? ?    echo = 1 (on)
? +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
? \p57
   realprecision = 57 significant digits
? Pi
% = 3.14159265358979323846264338327950288419716939937510582097
? \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)
? plotinit(0,500,500)
? ? abs(-0.01)
% = 0.0099999999999999999999999999999999999999
? acos(0.5)
% = 1.0471975511965977461542144610931676280
? acosh(3)
% = 1.7627471740390860504652186499595846180
? addprimes([nextprime(10^9),nextprime(10^10)])
% = [1000000007, 10000000019]
? matadjoint([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
? algdep(2*cos(2*Pi/13),6,15)
% = x^6 + x^5 - 5*x^4 - 4*x^3 + 6*x^2 + 3*x - 1
? ? nfpol=x^5-5*x^3+5*x+25
% = x^5 - 5*x^3 + 5*x + 25
? nf=nfinit(nfpol)
% = [x^5 - 5*x^3 + 5*x + 25, [1, 2], 595125, 45, [[1, -2.42851749071941860
68992069565359418364, 5.8976972027301414394898806541072047941, -7.07345267
15090929269887668671457811020, 3.8085820570096366144649278594400435257; 1,
 1.9647119211288133163138753392090569931 + 0.80971492418897895128294082219
556466857*I, 3.2044546745713084269203768790545260356 + 3.18171312854000053
41145852263331539899*I, -0.16163499313031744537610982231988834519 + 1.8880
437862007056931906454476483475283*I, 2.06607095383724806326989711488010906
92 + 2.6898967519623140991170523711857387388*I; 1, -0.75045317576910401286
427186094108607489 + 1.3101462685358123283560773619310445915*I, -1.1533032
759363791466653172061081284327 - 1.9664068558894834311780119356739268309*I
, 1.1983613288848639088704932558927788962 + 0.6437023807625698889957032567
1192132449*I, -0.47036198234206637050236104460013083212 + 0.08362826671158
9186119416762685933385421*I], [1, 2, 2; -2.4285174907194186068992069565359
418364, 3.9294238422576266326277506784181139862 - 1.6194298483779579025658
816443911293371*I, -1.5009063515382080257285437218821721497 - 2.6202925370
716246567121547238620891831*I; 5.8976972027301414394898806541072047941, 6.
4089093491426168538407537581090520712 - 6.36342625708000106822917045266630
79798*I, -2.3066065518727582933306344122162568654 + 3.93281371177896686235
60238713478536619*I; -7.0734526715090929269887668671457811020, -0.32326998
626063489075221964463977669038 - 3.7760875724014113863812908952966950567*I
, 2.3967226577697278177409865117855577924 - 1.2874047615251397779914065134
238426489*I; 3.8085820570096366144649278594400435257, 4.132141907674496126
5397942297602181385 - 5.3797935039246281982341047423714774776*I, -0.940723
96468413274100472208920026166424 - 0.1672565334231783722388335253718667708
4*I], [5, 4.0215293653309345240000000000000000000 E-87, 10.000000000000000
000000000000000000000, -5.0000000000000000000000000000000000000, 7.0000000
000000000000000000000000000000; 4.0215293653309345240000000000000000000 E-
87, 19.488486013650707197449403270536023970, 8.043058730661869049000000000
0000000000 E-86, 19.488486013650707197449403270536023970, 4.15045922467060
85588902013976045703227; 10.000000000000000000000000000000000000, 8.043058
7306618690490000000000000000000 E-86, 85.960217420851846480305133936577594
605, -36.034268291482979838267056239752434596, 53.576130452511107888183080
361946556763; -5.0000000000000000000000000000000000000, 19.488486013650707
197449403270536023970, -36.034268291482979838267056239752434596, 60.916248
374441986300937507618575151517, -18.470101750219179344070032346246890434; 
7.0000000000000000000000000000000000000, 4.1504592246706085588902013976045
703227, 53.576130452511107888183080361946556763, -18.470101750219179344070
032346246890434, 37.970152892842367340897384258599214282], [5, 0, 10, -5, 
7; 0, 10, 0, 10, -5; 10, 0, 30, -55, 20; -5, 10, -55, 45, -39; 7, -5, 20, 
-39, 9], [345, 0, 340, 167, 150; 0, 345, 110, 220, 153; 0, 0, 5, 2, 1; 0, 
0, 0, 1, 0; 0, 0, 0, 0, 1], [132825, -18975, -5175, 27600, 17250; -18975, 
34500, 41400, 3450, -43125; -5175, 41400, -41400, -15525, 51750; 27600, 34
50, -15525, -3450, 0; 17250, -43125, 51750, 0, -86250], [595125, 0, 0, 581
325, 474375; 0, 119025, 0, 117300, 63825; 0, 0, 119025, 67275, 113850; 0, 
0, 0, 1725, 0; 0, 0, 0, 0, 8625]], [-2.42851749071941860689920695653594183
64, 1.9647119211288133163138753392090569931 + 0.80971492418897895128294082
219556466857*I, -0.75045317576910401286427186094108607489 + 1.310146268535
8123283560773619310445915*I], [1, x, x^2, 1/3*x^3 - 1/3*x^2 - 1/3, 1/15*x^
4 + 1/3*x^2 + 1/3*x + 1/3], [1, 0, 0, 1, -5; 0, 1, 0, 0, -5; 0, 0, 1, 1, -
5; 0, 0, 0, 3, 0; 0, 0, 0, 0, 15], [1, 0, 0, 0, 0, 0, 0, 1, -2, -1, 0, 1, 
-5, -5, -3, 0, -2, -5, 1, -4, 0, -1, -3, -4, -3; 0, 1, 0, 0, 0, 1, 0, 0, -
2, 0, 0, 0, -5, 0, -5, 0, -2, 0, -5, 0, 0, 0, -5, 0, -4; 0, 0, 1, 0, 0, 0,
 1, 1, -2, 1, 1, 1, -5, 3, -3, 0, -2, 3, -5, 1, 0, 1, -3, 1, -2; 0, 0, 0, 
1, 0, 0, 0, 3, -1, 2, 0, 3, 0, 5, 1, 1, -1, 5, -4, 3, 0, 2, 1, 3, 1; 0, 0,
 0, 0, 1, 0, 0, 0, 5, 0, 0, 0, 15, -5, 10, 0, 5, -5, 10, -2, 1, 0, 10, -2,
 7]]
? ba=nfalgtobasis(nf,Mod(x^3+5,nfpol))
% = [6, 0, 1, 3, 0]~
? apol=x^3+5*x+1
% = x^3 + 5*x + 1
? 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)]~
? 4*arg(3+3*I)
% = 3.1415926535897932384626433832795028842
? 3*asin(sqrt(3)/2)
% = 3.1415926535897932384626433832795028841
? asinh(0.5)
% = 0.48121182505960344749775891342436842313
? matcompanion(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
? ? 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)
? 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
? binomial(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
? plotmove(0,0,0);plotbox(0,500,500)
? setrand(1);quadclassunit(1-10^7,,[1,1])
% = [2416, [1208, 2], [Qfb(277, 55, 9028), Qfb(1700, 1249, 1700)], 1, 0.99
984980753776002339750644800000000000]
? setrand(1);bnf=bnfinit(x^2-x-57,2,[0.2,0.2])
% = [Mat([3]), Mat([1, 2, 1, 2, 1, 2, 1, 2, 1]), [2.7124653051843439746808
795106061300699 + 3.1415926535897932384626433832795028842*I; -2.7124653051
843439746808795106061300699 + 6.2831853071795864769252867665590057684*I], 
[-575.96476824756753723069812383847548501 + 3.1415926535897932384626433832
795028842*I, 551.92021890548710036272154926028390729 + 3.14159265358979323
84626433832795028842*I, -2182.8330851707114713996393899372203372 + 9.42477
79607693797153879301498385086526*I, 22773.85870232775201142066437104906806
6 + 6.7262326274067163460000000000000000000 E-44*I, 22749.9470943847253715
22362658767003613 + 8.9683101698756217950000000000000000000 E-44*I, -22485
.248523724199248946630547104902428 + 3.14159265358979323846264338327950288
42*I, 24764.229400428850901332468152110725047 + 4.484155084937810897000000
0000000000000 E-44*I, -0.34328764427702709438988786673341921876 + 3.141592
6535897932384626433832795028842*I, -22509.02540427005566223247521509196639
4 + 3.1415926535897932384626433832795028842*I, 22773.924880629634757152849
739541391231 + 9.4247779607693797153879301498385086526*I; 575.964768247567
53723069812383847548501 + 12.566370614359172953850573533118011536*I, -551.
92021890548710036272154926028390729 + 3.1415926535897932384626433832795028
842*I, 2182.8330851707114713996393899372203372 + 12.5663706143591729538505
73533118011536*I, -22773.858702327752011420664371049068066 + 8.96831016987
56217950000000000000000000 E-44*I, -22749.94709438472537152236265876700361
3 + 6.7262326274067163460000000000000000000 E-44*I, 22485.2485237241992489
46630547104902428 + 9.4247779607693797153879301498385086526*I, -24764.2294
00428850901332468152110725047 + 1.3452465254813432690000000000000000000 E-
43*I, 0.34328764427702709438988786673341921876 + 0.E-48*I, 22509.025404270
055662232475215091966394 + 9.4247779607693797153879301498385086526*I, -227
73.924880629634757152849739541391231 + 8.968310169875621795000000000000000
0000 E-44*I], [[3, [-1, 1]~, 1, 1, [0, 1]~], [3, [0, 1]~, 1, 1, [-1, 1]~],
 [5, [-2, 1]~, 1, 1, [1, 1]~], [5, [1, 1]~, 1, 1, [-2, 1]~], [11, [-2, 1]~
, 1, 1, [1, 1]~], [11, [1, 1]~, 1, 1, [-2, 1]~], [17, [-3, 1]~, 1, 1, [2, 
1]~], [17, [2, 1]~, 1, 1, [-3, 1]~], [19, [-1, 1]~, 1, 1, [0, 1]~], [19, [
0, 1]~, 1, 1, [-1, 1]~]]~, [1, 3, 5, 2, 4, 6, 7, 8, 10, 9]~, [x^2 - x - 57
, [2, 0], 229, 1, [[1, -7.0663729752107779635959310246705326058; 1, 8.0663
729752107779635959310246705326058], [1, 1; -7.0663729752107779635959310246
705326058, 8.0663729752107779635959310246705326058], [2, 1.000000000000000
0000000000000000000000; 1.0000000000000000000000000000000000000, 115.00000
000000000000000000000000000000], [2, 1; 1, 115], [229, 114; 0, 1], [115, -
1; -1, 2], [229, 114; 0, 1]], [-7.0663729752107779635959310246705326058, 8
.0663729752107779635959310246705326058], [1, x], [1, 0; 0, 1], [1, 0, 0, 5
7; 0, 1, 1, 1]], [[3, [3], [[3, 2; 0, 1]]], 2.7124653051843439746808795106
061300699, 0.88144225126545793690341704100000000000, [2, -1]], [Mat([1]), 
Mat([1]), [[[3, 2; 0, 1], [0.E-48, 0.E-48]]]], 0]
? bnfcertify(bnf)
% = 1
? bnfunit(bnf)
% = [[x + 7], 141]
? setrand(1);bnfinit(x^2-x-100000,1)
% = [Mat([5]), Mat([3, 2, 1, 2, 0, 3, 2, 3, 0, 0, 4, 1, 3, 2, 2, 3, 3, 2])
, [-129.82045011403975460991182396195022419 + 6.28318530717958647692528676
65590057684*I; 129.82045011403975460991182396195022419 + 6.283185307179586
4769252867665590057684*I], [-41.811264589129943393339502258694361489 + 12.
566370614359172953850573533118011536*I, 7798.46690725717550557634706376089
75446 + 3.2944368571043014520000000000000000000 E-83*I, 10373.761399242104
962067848600958586774 + 12.566370614359172953850573533118011536*I, -158900
.23093958465964253207252942707441 + 12.56637061435917295385057353311801153
6*I, -325121.45825055946571559418432902593983 + 9.424777960769379715387930
1498385086526*I, -145593.63480289558479501611057332717643 + 3.141592653589
7932384626433832795028842*I, -145558.66123254661945437939684760746451 + 6.
2831853071795864769252867665590057684*I, 184597.94231098623536723383343794
216416 + 9.4247779607693797153879301498385086526*I, -132841.39398007350322
127235517938271907 + 3.1415926535897932384626433832795028842*I, -12674.735
792104327717774025829788414282 + 6.2831853071795864769252867665590057684*I
, -140643.21579257662247653183826927480048 + 6.283185307179586476925286766
5590057684*I, -228948.39559706781480223963544800452232 + 3.141592653589793
2384626433832795028842*I, 26127.041254348588158164026917179577779 + 9.4247
779607693797153879301498385086526*I, -135417.70965704811267121166315150337
705 + 12.566370614359172953850573533118011536*I, -17942.053192221967466487
540449818532080 + 1.1201085313223302360000000000000000000 E-81*I, 7639.699
8076618294564723087059201850803 + 12.566370614359172953850573533118011536*
I, -88300.010593069647012620890888549968664 + 3.14159265358979323846264338
32795028842*I, -90920.002638063436052838364758102886803 + 5.27109897136688
23240000000000000000000 E-82*I, 20904.968762006878374702552140353021602 + 
9.4247779607693797153879301498385086526*I; 41.8112645891299433933395022586
94361489 + 6.2831853071795864769252867665590057684*I, -7798.46690725717550
55763470637608975446 + 9.4247779607693797153879301498385086526*I, -10373.7
61399242104962067848600958586774 + 9.4247779607693797153879301498385086526
*I, 158900.23093958465964253207252942707441 + 12.5663706143591729538505735
33118011536*I, 325121.45825055946571559418432902593983 + 12.56637061435917
2953850573533118011536*I, 145593.63480289558479501611057332717643 + 6.2831
853071795864769252867665590057684*I, 145558.661232546619454379396847607464
51 + 9.4247779607693797153879301498385086526*I, -184597.942310986235367233
83343794216416 + 6.2831853071795864769252867665590057684*I, 132841.3939800
7350322127235517938271907 + 12.566370614359172953850573533118011536*I, 126
74.735792104327717774025829788414282 + 6.588873714208602905000000000000000
0000 E-83*I, 140643.21579257662247653183826927480048 + 6.28318530717958647
69252867665590057684*I, 228948.39559706781480223963544800452232 + 3.141592
6535897932384626433832795028842*I, -26127.04125434858815816402691717957777
9 + 3.1415926535897932384626433832795028842*I, 135417.70965704811267121166
315150337705 + 3.1415926535897932384626433832795028842*I, 17942.0531922219
67466487540449818532080 + 9.4247779607693797153879301498385086526*I, -7639
.6998076618294564723087059201850803 + 3.1415926535897932384626433832795028
842*I, 88300.010593069647012620890888549968664 + 6.28318530717958647692528
67665590057684*I, 90920.002638063436052838364758102886803 + 12.56637061435
9172953850573533118011536*I, -20904.968762006878374702552140353021602 + 3.
1415926535897932384626433832795028842*I], [[2, [1, 1]~, 1, 1, [0, 1]~], [2
, [2, 1]~, 1, 1, [1, 1]~], [5, [4, 1]~, 1, 1, [0, 1]~], [5, [5, 1]~, 1, 1,
 [-1, 1]~], [7, [3, 1]~, 2, 1, [3, 1]~], [13, [-6, 1]~, 1, 1, [5, 1]~], [1
3, [5, 1]~, 1, 1, [-6, 1]~], [17, [14, 1]~, 1, 1, [2, 1]~], [17, [19, 1]~,
 1, 1, [-3, 1]~], [23, [6, 1]~, 1, 1, [-7, 1]~], [23, [-7, 1]~, 1, 1, [6, 
1]~], [29, [13, 1]~, 1, 1, [-14, 1]~], [29, [-14, 1]~, 1, 1, [13, 1]~], [3
1, [23, 1]~, 1, 1, [7, 1]~], [31, [38, 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]~], [43, [15, 1]~, 1, 1, [-16, 1]~]]~, [1, 3, 6, 2, 4, 5, 7, 9, 8, 11,
 10, 13, 12, 15, 14, 17, 16, 19, 18]~, [x^2 - x - 100000, [2, 0], 400001, 
1, [[1, -315.72816130129840161392089489603747004; 1, 316.72816130129840161
392089489603747004], [1, 1; -315.72816130129840161392089489603747004, 316.
72816130129840161392089489603747004], [2, 1.000000000000000000000000000000
0000000; 1.0000000000000000000000000000000000000, 200001.00000000000000000
000000000000000], [2, 1; 1, 200001], [400001, 200000; 0, 1], [200001, -1; 
-1, 2], [400001, 200000; 0, 1]], [-315.72816130129840161392089489603747004
, 316.72816130129840161392089489603747004], [1, x], [1, 0; 0, 1], [1, 0, 0
, 100000; 0, 1, 1, 1]], [[5, [5], [[2, 1; 0, 1]]], 129.8204501140397546099
1182396195022419, 0.98765369790690472391212970100000000000, [2, -1], [3795
54884019013781006303254896369154068336082609238336*x + 1198361656442507899
90462835950022871665178127611316131167], 80], [Mat([1]), Mat([1]), [[[2, 1
; 0, 1], [0.E-86, 0.E-86]]]], 0]
? setrand(1);bnf=bnfinit(x^2-x-57,,[0.2,0.2])
% = [Mat([3]), Mat([1, 2, 1, 2, 1, 2, 1, 2, 1]), [-2.712465305184343974680
8795106061300699 - 3.1415926535897932384626433832795028842*I; 2.7124653051
843439746808795106061300699 - 6.2831853071795864769252867665590057684*I], 
[-575.96476824756753723069812383847548501 + 3.1415926535897932384626433832
795028842*I, 551.92021890548710036272154926028390729 + 3.14159265358979323
84626433832795028842*I, -2182.8330851707114713996393899372203372 + 9.42477
79607693797153879301498385086526*I, 22773.85870232775201142066437104906806
6 + 6.7262326274067163460000000000000000000 E-44*I, 22749.9470943847253715
22362658767003613 + 8.9683101698756217950000000000000000000 E-44*I, -22485
.248523724199248946630547104902428 + 3.14159265358979323846264338327950288
42*I, 24764.229400428850901332468152110725047 + 4.484155084937810897000000
0000000000000 E-44*I, -0.34328764427702709438988786673341921876 + 3.141592
6535897932384626433832795028842*I, -22509.02540427005566223247521509196639
4 + 3.1415926535897932384626433832795028842*I, 22773.924880629634757152849
739541391231 + 9.4247779607693797153879301498385086526*I; 575.964768247567
53723069812383847548501 + 12.566370614359172953850573533118011536*I, -551.
92021890548710036272154926028390729 + 3.1415926535897932384626433832795028
842*I, 2182.8330851707114713996393899372203372 + 12.5663706143591729538505
73533118011536*I, -22773.858702327752011420664371049068066 + 8.96831016987
56217950000000000000000000 E-44*I, -22749.94709438472537152236265876700361
3 + 6.7262326274067163460000000000000000000 E-44*I, 22485.2485237241992489
46630547104902428 + 9.4247779607693797153879301498385086526*I, -24764.2294
00428850901332468152110725047 + 1.3452465254813432690000000000000000000 E-
43*I, 0.34328764427702709438988786673341921876 + 0.E-48*I, 22509.025404270
055662232475215091966394 + 9.4247779607693797153879301498385086526*I, -227
73.924880629634757152849739541391231 + 8.968310169875621795000000000000000
0000 E-44*I], [[3, [-1, 1]~, 1, 1, [0, 1]~], [3, [0, 1]~, 1, 1, [-1, 1]~],
 [5, [-2, 1]~, 1, 1, [1, 1]~], [5, [1, 1]~, 1, 1, [-2, 1]~], [11, [-2, 1]~
, 1, 1, [1, 1]~], [11, [1, 1]~, 1, 1, [-2, 1]~], [17, [-3, 1]~, 1, 1, [2, 
1]~], [17, [2, 1]~, 1, 1, [-3, 1]~], [19, [-1, 1]~, 1, 1, [0, 1]~], [19, [
0, 1]~, 1, 1, [-1, 1]~]]~, [1, 3, 5, 2, 4, 6, 7, 8, 10, 9]~, [x^2 - x - 57
, [2, 0], 229, 1, [[1, -7.0663729752107779635959310246705326058; 1, 8.0663
729752107779635959310246705326058], [1, 1; -7.0663729752107779635959310246
705326058, 8.0663729752107779635959310246705326058], [2, 1.000000000000000
0000000000000000000000; 1.0000000000000000000000000000000000000, 115.00000
000000000000000000000000000000], [2, 1; 1, 115], [229, 114; 0, 1], [115, -
1; -1, 2], [229, 114; 0, 1]], [-7.0663729752107779635959310246705326058, 8
.0663729752107779635959310246705326058], [1, x], [1, 0; 0, 1], [1, 0, 0, 5
7; 0, 1, 1, 1]], [[3, [3], [[3, 2; 0, 1]]], 2.7124653051843439746808795106
061300699, 0.88144225126545793690341704100000000000, [2, -1], [x + 7], 141
], [Mat([1]), Mat([1]), [[[3, 2; 0, 1], [0.E-48, 0.E-48]]]], 0]
? setrand(1);quadclassunit(10^9-3,,[0.5,0.5])
% = [4, [4], [Qfb(3, 1, -83333333, 0.E-48)], 2800.625251907016076486370621
7370745513, 0.99903694589643832327024650000000000000]
? setrand(1);bnfclassunit(x^4-7,2,[0.2,0.2])
% = 
[x^4 - 7]

