Annotation of OpenXM_contrib/pari-2.2/src/test/64/compat, Revision 1.1
1.1 ! noro 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, 0.E-77, 10.0000000000000000000000000000000
! 98: 00000, -5.0000000000000000000000000000000000000, 7.0000000000000000000000000
! 99: 000000000000; 0.E-77, 19.488486013650707197449403270536023970, 2.07268045322
! 100: 2666710 E-76, 19.488486013650707197449403270536023970, 4.1504592246706085588
! 101: 902013976045703227; 10.000000000000000000000000000000000000, 2.0726804532226
! 102: 66710 E-76, 85.960217420851846480305133936577594605, -36.0342682914829798382
! 103: 67056239752434596, 53.576130452511107888183080361946556763; -5.0000000000000
! 104: 000000000000000000000000, 19.488486013650707197449403270536023970, -36.03426
! 105: 8291482979838267056239752434596, 60.916248374441986300937507618575151517, -1
! 106: 8.470101750219179344070032346246890434; 7.0000000000000000000000000000000000
! 107: 000, 4.1504592246706085588902013976045703227, 53.576130452511107888183080361
! 108: 946556763, -18.470101750219179344070032346246890434, 37.97015289284236734089
! 109: 7384258599214282], [5, 0, 10, -5, 7; 0, 10, 0, 10, -5; 10, 0, 30, -55, 20; -
! 110: 5, 10, -55, 45, -39; 7, -5, 20, -39, 9], [345, 0, 340, 167, 150; 0, 345, 110
! 111: , 220, 153; 0, 0, 5, 2, 1; 0, 0, 0, 1, 0; 0, 0, 0, 0, 1], [132825, -18975, -
! 112: 5175, 27600, 17250; -18975, 34500, 41400, 3450, -43125; -5175, 41400, -41400
! 113: , -15525, 51750; 27600, 3450, -15525, -3450, 0; 17250, -43125, 51750, 0, -86
! 114: 250], [595125, [-13800, 117300, 67275, 1725, 0]~]], [-2.42851749071941860689
! 115: 92069565359418364, 1.9647119211288133163138753392090569931 + 0.8097149241889
! 116: 7895128294082219556466857*I, -0.75045317576910401286427186094108607489 + 1.3
! 117: 101462685358123283560773619310445915*I], [1, x, x^2, 1/3*x^3 - 1/3*x^2 - 1/3
! 118: , 1/15*x^4 + 1/3*x^2 + 1/3*x + 1/3], [1, 0, 0, 1, -5; 0, 1, 0, 0, -5; 0, 0,
! 119: 1, 1, -5; 0, 0, 0, 3, 0; 0, 0, 0, 0, 15], [1, 0, 0, 0, 0, 0, 0, 1, -2, -1, 0
! 120: , 1, -5, -5, -3, 0, -2, -5, 1, -4, 0, -1, -3, -4, -3; 0, 1, 0, 0, 0, 1, 0, 0
! 121: , -2, 0, 0, 0, -5, 0, -5, 0, -2, 0, -5, 0, 0, 0, -5, 0, -4; 0, 0, 1, 0, 0, 0
! 122: , 1, 1, -2, 1, 1, 1, -5, 3, -3, 0, -2, 3, -5, 1, 0, 1, -3, 1, -2; 0, 0, 0, 1
! 123: , 0, 0, 0, 3, -1, 2, 0, 3, 0, 5, 1, 1, -1, 5, -4, 3, 0, 2, 1, 3, 1; 0, 0, 0,
! 124: 0, 1, 0, 0, 0, 5, 0, 0, 0, 15, -5, 10, 0, 5, -5, 10, -2, 1, 0, 10, -2, 7]]
! 125: ? ba=algtobasis(nf,mod(x^3+5,nfpol))
! 126: [6, 0, 1, 3, 0]~
! 127: ? anell(acurve,100)
! 128: [1, -2, -3, 2, -2, 6, -1, 0, 6, 4, -5, -6, -2, 2, 6, -4, 0, -12, 0, -4, 3, 1
! 129: 0, 2, 0, -1, 4, -9, -2, 6, -12, -4, 8, 15, 0, 2, 12, -1, 0, 6, 0, -9, -6, 2,
! 130: -10, -12, -4, -9, 12, -6, 2, 0, -4, 1, 18, 10, 0, 0, -12, 8, 12, -8, 8, -6,
! 131: -8, 4, -30, 8, 0, -6, -4, 9, 0, -1, 2, 3, 0, 5, -12, 4, 8, 9, 18, -15, 6, 0
! 132: , -4, -18, 0, 4, 24, 2, 4, 12, 18, 0, -24, 4, 12, -30, -2]
! 133: ? apell(acurve,10007)
! 134: 66
! 135: ? apell2(acurve,10007)
! 136: 66
! 137: ? apol=x^3+5*x+1
! 138: x^3 + 5*x + 1
! 139: ? apprpadic(apol,1+o(7^8))
! 140: [1 + 6*7 + 4*7^2 + 4*7^3 + 3*7^4 + 4*7^5 + 6*7^7 + O(7^8)]
! 141: ? apprpadic(x^3+5*x+1,mod(x*(1+o(7^8)),x^2+x-1))
! 142: [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 +
! 143: (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)
! 144: ]~
! 145: ? 4*arg(3+3*i)
! 146: 3.1415926535897932384626433832795028842
! 147: ? 3*asin(sqrt(3)/2)
! 148: 3.1415926535897932384626433832795028841
! 149: ? asinh(0.5)
! 150: 0.48121182505960344749775891342436842313
! 151: ? assmat(x^5-12*x^3+0.0005)
! 152:
! 153: [0 0 0 0 -0.00049999999999999999999999999999999999999]
! 154:
! 155: [1 0 0 0 0]
! 156:
! 157: [0 1 0 0 0]
! 158:
! 159: [0 0 1 0 12]
! 160:
! 161: [0 0 0 1 0]
! 162:
! 163: ? 3*atan(sqrt(3))
! 164: 3.1415926535897932384626433832795028841
! 165: ? atanh(0.5)
! 166: 0.54930614433405484569762261846126285232
! 167: ? basis(x^3+4*x+5)
! 168: [1, x, 1/7*x^2 - 1/7*x - 2/7]
! 169: ? basis2(x^3+4*x+5)
! 170: [1, x, 1/7*x^2 - 1/7*x - 2/7]
! 171: ? basistoalg(nf,ba)
! 172: mod(x^3 + 5, x^5 - 5*x^3 + 5*x + 25)
! 173: ? bernreal(12)
! 174: -0.25311355311355311355311355311355311354
! 175: ? bernvec(6)
! 176: [1, 1/6, -1/30, 1/42, -1/30, 5/66, -691/2730]
! 177: ? bestappr(pi,10000)
! 178: 355/113
! 179: ? bezout(123456789,987654321)
! 180: [-8, 1, 9]
! 181: ? bigomega(12345678987654321)
! 182: 8
! 183: ? mcurve=initell([0,0,0,-17,0])
! 184: [0, 0, 0, -17, 0, 0, -34, 0, -289, 816, 0, 314432, 1728, [4.1231056256176605
! 185: 498214098559740770251, 0.E-38, -4.1231056256176605498214098559740770251]~, 1
! 186: .2913084409290072207105564235857096009, 1.2913084409290072207105564235857096
! 187: 009*I, -1.2164377440798088266474269946818791934, -3.649313232239426479942280
! 188: 9840456375802*I, 1.6674774896145033307120230298772362381]
! 189: ? mpoints=[[-1,4],[-4,2]]~
! 190: [[-1, 4], [-4, 2]]~
! 191: ? mhbi=bilhell(mcurve,mpoints,[9,24])
! 192: [-0.72448571035980184146215805860545027438, 1.307328627832055544492943428892
! 193: 1943055]~
! 194: ? bin(1.1,5)
! 195: -0.0045457499999999999999999999999999999997
! 196: ? binary(65537)
! 197: [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1]
! 198: ? bittest(10^100,100)
! 199: 1
! 200: ? boundcf(pi,5)
! 201: [3, 7, 15, 1, 292]
! 202: ? boundfact(40!+1,100000)
! 203:
! 204: [41 1]
! 205:
! 206: [59 1]
! 207:
! 208: [277 1]
! 209:
! 210: [1217669507565553887239873369513188900554127 1]
! 211:
! 212: ? move(0,0,0);box(0,500,500)
! 213: ? setrand(1);buchimag(1-10^7,1,1)
! 214: *** Warning: not a fundamental discriminant in quadclassunit.
! 215: [2416, [1208, 2], [qfi(277, 55, 9028), qfi(1700, 1249, 1700)], 1, 0.99984980
! 216: 75377600233]
! 217: ? setrand(1);bnf=buchinitfu(x^2-x-57,0.2,0.2)
! 218: [mat(3), mat([1, 2, 1, 2, 1, 2, 1, 2, 1]), [-2.71246530518434397468087951060
! 219: 61300699 + 3.1415926535897932384626433832795028842*I; 2.71246530518434397468
! 220: 08795106061300699 - 6.2831853071795864769252867665590057684*I], [9.927737672
! 221: 2507613003718504524486100858 + 3.1415926535897932384626433832795028842*I, 1.
! 222: 2897619530652735025030086072395031017 + 0.E-57*I, -2.01097980249891575621226
! 223: 34098917610612 + 3.1415926535897932384626433832795028842*I, 24.4121877466590
! 224: 95772127915595455170629 + 6.2831853071795864769252867665590057684*I, 30.3376
! 225: 98160660239595315877930058147543 + 9.4247779607693797153879301498385086526*I
! 226: , -20.610866187462450639586440264933189691 + 9.42477796076937971538793014983
! 227: 85086526*I, 29.258282452818196217527894893424939793 + 9.42477796076937971538
! 228: 79301498385086526*I, -0.34328764427702709438988786673341921876 + 3.141592653
! 229: 5897932384626433832795028842*I, -14.550628376291080203941433635329724736 + 0
! 230: .E-56*I, 24.478366048541841504313284087778334822 + 3.14159265358979323846264
! 231: 33832795028842*I; -9.9277376722507613003718504524486100858 + 6.2831853071795
! 232: 864769252867665590057684*I, -1.2897619530652735025030086072395031017 + 9.424
! 233: 7779607693797153879301498385086526*I, 2.010979802498915756212263409891761061
! 234: 2 + 0.E-57*I, -24.412187746659095772127915595455170629 + 3.14159265358979323
! 235: 84626433832795028842*I, -30.337698160660239595315877930058147543 + 3.1415926
! 236: 535897932384626433832795028842*I, 20.610866187462450639586440264933189691 +
! 237: 3.1415926535897932384626433832795028842*I, -29.25828245281819621752789489342
! 238: 4939793 + 6.2831853071795864769252867665590057684*I, 0.343287644277027094389
! 239: 88786673341921876 + 0.E-57*I, 14.550628376291080203941433635329724736 + 3.14
! 240: 15926535897932384626433832795028842*I, -24.478366048541841504313284087778334
! 241: 822 + 3.1415926535897932384626433832795028842*I], [[3, [-1, 1]~, 1, 1, [0, 1
! 242: ]~], [3, [0, 1]~, 1, 1, [-1, 1]~], [5, [-2, 1]~, 1, 1, [1, 1]~], [5, [1, 1]~
! 243: , 1, 1, [-2, 1]~], [11, [-2, 1]~, 1, 1, [1, 1]~], [11, [1, 1]~, 1, 1, [-2, 1
! 244: ]~], [17, [-3, 1]~, 1, 1, [2, 1]~], [17, [2, 1]~, 1, 1, [-3, 1]~], [19, [-1,
! 245: 1]~, 1, 1, [0, 1]~], [19, [0, 1]~, 1, 1, [-1, 1]~]]~, [1, 3, 5, 2, 4, 6, 7,
! 246: 8, 10, 9], [x^2 - x - 57, [2, 0], 229, 1, [[1, -7.0663729752107779635959310
! 247: 246705326058; 1, 8.0663729752107779635959310246705326058], [1, 1; -7.0663729
! 248: 752107779635959310246705326058, 8.0663729752107779635959310246705326058], [2
! 249: , 1.0000000000000000000000000000000000000; 1.0000000000000000000000000000000
! 250: 000000, 115.00000000000000000000000000000000000], [2, 1; 1, 115], [229, 114;
! 251: 0, 1], [115, -1; -1, 2], [229, [114, 1]~]], [-7.066372975210777963595931024
! 252: 6705326058, 8.0663729752107779635959310246705326058], [1, x], [1, 0; 0, 1],
! 253: [1, 0, 0, 57; 0, 1, 1, 1]], [[3, [3], [[3, 2; 0, 1]]], 2.7124653051843439746
! 254: 808795106061300699, 0.8814422512654579369, [2, -1], [x + 7], 185], [mat(1),
! 255: [[0, 0]], [[9.9277376722507613003718504524486100858 + 3.14159265358979323846
! 256: 26433832795028842*I, -9.9277376722507613003718504524486100858 + 6.2831853071
! 257: 795864769252867665590057684*I]]], 0]
! 258: ? buchcertify(bnf)
! 259: 1
! 260: ? buchfu(bnf)
! 261: [[x + 7], 185]
! 262: ? setrand(1);buchinitforcefu(x^2-x-100000)
! 263: [mat(5), mat([3, 2, 1, 2, 0, 3, 2, 3, 0, 0, 1, 4, 3, 2, 2, 3, 3, 2]), [-129.
! 264: 82045011403975460991182396195022419 - 6.283185307179586476925286766559005768
! 265: 4*I; 129.82045011403975460991182396195022419 - 12.56637061435917295385057353
! 266: 3118011536*I], [-41.811264589129943393339502258694361489 + 8.121413879410077
! 267: 514 E-115*I, 9.2399004147902289816376260438840931575 + 3.1415926535897932384
! 268: 626433832795028842*I, -11.874609881075406725097315997431161032 + 9.424777960
! 269: 7693797153879301498385086526*I, 389.46135034211926382973547188585067257 + 12
! 270: .566370614359172953850573533118011536*I, -440.512515346039436204712600188429
! 271: 12722 + 0.E-113*I, -324.55112528509938652477955990487556047 + 6.283185307179
! 272: 5864769252867665590057684*I, 229.70424552002497255158146166263724792 + 3.141
! 273: 5926535897932384626433832795028842*I, -785.660451862534215720251179722755983
! 274: 25 + 6.2831853071795864769252867665590057684*I, -554.35531386699327377220656
! 275: 215544062014 + 6.2831853071795864769252867665590057684*I, -47.66831907156823
! 276: 3997332918482707687879 + 9.4247779607693797153879301498385086526*I, 177.4887
! 277: 6918560798860724474244465791207 + 6.497131103528062011 E-114*I, -875.6123693
! 278: 7168080069763246690606885226 + 2.598852441411224804 E-113*I, 54.878404098312
! 279: 329644822020875673145627 + 9.4247779607693797153879301498385086526*I, -404.4
! 280: 4153844676787690336623107514389175 + 0.E-113*I, 232.809823743598178900114904
! 281: 85449930607 + 6.2831853071795864769252867665590057684*I, -668.80899963671483
! 282: 856204802764462926790 + 9.4247779607693797153879301498385086526*I, 367.35683
! 283: 481950538594888487746203445802 + 12.566370614359172953850573533118011536*I,
! 284: -1214.0716092619656173892944003952818868 + 9.4247779607693797153879301498385
! 285: 086526*I, -125.94415646756187210316334148291471657 + 6.283185307179586476925
! 286: 2867665590057684*I; 41.811264589129943393339502258694361489 + 6.283185307179
! 287: 5864769252867665590057684*I, -9.2399004147902289816376260438840931575 + 12.5
! 288: 66370614359172953850573533118011536*I, 11.8746098810754067250973159974311610
! 289: 32 + 8.121413879410077514 E-115*I, -389.46135034211926382973547188585067257
! 290: + 6.2831853071795864769252867665590057684*I, 440.512515346039436204712600188
! 291: 42912722 + 3.1415926535897932384626433832795028842*I, 324.551125285099386524
! 292: 77955990487556047 + 9.4247779607693797153879301498385086526*I, -229.70424552
! 293: 002497255158146166263724792 + 6.2831853071795864769252867665590057684*I, 785
! 294: .66045186253421572025117972275598325 + 9.42477796076937971538793014983850865
! 295: 26*I, 554.35531386699327377220656215544062014 + 3.14159265358979323846264338
! 296: 32795028842*I, 47.668319071568233997332918482707687878 + 3.14159265358979323
! 297: 84626433832795028842*I, -177.48876918560798860724474244465791207 + 6.2831853
! 298: 071795864769252867665590057684*I, 875.61236937168080069763246690606885226 +
! 299: 6.497131103528062011 E-114*I, -54.878404098312329644822020875673145627 + 9.4
! 300: 247779607693797153879301498385086526*I, 404.44153844676787690336623107514389
! 301: 175 + 9.4247779607693797153879301498385086526*I, -232.8098237435981789001149
! 302: 0485449930607 + 3.1415926535897932384626433832795028842*I, 668.8089996367148
! 303: 3856204802764462926790 + 6.2831853071795864769252867665590057684*I, -367.356
! 304: 83481950538594888487746203445803 + 3.1415926535897932384626433832795028842*I
! 305: , 1214.0716092619656173892944003952818868 + 3.141592653589793238462643383279
! 306: 5028842*I, 125.94415646756187210316334148291471657 + 6.283185307179586476925
! 307: 2867665590057684*I], [[2, [1, 1]~, 1, 1, [0, 1]~], [2, [2, 1]~, 1, 1, [1, 1]
! 308: ~], [5, [4, 1]~, 1, 1, [0, 1]~], [5, [5, 1]~, 1, 1, [-1, 1]~], [7, [3, 1]~,
! 309: 2, 1, [3, 1]~], [13, [-6, 1]~, 1, 1, [5, 1]~], [13, [5, 1]~, 1, 1, [-6, 1]~]
! 310: , [17, [14, 1]~, 1, 1, [2, 1]~], [17, [19, 1]~, 1, 1, [-3, 1]~], [23, [-7, 1
! 311: ]~, 1, 1, [6, 1]~], [23, [6, 1]~, 1, 1, [-7, 1]~], [29, [-14, 1]~, 1, 1, [13
! 312: , 1]~], [29, [13, 1]~, 1, 1, [-14, 1]~], [31, [23, 1]~, 1, 1, [7, 1]~], [31,
! 313: [38, 1]~, 1, 1, [-8, 1]~], [41, [-7, 1]~, 1, 1, [6, 1]~], [41, [6, 1]~, 1,
! 314: 1, [-7, 1]~], [43, [-16, 1]~, 1, 1, [15, 1]~], [43, [15, 1]~, 1, 1, [-16, 1]
! 315: ~]]~, [1, 3, 6, 2, 4, 5, 7, 9, 8, 11, 10, 13, 12, 15, 14, 17, 16, 19, 18], [
! 316: x^2 - x - 100000, [2, 0], 400001, 1, [[1, -315.72816130129840161392089489603
! 317: 747004; 1, 316.72816130129840161392089489603747004], [1, 1; -315.72816130129
! 318: 840161392089489603747004, 316.72816130129840161392089489603747004], [2, 1.00
! 319: 00000000000000000000000000000000000; 1.0000000000000000000000000000000000000
! 320: , 200001.00000000000000000000000000000000], [2, 1; 1, 200001], [400001, 2000
! 321: 00; 0, 1], [200001, -1; -1, 2], [400001, [200000, 1]~]], [-315.7281613012984
! 322: 0161392089489603747004, 316.72816130129840161392089489603747004], [1, x], [1
! 323: , 0; 0, 1], [1, 0, 0, 100000; 0, 1, 1, 1]], [[5, [5], [[2, 1; 0, 1]]], 129.8
! 324: 2045011403975460991182396195022419, 0.9876536979069047239, [2, -1], [3795548
! 325: 84019013781006303254896369154068336082609238336*x + 119836165644250789990462
! 326: 835950022871665178127611316131167], 186], [mat(1), [[0, 0]], [[-41.811264589
! 327: 129943393339502258694361489 + 8.121413879410077514 E-115*I, 41.8112645891299
! 328: 43393339502258694361489 + 6.2831853071795864769252867665590057684*I]]], 0]
! 329: ? setrand(1);bnf=buchinitfu(x^2-x-57,0.2,0.2)
! 330: [mat(3), mat([1, 2, 1, 2, 1, 2, 1, 2, 1]), [-2.71246530518434397468087951060
! 331: 61300699 + 3.1415926535897932384626433832795028842*I; 2.71246530518434397468
! 332: 08795106061300699 - 6.2831853071795864769252867665590057684*I], [9.927737672
! 333: 2507613003718504524486100858 + 3.1415926535897932384626433832795028842*I, 1.
