File: [local] / OpenXM_contrib / pari-2.2 / src / test / 32 / Attic / compat (download)
Revision 1.2, Wed Sep 11 07:27:09 2002 UTC (21 years, 9 months ago) by noro
Branch: MAIN
CVS Tags: RELEASE_1_2_3, RELEASE_1_2_2_KNOPPIX_b, RELEASE_1_2_2_KNOPPIX, RELEASE_1_2_2
Changes since 1.1: +523 -688
lines
Upgraded pari-2.2 to pari-2.2.4.
|
echo = 1 (on)
? default(compatible,3)
compatible = 3 (use old functions, ignore case)
*** Warning: user functions re-initialized.
? +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
? \precision=57
realprecision = 57 significant digits
? pi
3.14159265358979323846264338327950288419716939937510582097
? \precision=38
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)
? initrect(0,500,500)
? abs(-0.01)
0.0099999999999999999999999999999999999999
? acos(0.5)
1.0471975511965977461542144610931676280
? acosh(3)
1.7627471740390860504652186499595846180
? acurve=initell([0,0,1,-1,0])
[0, 0, 1, -1, 0, 0, -2, 1, -1, 48, -216, 37, 110592/37, [0.83756543528332303
544481089907503024040, 0.26959443640544455826293795134926000404, -1.10715987
16887675937077488504242902444]~, 2.9934586462319596298320099794525081778, 2.
4513893819867900608542248318665252253*I, -0.47131927795681147588259389708033
769964, -1.4354565186686843187232088566788165076*I, 7.3381327407895767390707
210033323055881]
? apoint=[2,2]
[2, 2]
? isoncurve(acurve,apoint)
1
? addell(acurve,apoint,apoint)
[21/25, -56/125]
? addprimes([nextprime(10^9),nextprime(10^10)])
[1000000007, 10000000019]
? adj([1,2;3,4])
[4 -2]
[-3 1]
? agm(1,2)
1.4567910310469068691864323832650819749
? agm(1+o(7^5),8+o(7^5))
1 + 4*7 + 6*7^2 + 5*7^3 + 2*7^4 + O(7^5)
? algdep(2*cos(2*pi/13),6)
x^6 + x^5 - 5*x^4 - 4*x^3 + 6*x^2 + 3*x - 1
? algdep2(2*cos(2*pi/13),6,15)
x^6 + x^5 - 5*x^4 - 4*x^3 + 6*x^2 + 3*x - 1
? akell(acurve,1000000007)
43800
? nfpol=x^5-5*x^3+5*x+25
x^5 - 5*x^3 + 5*x + 25
? nf=initalg(nfpol)
[x^5 - 5*x^3 + 5*x + 25, [1, 2], 595125, 45, [[1, -1.08911514572050482502495
27946671612683, -2.4285174907194186068992069565359418364, 0.7194669112891317
8943997506477288225728, -2.5558200350691694950646071159426779970; 1, -0.1383
8372073406036365047976417441696635 - 0.4918163765776864349975328551474152510
7*I, 1.9647119211288133163138753392090569931 + 0.809714924188978951282940822
19556466856*I, -0.072312766896812300380582649294307897098 + 2.19808037538462
76641195195160383234877*I, -0.98796319352507039803950539735452837196 + 1.570
1452385894131769052374806001981108*I; 1, 1.682941293594312776162956161507997
6005 + 2.0500351226010726172974286983598602163*I, -0.75045317576910401286427
186094108607489 + 1.3101462685358123283560773619310445915*I, -0.787420688747
75359433940488309213323154 + 2.1336633893126618034168454610457936017*I, 1.26
58732110596551455718089553258673705 - 2.716479010374315056657802803578983483
4*I], [1, -1.0891151457205048250249527946671612683, -2.428517490719418606899
2069565359418364, 0.71946691128913178943997506477288225728, -2.5558200350691
694950646071159426779970; 1.4142135623730950488016887242096980785, -0.195704
13467375904264179382543977540672, 2.7785222450164664309920925654093065576, -
0.10226569567819614506098907018896260032, -1.3971909474085893198147151262541
540506; 0, -0.69553338995335755797766403996841143190, 1.14510982744395651299
26149974389115722, 3.1085550780550843138423672171643499921, 2.22052069130868
72788181483285734827868; 1.4142135623730950488016887242096980785, 2.38003840
20787979181834702019470475018, -1.0613010590986270398182318786558994412, -1.
1135810173202366904448352912286604470, 1.79021506332534372536778891648110361
60; 0, 2.8991874737236275652408825679737171586, 1.85282662165584876344468105
12816401036, 3.0174557027049114270734649132936867272, -3.8416814583731999185
306312841432940660], 0, [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], [108675, 5175, 0
, -10350, -15525; 5175, 13800, -8625, -1725, 27600; 0, -8625, 37950, -17250,
0; -10350, -1725, -17250, -24150, -15525; -15525, 27600, 0, -15525, -3450],
[595125, [238050, -296700, 91425, 1725, 0]~]], [-2.428517490719418606899206
9565359418364, 1.9647119211288133163138753392090569931 + 0.80971492418897895
128294082219556466856*I, -0.75045317576910401286427186094108607489 + 1.31014
62685358123283560773619310445915*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]]
? ba=algtobasis(nf,mod(x^3+5,nfpol))
[6, 1, 3, 1, 3]~
? anell(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]
? apell(acurve,10007)
66
? apell2(acurve,10007)
66
? apol=x^3+5*x+1
x^3 + 5*x + 1
? apprpadic(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)]
? apprpadic(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)
]~
? 4*arg(3+3*i)
3.1415926535897932384626433832795028842
? 3*asin(sqrt(3)/2)
3.1415926535897932384626433832795028841
? asinh(0.5)
0.48121182505960344749775891342436842313
? assmat(x^5-12*x^3+0.0005)
[0 0 0 0 -0.00049999999999999999999999999999999999999]
[1 0 0 0 0]
[0 1 0 0 0]
[0 0 1 0 12]
[0 0 0 1 0]
? 3*atan(sqrt(3))
3.1415926535897932384626433832795028841
? atanh(0.5)
0.54930614433405484569762261846126285232
? basis(x^3+4*x+5)
[1, x, 1/7*x^2 - 1/7*x - 2/7]
? basis2(x^3+4*x+5)
[1, x, 1/7*x^2 - 1/7*x - 2/7]
? basistoalg(nf,ba)
mod(x^3 + 5, x^5 - 5*x^3 + 5*x + 25)
? bernreal(12)
-0.25311355311355311355311355311355311354
? bernvec(6)
[1, 1/6, -1/30, 1/42, -1/30, 5/66, -691/2730]
? bestappr(pi,10000)
355/113
? bezout(123456789,987654321)
[-8, 1, 9]
? bigomega(12345678987654321)
8
? mcurve=initell([0,0,0,-17,0])
[0, 0, 0, -17, 0, 0, -34, 0, -289, 816, 0, 314432, 1728, [4.1231056256176605
498214098559740770251, 0.E-38, -4.1231056256176605498214098559740770251]~, 1
.2913084409290072207105564235857096009, 1.2913084409290072207105564235857096
009*I, -1.2164377440798088266474269946818791934, -3.649313232239426479942280
9840456375802*I, 1.6674774896145033307120230298772362381]
? mpoints=[[-1,4],[-4,2]]~
[[-1, 4], [-4, 2]]~
? mhbi=bilhell(mcurve,mpoints,[9,24])
[-0.72448571035980184146215805860545027439, 1.307328627832055544492943428892
1943055]~
? bin(1.1,5)
-0.0045457499999999999999999999999999999997
? binary(65537)
[1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1]
? bittest(10^100,100)
1
? boundcf(pi,5)
[3, 7, 15, 1, 292]
? boundfact(40!+1,100000)
[41 1]
[59 1]
[277 1]
[1217669507565553887239873369513188900554127 1]
? move(0,0,0);box(0,500,500)
? setrand(1);buchimag(1-10^7,1,1)
*** Warning: not a fundamental discriminant in quadclassunit.
[2416, [1208, 2], [qfi(277, 55, 9028), qfi(1700, 1249, 1700)], 1, 1.00257481
6299307750]
? setrand(1);bnf=buchinitfu(x^2-x-57,0.2,0.2)
[mat(3), mat([1, 2, 1, 2, 1, 2, 1, 2, 1]), [-2.71246530518434397468087951060
61300698 + 3.1415926535897932384626433832795028842*I; 2.71246530518434397468
08795106061300699], [1.7903417566977293763292119206302198761, 1.289761953065
2735025030086072395031017 + 3.1415926535897932384626433832795028842*I, 0.701
48550268542821846861610071436900868, -1.36845553 E-48, 0.5005798036324558738
2620331339071677436 + 3.1415926535897932384626433832795028842*I, 1.088856254
0123011578605958199158508674, 1.7241634548149836441438434283070556826 + 3.14
15926535897932384626433832795028842*I, -0.3432876442770270943898878667334192
1876 + 3.1415926535897932384626433832795028842*I, 2.133629400974756470719099
7873636390948 + 3.1415926535897932384626433832795028842*I, 0.066178301882745
732185368492323164193433 + 3.1415926535897932384626433832795028842*I; -1.790
3417566977293763292119206302198760, -1.2897619530652735025030086072395031017
, -0.70148550268542821846861610071436900868, 1.36845553 E-48, -0.50057980363
245587382620331339071677436, -1.0888562540123011578605958199158508674, -1.72
41634548149836441438434283070556826, 0.3432876442770270943898878667334192187
6, -2.1336294009747564707190997873636390948, -0.0661783018827457321853684923
23164193433], [[3, [0, 1]~, 1, 1, [1, 1]~], [5, [-1, 1]~, 1, 1, [2, 1]~], [1
1, [-1, 1]~, 1, 1, [2, 1]~], [3, [1, 1]~, 1, 1, [0, 1]~], [5, [2, 1]~, 1, 1,
[-1, 1]~], [11, [2, 1]~, 1, 1, [-1, 1]~], [19, [1, 1]~, 1, 1, [0, 1]~], [17
, [3, 1]~, 1, 1, [-2, 1]~], [17, [-2, 1]~, 1, 1, [3, 1]~], [19, [0, 1]~, 1,
1, [1, 1]~]], 0, [x^2 - x - 57, [2, 0], 229, 1, [[1, -8.06637297521077796359
59310246705326058; 1, 7.0663729752107779635959310246705326058], [1, -8.06637
29752107779635959310246705326058; 1, 7.0663729752107779635959310246705326058
], 0, [2, -1; -1, 115], [229, 115; 0, 1], [115, 1; 1, 2], [229, [115, 1]~]],
[-7.0663729752107779635959310246705326058, 8.066372975210777963595931024670
5326058], [1, x - 1], [1, 1; 0, 1], [1, 0, 0, 57; 0, 1, 1, -1]], [[3, [3], [
[3, 0; 0, 1]]], 2.7124653051843439746808795106061300699, 0.88144225126545793
64, [2, -1], [x + 7], 155], [mat(1), [[0, 0]], [[1.7903417566977293763292119
206302198761, -1.7903417566977293763292119206302198760]]], 0]
? buchcertify(bnf)
1
? buchfu(bnf)
[[x + 7], 155]
? setrand(1);buchinitforcefu(x^2-x-100000)
[mat(5), mat([3, 2, 1, 2, 0, 3, 0, 2, 2, 3, 1, 4, 3, 2, 2, 3, 3, 0]), [-129.