[[2, 1]]

[[-87808, 1]]

[[1, x, x^2, x^3]]

[[2, [2], [[2, 1, 1, 1; 0, 1, 0, 0; 0, 0, 1, 0; 0, 0, 0, 1]]]]

[14.229975145405511722395637833443108790]

[1.1211171071527562299744232290000000000]

? setrand(1);bnfclassunit(x^2-x-100000)
  ***   Warning: insufficient precision for fundamental units, not given.
% = 
[x^2 - x - 100000]

[[2, 0]]

[[400001, 1]]

[[1, x]]

[[5, [5], [[2, 1; 0, 1]]]]

[129.82045011403975460991182396195022419]

[0.98765369790690472391212970100000000000]

[[2, -1]]

[[;]]

[0]

? setrand(1);bnfclassunit(x^2-x-100000,1)
% = 
[x^2 - x - 100000]

[[2, 0]]

[[400001, 1]]

[[1, x]]

[[5, [5], [[2, 1; 0, 1]]]]

[129.82045011403975460991182396195022419]

[0.98765369790690472391212970100000000000]

[[2, -1]]

[[379554884019013781006303254896369154068336082609238336*x + 1198361656442
50789990462835950022871665178127611316131167]]

[80]

? setrand(1);bnfclassunit(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, x, 1/3*x^2, 1/1029*x^3 + 33/343*x^2 - 155/343*x - 58/343]]

[[4, [4], [[7, 5, 1, 0; 0, 1, 0, 0; 0, 0, 1, 0; 0, 0, 0, 1]]]]

[3.7941269688216589341408274220859400302]

[0.88260182866555813061644128400000000000]

[[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]]

[137]