! 334: 2897619530652735025030086072395031017 + 0.E-57*I, -2.01097980249891575621226
! 335: 34098917610612 + 3.1415926535897932384626433832795028842*I, 24.4121877466590
! 336: 95772127915595455170629 + 6.2831853071795864769252867665590057684*I, 30.3376
! 337: 98160660239595315877930058147543 + 9.4247779607693797153879301498385086526*I
! 338: , -20.610866187462450639586440264933189691 + 9.42477796076937971538793014983
! 339: 85086526*I, 29.258282452818196217527894893424939793 + 9.42477796076937971538
! 340: 79301498385086526*I, -0.34328764427702709438988786673341921876 + 3.141592653
! 341: 5897932384626433832795028842*I, -14.550628376291080203941433635329724736 + 0
! 342: .E-56*I, 24.478366048541841504313284087778334822 + 3.14159265358979323846264
! 343: 33832795028842*I; -9.9277376722507613003718504524486100858 + 6.2831853071795
! 344: 864769252867665590057684*I, -1.2897619530652735025030086072395031017 + 9.424
! 345: 7779607693797153879301498385086526*I, 2.010979802498915756212263409891761061
! 346: 2 + 0.E-57*I, -24.412187746659095772127915595455170629 + 3.14159265358979323
! 347: 84626433832795028842*I, -30.337698160660239595315877930058147543 + 3.1415926
! 348: 535897932384626433832795028842*I, 20.610866187462450639586440264933189691 +
! 349: 3.1415926535897932384626433832795028842*I, -29.25828245281819621752789489342
! 350: 4939793 + 6.2831853071795864769252867665590057684*I, 0.343287644277027094389
! 351: 88786673341921876 + 0.E-57*I, 14.550628376291080203941433635329724736 + 3.14
! 352: 15926535897932384626433832795028842*I, -24.478366048541841504313284087778334
! 353: 822 + 3.1415926535897932384626433832795028842*I], [[3, [-1, 1]~, 1, 1, [0, 1
! 354: ]~], [3, [0, 1]~, 1, 1, [-1, 1]~], [5, [-2, 1]~, 1, 1, [1, 1]~], [5, [1, 1]~
! 355: , 1, 1, [-2, 1]~], [11, [-2, 1]~, 1, 1, [1, 1]~], [11, [1, 1]~, 1, 1, [-2, 1
! 356: ]~], [17, [-3, 1]~, 1, 1, [2, 1]~], [17, [2, 1]~, 1, 1, [-3, 1]~], [19, [-1,
! 357: 1]~, 1, 1, [0, 1]~], [19, [0, 1]~, 1, 1, [-1, 1]~]]~, [1, 3, 5, 2, 4, 6, 7,
! 358: 8, 10, 9], [x^2 - x - 57, [2, 0], 229, 1, [[1, -7.0663729752107779635959310
! 359: 246705326058; 1, 8.0663729752107779635959310246705326058], [1, 1; -7.0663729
! 360: 752107779635959310246705326058, 8.0663729752107779635959310246705326058], [2
! 361: , 1.0000000000000000000000000000000000000; 1.0000000000000000000000000000000
! 362: 000000, 115.00000000000000000000000000000000000], [2, 1; 1, 115], [229, 114;
! 363: 0, 1], [115, -1; -1, 2], [229, [114, 1]~]], [-7.066372975210777963595931024
! 364: 6705326058, 8.0663729752107779635959310246705326058], [1, x], [1, 0; 0, 1],
! 365: [1, 0, 0, 57; 0, 1, 1, 1]], [[3, [3], [[3, 2; 0, 1]]], 2.7124653051843439746
! 366: 808795106061300699, 0.8814422512654579369, [2, -1], [x + 7], 185], [mat(1),
! 367: [[0, 0]], [[9.9277376722507613003718504524486100858 + 3.14159265358979323846
! 368: 26433832795028842*I, -9.9277376722507613003718504524486100858 + 6.2831853071
! 369: 795864769252867665590057684*I]]], 0]
! 370: ? setrand(1);buchreal(10^9-3,0,0.5,0.5)
! 371: [4, [4], [qfr(3, 1, -83333333, 0.E-57)], 2800.625251907016076486370621737074
! 372: 5514, 0.9990369458964383232]
! 373: ? setrand(1);buchgen(x^4-7,0.2,0.2)
! 374:
! 375: [x^4 - 7]
! 376:
! 377: [[2, 1]]
! 378:
! 379: [[-87808, 1]]
! 380:
! 381: [[1, x, x^2, x^3]]
! 382:
! 383: [[2, [2], [[3, 1, 2, 1; 0, 1, 0, 0; 0, 0, 1, 0; 0, 0, 0, 1]]]]
! 384:
! 385: [14.229975145405511722395637833443108790]
! 386:
! 387: [1.121117107152756229]
! 388:
! 389: ? setrand(1);buchgenfu(x^2-x-100000)
! 390: *** Warning: insufficient precision for fundamental units, not given.
! 391:
! 392: [x^2 - x - 100000]
! 393:
! 394: [[2, 0]]
! 395:
! 396: [[400001, 1]]
! 397:
! 398: [[1, x]]
! 399:
! 400: [[5, [5], [[2, 1; 0, 1]]]]
! 401:
! 402: [129.82045011403975460991182396195022419]
! 403:
! 404: [0.9876536979069047239]
! 405:
! 406: [[2, -1]]
! 407:
! 408: [[;]]
! 409:
! 410: [0]
! 411:
! 412: ? setrand(1);buchgenforcefu(x^2-x-100000)
! 413:
! 414: [x^2 - x - 100000]
! 415:
! 416: [[2, 0]]
! 417:
! 418: [[400001, 1]]
! 419:
! 420: [[1, x]]
! 421:
! 422: [[5, [5], [[2, 1; 0, 1]]]]
! 423:
! 424: [129.82045011403975460991182396195022419]
! 425:
! 426: [0.9876536979069047239]
! 427:
! 428: [[2, -1]]
! 429:
! 430: [[379554884019013781006303254896369154068336082609238336*x + 119836165644250
! 431: 789990462835950022871665178127611316131167]]
! 432:
! 433: [186]
! 434:
! 435: ? setrand(1);buchgenfu(x^4+24*x^2+585*x+1791,0.1,0.1)
! 436:
! 437: [x^4 + 24*x^2 + 585*x + 1791]
! 438:
! 439: [[0, 2]]
! 440:
! 441: [[18981, 3087]]
! 442:
! 443: [[1, x, 1/3*x^2, 1/1029*x^3 + 33/343*x^2 - 155/343*x - 58/343]]
! 444:
! 445: [[4, [4], [[7, 6, 2, 4; 0, 1, 0, 0; 0, 0, 1, 0; 0, 0, 0, 1]]]]
! 446:
! 447: [3.7941269688216589341408274220859400302]
! 448:
! 449: [0.8826018286655581306]
! 450:
! 451: [[6, -10/1029*x^3 + 13/343*x^2 - 165/343*x - 1135/343]]
! 452:
! 453: [[1/147*x^3 + 1/147*x^2 - 8/49*x - 9/49]]
! 454:
! 455: [182]
! 456:
! 457: ? buchnarrow(bnf)
! 458: [3, [3], [[3, 2; 0, 1]]]
! 459: ? buchray(bnf,[[5,3;0,1],[1,0]])
! 460: [12, [12], [[3, 2; 0, 1]]]
! 461: ? bnr=buchrayinitgen(bnf,[[5,3;0,1],[1,0]])
! 462: [[mat(3), mat([1, 2, 1, 2, 1, 2, 1, 2, 1]), [-2.7124653051843439746808795106
! 463: 061300699 + 3.1415926535897932384626433832795028842*I; 2.7124653051843439746
! 464: 808795106061300699 - 6.2831853071795864769252867665590057684*I], [9.92773767
! 465: 22507613003718504524486100858 + 3.1415926535897932384626433832795028842*I, 1
! 466: .2897619530652735025030086072395031017 + 0.E-57*I, -2.0109798024989157562122
! 467: 634098917610612 + 3.1415926535897932384626433832795028842*I, 24.412187746659
! 468: 095772127915595455170629 + 6.2831853071795864769252867665590057684*I, 30.337
! 469: 698160660239595315877930058147543 + 9.4247779607693797153879301498385086526*
! 470: I, -20.610866187462450639586440264933189691 + 9.4247779607693797153879301498
! 471: 385086526*I, 29.258282452818196217527894893424939793 + 9.4247779607693797153
! 472: 879301498385086526*I, -0.34328764427702709438988786673341921876 + 3.14159265
! 473: 35897932384626433832795028842*I, -14.550628376291080203941433635329724736 +
! 474: 0.E-56*I, 24.478366048541841504313284087778334822 + 3.1415926535897932384626
! 475: 433832795028842*I; -9.9277376722507613003718504524486100858 + 6.283185307179
! 476: 5864769252867665590057684*I, -1.2897619530652735025030086072395031017 + 9.42
! 477: 47779607693797153879301498385086526*I, 2.01097980249891575621226340989176106
! 478: 12 + 0.E-57*I, -24.412187746659095772127915595455170629 + 3.1415926535897932
! 479: 384626433832795028842*I, -30.337698160660239595315877930058147543 + 3.141592
! 480: 6535897932384626433832795028842*I, 20.610866187462450639586440264933189691 +
! 481: 3.1415926535897932384626433832795028842*I, -29.2582824528181962175278948934
! 482: 24939793 + 6.2831853071795864769252867665590057684*I, 0.34328764427702709438
! 483: 988786673341921876 + 0.E-57*I, 14.550628376291080203941433635329724736 + 3.1
! 484: 415926535897932384626433832795028842*I, -24.47836604854184150431328408777833
! 485: 4822 + 3.1415926535897932384626433832795028842*I], [[3, [-1, 1]~, 1, 1, [0,
! 486: 1]~], [3, [0, 1]~, 1, 1, [-1, 1]~], [5, [-2, 1]~, 1, 1, [1, 1]~], [5, [1, 1]
! 487: ~, 1, 1, [-2, 1]~], [11, [-2, 1]~, 1, 1, [1, 1]~], [11, [1, 1]~, 1, 1, [-2,
! 488: 1]~], [17, [-3, 1]~, 1, 1, [2, 1]~], [17, [2, 1]~, 1, 1, [-3, 1]~], [19, [-1
! 489: , 1]~, 1, 1, [0, 1]~], [19, [0, 1]~, 1, 1, [-1, 1]~]]~, [1, 3, 5, 2, 4, 6, 7
! 490: , 8, 10, 9], [x^2 - x - 57, [2, 0], 229, 1, [[1, -7.066372975210777963595931
! 491: 0246705326058; 1, 8.0663729752107779635959310246705326058], [1, 1; -7.066372
! 492: 9752107779635959310246705326058, 8.0663729752107779635959310246705326058], [
! 493: 2, 1.0000000000000000000000000000000000000; 1.000000000000000000000000000000
! 494: 0000000, 115.00000000000000000000000000000000000], [2, 1; 1, 115], [229, 114
! 495: ; 0, 1], [115, -1; -1, 2], [229, [114, 1]~]], [-7.06637297521077796359593102
! 496: 46705326058, 8.0663729752107779635959310246705326058], [1, x], [1, 0; 0, 1],
! 497: [1, 0, 0, 57; 0, 1, 1, 1]], [[3, [3], [[3, 2; 0, 1]]], 2.712465305184343974
! 498: 6808795106061300699, 0.8814422512654579369, [2, -1], [x + 7], 185], [mat(1),
! 499: [[0, 0]], [[9.9277376722507613003718504524486100858 + 3.1415926535897932384
! 500: 626433832795028842*I, -9.9277376722507613003718504524486100858 + 6.283185307
! 501: 1795864769252867665590057684*I]]], [0, [mat([[5, 1]~, 1])]]], [[[5, 3; 0, 1]
! 502: , [1, 0]], [8, [4, 2], [[2, 0]~, [-1, 1]~]], mat([[5, [-2, 1]~, 1, 1, [1, 1]
! 503: ~], 1]), [[[[4], [[2, 0]~], [[2, 0]~], [[mod(0, 2)]~], 1]], [[2], [[-1, 1]~]
! 504: , mat(1)]], [1, 0; 0, 1]], [1], [1, -3, -6; 0, 0, 1; 0, 1, 0], [12, [12], [[
! 505: 3, 2; 0, 1]]], [[1/2, 0; 0, 0], [1, -1; 1, 1]]]
! 506: ? bnr2=buchrayinitgen(bnf,[[25,13;0,1],[1,1]])
! 507: [[mat(3), mat([1, 2, 1, 2, 1, 2, 1, 2, 1]), [-2.7124653051843439746808795106
! 508: 061300699 + 3.1415926535897932384626433832795028842*I; 2.7124653051843439746
! 509: 808795106061300699 - 6.2831853071795864769252867665590057684*I], [9.92773767
! 510: 22507613003718504524486100858 + 3.1415926535897932384626433832795028842*I, 1
! 511: .2897619530652735025030086072395031017 + 0.E-57*I, -2.0109798024989157562122
! 512: 634098917610612 + 3.1415926535897932384626433832795028842*I, 24.412187746659
! 513: 095772127915595455170629 + 6.2831853071795864769252867665590057684*I, 30.337
! 514: 698160660239595315877930058147543 + 9.4247779607693797153879301498385086526*
! 515: I, -20.610866187462450639586440264933189691 + 9.4247779607693797153879301498
! 516: 385086526*I, 29.258282452818196217527894893424939793 + 9.4247779607693797153
! 517: 879301498385086526*I, -0.34328764427702709438988786673341921876 + 3.14159265
! 518: 35897932384626433832795028842*I, -14.550628376291080203941433635329724736 +
! 519: 0.E-56*I, 24.478366048541841504313284087778334822 + 3.1415926535897932384626
! 520: 433832795028842*I; -9.9277376722507613003718504524486100858 + 6.283185307179
! 521: 5864769252867665590057684*I, -1.2897619530652735025030086072395031017 + 9.42
! 522: 47779607693797153879301498385086526*I, 2.01097980249891575621226340989176106
! 523: 12 + 0.E-57*I, -24.412187746659095772127915595455170629 + 3.1415926535897932
! 524: 384626433832795028842*I, -30.337698160660239595315877930058147543 + 3.141592
! 525: 6535897932384626433832795028842*I, 20.610866187462450639586440264933189691 +
! 526: 3.1415926535897932384626433832795028842*I, -29.2582824528181962175278948934
! 527: 24939793 + 6.2831853071795864769252867665590057684*I, 0.34328764427702709438
! 528: 988786673341921876 + 0.E-57*I, 14.550628376291080203941433635329724736 + 3.1
! 529: 415926535897932384626433832795028842*I, -24.47836604854184150431328408777833
! 530: 4822 + 3.1415926535897932384626433832795028842*I], [[3, [-1, 1]~, 1, 1, [0,
! 531: 1]~], [3, [0, 1]~, 1, 1, [-1, 1]~], [5, [-2, 1]~, 1, 1, [1, 1]~], [5, [1, 1]
! 532: ~, 1, 1, [-2, 1]~], [11, [-2, 1]~, 1, 1, [1, 1]~], [11, [1, 1]~, 1, 1, [-2,
! 533: 1]~], [17, [-3, 1]~, 1, 1, [2, 1]~], [17, [2, 1]~, 1, 1, [-3, 1]~], [19, [-1
! 534: , 1]~, 1, 1, [0, 1]~], [19, [0, 1]~, 1, 1, [-1, 1]~]]~, [1, 3, 5, 2, 4, 6, 7
! 535: , 8, 10, 9], [x^2 - x - 57, [2, 0], 229, 1, [[1, -7.066372975210777963595931
! 536: 0246705326058; 1, 8.0663729752107779635959310246705326058], [1, 1; -7.066372
! 537: 9752107779635959310246705326058, 8.0663729752107779635959310246705326058], [
! 538: 2, 1.0000000000000000000000000000000000000; 1.000000000000000000000000000000
! 539: 0000000, 115.00000000000000000000000000000000000], [2, 1; 1, 115], [229, 114
! 540: ; 0, 1], [115, -1; -1, 2], [229, [114, 1]~]], [-7.06637297521077796359593102
! 541: 46705326058, 8.0663729752107779635959310246705326058], [1, x], [1, 0; 0, 1],
! 542: [1, 0, 0, 57; 0, 1, 1, 1]], [[3, [3], [[3, 2; 0, 1]]], 2.712465305184343974
! 543: 6808795106061300699, 0.8814422512654579369, [2, -1], [x + 7], 185], [mat(1),
! 544: [[0, 0]], [[9.9277376722507613003718504524486100858 + 3.1415926535897932384
! 545: 626433832795028842*I, -9.9277376722507613003718504524486100858 + 6.283185307
! 546: 1795864769252867665590057684*I]]], [0, [mat([[5, 1]~, 1])]]], [[[25, 13; 0,
! 547: 1], [1, 1]], [80, [20, 2, 2], [[2, 0]~, [0, -2]~, [2, 2]~]], mat([[5, [-2, 1
! 548: ]~, 1, 1, [1, 1]~], 2]), [[[[4], [[2, 0]~], [[2, 0]~], [[mod(0, 2), mod(0, 2
! 549: )]~], 1], [[5], [[6, 0]~], [[6, 0]~], [[mod(0, 2), mod(0, 2)]~], mat([1/5, -
! 550: 13/5])]], [[2, 2], [[0, -2]~, [2, 2]~], [0, 1; 1, 0]]], [1, -12, 0, 0; 0, 0,
! 551: 1, 0; 0, 0, 0, 1]], [1], [1, -3, 0, -6; 0, 0, 1, 0; 0, 0, 0, 1; 0, 1, 0, 0]
! 552: , [12, [12], [[3, 2; 0, 1]]], [[1, 9, -18; -1/2, -5, 10], [-2, 0; 0, 10]]]
! 553: ? bytesize(%)
! 554: 14120
! 555: ? ceil(-2.5)
! 556: -2
! 557: ? centerlift(mod(456,555))
! 558: -99
! 559: ? cf(pi)
! 560: [3, 7, 15, 1, 292, 1, 1, 1, 2, 1, 3, 1, 14, 2, 1, 1, 2, 2, 2, 2, 1, 84, 2, 1
! 561: , 1, 15, 3, 13, 1, 4, 2, 6, 6]
! 562: ? cf2([1,3,5,7,9],(exp(1)-1)/(exp(1)+1))
! 563: [0, 6, 10, 42, 30]
! 564: ? changevar(x+y,[z,t])
! 565: y + z
! 566: ? char([1,2;3,4],z)
! 567: z^2 - 5*z - 2
! 568: ? char(mod(x^2+x+1,x^3+5*x+1),z)
! 569: z^3 + 7*z^2 + 16*z - 19
! 570: ? char1([1,2;3,4],z)
! 571: z^2 - 5*z - 2
! 572: ? char2(mod(1,8191)*[1,2;3,4],z)
! 573: z^2 + mod(8186, 8191)*z + mod(8189, 8191)
! 574: ? acurve=chell(acurve,[-1,1,2,3])
! 575: [-4, -1, -7, -12, -12, 12, 4, 1, -1, 48, -216, 37, 110592/37, [-0.1624345647
! 576: 1667696455518910092496975959, -0.73040556359455544173706204865073999595, -2.