82045011403975460991182396195022419 + 6.283185307179586476925286766559005768
4*I; 129.82045011403975460991182396195022419], [-41.811264589129943393339502
258694361489 + 6.2831853071795864769252867665590057684*I, 9.2399004147902289
816376260438840931575 + 3.1415926535897932384626433832795028842*I, -11.87460
9881075406725097315997431161032 + 3.1415926535897932384626433832795028842*I,
0.E-67, -51.051165003920172374977128302578454646 + 3.1415926535897932384626
433832795028842*I, -64.910225057019877304955911980975112095 + 3.141592653589
7932384626433832795028842*I, -29.936654708054536668242186261263200456 + 3.14
15926535897932384626433832795028842*I, -47.668319071568233997332918482707687
878 + 6.2831853071795864769252867665590057684*I, 3.8762936464778825067484824
790355076166, -6.7377511782956880607802359510546381087 + 3.14159265358979323
84626433832795028842*I, -35.073513410834255332559266307639723380 + 3.1415926
535897932384626433832795028842*I, 33.130781426597481571750300827582717074 +
2.96736492 E-67*I, 54.878404098312329644822020875673145627 + 5.93472984 E-67
*I, -14.980188104648613073630759189293219180 + 3.141592653589793238462643383
2795028842*I, -26.831076484481330319708743069401142308 + 3.14159265358979323
84626433832795028842*I, -19.706749066516065512488907834878146944 + 3.1415926
535897932384626433832795028842*I, -22.104515522613877880850594423816214544 +
3.1415926535897932384626433832795028842*I, -45.6875582356078259000879847377
29869105 + 6.2831853071795864769252867665590057684*I, 47.6683190715682339973
32918482707687879 + 1.18694596 E-66*I; 41.8112645891299433933395022586943614
89, -9.2399004147902289816376260438840931575, 11.874609881075406725097315997
431161032, 0.E-67, 51.051165003920172374977128302578454646, 64.9102250570198
77304955911980975112095, 29.936654708054536668242186261263200456, 47.6683190
71568233997332918482707687879, -3.8762936464778825067484824790355076166, 6.7
377511782956880607802359510546381087, 35.07351341083425533255926630763972338
0, -33.130781426597481571750300827582717074, -54.878404098312329644822020875
673145627, 14.980188104648613073630759189293219180, 26.831076484481330319708
743069401142309, 19.706749066516065512488907834878146944, 22.104515522613877
880850594423816214544, 45.687558235607825900087984737729869105, -47.66831907
1568233997332918482707687878], [[2, [2, 1]~, 1, 1, [1, 1]~], [5, [5, 1]~, 1,
1, [1, 1]~], [13, [-5, 1]~, 1, 1, [6, 1]~], [2, [3, 1]~, 1, 1, [0, 1]~], [5
, [6, 1]~, 1, 1, [0, 1]~], [7, [4, 1]~, 2, 1, [-3, 1]~], [13, [6, 1]~, 1, 1,
[-5, 1]~], [23, [7, 1]~, 1, 1, [-6, 1]~], [43, [-15, 1]~, 1, 1, [16, 1]~],
[17, [20, 1]~, 1, 1, [-2, 1]~], [17, [15, 1]~, 1, 1, [3, 1]~], [29, [14, 1]~
, 1, 1, [-13, 1]~], [29, [-13, 1]~, 1, 1, [14, 1]~], [31, [39, 1]~, 1, 1, [-
7, 1]~], [31, [24, 1]~, 1, 1, [8, 1]~], [41, [7, 1]~, 1, 1, [-6, 1]~], [41,
[-6, 1]~, 1, 1, [7, 1]~], [43, [16, 1]~, 1, 1, [-15, 1]~], [23, [-6, 1]~, 1,
1, [7, 1]~]], 0, [x^2 - x - 100000, [2, 0], 400001, 1, [[1, -316.7281613012
9840161392089489603747004; 1, 315.72816130129840161392089489603747004], [1,
-316.72816130129840161392089489603747004; 1, 315.728161301298401613920894896
03747004], 0, [2, -1; -1, 200001], [400001, 200001; 0, 1], [200001, 1; 1, 2]
, [400001, [200001, 1]~]], [-315.72816130129840161392089489603747004, 316.72
816130129840161392089489603747004], [1, x - 1], [1, 1; 0, 1], [1, 0, 0, 1000
00; 0, 1, 1, -1]], [[5, [5], [[2, 0; 0, 1]]], 129.82045011403975460991182396
195022419, 0.9876536979069047228, [2, -1], [37955488401901378100630325489636
9154068336082609238336*x + 1198361656442507899904628359500228716651781276113
16131167], 24], [mat(1), [[0, 0]], [[-41.81126458912994339333950225869436148
9 + 6.2831853071795864769252867665590057684*I, 41.81126458912994339333950225
8694361489]]], 0]
? setrand(1);bnf=buchinitfu(x^2-x-57,0.2,0.2)
[mat(3), mat([1, 2, 1, 2, 1, 2, 1, 2, 1]), [-2.71246530518434397468087951060
61300698 + 3.1415926535897932384626433832795028842*I; 2.71246530518434397468
08795106061300699], [1.7903417566977293763292119206302198761, 1.289761953065
2735025030086072395031017 + 3.1415926535897932384626433832795028842*I, 0.701
48550268542821846861610071436900868, -1.36845553 E-48, 0.5005798036324558738
2620331339071677436 + 3.1415926535897932384626433832795028842*I, 1.088856254
0123011578605958199158508674, 1.7241634548149836441438434283070556826 + 3.14
15926535897932384626433832795028842*I, -0.3432876442770270943898878667334192
1876 + 3.1415926535897932384626433832795028842*I, 2.133629400974756470719099
7873636390948 + 3.1415926535897932384626433832795028842*I, 0.066178301882745
732185368492323164193433 + 3.1415926535897932384626433832795028842*I; -1.790
3417566977293763292119206302198760, -1.2897619530652735025030086072395031017
, -0.70148550268542821846861610071436900868, 1.36845553 E-48, -0.50057980363
245587382620331339071677436, -1.0888562540123011578605958199158508674, -1.72
41634548149836441438434283070556826, 0.3432876442770270943898878667334192187
6, -2.1336294009747564707190997873636390948, -0.0661783018827457321853684923
23164193433], [[3, [0, 1]~, 1, 1, [1, 1]~], [5, [-1, 1]~, 1, 1, [2, 1]~], [1
1, [-1, 1]~, 1, 1, [2, 1]~], [3, [1, 1]~, 1, 1, [0, 1]~], [5, [2, 1]~, 1, 1,
[-1, 1]~], [11, [2, 1]~, 1, 1, [-1, 1]~], [19, [1, 1]~, 1, 1, [0, 1]~], [17
, [3, 1]~, 1, 1, [-2, 1]~], [17, [-2, 1]~, 1, 1, [3, 1]~], [19, [0, 1]~, 1,
1, [1, 1]~]], 0, [x^2 - x - 57, [2, 0], 229, 1, [[1, -8.06637297521077796359
59310246705326058; 1, 7.0663729752107779635959310246705326058], [1, -8.06637
29752107779635959310246705326058; 1, 7.0663729752107779635959310246705326058
], 0, [2, -1; -1, 115], [229, 115; 0, 1], [115, 1; 1, 2], [229, [115, 1]~]],
[-7.0663729752107779635959310246705326058, 8.066372975210777963595931024670
5326058], [1, x - 1], [1, 1; 0, 1], [1, 0, 0, 57; 0, 1, 1, -1]], [[3, [3], [
[3, 0; 0, 1]]], 2.7124653051843439746808795106061300699, 0.88144225126545793
64, [2, -1], [x + 7], 155], [mat(1), [[0, 0]], [[1.7903417566977293763292119
206302198761, -1.7903417566977293763292119206302198760]]], 0]
? setrand(1);buchreal(10^9-3,0,0.5,0.5)
[4, [4], [qfr(3, 1, -83333333, 0.E-48)], 2800.625251907016076486370621737074
5514, 0.9849577285369119736]
? setrand(1);buchgen(x^4-7,0.2,0.2)
[x^4 - 7]
[[2, 1]]
[[-87808, 1]]
[[1, x, x^2, x^3]]
[[2, [2], [[3, 1, 2, 1; 0, 1, 0, 0; 0, 0, 1, 0; 0, 0, 0, 1]]]]
[14.229975145405511722395637833443108790]
[1.121117107152756229]
? setrand(1);buchgenfu(x^2-x-100000)
*** Warning: insufficient precision for fundamental units, not given.
[x^2 - x - 100000]
[[2, 0]]
[[400001, 1]]
[[1, x - 1]]
[[5, [5], [[2, 0; 0, 1]]]]
[129.82045011403975460991182396195022419]
[0.9876536979069047228]
[[2, -1]]
[[;]]
[-27]
? setrand(1);buchgenforcefu(x^2-x-100000)
[x^2 - x - 100000]
[[2, 0]]
[[400001, 1]]
[[1, x - 1]]
[[5, [5], [[2, 0; 0, 1]]]]
[129.82045011403975460991182396195022419]
[0.9876536979069047228]
[[2, -1]]
[[379554884019013781006303254896369154068336082609238336*x + 119836165644250
789990462835950022871665178127611316131167]]
[24]
? setrand(1);buchgenfu(x^4+24*x^2+585*x+1791,0.1,0.1)
[x^4 + 24*x^2 + 585*x + 1791]
[[0, 2]]
[[18981, 3087]]
[[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, -11/343*x^3 + 163/1029*x^2 - 373/343*x - 4260/3
43]]
[[4, [4], [[7, 2, 4, 0; 0, 1, 0, 0; 0, 0, 1, 0; 0, 0, 0, 1]]]]
[3.7941269688216589341408274220859400302]
[0.8826018286655581299]
[[6, 10/1029*x^3 - 13/343*x^2 + 165/343*x + 1478/343]]
[[1/343*x^3 - 46/1029*x^2 - 122/343*x - 174/343]]
[154]
? buchnarrow(bnf)
[3, [3], [[3, 0; 0, 1]]]
? buchray(bnf,[[5,4;0,1],[1,0]])
[12, [12], [[3, 0; 0, 1]]]
? bnr=buchrayinitgen(bnf,[[5,4;0,1],[1,0]])
[[mat(3), mat([1, 2, 1, 2, 1, 2, 1, 2, 1]), [-2.7124653051843439746808795106
061300698 + 3.1415926535897932384626433832795028842*I; 2.7124653051843439746
808795106061300699], [1.7903417566977293763292119206302198761, 1.28976195306
52735025030086072395031017 + 3.1415926535897932384626433832795028842*I, 0.70
148550268542821846861610071436900868, -1.36845553 E-48, 0.500579803632455873
82620331339071677436 + 3.1415926535897932384626433832795028842*I, 1.08885625
40123011578605958199158508674, 1.7241634548149836441438434283070556826 + 3.1
415926535897932384626433832795028842*I, -0.343287644277027094389887866733419
21876 + 3.1415926535897932384626433832795028842*I, 2.13362940097475647071909
97873636390948 + 3.1415926535897932384626433832795028842*I, 0.06617830188274
5732185368492323164193433 + 3.1415926535897932384626433832795028842*I; -1.79
03417566977293763292119206302198760, -1.289761953065273502503008607239503101
7, -0.70148550268542821846861610071436900868, 1.36845553 E-48, -0.5005798036
3245587382620331339071677436, -1.0888562540123011578605958199158508674, -1.7
241634548149836441438434283070556826, 0.343287644277027094389887866733419218
76, -2.1336294009747564707190997873636390948, -0.066178301882745732185368492
323164193433], [[3, [0, 1]~, 1, 1, [1, 1]~], [5, [-1, 1]~, 1, 1, [2, 1]~], [