? bnfnarrow(bnf)
% = [3, [3], [[3, 2; 0, 1]]]
? bnrclass(bnf,[[5,3;0,1],[1,0]])
% = [12, [12], [[3, 2; 0, 1]]]
? bnr=bnrclass(bnf,[[5,3;0,1],[1,0]],2)
% = [[Mat([3]), Mat([1, 2, 1, 2, 1, 2, 1, 2, 1]), [-2.71246530518434397468
08795106061300699 - 3.1415926535897932384626433832795028842*I; 2.712465305
1843439746808795106061300699 - 6.2831853071795864769252867665590057684*I],
 [-575.96476824756753723069812383847548501 + 3.141592653589793238462643383
2795028842*I, 551.92021890548710036272154926028390729 + 3.1415926535897932
384626433832795028842*I, -2182.8330851707114713996393899372203372 + 9.4247
779607693797153879301498385086526*I, 22773.8587023277520114206643710490680
66 + 6.7262326274067163460000000000000000000 E-44*I, 22749.947094384725371
522362658767003613 + 8.9683101698756217950000000000000000000 E-44*I, -2248
5.248523724199248946630547104902428 + 3.1415926535897932384626433832795028
842*I, 24764.229400428850901332468152110725047 + 4.48415508493781089700000
00000000000000 E-44*I, -0.34328764427702709438988786673341921876 + 3.14159
26535897932384626433832795028842*I, -22509.0254042700556622324752150919663
94 + 3.1415926535897932384626433832795028842*I, 22773.92488062963475715284
9739541391231 + 9.4247779607693797153879301498385086526*I; 575.96476824756
753723069812383847548501 + 12.566370614359172953850573533118011536*I, -551
.92021890548710036272154926028390729 + 3.141592653589793238462643383279502
8842*I, 2182.8330851707114713996393899372203372 + 12.566370614359172953850
573533118011536*I, -22773.858702327752011420664371049068066 + 8.9683101698
756217950000000000000000000 E-44*I, -22749.9470943847253715223626587670036
13 + 6.7262326274067163460000000000000000000 E-44*I, 22485.248523724199248
946630547104902428 + 9.4247779607693797153879301498385086526*I, -24764.229
400428850901332468152110725047 + 1.3452465254813432690000000000000000000 E
-43*I, 0.34328764427702709438988786673341921876 + 0.E-48*I, 22509.02540427
0055662232475215091966394 + 9.4247779607693797153879301498385086526*I, -22
773.924880629634757152849739541391231 + 8.96831016987562179500000000000000
00000 E-44*I], [[3, [-1, 1]~, 1, 1, [0, 1]~], [3, [0, 1]~, 1, 1, [-1, 1]~]
, [5, [-2, 1]~, 1, 1, [1, 1]~], [5, [1, 1]~, 1, 1, [-2, 1]~], [11, [-2, 1]
~, 1, 1, [1, 1]~], [11, [1, 1]~, 1, 1, [-2, 1]~], [17, [-3, 1]~, 1, 1, [2,
 1]~], [17, [2, 1]~, 1, 1, [-3, 1]~], [19, [-1, 1]~, 1, 1, [0, 1]~], [19, 
[0, 1]~, 1, 1, [-1, 1]~]]~, [1, 3, 5, 2, 4, 6, 7, 8, 10, 9]~, [x^2 - x - 5
7, [2, 0], 229, 1, [[1, -7.0663729752107779635959310246705326058; 1, 8.066
3729752107779635959310246705326058], [1, 1; -7.066372975210777963595931024
6705326058, 8.0663729752107779635959310246705326058], [2, 1.00000000000000
00000000000000000000000; 1.0000000000000000000000000000000000000, 115.0000
0000000000000000000000000000000], [2, 1; 1, 115], [229, 114; 0, 1], [115, 
-1; -1, 2], [229, 114; 0, 1]], [-7.0663729752107779635959310246705326058, 
8.0663729752107779635959310246705326058], [1, x], [1, 0; 0, 1], [1, 0, 0, 
57; 0, 1, 1, 1]], [[3, [3], [[3, 2; 0, 1]]], 2.712465305184343974680879510
6061300699, 0.88144225126545793690341704100000000000, [2, -1], [x + 7], 14
1], [Mat([1]), Mat([1]), [[[3, 2; 0, 1], [0.E-48, 0.E-48]]]], 0], [[[5, 3;
 0, 1], [1, 0]], [8, [4, 2], [[2, 0]~, [-4, 0]~]], Mat([[5, [-2, 1]~, 1, 1
, [1, 1]~], 1]), [[[[4], [[2, 0]~], [[2, 0]~], [[Mod(0, 2)]~], 1]], [[2], 
[[-4, 0]~], Mat([1])]], [1, 0; 0, 1]], [[1, 0]~], [1, -3, -6; 0, 0, 1; 0, 
1, 0], [12, [12], [[3, 2; 0, 1]]], [[0, 0; 0, 1], [-1, -1; 1, -1]]]
? bnr2=bnrclass(bnf,[[25,13;0,1],[1,1]],2)
% = [[Mat([3]), Mat([1, 2, 1, 2, 1, 2, 1, 2, 1]), [-2.71246530518434397468
08795106061300699 - 3.1415926535897932384626433832795028842*I; 2.712465305
1843439746808795106061300699 - 6.2831853071795864769252867665590057684*I],
 [-575.96476824756753723069812383847548501 + 3.141592653589793238462643383
2795028842*I, 551.92021890548710036272154926028390729 + 3.1415926535897932
384626433832795028842*I, -2182.8330851707114713996393899372203372 + 9.4247
779607693797153879301498385086526*I, 22773.8587023277520114206643710490680
66 + 6.7262326274067163460000000000000000000 E-44*I, 22749.947094384725371
522362658767003613 + 8.9683101698756217950000000000000000000 E-44*I, -2248
5.248523724199248946630547104902428 + 3.1415926535897932384626433832795028
842*I, 24764.229400428850901332468152110725047 + 4.48415508493781089700000
00000000000000 E-44*I, -0.34328764427702709438988786673341921876 + 3.14159
26535897932384626433832795028842*I, -22509.0254042700556622324752150919663
94 + 3.1415926535897932384626433832795028842*I, 22773.92488062963475715284
9739541391231 + 9.4247779607693797153879301498385086526*I; 575.96476824756
753723069812383847548501 + 12.566370614359172953850573533118011536*I, -551
.92021890548710036272154926028390729 + 3.141592653589793238462643383279502
8842*I, 2182.8330851707114713996393899372203372 + 12.566370614359172953850
573533118011536*I, -22773.858702327752011420664371049068066 + 8.9683101698
756217950000000000000000000 E-44*I, -22749.9470943847253715223626587670036
13 + 6.7262326274067163460000000000000000000 E-44*I, 22485.248523724199248
946630547104902428 + 9.4247779607693797153879301498385086526*I, -24764.229
400428850901332468152110725047 + 1.3452465254813432690000000000000000000 E
-43*I, 0.34328764427702709438988786673341921876 + 0.E-48*I, 22509.02540427
0055662232475215091966394 + 9.4247779607693797153879301498385086526*I, -22
773.924880629634757152849739541391231 + 8.96831016987562179500000000000000
00000 E-44*I], [[3, [-1, 1]~, 1, 1, [0, 1]~], [3, [0, 1]~, 1, 1, [-1, 1]~]
, [5, [-2, 1]~, 1, 1, [1, 1]~], [5, [1, 1]~, 1, 1, [-2, 1]~], [11, [-2, 1]
~, 1, 1, [1, 1]~], [11, [1, 1]~, 1, 1, [-2, 1]~], [17, [-3, 1]~, 1, 1, [2,
 1]~], [17, [2, 1]~, 1, 1, [-3, 1]~], [19, [-1, 1]~, 1, 1, [0, 1]~], [19, 
[0, 1]~, 1, 1, [-1, 1]~]]~, [1, 3, 5, 2, 4, 6, 7, 8, 10, 9]~, [x^2 - x - 5
7, [2, 0], 229, 1, [[1, -7.0663729752107779635959310246705326058; 1, 8.066
3729752107779635959310246705326058], [1, 1; -7.066372975210777963595931024
6705326058, 8.0663729752107779635959310246705326058], [2, 1.00000000000000
00000000000000000000000; 1.0000000000000000000000000000000000000, 115.0000
0000000000000000000000000000000], [2, 1; 1, 115], [229, 114; 0, 1], [115, 
-1; -1, 2], [229, 114; 0, 1]], [-7.0663729752107779635959310246705326058, 
8.0663729752107779635959310246705326058], [1, x], [1, 0; 0, 1], [1, 0, 0, 
57; 0, 1, 1, 1]], [[3, [3], [[3, 2; 0, 1]]], 2.712465305184343974680879510
6061300699, 0.88144225126545793690341704100000000000, [2, -1], [x + 7], 14
1], [Mat([1]), Mat([1]), [[[3, 2; 0, 1], [0.E-48, 0.E-48]]]], 0], [[[25, 1
3; 0, 1], [1, 1]], [80, [20, 2, 2], [[2, 0]~, [11, -5]~, [15, 3]~]], Mat([
[5, [-2, 1]~, 1, 1, [1, 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, -13/5])]], [[2, 2], [[11, -5]~, [15, 3]~], [0, 1; 1, 0]]], [1
, -12, 0, 0; 0, 0, 1, 0; 0, 0, 0, 1]], [[1, 0]~], [1, -3, 0, -6; 0, 0, 1, 
0; 0, 0, 0, 1; 0, 1, 0, 0], [12, [12], [[3, 2; 0, 1]]], [[1/2, 5, -9; -1/2
, -5, 10], [-2, 0; 0, 10]]]
? sizebyte(%)
% = 7488
? ? ceil(-2.5)
% = -2
? centerlift(Mod(456,555))
% = -99
? 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]
? changevar(x+y,[z,t])
% = y + z
? 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)
? chinese(Mod(7,15),Mod(13,21))
% = Mod(97, 105)
? qfbclassno(-12391)
% = 63
? qfbclassno(1345)
% = 6
? qfbclassno(-12391,1)
% = 63
? qfbclassno(1345,1)
% = 6
? polcoeff(sin(x),7)
% = -1/5040
? Qfb(2,1,3)*Qfb(2,1,3)
% = Qfb(2, -1, 3)
? component(1+O(7^4),3)
% = 1
? 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 + 12991661155
2/29063006931199*x^10 + 1272919322296/29063006931199*x^9 - 2813750209005/2
9063006931199*x^8 - 2859411937992/29063006931199*x^7 - 414533880536/290630
06931199*x^6 - 35713977492936/29063006931199*x^5 - 17432607267590/29063006
931199*x^4 + 49785595543672/29063006931199*x^3 + 9423768373204/29063006931
199*x^2 - 42779776146743/29063006931199*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), Mod(-279140305176/29063006931199*x^11 + 129916611552/29
063006931199*x^10 + 1272919322296/29063006931199*x^9 - 2813750209005/29063
006931199*x^8 - 2859411937992/29063006931199*x^7 - 414533880536/2906300693
1199*x^6 - 35713977492936/29063006931199*x^5 - 17432607267590/290630069311
99*x^4 + 49785595543672/29063006931199*x^3 + 9423768373204/29063006931199*
x^2 - 13716769215544/29063006931199*x + 37962587857138/29063006931199, x^1
2 - 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]]
? qfbcompraw(Qfb(5,3,-1,0.),Qfb(7,1,-1,0.))
% = Qfb(35, 43, 13, 0.E-38)
? concat([1,2],[3,4])
% = [1, 2, 3, 4]
? bnrconductor(bnf,[[25,13;0,1],[1,1]])
% = [[5, 3; 0, 1], [1, 0]]
? bnrconductorofchar(bnr,[2])
% = [[5, 3; 0, 1], [0, 0]]
? conj(1+I)
% = 1 - I
? %_
  ***   unused characters: %_
                            ^

? conjvec(Mod(x^2+x+1,x^3-x-1))
% = [4.0795956234914387860104177508366260325, 0.46020218825428060699479112
458168698369 + 0.18258225455744299269398828369501930573*I, 0.4602021882542
8060699479112458168698369 - 0.18258225455744299269398828369501930573*I]~
? content([123,456,789,234])
% = 3
? serconvol(sin(x),x*cos(x))
% = x + 1/12*x^3 + 1/2880*x^5 + 1/3628800*x^7 + 1/14631321600*x^9 + 1/1448
50083840000*x^11 + 1/2982752926433280000*x^13 + 1/114000816848279961600000
*x^15 + O(x^16)
? core(54713282649239)
% = 5471
? core(54713282649239,1)
% = [5471, 100003]
? coredisc(54713282649239)
% = 21884
? coredisc(54713282649239,1)
% = [21884, 100003/2]
? cos(1)
% = 0.54030230586813971740093660744297660373
? cosh(1)
% = 1.5430806348152437784779056207570616825
? plotmove(0,200,150)
? plotcursor(0)
% = [200, 150]
? truncate(1.7,1)
% = 1
? 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^15 + x^14 + x^13 + x^12 - x^9 - x^8 - 2*x^7 - x^6 - x^5 + x^2 + x +
 1
? ? poldegree(x^3/(x-1))
% = 2
? denominator(12345/54321)
% = 18107
? lindep(Mod(1,7)*[2,-1;1,3],-1)
% = [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
? 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]

? 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]
? acurve=ellinit([0,0,1,-1,0])
% = [0, 0, 1, -1, 0, 0, -2, 1, -1, 48, -216, 37, 110592/37, [0.83756543528
332303544481089907503024040, 0.26959443640544455826293795134926000404, -1.
1071598716887675937077488504242902444]~, 2.9934586462319596298320099794525
081778, 2.4513893819867900608542248318665252253*I, -0.47131927795681147588
259389708033769964, -1.4354565186686843187232088566788165076*I, 7.33813274
07895767390707210033323055881]
? apoint=[2,2]
% = [2, 2]
? ellisoncurve(acurve,apoint)
% = 1
? 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, 10, 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, 1
8, -15, 6, 0, -4, -18, 0, 4, 24, 2, 4, 12, 18, 0, -24, 4, 12, -30, -2]
? ellap(acurve,10007)
% = 66
? ellap(acurve,10007,1)
% = 66
? ellan(acurve,100)==deu
% = 0
? 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, 10, 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, 1
8, -15, 6, 0, -4, -18, 0, 4, 24, 2, 4, 12, 18, 0, -24, 4, 12, -30, -2]
? acurve=ellchangecurve(acurve,[-1,1,2,3])
% = [-4, -1, -7, -12, -12, 12, 4, 1, -1, 48, -216, 37, 110592/37, [-0.1624
3456471667696455518910092496975959, -0.73040556359455544173706204865073999
595, -2.1071598716887675937077488504242902444]~, -2.9934586462319596298320
099794525081778, -2.4513893819867900608542248318665252253*I, 0.47131927795
681147588259389708033769964, 1.4354565186686843187232088566788165076*I, 7.
3381327407895767390707210033323055881]
? apoint=ellchangepoint(apoint,[-1,1,2,3])
% = [1, 3]
? ellisoncurve(acurve,apoint)
% = 1
? mcurve=ellinit([0,0,0,-17,0])
% = [0, 0, 0, -17, 0, 0, -34, 0, -289, 816, 0, 314432, 1728, [4.1231056256
176605498214098559740770251, 0.E-38, -4.1231056256176605498214098559740770
251]~, 1.2913084409290072207105564235857096009, 1.291308440929007220710556
4235857096009*I, -1.2164377440798088266474269946818791934, -3.649313232239
4264799422809840456375802*I, 1.6674774896145033307120230298772362381]
? mpoints=[[-1,4],[-4,2]]~
% = [[-1, 4], [-4, 2]]~
? mhbi=ellbil(mcurve,mpoints,[9,24])
% = [-0.72448571035980184146215805860545027439, 1.307328627832055544492943
4288921943055]~
? 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(nfinit(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]
? poldisc(x^3+4*x+12)
% = -4144
? nfdisc(x^3+4*x+12)
% = -1036
? nfdisc(x^3+4*x+12,1)
% = -1036
? bnrdisc(bnr,Mat(6))
% = [12, 12, 18026977100265125]
? bnrdisc(bnr)
% = [24, 12, 40621487921685401825918161408203125]
? bnrdisc(bnr2,,,2)
% = 0
? lu=ideallist(bnf,55,3);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, 12]]], [[]], [[], []], [], [[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]], [12, 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, 12, [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,,1)
% = [[[[matrix(0,2,j,k,0), [[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], [0, 0, 0], [12, 6, [-1, 1; 
3, 3; 229, 6]], [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]], [0, 0, 0], [24, 12, [5, 9; 229, 12]], [0, 0, 0]]]], [], [], [], [[M
at([12, 2]), [[0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0]]], [[12, 1; 13, 1
], [[0, 0, 0], [12, 6, [-1, 1; 3, 6; 229, 6]], [0, 0, 0], [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], [0, 0, 0], [12, 6, [-1, 1; 11, 3; 229, 6
]], [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, 24]]]], [[13, 1; 20, 1], [[0, 0, 0]
, [24, 12, [3, 6; 5, 9; 229, 12]], [24, 12, [3, 6; 5, 6; 229, 12]], [48, 0
, [3, 12; 5, 18; 229, 24]]]], [[12, 1; 21, 1], [[0, 0, 0], [24, 12, [3, 6;
 5, 9; 229, 12]], [0, 0, 0], [48, 0, [3, 12; 5, 18; 229, 24]]]], [[13, 1; 
21, 1], [[24, 24, [3, 6; 5, 9; 229, 12]], [0, 0, 0], [48, 24, [3, 12; 5, 1
8; 229, 24]], [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], [12, 6, [-1, 1; 17, 3; 229, 6]], [0, 0, 0]
, [0, 0, 0]]], [Mat([69, 1]), [[0, 0, 0], [12, 6, [-1, 1; 17, 3; 229, 6]],
 [0, 0, 0], [0, 0, 0]]]], [], [[Mat([76, 1]), [[18, 18, [19, 6; 229, 9]], 
[0, 0, 0], [0, 0, 0], [36, 0, [19, 15; 229, 18]]]], [Mat([77, 1]), [[18, 1
8, [19, 6; 229, 9]], [0, 0, 0], [36, 18, [-1, 1; 19, 15; 229, 18]], [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]]]]]]
? bnrdisc(bnr,Mat(6),,1)
% = [6, 2, [125, 13; 0, 1]]
? bnrdisc(bnr,,,1)
% = [12, 1, [1953125, 1160888; 0, 1]]
? bnrdisc(bnr2,,,3)
% = 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, 120, 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, 67
2, 720, 840, 896, 960, 1008, 1120, 1152, 1260, 1344, 1440, 1680, 1920, 201
6, 2240, 2520, 2688, 2880, 3360, 4032, 4480, 5040, 5760, 6720, 8064, 10080
, 13440, 20160, 40320]
? divrem(345,123)
% = [2, 99]~
? divrem(x^7-1,x^5+1)
% = [x^2, -x^2 - 1]~
? sumdiv(8!,x,x)
% = 159120
? psdraw([0,0,0])
? ? mateigen([1,2,3;4,5,6;7,8,9])
% = 
[0.28334945180064027179781065475712672521 + 0.E-39*I 1 -1.2833494518006402
717978106547571267252 + 0.E-38*I]

