Annotation of OpenXM_contrib/pari/src/test/32/compat, Revision 1.1
1.1 ! maekawa 1: echo = 1 (on)
! 2: ? default(compatible,3)
! 3: compatible = 3 (use old functions, ignore case)
! 4: *** Warning: user functions re-initialized.
! 5: ? +3
! 6: 3
! 7: ? -5
! 8: -5
! 9: ? 5+3
! 10: 8
! 11: ? 5-3
! 12: 2
! 13: ? 5/3
! 14: 5/3
! 15: ? 5\3
! 16: 1
! 17: ? 5\/3
! 18: 2
! 19: ? 5%3
! 20: 2
! 21: ? 5^3
! 22: 125
! 23: ? \precision=57
! 24: realprecision = 57 significant digits
! 25: ? pi
! 26: 3.14159265358979323846264338327950288419716939937510582097
! 27: ? \precision=38
! 28: realprecision = 38 significant digits
! 29: ? o(x^12)
! 30: O(x^12)
! 31: ? padicno=(5/3)*127+O(127^5)
! 32: 44*127 + 42*127^2 + 42*127^3 + 42*127^4 + O(127^5)
! 33: ? initrect(0,500,500)
! 34: ? abs(-0.01)
! 35: 0.0099999999999999999999999999999999999999
! 36: ? acos(0.5)
! 37: 1.0471975511965977461542144610931676280
! 38: ? acosh(3)
! 39: 1.7627471740390860504652186499595846180
! 40: ? acurve=initell([0,0,1,-1,0])
! 41: [0, 0, 1, -1, 0, 0, -2, 1, -1, 48, -216, 37, 110592/37, [0.83756543528332303
! 42: 544481089907503024040, 0.26959443640544455826293795134926000404, -1.10715987
! 43: 16887675937077488504242902444]~, 2.9934586462319596298320099794525081778, 2.
! 44: 4513893819867900608542248318665252253*I, -0.47131927795681147588259389708033
! 45: 769964, -1.4354565186686843187232088566788165076*I, 7.3381327407895767390707
! 46: 210033323055881]
! 47: ? apoint=[2,2]
! 48: [2, 2]
! 49: ? isoncurve(acurve,apoint)
! 50: 1
! 51: ? addell(acurve,apoint,apoint)
! 52: [21/25, -56/125]
! 53: ? addprimes([nextprime(10^9),nextprime(10^10)])
! 54: [1000000007, 10000000019]
! 55: ? adj([1,2;3,4])
! 56:
! 57: [4 -2]
! 58:
! 59: [-3 1]
! 60:
! 61: ? agm(1,2)
! 62: 1.4567910310469068691864323832650819749
! 63: ? agm(1+o(7^5),8+o(7^5))
! 64: 1 + 4*7 + 6*7^2 + 5*7^3 + 2*7^4 + O(7^5)
! 65: ? algdep(2*cos(2*pi/13),6)
! 66: x^6 + x^5 - 5*x^4 - 4*x^3 + 6*x^2 + 3*x - 1
! 67: ? algdep2(2*cos(2*pi/13),6,15)
! 68: x^6 + x^5 - 5*x^4 - 4*x^3 + 6*x^2 + 3*x - 1
! 69: ? akell(acurve,1000000007)
! 70: 43800
! 71: ? nfpol=x^5-5*x^3+5*x+25
! 72: x^5 - 5*x^3 + 5*x + 25
! 73: ? nf=initalg(nfpol)
! 74: [x^5 - 5*x^3 + 5*x + 25, [1, 2], 595125, 45, [[1, -2.42851749071941860689920
! 75: 69565359418364, 5.8976972027301414394898806541072047941, -7.0734526715090929
! 76: 269887668671457811020, 3.8085820570096366144649278594400435257; 1, 1.9647119
! 77: 211288133163138753392090569931 + 0.80971492418897895128294082219556466857*I,
! 78: 3.2044546745713084269203768790545260356 + 3.1817131285400005341145852263331
! 79: 539899*I, -0.16163499313031744537610982231988834519 + 1.88804378620070569319
! 80: 06454476483475283*I, 2.0660709538372480632698971148801090692 + 2.68989675196
! 81: 23140991170523711857387388*I; 1, -0.75045317576910401286427186094108607489 +
! 82: 1.3101462685358123283560773619310445915*I, -1.15330327593637914666531720610
! 83: 81284327 - 1.9664068558894834311780119356739268309*I, 1.19836132888486390887
! 84: 04932558927788962 + 0.64370238076256988899570325671192132449*I, -0.470361982
! 85: 34206637050236104460013083212 + 0.083628266711589186119416762685933385421*I]
! 86: , [1, 2, 2; -2.4285174907194186068992069565359418364, 3.92942384225762663262
! 87: 77506784181139862 - 1.6194298483779579025658816443911293371*I, -1.5009063515
! 88: 382080257285437218821721497 - 2.6202925370716246567121547238620891831*I; 5.8
! 89: 976972027301414394898806541072047941, 6.408909349142616853840753758109052071
! 90: 2 - 6.3634262570800010682291704526663079798*I, -2.30660655187275829333063441
! 91: 22162568654 + 3.9328137117789668623560238713478536619*I; -7.0734526715090929
! 92: 269887668671457811020, -0.32326998626063489075221964463977669038 - 3.7760875
! 93: 724014113863812908952966950567*I, 2.3967226577697278177409865117855577924 -
! 94: 1.2874047615251397779914065134238426489*I; 3.8085820570096366144649278594400
! 95: 435257, 4.1321419076744961265397942297602181385 - 5.379793503924628198234104
! 96: 7423714774776*I, -0.94072396468413274100472208920026166424 - 0.1672565334231
! 97: 7837223883352537186677084*I], [5, 4.0215293653309345240000000000000000000 E-
! 98: 87, 10.000000000000000000000000000000000000, -5.0000000000000000000000000000
! 99: 000000000, 7.0000000000000000000000000000000000000; 4.0215293653309345240000
! 100: 000000000000000 E-87, 19.488486013650707197449403270536023970, 8.04305873066
! 101: 18690490000000000000000000 E-86, 19.488486013650707197449403270536023970, 4.
! 102: 1504592246706085588902013976045703227; 10.0000000000000000000000000000000000
! 103: 00, 8.0430587306618690490000000000000000000 E-86, 85.96021742085184648030513
! 104: 3936577594605, -36.034268291482979838267056239752434596, 53.5761304525111078
! 105: 88183080361946556763; -5.0000000000000000000000000000000000000, 19.488486013
! 106: 650707197449403270536023970, -36.034268291482979838267056239752434596, 60.91
! 107: 6248374441986300937507618575151517, -18.470101750219179344070032346246890434
! 108: ; 7.0000000000000000000000000000000000000, 4.1504592246706085588902013976045
! 109: 703227, 53.576130452511107888183080361946556763, -18.47010175021917934407003
! 110: 2346246890434, 37.970152892842367340897384258599214282], [5, 0, 10, -5, 7; 0
! 111: , 10, 0, 10, -5; 10, 0, 30, -55, 20; -5, 10, -55, 45, -39; 7, -5, 20, -39, 9
! 112: ], [345, 0, 340, 167, 150; 0, 345, 110, 220, 153; 0, 0, 5, 2, 1; 0, 0, 0, 1,
! 113: 0; 0, 0, 0, 0, 1], [132825, -18975, -5175, 27600, 17250; -18975, 34500, 414
! 114: 00, 3450, -43125; -5175, 41400, -41400, -15525, 51750; 27600, 3450, -15525,
! 115: -3450, 0; 17250, -43125, 51750, 0, -86250], [595125, [-120750, 63825, 113850
! 116: , 0, 8625]~, 125439056256992431640625]], [-2.4285174907194186068992069565359
! 117: 418364, 1.9647119211288133163138753392090569931 + 0.809714924188978951282940
! 118: 82219556466857*I, -0.75045317576910401286427186094108607489 + 1.310146268535
! 119: 8123283560773619310445915*I], [1, x, x^2, 1/3*x^3 - 1/3*x^2 - 1/3, 1/15*x^4
! 120: + 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
! 121: , 0, 0, 3, 0; 0, 0, 0, 0, 15], [1, 0, 0, 0, 0, 0, 0, 1, -2, -1, 0, 1, -5, -5
! 122: , -3, 0, -2, -5, 1, -4, 0, -1, -3, -4, -3; 0, 1, 0, 0, 0, 1, 0, 0, -2, 0, 0,
! 123: 0, -5, 0, -5, 0, -2, 0, -5, 0, 0, 0, -5, 0, -4; 0, 0, 1, 0, 0, 0, 1, 1, -2,
! 124: 1, 1, 1, -5, 3, -3, 0, -2, 3, -5, 1, 0, 1, -3, 1, -2; 0, 0, 0, 1, 0, 0, 0,
! 125: 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
! 126: , 0, 5, 0, 0, 0, 15, -5, 10, 0, 5, -5, 10, -2, 1, 0, 10, -2, 7]]
! 127: ? ba=algtobasis(nf,mod(x^3+5,nfpol))
! 128: [6, 0, 1, 3, 0]~
! 129: ? anell(acurve,100)
! 130: [1, -2, -3, 2, -2, 6, -1, 0, 6, 4, -5, -6, -2, 2, 6, -4, 0, -12, 0, -4, 3, 1
! 131: 0, 2, 0, -1, 4, -9, -2, 6, -12, -4, 8, 15, 0, 2, 12, -1, 0, 6, 0, -9, -6, 2,
! 132: -10, -12, -4, -9, 12, -6, 2, 0, -4, 1, 18, 10, 0, 0, -12, 8, 12, -8, 8, -6,
! 133: -8, 4, -30, 8, 0, -6, -4, 9, 0, -1, 2, 3, 0, 5, -12, 4, 8, 9, 18, -15, 6, 0
! 134: , -4, -18, 0, 4, 24, 2, 4, 12, 18, 0, -24, 4, 12, -30, -2]
! 135: ? apell(acurve,10007)
! 136: 66
! 137: ? apell2(acurve,10007)
! 138: 66
! 139: ? apol=x^3+5*x+1
! 140: x^3 + 5*x + 1
! 141: ? apprpadic(apol,1+O(7^8))
! 142: [1 + 6*7 + 4*7^2 + 4*7^3 + 3*7^4 + 4*7^5 + 6*7^7 + O(7^8)]
! 143: ? apprpadic(x^3+5*x+1,mod(x*(1+O(7^8)),x^2+x-1))
! 144: [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 +
! 145: (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)
! 146: ]~
! 147: ? 4*arg(3+3*i)
! 148: 3.1415926535897932384626433832795028842
! 149: ? 3*asin(sqrt(3)/2)
! 150: 3.1415926535897932384626433832795028841
! 151: ? asinh(0.5)
! 152: 0.48121182505960344749775891342436842313
! 153: ? assmat(x^5-12*x^3+0.0005)
! 154:
! 155: [0 0 0 0 -0.00049999999999999999999999999999999999999]
! 156:
! 157: [1 0 0 0 0]
! 158:
! 159: [0 1 0 0 0]
! 160:
! 161: [0 0 1 0 12]
! 162:
! 163: [0 0 0 1 0]
! 164:
! 165: ? 3*atan(sqrt(3))
! 166: 3.1415926535897932384626433832795028841
! 167: ? atanh(0.5)
! 168: 0.54930614433405484569762261846126285232
! 169: ? basis(x^3+4*x+5)
! 170: [1, x, 1/7*x^2 - 1/7*x - 2/7]
! 171: ? basis2(x^3+4*x+5)
! 172: [1, x, 1/7*x^2 - 1/7*x - 2/7]
! 173: ? basistoalg(nf,ba)
! 174: mod(x^3 + 5, x^5 - 5*x^3 + 5*x + 25)
! 175: ? bernreal(12)
! 176: -0.25311355311355311355311355311355311354
! 177: ? bernvec(6)
! 178: [1, 1/6, -1/30, 1/42, -1/30, 5/66, -691/2730]
! 179: ? bestappr(pi,10000)
! 180: 355/113
! 181: ? bezout(123456789,987654321)
! 182: [-8, 1, 9]
! 183: ? bigomega(12345678987654321)
! 184: 8
! 185: ? mcurve=initell([0,0,0,-17,0])
! 186: [0, 0, 0, -17, 0, 0, -34, 0, -289, 816, 0, 314432, 1728, [4.1231056256176605
! 187: 498214098559740770251, 0.E-38, -4.1231056256176605498214098559740770251]~, 1
! 188: .2913084409290072207105564235857096009, 1.2913084409290072207105564235857096
! 189: 009*I, -1.2164377440798088266474269946818791934, -3.649313232239426479942280
! 190: 9840456375802*I, 1.6674774896145033307120230298772362381]
! 191: ? mpoints=[[-1,4],[-4,2]]~
! 192: [[-1, 4], [-4, 2]]~
! 193: ? mhbi=bilhell(mcurve,mpoints,[9,24])
! 194: [-0.72448571035980184146215805860545027439, 1.307328627832055544492943428892
! 195: 1943055]~
! 196: ? bin(1.1,5)
! 197: -0.0045457499999999999999999999999999999997
! 198: ? binary(65537)
! 199: [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1]
! 200: ? bittest(10^100,100)
! 201: 1
! 202: ? boundcf(pi,5)
! 203: [3, 7, 15, 1, 292]
! 204: ? boundfact(40!+1,100000)
! 205:
! 206: [41 1]
! 207:
! 208: [59 1]
! 209:
! 210: [277 1]
! 211:
! 212: [1217669507565553887239873369513188900554127 1]
! 213:
! 214: ? move(0,0,0);box(0,500,500)
! 215: ? setrand(1);buchimag(1-10^7,1,1)
! 216: *** Warning: not a fundamental discriminant in quadclassunit.
! 217: [2416, [1208, 2], [qfi(277, 55, 9028), qfi(1700, 1249, 1700)], 1, 0.99984980
! 218: 753776002339750644800000000000]
! 219: ? setrand(1);bnf=buchinitfu(x^2-x-57,0.2,0.2)
! 220: [mat(3), mat([1, 2, 1, 2, 1, 2, 1, 2, 1]), [-2.71246530518434397468087951060
! 221: 61300699 + 3.1415926535897932384626433832795028842*I; 2.71246530518434397468
! 222: 08795106061300699 - 6.2831853071795864769252867665590057684*I], [23347.97922
! 223: 3478346319454659159707591731 + 6.2831853071795864769252867665590057684*I, 86
! 224: 6.56619430687100142570357249059499540 + 6.2831853071795864769252867665590057
! 225: 684*I, 2881.3396396084587293295626563644245032 + 3.1415926535897932384626433
! 226: 832795028842*I, 27379.624790530768080428797780058276925 + 1.9281866867095232
! 227: 000000000000000000000 E-42*I, 57933.334567930851067108050790839116749 + 2.69
! 228: 04930509626865380000000000000000000 E-42*I, -34585.5562501515577199980340439
! 229: 18848670 + 9.4247779607693797153879301498385086526*I, 23348.3225111226233465
! 230: 49049047574325150 + 3.1415926535897932384626433832795028842*I, -0.3432876442
! 231: 7702709438988786673341921876 + 3.1415926535897932384626433832795028842*I, -4
! 232: 031.7117453543045067063239888430083582 + 9.424777960769379715387930149838508
! 233: 6526*I, 27379.690968832650826160983148550600089 + 9.424777960769379715387930
! 234: 1498385086526*I; -23347.979223478346319454659159707591731 + 9.42477796076937
! 235: 97153879301498385086526*I, -866.56619430687100142570357249059499540 + 2.1019
! 236: 476959481835360000000000000000000 E-45*I, -2881.3396396084587293295626563644
! 237: 245032 + 9.4247779607693797153879301498385086526*I, -27379.62479053076808042
! 238: 8797780058276925 + 6.2831853071795864769252867665590057684*I, -57933.3345679
! 239: 30851067108050790839116749 + 3.1415926535897932384626433832795028842*I, 3458
! 240: 5.556250151557719998034043918848670 + 6.283185307179586476925286766559005768
! 241: 4*I, -23348.322511122623346549049047574325150 + 9.42477796076937971538793014
! 242: 98385086526*I, 0.34328764427702709438988786673341921876 + 0.E-48*I, 4031.711
! 243: 7453543045067063239888430083582 + 3.1415926535897932384626433832795028842*I,
! 244: -27379.690968832650826160983148550600089 + 6.283185307179586476925286766559
! 245: 0057684*I], [[3, [-1, 1]~, 1, 1, [0, 1]~], [3, [0, 1]~, 1, 1, [-1, 1]~], [5,
! 246: [-2, 1]~, 1, 1, [1, 1]~], [5, [1, 1]~, 1, 1, [-2, 1]~], [11, [-2, 1]~, 1, 1
! 247: , [1, 1]~], [11, [1, 1]~, 1, 1, [-2, 1]~], [17, [-3, 1]~, 1, 1, [2, 1]~], [1
! 248: 7, [2, 1]~, 1, 1, [-3, 1]~], [19, [-1, 1]~, 1, 1, [0, 1]~], [19, [0, 1]~, 1,
! 249: 1, [-1, 1]~]]~, [1, 3, 5, 2, 4, 6, 7, 8, 10, 9]~, [x^2 - x - 57, [2, 0], 22
! 250: 9, 1, [[1, -7.0663729752107779635959310246705326058; 1, 8.066372975210777963
! 251: 5959310246705326058], [1, 1; -7.0663729752107779635959310246705326058, 8.066
! 252: 3729752107779635959310246705326058], [2, 1.000000000000000000000000000000000
! 253: 0000; 1.0000000000000000000000000000000000000, 115.0000000000000000000000000
! 254: 0000000000], [2, 1; 1, 115], [229, 114; 0, 1], [115, -1; -1, 2], [229, [114,
! 255: 1]~, 229]], [-7.0663729752107779635959310246705326058, 8.066372975210777963
! 256: 5959310246705326058], [1, x], [1, 0; 0, 1], [1, 0, 0, 57; 0, 1, 1, 1]], [[3,
! 257: [3], [[3, 2; 0, 1]]], 2.7124653051843439746808795106061300699, 0.8814422512
! 258: 6545793690341704100000000000, [2, -1], [x + 7], 130], [mat(1), mat(1), [[[3,
! 259: 2; 0, 1], [0, 0]]]], 0]
! 260: ? buchcertify(bnf)
! 261: 1
! 262: ? buchfu(bnf)
! 263: [[x + 7], 130]
! 264: ? setrand(1);buchinitforcefu(x^2-x-100000)
! 265: [mat(5), mat([3, 2, 1, 2, 0, 3, 2, 3, 0, 0, 1, 4, 3, 2, 2, 3, 3, 2]), [-129.
! 266: 82045011403975460991182396195022419 + 6.283185307179586476925286766559005768
! 267: 4*I; 129.82045011403975460991182396195022419 + 4.907207226380705833000000000
! 268: 0000000000 E-95*I], [2093832.2286247580721598744691800364716 + 9.42477796076
! 269: 93797153879301498385086526*I, 463727.88770776479369558667281813008490 + 6.28
! 270: 31853071795864769252867665590057684*I, 229510.681191741210743599007448730565
! 271: 20 + 3.1415926535897932384626433832795028842*I, -13814064.276184856248286107
! 272: 275967161406 + 6.2831853071795864769252867665590057684*I, 10975229.442376145
! 273: 014058790444262893275 + 9.4247779607693797153879301498385086526*I, 12628868.