11, [-1, 1]~, 1, 1, [2, 1]~], [3, [1, 1]~, 1, 1, [0, 1]~], [5, [2, 1]~, 1, 1
, [-1, 1]~], [11, [2, 1]~, 1, 1, [-1, 1]~], [19, [1, 1]~, 1, 1, [0, 1]~], [1
7, [3, 1]~, 1, 1, [-2, 1]~], [17, [-2, 1]~, 1, 1, [3, 1]~], [19, [0, 1]~, 1,
1, [1, 1]~]], 0, [x^2 - x - 57, [2, 0], 229, 1, [[1, -8.0663729752107779635
959310246705326058; 1, 7.0663729752107779635959310246705326058], [1, -8.0663
729752107779635959310246705326058; 1, 7.066372975210777963595931024670532605
8], 0, [2, -1; -1, 115], [229, 115; 0, 1], [115, 1; 1, 2], [229, [115, 1]~]]
, [-7.0663729752107779635959310246705326058, 8.06637297521077796359593102467
05326058], [1, x - 1], [1, 1; 0, 1], [1, 0, 0, 57; 0, 1, 1, -1]], [[3, [3],
[[3, 0; 0, 1]]], 2.7124653051843439746808795106061300699, 0.8814422512654579
364, [2, -1], [x + 7], 155], [mat(1), [[0, 0]], [[1.790341756697729376329211
9206302198761, -1.7903417566977293763292119206302198760]]], [0, [mat([[6, 1]
~, 1])]]], [[[5, 4; 0, 1], [1, 0]], [8, [4, 2], [[2, 0]~, [0, 1]~]], mat([[5
, [-1, 1]~, 1, 1, [2, 1]~], 1]), [[[[4], [[2, 0]~], [[2, 0]~], [[mod(0, 2)]~
], 1]], [[2], [[0, 1]~], mat(1)]], [1, 0; 0, 1]], [1], mat([1, -3, -6]), [12
, [12], [[3, 0; 0, 1]]], [[1/2, 0; 0, 0], [1, -1; 1, 1]]]
? bnr2=buchrayinitgen(bnf,[[25,14;0,1],[1,1]])
[[mat(3), mat([1, 2, 1, 2, 1, 2, 1, 2, 1]), [-2.7124653051843439746808795106
061300698 + 3.1415926535897932384626433832795028842*I; 2.7124653051843439746
808795106061300699], [1.7903417566977293763292119206302198761, 1.28976195306
52735025030086072395031017 + 3.1415926535897932384626433832795028842*I, 0.70
148550268542821846861610071436900868, -1.36845553 E-48, 0.500579803632455873
82620331339071677436 + 3.1415926535897932384626433832795028842*I, 1.08885625
40123011578605958199158508674, 1.7241634548149836441438434283070556826 + 3.1
415926535897932384626433832795028842*I, -0.343287644277027094389887866733419
21876 + 3.1415926535897932384626433832795028842*I, 2.13362940097475647071909
97873636390948 + 3.1415926535897932384626433832795028842*I, 0.06617830188274
5732185368492323164193433 + 3.1415926535897932384626433832795028842*I; -1.79
03417566977293763292119206302198760, -1.289761953065273502503008607239503101
7, -0.70148550268542821846861610071436900868, 1.36845553 E-48, -0.5005798036
3245587382620331339071677436, -1.0888562540123011578605958199158508674, -1.7
241634548149836441438434283070556826, 0.343287644277027094389887866733419218
76, -2.1336294009747564707190997873636390948, -0.066178301882745732185368492
323164193433], [[3, [0, 1]~, 1, 1, [1, 1]~], [5, [-1, 1]~, 1, 1, [2, 1]~], [
11, [-1, 1]~, 1, 1, [2, 1]~], [3, [1, 1]~, 1, 1, [0, 1]~], [5, [2, 1]~, 1, 1
, [-1, 1]~], [11, [2, 1]~, 1, 1, [-1, 1]~], [19, [1, 1]~, 1, 1, [0, 1]~], [1
7, [3, 1]~, 1, 1, [-2, 1]~], [17, [-2, 1]~, 1, 1, [3, 1]~], [19, [0, 1]~, 1,
1, [1, 1]~]], 0, [x^2 - x - 57, [2, 0], 229, 1, [[1, -8.0663729752107779635
959310246705326058; 1, 7.0663729752107779635959310246705326058], [1, -8.0663
729752107779635959310246705326058; 1, 7.066372975210777963595931024670532605
8], 0, [2, -1; -1, 115], [229, 115; 0, 1], [115, 1; 1, 2], [229, [115, 1]~]]
, [-7.0663729752107779635959310246705326058, 8.06637297521077796359593102467
05326058], [1, x - 1], [1, 1; 0, 1], [1, 0, 0, 57; 0, 1, 1, -1]], [[3, [3],
[[3, 0; 0, 1]]], 2.7124653051843439746808795106061300699, 0.8814422512654579
364, [2, -1], [x + 7], 155], [mat(1), [[0, 0]], [[1.790341756697729376329211
9206302198761, -1.7903417566977293763292119206302198760]]], [0, [mat([[6, 1]
~, 1])]]], [[[25, 14; 0, 1], [1, 1]], [80, [20, 2, 2], [[2, 0]~, [4, 2]~, [-
2, -2]~]], mat([[5, [-1, 1]~, 1, 1, [2, 1]~], 2]), [[[[4], [[2, 0]~], [[2, 0
]~], [[mod(0, 2), mod(0, 2)]~], 1], [[5], [[6, 0]~], [[6, 0]~], [[mod(0, 2),
mod(0, 2)]~], mat([1/5, -14/5])]], [[2, 2], [[4, 2]~, [-2, -2]~], [1, 0; 0,
1]]], [1, -12, 0, 0; 0, 0, 1, 0; 0, 0, 0, 1]], [1], mat([1, -3, -6, 0]), [1
2, [12], [[3, 0; 0, 1]]], [[1, -18, 9; -1/2, 10, -5], [-2, 0; 0, -10]]]
? bytesize(%)
6372
? ceil(-2.5)
-2
? centerlift(mod(456,555))
-99
? cf(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]
? cf2([1,3,5,7,9],(exp(1)-1)/(exp(1)+1))
[0, 6, 10, 42, 30]
? changevar(x+y,[z,t])
y + z
? char([1,2;3,4],z)
z^2 - 5*z - 2
? char(mod(x^2+x+1,x^3+5*x+1),z)
z^3 + 7*z^2 + 16*z - 19
? char1([1,2;3,4],z)
z^2 - 5*z - 2
? char2(mod(1,8191)*[1,2;3,4],z)
z^2 + mod(8186, 8191)*z + mod(8189, 8191)
? acurve=chell(acurve,[-1,1,2,3])
[-4, -1, -7, -12, -12, 12, 4, 1, -1, 48, -216, 37, 110592/37, [-0.1624345647
1667696455518910092496975959, -0.73040556359455544173706204865073999594, -2.
1071598716887675937077488504242902444]~, -2.99345864623195962983200997945250
81778, -2.4513893819867900608542248318665252253*I, 0.47131927795681147588259
389708033769964, 1.4354565186686843187232088566788165076*I, 7.33813274078957
67390707210033323055881]
? chinese(mod(7,15),mod(13,21))
mod(97, 105)
? apoint=chptell(apoint,[-1,1,2,3])
[1, 3]
? isoncurve(acurve,apoint)
1
? classno(-12391)
63
? classno(1345)
6
? classno2(-12391)
63
? classno2(1345)
6
? coeff(sin(x),7)
-1/5040
? compimag(qfi(2,1,3),qfi(2,1,3))
qfi(2, -1, 3)
? compo(1+o(7^4),3)
1
? compositum(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]
? compositum2(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, 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]]
? comprealraw(qfr(5,3,-1,0.),qfr(7,1,-1,0.))
qfr(35, 43, 13, 0.E-38)
? concat([1,2],[3,4])
[1, 2, 3, 4]
? conductor(bnf,[[25,14;0,1],[1,1]])
[[[5, 4; 0, 1], [1, 0]], [12, [12], [[3, 0; 0, 1]]], mat(12)]
? conductorofchar(bnr,[2])
[[5, 4; 0, 1], [0, 0]]
? conj(1+i)
1 - I
? conjvec(mod(x^2+x+1,x^3-x-1))
[4.0795956234914387860104177508366260325, 0.46020218825428060699479112458168
698369 + 0.18258225455744299269398828369501930573*I, 0.460202188254280606994
79112458168698369 - 0.18258225455744299269398828369501930573*I]~
? content([123,456,789,234])
3
? convol(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^16)
? core(54713282649239)
5471
? core2(54713282649239)
[5471, 100003]
? coredisc(54713282649239)
21884
? coredisc2(54713282649239)
[21884, 100003/2]
? cos(1)
0.54030230586813971740093660744297660373
? cosh(1)
1.5430806348152437784779056207570616825
? move(0,200,150)
? cursor(0)
? cvtoi(1.7)
1
? cyclo(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
? degree(x^3/(x-1))
2
? denom(12345/54321)
18107
? deplin(mod(1,7)*[2,-1;1,3])
[mod(6, 7), mod(5, 7)]~
? 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
? det([1,2,3;1,5,6;9,8,7])
-30
? det2([1,2,3;1,5,6;9,8,7])
-30
? detint([1,2,3;4,5,6])
3
? diagonal([2,4,6])
[2 0 0]
[0 4 0]
[0 0 6]
? dilog(0.5)
0.58224052646501250590265632015968010858
? 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]
? deu=direuler(p=2,100,1/(1-apell(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]
? anell(acurve,100)==deu
1
? 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]
? dirzetak(initalg(x^3-10*x+8),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]
? disc(x^3+4*x+12)
-4144
? discf(x^3+4*x+12)
-1036
? discrayabs(bnr,mat(6))
[12, 12, 18026977100265125]
? discrayabs(bnr)
[24, 12, 40621487921685401825918161408203125]
? discrayabscond(bnr2)
0
? lu=ideallistunitgen(bnf,55);discrayabslist(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]]
, []]]
? discrayabslistlong(bnf,20)
[[[[matrix(0,2,j,k,0), 6, 6, mat([229, 3])]], [], [[mat([12, 1]), 0, 0, 0],
[mat([13, 1]), 0, 0, 0]], [[mat([10, 1]), 0, 0, 0]], [[mat([20, 1]), 12, 12,
[5, 3; 229, 6]], [mat([21, 1]), 12, 12, [5, 3; 229, 6]]], [], [], [], [[mat
([12, 2]), 0, 0, 0], [[12, 1; 13, 1], 0, 0, 0], [mat([13, 2]), 0, 0, 0]], []
, [[mat([44, 1]), 0, 0, 0], [mat([45, 1]), 0, 0, 0]], [[[10, 1; 12, 1], 0, 0
, 0], [[10, 1; 13, 1], 0, 0, 0]], [], [], [[[12, 1; 20, 1], 24, 24, [3, 6; 5
, 9; 229, 12]], [[13, 1; 20, 1], 0, 0, 0], [[12, 1; 21, 1], 0, 0, 0], [[13,
1; 21, 1], 24, 24, [3, 6; 5, 9; 229, 12]]], [[mat([10, 2]), 0, 0, 0]], [[mat
([68, 1]), 0, 0, 0], [mat([69, 1]), 0, 0, 0]], [], [[mat([76, 1]), 18, 18, [
19, 6; 229, 9]], [mat([77, 1]), 18, 18, [19, 6; 229, 9]]], [[[10, 1; 20, 1],
0, 0, 0], [[10, 1; 21, 1], 0, 0, 0]]]]
? discrayrel(bnr,mat(6))
[6, 2, [125, 14; 0, 1]]
? discrayrel(bnr)
[12, 1, [1953125, 1160889; 0, 1]]
? discrayrelcond(bnr2)
0
? 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]
? divres(345,123)
[2, 99]~
? divres(x^7-1,x^5+1)
[x^2, -x^2 - 1]~
? divsum(8!,x,x)
159120
? postdraw([0,0,0])
? eigen([1,2,3;4,5,6;7,8,9])
[-1.2833494518006402717978106547571267252 1 0.283349451800640271797810654757
12672521]
[-0.14167472590032013589890532737856336260 -2 0.6416747259003201358989053273
7856336260]
[1 1 1]
? eint1(2)
0.048900510708061119567239835228049522206
? erfc(2)
0.0046777349810472658379307436327470713891
? eta(q)
1 - q - q^2 + q^5 + q^7 - q^12 - q^15 + O(q^16)
? euler
0.57721566490153286060651209008240243104
? z=y;y=x;eval(z)
x
? exp(1)
2.7182818284590452353602874713526624977
? extract([1,2,3,4,5,6,7,8,9,10],1000)
[4, 6, 7, 8, 9, 10]
? 10!