[0.64167472590032013589890532737856336260 + 0.E-38*I -2 -0.141674725900320
13589890532737856336259 + 0.E-39*I]

[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
% = euler
? z=y;y=x;eval(z)
% = x
? exp(1)
% = 2.7182818284590452353602874713526624977
? vecextract([1,2,3,4,5,6,7,8,9,10],1000)
% = [4, 6, 7, 8, 9, 10]
? ? 10!
% = 3628800
? factorial(10)
% = 3628800.0000000000000000000000000000000
? 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 + Mo
d(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^2 - 1) 1]

[x + (t^2 + t - 1) 1]

[x - t 1]

? factormod(x^11+1,7)
% = 
[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 + Mo
d(6, 7)*x + Mod(1, 7) 1]

[Mod(1, 7)*x + Mod(1, 7) 1]

? factormod(x^11+1,7,1)
% = 
[1 1]

[10 1]

? factor(17!+1)
% = 
[661 1]

[537913 1]

[1000357 1]

? factor(100!+1,0)
% = 
[101 1]

[14303 1]

[149239 1]

[4328852738498929626130718009186589490596793086850244817957407655275684930
10727023757461397498800981521440877813288657839195622497225621499427628453
 1]

? factor(40!+1,100000)
% = 
[41 1]

[59 1]

[277 1]

[1217669507565553887239873369513188900554127 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 + 385389
0514072057
? fa=[11699,6;2392997,2;4987333019653,2]
% = 
[11699 6]

[2392997 2]

[4987333019653 2]

? nfbasis(p,0,fa)
% = [1, x, x^2, 1/11699*x^3 + 1847/11699*x^2 - 132/11699*x - 2641/11699, 1
/139623738889203638909659*x^4 - 1552451622081122020/1396237388892036389096
59*x^3 + 418509858130821123141/139623738889203638909659*x^2 - 681091379850
75994073134/139623738889203638909659*x - 13185339461968406/583468089969204
47]
? nfdisc(p,0,fa)
% = 136866601
? polred(p,0,fa)
% = [x - 1, 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, x^5 - 2*x^4 - 53*x^3 - 46*x^2 + 508*x + 913, x^5 -
 2*x^4 - 62*x^3 + 85*x^2 + 818*x + 1]~
? polred(p,1,fa)
% = [x - 1, 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, x^5 - 2*x^4 - 53*x^3 - 46*x^2 + 508*x + 913, x^5 -
 2*x^4 - 62*x^3 + 85*x^2 + 818*x + 1]~
? 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]

? 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]

? fibonacci(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
0.86602540378443864676372317075293618346
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
? ? polgalois(x^6-3*x^2-1)
% = [12, 1, 1]
? nf3=nfinit(x^6+108);nfgaloisconj(nf3)
% = [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, -x]
? nfgaloisconj(nf3,1)
% = [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, -x]
? aut=%[2];nfgaloisapply(nf3,aut,Mod(x^5,x^6+108))
% = Mod(-1/2*x^5 + 9*x^2, x^6 + 108)
? gammah(10)
% = 1133278.3889487855673345741655888924755
? gamma(10.5)
% = 1133278.3889487855673345741655888924755
? matsolve(mathilbert(10),[1,2,3,4,5,6,7,8,9,0]~)
% = [9236800, -831303990, 18288515520, -170691240720, 832112321040, -23298
94066500, 3883123564320, -3803844432960, 2020775945760, -449057772020]~
? matsolvemod([2,3;5,4],[7,11],[1,4]~)
% = [[-5, -1]~, [-77, 723; 0, 1]]
? matsolvemod([2,3;5,4],[7,11],[1,4]~,1)
% = [-5, -1]~
? gcd(12345678,87654321)
% = 9
? gcd(x^10-1,x^15-1,2)
% = x^5 - 1
? getheap
% = [221, 50221]
? getrand
% = 268436848
? ellglobalred(acurve)
% = [37, [1, -1, 2, 2], 1]
? getheap
% = [224, 50272]
? ? qfbhclassno(2000003)
% = 357
? ellheight(acurve,apoint)
% = 0.40889126591975072188708879805553617287
? ellheight(acurve,apoint,1)
% = 0.40889126591975072188708879805553617296
? mathnf(amat=1/mathilbert(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]

? 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; 210, 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, 1
866]]
? mathnf(amat,2)
% = [[360360, 0, 0, 0, 0, 144144, 300300; 0, 27720, 0, 0, 0, 0, 22176; 0, 
0, 27720, 0, 0, 0, 6930; 0, 0, 0, 2520, 0, 0, 840; 0, 0, 0, 0, 2520, 0, 12
60; 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, 3080, 315, 360, 13132, 30574; 30030, 2520, 2772, 280, 315, 12
036, 27986; 27720, 2310, 2520, 252, 280, 11109, 25803], [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]

? mathnf(amat,3)
% = [[360360, 0, 0, 0, 0, 144144, 300300; 0, 27720, 0, 0, 0, 0, 22176; 0, 
0, 27720, 0, 0, 0, 6930; 0, 0, 0, 2520, 0, 0, 840; 0, 0, 0, 0, 2520, 0, 12
60; 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, 3080, 315, 360, 13132, 30574; 30030, 2520, 2772, 280, 315, 12
036, 27986; 27720, 2310, 2520, 252, 280, 11109, 25803], [7, 6, 5, 4, 3, 2,
 1]]
? mathess(mathilbert(7))
% = 
[1 90281/58800 -1919947/4344340 4858466341/1095033030 -77651417539/8196787
326 3386888964/106615355 1/2]

[1/3 43/48 38789/5585580 268214641/109503303 -581330123627/126464718744 43
65450643/274153770 1/4]

[0 217/2880 442223/7447440 53953931/292008808 -32242849453/168619624992 14
75457901/1827691800 1/80]

[0 0 1604444/264539275 24208141/149362505292 847880210129/47916076768560 -
4544407141/103873817300 -29/40920]

[0 0 0 9773092581/35395807550620 -24363634138919/107305824577186620 721182
03606917/60481351061158500 55899/3088554700]

[0 0 0 0 67201501179065/8543442888354179988 -9970556426629/740828619992676
600 -3229/13661312210]

[0 0 0 0 0 -258198800769/9279048099409000 -13183/38381527800]

? hilbert(2/3,3/4,5)
% = 1
? 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]