! 274: 476868730308574917279106536834 + 6.2831853071795864769252867665590057684*I,
! 275: 2595210.6815750606798700790306370856686 + 3.14159265358979323846264338327950
! 276: 28842*I, 21463208.279603014333968661075393279510 + 6.28318530717958647692528
! 277: 67665590057684*I, 9340416.4917416354701732132629720490406 + 9.42477796076937
! 278: 97153879301498385086526*I, 224801.35127844528675036994618361508061 + 12.5663
! 279: 70614359172953850573533118011536*I, -224801.35127844528675036994618361508061
! 280: + 2.1125754163178543118626478980000000000 E-90*I, 40271115.6788572427160038
! 281: 79014241558828 + 6.2831853071795864769252867665590057684*I, -10066612.284788
! 282: 886379386747743460630561 + 9.4600667685469491310218392850000000000 E-89*I, 1
! 283: 0267873.880681641662748682261863339788 + 12.56637061435917295385057353311801
! 284: 1536*I, -4435991.6114732228963510067335229085617 + 6.28318530717958647692528
! 285: 67665590057684*I, 8361196.2032957779193404684451855312611 + 9.42477796076937
! 286: 97153879301498385086526*I, -10272584.501589374356405593568879583106 + 9.4247
! 287: 779607693797153879301498385086526*I, 41648172.195327314227598351804544361493
! 288: + 9.4247779607693797153879301498385086526*I, -2117367.665066341919805155100
! 289: 3369291210 + 1.9897854874556092437572207830000000000 E-89*I; -2093832.228624
! 290: 7580721598744691800364716 + 3.1415926535897932384626433832795028842*I, -4637
! 291: 27.88770776479369558667281813008490 + 9.424777960769379715387930149838508652
! 292: 6*I, -229510.68119174121074359900744873056520 + 12.5663706143591729538505735
! 293: 33118011536*I, 13814064.276184856248286107275967161405 + 5.22154890000820159
! 294: 90000000000000000000 E-90*I, -10975229.442376145014058790444262893275 + 12.5
! 295: 66370614359172953850573533118011536*I, -12628868.476868730308574917279106536
! 296: 834 + 3.1415926535897932384626433832795028842*I, -2595210.681575060679870079
! 297: 0306370856686 + 12.566370614359172953850573533118011536*I, -21463208.2796030
! 298: 14333968661075393279510 + 9.4247779607693797153879301498385086526*I, -934041
! 299: 6.4917416354701732132629720490406 + 6.2831853071795864769252867665590057684*
! 300: I, -224801.35127844528675036994618361508061 + 12.566370614359172953850573533
! 301: 118011536*I, 224801.35127844528675036994618361508061 + 8.4971798285841941830
! 302: 000000000000000000 E-92*I, -40271115.678857242716003879014241558828 + 12.566
! 303: 370614359172953850573533118011536*I, 10066612.284788886379386747743460630561
! 304: + 3.8050554944202303880000000000000000000 E-90*I, -10267873.880681641662748
! 305: 682261863339788 + 3.1415926535897932384626433832795028842*I, 4435991.6114732
! 306: 228963510067335229085617 + 9.4247779607693797153879301498385086526*I, -83611
! 307: 96.2032957779193404684451855312611 + 12.566370614359172953850573533118011536
! 308: *I, 10272584.501589374356405593568879583106 + 3.8829118423163890830000000000
! 309: 000000000 E-90*I, -41648172.195327314227598351804544361493 + 3.1415926535897
! 310: 932384626433832795028842*I, 2117367.6650663419198051551003369291210 + 8.0033
! 311: 745765686035150000000000000000000 E-91*I], [[2, [1, 1]~, 1, 1, [0, 1]~], [2,
! 312: [2, 1]~, 1, 1, [1, 1]~], [5, [4, 1]~, 1, 1, [0, 1]~], [5, [5, 1]~, 1, 1, [-
! 313: 1, 1]~], [7, [3, 1]~, 2, 1, [3, 1]~], [13, [-6, 1]~, 1, 1, [5, 1]~], [13, [5
! 314: , 1]~, 1, 1, [-6, 1]~], [17, [14, 1]~, 1, 1, [2, 1]~], [17, [19, 1]~, 1, 1,
! 315: [-3, 1]~], [23, [-7, 1]~, 1, 1, [6, 1]~], [23, [6, 1]~, 1, 1, [-7, 1]~], [29
! 316: , [-14, 1]~, 1, 1, [13, 1]~], [29, [13, 1]~, 1, 1, [-14, 1]~], [31, [23, 1]~
! 317: , 1, 1, [7, 1]~], [31, [38, 1]~, 1, 1, [-8, 1]~], [41, [-7, 1]~, 1, 1, [6, 1
! 318: ]~], [41, [6, 1]~, 1, 1, [-7, 1]~], [43, [-16, 1]~, 1, 1, [15, 1]~], [43, [1
! 319: 5, 1]~, 1, 1, [-16, 1]~]]~, [1, 3, 6, 2, 4, 5, 7, 9, 8, 11, 10, 13, 12, 15,
! 320: 14, 17, 16, 19, 18]~, [x^2 - x - 100000, [2, 0], 400001, 1, [[1, -315.728161
! 321: 30129840161392089489603747004; 1, 316.72816130129840161392089489603747004],
! 322: [1, 1; -315.72816130129840161392089489603747004, 316.72816130129840161392089
! 323: 489603747004], [2, 1.0000000000000000000000000000000000000; 1.00000000000000
! 324: 00000000000000000000000, 200001.00000000000000000000000000000000], [2, 1; 1,
! 325: 200001], [400001, 200000; 0, 1], [200001, -1; -1, 2], [400001, [200000, 1]~
! 326: , 400001]], [-315.72816130129840161392089489603747004, 316.72816130129840161
! 327: 392089489603747004], [1, x], [1, 0; 0, 1], [1, 0, 0, 100000; 0, 1, 1, 1]], [
! 328: [5, [5], [[2, 1; 0, 1]]], 129.82045011403975460991182396195022419, 0.9876536
! 329: 9790690472391212970100000000000, [2, -1], [379554884019013781006303254896369
! 330: 154068336082609238336*x + 11983616564425078999046283595002287166517812761131
! 331: 6131167], 124], [mat(1), mat(1), [[[2, 1; 0, 1], [0, 0]]]], 0]
! 332: ? setrand(1);bnf=buchinitfu(x^2-x-57,0.2,0.2)
! 333: [mat(3), mat([1, 2, 1, 2, 1, 2, 1, 2, 1]), [-2.71246530518434397468087951060
! 334: 61300699 + 3.1415926535897932384626433832795028842*I; 2.71246530518434397468
! 335: 08795106061300699 - 6.2831853071795864769252867665590057684*I], [23347.97922
! 336: 3478346319454659159707591731 + 6.2831853071795864769252867665590057684*I, 86
! 337: 6.56619430687100142570357249059499540 + 6.2831853071795864769252867665590057
! 338: 684*I, 2881.3396396084587293295626563644245032 + 3.1415926535897932384626433
! 339: 832795028842*I, 27379.624790530768080428797780058276925 + 1.9281866867095232
! 340: 000000000000000000000 E-42*I, 57933.334567930851067108050790839116749 + 2.69
! 341: 04930509626865380000000000000000000 E-42*I, -34585.5562501515577199980340439
! 342: 18848670 + 9.4247779607693797153879301498385086526*I, 23348.3225111226233465
! 343: 49049047574325150 + 3.1415926535897932384626433832795028842*I, -0.3432876442
! 344: 7702709438988786673341921876 + 3.1415926535897932384626433832795028842*I, -4
! 345: 031.7117453543045067063239888430083582 + 9.424777960769379715387930149838508
! 346: 6526*I, 27379.690968832650826160983148550600089 + 9.424777960769379715387930
! 347: 1498385086526*I; -23347.979223478346319454659159707591731 + 9.42477796076937
! 348: 97153879301498385086526*I, -866.56619430687100142570357249059499540 + 2.1019
! 349: 476959481835360000000000000000000 E-45*I, -2881.3396396084587293295626563644
! 350: 245032 + 9.4247779607693797153879301498385086526*I, -27379.62479053076808042
! 351: 8797780058276925 + 6.2831853071795864769252867665590057684*I, -57933.3345679
! 352: 30851067108050790839116749 + 3.1415926535897932384626433832795028842*I, 3458
! 353: 5.556250151557719998034043918848670 + 6.283185307179586476925286766559005768
! 354: 4*I, -23348.322511122623346549049047574325150 + 9.42477796076937971538793014
! 355: 98385086526*I, 0.34328764427702709438988786673341921876 + 0.E-48*I, 4031.711
! 356: 7453543045067063239888430083582 + 3.1415926535897932384626433832795028842*I,
! 357: -27379.690968832650826160983148550600089 + 6.283185307179586476925286766559
! 358: 0057684*I], [[3, [-1, 1]~, 1, 1, [0, 1]~], [3, [0, 1]~, 1, 1, [-1, 1]~], [5,
! 359: [-2, 1]~, 1, 1, [1, 1]~], [5, [1, 1]~, 1, 1, [-2, 1]~], [11, [-2, 1]~, 1, 1
! 360: , [1, 1]~], [11, [1, 1]~, 1, 1, [-2, 1]~], [17, [-3, 1]~, 1, 1, [2, 1]~], [1
! 361: 7, [2, 1]~, 1, 1, [-3, 1]~], [19, [-1, 1]~, 1, 1, [0, 1]~], [19, [0, 1]~, 1,
! 362: 1, [-1, 1]~]]~, [1, 3, 5, 2, 4, 6, 7, 8, 10, 9]~, [x^2 - x - 57, [2, 0], 22
! 363: 9, 1, [[1, -7.0663729752107779635959310246705326058; 1, 8.066372975210777963
! 364: 5959310246705326058], [1, 1; -7.0663729752107779635959310246705326058, 8.066
! 365: 3729752107779635959310246705326058], [2, 1.000000000000000000000000000000000
! 366: 0000; 1.0000000000000000000000000000000000000, 115.0000000000000000000000000
! 367: 0000000000], [2, 1; 1, 115], [229, 114; 0, 1], [115, -1; -1, 2], [229, [114,
! 368: 1]~, 229]], [-7.0663729752107779635959310246705326058, 8.066372975210777963
! 369: 5959310246705326058], [1, x], [1, 0; 0, 1], [1, 0, 0, 57; 0, 1, 1, 1]], [[3,
! 370: [3], [[3, 2; 0, 1]]], 2.7124653051843439746808795106061300699, 0.8814422512
! 371: 6545793690341704100000000000, [2, -1], [x + 7], 130], [mat(1), mat(1), [[[3,
! 372: 2; 0, 1], [0, 0]]]], 0]
! 373: ? setrand(1);buchreal(10^9-3,0,0.5,0.5)
! 374: [4, [4], [qfr(3, 1, -83333333, 0.E-48)], 2800.625251907016076486370621737074
! 375: 5513, 0.99903694589643832327024650000000000000]
! 376: ? setrand(1);buchgen(x^4-7,0.2,0.2)
! 377:
! 378: [x^4 - 7]
! 379:
! 380: [[2, 1]]
! 381:
! 382: [[-87808, 1]]
! 383:
! 384: [[1, x, x^2, x^3]]
! 385:
! 386: [[2, [2], [[2, 1, 1, 1; 0, 1, 0, 0; 0, 0, 1, 0; 0, 0, 0, 1]]]]
! 387:
! 388: [14.229975145405511722395637833443108790]
! 389:
! 390: [1.1211171071527562299744232290000000000]
! 391:
! 392: ? setrand(1);buchgenfu(x^2-x-100000)
! 393: *** Warning: insufficient precision for fundamental units, not given.
! 394:
! 395: [x^2 - x - 100000]
! 396:
! 397: [[2, 0]]
! 398:
! 399: [[400001, 1]]
! 400:
! 401: [[1, x]]
! 402:
! 403: [[5, [5], [[2, 1; 0, 1]]]]
! 404:
! 405: [129.82045011403975460991182396195022419]
! 406:
! 407: [0.98765369790690472391212970100000000000]
! 408:
! 409: [[2, -1]]
! 410:
! 411: [[;]]
! 412:
! 413: [0]
! 414:
! 415: ? setrand(1);buchgenforcefu(x^2-x-100000)
! 416:
! 417: [x^2 - x - 100000]
! 418:
! 419: [[2, 0]]
! 420:
! 421: [[400001, 1]]
! 422:
! 423: [[1, x]]
! 424:
! 425: [[5, [5], [[2, 1; 0, 1]]]]
! 426:
! 427: [129.82045011403975460991182396195022419]
! 428:
! 429: [0.98765369790690472391212970100000000000]
! 430:
! 431: [[2, -1]]
! 432:
! 433: [[379554884019013781006303254896369154068336082609238336*x + 119836165644250
! 434: 789990462835950022871665178127611316131167]]
! 435:
! 436: [124]
! 437:
! 438: ? setrand(1);buchgenfu(x^4+24*x^2+585*x+1791,0.1,0.1)
! 439:
! 440: [x^4 + 24*x^2 + 585*x + 1791]
! 441:
! 442: [[0, 2]]
! 443:
! 444: [[18981, 3087]]
! 445:
! 446: [[1, x, 1/3*x^2, 1/1029*x^3 + 33/343*x^2 - 155/343*x - 58/343]]
! 447:
! 448: [[4, [4], [[7, 6, 2, 4; 0, 1, 0, 0; 0, 0, 1, 0; 0, 0, 0, 1]]]]
! 449:
! 450: [3.7941269688216589341408274220859400302]
! 451:
! 452: [0.88260182866555813061644128400000000000]
! 453:
! 454: [[6, 10/1029*x^3 - 13/343*x^2 + 165/343*x + 1478/343]]
! 455:
! 456: [[4/1029*x^3 + 53/1029*x^2 + 66/343*x + 111/343]]
! 457:
! 458: [103]
! 459:
! 460: ? buchnarrow(bnf)
! 461: [3, [3], [[3, 2; 0, 1]]]
! 462: ? buchray(bnf,[[5,3;0,1],[1,0]])
! 463: [12, [12], [[3, 2; 0, 1]]]
! 464: ? bnr=buchrayinitgen(bnf,[[5,3;0,1],[1,0]])
! 465: [[mat(3), mat([1, 2, 1, 2, 1, 2, 1, 2, 1]), [-2.7124653051843439746808795106
! 466: 061300699 + 3.1415926535897932384626433832795028842*I; 2.7124653051843439746
! 467: 808795106061300699 - 6.2831853071795864769252867665590057684*I], [23347.9792
! 468: 23478346319454659159707591731 + 6.2831853071795864769252867665590057684*I, 8
! 469: 66.56619430687100142570357249059499540 + 6.283185307179586476925286766559005
! 470: 7684*I, 2881.3396396084587293295626563644245032 + 3.141592653589793238462643
! 471: 3832795028842*I, 27379.624790530768080428797780058276925 + 1.928186686709523
! 472: 2000000000000000000000 E-42*I, 57933.334567930851067108050790839116749 + 2.6
! 473: 904930509626865380000000000000000000 E-42*I, -34585.556250151557719998034043
! 474: 918848670 + 9.4247779607693797153879301498385086526*I, 23348.322511122623346
! 475: 549049047574325150 + 3.1415926535897932384626433832795028842*I, -0.343287644
! 476: 27702709438988786673341921876 + 3.1415926535897932384626433832795028842*I, -
! 477: 4031.7117453543045067063239888430083582 + 9.42477796076937971538793014983850
! 478: 86526*I, 27379.690968832650826160983148550600089 + 9.42477796076937971538793
! 479: 01498385086526*I; -23347.979223478346319454659159707591731 + 9.4247779607693
! 480: 797153879301498385086526*I, -866.56619430687100142570357249059499540 + 2.101
! 481: 9476959481835360000000000000000000 E-45*I, -2881.339639608458729329562656364
! 482: 4245032 + 9.4247779607693797153879301498385086526*I, -27379.6247905307680804
! 483: 28797780058276925 + 6.2831853071795864769252867665590057684*I, -57933.334567
! 484: 930851067108050790839116749 + 3.1415926535897932384626433832795028842*I, 345
! 485: 85.556250151557719998034043918848670 + 6.28318530717958647692528676655900576
! 486: 84*I, -23348.322511122623346549049047574325150 + 9.4247779607693797153879301
! 487: 498385086526*I, 0.34328764427702709438988786673341921876 + 0.E-48*I, 4031.71
! 488: 17453543045067063239888430083582 + 3.1415926535897932384626433832795028842*I
! 489: , -27379.690968832650826160983148550600089 + 6.28318530717958647692528676655
! 490: 90057684*I], [[3, [-1, 1]~, 1, 1, [0, 1]~], [3, [0, 1]~, 1, 1, [-1, 1]~], [5
! 491: , [-2, 1]~, 1, 1, [1, 1]~], [5, [1, 1]~, 1, 1, [-2, 1]~], [11, [-2, 1]~, 1,
! 492: 1, [1, 1]~], [11, [1, 1]~, 1, 1, [-2, 1]~], [17, [-3, 1]~, 1, 1, [2, 1]~], [
! 493: 17, [2, 1]~, 1, 1, [-3, 1]~], [19, [-1, 1]~, 1, 1, [0, 1]~], [19, [0, 1]~, 1
! 494: , 1, [-1, 1]~]]~, [1, 3, 5, 2, 4, 6, 7, 8, 10, 9]~, [x^2 - x - 57, [2, 0], 2
! 495: 29, 1, [[1, -7.0663729752107779635959310246705326058; 1, 8.06637297521077796
! 496: 35959310246705326058], [1, 1; -7.0663729752107779635959310246705326058, 8.06
! 497: 63729752107779635959310246705326058], [2, 1.00000000000000000000000000000000
! 498: 00000; 1.0000000000000000000000000000000000000, 115.000000000000000000000000
! 499: 00000000000], [2, 1; 1, 115], [229, 114; 0, 1], [115, -1; -1, 2], [229, [114
! 500: , 1]~, 229]], [-7.0663729752107779635959310246705326058, 8.06637297521077796
! 501: 35959310246705326058], [1, x], [1, 0; 0, 1], [1, 0, 0, 57; 0, 1, 1, 1]], [[3
! 502: , [3], [[3, 2; 0, 1]]], 2.7124653051843439746808795106061300699, 0.881442251
! 503: 26545793690341704100000000000, [2, -1], [x + 7], 130], [mat(1), mat(1), [[[3
! 504: , 2; 0, 1], [0, 0]]]], 0], [[[5, 3; 0, 1], [1, 0]], [8, [4, 2], [[2, 0]~, [-
! 505: 1, 1]~]], mat([[5, [-2, 1]~, 1, 1, [1, 1]~], 1]), [[[[4], [[2, 0]~], [[2, 0]
! 506: ~], [[mod(0, 2)]~], 1]], [[2], [[-1, 1]~], mat(1)]], [1, 0; 0, 1]], [[1, 0]~
! 507: ], [1, -3, -6; 0, 0, 1; 0, 1, 0], [12, [12], [[3, 2; 0, 1]]], [[0, 0; 0, 1],
! 508: [1, -1; 1, 1]]]
! 509: ? bnr2=buchrayinitgen(bnf,[[25,13;0,1],[1,1]])
! 510: [[mat(3), mat([1, 2, 1, 2, 1, 2, 1, 2, 1]), [-2.7124653051843439746808795106
! 511: 061300699 + 3.1415926535897932384626433832795028842*I; 2.7124653051843439746
! 512: 808795106061300699 - 6.2831853071795864769252867665590057684*I], [23347.9792
! 513: 23478346319454659159707591731 + 6.2831853071795864769252867665590057684*I, 8
! 514: 66.56619430687100142570357249059499540 + 6.283185307179586476925286766559005
! 515: 7684*I, 2881.3396396084587293295626563644245032 + 3.141592653589793238462643
! 516: 3832795028842*I, 27379.624790530768080428797780058276925 + 1.928186686709523
! 517: 2000000000000000000000 E-42*I, 57933.334567930851067108050790839116749 + 2.6
! 518: 904930509626865380000000000000000000 E-42*I, -34585.556250151557719998034043
! 519: 918848670 + 9.4247779607693797153879301498385086526*I, 23348.322511122623346
! 520: 549049047574325150 + 3.1415926535897932384626433832795028842*I, -0.343287644
! 521: 27702709438988786673341921876 + 3.1415926535897932384626433832795028842*I, -
! 522: 4031.7117453543045067063239888430083582 + 9.42477796076937971538793014983850
! 523: 86526*I, 27379.690968832650826160983148550600089 + 9.42477796076937971538793
! 524: 01498385086526*I; -23347.979223478346319454659159707591731 + 9.4247779607693
! 525: 797153879301498385086526*I, -866.56619430687100142570357249059499540 + 2.101
! 526: 9476959481835360000000000000000000 E-45*I, -2881.339639608458729329562656364
! 527: 4245032 + 9.4247779607693797153879301498385086526*I, -27379.6247905307680804
! 528: 28797780058276925 + 6.2831853071795864769252867665590057684*I, -57933.334567
! 529: 930851067108050790839116749 + 3.1415926535897932384626433832795028842*I, 345
! 530: 85.556250151557719998034043918848670 + 6.28318530717958647692528676655900576
! 531: 84*I, -23348.322511122623346549049047574325150 + 9.4247779607693797153879301
! 532: 498385086526*I, 0.34328764427702709438988786673341921876 + 0.E-48*I, 4031.71
! 533: 17453543045067063239888430083582 + 3.1415926535897932384626433832795028842*I
! 534: , -27379.690968832650826160983148550600089 + 6.28318530717958647692528676655
! 535: 90057684*I], [[3, [-1, 1]~, 1, 1, [0, 1]~], [3, [0, 1]~, 1, 1, [-1, 1]~], [5
! 536: , [-2, 1]~, 1, 1, [1, 1]~], [5, [1, 1]~, 1, 1, [-2, 1]~], [11, [-2, 1]~, 1,
! 537: 1, [1, 1]~], [11, [1, 1]~, 1, 1, [-2, 1]~], [17, [-3, 1]~, 1, 1, [2, 1]~], [
! 538: 17, [2, 1]~, 1, 1, [-3, 1]~], [19, [-1, 1]~, 1, 1, [0, 1]~], [19, [0, 1]~, 1
! 539: , 1, [-1, 1]~]]~, [1, 3, 5, 2, 4, 6, 7, 8, 10, 9]~, [x^2 - x - 57, [2, 0], 2
! 540: 29, 1, [[1, -7.0663729752107779635959310246705326058; 1, 8.06637297521077796
! 541: 35959310246705326058], [1, 1; -7.0663729752107779635959310246705326058, 8.06
! 542: 63729752107779635959310246705326058], [2, 1.00000000000000000000000000000000
! 543: 00000; 1.0000000000000000000000000000000000000, 115.000000000000000000000000
! 544: 00000000000], [2, 1; 1, 115], [229, 114; 0, 1], [115, -1; -1, 2], [229, [114
! 545: , 1]~, 229]], [-7.0663729752107779635959310246705326058, 8.06637297521077796
! 546: 35959310246705326058], [1, x], [1, 0; 0, 1], [1, 0, 0, 57; 0, 1, 1, 1]], [[3
! 547: , [3], [[3, 2; 0, 1]]], 2.7124653051843439746808795106061300699, 0.881442251
! 548: 26545793690341704100000000000, [2, -1], [x + 7], 130], [mat(1), mat(1), [[[3
! 549: , 2; 0, 1], [0, 0]]]], 0], [[[25, 13; 0, 1], [1, 1]], [80, [20, 2, 2], [[2,
! 550: 0]~, [0, -2]~, [2, 2]~]], mat([[5, [-2, 1]~, 1, 1, [1, 1]~], 2]), [[[[4], [[
! 551: 2, 0]~], [[2, 0]~], [[mod(0, 2), mod(0, 2)]~], 1], [[5], [[6, 0]~], [[6, 0]~
! 552: ], [[mod(0, 2), mod(0, 2)]~], mat([1/5, -13/5])]], [[2, 2], [[0, -2]~, [2, 2
! 553: ]~], [0, 1; 1, 0]]], [1, -12, 0, 0; 0, 0, 1, 0; 0, 0, 0, 1]], [[1, 0]~], [1,
! 554: -3, 0, -6; 0, 0, 1, 0; 0, 0, 0, 1; 0, 1, 0, 0], [12, [12], [[3, 2; 0, 1]]],
! 555: [[1/2, 5, -9; -1/2, -5, 10], [-2, 0; 0, 10]]]
! 556: ? bytesize(%)
! 557: 7532
! 558: ? ceil(-2.5)
! 559: -2
! 560: ? centerlift(mod(456,555))
! 561: -99
! 562: ? cf(pi)
! 563: [3, 7, 15, 1, 292, 1, 1, 1, 2, 1, 3, 1, 14, 2, 1, 1, 2, 2, 2, 2, 1, 84, 2, 1
! 564: , 1, 15, 3, 13, 1, 4, 2, 6, 6]
! 565: ? cf2([1,3,5,7,9],(exp(1)-1)/(exp(1)+1))
! 566: [0, 6, 10, 42, 30]
! 567: ? changevar(x+y,[z,t])
! 568: y + z
! 569: ? char([1,2;3,4],z)
! 570: z^2 - 5*z - 2
! 571: ? char(mod(x^2+x+1,x^3+5*x+1),z)
! 572: z^3 + 7*z^2 + 16*z - 19
! 573: ? char1([1,2;3,4],z)
! 574: z^2 - 5*z - 2
! 575: ? char2(mod(1,8191)*[1,2;3,4],z)
! 576: mod(1, 8191)*z^2 + mod(8186, 8191)*z + mod(8189, 8191)
! 577: ? acurve=chell(acurve,[-1,1,2,3])
! 578: [-4, -1, -7, -12, -12, 12, 4, 1, -1, 48, -216, 37, 110592/37, [-0.1624345647
! 579: 1667696455518910092496975959, -0.73040556359455544173706204865073999595, -2.