! 577: 1071598716887675937077488504242902444]~, -2.99345864623195962983200997945250
! 578: 81778, -2.4513893819867900608542248318665252253*I, 0.47131927795681147588259
! 579: 389708033769964, 1.4354565186686843187232088566788165076*I, 7.33813274078957
! 580: 67390707210033323055881]
! 581: ? chinese(mod(7,15),mod(13,21))
! 582: mod(97, 105)
! 583: ? apoint=chptell(apoint,[-1,1,2,3])
! 584: [1, 3]
! 585: ? isoncurve(acurve,apoint)
! 586: 1
! 587: ? classno(-12391)
! 588: 63
! 589: ? classno(1345)
! 590: 6
! 591: ? classno2(-12391)
! 592: 63
! 593: ? classno2(1345)
! 594: 6
! 595: ? coeff(sin(x),7)
! 596: -1/5040
! 597: ? compimag(qfi(2,1,3),qfi(2,1,3))
! 598: qfi(2, -1, 3)
! 599: ? compo(1+o(7^4),3)
! 600: 1
! 601: ? compositum(x^4-4*x+2,x^3-x-1)
! 602: [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
! 603: ^2 - 128*x - 5]
! 604: ? compositum2(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*
! 606: x^2 - 128*x - 5, mod(-279140305176/29063006931199*x^11 + 129916611552/290630
! 607: 06931199*x^10 + 1272919322296/29063006931199*x^9 - 2813750209005/29063006931
! 608: 199*x^8 - 2859411937992/29063006931199*x^7 - 414533880536/29063006931199*x^6
! 609: - 35713977492936/29063006931199*x^5 - 17432607267590/29063006931199*x^4 + 4
! 610: 9785595543672/29063006931199*x^3 + 9423768373204/29063006931199*x^2 - 427797
! 611: 76146743/29063006931199*x + 37962587857138/29063006931199, x^12 - 4*x^10 + 8
! 612: *x^9 + 12*x^8 + 12*x^7 + 138*x^6 + 132*x^5 - 43*x^4 + 58*x^2 - 128*x - 5), m
! 613: od(-279140305176/29063006931199*x^11 + 129916611552/29063006931199*x^10 + 12
! 614: 72919322296/29063006931199*x^9 - 2813750209005/29063006931199*x^8 - 28594119
! 615: 37992/29063006931199*x^7 - 414533880536/29063006931199*x^6 - 35713977492936/
! 616: 29063006931199*x^5 - 17432607267590/29063006931199*x^4 + 49785595543672/2906
! 617: 3006931199*x^3 + 9423768373204/29063006931199*x^2 - 13716769215544/290630069
! 618: 31199*x + 37962587857138/29063006931199, x^12 - 4*x^10 + 8*x^9 + 12*x^8 + 12
! 619: *x^7 + 138*x^6 + 132*x^5 - 43*x^4 + 58*x^2 - 128*x - 5), -1]]
! 620: ? comprealraw(qfr(5,3,-1,0.),qfr(7,1,-1,0.))
! 621: qfr(35, 43, 13, 0.E-38)
! 622: ? concat([1,2],[3,4])
! 623: [1, 2, 3, 4]
! 624: ? conductor(bnf,[[25,13;0,1],[1,1]])
! 625: [[[5, 3; 0, 1], [1, 0]], [12, [12], [[3, 2; 0, 1]]], mat(12)]
! 626: ? conductorofchar(bnr,[2])
! 627: [[5, 3; 0, 1], [0, 0]]
! 628: ? conj(1+i)
! 629: 1 - I
! 630: ? conjvec(mod(x^2+x+1,x^3-x-1))
! 631: [4.0795956234914387860104177508366260325, 0.46020218825428060699479112458168
! 632: 698369 + 0.18258225455744299269398828369501930573*I, 0.460202188254280606994
! 633: 79112458168698369 - 0.18258225455744299269398828369501930573*I]~
! 634: ? content([123,456,789,234])
! 635: 3
! 636: ? convol(sin(x),x*cos(x))
! 637: x + 1/12*x^3 + 1/2880*x^5 + 1/3628800*x^7 + 1/14631321600*x^9 + 1/1448500838
! 638: 40000*x^11 + 1/2982752926433280000*x^13 + 1/114000816848279961600000*x^15 +
! 639: O(x^16)
! 640: ? core(54713282649239)
! 641: 5471
! 642: ? core2(54713282649239)
! 643: [5471, 100003]
! 644: ? coredisc(54713282649239)
! 645: 21884
! 646: ? coredisc2(54713282649239)
! 647: [21884, 100003/2]
! 648: ? cos(1)
! 649: 0.54030230586813971740093660744297660373
! 650: ? cosh(1)
! 651: 1.5430806348152437784779056207570616825
! 652: ? move(0,200,150)
! 653: ? cursor(0)
! 654: ? cvtoi(1.7)
! 655: 1
! 656: ? cyclo(105)
! 657: x^48 + x^47 + x^46 - x^43 - x^42 - 2*x^41 - x^40 - x^39 + x^36 + x^35 + x^34
! 658: + x^33 + x^32 + x^31 - x^28 - x^26 - x^24 - x^22 - x^20 + x^17 + x^16 + x^1
! 659: 5 + x^14 + x^13 + x^12 - x^9 - x^8 - 2*x^7 - x^6 - x^5 + x^2 + x + 1
! 660: ? degree(x^3/(x-1))
! 661: 2
! 662: ? denom(12345/54321)
! 663: 18107
! 664: ? deplin(mod(1,7)*[2,-1;1,3])
! 665: [mod(6, 7), mod(5, 7)]~
! 666: ? deriv((x+y)^5,y)
! 667: 5*x^4 + 20*y*x^3 + 30*y^2*x^2 + 20*y^3*x + 5*y^4
! 668: ? ((x+y)^5)'
! 669: 5*x^4 + 20*y*x^3 + 30*y^2*x^2 + 20*y^3*x + 5*y^4
! 670: ? det([1,2,3;1,5,6;9,8,7])
! 671: -30
! 672: ? det2([1,2,3;1,5,6;9,8,7])
! 673: -30
! 674: ? detint([1,2,3;4,5,6])
! 675: 3
! 676: ? diagonal([2,4,6])
! 677:
! 678: [2 0 0]
! 679:
! 680: [0 4 0]
! 681:
! 682: [0 0 6]
! 683:
! 684: ? dilog(0.5)
! 685: 0.58224052646501250590265632015968010858
! 686: ? dz=vector(30,k,1);dd=vector(30,k,k==1);dm=dirdiv(dd,dz)
! 687: [1, -1, -1, 0, -1, 1, -1, 0, 0, 1, -1, 0, -1, 1, 1, 0, -1, 0, -1, 0, 1, 1, -
! 688: 1, 0, 0, 1, 0, 0, -1, -1]
! 689: ? deu=direuler(p=2,100,1/(1-apell(acurve,p)*x+if(acurve[12]%p,p,0)*x^2))
! 690: [1, -2, -3, 2, -2, 6, -1, 0, 6, 4, -5, -6, -2, 2, 6, -4, 0, -12, 0, -4, 3, 1
! 691: 0, 2, 0, -1, 4, -9, -2, 6, -12, -4, 8, 15, 0, 2, 12, -1, 0, 6, 0, -9, -6, 2,
! 692: -10, -12, -4, -9, 12, -6, 2, 0, -4, 1, 18, 10, 0, 0, -12, 8, 12, -8, 8, -6,
! 693: -8, 4, -30, 8, 0, -6, -4, 9, 0, -1, 2, 3, 0, 5, -12, 4, 8, 9, 18, -15, 6, 0
! 694: , -4, -18, 0, 4, 24, 2, 4, 12, 18, 0, -24, 4, 12, -30, -2]
! 695: ? anell(acurve,100)==deu
! 696: 1
! 697: ? dirmul(abs(dm),dz)
! 698: [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,
! 699: 4, 2, 4, 2, 8]
! 700: ? dirzetak(initalg(x^3-10*x+8),30)
! 701: [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,
! 702: 0, 1, 0, 1, 0]
! 703: ? disc(x^3+4*x+12)
! 704: -4144
! 705: ? discf(x^3+4*x+12)
! 706: -1036
! 707: ? discrayabs(bnr,mat(6))
! 708: [12, 12, 18026977100265125]
! 709: ? discrayabs(bnr)
! 710: [24, 12, 40621487921685401825918161408203125]
! 711: ? discrayabscond(bnr2)
! 712: 0
! 713: ? lu=ideallistunitgen(bnf,55);discrayabslist(bnf,lu)
! 714: [[[6, 6, mat([229, 3])]], [], [[], []], [[]], [[12, 12, [5, 3; 229, 6]], [12
! 715: , 12, [5, 3; 229, 6]]], [], [], [], [[], [], []], [], [[], []], [[], []], []
! 716: , [], [[24, 24, [3, 6; 5, 9; 229, 12]], [], [], [24, 24, [3, 6; 5, 9; 229, 1
! 717: 2]]], [[]], [[], []], [], [[18, 18, [19, 6; 229, 9]], [18, 18, [19, 6; 229,
! 718: 9]]], [[], []], [], [], [], [], [[], [24, 24, [5, 12; 229, 12]], []], [], [[
! 719: ], [], [], []], [], [], [], [], [], [[], [12, 12, [3, 3; 11, 3; 229, 6]], [1
! 720: 2, 12, [3, 3; 11, 3; 229, 6]], []], [], [], [[18, 18, [2, 12; 3, 12; 229, 9]
! 721: ], [], [18, 18, [2, 12; 3, 12; 229, 9]]], [[12, 12, [37, 3; 229, 6]], [12, 1
! 722: 2, [37, 3; 229, 6]]], [], [], [], [], [], [[], []], [[], []], [[], [], [], [
! 723: ], [], []], [], [], [[12, 12, [2, 12; 3, 3; 229, 6]], [12, 12, [2, 12; 3, 3;
! 724: 229, 6]]], [[18, 18, [7, 12; 229, 9]]], [], [[], [], [], []], [], [[], []],
! 725: [], [[], [24, 24, [5, 9; 11, 6; 229, 12]], [24, 24, [5, 9; 11, 6; 229, 12]]
! 726: , []]]
! 727: ? discrayabslistlong(bnf,20)
! 728: [[[[matrix(0,2,j,k,0), 6, 6, mat([229, 3])]], [], [[mat([12, 1]), 0, 0, 0],
! 729: [mat([13, 1]), 0, 0, 0]], [[mat([10, 1]), 0, 0, 0]], [[mat([20, 1]), 12, 12,
! 730: [5, 3; 229, 6]], [mat([21, 1]), 12, 12, [5, 3; 229, 6]]], [], [], [], [[mat
! 731: ([12, 2]), 0, 0, 0], [[12, 1; 13, 1], 0, 0, 0], [mat([13, 2]), 0, 0, 0]], []
! 732: , [[mat([44, 1]), 0, 0, 0], [mat([45, 1]), 0, 0, 0]], [[[10, 1; 12, 1], 0, 0
! 733: , 0], [[10, 1; 13, 1], 0, 0, 0]], [], [], [[[12, 1; 20, 1], 24, 24, [3, 6; 5
! 734: , 9; 229, 12]], [[13, 1; 20, 1], 0, 0, 0], [[12, 1; 21, 1], 0, 0, 0], [[13,
! 735: 1; 21, 1], 24, 24, [3, 6; 5, 9; 229, 12]]], [[mat([10, 2]), 0, 0, 0]], [[mat
! 736: ([68, 1]), 0, 0, 0], [mat([69, 1]), 0, 0, 0]], [], [[mat([76, 1]), 18, 18, [
! 737: 19, 6; 229, 9]], [mat([77, 1]), 18, 18, [19, 6; 229, 9]]], [[[10, 1; 20, 1],
! 738: 0, 0, 0], [[10, 1; 21, 1], 0, 0, 0]]]]
! 739: ? discrayrel(bnr,mat(6))
! 740: [6, 2, [125, 13; 0, 1]]
! 741: ? discrayrel(bnr)
! 742: [12, 1, [1953125, 1160888; 0, 1]]
! 743: ? discrayrelcond(bnr2)
! 744: 0
! 745: ? divisors(8!)
! 746: [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 14, 15, 16, 18, 20, 21, 24, 28, 30, 32,
! 747: 35, 36, 40, 42, 45, 48, 56, 60, 63, 64, 70, 72, 80, 84, 90, 96, 105, 112, 12
! 748: 0, 126, 128, 140, 144, 160, 168, 180, 192, 210, 224, 240, 252, 280, 288, 315
! 749: , 320, 336, 360, 384, 420, 448, 480, 504, 560, 576, 630, 640, 672, 720, 840,
! 750: 896, 960, 1008, 1120, 1152, 1260, 1344, 1440, 1680, 1920, 2016, 2240, 2520,
! 751: 2688, 2880, 3360, 4032, 4480, 5040, 5760, 6720, 8064, 10080, 13440, 20160,
! 752: 40320]
! 753: ? divres(345,123)
! 754: [2, 99]~
! 755: ? divres(x^7-1,x^5+1)
! 756: [x^2, -x^2 - 1]~
! 757: ? divsum(8!,x,x)
! 758: 159120
! 759: ? postdraw([0,0,0])
! 760: ? eigen([1,2,3;4,5,6;7,8,9])
! 761:
! 762: [-1.2833494518006402717978106547571267252 1 0.283349451800640271797810654757
! 763: 12672521]
! 764:
! 765: [-0.14167472590032013589890532737856336260 -2 0.6416747259003201358989053273
! 766: 7856336260]
! 767:
! 768: [1 1 1]
! 769:
! 770: ? eint1(2)
! 771: 0.048900510708061119567239835228049522206
! 772: ? erfc(2)
! 773: 0.0046777349810472658379307436327470713891
! 774: ? eta(q)
! 775: 1 - q - q^2 + q^5 + q^7 - q^12 - q^15 + O(q^16)
! 776: ? euler
! 777: 0.57721566490153286060651209008240243104
! 778: ? z=y;y=x;eval(z)
! 779: x
! 780: ? exp(1)
! 781: 2.7182818284590452353602874713526624977
! 782: ? extract([1,2,3,4,5,6,7,8,9,10],1000)
! 783: [4, 6, 7, 8, 9, 10]
! 784: ? 10!
! 785: 3628800
! 786: ? fact(10)
! 787: 3628800.0000000000000000000000000000000
! 788: ? factcantor(x^11+1,7)
! 789:
! 790: [mod(1, 7)*x + mod(1, 7) 1]
! 791:
! 792: [mod(1, 7)*x^10 + mod(6, 7)*x^9 + mod(1, 7)*x^8 + mod(6, 7)*x^7 + mod(1, 7)*
! 793: x^6 + mod(6, 7)*x^5 + mod(1, 7)*x^4 + mod(6, 7)*x^3 + mod(1, 7)*x^2 + mod(6,
! 794: 7)*x + mod(1, 7) 1]
! 795:
! 796: ? centerlift(lift(factfq(x^3+x^2+x-1,3,t^3+t^2+t-1)))
! 797:
! 798: [x - t 1]
! 799:
! 800: [x + (t^2 + t - 1) 1]
! 801:
! 802: [x + (-t^2 - 1) 1]
! 803:
! 804: ? factmod(x^11+1,7)
! 805:
! 806: [mod(1, 7)*x + mod(1, 7) 1]
! 807:
! 808: [mod(1, 7)*x^10 + mod(6, 7)*x^9 + mod(1, 7)*x^8 + mod(6, 7)*x^7 + mod(1, 7)*
! 809: x^6 + mod(6, 7)*x^5 + mod(1, 7)*x^4 + mod(6, 7)*x^3 + mod(1, 7)*x^2 + mod(6,
! 810: 7)*x + mod(1, 7) 1]
! 811:
! 812: ? factor(17!+1)
! 813:
! 814: [661 1]
! 815:
! 816: [537913 1]
! 817:
! 818: [1000357 1]
! 819:
! 820: ? p=x^5+3021*x^4-786303*x^3-6826636057*x^2-546603588746*x+3853890514072057
! 821: x^5 + 3021*x^4 - 786303*x^3 - 6826636057*x^2 - 546603588746*x + 385389051407
! 822: 2057
! 823: ? fa=[11699,6;2392997,2;4987333019653,2]
! 824:
! 825: [11699 6]
! 826:
! 827: [2392997 2]
! 828:
! 829: [4987333019653 2]
! 830:
! 831: ? factoredbasis(p,fa)
! 832: [1, x, x^2, 1/11699*x^3 + 1847/11699*x^2 - 132/11699*x - 2641/11699, 1/13962
! 833: 3738889203638909659*x^4 - 1552451622081122020/139623738889203638909659*x^3 +
! 834: 418509858130821123141/139623738889203638909659*x^2 - 6810913798507599407313
! 835: 4/139623738889203638909659*x - 13185339461968406/58346808996920447]
! 836: ? factoreddiscf(p,fa)
! 837: 136866601
! 838: ? factoredpolred(p,fa)
! 839: [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
! 840: *x^2 + 508*x + 913, x^5 - 2*x^4 - 13*x^3 + 37*x^2 - 21*x - 1, x^5 - x^4 - 52
! 841: *x^3 - 197*x^2 - 273*x - 127]
! 842: ? factoredpolred2(p,fa)
! 843:
! 844: [1 x - 1]
! 845:
! 846: [320031469790/139623738889203638909659*x^4 + 525154323698149/139623738889203
! 847: 638909659*x^3 + 68805502220272624/139623738889203638909659*x^2 + 11626197624
! 848: 4907072724/139623738889203638909659*x - 265513916545157609/58346808996920447
! 849: x^5 - 2*x^4 - 62*x^3 + 85*x^2 + 818*x + 1]
! 850:
! 851: [-649489679500/139623738889203638909659*x^4 - 1004850936416946/1396237388892
! 852: 03638909659*x^3 + 1850137668999773331/139623738889203638909659*x^2 + 1162464
! 853: 435118744503168/139623738889203638909659*x - 744221404070129897/583468089969
! 854: 20447 x^5 - 2*x^4 - 53*x^3 - 46*x^2 + 508*x + 913]
! 855:
! 856: [404377049971/139623738889203638909659*x^4 + 1028343729806593/13962373888920
! 857: 3638909659*x^3 - 220760129739668913/139623738889203638909659*x^2 - 139192454
! 858: 3479498840309/139623738889203638909659*x - 21580477171925514/583468089969204
! 859: 47 x^5 - 2*x^4 - 13*x^3 + 37*x^2 - 21*x - 1]
! 860:
! 861: [160329790087/139623738889203638909659*x^4 + 1043812506369034/13962373888920
! 862: 3638909659*x^3 + 1517006779298914407/139623738889203638909659*x^2 - 52234888
! 863: 8528537141362/139623738889203638909659*x - 677624890046649103/58346808996920
! 864: 447 x^5 - x^4 - 52*x^3 - 197*x^2 - 273*x - 127]
! 865:
! 866: ? factornf(x^3+x^2-2*x-1,t^3+t^2-2*t-1)
! 867:
! 868: [mod(1, t^3 + t^2 - 2*t - 1)*x + mod(-t, t^3 + t^2 - 2*t - 1) 1]
! 869:
! 870: [mod(1, t^3 + t^2 - 2*t - 1)*x + mod(-t^2 + 2, t^3 + t^2 - 2*t - 1) 1]
! 871:
! 872: [mod(1, t^3 + t^2 - 2*t - 1)*x + mod(t^2 + t - 1, t^3 + t^2 - 2*t - 1) 1]
! 873:
! 874: ? factorpadic(apol,7,8)
! 875:
! 876: [(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]
! 877:
! 878: [(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
! 879: ))*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]
! 880:
! 881: ? factorpadic2(apol,7,8)
! 882:
! 883: [(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]
! 884:
! 885: [(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
! 886: ))*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]
! 887:
! 888: ? factpol(x^15-1,3,1)
! 889:
! 890: [x - 1 1]
! 891:
! 892: [x^2 + x + 1 1]
! 893:
! 894: [x^4 + x^3 + x^2 + x + 1 1]
! 895:
! 896: [x^8 - x^7 + x^5 - x^4 + x^3 - x + 1 1]
! 897:
! 898: ? factpol(x^15-1,0,1)
! 899:
! 900: [x - 1 1]
! 901:
! 902: [x^2 + x + 1 1]
! 903:
! 904: [x^4 + x^3 + x^2 + x + 1 1]
! 905:
! 906: [x^8 - x^7 + x^5 - x^4 + x^3 - x + 1 1]
! 907:
! 908: ? factpol2(x^15-1,0)
! 909: *** this function has been suppressed.