? hilbert(Mod(5,7),Mod(6,7))
% = 1
? hyperu(1,1,1)
% = 0.59634736232319407434107849936927937603
? ? I^2
% = -1
? nf1=nfinit(nfpol,2)
% = [x^5 - 2*x^4 + 3*x^3 + 8*x^2 + 3*x + 2, [1, 2], 595125, 4, [[1, -1.089
1151457205048250249527946671612684, 1.186171800637796459479629386048398986
0, -0.59741050929194782733001765987770358483, 0.15894419745390376206549481
671071894289; 1, -0.13838372073406036365047976417441696637 + 0.49181637657
768643499753285514741525107*I, -0.22273329410580226599155701611419649154 -
 0.13611876021752805221674918029071012580*I, -0.13167445871785818798769651
537619416009 + 0.13249517760521973840801462296650806543*I, -0.053650958656
997725359297528357602608116 + 0.27622636814169107038138284681568361486*I; 
1, 1.6829412935943127761629561615079976005 + 2.050035122601072617297428698
3598602163*I, -1.3703526062130959637482576769100030014 + 6.900177522288049
4773720769629846373016*I, -8.0696202866361678983472946546849540475 + 8.876
7676785971042450885284301348051602*I, -22.02582114006995415567344987999775
6863 - 8.4306586896999153544710860185447589664*I], [1, 2, 2; -1.0891151457
205048250249527946671612684, -0.27676744146812072730095952834883393274 - 0
.98363275315537286999506571029483050214*I, 3.36588258718862555232591232301
59952011 - 4.1000702452021452345948573967197204327*I; 1.186171800637796459
4796293860483989860, -0.44546658821160453198311403222839298308 + 0.2722375
2043505610443349836058142025160*I, -2.740705212426191927496515353820006002
9 - 13.800355044576098954744153925969274603*I; -0.597410509291947827330017
65987770358483, -0.26334891743571637597539303075238832018 - 0.264990355210
43947681602924593301613087*I, -16.139240573272335796694589309369908095 - 1
7.753535357194208490177056860269610320*I; 0.158944197453903762065494816710
71894289, -0.10730191731399545071859505671520521623 - 0.552452736283382140
76276569363136722973*I, -44.051642280139908311346899759995513726 + 16.8613
17379399830708942172037089517932*I], [5, 2.0000000000000000000000000000000
000000, -2.0000000000000000000000000000000000000, -17.00000000000000000000
0000000000000000, -44.000000000000000000000000000000000000; 2.000000000000
0000000000000000000000000, 15.778109408671998044836357471283695361, 22.314
643349754061651916553814602769764, 10.051395257831478275499932716306366248
, -108.58917507620841447456569092094763671; -2.000000000000000000000000000
0000000000, 22.314643349754061651916553814602769764, 100.52391262388960975
827806174040462368, 143.93295090847353519436673793501057176, -55.842564718
082452641322500190813370023; -17.000000000000000000000000000000000000, 10.
051395257831478275499932716306366248, 143.93295090847353519436673793501057
176, 288.25823756749944693139292174819167135, 205.798400382776623757201806
49465932302; -44.000000000000000000000000000000000000, -108.58917507620841
447456569092094763671, -55.842564718082452641322500190813370023, 205.79840
038277662375720180649465932302, 1112.6092277946777707779250962522343036], 
[5, 2, -2, -17, -44; 2, -2, -34, -63, -40; -2, -34, -90, -101, 177; -17, -
63, -101, -27, 505; -44, -40, 177, 505, 828], [345, 0, 160, 252, 156; 0, 3
45, 215, 311, 306; 0, 0, 5, 3, 2; 0, 0, 0, 1, 0; 0, 0, 0, 0, 1], [163875, 
-388125, -296700, 234600, -89700; -388125, -1593900, -677925, 595125, -315
675; -296700, -677925, 17250, 58650, -87975; 234600, 595125, 58650, -10005
0, 89700; -89700, -315675, -87975, 89700, -55200], [595125, 0, 357075, 427
800, 326025; 0, 595125, 119025, 512325, 191475; 0, 0, 119025, 79350, 75900
; 0, 0, 0, 1725, 0; 0, 0, 0, 0, 1725]], [-1.089115145720504825024952794667
1612684, -0.13838372073406036365047976417441696637 + 0.4918163765776864349
9753285514741525107*I, 1.6829412935943127761629561615079976005 + 2.0500351
226010726172974286983598602163*I], [1, x, x^2, 1/2*x^3 + 1/2*x^2 + 1/2*x, 
1/2*x^4 + 1/2*x], [1, 0, 0, 0, 0; 0, 1, 0, -1, -1; 0, 0, 1, -1, 0; 0, 0, 0
, 2, 0; 0, 0, 0, 0, 2], [1, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, -1, -2, 0
, 0, -1, -2, -2, 0, -1, -2, -2, 5; 0, 1, 0, 0, 0, 1, 0, -1, -1, -1, 0, -1,
 -1, -2, 2, 0, -1, -2, -1, 7, 0, -1, 2, 7, 14; 0, 0, 1, 0, 0, 0, 1, -1, 0,
 -2, 1, -1, 0, -3, -3, 0, 0, -3, -4, -1, 0, -2, -3, -1, 15; 0, 0, 0, 1, 0,
 0, 0, 2, 1, -3, 0, 2, 0, -2, -13, 1, 1, -2, -9, -19, 0, -3, -13, -19, 7; 
0, 0, 0, 0, 1, 0, 0, 0, 1, 2, 0, 0, 2, 3, 1, 0, 1, 3, 4, -4, 1, 2, 1, -4, 
-21]]
? nfinit(nfpol,3)
% = [[x^5 - 2*x^4 + 3*x^3 + 8*x^2 + 3*x + 2, [1, 2], 595125, 4, [[1, -1.08
91151457205048250249527946671612684, 1.18617180063779645947962938604839898
60, -0.59741050929194782733001765987770358483, 0.1589441974539037620654948
1671071894289; 1, -0.13838372073406036365047976417441696637 + 0.4918163765
7768643499753285514741525107*I, -0.22273329410580226599155701611419649154 
- 0.13611876021752805221674918029071012580*I, -0.1316744587178581879876965
1537619416009 + 0.13249517760521973840801462296650806543*I, -0.05365095865
6997725359297528357602608116 + 0.27622636814169107038138284681568361486*I;
 1, 1.6829412935943127761629561615079976005 + 2.05003512260107261729742869
83598602163*I, -1.3703526062130959637482576769100030014 + 6.90017752228804
94773720769629846373016*I, -8.0696202866361678983472946546849540475 + 8.87
67676785971042450885284301348051602*I, -22.0258211400699541556734498799977
56863 - 8.4306586896999153544710860185447589664*I], [1, 2, 2; -1.089115145
7205048250249527946671612684, -0.27676744146812072730095952834883393274 - 
0.98363275315537286999506571029483050214*I, 3.3658825871886255523259123230
159952011 - 4.1000702452021452345948573967197204327*I; 1.18617180063779645
94796293860483989860, -0.44546658821160453198311403222839298308 + 0.272237
52043505610443349836058142025160*I, -2.74070521242619192749651535382000600
29 - 13.800355044576098954744153925969274603*I; -0.59741050929194782733001
765987770358483, -0.26334891743571637597539303075238832018 - 0.26499035521
043947681602924593301613087*I, -16.139240573272335796694589309369908095 - 
17.753535357194208490177056860269610320*I; 0.15894419745390376206549481671
071894289, -0.10730191731399545071859505671520521623 - 0.55245273628338214
076276569363136722973*I, -44.051642280139908311346899759995513726 + 16.861
317379399830708942172037089517932*I], [5, 2.000000000000000000000000000000
0000000, -2.0000000000000000000000000000000000000, -17.0000000000000000000
00000000000000000, -44.000000000000000000000000000000000000; 2.00000000000
00000000000000000000000000, 15.778109408671998044836357471283695361, 22.31
4643349754061651916553814602769764, 10.05139525783147827549993271630636624
8, -108.58917507620841447456569092094763671; -2.00000000000000000000000000
00000000000, 22.314643349754061651916553814602769764, 100.5239126238896097
5827806174040462368, 143.93295090847353519436673793501057176, -55.84256471
8082452641322500190813370023; -17.000000000000000000000000000000000000, 10
.051395257831478275499932716306366248, 143.9329509084735351943667379350105
7176, 288.25823756749944693139292174819167135, 205.79840038277662375720180
649465932302; -44.000000000000000000000000000000000000, -108.5891750762084
1447456569092094763671, -55.842564718082452641322500190813370023, 205.7984
0038277662375720180649465932302, 1112.6092277946777707779250962522343036],
 [5, 2, -2, -17, -44; 2, -2, -34, -63, -40; -2, -34, -90, -101, 177; -17, 
-63, -101, -27, 505; -44, -40, 177, 505, 828], [345, 0, 160, 252, 156; 0, 
345, 215, 311, 306; 0, 0, 5, 3, 2; 0, 0, 0, 1, 0; 0, 0, 0, 0, 1], [163875,
 -388125, -296700, 234600, -89700; -388125, -1593900, -677925, 595125, -31
5675; -296700, -677925, 17250, 58650, -87975; 234600, 595125, 58650, -1000
50, 89700; -89700, -315675, -87975, 89700, -55200], [595125, 0, 357075, 42
7800, 326025; 0, 595125, 119025, 512325, 191475; 0, 0, 119025, 79350, 7590
0; 0, 0, 0, 1725, 0; 0, 0, 0, 0, 1725]], [-1.08911514572050482502495279466
71612684, -0.13838372073406036365047976417441696637 + 0.491816376577686434
99753285514741525107*I, 1.6829412935943127761629561615079976005 + 2.050035
1226010726172974286983598602163*I], [1, x, x^2, 1/2*x^3 + 1/2*x^2 + 1/2*x,
 1/2*x^4 + 1/2*x], [1, 0, 0, 0, 0; 0, 1, 0, -1, -1; 0, 0, 1, -1, 0; 0, 0, 
0, 2, 0; 0, 0, 0, 0, 2], [1, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, -1, -2, 
0, 0, -1, -2, -2, 0, -1, -2, -2, 5; 0, 1, 0, 0, 0, 1, 0, -1, -1, -1, 0, -1
, -1, -2, 2, 0, -1, -2, -1, 7, 0, -1, 2, 7, 14; 0, 0, 1, 0, 0, 0, 1, -1, 0
, -2, 1, -1, 0, -3, -3, 0, 0, -3, -4, -1, 0, -2, -3, -1, 15; 0, 0, 0, 1, 0
, 0, 0, 2, 1, -3, 0, 2, 0, -2, -13, 1, 1, -2, -9, -19, 0, -3, -13, -19, 7;
 0, 0, 0, 0, 1, 0, 0, 0, 1, 2, 0, 0, 2, 3, 1, 0, 1, 3, 4, -4, 1, 2, 1, -4,
 -21]], 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)]
? nfinit(nfpol,4)
% = [x^5 - 2*x^4 + 3*x^3 + 8*x^2 + 3*x + 2, [1, 2], 595125, 4, [[1, -1.089
1151457205048250249527946671612684, 1.186171800637796459479629386048398986
0, -0.59741050929194782733001765987770358483, 0.15894419745390376206549481
671071894289; 1, -0.13838372073406036365047976417441696637 + 0.49181637657
768643499753285514741525107*I, -0.22273329410580226599155701611419649154 -
 0.13611876021752805221674918029071012580*I, -0.13167445871785818798769651
537619416009 + 0.13249517760521973840801462296650806543*I, -0.053650958656
997725359297528357602608116 + 0.27622636814169107038138284681568361486*I; 
1, 1.6829412935943127761629561615079976005 + 2.050035122601072617297428698
3598602163*I, -1.3703526062130959637482576769100030014 + 6.900177522288049
4773720769629846373016*I, -8.0696202866361678983472946546849540475 + 8.876
7676785971042450885284301348051602*I, -22.02582114006995415567344987999775
6863 - 8.4306586896999153544710860185447589664*I], [1, 2, 2; -1.0891151457
205048250249527946671612684, -0.27676744146812072730095952834883393274 - 0
.98363275315537286999506571029483050214*I, 3.36588258718862555232591232301
59952011 - 4.1000702452021452345948573967197204327*I; 1.186171800637796459
4796293860483989860, -0.44546658821160453198311403222839298308 + 0.2722375
2043505610443349836058142025160*I, -2.740705212426191927496515353820006002
9 - 13.800355044576098954744153925969274603*I; -0.597410509291947827330017
65987770358483, -0.26334891743571637597539303075238832018 - 0.264990355210
43947681602924593301613087*I, -16.139240573272335796694589309369908095 - 1
7.753535357194208490177056860269610320*I; 0.158944197453903762065494816710
71894289, -0.10730191731399545071859505671520521623 - 0.552452736283382140
76276569363136722973*I, -44.051642280139908311346899759995513726 + 16.8613
17379399830708942172037089517932*I], [5, 2.0000000000000000000000000000000
000000, -2.0000000000000000000000000000000000000, -17.00000000000000000000
0000000000000000, -44.000000000000000000000000000000000000; 2.000000000000
0000000000000000000000000, 15.778109408671998044836357471283695361, 22.314
643349754061651916553814602769764, 10.051395257831478275499932716306366248
, -108.58917507620841447456569092094763671; -2.000000000000000000000000000
0000000000, 22.314643349754061651916553814602769764, 100.52391262388960975
827806174040462368, 143.93295090847353519436673793501057176, -55.842564718
082452641322500190813370023; -17.000000000000000000000000000000000000, 10.
051395257831478275499932716306366248, 143.93295090847353519436673793501057
176, 288.25823756749944693139292174819167135, 205.798400382776623757201806
49465932302; -44.000000000000000000000000000000000000, -108.58917507620841
447456569092094763671, -55.842564718082452641322500190813370023, 205.79840
038277662375720180649465932302, 1112.6092277946777707779250962522343036], 
[5, 2, -2, -17, -44; 2, -2, -34, -63, -40; -2, -34, -90, -101, 177; -17, -
63, -101, -27, 505; -44, -40, 177, 505, 828], [345, 0, 160, 252, 156; 0, 3
45, 215, 311, 306; 0, 0, 5, 3, 2; 0, 0, 0, 1, 0; 0, 0, 0, 0, 1], [163875, 
-388125, -296700, 234600, -89700; -388125, -1593900, -677925, 595125, -315
675; -296700, -677925, 17250, 58650, -87975; 234600, 595125, 58650, -10005
0, 89700; -89700, -315675, -87975, 89700, -55200], [595125, 0, 357075, 427
800, 326025; 0, 595125, 119025, 512325, 191475; 0, 0, 119025, 79350, 75900
; 0, 0, 0, 1725, 0; 0, 0, 0, 0, 1725]], [-1.089115145720504825024952794667
1612684, -0.13838372073406036365047976417441696637 + 0.4918163765776864349
9753285514741525107*I, 1.6829412935943127761629561615079976005 + 2.0500351
226010726172974286983598602163*I], [1, x, x^2, 1/2*x^3 + 1/2*x^2 + 1/2*x, 
1/2*x^4 + 1/2*x], [1, 0, 0, 0, 0; 0, 1, 0, -1, -1; 0, 0, 1, -1, 0; 0, 0, 0
, 2, 0; 0, 0, 0, 0, 2], [1, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, -1, -2, 0
, 0, -1, -2, -2, 0, -1, -2, -2, 5; 0, 1, 0, 0, 0, 1, 0, -1, -1, -1, 0, -1,
 -1, -2, 2, 0, -1, -2, -1, 7, 0, -1, 2, 7, 14; 0, 0, 1, 0, 0, 0, 1, -1, 0,
 -2, 1, -1, 0, -3, -3, 0, 0, -3, -4, -1, 0, -2, -3, -1, 15; 0, 0, 0, 1, 0,
 0, 0, 2, 1, -3, 0, 2, 0, -2, -13, 1, 1, -2, -9, -19, 0, -3, -13, -19, 7; 
0, 0, 0, 0, 1, 0, 0, 0, 1, 2, 0, 0, 2, 3, 1, 0, 1, 3, 4, -4, 1, 2, 1, -4, 
-21]]
? vp=idealprimedec(nf,3)[1]
% = [3, [1, 1, 0, 0, 0]~, 1, 1, [1, -1, -1, 0, 0]~]
? idx=idealmul(nf,matid(5),vp)
% = 
[3 1 2 2 2]

[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 2/3 0 0]

[0 1 1/3 0 0]

[0 0 1/3 0 0]

[0 0 0 1 0]

[0 0 0 0 1]

? idy=idealred(nf,idx,[1,5,6])
% = 
[5 0 0 2 0]

[0 5 0 0 0]

[0 0 5 2 0]

[0 0 0 1 0]

[0 0 0 0 5]

? 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)
% = [[3, 0, 2, 1, 0]~, [-2, 0, -2, -1, 0]~]
? idealaddtoone(nf,[idy,idx])
% = [[-5, 0, 0, 0, 0]~, [6, 0, 0, 0, 0]~]
? idealappr(nf,idy)
% = [-2, 0, -2, 4, 0]~
? idealappr(nf,idealfactor(nf,idy),1)
% = [-2, 0, -2, 4, 0]~
? idealcoprime(nf,idx,idx)
% = [7/3, 2/3, -1/3, -1, 0]~
? idz=idealintersect(nf,idx,idy)
% = 
[15 5 10 12 10]

[0 5 0 0 0]

[0 0 5 2 0]

[0 0 0 1 0]

[0 0 0 0 5]

? idealfactor(nf,idz)
% = 
[[3, [1, 1, 0, 0, 0]~, 1, 1, [1, -1, -1, 0, 0]~] 1]

[[5, [0, 0, 0, 0, 1]~, 4, 1, [2, 5, 2, 1, 0]~] 3]

[[5, [-2, 0, 0, 0, 1]~, 1, 1, [2, 2, 1, 1, 4]~] 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]]]
? idx2=idealmul(nf,idx,idx)
% = 
[9 7 5 8 2]

[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 1]

[0 2 0 0 1]

[0 0 2 0 0]

[0 0 0 2 1]

[0 0 0 0 1]

? idealdiv(nf,idy,idt)
% = 
[5 5/2 5/2 7/2 0]

[0 5/2 0 0 0]

[0 0 5/2 1 0]

[0 0 0 1/2 0]

[0 0 0 0 5/2]

? idealdiv(nf,idx2,idx,1)
% = 
[3 1 2 2 2]

[0 1 0 0 0]

[0 0 1 0 0]

[0 0 0 1 0]

[0 0 0 0 1]

? idealhnf(nf,vp)
% = 
[3 1 2 2 2]

[0 1 0 0 0]

[0 0 1 0 0]

[0 0 0 1 0]

[0 0 0 0 1]

? idealhnf(nf,vp[2],3)
% = 
[3 1 2 2 2]

[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 1807 2129 692 1379]

[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)
% = 
[2 0 0 0 1]

[0 2 0 0 1]

[0 0 2 0 0]

[0 0 0 2 1]

[0 0 0 0 1]

? idealtwoelt(nf,idy)
% = [5, [2, 0, 2, 1, 0]~]
? idealtwoelt(nf,idy,10)
% = [-2, 0, -2, -1, 0]~
? idealval(nf,idp,vp)
% = 7
? 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]

? if(3<2,print("bof"),print("ok"));
ok
? imag(2+3*I)
% = 3
? matimage([1,3,5;2,4,6;3,5,7])
% = 
[1 3]

[2 4]

[3 5]

? matimage(Pi*[1,3,5;2,4,6;3,5,7])
% = 
[3.1415926535897932384626433832795028841 9.4247779607693797153879301498385
086525]

[6.2831853071795864769252867665590057683 12.566370614359172953850573533118
011536]

[9.4247779607693797153879301498385086525 15.707963267948966192313216916397
514420]

? incgam(2,1)
% = 0.73575888234288464319104754032292173491
? incgam(4,1,6)
% = 5.8860710587430771455283803225833738791
? matindexrank([1,1,1;1,1,1;1,1,2])
% = [[1, 3], [1, 3]]
? vecindexsort([8,7,6,5])
% = [4, 3, 2, 1]
? ellinit([0,0,0,-1,0])
% = [0, 0, 0, -1, 0, 0, -2, 0, -1, 48, 0, 64, 1728, [1.0000000000000000000
000000000000000000, 0.E-38, -1.0000000000000000000000000000000000000]~, 2.
6220575542921198104648395898911194136, 2.622057554292119810464839589891119
4136*I, -0.59907011736779610371996124614016193910, -1.79721035210338831115
98837384204858173*I, 6.8751858180203728274900957798105571979]
? ellinit([0,0,0,-17,0],1)
% = [0, 0, 0, -17, 0, 0, -34, 0, -289, 816, 0, 314432, 1728]
? plotinit(1,700,700)
? nfz=zetakinit(x^2-2);
? intformal(sin(x),x)
% = 1/2*x^2 - 1/24*x^4 + 1/720*x^6 - 1/40320*x^8 + 1/3628800*x^10 - 1/4790
01600*x^12 + 1/87178291200*x^14 - 1/20922789888000*x^16 + O(x^17)
? intformal((-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)
? matintersect([1,2;3,4;5,6],[2,3;7,8;8,9])
% = 
[-1]

[-1]

[-1]

