 0.004375616572659815434 + 3.141592
- 653589793239*I, -0.8305625946607188642 + 3.141592653589793239*I, -1.99005644
- 5584799713 + 3.141592653589793239*I, 0, -1.977791147836553954, 0.36772620140
- 27817707; 0.6716827432867392935, -0.8333219883742404172, -0.2461086674077943
- 078 + 3.141592653589793239*I, -0.8738318043071131266, -1.552661549868775854,
-  0.5379005671092853266, 0, 0.5774919091398324094, 0.9729063188316092381 + 3.
- 141592653589793239*I; -1.918029732621558454 + 3.141592653589793239*I, 0.2929
- 213507612934446 + 3.141592653589793239*I, 0.9387477816548985924 + 3.14159265
- 3589793239*I, 0.8694561877344533112, 2.383224144529494719, 1.452155878475514
- 387, 0, 1.400299238696721545, -1.340632520234391008 + 3.141592653589793239*I
- ], [[3, [-1, 1, 0]~, 1, 1, [1, 1, 1]~], [5, [-1, 1, 0]~, 1, 1, [0, 1, 1]~], 
- [5, [2, 1, 0]~, 1, 1, [1, -2, 1]~], [11, [1, 1, 0]~, 1, 1, [-3, -1, 1]~], [1
- 3, [19, 1, 0]~, 1, 1, [-2, -6, 1]~], [5, [3, 1, 0]~, 1, 1, [2, 2, 1]~], [3, 
- [10, 1, 1]~, 1, 2, [-1, 1, 0]~], [19, [-6, 1, 0]~, 1, 1, [6, 6, 1]~], [23, [
- -10, 1, 0]~, 1, 1, [-7, 10, 1]~]]~, 0, [x^3 - x^2 - 14*x - 1, [3, 0], 10889,
-  1, [[1, -3.233732695981516673, 4.690759845041404812; 1, -0.0718235090274363
- 6345, -8.923017874523549404; 1, 4.305556205008953037, 5.232258029482144592],
-  [1, -3.233732695981516673, 4.690759845041404812; 1, -0.07182350902743636345
- , -8.923017874523549404; 1, 4.305556205008953037, 5.232258029482144592], [1,
-  -3, 5; 1, 0, -9; 1, 4, 5], [3, 1, 1; 1, 29, 8; 1, 8, 129], [10889, 5698, 89
- 94; 0, 1, 0; 0, 0, 1], [3677, -121, -21; -121, 386, -23; -21, -23, 86], [108
- 89, [1899, 46720, 5235; 5191, 7095, 25956; 1, 5191, 1895]]], [-3.23373269598
- 1516673, -0.07182350902743636345, 4.305556205008953037], [1, x, x^2 - x - 9]
- , [1, 0, 9; 0, 1, 1; 0, 0, 1], [1, 0, 0, 0, 9, 1, 0, 1, 44; 0, 1, 0, 1, 1, 5
- , 0, 5, 1; 0, 0, 1, 0, 1, 0, 1, 0, -4]], [[2, [2], [[3, 2, 0; 0, 1, 0; 0, 0,
-  1]]], 10.34800724602768001, 1, [2, -1], [x, x^2 + 2*x - 4]], [Mat(1), [[0, 
- 0, 0]], [[1.246346989334819161, 0.6716827432867392935, -1.918029732621558454
-  + 3.141592653589793239*I]]], [[[4, -1, 0]~, [1, -1, 0]~, [-2, -1, 0]~, [1, 
- 1, 0]~, [10, 5, 1]~, [3, 1, 0]~, [3, 0, 0]~, [7, 2, 0]~, [-2, -1, 1]~], 0]]
- ? \p38
-    realprecision = 38 significant digits
- ? bnfnarrow(bnf)
- [3, [3], [[3, 2; 0, 1]]]
- ? bnfsignunit(bnf)
- 
- [-1]
- 
- [1]
- 
- ? bnr2=bnrinit(bnf,[[25,13;0,1],[1,1]],1)
- [[Mat(3), Mat([1, 2, 1, 2, 1, 2, 1, 1, 2]), [-2.7124653051843439746808795106
- 061300701 - 3.1415926535897932384626433832795028843*I; 2.7124653051843439746
- 808795106061300701 - 6.2831853071795864769252867665590057684*I], [-0.9221235
- 4848661459835166758997591019383 + 3.1415926535897932384626433832795028842*I,
-  -1.4227033521190704721778709033666269682, 0.7014855026854282184686161007143
- 6900869 + 3.1415926535897932384626433832795028842*I, 0.E-38, 0.5005798036324
