            GP/PARI CALCULATOR Version 1.39
                   (Alpha 64-bit version)

Copyright 1989-1994 by C. Batut, D. Bernardi, H. Cohen and M. Olivier

Type ? for help

\precision      = 38
\serieslength   = 16
\format         = g0.38
\prompt         = ? 
stacksize = 10000000, prime limit = 500000, buffersize = 30000
? ? +3
%1 = 3
? -5
%2 = -5
? 5+3
%3 = 8
? 5-3
%4 = 2
? 5/3
%5 = 5/3
? 5\3
%6 = 1
? 5\/3
%7 = 2
? 5%3
%8 = 2
? 5^3
%9 = 125
? \precision=57
   precision = 57 significant digits
? pi
%10 = 3.14159265358979323846264338327950288419716939937510582097
? \precision=38
   precision = 38 significant digits
? o(x^12)
%11 = O(x^12)
? padicno=(5/3)*127+O(127^5)
%12 = 44*127 + 42*127^2  + 42*127^3  + 42*127^4  + O(127^5)
? initrect(0,500,500)
? \\ A
? abs(-0.01)
%13 = 0.0099999999999999999999999999999999999999
? acos(0.5)
%14 = 1.0471975511965977461542144610931676280
? acosh(3)
%15 = 1.7627471740390860504652186499595846180
? acurve=initell([0,0,1,-1,0])
%16 = [0, 0, 1, -1, 0, 0, -2, 1, -1, 48, -216, 37, 110592/37, [0.83756543528332303544481089907503024040, 0.26959443640544455826293795134926000404, -1.1071598716887675937077488504242902444]~, 2.9934586462319596298320099794525081778, 2.4513893819867900608542248318665252253*i, -0.47131927795681147588259389708033769964, -1.4354565186686843187232088566788165076*i, 7.3381327407895767390707210033323055881]
? apoint=[2,2]
%17 = [2, 2]
? isoncurve(acurve,apoint)
%18 = 1
? addell(acurve,apoint,apoint)
%19 = [21/25, -56/125]
? addprimes([nextprime(10^9),nextprime(10^10)])
%20 = [1000000007, 10000000019, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]
? adj([1,2;3,4])
%21 = 
[4 -2]

[-3 1]

? agm(1,2)
%22 = 1.4567910310469068691864323832650819749
? agm(1+o(7^5),8+o(7^5))
%23 = 1 + 4*7 + 6*7^2  + 5*7^3  + 2*7^4  + O(7^5)
? algdep(2*cos(2*pi/13),6)
%24 = x^6 + x^5 - 5*x^4 - 4*x^3 + 6*x^2 + 3*x - 1
? algdep2(2*cos(2*pi/13),6,15)
%25 = x^6 + x^5 - 5*x^4 - 4*x^3 + 6*x^2 + 3*x - 1
? \\allocatemem(3000000)
? akell(acurve,1000000007)
%26 = 43800
? nfpol=x^5-5*x^3+5*x+25
%27 = x^5 - 5*x^3 + 5*x + 25
? nf=initalg(nfpol)
%28 = [x^5 - 5*x^3 + 5*x + 25, [1, 2], 595125, 45, [[1, -2.4285174907194186068992069565359418364, 5.8976972027301414394898806541072047941, -7.0734526715090929269887668671457811020, 3.8085820570096366144649278594400435257; 1, 1.9647119211288133163138753392090569931 - 0.80971492418897895128294082219556466857*i, 3.2044546745713084269203768790545260356 - 3.1817131285400005341145852263331539899*i, -0.16163499313031744537610982231988834519 - 1.8880437862007056931906454476483475283*i, 2.0660709538372480632698971148801090692 - 2.6898967519623140991170523711857387388*i; 1, -0.75045317576910401286427186094108607489 - 1.3101462685358123283560773619310445915*i, -1.1533032759363791466653172061081284327 + 1.9664068558894834311780119356739268309*i, 1.1983613288848639088704932558927788962 - 0.64370238076256988899570325671192132449*i, -0.47036198234206637050236104460013083212 - 0.083628266711589186119416762685933385421*i], [1, 2, 2; -2.4285174907194186068992069565359418364, 3.9294238422576266326277506784181139862 + 1.6194298483779579025658816443911293371*i, -1.5009063515382080257285437218821721497 + 2.6202925370716246567121547238620891831*i; 5.8976972027301414394898806541072047941, 6.4089093491426168538407537581090520712 + 6.3634262570800010682291704526663079798*i, -2.3066065518727582933306344122162568654 - 3.9328137117789668623560238713478536619*i; -7.0734526715090929269887668671457811020, -0.32326998626063489075221964463977669038 + 3.7760875724014113863812908952966950567*i, 2.3967226577697278177409865117855577924 + 1.2874047615251397779914065134238426489*i; 3.8085820570096366144649278594400435257, 4.1321419076744961265397942297602181385 + 5.3797935039246281982341047423714774776*i, -0.94072396468413274100472208920026166424 + 0.16725653342317837223883352537186677084*i], [5,  0.E-192, 10.000000000000000000000000000000000000, -5.0000000000000000000000000000000000000, 7.0000000000000000000000000000000000000;  0.E-192, 19.488486013650707197449403270536023970, 1.7534474792067224317455159660000000000 E-192, 19.488486013650707197449403270536023970, 4.1504592246706085588902013976045703227; 10.000000000000000000000000000000000000, 1.7534474792067224317455159660000000000 E-192, 85.960217420851846480305133936577594605, -36.034268291482979838267056239752434596, 53.576130452511107888183080361946556763; -5.0000000000000000000000000000000000000, 19.488486013650707197449403270536023970, -36.034268291482979838267056239752434596, 60.916248374441986300937507618575151517, -18.470101750219179344070032346246890434; 7.0000000000000000000000000000000000000, 4.1504592246706085588902013976045703227, 53.576130452511107888183080361946556763, -18.470101750219179344070032346246890434, 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, 3450, -15525, -3450, 0; 17250, -43125, 51750, 0, -86250], [595125, 0, 0, 581325, 474375; 0, 119025, 0, 117300, 63825; 0, 0, 119025, 67275, 113850; 0, 0, 0, 1725, 0; 0, 0, 0, 0, 8625]], [-2.4285174907194186068992069565359418364, 1.9647119211288133163138753392090569931 - 0.80971492418897895128294082219556466857*i, -0.75045317576910401286427186094108607489 - 1.3101462685358123283560773619310445915*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=algtobasis(nf,mod(x^3+5,nfpol))
%29 = [6, 0, 1, 3, 0]~
? anell(acurve,100)
%30 = [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, 18, -15, 6, 0, -4, -18, 0, 4, 24, 2, 4, 12, 18, 0, -24, 4, 12, -30, -2]
? apell(acurve,10007)
%31 = 66
? apell2(acurve,10007)
%32 = 66
? apol=x^3+5*x+1
%33 = x^3 + 5*x + 1
? apprpadic(apol,1+O(7^8))
%34 = [1 + 6*7 + 4*7^2  + 4*7^3  + 3*7^4  + 4*7^5  + 6*7^7  + O(7^8)]
? apprpadic(x^3+5*x+1,mod(x*(1+O(7^8)),x^2+x-1))
%35 = [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)
%36 = 3.1415926535897932384626433832795028842
? 3*asin(sqrt(3)/2)
%37 = 3.1415926535897932384626433832795028841
? asinh(0.5)
%38 = 0.48121182505960344749775891342436842313
? assmat(x^5-12*x^3+0.0005)
%39 = 
[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))
%40 = 3.1415926535897932384626433832795028841
? atanh(0.5)
%41 = 0.54930614433405484569762261846126285232
? \\ B
? basis(x^3+4*x+5)
%42 = [1, x, 1/7*x^2 - 1/7*x - 2/7]
? basis2(x^3+4*x+5)
%43 = [1, x, 1/7*x^2 - 1/7*x - 2/7]
? basistoalg(nf,ba)
%44 = mod(x^3 + 5, x^5 - 5*x^3 + 5*x + 25)
? bernreal(12)
%45 = -0.25311355311355311355311355311355311354
? bernvec(6)
%46 = [1, 1/6, -1/30, 1/42, -1/30, 5/66, -691/2730]
? bestappr(pi,10000)
%47 = 355/113
? bezout(123456789,987654321)
%48 = [-8, 1, 9]
? bigomega(12345678987654321)
%49 = 8
? mcurve=initell([0,0,0,-17,0])
%50 = [0, 0, 0, -17, 0, 0, -34, 0, -289, 816, 0, 314432, 1728, [4.1231056256176605498214098559740770251,  0.E-38, -4.1231056256176605498214098559740770251]~, 1.2913084409290072207105564235857096009, 1.2913084409290072207105564235857096009*i, -1.2164377440798088266474269946818791934, -3.6493132322394264799422809840456375802*i, 1.6674774896145033307120230298772362381]
? mpoints=[[-1,4],[-4,2]]~
%51 = [[-1, 4], [-4, 2]]~
? mhbi=bilhell(mcurve,mpoints,[9,24])
%52 = [-0.72448571035980184146215805860545027438, 1.3073286278320555444929434288921943055]~
? bin(1.1,5)
%53 = -0.0045457499999999999999999999999999999997
? binary(65537)
%54 = [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1]
? bittest(10^100,100)
%55 = 1
? boundcf(pi,5)
%56 = [3, 7, 15, 1, 292]
? boundfact(40!+1,100000)
%57 = 
[41 1]

[59 1]

[277 1]

[1217669507565553887239873369513188900554127 1]