! 910: ? fibo(100)
! 911: 354224848179261915075
! 912: ? floor(-1/2)
! 913: -1
! 914: ? floor(-2.5)
! 915: -3
! 916: ? for(x=1,5,print(x!))
! 917: 1
! 918: 2
! 919: 6
! 920: 24
! 921: 120
! 922: ? fordiv(10,x,print(x))
! 923: 1
! 924: 2
! 925: 5
! 926: 10
! 927: ? forprime(p=1,30,print(p))
! 928: 2
! 929: 3
! 930: 5
! 931: 7
! 932: 11
! 933: 13
! 934: 17
! 935: 19
! 936: 23
! 937: 29
! 938: ? forstep(x=0,pi,pi/12,print(sin(x)))
! 939: 0.E-38
! 940: 0.25881904510252076234889883762404832834
! 941: 0.49999999999999999999999999999999999999
! 942: 0.70710678118654752440084436210484903928
! 943: 0.86602540378443864676372317075293618346
! 944: 0.96592582628906828674974319972889736763
! 945: 1.0000000000000000000000000000000000000
! 946: 0.96592582628906828674974319972889736764
! 947: 0.86602540378443864676372317075293618348
! 948: 0.70710678118654752440084436210484903930
! 949: 0.50000000000000000000000000000000000002
! 950: 0.25881904510252076234889883762404832838
! 951: 4.7019774032891500318749461488889827112 E-38
! 952: ? forvec(x=[[1,3],[-2,2]],print1([x[1],x[2]]," "));print(" ");
! 953: [1, -2] [1, -1] [1, 0] [1, 1] [1, 2] [2, -2] [2, -1] [2, 0] [2, 1] [2, 2] [3
! 954: , -2] [3, -1] [3, 0] [3, 1] [3, 2]
! 955: ? frac(-2.7)
! 956: 0.30000000000000000000000000000000000000
! 957: ? galois(x^6-3*x^2-1)
! 958: [12, 1, 1]
! 959: ? nf3=initalg(x^6+108);galoisconj(nf3)
! 960: [-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
! 961: /2*x]~
! 962: ? aut=%[2];galoisapply(nf3,aut,mod(x^5,x^6+108))
! 963: mod(x^5, x^6 + 108)
! 964: ? gamh(10)
! 965: 1133278.3889487855673345741655888924755
! 966: ? gamma(10.5)
! 967: 1133278.3889487855673345741655888924755
! 968: ? gauss(hilbert(10),[1,2,3,4,5,6,7,8,9,0]~)
! 969: [9236800, -831303990, 18288515520, -170691240720, 832112321040, -23298940665
! 970: 00, 3883123564320, -3803844432960, 2020775945760, -449057772020]~
! 971: ? gaussmodulo([2,3;5,4],[7,11],[1,4]~)
! 972: [-5, -1]~
! 973: ? gaussmodulo2([2,3;5,4],[7,11],[1,4]~)
! 974: [[-5, -1]~, [-77, 723; 0, 1]]
! 975: ? gcd(12345678,87654321)
! 976: 9
! 977: ? getheap()
! 978: [214, 46166]
! 979: ? getrand()
! 980: 1939683225
! 981: ? getstack()
! 982: 0
! 983: ? globalred(acurve)
! 984: [37, [1, -1, 2, 2], 1]
! 985: ? getstack()
! 986: 0
! 987: ? hclassno(2000003)
! 988: 357
! 989: ? hell(acurve,apoint)
! 990: 0.40889126591975072188708879805553617287
! 991: ? hell2(acurve,apoint)
! 992: 0.40889126591975072188708879805553617296
! 993: ? hermite(amat=1/hilbert(7))
! 994:
! 995: [420 0 0 0 210 168 175]
! 996:
! 997: [0 840 0 0 0 0 504]
! 998:
! 999: [0 0 2520 0 0 0 1260]
! 1000:
! 1001: [0 0 0 2520 0 0 840]
! 1002:
! 1003: [0 0 0 0 13860 0 6930]
! 1004:
! 1005: [0 0 0 0 0 5544 0]
! 1006:
! 1007: [0 0 0 0 0 0 12012]
! 1008:
! 1009: ? hermite2(amat)
! 1010: [[420, 0, 0, 0, 210, 168, 175; 0, 840, 0, 0, 0, 0, 504; 0, 0, 2520, 0, 0, 0,
! 1011: 1260; 0, 0, 0, 2520, 0, 0, 840; 0, 0, 0, 0, 13860, 0, 6930; 0, 0, 0, 0, 0,
! 1012: 5544, 0; 0, 0, 0, 0, 0, 0, 12012], [420, 420, 840, 630, 2982, 1092, 4159; 21
! 1013: 0, 280, 630, 504, 2415, 876, 3395; 140, 210, 504, 420, 2050, 749, 2901; 105,
! 1014: 168, 420, 360, 1785, 658, 2542; 84, 140, 360, 315, 1582, 588, 2266; 70, 120
! 1015: , 315, 280, 1421, 532, 2046; 60, 105, 280, 252, 1290, 486, 1866]]
! 1016: ? hermitehavas(amat)
! 1017: *** this function has been suppressed.
! 1018: ? hermitemod(amat,detint(amat))
! 1019:
! 1020: [420 0 0 0 210 168 175]
! 1021:
! 1022: [0 840 0 0 0 0 504]
! 1023:
! 1024: [0 0 2520 0 0 0 1260]
! 1025:
! 1026: [0 0 0 2520 0 0 840]
! 1027:
! 1028: [0 0 0 0 13860 0 6930]
! 1029:
! 1030: [0 0 0 0 0 5544 0]
! 1031:
! 1032: [0 0 0 0 0 0 12012]
! 1033:
! 1034: ? hermiteperm(amat)
! 1035: [[360360, 0, 0, 0, 0, 144144, 300300; 0, 27720, 0, 0, 0, 0, 22176; 0, 0, 277
! 1036: 20, 0, 0, 0, 6930; 0, 0, 0, 2520, 0, 0, 840; 0, 0, 0, 0, 2520, 0, 1260; 0, 0
! 1037: , 0, 0, 0, 168, 0; 0, 0, 0, 0, 0, 0, 7], [51480, 4620, 5544, 630, 840, 20676
! 1038: , 48619; 45045, 3960, 4620, 504, 630, 18074, 42347; 40040, 3465, 3960, 420,
! 1039: 504, 16058, 37523; 36036, 3080, 3465, 360, 420, 14448, 33692; 32760, 2772, 3
! 1040: 080, 315, 360, 13132, 30574; 30030, 2520, 2772, 280, 315, 12036, 27986; 2772
! 1041: 0, 2310, 2520, 252, 280, 11109, 25803], [7, 6, 5, 4, 3, 2, 1]]
! 1042: ? hess(hilbert(7))
! 1043:
! 1044: [1 90281/58800 -1919947/4344340 4858466341/1095033030 -77651417539/819678732
! 1045: 6 3386888964/106615355 1/2]
! 1046:
! 1047: [1/3 43/48 38789/5585580 268214641/109503303 -581330123627/126464718744 4365
! 1048: 450643/274153770 1/4]
! 1049:
! 1050: [0 217/2880 442223/7447440 53953931/292008808 -32242849453/168619624992 1475
! 1051: 457901/1827691800 1/80]
! 1052:
! 1053: [0 0 1604444/264539275 24208141/149362505292 847880210129/47916076768560 -45
! 1054: 44407141/103873817300 -29/40920]
! 1055:
! 1056: [0 0 0 9773092581/35395807550620 -24363634138919/107305824577186620 72118203
! 1057: 606917/60481351061158500 55899/3088554700]
! 1058:
! 1059: [0 0 0 0 67201501179065/8543442888354179988 -9970556426629/74082861999267660
! 1060: 0 -3229/13661312210]
! 1061:
! 1062: [0 0 0 0 0 -258198800769/9279048099409000 -13183/38381527800]
! 1063:
! 1064: ? hilb(2/3,3/4,5)
! 1065: 1
! 1066: ? hilbert(5)
! 1067:
! 1068: [1 1/2 1/3 1/4 1/5]
! 1069:
! 1070: [1/2 1/3 1/4 1/5 1/6]
! 1071:
! 1072: [1/3 1/4 1/5 1/6 1/7]
! 1073:
! 1074: [1/4 1/5 1/6 1/7 1/8]
! 1075:
! 1076: [1/5 1/6 1/7 1/8 1/9]
! 1077:
! 1078: ? hilbp(mod(5,7),mod(6,7))
! 1079: 1
! 1080: ? hvector(10,x,1/x)
! 1081: [1, 1/2, 1/3, 1/4, 1/5, 1/6, 1/7, 1/8, 1/9, 1/10]
! 1082: ? hyperu(1,1,1)
! 1083: 0.59634736232319407434107849936927937488
! 1084: ? i^2
! 1085: -1
! 1086: ? nf1=initalgred(nfpol)
! 1087: [x^5 - 2*x^4 + 3*x^3 + 8*x^2 + 3*x + 2, [1, 2], 595125, 4, [[1, -1.089115145
! 1088: 7205048250249527946671612684, 1.1861718006377964594796293860483989860, -0.59
! 1089: 741050929194782733001765987770358483, 0.158944197453903762065494816710718942
! 1090: 89; 1, -0.13838372073406036365047976417441696637 + 0.49181637657768643499753
! 1091: 285514741525107*I, -0.22273329410580226599155701611419649154 - 0.13611876021
! 1092: 752805221674918029071012580*I, -0.13167445871785818798769651537619416009 + 0
! 1093: .13249517760521973840801462296650806543*I, -0.053650958656997725359297528357
! 1094: 602608116 + 0.27622636814169107038138284681568361486*I; 1, 1.682941293594312
! 1095: 7761629561615079976005 + 2.0500351226010726172974286983598602163*I, -1.37035
! 1096: 26062130959637482576769100030014 + 6.9001775222880494773720769629846373016*I
! 1097: , -8.0696202866361678983472946546849540475 + 8.87676767859710424508852843013
! 1098: 48051602*I, -22.025821140069954155673449879997756863 - 8.4306586896999153544
! 1099: 710860185447589664*I], [1, 2, 2; -1.0891151457205048250249527946671612684, -
! 1100: 0.27676744146812072730095952834883393274 - 0.9836327531553728699950657102948
! 1101: 3050214*I, 3.3658825871886255523259123230159952011 - 4.100070245202145234594
! 1102: 8573967197204327*I; 1.1861718006377964594796293860483989860, -0.445466588211
! 1103: 60453198311403222839298308 + 0.27223752043505610443349836058142025160*I, -2.
! 1104: 7407052124261919274965153538200060029 - 13.800355044576098954744153925969274
! 1105: 603*I; -0.59741050929194782733001765987770358483, -0.26334891743571637597539
! 1106: 303075238832018 - 0.26499035521043947681602924593301613087*I, -16.1392405732
! 1107: 72335796694589309369908095 - 17.753535357194208490177056860269610320*I; 0.15
! 1108: 894419745390376206549481671071894289, -0.10730191731399545071859505671520521
! 1109: 623 - 0.55245273628338214076276569363136722973*I, -44.0516422801399083113468
! 1110: 99759995513726 + 16.861317379399830708942172037089517932*I], [5, 2.000000000
! 1111: 0000000000000000000000000000, -2.0000000000000000000000000000000000000, -17.
! 1112: 000000000000000000000000000000000000, -44.0000000000000000000000000000000000
! 1113: 00; 2.0000000000000000000000000000000000000, 15.7781094086719980448363574712
! 1114: 83695361, 22.314643349754061651916553814602769764, 10.0513952578314782754999
! 1115: 32716306366248, -108.58917507620841447456569092094763671; -2.000000000000000
! 1116: 0000000000000000000000, 22.314643349754061651916553814602769764, 100.5239126
! 1117: 2388960975827806174040462368, 143.93295090847353519436673793501057176, -55.8
! 1118: 42564718082452641322500190813370023; -17.00000000000000000000000000000000000
! 1119: 0, 10.051395257831478275499932716306366248, 143.9329509084735351943667379350
! 1120: 1057176, 288.25823756749944693139292174819167135, 205.7984003827766237572018
! 1121: 0649465932302; -44.000000000000000000000000000000000000, -108.58917507620841
! 1122: 447456569092094763671, -55.842564718082452641322500190813370023, 205.7984003
! 1123: 8277662375720180649465932302, 1112.6092277946777707779250962522343036], [5,
! 1124: 2, -2, -17, -44; 2, -2, -34, -63, -40; -2, -34, -90, -101, 177; -17, -63, -1
! 1125: 01, -27, 505; -44, -40, 177, 505, 828], [345, 0, 160, 252, 156; 0, 345, 215,
! 1126: 311, 306; 0, 0, 5, 3, 2; 0, 0, 0, 1, 0; 0, 0, 0, 0, 1], [163875, -388125, -
! 1127: 296700, 234600, -89700; -388125, -1593900, -677925, 595125, -315675; -296700
! 1128: , -677925, 17250, 58650, -87975; 234600, 595125, 58650, -100050, 89700; -897
! 1129: 00, -315675, -87975, 89700, -55200], [595125, [-167325, -82800, 79350, 1725,
! 1130: 0]~]], [-1.0891151457205048250249527946671612684, -0.1383837207340603636504
! 1131: 7976417441696637 + 0.49181637657768643499753285514741525107*I, 1.68294129359
! 1132: 43127761629561615079976005 + 2.0500351226010726172974286983598602163*I], [1,
! 1133: x, x^2, 1/2*x^3 + 1/2*x^2 + 1/2*x, 1/2*x^4 + 1/2*x], [1, 0, 0, 0, 0; 0, 1,
! 1134: 0, -1, -1; 0, 0, 1, -1, 0; 0, 0, 0, 2, 0; 0, 0, 0, 0, 2], [1, 0, 0, 0, 0, 0,
! 1135: 0, 0, 0, -1, 0, 0, 0, -1, -2, 0, 0, -1, -2, -2, 0, -1, -2, -2, 5; 0, 1, 0,
! 1136: 0, 0, 1, 0, -1, -1, -1, 0, -1, -1, -2, 2, 0, -1, -2, -1, 7, 0, -1, 2, 7, 14;
! 1137: 0, 0, 1, 0, 0, 0, 1, -1, 0, -2, 1, -1, 0, -3, -3, 0, 0, -3, -4, -1, 0, -2,
! 1138: -3, -1, 15; 0, 0, 0, 1, 0, 0, 0, 2, 1, -3, 0, 2, 0, -2, -13, 1, 1, -2, -9, -
! 1139: 19, 0, -3, -13, -19, 7; 0, 0, 0, 0, 1, 0, 0, 0, 1, 2, 0, 0, 2, 3, 1, 0, 1, 3
! 1140: , 4, -4, 1, 2, 1, -4, -21]]
! 1141: ? initalgred2(nfpol)
! 1142: [[x^5 - 2*x^4 + 3*x^3 + 8*x^2 + 3*x + 2, [1, 2], 595125, 4, [[1, -1.08911514
! 1143: 57205048250249527946671612684, 1.1861718006377964594796293860483989860, -0.5
! 1144: 9741050929194782733001765987770358483, 0.15894419745390376206549481671071894
! 1145: 289; 1, -0.13838372073406036365047976417441696637 + 0.4918163765776864349975
! 1146: 3285514741525107*I, -0.22273329410580226599155701611419649154 - 0.1361187602
! 1147: 1752805221674918029071012580*I, -0.13167445871785818798769651537619416009 +
! 1148: 0.13249517760521973840801462296650806543*I, -0.05365095865699772535929752835
! 1149: 7602608116 + 0.27622636814169107038138284681568361486*I; 1, 1.68294129359431
! 1150: 27761629561615079976005 + 2.0500351226010726172974286983598602163*I, -1.3703
! 1151: 526062130959637482576769100030014 + 6.9001775222880494773720769629846373016*
! 1152: I, -8.0696202866361678983472946546849540475 + 8.8767676785971042450885284301
! 1153: 348051602*I, -22.025821140069954155673449879997756863 - 8.430658689699915354
! 1154: 4710860185447589664*I], [1, 2, 2; -1.0891151457205048250249527946671612684,
! 1155: -0.27676744146812072730095952834883393274 - 0.983632753155372869995065710294
! 1156: 83050214*I, 3.3658825871886255523259123230159952011 - 4.10007024520214523459
! 1157: 48573967197204327*I; 1.1861718006377964594796293860483989860, -0.44546658821
! 1158: 160453198311403222839298308 + 0.27223752043505610443349836058142025160*I, -2
! 1159: .7407052124261919274965153538200060029 - 13.80035504457609895474415392596927
! 1160: 4603*I; -0.59741050929194782733001765987770358483, -0.2633489174357163759753
! 1161: 9303075238832018 - 0.26499035521043947681602924593301613087*I, -16.139240573
! 1162: 272335796694589309369908095 - 17.753535357194208490177056860269610320*I; 0.1
! 1163: 5894419745390376206549481671071894289, -0.1073019173139954507185950567152052
! 1164: 1623 - 0.55245273628338214076276569363136722973*I, -44.051642280139908311346
! 1165: 899759995513726 + 16.861317379399830708942172037089517932*I], [5, 2.00000000
! 1166: 00000000000000000000000000000, -2.0000000000000000000000000000000000000, -17
! 1167: .000000000000000000000000000000000000, -44.000000000000000000000000000000000
! 1168: 000; 2.0000000000000000000000000000000000000, 15.778109408671998044836357471
! 1169: 283695361, 22.314643349754061651916553814602769764, 10.051395257831478275499
! 1170: 932716306366248, -108.58917507620841447456569092094763671; -2.00000000000000
! 1171: 00000000000000000000000, 22.314643349754061651916553814602769764, 100.523912
! 1172: 62388960975827806174040462368, 143.93295090847353519436673793501057176, -55.