- 5587382620331339071677438 + 3.1415926535897932384626433832795028842*I, -1.62
- 36090511720428168202836906902792025, -0.578835904209587503961779723242490975
- 04, -0.34328764427702709438988786673341921877 + 3.14159265358979323846264338
- 32795028842*I, 0.066178301882745732185368492323164193427 + 3.141592653589793
- 2384626433832795028842*I, -0.98830185036936033053703608229907438725; 0.92212
- 354848661459835166758997591019383, 1.4227033521190704721778709033666269682, 
- -0.70148550268542821846861610071436900869 + 3.141592653589793238462643383279
- 5028842*I, 0.E-38, -0.50057980363245587382620331339071677436, 1.623609051172
- 0428168202836906902792025 + 3.1415926535897932384626433832795028842*I, 0.578
- 83590420958750396177972324249097504, 0.3432876442770270943898878667334192187
- 7, -0.066178301882745732185368492323164193427, 0.988301850369360330537036082
- 29907438725], [[3, [-1, 1]~, 1, 1, [0, 57; 1, 1]], [5, [-2, 1]~, 1, 1, [1, 5
- 7; 1, 2]], [11, [-2, 1]~, 1, 1, [1, 57; 1, 2]], [3, [0, 1]~, 1, 1, [-1, 57; 
- 1, 0]], [5, [1, 1]~, 1, 1, [-2, 57; 1, -1]], [11, [1, 1]~, 1, 1, [-2, 57; 1,
-  -1]], [17, [-3, 1]~, 1, 1, [2, 57; 1, 3]], [17, [2, 1]~, 1, 1, [-3, 57; 1, 
- -2]], [19, [-1, 1]~, 1, 1, [0, 57; 1, 1]], [19, [0, 1]~, 1, 1, [-1, 57; 1, 0
- ]]], 0, [x^2 - x - 57, [2, 0], 229, 1, [[1, -7.06637297521077796359593102467
- 05326059; 1, 8.0663729752107779635959310246705326059], [1, -7.06637297521077
- 79635959310246705326059; 1, 8.0663729752107779635959310246705326059], [1, -7
- ; 1, 8], [2, 1; 1, 115], [229, 114; 0, 1], [115, -1; -1, 2], [229, [114, 57;
-  1, 115]]], [-7.0663729752107779635959310246705326059, 8.0663729752107779635
- 959310246705326059], [1, x], [1, 0; 0, 1], [1, 0, 0, 57; 0, 1, 1, 1]], [[3, 
- [3], [[3, 2; 0, 1]]], 2.7124653051843439746808795106061300701, 1, [2, -1], [
- x + 7]], [Mat(1), [[0, 0]], [[-0.92212354848661459835166758997591019383 + 3.
- 1415926535897932384626433832795028842*I, 0.922123548486614598351667589975910
- 19383]]], [0, [Mat([[5, 1]~, 1])]]], [[[25, 13; 0, 1], [1, 1]], [80, [20, 2,
-  2], [2, [-24, 0]~, [2, 2]~]], Mat([[5, [-2, 1]~, 1, 1, [1, 1]~], 2]), [[[[4
- ], [[2, 0]~], [[2, 0]~], [Vecsmall([0, 0])], 1], [[5], [[6, 0]~], [[6, 0]~],
-  [Vecsmall([0, 0])], Mat([1/5, -13/5])]], [[2, 2], [-24, [2, 2]~], [Vecsmall
- ([0, 1]), Vecsmall([1, 1])]]], [1, -12, 0, 0; 0, 0, 1, 0; 0, 0, 0, 1]], [1],
-  Mat([1, -3, -6, -6]), [12, [12], [[3, 2; 0, 1]]], [[0, 2, 0; -1, 10, 0], [-
- 2, 0; 0, -10], 2]]
- ? bnrclassno(bnf,[[5,3;0,1],[1,0]])
- 12
- ? lu=ideallist(bnf,55,3);
- ? bnrclassnolist(bnf,lu)
- [[3], [], [3, 3], [3], [6, 6], [], [], [], [3, 3, 3], [], [3, 3], [3, 3], []
- , [], [12, 6, 6, 12], [3], [3, 3], [], [9, 9], [6, 6], [], [], [], [], [6, 1
- 2, 6], [], [3, 3, 3, 3], [], [], [], [], [], [3, 6, 6, 3], [], [], [9, 3, 9]
- , [6, 6], [], [], [], [], [], [3, 3], [3, 3], [12, 12, 6, 6, 12, 12], [], []
- , [6, 6], [9], [], [3, 3, 3, 3], [], [3, 3], [], [6, 12, 12, 6]]