? move(0,0,0);box(0,500,500)
? setrand(1);buchimag(1-10^7,1,1)
%58 = [2416, [1208, 2], [qfi(277, 55, 9028), qfi(1700, 1249, 1700)], 0.99984980753775999737665430800000000000]
? setrand(1);bnf=buchinit(x^2-x-57,0.2,0.2)
%59 = [[3], [2, 2, -2, -2, -2], [-2.7124653051843439746808795106061300699 + 9.4247779607693797153879301498385086526*i; 2.7124653051843439746808795106061300699 + 12.566370614359172953850573533118011536*i], [10275.740699586781590689523253765996614 + 3.1415926535897932384626433832795028842*i, 634.21630160950403420149960216844371958 + 12.566370614359172953850573533118011536*i, 634.01539591045106185685718938112006734 + 9.4247779607693797153879301498385086526*i, 79802.519620280097464487804413952976876 + 6.2831853071795864769252867665590057684*i, 35395.460347154136981484622937212781998 + 3.1415926535897932384626433832795028842*i, 41864.891005717850333443162982795725867 + 9.4247779607693797153879301498385086526*i; -10275.740699586781590689523253765996615 + 6.2831853071795864769252867665590057684*i, -634.21630160950403420149960216844371958 + 3.1415926535897932384626433832795028842*i, -634.01539591045106185685718938112006734 + 3.1415926535897932384626433832795028842*i, -79802.519620280097464487804413952976876 + 6.2831853071795864769252867665590057684*i, -35395.460347154136981484622937212781998 + 9.4247779607693797153879301498385086526*i, -41864.891005717850333443162982795725867 + 3.1415926535897932384626433832795028842*i], [[3, [0, 1]~, 1, 1, [-1, 1]~], [3, [-1, 1]~, 1, 1, [0, 1]~], [5, [-2, 1]~, 1, 1, [1, 1]~], [5, [1, 1]~, 1, 1, [-2, 1]~], [11, [1, 1]~, 1, 1, [-2, 1]~], [11, [-2, 1]~, 1, 1, [1, 1]~]]~, [1, 3, 5, 2, 4, 6]~, [x^2 - x - 57, [2, 0], 229, 1, [[1, -7.0663729752107779635959310246705326058; 1, 8.0663729752107779635959310246705326058], [1, 1; -7.0663729752107779635959310246705326058, 8.0663729752107779635959310246705326058], [2, 1.0000000000000000000000000000000000000; 1.0000000000000000000000000000000000000, 115.00000000000000000000000000000000000], [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, 0; 0, 1]]], 2.7124653051843439746808795106061300699, 0.91251874089340677398407564100000000000, [2, -1]]]
? buchfu(bnf)
%60 = [[x + 7], 163]
? setrand(1);buchinitforcefu(x^2-x-100000)
%61 = [[5], [3, 2, -4, -3, 0, 3, -3, -2, 0, 0, -1, -4, -2, 2, -3, 3, 3, -3], [-129.82045011403975460991182396195022419 - 1.1678921863132358901398236130000000000 E-83*i; 129.82045011403975460991182396195022419 - 6.2831853071795864769252867665590057684*i], [-12524210.095116346376425416732583482672 + 9.4247779607693797153879301498385086526*i, -2068419.9917665806199707434535597090379 - 7.8545495444763624849453254030000000000 E-90*i, 37895.696823418532939369155280892034302 + 3.1415926535897932384626433832795028842*i, -39337891.341391509232442867733799974339 + 6.2831853071795864769252867665590057684*i, -71463181.157326676788629412756728517446 + 7.5403675626973079852873038660000000000 E-88*i, 68826323.844934943522641207106699321583 + 9.4247779607693797153879301498385086526*i, 142244237.25329865107154371727292259938 + 12.566370614359172953850573533118011536*i, -142661085.58175612994387747982258437517 + 9.4247779607693797153879301498385086526*i, -232853741.81379736795792638138735568806 + 9.4247779607693797153879301498385086526*i, 2182104.2776478226670040105160579386107 + 6.2831853071795864769252867665590057684*i, -2182104.2776478226670040105160579386107 + 6.2831853071795864769252867665590057684*i, -115089497.12948086217229748122364063593 + 6.2831853071795864769252867665590057684*i, -39868434.390226163112052005608031637323 + 1.2567279271162179975478839770000000000 E-88*i, -63000020.122965411874295349694455907095 + 3.1415926535897932384626433832795028842*i, 33587379.663328108910855287210340616502 + 6.2831853071795864769252867665590057684*i, -205130569.32517983404278989130992274493 + 3.1415926535897932384626433832795028842*i, 77668437.507911725615121725542065308512 + 3.1415926535897932384626433832795028842*i, -7645301.8152241507965582173129279483827 + 9.4247779607693797153879301498385086526*i, -138221085.75336103152289331800254328546 + 6.2831853071795864769252867665590057684*i; 12524210.095116346376425416732583482672 + 3.1415926535897932384626433832795028842*i, 2068419.9917665806199707434535597090379 + 3.1415926535897932384626433832795028842*i, -37895.696823418532939369155280892034302 + 12.566370614359172953850573533118011536*i, 39337891.341391509232442867733799974339 - 1.5709099088952724969890650800000000000 E-89*i, 71463181.157326676788629412756728517446 + 9.4247779607693797153879301498385086526*i, -68826323.844934943522641207106699321583 + 12.566370614359172953850573533118011536*i, -142244237.25329865107154371727292259938 + 3.1415926535897932384626433832795028842*i, 142661085.58175612994387747982258437517 + 6.2831853071795864769252867665590057684*i, 232853741.81379736795792638138735568806 + 6.2831853071795864769252867665590057684*i, -2182104.2776478226670040105160579386107 + 6.2831853071795864769252867665590057684*i, 2182104.2776478226670040105160579386107 + 6.2831853071795864769252867665590057684*i, 115089497.12948086217229748122364063593 + 6.2831853071795864769252867665590057684*i, 39868434.390226163112052005608031637323 + 6.2831853071795864769252867665590057684*i, 63000020.122965411874295349694455907095 +  0.E-88*i, -33587379.663328108910855287210340616502 + 9.4247779607693797153879301498385086526*i, 205130569.32517983404278989130992274493 + 6.2831853071795864769252867665590057684*i, -77668437.507911725615121725542065308512 + 6.2831853071795864769252867665590057684*i, 7645301.8152241507965582173129279483827 + 3.1415926535897932384626433832795028842*i, 138221085.75336103152289331800254328546 + 6.2831853071795864769252867665590057684*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]~], [13, [5, 1]~, 1, 1, [-6, 1]~], [17, [14, 1]~, 1, 1, [2, 1]~], [17, [19, 1]~, 1, 1, [-3, 1]~], [23, [-7, 1]~, 1, 1, [6, 1]~], [23, [6, 1]~, 1, 1, [-7, 1]~], [29, [13, 1]~, 1, 1, [-14, 1]~], [29, [-14, 1]~, 1, 1, [13, 1]~], [31, [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, 316.72816130129840161392089489603747004], [1, 1; -315.72816130129840161392089489603747004, 316.72816130129840161392089489603747004], [2, 1.0000000000000000000000000000000000000; 1.0000000000000000000000000000000000000, 200001.00000000000000000000000000000000], [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]]], 129.82045011403975460991182396195022419, 0.98765369790690472391212970100000000000, [2, -1], [379554884019013781006303254896369154068336082609238336*x + 119836165644250789990462835950022871665178127611316131167], 89]]
? setrand(1);bnf=buchinitfu(x^2-x-57,0.2,0.2)
%62 = [[3], [2, 2, -2, -2, -2], [-2.7124653051843439746808795106061300699 + 9.4247779607693797153879301498385086526*i; 2.7124653051843439746808795106061300699 + 12.566370614359172953850573533118011536*i], [10275.740699586781590689523253765996614 + 3.1415926535897932384626433832795028842*i, 634.21630160950403420149960216844371958 + 12.566370614359172953850573533118011536*i, 634.01539591045106185685718938112006734 + 9.4247779607693797153879301498385086526*i, 79802.519620280097464487804413952976876 + 6.2831853071795864769252867665590057684*i, 35395.460347154136981484622937212781998 + 3.1415926535897932384626433832795028842*i, 41864.891005717850333443162982795725867 + 9.4247779607693797153879301498385086526*i; -10275.740699586781590689523253765996615 + 6.2831853071795864769252867665590057684*i, -634.21630160950403420149960216844371958 + 3.1415926535897932384626433832795028842*i, -634.01539591045106185685718938112006734 + 3.1415926535897932384626433832795028842*i, -79802.519620280097464487804413952976876 + 6.2831853071795864769252867665590057684*i, -35395.460347154136981484622937212781998 + 9.4247779607693797153879301498385086526*i, -41864.891005717850333443162982795725867 + 3.1415926535897932384626433832795028842*i], [[3, [0, 1]~, 1, 1, [-1, 1]~], [3, [-1, 1]~, 1, 1, [0, 1]~], [5, [-2, 1]~, 1, 1, [1, 1]~], [5, [1, 1]~, 1, 1, [-2, 1]~], [11, [1, 1]~, 1, 1, [-2, 1]~], [11, [-2, 1]~, 1, 1, [1, 1]~]]~, [1, 3, 5, 2, 4, 6]~, [x^2 - x - 57, [2, 0], 229, 1, [[1, -7.0663729752107779635959310246705326058; 1, 8.0663729752107779635959310246705326058], [1, 1; -7.0663729752107779635959310246705326058, 8.0663729752107779635959310246705326058], [2, 1.0000000000000000000000000000000000000; 1.0000000000000000000000000000000000000, 115.00000000000000000000000000000000000], [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, 0; 0, 1]]], 2.7124653051843439746808795106061300699, 0.91251874089340677398407564100000000000, [2, -1], [x + 7], 163]]
? setrand(1);buchreal(10^9-3,0,0.5,0.5)
%63 = [4, [4], [qfr(3, 1, -83333333,  0.E-57)], 2800.6252519070160764863706217370745514, 0.99903694589643828667842317900000000000]
? setrand(1);buchgen(x^4-7,0.2,0.2)
%64 = 
[x^4 - 7]

[[2, 1]]

[[-87808, 1]]

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

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

[14.229975145405511722395637833443108790]

[1.1211171071527562299744232290000000000]

? setrand(1);buchgenfu(x^2-x-100000)

  ***   Warning: fundamental units too large, not given
%65 = 
[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);buchgenforcefu(x^2-x-100000)
%66 = 
[x^2 - x - 100000]

[[2, 0]]

[[400001, 1]]

[[1, x]]

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

[129.82045011403975460991182396195022419]

[0.98765369790690472391212970100000000000]

[[2, -1]]

[[379554884019013781006303254896369154068336082609238336*x + 119836165644250789990462835950022871665178127611316131167]]

[89]

? setrand(1);buchgenfu(x^4+24*x^2+585*x+1791,0.1,0.1)
%67 = 
[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, 0, 3, 0; 0, 7, 6, 0; 0, 0, 1, 0; 0, 0, 0, 7]]]]

[3.7941269688216589341408274220859400302]

[1.2552005425029209450702924460000000000]

[[6, -10/1029*x^3 + 13/343*x^2 - 165/343*x - 1135/343]]

[[1/147*x^3 + 1/147*x^2 - 8/49*x - 9/49]]

[153]