! 1173: 842564718082452641322500190813370023; -17.0000000000000000000000000000000000
! 1174: 00, 10.051395257831478275499932716306366248, 143.932950908473535194366737935
! 1175: 01057176, 288.25823756749944693139292174819167135, 205.798400382776623757201
! 1176: 80649465932302; -44.000000000000000000000000000000000000, -108.5891750762084
! 1177: 1447456569092094763671, -55.842564718082452641322500190813370023, 205.798400
! 1178: 38277662375720180649465932302, 1112.6092277946777707779250962522343036], [5,
! 1179: 2, -2, -17, -44; 2, -2, -34, -63, -40; -2, -34, -90, -101, 177; -17, -63, -
! 1180: 101, -27, 505; -44, -40, 177, 505, 828], [345, 0, 160, 252, 156; 0, 345, 215
! 1181: , 311, 306; 0, 0, 5, 3, 2; 0, 0, 0, 1, 0; 0, 0, 0, 0, 1], [163875, -388125,
! 1182: -296700, 234600, -89700; -388125, -1593900, -677925, 595125, -315675; -29670
! 1183: 0, -677925, 17250, 58650, -87975; 234600, 595125, 58650, -100050, 89700; -89
! 1184: 700, -315675, -87975, 89700, -55200], [595125, [-167325, -82800, 79350, 1725
! 1185: , 0]~]], [-1.0891151457205048250249527946671612684, -0.138383720734060363650
! 1186: 47976417441696637 + 0.49181637657768643499753285514741525107*I, 1.6829412935
! 1187: 943127761629561615079976005 + 2.0500351226010726172974286983598602163*I], [1
! 1188: , x, x^2, 1/2*x^3 + 1/2*x^2 + 1/2*x, 1/2*x^4 + 1/2*x], [1, 0, 0, 0, 0; 0, 1,
! 1189: 0, -1, -1; 0, 0, 1, -1, 0; 0, 0, 0, 2, 0; 0, 0, 0, 0, 2], [1, 0, 0, 0, 0, 0
! 1190: , 0, 0, 0, -1, 0, 0, 0, -1, -2, 0, 0, -1, -2, -2, 0, -1, -2, -2, 5; 0, 1, 0,
! 1191: 0, 0, 1, 0, -1, -1, -1, 0, -1, -1, -2, 2, 0, -1, -2, -1, 7, 0, -1, 2, 7, 14
! 1192: ; 0, 0, 1, 0, 0, 0, 1, -1, 0, -2, 1, -1, 0, -3, -3, 0, 0, -3, -4, -1, 0, -2,
! 1193: -3, -1, 15; 0, 0, 0, 1, 0, 0, 0, 2, 1, -3, 0, 2, 0, -2, -13, 1, 1, -2, -9,
! 1194: -19, 0, -3, -13, -19, 7; 0, 0, 0, 0, 1, 0, 0, 0, 1, 2, 0, 0, 2, 3, 1, 0, 1,
! 1195: 3, 4, -4, 1, 2, 1, -4, -21]], mod(-1/2*x^4 + 3/2*x^3 - 5/2*x^2 - 2*x + 1, x^
! 1196: 5 - 2*x^4 + 3*x^3 + 8*x^2 + 3*x + 2)]
! 1197: ? vp=primedec(nf,3)[1]
! 1198: [3, [1, 1, 0, 0, 0]~, 1, 1, [1, -1, -1, 0, 0]~]
! 1199: ? idx=idealmul(nf,idmat(5),vp)
! 1200:
! 1201: [3 1 2 2 2]
! 1202:
! 1203: [0 1 0 0 0]
! 1204:
! 1205: [0 0 1 0 0]
! 1206:
! 1207: [0 0 0 1 0]
! 1208:
! 1209: [0 0 0 0 1]
! 1210:
! 1211: ? idealinv(nf,idx)
! 1212:
! 1213: [1 0 2/3 0 0]
! 1214:
! 1215: [0 1 1/3 0 0]
! 1216:
! 1217: [0 0 1/3 0 0]
! 1218:
! 1219: [0 0 0 1 0]
! 1220:
! 1221: [0 0 0 0 1]
! 1222:
! 1223: ? idy=ideallllred(nf,idx,[1,5,6])
! 1224:
! 1225: [5 0 0 2 0]
! 1226:
! 1227: [0 5 0 0 0]
! 1228:
! 1229: [0 0 5 2 0]
! 1230:
! 1231: [0 0 0 1 0]
! 1232:
! 1233: [0 0 0 0 5]
! 1234:
! 1235: ? idealadd(nf,idx,idy)
! 1236:
! 1237: [1 0 0 0 0]
! 1238:
! 1239: [0 1 0 0 0]
! 1240:
! 1241: [0 0 1 0 0]
! 1242:
! 1243: [0 0 0 1 0]
! 1244:
! 1245: [0 0 0 0 1]
! 1246:
! 1247: ? idealaddone(nf,idx,idy)
! 1248: [[3, 0, 2, 1, 0]~, [-2, 0, -2, -1, 0]~]
! 1249: ? idealaddmultone(nf,[idy,idx])
! 1250: [[-5, 0, 0, 0, 0]~, [6, 0, 0, 0, 0]~]
! 1251: ? idealappr(nf,idy)
! 1252: [-2, 0, -2, 4, 0]~
! 1253: ? idealapprfact(nf,idealfactor(nf,idy))
! 1254: [-2, 0, -2, 4, 0]~
! 1255: ? idealcoprime(nf,idx,idx)
! 1256: [-2/3, 2/3, -1/3, 0, 0]~
! 1257: ? idz=idealintersect(nf,idx,idy)
! 1258:
! 1259: [15 5 10 12 10]
! 1260:
! 1261: [0 5 0 0 0]
! 1262:
! 1263: [0 0 5 2 0]
! 1264:
! 1265: [0 0 0 1 0]
! 1266:
! 1267: [0 0 0 0 5]
! 1268:
! 1269: ? idealfactor(nf,idz)
! 1270:
! 1271: [[3, [1, 1, 0, 0, 0]~, 1, 1, [1, -1, -1, 0, 0]~] 1]
! 1272:
! 1273: [[5, [-2, 0, 0, 0, 1]~, 1, 1, [2, 2, 1, 1, 4]~] 1]
! 1274:
! 1275: [[5, [0, 0, -1, 0, 1]~, 4, 1, [4, 5, 4, 2, 0]~] 3]
! 1276:
! 1277: ? ideallist(bnf,20)
! 1278: [[[1, 0; 0, 1]], [], [[3, 2; 0, 1], [3, 0; 0, 1]], [[2, 0; 0, 2]], [[5, 3; 0
! 1279: , 1], [5, 1; 0, 1]], [], [], [], [[9, 5; 0, 1], [3, 0; 0, 3], [9, 3; 0, 1]],
! 1280: [], [[11, 9; 0, 1], [11, 1; 0, 1]], [[6, 4; 0, 2], [6, 0; 0, 2]], [], [], [
! 1281: [15, 8; 0, 1], [15, 3; 0, 1], [15, 11; 0, 1], [15, 6; 0, 1]], [[4, 0; 0, 4]]
! 1282: , [[17, 14; 0, 1], [17, 2; 0, 1]], [], [[19, 18; 0, 1], [19, 0; 0, 1]], [[10
! 1283: , 6; 0, 2], [10, 2; 0, 2]]]
! 1284: ? idx2=idealmul(nf,idx,idx)
! 1285:
! 1286: [9 7 5 8 2]
! 1287:
! 1288: [0 1 0 0 0]
! 1289:
! 1290: [0 0 1 0 0]
! 1291:
! 1292: [0 0 0 1 0]
! 1293:
! 1294: [0 0 0 0 1]
! 1295:
! 1296: ? idt=idealmulred(nf,idx,idx)
! 1297:
! 1298: [2 0 0 0 1]
! 1299:
! 1300: [0 2 0 0 1]
! 1301:
! 1302: [0 0 2 0 0]
! 1303:
! 1304: [0 0 0 2 1]
! 1305:
! 1306: [0 0 0 0 1]
! 1307:
! 1308: ? idealdiv(nf,idy,idt)
! 1309:
! 1310: [5 5/2 5/2 7/2 0]
! 1311:
! 1312: [0 5/2 0 0 0]
! 1313:
! 1314: [0 0 5/2 1 0]
! 1315:
! 1316: [0 0 0 1/2 0]
! 1317:
! 1318: [0 0 0 0 5/2]
! 1319:
! 1320: ? idealdivexact(nf,idx2,idx)
! 1321:
! 1322: [3 1 2 2 2]
! 1323:
! 1324: [0 1 0 0 0]
! 1325:
! 1326: [0 0 1 0 0]
! 1327:
! 1328: [0 0 0 1 0]
! 1329:
! 1330: [0 0 0 0 1]
! 1331:
! 1332: ? idealhermite(nf,vp)
! 1333:
! 1334: [3 1 2 2 2]
! 1335:
! 1336: [0 1 0 0 0]
! 1337:
! 1338: [0 0 1 0 0]
! 1339:
! 1340: [0 0 0 1 0]
! 1341:
! 1342: [0 0 0 0 1]
! 1343:
! 1344: ? idealhermite2(nf,vp[2],3)
! 1345:
! 1346: [3 1 2 2 2]
! 1347:
! 1348: [0 1 0 0 0]
! 1349:
! 1350: [0 0 1 0 0]
! 1351:
! 1352: [0 0 0 1 0]
! 1353:
! 1354: [0 0 0 0 1]
! 1355:
! 1356: ? idealnorm(nf,idt)
! 1357: 16
! 1358: ? idp=idealpow(nf,idx,7)
! 1359:
! 1360: [2187 1807 2129 692 1379]
! 1361:
! 1362: [0 1 0 0 0]
! 1363:
! 1364: [0 0 1 0 0]
! 1365:
! 1366: [0 0 0 1 0]
! 1367:
! 1368: [0 0 0 0 1]
! 1369:
! 1370: ? idealpowred(nf,idx,7)
! 1371:
! 1372: [5 0 0 2 0]
! 1373:
! 1374: [0 5 0 0 0]
! 1375:
! 1376: [0 0 5 2 0]
! 1377:
! 1378: [0 0 0 1 0]
! 1379:
! 1380: [0 0 0 0 5]
! 1381:
! 1382: ? idealtwoelt(nf,idy)
! 1383: [5, [2, 0, 2, 1, 0]~]
! 1384: ? idealtwoelt2(nf,idy,10)
! 1385: [-2, 0, -2, -1, 0]~
! 1386: ? idealval(nf,idp,vp)
! 1387: 7
! 1388: ? idmat(5)
! 1389:
! 1390: [1 0 0 0 0]
! 1391:
! 1392: [0 1 0 0 0]
! 1393:
! 1394: [0 0 1 0 0]
! 1395:
! 1396: [0 0 0 1 0]
! 1397:
! 1398: [0 0 0 0 1]
! 1399:
! 1400: ? if(3<2,print("bof"),print("ok"));
! 1401: ok
! 1402: ? imag(2+3*i)
! 1403: 3
! 1404: ? image([1,3,5;2,4,6;3,5,7])
! 1405:
! 1406: [1 3]
! 1407:
! 1408: [2 4]
! 1409:
! 1410: [3 5]
! 1411:
! 1412: ? image(pi*[1,3,5;2,4,6;3,5,7])
! 1413:
! 1414: [9.4247779607693797153879301498385086525 15.70796326794896619231321691639751
! 1415: 4420]
! 1416:
! 1417: [12.566370614359172953850573533118011536 18.84955592153875943077586029967701
! 1418: 7305]
! 1419:
! 1420: [15.707963267948966192313216916397514420 21.99114857512855266923850368295652
! 1421: 0189]
! 1422:
! 1423: ? incgam(2,1)
! 1424: 0.73575888234288464319104754032292173491
! 1425: ? incgam1(2,1)
! 1426: -0.26424111765711535680895245967678075578
! 1427: ? incgam2(2,1)
! 1428: 0.73575888234288464319104754032292173489
! 1429: ? incgam3(2,1)
! 1430: 0.26424111765711535680895245967707826508
! 1431: ? incgam4(4,1,6)
! 1432: 5.8860710587430771455283803225833738791
! 1433: ? indexrank([1,1,1;1,1,1;1,1,2])
! 1434: [[1, 3], [1, 3]]
! 1435: ? indsort([8,7,6,5])
! 1436: [4, 3, 2, 1]
! 1437: ? initell([0,0,0,-1,0])
! 1438: [0, 0, 0, -1, 0, 0, -2, 0, -1, 48, 0, 64, 1728, [1.0000000000000000000000000
! 1439: 000000000000, 0.E-38, -1.0000000000000000000000000000000000000]~, 2.62205755
! 1440: 42921198104648395898911194136, 2.6220575542921198104648395898911194136*I, -0
! 1441: .59907011736779610371996124614016193910, -1.79721035210338831115988373842048
! 1442: 58173*I, 6.8751858180203728274900957798105571979]
! 1443: ? initrect(1,700,700)
! 1444: ? nfz=initzeta(x^2-2);
! 1445: ? integ(sin(x),x)
! 1446: 1/2*x^2 - 1/24*x^4 + 1/720*x^6 - 1/40320*x^8 + 1/3628800*x^10 - 1/479001600*
! 1447: x^12 + 1/87178291200*x^14 - 1/20922789888000*x^16 + O(x^17)
! 1448: ? integ((-x^2-2*a*x+8*a)/(x^4-14*x^3+(2*a+49)*x^2-14*a*x+a^2),x)
! 1449: (x + a)/(x^2 - 7*x + a)
! 1450: ? intersect([1,2;3,4;5,6],[2,3;7,8;8,9])
! 1451:
! 1452: [-1]
! 1453:
! 1454: [-1]
! 1455:
! 1456: [-1]
! 1457:
! 1458: ? \precision=19
! 1459: realprecision = 19 significant digits
! 1460: ? intgen(x=0,pi,sin(x))
! 1461: 2.000000000000000017
! 1462: ? sqr(2*intgen(x=0,4,exp(-x^2)))
! 1463: 3.141592556720305685
! 1464: ? 4*intinf(x=1,10^20,1/(1+x^2))
! 1465: 3.141592653589793208
! 1466: ? intnum(x=-0.5,0.5,1/sqrt(1-x^2))
! 1467: 1.047197551196597747
! 1468: ? 2*intopen(x=0,100,sin(x)/x)
! 1469: 3.124450933778112629
! 1470: ? \precision=38
! 1471: realprecision = 38 significant digits
! 1472: ? inverseimage([1,1;2,3;5,7],[2,2,6]~)
! 1473: [4, -2]~
! 1474: ? isdiagonal([1,0,0;0,5,0;0,0,0])
! 1475: 1
! 1476: ? isfund(12345)
! 1477: 1
! 1478: ? isideal(bnf[7],[5,1;0,1])
! 1479: 1
! 1480: ? isincl(x^2+1,x^4+1)
! 1481: [-x^2, x^2]
! 1482: ? isinclfast(initalg(x^2+1),initalg(x^4+1))
! 1483: [-x^2, x^2]
! 1484: ? isirreducible(x^5+3*x^3+5*x^2+15)
! 1485: 0
! 1486: ? isisom(x^3+x^2-2*x-1,x^3+x^2-2*x-1)
! 1487: [x, -x^2 - x + 1, x^2 - 2]
! 1488: ? isisomfast(initalg(x^3-2),initalg(x^3-6*x^2-6*x-30))
! 1489: [-1/25*x^2 + 13/25*x - 2/5]
! 1490: ? isprime(12345678901234567)
! 1491: 0
! 1492: ? isprincipal(bnf,[5,1;0,1])
! 1493: [1]~
! 1494: ? isprincipalgen(bnf,[5,1;0,1])
! 1495: [[1]~, [-2, -1/3]~, 181]
! 1496: ? isprincipalraygen(bnr,primedec(bnf,7)[1])
! 1497: [[9]~, [-2170/6561, -931/19683]~, 256]
! 1498: ? ispsp(73!+1)
! 1499: 1
! 1500: ? isqrt(10!^2+1)
! 1501: 3628800
! 1502: ? isset([-3,5,7,7])
! 1503: 0
! 1504: ? issqfree(123456789876543219)
! 1505: 0
! 1506: ? issquare(12345678987654321)
! 1507: 1
! 1508: ? isunit(bnf,mod(3405*x-27466,x^2-x-57))
! 1509: [-4, mod(1, 2)]~
! 1510: ? jacobi(hilbert(6))
! 1511: [[1.6188998589243390969705881471257800712, 0.2423608705752095521357284158507
! 1512: 0114077, 0.000012570757122625194922982397996498755027, 0.0000001082799484565
! 1513: 5497685388772372251711485, 0.016321521319875822124345079564191505890, 0.0006
! 1514: 1574835418265769764919938428527140264]~, [0.74871921887909485900280109200517
! 1515: 845109, -0.61454482829258676899320019644273870645, 0.01114432093072471053067
! 1516: 8340374220998541, -0.0012481940840821751169398163046387834473, 0.24032536934
! 1517: 252330399154228873240534568, -0.062226588150197681775152126611810492910; 0.4
! 1518: 4071750324351206127160083580231701801, 0.21108248167867048675227675845247769
! 1519: 095, -0.17973275724076003758776897803740640964, 0.03560664294428763526612284
! 1520: 8131812048466, -0.69765137527737012296208335046678265583, 0.4908392097109243
! 1521: 6297498316169060044997; 0.32069686982225190106359024326699463106, 0.36589360
! 1522: 730302614149086554211117169622, 0.60421220675295973004426567844103062241, -0
! 1523: .24067907958842295837736719558855679285, -0.23138937333290388042251363554209
! 1524: 048309, -0.53547692162107486593474491750949545456; 0.25431138634047419251788
! 1525: 312792590944672, 0.39470677609501756783094636145991581708, -0.44357471627623
! 1526: 954554460416705180105301, 0.62546038654922724457753441039459331059, 0.132863
! 1527: 15850933553530333839628101576050, -0.41703769221897886840494514780771076439;
! 1528: 0.21153084007896524664213667673977991959, 0.3881904338738864286311144882599
! 1529: 2418973, -0.44153664101228966222143649752977203423, -0.689807199293836684198
! 1530: 01738006926829419, 0.36271492146487147525299457604461742111, 0.0470340189331
! 1531: 15649705614518466541243873; 0.18144297664876947372217005457727093715, 0.3706
! 1532: 9590776736280861775501084807394603, 0.45911481681642960284551392793050866602
! 1533: , 0.27160545336631286930015536176213647001, 0.502762866757515384892605663686
! 1534: 47786272, 0.54068156310385293880022293448123782121]]
! 1535: ? jbesselh(1,1)
! 1536: 0.24029783912342701089584304474193368045
! 1537: ? jell(i)
! 1538: 1728.0000000000000000000000000000000000 + 0.E-54*I
! 1539: ? kbessel(1+i,1)
! 1540: 0.32545977186584141085464640324923711863 + 0.2894280370259921276345671592415
! 1541: 2302704*I
! 1542: ? kbessel2(1+i,1)
! 1543: 0.32545977186584141085464640324923711863 + 0.2894280370259921276345671592415
! 1544: 2302704*I
! 1545: ? x
! 1546: x
! 1547: ? y
! 1548: x
! 1549: ? ker(matrix(4,4,x,y,x/y))
! 1550:
! 1551: [-1/2 -1/3 -1/4]
! 1552:
! 1553: [1 0 0]
! 1554:
! 1555: [0 1 0]
! 1556:
! 1557: [0 0 1]
! 1558:
! 1559: ? ker(matrix(4,4,x,y,sin(x+y)))
! 1560:
! 1561: [0.72968694572192883282306463453582002359]
! 1562:
! 1563: [0.2114969213291234874]
! 1564:
! 1565: [-0.3509176660143506019]
! 1566:
! 1567: [1]
! 1568:
! 1569: ? keri(matrix(4,4,x,y,x+y))
! 1570:
! 1571: [1 2]
! 1572:
! 1573: [-2 -3]
! 1574:
! 1575: [1 0]
! 1576:
! 1577: [0 1]
! 1578:
! 1579: ? kerint(matrix(4,4,x,y,x*y))