- ? bnrdisc(bnr,Mat(6))
- [12, 12, 18026977100265125]
- ? bnrdisc(bnr)
- [24, 12, 40621487921685401825918161408203125]
- ? bnrdisc(bnr2,,,2)
- 0
- ? bnrdisc(bnr,Mat(6),,1)
- [6, 2, [125, 13; 0, 1]]
- ? bnrdisc(bnr,,,1)
- [12, 1, [1953125, 1160888; 0, 1]]
- ? bnrdisc(bnr2,,,3)
- 0
- ? bnrdisclist(bnf,lu)
- [[[6, 6, Mat([229, 3])]], [], [[], []], [[]], [[12, 12, [5, 3; 229, 6]], [12
- , 12, [5, 3; 229, 6]]], [], [], [], [[], [], []], [], [[], []], [[], []], []
- , [], [[24, 24, [3, 6; 5, 9; 229, 12]], [], [], [24, 24, [3, 6; 5, 9; 229, 1
- 2]]], [[]], [[], []], [], [[18, 18, [19, 6; 229, 9]], [18, 18, [19, 6; 229, 
- 9]]], [[], []], [], [], [], [], [[], [24, 24, [5, 12; 229, 12]], []], [], [[
- ], [], [], []], [], [], [], [], [], [[], [12, 12, [3, 3; 11, 3; 229, 6]], [1
- 2, 12, [3, 3; 11, 3; 229, 6]], []], [], [], [[18, 18, [2, 12; 3, 12; 229, 9]
- ], [], [18, 18, [2, 12; 3, 12; 229, 9]]], [[12, 12, [37, 3; 229, 6]], [12, 1
- 2, [37, 3; 229, 6]]], [], [], [], [], [], [[], []], [[], []], [[], [], [], [
- ], [], []], [], [], [[12, 12, [2, 12; 3, 3; 229, 6]], [12, 12, [2, 12; 3, 3;
-  229, 6]]], [[18, 18, [7, 12; 229, 9]]], [], [[], [], [], []], [], [[], []],
-  [], [[], [24, 24, [5, 9; 11, 6; 229, 12]], [24, 24, [5, 9; 11, 6; 229, 12]]
- , []]]
- ? bnrdisclist(bnf,20)
- [[[[matrix(0,2), [[6, 6, Mat([229, 3])], [0, 0, 0], [0, 0, 0], [0, 0, 0]]]],
-  [], [[Mat([12, 1]), [[0, 0, 0], [0, 0, 0], [0, 0, 0], [12, 0, [3, 3; 229, 6
- ]]]], [Mat([13, 1]), [[0, 0, 0], [12, 6, [-1, 1; 3, 3; 229, 6]], [0, 0, 0], 
- [0, 0, 0]]]], [[Mat([10, 1]), [[0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0]]]]
- , [[Mat([20, 1]), [[12, 12, [5, 3; 229, 6]], [0, 0, 0], [0, 0, 0], [24, 0, [
- 5, 9; 229, 12]]]], [Mat([21, 1]), [[12, 12, [5, 3; 229, 6]], [24, 12, [5, 9;
-  229, 12]], [0, 0, 0], [0, 0, 0]]]], [], [], [], [[Mat([12, 2]), [[0, 0, 0],
-  [0, 0, 0], [0, 0, 0], [0, 0, 0]]], [[12, 1; 13, 1], [[0, 0, 0], [0, 0, 0], 
- [12, 6, [-1, 1; 3, 6; 229, 6]], [24, 0, [3, 12; 229, 12]]]], [Mat([13, 2]), 
- [[0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0]]]], [], [[Mat([44, 1]), [[0, 0, 
- 0], [12, 6, [-1, 1; 11, 3; 229, 6]], [0, 0, 0], [0, 0, 0]]], [Mat([45, 1]), 
- [[0, 0, 0], [0, 0, 0], [0, 0, 0], [12, 0, [11, 3; 229, 6]]]]], [[[10, 1; 12,
-  1], [[0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0]]], [[10, 1; 13, 1], [[0, 0,
-  0], [0, 0, 0], [0, 0, 0], [0, 0, 0]]]], [], [], [[[12, 1; 20, 1], [[24, 24,
-  [3, 6; 5, 9; 229, 12]], [0, 0, 0], [0, 0, 0], [48, 0, [3, 12; 5, 18; 229, 2
- 4]]]], [[13, 1; 20, 1], [[0, 0, 0], [24, 12, [3, 6; 5, 6; 229, 12]], [24, 12
- , [3, 6; 5, 9; 229, 12]], [48, 0, [3, 12; 5, 18; 229, 24]]]], [[12, 1; 21, 1
- ], [[0, 0, 0], [0, 0, 0], [24, 12, [3, 6; 5, 9; 229, 12]], [48, 0, [3, 12; 5
- , 18; 229, 24]]]], [[13, 1; 21, 1], [[24, 24, [3, 6; 5, 9; 229, 12]], [48, 2
- 4, [3, 12; 5, 18; 229, 24]], [0, 0, 0], [0, 0, 0]]]], [[Mat([10, 2]), [[0, 0