3628800
? fact(10)
3628800.0000000000000000000000000000000
? factcantor(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(factfq(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]
? factmod(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]
? factor(17!+1)
[661 1]
[537913 1]
[1000357 1]
? p=x^5+3021*x^4-786303*x^3-6826636057*x^2-546603588746*x+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]
? factoredbasis(p,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]
? factoreddiscf(p,fa)
136866601
? factoredpolred(p,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]
? factoredpolred2(p,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]
? factornf(x^3+x^2-2*x-1,t^3+t^2-2*t-1)
[mod(1, t^3 + t^2 - 2*t - 1)*x + mod(-t, t^3 + t^2 - 2*t - 1) 1]
[mod(1, t^3 + t^2 - 2*t - 1)*x + mod(-t^2 + 2, t^3 + t^2 - 2*t - 1) 1]
[mod(1, t^3 + t^2 - 2*t - 1)*x + mod(t^2 + t - 1, t^3 + t^2 - 2*t - 1) 1]
? 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]
? factorpadic2(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]
? factpol(x^15-1,3,1)
[x - 1 1]
[x^2 + x + 1 1]
[x^4 + x^3 + x^2 + x + 1 1]
[x^8 - x^7 + x^5 - x^4 + x^3 - x + 1 1]
? factpol(x^15-1,0,1)
[x - 1 1]
[x^2 + x + 1 1]
[x^4 + x^3 + x^2 + x + 1 1]
[x^8 - x^7 + x^5 - x^4 + x^3 - x + 1 1]
? factpol2(x^15-1,0)
*** this function has been suppressed.
? fibo(100)
354224848179261915075
? floor(-1/2)
-1
? floor(-2.5)
-3
? 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
0.25881904510252076234889883762404832834
0.49999999999999999999999999999999999999
0.70710678118654752440084436210484903928
0.86602540378443864676372317075293618347
0.96592582628906828674974319972889736763
1.0000000000000000000000000000000000000
0.96592582628906828674974319972889736764
0.86602540378443864676372317075293618348
0.70710678118654752440084436210484903930
0.50000000000000000000000000000000000002
0.25881904510252076234889883762404832838
4.7019774032891500318749461488889827112 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]
? frac(-2.7)
0.30000000000000000000000000000000000000
? galois(x^6-3*x^2-1)
[12, 1, 1]
? nf3=initalg(x^6+108);galoisconj(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]~
? aut=%[2];galoisapply(nf3,aut,mod(x^5,x^6+108))
mod(x^5, x^6 + 108)
? gamh(10)
1133278.3889487855673345741655888924755
? gamma(10.5)
1133278.3889487855673345741655888924755
? gauss(hilbert(10),[1,2,3,4,5,6,7,8,9,0]~)
[9236800, -831303990, 18288515520, -170691240720, 832112321040, -23298940665
00, 3883123564320, -3803844432960, 2020775945760, -449057772020]~
? gaussmodulo([2,3;5,4],[7,11],[1,4]~)
[-5, -1]~
? gaussmodulo2([2,3;5,4],[7,11],[1,4]~)
[[-5, -1]~, [-77, 723; 0, 1]]
? gcd(12345678,87654321)
9
? getheap()
[215, 44753]
? getrand()
498199132
? getstack()
0
? globalred(acurve)
[37, [1, -1, 2, 2], 1]
? getstack()
0
? hclassno(2000003)
357
? hell(acurve,apoint)
0.40889126591975072188708879805553617287
? hell2(acurve,apoint)
0.40889126591975072188708879805553617296
? hermite(amat=1/hilbert(7))
[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]
? hermite2(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], [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]]
? hermitehavas(amat)
*** this function has been suppressed.
? hermitemod(amat,detint(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]
? hermiteperm(amat)
[[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], [7, 6, 5, 4, 3, 2, 1]]
? hess(hilbert(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]
? hilb(2/3,3/4,5)
1
? hilbert(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]
? hilbp(mod(5,7),mod(6,7))
1
? hvector(10,x,1/x)
[1, 1/2, 1/3, 1/4, 1/5, 1/6, 1/7, 1/8, 1/9, 1/10]
? hyperu(1,1,1)
0.59634736232319407434107849936927937488
? i^2
-1
? nf1=initalgred(nfpol)
[x^5 - 2*x^4 + 3*x^3 + 8*x^2 + 3*x + 2, [1, 2], 595125, 4, [[1, -1.089115145
7205048250249527946671612684, 2.4285174907194186068992069565359418363, -0.71
946691128913178943997506477288225737, 2.555820035069169495064607115942677997
0; 1, -0.13838372073406036365047976417441696637 + 0.491816376577686434997532
85514741525107*I, -1.9647119211288133163138753392090569931 + 0.8097149241889
7895128294082219556466856*I, 0.072312766896812300380582649294307897128 + 2.1
980803753846276641195195160383234877*I, 0.9879631935250703980395053973545283
7195 + 1.5701452385894131769052374806001981108*I; 1, 1.682941293594312776162
9561615079976005 + 2.0500351226010726172974286983598602163*I, 0.750453175769
10401286427186094108607491 - 1.3101462685358123283560773619310445914*I, 0.78
742068874775359433940488309213323161 - 2.13366338931266180341684546104579360
16*I, -1.2658732110596551455718089553258673704 + 2.7164790103743150566578028
035789834835*I], [1, -1.0891151457205048250249527946671612684, 2.42851749071
94186068992069565359418363, -0.71946691128913178943997506477288225737, 2.555
8200350691694950646071159426779970; 1.4142135623730950488016887242096980785,
-0.19570413467375904264179382543977540673, -2.77852224501646643099209256540
93065576, 0.10226569567819614506098907018896260036, 1.3971909474085893198147
151262541540506; 0, 0.69553338995335755797766403996841143190, 1.145109827443
9565129926149974389115722, 3.1085550780550843138423672171643499921, 2.220520
6913086872788181483285734827868; 1.4142135623730950488016887242096980785, 2.
3800384020787979181834702019470475018, 1.06130105909862703981823187865589944
13, 1.1135810173202366904448352912286604471, -1.7902150633253437253677889164
811036159; 0, 2.8991874737236275652408825679737171587, -1.852826621655848763
4446810512816401034, -3.0174557027049114270734649132936867271, 3.84168145837
31999185306312841432940662], 0, [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, 145, 235, 168; 0, 3
45, 250, 344, 200; 0, 0, 5, 4, 3; 0, 0, 0, 1, 0; 0, 0, 0, 0, 1], [108675, 51
75, 0, 10350, 15525; 5175, 13800, 8625, 1725, -27600; 0, 8625, 37950, -17250
, 0; 10350, 1725, -17250, -24150, -15525; 15525, -27600, 0, -15525, -3450],
[595125, [-238050, 296700, 91425, 1725, 0]~]], [-1.0891151457205048250249527
946671612684, -0.13838372073406036365047976417441696637 + 0.4918163765776864
3499753285514741525107*I, 1.6829412935943127761629561615079976005 + 2.050035
1226010726172974286983598602163*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]]
? initalgred2(nfpol)
[[x^5 - 2*x^4 + 3*x^3 + 8*x^2 + 3*x + 2, [1, 2], 595125, 4, [[1, -1.08911514
57205048250249527946671612684, 2.4285174907194186068992069565359418363, -0.7
1946691128913178943997506477288225737, 2.55582003506916949506460711594267799
70; 1, -0.13838372073406036365047976417441696637 + 0.49181637657768643499753
285514741525107*I, -1.9647119211288133163138753392090569931 + 0.809714924188
97895128294082219556466856*I, 0.072312766896812300380582649294307897128 + 2.
1980803753846276641195195160383234877*I, 0.987963193525070398039505397354528
37195 + 1.5701452385894131769052374806001981108*I; 1, 1.68294129359431277616
29561615079976005 + 2.0500351226010726172974286983598602163*I, 0.75045317576
910401286427186094108607491 - 1.3101462685358123283560773619310445914*I, 0.7
8742068874775359433940488309213323161 - 2.1336633893126618034168454610457936
016*I, -1.2658732110596551455718089553258673704 + 2.716479010374315056657802
8035789834835*I], [1, -1.0891151457205048250249527946671612684, 2.4285174907
194186068992069565359418363, -0.71946691128913178943997506477288225737, 2.55
58200350691694950646071159426779970; 1.4142135623730950488016887242096980785
, -0.19570413467375904264179382543977540673, -2.7785222450164664309920925654
093065576, 0.10226569567819614506098907018896260036, 1.397190947408589319814
7151262541540506; 0, 0.69553338995335755797766403996841143190, 1.14510982744
39565129926149974389115722, 3.1085550780550843138423672171643499921, 2.22052
06913086872788181483285734827868; 1.4142135623730950488016887242096980785, 2
.3800384020787979181834702019470475018, 1.0613010590986270398182318786558994
413, 1.1135810173202366904448352912286604471, -1.790215063325343725367788916
4811036159; 0, 2.8991874737236275652408825679737171587, -1.85282662165584876
34446810512816401034, -3.0174557027049114270734649132936867271, 3.8416814583
731999185306312841432940662], 0, [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, 145, 235, 168; 0,
345, 250, 344, 200; 0, 0, 5, 4, 3; 0, 0, 0, 1, 0; 0, 0, 0, 0, 1], [108675, 5
175, 0, 10350, 15525; 5175, 13800, 8625, 1725, -27600; 0, 8625, 37950, -1725
0, 0; 10350, 1725, -17250, -24150, -15525; 15525, -27600, 0, -15525, -3450],
[595125, [-238050, 296700, 91425, 1725, 0]~]], [-1.089115145720504825024952
7946671612684, -0.13838372073406036365047976417441696637 + 0.491816376577686
43499753285514741525107*I, 1.6829412935943127761629561615079976005 + 2.05003
51226010726172974286983598602163*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)]
? vp=primedec(nf,3)[1]
[3, [1, 0, 1, 0, 0]~, 1, 1, [1, -1, -1, -1, 0]~]
? idx=idealmul(nf,idmat(5),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]
? idealinv(nf,idx)
[1 0 0 2/3 0]
[0 1 0 1/3 0]
[0 0 1 1/3 0]
[0 0 0 1/3 0]
[0 0 0 0 1]
? idy=ideallllred(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]
? 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]
? idealaddone(nf,idx,idy)
[[3, 2, 1, 2, 1]~, [-2, -2, -1, -2, -1]~]
? idealaddmultone(nf,[idy,idx])
[[-5, 0, 0, 0, 0]~, [6, 0, 0, 0, 0]~]
? idealappr(nf,idy)
[-2, -2, -1, -2, -1]~
? idealapprfact(nf,idealfactor(nf,idy))
[-2, -2, -1, -2, -1]~
? idealcoprime(nf,idx,idx)
[1/3, -1/3, -1/3, -1/3, 0]~
? 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]
? idealfactor(nf,idz)