! 1580:
! 1581: [-1 -1 -1]
! 1582:
! 1583: [-1 0 1]
! 1584:
! 1585: [1 -1 1]
! 1586:
! 1587: [0 1 -1]
! 1588:
! 1589: ? kerint1(matrix(4,4,x,y,x*y))
! 1590:
! 1591: [-1 -1 -1]
! 1592:
! 1593: [-1 0 1]
! 1594:
! 1595: [1 -1 1]
! 1596:
! 1597: [0 1 -1]
! 1598:
! 1599: ? kerint2(matrix(4,6,x,y,2520/(x+y)))
! 1600:
! 1601: [3 1]
! 1602:
! 1603: [-30 -15]
! 1604:
! 1605: [70 70]
! 1606:
! 1607: [0 -140]
! 1608:
! 1609: [-126 126]
! 1610:
! 1611: [84 -42]
! 1612:
! 1613: ? f(u)=u+1;
! 1614: ? print(f(5));kill(f);
! 1615: 6
! 1616: ? f=12
! 1617: 12
! 1618: ? killrect(1)
! 1619: ? kro(5,7)
! 1620: -1
! 1621: ? kro(3,18)
! 1622: 0
! 1623: ? laplace(x*exp(x*y)/(exp(x)-1))
! 1624: 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 +
! 1625: 22133/10*x^8 - 7560*x^9 + 2775767/66*x^10 - 166320*x^11 + 2655339269/2730*x
! 1626: ^12 - 4324320*x^13 + 264873251/10*x^14 + O(x^15)
! 1627: ? lcm(15,-21)
! 1628: 105
! 1629: ? length(divisors(1000))
! 1630: 16
! 1631: ? legendre(10)
! 1632: 46189/256*x^10 - 109395/256*x^8 + 45045/128*x^6 - 15015/128*x^4 + 3465/256*x
! 1633: ^2 - 63/256
! 1634: ? lex([1,3],[1,3,5])
! 1635: -1
! 1636: ? lexsort([[1,5],[2,4],[1,5,1],[1,4,2]])
! 1637: [[1, 4, 2], [1, 5], [1, 5, 1], [2, 4]]
! 1638: ? lift(chinese(mod(7,15),mod(4,21)))
! 1639: 67
! 1640: ? lindep([(1-3*sqrt(2))/(3-2*sqrt(3)),1,sqrt(2),sqrt(3),sqrt(6)])
! 1641: [-3, -3, 9, -2, 6]
! 1642: ? lindep2([(1-3*sqrt(2))/(3-2*sqrt(3)),1,sqrt(2),sqrt(3),sqrt(6)],14)
! 1643: [-3, -3, 9, -2, 6]
! 1644: ? move(0,0,900);line(0,900,0)
! 1645: ? lines(0,vector(5,k,50*k),vector(5,k,10*k*k))
! 1646: ? m=1/hilbert(7)
! 1647:
! 1648: [49 -1176 8820 -29400 48510 -38808 12012]
! 1649:
! 1650: [-1176 37632 -317520 1128960 -1940400 1596672 -504504]
! 1651:
! 1652: [8820 -317520 2857680 -10584000 18711000 -15717240 5045040]
! 1653:
! 1654: [-29400 1128960 -10584000 40320000 -72765000 62092800 -20180160]
! 1655:
! 1656: [48510 -1940400 18711000 -72765000 133402500 -115259760 37837800]
! 1657:
! 1658: [-38808 1596672 -15717240 62092800 -115259760 100590336 -33297264]
! 1659:
! 1660: [12012 -504504 5045040 -20180160 37837800 -33297264 11099088]
! 1661:
! 1662: ? mp=concat(m,idmat(7))
! 1663:
! 1664: [49 -1176 8820 -29400 48510 -38808 12012 1 0 0 0 0 0 0]
! 1665:
! 1666: [-1176 37632 -317520 1128960 -1940400 1596672 -504504 0 1 0 0 0 0 0]
! 1667:
! 1668: [8820 -317520 2857680 -10584000 18711000 -15717240 5045040 0 0 1 0 0 0 0]
! 1669:
! 1670: [-29400 1128960 -10584000 40320000 -72765000 62092800 -20180160 0 0 0 1 0 0
! 1671: 0]
! 1672:
! 1673: [48510 -1940400 18711000 -72765000 133402500 -115259760 37837800 0 0 0 0 1 0
! 1674: 0]
! 1675:
! 1676: [-38808 1596672 -15717240 62092800 -115259760 100590336 -33297264 0 0 0 0 0
! 1677: 1 0]
! 1678:
! 1679: [12012 -504504 5045040 -20180160 37837800 -33297264 11099088 0 0 0 0 0 0 1]
! 1680:
! 1681: ? lll(m)
! 1682:
! 1683: [-420 -420 840 630 -1092 -83 2562]
! 1684:
! 1685: [-210 -280 630 504 -876 70 2205]
! 1686:
! 1687: [-140 -210 504 420 -749 137 1910]
! 1688:
! 1689: [-105 -168 420 360 -658 169 1680]
! 1690:
! 1691: [-84 -140 360 315 -588 184 1498]
! 1692:
! 1693: [-70 -120 315 280 -532 190 1351]
! 1694:
! 1695: [-60 -105 280 252 -486 191 1230]
! 1696:
! 1697: ? lll1(m)
! 1698:
! 1699: [-420 -420 840 630 -1092 -83 2562]
! 1700:
! 1701: [-210 -280 630 504 -876 70 2205]
! 1702:
! 1703: [-140 -210 504 420 -749 137 1910]
! 1704:
! 1705: [-105 -168 420 360 -658 169 1680]
! 1706:
! 1707: [-84 -140 360 315 -588 184 1498]
! 1708:
! 1709: [-70 -120 315 280 -532 190 1351]
! 1710:
! 1711: [-60 -105 280 252 -486 191 1230]
! 1712:
! 1713: ? lllgram(m)
! 1714:
! 1715: [1 1 27 -27 69 0 141]
! 1716:
! 1717: [0 1 4 -22 34 -24 49]
! 1718:
! 1719: [0 1 3 -21 18 -24 23]
! 1720:
! 1721: [0 1 3 -20 10 -19 13]
! 1722:
! 1723: [0 1 3 -19 6 -14 8]
! 1724:
! 1725: [0 1 3 -18 4 -10 5]
! 1726:
! 1727: [0 1 3 -17 3 -7 3]
! 1728:
! 1729: ? lllgram1(m)
! 1730:
! 1731: [1 1 27 -27 69 0 141]
! 1732:
! 1733: [0 1 4 -22 34 -24 49]
! 1734:
! 1735: [0 1 3 -21 18 -24 23]
! 1736:
! 1737: [0 1 3 -20 10 -19 13]
! 1738:
! 1739: [0 1 3 -19 6 -14 8]
! 1740:
! 1741: [0 1 3 -18 4 -10 5]
! 1742:
! 1743: [0 1 3 -17 3 -7 3]
! 1744:
! 1745: ? lllgramint(m)
! 1746:
! 1747: [1 1 27 -27 69 0 141]
! 1748:
! 1749: [0 1 4 -23 34 -24 91]
! 1750:
! 1751: [0 1 3 -22 18 -24 65]
! 1752:
! 1753: [0 1 3 -21 10 -19 49]
! 1754:
! 1755: [0 1 3 -20 6 -14 38]
! 1756:
! 1757: [0 1 3 -19 4 -10 30]
! 1758:
! 1759: [0 1 3 -18 3 -7 24]
! 1760:
! 1761: ? lllgramkerim(mp~*mp)
! 1762: [[-420, -420, 840, 630, 2982, -1092, -83; -210, -280, 630, 504, 2415, -876,
! 1763: 70; -140, -210, 504, 420, 2050, -749, 137; -105, -168, 420, 360, 1785, -658,
! 1764: 169; -84, -140, 360, 315, 1582, -588, 184; -70, -120, 315, 280, 1421, -532,
! 1765: 190; -60, -105, 280, 252, 1290, -486, 191; 420, 0, 0, 0, -210, 168, 35; 0,
! 1766: 840, 0, 0, 0, 0, 336; 0, 0, -2520, 0, 0, 0, 1260; 0, 0, 0, -2520, 0, 0, -840
! 1767: ; 0, 0, 0, 0, -13860, 0, 6930; 0, 0, 0, 0, 0, 5544, 0; 0, 0, 0, 0, 0, 0, -12
! 1768: 012], [0, 0, 0, 0, 0, 0, 0; 0, 0, 0, 0, 0, 0, 0; 0, 0, 0, 0, 0, 0, 0; 0, 0,
! 1769: 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
! 1770: ; 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,
! 1771: 0, 0, 0; 0, 0, 0, 0, 1, 0, 0; 0, 0, 0, 0, 0, 1, 0; 0, 0, 0, 0, 0, 0, 1]]
! 1772: ? lllint(m)
! 1773:
! 1774: [-420 -420 840 630 -1092 -83 2982]
! 1775:
! 1776: [-210 -280 630 504 -876 70 2415]
! 1777:
! 1778: [-140 -210 504 420 -749 137 2050]
! 1779:
! 1780: [-105 -168 420 360 -658 169 1785]
! 1781:
! 1782: [-84 -140 360 315 -588 184 1582]
! 1783:
! 1784: [-70 -120 315 280 -532 190 1421]
! 1785:
! 1786: [-60 -105 280 252 -486 191 1290]
! 1787:
! 1788: ? lllintpartial(m)
! 1789:
! 1790: [-420 -420 -630 840 1092 2982 -83]
! 1791:
! 1792: [-210 -280 -504 630 876 2415 70]
! 1793:
! 1794: [-140 -210 -420 504 749 2050 137]
! 1795:
! 1796: [-105 -168 -360 420 658 1785 169]
! 1797:
! 1798: [-84 -140 -315 360 588 1582 184]
! 1799:
! 1800: [-70 -120 -280 315 532 1421 190]
! 1801:
! 1802: [-60 -105 -252 280 486 1290 191]
! 1803:
! 1804: ? lllkerim(mp)
! 1805: [[-420, -420, 840, 630, 2982, -1092, -83; -210, -280, 630, 504, 2415, -876,
! 1806: 70; -140, -210, 504, 420, 2050, -749, 137; -105, -168, 420, 360, 1785, -658,
! 1807: 169; -84, -140, 360, 315, 1582, -588, 184; -70, -120, 315, 280, 1421, -532,
! 1808: 190; -60, -105, 280, 252, 1290, -486, 191; 420, 0, 0, 0, -210, 168, 35; 0,
! 1809: 840, 0, 0, 0, 0, 336; 0, 0, -2520, 0, 0, 0, 1260; 0, 0, 0, -2520, 0, 0, -840
! 1810: ; 0, 0, 0, 0, -13860, 0, 6930; 0, 0, 0, 0, 0, 5544, 0; 0, 0, 0, 0, 0, 0, -12
! 1811: 012], [0, 0, 0, 0, 0, 0, 0; 0, 0, 0, 0, 0, 0, 0; 0, 0, 0, 0, 0, 0, 0; 0, 0,
! 1812: 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
! 1813: ; 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,
! 1814: 0, 0, 0; 0, 0, 0, 0, 1, 0, 0; 0, 0, 0, 0, 0, 1, 0; 0, 0, 0, 0, 0, 0, 1]]
! 1815: ? lllrat(m)
! 1816:
! 1817: [-420 -420 840 630 -1092 -83 2982]
! 1818:
! 1819: [-210 -280 630 504 -876 70 2415]
! 1820:
! 1821: [-140 -210 504 420 -749 137 2050]
! 1822:
! 1823: [-105 -168 420 360 -658 169 1785]
! 1824:
! 1825: [-84 -140 360 315 -588 184 1582]
! 1826:
! 1827: [-70 -120 315 280 -532 190 1421]
! 1828:
! 1829: [-60 -105 280 252 -486 191 1290]
! 1830:
! 1831: ? \precision=96
! 1832: realprecision = 96 significant digits
! 1833: ? ln(2)
! 1834: 0.69314718055994530941723212145817656807550013436025525412068000949339362196
! 1835: 9694715605863326996418
! 1836: ? lngamma(10^50*i)
! 1837: -157079632679489661923132169163975144209858469968811.93673753887608474948977
! 1838: 0941153418951907406847 - 2.5258126069288717421377720813802613884088088474975
! 1839: 8842763772207531866369674037379004058787354391*I
! 1840: ? \precision=2000
! 1841: realprecision = 2003 significant digits (2000 digits displayed)
! 1842: ? log(2)
! 1843: 0.69314718055994530941723212145817656807550013436025525412068000949339362196
! 1844: 9694715605863326996418687542001481020570685733685520235758130557032670751635
! 1845: 0759619307275708283714351903070386238916734711233501153644979552391204751726
! 1846: 8157493206515552473413952588295045300709532636664265410423915781495204374043
! 1847: 0385500801944170641671518644712839968171784546957026271631064546150257207402
! 1848: 4816377733896385506952606683411372738737229289564935470257626520988596932019
! 1849: 6505855476470330679365443254763274495125040606943814710468994650622016772042
! 1850: 4524529612687946546193165174681392672504103802546259656869144192871608293803
! 1851: 1727143677826548775664850856740776484514644399404614226031930967354025744460
! 1852: 7030809608504748663852313818167675143866747664789088143714198549423151997354
! 1853: 8803751658612753529166100071053558249879414729509293113897155998205654392871
! 1854: 7000721808576102523688921324497138932037843935308877482597017155910708823683
! 1855: 6275898425891853530243634214367061189236789192372314672321720534016492568727
! 1856: 4778234453534764811494186423867767744060695626573796008670762571991847340226
! 1857: 5146283790488306203306114463007371948900274364396500258093651944304119115060
! 1858: 8094879306786515887090060520346842973619384128965255653968602219412292420757
! 1859: 4321757489097706752687115817051137009158942665478595964890653058460258668382
! 1860: 9400228330053820740056770530467870018416240441883323279838634900156312188956
! 1861: 0650553151272199398332030751408426091479001265168243443893572472788205486271
! 1862: 5527418772430024897945401961872339808608316648114909306675193393128904316413
! 1863: 7068139777649817697486890388778999129650361927071088926410523092478391737350
! 1864: 1229842420499568935992206602204654941510613918788574424557751020683703086661
! 1865: 9480896412186807790208181588580001688115973056186676199187395200766719214592
! 1866: 2367206025395954365416553112951759899400560003665135675690512459268257439464
! 1867: 8316833262490180382424082423145230614096380570070255138770268178516306902551
! 1868: 3703234053802145019015374029509942262995779647427138157363801729873940704242
! 1869: 17997226696297993931270693
! 1870: ? logagm(2)
! 1871: 0.69314718055994530941723212145817656807550013436025525412068000949339362196
! 1872: 9694715605863326996418687542001481020570685733685520235758130557032670751635
! 1873: 0759619307275708283714351903070386238916734711233501153644979552391204751726
! 1874: 8157493206515552473413952588295045300709532636664265410423915781495204374043
! 1875: 0385500801944170641671518644712839968171784546957026271631064546150257207402
! 1876: 4816377733896385506952606683411372738737229289564935470257626520988596932019
! 1877: 6505855476470330679365443254763274495125040606943814710468994650622016772042
! 1878: 4524529612687946546193165174681392672504103802546259656869144192871608293803
! 1879: 1727143677826548775664850856740776484514644399404614226031930967354025744460
! 1880: 7030809608504748663852313818167675143866747664789088143714198549423151997354
! 1881: 8803751658612753529166100071053558249879414729509293113897155998205654392871
! 1882: 7000721808576102523688921324497138932037843935308877482597017155910708823683
! 1883: 6275898425891853530243634214367061189236789192372314672321720534016492568727
! 1884: 4778234453534764811494186423867767744060695626573796008670762571991847340226
! 1885: 5146283790488306203306114463007371948900274364396500258093651944304119115060
! 1886: 8094879306786515887090060520346842973619384128965255653968602219412292420757
! 1887: 4321757489097706752687115817051137009158942665478595964890653058460258668382
! 1888: 9400228330053820740056770530467870018416240441883323279838634900156312188956
! 1889: 0650553151272199398332030751408426091479001265168243443893572472788205486271
! 1890: 5527418772430024897945401961872339808608316648114909306675193393128904316413
! 1891: 7068139777649817697486890388778999129650361927071088926410523092478391737350
! 1892: 1229842420499568935992206602204654941510613918788574424557751020683703086661
! 1893: 9480896412186807790208181588580001688115973056186676199187395200766719214592
! 1894: 2367206025395954365416553112951759899400560003665135675690512459268257439464
! 1895: 8316833262490180382424082423145230614096380570070255138770268178516306902551
! 1896: 3703234053802145019015374029509942262995779647427138157363801729873940704242
! 1897: 17997226696297993931270693
! 1898: ? \precision=19
! 1899: realprecision = 19 significant digits
! 1900: ? bcurve=initell([0,0,0,-3,0])
! 1901: [0, 0, 0, -3, 0, 0, -6, 0, -9, 144, 0, 1728, 1728, [1.732050807568877293, 0.