- , 0], [12, 6, [-1, 1; 2, 12; 229, 6]], [12, 6, [-1, 1; 2, 12; 229, 6]], [24,
-  0, [2, 36; 229, 12]]]]], [[Mat([68, 1]), [[0, 0, 0], [0, 0, 0], [12, 6, [-1
- , 1; 17, 3; 229, 6]], [0, 0, 0]]], [Mat([69, 1]), [[0, 0, 0], [0, 0, 0], [12
- , 6, [-1, 1; 17, 3; 229, 6]], [0, 0, 0]]]], [], [[Mat([76, 1]), [[18, 18, [1
- 9, 6; 229, 9]], [0, 0, 0], [0, 0, 0], [36, 0, [19, 15; 229, 18]]]], [Mat([77
- , 1]), [[18, 18, [19, 6; 229, 9]], [36, 18, [-1, 1; 19, 15; 229, 18]], [0, 0
- , 0], [0, 0, 0]]]], [[[10, 1; 20, 1], [[0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 
- 0, 0]]], [[10, 1; 21, 1], [[0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0]]]]]]
- ? bnrisprincipal(bnr,idealprimedec(bnf,7)[1])
- [[9]~, [32879/6561, 13958/19683]~]
- ? dirzetak(nf4,30)
- [1, 2, 0, 3, 1, 0, 0, 4, 0, 2, 1, 0, 0, 0, 0, 5, 1, 0, 0, 3, 0, 2, 0, 0, 2, 
- 0, 1, 0, 1, 0]
- ? factornf(x^3+x^2-2*x-1,t^3+t^2-2*t-1)
- 
- [x + Mod(-t, t^3 + t^2 - 2*t - 1) 1]
- 
- [x + Mod(-t^2 + 2, t^3 + t^2 - 2*t - 1) 1]
- 
- [x + Mod(t^2 + t - 1, t^3 + t^2 - 2*t - 1) 1]
- 
- ? vp=idealprimedec(nf,3)[1]
- [3, [1, 0, 1, 0, 0]~, 1, 1, [1, -1, -1, -1, 0]~]
- ? idx=idealhnf(nf,vp)
- 
- [3 2 1 0 1]
- 
- [0 1 0 0 0]
- 
- [0 0 1 0 0]
- 
- [0 0 0 1 0]
- 
- [0 0 0 0 1]
- 
- ? idy=idealred(nf,idx,[1,5,6])
- 
- [5 0 0 0 2]
- 
- [0 5 0 0 2]
- 
- [0 0 5 0 1]
- 
- [0 0 0 5 2]
- 
- [0 0 0 0 1]
- 
- ? idx2=idealmul(nf,idx,idx)
- 
- [9 5 7 0 4]
- 
- [0 1 0 0 0]
- 
- [0 0 1 0 0]
- 
- [0 0 0 1 0]
- 
- [0 0 0 0 1]
- 
- ? idt=idealmul(nf,idx,idx,1)
- 
- [2 0 0 0 0]
- 
- [0 2 0 0 0]
- 
- [0 0 2 0 0]
- 
- [0 0 0 2 1]
- 
- [0 0 0 0 1]
- 
- ? idz=idealintersect(nf,idx,idy)
- 
- [15 10 5 0 12]
- 
- [0 5 0 0 2]
- 
- [0 0 5 0 1]
- 
- [0 0 0 5 2]
- 
- [0 0 0 0 1]
- 
- ? aid=[idx,idy,idz,1,idx]
- [[3, 2, 1, 0, 1; 0, 1, 0, 0, 0; 0, 0, 1, 0, 0; 0, 0, 0, 1, 0; 0, 0, 0, 0, 1]
- , [5, 0, 0, 0, 2; 0, 5, 0, 0, 2; 0, 0, 5, 0, 1; 0, 0, 0, 5, 2; 0, 0, 0, 0, 1
- ], [15, 10, 5, 0, 12; 0, 5, 0, 0, 2; 0, 0, 5, 0, 1; 0, 0, 0, 5, 2; 0, 0, 0, 
- 0, 1], 1, [3, 2, 1, 0, 1; 0, 1, 0, 0, 0; 0, 0, 1, 0, 0; 0, 0, 0, 1, 0; 0, 0,
-  0, 0, 1]]
- ? idealadd(nf,idx,idy)
- 
- [1 0 0 0 0]
- 
- [0 1 0 0 0]
- 
- [0 0 1 0 0]
- 
- [0 0 0 1 0]
- 
- [0 0 0 0 1]
- 
- ? idealaddtoone(nf,idx,idy)
- [[0, -1, -3, -1, 2]~, [1, 1, 3, 1, -2]~]
- ? idealaddtoone(nf,[idy,idx])
- [[-5, 0, 0, 0, 0]~, [6, 0, 0, 0, 0]~]
- ? idealappr(nf,idy)
- [-1, 4, 2, -1, -3]~
- ? idealappr(nf,idealfactor(nf,idy),1)
- [-1, 4, 2, -1, -3]~
- ? idealcoprime(nf,idx,idx)
- [-1/3, 1/3, 1/3, 1/3, 0]~
- ? idealdiv(nf,idy,idt)
- 
- [5 0 5/2 0 1]
- 
- [0 5/2 0 0 1]
- 
- [0 0 5/2 0 1/2]
- 
- [0 0 0 5/2 1]
- 
- [0 0 0 0 1/2]
- 
- ? idealdiv(nf,idx2,idx,1)
- 
- [3 2 1 0 1]
- 
- [0 1 0 0 0]
- 
- [0 0 1 0 0]
- 
- [0 0 0 1 0]
- 
- [0 0 0 0 1]
- 
- ? idealfactor(nf,idz)
- 
- [[3, [1, 0, 1, 0, 0]~, 1, 1, [1, -1, -1, -1, 0]~] 1]
- 
- [[5, [-1, 0, 0, 0, 2]~, 4, 1, [2, 2, 1, 2, 1]~] 3]
- 