? \p19
   realprecision = 19 significant digits
? intnum(x=0,Pi,sin(x),1)
% = 2.000000000000000017
? sqr(2*intnum(x=0,4,exp(-x^2),1))
% = 3.141592556720305685
? 4*intnum(x=1,10^20,1/(1+x^2),2)
% = 3.141592653589793208
? intnum(x=-0.5,0.5,1/sqrt(1-x^2))
% = 1.047197551196597747
? 2*intnum(x=0,100,sin(x)/x,3)
% = 3.124450933778112629
? \p38
   realprecision = 38 significant digits
? matinverseimage([1,1;2,3;5,7],[2,2,6]~)
% = [4, -2]~
? matisdiagonal([1,0,0;0,5,0;0,0,0])
% = 1
? isfundamental(12345)
% = 1
? nfisideal(bnf[7],[5,1;0,1])
% = 1
? nfisincl(x^2+1,x^4+1)
% = [x^2, -x^2]
? nfisincl(nfinit(x^2+1),nfinit(x^4+1),1)
% = [x^2, -x^2]
? polisirreducible(x^5+3*x^3+5*x^2+15)
% = 0
? nfisisom(x^3+x^2-2*x-1,x^3+x^2-2*x-1)
% = [x, x^2 - 2, -x^2 - x + 1]
? nfisisom(nfinit(x^3-2),nfinit(x^3-6*x^2-6*x-30),1)
% = [-1/25*x^2 + 13/25*x - 2/5]
? isprime(12345678901234567)
% = 0
? bnfisprincipal(bnf,[5,1;0,1],0)
% = [1]~
? bnfisprincipal(bnf,[5,1;0,1])
% = [[1]~, [2, 1/3]~, 129]
? bnrisprincipal(bnr,idealprimedec(bnf,7)[1])
% = [[9]~, [329/6561, -7/19683]~, 125]
? ispseudoprime(73!+1)
% = 1
? sqrtint(10!^2+1)
% = 3628800
? setisset([-3,5,7,7])
% = 0
? issquarefree(123456789876543219)
% = 0
? issquare(12345678987654321)
% = 1
? bnfisunit(bnf,Mod(3405*x-27466,x^2-x-57))
% = [-4, Mod(1, 2)]~
? ? qfjacobi(mathilbert(6))
% = [[1.6188998589243390969705881471257800712, 0.2423608705752095521357284
1585070114077, 0.000012570757122625194922982397996498755027, 0.00000010827
994845655497685388772372251711485, 0.0163215213198758221243450795641915058
90, 0.00061574835418265769764919938428527140264]~, [0.74871921887909485900
280109200517845109, -0.61454482829258676899320019644273870645, 0.011144320
930724710530678340374220998541, -0.001248194084082175116939816304638783447
3, 0.24032536934252330399154228873240534568, -0.06222658815019768177515212
6611810492910; 0.44071750324351206127160083580231701801, 0.211082481678670
48675227675845247769095, -0.17973275724076003758776897803740640964, 0.0356
06642944287635266122848131812048466, -0.6976513752773701229620833504667826
5583, 0.49083920971092436297498316169060044997; 0.320696869822251901063590
24326699463106, 0.36589360730302614149086554211117169622, 0.60421220675295
973004426567844103062241, -0.24067907958842295837736719558855679285, -0.23
138937333290388042251363554209048309, -0.535476921621074865934744917509495
45456; 0.25431138634047419251788312792590944672, 0.39470677609501756783094
636145991581708, -0.44357471627623954554460416705180105301, 0.625460386549
22724457753441039459331059, 0.13286315850933553530333839628101576050, -0.4
1703769221897886840494514780771076439; 0.211530840078965246642136676739779
91959, 0.38819043387388642863111448825992418973, -0.4415366410122896622214
3649752977203423, -0.68980719929383668419801738006926829419, 0.36271492146
487147525299457604461742111, 0.047034018933115649705614518466541243873; 0.
18144297664876947372217005457727093715, 0.37069590776736280861775501084807
394603, 0.45911481681642960284551392793050866602, 0.2716054533663128693001
5536176213647001, 0.50276286675751538489260566368647786272, 0.540681563103
85293880022293448123782121]]
? besseljh(1,1)
% = 0.24029783912342701089584304474193368045
? ellj(I)
% = 1728.0000000000000000000000000000000000 + 0.E-45*I
? ? besselk(1+I,1)
% = 0.32545977186584141085464640324923711948 + 0.2894280370259921276345671
5924152302740*I
? besselk(1+I,1,1)
% = 0.32545977186584141085464640324923711948 + 0.2894280370259921276345671
5924152302740*I
? x
% = x
? y
% = x
? 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 1.0806046117362794348018732148859
532074]

[-1.0806046117362794348018732148859532074 -0.16770632690571522600486354099
847562046]

[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)),2)
% = 
[3 1]

[-30 -15]

[70 70]

[0 -140]

[-126 126]

[84 -42]

? f(u)=u+1;
? print(f(5));kill(f);
6
? f=12
% = 12
? plotkill(1)
? kronecker(5,7)
% = -1
? kronecker(3,18)
% = 0
? ? serlaplace(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 + 265533926
9/2730*x^12 - 4324320*x^13 + 264873251/10*x^14 + O(x^15)
? lcm(15,-21)
% = 105
? length(divisors(1000))
% = 16
? pollegendre(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
? veclexsort([[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]
? lindep([(1-3*sqrt(2))/(3-2*sqrt(3)),1,sqrt(2),sqrt(3),sqrt(6)],14)
% = [-3, -3, 9, -2, 6]
? plotmove(0,0,900);plotlines(0,900,0)
? plotlines(0,vector(5,k,50*k),vector(5,k,10*k*k))
? 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]

? qflll(m,7)
% = 
[-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 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]

? qflllgram(m,7)
% = 
[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]

? qflllgram(m,1)
% = 
[1 1 27 -27 69 0 141]

[0 1 4 -23 34 -24 49]

[0 1 3 -22 18 -24 23]

[0 1 3 -21 10 -19 13]

[0 1 3 -20 6 -14 8]

[0 1 3 -19 4 -10 5]

[0 1 3 -18 3 -7 3]

? 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, 17
85, -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, -840; 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, 17
85, -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, -840; 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,3)
% = 
[-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]

? \p96
   realprecision = 96 significant digits
? alias(ln,log)
? ln(2)
% = 0.69314718055994530941723212145817656807550013436025525412068000949339
3621969694715605863326996418
? lngamma(10^50*I)
% = -157079632679489661923132169163975144209858469968811.93673753887608474
9489770941153418951907406847 - 2.52581260692887174213777208138026138840880
884749758842685248040385012601916745265645208759475328*I
? \p2000
   realprecision = 2000 significant digits
? log(2)
% = 0.69314718055994530941723212145817656807550013436025525412068000949339
36219696947156058633269964186875420014810205706857336855202357581305570326
70751635075961930727570828371435190307038623891673471123350115364497955239
12047517268157493206515552473413952588295045300709532636664265410423915781
49520437404303855008019441706416715186447128399681717845469570262716310645
46150257207402481637773389638550695260668341137273873722928956493547025762
65209885969320196505855476470330679365443254763274495125040606943814710468
99465062201677204245245296126879465461931651746813926725041038025462596568
69144192871608293803172714367782654877566485085674077648451464439940461422
60319309673540257444607030809608504748663852313818167675143866747664789088
14371419854942315199735488037516586127535291661000710535582498794147295092
93113897155998205654392871700072180857610252368892132449713893203784393530
88774825970171559107088236836275898425891853530243634214367061189236789192
37231467232172053401649256872747782344535347648114941864238677677440606956
26573796008670762571991847340226514628379048830620330611446300737194890027
43643965002580936519443041191150608094879306786515887090060520346842973619
38412896525565396860221941229242075743217574890977067526871158170511370091
58942665478595964890653058460258668382940022833005382074005677053046787001
84162404418833232798386349001563121889560650553151272199398332030751408426
09147900126516824344389357247278820548627155274187724300248979454019618723
39808608316648114909306675193393128904316413706813977764981769748689038877
89991296503619270710889264105230924783917373501229842420499568935992206602
20465494151061391878857442455775102068370308666194808964121868077902081815
88580001688115973056186676199187395200766719214592236720602539595436541655
31129517598994005600036651356756905124592682574394648316833262490180382424
08242314523061409638057007025513877026817851630690255137032340538021450190
15374029509942262995779647427138157363801729873940704242179972266962979939
31270693
? log(2,1)
% = 0.69314718055994530941723212145817656807550013436025525412068000949339
36219696947156058633269964186875420014810205706857336855202357581305570326
70751635075961930727570828371435190307038623891673471123350115364497955239
12047517268157493206515552473413952588295045300709532636664265410423915781
49520437404303855008019441706416715186447128399681717845469570262716310645
46150257207402481637773389638550695260668341137273873722928956493547025762
65209885969320196505855476470330679365443254763274495125040606943814710468
99465062201677204245245296126879465461931651746813926725041038025462596568
69144192871608293803172714367782654877566485085674077648451464439940461422
60319309673540257444607030809608504748663852313818167675143866747664789088
14371419854942315199735488037516586127535291661000710535582498794147295092
93113897155998205654392871700072180857610252368892132449713893203784393530
88774825970171559107088236836275898425891853530243634214367061189236789192
37231467232172053401649256872747782344535347648114941864238677677440606956
26573796008670762571991847340226514628379048830620330611446300737194890027
43643965002580936519443041191150608094879306786515887090060520346842973619
38412896525565396860221941229242075743217574890977067526871158170511370091
58942665478595964890653058460258668382940022833005382074005677053046787001
84162404418833232798386349001563121889560650553151272199398332030751408426
09147900126516824344389357247278820548627155274187724300248979454019618723
39808608316648114909306675193393128904316413706813977764981769748689038877
89991296503619270710889264105230924783917373501229842420499568935992206602
20465494151061391878857442455775102068370308666194808964121868077902081815
88580001688115973056186676199187395200766719214592236720602539595436541655
31129517598994005600036651356756905124592682574394648316833262490180382424
08242314523061409638057007025513877026817851630690255137032340538021450190
15374029509942262995779647427138157363801729873940704242179972266962979939
31270693
? \p19
   realprecision = 19 significant digits
? bcurve=ellinit([0,0,0,-3,0])
% = [0, 0, 0, -3, 0, 0, -6, 0, -9, 144, 0, 1728, 1728, [1.7320508075688772
93, 0.E-19, -1.732050807568877293]~, 1.992332899583490707, 1.9923328995834
90708*I, -0.7884206134041560682, -2.365261840212468204*I, 3.96939038276275
9668]
? elllocalred(bcurve,2)
% = [6, 2, [1, 1, 1, 0], 1]
? ccurve=ellinit([0,0,-1,-1,0])
% = [0, 0, -1, -1, 0, 0, -2, 1, -1, 48, -216, 37, 110592/37, [0.8375654352
833230353, 0.2695944364054445582, -1.107159871688767593]~, 2.9934586462319
59630, 2.451389381986790061*I, -0.4713192779568114757, -1.4354565186686843
18*I, 7.338132740789576742]
? l=elllseries(ccurve,2,-37,1)
% = 0.3815754082607112112
? elllseries(ccurve,2,-37,1.2)-l
% = -1.355252715293318033 E-19
? ? setrand(1);sbnf=bnfinit(x^3-x^2-14*x-1,3)
% = [x^3 - x^2 - 14*x - 1, 3, 10889, [1, x, x^2], [-3.233732695981516673, 
-0.07182350902743636344, 4.305556205008953036], [10889, 5698, 3794; 0, 1, 
0; 0, 0, 1], Mat([2]), Mat([1, 0, 1, 1, 0, 1, 1, 1]), [9, 15, 16, 17, 10, 
33, 39, 69, 57], [2, [-1, 0, 0]~], [[0, 1, 0]~, [-4, 2, 1]~], [-4, 2, 3, -
1, 3, 1, -1, 11, -7; 1, 1, 1, 1, 0, 1, -4, 2, -2; 0, 0, 0, 0, 0, 0, -1, -1
, 0]]
? bnfmake(sbnf)
% = [Mat([2]), Mat([1, 0, 1, 1, 0, 1, 1, 1]), [1.173637103435061715 + 3.14
1592653589793238*I, -4.562279014988837901 + 3.141592653589793238*I; -2.633
543432738976049 + 3.141592653589793238*I, 1.420330600779487358 + 3.1415926
53589793238*I; 1.459906329303914334, 3.141948414209350543], [1.24634698933
4819161 + 3.141592653589793238*I, -0.6926391142471042845 + 3.1415926535897
93238*I, -1.990056445584799713 + 3.141592653589793238*I, 0.540400637612946
9727 + 3.141592653589793238*I, 0.E-96, 0.004375616572659815402 + 3.1415926
53589793238*I, -0.8305625946607188639, 0.3677262014027817705 + 3.141592653
589793238*I, -1.977791147836553953 + 3.141592653589793238*I; 0.67168274328
67392935 + 3.141592653589793238*I, -0.2461086674077943078, 0.5379005671092
853266, -0.8333219883742404172 + 3.141592653589793238*I, 0.E-96, -0.873831
8043071131265, -1.552661549868775853 + 3.141592653589793238*I, 0.972906318
8316092378, 0.5774919091398324092 + 3.141592653589793238*I; -1.91802973262
1558454, 0.9387477816548985923, 1.452155878475514386, 0.292921350761293444
4, 0.E-96, 0.8694561877344533111, 2.383224144529494717 + 3.141592653589793
238*I, -1.340632520234391008, 1.400299238696721544 + 3.141592653589793238*
I], [[3, [-1, 1, 0]~, 1, 1, [1, 0, 1]~], [5, [2, 1, 0]~, 1, 1, [2, 2, 1]~]
, [5, [3, 1, 0]~, 1, 1, [-2, 1, 1]~], [5, [-1, 1, 0]~, 1, 1, [1, 0, 1]~], 
[3, [1, 0, 1]~, 1, 2, [-1, 1, 0]~], [11, [1, 1, 0]~, 1, 1, [-1, -2, 1]~], 
[13, [19, 1, 0]~, 1, 1, [2, 6, 1]~], [23, [-10, 1, 0]~, 1, 1, [7, 9, 1]~],
 [19, [-6, 1, 0]~, 1, 1, [-3, 5, 1]~]]~, [1, 2, 3, 4, 5, 6, 7, 8, 9]~, [x^
3 - x^2 - 14*x - 1, [3, 0], 10889, 1, [[1, -3.233732695981516673, 10.45702
714905988813; 1, -0.07182350902743636344, 0.005158616449014232794; 1, 4.30
5556205008953036, 18.53781423449109762], [1, 1, 1; -3.233732695981516673, 
-0.07182350902743636344, 4.305556205008953036; 10.45702714905988813, 0.005
158616449014232794, 18.53781423449109762], [3, 1.000000000000000000, 29.00
000000000000000; 1.000000000000000000, 29.00000000000000000, 46.0000000000
0000000; 29.00000000000000000, 46.00000000000000000, 453.0000000000000000]
, [3, 1, 29; 1, 29, 46; 29, 46, 453], [10889, 5698, 3794; 0, 1, 0; 0, 0, 1
], [11021, 881, -795; 881, 518, -109; -795, -109, 86], [10889, 0, 1890; 0,
 10889, 5190; 0, 0, 1]], [-3.233732695981516673, -0.07182350902743636344, 
4.305556205008953036], [1, x, x^2], [1, 0, 0; 0, 1, 0; 0, 0, 1], [1, 0, 0,
 0, 0, 1, 0, 1, 1; 0, 1, 0, 1, 0, 14, 0, 14, 15; 0, 0, 1, 0, 1, 1, 1, 1, 1
5]], [[2, [2], [[3, 2, 2; 0, 1, 0; 0, 0, 1]]], 10.34800724602767998, 1.000
000000000000000, [2, -1], [x, x^2 + 2*x - 4], 1000], [Mat([1]), Mat([1]), 
[[[3, 2, 2; 0, 1, 0; 0, 0, 1], [0.E-96, 0.E-96, 0.E-96]]]], 0]
? concat(Mat(vector(4,x,x)~),vector(4,x,10+x)~)
% = 
[1 11]