? buchnarrow(bnf)
%68 = [3, [3], [[3, 0; 0, 1]]]
? bytesize(%)
%69 = 264
? \\ C
? ceil(-2.5)
%70 = -2
? centerlift(mod(456,555))
%71 = -99
? cf(pi)
%72 = [3, 7, 15, 1, 292, 1, 1, 1, 2, 1, 3, 1, 14, 2, 1, 1, 2, 2, 2, 2, 1, 84, 2, 1, 1, 15, 3, 13, 1, 4, 2, 6, 6]
? cf2([1,3,5,7,9],(exp(1)-1)/(exp(1)+1))
%73 = [0, 6, 10, 42, 30]
? changevar(x+y,[z,t])
%74 = y + z
? char([1,2;3,4],z)
%75 = z^2 - 5*z - 2
? char(mod(x^2+x+1,x^3+5*x+1),z)
%76 = z^3 + 7*z^2 + 16*z - 19
? char1([1,2;3,4],z)
%77 = z^2 - 5*z - 2
? char2(mod(1,8191)*[1,2;3,4],z)
%78 = z^2 + mod(8186, 8191)*z + mod(8189, 8191)
? acurve=chell(acurve,[-1,1,2,3])
%79 = [-4, -1, -7, -12, -12, 12, 4, 1, -1, 48, -216, 37, 110592/37, [-0.16243456471667696455518910092496975959, -0.73040556359455544173706204865073999595, -2.1071598716887675937077488504242902444]~, -2.9934586462319596298320099794525081778, -2.4513893819867900608542248318665252253*i, 0.47131927795681147588259389708033769964, 1.4354565186686843187232088566788165076*i, 7.3381327407895767390707210033323055881]
? chinese(mod(7,15),mod(13,21))
%80 = mod(97, 105)
? apoint=chptell(apoint,[-1,1,2,3])
%81 = [1, 3]
? isoncurve(acurve,apoint)
%82 = 1
? classno(-12391)
%83 = 63
? classno(1345)
%84 = 6
? classno2(-12391)
%85 = 63
? classno2(1345)
%86 = 6
? coeff(sin(x),7)
%87 = -1/5040
? compimag(qfi(2,1,3),qfi(2,1,3))
%88 = qfi(2, -1, 3)
? compo(1+o(7^4),3)
%89 = 1
? compositum(x^4-4*x+2,x^3-x-1)
%90 = x^12 - 4*x^10 - 16*x^9 + 12*x^8 + 12*x^7 - 6*x^6 + 36*x^5 + 173*x^4 - 208*x^3 + 154*x^2 - 40*x + 59
? comprealraw(qfr(5,3,-1,0.),qfr(7,1,-1,0.))
%91 = qfr(35, 43, 13,  0.E-38)
? concat([1,2],[3,4])
%92 = [1, 2, 3, 4]
? conj(1+i)
%93 = 1 - i
? %_
%94 = 1 + i
? conjvec(mod(x^2+x+1,x^3-x-1))
%95 = [4.0795956234914387860104177508366260326 +  0.E-38*i, 0.46020218825428060699479112458168698369 - 0.18258225455744299269398828369501930573*i, 0.46020218825428060699479112458168698369 + 0.18258225455744299269398828369501930573*i]~
? content([123,456,789,234])
%96 = 3
? convol(sin(x),x*cos(x))
%97 = x + 1/12*x^3 + 1/2880*x^5 + 1/3628800*x^7 + 1/14631321600*x^9 + 1/144850083840000*x^11 + 1/2982752926433280000*x^13 + 1/114000816848279961600000*x^15 + O(x^16)
? cos(1)
%98 = 0.54030230586813971740093660744297660373
? cosh(1)
%99 = 1.5430806348152437784779056207570616825
? move(0,200,150)
? cursor(0)
%100 = [200.00000000000000000000000000000000000, 150.00000000000000000000000000000000000]
? cvtoi(1.7)
%101 = 1
? cyclo(105)
%102 = 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
? \\ D
? denom(12345/54321)
%103 = 18107
? deplin(mod(1,7)*[2,-1;1,3])
%104 = [mod(6, 7), mod(5, 7)]~
? deriv((x+y)^5,y)
%105 = 5*x^4 + 20*y*x^3 + 30*y^2*x^2 + 20*y^3*x + 5*y^4
? ((x+y)^5)'
%106 = 5*x^4 + 20*y*x^3 + 30*y^2*x^2 + 20*y^3*x + 5*y^4
? det([1,2,3;1,5,6;9,8,7])
%107 = -30
? det2([1,2,3;1,5,6;9,8,7])
%108 = -30
? detint([1,2,3;4,5,6])
%109 = 3
? detr([1,2,3;1,5,6;9,8,7])
%110 = -30
? dilog(0.5)
%111 = 0.58224052646501250590265632015968010858
? dz=vector(30,k,1);dd=vector(30,k,k==1);dm=dirdiv(dd,dz)
%112 = [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]
? dirmul(abs(dm),dz)
%113 = [1, 2, 2, 2, 2, 4, 2, 2, 2, 4, 2, 4, 2, 4, 4, 2, 2, 4, 2, 4, 4, 4, 2, 4, 2, 4, 2, 4, 2, 8]
? dirzetak(initalg(x^3-10*x+8),30)
%114 = [1, 2, 0, 3, 1, 0, 0, 4, 0, 2, 1, 0, 0, 0, 0, 5, 1, 0, 0, 3, 0, 2, 0, 0, 2, 0, 1, 0, 1, 0]
? disc(x^3+4*x+12)
%115 = -4144
? discf(x^3+4*x+12)
%116 = -1036
? divisors(8!)
%117 = [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, 672, 720, 840, 896, 960, 1008, 1120, 1152, 1260, 1344, 1440, 1680, 1920, 2016, 2240, 2520, 2688, 2880, 3360, 4032, 4480, 5040, 5760, 6720, 8064, 10080, 13440, 20160, 40320]
? divres(345,123)
%118 = [2, 99]~
? divres(x^7-1,x^5+1)
%119 = [x^2, -x^2 - 1]~
? divsum(8!,x,x)
%120 = 159120
? \\draw([0,0,0])
? postdraw([0,0,0])
? \\ E
? eigen([1,2,3;4,5,6;7,8,9])
%121 = 
[-1.2833494518006402717978106547571267252 +  0.E-38*i 1 0.28334945180064027179781065475712672521 +  0.E-39*i]

[-0.14167472590032013589890532737856336259 +  0.E-39*i -2 0.64167472590032013589890532737856336260 +  0.E-38*i]

[1 1 1]

? eint1(2)
%122 = 0.048900510708061119567239835228049522206
? erfc(2)
%123 = 0.0046777349810472658379307436327470713891
? eta(q)
%124 = 1 - q - q^2 + q^5 + q^7 - q^12 - q^15 + O(q^16)
? euler
%125 = 0.57721566490153286060651209008240243104
? z=y;y=x;eval(z)
%126 = x
? exp(1)
%127 = 2.7182818284590452353602874713526624977
? extract([1,2,3,4,5,6,7,8,9,10],1000)
%128 = [4, 6, 7, 8, 9, 10]
? \\ F
? 10!
%129 = 3628800
? fact(10)
%130 = 3628800.0000000000000000000000000000000
? factcantor(x^11+1,7)
%131 = 
[mod(1, 7)*x + mod(1, 7) 1]

[mod(1, 7)*x^10 + mod(6, 7)*x^9 + mod(1, 7)*x^8 + mod(6, 7)*x^7 + mod(1, 7)*x^6 + mod(6, 7)*x^5 + mod(1, 7)*x^4 + mod(6, 7)*x^3 + mod(1, 7)*x^2 + mod(6, 7)*x + mod(1, 7) 1]

? centerlift(lift(factfq(x^3+x^2+x-1,3,t^3+t^2+t-1)))
%132 = 
[x + (-t^2 - 1) 1]

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

[x - t 1]

? factmod(x^11+1,7)
%133 = 
[mod(1, 7)*x + mod(1, 7) 1]

[mod(1, 7)*x^10 + mod(6, 7)*x^9 + mod(1, 7)*x^8 + mod(6, 7)*x^7 + mod(1, 7)*x^6 + mod(6, 7)*x^5 + mod(1, 7)*x^4 + mod(6, 7)*x^3 + mod(1, 7)*x^2 + mod(6, 7)*x + mod(1, 7) 1]

? factor(17!+1)
%134 = 
[661 1]

[537913 1]

[1000357 1]

? p=x^5+3021*x^4-786303*x^3-6826636057*x^2-546603588746*x+3853890514072057
%135 = x^5 + 3021*x^4 - 786303*x^3 - 6826636057*x^2 - 546603588746*x + 3853890514072057
? fa=[11699,6;2392997,2;4987333019653,2]
%136 = 
[11699 6]

[2392997 2]

[4987333019653 2]

? factoredbasis(p,fa)
%137 = [1, x, x^2, 1/11699*x^3 + 1847/11699*x^2 - 132/11699*x - 2641/11699, 1/139623738889203638909659*x^4 - 1552451622081122020/139623738889203638909659*x^3 + 418509858130821123141/139623738889203638909659*x^2 - 68109137985075994073134/139623738889203638909659*x - 13185339461968406/58346808996920447]
? factoreddiscf(p,fa)
%138 = 136866601
? factoredpolred(p,fa)
%139 = [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]~
? factoredpolred2(p,fa)
%140 = 
[1 x - 1]

[404377049971/139623738889203638909659*x^4 + 1028343729806593/139623738889203638909659*x^3 - 220760129739668913/139623738889203638909659*x^2 - 1391924543479498840309/139623738889203638909659*x - 21580477171925514/58346808996920447 x^5 - 2*x^4 - 13*x^3 + 37*x^2 - 21*x - 1]

[160329790087/139623738889203638909659*x^4 + 1043812506369034/139623738889203638909659*x^3 + 1517006779298914407/139623738889203638909659*x^2 - 522348888528537141362/139623738889203638909659*x - 677624890046649103/58346808996920447 x^5 - x^4 - 52*x^3 - 197*x^2 - 273*x - 127]

[-649489679500/139623738889203638909659*x^4 - 1004850936416946/139623738889203638909659*x^3 + 1850137668999773331/139623738889203638909659*x^2 + 1162464435118744503168/139623738889203638909659*x - 744221404070129897/58346808996920447 x^5 - 2*x^4 - 53*x^3 - 46*x^2 + 508*x + 913]

[320031469790/139623738889203638909659*x^4 + 525154323698149/139623738889203638909659*x^3 + 68805502220272624/139623738889203638909659*x^2 + 116261976244907072724/139623738889203638909659*x - 265513916545157609/58346808996920447 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)
%141 = 
[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)
%142 = 
[(1 + O(7^8))*x + (6 + 2*7^2  + 2*7^3  + 3*7^4  + 2*7^5  + 6*7^6  + O(7^8)) 1]

[(1 + O(7^8))*x^2 + (1 + 6*7 + 4*7^2  + 4*7^3  + 3*7^4  + 4*7^5  + 6*7^7  + O(7^8))*x + (6 + 5*7 + 3*7^2  + 6*7^3  + 7^4  + 3*7^5  + 2*7^6  + 5*7^7  + O(7^8)) 1]

? factorpadic2(apol,7,8)
%143 = 
[(1 + O(7^8))*x + (6 + 2*7^2  + 2*7^3  + 3*7^4  + 2*7^5  + 6*7^6  + O(7^8)) 1]

[(1 + O(7^8))*x^2 + (1 + 6*7 + 4*7^2  + 4*7^3  + 3*7^4  + 4*7^5  + 6*7^7  + O(7^8))*x + (6 + 5*7 + 3*7^2  + 6*7^3  + 7^4  + 3*7^5  + 2*7^6  + 5*7^7  + O(7^8)) 1]

? factpol(x^15-1,3,1)
%144 = 
[x^2 + x + 1 1]

[x - 1 1]

[x^12 + x^9 + x^6 + x^3 + 1 1]

? factpol(x^15-1,0,1)
%145 = 
[x^4 + x^3 + x^2 + x + 1 1]

[x^2 + x + 1 1]

[x - 1 1]

[x^8 - x^7 + x^5 - x^4 + x^3 - x + 1 1]

? factpol2(x^15-1,0)
%146 = 
[x - 1 1]

[x^2 + x + 1 1]

[x^4 + x^3 + x^2 + x + 1 1]

[x^8 - x^7 + x^5 - x^4 + x^3 - x + 1 1]

? fibo(100)
%147 = 354224848179261915075
? floor(-1/2)
%148 = -1
? floor(-2.5)
%149 = -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)
%150 = 0.30000000000000000000000000000000000000
? \\ G
? galois(x^6-3*x^2-1)
%151 = [12, 1, 1]
? nf3=initalg(x^6+108);galoisconj(nf3)
%152 = [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]
? galoisconjforce(nf3)
%153 = [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];galoisapply(nf3,aut,mod(x^5,x^6+108))
%154 = mod(-1/2*x^5 + 9*x^2, x^6 + 108)
? gamh(10)
%155 = 1133278.3889487855673345741655888924755
? gamma(10.5)
%156 = 1133278.3889487855673345741655888924755
? gauss(hilbert(10),[1,2,3,4,5,6,7,8,9,0]~)
%157 = [9236800, -831303990, 18288515520, -170691240720, 832112321040, -2329894066500, 3883123564320, -3803844432960, 2020775945760, -449057772020]~
? gcd(12345678,87654321)
%158 = 9
? getheap()
%159 = [44, 7452]
? getrand()
%160 = 1438343478
? getstack()
%161 = 167864
? \\gettime()isattheend
? globalred(acurve)
%162 = [37, [1, -1, 2, 2], 1]
? getstack()
%163 = 168104
? k=4;goto(k%2);label(0);print("even");goto(3);label(1);print("odd");label(3);
even
? \\ H
? hclassno(2000003)
%164 = 357
? hell(acurve,apoint)
%165 = 0.40889126591975072188708879805553617287
? hell2(acurve,apoint)
%166 = 0.40889126591975072188708879805553617296
? hermite(amat=1/hilbert(7))
%167 = 
[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]

? hermitebatut(amat)
%168 = [[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, 1866]]
? hermitehavas(amat)
%169 = [[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, 1260; 0, 0, 0, 0, 0, 168, 0; 0, 0, 0, 0, 0, 0, 7], [51480, 4620, 5544, 630, 840, 20676, 48619; 45045, 3960, 4620, 504, 630, 18074, 42347; 40040, 3465, 3960, 420, 504, 16058, 37523; 36036, 3080, 3465, 360, 420, 14448, 33692; 32760, 2772, 3080, 315, 360, 13132, 30574; 30030, 2520, 2772, 280, 315, 12036, 27986; 27720, 2310, 2520, 252, 280, 11109, 25803], [7, 6, 5, 4, 3, 2, 1]]
? hermitemod(amat,detint(amat))
%170 = 
[420 0 0 0 210 168 175]