- [[5, [2, 0, 0, 0, -2]~, 1, 1, [2, 0, 3, 0, 1]~] 1]
- 
- ? idealhnf(nf,vp[2],3)
- 
- [3 2 1 0 1]
- 
- [0 1 0 0 0]
- 
- [0 0 1 0 0]
- 
- [0 0 0 1 0]
- 
- [0 0 0 0 1]
- 
- ? ideallist(bnf,20)
- [[[1, 0; 0, 1]], [], [[3, 2; 0, 1], [3, 0; 0, 1]], [[2, 0; 0, 2]], [[5, 3; 0
- , 1], [5, 1; 0, 1]], [], [], [], [[9, 5; 0, 1], [3, 0; 0, 3], [9, 3; 0, 1]],
-  [], [[11, 9; 0, 1], [11, 1; 0, 1]], [[6, 4; 0, 2], [6, 0; 0, 2]], [], [], [
- [15, 8; 0, 1], [15, 3; 0, 1], [15, 11; 0, 1], [15, 6; 0, 1]], [[4, 0; 0, 4]]
- , [[17, 14; 0, 1], [17, 2; 0, 1]], [], [[19, 18; 0, 1], [19, 0; 0, 1]], [[10
- , 6; 0, 2], [10, 2; 0, 2]]]
- ? bid=idealstar(nf2,54)
- [[[54, 0, 0; 0, 54, 0; 0, 0, 54], [0]], [132678, [1638, 9, 9]], [[2, [2, 0, 
- 0]~, 1, 3, 1], 1; [3, [3, 0, 0]~, 1, 3, 1], 3], [[[[7], [[1, 1, 0]~], [[1, -
- 27, 0]~], [Vecsmall([])], 1]], [[[26], [[4, 2, 1]~], [[-23, 2, -26]~], [Vecs
- mall([])], 1], [[3, 3, 3], [[4, 0, 0]~, [1, 3, 0]~, [1, 0, 3]~], [[-23, 0, 0
- ]~, [1, -24, 0]~, [1, 0, -24]~], [Vecsmall([]), Vecsmall([]), Vecsmall([])],
-  [1/3, 0, 0; 0, 1/3, 0; 0, 0, 1/3]], [[3, 3, 3], [[10, 0, 0]~, [1, 9, 0]~, [
- 1, 0, 9]~], [[-17, 0, 0]~, [1, -18, 0]~, [1, 0, -18]~], [Vecsmall([]), Vecsm
- all([]), Vecsmall([])], [1/9, 0, 0; 0, 1/9, 0; 0, 0, 1/9]]], [[], [], []]], 
- [468, -77, 0, 728, -1456, 0, 546, -1092; 0, 0, 1, 0, -1, -6, 0, -3; 0, 1, 0,
-  -1, 1, 0, -3, 3]]
- ? ideallog(nf2,y,bid)
- [752, 1, 1]~
- ? idealmin(nf,idx,[1,2,3])
- [1, 0, 1, 0, 0]~
- ? idealnorm(nf,idt)
- 16
- ? idp=idealpow(nf,idx,7)
- 
- [2187 1436 1807 630 1822]
- 
- [0 1 0 0 0]
- 
- [0 0 1 0 0]
- 
- [0 0 0 1 0]
- 
- [0 0 0 0 1]
- 
- ? idealpow(nf,idx,7,1)
- 
- [1 0 0 0 0]
- 
- [0 1 0 0 0]
- 
- [0 0 1 0 0]
- 
- [0 0 0 1 0]
- 
- [0 0 0 0 1]
- 
- ? idealprimedec(nf,2)
- [[2, [3, 0, 1, 0, 0]~, 1, 1, [0, 0, 0, 1, 1]~], [2, [12, -4, -2, 11, 3]~, 1,
-  4, [1, 0, 1, 0, 0]~]]
- ? idealprimedec(nf,3)
- [[3, [1, 0, 1, 0, 0]~, 1, 1, [1, -1, -1, -1, 0]~], [3, [1, 1, 1, 0, 0]~, 2, 
- 2, [0, 2, 2, 1, 0]~]]
- ? idealprimedec(nf,11)
- [[11, [11, 0, 0, 0, 0]~, 1, 5, 1]]
- ? idealtwoelt(nf,idy)
- [5, [2, 2, 1, 2, 1]~]
- ? idealtwoelt(nf,idy,10)
- [-1, 4, 2, 4, 2]~
- ? idealstar(nf2,54)
- [[[54, 0, 0; 0, 54, 0; 0, 0, 54], [0]], [132678, [1638, 9, 9]], [[2, [2, 0, 
- 0]~, 1, 3, 1], 1; [3, [3, 0, 0]~, 1, 3, 1], 3], [[[[7], [[2, 1, 1]~], [[-26,
-  -27, -27]~], [Vecsmall([])], 1]], [[[26], [[2, 1, 0]~], [[-25, -26, 0]~], [
- Vecsmall([])], 1], [[3, 3, 3], [[4, 0, 0]~, [1, 3, 0]~, [1, 0, 3]~], [[-23, 
- 0, 0]~, [1, -24, 0]~, [1, 0, -24]~], [Vecsmall([]), Vecsmall([]), Vecsmall([
- ])], [1/3, 0, 0; 0, 1/3, 0; 0, 0, 1/3]], [[3, 3, 3], [[10, 0, 0]~, [1, 9, 0]
- ~, [1, 0, 9]~], [[-17, 0, 0]~, [1, -18, 0]~, [1, 0, -18]~], [Vecsmall([]), V
- ecsmall([]), Vecsmall([])], [1/9, 0, 0; 0, 1/9, 0; 0, 0, 1/9]]], [[], [], []
- ]], [468, -77, 0, 728, -546, 0, 546, 0; 0, 0, 1, 0, -2, -6, 0, -6; 0, 1, 0, 
- -1, 1, 0, -3, 3]]
- ? idealval(nf,idp,vp)
- 7