[2 12]

[3 13]

[4 14]

? 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]

? ma=ellheightmatrix(mcurve,mpoints)
% = 
[1.172183098700697010 0.4476973883408951692]

[0.4476973883408951692 1.755026016172950713]

? matsolve(ma,mhbi)
% = [-1.000000000000000000, 1.000000000000000000]~
? (1.*mathilbert(7))^(-1)
% = 
[48.99999999998655186 -1175.999999999491507 8819.999999995287112 -29399.99
999998221801 48509.99999996815267 -38807.99999997300892 12011.999999991281
35]

[-1175.999999999490476 37631.99999998079928 -317519.9999998225325 1128959.
999999331688 -1940399.999998805393 1596671.999998988919 -504503.9999996737
196]

[8819.999999995268284 -317519.9999998221492 2857679.999998359414 -10583999
.99999383116 18710999.99998898732 -15717239.99999068887 5045039.9999969978
89]

[-29399.99999998210586 1128959.999999328755 -10583999.99999381752 40319999
.99997678085 -72764999.99995859005 62092799.99996501723 -20180159.99998872
876]

[48509.99999996789781 -1940399.999998797710 18710999.99998893989 -72764999
.99995850268 133402499.9999260516 -115259759.9999375712 37837799.999979897
47]

[-38807.99999997274165 1596671.999998980465 -15717239.99999063055 62092799
.99996487447 -115259759.9999374480 100590335.9999472221 -33297263.99998301
333]

[12011.99999999117839 -504503.9999996704128 5045039.999996973695 -20180159
.99998866230 37837799.99997982113 -33297263.99998298231 11099087.999994525
07]

? 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]

? 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]

? max(2,3)
% = 3
? min(2,3)
% = 2
? qfminim([2,1;1,2],4,6)
% = [6, 2, [0, -1, 1; 1, 1, 0]]
? Mod(-12,7)
% = Mod(2, 7)
? Mod(-12,7,1)
% = 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)
? plotmove(0,243,583);plotcursor(0)
% = [243, 583]
? moebius(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,vectorv(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,matid(5),idx]
% = [[3, 1, 2, 2, 2; 0, 1, 0, 0, 0; 0, 0, 1, 0, 0; 0, 0, 0, 1, 0; 0, 0, 0,
 0, 1], [5, 0, 0, 2, 0; 0, 5, 0, 0, 0; 0, 0, 5, 2, 0; 0, 0, 0, 1, 0; 0, 0,
 0, 0, 5], [15, 5, 10, 12, 10; 0, 5, 0, 0, 0; 0, 0, 5, 2, 0; 0, 0, 0, 1, 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], [3, 1, 2, 2, 2; 0, 1, 0, 0, 0; 0, 0, 1, 0, 0; 0, 0, 0
, 1, 0; 0, 0, 0, 0, 1]]
? bb=nfalgtobasis(nf,Mod(x^3+x,nfpol))
% = [1, 1, 1, 3, 0]~
? da=nfdetint(nf,[a,aid])
% = 
[30 5 25 27 10]

[0 5 0 0 0]

[0 0 5 2 0]

[0 0 0 1 0]

[0 0 0 0 5]

? nfeltdiv(nf,ba,bb)
% = [755/373, -152/373, 159/373, 120/373, -264/373]~
? nfeltdiveuc(nf,ba,bb)
% = [2, 0, 0, 0, -1]~
? nfeltdivrem(nf,ba,bb)
% = [[2, 0, 0, 0, -1]~, [-12, -7, 0, 9, 5]~]
? nfhnf(nf,[a,aid])
% = [[[1, 0, 0, 0, 0]~, [0, 0, 0, 0, 0]~, [0, 0, 0, 0, 0]~; [0, 0, 0, 0, 0
]~, [1, 0, 0, 0, 0]~, [0, 0, 0, 0, 0]~; [0, 0, 0, 0, 0]~, [0, 0, 0, 0, 0]~
, [1, 0, 0, 0, 0]~], [[2, 1, 1, 1, 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], [3, 1, 2, 2, 2; 0, 1, 0, 0, 0; 0, 0, 1, 0, 0; 
0, 0, 0, 1, 0; 0, 0, 0, 0, 1]]]
? nfhnfmod(nf,[a,aid],da)
% = [[[1, 0, 0, 0, 0]~, [0, 0, 0, 0, 0]~, [0, 0, 0, 0, 0]~; [0, 0, 0, 0, 0
]~, [1, 0, 0, 0, 0]~, [0, 0, 0, 0, 0]~; [0, 0, 0, 0, 0]~, [0, 0, 0, 0, 0]~
, [1, 0, 0, 0, 0]~], [[2, 1, 1, 1, 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], [3, 1, 2, 2, 2; 0, 1, 0, 0, 0; 0, 0, 1, 0, 0; 
0, 0, 0, 1, 0; 0, 0, 0, 0, 1]]]
? nfeltmod(nf,ba,bb)
% = [-12, -7, 0, 9, 5]~
? nfeltmul(nf,ba,bb)
% = [-25, -50, -30, 15, 90]~
? nfeltpow(nf,bb,5)
% = [23455, 156370, 115855, 74190, -294375]~
? nfeltreduce(nf,ba,idx)
% = [1, 0, 0, 0, 0]~
? setrand(1);as=matrix(3,3,j,k,vectorv(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,matid(5)]
% = [[3, 1, 2, 2, 2; 0, 1, 0, 0, 0; 0, 0, 1, 0, 0; 0, 0, 0, 1, 0; 0, 0, 0,
 0, 1], [5, 0, 0, 2, 0; 0, 5, 0, 0, 0; 0, 0, 5, 2, 0; 0, 0, 0, 1, 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]]
? haid=[matid(5),matid(5),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], [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]]
? nfsnf(nf,[as,haid,vaid])
% = [[10951073973332888246310, 5442457637639729109215, 2693780223637146570
055, 3910837124677073032737, 3754666252923836621170; 0, 5, 0, 0, 0; 0, 0, 
5, 2, 0; 0, 0, 0, 1, 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]]
? nfeltval(nf,ba,vp)
% = 0
? norm(1+I)
% = 2
? norm(Mod(x+5,x^3+x+1))
% = 129
? norml2(vector(10,x,x))
% = 385
? 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)
? numdiv(2^99*3^49)
% = 5000
? numerator((x+1)/(x-1))
% = x + 1
? qfbnupow(form,111)
% = Qfb(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
? ellordinate(acurve,1)
% = [8, 3]
? tcurve=ellinit([1,0,1,-19,26],1)
% = [1, 0, 1, -19, 26, 1, -37, 105, -316, 889, -24013, 72900, 702595369/72
900]
? ellorder(tcurve,[1,2])
% = 6
? ellztopoint(acurve,ellpointtoz(acurve,apoint))
% = [0.9999999999999999993 + 0.E-19*I, 3.000000000000000000 + 0.E-18*I]
? ellpow(acurve,apoint,10)
% = [-28919032218753260057646013785951999/29273632532924812765148468064016
0000, 478051489392386968218136375373985436596569736643531551/1583853196263
08443937475969221994173751192384064000000]
? cmcurve=ellinit([0,-3/4,0,-2,-1])
% = [0, -3/4, 0, -2, -1, -3, -4, -4, -1, 105, 1323, -343, -3375, [2.000000
000000000000, -0.6250000000000000000 + 0.3307189138830738238*I, -0.6250000
000000000000 - 0.3307189138830738238*I]~, 1.933311705616811546, 0.96665585
28084057733 + 2.557530989916099474*I, -0.8558486330998558525 - 4.598829817
026853561 E-20*I, -0.4279243165499279261 - 2.757161217166147204*I, 4.94450
4600282546727]
? ellpow(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 + 28*w))]
? ellpointtoz(acurve,apoint)
% = 0.7249122149096230677 + 0.E-58*I
? polredord(x^3-12*x+45*x-1)
% = [x - 1, x^3 + 33*x - 1, x^3 - 363*x - 2663]~
? ? padicprec(padicno,127)
% = 5
? 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]

? qfperfection([2,0,1;0,2,1;1,1,2])
% = 6
? numtoperm(7,1035)
% = [4, 7, 1, 6, 3, 5, 2]
? permtonum([4,7,1,6,3,5,2])
% = 1035
? qfbprimeform(-44,3)
% = Qfb(3, 2, 4)
? eulerphi(257^2)
% = 65792
? Pi
% = 3.141592653589793238
? plot(x=-5,5,sin(x))

      0.999 xxxx---------------------------------xxxx------------------|
            |   x                               x    xx                |
            |    x                             x       x               |
            |     x                           x                        |
            |      x                         x          x              |
            |       x                                    x             |
            |                               x                          |
            |        x                     x              x            |
            |         x                                    x           |
            |                             x                            |
            -----------x------------------------------------x-----------
            |                            x                             |
            |           x                                    x         |
            |            x              x                     x        |
            |                          x                               |
            |             x                                    x       |
            |              x          x                         x      |
            |                        x                           x     |
            |               x       x                             x    |
            |                xx    x                               x   |
     -0.999 |------------------xxxx---------------------------------xxxx
             -5.000                                                   5.00
0

? 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]

? plotpoints(0,225,334)
? plotpoints(0,vector(10,k,10*k),vector(10,k,5*k*k))
? ? polinterpolate([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 + 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, x^5 - x^4 - 6*x^3 + 6*x^2 + 13*x - 
5]~
? polred(x^4-28*x^3-458*x^2+9156*x-25321,3)
% = 
[1 x - 1]

[1/4485*x^3 - 7/1495*x^2 - 1034/4485*x + 7924/4485 x^4 - 8*x^2 + 6]

[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]

? polred(x^4+576,1)
% = [x - 1, x^2 + 1, x^4 - x^2 + 1, x^2 - x + 1]~
? polred(x^4+576,3)
% = 
[1 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]

[-1/192*x^3 - 1/8*x + 1/2 x^2 - x + 1]

? 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)]
? polsym(x^17-1,17)
% = [17, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 17]~
? variable(name^4-other)
% = name
? Pol(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)
? polylog(5,0.5,1)
% = 1.033792745541689061
? polylog(5,0.5,2)
% = 1.034459423449010483
? polylog(5,0.5,3)
% = 0.9495693489964922581
? Pol([1,2,3,4,5],x)
% = x^4 + 2*x^3 + 3*x^2 + 4*x + 5
? Polrev([1,2,3,4,5],x)
% = 5*x^4 + 4*x^3 + 3*x^2 + 2*x + 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
? psdraw([0,20,20])
? psploth(x=-5,5,sin(x))
% = [-5.000000000000000000, 5.000000000000000000, -0.9999964107564721649, 
0.9999964107564721649]
? psploth(t=0,2*Pi,[sin(5*t),sin(7*t)],1,100)
% = [-0.9998741276738750682, 0.9998741276738750682, -0.9998741276738750682
, 0.9998741276738750682]
? psplothraw(vector(100,k,k),vector(100,k,k*k/100))
% = [1.000000000000000000, 100.0000000000000000, 0.01000000000000000020, 1
00.0000000000000000]
? qfbpowraw(Qfb(5,3,-1,0.),3)
% = Qfb(125, 23, 1, 0.E-18)
? print((x-12*y)/(y+13*x));
-11/14
? print([1,2;3,4])
[1, 2; 3, 4]
? print1(x+y);print(x+y);
2*x2*x
? \p96
   realprecision = 96 significant digits
? Pi
% = 3.14159265358979323846264338327950288419716939937510582097494459230781
640628620899862803482534211
? precision(Pi,20)
% = 3.14159265358979323846264338325408976600000000000000000000000000000000
000000000000000000000000000
? precision(cmcurve)
% = 19
? \p38
   realprecision = 38 significant digits
? prime(100)
% = 541
? idealprimedec(nf,2)
% = [[2, [3, 1, 0, 0, 0]~, 1, 1, [1, 1, 0, 1, 1]~], [2, [-3, -5, -4, 3, 15
]~, 1, 4, [1, 1, 0, 0, 0]~]]
? idealprimedec(nf,3)
% = [[3, [1, 1, 0, 0, 0]~, 1, 1, [1, -1, -1, 0, 0]~], [3, [0, 0, 1, 1, 0]~
, 2, 2, [2, 1, 3, 2, 0]~]]
? idealprimedec(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, 6
7, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 14
9, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199, 211, 223, 227, 2
29, 233, 239, 241, 251, 257, 263, 269, 271, 277, 281, 283, 293, 307, 311, 
313, 317, 331, 337, 347, 349, 353, 359, 367, 373, 379, 383, 389, 397, 401,
 409, 419, 421, 431, 433, 439, 443, 449, 457, 461, 463, 467, 479, 487, 491
, 499, 503, 509, 521, 523, 541]
? 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
? idealprincipal(nf,Mod(x^3+5,nfpol))
% = 
[6]