! 1902: E-19, -1.732050807568877293]~, 1.992332899583490707, 1.992332899583490708*I,
! 1903: -0.7884206134041560682, -2.365261840212468204*I, 3.969390382762759668]
! 1904: ? localred(bcurve,2)
! 1905: [6, 2, [1, 1, 1, 0], 1]
! 1906: ? ccurve=initell([0,0,-1,-1,0])
! 1907: [0, 0, -1, -1, 0, 0, -2, 1, -1, 48, -216, 37, 110592/37, [0.8375654352833230
! 1908: 353, 0.2695944364054445582, -1.107159871688767593]~, 2.993458646231959630, 2
! 1909: .451389381986790061*I, -0.4713192779568114757, -1.435456518668684318*I, 7.33
! 1910: 8132740789576742]
! 1911: ? l=lseriesell(ccurve,2,-37,1)
! 1912: 0.3815754082607112111
! 1913: ? lseriesell(ccurve,2,-37,1.2)-l
! 1914: -1.084202172485504434 E-19
! 1915: ? sbnf=smallbuchinit(x^3-x^2-14*x-1)
! 1916: [x^3 - x^2 - 14*x - 1, 3, 10889, [1, x, x^2], [-3.233732695981516673, -0.071
! 1917: 82350902743636344, 4.305556205008953036], [10889, 5698, 3794; 0, 1, 0; 0, 0,
! 1918: 1], mat(2), mat([0, 1, 1, 1, 1, 0, 1, 1]), [9, 15, 16, 17, 10, 69, 33, 39,
! 1919: 57], [2, [-1, 0, 0]~], [[0, 1, 0]~, [-4, 2, 1]~], [-4, 3, -1, 2, -3, 11, 1,
! 1920: -1, -7; 1, 1, 1, 1, 0, 2, 1, -4, -2; 0, 0, 0, 0, 0, -1, 0, -1, 0]]
! 1921: ? makebigbnf(sbnf)
! 1922: [mat(2), mat([0, 1, 1, 1, 1, 0, 1, 1]), [1.173637103435061715 + 3.1415926535
! 1923: 89793238*I, -4.562279014988837901 + 3.141592653589793238*I; -2.6335434327389
! 1924: 76049 + 3.141592653589793238*I, 1.420330600779487357 + 3.141592653589793238*
! 1925: I; 1.459906329303914334, 3.141948414209350543], [1.246346989334819161 + 3.14
! 1926: 1592653589793238*I, -1.990056445584799713 + 3.141592653589793238*I, 0.540400
! 1927: 6376129469727 + 3.141592653589793238*I, -0.6926391142471042845 + 3.141592653
! 1928: 589793238*I, 0.E-96 + 3.141592653589793238*I, 0.3677262014027817705 + 3.1415
! 1929: 92653589793238*I, 0.004375616572659815402 + 3.141592653589793238*I, -0.83056
! 1930: 25946607188639, -1.977791147836553953 + 3.141592653589793238*I; 0.6716827432
! 1931: 867392935 + 3.141592653589793238*I, 0.5379005671092853266, -0.83332198837424
! 1932: 04172 + 3.141592653589793238*I, -0.2461086674077943078, 0.E-96 + 3.141592653
! 1933: 589793238*I, 0.9729063188316092378, -0.8738318043071131265, -1.5526615498687
! 1934: 75853 + 3.141592653589793238*I, 0.5774919091398324092 + 3.141592653589793238
! 1935: *I; -1.918029732621558454, 1.452155878475514386, 0.2929213507612934444, 0.93
! 1936: 87477816548985923, 0.E-96 + 3.141592653589793238*I, -1.340632520234391008, 0
! 1937: .8694561877344533111, 2.383224144529494717 + 3.141592653589793238*I, 1.40029
! 1938: 9238696721544 + 3.141592653589793238*I], [[3, [-1, 1, 0]~, 1, 1, [1, 0, 1]~]
! 1939: , [5, [3, 1, 0]~, 1, 1, [-2, 1, 1]~], [5, [-1, 1, 0]~, 1, 1, [1, 0, 1]~], [5
! 1940: , [2, 1, 0]~, 1, 1, [2, 2, 1]~], [3, [1, 0, 1]~, 1, 2, [-1, 1, 0]~], [23, [-
! 1941: 10, 1, 0]~, 1, 1, [7, 9, 1]~], [11, [1, 1, 0]~, 1, 1, [-1, -2, 1]~], [13, [1
! 1942: 9, 1, 0]~, 1, 1, [2, 6, 1]~], [19, [-6, 1, 0]~, 1, 1, [-3, 5, 1]~]]~, [1, 2,
! 1943: 3, 4, 5, 6, 7, 8, 9]~, [x^3 - x^2 - 14*x - 1, [3, 0], 10889, 1, [[1, -3.233
! 1944: 732695981516673, 10.45702714905988813; 1, -0.07182350902743636344, 0.0051586
! 1945: 16449014232794; 1, 4.305556205008953036, 18.53781423449109762], [1, 1, 1; -3
! 1946: .233732695981516673, -0.07182350902743636344, 4.305556205008953036; 10.45702
! 1947: 714905988813, 0.005158616449014232794, 18.53781423449109762], [3, 1.00000000
! 1948: 0000000000, 29.00000000000000000; 1.000000000000000000, 29.00000000000000000
! 1949: , 46.00000000000000000; 29.00000000000000000, 46.00000000000000000, 453.0000
! 1950: 000000000000], [3, 1, 29; 1, 29, 46; 29, 46, 453], [10889, 5698, 3794; 0, 1,
! 1951: 0; 0, 0, 1], [11021, 881, -795; 881, 518, -109; -795, -109, 86], [10889, [1
! 1952: 890, 5190, 1]~]], [-3.233732695981516673, -0.07182350902743636344, 4.3055562
! 1953: 05008953036], [1, x, x^2], [1, 0, 0; 0, 1, 0; 0, 0, 1], [1, 0, 0, 0, 0, 1, 0
! 1954: , 1, 1; 0, 1, 0, 1, 0, 14, 0, 14, 15; 0, 0, 1, 0, 1, 1, 1, 1, 15]], [[2, [2]
! 1955: , [[3, 2, 2; 0, 1, 0; 0, 0, 1]]], 10.34800724602767998, 1.000000000000000000
! 1956: , [2, -1], [x, x^2 + 2*x - 4], 1000], [mat(1), [[0, 0, 0]], [[1.246346989334
! 1957: 819161 + 3.141592653589793238*I, 0.6716827432867392935 + 3.14159265358979323
! 1958: 8*I, -1.918029732621558454]]], [-4, 3, -1, 2, -3, 11, 1, -1, -7; 1, 1, 1, 1,
! 1959: 0, 2, 1, -4, -2; 0, 0, 0, 0, 0, -1, 0, -1, 0]]
! 1960: ? concat(mat(vector(4,x,x)~),vector(4,x,10+x)~)
! 1961:
! 1962: [1 11]
! 1963:
! 1964: [2 12]
! 1965:
! 1966: [3 13]
! 1967:
! 1968: [4 14]
! 1969:
! 1970: ? matextract(matrix(15,15,x,y,x+y),vector(5,x,3*x),vector(3,y,3*y))
! 1971:
! 1972: [6 9 12]
! 1973:
! 1974: [9 12 15]
! 1975:
! 1976: [12 15 18]
! 1977:
! 1978: [15 18 21]
! 1979:
! 1980: [18 21 24]
! 1981:
! 1982: ? ma=mathell(mcurve,mpoints)
! 1983:
! 1984: [1.172183098700697010 0.4476973883408951692]
! 1985:
! 1986: [0.4476973883408951692 1.755026016172950713]
! 1987:
! 1988: ? gauss(ma,mhbi)
! 1989: [-1.000000000000000000, 1.000000000000000000]~
! 1990: ? (1.*hilbert(7))^(-1)
! 1991:
! 1992: [48.99999999999354616 -1175.999999999759026 8819.999999997789586 -29399.9999
! 1993: 9999171836 48509.99999998526254 -38807.99999998756766 12011.99999999599856]
! 1994:
! 1995: [-1175.999999999756499 37631.99999999093860 -317519.9999999170483 1128959.99
! 1996: 9999689868 -1940399.999999448886 1596671.999999535762 -504503.9999998507690]
! 1997:
! 1998: [8819.999999997745604 -317519.9999999163090 2857679.999999235184 -10583999.9
! 1999: 9999714478 18710999.99999493212 -15717239.99999573533 5045039.999998630382]
! 2000:
! 2001: [-29399.99999999149442 1128959.999999684822 -10583999.99999712372 40319999.9
! 2002: 9998927448 -72764999.99998098063 62092799.99998400783 -20180159.99999486766]
! 2003:
! 2004: [48509.99999998476962 -1940399.999999436456 18710999.99999486299 -72764999.9
! 2005: 9998086196 133402499.9999660890 -115259759.9999715052 37837799.99999086044]
! 2006:
! 2007: [-38807.99999998708779 1596671.999999522805 -15717239.99999565420 62092799.9
! 2008: 9998382209 -115259759.9999713525 100590335.9999759413 -33297263.99999228701]
! 2009:
! 2010: [12011.99999999582671 -504503.9999998459239 5045039.999998597949 -20180159.9
! 2011: 9999478405 37837799.99999076882 -33297263.99999225112 11099087.99999751679]
! 2012:
! 2013: ? matsize([1,2;3,4;5,6])
! 2014: [3, 2]
! 2015: ? matrix(5,5,x,y,gcd(x,y))
! 2016:
! 2017: [1 1 1 1 1]
! 2018:
! 2019: [1 2 1 2 1]
! 2020:
! 2021: [1 1 3 1 1]
! 2022:
! 2023: [1 2 1 4 1]
! 2024:
! 2025: [1 1 1 1 5]
! 2026:
! 2027: ? matrixqz([1,3;3,5;5,7],0)
! 2028:
! 2029: [1 1]
! 2030:
! 2031: [3 2]
! 2032:
! 2033: [5 3]
! 2034:
! 2035: ? matrixqz2([1/3,1/4,1/6;1/2,1/4,-1/4;1/3,1,0])
! 2036:
! 2037: [19 12 2]
! 2038:
! 2039: [0 1 0]
! 2040:
! 2041: [0 0 1]
! 2042:
! 2043: ? matrixqz3([1,3;3,5;5,7])
! 2044:
! 2045: [2 -1]
! 2046:
! 2047: [1 0]
! 2048:
! 2049: [0 1]
! 2050:
! 2051: ? max(2,3)
! 2052: 3
! 2053: ? min(2,3)
! 2054: 2
! 2055: ? minim([2,1;1,2],4,6)
! 2056: [6, 2, [0, -1, 1; 1, 1, 0]]
! 2057: ? mod(-12,7)
! 2058: mod(2, 7)
! 2059: ? modp(-12,7)
! 2060: mod(2, 7)
! 2061: ? mod(10873,49649)^-1
! 2062: *** impossible inverse modulo: mod(131, 49649).
! 2063: ? modreverse(mod(x^2+1,x^3-x-1))
! 2064: mod(x^2 - 3*x + 2, x^3 - 5*x^2 + 8*x - 5)
! 2065: ? move(0,243,583);cursor(0)
! 2066: ? mu(3*5*7*11*13)
! 2067: -1
! 2068: ? newtonpoly(x^4+3*x^3+27*x^2+9*x+81,3)
! 2069: [2, 2/3, 2/3, 2/3]
! 2070: ? nextprime(100000000000000000000000)
! 2071: 100000000000000000000117
! 2072: ? setrand(1);a=matrix(3,5,j,k,vvector(5,l,random()\10^8))
! 2073:
! 2074: [[10, 7, 8, 7, 18]~ [17, 0, 9, 20, 10]~ [5, 4, 7, 18, 20]~ [0, 16, 4, 2, 0]~
! 2075: [17, 19, 17, 1, 14]~]
! 2076:
! 2077: [[17, 16, 6, 3, 6]~ [17, 13, 9, 19, 6]~ [1, 14, 12, 20, 8]~ [6, 1, 8, 17, 21
! 2078: ]~ [18, 17, 9, 10, 13]~]
! 2079:
! 2080: [[4, 13, 3, 17, 14]~ [14, 16, 11, 5, 4]~ [9, 11, 13, 7, 15]~ [19, 21, 2, 4,
! 2081: 5]~ [14, 16, 6, 20, 14]~]
! 2082:
! 2083: ? aid=[idx,idy,idz,idmat(5),idx]
! 2084: [[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]
! 2085: , [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
! 2086: ], [15, 5, 10, 12, 10; 0, 5, 0, 0, 0; 0, 0, 5, 2, 0; 0, 0, 0, 1, 0; 0, 0, 0,
! 2087: 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
! 2088: , 0, 1], [3, 1, 2, 2, 2; 0, 1, 0, 0, 0; 0, 0, 1, 0, 0; 0, 0, 0, 1, 0; 0, 0,
! 2089: 0, 0, 1]]
! 2090: ? bb=algtobasis(nf,mod(x^3+x,nfpol))
! 2091: [1, 1, 1, 3, 0]~
! 2092: ? da=nfdetint(nf,[a,aid])
! 2093:
! 2094: [30 5 25 27 10]
! 2095:
! 2096: [0 5 0 0 0]
! 2097:
! 2098: [0 0 5 2 0]
! 2099:
! 2100: [0 0 0 1 0]
! 2101:
! 2102: [0 0 0 0 5]
! 2103:
! 2104: ? nfdiv(nf,ba,bb)
! 2105: [755/373, -152/373, 159/373, 120/373, -264/373]~
! 2106: ? nfdiveuc(nf,ba,bb)
! 2107: [2, 0, 0, 0, -1]~
! 2108: ? nfdivres(nf,ba,bb)
! 2109: [[2, 0, 0, 0, -1]~, [-12, -7, 0, 9, 5]~]
! 2110: ? nfhermite(nf,[a,aid])
! 2111: [[[1, 0, 0, 0, 0]~, [0, 0, 0, 0, 0]~, [0, 0, 0, 0, 0]~; [0, 0, 0, 0, 0]~, [1
! 2112: , 0, 0, 0, 0]~, [0, 0, 0, 0, 0]~; [0, 0, 0, 0, 0]~, [0, 0, 0, 0, 0]~, [1, 0,
! 2113: 0, 0, 0]~], [[2, 1, 1, 1, 0; 0, 1, 0, 0, 0; 0, 0, 1, 0, 0; 0, 0, 0, 1, 0; 0
! 2114: , 0, 0, 0, 1], [1, 0, 0, 0, 0; 0, 1, 0, 0, 0; 0, 0, 1, 0, 0; 0, 0, 0, 1, 0;
! 2115: 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;
! 2116: 0, 0, 0, 0, 1]]]
! 2117: ? nfhermitemod(nf,[a,aid],da)
! 2118: [[[1, 0, 0, 0, 0]~, [0, 0, 0, 0, 0]~, [0, 0, 0, 0, 0]~; [0, 0, 0, 0, 0]~, [1
! 2119: , 0, 0, 0, 0]~, [0, 0, 0, 0, 0]~; [0, 0, 0, 0, 0]~, [0, 0, 0, 0, 0]~, [1, 0,
! 2120: 0, 0, 0]~], [[2, 1, 1, 1, 0; 0, 1, 0, 0, 0; 0, 0, 1, 0, 0; 0, 0, 0, 1, 0; 0
! 2121: , 0, 0, 0, 1], [1, 0, 0, 0, 0; 0, 1, 0, 0, 0; 0, 0, 1, 0, 0; 0, 0, 0, 1, 0;
! 2122: 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;
! 2123: 0, 0, 0, 0, 1]]]
! 2124: ? nfmod(nf,ba,bb)
! 2125: [-12, -7, 0, 9, 5]~
! 2126: ? nfmul(nf,ba,bb)
! 2127: [-25, -50, -30, 15, 90]~
! 2128: ? nfpow(nf,bb,5)
! 2129: [23455, 156370, 115855, 74190, -294375]~
! 2130: ? nfreduce(nf,ba,idx)
! 2131: [1, 0, 0, 0, 0]~
! 2132: ? setrand(1);as=matrix(3,3,j,k,vvector(5,l,random()\10^8))
! 2133:
! 2134: [[10, 7, 8, 7, 18]~ [17, 0, 9, 20, 10]~ [5, 4, 7, 18, 20]~]
! 2135:
! 2136: [[17, 16, 6, 3, 6]~ [17, 13, 9, 19, 6]~ [1, 14, 12, 20, 8]~]
! 2137:
! 2138: [[4, 13, 3, 17, 14]~ [14, 16, 11, 5, 4]~ [9, 11, 13, 7, 15]~]
! 2139:
! 2140: ? vaid=[idx,idy,idmat(5)]
! 2141: [[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]
! 2142: , [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
! 2143: ], [1, 0, 0, 0, 0; 0, 1, 0, 0, 0; 0, 0, 1, 0, 0; 0, 0, 0, 1, 0; 0, 0, 0, 0,
! 2144: 1]]
! 2145: ? haid=[idmat(5),idmat(5),idmat(5)]
! 2146: [[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]
! 2147: , [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
! 2148: ], [1, 0, 0, 0, 0; 0, 1, 0, 0, 0; 0, 0, 1, 0, 0; 0, 0, 0, 1, 0; 0, 0, 0, 0,
! 2149: 1]]
! 2150: ? nfsmith(nf,[as,haid,vaid])
! 2151: [[10951073973332888246310, 5442457637639729109215, 2693780223637146570055, 3
! 2152: 910837124677073032737, 3754666252923836621170; 0, 5, 0, 0, 0; 0, 0, 5, 2, 0;
! 2153: 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
! 2154: ; 0, 0, 0, 1, 0; 0, 0, 0, 0, 1], [1, 0, 0, 0, 0; 0, 1, 0, 0, 0; 0, 0, 1, 0,
! 2155: 0; 0, 0, 0, 1, 0; 0, 0, 0, 0, 1]]
! 2156: ? nfval(nf,ba,vp)
! 2157: 0
! 2158: ? norm(1+i)
! 2159: 2
! 2160: ? norm(mod(x+5,x^3+x+1))
! 2161: 129
! 2162: ? norml2(vector(10,x,x))
! 2163: 385
! 2164: ? nucomp(qfi(2,1,9),qfi(4,3,5),3)
! 2165: qfi(2, -1, 9)
! 2166: ? form=qfi(2,1,9);nucomp(form,form,3)
! 2167: qfi(4, -3, 5)
! 2168: ? numdiv(2^99*3^49)
! 2169: 5000
! 2170: ? numer((x+1)/(x-1))
! 2171: x + 1
! 2172: ? nupow(form,111)
! 2173: qfi(2, -1, 9)
! 2174: ? 1/(1+x)+o(x^20)
! 2175: 1 - x + x^2 - x^3 + x^4 - x^5 + x^6 - x^7 + x^8 - x^9 + x^10 - x^11 + x^12 -
! 2176: x^13 + x^14 - x^15 + x^16 - x^17 + x^18 - x^19 + O(x^20)
! 2177: ? omega(100!)
! 2178: 25
! 2179: ? ordell(acurve,1)
! 2180: [8, 3]
! 2181: ? order(mod(33,2^16+1))
! 2182: 2048
! 2183: ? tcurve=initell([1,0,1,-19,26]);
! 2184: ? orderell(tcurve,[1,2])
! 2185: 6
! 2186: ? ordred(x^3-12*x+45*x-1)
! 2187: [x - 1, x^3 - 363*x - 2663, x^3 + 33*x - 1]
! 2188: ? padicprec(padicno,127)
! 2189: 5
! 2190: ? pascal(8)
! 2191:
! 2192: [1 0 0 0 0 0 0 0 0]
! 2193:
! 2194: [1 1 0 0 0 0 0 0 0]
! 2195:
! 2196: [1 2 1 0 0 0 0 0 0]
! 2197:
! 2198: [1 3 3 1 0 0 0 0 0]
! 2199:
! 2200: [1 4 6 4 1 0 0 0 0]
! 2201:
! 2202: [1 5 10 10 5 1 0 0 0]
! 2203:
! 2204: [1 6 15 20 15 6 1 0 0]
! 2205:
! 2206: [1 7 21 35 35 21 7 1 0]
! 2207:
! 2208: [1 8 28 56 70 56 28 8 1]
! 2209:
! 2210: ? perf([2,0,1;0,2,1;1,1,2])
! 2211: 6
! 2212: ? permutation(7,1035)
! 2213: [4, 7, 1, 6, 3, 5, 2]
! 2214: ? permutation2num([4,7,1,6,3,5,2])
! 2215: 1035
! 2216: ? pf(-44,3)
! 2217: qfi(3, 2, 4)
! 2218: ? phi(257^2)
! 2219: 65792
! 2220: ? pi
! 2221: 3.141592653589793238
! 2222: ? plot(x=-5,5,sin(x))
! 2223:
! 2224: 0.9995545 x""x_''''''''''''''''''''''''''''''''''_x""x'''''''''''''''''''|
! 2225: | x _ "_ |
! 2226: | x _ _ |
! 2227: | x _ |
! 2228: | _ " |
! 2229: | " x |
! 2230: | x _ |
! 2231: | " |
! 2232: | " x _ |
! 2233: | _ |
! 2234: | " x |
! 2235: ````````````x``````````````````_````````````````````````````````
! 2236: | " |
! 2237: | " x _ |
! 2238: | _ |
! 2239: | " x |
! 2240: | x _ |
! 2241: | _ " |
! 2242: | " x |
! 2243: | " " x |
! 2244: | "_ " x |
! 2245: -0.999555 |...................x__x".................................."x__x
! 2246: -5 5
! 2247: ? pnqn([2,6,10,14,18,22,26])
! 2248:
! 2249: [19318376 741721]
! 2250:
! 2251: [8927353 342762]
! 2252:
! 2253: ? pnqn([1,1,1,1,1,1,1,1;1,1,1,1,1,1,1,1])
! 2254:
! 2255: [34 21]
! 2256:
! 2257: [21 13]
! 2258:
! 2259: ? point(0,225,334)
! 2260: ? points(0,vector(10,k,10*k),vector(10,k,5*k*k))
! 2261: ? pointell(acurve,zell(acurve,apoint))
! 2262: [0.9999999999999999986 + 0.E-19*I, 2.999999999999999998 + 0.E-18*I]
! 2263: ? polint([0,2,3],[0,4,9],5)
! 2264: 25
! 2265: ? polred(x^5-2*x^4-4*x^3-96*x^2-352*x-568)
! 2266: [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
! 2267: - 1, x^5 - x^4 + 4*x^3 - 2*x^2 + x - 1, x^5 + 4*x^3 - 4*x^2 + 8*x - 8]
! 2268: ? polred2(x^4-28*x^3-458*x^2+9156*x-25321)
! 2269:
! 2270: [1 x - 1]
! 2271:
! 2272: [1/115*x^2 - 14/115*x - 327/115 x^2 - 10]
! 2273:
! 2274: [3/1495*x^3 - 63/1495*x^2 - 1607/1495*x + 13307/1495 x^4 - 32*x^2 + 216]
! 2275:
! 2276: [1/4485*x^3 - 7/1495*x^2 - 1034/4485*x + 7924/4485 x^4 - 8*x^2 + 6]
! 2277:
! 2278: ? polredabs(x^5-2*x^4-4*x^3-96*x^2-352*x-568)
! 2279: x^5 - x^4 + 2*x^3 - 4*x^2 + x - 1
! 2280: ? polredabs2(x^5-2*x^4-4*x^3-96*x^2-352*x-568)
! 2281: [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 -
! 2282: x^4 + 2*x^3 - 4*x^2 + x - 1)]
! 2283: ? polsym(x^17-1,17)
! 2284: [17, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 17]~
! 2285: ? polvar(name^4-other)
! 2286: name
! 2287: ? poly(sin(x),x)
! 2288: -1/1307674368000*x^15 + 1/6227020800*x^13 - 1/39916800*x^11 + 1/362880*x^9 -
! 2289: 1/5040*x^7 + 1/120*x^5 - 1/6*x^3 + x
! 2290: ? polylog(5,0.5)
! 2291: 0.5084005792422687065
! 2292: ? polylog(-4,t)
! 2293: (t^4 + 11*t^3 + 11*t^2 + t)/(-t^5 + 5*t^4 - 10*t^3 + 10*t^2 - 5*t + 1)
! 2294: ? polylogd(5,0.5)
! 2295: 1.033792745541689061
! 2296: ? polylogdold(5,0.5)
! 2297: 1.034459423449010483
! 2298: ? polylogp(5,0.5)
! 2299: 0.9495693489964922581
! 2300: ? poly([1,2,3,4,5],x)
! 2301: x^4 + 2*x^3 + 3*x^2 + 4*x + 5
! 2302: ? polyrev([1,2,3,4,5],x)
! 2303: 5*x^4 + 4*x^3 + 3*x^2 + 2*x + 1
! 2304: ? polzag(6,3)
! 2305: 4608*x^6 - 13824*x^5 + 46144/3*x^4 - 23168/3*x^3 + 5032/3*x^2 - 120*x + 1
! 2306: ? postdraw([0,20,20])
! 2307: ? postploth(x=-5,5,sin(x))
! 2308: [-5.000000000000000000, 5.000000000000000000, -0.9999964107564721649, 0.9999
! 2309: 964107564721649]
! 2310: ? postploth2(t=0,2*pi,[sin(5*t),sin(7*t)])
! 2311: [-0.9999994509568810308, 0.9999994509568810308, -0.9999994509568810308, 0.99
! 2312: 99994509568810308]
! 2313: ? postplothraw(vector(100,k,k),vector(100,k,k*k/100))
! 2314: [1.000000000000000000, 100.0000000000000000, 0.01000000000000000020, 100.000
! 2315: 0000000000000]
! 2316: ? powell(acurve,apoint,10)
! 2317: [-28919032218753260057646013785951999/292736325329248127651484680640160000,
! 2318: 478051489392386968218136375373985436596569736643531551/158385319626308443937
! 2319: 475969221994173751192384064000000]
! 2320: ? cmcurve=initell([0,-3/4,0,-2,-1])
! 2321: [0, -3/4, 0, -2, -1, -3, -4, -4, -1, 105, 1323, -343, -3375, [2.000000000000
! 2322: 000000, -0.6249999999999999999 + 0.3307189138830738238*I, -0.624999999999999
! 2323: 9999 - 0.3307189138830738238*I]~, 1.933311705616811546, 0.966655852808405773
! 2324: 3 + 2.557530989916099474*I, -0.8558486330998558525 - 4.598829819117624524 E-
! 2325: 20*I, -0.4279243165499279261 - 2.757161217166147204*I, 4.944504600282546727]
! 2326: ? powell(cmcurve,[x,y],quadgen(-7))
! 2327: [((-2 + 3*w)*x^2 + (6 - w))/((-2 - 5*w)*x + (-4 - 2*w)), ((34 - 11*w)*x^3 +
! 2328: (40 - 28*w)*x^2 + (22 + 23*w)*x)/((-90 - w)*x^2 + (-136 + 44*w)*x + (-40 + 2
! 2329: 8*w))]
! 2330: ? powrealraw(qfr(5,3,-1,0.),3)
! 2331: qfr(125, 23, 1, 0.E-18)
! 2332: ? pprint((x-12*y)/(y+13*x));
! 2333: (-(11 /14))
! 2334: ? pprint([1,2;3,4])
! 2335:
! 2336: [1 2]
! 2337:
! 2338: [3 4]
! 2339:
! 2340: ? pprint1(x+y);pprint(x+y);
! 2341: (2 x)(2 x)
! 2342: ? \precision=96
! 2343: realprecision = 96 significant digits
! 2344: ? pi
! 2345: 3.14159265358979323846264338327950288419716939937510582097494459230781640628
! 2346: 620899862803482534211
! 2347: ? prec(pi,20)
! 2348: 3.1415926535897932384626433832795028841
! 2349: ? precision(cmcurve)
! 2350: 19
! 2351: ? \precision=38
! 2352: realprecision = 38 significant digits
! 2353: ? prime(100)
! 2354: 541
! 2355: ? primedec(nf,2)
! 2356: [[2, [3, 1, 0, 0, 0]~, 1, 1, [1, 1, 0, 1, 1]~], [2, [-3, -5, -4, 3, 15]~, 1,
! 2357: 4, [1, 1, 0, 0, 0]~]]
! 2358: ? primedec(nf,3)
! 2359: [[3, [1, 1, 0, 0, 0]~, 1, 1, [1, -1, -1, 0, 0]~], [3, [-1, 1, -1, 0, 1]~, 2,
! 2360: 2, [1, 2, 3, 1, 0]~]]
! 2361: ? primedec(nf,11)
! 2362: [[11, [11, 0, 0, 0, 0]~, 1, 5, [1, 0, 0, 0, 0]~]]
! 2363: ? primes(100)
! 2364: [2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71,
! 2365: 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151,
! 2366: 157, 163, 167, 173, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229, 233, 2
! 2367: 39, 241, 251, 257, 263, 269, 271, 277, 281, 283, 293, 307, 311, 313, 317, 33
! 2368: 1, 337, 347, 349, 353, 359, 367, 373, 379, 383, 389, 397, 401, 409, 419, 421
! 2369: , 431, 433, 439, 443, 449, 457, 461, 463, 467, 479, 487, 491, 499, 503, 509,
! 2370: 521, 523, 541]
! 2371: ? forprime(p=2,100,print(p," ",lift(primroot(p))))
! 2372: 2 1
! 2373: 3 2
! 2374: 5 2
! 2375: 7 3
! 2376: 11 2
! 2377: 13 2
! 2378: 17 3
! 2379: 19 2
! 2380: 23 5
! 2381: 29 2
! 2382: 31 3
! 2383: 37 2
! 2384: 41 6
! 2385: 43 3
! 2386: 47 5
! 2387: 53 2
! 2388: 59 2
! 2389: 61 2
! 2390: 67 2
! 2391: 71 7
! 2392: 73 5
! 2393: 79 3
! 2394: 83 2
! 2395: 89 3
! 2396: 97 5
! 2397: ? principalideal(nf,mod(x^3+5,nfpol))
! 2398:
! 2399: [6]
! 2400:
! 2401: [0]
! 2402:
! 2403: [1]
! 2404:
! 2405: [3]
! 2406:
! 2407: [0]
! 2408:
! 2409: ? principalidele(nf,mod(x^3+5,nfpol))
! 2410: [[6; 0; 1; 3; 0], [2.2324480827796254080981385584384939684 + 3.1415926535897
! 2411: 932384626433832795028842*I, 5.0387659675158716386435353106610489968 + 1.5851
! 2412: 760343512250049897278861965702423*I, 4.2664040272651028743625910797589683173
! 2413: - 0.0083630478144368246110910258645462996191*I]]
! 2414: ? print((x-12*y)/(y+13*x));
! 2415: -11/14
! 2416: ? print([1,2;3,4])
! 2417: [1, 2; 3, 4]
! 2418: ? print1(x+y);print1(" equals ");print(x+y);
! 2419: 2*x equals 2*x
! 2420: ? prod(1,k=1,10,1+1/k!)