[0 840 0 0 0 0 504]

[0 0 2520 0 0 0 1260]

[0 0 0 2520 0 0 840]

[0 0 0 0 13860 0 6930]

[0 0 0 0 0 5544 0]

[0 0 0 0 0 0 12012]

? hermiteperm(amat)
%171 = [[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, 1260; 0, 0, 0, 0, 0, 168, 0; 0, 0, 0, 0, 0, 0, 7], [51480, 4620, 5544, 630, 840, 20676, 48619; 45045, 3960, 4620, 504, 630, 18074, 42347; 40040, 3465, 3960, 420, 504, 16058, 37523; 36036, 3080, 3465, 360, 420, 14448, 33692; 32760, 2772, 3080, 315, 360, 13132, 30574; 30030, 2520, 2772, 280, 315, 12036, 27986; 27720, 2310, 2520, 252, 280, 11109, 25803], [7, 6, 5, 4, 3, 2, 1]]
? hess(hilbert(7))
%172 = 
[1 90281/58800 -1919947/4344340 4858466341/1095033030 -77651417539/8196787326 3386888964/106615355 1/2]

[1/3 43/48 38789/5585580 268214641/109503303 -581330123627/126464718744 4365450643/274153770 1/4]

[0 217/2880 442223/7447440 53953931/292008808 -32242849453/168619624992 1475457901/1827691800 1/80]

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

[0 0 0 9773092581/35395807550620 -24363634138919/107305824577186620 72118203606917/60481351061158500 55899/3088554700]

[0 0 0 0 67201501179065/8543442888354179988 -9970556426629/740828619992676600 -3229/13661312210]

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

? hilb(2/3,3/4,5)
%173 = 1
? hilbert(5)
%174 = 
[1 1/2 1/3 1/4 1/5]

[1/2 1/3 1/4 1/5 1/6]

[1/3 1/4 1/5 1/6 1/7]

[1/4 1/5 1/6 1/7 1/8]

[1/5 1/6 1/7 1/8 1/9]

? hilbp(mod(5,7),mod(6,7))
%175 = 1
? hvector(10,x,1/x)
%176 = [1, 1/2, 1/3, 1/4, 1/5, 1/6, 1/7, 1/8, 1/9, 1/10]
? hyperu(1,1,1)
%177 = 0.59634736232319407434107849936927937488
? \\ I
? i^2
%178 = -1
? nf1=initalgred(nfpol)
%179 = [x^5 - 2*x^4 + 3*x^3 + 8*x^2 + 3*x + 2, [1, 2], 595125, 4, [[1, -1.0891151457205048250249527946671612684, 1.1861718006377964594796293860483989860, -0.59741050929194782733001765987770358482, 0.15894419745390376206549481671071894288; 1, -0.13838372073406036365047976417441696637 - 0.49181637657768643499753285514741525107*i, -0.22273329410580226599155701611419649154 + 0.13611876021752805221674918029071012579*i, -0.13167445871785818798769651537619416009 - 0.13249517760521973840801462296650806543*i, -0.053650958656997725359297528357602608115 - 0.27622636814169107038138284681568361486*i; 1, 1.6829412935943127761629561615079976005 - 2.0500351226010726172974286983598602163*i, -1.3703526062130959637482576769100030014 - 6.9001775222880494773720769629846373016*i, -8.0696202866361678983472946546849540474 - 8.8767676785971042450885284301348051602*i, -22.025821140069954155673449879997756863 + 8.4306586896999153544710860185447589662*i], [1, 2, 2; -1.0891151457205048250249527946671612684, -0.27676744146812072730095952834883393274 + 0.98363275315537286999506571029483050214*i, 3.3658825871886255523259123230159952011 + 4.1000702452021452345948573967197204327*i; 1.1861718006377964594796293860483989860, -0.44546658821160453198311403222839298308 - 0.27223752043505610443349836058142025159*i, -2.7407052124261919274965153538200060029 + 13.800355044576098954744153925969274603*i; -0.59741050929194782733001765987770358482, -0.26334891743571637597539303075238832018 + 0.26499035521043947681602924593301613087*i, -16.139240573272335796694589309369908094 + 17.753535357194208490177056860269610320*i; 0.15894419745390376206549481671071894288, -0.10730191731399545071859505671520521623 + 0.55245273628338214076276569363136722973*i, -44.051642280139908311346899759995513726 - 16.861317379399830708942172037089517932*i], [5, 2.0000000000000000000000000000000000000, -1.9999999999999999999999999999999999999, -16.999999999999999999999999999999999999, -43.999999999999999999999999999999999999; 2.0000000000000000000000000000000000000, 15.778109408671998044836357471283695361, 22.314643349754061651916553814602769764, 10.051395257831478275499932716306366248, -108.58917507620841447456569092094763671; -1.9999999999999999999999999999999999999, 22.314643349754061651916553814602769764, 100.52391262388960975827806174040462367, 143.93295090847353519436673793501057175, -55.842564718082452641322500190813370021; -16.999999999999999999999999999999999999, 10.051395257831478275499932716306366248, 143.93295090847353519436673793501057175, 288.25823756749944693139292174819167135, 205.79840038277662375720180649465932302; -43.999999999999999999999999999999999999, -108.58917507620841447456569092094763671, -55.842564718082452641322500190813370021, 205.79840038277662375720180649465932302, 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, -315675; -296700, -677925, 17250, 58650, -87975; 234600, 595125, 58650, -100050, 89700; -89700, -315675, -87975, 89700, -55200], [595125, 0, 357075, 427800, 326025; 0, 595125, 119025, 512325, 191475; 0, 0, 119025, 79350, 75900; 0, 0, 0, 1725, 0; 0, 0, 0, 0, 1725]], [-1.0891151457205048250249527946671612684, -0.13838372073406036365047976417441696637 - 0.49181637657768643499753285514741525107*i, 1.6829412935943127761629561615079976005 - 2.0500351226010726172974286983598602163*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]]
? initalgred2(nfpol)
%180 = mod(-1/2*x^4 + 3/2*x^3 - 5/2*x^2 - 2*x + 1, x^5 - 2*x^4 + 3*x^3 + 8*x^2 + 3*x + 2)
? vp=primedec(nf,3)[1]
%181 = [3, [1, 1, 0, 0, 0]~, 1, 1, [1, -1, -1, 0, 0]~]
? idx=idealmul(nf,idmat(5),vp)
%182 = 
[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)
%183 = 
[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=ideallllred(nf,idx,[1,3,5])
%184 = 
[6 0 4 0 3]

[0 6 2 0 3]

[0 0 2 0 0]

[0 0 0 6 3]

[0 0 0 0 3]

? idealadd(nf,idx,idy)
%185 = 
[1 0 0 0 0]

[0 1 0 0 0]

[0 0 1 0 0]

[0 0 0 1 0]

[0 0 0 0 1]

? idealaddone(nf,idx,idy)
%186 = [[3, -2, -2, 0, 0]~, [-2, 2, 2, 0, 0]~]
? idealaddmultone(nf,[idy,idx])
%187 = [[-14, 14, -4, 0, 0]~, [15, -14, 4, 0, 0]~]
? idealappr(nf,idy)
%188 = [-4, -2, -2, 0, 6]~
? idealapprfact(nf,idealfactor(nf,idy))
%189 = [-4, -2, -2, 0, 6]~
? idealcoprime(nf,idx,idx)
%190 = [7/3, 2/3, -1/3, -1, 0]~
? idz=idealintersect(nf,idx,idy)
%191 = 
[6 0 0 0 3]

[0 6 0 0 3]

[0 0 6 0 0]

[0 0 0 6 3]

[0 0 0 0 3]

? idealfactor(nf,idz)
%192 = 
[[2, [-3, -5, -4, 3, 15]~, 1, 4, [1, 1, 0, 0, 0]~] 1]

[[3, [1, 1, 0, 0, 0]~, 1, 1, [1, -1, -1, 0, 0]~] 1]

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

? idx2=idealmul(nf,idx,idx)
%193 = 
[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=idealmulred(nf,idx,idx)
%194 = 
[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)
%195 = 
[3 0 2 0 0]

[0 3 1 0 0]

[0 0 1 0 0]

[0 0 0 3 0]

[0 0 0 0 3]

? idealdivexact(nf,idx2,idx)
%196 = 
[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]

? idealhermite(nf,vp)
%197 = 
[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]

? idealhermite2(nf,vp[2],3)
%198 = 
[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)
%199 = 16
? idp=idealpow(nf,idx,7)
%200 = 
[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]

? idealpowred(nf,idx,7)
%201 = 
[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)
%202 = [6, [1, -1, 2, 3, 3]~]
? idealtwoelt2(nf,idy,6)
%203 = [1, -1, 2, 3, 3]~
? idealval(nf,idp,vp)
%204 = 7
? idmat(5)
%205 = 
[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)
%206 = 3
? image([1,3,5;2,4,6;3,5,7])
%207 = 
[1 3]

[2 4]

[3 5]

? imager(pi*[1,3,5;2,4,6;3,5,7])
%208 = 
[3.1415926535897932384626433832795028841 9.4247779607693797153879301498385086525]

[6.2831853071795864769252867665590057683 12.566370614359172953850573533118011536]

[9.4247779607693797153879301498385086525 15.707963267948966192313216916397514420]

? incgam(2,1)
%209 = 0.73575888234288464319104754032292173491
? incgam1(2,1)
%210 = -0.26424111765711535680895245967678075578
? incgam2(2,1)
%211 = 0.73575888234288464319104754032292173489
? incgam3(2,1)
%212 = 0.26424111765711535680895245967707826508
? incgam4(4,1,6)
%213 = 5.8860710587430771455283803225833738791
? indexrank([1,1,1;1,1,1;1,1,2])
%214 = [[1, 3], [1, 3]]
? indsort([8,7,6,5])
%215 = [4, 3, 2, 1]
? initell([0,0,0,-1,0])
%216 = [0, 0, 0, -1, 0, 0, -2, 0, -1, 48, 0, 64, 1728, [1.0000000000000000000000000000000000000,  0.E-38, -1.0000000000000000000000000000000000000]~, 2.6220575542921198104648395898911194136, 2.6220575542921198104648395898911194136*i, -0.59907011736779610371996124614016193910, -1.7972103521033883111598837384204858173*i, 6.8751858180203728274900957798105571979]
? initell2([0,0,0,0,-1])
%217 = [0, 0, 0, 0, -1, 0, 0, -4, 0, 0, 864, -432, 0, [0.99999999999999999999999999999999999999, -0.50000000000000000000000000000000000000 + 0.86602540378443864676372317075293618346*i, -0.50000000000000000000000000000000000000 - 0.86602540378443864676372317075293618346*i]~, 2.4286506478875816118199416897809312485, 1.2143253239437908059099708448904656242 + 2.1032731579881813917625286185754412032*i, -0.74683420022218681310347088055619015637 - 5.6699442800036638973916469640000000000 E-39*i, -0.37341710011109340655173544027809507817 - 1.9403321694223429012151362688484087282*i, 5.1081157178325565351221945057517738028]
? initrect(1,700,700)
? nfz=initzeta(x^2-2);
? integ(sin(x),x)
%219 = 1/2*x^2 - 1/24*x^4 + 1/720*x^6 - 1/40320*x^8 + 1/3628800*x^10 - 1/479001600*x^12 + 1/87178291200*x^14 - 1/20922789888000*x^16 + O(x^17)
? integ((-x^2-2*a*x+8*a)/(x^4-14*x^3+(2*a+49)*x^2-14*a*x+a^2),x)
%220 = (x + a)/(x^2 - 7*x + a)
? intersect([1,2;3,4;5,6],[2,3;7,8;8,9])
%221 = 
[-1]