- ? ba=nfalgtobasis(nf,x^3+5)
- [6, 1, 3, 1, 3]~
- ? bb=nfalgtobasis(nf,x^3+x)
- [1, 1, 4, 1, 3]~
- ? bc=matalgtobasis(nf,[x^2+x;x^2+1])
- 
- [[3, -2, 1, 1, 0]~]
- 
- [[4, -2, 0, 1, 0]~]
- 
- ? matbasistoalg(nf,bc)
- 
- [Mod(x^2 + x, x^5 - 5*x^3 + 5*x + 25)]
- 
- [Mod(x^2 + 1, x^5 - 5*x^3 + 5*x + 25)]
- 
- ? nfbasis(x^3+4*x+5)
- [1, x, 1/7*x^2 - 1/7*x - 2/7]
- ? nfbasis(x^3+4*x+5,2)
- [1, x, 1/7*x^2 - 1/7*x - 2/7]
- ? nfbasis(x^3+4*x+12,1)
- [1, x, 1/2*x^2]
- ? nfbasistoalg(nf,ba)
- Mod(x^3 + 5, x^5 - 5*x^3 + 5*x + 25)
- ? nfbasis(p2,0,fa)
- [1, x, x^2, 1/11699*x^3 + 1847/11699*x^2 - 132/11699*x - 2641/11699, 1/13962
- 3738889203638909659*x^4 - 1552451622081122020/139623738889203638909659*x^3 +
-  418509858130821123141/139623738889203638909659*x^2 - 6810913798507599407313
- 4/139623738889203638909659*x - 13185339461968406/58346808996920447]
- ? nfdisc(x^3+4*x+12)
- -1036
- ? nfdisc(x^3+4*x+12,1)
- -1036
- ? nfdisc(p2,0,fa)
- 136866601
- ? nfeltdiv(nf,ba,bb)
- [584/373, 66/373, -32/373, -105/373, 120/373]~
- ? nfeltdiveuc(nf,ba,bb)
- [2, 0, 0, 0, 0]~
- ? nfeltdivrem(nf,ba,bb)
- [[2, 0, 0, 0, 0]~, [4, -1, -5, -1, -3]~]
- ? nfeltmod(nf,ba,bb)
- [4, -1, -5, -1, -3]~
- ? nfeltmul(nf,ba,bb)
- [50, -15, -35, 60, 15]~
- ? nfeltpow(nf,bb,5)
- [-291920, 136855, 230560, -178520, 74190]~
- ? nfeltreduce(nf,ba,idx)
- [1, 0, 0, 0, 0]~
- ? nfeltval(nf,ba,vp)
- 0
- ? nffactor(nf2,x^3+x)
- 
- [x 1]
- 
- [x^2 + 1 1]
- 
- ? aut=nfgaloisconj(nf3)
- [-x, x, -1/12*x^4 - 1/2*x, -1/12*x^4 + 1/2*x, 1/12*x^4 - 1/2*x, 1/12*x^4 + 1
- /2*x]~
- ? nfgaloisapply(nf3,aut[5],Mod(x^5,x^6+108))
- Mod(-1/2*x^5 + 9*x^2, x^6 + 108)
- ? nfhilbert(nf,3,5)
- -1
- ? nfhilbert(nf,3,5,vp)
- -1
- ? nfhnf(nf,[a,aid])
- [[1, 1, 4; 0, 1, 0; 0, 0, 1], [[15, 2, 10, 12, 4; 0, 1, 0, 0, 0; 0, 0, 1, 0,
-  0; 0, 0, 0, 1, 0; 0, 0, 0, 0, 1], [1, 0, 0, 0, 0; 0, 1, 0, 0, 0; 0, 0, 1, 0
- , 0; 0, 0, 0, 1, 0; 0, 0, 0, 0, 1], [1, 0, 0, 0, 0; 0, 1, 0, 0, 0; 0, 0, 1, 
- 0, 0; 0, 0, 0, 1, 0; 0, 0, 0, 0, 1]]]
- ? da=nfdetint(nf,[a,aid])
- 
- [15 10 5 0 12]
- 
- [0 5 0 0 2]
- 
- [0 0 5 0 1]
- 
- [0 0 0 5 2]
- 
- [0 0 0 0 1]
- 
- ? nfhnfmod(nf,[a,aid],da)
- [[1, 1, 4; 0, 1, 0; 0, 0, 1], [[15, 2, 10, 12, 4; 0, 1, 0, 0, 0; 0, 0, 1, 0,
-  0; 0, 0, 0, 1, 0; 0, 0, 0, 0, 1], [1, 0, 0, 0, 0; 0, 1, 0, 0, 0; 0, 0, 1, 0
- , 0; 0, 0, 0, 1, 0; 0, 0, 0, 0, 1], [1, 0, 0, 0, 0; 0, 1, 0, 0, 0; 0, 0, 1, 
- 0, 0; 0, 0, 0, 1, 0; 0, 0, 0, 0, 1]]]
- ? nfisideal(bnf[7],[5,1;0,1])
- 1
- ? nfisincl(x^2+1,x^4+1)
- [-x^2, x^2]
- ? nfisincl(x^2+1,nfinit(x^4+1))
- [-x^2, x^2]
- ? nfisisom(x^3+x^2-2*x-1,x^3+x^2-2*x-1)
- [x, -x^2 - x + 1, x^2 - 2]
- ? nfisisom(x^3-2,nfinit(x^3-6*x^2-6*x-30))
- [-1/25*x^2 + 13/25*x - 2/5]
- ? nfroots(nf2,x+2)
- [Mod(-2, y^3 - y - 1)]
- ? nfrootsof1(nf)
- [2, -1]
- ? nfsnf(nf,[as,[1,1,1],[idealinv(nf,idx),idealinv(nf,idy),1]])
- [[15706993357777254170417850, 1636878763571210697462070, 1307908830618593502
- 9427775, 1815705333955314515809980, 7581330311082212790621785; 0, 5, 0, 0, 0