[[3, [1, 0, 1, 0, 0]~, 1, 1, [1, -1, -1, -1, 0]~] 1]
[[5, [-1, 0, 0, 0, 1]~, 1, 1, [2, 0, 3, 0, 1]~] 1]
[[5, [2, 0, 0, 0, 1]~, 4, 1, [2, 2, 1, 2, 1]~] 3]
? ideallist(bnf,20)
[[[1, 0; 0, 1]], [], [[3, 0; 0, 1], [3, 1; 0, 1]], [[2, 0; 0, 2]], [[5, 4; 0
, 1], [5, 2; 0, 1]], [], [], [], [[9, 6; 0, 1], [3, 0; 0, 3], [9, 4; 0, 1]],
[], [[11, 10; 0, 1], [11, 2; 0, 1]], [[6, 0; 0, 2], [6, 2; 0, 2]], [], [],
[[15, 9; 0, 1], [15, 4; 0, 1], [15, 12; 0, 1], [15, 7; 0, 1]], [[4, 0; 0, 4]
], [[17, 15; 0, 1], [17, 3; 0, 1]], [], [[19, 0; 0, 1], [19, 1; 0, 1]], [[10
, 8; 0, 2], [10, 4; 0, 2]]]
? 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=idealmulred(nf,idx,idx)
[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]
? 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]
? idealdivexact(nf,idx2,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]
? idealhermite(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]
? idealhermite2(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]
? 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]
? idealpowred(nf,idx,7)
[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]
? idealtwoelt(nf,idy)
[5, [2, 2, 1, 2, 1]~]
? idealtwoelt2(nf,idy,10)
[-2, -2, -1, -2, -1]~
? idealval(nf,idp,vp)
7
? idmat(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]
? if(3<2,print("bof"),print("ok"));
ok
? imag(2+3*i)
3
? image([1,3,5;2,4,6;3,5,7])
[1 3]
[2 4]
[3 5]
? image(pi*[1,3,5;2,4,6;3,5,7])
[9.4247779607693797153879301498385086525 15.70796326794896619231321691639751
4420]
[12.566370614359172953850573533118011536 18.84955592153875943077586029967701
7305]
[15.707963267948966192313216916397514420 21.99114857512855266923850368295652
0189]
? incgam(2,1)
0.73575888234288464319104754032292173491
? incgam1(2,1)
-0.26424111765711535680895245967678075578
? incgam2(2,1)
0.73575888234288464319104754032292173489
? incgam3(2,1)
0.26424111765711535680895245967707826508
? incgam4(4,1,6)
5.8860710587430771455283803225833738791
? indexrank([1,1,1;1,1,1;1,1,2])
[[1, 3], [1, 3]]
? indsort([8,7,6,5])
[4, 3, 2, 1]
? initell([0,0,0,-1,0])
[0, 0, 0, -1, 0, 0, -2, 0, -1, 48, 0, 64, 1728, [1.0000000000000000000000000
000000000000, 0.E-38, -1.0000000000000000000000000000000000000]~, 2.62205755
42921198104648395898911194136, 2.6220575542921198104648395898911194136*I, -0
.59907011736779610371996124614016193910, -1.79721035210338831115988373842048
58173*I, 6.8751858180203728274900957798105571979]
? initrect(1,700,700)
? nfz=initzeta(x^2-2);
? integ(sin(x),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^17)
? integ((-x^2-2*a*x+8*a)/(x^4-14*x^3+(2*a+49)*x^2-14*a*x+a^2),x)
(x + a)/(x^2 - 7*x + a)
? intersect([1,2;3,4;5,6],[2,3;7,8;8,9])
[-1]
[-1]
[-1]
? \precision=19
realprecision = 19 significant digits
? intgen(x=0,pi,sin(x))
2.000000000000000017
? sqr(2*intgen(x=0,4,exp(-x^2)))
3.141592556720305685
? 4*intinf(x=1,10^20,1/(1+x^2))
3.141592653589793208
? intnum(x=-0.5,0.5,1/sqrt(1-x^2))
1.047197551196597747
? 2*intopen(x=0,100,sin(x)/x)
3.124450933778112629
? \precision=38
realprecision = 38 significant digits
? inverseimage([1,1;2,3;5,7],[2,2,6]~)
[4, -2]~
? isdiagonal([1,0,0;0,5,0;0,0,0])
1
? isfund(12345)
1
? isideal(bnf[7],[5,2;0,1])
1
? isincl(x^2+1,x^4+1)
[-x^2, x^2]
? isinclfast(initalg(x^2+1),initalg(x^4+1))
[-x^2, x^2]
? isirreducible(x^5+3*x^3+5*x^2+15)
0
? isisom(x^3+x^2-2*x-1,x^3+x^2-2*x-1)
[x, -x^2 - x + 1, x^2 - 2]
? isisomfast(initalg(x^3-2),initalg(x^3-6*x^2-6*x-30))
[-1/25*x^2 + 13/25*x - 2/5]
? isprime(12345678901234567)
0
? isprincipal(bnf,[5,2;0,1])
[1]~
? isprincipalgen(bnf,[5,2;0,1])
[[1]~, [7/3, 1/3]~, 155]
? isprincipalraygen(bnr,primedec(bnf,7)[1])
[[9]~, [112595/19683, 13958/19683]~, 192]
? ispsp(73!+1)
1
? isqrt(10!^2+1)
3628800
? isset([-3,5,7,7])
0
? issqfree(123456789876543219)
0
? issquare(12345678987654321)
1
? isunit(bnf,mod(3405*x-27466,x^2-x-57))
[-4, mod(1, 2)]~
? jacobi(hilbert(6))
[[1.6188998589243390969705881471257800712, 0.2423608705752095521357284158507
0114077, 0.000012570757122625194922982397996498755027, 0.0000001082799484565
5497685388772372251711485, 0.016321521319875822124345079564191505890, 0.0006
1574835418265769764919938428527140264]~, [0.74871921887909485900280109200517
845109, -0.61454482829258676899320019644273870645, 0.01114432093072471053067
8340374220998541, -0.0012481940840821751169398163046387834473, 0.24032536934
252330399154228873240534568, -0.062226588150197681775152126611810492910; 0.4
4071750324351206127160083580231701801, 0.21108248167867048675227675845247769
095, -0.17973275724076003758776897803740640964, 0.03560664294428763526612284
8131812048466, -0.69765137527737012296208335046678265583, 0.4908392097109243
6297498316169060044997; 0.32069686982225190106359024326699463106, 0.36589360
730302614149086554211117169622, 0.60421220675295973004426567844103062241, -0
.24067907958842295837736719558855679285, -0.23138937333290388042251363554209
048309, -0.53547692162107486593474491750949545456; 0.25431138634047419251788
312792590944672, 0.39470677609501756783094636145991581708, -0.44357471627623
954554460416705180105301, 0.62546038654922724457753441039459331059, 0.132863
15850933553530333839628101576050, -0.41703769221897886840494514780771076439;
0.21153084007896524664213667673977991959, 0.3881904338738864286311144882599
2418973, -0.44153664101228966222143649752977203423, -0.689807199293836684198
01738006926829419, 0.36271492146487147525299457604461742111, 0.0470340189331
15649705614518466541243873; 0.18144297664876947372217005457727093715, 0.3706
9590776736280861775501084807394603, 0.45911481681642960284551392793050866602
, 0.27160545336631286930015536176213647001, 0.502762866757515384892605663686
47786272, 0.54068156310385293880022293448123782121]]
? jbesselh(1,1)
0.24029783912342701089584304474193368045
? jell(i)
1728.0000000000000000000000000000000000 + 0.E-45*I
? kbessel(1+i,1)
0.32545977186584141085464640324923711863 + 0.2894280370259921276345671592415
2302704*I
? kbessel2(1+i,1)
0.32545977186584141085464640324923711863 + 0.2894280370259921276345671592415
2302704*I
? x
x
? y
x
? ker(matrix(4,4,x,y,x/y))
[-1/2 -1/3 -1/4]
[1 0 0]
[0 1 0]
[0 0 1]
? ker(matrix(4,4,x,y,sin(x+y)))
[1.0000000000000000000000000000000000000 1.080604611736279434801873214885953
2074]
[-1.0806046117362794348018732148859532074 -0.1677063269057152260048635409984
7562046]
[1 0]
[0 1]
? keri(matrix(4,4,x,y,x+y))
[1 2]
[-2 -3]
[1 0]
[0 1]
? kerint(matrix(4,4,x,y,x*y))
[-1 -1 -1]
[-1 0 1]
[1 -1 1]
[0 1 -1]
? kerint1(matrix(4,4,x,y,x*y))
[-1 -1 -1]
[-1 0 1]
[1 -1 1]
[0 1 -1]
? kerint2(matrix(4,6,x,y,2520/(x+y)))
*** this function has been suppressed.
? f(u)=u+1;
? print(f(5));kill(f);
6
? f=12
12
? killrect(1)
? kro(5,7)
-1
? kro(3,18)
0
? laplace(x*exp(x*y)/(exp(x)-1))
1 - 1/2*x + 13/6*x^2 - 3*x^3 + 419/30*x^4 - 30*x^5 + 6259/42*x^6 - 420*x^7 +
22133/10*x^8 - 7560*x^9 + 2775767/66*x^10 - 166320*x^11 + 2655339269/2730*x
^12 - 4324320*x^13 + 264873251/10*x^14 + O(x^15)
? lcm(15,-21)
105
? length(divisors(1000))
16
? legendre(10)
46189/256*x^10 - 109395/256*x^8 + 45045/128*x^6 - 15015/128*x^4 + 3465/256*x
^2 - 63/256
? lex([1,3],[1,3,5])
-1
? lexsort([[1,5],[2,4],[1,5,1],[1,4,2]])
[[1, 4, 2], [1, 5], [1, 5, 1], [2, 4]]
? lift(chinese(mod(7,15),mod(4,21)))
67
? lindep([(1-3*sqrt(2))/(3-2*sqrt(3)),1,sqrt(2),sqrt(3),sqrt(6)])
[-3, -3, 9, -2, 6]
? lindep2([(1-3*sqrt(2))/(3-2*sqrt(3)),1,sqrt(2),sqrt(3),sqrt(6)],14)
[-3, -3, 9, -2, 6]
? move(0,0,900);line(0,900,0)
? lines(0,vector(5,k,50*k),vector(5,k,10*k*k))
? m=1/hilbert(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,idmat(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]
? lll(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]
? lll1(m)
*** this function has been suppressed.
? lllgram(m)
[1 1 27 -27 69 0 141]
[0 1 4 -22 34 -24 49]
[0 1 3 -21 18 -24 23]
[0 1 3 -20 10 -19 13]
[0 1 3 -19 6 -14 8]
[0 1 3 -18 4 -10 5]
[0 1 3 -17 3 -7 3]
? lllgram1(m)
*** this function has been suppressed.
? lllgramint(m)
[1 1 27 -27 69 0 141]
[0 1 4 -23 34 -24 91]
[0 1 3 -22 18 -24 65]
[0 1 3 -21 10 -19 49]
[0 1 3 -20 6 -14 38]
[0 1 3 -19 4 -10 30]
[0 1 3 -18 3 -7 24]
? lllgramkerim(mp~*mp)
[[-420, -420, 840, 630, 2982, -1092, -83; -210, -280, 630, 504, 2415, -876,
70; -140, -210, 504, 420, 2050, -749, 137; -105, -168, 420, 360, 1785, -658,
169; -84, -140, 360, 315, 1582, -588, 184; -70, -120, 315, 280, 1421, -532,
190; -60, -105, 280, 252, 1290, -486, 191; 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, -840
; 0, 0, 0, 0, -13860, 0, 6930; 0, 0, 0, 0, 0, 5544, 0; 0, 0, 0, 0, 0, 0, -12
012], [0, 0, 0, 0, 0, 0, 0; 0, 0, 0, 0, 0, 0, 0; 0, 0, 0, 0, 0, 0, 0; 0, 0,
0, 0, 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]]
? lllint(m)
[-420 -420 840 630 -1092 -83 2982]
[-210 -280 630 504 -876 70 2415]
[-140 -210 504 420 -749 137 2050]
[-105 -168 420 360 -658 169 1785]
[-84 -140 360 315 -588 184 1582]
[-70 -120 315 280 -532 190 1421]
[-60 -105 280 252 -486 191 1290]
? lllintpartial(m)
[-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]
? lllkerim(mp)
[[-420, -420, 840, 630, 2982, -1092, -83; -210, -280, 630, 504, 2415, -876,
70; -140, -210, 504, 420, 2050, -749, 137; -105, -168, 420, 360, 1785, -658,
169; -84, -140, 360, 315, 1582, -588, 184; -70, -120, 315, 280, 1421, -532,
190; -60, -105, 280, 252, 1290, -486, 191; 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, -840
; 0, 0, 0, 0, -13860, 0, 6930; 0, 0, 0, 0, 0, 5544, 0; 0, 0, 0, 0, 0, 0, -12
012], [0, 0, 0, 0, 0, 0, 0; 0, 0, 0, 0, 0, 0, 0; 0, 0, 0, 0, 0, 0, 0; 0, 0,
0, 0, 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]]
? lllrat(m)