[-1]

[-1]

? \precision=19
   precision = 19 significant digits
? intgen(x=0,pi,sin(x))
%222 = 2.000000000000000017
? sqr(2*intgen(x=0,4,exp(-x^2)))
%223 = 3.141592556720305685
? 4*intinf(x=1,10^20,1/(1+x^2))
%224 = 3.141592653589793208
? intnum(x=-0.5,0.5,1/sqrt(1-x^2))
%225 = 1.047197551196597747
? 2*intopen(x=0,100,sin(x)/x)
%226 = 3.124450933778112629
? \precision=38
   precision = 38 significant digits
? inverseimage([1,1;2,3;5,7],[2,2,6]~)
%227 = [4, -2]~
? isfund(12345)
%228 = 1
? isideal(bnf[7],[5,1;0,1])
%229 = 1
? isincl(x^2+1,x^4+1)
%230 = [x^2, -x^2]
? isinclfast(initalg(x^2+1),initalg(x^4+1))
%231 = [x^2, -x^2]
? isirreducible(x^5+3*x^3+5*x^2+15)
%232 = 0
? isisom(x^3+x^2-2*x-1,x^3+x^2-2*x-1)
%233 = [x, x^2 - 2, -x^2 - x + 1]
? isisomfast(initalg(x^3-2),initalg(x^3-6*x^2-6*x-30))
%234 = [-1/25*x^2 + 13/25*x - 2/5]
? isprime(12345678901234567)
%235 = 0
? isprincipal(bnf,[5,1;0,1])
%236 = [2]~
? isprincipalgen(bnf,[5,1;0,1])
%237 = [[2]~, [4/9, -1/9]~, 149]
? ispsp(73!+1)
%238 = 1
? isqrt(10!^2+1)
%239 = 3628800
? isset([-3,5,7,7])
%240 = 0
? issqfree(123456789876543219)
%241 = 0
? issquare(12345678987654321)
%242 = 1
? isunit(bnf,mod(3405*x-27466,x^2-x-57))
%243 = [-4, mod(1, 2)]
? \\ J
? jacobi(hilbert(6))
%244 = [[1.6188998589243390969705881471257800712, 0.24236087057520955213572841585070114077, 0.000012570757122625194922982397996498755027, 0.00000010827994845655497685388772372251711485, 0.016321521319875822124345079564191505890, 0.00061574835418265769764919938428527140264]~, [0.74871921887909485900280109200517845109, -0.61454482829258676899320019644273870645, 0.011144320930724710530678340374220998541, -0.0012481940840821751169398163046387834473, 0.24032536934252330399154228873240534568, -0.062226588150197681775152126611810492910; 0.44071750324351206127160083580231701801, 0.21108248167867048675227675845247769095, -0.17973275724076003758776897803740640964, 0.035606642944287635266122848131812048466, -0.69765137527737012296208335046678265583, 0.49083920971092436297498316169060044997; 0.32069686982225190106359024326699463106, 0.36589360730302614149086554211117169622, 0.60421220675295973004426567844103062241, -0.24067907958842295837736719558855679285, -0.23138937333290388042251363554209048309, -0.53547692162107486593474491750949545456; 0.25431138634047419251788312792590944672, 0.39470677609501756783094636145991581708, -0.44357471627623954554460416705180105301, 0.62546038654922724457753441039459331059, 0.13286315850933553530333839628101576050, -0.41703769221897886840494514780771076439; 0.21153084007896524664213667673977991959, 0.38819043387388642863111448825992418973, -0.44153664101228966222143649752977203423, -0.68980719929383668419801738006926829419, 0.36271492146487147525299457604461742111, 0.047034018933115649705614518466541243873; 0.18144297664876947372217005457727093715, 0.37069590776736280861775501084807394603, 0.45911481681642960284551392793050866602, 0.27160545336631286930015536176213647001, 0.50276286675751538489260566368647786272, 0.54068156310385293880022293448123782121]]
? jbesselh(1,1)
%245 = 0.24029783912342701089584304474193368045
? jell(i)
%246 = 1728.0000000000000000000000000000000000 +  0.E-35*i
? \\ K
? kbessel(1+i,1)
%247 = 0.32545977186584141085464640324923711884 + 0.28942803702599212763456715924152302708*i
? kbessel2(1+i,1)
%248 = 0.32545977186584141085464640324923711884 + 0.28942803702599212763456715924152302708*i
? x
%249 = x
? y
%250 = x
? ker(matrix(4,4,x,y,x/y))
%251 = 
[-1/2 -1/3 -1/4]

[1 0 0]

[0 1 0]

[0 0 1]

? keri(matrix(4,4,x,y,x+y))
%252 = 
[1 2]

[-2 -3]

[1 0]

[0 1]

? kerint(matrix(4,4,x,y,x*y))
%253 = 
[-1 -1 -1]

[-1 0 1]

[1 -1 1]

[0 1 -1]

? kerint1(matrix(4,4,x,y,x*y))
%254 = 
[-1 -1 -1]

[-1 0 1]

[1 -1 1]

[0 1 -1]

? kerint2(matrix(4,6,x,y,2520/(x+y)))
%255 = 
[3 1]

[-30 -15]

[70 70]

[0 -140]

[-126 126]

[84 -42]

? kerr(matrix(4,4,x,y,sin(x+y)))
%256 = 
[1.0000000000000000000000000000000000000 1.0806046117362794348018732148859532074]

[-1.0806046117362794348018732148859532074 -0.16770632690571522600486354099847562046]

[1 0]

[0 1]

? f(u)=u+1;
? print(f(5));kill(f);
6
? f=12
%257 = 12
? killrect(1)
? kro(5,7)
%258 = -1
? kro(3,18)
%259 = 0
? \\ L
? k=4;goto(k%2);label(0);print("even");goto(3);label(1);print("odd");label(3);
even
? laplace(x*exp(x*y)/(exp(x)-1))
%260 = 1 - 1/2*x + 13/6*x^2 - 3*x^3 + 419/30*x^4 - 30*x^5 + 6259/42*x^6 - 420*x^7 + 22133/10*x^8 - 7560*x^9 + 2775767/66*x^10 - 166320*x^11 + 2655339269/2730*x^12 - 4324320*x^13 + 264873251/10*x^14 + O(x^15)
? lcm(15,-21)
%261 = 105
? length(divisors(1000))
%262 = 16
? legendre(10)
%263 = 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])
%264 = -1
? lexsort([[1,5],[2,4],[1,5,1],[1,4,2]])
%265 = [[1, 4, 2], [1, 5], [1, 5, 1], [2, 4]]
? lift(chinese(mod(7,15),mod(4,21)))
%266 = 67
? lindep([(1-3*sqrt(2))/(3-2*sqrt(3)),1,sqrt(2),sqrt(3),sqrt(6)])
%267 = [-3, -3, 9, -2, 6]
? lindep2([(1-3*sqrt(2))/(3-2*sqrt(3)),1,sqrt(2),sqrt(3),sqrt(6)],14)
%268 = [-3, -3, 9, -2, 6]
? move(0,0,900);line(0,900,0)
? lines(0,vector(5,k,50*k),vector(5,k,10*k*k))
? m=1/hilbert(7)
%269 = 
[49 -1176 8820 -29400 48510 -38808 12012]

[-1176 37632 -317520 1128960 -1940400 1596672 -504504]

[8820 -317520 2857680 -10584000 18711000 -15717240 5045040]

[-29400 1128960 -10584000 40320000 -72765000 62092800 -20180160]

[48510 -1940400 18711000 -72765000 133402500 -115259760 37837800]

[-38808 1596672 -15717240 62092800 -115259760 100590336 -33297264]

[12012 -504504 5045040 -20180160 37837800 -33297264 11099088]

? mp=concat(m,idmat(7))
%270 = 
[49 -1176 8820 -29400 48510 -38808 12012 1 0 0 0 0 0 0]

[-1176 37632 -317520 1128960 -1940400 1596672 -504504 0 1 0 0 0 0 0]

[8820 -317520 2857680 -10584000 18711000 -15717240 5045040 0 0 1 0 0 0 0]

[-29400 1128960 -10584000 40320000 -72765000 62092800 -20180160 0 0 0 1 0 0 0]

[48510 -1940400 18711000 -72765000 133402500 -115259760 37837800 0 0 0 0 1 0 0]

[-38808 1596672 -15717240 62092800 -115259760 100590336 -33297264 0 0 0 0 0 1 0]

[12012 -504504 5045040 -20180160 37837800 -33297264 11099088 0 0 0 0 0 0 1]

? lll(m)
%271 = 
[-420 -420 840 630 -1092 -83 2562]

[-210 -280 630 504 -876 70 2205]

[-140 -210 504 420 -749 137 1910]

[-105 -168 420 360 -658 169 1680]

[-84 -140 360 315 -588 184 1498]

[-70 -120 315 280 -532 190 1351]

[-60 -105 280 252 -486 191 1230]

? lll1(m)
%272 = 
[-420 -420 840 630 -1092 -83 2562]

[-210 -280 630 504 -876 70 2205]

[-140 -210 504 420 -749 137 1910]

[-105 -168 420 360 -658 169 1680]

[-84 -140 360 315 -588 184 1498]

[-70 -120 315 280 -532 190 1351]

[-60 -105 280 252 -486 191 1230]

? lllgram(m)
%273 = 
[1 1 27 -27 69 0 141]

[0 1 4 -22 34 -24 49]

[0 1 3 -21 18 -24 23]

[0 1 3 -20 10 -19 13]

[0 1 3 -19 6 -14 8]

[0 1 3 -18 4 -10 5]

[0 1 3 -17 3 -7 3]

? lllgram1(m)
%274 = 
[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]

? lllgramint(m)
%275 = 
[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]

? lllgramkerim(mp~*mp)
%276 = [[-420, -420, 840, 630, 2982, -1092, 757; -210, -280, 630, 504, 2415, -876, 700; -140, -210, 504, 420, 2050, -749, 641; -105, -168, 420, 360, 1785, -658, 589; -84, -140, 360, 315, 1582, -588, 544; -70, -120, 315, 280, 1421, -532, 505; -60, -105, 280, 252, 1290, -486, 471; 420, 0, 0, 0, -210, 168, 35; 0, 840, 0, 0, 0, 0, 336; 0, 0, -2520, 0, 0, 0, -1260; 0, 0, 0, -2520, 0, 0, -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]]
? lllint(m)
%277 = 
[-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]

? lllintpartial(m)
%278 = 
[-420 -420 -630 840 1092 2982 -83]

[-210 -280 -504 630 876 2415 70]

[-140 -210 -420 504 749 2050 137]

[-105 -168 -360 420 658 1785 169]

[-84 -140 -315 360 588 1582 184]

[-70 -120 -280 315 532 1421 190]

[-60 -105 -252 280 486 1290 191]

? lllkerim(mp)
%279 = [[-420, -420, 840, 630, 2982, -1092, 757; -210, -280, 630, 504, 2415, -876, 700; -140, -210, 504, 420, 2050, -749, 641; -105, -168, 420, 360, 1785, -658, 589; -84, -140, 360, 315, 1582, -588, 544; -70, -120, 315, 280, 1421, -532, 505; -60, -105, 280, 252, 1290, -486, 471; 420, 0, 0, 0, -210, 168, 35; 0, 840, 0, 0, 0, 0, 336; 0, 0, -2520, 0, 0, 0, -1260; 0, 0, 0, -2520, 0, 0, -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]]
? lllrat(m)
%280 = 
[-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]