[0]

[1]

[3]

[0]

? ideleprincipal(nf,Mod(x^3+5,nfpol))
% = [[6; 0; 1; 3; 0], [2.2324480827796254080981385584384939684 + 3.1415926
535897932384626433832795028842*I, 5.0387659675158716386435353106610489968 
+ 1.5851760343512250049897278861965702423*I, 4.266404027265102874362591079
7589683173 - 0.0083630478144368246110910258645462996191*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(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)
% = 1.0000098157493066238697591433298145174
? prodinf(n=0,(1+2^-n)/(1+2^(-n+1)))
% = 0.33333333333333333333333333333333333322
? prodinf(n=0,-2^-n/(1+2^(-n+1)),1)
% = 0.33333333333333333333333333333333333322
? psi(1)
% = -0.57721566490153286060651209008240243102
? ? quaddisc(-252)
% = -7
? quadgen(-11)
% = w
? quadpoly(-11)
% = x^2 - x + 3
? quadregulator(17)
% = 2.0947125472611012942448228460655286534
? ? matrank(matrix(5,5,x,y,x+y))
% = 2
? bnrclassno(bnf,[[5,3;0,1],[1,0]])
% = 12
? 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, 12, 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
]]
? plotmove(0,50,50);plotrbox(0,50,50)
? print1("give a value for s? ");s=input();print(1/s)
give a value for s? 37.
0.027027027027027027027027027027027027026
? real(5-7*I)
% = 5
? polrecip(3*x^7-5*x^3+6*x-9)
% = -9*x^7 + 6*x^6 - 5*x^4 + 3
? 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, 2.1074451073987839947135880252731470615)
? qfbred(Qfb(3,10,-20,1.5),3,,18)
% = Qfb(-20, -10, 3, 1.5000000000000000000000000000000000000)
? poldiscreduced(x^3+4*x+12)
% = [1036, 4, 1]
? kill(y);print(x+y);reorder([x,y]);print(x+y);
x + y
x + y
? polresultant(x^3-1,x^3+1)
% = 8
? polresultant(x^3-1.,x^3+1.,1)
% = 8.0000000000000000000000000000000000000
? 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^15 + O(x^16)
? plotrline(0,200,150)
? plotcursor(0)
% = [250, 200]
? plotrmove(0,5,5);plotcursor(0)
% = [255, 205]
? round(prod(k=1,17,x-exp(2*I*Pi*k/17)),1)
% = x^17 - 1
? qpol=y^3-y-1;setrand(1);bnf2=bnfinit(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, 3/5; 0, 1, 2/5; 0, 0, 1/5], [1, 0, 8/2
5; 0, 1, 22/25; 0, 0, 1/25]], [416134375, 212940625, 388649575; 0, 3125, 5
50; 0, 0, 25], [-1280, 5, 5]~]
? rnfbasis(bnf2,aa)
% = 
[[1, 0, 0]~ [0, 0, 0]~ [0, 0, 0]~ [4/5, -4/5, -2/5]~ [-187/25, -208/25, 61
/25]~]

[[0, 0, 0]~ [1, 0, 0]~ [0, 0, 0]~ [-4/5, 4/5, 2/5]~ [196/25, 214/25, -88/2
5]~]

[[0, 0, 0]~ [0, 0, 0]~ [1, 0, 0]~ [-2/5, 2/5, 1/5]~ [122/25, 123/25, -116/
25]~]

[[0, 0, 0]~ [0, 0, 0]~ [0, 0, 0]~ [-2/5, 2/5, 1/5]~ [104/25, 111/25, -62/2
5]~]

[[0, 0, 0]~ [0, 0, 0]~ [0, 0, 0]~ [0, 0, 0]~ [3/25, 2/25, -9/25]~]

? rnfdisc(nf2,p)
% = [[416134375, 212940625, 388649575; 0, 3125, 550; 0, 0, 25], [-1280, 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 - 15*x^11 + 75*x^7 - x^5 - 125*x^3 + 5*x + 1), 0]
? rnfhnfbasis(bnf2,aa)
% = 
[[1, 0, 0]~ [0, 0, 0]~ [0, 0, 0]~ [-2/5, 2/5, -4/5]~ [11/25, 99/25, -33/25
]~]

[[0, 0, 0]~ [1, 0, 0]~ [0, 0, 0]~ [2/5, -2/5, 4/5]~ [-8/25, -72/25, 24/25]
~]

[[0, 0, 0]~ [0, 0, 0]~ [1, 0, 0]~ [1/5, -1/5, 2/5]~ [4/25, 36/25, -12/25]~
]

[[0, 0, 0]~ [0, 0, 0]~ [0, 0, 0]~ [1/5, -1/5, 2/5]~ [-2/25, -18/25, 6/25]~
]

[[0, 0, 0]~ [0, 0, 0]~ [0, 0, 0]~ [0, 0, 0]~ [1/25, 9/25, -3/25]~]

? rnfisfree(bnf2,aa)
% = 1
? rnfsteinitz(nf2,aa)
% = [[[1, 0, 0]~, [0, 0, 0]~, [0, 0, 0]~, [4/5, -4/5, -2/5]~, [39/125, 11/
125, 11/125]~; [0, 0, 0]~, [1, 0, 0]~, [0, 0, 0]~, [-4/5, 4/5, 2/5]~, [-42
/125, -8/125, -8/125]~; [0, 0, 0]~, [0, 0, 0]~, [1, 0, 0]~, [-2/5, 2/5, 1/
5]~, [-29/125, 4/125, 4/125]~; [0, 0, 0]~, [0, 0, 0]~, [0, 0, 0]~, [-2/5, 
2/5, 1/5]~, [-23/125, -2/125, -2/125]~; [0, 0, 0]~, [0, 0, 0]~, [0, 0, 0]~
, [0, 0, 0]~, [-1/125, 1/125, 1/125]~], [[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, 108; 0, 125, 22; 0, 0, 1]], [416134375, 212940625, 38864
9575; 0, 3125, 550; 0, 0, 25], [-1280, 5, 5]~]
? 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 + 25*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)]
? polroots(x^5-5*x^2-5*x-5)
% = [2.0509134529831982130058170163696514536 + 0.E-38*I, -0.67063790319207
539268663382582902335603 + 0.84813118358634026680538906224199030917*I, -0.
67063790319207539268663382582902335603 - 0.8481311835863402668053890622419
9030917*I, -0.35481882329952371381627468235580237077 + 1.39980287391035466
98297522834062081964*I, -0.35481882329952371381627468235580237077 - 1.3998
028739103546698297522834062081964*I]~
? polroots(x^4-1000000000000000000000,1)
% = [-177827.94100389228012254211951926848447 + 0.E-38*I, 177827.941003892
28012254211951926848447 + 0.E-38*I, 6.653062250012735499859458931636420075
3 E-111 + 177827.94100389228012254211951926848447*I, 6.6530622500127354998
594589316364200753 E-111 - 177827.94100389228012254211951926848447*I]~
? round(prod(k=1,17,x-exp(2*I*Pi*k/17)))
% = x^17 - 1
? rounderror(prod(k=1,17,x-exp(2*I*Pi*k/17)))
% = -35
? plotrpoint(0,20,20)
? ? plotinit(3,600,600);plotscale(3,-7,7,-2,2);plotcursor(3)
% = [-7, 2]
? 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^62 - 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 + 2
4*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"]
? default(realprecision,28)
   realprecision = 28 significant digits
? setrand(10)
% = 10
? setsearch(aset,3)
% = 3
? setsearch(bset,3)
% = 0
? default(seriesprecision,12)
   seriesprecision = 12 significant terms
? setunion(aset,bset)
% = ["-2", "-5", "1", "2", "3", "5", "7"]
? arat=(x^3+x+1)/x^3;type(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
? sigma(100,2)
% = 13671
? sigma(100,-3)
% = 1149823/1000000
? sign(-1)
% = -1
? sign(0)
% = 0
? sign(0.)
% = 0
? qfsign(mathilbert(5)-0.11*matid(5))
% = [2, 3]
? bnfsignunit(bnf)
% = 
[-1]

[1]

? simplify(((x+I+1)^2-x^2-2*x*(I+1))^2)
% = -4
? sin(Pi/6)
% = 0.4999999999999999999999999999
? sinh(1)
% = 1.175201193643801456882381850
? sizedigit([1.3*10^5,2*I*Pi*exp(4*Pi)])
% = 7
? matsnf(matrix(5,5,j,k,random))
% = [1442459322553825252071178240, 2147483648, 2147483648, 1, 1]
? 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]
? solve(x=1,4,sin(x))
% = 3.141592653589793238462643383
? vecsort(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)
? 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]

? sqrt(13+O(127^12))
% = 34 + 125*127 + 83*127^2 + 107*127^3 + 53*127^4 + 42*127^5 + 22*127^6 +
 98*127^7 + 127^8 + 23*127^9 + 122*127^10 + 79*127^11 + O(127^12)
? plotmove(0,100,100);plotstring(0,Pi)
? plotmove(0,200,200);plotstring(0,"(0,0)")
? psdraw([0,10,10])
? apol=0.3+pollegendre(10)
% = 46189/256*x^10 - 109395/256*x^8 + 45045/128*x^6 - 15015/128*x^4 + 3465
/256*x^2 + 0.05390624999999999999999999999
? polsturm(apol)
% = 4
? polsturm(apol,0.91,1)
% = 1
? polsubcyclo(31,5)
% = x^5 + x^4 - 12*x^3 - 21*x^2 + x + 5
? ellsub(ellinit([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^1
2)
? sum(k=1,10,2^-k)
% = 1023/1024
? sum(k=1,10,2.^-k)
% = 0.9990234375000000000000000000
? polsylvestermatrix(a2*x^2+a1*x+a0,b1*x+b0)
% = 
[a2 b1 0]

[a1 b0 b1]

[a0 0 b0]

? \p38
   realprecision = 38 significant digits
? 4*sumalt(n=0,(-1)^n/(2*n+1))
% = 3.1415926535897932384626433832795028841
? 4*sumalt(n=0,(-1)^n/(2*n+1),1)
% = 3.1415926535897932384626433832795028842
? suminf(n=1,2.^-n)
% = 0.99999999999999999999999999999999999999
? 6/Pi^2*sumpos(n=1,n^-2)
% = 0.99999999999999999999999999999999999999
? matsupplement([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
? elltaniyama(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
? poltchebi(10)
% = 512*x^10 - 1280*x^8 + 1120*x^6 - 400*x^4 + 50*x^2 - 1
? teichmuller(7+O(127^12))
% = 7 + 57*127 + 58*127^2 + 83*127^3 + 52*127^4 + 109*127^5 + 74*127^6 + 1
6*127^7 + 60*127^8 + 47*127^9 + 65*127^10 + 5*127^11 + O(127^12)
? printtex((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
? elltors(tcurve)
% = [12, [6, 2], [[1, 2], [7/4, -11/8]]]
? trace(1+I)
% = 2
? trace(Mod(x+5,x^3+x+1))
% = 15
? mattranspose(vector(2,x,x))
% = [1, 2]~
? %*%~
% = 
[1 2]

[2 4]

? truncate(-2.7)
% = -2
? truncate(sin(x^2))
% = 1/120*x^10 - 1/6*x^6 + x^2
? poltschirnhaus(x^5-x-1)
% = x^5 + 10*x^4 + 38*x^3 + 69*x^2 + 65*x + 29
? type(Mod(x,x^2+1))
% = "t_POLMOD"
? ? quadunit(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
? vector(10,x,1/x)
% = [1, 1/2, 1/3, 1/4, 1/5, 1/6, 1/7, 1/8, 1/9, 1/10]
? 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]]
? ? ellwp(acurve)
% = x^-2 + 1/5*x^2 - 1/28*x^4 + 1/75*x^6 - 3/1540*x^8 + 1943/3822000*x^10 
- 1/11550*x^12 + 193/10510500*x^14 - 1269/392392000*x^16 + 21859/346846500
00*x^18 - 1087/9669660000*x^20 + O(x^22)
? weber(I)
% = 1.1892071150027210667174999705604759152 - 1.17549435049295425400000000
00000000000 E-38*I
? weber(I,1)
% = 1.0905077326652576592070106557607079789 + 0.E-38*I
? weber(I,2)
% = 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 
? ? zeta(3)
% = 1.2020569031595942853997381615114499907
? zeta(0.5+14.1347251*I)
% = 0.0000000052043097453468479398562848599419244554 - 0.00000003269063986
9786982176409251733800562846*I
? zetak(nfz,-3)
% = 0.091666666666666666666666666666666666666
? zetak(nfz,1.5+3*I)
% = 0.88324345992059326405525724366416928890 - 0.2067536250233895222724230
8991427938845*I
? idealstar(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], [[0, 1, 0]~], [[-26, -27, 0]~], [[]~], 1]], [[[26], [[0, 2, 0]~], [[
-27, 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]]], [[], [], [;]]], [468, 469, 0, 0, -48776, 0, 0, -3
6582; 0, 0, 1, 0, -7, -6, 0, -3; 0, 0, 0, 1, -3, 0, -6, 0]]
? bid=idealstar(nf2,54,1)
% = [[[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], [[0, 1, 0]~], [[-26, -27, 0]~], [[]~], 1]], [[[26], [[0, 2, 0]~], [[
-27, 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]]], [[], [], [;]]], [468, 469, 0, 0, -48776, 0, 0, -3
6582; 0, 0, 1, 0, -7, -6, 0, -3; 0, 0, 0, 1, -3, 0, -6, 0]]
? ideallog(nf2,w,bid)
% = [1574, 8, 6]~
? znstar(3120)
% = [768, [12, 4, 4, 2, 2], [Mod(67, 3120), Mod(2341, 3120), Mod(1847, 312
0), Mod(391, 3120), Mod(2081, 3120)]]
? znorder(Mod(33,2^16+1))
% = 2048
? getheap
% = [630, 130827]
? print("Total time spent: ",gettime);
Total time spent: 26457
? \q
Good bye!