! 580: 1071598716887675937077488504242902444]~, -2.99345864623195962983200997945250
! 581: 81778, -2.4513893819867900608542248318665252253*I, 0.47131927795681147588259
! 582: 389708033769964, 1.4354565186686843187232088566788165076*I, 7.33813274078957
! 583: 67390707210033323055881]
! 584: ? chinese(mod(7,15),mod(13,21))
! 585: mod(97, 105)
! 586: ? apoint=chptell(apoint,[-1,1,2,3])
! 587: [1, 3]
! 588: ? isoncurve(acurve,apoint)
! 589: 1
! 590: ? classno(-12391)
! 591: 63
! 592: ? classno(1345)
! 593: 6
! 594: ? classno2(-12391)
! 595: 63
! 596: ? classno2(1345)
! 597: 6
! 598: ? coeff(sin(x),7)
! 599: -1/5040
! 600: ? compimag(qfi(2,1,3),qfi(2,1,3))
! 601: qfi(2, -1, 3)
! 602: ? compo(1+o(7^4),3)
! 603: 1
! 604: ? compositum(x^4-4*x+2,x^3-x-1)
! 605: [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
! 606: ^2 - 128*x - 5]~
! 607: ? compositum2(x^4-4*x+2,x^3-x-1)
! 608: [[x^12 - 4*x^10 + 8*x^9 + 12*x^8 + 12*x^7 + 138*x^6 + 132*x^5 - 43*x^4 + 58*
! 609: x^2 - 128*x - 5, mod(-279140305176/29063006931199*x^11 + 129916611552/290630
! 610: 06931199*x^10 + 1272919322296/29063006931199*x^9 - 2813750209005/29063006931
! 611: 199*x^8 - 2859411937992/29063006931199*x^7 - 414533880536/29063006931199*x^6
! 612: - 35713977492936/29063006931199*x^5 - 17432607267590/29063006931199*x^4 + 4
! 613: 9785595543672/29063006931199*x^3 + 9423768373204/29063006931199*x^2 - 427797
! 614: 76146743/29063006931199*x + 37962587857138/29063006931199, x^12 - 4*x^10 + 8
! 615: *x^9 + 12*x^8 + 12*x^7 + 138*x^6 + 132*x^5 - 43*x^4 + 58*x^2 - 128*x - 5), m
! 616: od(-279140305176/29063006931199*x^11 + 129916611552/29063006931199*x^10 + 12
! 617: 72919322296/29063006931199*x^9 - 2813750209005/29063006931199*x^8 - 28594119
! 618: 37992/29063006931199*x^7 - 414533880536/29063006931199*x^6 - 35713977492936/
! 619: 29063006931199*x^5 - 17432607267590/29063006931199*x^4 + 49785595543672/2906
! 620: 3006931199*x^3 + 9423768373204/29063006931199*x^2 - 13716769215544/290630069
! 621: 31199*x + 37962587857138/29063006931199, x^12 - 4*x^10 + 8*x^9 + 12*x^8 + 12
! 622: *x^7 + 138*x^6 + 132*x^5 - 43*x^4 + 58*x^2 - 128*x - 5), -1]]
! 623: ? comprealraw(qfr(5,3,-1,0.),qfr(7,1,-1,0.))
! 624: qfr(35, 43, 13, 0.E-38)
! 625: ? concat([1,2],[3,4])
! 626: [1, 2, 3, 4]
! 627: ? conductor(bnf,[[25,13;0,1],[1,1]])
! 628: [[[5, 3; 0, 1], [1, 0]], [12, [12], [[3, 2; 0, 1]]], mat(12)]
! 629: ? conductorofchar(bnr,[2])
! 630: [[5, 3; 0, 1], [0, 0]]
! 631: ? conj(1+i)
! 632: 1 - I
! 633: ? conjvec(mod(x^2+x+1,x^3-x-1))
! 634: [4.0795956234914387860104177508366260325, 0.46020218825428060699479112458168
! 635: 698369 + 0.18258225455744299269398828369501930573*I, 0.460202188254280606994
! 636: 79112458168698369 - 0.18258225455744299269398828369501930573*I]~
! 637: ? content([123,456,789,234])
! 638: 3
! 639: ? convol(sin(x),x*cos(x))
! 640: x + 1/12*x^3 + 1/2880*x^5 + 1/3628800*x^7 + 1/14631321600*x^9 + 1/1448500838
! 641: 40000*x^11 + 1/2982752926433280000*x^13 + 1/114000816848279961600000*x^15 +
! 642: O(x^16)
! 643: ? core(54713282649239)
! 644: 5471
! 645: ? core2(54713282649239)
! 646: [5471, 100003]
! 647: ? coredisc(54713282649239)
! 648: 21884
! 649: ? coredisc2(54713282649239)
! 650: [21884, 100003/2]
! 651: ? cos(1)
! 652: 0.54030230586813971740093660744297660373
! 653: ? cosh(1)
! 654: 1.5430806348152437784779056207570616825
! 655: ? move(0,200,150)
! 656: ? cursor(0)
! 657: ? cvtoi(1.7)
! 658: 1
! 659: ? cyclo(105)
! 660: x^48 + x^47 + x^46 - x^43 - x^42 - 2*x^41 - x^40 - x^39 + x^36 + x^35 + x^34
! 661: + x^33 + x^32 + x^31 - x^28 - x^26 - x^24 - x^22 - x^20 + x^17 + x^16 + x^1
! 662: 5 + x^14 + x^13 + x^12 - x^9 - x^8 - 2*x^7 - x^6 - x^5 + x^2 + x + 1
! 663: ? degree(x^3/(x-1))
! 664: 2
! 665: ? denom(12345/54321)
! 666: 18107
! 667: ? deplin(mod(1,7)*[2,-1;1,3])
! 668: [mod(6, 7), mod(5, 7)]~
! 669: ? deriv((x+y)^5,y)
! 670: 5*x^4 + 20*y*x^3 + 30*y^2*x^2 + 20*y^3*x + 5*y^4
! 671: ? ((x+y)^5)'
! 672: 5*x^4 + 20*y*x^3 + 30*y^2*x^2 + 20*y^3*x + 5*y^4
! 673: ? det([1,2,3;1,5,6;9,8,7])
! 674: -30
! 675: ? det2([1,2,3;1,5,6;9,8,7])
! 676: -30
! 677: ? detint([1,2,3;4,5,6])
! 678: 3
! 679: ? diagonal([2,4,6])
! 680:
! 681: [2 0 0]
! 682:
! 683: [0 4 0]
! 684:
! 685: [0 0 6]
! 686:
! 687: ? dilog(0.5)
! 688: 0.58224052646501250590265632015968010858
! 689: ? dz=vector(30,k,1);dd=vector(30,k,k==1);dm=dirdiv(dd,dz)
! 690: [1, -1, -1, 0, -1, 1, -1, 0, 0, 1, -1, 0, -1, 1, 1, 0, -1, 0, -1, 0, 1, 1, -
! 691: 1, 0, 0, 1, 0, 0, -1, -1]
! 692: ? deu=direuler(p=2,100,1/(1-apell(acurve,p)*x+if(acurve[12]%p,p,0)*x^2))
! 693: [1, -2, -3, 2, -2, 6, -1, 0, 6, 4, -5, -6, -2, 2, 6, -4, 0, -12, 0, -4, 3, 1
! 694: 0, 2, 0, -1, 4, -9, -2, 6, -12, -4, 8, 15, 0, 2, 12, -1, 0, 6, 0, -9, -6, 2,
! 695: -10, -12, -4, -9, 12, -6, 2, 0, -4, 1, 18, 10, 0, 0, -12, 8, 12, -8, 8, -6,
! 696: -8, 4, -30, 8, 0, -6, -4, 9, 0, -1, 2, 3, 0, 5, -12, 4, 8, 9, 18, -15, 6, 0
! 697: , -4, -18, 0, 4, 24, 2, 4, 12, 18, 0, -24, 4, 12, -30, -2]
! 698: ? anell(acurve,100)==deu
! 699: 1
! 700: ? dirmul(abs(dm),dz)
! 701: [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,
! 702: 4, 2, 4, 2, 8]
! 703: ? dirzetak(initalg(x^3-10*x+8),30)
! 704: [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,
! 705: 0, 1, 0, 1, 0]
! 706: ? disc(x^3+4*x+12)
! 707: -4144
! 708: ? discf(x^3+4*x+12)
! 709: -1036
! 710: ? discrayabs(bnr,mat(6))
! 711: [12, 12, 18026977100265125]
! 712: ? discrayabs(bnr)
! 713: [24, 12, 40621487921685401825918161408203125]
! 714: ? discrayabscond(bnr2)
! 715: 0
! 716: ? lu=ideallistunitgen(bnf,55);discrayabslist(bnf,lu)
! 717: [[[6, 6, mat([229, 3])]], [], [[], []], [[]], [[12, 12, [5, 3; 229, 6]], [12
! 718: , 12, [5, 3; 229, 6]]], [], [], [], [[], [], []], [], [[], []], [[], []], []
! 719: , [], [[24, 24, [3, 6; 5, 9; 229, 12]], [], [], [24, 24, [3, 6; 5, 9; 229, 1
! 720: 2]]], [[]], [[], []], [], [[18, 18, [19, 6; 229, 9]], [18, 18, [19, 6; 229,
! 721: 9]]], [[], []], [], [], [], [], [[], [24, 24, [5, 12; 229, 12]], []], [], [[
! 722: ], [], [], []], [], [], [], [], [], [[], [12, 12, [3, 3; 11, 3; 229, 6]], [1
! 723: 2, 12, [3, 3; 11, 3; 229, 6]], []], [], [], [[18, 18, [2, 12; 3, 12; 229, 9]
! 724: ], [], [18, 18, [2, 12; 3, 12; 229, 9]]], [[12, 12, [37, 3; 229, 6]], [12, 1
! 725: 2, [37, 3; 229, 6]]], [], [], [], [], [], [[], []], [[], []], [[], [], [], [
! 726: ], [], []], [], [], [[12, 12, [2, 12; 3, 3; 229, 6]], [12, 12, [2, 12; 3, 3;
! 727: 229, 6]]], [[18, 18, [7, 12; 229, 9]]], [], [[], [], [], []], [], [[], []],
! 728: [], [[], [24, 24, [5, 9; 11, 6; 229, 12]], [24, 24, [5, 9; 11, 6; 229, 12]]
! 729: , []]]
! 730: ? discrayabslistlong(bnf,20)
! 731: [[[[matrix(0,2,j,k,0), 6, 6, mat([229, 3])]], [], [[mat([12, 1]), 0, 0, 0],
! 732: [mat([13, 1]), 0, 0, 0]], [[mat([10, 1]), 0, 0, 0]], [[mat([20, 1]), 12, 12,
! 733: [5, 3; 229, 6]], [mat([21, 1]), 12, 12, [5, 3; 229, 6]]], [], [], [], [[mat
! 734: ([12, 2]), 0, 0, 0], [[12, 1; 13, 1], 0, 0, 0], [mat([13, 2]), 0, 0, 0]], []
! 735: , [[mat([44, 1]), 0, 0, 0], [mat([45, 1]), 0, 0, 0]], [[[10, 1; 12, 1], 0, 0
! 736: , 0], [[10, 1; 13, 1], 0, 0, 0]], [], [], [[[12, 1; 20, 1], 24, 24, [3, 6; 5
! 737: , 9; 229, 12]], [[13, 1; 20, 1], 0, 0, 0], [[12, 1; 21, 1], 0, 0, 0], [[13,
! 738: 1; 21, 1], 24, 24, [3, 6; 5, 9; 229, 12]]], [[mat([10, 2]), 0, 0, 0]], [[mat
! 739: ([68, 1]), 0, 0, 0], [mat([69, 1]), 0, 0, 0]], [], [[mat([76, 1]), 18, 18, [
! 740: 19, 6; 229, 9]], [mat([77, 1]), 18, 18, [19, 6; 229, 9]]], [[[10, 1; 20, 1],
! 741: 0, 0, 0], [[10, 1; 21, 1], 0, 0, 0]]]]
! 742: ? discrayrel(bnr,mat(6))
! 743: [6, 2, [125, 13; 0, 1]]
! 744: ? discrayrel(bnr)
! 745: [12, 1, [1953125, 1160888; 0, 1]]
! 746: ? discrayrelcond(bnr2)
! 747: 0
! 748: ? divisors(8!)
! 749: [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 14, 15, 16, 18, 20, 21, 24, 28, 30, 32,
! 750: 35, 36, 40, 42, 45, 48, 56, 60, 63, 64, 70, 72, 80, 84, 90, 96, 105, 112, 12
! 751: 0, 126, 128, 140, 144, 160, 168, 180, 192, 210, 224, 240, 252, 280, 288, 315
! 752: , 320, 336, 360, 384, 420, 448, 480, 504, 560, 576, 630, 640, 672, 720, 840,
! 753: 896, 960, 1008, 1120, 1152, 1260, 1344, 1440, 1680, 1920, 2016, 2240, 2520,
! 754: 2688, 2880, 3360, 4032, 4480, 5040, 5760, 6720, 8064, 10080, 13440, 20160,
! 755: 40320]
! 756: ? divres(345,123)
! 757: [2, 99]~
! 758: ? divres(x^7-1,x^5+1)
! 759: [x^2, -x^2 - 1]~
! 760: ? divsum(8!,x,x)
! 761: 159120
! 762: ? postdraw([0,0,0])
! 763: ? eigen([1,2,3;4,5,6;7,8,9])
! 764:
! 765: [-1.2833494518006402717978106547571267252 1 0.283349451800640271797810654757
! 766: 12672521]
! 767:
! 768: [-0.14167472590032013589890532737856336261 -2 0.6416747259003201358989053273
! 769: 7856336260]
! 770:
! 771: [1 1 1]
! 772:
! 773: ? eint1(2)
! 774: 0.048900510708061119567239835228049522206
! 775: ? erfc(2)
! 776: 0.0046777349810472658379307436327470713891
! 777: ? eta(q)
! 778: 1 - q - q^2 + q^5 + q^7 - q^12 - q^15 + O(q^16)
! 779: ? euler
! 780: 0.57721566490153286060651209008240243104
! 781: ? z=y;y=x;eval(z)
! 782: x
! 783: ? exp(1)
! 784: 2.7182818284590452353602874713526624977
! 785: ? extract([1,2,3,4,5,6,7,8,9,10],1000)
! 786: [4, 6, 7, 8, 9, 10]
! 787: ? 10!
! 788: 3628800
! 789: ? fact(10)
! 790: 3628800.0000000000000000000000000000000
! 791: ? factcantor(x^11+1,7)
! 792:
! 793: [mod(1, 7)*x + mod(1, 7) 1]
! 794:
! 795: [mod(1, 7)*x^10 + mod(6, 7)*x^9 + mod(1, 7)*x^8 + mod(6, 7)*x^7 + mod(1, 7)*
! 796: x^6 + mod(6, 7)*x^5 + mod(1, 7)*x^4 + mod(6, 7)*x^3 + mod(1, 7)*x^2 + mod(6,
! 797: 7)*x + mod(1, 7) 1]
! 798:
! 799: ? centerlift(lift(factfq(x^3+x^2+x-1,3,t^3+t^2+t-1)))
! 800:
! 801: [x - t 1]
! 802:
! 803: [x + (t^2 + t - 1) 1]
! 804:
! 805: [x + (-t^2 - 1) 1]
! 806:
! 807: ? factmod(x^11+1,7)
! 808:
! 809: [mod(1, 7)*x + mod(1, 7) 1]
! 810:
! 811: [mod(1, 7)*x^10 + mod(6, 7)*x^9 + mod(1, 7)*x^8 + mod(6, 7)*x^7 + mod(1, 7)*
! 812: x^6 + mod(6, 7)*x^5 + mod(1, 7)*x^4 + mod(6, 7)*x^3 + mod(1, 7)*x^2 + mod(6,
! 813: 7)*x + mod(1, 7) 1]
! 814:
! 815: ? factor(17!+1)
! 816:
! 817: [661 1]
! 818:
! 819: [537913 1]
! 820:
! 821: [1000357 1]
! 822:
! 823: ? p=x^5+3021*x^4-786303*x^3-6826636057*x^2-546603588746*x+3853890514072057
! 824: x^5 + 3021*x^4 - 786303*x^3 - 6826636057*x^2 - 546603588746*x + 385389051407
! 825: 2057
! 826: ? fa=[11699,6;2392997,2;4987333019653,2]
! 827:
! 828: [11699 6]
! 829:
! 830: [2392997 2]
! 831:
! 832: [4987333019653 2]
! 833:
! 834: ? factoredbasis(p,fa)
! 835: [1, x, x^2, 1/11699*x^3 + 1847/11699*x^2 - 132/11699*x - 2641/11699, 1/13962
! 836: 3738889203638909659*x^4 - 1552451622081122020/139623738889203638909659*x^3 +
! 837: 418509858130821123141/139623738889203638909659*x^2 - 6810913798507599407313
! 838: 4/139623738889203638909659*x - 13185339461968406/58346808996920447]
! 839: ? factoreddiscf(p,fa)
! 840: 136866601
! 841: ? factoredpolred(p,fa)
! 842: [x - 1, x^5 - 2*x^4 - 62*x^3 + 85*x^2 + 818*x + 1, x^5 - 2*x^4 - 53*x^3 - 46
! 843: *x^2 + 508*x + 913, x^5 - 2*x^4 - 13*x^3 + 37*x^2 - 21*x - 1, x^5 - x^4 - 52
! 844: *x^3 - 197*x^2 - 273*x - 127]
! 845: ? factoredpolred2(p,fa)
! 846:
! 847: [1 x - 1]
! 848:
! 849: [320031469790/139623738889203638909659*x^4 + 525154323698149/139623738889203
! 850: 638909659*x^3 + 68805502220272624/139623738889203638909659*x^2 + 11626197624
! 851: 4907072724/139623738889203638909659*x - 265513916545157609/58346808996920447
! 852: x^5 - 2*x^4 - 62*x^3 + 85*x^2 + 818*x + 1]
! 853:
! 854: [-649489679500/139623738889203638909659*x^4 - 1004850936416946/1396237388892
! 855: 03638909659*x^3 + 1850137668999773331/139623738889203638909659*x^2 + 1162464
! 856: 435118744503168/139623738889203638909659*x - 744221404070129897/583468089969
! 857: 20447 x^5 - 2*x^4 - 53*x^3 - 46*x^2 + 508*x + 913]
! 858:
! 859: [404377049971/139623738889203638909659*x^4 + 1028343729806593/13962373888920
! 860: 3638909659*x^3 - 220760129739668913/139623738889203638909659*x^2 - 139192454
! 861: 3479498840309/139623738889203638909659*x - 21580477171925514/583468089969204
! 862: 47 x^5 - 2*x^4 - 13*x^3 + 37*x^2 - 21*x - 1]
! 863:
! 864: [160329790087/139623738889203638909659*x^4 + 1043812506369034/13962373888920
! 865: 3638909659*x^3 + 1517006779298914407/139623738889203638909659*x^2 - 52234888
! 866: 8528537141362/139623738889203638909659*x - 677624890046649103/58346808996920
! 867: 447 x^5 - x^4 - 52*x^3 - 197*x^2 - 273*x - 127]
! 868:
! 869: ? factornf(x^3+x^2-2*x-1,t^3+t^2-2*t-1)
! 870:
! 871: [mod(1, t^3 + t^2 - 2*t - 1)*x + mod(-t, t^3 + t^2 - 2*t - 1) 1]
! 872:
! 873: [mod(1, t^3 + t^2 - 2*t - 1)*x + mod(-t^2 + 2, t^3 + t^2 - 2*t - 1) 1]
! 874:
! 875: [mod(1, t^3 + t^2 - 2*t - 1)*x + mod(t^2 + t - 1, t^3 + t^2 - 2*t - 1) 1]
! 876:
! 877: ? factorpadic(apol,7,8)
! 878:
! 879: [(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]
! 880:
! 881: [(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
! 882: ))*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]
! 883:
! 884: ? factorpadic2(apol,7,8)
! 885:
! 886: [(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]
! 887:
! 888: [(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
! 889: ))*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]
! 890:
! 891: ? factpol(x^15-1,3,1)
! 892:
! 893: [x - 1 1]
! 894:
! 895: [x^2 + x + 1 1]
! 896:
! 897: [x^12 + x^9 + x^6 + x^3 + 1 1]
! 898:
! 899: ? factpol(x^15-1,0,1)
! 900:
! 901: [x - 1 1]
! 902:
! 903: [x^2 + x + 1 1]
! 904:
! 905: [x^4 + x^3 + x^2 + x + 1 1]
! 906:
! 907: [x^8 - x^7 + x^5 - x^4 + x^3 - x + 1 1]
! 908:
! 909: ? factpol2(x^15-1,0)
! 910:
! 911: [x - 1 1]
! 912:
! 913: [x^2 + x + 1 1]
! 914:
! 915: [x^4 + x^3 + x^2 + x + 1 1]
! 916:
! 917: [x^8 - x^7 + x^5 - x^4 + x^3 - x + 1 1]
! 918:
! 919: ? fibo(100)
! 920: 354224848179261915075
! 921: ? floor(-1/2)
! 922: -1
! 923: ? floor(-2.5)
! 924: -3
! 925: ? for(x=1,5,print(x!))
! 926: 1
! 927: 2
! 928: 6
! 929: 24
! 930: 120
! 931: ? fordiv(10,x,print(x))
! 932: 1
! 933: 2
! 934: 5
! 935: 10
! 936: ? forprime(p=1,30,print(p))
! 937: 2
! 938: 3
! 939: 5
! 940: 7
! 941: 11
! 942: 13
! 943: 17
! 944: 19
! 945: 23
! 946: 29
! 947: ? forstep(x=0,pi,pi/12,print(sin(x)))
! 948: 0.E-38
! 949: 0.25881904510252076234889883762404832834
! 950: 0.49999999999999999999999999999999999999
! 951: 0.70710678118654752440084436210484903928
! 952: 0.86602540378443864676372317075293618346
! 953: 0.96592582628906828674974319972889736763
! 954: 1.0000000000000000000000000000000000000
! 955: 0.96592582628906828674974319972889736764
! 956: 0.86602540378443864676372317075293618348
! 957: 0.70710678118654752440084436210484903930
! 958: 0.50000000000000000000000000000000000002
! 959: 0.25881904510252076234889883762404832838
! 960: 4.7019774032891500318749461488889827112 E-38
! 961: ? forvec(x=[[1,3],[-2,2]],print1([x[1],x[2]]," "));print(" ");
! 962: [1, -2] [1, -1] [1, 0] [1, 1] [1, 2] [2, -2] [2, -1] [2, 0] [2, 1] [2, 2] [3
! 963: , -2] [3, -1] [3, 0] [3, 1] [3, 2]
! 964: ? frac(-2.7)
! 965: 0.30000000000000000000000000000000000000
! 966: ? galois(x^6-3*x^2-1)
! 967: [12, 1, 1]
! 968: ? nf3=initalg(x^6+108);galoisconj(nf3)
! 969: [-x, x, -1/12*x^4 - 1/2*x, -1/12*x^4 + 1/2*x, 1/12*x^4 - 1/2*x, 1/12*x^4 + 1
! 970: /2*x]~
! 971: ? galoisconjforce(nf3)
! 972: *** this function has been suppressed.