? \precision=96
   precision = 96 significant digits
? ln(2)
%281 = 0.693147180559945309417232121458176568075500134360255254120680009493393621969694715605863326996418
? lngamma(10^50*i)
%282 = -157079632679489661923132169163975144209858469968811.936737538876084749489770941153418951907406847 + 11412925464970228420089957273421821038005507443143864.0947684761073895534327259165813042649761556*i
? \precision=2000
   precision = 2000 significant digits
? log(2)
%283 = 0.69314718055994530941723212145817656807550013436025525412068000949339362196969471560586332699641868754200148102057068573368552023575813055703267075163507596193072757082837143519030703862389167347112335011536449795523912047517268157493206515552473413952588295045300709532636664265410423915781495204374043038550080194417064167151864471283996817178454695702627163106454615025720740248163777338963855069526066834113727387372292895649354702576265209885969320196505855476470330679365443254763274495125040606943814710468994650622016772042452452961268794654619316517468139267250410380254625965686914419287160829380317271436778265487756648508567407764845146443994046142260319309673540257444607030809608504748663852313818167675143866747664789088143714198549423151997354880375165861275352916610007105355824987941472950929311389715599820565439287170007218085761025236889213244971389320378439353088774825970171559107088236836275898425891853530243634214367061189236789192372314672321720534016492568727477823445353476481149418642386776774406069562657379600867076257199184734022651462837904883062033061144630073719489002743643965002580936519443041191150608094879306786515887090060520346842973619384128965255653968602219412292420757432175748909770675268711581705113700915894266547859596489065305846025866838294002283300538207400567705304678700184162404418833232798386349001563121889560650553151272199398332030751408426091479001265168243443893572472788205486271552741877243002489794540196187233980860831664811490930667519339312890431641370681397776498176974868903887789991296503619270710889264105230924783917373501229842420499568935992206602204654941510613918788574424557751020683703086661948089641218680779020818158858000168811597305618667619918739520076671921459223672060253959543654165531129517598994005600036651356756905124592682574394648316833262490180382424082423145230614096380570070255138770268178516306902551370323405380214501901537402950994226299577964742713815736380172987394070424217997226696297993931270693
? logagm(2)
%284 = 0.69314718055994530941723212145817656807550013436025525412068000949339362196969471560586332699641868754200148102057068573368552023575813055703267075163507596193072757082837143519030703862389167347112335011536449795523912047517268157493206515552473413952588295045300709532636664265410423915781495204374043038550080194417064167151864471283996817178454695702627163106454615025720740248163777338963855069526066834113727387372292895649354702576265209885969320196505855476470330679365443254763274495125040606943814710468994650622016772042452452961268794654619316517468139267250410380254625965686914419287160829380317271436778265487756648508567407764845146443994046142260319309673540257444607030809608504748663852313818167675143866747664789088143714198549423151997354880375165861275352916610007105355824987941472950929311389715599820565439287170007218085761025236889213244971389320378439353088774825970171559107088236836275898425891853530243634214367061189236789192372314672321720534016492568727477823445353476481149418642386776774406069562657379600867076257199184734022651462837904883062033061144630073719489002743643965002580936519443041191150608094879306786515887090060520346842973619384128965255653968602219412292420757432175748909770675268711581705113700915894266547859596489065305846025866838294002283300538207400567705304678700184162404418833232798386349001563121889560650553151272199398332030751408426091479001265168243443893572472788205486271552741877243002489794540196187233980860831664811490930667519339312890431641370681397776498176974868903887789991296503619270710889264105230924783917373501229842420499568935992206602204654941510613918788574424557751020683703086661948089641218680779020818158858000168811597305618667619918739520076671921459223672060253959543654165531129517598994005600036651356756905124592682574394648316833262490180382424082423145230614096380570070255138770268178516306902551370323405380214501901537402950994226299577964742713815736380172987394070424217997226696297993931270693
? \precision=19
   precision = 19 significant digits
? bcurve=initell([0,0,0,-3,0])
%285 = [0, 0, 0, -3, 0, 0, -6, 0, -9, 144, 0, 1728, 1728, [1.732050807568877293,  0.E-19, -1.732050807568877293]~, 1.992332899583490707, 1.992332899583490708*i, -0.7884206134041560682, -2.365261840212468204*i, 3.969390382762759668]
? localred(bcurve,2)
%286 = [6, 2, [1, 1, 1, 0], 1]
? ccurve=initell([0,0,-1,-1,0])
%287 = [0, 0, -1, -1, 0, 0, -2, 1, -1, 48, -216, 37, 110592/37, [0.8375654352833230353, 0.2695944364054445582, -1.107159871688767593]~, 2.993458646231959630, 2.451389381986790061*i, -0.4713192779568114757, -1.435456518668684318*i, 7.338132740789576742]
? l=lseriesell(ccurve,2,-37,1)
%288 = 0.3815754082607112112
? lseriesell(ccurve,2,-37,1.2)-l
%289 = -1.355252715606880542 E-19
? \\ M
? concat(mat(vector(4,x,x)~),vector(4,x,10+x)~)
%290 = 
[1 11]

[2 12]

[3 13]

[4 14]

? matextract(matrix(15,15,x,y,x+y),vector(5,x,3*x),vector(3,y,3*y))
%291 = 
[6 9 12]

[9 12 15]

[12 15 18]

[15 18 21]

[18 21 24]

? ma=mathell(mcurve,mpoints)
%292 = 
[1.172183098700697010 0.4476973883408951692]

[0.4476973883408951692 1.755026016172950713]

? gauss(ma,mhbi)
%293 = [-1.000000000000000000, 1.000000000000000000]~
? matinvr(1.*hilbert(7))
%294 = 
[48.99999999998655186 -1175.999999999491507 8819.999999995287112 -29399.99999998221801 48509.99999996815267 -38807.99999997300892 12011.99999999128135]

[-1175.999999999490476 37631.99999998079928 -317519.9999998225325 1128959.999999331688 -1940399.999998805393 1596671.999998988919 -504503.9999996737196]

[8819.999999995268284 -317519.9999998221492 2857679.999998359414 -10583999.99999383116 18710999.99998898732 -15717239.99999068887 5045039.999996997889]

[-29399.99999998210586 1128959.999999328755 -10583999.99999381752 40319999.99997678085 -72764999.99995859005 62092799.99996501723 -20180159.99998872876]

[48509.99999996789781 -1940399.999998797710 18710999.99998893989 -72764999.99995850268 133402499.9999260516 -115259759.9999375712 37837799.99997989747]

[-38807.99999997274165 1596671.999998980465 -15717239.99999063055 62092799.99996487447 -115259759.9999374480 100590335.9999472221 -33297263.99998301333]

[12011.99999999117839 -504503.9999996704128 5045039.999996973695 -20180159.99998866230 37837799.99997982113 -33297263.99998298231 11099087.99999452507]

? matsize([1,2;3,4;5,6])
%295 = [3, 2]
? matrix(5,5,x,y,gcd(x,y))
%296 = 
[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)
%297 = 
[1 1]

[3 2]

[5 3]

? matrixqz2([1/3,1/4,1/6;1/2,1/4,-1/4;1/3,1,0])
%298 = 
[19 12 2]

[0 1 0]

[0 0 1]

? matrixqz3([1,3;3,5;5,7])
%299 = 
[2 -1]

[1 0]

[0 1]

? max(2,3)
%300 = 3
? min(2,3)
%301 = 2
? minim([2,1;1,2],4,6)
%302 = [6, 2, [0, -1, 1; 1, 1, 0]]
? mod(-12,7)
%303 = mod(2, 7)
? modp(-12,7)
%304 = mod(2, 7)
? mod(10873,49649)^-1
  ***   impossible inverse modulo: mod(131, 49649)
? modreverse(mod(x^2+1,x^3-x-1))
%305 = mod(x^2 - 3*x + 2, x^3 - 5*x^2 + 8*x - 5)
? move(0,243,583);cursor(0)
%306 = [243.0000000000000000, 583.0000000000000000]
? mu(3*5*7*11*13)
%307 = -1
? \\ N
? newtonpoly(x^4+3*x^3+27*x^2+9*x+81,3)
%308 = [2, 2/3, 2/3, 2/3]
? nextprime(100000000000000000000000)
%309 = 100000000000000000000117
? setrand(1);a=matrix(3,5,j,k,vvector(5,l,random()\10^8))
%310 = 
[[10, 7, 8, 7, 18]~ [17, 0, 9, 20, 10]~ [5, 4, 7, 18, 20]~ [0, 16, 4, 2, 0]~ [17, 19, 17, 1, 14]~]

[[17, 16, 6, 3, 6]~ [17, 13, 9, 19, 6]~ [1, 14, 12, 20, 8]~ [6, 1, 8, 17, 21]~ [18, 17, 9, 10, 13]~]

[[4, 13, 3, 17, 14]~ [14, 16, 11, 5, 4]~ [9, 11, 13, 7, 15]~ [19, 21, 2, 4, 5]~ [14, 16, 6, 20, 14]~]

? aid=[idx,idy,idz,idmat(5),idx]
%311 = [[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], [6, 0, 4, 0, 3; 0, 6, 2, 0, 3; 0, 0, 2, 0, 0; 0, 0, 0, 6, 3; 0, 0, 0, 0, 3], [6, 0, 0, 0, 3; 0, 6, 0, 0, 3; 0, 0, 6, 0, 0; 0, 0, 0, 6, 3; 0, 0, 0, 0, 3], [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=algtobasis(nf,mod(x^3+x,nfpol))
%312 = [1, 1, 1, 3, 0]~
? da=nfdetint(nf,[a,aid])
%313 = 
[6 0 0 0 0]

[0 6 0 0 0]

[0 0 6 0 0]

[0 0 0 6 0]

[0 0 0 0 6]

? nfdiv(nf,ba,bb)
%314 = [755/373, -152/373, 159/373, 120/373, -264/373]~
? nfdiveuc(nf,ba,bb)
%315 = [2, 0, 0, 0, -1]~
? nfdivres(nf,ba,bb)
%316 = [[2, 0, 0, 0, -1]~, [-12, -7, 0, 9, 5]~]
? nfhermite(nf,[a,aid])
%317 = [[[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]]]
? nfhermitemod(nf,[a,aid],da)
%318 = [[[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]]]
? nfmod(nf,ba,bb)
%319 = [-12, -7, 0, 9, 5]~
? nfmul(nf,ba,bb)
%320 = [-25, -50, -30, 15, 90]~
? nfpow(nf,bb,5)
%321 = [23455, 156370, 115855, 74190, -294375]~
? nfreduce(nf,ba,idx)
%322 = [1, 0, 0, 0, 0]~
? setrand(1);as=matrix(3,3,j,k,vvector(5,l,random()\10^8))
%323 = 
[[10, 7, 8, 7, 18]~ [17, 0, 9, 20, 10]~ [5, 4, 7, 18, 20]~]

[[17, 16, 6, 3, 6]~ [17, 13, 9, 19, 6]~ [1, 14, 12, 20, 8]~]

[[4, 13, 3, 17, 14]~ [14, 16, 11, 5, 4]~ [9, 11, 13, 7, 15]~]