- ; 0, 0, 5, 0, 0; 0, 0, 0, 5, 0; 0, 0, 0, 0, 5], [1, 0, 0, 0, 0; 0, 1, 0, 0, 
- 0; 0, 0, 1, 0, 0; 0, 0, 0, 1, 0; 0, 0, 0, 0, 1], [1, 0, 0, 0, 0; 0, 1, 0, 0,
-  0; 0, 0, 1, 0, 0; 0, 0, 0, 1, 0; 0, 0, 0, 0, 1]]
- ? nfsubfields(nf)
- [[x, 0], [x^5 - 5*x^3 + 5*x + 25, x]]
- ? polcompositum(x^4-4*x+2,x^3-x-1)
- [x^12 - 4*x^10 + 8*x^9 + 12*x^8 + 12*x^7 + 138*x^6 + 132*x^5 - 43*x^4 + 58*x
- ^2 - 128*x - 5]
- ? polcompositum(x^4-4*x+2,x^3-x-1,1)
- [[x^12 - 4*x^10 + 8*x^9 + 12*x^8 + 12*x^7 + 138*x^6 + 132*x^5 - 43*x^4 + 58*
- x^2 - 128*x - 5, Mod(-279140305176/29063006931199*x^11 + 129916611552/290630
- 06931199*x^10 + 1272919322296/29063006931199*x^9 - 2813750209005/29063006931
- 199*x^8 - 2859411937992/29063006931199*x^7 - 414533880536/29063006931199*x^6
-  - 35713977492936/29063006931199*x^5 - 17432607267590/29063006931199*x^4 + 4
- 9785595543672/29063006931199*x^3 + 9423768373204/29063006931199*x^2 - 427797
- 76146743/29063006931199*x + 37962587857138/29063006931199, x^12 - 4*x^10 + 8
- *x^9 + 12*x^8 + 12*x^7 + 138*x^6 + 132*x^5 - 43*x^4 + 58*x^2 - 128*x - 5), M
- od(-279140305176/29063006931199*x^11 + 129916611552/29063006931199*x^10 + 12
- 72919322296/29063006931199*x^9 - 2813750209005/29063006931199*x^8 - 28594119
- 37992/29063006931199*x^7 - 414533880536/29063006931199*x^6 - 35713977492936/
- 29063006931199*x^5 - 17432607267590/29063006931199*x^4 + 49785595543672/2906
- 3006931199*x^3 + 9423768373204/29063006931199*x^2 - 13716769215544/290630069
- 31199*x + 37962587857138/29063006931199, x^12 - 4*x^10 + 8*x^9 + 12*x^8 + 12
- *x^7 + 138*x^6 + 132*x^5 - 43*x^4 + 58*x^2 - 128*x - 5), -1]]
- ? polgalois(x^6-3*x^2-1)
- [12, 1, 1, "A_4(6) = [2^2]3"]
- ? polred(x^5-2*x^4-4*x^3-96*x^2-352*x-568)
- [x - 1, x^5 - x^4 - 6*x^3 + 6*x^2 + 13*x - 5, x^5 - x^4 + 2*x^3 - 4*x^2 + x 
- - 1, x^5 - x^4 + 4*x^3 - 2*x^2 + x - 1, x^5 + 4*x^3 - 4*x^2 + 8*x - 8]
- ? polred(x^4-28*x^3-458*x^2+9156*x-25321,3)
- 
- [1 x - 1]
- 
- [1/115*x^2 - 14/115*x - 327/115 x^2 - 10]
- 
- [2/897*x^3 - 14/299*x^2 - 1171/897*x + 9569/897 x^4 - 32*x^2 + 6]
- 
- [1/4485*x^3 - 7/1495*x^2 - 1034/4485*x + 7924/4485 x^4 - 8*x^2 + 6]
- 
- ? polred(x^4+576,1)
- [x - 1, x^2 - x + 1, x^2 + 1, x^4 - x^2 + 1]
- ? polred(x^4+576,3)
- 
- [1 x - 1]
- 
- [-1/192*x^3 - 1/8*x + 1/2 x^2 - x + 1]
- 
- [1/24*x^2 x^2 + 1]
- 
- [1/192*x^3 + 1/48*x^2 - 1/8*x x^4 - x^2 + 1]
- 
- ? polred(p2,0,fa)
- [x - 1, x^5 - 2*x^4 - 62*x^3 + 85*x^2 + 818*x + 1, x^5 - 2*x^4 - 53*x^3 - 46
- *x^2 + 508*x + 913, x^5 - 2*x^4 - 13*x^3 + 37*x^2 - 21*x - 1, x^5 - x^4 - 52
- *x^3 - 197*x^2 - 273*x - 127]
- ? polred(p2,1,fa)
- [x - 1, x^5 - 2*x^4 - 62*x^3 + 85*x^2 + 818*x + 1, x^5 - 2*x^4 - 53*x^3 - 46
- *x^2 + 508*x + 913, x^5 - 2*x^4 - 13*x^3 + 37*x^2 - 21*x - 1, x^5 - x^4 - 52
- *x^3 - 197*x^2 - 273*x - 127]
- ? polredabs(x^5-2*x^4-4*x^3-96*x^2-352*x-568)
- x^5 - x^4 + 2*x^3 - 4*x^2 + x - 1
- ? polredabs(x^5-2*x^4-4*x^3-96*x^2-352*x-568,1)