! 973:
! 974: ? aut=%[2];galoisapply(nf3,aut,mod(x^5,x^6+108))
! 975: mod(x^5, x^6 + 108)
! 976: ? gamh(10)
! 977: 1133278.3889487855673345741655888924755
! 978: ? gamma(10.5)
! 979: 1133278.3889487855673345741655888924755
! 980: ? gauss(hilbert(10),[1,2,3,4,5,6,7,8,9,0]~)
! 981: [9236800, -831303990, 18288515520, -170691240720, 832112321040, -23298940665
! 982: 00, 3883123564320, -3803844432960, 2020775945760, -449057772020]~
! 983: ? gaussmodulo([2,3;5,4],[7,11],[1,4]~)
! 984: [-5, -1]~
! 985: ? gaussmodulo2([2,3;5,4],[7,11],[1,4]~)
! 986: [[-5, -1]~, [-77, 723; 0, 1]]
! 987: ? gcd(12345678,87654321)
! 988: 9
! 989: ? getheap()
! 990: [214, 48887]
! 991: ? getrand()
! 992: 1285582432
! 993: ? getstack()
! 994: 0
! 995: ? globalred(acurve)
! 996: [37, [1, -1, 2, 2], 1]
! 997: ? getstack()
! 998: 0
! 999: ? hclassno(2000003)
! 1000: 357
! 1001: ? hell(acurve,apoint)
! 1002: 0.40889126591975072188708879805553617287
! 1003: ? hell2(acurve,apoint)
! 1004: 0.40889126591975072188708879805553617296
! 1005: ? hermite(amat=1/hilbert(7))
! 1006:
! 1007: [420 0 0 0 210 168 175]
! 1008:
! 1009: [0 840 0 0 0 0 504]
! 1010:
! 1011: [0 0 2520 0 0 0 1260]
! 1012:
! 1013: [0 0 0 2520 0 0 840]
! 1014:
! 1015: [0 0 0 0 13860 0 6930]
! 1016:
! 1017: [0 0 0 0 0 5544 0]
! 1018:
! 1019: [0 0 0 0 0 0 12012]
! 1020:
! 1021: ? hermite2(amat)
! 1022: [[420, 0, 0, 0, 210, 168, 175; 0, 840, 0, 0, 0, 0, 504; 0, 0, 2520, 0, 0, 0,
! 1023: 1260; 0, 0, 0, 2520, 0, 0, 840; 0, 0, 0, 0, 13860, 0, 6930; 0, 0, 0, 0, 0,
! 1024: 5544, 0; 0, 0, 0, 0, 0, 0, 12012], [420, 420, 840, 630, 2982, 1092, 4159; 21
! 1025: 0, 280, 630, 504, 2415, 876, 3395; 140, 210, 504, 420, 2050, 749, 2901; 105,
! 1026: 168, 420, 360, 1785, 658, 2542; 84, 140, 360, 315, 1582, 588, 2266; 70, 120
! 1027: , 315, 280, 1421, 532, 2046; 60, 105, 280, 252, 1290, 486, 1866]]
! 1028: ? hermitehavas(amat)
! 1029: [[360360, 0, 0, 0, 0, 144144, 300300; 0, 27720, 0, 0, 0, 0, 22176; 0, 0, 277
! 1030: 20, 0, 0, 0, 6930; 0, 0, 0, 2520, 0, 0, 840; 0, 0, 0, 0, 2520, 0, 1260; 0, 0
! 1031: , 0, 0, 0, 168, 0; 0, 0, 0, 0, 0, 0, 7], [51480, 4620, 5544, 630, 840, 20676
! 1032: , 48619; 45045, 3960, 4620, 504, 630, 18074, 42347; 40040, 3465, 3960, 420,
! 1033: 504, 16058, 37523; 36036, 3080, 3465, 360, 420, 14448, 33692; 32760, 2772, 3
! 1034: 080, 315, 360, 13132, 30574; 30030, 2520, 2772, 280, 315, 12036, 27986; 2772
! 1035: 0, 2310, 2520, 252, 280, 11109, 25803], [7, 6, 5, 4, 3, 2, 1]]
! 1036: ? hermitemod(amat,detint(amat))
! 1037:
! 1038: [420 0 0 0 210 168 175]
! 1039:
! 1040: [0 840 0 0 0 0 504]
! 1041:
! 1042: [0 0 2520 0 0 0 1260]
! 1043:
! 1044: [0 0 0 2520 0 0 840]
! 1045:
! 1046: [0 0 0 0 13860 0 6930]
! 1047:
! 1048: [0 0 0 0 0 5544 0]
! 1049:
! 1050: [0 0 0 0 0 0 12012]
! 1051:
! 1052: ? hermiteperm(amat)
! 1053: [[360360, 0, 0, 0, 0, 144144, 300300; 0, 27720, 0, 0, 0, 0, 22176; 0, 0, 277
! 1054: 20, 0, 0, 0, 6930; 0, 0, 0, 2520, 0, 0, 840; 0, 0, 0, 0, 2520, 0, 1260; 0, 0
! 1055: , 0, 0, 0, 168, 0; 0, 0, 0, 0, 0, 0, 7], [51480, 4620, 5544, 630, 840, 20676
! 1056: , 48619; 45045, 3960, 4620, 504, 630, 18074, 42347; 40040, 3465, 3960, 420,
! 1057: 504, 16058, 37523; 36036, 3080, 3465, 360, 420, 14448, 33692; 32760, 2772, 3
! 1058: 080, 315, 360, 13132, 30574; 30030, 2520, 2772, 280, 315, 12036, 27986; 2772
! 1059: 0, 2310, 2520, 252, 280, 11109, 25803], [7, 6, 5, 4, 3, 2, 1]]
! 1060: ? hess(hilbert(7))
! 1061:
! 1062: [1 90281/58800 -1919947/4344340 4858466341/1095033030 -77651417539/819678732
! 1063: 6 3386888964/106615355 1/2]
! 1064:
! 1065: [1/3 43/48 38789/5585580 268214641/109503303 -581330123627/126464718744 4365
! 1066: 450643/274153770 1/4]
! 1067:
! 1068: [0 217/2880 442223/7447440 53953931/292008808 -32242849453/168619624992 1475
! 1069: 457901/1827691800 1/80]
! 1070:
! 1071: [0 0 1604444/264539275 24208141/149362505292 847880210129/47916076768560 -45
! 1072: 44407141/103873817300 -29/40920]
! 1073:
! 1074: [0 0 0 9773092581/35395807550620 -24363634138919/107305824577186620 72118203
! 1075: 606917/60481351061158500 55899/3088554700]
! 1076:
! 1077: [0 0 0 0 67201501179065/8543442888354179988 -9970556426629/74082861999267660
! 1078: 0 -3229/13661312210]
! 1079:
! 1080: [0 0 0 0 0 -258198800769/9279048099409000 -13183/38381527800]
! 1081:
! 1082: ? hilb(2/3,3/4,5)
! 1083: 1
! 1084: ? hilbert(5)
! 1085:
! 1086: [1 1/2 1/3 1/4 1/5]
! 1087:
! 1088: [1/2 1/3 1/4 1/5 1/6]
! 1089:
! 1090: [1/3 1/4 1/5 1/6 1/7]
! 1091:
! 1092: [1/4 1/5 1/6 1/7 1/8]
! 1093:
! 1094: [1/5 1/6 1/7 1/8 1/9]
! 1095:
! 1096: ? hilbp(mod(5,7),mod(6,7))
! 1097: 1
! 1098: ? hvector(10,x,1/x)
! 1099: [1, 1/2, 1/3, 1/4, 1/5, 1/6, 1/7, 1/8, 1/9, 1/10]
! 1100: ? hyperu(1,1,1)
! 1101: 0.59634736232319407434107849936927937488
! 1102: ? i^2
! 1103: -1
! 1104: ? nf1=initalgred(nfpol)
! 1105: [x^5 - 2*x^4 + 3*x^3 + 8*x^2 + 3*x + 2, [1, 2], 595125, 4, [[1, -1.089115145
! 1106: 7205048250249527946671612684, 1.1861718006377964594796293860483989860, -0.59
! 1107: 741050929194782733001765987770358483, 0.158944197453903762065494816710718942
! 1108: 89; 1, -0.13838372073406036365047976417441696637 + 0.49181637657768643499753
! 1109: 285514741525107*I, -0.22273329410580226599155701611419649154 - 0.13611876021
! 1110: 752805221674918029071012580*I, -0.13167445871785818798769651537619416009 + 0
! 1111: .13249517760521973840801462296650806543*I, -0.053650958656997725359297528357
! 1112: 602608116 + 0.27622636814169107038138284681568361486*I; 1, 1.682941293594312
! 1113: 7761629561615079976005 + 2.0500351226010726172974286983598602163*I, -1.37035
! 1114: 26062130959637482576769100030014 + 6.9001775222880494773720769629846373016*I
! 1115: , -8.0696202866361678983472946546849540475 + 8.87676767859710424508852843013
! 1116: 48051602*I, -22.025821140069954155673449879997756863 - 8.4306586896999153544
! 1117: 710860185447589664*I], [1, 2, 2; -1.0891151457205048250249527946671612684, -
! 1118: 0.27676744146812072730095952834883393274 - 0.9836327531553728699950657102948
! 1119: 3050214*I, 3.3658825871886255523259123230159952011 - 4.100070245202145234594
! 1120: 8573967197204327*I; 1.1861718006377964594796293860483989860, -0.445466588211
! 1121: 60453198311403222839298308 + 0.27223752043505610443349836058142025160*I, -2.
! 1122: 7407052124261919274965153538200060029 - 13.800355044576098954744153925969274
! 1123: 603*I; -0.59741050929194782733001765987770358483, -0.26334891743571637597539
! 1124: 303075238832018 - 0.26499035521043947681602924593301613087*I, -16.1392405732
! 1125: 72335796694589309369908095 - 17.753535357194208490177056860269610320*I; 0.15
! 1126: 894419745390376206549481671071894289, -0.10730191731399545071859505671520521
! 1127: 623 - 0.55245273628338214076276569363136722973*I, -44.0516422801399083113468
! 1128: 99759995513726 + 16.861317379399830708942172037089517932*I], [5, 2.000000000
! 1129: 0000000000000000000000000000, -2.0000000000000000000000000000000000000, -17.
! 1130: 000000000000000000000000000000000000, -44.0000000000000000000000000000000000
! 1131: 00; 2.0000000000000000000000000000000000000, 15.7781094086719980448363574712
! 1132: 83695361, 22.314643349754061651916553814602769764, 10.0513952578314782754999
! 1133: 32716306366248, -108.58917507620841447456569092094763671; -2.000000000000000
! 1134: 0000000000000000000000, 22.314643349754061651916553814602769764, 100.5239126
! 1135: 2388960975827806174040462368, 143.93295090847353519436673793501057176, -55.8
! 1136: 42564718082452641322500190813370023; -17.00000000000000000000000000000000000
! 1137: 0, 10.051395257831478275499932716306366248, 143.9329509084735351943667379350
! 1138: 1057176, 288.25823756749944693139292174819167135, 205.7984003827766237572018
! 1139: 0649465932302; -44.000000000000000000000000000000000000, -108.58917507620841
! 1140: 447456569092094763671, -55.842564718082452641322500190813370023, 205.7984003
! 1141: 8277662375720180649465932302, 1112.6092277946777707779250962522343036], [5,
! 1142: 2, -2, -17, -44; 2, -2, -34, -63, -40; -2, -34, -90, -101, 177; -17, -63, -1
! 1143: 01, -27, 505; -44, -40, 177, 505, 828], [345, 0, 160, 252, 156; 0, 345, 215,
! 1144: 311, 306; 0, 0, 5, 3, 2; 0, 0, 0, 1, 0; 0, 0, 0, 0, 1], [163875, -388125, -
! 1145: 296700, 234600, -89700; -388125, -1593900, -677925, 595125, -315675; -296700
! 1146: , -677925, 17250, 58650, -87975; 234600, 595125, 58650, -100050, 89700; -897
! 1147: 00, -315675, -87975, 89700, -55200], [595125, [-167325, -82800, 79350, 1725,
! 1148: 0]~, 125439056256992431640625]], [-1.0891151457205048250249527946671612684,
! 1149: -0.13838372073406036365047976417441696637 + 0.49181637657768643499753285514
! 1150: 741525107*I, 1.6829412935943127761629561615079976005 + 2.0500351226010726172
! 1151: 974286983598602163*I], [1, x, x^2, 1/2*x^3 + 1/2*x^2 + 1/2*x, 1/2*x^4 + 1/2*
! 1152: x], [1, 0, 0, 0, 0; 0, 1, 0, -1, -1; 0, 0, 1, -1, 0; 0, 0, 0, 2, 0; 0, 0, 0,
! 1153: 0, 2], [1, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, -1, -2, 0, 0, -1, -2, -2, 0
! 1154: , -1, -2, -2, 5; 0, 1, 0, 0, 0, 1, 0, -1, -1, -1, 0, -1, -1, -2, 2, 0, -1, -
! 1155: 2, -1, 7, 0, -1, 2, 7, 14; 0, 0, 1, 0, 0, 0, 1, -1, 0, -2, 1, -1, 0, -3, -3,
! 1156: 0, 0, -3, -4, -1, 0, -2, -3, -1, 15; 0, 0, 0, 1, 0, 0, 0, 2, 1, -3, 0, 2, 0
! 1157: , -2, -13, 1, 1, -2, -9, -19, 0, -3, -13, -19, 7; 0, 0, 0, 0, 1, 0, 0, 0, 1,
! 1158: 2, 0, 0, 2, 3, 1, 0, 1, 3, 4, -4, 1, 2, 1, -4, -21]]
! 1159: ? initalgred2(nfpol)
! 1160: [[x^5 - 2*x^4 + 3*x^3 + 8*x^2 + 3*x + 2, [1, 2], 595125, 4, [[1, -1.08911514
! 1161: 57205048250249527946671612684, 1.1861718006377964594796293860483989860, -0.5
! 1162: 9741050929194782733001765987770358483, 0.15894419745390376206549481671071894
! 1163: 289; 1, -0.13838372073406036365047976417441696637 + 0.4918163765776864349975
! 1164: 3285514741525107*I, -0.22273329410580226599155701611419649154 - 0.1361187602
! 1165: 1752805221674918029071012580*I, -0.13167445871785818798769651537619416009 +
! 1166: 0.13249517760521973840801462296650806543*I, -0.05365095865699772535929752835
! 1167: 7602608116 + 0.27622636814169107038138284681568361486*I; 1, 1.68294129359431
! 1168: 27761629561615079976005 + 2.0500351226010726172974286983598602163*I, -1.3703
! 1169: 526062130959637482576769100030014 + 6.9001775222880494773720769629846373016*
! 1170: I, -8.0696202866361678983472946546849540475 + 8.8767676785971042450885284301
! 1171: 348051602*I, -22.025821140069954155673449879997756863 - 8.430658689699915354
! 1172: 4710860185447589664*I], [1, 2, 2; -1.0891151457205048250249527946671612684,
! 1173: -0.27676744146812072730095952834883393274 - 0.983632753155372869995065710294
! 1174: 83050214*I, 3.3658825871886255523259123230159952011 - 4.10007024520214523459
! 1175: 48573967197204327*I; 1.1861718006377964594796293860483989860, -0.44546658821
! 1176: 160453198311403222839298308 + 0.27223752043505610443349836058142025160*I, -2
! 1177: .7407052124261919274965153538200060029 - 13.80035504457609895474415392596927
! 1178: 4603*I; -0.59741050929194782733001765987770358483, -0.2633489174357163759753
! 1179: 9303075238832018 - 0.26499035521043947681602924593301613087*I, -16.139240573
! 1180: 272335796694589309369908095 - 17.753535357194208490177056860269610320*I; 0.1
! 1181: 5894419745390376206549481671071894289, -0.1073019173139954507185950567152052
! 1182: 1623 - 0.55245273628338214076276569363136722973*I, -44.051642280139908311346
! 1183: 899759995513726 + 16.861317379399830708942172037089517932*I], [5, 2.00000000
! 1184: 00000000000000000000000000000, -2.0000000000000000000000000000000000000, -17
! 1185: .000000000000000000000000000000000000, -44.000000000000000000000000000000000
! 1186: 000; 2.0000000000000000000000000000000000000, 15.778109408671998044836357471
! 1187: 283695361, 22.314643349754061651916553814602769764, 10.051395257831478275499
! 1188: 932716306366248, -108.58917507620841447456569092094763671; -2.00000000000000
! 1189: 00000000000000000000000, 22.314643349754061651916553814602769764, 100.523912
! 1190: 62388960975827806174040462368, 143.93295090847353519436673793501057176, -55.