? vaid=[idx,idy,idmat(5)]
%324 = [[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], [6, 0, 4, 0, 3; 0, 6, 2, 0, 3; 0, 0, 2, 0, 0; 0, 0, 0, 6, 3; 0, 0, 0, 0, 3], [1, 0, 0, 0, 0; 0, 1, 0, 0, 0; 0, 0, 1, 0, 0; 0, 0, 0, 1, 0; 0, 0, 0, 0, 1]]
? haid=[idmat(5),idmat(5),idmat(5)]
%325 = [[1, 0, 0, 0, 0; 0, 1, 0, 0, 0; 0, 0, 1, 0, 0; 0, 0, 0, 1, 0; 0, 0, 0, 0, 1], [1, 0, 0, 0, 0; 0, 1, 0, 0, 0; 0, 0, 1, 0, 0; 0, 0, 0, 1, 0; 0, 0, 0, 0, 1], [1, 0, 0, 0, 0; 0, 1, 0, 0, 0; 0, 0, 1, 0, 0; 0, 0, 0, 1, 0; 0, 0, 0, 0, 1]]
? nfsmith(nf,[as,haid,vaid])
%326 = [[2190214794666577649262, 2150519575834519632534, 1042321473697998234804, 1668446648667242883456, 125169914175448646880; 0, 6, 0, 0, 0; 0, 0, 6, 0, 0; 0, 0, 0, 6, 0; 0, 0, 0, 0, 6], [1, 0, 0, 0, 0; 0, 1, 0, 0, 0; 0, 0, 1, 0, 0; 0, 0, 0, 1, 0; 0, 0, 0, 0, 1], [1, 0, 0, 0, 0; 0, 1, 0, 0, 0; 0, 0, 1, 0, 0; 0, 0, 0, 1, 0; 0, 0, 0, 0, 1]]
? nfval(nf,ba,vp)
%327 = 0
? norm(1+i)
%328 = 2
? norm(mod(x+5,x^3+x+1))
%329 = 129
? norml2(vector(10,x,x))
%330 = 385
? nucomp(qfi(2,1,9),qfi(4,3,5),3)
%331 = qfi(2, -1, 9)
? form=qfi(2,1,9);nucomp(form,form,3)
%332 = qfi(4, -3, 5)
? numdiv(2^99*3^49)
%333 = 5000
? numer((x+1)/(x-1))
%334 = x + 1
? nupow(form,111)
%335 = qfi(2, -1, 9)
? \\ O
? 1/(1+x)+o(x^20)
%336 = 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!)
%337 = 25
? ordell(acurve,1)
%338 = [8, 3]
? order(mod(33,2^16+1))
%339 = 2048
? tcurve=smallinitell([1,0,1,-19,26])
%340 = [1, 0, 1, -19, 26, 1, -37, 105, -316, 889, -24013, 72900, 702595369/72900]
? orderell(tcurve,[1,2])
%341 = 6
? ordred(x^3-12*x+45*x-1)
%342 = [x - 1, x^3 + 33*x - 1, x^3 - 363*x - 2663]~
? \\ P
? padicprec(padicno,127)
%343 = 5
? pascal(8)
%344 = 
[1 0 0 0 0 0 0 0 0]

[1 1 0 0 0 0 0 0 0]

[1 2 1 0 0 0 0 0 0]

[1 3 3 1 0 0 0 0 0]

[1 4 6 4 1 0 0 0 0]

[1 5 10 10 5 1 0 0 0]

[1 6 15 20 15 6 1 0 0]

[1 7 21 35 35 21 7 1 0]

[1 8 28 56 70 56 28 8 1]

? perf([2,0,1;0,2,1;1,1,2])
%345 = 6
? permutation(7,1035)
%346 = [4, 7, 1, 6, 3, 5, 2]
? permutation2num([4,7,1,6,3,5,2])
%347 = 1035
? pf(-44,3)
%348 = qfi(3, 2, 4)
? phi(257^2)
%349 = 65792
? pi
%350 = 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                                                   5.000

? \\ploth(x=-5,5,sin(x))
? \\ploth2(t=0,2*pi,[sin(5*t),sin(7*t)])
? \\plothraw(vector(100,k,k),vector(100,k,k*k/100))
? pnqn([2,6,10,14,18,22,26])
%351 = 
[19318376 741721]

[8927353 342762]

? pnqn([1,1,1,1,1,1,1,1;1,1,1,1,1,1,1,1])
%352 = 
[34 21]

[21 13]

? point(0,225,334)
? points(0,vector(10,k,10*k),vector(10,k,5*k*k))
? pointell(acurve,zell(acurve,apoint))
%353 = [0.9999999999999999993 +  0.E-19*i, 3.000000000000000000 +  0.E-18*i]
? polint([0,2,3],[0,4,9],5)
%354 = 25
? polred(x^5-2*x^4-4*x^3-96*x^2-352*x-568)
%355 = [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]~
? polred2(x^4-28*x^3-458*x^2+9156*x-25321)
%356 = 
[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]

? polredabs(x^5-2*x^4-4*x^3-96*x^2-352*x-568)
%357 = x^5 - x^4 + 2*x^3 - 4*x^2 + x - 1
? polsym(x^17-1,17)
%358 = [17, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 17]~
? polvar(name^4-other)
%359 = name
? poly(sin(x),x)
%360 = -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)
%361 = 0.5084005792422687065
? polylog(-4,t)
%362 = (t^4 + 11*t^3 + 11*t^2 + t)/(-t^5 + 5*t^4 - 10*t^3 + 10*t^2 - 5*t + 1)
? polylogd(5,0.5)
%363 = 0.9390354985726916212
? polylogdold(5,0.5)
%364 = 1.034459423449010483
? polylogp(5,0.5)
%365 = 0.9495693489964922581
? poly([1,2,3,4,5],x)
%366 = x^4 + 2*x^3 + 3*x^2 + 4*x + 5
? polyrev([1,2,3,4,5],x)
%367 = 5*x^4 + 4*x^3 + 3*x^2 + 2*x + 1
? \\draw([0,20,20])
? postdraw([0,20,20])
? postploth(x=-5,5,sin(x))
? postploth2(t=0,2*pi,[sin(5*t),sin(7*t)])
? postplothraw(vector(100,k,k),vector(100,k,k*k/100))
? powell(acurve,apoint,10)
%368 = [-28919032218753260057646013785951999/292736325329248127651484680640160000, 478051489392386968218136375373985436596569736643531551/158385319626308443937475969221994173751192384064000000]
? powrealraw(qfr(5,3,-1,0.),3)
%369 = qfr(125, 23, 1,  0.E-18)
? pprint((x-12*y)/(y+13*x));
(-(11 /14))
? pprint([1,2;3,4])

[1 2]

[3 4]

%371 = 
[1 2]

[3 4]

? pprint1(x+y);pprint(x+y);
(2 x )(2 x )
? \precision=96
   precision = 96 significant digits
? pi
%373 = 3.14159265358979323846264338327950288419716939937510582097494459230781640628620899862803482534211
? prec(pi,20)
%374 = 3.14159265358979323846264338327950288419528635800000000000000000000000000000000000000000000000000
? \precision=38
   precision = 38 significant digits
? prime(100)
%375 = 541
? primedec(nf,2)
%376 = [[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]~]]
? primedec(nf,3)
%377 = [[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]~]]
? primedec(nf,11)
%378 = [[11, [11, 0, 0, 0, 0]~, 1, 5, [1, 0, 0, 0, 0]~]]
? primes(100)
%379 = [2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229, 233, 239, 241, 251, 257, 263, 269, 271, 277, 281, 283, 293, 307, 311, 313, 317, 331, 337, 347, 349, 353, 359, 367, 373, 379, 383, 389, 397, 401, 409, 419, 421, 431, 433, 439, 443, 449, 457, 461, 463, 467, 479, 487, 491, 499, 503, 509, 521, 523, 541]
? forprime(p=2,100,print(p," ",lift(primroot(p))))
2 1
3 2
5 2
7 3
11 2
13 2
17 3
19 2
23 5
29 2
31 3
37 2
41 6
43 3
47 5
53 2
59 2
61 2
67 2
71 7
73 5
79 3
83 2
89 3
97 5
? principalideal(nf,mod(x^3+5,nfpol))
%380 = 
[6]

[0]

[1]

[3]

[0]

? principalidele(nf,mod(x^3+5,nfpol))
%381 = [[6; 0; 1; 3; 0], [2.2324480827796254080981385584384939684 + 3.1415926535897932384626433832795028842*i, 5.0387659675158716386435353106610489968 - 1.5851760343512250049897278861965702423*i, 4.2664040272651028743625910797589683173 + 0.0083630478144368246110910258645462996191*i]~]
? print((x-12*y)/(y+13*x));
-11/14
? print([1,2;3,4])
[1, 2; 3, 4]
%383 = 
[1 2]

[3 4]

? print1(x+y);print1(" equals ");print(x+y);
2*x equals 2*x
? prod(1,k=1,10,1+1/k!)
%385 = 3335784368058308553334783/905932868585678438400000
? prod(1.,k=1,10,1+1/k!)
%386 = 3.6821540356142043935732308433185262945
? pi^2/6*prodeuler(p=2,10000,1-p^-2)
%387 = 1.0000098157493066238697591433298145174
? prodinf(n=0,(1+2^-n)/(1+2^(-n+1)))
%388 = 0.33333333333333333333333333333333333320
? prodinf1(n=0,-2^-n/(1+2^(-n+1)))
%389 = 0.33333333333333333333333333333333333320
? psi(1)
%390 = -0.57721566490153286060651209008240243102
? \\ Q
? quaddisc(-252)
%391 = -7
? quadgen(-11)
%392 = w
? quadpoly(-11)
%393 = x^2 - x + 3
? \\ R
? smith(matrix(5,5,j,k,random()))
%394 = [483591676615786906404257792, 2147483648, 2147483648, 1, 1]
? rank(matrix(5,5,x,y,x+y))
%395 = 2
? move(0,50,50);rbox(0,50,50)
? print1("give a value for s? ");s=read();print(1/s)
give a value for s? 37.
0.027027027027027027027027027027027027026
%396 = 0.027027027027027027027027027027027027026
? real(5-7*i)
%397 = 5
? recip(3*x^7-5*x^3+6*x-9)
%398 = -9*x^7 + 6*x^6 - 5*x^4 + 3
? redimag(qfi(3,10,12))
%399 = qfi(3, -2, 4)
? redreal(qfr(3,10,-20,1.5))
%400 = qfr(3, 16, -7, 1.5000000000000000000000000000000000000)
? redrealnod(qfr(3,10,-20,1.5),18)
%401 = qfr(3, 16, -7, 1.5000000000000000000000000000000000000)
? regula(17)
%402 = 2.0947125472611012942448228460655286534
? kill(y);print(x+y);reorder([x,y]);print(x+y);
x + y
x + y
? resultant(x^3-1,x^3+1)
%404 = 8
? resultant2(x^3-1.,x^3+1.)
%405 = 8.0000000000000000000000000000000000000
? reverse(tan(x))
%406 = 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)
? rhoreal(qfr(3,10,-20,1.5))
%407 = qfr(-20, -10, 3, 2.1074451073987839947135880252731470615)
? rhorealnod(qfr(3,10,-20,1.5),18)
%408 = qfr(-20, -10, 3, 1.5000000000000000000000000000000000000)
? rline(0,200,150)
? cursor(0)
%409 = [250.00000000000000000000000000000000000, 200.00000000000000000000000000000000000]
? rmove(0,5,5);cursor(0)
%410 = [255.00000000000000000000000000000000000, 205.00000000000000000000000000000000000]
? rndtoi(prod(1,k=1,17,x-exp(2*i*pi*k/17)))
%411 = x^17 - 1
? qpol=y^3-y-1;setrand(1);bnf2=buchinit(qpol);nf2=bnf2[7];
? un=mod(1,qpol);w=mod(y,qpol);p=un*(x^5-5*x+w)
%413 = 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)
%414 = [[[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, 8/25; 0, 1, 22/25; 0, 0, 1/25]], [416134375, 212940625, 388649575; 0, 3125, 550; 0, 0, 25], [-1280, 5, 5]~]
? rnfbasis(bnf2,aa)
%415 = 
[[1, 0, 0]~ [0, 0, 0]~ [0, 0, 0]~ [4/5, -4/5, -2/5]~ [-253/25, -252/25, 259/25]~]

[[0, 0, 0]~ [1, 0, 0]~ [0, 0, 0]~ [-4/5, 4/5, 2/5]~ [244/25, 246/25, -232/25]~]

[[0, 0, 0]~ [0, 0, 0]~ [1, 0, 0]~ [-2/5, 2/5, 1/5]~ [98/25, 107/25, -44/25]~]