- [x^5 - x^4 + 2*x^3 - 4*x^2 + x - 1, Mod(2*x^4 - x^3 + 3*x^2 - 3*x - 1, x^5 -
-  x^4 + 2*x^3 - 4*x^2 + x - 1)]
- ? polredord(x^3-12*x+45*x-1)
- [x - 1, x^3 - 363*x - 2663, x^3 + 33*x - 1]
- ? polsubcyclo(31,5)
- x^5 + x^4 - 12*x^3 - 21*x^2 + x + 5
- ? setrand(1);poltschirnhaus(x^5-x-1)
- x^5 + 10*x^4 + 32*x^3 - 100*x^2 - 879*x - 1457
- ? p=x^5-5*x+y;aa=rnfpseudobasis(nf2,p)
- [[1, 0, 0, -2, [3, 1, 0]~; 0, 1, 0, 2, [0, -1, 0]~; 0, 0, 1, 1, [-5, -2, 0]~
- ; 0, 0, 0, 1, -2; 0, 0, 0, 0, 1], [1, 1, 1, [1, 0, 2/5; 0, 1, 3/5; 0, 0, 1/5
- ], [1, 0, 22/25; 0, 1, 8/25; 0, 0, 1/25]], [416134375, 202396875, 60056800; 
- 0, 3125, 2700; 0, 0, 25], [-1275, 5, 5]~]
- ? rnfbasis(bnf2,aa)
- 
- [1 0 0 [-26/25, 11/25, -8/25]~ [0, 4, -7]~]
- 
- [0 1 0 [53/25, -8/25, -1/25]~ [6/5, -41/5, 53/5]~]
- 
- [0 0 1 [-14/25, -21/25, 13/25]~ [-16/5, 1/5, 7/5]~]
- 
- [0 0 0 [7/25, -2/25, 6/25]~ [2/5, -2/5, 11/5]~]
- 
- [0 0 0 [9/25, 1/25, -3/25]~ [2/5, -7/5, 6/5]~]
- 
- ? rnfdisc(nf2,p)
- [[416134375, 202396875, 60056800; 0, 3125, 2700; 0, 0, 25], [-1275, 5, 5]~]
- ? rnfequation(nf2,p)
- x^15 - 15*x^11 + 75*x^7 - x^5 - 125*x^3 + 5*x + 1
- ? rnfequation(nf2,p,1)
- [x^15 - 15*x^11 + 75*x^7 - x^5 - 125*x^3 + 5*x + 1, Mod(-x^5 + 5*x, x^15 - 1
- 5*x^11 + 75*x^7 - x^5 - 125*x^3 + 5*x + 1), 0]
- ? rnfhnfbasis(bnf2,aa)
- 
- [1 0 0 [-6/5, -4/5, 2/5]~ [3/25, -8/25, 24/25]~]
- 
- [0 1 0 [6/5, 4/5, -2/5]~ [-9/25, -1/25, 3/25]~]
- 
- [0 0 1 [3/5, 2/5, -1/5]~ [-8/25, 13/25, -39/25]~]
- 
- [0 0 0 [3/5, 2/5, -1/5]~ [4/25, 6/25, -18/25]~]
- 
- [0 0 0 0 [-2/25, -3/25, 9/25]~]
- 
- ? rnfisfree(bnf2,aa)
- 1
- ? rnfsteinitz(nf2,aa)
- [[1, 0, 0, [-26/25, 11/25, -8/25]~, [29/125, -2/25, 8/125]~; 0, 1, 0, [53/25
- , -8/25, -1/25]~, [-53/125, 7/125, 1/125]~; 0, 0, 1, [-14/25, -21/25, 13/25]
- ~, [9/125, 19/125, -13/125]~; 0, 0, 0, [7/25, -2/25, 6/25]~, [-9/125, 2/125,
-  -6/125]~; 0, 0, 0, [9/25, 1/25, -3/25]~, [-8/125, -1/125, 3/125]~], [1, 1, 
- 1, 1, [125, 0, 22; 0, 125, 108; 0, 0, 1]], [416134375, 202396875, 60056800; 
- 0, 3125, 2700; 0, 0, 25], [-1275, 5, 5]~]
- ? nfz=zetakinit(x^2-2);
- ? zetak(nfz,-3)
- 0.091666666666666666666666666666666666668
- ? zetak(nfz,1.5+3*I)
- 0.88324345992059326405525724366416928892 - 0.2067536250233895222724230899142
- 7938853*I
- ? setrand(1);quadclassunit(1-10^7,,[1,1])
- [2416, [1208, 2], [Qfb(277, 55, 9028), Qfb(1700, 1249, 1700)], 1]
- ? setrand(1);quadclassunit(10^9-3,,[0.5,0.5])
- [4, [4], [Qfb(283, 31285, -18771, 0.E-57)], 2800.625251907016076486370621737
- 0745514]
- ? sizebyte(%)
- 288
- ? getheap
- [175, 102929]
- ? print("Total time spent: ",gettime);
- Total time spent: 84
--- 0 ----

>Cheers,
>Bill.

Regards,
Bill

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Bill Allombert <allomber@math.u-bordeaux.fr>. Last modified: Sat Aug 26 17:16:36 2023; Machine Name: pari

PARI/GP Bug tracking system

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