*** this function has been suppressed.
? \precision=96
realprecision = 96 significant digits
? ln(2)
0.69314718055994530941723212145817656807550013436025525412068000949339362196
9694715605863326996418
? lngamma(10^50*i)
-157079632679489661923132169163975144209858469968811.93673753887608474948977
0941153418951907406847 - 2.5258126069288717421377720813802613884088088474975
8842685248040385012601916745265645208759475328*I
? \precision=2000
realprecision = 2003 significant digits (2000 digits displayed)
? log(2)
0.69314718055994530941723212145817656807550013436025525412068000949339362196
9694715605863326996418687542001481020570685733685520235758130557032670751635
0759619307275708283714351903070386238916734711233501153644979552391204751726
8157493206515552473413952588295045300709532636664265410423915781495204374043
0385500801944170641671518644712839968171784546957026271631064546150257207402
4816377733896385506952606683411372738737229289564935470257626520988596932019
6505855476470330679365443254763274495125040606943814710468994650622016772042
4524529612687946546193165174681392672504103802546259656869144192871608293803
1727143677826548775664850856740776484514644399404614226031930967354025744460
7030809608504748663852313818167675143866747664789088143714198549423151997354
8803751658612753529166100071053558249879414729509293113897155998205654392871
7000721808576102523688921324497138932037843935308877482597017155910708823683
6275898425891853530243634214367061189236789192372314672321720534016492568727
4778234453534764811494186423867767744060695626573796008670762571991847340226
5146283790488306203306114463007371948900274364396500258093651944304119115060
8094879306786515887090060520346842973619384128965255653968602219412292420757
4321757489097706752687115817051137009158942665478595964890653058460258668382
9400228330053820740056770530467870018416240441883323279838634900156312188956
0650553151272199398332030751408426091479001265168243443893572472788205486271
5527418772430024897945401961872339808608316648114909306675193393128904316413
7068139777649817697486890388778999129650361927071088926410523092478391737350
1229842420499568935992206602204654941510613918788574424557751020683703086661
9480896412186807790208181588580001688115973056186676199187395200766719214592
2367206025395954365416553112951759899400560003665135675690512459268257439464
8316833262490180382424082423145230614096380570070255138770268178516306902551
3703234053802145019015374029509942262995779647427138157363801729873940704242
17997226696297993931270693
? logagm(2)
0.69314718055994530941723212145817656807550013436025525412068000949339362196
9694715605863326996418687542001481020570685733685520235758130557032670751635
0759619307275708283714351903070386238916734711233501153644979552391204751726
8157493206515552473413952588295045300709532636664265410423915781495204374043
0385500801944170641671518644712839968171784546957026271631064546150257207402
4816377733896385506952606683411372738737229289564935470257626520988596932019
6505855476470330679365443254763274495125040606943814710468994650622016772042
4524529612687946546193165174681392672504103802546259656869144192871608293803
1727143677826548775664850856740776484514644399404614226031930967354025744460
7030809608504748663852313818167675143866747664789088143714198549423151997354
8803751658612753529166100071053558249879414729509293113897155998205654392871
7000721808576102523688921324497138932037843935308877482597017155910708823683
6275898425891853530243634214367061189236789192372314672321720534016492568727
4778234453534764811494186423867767744060695626573796008670762571991847340226
5146283790488306203306114463007371948900274364396500258093651944304119115060
8094879306786515887090060520346842973619384128965255653968602219412292420757
4321757489097706752687115817051137009158942665478595964890653058460258668382
9400228330053820740056770530467870018416240441883323279838634900156312188956
0650553151272199398332030751408426091479001265168243443893572472788205486271
5527418772430024897945401961872339808608316648114909306675193393128904316413
7068139777649817697486890388778999129650361927071088926410523092478391737350
1229842420499568935992206602204654941510613918788574424557751020683703086661
9480896412186807790208181588580001688115973056186676199187395200766719214592
2367206025395954365416553112951759899400560003665135675690512459268257439464
8316833262490180382424082423145230614096380570070255138770268178516306902551
3703234053802145019015374029509942262995779647427138157363801729873940704242
17997226696297993931270693
? \precision=19
realprecision = 19 significant digits
? bcurve=initell([0,0,0,-3,0])
[0, 0, 0, -3, 0, 0, -6, 0, -9, 144, 0, 1728, 1728, [1.732050807568877293, 0.
E-19, -1.732050807568877293]~, 1.992332899583490707, 1.992332899583490708*I,
-0.7884206134041560682, -2.365261840212468204*I, 3.969390382762759668]
? localred(bcurve,2)
[6, 2, [1, 1, 1, 0], 1]
? ccurve=initell([0,0,-1,-1,0])
[0, 0, -1, -1, 0, 0, -2, 1, -1, 48, -216, 37, 110592/37, [0.8375654352833230
353, 0.2695944364054445582, -1.107159871688767593]~, 2.993458646231959630, 2
.451389381986790061*I, -0.4713192779568114757, -1.435456518668684318*I, 7.33
8132740789576742]
? l=lseriesell(ccurve,2,-37,1)
0.3815754082607112111
? lseriesell(ccurve,2,-37,1.2)-l
-1.08420217 E-19
? sbnf=smallbuchinit(x^3-x^2-14*x-1)
[x^3 - x^2 - 14*x - 1, 3, 10889, [1, x, x^2 - x - 9], [-3.233732695981516672
, -0.07182350902743636344, 4.305556205008953036], [10889, 5698, 8994; 0, 1,
0; 0, 0, 1], mat(2), mat([1, 1, 0, 1, 1, 0, 1, 1]), [9, 15, 16, 17, 39, 10,
33, 57, 69], [2, [-1, 0, 0]~], [[0, 1, 0]~, [5, 3, 1]~], [-4, -1, 2, 3, 10,
3, 1, 7, 2; 1, 1, 1, 1, 5, 0, 1, 2, 1; 0, 0, 0, 0, 1, 0, 0, 0, -1]]
? makebigbnf(sbnf)
[mat(2), mat([1, 1, 0, 1, 1, 0, 1, 1]), [1.173637103435061715 + 3.1415926535
89793238*I, -4.562279014988837952 + 3.141592653589793238*I; -2.6335434327389
76049 + 3.141592653589793238*I, 1.420330600779487357 + 3.141592653589793238*
I; 1.459906329303914334, 3.141948414209350543], [1.246346989334819161 + 3.14
1592653589793238*I, 0.5404006376129469727 + 3.141592653589793238*I, -0.69263
91142471042844 + 3.141592653589793238*I, -1.990056445584799713 + 3.141592653
589793238*I, -0.8305625946607188643 + 3.141592653589793238*I, 0.E-57, 0.0043
75616572659815433 + 3.141592653589793238*I, -1.977791147836553953, 0.3677262
014027817708 + 3.141592653589793238*I; 0.6716827432867392938 + 3.14159265358
9793238*I, -0.8333219883742404170 + 3.141592653589793238*I, -0.2461086674077
943076, 0.5379005671092853269, -1.552661549868775853, 0.E-57, -0.87383180430
71131263, 0.5774919091398324092, 0.9729063188316092380; -1.91802973262155845
5, 0.2929213507612934444, 0.9387477816548985923, 1.452155878475514386, 2.383
224144529494717, 0.E-57, 0.8694561877344533111, 1.400299238696721544, -1.340
632520234391008], [[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]~], [5, [3, 1, 0]~, 1, 1, [2,
2, 1]~], [13, [19, 1, 0]~, 1, 1, [-2, -6, 1]~], [3, [10, 1, 1]~, 1, 2, [-1,
1, 0]~], [11, [1, 1, 0]~, 1, 1, [-3, -1, 1]~], [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, -3.233732695981516672, 4.690759845041404811; 1, -0.0
7182350902743636344, -8.923017874523549402; 1, 4.305556205008953036, 5.23225
8029482144592], [1, -3.233732695981516672, 4.690759845041404811; 1, -0.07182
350902743636344, -8.923017874523549402; 1, 4.305556205008953036, 5.232258029
482144592], 0, [3, 1, 1; 1, 29, 8; 1, 8, 129], [10889, 5698, 8994; 0, 1, 0;
0, 0, 1], [3677, -121, -21; -121, 386, -23; -21, -23, 86], [10889, [1899, 51
91, 1]~]], [-3.233732695981516672, -0.07182350902743636344, 4.30555620500895
3036], [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]]], 10.34800724602768011, 1.000000000000000000,
[2, -1], [x, x^2 + 2*x - 4], 1000], [mat(1), [[0.E-57, 0.E-57, 0.E-57]], [[
1.246346989334819161 + 3.141592653589793238*I, 0.6716827432867392938 + 3.141
592653589793238*I, -1.918029732621558455]]], [-4, -1, 2, 3, 10, 3, 1, 7, 2;
1, 1, 1, 1, 5, 0, 1, 2, 1; 0, 0, 0, 0, 1, 0, 0, 0, -1]]
? concat(mat(vector(4,x,x)~),vector(4,x,10+x)~)
[1 11]
[2 12]
[3 13]
[4 14]
? matextract(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]
? ma=mathell(mcurve,mpoints)
[1.172183098700697010 0.4476973883408951692]
[0.4476973883408951692 1.755026016172950713]
? gauss(ma,mhbi)
[-1.000000000000000000, 1.000000000000000000]~
? (1.*hilbert(7))^(-1)
[48.99999999999354616 -1175.999999999759026 8819.999999997789586 -29399.9999
9999171836 48509.99999998526254 -38807.99999998756766 12011.99999999599856]
[-1175.999999999756499 37631.99999999093860 -317519.9999999170483 1128959.99
9999689868 -1940399.999999448886 1596671.999999535762 -504503.9999998507690]
[8819.999999997745604 -317519.9999999163090 2857679.999999235184 -10583999.9
9999714478 18710999.99999493212 -15717239.99999573533 5045039.999998630382]
[-29399.99999999149442 1128959.999999684822 -10583999.99999712372 40319999.9
9998927448 -72764999.99998098063 62092799.99998400783 -20180159.99999486766]
[48509.99999998476962 -1940399.999999436456 18710999.99999486299 -72764999.9
9998086196 133402499.9999660890 -115259759.9999715052 37837799.99999086044]
[-38807.99999998708779 1596671.999999522805 -15717239.99999565420 62092799.9
9998382209 -115259759.9999713525 100590335.9999759413 -33297263.99999228701]
[12011.99999999582671 -504503.9999998459239 5045039.999998597949 -20180159.9
9999478405 37837799.99999076882 -33297263.99999225112 11099087.99999751679]
? matsize([1,2;3,4;5,6])
[3, 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]
? matrixqz2([1/3,1/4,1/6;1/2,1/4,-1/4;1/3,1,0])
[19 12 2]
[0 1 0]
[0 0 1]
? matrixqz3([1,3;3,5;5,7])
[2 -1]
[1 0]
[0 1]
? max(2,3)
3
? min(2,3)
2
? minim([2,1;1,2],4,6)
[6, 2, [0, -1, 1; 1, 1, 0]]
? mod(-12,7)
mod(2, 7)
? modp(-12,7)
mod(2, 7)
? mod(10873,49649)^-1
*** impossible inverse modulo: mod(131, 49649).
? modreverse(mod(x^2+1,x^3-x-1))
mod(x^2 - 3*x + 2, x^3 - 5*x^2 + 8*x - 5)
? move(0,243,583);cursor(0)
? mu(3*5*7*11*13)
-1
? newtonpoly(x^4+3*x^3+27*x^2+9*x+81,3)
[2, 2/3, 2/3, 2/3]
? nextprime(100000000000000000000000)
100000000000000000000117
? setrand(1);a=matrix(3,5,j,k,vvector(5,l,random()\10^8))
[[10, 7, 8, 7, 18]~ [17, 0, 9, 20, 10]~ [5, 4, 7, 18, 20]~ [0, 16, 4, 2, 0]~
[17, 19, 17, 1, 14]~]
[[17, 16, 6, 3, 6]~ [17, 13, 9, 19, 6]~ [1, 14, 12, 20, 8]~ [6, 1, 8, 17, 21
]~ [18, 17, 9, 10, 13]~]
[[4, 13, 3, 17, 14]~ [14, 16, 11, 5, 4]~ [9, 11, 13, 7, 15]~ [19, 21, 2, 4,
5]~ [14, 16, 6, 20, 14]~]
? aid=[idx,idy,idz,idmat(5),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, 0, 0, 0, 0; 0, 1, 0, 0, 0; 0, 0, 1, 0, 0; 0, 0, 0, 1, 0; 0, 0, 0,
0, 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]]
? bb=algtobasis(nf,mod(x^3+x,nfpol))
[1, 1, 4, 1, 3]~
? da=nfdetint(nf,[a,aid])
[90 70 35 0 65]
[0 5 0 0 0]
[0 0 5 0 0]
[0 0 0 5 0]
[0 0 0 0 5]
? nfdiv(nf,ba,bb)
[584/373, 66/373, -32/373, -105/373, 120/373]~
? nfdiveuc(nf,ba,bb)
[2, 0, 0, 0, 0]~
? nfdivres(nf,ba,bb)
[[2, 0, 0, 0, 0]~, [4, -1, -5, -1, -3]~]
? nfhermite(nf,[a,aid])
[[[1, 0, 0, 0, 0]~, [-2, 0, 0, 0, 0]~, [0, 0, 0, 0, 0]~; [0, 0, 0, 0, 0]~, [
1, 0, 0, 0, 0]~, [0, 0, 0, 0, 0]~; [0, 0, 0, 0, 0]~, [0, 0, 0, 0, 0]~, [1, 0
, 0, 0, 0]~], [[10, 4, 5, 6, 7; 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], [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]]]
? nfhermitemod(nf,[a,aid],da)
[[[1, 0, 0, 0, 0]~, [-2, 0, 0, 0, 0]~, [0, 0, 0, 0, 0]~; [0, 0, 0, 0, 0]~, [
1, 0, 0, 0, 0]~, [0, 0, 0, 0, 0]~; [0, 0, 0, 0, 0]~, [0, 0, 0, 0, 0]~, [1, 0
, 0, 0, 0]~], [[10, 4, 5, 6, 7; 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], [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]]]
? nfmod(nf,ba,bb)
[4, -1, -5, -1, -3]~
? nfmul(nf,ba,bb)
[50, -15, -35, 60, 15]~
? nfpow(nf,bb,5)
[-291920, 136855, 230560, -178520, 74190]~
? nfreduce(nf,ba,idx)
[1, 0, 0, 0, 0]~
? setrand(1);as=matrix(3,3,j,k,vvector(5,l,random()\10^8))
[[10, 7, 8, 7, 18]~ [17, 0, 9, 20, 10]~ [5, 4, 7, 18, 20]~]
[[17, 16, 6, 3, 6]~ [17, 13, 9, 19, 6]~ [1, 14, 12, 20, 8]~]
[[4, 13, 3, 17, 14]~ [14, 16, 11, 5, 4]~ [9, 11, 13, 7, 15]~]
? vaid=[idx,idy,idmat(5)]
[[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
], [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]]
? haid=[idmat(5),idmat(5),idmat(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
], [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]]
? nfsmith(nf,[as,haid,vaid])
[[2562748315629757085585610, 436545976069778274371140, 123799938628701108220
1405, 2356446991473627724963350, 801407102592194537169612; 0, 5, 0, 0, 2; 0,
0, 5, 0, 1; 0, 0, 0, 5, 2; 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]]
? nfval(nf,ba,vp)
0
? norm(1+i)
2
? norm(mod(x+5,x^3+x+1))
129
? norml2(vector(10,x,x))
385
? nucomp(qfi(2,1,9),qfi(4,3,5),3)
qfi(2, -1, 9)
? form=qfi(2,1,9);nucomp(form,form,3)
qfi(4, -3, 5)
? numdiv(2^99*3^49)
5000
? numer((x+1)/(x-1))
x + 1
? nupow(form,111)
qfi(2, -1, 9)
? 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)
? omega(100!)