! 1191: 842564718082452641322500190813370023; -17.0000000000000000000000000000000000
! 1192: 00, 10.051395257831478275499932716306366248, 143.932950908473535194366737935
! 1193: 01057176, 288.25823756749944693139292174819167135, 205.798400382776623757201
! 1194: 80649465932302; -44.000000000000000000000000000000000000, -108.5891750762084
! 1195: 1447456569092094763671, -55.842564718082452641322500190813370023, 205.798400
! 1196: 38277662375720180649465932302, 1112.6092277946777707779250962522343036], [5,
! 1197: 2, -2, -17, -44; 2, -2, -34, -63, -40; -2, -34, -90, -101, 177; -17, -63, -
! 1198: 101, -27, 505; -44, -40, 177, 505, 828], [345, 0, 160, 252, 156; 0, 345, 215
! 1199: , 311, 306; 0, 0, 5, 3, 2; 0, 0, 0, 1, 0; 0, 0, 0, 0, 1], [163875, -388125,
! 1200: -296700, 234600, -89700; -388125, -1593900, -677925, 595125, -315675; -29670
! 1201: 0, -677925, 17250, 58650, -87975; 234600, 595125, 58650, -100050, 89700; -89
! 1202: 700, -315675, -87975, 89700, -55200], [595125, [-167325, -82800, 79350, 1725
! 1203: , 0]~, 125439056256992431640625]], [-1.0891151457205048250249527946671612684
! 1204: , -0.13838372073406036365047976417441696637 + 0.4918163765776864349975328551
! 1205: 4741525107*I, 1.6829412935943127761629561615079976005 + 2.050035122601072617
! 1206: 2974286983598602163*I], [1, x, x^2, 1/2*x^3 + 1/2*x^2 + 1/2*x, 1/2*x^4 + 1/2
! 1207: *x], [1, 0, 0, 0, 0; 0, 1, 0, -1, -1; 0, 0, 1, -1, 0; 0, 0, 0, 2, 0; 0, 0, 0
! 1208: , 0, 2], [1, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, -1, -2, 0, 0, -1, -2, -2,
! 1209: 0, -1, -2, -2, 5; 0, 1, 0, 0, 0, 1, 0, -1, -1, -1, 0, -1, -1, -2, 2, 0, -1,
! 1210: -2, -1, 7, 0, -1, 2, 7, 14; 0, 0, 1, 0, 0, 0, 1, -1, 0, -2, 1, -1, 0, -3, -3
! 1211: , 0, 0, -3, -4, -1, 0, -2, -3, -1, 15; 0, 0, 0, 1, 0, 0, 0, 2, 1, -3, 0, 2,
! 1212: 0, -2, -13, 1, 1, -2, -9, -19, 0, -3, -13, -19, 7; 0, 0, 0, 0, 1, 0, 0, 0, 1
! 1213: , 2, 0, 0, 2, 3, 1, 0, 1, 3, 4, -4, 1, 2, 1, -4, -21]], mod(-1/2*x^4 + 3/2*x
! 1214: ^3 - 5/2*x^2 - 2*x + 1, x^5 - 2*x^4 + 3*x^3 + 8*x^2 + 3*x + 2)]
! 1215: ? vp=primedec(nf,3)[1]
! 1216: [3, [1, 1, 0, 0, 0]~, 1, 1, [1, -1, -1, 0, 0]~]
! 1217: ? idx=idealmul(nf,idmat(5),vp)
! 1218:
! 1219: [3 1 2 2 2]
! 1220:
! 1221: [0 1 0 0 0]
! 1222:
! 1223: [0 0 1 0 0]
! 1224:
! 1225: [0 0 0 1 0]
! 1226:
! 1227: [0 0 0 0 1]
! 1228:
! 1229: ? idealinv(nf,idx)
! 1230:
! 1231: [1 0 2/3 0 0]
! 1232:
! 1233: [0 1 1/3 0 0]
! 1234:
! 1235: [0 0 1/3 0 0]
! 1236:
! 1237: [0 0 0 1 0]
! 1238:
! 1239: [0 0 0 0 1]
! 1240:
! 1241: ? idy=ideallllred(nf,idx,[1,5,6])
! 1242:
! 1243: [5 0 0 2 0]
! 1244:
! 1245: [0 5 0 0 0]
! 1246:
! 1247: [0 0 5 2 0]
! 1248:
! 1249: [0 0 0 1 0]
! 1250:
! 1251: [0 0 0 0 5]
! 1252:
! 1253: ? idealadd(nf,idx,idy)
! 1254:
! 1255: [1 0 0 0 0]
! 1256:
! 1257: [0 1 0 0 0]
! 1258:
! 1259: [0 0 1 0 0]
! 1260:
! 1261: [0 0 0 1 0]
! 1262:
! 1263: [0 0 0 0 1]
! 1264:
! 1265: ? idealaddone(nf,idx,idy)
! 1266: [[3, 0, 2, 1, 0]~, [-2, 0, -2, -1, 0]~]
! 1267: ? idealaddmultone(nf,[idy,idx])
! 1268: [[-5, 0, 0, 0, 0]~, [6, 0, 0, 0, 0]~]
! 1269: ? idealappr(nf,idy)
! 1270: [-2, 0, -2, 4, 0]~
! 1271: ? idealapprfact(nf,idealfactor(nf,idy))
! 1272: [-2, 0, -2, 4, 0]~
! 1273: ? idealcoprime(nf,idx,idx)
! 1274: [-2/3, 2/3, -1/3, 0, 0]~
! 1275: ? idz=idealintersect(nf,idx,idy)
! 1276:
! 1277: [15 5 10 12 10]
! 1278:
! 1279: [0 5 0 0 0]
! 1280:
! 1281: [0 0 5 2 0]
! 1282:
! 1283: [0 0 0 1 0]
! 1284:
! 1285: [0 0 0 0 5]
! 1286:
! 1287: ? idealfactor(nf,idz)
! 1288:
! 1289: [[3, [1, 1, 0, 0, 0]~, 1, 1, [1, -1, -1, 0, 0]~] 1]
! 1290:
! 1291: [[5, [-2, 0, 0, 0, 1]~, 1, 1, [2, 2, 1, 1, 4]~] 1]
! 1292:
! 1293: [[5, [0, 0, -1, 0, 1]~, 4, 1, [4, 5, 4, 2, 0]~] 3]
! 1294:
! 1295: ? ideallist(bnf,20)
! 1296: [[[1, 0; 0, 1]], [], [[3, 2; 0, 1], [3, 0; 0, 1]], [[2, 0; 0, 2]], [[5, 3; 0
! 1297: , 1], [5, 1; 0, 1]], [], [], [], [[9, 5; 0, 1], [3, 0; 0, 3], [9, 3; 0, 1]],
! 1298: [], [[11, 9; 0, 1], [11, 1; 0, 1]], [[6, 4; 0, 2], [6, 0; 0, 2]], [], [], [
! 1299: [15, 8; 0, 1], [15, 3; 0, 1], [15, 11; 0, 1], [15, 6; 0, 1]], [[4, 0; 0, 4]]
! 1300: , [[17, 14; 0, 1], [17, 2; 0, 1]], [], [[19, 18; 0, 1], [19, 0; 0, 1]], [[10
! 1301: , 6; 0, 2], [10, 2; 0, 2]]]
! 1302: ? idx2=idealmul(nf,idx,idx)
! 1303:
! 1304: [9 7 5 8 2]
! 1305:
! 1306: [0 1 0 0 0]
! 1307:
! 1308: [0 0 1 0 0]
! 1309:
! 1310: [0 0 0 1 0]
! 1311:
! 1312: [0 0 0 0 1]
! 1313:
! 1314: ? idt=idealmulred(nf,idx,idx)
! 1315:
! 1316: [2 0 0 0 1]
! 1317:
! 1318: [0 2 0 0 1]
! 1319:
! 1320: [0 0 2 0 0]
! 1321:
! 1322: [0 0 0 2 1]
! 1323:
! 1324: [0 0 0 0 1]
! 1325:
! 1326: ? idealdiv(nf,idy,idt)
! 1327:
! 1328: [5 5/2 5/2 7/2 0]
! 1329:
! 1330: [0 5/2 0 0 0]
! 1331:
! 1332: [0 0 5/2 1 0]
! 1333:
! 1334: [0 0 0 1/2 0]
! 1335:
! 1336: [0 0 0 0 5/2]
! 1337:
! 1338: ? idealdivexact(nf,idx2,idx)
! 1339:
! 1340: [3 1 2 2 2]
! 1341:
! 1342: [0 1 0 0 0]
! 1343:
! 1344: [0 0 1 0 0]
! 1345:
! 1346: [0 0 0 1 0]
! 1347:
! 1348: [0 0 0 0 1]
! 1349:
! 1350: ? idealhermite(nf,vp)
! 1351:
! 1352: [3 1 2 2 2]
! 1353:
! 1354: [0 1 0 0 0]
! 1355:
! 1356: [0 0 1 0 0]
! 1357:
! 1358: [0 0 0 1 0]
! 1359:
! 1360: [0 0 0 0 1]
! 1361:
! 1362: ? idealhermite2(nf,vp[2],3)
! 1363:
! 1364: [3 1 2 2 2]
! 1365:
! 1366: [0 1 0 0 0]
! 1367:
! 1368: [0 0 1 0 0]
! 1369:
! 1370: [0 0 0 1 0]
! 1371:
! 1372: [0 0 0 0 1]
! 1373:
! 1374: ? idealnorm(nf,idt)
! 1375: 16
! 1376: ? idp=idealpow(nf,idx,7)
! 1377:
! 1378: [2187 1807 2129 692 1379]
! 1379:
! 1380: [0 1 0 0 0]
! 1381:
! 1382: [0 0 1 0 0]
! 1383:
! 1384: [0 0 0 1 0]
! 1385:
! 1386: [0 0 0 0 1]
! 1387:
! 1388: ? idealpowred(nf,idx,7)
! 1389:
! 1390: [2 0 0 0 1]
! 1391:
! 1392: [0 2 0 0 1]
! 1393:
! 1394: [0 0 2 0 0]
! 1395:
! 1396: [0 0 0 2 1]
! 1397:
! 1398: [0 0 0 0 1]
! 1399:
! 1400: ? idealtwoelt(nf,idy)
! 1401: [5, [2, 0, 2, 1, 0]~]
! 1402: ? idealtwoelt2(nf,idy,10)
! 1403: [-2, 0, -2, -1, 0]~
! 1404: ? idealval(nf,idp,vp)
! 1405: 7
! 1406: ? idmat(5)
! 1407:
! 1408: [1 0 0 0 0]
! 1409:
! 1410: [0 1 0 0 0]
! 1411:
! 1412: [0 0 1 0 0]
! 1413:
! 1414: [0 0 0 1 0]
! 1415:
! 1416: [0 0 0 0 1]
! 1417:
! 1418: ? if(3<2,print("bof"),print("ok"));
! 1419: ok
! 1420: ? imag(2+3*i)
! 1421: 3
! 1422: ? image([1,3,5;2,4,6;3,5,7])
! 1423:
! 1424: [1 3]
! 1425:
! 1426: [2 4]
! 1427:
! 1428: [3 5]
! 1429:
! 1430: ? image(pi*[1,3,5;2,4,6;3,5,7])
! 1431:
! 1432: [3.1415926535897932384626433832795028841 9.424777960769379715387930149838508
! 1433: 6525]
! 1434:
! 1435: [6.2831853071795864769252867665590057683 12.56637061435917295385057353311801
! 1436: 1536]
! 1437:
! 1438: [9.4247779607693797153879301498385086525 15.70796326794896619231321691639751
! 1439: 4420]
! 1440:
! 1441: ? incgam(2,1)
! 1442: 0.73575888234288464319104754032292173491
! 1443: ? incgam1(2,1)
! 1444: -0.26424111765711535680895245967678075578
! 1445: ? incgam2(2,1)
! 1446: 0.73575888234288464319104754032292173489
! 1447: ? incgam3(2,1)
! 1448: 0.26424111765711535680895245967707826508
! 1449: ? incgam4(4,1,6)
! 1450: 5.8860710587430771455283803225833738791
! 1451: ? indexrank([1,1,1;1,1,1;1,1,2])
! 1452: [[1, 3], [1, 3]]
! 1453: ? indsort([8,7,6,5])
! 1454: [4, 3, 2, 1]
! 1455: ? initell([0,0,0,-1,0])
! 1456: [0, 0, 0, -1, 0, 0, -2, 0, -1, 48, 0, 64, 1728, [1.0000000000000000000000000
! 1457: 000000000000, 0.E-38, -1.0000000000000000000000000000000000000]~, 2.62205755
! 1458: 42921198104648395898911194136, 2.6220575542921198104648395898911194136*I, -0
! 1459: .59907011736779610371996124614016193910, -1.79721035210338831115988373842048
! 1460: 58173*I, 6.8751858180203728274900957798105571979]
! 1461: ? initrect(1,700,700)
! 1462: ? nfz=initzeta(x^2-2);
! 1463: ? integ(sin(x),x)
! 1464: 1/2*x^2 - 1/24*x^4 + 1/720*x^6 - 1/40320*x^8 + 1/3628800*x^10 - 1/479001600*
! 1465: x^12 + 1/87178291200*x^14 - 1/20922789888000*x^16 + O(x^17)
! 1466: ? integ((-x^2-2*a*x+8*a)/(x^4-14*x^3+(2*a+49)*x^2-14*a*x+a^2),x)
! 1467: (x + a)/(x^2 - 7*x + a)
! 1468: ? intersect([1,2;3,4;5,6],[2,3;7,8;8,9])
! 1469:
! 1470: [-1]
! 1471:
! 1472: [-1]
! 1473:
! 1474: [-1]
! 1475:
! 1476: ? \precision=19
! 1477: realprecision = 19 significant digits
! 1478: ? intgen(x=0,pi,sin(x))
! 1479: 2.000000000000000017
! 1480: ? sqr(2*intgen(x=0,4,exp(-x^2)))
! 1481: 3.141592556720305685
! 1482: ? 4*intinf(x=1,10^20,1/(1+x^2))
! 1483: 3.141592653589793208
! 1484: ? intnum(x=-0.5,0.5,1/sqrt(1-x^2))
! 1485: 1.047197551196597747
! 1486: ? 2*intopen(x=0,100,sin(x)/x)
! 1487: 3.124450933778112629
! 1488: ? \precision=38
! 1489: realprecision = 38 significant digits
! 1490: ? inverseimage([1,1;2,3;5,7],[2,2,6]~)
! 1491: [4, -2]~
! 1492: ? isdiagonal([1,0,0;0,5,0;0,0,0])
! 1493: 1
! 1494: ? isfund(12345)
! 1495: 1
! 1496: ? isideal(bnf[7],[5,1;0,1])
! 1497: 1
! 1498: ? isincl(x^2+1,x^4+1)
! 1499: [-x^2, x^2]
! 1500: ? isinclfast(initalg(x^2+1),initalg(x^4+1))
! 1501: [-x^2, x^2]
! 1502: ? isirreducible(x^5+3*x^3+5*x^2+15)
! 1503: 0
! 1504: ? isisom(x^3+x^2-2*x-1,x^3+x^2-2*x-1)
! 1505: [x, -x^2 - x + 1, x^2 - 2]
! 1506: ? isisomfast(initalg(x^3-2),initalg(x^3-6*x^2-6*x-30))
! 1507: [-1/25*x^2 + 13/25*x - 2/5]
! 1508: ? isprime(12345678901234567)
! 1509: 0
! 1510: ? isprincipal(bnf,[5,1;0,1])
! 1511: [1]~
! 1512: ? isprincipalgen(bnf,[5,1;0,1])
! 1513: [[1]~, [2, 1/3]~, 117]
! 1514: ? isprincipalraygen(bnr,primedec(bnf,7)[1])
! 1515: [[9]~, [-2170/6561, -931/19683]~, 113]
! 1516: ? ispsp(73!+1)
! 1517: 1
! 1518: ? isqrt(10!^2+1)
! 1519: 3628800
! 1520: ? isset([-3,5,7,7])
! 1521: 0
! 1522: ? issqfree(123456789876543219)
! 1523: 0
! 1524: ? issquare(12345678987654321)
! 1525: 1
! 1526: ? isunit(bnf,mod(3405*x-27466,x^2-x-57))
! 1527: [-4, mod(1, 2)]~
! 1528: ? jacobi(hilbert(6))
! 1529: [[1.6188998589243390969705881471257800712, 0.2423608705752095521357284158507
! 1530: 0114077, 0.000012570757122625194922982397996498755027, 0.0000001082799484565
! 1531: 5497685388772372251711485, 0.016321521319875822124345079564191505890, 0.0006
! 1532: 1574835418265769764919938428527140264]~, [0.74871921887909485900280109200517
! 1533: 845109, -0.61454482829258676899320019644273870645, 0.01114432093072471053067
! 1534: 8340374220998541, -0.0012481940840821751169398163046387834473, 0.24032536934
! 1535: 252330399154228873240534568, -0.062226588150197681775152126611810492910; 0.4
! 1536: 4071750324351206127160083580231701801, 0.21108248167867048675227675845247769
! 1537: 095, -0.17973275724076003758776897803740640964, 0.03560664294428763526612284
! 1538: 8131812048466, -0.69765137527737012296208335046678265583, 0.4908392097109243
! 1539: 6297498316169060044997; 0.32069686982225190106359024326699463106, 0.36589360
! 1540: 730302614149086554211117169622, 0.60421220675295973004426567844103062241, -0
! 1541: .24067907958842295837736719558855679285, -0.23138937333290388042251363554209
! 1542: 048309, -0.53547692162107486593474491750949545456; 0.25431138634047419251788
! 1543: 312792590944672, 0.39470677609501756783094636145991581708, -0.44357471627623
! 1544: 954554460416705180105301, 0.62546038654922724457753441039459331059, 0.132863
! 1545: 15850933553530333839628101576050, -0.41703769221897886840494514780771076439;
! 1546: 0.21153084007896524664213667673977991959, 0.3881904338738864286311144882599
! 1547: 2418973, -0.44153664101228966222143649752977203423, -0.689807199293836684198
! 1548: 01738006926829419, 0.36271492146487147525299457604461742111, 0.0470340189331
! 1549: 15649705614518466541243873; 0.18144297664876947372217005457727093715, 0.3706
! 1550: 9590776736280861775501084807394603, 0.45911481681642960284551392793050866602
! 1551: , 0.27160545336631286930015536176213647001, 0.502762866757515384892605663686
! 1552: 47786272, 0.54068156310385293880022293448123782121]]
! 1553: ? jbesselh(1,1)
! 1554: 0.24029783912342701089584304474193368045
! 1555: ? jell(i)
! 1556: 1728.0000000000000000000000000000000000 + 0.E-45*I
! 1557: ? kbessel(1+i,1)
! 1558: 0.32545977186584141085464640324923711863 + 0.2894280370259921276345671592415
! 1559: 2302704*I
! 1560: ? kbessel2(1+i,1)
! 1561: 0.32545977186584141085464640324923711863 + 0.2894280370259921276345671592415
! 1562: 2302704*I
! 1563: ? x
! 1564: x
! 1565: ? y
! 1566: x
! 1567: ? ker(matrix(4,4,x,y,x/y))
! 1568:
! 1569: [-1/2 -1/3 -1/4]
! 1570:
! 1571: [1 0 0]
! 1572:
! 1573: [0 1 0]
! 1574:
! 1575: [0 0 1]
! 1576:
! 1577: ? ker(matrix(4,4,x,y,sin(x+y)))
! 1578:
! 1579: [1.0000000000000000000000000000000000000 1.080604611736279434801873214885953
! 1580: 2074]
! 1581:
! 1582: [-1.0806046117362794348018732148859532074 -0.1677063269057152260048635409984
! 1583: 7562046]
! 1584:
! 1585: [1 0]
! 1586:
! 1587: [0 1]
! 1588:
! 1589: ? keri(matrix(4,4,x,y,x+y))
! 1590:
! 1591: [1 2]
! 1592:
! 1593: [-2 -3]
! 1594:
! 1595: [1 0]
! 1596:
! 1597: [0 1]
! 1598:
! 1599: ? kerint(matrix(4,4,x,y,x*y))
! 1600:
! 1601: [-1 -1 -1]
! 1602:
! 1603: [-1 0 1]
! 1604:
! 1605: [1 -1 1]
! 1606:
! 1607: [0 1 -1]
! 1608:
! 1609: ? kerint1(matrix(4,4,x,y,x*y))
! 1610:
! 1611: [-1 -1 -1]
! 1612:
! 1613: [-1 0 1]
! 1614:
! 1615: [1 -1 1]
! 1616:
! 1617: [0 1 -1]
! 1618:
! 1619: ? kerint2(matrix(4,6,x,y,2520/(x+y)))
! 1620:
! 1621: [3 1]
! 1622:
! 1623: [-30 -15]
! 1624:
! 1625: [70 70]
! 1626:
! 1627: [0 -140]
! 1628:
! 1629: [-126 126]
! 1630:
! 1631: [84 -42]
! 1632:
! 1633: ? f(u)=u+1;
! 1634: ? print(f(5));kill(f);
! 1635: 6
! 1636: ? f=12
! 1637: 12
! 1638: ? killrect(1)
! 1639: ? kro(5,7)
! 1640: -1
! 1641: ? kro(3,18)
! 1642: 0
! 1643: ? laplace(x*exp(x*y)/(exp(x)-1))
! 1644: 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 +
! 1645: 22133/10*x^8 - 7560*x^9 + 2775767/66*x^10 - 166320*x^11 + 2655339269/2730*x
! 1646: ^12 - 4324320*x^13 + 264873251/10*x^14 + O(x^15)
! 1647: ? lcm(15,-21)
! 1648: 105
! 1649: ? length(divisors(1000))
! 1650: 16
! 1651: ? legendre(10)
! 1652: 46189/256*x^10 - 109395/256*x^8 + 45045/128*x^6 - 15015/128*x^4 + 3465/256*x
! 1653: ^2 - 63/256
! 1654: ? lex([1,3],[1,3,5])
! 1655: -1
! 1656: ? lexsort([[1,5],[2,4],[1,5,1],[1,4,2]])
! 1657: [[1, 4, 2], [1, 5], [1, 5, 1], [2, 4]]
! 1658: ? lift(chinese(mod(7,15),mod(4,21)))
! 1659: 67
! 1660: ? lindep([(1-3*sqrt(2))/(3-2*sqrt(3)),1,sqrt(2),sqrt(3),sqrt(6)])
! 1661: [-3, -3, 9, -2, 6]
! 1662: ? lindep2([(1-3*sqrt(2))/(3-2*sqrt(3)),1,sqrt(2),sqrt(3),sqrt(6)],14)
! 1663: [-3, -3, 9, -2, 6]
! 1664: ? move(0,0,900);line(0,900,0)
! 1665: ? lines(0,vector(5,k,50*k),vector(5,k,10*k*k))
! 1666: ? m=1/hilbert(7)
! 1667:
! 1668: [49 -1176 8820 -29400 48510 -38808 12012]
! 1669:
! 1670: [-1176 37632 -317520 1128960 -1940400 1596672 -504504]
! 1671:
! 1672: [8820 -317520 2857680 -10584000 18711000 -15717240 5045040]
! 1673:
! 1674: [-29400 1128960 -10584000 40320000 -72765000 62092800 -20180160]
! 1675:
! 1676: [48510 -1940400 18711000 -72765000 133402500 -115259760 37837800]
! 1677:
! 1678: [-38808 1596672 -15717240 62092800 -115259760 100590336 -33297264]
! 1679:
! 1680: [12012 -504504 5045040 -20180160 37837800 -33297264 11099088]
! 1681:
! 1682: ? mp=concat(m,idmat(7))
! 1683:
! 1684: [49 -1176 8820 -29400 48510 -38808 12012 1 0 0 0 0 0 0]
! 1685:
! 1686: [-1176 37632 -317520 1128960 -1940400 1596672 -504504 0 1 0 0 0 0 0]
! 1687:
! 1688: [8820 -317520 2857680 -10584000 18711000 -15717240 5045040 0 0 1 0 0 0 0]
! 1689:
! 1690: [-29400 1128960 -10584000 40320000 -72765000 62092800 -20180160 0 0 0 1 0 0
! 1691: 0]
! 1692:
! 1693: [48510 -1940400 18711000 -72765000 133402500 -115259760 37837800 0 0 0 0 1 0
! 1694: 0]
! 1695:
! 1696: [-38808 1596672 -15717240 62092800 -115259760 100590336 -33297264 0 0 0 0 0
! 1697: 1 0]
! 1698:
! 1699: [12012 -504504 5045040 -20180160 37837800 -33297264 11099088 0 0 0 0 0 0 1]
! 1700:
! 1701: ? lll(m)
! 1702:
! 1703: [-420 -420 840 630 -1092 757 2982]
! 1704:
! 1705: [-210 -280 630 504 -876 700 2415]
! 1706:
! 1707: [-140 -210 504 420 -749 641 2050]
! 1708:
! 1709: [-105 -168 420 360 -658 589 1785]
! 1710:
! 1711: [-84 -140 360 315 -588 544 1582]
! 1712:
! 1713: [-70 -120 315 280 -532 505 1421]
! 1714:
! 1715: [-60 -105 280 252 -486 471 1290]
! 1716:
! 1717: ? lll1(m)
! 1718:
! 1719: [-420 -420 840 630 -1092 757 2982]
! 1720:
! 1721: [-210 -280 630 504 -876 700 2415]
! 1722:
! 1723: [-140 -210 504 420 -749 641 2050]
! 1724:
! 1725: [-105 -168 420 360 -658 589 1785]
! 1726:
! 1727: [-84 -140 360 315 -588 544 1582]
! 1728:
! 1729: [-70 -120 315 280 -532 505 1421]
! 1730:
! 1731: [-60 -105 280 252 -486 471 1290]
! 1732:
! 1733: ? lllgram(m)
! 1734:
! 1735: [1 1 27 -27 69 0 141]
! 1736:
! 1737: [0 1 4 -22 34 -24 49]
! 1738:
! 1739: [0 1 3 -21 18 -24 23]
! 1740:
! 1741: [0 1 3 -20 10 -19 13]
! 1742:
! 1743: [0 1 3 -19 6 -14 8]
! 1744:
! 1745: [0 1 3 -18 4 -10 5]
! 1746:
! 1747: [0 1 3 -17 3 -7 3]
! 1748:
! 1749: ? lllgram1(m)
! 1750:
! 1751: [1 1 27 -27 69 0 141]
! 1752:
! 1753: [0 1 4 -22 34 -24 49]
! 1754:
! 1755: [0 1 3 -21 18 -24 23]
! 1756:
! 1757: [0 1 3 -20 10 -19 13]
! 1758:
! 1759: [0 1 3 -19 6 -14 8]
! 1760:
! 1761: [0 1 3 -18 4 -10 5]
! 1762:
! 1763: [0 1 3 -17 3 -7 3]
! 1764:
! 1765: ? lllgramint(m)
! 1766:
! 1767: [1 1 27 -27 69 0 141]
! 1768:
! 1769: [0 1 4 -23 34 -24 91]
! 1770:
! 1771: [0 1 3 -22 18 -24 65]
! 1772:
! 1773: [0 1 3 -21 10 -19 49]
! 1774:
! 1775: [0 1 3 -20 6 -14 38]
! 1776:
! 1777: [0 1 3 -19 4 -10 30]
! 1778:
! 1779: [0 1 3 -18 3 -7 24]
! 1780:
! 1781: ? lllgramkerim(mp~*mp)
! 1782: [[-420, -420, 840, 630, 2982, -1092, -83; -210, -280, 630, 504, 2415, -876,
! 1783: 70; -140, -210, 504, 420, 2050, -749, 137; -105, -168, 420, 360, 1785, -658,
! 1784: 169; -84, -140, 360, 315, 1582, -588, 184; -70, -120, 315, 280, 1421, -532,
! 1785: 190; -60, -105, 280, 252, 1290, -486, 191; 420, 0, 0, 0, -210, 168, 35; 0,
! 1786: 840, 0, 0, 0, 0, 336; 0, 0, -2520, 0, 0, 0, 1260; 0, 0, 0, -2520, 0, 0, -840
! 1787: ; 0, 0, 0, 0, -13860, 0, 6930; 0, 0, 0, 0, 0, 5544, 0; 0, 0, 0, 0, 0, 0, -12
! 1788: 012], [0, 0, 0, 0, 0, 0, 0; 0, 0, 0, 0, 0, 0, 0; 0, 0, 0, 0, 0, 0, 0; 0, 0,
! 1789: 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
! 1790: ; 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,
! 1791: 0, 0, 0; 0, 0, 0, 0, 1, 0, 0; 0, 0, 0, 0, 0, 1, 0; 0, 0, 0, 0, 0, 0, 1]]
! 1792: ? lllint(m)
! 1793:
! 1794: [-420 -420 840 630 -1092 -83 2982]
! 1795:
! 1796: [-210 -280 630 504 -876 70 2415]
! 1797:
! 1798: [-140 -210 504 420 -749 137 2050]
! 1799:
! 1800: [-105 -168 420 360 -658 169 1785]
! 1801:
! 1802: [-84 -140 360 315 -588 184 1582]
! 1803:
! 1804: [-70 -120 315 280 -532 190 1421]
! 1805:
! 1806: [-60 -105 280 252 -486 191 1290]
! 1807:
! 1808: ? lllintpartial(m)
! 1809:
! 1810: [-420 -420 -630 840 1092 2982 -83]
! 1811:
! 1812: [-210 -280 -504 630 876 2415 70]
! 1813:
! 1814: [-140 -210 -420 504 749 2050 137]
! 1815:
! 1816: [-105 -168 -360 420 658 1785 169]
! 1817:
! 1818: [-84 -140 -315 360 588 1582 184]
! 1819:
! 1820: [-70 -120 -280 315 532 1421 190]
! 1821:
! 1822: [-60 -105 -252 280 486 1290 191]
! 1823:
! 1824: ? lllkerim(mp)
! 1825: [[-420, -420, 840, 630, 2982, -1092, -83; -210, -280, 630, 504, 2415, -876,
! 1826: 70; -140, -210, 504, 420, 2050, -749, 137; -105, -168, 420, 360, 1785, -658,
! 1827: 169; -84, -140, 360, 315, 1582, -588, 184; -70, -120, 315, 280, 1421, -532,
! 1828: 190; -60, -105, 280, 252, 1290, -486, 191; 420, 0, 0, 0, -210, 168, 35; 0,
! 1829: 840, 0, 0, 0, 0, 336; 0, 0, -2520, 0, 0, 0, 1260; 0, 0, 0, -2520, 0, 0, -840
! 1830: ; 0, 0, 0, 0, -13860, 0, 6930; 0, 0, 0, 0, 0, 5544, 0; 0, 0, 0, 0, 0, 0, -12
! 1831: 012], [0, 0, 0, 0, 0, 0, 0; 0, 0, 0, 0, 0, 0, 0; 0, 0, 0, 0, 0, 0, 0; 0, 0,
! 1832: 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
! 1833: ; 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,
! 1834: 0, 0, 0; 0, 0, 0, 0, 1, 0, 0; 0, 0, 0, 0, 0, 1, 0; 0, 0, 0, 0, 0, 0, 1]]
! 1835: ? lllrat(m)
! 1836:
! 1837: [-420 -420 840 630 -1092 -83 2982]
! 1838:
! 1839: [-210 -280 630 504 -876 70 2415]
! 1840:
! 1841: [-140 -210 504 420 -749 137 2050]
! 1842:
! 1843: [-105 -168 420 360 -658 169 1785]
! 1844:
! 1845: [-84 -140 360 315 -588 184 1582]
! 1846:
! 1847: [-70 -120 315 280 -532 190 1421]
! 1848:
! 1849: [-60 -105 280 252 -486 191 1290]
! 1850:
! 1851: ? \precision=96
! 1852: realprecision = 96 significant digits
! 1853: ? ln(2)
! 1854: 0.69314718055994530941723212145817656807550013436025525412068000949339362196
! 1855: 9694715605863326996418
! 1856: ? lngamma(10^50*i)
! 1857: -157079632679489661923132169163975144209858469968811.93673753887608474948977
! 1858: 0941153418951907406847 - 2.5258126069288717421377720813802613884088088474975
! 1859: 8842685248040385012601916745265645208759475328*I
! 1860: ? \precision=2000
! 1861: realprecision = 2003 significant digits (2000 digits displayed)
! 1862: ? log(2)
! 1863: 0.69314718055994530941723212145817656807550013436025525412068000949339362196
! 1864: 9694715605863326996418687542001481020570685733685520235758130557032670751635
! 1865: 0759619307275708283714351903070386238916734711233501153644979552391204751726
! 1866: 8157493206515552473413952588295045300709532636664265410423915781495204374043
! 1867: 0385500801944170641671518644712839968171784546957026271631064546150257207402
! 1868: 4816377733896385506952606683411372738737229289564935470257626520988596932019
! 1869: 6505855476470330679365443254763274495125040606943814710468994650622016772042
! 1870: 4524529612687946546193165174681392672504103802546259656869144192871608293803
! 1871: 1727143677826548775664850856740776484514644399404614226031930967354025744460
! 1872: 7030809608504748663852313818167675143866747664789088143714198549423151997354
! 1873: 8803751658612753529166100071053558249879414729509293113897155998205654392871
! 1874: 7000721808576102523688921324497138932037843935308877482597017155910708823683
! 1875: 6275898425891853530243634214367061189236789192372314672321720534016492568727
! 1876: 4778234453534764811494186423867767744060695626573796008670762571991847340226
! 1877: 5146283790488306203306114463007371948900274364396500258093651944304119115060
! 1878: 8094879306786515887090060520346842973619384128965255653968602219412292420757
! 1879: 4321757489097706752687115817051137009158942665478595964890653058460258668382
! 1880: 9400228330053820740056770530467870018416240441883323279838634900156312188956
! 1881: 0650553151272199398332030751408426091479001265168243443893572472788205486271
! 1882: 5527418772430024897945401961872339808608316648114909306675193393128904316413
! 1883: 7068139777649817697486890388778999129650361927071088926410523092478391737350
! 1884: 1229842420499568935992206602204654941510613918788574424557751020683703086661
! 1885: 9480896412186807790208181588580001688115973056186676199187395200766719214592
! 1886: 2367206025395954365416553112951759899400560003665135675690512459268257439464
! 1887: 8316833262490180382424082423145230614096380570070255138770268178516306902551
! 1888: 3703234053802145019015374029509942262995779647427138157363801729873940704242
! 1889: 17997226696297993931270693
! 1890: ? logagm(2)
! 1891: 0.69314718055994530941723212145817656807550013436025525412068000949339362196
! 1892: 9694715605863326996418687542001481020570685733685520235758130557032670751635
! 1893: 0759619307275708283714351903070386238916734711233501153644979552391204751726
! 1894: 8157493206515552473413952588295045300709532636664265410423915781495204374043
! 1895: 0385500801944170641671518644712839968171784546957026271631064546150257207402
! 1896: 4816377733896385506952606683411372738737229289564935470257626520988596932019
! 1897: 6505855476470330679365443254763274495125040606943814710468994650622016772042
! 1898: 4524529612687946546193165174681392672504103802546259656869144192871608293803
! 1899: 1727143677826548775664850856740776484514644399404614226031930967354025744460
! 1900: 7030809608504748663852313818167675143866747664789088143714198549423151997354
! 1901: 8803751658612753529166100071053558249879414729509293113897155998205654392871
! 1902: 7000721808576102523688921324497138932037843935308877482597017155910708823683
! 1903: 6275898425891853530243634214367061189236789192372314672321720534016492568727
! 1904: 4778234453534764811494186423867767744060695626573796008670762571991847340226
! 1905: 5146283790488306203306114463007371948900274364396500258093651944304119115060
! 1906: 8094879306786515887090060520346842973619384128965255653968602219412292420757
! 1907: 4321757489097706752687115817051137009158942665478595964890653058460258668382
! 1908: 9400228330053820740056770530467870018416240441883323279838634900156312188956
! 1909: 0650553151272199398332030751408426091479001265168243443893572472788205486271
! 1910: 5527418772430024897945401961872339808608316648114909306675193393128904316413
! 1911: 7068139777649817697486890388778999129650361927071088926410523092478391737350
! 1912: 1229842420499568935992206602204654941510613918788574424557751020683703086661
! 1913: 9480896412186807790208181588580001688115973056186676199187395200766719214592
! 1914: 2367206025395954365416553112951759899400560003665135675690512459268257439464
! 1915: 8316833262490180382424082423145230614096380570070255138770268178516306902551
! 1916: 3703234053802145019015374029509942262995779647427138157363801729873940704242
! 1917: 17997226696297993931270693
! 1918: ? \precision=19
! 1919: realprecision = 19 significant digits
! 1920: ? bcurve=initell([0,0,0,-3,0])
! 1921: [0, 0, 0, -3, 0, 0, -6, 0, -9, 144, 0, 1728, 1728, [1.732050807568877293, 0.
! 1922: E-19, -1.732050807568877293]~, 1.992332899583490707, 1.992332899583490708*I,
! 1923: -0.7884206134041560682, -2.365261840212468204*I, 3.969390382762759668]
! 1924: ? localred(bcurve,2)
! 1925: [6, 2, [1, 1, 1, 0], 1]
! 1926: ? ccurve=initell([0,0,-1,-1,0])
! 1927: [0, 0, -1, -1, 0, 0, -2, 1, -1, 48, -216, 37, 110592/37, [0.8375654352833230
! 1928: 353, 0.2695944364054445582, -1.107159871688767593]~, 2.993458646231959630, 2
! 1929: .451389381986790061*I, -0.4713192779568114757, -1.435456518668684318*I, 7.33
! 1930: 8132740789576742]
! 1931: ? l=lseriesell(ccurve,2,-37,1)
! 1932: 0.3815754082607112111
! 1933: ? lseriesell(ccurve,2,-37,1.2)-l
! 1934: -1.084202172234654426 E-19
! 1935: ? sbnf=smallbuchinit(x^3-x^2-14*x-1)
! 1936: [x^3 - x^2 - 14*x - 1, 3, 10889, [1, x, x^2], [-3.233732695981516673, -0.071
! 1937: 82350902743636344, 4.305556205008953036], [10889, 5698, 3794; 0, 1, 0; 0, 0,
! 1938: 1], mat(2), mat([0, 1, 1, 1, 0, 1, 1, 1]), [9, 15, 16, 17, 10, 33, 69, 39,
! 1939: 57], [2, [-1, 0, 0]~], [[0, 1, 0]~, [-4, 2, 1]~], [-4, -3, -1, 2, 3, 1, 11,
! 1940: -1, -7; 1, -1, 1, 1, 0, 1, 2, -4, -2; 0, 0, 0, 0, 0, 0, -1, -1, 0]]
! 1941: ? makebigbnf(sbnf)
! 1942: [mat(2), mat([0, 1, 1, 1, 0, 1, 1, 1]), [1.173637103435061715 + 3.1415926535
! 1943: 89793238*I, -4.562279014988837901 + 3.141592653589793238*I; -2.6335434327389
! 1944: 76049 + 3.141592653589793238*I, 1.420330600779487358 + 3.141592653589793238*
! 1945: I; 1.459906329303914334, 3.141948414209350543], [1.246346989334819161 + 3.14
! 1946: 1592653589793238*I, -1.990056445584799713, 0.5404006376129469727 + 3.1415926
! 1947: 53589793238*I, -0.6926391142471042845 + 3.141592653589793238*I, 0.E-96, 0.00
! 1948: 4375616572659815402 + 3.141592653589793238*I, 0.3677262014027817705 + 3.1415
! 1949: 92653589793238*I, -0.8305625946607188639, -1.977791147836553953 + 3.14159265
! 1950: 3589793238*I; 0.6716827432867392935 + 3.141592653589793238*I, 0.537900567109
! 1951: 2853266 + 3.141592653589793238*I, -0.8333219883742404172 + 3.141592653589793
! 1952: 238*I, -0.2461086674077943078, 0.E-96, -0.8738318043071131265, 0.97290631883
! 1953: 16092378, -1.552661549868775853 + 3.141592653589793238*I, 0.5774919091398324
! 1954: 092 + 3.141592653589793238*I; -1.918029732621558454, 1.452155878475514386 +
! 1955: 3.141592653589793238*I, 0.2929213507612934444, 0.9387477816548985923, 0.E-96
! 1956: , 0.8694561877344533111, -1.340632520234391008, 2.383224144529494717 + 3.141
! 1957: 592653589793238*I, 1.400299238696721544 + 3.141592653589793238*I], [[3, [-1,
! 1958: 1, 0]~, 1, 1, [1, 0, 1]~], [5, [3, 1, 0]~, 1, 1, [-2, 1, 1]~], [5, [-1, 1,
! 1959: 0]~, 1, 1, [1, 0, 1]~], [5, [2, 1, 0]~, 1, 1, [2, 2, 1]~], [3, [1, 0, 1]~, 1
! 1960: , 2, [-1, 1, 0]~], [11, [1, 1, 0]~, 1, 1, [-1, -2, 1]~], [23, [-10, 1, 0]~,
! 1961: 1, 1, [7, 9, 1]~], [13, [19, 1, 0]~, 1, 1, [2, 6, 1]~], [19, [-6, 1, 0]~, 1,
! 1962: 1, [-3, 5, 1]~]]~, [1, 2, 3, 4, 5, 6, 7, 8, 9]~, [x^3 - x^2 - 14*x - 1, [3,
! 1963: 0], 10889, 1, [[1, -3.233732695981516673, 10.45702714905988813; 1, -0.07182
! 1964: 350902743636344, 0.005158616449014232794; 1, 4.305556205008953036, 18.537814
! 1965: 23449109762], [1, 1, 1; -3.233732695981516673, -0.07182350902743636344, 4.30
! 1966: 5556205008953036; 10.45702714905988813, 0.005158616449014232794, 18.53781423
! 1967: 449109762], [3, 1.000000000000000000, 29.00000000000000000; 1.00000000000000
! 1968: 0000, 29.00000000000000000, 46.00000000000000000; 29.00000000000000000, 46.0
! 1969: 0000000000000000, 453.0000000000000000], [3, 1, 29; 1, 29, 46; 29, 46, 453],
! 1970: [10889, 5698, 3794; 0, 1, 0; 0, 0, 1], [11021, 881, -795; 881, 518, -109; -
! 1971: 795, -109, 86], [10889, [1890, 5190, 1]~, 118570321]], [-3.23373269598151667
! 1972: 3, -0.07182350902743636344, 4.305556205008953036], [1, x, x^2], [1, 0, 0; 0,
! 1973: 1, 0; 0, 0, 1], [1, 0, 0, 0, 0, 1, 0, 1, 1; 0, 1, 0, 1, 0, 14, 0, 14, 15; 0
! 1974: , 0, 1, 0, 1, 1, 1, 1, 15]], [[2, [2], [[3, 2, 2; 0, 1, 0; 0, 0, 1]]], 10.34
! 1975: 800724602767998, 1.000000000000000000, [2, -1], [x, x^2 + 2*x - 4], 1000], [
! 1976: mat(1), mat(1), [[[3, 2, 2; 0, 1, 0; 0, 0, 1], [0, 0, 0]]]], 0]
! 1977: ? concat(mat(vector(4,x,x)~),vector(4,x,10+x)~)
! 1978:
! 1979: [1 11]
! 1980:
! 1981: [2 12]
! 1982:
! 1983: [3 13]
! 1984:
! 1985: [4 14]
! 1986:
! 1987: ? matextract(matrix(15,15,x,y,x+y),vector(5,x,3*x),vector(3,y,3*y))
! 1988:
! 1989: [6 9 12]
! 1990:
! 1991: [9 12 15]
! 1992:
! 1993: [12 15 18]
! 1994:
! 1995: [15 18 21]
! 1996:
! 1997: [18 21 24]
! 1998:
! 1999: ? ma=mathell(mcurve,mpoints)
! 2000:
! 2001: [1.172183098700697010 0.4476973883408951692]
! 2002:
! 2003: [0.4476973883408951692 1.755026016172950713]
! 2004:
! 2005: ? gauss(ma,mhbi)
! 2006: [-1.000000000000000000, 1.000000000000000000]~
! 2007: ? (1.*hilbert(7))^(-1)
! 2008:
! 2009: [48.99999999999354616 -1175.999999999759026 8819.999999997789586 -29399.9999
! 2010: 9999171836 48509.99999998526254 -38807.99999998756766 12011.99999999599856]
! 2011:
! 2012: [-1175.999999999756499 37631.99999999093860 -317519.9999999170483 1128959.99
! 2013: 9999689868 -1940399.999999448886 1596671.999999535762 -504503.9999998507690]
! 2014:
! 2015: [8819.999999997745604 -317519.9999999163090 2857679.999999235184 -10583999.9
! 2016: 9999714478 18710999.99999493212 -15717239.99999573533 5045039.999998630382]
! 2017:
! 2018: [-29399.99999999149442 1128959.999999684822 -10583999.99999712372 40319999.9
! 2019: 9998927448 -72764999.99998098063 62092799.99998400783 -20180159.99999486766]
! 2020:
! 2021: [48509.99999998476962 -1940399.999999436456 18710999.99999486299 -72764999.9
! 2022: 9998086196 133402499.9999660890 -115259759.9999715052 37837799.99999086044]
! 2023:
! 2024: [-38807.99999998708779 1596671.999999522805 -15717239.99999565420 62092799.9
! 2025: 9998382209 -115259759.9999713525 100590335.9999759413 -33297263.99999228701]
! 2026:
! 2027: [12011.99999999582671 -504503.9999998459239 5045039.999998597949 -20180159.9
! 2028: 9999478405 37837799.99999076882 -33297263.99999225112 11099087.99999751679]
! 2029:
! 2030: ? matsize([1,2;3,4;5,6])
! 2031: [3, 2]
! 2032: ? matrix(5,5,x,y,gcd(x,y))
! 2033:
! 2034: [1 1 1 1 1]
! 2035:
! 2036: [1 2 1 2 1]
! 2037:
! 2038: [1 1 3 1 1]
! 2039:
! 2040: [1 2 1 4 1]
! 2041:
! 2042: [1 1 1 1 5]
! 2043:
! 2044: ? matrixqz([1,3;3,5;5,7],0)
! 2045:
! 2046: [1 1]
! 2047:
! 2048: [3 2]
! 2049:
! 2050: [5 3]
! 2051:
! 2052: ? matrixqz2([1/3,1/4,1/6;1/2,1/4,-1/4;1/3,1,0])
! 2053:
! 2054: [19 12 2]
! 2055:
! 2056: [0 1 0]
! 2057:
! 2058: [0 0 1]
! 2059:
! 2060: ? matrixqz3([1,3;3,5;5,7])
! 2061:
! 2062: [2 -1]
! 2063:
! 2064: [1 0]
! 2065:
! 2066: [0 1]
! 2067:
! 2068: ? max(2,3)
! 2069: 3
! 2070: ? min(2,3)
! 2071: 2
! 2072: ? minim([2,1;1,2],4,6)
! 2073: [6, 2, [0, -1, 1; 1, 1, 0]]
! 2074: ? mod(-12,7)
! 2075: mod(2, 7)
! 2076: ? modp(-12,7)
! 2077: mod(2, 7)
! 2078: ? mod(10873,49649)^-1
! 2079: *** impossible inverse modulo: mod(131, 49649).