[[0, 0, 0]~ [0, 0, 0]~ [0, 0, 0]~ [-2/5, 2/5, 1/5]~ [116/25, 119/25, -98/25]~]

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

? rnfdiscf(nf2,p)
%416 = [[416134375, 212940625, 388649575; 0, 3125, 550; 0, 0, 25], [-1280, 5, 5]~]
? rnfhermitebasis(bnf2,aa)
%417 = 
[[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)
%418 = 1
? rnfsteinitz(nf2,aa)
%419 = [[[1, 0, 0]~, [0, 0, 0]~, [0, 0, 0]~, [4/5, -4/5, -2/5]~, [-61/125, 11/125, 11/125]~; [0, 0, 0]~, [1, 0, 0]~, [0, 0, 0]~, [-4/5, 4/5, 2/5]~, [58/125, -8/125, -8/125]~; [0, 0, 0]~, [0, 0, 0]~, [1, 0, 0]~, [-2/5, 2/5, 1/5]~, [21/125, 4/125, 4/125]~; [0, 0, 0]~, [0, 0, 0]~, [0, 0, 0]~, [-2/5, 2/5, 1/5]~, [27/125, -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, 388649575; 0, 3125, 550; 0, 0, 25], [-1280, 5, 5]~]
? rootmod(x^16-1,41)
%420 = [mod(1, 41), mod(3, 41), mod(9, 41), mod(14, 41), mod(27, 41), mod(32, 41), mod(38, 41), mod(40, 41)]
? rootpadic(x^4+1,41,6)
%421 = [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)]
? roots(x^5-1)
%422 = [0.99999999999999999999999999999999999999 +  0.E-38*i, -0.80901699437494742410229341718281905886 + 0.58778525229247312916870595463907276859*i, -0.80901699437494742410229341718281905886 - 0.58778525229247312916870595463907276859*i, 0.30901699437494742410229341718281905886 + 0.95105651629515357211643933337938214340*i, 0.30901699437494742410229341718281905886 - 0.95105651629515357211643933337938214340*i]~
? rootslong(x^4-1000000000000000000000)
%423 = [-177827.94100389228012254211951926848447 +  0.E-38*i, 177827.94100389228012254211951926848447 +  0.E-38*i, 6.4133387520287128895875457643205185532 E-291 + 177827.94100389228012254211951926848447*i, 6.4133387520287128895875457643205185532 E-291 - 177827.94100389228012254211951926848447*i]~
? round(prod(1,k=1,17,x-exp(2*i*pi*k/17)))
%424 = x^17 - 1
? rounderror(prod(1,k=1,17,x-exp(2*i*pi*k/17)))
%425 = -35
? rpoint(0,20,20)
? \\ S
? initrect(3,600,600);scale(3,-7,7,-2,2);cursor(3)
%426 = [-7.0000000000000000000000000000000000000, 2.0000000000000000000000000000000000000]
? q*series(anell(acurve,100),q)
%427 = 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 + 24*q^90 + 2*q^91 + 4*q^92 + 12*q^93 + 18*q^94 - 24*q^96 + 4*q^97 + 12*q^98 - 30*q^99 - 2*q^100 + O(q^101)
? aset=set([5,-2,7,3,5,1])
%428 = [-2, 1, 3, 5, 7]
? bset=set([7,5,-5,7,2])
%429 = [-5, 2, 5, 7]
? setintersect(aset,bset)
%430 = [5, 7]
? setminus(aset,bset)
%431 = [-2, 1, 3]
? setprecision(28)
%432 = 38
? setrand(10)
%433 = 10
? setsearch(aset,3)
%434 = 3
? setsearch(bset,3)
%435 = 0
? setserieslength(12)
%436 = 16
? setunion(aset,bset)
%437 = [-5, -2, 1, 2, 3, 5, 7]
? arat=(x^3+x+1)/x^3;settype(arat,14)
%438 = (x^3 + x + 1)/x^3
? shift(1,50)
%439 = 1125899906842624
? shift([3,4,-11,-12],-2)
%440 = [0, 1, -2, -3]
? shiftmul([3,4,-11,-12],-2)
%441 = [3/4, 1, -11/4, -3]
? sigma(100)
%442 = 217
? sigmak(2,100)
%443 = 13671
? sigmak(-3,100)
%444 = 1149823/1000000
? sign(-1)
%445 = -1
? sign(0)
%446 = 0
? sign(0.)
%447 = 0
? signat(hilbert(5)-0.11*idmat(5))
%448 = [2, 3]
? signunit(bnf)
%449 = 
[-1]

[1]

? simplefactmod(x^11+1,7)
%450 = 
[1 1]

[10 1]

? simplify(((x+i+1)^2-x^2-2*x*(i+1))^2)
%451 = -4
? sin(pi/6)
%452 = 0.5000000000000000000000000000
? sinh(1)
%453 = 1.175201193643801456882381850
? size([1.3*10^5,2*i*pi*exp(4*pi)])
%454 = 7
? smallbasis(x^3+4*x+12)
%455 = [1, x, 1/2*x^2]
? smalldiscf(x^3+4*x+12)
%456 = -1036
? smallfact(100!+1)
%457 = 
[101 1]

[14303 1]

[149239 1]

[432885273849892962613071800918658949059679308685024481795740765527568493010727023757461397498800981521440877813288657839195622497225621499427628453 1]

? smallinitell([0,0,0,-17,0])
%458 = [0, 0, 0, -17, 0, 0, -34, 0, -289, 816, 0, 314432, 1728]
? smallpolred(x^4+576)
%459 = [x - 1, x^2 + 1, x^4 - x^2 + 1, x^2 - x + 1]~
? smallpolred2(x^4+576)
%460 = 
[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]

? smith(1/hilbert(6))
%461 = [27720, 2520, 2520, 840, 210, 6]
? solve(x=1,4,sin(x))
%462 = 3.141592653589793238462643383
? sort(vector(17,x,5*x%17))
%463 = [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16]
? sqr(1+o(2))
%464 = 1 + O(2^3)
? sqred(hilbert(5))
%465 = 
[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))
%466 = 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)
? srgcd(x^10-1,x^15-1)
%467 = x^5 - 1
? move(0,100,100);string(0,pi)
? move(0,200,200);string(0,"(0,0)")
? \\draw([0,10,10])
? postdraw([0,10,10])
? apol=0.3+legendre(10)
%468 = 46189/256*x^10 - 109395/256*x^8 + 45045/128*x^6 - 15015/128*x^4 + 3465/256*x^2 + 0.05390625000000000000000000000
? sturm(apol)
%469 = 4
? sturmpart(apol,0.91,1)
%470 = 1
? subell(initell([0,0,0,-17,0]),[-1,4],[-4,2])
%471 = [9, -24]
? subst(sin(x),x,y)
%472 = 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)
%473 = x + x^2 - 1/6*x^3 - 1/2*x^4 - 59/120*x^5 - 1/8*x^6 + 419/5040*x^7 + 59/720*x^8 + 13609/362880*x^9 + 19/13440*x^10 - 273241/39916800*x^11 + O(x^12)
? sum(0,k=1,10,2^-k)
%474 = 1023/1024
? sum(0.,k=1,10,2^-k)
%475 = 0.9990234375000000000000000000
? sylvestermatrix(a2*x^2+a1*x+a0,b1*x+b0)
%476 = 
[a2 b1 0]

[a1 b0 b1]

[a0 0 b0]

? \precision=38
   precision = 38 significant digits
? 4*sumalt(n=0,(-1)^n/(2*n+1))
%477 = 3.1415926535897932384626433832795028841
? 4*sumalt2(n=0,(-1)^n/(2*n+1))
%478 = 3.1415926535897932384626433832795028842
? suminf(n=1,2.^-n)
%479 = 1.0000000000000000000000000000000000000
? 6/pi^2*sumpos(n=1,n^-2)
%480 = 0.99999999999999999999999999999999999933
? supplement([1,3;2,4;3,6])
%481 = 
[1 3 0]

[2 4 0]

[3 6 1]

? \\ T
? sqr(tan(pi/3))
%482 = 2.9999999999999999999999999999999999999
? tanh(1)
%483 = 0.76159415595576488811945828260479359041
? taniyama(bcurve)
%484 = [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)
%485 = (O(y^12)*x^11 + y*x^10 + y^2*x^9 + y^3*x^8 + y^4*x^7 + y^5*x^6 + y^6*x^5 + y^7*x^4 + y^8*x^3 + y^9*x^2 + y^10*x + y^11)/x^11
? tchebi(10)
%486 = 512*x^10 - 1280*x^8 + 1120*x^6 - 400*x^4 + 50*x^2 - 1
? teich(7+o(127^12))
%487 = 7 + 57*127 + 58*127^2  + 83*127^3  + 52*127^4  + 109*127^5  + 74*127^6  + 16*127^7  + 60*127^8  + 47*127^9  + 65*127^10  + 5*127^11  + O(127^12)
? texprint((x+y)^3/(x-y)^2)
{{x^{3} + {{3}y}x^{2} + {{3}y^{2}}x + {y^{3}}}\over{x^{2} - {{2}y}x + {y^{2}}}}
%488 = (x^3 + 3*y*x^2 + 3*y^2*x + y^3)/(x^2 - 2*y*x + y^2)
? theta(0.5,3)
%489 = 0.080806418251894691299871683210466298535
? thetanullk(0.5,7)
%490 = -804.63037320243369422783730584965684022
? torsell(tcurve)
%491 = [12, [6, 2], [[1, 2], [7/4, -11/8]]]
? trace(1+i)
%492 = 2
? trace(mod(x+5,x^3+x+1))
%493 = 15
? trans(vector(2,x,x))
%494 = [1, 2]~
? %*%~
%495 = 
[1 2]

[2 4]

? trunc(-2.7)
%496 = -2
? trunc(sin(x^2))
%497 = 1/120*x^10 - 1/6*x^6 + x^2
? tschirnhaus(x^5-x-1)
%498 = x^5 + 5*x^4 + 8*x^3 - 40*x^2 - 24*x + 1039
? type(mod(x,x^2+1))
%499 = 9
? \\ U
? unit(17)
%500 = 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
%501 = 1
? \\ V
? valuation(6^10000-1,5)
%502 = 5
? vec(sin(x))
%503 = [1, 0, -1/6, 0, 1/120, 0, -1/5040, 0, 1/362880, 0, -1/39916800]
? vecmax([-3,7,-2,11])
%504 = 11
? vecmin([-3,7,-2,11])
%505 = -3
? vecsort([[1,8,5],[2,5,8],[3,6,-6],[4,8,6]],2)
%506 = [[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])
%507 = [[2, 5, 8], [3, 6, -6], [1, 8, 5], [4, 8, 6]]
? \\ W
? wf(i)
%508 = 1.1892071150027210667174999705604759152 + 5.8194659955999840398807587680000000000 E-40*i
? wf2(i)
%509 = 1.0905077326652576592070106557607079789 +  0.E-38*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 
? \\ Z
? zell(acurve,apoint)
%510 = 0.72491221490962306778878739838332384646 - 1.7272337110188889250459581820000000000 E-77*i
? zeta(3)
%511 = 1.2020569031595942853997381615114499907
? zeta(0.5+14.1347251*i)
%512 = 0.0000000052043097453468479398562848599419244555 - 0.000000032690639869786982176409251733800562846*i
? zetak(nfz,-3)
%513 = 0.091666666666666666666666666666666666666
? zetak(nfz,1.5+3*i)
%514 = 0.88324345992059326405525724366416928890 - 0.20675362502338952227242308991427938845*i
? znstar(3120)
%515 = [768, [12, 4, 4, 2, 2], [mod(67, 3120), mod(2341, 3120), mod(1847, 3120), mod(391, 3120), mod(2081, 3120)]]
? getstack()
%516 = 462136
? getheap()
%517 = [97, 27934]
? print("Total time spent: ",gettime());
Total time spent: 79581
? \q
Good bye!