25
? ordell(acurve,1)
[8, 3]
? order(mod(33,2^16+1))
2048
? tcurve=initell([1,0,1,-19,26]);
? orderell(tcurve,[1,2])
6
? ordred(x^3-12*x+45*x-1)
[x - 1, x^3 - 363*x - 2663, x^3 + 33*x - 1]
? padicprec(padicno,127)
5
? pascal(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]
? perf([2,0,1;0,2,1;1,1,2])
6
? permutation(7,1035)
[4, 7, 1, 6, 3, 5, 2]
? permutation2num([4,7,1,6,3,5,2])
1035
? pf(-44,3)
qfi(3, 2, 4)
? phi(257^2)
65792
? pi
3.141592653589793238
? 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
? pnqn([2,6,10,14,18,22,26])
[19318376 741721]
[8927353 342762]
? pnqn([1,1,1,1,1,1,1,1;1,1,1,1,1,1,1,1])
[34 21]
[21 13]
? point(0,225,334)
? points(0,vector(10,k,10*k),vector(10,k,5*k*k))
? pointell(acurve,zell(acurve,apoint))
[0.9999999999999999986 + 0.E-19*I, 2.999999999999999998 + 0.E-18*I]
? polint([0,2,3],[0,4,9],5)
25
? 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]
? polred2(x^4-28*x^3-458*x^2+9156*x-25321)
[1 x - 1]
[1/115*x^2 - 14/115*x - 327/115 x^2 - 10]
[3/1495*x^3 - 63/1495*x^2 - 1607/1495*x + 13307/1495 x^4 - 32*x^2 + 216]
[1/4485*x^3 - 7/1495*x^2 - 1034/4485*x + 7924/4485 x^4 - 8*x^2 + 6]
? 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
? polredabs2(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, mod(2*x^4 - x^3 + 3*x^2 - 3*x - 1, x^5 -
x^4 + 2*x^3 - 4*x^2 + x - 1)]
? polsym(x^17-1,17)
[17, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 17]~
? polvar(name^4-other)
name
? poly(sin(x),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
? polylog(5,0.5)
0.5084005792422687065
? 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)
? polylogd(5,0.5)
1.033792745541689061
? polylogdold(5,0.5)
1.034459423449010483
? polylogp(5,0.5)
0.9495693489964922581
? poly([1,2,3,4,5],x)
x^4 + 2*x^3 + 3*x^2 + 4*x + 5
? polyrev([1,2,3,4,5],x)
5*x^4 + 4*x^3 + 3*x^2 + 2*x + 1
? polzag(6,3)
4608*x^6 - 13824*x^5 + 46144/3*x^4 - 23168/3*x^3 + 5032/3*x^2 - 120*x + 1
? postdraw([0,20,20])
? postploth(x=-5,5,sin(x))
[-5.000000000000000000, 5.000000000000000000, -0.9999964107564721649, 0.9999
964107564721649]
? postploth2(t=0,2*pi,[sin(5*t),sin(7*t)])
[-0.9999994509568810308, 0.9999994509568810308, -0.9999994509568810308, 0.99
99994509568810308]
? postplothraw(vector(100,k,k),vector(100,k,k*k/100))
[1.000000000000000000, 100.0000000000000000, 0.01000000000000000020, 100.000
0000000000000]
? powell(acurve,apoint,10)
[-28919032218753260057646013785951999/292736325329248127651484680640160000,
478051489392386968218136375373985436596569736643531551/158385319626308443937
475969221994173751192384064000000]
? cmcurve=initell([0,-3/4,0,-2,-1])
[0, -3/4, 0, -2, -1, -3, -4, -4, -1, 105, 1323, -343, -3375, [2.000000000000
000000, -0.6250000000000000000 + 0.3307189138830738238*I, -0.625000000000000
0000 - 0.3307189138830738238*I]~, 1.933311705616811546, 0.966655852808405773
3 + 2.557530989916099474*I, -0.8558486330998558525 - 4.59882981 E-20*I, -0.4
279243165499279261 - 2.757161217166147204*I, 4.944504600282546727]
? powell(cmcurve,[x,y],quadgen(-7))
[((-2 + 3*w)*x^2 + (6 - w))/((-2 - 5*w)*x + (-4 - 2*w)), ((34 - 11*w)*x^3 +
(40 - 28*w)*x^2 + (22 + 23*w)*x)/((-90 - w)*x^2 + (-136 + 44*w)*x + (-40 + 2
8*w))]
? powrealraw(qfr(5,3,-1,0.),3)
qfr(125, 23, 1, 0.E-18)
? pprint((x-12*y)/(y+13*x));
(-(11 /14))
? pprint([1,2;3,4])
[1 2]
[3 4]
? pprint1(x+y);pprint(x+y);
(2 x)(2 x)
? \precision=96
realprecision = 96 significant digits
? pi
3.14159265358979323846264338327950288419716939937510582097494459230781640628
620899862803482534211
? prec(pi,20)
3.141592653589793238462643383
? precision(cmcurve)
19
? \precision=38
realprecision = 38 significant digits
? prime(100)
541
? primedec(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]~]]
? primedec(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]~]]
? primedec(nf,11)
[[11, [11, 0, 0, 0, 0]~, 1, 5, [1, 0, 0, 0, 0]~]]
? 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]
? forprime(p=2,100,print(p," ",lift(primroot(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
? principalideal(nf,mod(x^3+5,nfpol))
[6]
[1]
[3]
[1]
[3]
? principalidele(nf,mod(x^3+5,nfpol))
[[6; 1; 3; 1; 3], [2.2324480827796254080981385584384939684 + 3.1415926535897
932384626433832795028841*I, 5.0387659675158716386435353106610489967 + 1.5851
760343512250049897278861965702423*I, 4.2664040272651028743625910797589683173
- 0.0083630478144368246110910258645462996226*I]]
? print((x-12*y)/(y+13*x));
-11/14
? print([1,2;3,4])
[1, 2; 3, 4]
? print1(x+y);print1(" equals ");print(x+y);
2*x equals 2*x
? prod(1,k=1,10,1+1/k!)
3335784368058308553334783/905932868585678438400000
? prod(1.,k=1,10,1+1/k!)
3.6821540356142043935732308433185262945
? pi^2/6*prodeuler(p=2,10000,1-p^-2)
1.0000098157493066238697591433298145166
? prodinf(n=0,(1+2^-n)/(1+2^(-n+1)))
0.33333333333333333333333333333333333313
? prodinf1(n=0,-2^-n/(1+2^(-n+1)))
0.33333333333333333333333333333333333313
? psi(1)
-0.57721566490153286060651209008240243104
? quaddisc(-252)
-7
? quadgen(-11)
w
? quadpoly(-11)
x^2 - x + 3
? rank(matrix(5,5,x,y,x+y))
2
? rayclassno(bnf,[[5,4;0,1],[1,0]])
12
? rayclassnolist(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]]
? move(0,50,50);rbox(0,50,50)
? print1("give a value for s? ");s=read();print(1/s)
give a value for s? 37.
0.027027027027027027027027027027027027026
? real(5-7*i)
5
? recip(3*x^7-5*x^3+6*x-9)
-9*x^7 + 6*x^6 - 5*x^4 + 3
? redimag(qfi(3,10,12))
qfi(3, -2, 4)
? redreal(qfr(3,10,-20,1.5))
qfr(3, 16, -7, 1.5000000000000000000000000000000000000)
? redrealnod(qfr(3,10,-20,1.5),18)
qfr(3, 16, -7, 1.5000000000000000000000000000000000000)
? reduceddisc(x^3+4*x+12)
[1036, 4, 1]
? regula(17)
2.0947125472611012942448228460655286534
? kill(y);print(x+y);reorder([x,y]);print(x+y);
x + y
x + y
? resultant(x^3-1,x^3+1)
8
? resultant2(x^3-1.,x^3+1.)