! 2080:
! 2081: ? modreverse(mod(x^2+1,x^3-x-1))
! 2082: mod(x^2 - 3*x + 2, x^3 - 5*x^2 + 8*x - 5)
! 2083: ? move(0,243,583);cursor(0)
! 2084: ? mu(3*5*7*11*13)
! 2085: -1
! 2086: ? newtonpoly(x^4+3*x^3+27*x^2+9*x+81,3)
! 2087: [2, 2/3, 2/3, 2/3]
! 2088: ? nextprime(100000000000000000000000)
! 2089: 100000000000000000000117
! 2090: ? setrand(1);a=matrix(3,5,j,k,vvector(5,l,random()\10^8))
! 2091:
! 2092: [[10, 7, 8, 7, 18]~ [17, 0, 9, 20, 10]~ [5, 4, 7, 18, 20]~ [0, 16, 4, 2, 0]~
! 2093: [17, 19, 17, 1, 14]~]
! 2094:
! 2095: [[17, 16, 6, 3, 6]~ [17, 13, 9, 19, 6]~ [1, 14, 12, 20, 8]~ [6, 1, 8, 17, 21
! 2096: ]~ [18, 17, 9, 10, 13]~]
! 2097:
! 2098: [[4, 13, 3, 17, 14]~ [14, 16, 11, 5, 4]~ [9, 11, 13, 7, 15]~ [19, 21, 2, 4,
! 2099: 5]~ [14, 16, 6, 20, 14]~]
! 2100:
! 2101: ? aid=[idx,idy,idz,idmat(5),idx]
! 2102: [[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]
! 2103: , [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
! 2104: ], [15, 5, 10, 12, 10; 0, 5, 0, 0, 0; 0, 0, 5, 2, 0; 0, 0, 0, 1, 0; 0, 0, 0,
! 2105: 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
! 2106: , 0, 1], [3, 1, 2, 2, 2; 0, 1, 0, 0, 0; 0, 0, 1, 0, 0; 0, 0, 0, 1, 0; 0, 0,
! 2107: 0, 0, 1]]
! 2108: ? bb=algtobasis(nf,mod(x^3+x,nfpol))
! 2109: [1, 1, 1, 3, 0]~
! 2110: ? da=nfdetint(nf,[a,aid])
! 2111:
! 2112: [30 5 25 27 10]
! 2113:
! 2114: [0 5 0 0 0]
! 2115:
! 2116: [0 0 5 2 0]
! 2117:
! 2118: [0 0 0 1 0]
! 2119:
! 2120: [0 0 0 0 5]
! 2121:
! 2122: ? nfdiv(nf,ba,bb)
! 2123: [755/373, -152/373, 159/373, 120/373, -264/373]~
! 2124: ? nfdiveuc(nf,ba,bb)
! 2125: [2, 0, 0, 0, -1]~
! 2126: ? nfdivres(nf,ba,bb)
! 2127: [[2, 0, 0, 0, -1]~, [-12, -7, 0, 9, 5]~]
! 2128: ? nfhermite(nf,[a,aid])
! 2129: [[[1, 0, 0, 0, 0]~, [0, 0, 0, 0, 0]~, [0, 0, 0, 0, 0]~; [0, 0, 0, 0, 0]~, [1
! 2130: , 0, 0, 0, 0]~, [0, 0, 0, 0, 0]~; [0, 0, 0, 0, 0]~, [0, 0, 0, 0, 0]~, [1, 0,
! 2131: 0, 0, 0]~], [[2, 1, 1, 1, 0; 0, 1, 0, 0, 0; 0, 0, 1, 0, 0; 0, 0, 0, 1, 0; 0
! 2132: , 0, 0, 0, 1], [1, 0, 0, 0, 0; 0, 1, 0, 0, 0; 0, 0, 1, 0, 0; 0, 0, 0, 1, 0;
! 2133: 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;
! 2134: 0, 0, 0, 0, 1]]]
! 2135: ? nfhermitemod(nf,[a,aid],da)
! 2136: [[[1, 0, 0, 0, 0]~, [0, 0, 0, 0, 0]~, [0, 0, 0, 0, 0]~; [0, 0, 0, 0, 0]~, [1
! 2137: , 0, 0, 0, 0]~, [0, 0, 0, 0, 0]~; [0, 0, 0, 0, 0]~, [0, 0, 0, 0, 0]~, [1, 0,
! 2138: 0, 0, 0]~], [[2, 1, 1, 1, 0; 0, 1, 0, 0, 0; 0, 0, 1, 0, 0; 0, 0, 0, 1, 0; 0
! 2139: , 0, 0, 0, 1], [1, 0, 0, 0, 0; 0, 1, 0, 0, 0; 0, 0, 1, 0, 0; 0, 0, 0, 1, 0;
! 2140: 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;
! 2141: 0, 0, 0, 0, 1]]]
! 2142: ? nfmod(nf,ba,bb)
! 2143: [-12, -7, 0, 9, 5]~
! 2144: ? nfmul(nf,ba,bb)
! 2145: [-25, -50, -30, 15, 90]~
! 2146: ? nfpow(nf,bb,5)
! 2147: [23455, 156370, 115855, 74190, -294375]~
! 2148: ? nfreduce(nf,ba,idx)
! 2149: [1, 0, 0, 0, 0]~
! 2150: ? setrand(1);as=matrix(3,3,j,k,vvector(5,l,random()\10^8))
! 2151:
! 2152: [[10, 7, 8, 7, 18]~ [17, 0, 9, 20, 10]~ [5, 4, 7, 18, 20]~]
! 2153:
! 2154: [[17, 16, 6, 3, 6]~ [17, 13, 9, 19, 6]~ [1, 14, 12, 20, 8]~]
! 2155:
! 2156: [[4, 13, 3, 17, 14]~ [14, 16, 11, 5, 4]~ [9, 11, 13, 7, 15]~]
! 2157:
! 2158: ? vaid=[idx,idy,idmat(5)]
! 2159: [[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]
! 2160: , [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
! 2161: ], [1, 0, 0, 0, 0; 0, 1, 0, 0, 0; 0, 0, 1, 0, 0; 0, 0, 0, 1, 0; 0, 0, 0, 0,
! 2162: 1]]
! 2163: ? haid=[idmat(5),idmat(5),idmat(5)]
! 2164: [[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]
! 2165: , [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
! 2166: ], [1, 0, 0, 0, 0; 0, 1, 0, 0, 0; 0, 0, 1, 0, 0; 0, 0, 0, 1, 0; 0, 0, 0, 0,
! 2167: 1]]
! 2168: ? nfsmith(nf,[as,haid,vaid])
! 2169: [[10951073973332888246310, 5442457637639729109215, 2693780223637146570055, 3
! 2170: 910837124677073032737, 3754666252923836621170; 0, 5, 0, 0, 0; 0, 0, 5, 2, 0;
! 2171: 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
! 2172: ; 0, 0, 0, 1, 0; 0, 0, 0, 0, 1], [1, 0, 0, 0, 0; 0, 1, 0, 0, 0; 0, 0, 1, 0,
! 2173: 0; 0, 0, 0, 1, 0; 0, 0, 0, 0, 1]]
! 2174: ? nfval(nf,ba,vp)
! 2175: 0
! 2176: ? norm(1+i)
! 2177: 2
! 2178: ? norm(mod(x+5,x^3+x+1))
! 2179: 129
! 2180: ? norml2(vector(10,x,x))
! 2181: 385
! 2182: ? nucomp(qfi(2,1,9),qfi(4,3,5),3)
! 2183: qfi(2, -1, 9)
! 2184: ? form=qfi(2,1,9);nucomp(form,form,3)
! 2185: qfi(4, -3, 5)
! 2186: ? numdiv(2^99*3^49)
! 2187: 5000
! 2188: ? numer((x+1)/(x-1))
! 2189: x + 1
! 2190: ? nupow(form,111)
! 2191: qfi(2, -1, 9)
! 2192: ? 1/(1+x)+o(x^20)
! 2193: 1 - x + x^2 - x^3 + x^4 - x^5 + x^6 - x^7 + x^8 - x^9 + x^10 - x^11 + x^12 -
! 2194: x^13 + x^14 - x^15 + x^16 - x^17 + x^18 - x^19 + O(x^20)
! 2195: ? omega(100!)
! 2196: 25
! 2197: ? ordell(acurve,1)
! 2198: [8, 3]
! 2199: ? order(mod(33,2^16+1))
! 2200: 2048
! 2201: ? tcurve=initell([1,0,1,-19,26]);
! 2202: ? orderell(tcurve,[1,2])
! 2203: 6
! 2204: ? ordred(x^3-12*x+45*x-1)
! 2205: [x - 1, x^3 - 363*x - 2663, x^3 + 33*x - 1]
! 2206: ? padicprec(padicno,127)
! 2207: 5
! 2208: ? pascal(8)
! 2209:
! 2210: [1 0 0 0 0 0 0 0 0]
! 2211:
! 2212: [1 1 0 0 0 0 0 0 0]
! 2213:
! 2214: [1 2 1 0 0 0 0 0 0]
! 2215:
! 2216: [1 3 3 1 0 0 0 0 0]
! 2217:
! 2218: [1 4 6 4 1 0 0 0 0]
! 2219:
! 2220: [1 5 10 10 5 1 0 0 0]
! 2221:
! 2222: [1 6 15 20 15 6 1 0 0]
! 2223:
! 2224: [1 7 21 35 35 21 7 1 0]
! 2225:
! 2226: [1 8 28 56 70 56 28 8 1]
! 2227:
! 2228: ? perf([2,0,1;0,2,1;1,1,2])
! 2229: 6
! 2230: ? permutation(7,1035)
! 2231: [4, 7, 1, 6, 3, 5, 2]
! 2232: ? permutation2num([4,7,1,6,3,5,2])
! 2233: 1035
! 2234: ? pf(-44,3)
! 2235: qfi(3, 2, 4)
! 2236: ? phi(257^2)
! 2237: 65792
! 2238: ? pi
! 2239: 3.141592653589793238
! 2240: ? plot(x=-5,5,sin(x))
! 2241:
! 2242: 0.9995545 x""x_''''''''''''''''''''''''''''''''''_x""x'''''''''''''''''''|
! 2243: | x _ "_ |
! 2244: | x _ _ |
! 2245: | x _ |
! 2246: | _ " |
! 2247: | " x |
! 2248: | x _ |
! 2249: | " |
! 2250: | " x _ |
! 2251: | _ |
! 2252: | " x |
! 2253: ````````````x``````````````````_````````````````````````````````
! 2254: | " |
! 2255: | " x _ |
! 2256: | _ |
! 2257: | " x |
! 2258: | x _ |
! 2259: | _ " |
! 2260: | " x |
! 2261: | " " x |
! 2262: | "_ " x |
! 2263: -0.999555 |...................x__x".................................."x__x
! 2264: -5 5
! 2265: ? pnqn([2,6,10,14,18,22,26])
! 2266:
! 2267: [19318376 741721]
! 2268:
! 2269: [8927353 342762]
! 2270:
! 2271: ? pnqn([1,1,1,1,1,1,1,1;1,1,1,1,1,1,1,1])
! 2272:
! 2273: [34 21]
! 2274:
! 2275: [21 13]
! 2276:
! 2277: ? point(0,225,334)
! 2278: ? points(0,vector(10,k,10*k),vector(10,k,5*k*k))
! 2279: ? pointell(acurve,zell(acurve,apoint))
! 2280: [0.9999999999999999986 + 0.E-19*I, 2.999999999999999998 + 0.E-18*I]
! 2281: ? polint([0,2,3],[0,4,9],5)
! 2282: 25
! 2283: ? polred(x^5-2*x^4-4*x^3-96*x^2-352*x-568)
! 2284: [x - 1, x^5 - x^4 - 6*x^3 + 6*x^2 + 13*x - 5, x^5 - x^4 + 2*x^3 - 4*x^2 + x
! 2285: - 1, x^5 - x^4 + 4*x^3 - 2*x^2 + x - 1, x^5 + 4*x^3 - 4*x^2 + 8*x - 8]
! 2286: ? polred2(x^4-28*x^3-458*x^2+9156*x-25321)
! 2287:
! 2288: [1 x - 1]
! 2289:
! 2290: [1/115*x^2 - 14/115*x - 327/115 x^2 - 10]
! 2291:
! 2292: [3/1495*x^3 - 63/1495*x^2 - 1607/1495*x + 13307/1495 x^4 - 32*x^2 + 216]
! 2293:
! 2294: [1/4485*x^3 - 7/1495*x^2 - 1034/4485*x + 7924/4485 x^4 - 8*x^2 + 6]
! 2295:
! 2296: ? polredabs(x^5-2*x^4-4*x^3-96*x^2-352*x-568)
! 2297: x^5 - x^4 + 2*x^3 - 4*x^2 + x - 1
! 2298: ? polredabs2(x^5-2*x^4-4*x^3-96*x^2-352*x-568)
! 2299: [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 -
! 2300: x^4 + 2*x^3 - 4*x^2 + x - 1)]
! 2301: ? polsym(x^17-1,17)
! 2302: [17, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 17]~
! 2303: ? polvar(name^4-other)
! 2304: name
! 2305: ? poly(sin(x),x)
! 2306: -1/1307674368000*x^15 + 1/6227020800*x^13 - 1/39916800*x^11 + 1/362880*x^9 -
! 2307: 1/5040*x^7 + 1/120*x^5 - 1/6*x^3 + x
! 2308: ? polylog(5,0.5)
! 2309: 0.5084005792422687065
! 2310: ? polylog(-4,t)
! 2311: (t^4 + 11*t^3 + 11*t^2 + t)/(-t^5 + 5*t^4 - 10*t^3 + 10*t^2 - 5*t + 1)
! 2312: ? polylogd(5,0.5)
! 2313: 1.033792745541689061
! 2314: ? polylogdold(5,0.5)
! 2315: 1.034459423449010483
! 2316: ? polylogp(5,0.5)
! 2317: 0.9495693489964922581
! 2318: ? poly([1,2,3,4,5],x)
! 2319: x^4 + 2*x^3 + 3*x^2 + 4*x + 5
! 2320: ? polyrev([1,2,3,4,5],x)
! 2321: 5*x^4 + 4*x^3 + 3*x^2 + 2*x + 1
! 2322: ? polzag(6,3)
! 2323: 4608*x^6 - 13824*x^5 + 46144/3*x^4 - 23168/3*x^3 + 5032/3*x^2 - 120*x + 1
! 2324: ? postdraw([0,20,20])
! 2325: ? postploth(x=-5,5,sin(x))
! 2326: [-5.000000000000000000, 5.000000000000000000, -0.9999964107564721649, 0.9999
! 2327: 964107564721649]
! 2328: ? postploth2(t=0,2*pi,[sin(5*t),sin(7*t)])
! 2329: [-0.9999994509568810308, 0.9999994509568810308, -0.9999994509568810308, 0.99
! 2330: 99994509568810308]
! 2331: ? postplothraw(vector(100,k,k),vector(100,k,k*k/100))
! 2332: [1.000000000000000000, 100.0000000000000000, 0.01000000000000000020, 100.000
! 2333: 0000000000000]
! 2334: ? powell(acurve,apoint,10)
! 2335: [-28919032218753260057646013785951999/292736325329248127651484680640160000,
! 2336: 478051489392386968218136375373985436596569736643531551/158385319626308443937
! 2337: 475969221994173751192384064000000]
! 2338: ? cmcurve=initell([0,-3/4,0,-2,-1])
! 2339: [0, -3/4, 0, -2, -1, -3, -4, -4, -1, 105, 1323, -343, -3375, [1.999999999999
! 2340: 999999, -0.6250000000000000000 + 0.3307189138830738238*I, -0.625000000000000
! 2341: 0000 - 0.3307189138830738238*I]~, 1.933311705616811546, 0.966655852808405773
! 2342: 4 + 2.557530989916099474*I, -0.8558486330998558523 - 4.598829817026853561 E-
! 2343: 20*I, -0.4279243165499279261 - 2.757161217166147204*I, 4.944504600282546729]
! 2344: ? powell(cmcurve,[x,y],quadgen(-7))
! 2345: [((-2 + 3*w)*x^2 + (6 - w))/((-2 - 5*w)*x + (-4 - 2*w)), ((34 - 11*w)*x^3 +
! 2346: (40 - 28*w)*x^2 + (22 + 23*w)*x)/((-90 - w)*x^2 + (-136 + 44*w)*x + (-40 + 2
! 2347: 8*w))]
! 2348: ? powrealraw(qfr(5,3,-1,0.),3)
! 2349: qfr(125, 23, 1, 0.E-18)
! 2350: ? pprint((x-12*y)/(y+13*x));
! 2351: (-(11 /14))
! 2352: ? pprint([1,2;3,4])
! 2353:
! 2354: [1 2]
! 2355:
! 2356: [3 4]
! 2357:
! 2358: ? pprint1(x+y);pprint(x+y);
! 2359: (2 x)(2 x)
! 2360: ? \precision=96
! 2361: realprecision = 96 significant digits
! 2362: ? pi
! 2363: 3.14159265358979323846264338327950288419716939937510582097494459230781640628
! 2364: 620899862803482534211
! 2365: ? prec(pi,20)
! 2366: 3.14159265358979323846264338325408976600000000000000000000000000000000000000
! 2367: 000000000000000000000
! 2368: ? precision(cmcurve)
! 2369: 19
! 2370: ? \precision=38
! 2371: realprecision = 38 significant digits
! 2372: ? prime(100)
! 2373: 541
! 2374: ? primedec(nf,2)
! 2375: [[2, [3, 1, 0, 0, 0]~, 1, 1, [1, 1, 0, 1, 1]~], [2, [-3, -5, -4, 3, 15]~, 1,
! 2376: 4, [1, 1, 0, 0, 0]~]]
! 2377: ? primedec(nf,3)
! 2378: [[3, [1, 1, 0, 0, 0]~, 1, 1, [1, -1, -1, 0, 0]~], [3, [-1, 1, -1, 0, 1]~, 2,
! 2379: 2, [1, 2, 3, 1, 0]~]]
! 2380: ? primedec(nf,11)
! 2381: [[11, [11, 0, 0, 0, 0]~, 1, 5, [1, 0, 0, 0, 0]~]]
! 2382: ? primes(100)
! 2383: [2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71,
! 2384: 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151,
! 2385: 157, 163, 167, 173, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229, 233, 2
! 2386: 39, 241, 251, 257, 263, 269, 271, 277, 281, 283, 293, 307, 311, 313, 317, 33
! 2387: 1, 337, 347, 349, 353, 359, 367, 373, 379, 383, 389, 397, 401, 409, 419, 421
! 2388: , 431, 433, 439, 443, 449, 457, 461, 463, 467, 479, 487, 491, 499, 503, 509,
! 2389: 521, 523, 541]
! 2390: ? forprime(p=2,100,print(p," ",lift(primroot(p))))
! 2391: 2 1
! 2392: 3 2
! 2393: 5 2
! 2394: 7 3
! 2395: 11 2
! 2396: 13 2
! 2397: 17 3
! 2398: 19 2
! 2399: 23 5
! 2400: 29 2
! 2401: 31 3
! 2402: 37 2
! 2403: 41 6
! 2404: 43 3
! 2405: 47 5
! 2406: 53 2
! 2407: 59 2
! 2408: 61 2
! 2409: 67 2
! 2410: 71 7
! 2411: 73 5
! 2412: 79 3
! 2413: 83 2
! 2414: 89 3
! 2415: 97 5
! 2416: ? principalideal(nf,mod(x^3+5,nfpol))
! 2417:
! 2418: [6]
! 2419:
! 2420: [0]
! 2421:
! 2422: [1]
! 2423:
! 2424: [3]
! 2425:
! 2426: [0]
! 2427:
! 2428: ? principalidele(nf,mod(x^3+5,nfpol))
! 2429: [[6; 0; 1; 3; 0], [2.2324480827796254080981385584384939684 + 3.1415926535897
! 2430: 932384626433832795028842*I, 5.0387659675158716386435353106610489968 + 1.5851
! 2431: 760343512250049897278861965702423*I, 4.2664040272651028743625910797589683173
! 2432: - 0.0083630478144368246110910258645462996191*I]]
! 2433: ? print((x-12*y)/(y+13*x));
! 2434: -11/14
! 2435: ? print([1,2;3,4])
! 2436: [1, 2; 3, 4]
! 2437: ? print1(x+y);print1(" equals ");print(x+y);
! 2438: 2*x equals 2*x
! 2439: ? prod(1,k=1,10,1+1/k!)
! 2440: 3335784368058308553334783/905932868585678438400000
! 2441: ? prod(1.,k=1,10,1+1/k!)
! 2442: 3.6821540356142043935732308433185262945
! 2443: ? pi^2/6*prodeuler(p=2,10000,1-p^-2)
! 2444: 1.0000098157493066238697591433298145174
! 2445: ? prodinf(n=0,(1+2^-n)/(1+2^(-n+1)))
! 2446: 0.33333333333333333333333333333333333322
! 2447: ? prodinf1(n=0,-2^-n/(1+2^(-n+1)))
! 2448: 0.33333333333333333333333333333333333322
! 2449: ? psi(1)
! 2450: -0.57721566490153286060651209008240243102
! 2451: ? quaddisc(-252)
! 2452: -7
! 2453: ? quadgen(-11)
! 2454: w
! 2455: ? quadpoly(-11)
! 2456: x^2 - x + 3
! 2457: ? rank(matrix(5,5,x,y,x+y))
! 2458: 2
! 2459: ? rayclassno(bnf,[[5,3;0,1],[1,0]])
! 2460: 12
! 2461: ? rayclassnolist(bnf,lu)
! 2462: [[3], [], [3, 3], [3], [6, 6], [], [], [], [3, 3, 3], [], [3, 3], [3, 3], []
! 2463: , [], [12, 6, 6, 12], [3], [3, 3], [], [9, 9], [6, 6], [], [], [], [], [6, 1
! 2464: 2, 6], [], [3, 3, 3, 3], [], [], [], [], [], [3, 6, 6, 3], [], [], [9, 3, 9]
! 2465: , [6, 6], [], [], [], [], [], [3, 3], [3, 3], [12, 12, 6, 6, 12, 12], [], []
! 2466: , [6, 6], [9], [], [3, 3, 3, 3], [], [3, 3], [], [6, 12, 12, 6]]
! 2467: ? move(0,50,50);rbox(0,50,50)
! 2468: ? print1("give a value for s? ");s=read();print(1/s)
! 2469: give a value for s? 37.
! 2470: 0.027027027027027027027027027027027027026
! 2471: ? real(5-7*i)
! 2472: 5
! 2473: ? recip(3*x^7-5*x^3+6*x-9)
! 2474: -9*x^7 + 6*x^6 - 5*x^4 + 3
! 2475: ? redimag(qfi(3,10,12))
! 2476: qfi(3, -2, 4)
! 2477: ? redreal(qfr(3,10,-20,1.5))
! 2478: qfr(3, 16, -7, 1.5000000000000000000000000000000000000)
! 2479: ? redrealnod(qfr(3,10,-20,1.5),18)
! 2480: qfr(3, 16, -7, 1.5000000000000000000000000000000000000)
! 2481: ? reduceddisc(x^3+4*x+12)
! 2482: [1036, 4, 1]
! 2483: ? regula(17)
! 2484: 2.0947125472611012942448228460655286534
! 2485: ? kill(y);print(x+y);reorder([x,y]);print(x+y);
! 2486: x + y
! 2487: x + y
! 2488: ? resultant(x^3-1,x^3+1)
! 2489: 8
! 2490: ? resultant2(x^3-1.,x^3+1.)
! 2491: 8.0000000000000000000000000000000000000
! 2492: ? reverse(tan(x))
! 2493: x - 1/3*x^3 + 1/5*x^5 - 1/7*x^7 + 1/9*x^9 - 1/11*x^11 + 1/13*x^13 - 1/15*x^1
! 2494: 5 + O(x^16)
! 2495: ? rhoreal(qfr(3,10,-20,1.5))
! 2496: qfr(-20, -10, 3, 2.1074451073987839947135880252731470615)
! 2497: ? rhorealnod(qfr(3,10,-20,1.5),18)
! 2498: qfr(-20, -10, 3, 1.5000000000000000000000000000000000000)
! 2499: ? rline(0,200,150)
! 2500: ? cursor(0)
! 2501: ? rmove(0,5,5);cursor(0)
! 2502: ? rndtoi(prod(1,k=1,17,x-exp(2*i*pi*k/17)))
! 2503: x^17 - 1
! 2504: ? qpol=y^3-y-1;setrand(1);bnf2=buchinit(qpol);nf2=bnf2[7];
! 2505: ? un=mod(1,qpol);w=mod(y,qpol);p=un*(x^5-5*x+w)
! 2506: mod(1, y^3 - y - 1)*x^5 + mod(-5, y^3 - y - 1)*x + mod(y, y^3 - y - 1)
! 2507: ? aa=rnfpseudobasis(nf2,p)
! 2508: [[[1, 0, 0]~, [0, 0, 0]~, [0, 0, 0]~, [-2, 0, 0]~, [11, 0, 0]~; [0, 0, 0]~,
! 2509: [1, 0, 0]~, [0, 0, 0]~, [2, 0, 0]~, [-8, 0, 0]~; [0, 0, 0]~, [0, 0, 0]~, [1,
! 2510: 0, 0]~, [1, 0, 0]~, [4, 0, 0]~; [0, 0, 0]~, [0, 0, 0]~, [0, 0, 0]~, [1, 0,
! 2511: 0]~, [-2, 0, 0]~; [0, 0, 0]~, [0, 0, 0]~, [0, 0, 0]~, [0, 0, 0]~, [1, 0, 0]~
! 2512: ], [[1, 0, 0; 0, 1, 0; 0, 0, 1], [1, 0, 0; 0, 1, 0; 0, 0, 1], [1, 0, 0; 0, 1
! 2513: , 0; 0, 0, 1], [1, 0, 3/5; 0, 1, 2/5; 0, 0, 1/5], [1, 0, 8/25; 0, 1, 22/25;
! 2514: 0, 0, 1/25]], [416134375, 212940625, 388649575; 0, 3125, 550; 0, 0, 25], [-1
! 2515: 280, 5, 5]~]
! 2516: ? rnfbasis(bnf2,aa)
! 2517:
! 2518: [[1, 0, 0]~ [0, 0, 0]~ [0, 0, 0]~ [4/5, -4/5, -2/5]~ [187/25, 208/25, -61/25
! 2519: ]~]
! 2520:
! 2521: [[0, 0, 0]~ [1, 0, 0]~ [0, 0, 0]~ [-4/5, 4/5, 2/5]~ [-196/25, -214/25, 88/25
! 2522: ]~]
! 2523:
! 2524: [[0, 0, 0]~ [0, 0, 0]~ [1, 0, 0]~ [-2/5, 2/5, 1/5]~ [-122/25, -123/25, 116/2
! 2525: 5]~]
! 2526:
! 2527: [[0, 0, 0]~ [0, 0, 0]~ [0, 0, 0]~ [-2/5, 2/5, 1/5]~ [-104/25, -111/25, 62/25
! 2528: ]~]
! 2529:
! 2530: [[0, 0, 0]~ [0, 0, 0]~ [0, 0, 0]~ [0, 0, 0]~ [-3/25, -2/25, 9/25]~]
! 2531:
! 2532: ? rnfdiscf(nf2,p)
! 2533: [[416134375, 212940625, 388649575; 0, 3125, 550; 0, 0, 25], [-1280, 5, 5]~]
! 2534: ? rnfequation(nf2,p)
! 2535: x^15 - 15*x^11 + 75*x^7 - x^5 - 125*x^3 + 5*x + 1
! 2536: ? rnfequation2(nf2,p)
! 2537: [x^15 - 15*x^11 + 75*x^7 - x^5 - 125*x^3 + 5*x + 1, mod(-x^5 + 5*x, x^15 - 1
! 2538: 5*x^11 + 75*x^7 - x^5 - 125*x^3 + 5*x + 1), 0]
! 2539: ? rnfhermitebasis(bnf2,aa)
! 2540:
! 2541: [[1, 0, 0]~ [0, 0, 0]~ [0, 0, 0]~ [-2/5, 2/5, -4/5]~ [11/25, 99/25, -33/25]~
! 2542: ]
! 2543:
! 2544: [[0, 0, 0]~ [1, 0, 0]~ [0, 0, 0]~ [2/5, -2/5, 4/5]~ [-8/25, -72/25, 24/25]~]
! 2545:
! 2546: [[0, 0, 0]~ [0, 0, 0]~ [1, 0, 0]~ [1/5, -1/5, 2/5]~ [4/25, 36/25, -12/25]~]
! 2547:
! 2548: [[0, 0, 0]~ [0, 0, 0]~ [0, 0, 0]~ [1/5, -1/5, 2/5]~ [-2/25, -18/25, 6/25]~]
! 2549:
! 2550: [[0, 0, 0]~ [0, 0, 0]~ [0, 0, 0]~ [0, 0, 0]~ [1/25, 9/25, -3/25]~]
! 2551:
! 2552: ? rnfisfree(bnf2,aa)
! 2553: 1
! 2554: ? rnfsteinitz(nf2,aa)
! 2555: [[[1, 0, 0]~, [0, 0, 0]~, [0, 0, 0]~, [4/5, -4/5, -2/5]~, [39/125, 11/125, 1
! 2556: 1/125]~; [0, 0, 0]~, [1, 0, 0]~, [0, 0, 0]~, [-4/5, 4/5, 2/5]~, [-42/125, -8
! 2557: /125, -8/125]~; [0, 0, 0]~, [0, 0, 0]~, [1, 0, 0]~, [-2/5, 2/5, 1/5]~, [-29/
! 2558: 125, 4/125, 4/125]~; [0, 0, 0]~, [0, 0, 0]~, [0, 0, 0]~, [-2/5, 2/5, 1/5]~,
! 2559: [-23/125, -2/125, -2/125]~; [0, 0, 0]~, [0, 0, 0]~, [0, 0, 0]~, [0, 0, 0]~,
! 2560: [-1/125, 1/125, 1/125]~], [[1, 0, 0; 0, 1, 0; 0, 0, 1], [1, 0, 0; 0, 1, 0; 0
! 2561: , 0, 1], [1, 0, 0; 0, 1, 0; 0, 0, 1], [1, 0, 0; 0, 1, 0; 0, 0, 1], [125, 0,
! 2562: 108; 0, 125, 22; 0, 0, 1]], [416134375, 212940625, 388649575; 0, 3125, 550;
! 2563: 0, 0, 25], [-1280, 5, 5]~]
! 2564: ? rootmod(x^16-1,41)
! 2565: [mod(1, 41), mod(3, 41), mod(9, 41), mod(14, 41), mod(27, 41), mod(32, 41),
! 2566: mod(38, 41), mod(40, 41)]~
! 2567: ? rootpadic(x^4+1,41,6)
! 2568: [3 + 22*41 + 27*41^2 + 15*41^3 + 27*41^4 + 33*41^5 + O(41^6), 14 + 20*41 + 2
! 2569: 5*41^2 + 24*41^3 + 4*41^4 + 18*41^5 + O(41^6), 27 + 20*41 + 15*41^2 + 16*41^
! 2570: 3 + 36*41^4 + 22*41^5 + O(41^6), 38 + 18*41 + 13*41^2 + 25*41^3 + 13*41^4 +
! 2571: 7*41^5 + O(41^6)]~
! 2572: ? roots(x^5-5*x^2-5*x-5)
! 2573: [2.0509134529831982130058170163696514536 + 0.E-38*I, -0.67063790319207539268
! 2574: 663382582902335603 + 0.84813118358634026680538906224199030917*I, -0.67063790
! 2575: 319207539268663382582902335603 - 0.84813118358634026680538906224199030917*I,
! 2576: -0.35481882329952371381627468235580237077 + 1.39980287391035466982975228340
! 2577: 62081964*I, -0.35481882329952371381627468235580237077 - 1.399802873910354669
! 2578: 8297522834062081964*I]~
! 2579: ? rootsold(x^4-1000000000000000000000)
! 2580: [-177827.94100389228012254211951926848447 + 0.E-38*I, 177827.941003892280122
! 2581: 54211951926848447 + 0.E-38*I, 6.6530622500127354998594589316364200753 E-111
! 2582: + 177827.94100389228012254211951926848447*I, 6.65306225001273549985945893163
! 2583: 64200753 E-111 - 177827.94100389228012254211951926848447*I]~
! 2584: ? round(prod(1,k=1,17,x-exp(2*i*pi*k/17)))
! 2585: x^17 - 1
! 2586: ? rounderror(prod(1,k=1,17,x-exp(2*i*pi*k/17)))
! 2587: -35
! 2588: ? rpoint(0,20,20)
! 2589: ? initrect(3,600,600);scale(3,-7,7,-2,2);cursor(3)
! 2590: ? q*series(anell(acurve,100),q)
! 2591: 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 -
! 2592: 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*
! 2593: 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
! 2594: + 8*q^32 + 15*q^33 + 2*q^35 + 12*q^36 - q^37 + 6*q^39 - 9*q^41 - 6*q^42 + 2*
! 2595: 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
! 2596: ^52 + q^53 + 18*q^54 + 10*q^55 - 12*q^58 + 8*q^59 + 12*q^60 - 8*q^61 + 8*q^6
! 2597: 2 - 6*q^63 - 8*q^64 + 4*q^65 - 30*q^66 + 8*q^67 - 6*q^69 - 4*q^70 + 9*q^71 -
! 2598: 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
! 2599: ^82 - 15*q^83 + 6*q^84 - 4*q^86 - 18*q^87 + 4*q^89 + 24*q^90 + 2*q^91 + 4*q^
! 2600: 92 + 12*q^93 + 18*q^94 - 24*q^96 + 4*q^97 + 12*q^98 - 30*q^99 - 2*q^100 + O(
! 2601: q^101)
! 2602: ? aset=set([5,-2,7,3,5,1])
! 2603: ["-2", "1", "3", "5", "7"]
! 2604: ? bset=set([7,5,-5,7,2])
! 2605: ["-5", "2", "5", "7"]
! 2606: ? setintersect(aset,bset)
! 2607: ["5", "7"]
! 2608: ? setminus(aset,bset)
! 2609: ["-2", "1", "3"]
! 2610: ? setprecision(28)
! 2611: 38
! 2612: ? setrand(10)
! 2613: 10
! 2614: ? setsearch(aset,3)
! 2615: 3
! 2616: ? setsearch(bset,3)
! 2617: 0
! 2618: ? setserieslength(12)
! 2619: 16
! 2620: ? setunion(aset,bset)
! 2621: ["-2", "-5", "1", "2", "3", "5", "7"]
! 2622: ? arat=(x^3+x+1)/x^3;settype(arat,14)
! 2623: (x^3 + x + 1)/x^3
! 2624: ? shift(1,50)
! 2625: 1125899906842624
! 2626: ? shift([3,4,-11,-12],-2)
! 2627: [0, 1, -2, -3]
! 2628: ? shiftmul([3,4,-11,-12],-2)
! 2629: [3/4, 1, -11/4, -3]
! 2630: ? sigma(100)
! 2631: 217
! 2632: ? sigmak(2,100)
! 2633: 13671
! 2634: ? sigmak(-3,100)
! 2635: 1149823/1000000
! 2636: ? sign(-1)
! 2637: -1
! 2638: ? sign(0)
! 2639: 0
! 2640: ? sign(0.)
! 2641: 0
! 2642: ? signat(hilbert(5)-0.11*idmat(5))
! 2643: [2, 3]
! 2644: ? signunit(bnf)
! 2645:
! 2646: [-1]
! 2647:
! 2648: [1]
! 2649:
! 2650: ? simplefactmod(x^11+1,7)
! 2651:
! 2652: [1 1]
! 2653:
! 2654: [10 1]
! 2655:
! 2656: ? simplify(((x+i+1)^2-x^2-2*x*(i+1))^2)
! 2657: -4
! 2658: ? sin(pi/6)
! 2659: 0.4999999999999999999999999999
! 2660: ? sinh(1)
! 2661: 1.175201193643801456882381850
! 2662: ? size([1.3*10^5,2*i*pi*exp(4*pi)])
! 2663: 7
! 2664: ? smallbasis(x^3+4*x+12)
! 2665: [1, x, 1/2*x^2]
! 2666: ? smalldiscf(x^3+4*x+12)
! 2667: -1036
! 2668: ? smallfact(100!+1)
! 2669:
! 2670: [101 1]
! 2671:
! 2672: [14303 1]
! 2673:
! 2674: [149239 1]
! 2675:
! 2676: [432885273849892962613071800918658949059679308685024481795740765527568493010
! 2677: 727023757461397498800981521440877813288657839195622497225621499427628453 1]
! 2678:
! 2679: ? smallinitell([0,0,0,-17,0])
! 2680: [0, 0, 0, -17, 0, 0, -34, 0, -289, 816, 0, 314432, 1728]
! 2681: ? smallpolred(x^4+576)
! 2682: [x - 1, x^2 - x + 1, x^2 + 1, x^4 - x^2 + 1]
! 2683: ? smallpolred2(x^4+576)
! 2684:
! 2685: [1 x - 1]
! 2686:
! 2687: [-1/192*x^3 - 1/8*x + 1/2 x^2 - x + 1]
! 2688:
! 2689: [-1/24*x^2 x^2 + 1]
! 2690:
! 2691: [-1/192*x^3 + 1/48*x^2 + 1/8*x x^4 - x^2 + 1]
! 2692:
! 2693: ? smith(matrix(5,5,j,k,random()))
! 2694: [434644616238830047700451328, 2147483648, 2147483648, 1, 1]
! 2695: ? smith(1/hilbert(6))
! 2696: [27720, 2520, 2520, 840, 210, 6]
! 2697: ? smithpol(x*idmat(5)-matrix(5,5,j,k,1))
! 2698: [x^2 - 5*x, x, x, x, 1]
! 2699: ? solve(x=1,4,sin(x))
! 2700: 3.141592653589793238462643383
! 2701: ? sort(vector(17,x,5*x%17))
! 2702: [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16]
! 2703: ? sqr(1+o(2))
! 2704: 1 + O(2^3)
! 2705: ? sqred(hilbert(5))
! 2706:
! 2707: [1 1/2 1/3 1/4 1/5]
! 2708:
! 2709: [0 1/12 1 9/10 4/5]
! 2710:
! 2711: [0 0 1/180 3/2 12/7]
! 2712:
! 2713: [0 0 0 1/2800 2]
! 2714:
! 2715: [0 0 0 0 1/44100]
! 2716:
! 2717: ? sqrt(13+o(127^12))
! 2718: 34 + 125*127 + 83*127^2 + 107*127^3 + 53*127^4 + 42*127^5 + 22*127^6 + 98*12
! 2719: 7^7 + 127^8 + 23*127^9 + 122*127^10 + 79*127^11 + O(127^12)
! 2720: ? srgcd(x^10-1,x^15-1)
! 2721: x^5 - 1
! 2722: ? move(0,100,100);string(0,pi)
! 2723: ? move(0,200,200);string(0,"(0,0)")
! 2724: ? postdraw([0,10,10])
! 2725: ? apol=0.3+legendre(10)
! 2726: 46189/256*x^10 - 109395/256*x^8 + 45045/128*x^6 - 15015/128*x^4 + 3465/256*x
! 2727: ^2 + 0.05390624999999999999999999999
! 2728: ? sturm(apol)
! 2729: 4
! 2730: ? sturmpart(apol,0.91,1)
! 2731: 1
! 2732: ? subcyclo(31,5)
! 2733: x^5 + x^4 - 12*x^3 - 21*x^2 + x + 5
! 2734: ? subell(initell([0,0,0,-17,0]),[-1,4],[-4,2])
! 2735: [9, -24]
! 2736: ? subst(sin(x),x,y)
! 2737: y - 1/6*y^3 + 1/120*y^5 - 1/5040*y^7 + 1/362880*y^9 - 1/39916800*y^11 + O(y^
! 2738: 12)
! 2739: ? subst(sin(x),x,x+x^2)
! 2740: 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
! 2741: ^8 + 13609/362880*x^9 + 19/13440*x^10 - 273241/39916800*x^11 + O(x^12)
! 2742: ? sum(0,k=1,10,2^-k)
! 2743: 1023/1024
! 2744: ? sum(0.,k=1,10,2^-k)
! 2745: 0.9990234375000000000000000000
! 2746: ? sylvestermatrix(a2*x^2+a1*x+a0,b1*x+b0)
! 2747:
! 2748: [a2 b1 0]
! 2749:
! 2750: [a1 b0 b1]
! 2751:
! 2752: [a0 0 b0]
! 2753:
! 2754: ? \precision=38
! 2755: realprecision = 38 significant digits
! 2756: ? 4*sumalt(n=0,(-1)^n/(2*n+1))
! 2757: 3.1415926535897932384626433832795028841
! 2758: ? 4*sumalt2(n=0,(-1)^n/(2*n+1))
! 2759: 3.1415926535897932384626433832795028842
! 2760: ? suminf(n=1,2.^-n)
! 2761: 0.99999999999999999999999999999999999999
! 2762: ? 6/pi^2*sumpos(n=1,n^-2)
! 2763: 0.99999999999999999999999999999999999999
! 2764: ? supplement([1,3;2,4;3,6])
! 2765:
! 2766: [1 3 0]
! 2767:
! 2768: [2 4 0]
! 2769:
! 2770: [3 6 1]
! 2771:
! 2772: ? sqr(tan(pi/3))
! 2773: 2.9999999999999999999999999999999999999
! 2774: ? tanh(1)
! 2775: 0.76159415595576488811945828260479359041
! 2776: ? taniyama(bcurve)
! 2777: [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
! 2778: )]
! 2779: ? taylor(y/(x-y),y)
! 2780: (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
! 2781: ^7*x^4 + y^8*x^3 + y^9*x^2 + y^10*x + y^11)/x^11
! 2782: ? tchebi(10)
! 2783: 512*x^10 - 1280*x^8 + 1120*x^6 - 400*x^4 + 50*x^2 - 1
! 2784: ? teich(7+o(127^12))
! 2785: 7 + 57*127 + 58*127^2 + 83*127^3 + 52*127^4 + 109*127^5 + 74*127^6 + 16*127^
! 2786: 7 + 60*127^8 + 47*127^9 + 65*127^10 + 5*127^11 + O(127^12)
! 2787: ? texprint((x+y)^3/(x-y)^2)
! 2788: {{x^{3} + {{3}y}x^{2} + {{3}y^{2}}x + {y^{3}}}\over{x^{2} - {{2}y}x + {y^{2}
! 2789: }}}
! 2790: ? theta(0.5,3)
! 2791: 0.080806418251894691299871683210466298535
! 2792: ? thetanullk(0.5,7)
! 2793: -804.63037320243369422783730584965684022
! 2794: ? torsell(tcurve)
! 2795: [12, [6, 2], [[-2, 8], [3, -2]]]
! 2796: ? trace(1+i)
! 2797: 2
! 2798: ? trace(mod(x+5,x^3+x+1))
! 2799: 15
! 2800: ? trans(vector(2,x,x))
! 2801: [1, 2]~
! 2802: ? %*%~
! 2803:
! 2804: [1 2]
! 2805:
! 2806: [2 4]
! 2807:
! 2808: ? trunc(-2.7)
! 2809: -2
! 2810: ? trunc(sin(x^2))
! 2811: 1/120*x^10 - 1/6*x^6 + x^2
! 2812: ? tschirnhaus(x^5-x-1)
! 2813: x^5 - 8*x^3 + 16*x - 32
! 2814: ? type(mod(x,x^2+1))
! 2815: 9
! 2816: ? unit(17)
! 2817: 3 + 2*w
! 2818: ? n=33;until(n==1,print1(n," ");if(n%2,n=3*n+1,n=n/2));print(1)
! 2819: 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
! 2820: ? valuation(6^10000-1,5)
! 2821: 5
! 2822: ? vec(sin(x))
! 2823: [1, 0, -1/6, 0, 1/120, 0, -1/5040, 0, 1/362880, 0, -1/39916800]
! 2824: ? vecmax([-3,7,-2,11])
! 2825: 11
! 2826: ? vecmin([-3,7,-2,11])
! 2827: -3
! 2828: ? vecsort([[1,8,5],[2,5,8],[3,6,-6],[4,8,6]],2)
! 2829: [[2, 5, 8], [3, 6, -6], [4, 8, 6], [1, 8, 5]]
! 2830: ? vecsort([[1,8,5],[2,5,8],[3,6,-6],[4,8,6]],[2,1])
! 2831: [[2, 5, 8], [3, 6, -6], [1, 8, 5], [4, 8, 6]]
! 2832: ? weipell(acurve)
! 2833: x^-2 + 1/5*x^2 - 1/28*x^4 + 1/75*x^6 - 3/1540*x^8 + 1943/3822000*x^10 - 1/11
! 2834: 550*x^12 + 193/10510500*x^14 - 1269/392392000*x^16 + 21859/34684650000*x^18
! 2835: - 1087/9669660000*x^20 + O(x^22)
! 2836: ? wf(i)
! 2837: 1.1892071150027210667174999705604759152 - 1.17549435049295425400000000000000
! 2838: 00000 E-38*I
! 2839: ? wf2(i)
! 2840: 1.0905077326652576592070106557607079789 + 0.E-48*I
! 2841: ? m=5;while(m<20,print1(m," ");m=m+1);print()
! 2842: 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19
! 2843: ? zell(acurve,apoint)
! 2844: 0.72491221490962306778878739838332384646 + 0.E-58*I
! 2845: ? zeta(3)
! 2846: 1.2020569031595942853997381615114499907
! 2847: ? zeta(0.5+14.1347251*i)
! 2848: 0.0000000052043097453468479398562848599419244554 - 0.00000003269063986978698
! 2849: 2176409251733800562846*I
! 2850: ? zetak(nfz,-3)
! 2851: 0.091666666666666666666666666666666666666
! 2852: ? zetak(nfz,1.5+3*i)
! 2853: 0.88324345992059326405525724366416928890 - 0.2067536250233895222724230899142
! 2854: 7938845*I
! 2855: ? zidealstar(nf2,54)
! 2856: [132678, [1638, 9, 9], [[-27, 2, -27]~, [1, -24, 0]~, [1, 0, -24]~]]
! 2857: ? bid=zidealstarinit(nf2,54)
! 2858: [[[54, 0, 0; 0, 54, 0; 0, 0, 54], [0]], [132678, [1638, 9, 9]], [[2, [2, 0,
! 2859: 0]~, 1, 3, [1, 0, 0]~], 1; [3, [3, 0, 0]~, 1, 3, [1, 0, 0]~], 3], [[[[7], [[
! 2860: 0, 1, 0]~], [[-26, -27, 0]~], [[]~], 1]], [[[26], [[0, 2, 0]~], [[-27, 2, 0]
! 2861: ~], [[]~], 1], [[3, 3, 3], [[1, 3, 0]~, [1, 0, 3]~, [4, 0, 0]~], [[1, -24, 0
! 2862: ]~, [1, 0, -24]~, [-23, 0, 0]~], [[]~, []~, []~], [0, 1/3, 0; 0, 0, 1/3; 1/3
! 2863: , 0, 0]], [[3, 3, 3], [[1, 9, 0]~, [1, 0, 9]~, [10, 0, 0]~], [[1, -18, 0]~,
! 2864: [1, 0, -18]~, [-17, 0, 0]~], [[]~, []~, []~], [0, 1/9, 0; 0, 0, 1/9; 1/9, 0,
! 2865: 0]]], [[], [], [;]]], [468, 469, 0, 0, -48776, 0, 0, -36582; 0, 0, 1, 0, -7
! 2866: , -6, 0, -3; 0, 0, 0, 1, -3, 0, -6, 0]]
! 2867: ? zideallog(nf2,w,bid)
! 2868: [1574, 8, 6]~
! 2869: ? znstar(3120)
! 2870: [768, [12, 4, 4, 2, 2], [mod(67, 3120), mod(2341, 3120), mod(1847, 3120), mo
! 2871: d(391, 3120), mod(2081, 3120)]]
! 2872: ? getstack()
! 2873: 0
! 2874: ? getheap()
! 2875: [625, 126641]
! 2876: ? print("Total time spent: ",gettime());
! 2877: Total time spent: 19852
! 2878: ? \q
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