8.0000000000000000000000000000000000000
? reverse(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^16)
? rhoreal(qfr(3,10,-20,1.5))
qfr(-20, -10, 3, 2.1074451073987839947135880252731470615)
? rhorealnod(qfr(3,10,-20,1.5),18)
qfr(-20, -10, 3, 1.5000000000000000000000000000000000000)
? rline(0,200,150)
? cursor(0)
? rmove(0,5,5);cursor(0)
? rndtoi(prod(1,k=1,17,x-exp(2*i*pi*k/17)))
x^17 - 1
? qpol=y^3-y-1;setrand(1);bnf2=buchinit(qpol);nf2=bnf2[7];
? un=mod(1,qpol);w=mod(y,qpol);p=un*(x^5-5*x+w)
mod(1, y^3 - y - 1)*x^5 + mod(-5, y^3 - y - 1)*x + mod(y, y^3 - y - 1)
? aa=rnfpseudobasis(nf2,p)
[[[1, 0, 0]~, [0, 0, 0]~, [0, 0, 0]~, [-2, 0, 0]~, [11, 0, 0]~; [0, 0, 0]~,
[1, 0, 0]~, [0, 0, 0]~, [2, 0, 0]~, [-8, 0, 0]~; [0, 0, 0]~, [0, 0, 0]~, [1,
0, 0]~, [1, 0, 0]~, [4, 0, 0]~; [0, 0, 0]~, [0, 0, 0]~, [0, 0, 0]~, [1, 0,
0]~, [-2, 0, 0]~; [0, 0, 0]~, [0, 0, 0]~, [0, 0, 0]~, [0, 0, 0]~, [1, 0, 0]~
], [[1, 0, 0; 0, 1, 0; 0, 0, 1], [1, 0, 0; 0, 1, 0; 0, 0, 1], [1, 0, 0; 0, 1
, 0; 0, 0, 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], [-1
275, 5, 5]~]
? rnfbasis(bnf2,aa)
[[1, 0, 0]~ [0, 0, 0]~ [0, 0, 0]~ [-6/25, 66/25, 77/25]~ [-391/25, -699/25,
197/25]~]
[[0, 0, 0]~ [1, 0, 0]~ [0, 0, 0]~ [18/25, -48/25, -56/25]~ [268/25, 552/25,
-206/25]~]
[[0, 0, 0]~ [0, 0, 0]~ [1, 0, 0]~ [41/25, 24/25, 28/25]~ [-194/25, -116/25,
-127/25]~]
[[0, 0, 0]~ [0, 0, 0]~ [0, 0, 0]~ [17/25, -12/25, -14/25]~ [52/25, 178/25, -
109/25]~]
[[0, 0, 0]~ [0, 0, 0]~ [0, 0, 0]~ [4/25, 6/25, 7/25]~ [-41/25, -49/25, -3/25
]~]
? rnfdiscf(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
? rnfequation2(nf2,p)
[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]
? rnfhermitebasis(bnf2,aa)
[[1, 0, 0]~ [0, 0, 0]~ [0, 0, 0]~ [6/5, 4/5, -2/5]~ [-22/25, -33/25, 99/25]~
]
[[0, 0, 0]~ [1, 0, 0]~ [0, 0, 0]~ [-6/5, -4/5, 2/5]~ [16/25, 24/25, -72/25]~
]
[[0, 0, 0]~ [0, 0, 0]~ [1, 0, 0]~ [-3/5, -2/5, 1/5]~ [-8/25, -12/25, 36/25]~
]
[[0, 0, 0]~ [0, 0, 0]~ [0, 0, 0]~ [-3/5, -2/5, 1/5]~ [4/25, 6/25, -18/25]~]
[[0, 0, 0]~ [0, 0, 0]~ [0, 0, 0]~ [0, 0, 0]~ [-2/25, -3/25, 9/25]~]
? rnfisfree(bnf2,aa)
1
? rnfsteinitz(nf2,aa)
[[[1, 0, 0]~, [0, 0, 0]~, [0, 0, 0]~, [-6/25, 66/25, 77/25]~, [17/125, -66/1
25, -77/125]~; [0, 0, 0]~, [1, 0, 0]~, [0, 0, 0]~, [18/25, -48/25, -56/25]~,
[-26/125, 48/125, 56/125]~; [0, 0, 0]~, [0, 0, 0]~, [1, 0, 0]~, [41/25, 24/
25, 28/25]~, [-37/125, -24/125, -28/125]~; [0, 0, 0]~, [0, 0, 0]~, [0, 0, 0]
~, [17/25, -12/25, -14/25]~, [-19/125, 12/125, 14/125]~; [0, 0, 0]~, [0, 0,
0]~, [0, 0, 0]~, [4/25, 6/25, 7/25]~, [-3/125, -6/125, -7/125]~], [[1, 0, 0;
0, 1, 0; 0, 0, 1], [1, 0, 0; 0, 1, 0; 0, 0, 1], [1, 0, 0; 0, 1, 0; 0, 0, 1]
, [1, 0, 0; 0, 1, 0; 0, 0, 1], [125, 0, 22; 0, 125, 108; 0, 0, 1]], [4161343
75, 202396875, 60056800; 0, 3125, 2700; 0, 0, 25], [-1275, 5, 5]~]
? rootmod(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)]~
? rootpadic(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)]~
? roots(x^5-5*x^2-5*x-5)
[2.0509134529831982130058170163696514536 + 0.E-38*I, -0.67063790319207539268
663382582902335603 + 0.84813118358634026680538906224199030917*I, -0.67063790
319207539268663382582902335603 - 0.84813118358634026680538906224199030917*I,
-0.35481882329952371381627468235580237077 + 1.39980287391035466982975228340
62081964*I, -0.35481882329952371381627468235580237077 - 1.399802873910354669
8297522834062081964*I]~
? rootsold(x^4-1000000000000000000000)
[-177827.94100389228012254211951926848447 + 0.E-38*I, 177827.941003892280122
54211951926848447 + 0.E-38*I, 6.6530622500127354998594589316364200753 E-111
+ 177827.94100389228012254211951926848447*I, 6.65306225001273549985945893163
64200753 E-111 - 177827.94100389228012254211951926848447*I]~
? round(prod(1,k=1,17,x-exp(2*i*pi*k/17)))
x^17 - 1
? rounderror(prod(1,k=1,17,x-exp(2*i*pi*k/17)))
-35
? rpoint(0,20,20)
? initrect(3,600,600);scale(3,-7,7,-2,2);cursor(3)
? q*series(anell(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)
? 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"]
? setminus(aset,bset)
["-2", "1", "3"]
? setprecision(28)
38
? setrand(10)
10
? setsearch(aset,3)
3
? setsearch(bset,3)
0
? setserieslength(12)
16
? setunion(aset,bset)
["-2", "-5", "1", "2", "3", "5", "7"]
? arat=(x^3+x+1)/x^3;settype(arat,14)
(x^3 + x + 1)/x^3
? 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]
? sigma(100)
217
? sigmak(2,100)
13671
? sigmak(-3,100)
1149823/1000000
? sign(-1)
-1
? sign(0)
0
? sign(0.)
0
? signat(hilbert(5)-0.11*idmat(5))
[2, 3]
? signunit(bnf)
[-1]
[1]
? simplefactmod(x^11+1,7)
[1 1]
[10 1]
? simplify(((x+i+1)^2-x^2-2*x*(i+1))^2)
-4
? sin(pi/6)
0.4999999999999999999999999999
? sinh(1)
1.175201193643801456882381850
? size([1.3*10^5,2*i*pi*exp(4*pi)])
7
? smallbasis(x^3+4*x+12)
[1, x, 1/2*x^2]
? smalldiscf(x^3+4*x+12)
-1036
? smallfact(100!+1)
[101 1]
[14303 1]
[149239 1]
[432885273849892962613071800918658949059679308685024481795740765527568493010
727023757461397498800981521440877813288657839195622497225621499427628453 1]
? smallinitell([0,0,0,-17,0])
[0, 0, 0, -17, 0, 0, -34, 0, -289, 816, 0, 314432, 1728]
? smallpolred(x^4+576)
[x - 1, x^2 - x + 1, x^2 + 1, x^4 - x^2 + 1]
? smallpolred2(x^4+576)
[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]
? smith(matrix(5,5,j,k,random()))
[239509529380671174817611776, 2147483648, 2147483648, 1, 1]
? smith(1/hilbert(6))
[27720, 2520, 2520, 840, 210, 6]
? smithpol(x*idmat(5)-matrix(5,5,j,k,1))
[x^2 - 5*x, x, x, x, 1]
? solve(x=1,4,sin(x))
3.141592653589793238462643383
? sort(vector(17,x,5*x%17))
[0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16]
? sqr(1+o(2))
1 + O(2^3)
? sqred(hilbert(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]
? 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)
? srgcd(x^10-1,x^15-1)
x^5 - 1
? move(0,100,100);string(0,pi)
? move(0,200,200);string(0,"(0,0)")
? postdraw([0,10,10])
? apol=0.3+legendre(10)
46189/256*x^10 - 109395/256*x^8 + 45045/128*x^6 - 15015/128*x^4 + 3465/256*x
^2 + 0.05390624999999999999999999999
? sturm(apol)
4
? sturmpart(apol,0.91,1)
1
? subcyclo(31,5)
x^5 + x^4 - 12*x^3 - 21*x^2 + x + 5
? subell(initell([0,0,0,-17,0]),[-1,4],[-4,2])
[9, -24]
? 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 + O(y^
12)
? 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 + O(x^12)
? sum(0,k=1,10,2^-k)
1023/1024
? sum(0.,k=1,10,2^-k)
0.9990234375000000000000000000
? sylvestermatrix(a2*x^2+a1*x+a0,b1*x+b0)
[a2 b1 0]
[a1 b0 b1]
[a0 0 b0]
? \precision=38
realprecision = 38 significant digits
? 4*sumalt(n=0,(-1)^n/(2*n+1))
3.1415926535897932384626433832795028841
? 4*sumalt2(n=0,(-1)^n/(2*n+1))
3.1415926535897932384626433832795028842
? suminf(n=1,2.^-n)
0.99999999999999999999999999999999999999
? 6/pi^2*sumpos(n=1,n^-2)
0.99999999999999999999999999999999999999
? supplement([1,3;2,4;3,6])
[1 3 0]
[2 4 0]
[3 6 1]
? sqr(tan(pi/3))
2.9999999999999999999999999999999999999
? tanh(1)
0.76159415595576488811945828260479359041
? taniyama(bcurve)
[x^-2 - x^2 + 3*x^6 - 2*x^10 + O(x^11), -x^-3 + 3*x - 3*x^5 + 8*x^9 + O(x^10
)]
? taylor(y/(x-y),y)
(O(y^12)*x^11 + y*x^10 + y^2*x^9 + y^3*x^8 + y^4*x^7 + y^5*x^6 + y^6*x^5 + y
^7*x^4 + y^8*x^3 + y^9*x^2 + y^10*x + y^11)/x^11
? tchebi(10)
512*x^10 - 1280*x^8 + 1120*x^6 - 400*x^4 + 50*x^2 - 1
? teich(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)
? texprint((x+y)^3/(x-y)^2)
{{x^{3} + {{3}y}x^{2} + {{3}y^{2}}x + {y^{3}}}\over{x^{2} - {{2}y}x + {y^{2}
}}}
? theta(0.5,3)
0.080806418251894691299871683210466298535
? thetanullk(0.5,7)
-804.63037320243369422783730584965684022
? torsell(tcurve)
[12, [6, 2], [[-2, 8], [3, -2]]]
? trace(1+i)
2
? trace(mod(x+5,x^3+x+1))
15
? trans(vector(2,x,x))
[1, 2]~
? %*%~
[1 2]
[2 4]
? trunc(-2.7)
-2
? trunc(sin(x^2))
1/120*x^10 - 1/6*x^6 + x^2
? tschirnhaus(x^5-x-1)
x^5 + 20*x^4 + 158*x^3 + 616*x^2 + 1185*x + 899
? type(mod(x,x^2+1))
9
? unit(17)
3 + 2*w
? 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
? valuation(6^10000-1,5)
5
? vec(sin(x))
[1, 0, -1/6, 0, 1/120, 0, -1/5040, 0, 1/362880, 0, -1/39916800]
? vecmax([-3,7,-2,11])
11
? vecmin([-3,7,-2,11])
-3
? vecsort([[1,8,5],[2,5,8],[3,6,-6],[4,8,6]],2)
[[2, 5, 8], [3, 6, -6], [4, 8, 6], [1, 8, 5]]
? 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]]
? weipell(acurve)
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 + O(x^22)
? wf(i)
1.1892071150027210667174999705604759152 - 1.17549435 E-38*I
? wf2(i)
1.0905077326652576592070106557607079789 + 0.E-48*I
? 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
? zell(acurve,apoint)
0.72491221490962306778878739838332384646 + 0.E-58*I
? zeta(3)
1.2020569031595942853997381615114499907
? zeta(0.5+14.1347251*i)
0.0000000052043097453468479398562848599419244606 - 0.00000003269063986978698
2176409251733800562856*I
? zetak(nfz,-3)
0.091666666666666666666666666666666666666
? zetak(nfz,1.5+3*i)
0.88324345992059326405525724366416928890 - 0.2067536250233895222724230899142
7938845*I
? zidealstar(nf2,54)
[132678, [1638, 9, 9], [[-14, -4, 19]~, [1, 0, -24]~, [7, -6, 6]~]]
? bid=zidealstarinit(nf2,54)
[[[54, 0, 0; 0, 54, 0; 0, 0, 54], [0]], [132678, [1638, 9, 9]], [[2, [2, 0,
0]~, 1, 3, [1, 0, 0]~], 1; [3, [3, 0, 0]~, 1, 3, [1, 0, 0]~], 3], [[[[7], [[
1, 0, 1]~], [[1, 0, -27]~], [[]~], 1]], [[[26], [[3, 2, 0]~], [[3, 2, 0]~],
[[]~], 1], [[3, 3, 3], [[1, 3, 0]~, [1, 0, 3]~, [4, 0, 0]~], [[1, -24, 0]~,
[1, 0, -24]~, [-23, 0, 0]~], [[]~, []~, []~], [0, 1/3, 0; 0, 0, 1/3; 1/3, 0,
0]], [[3, 3, 3], [[1, 9, 0]~, [1, 0, 9]~, [10, 0, 0]~], [[1, -18, 0]~, [1,
0, -18]~, [-17, 0, 0]~], [[]~, []~, []~], [0, 1/9, 0; 0, 0, 1/9; 1/9, 0, 0]]
], [[], [], [;]]], [2106, -77, 0, -11102, 2184, 0, 6006, -13104; 0, 0, 1, -3
, 0, -6, 0, 0; -27, 1, 0, 142, -28, 0, -78, 168]]
? zideallog(nf2,w,bid)
[1234, 0, 5]~
? znstar(3120)
[768, [12, 4, 4, 2, 2], [mod(67, 3120), mod(2341, 3120), mod(1847, 3120), mo
d(391, 3120), mod(2081, 3120)]]
? getstack()
0
? getheap()
[620, 118299]
? print("Total time spent: ",gettime());
Total time spent: 1400
? \q
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