! 2421: 3335784368058308553334783/905932868585678438400000
! 2422: ? prod(1.,k=1,10,1+1/k!)
! 2423: 3.6821540356142043935732308433185262945
! 2424: ? pi^2/6*prodeuler(p=2,10000,1-p^-2)
! 2425: 1.0000098157493066238697591433298145174
! 2426: ? prodinf(n=0,(1+2^-n)/(1+2^(-n+1)))
! 2427: 0.33333333333333333333333333333333333320
! 2428: ? prodinf1(n=0,-2^-n/(1+2^(-n+1)))
! 2429: 0.33333333333333333333333333333333333320
! 2430: ? psi(1)
! 2431: -0.57721566490153286060651209008240243102
! 2432: ? quaddisc(-252)
! 2433: -7
! 2434: ? quadgen(-11)
! 2435: w
! 2436: ? quadpoly(-11)
! 2437: x^2 - x + 3
! 2438: ? rank(matrix(5,5,x,y,x+y))
! 2439: 2
! 2440: ? rayclassno(bnf,[[5,3;0,1],[1,0]])
! 2441: 12
! 2442: ? rayclassnolist(bnf,lu)
! 2443: [[3], [], [3, 3], [3], [6, 6], [], [], [], [3, 3, 3], [], [3, 3], [3, 3], []
! 2444: , [], [12, 6, 6, 12], [3], [3, 3], [], [9, 9], [6, 6], [], [], [], [], [6, 1
! 2445: 2, 6], [], [3, 3, 3, 3], [], [], [], [], [], [3, 6, 6, 3], [], [], [9, 3, 9]
! 2446: , [6, 6], [], [], [], [], [], [3, 3], [3, 3], [12, 12, 6, 6, 12, 12], [], []
! 2447: , [6, 6], [9], [], [3, 3, 3, 3], [], [3, 3], [], [6, 12, 12, 6]]
! 2448: ? move(0,50,50);rbox(0,50,50)
! 2449: ? print1("give a value for s? ");s=read();print(1/s)
! 2450: give a value for s? 37.
! 2451: 0.027027027027027027027027027027027027026
! 2452: ? real(5-7*i)
! 2453: 5
! 2454: ? recip(3*x^7-5*x^3+6*x-9)
! 2455: -9*x^7 + 6*x^6 - 5*x^4 + 3
! 2456: ? redimag(qfi(3,10,12))
! 2457: qfi(3, -2, 4)
! 2458: ? redreal(qfr(3,10,-20,1.5))
! 2459: qfr(3, 16, -7, 1.5000000000000000000000000000000000000)
! 2460: ? redrealnod(qfr(3,10,-20,1.5),18)
! 2461: qfr(3, 16, -7, 1.5000000000000000000000000000000000000)
! 2462: ? reduceddisc(x^3+4*x+12)
! 2463: [1036, 4, 1]
! 2464: ? regula(17)
! 2465: 2.0947125472611012942448228460655286534
! 2466: ? kill(y);print(x+y);reorder([x,y]);print(x+y);
! 2467: x + y
! 2468: x + y
! 2469: ? resultant(x^3-1,x^3+1)
! 2470: 8
! 2471: ? resultant2(x^3-1.,x^3+1.)
! 2472: 8.0000000000000000000000000000000000000
! 2473: ? reverse(tan(x))
! 2474: 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
! 2475: 5 + O(x^16)
! 2476: ? rhoreal(qfr(3,10,-20,1.5))
! 2477: qfr(-20, -10, 3, 2.1074451073987839947135880252731470615)
! 2478: ? rhorealnod(qfr(3,10,-20,1.5),18)
! 2479: qfr(-20, -10, 3, 1.5000000000000000000000000000000000000)
! 2480: ? rline(0,200,150)
! 2481: ? cursor(0)
! 2482: ? rmove(0,5,5);cursor(0)
! 2483: ? rndtoi(prod(1,k=1,17,x-exp(2*i*pi*k/17)))
! 2484: x^17 - 1
! 2485: ? qpol=y^3-y-1;setrand(1);bnf2=buchinit(qpol);nf2=bnf2[7];
! 2486: ? un=mod(1,qpol);w=mod(y,qpol);p=un*(x^5-5*x+w)
! 2487: mod(1, y^3 - y - 1)*x^5 + mod(-5, y^3 - y - 1)*x + mod(y, y^3 - y - 1)
! 2488: ? aa=rnfpseudobasis(nf2,p)
! 2489: [[[1, 0, 0]~, [0, 0, 0]~, [0, 0, 0]~, [-2, 0, 0]~, [11, 0, 0]~; [0, 0, 0]~,
! 2490: [1, 0, 0]~, [0, 0, 0]~, [2, 0, 0]~, [-8, 0, 0]~; [0, 0, 0]~, [0, 0, 0]~, [1,
! 2491: 0, 0]~, [1, 0, 0]~, [4, 0, 0]~; [0, 0, 0]~, [0, 0, 0]~, [0, 0, 0]~, [1, 0,
! 2492: 0]~, [-2, 0, 0]~; [0, 0, 0]~, [0, 0, 0]~, [0, 0, 0]~, [0, 0, 0]~, [1, 0, 0]~
! 2493: ], [[1, 0, 0; 0, 1, 0; 0, 0, 1], [1, 0, 0; 0, 1, 0; 0, 0, 1], [1, 0, 0; 0, 1
! 2494: , 0; 0, 0, 1], [1, 0, 3/5; 0, 1, 2/5; 0, 0, 1/5], [1, 0, 8/25; 0, 1, 22/25;
! 2495: 0, 0, 1/25]], [416134375, 212940625, 388649575; 0, 3125, 550; 0, 0, 25], [-1
! 2496: 280, 5, 5]~]
! 2497: ? rnfbasis(bnf2,aa)
! 2498:
! 2499: [[1, 0, 0]~ [0, 0, 0]~ [0, 0, 0]~ [38/25, -33/25, 11/25]~ [-11, -4, 9]~]
! 2500:
! 2501: [[0, 0, 0]~ [1, 0, 0]~ [0, 0, 0]~ [-14/25, 24/25, -8/25]~ [28/5, 2/5, -24/5]
! 2502: ~]
! 2503:
! 2504: [[0, 0, 0]~ [0, 0, 0]~ [1, 0, 0]~ [57/25, -12/25, 4/25]~ [-58/5, -47/5, 44/5
! 2505: ]~]
! 2506:
! 2507: [[0, 0, 0]~ [0, 0, 0]~ [0, 0, 0]~ [9/25, 6/25, -2/25]~ [-4/5, -11/5, 2/5]~]
! 2508:
! 2509: [[0, 0, 0]~ [0, 0, 0]~ [0, 0, 0]~ [8/25, -3/25, 1/25]~ [-9/5, -6/5, 7/5]~]
! 2510:
! 2511: ? rnfdiscf(nf2,p)
! 2512: [[416134375, 212940625, 388649575; 0, 3125, 550; 0, 0, 25], [-1280, 5, 5]~]
! 2513: ? rnfequation(nf2,p)
! 2514: x^15 - 15*x^11 + 75*x^7 - x^5 - 125*x^3 + 5*x + 1
! 2515: ? rnfequation2(nf2,p)
! 2516: [x^15 - 15*x^11 + 75*x^7 - x^5 - 125*x^3 + 5*x + 1, mod(-x^5 + 5*x, x^15 - 1
! 2517: 5*x^11 + 75*x^7 - x^5 - 125*x^3 + 5*x + 1), 0]
! 2518: ? rnfhermitebasis(bnf2,aa)
! 2519:
! 2520: [[1, 0, 0]~ [0, 0, 0]~ [0, 0, 0]~ [-2/5, 2/5, -4/5]~ [11/25, 99/25, -33/25]~
! 2521: ]
! 2522:
! 2523: [[0, 0, 0]~ [1, 0, 0]~ [0, 0, 0]~ [2/5, -2/5, 4/5]~ [-8/25, -72/25, 24/25]~]
! 2524:
! 2525: [[0, 0, 0]~ [0, 0, 0]~ [1, 0, 0]~ [1/5, -1/5, 2/5]~ [4/25, 36/25, -12/25]~]
! 2526:
! 2527: [[0, 0, 0]~ [0, 0, 0]~ [0, 0, 0]~ [1/5, -1/5, 2/5]~ [-2/25, -18/25, 6/25]~]
! 2528:
! 2529: [[0, 0, 0]~ [0, 0, 0]~ [0, 0, 0]~ [0, 0, 0]~ [1/25, 9/25, -3/25]~]
! 2530:
! 2531: ? rnfisfree(bnf2,aa)
! 2532: 1
! 2533: ? rnfsteinitz(nf2,aa)
! 2534: [[[1, 0, 0]~, [0, 0, 0]~, [0, 0, 0]~, [38/25, -33/25, 11/25]~, [-27/125, 33/
! 2535: 125, -11/125]~; [0, 0, 0]~, [1, 0, 0]~, [0, 0, 0]~, [-14/25, 24/25, -8/25]~,
! 2536: [6/125, -24/125, 8/125]~; [0, 0, 0]~, [0, 0, 0]~, [1, 0, 0]~, [57/25, -12/2
! 2537: 5, 4/25]~, [-53/125, 12/125, -4/125]~; [0, 0, 0]~, [0, 0, 0]~, [0, 0, 0]~, [
! 2538: 9/25, 6/25, -2/25]~, [-11/125, -6/125, 2/125]~; [0, 0, 0]~, [0, 0, 0]~, [0,
! 2539: 0, 0]~, [8/25, -3/25, 1/25]~, [-7/125, 3/125, -1/125]~], [[1, 0, 0; 0, 1, 0;
! 2540: 0, 0, 1], [1, 0, 0; 0, 1, 0; 0, 0, 1], [1, 0, 0; 0, 1, 0; 0, 0, 1], [1, 0,
! 2541: 0; 0, 1, 0; 0, 0, 1], [125, 0, 108; 0, 125, 22; 0, 0, 1]], [416134375, 21294
! 2542: 0625, 388649575; 0, 3125, 550; 0, 0, 25], [-1280, 5, 5]~]
! 2543: ? rootmod(x^16-1,41)
! 2544: [mod(1, 41), mod(3, 41), mod(9, 41), mod(14, 41), mod(27, 41), mod(32, 41),
! 2545: mod(38, 41), mod(40, 41)]~
! 2546: ? rootpadic(x^4+1,41,6)
! 2547: [3 + 22*41 + 27*41^2 + 15*41^3 + 27*41^4 + 33*41^5 + O(41^6), 14 + 20*41 + 2
! 2548: 5*41^2 + 24*41^3 + 4*41^4 + 18*41^5 + O(41^6), 27 + 20*41 + 15*41^2 + 16*41^
! 2549: 3 + 36*41^4 + 22*41^5 + O(41^6), 38 + 18*41 + 13*41^2 + 25*41^3 + 13*41^4 +
! 2550: 7*41^5 + O(41^6)]~
! 2551: ? roots(x^5-5*x^2-5*x-5)
! 2552: [2.0509134529831982130058170163696514536 + 0.E-38*I, -0.67063790319207539268
! 2553: 663382582902335603 + 0.84813118358634026680538906224199030917*I, -0.67063790
! 2554: 319207539268663382582902335603 - 0.84813118358634026680538906224199030917*I,
! 2555: -0.35481882329952371381627468235580237077 + 1.39980287391035466982975228340
! 2556: 62081964*I, -0.35481882329952371381627468235580237077 - 1.399802873910354669
! 2557: 8297522834062081964*I]~
! 2558: ? rootsold(x^4-1000000000000000000000)
! 2559: [-177827.94100389228012254211951926848447 + 0.E-38*I, 177827.941003892280122
! 2560: 54211951926848447 + 0.E-38*I, 6.7178761075670887517909655889502271295 E-139
! 2561: + 177827.94100389228012254211951926848447*I, 6.71787610756708875179096558895
! 2562: 02271295 E-139 - 177827.94100389228012254211951926848447*I]~
! 2563: ? round(prod(1,k=1,17,x-exp(2*i*pi*k/17)))
! 2564: x^17 - 1
! 2565: ? rounderror(prod(1,k=1,17,x-exp(2*i*pi*k/17)))
! 2566: -35
! 2567: ? rpoint(0,20,20)
! 2568: ? initrect(3,600,600);scale(3,-7,7,-2,2);cursor(3)
! 2569: ? q*series(anell(acurve,100),q)
! 2570: 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 -
! 2571: 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*
! 2572: 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
! 2573: + 8*q^32 + 15*q^33 + 2*q^35 + 12*q^36 - q^37 + 6*q^39 - 9*q^41 - 6*q^42 + 2*
! 2574: 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
! 2575: ^52 + q^53 + 18*q^54 + 10*q^55 - 12*q^58 + 8*q^59 + 12*q^60 - 8*q^61 + 8*q^6
! 2576: 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 -
! 2577: 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
! 2578: ^82 - 15*q^83 + 6*q^84 - 4*q^86 - 18*q^87 + 4*q^89 + 24*q^90 + 2*q^91 + 4*q^
! 2579: 92 + 12*q^93 + 18*q^94 - 24*q^96 + 4*q^97 + 12*q^98 - 30*q^99 - 2*q^100 + O(
! 2580: q^101)
! 2581: ? aset=set([5,-2,7,3,5,1])
! 2582: ["-2", "1", "3", "5", "7"]
! 2583: ? bset=set([7,5,-5,7,2])
! 2584: ["-5", "2", "5", "7"]
! 2585: ? setintersect(aset,bset)
! 2586: ["5", "7"]
! 2587: ? setminus(aset,bset)
! 2588: ["-2", "1", "3"]
! 2589: ? setprecision(28)
! 2590: 38
! 2591: ? setrand(10)
! 2592: 10
! 2593: ? setsearch(aset,3)
! 2594: 3
! 2595: ? setsearch(bset,3)
! 2596: 0
! 2597: ? setserieslength(12)
! 2598: 16
! 2599: ? setunion(aset,bset)
! 2600: ["-2", "-5", "1", "2", "3", "5", "7"]
! 2601: ? arat=(x^3+x+1)/x^3;settype(arat,14)
! 2602: (x^3 + x + 1)/x^3
! 2603: ? shift(1,50)
! 2604: 1125899906842624
! 2605: ? shift([3,4,-11,-12],-2)
! 2606: [0, 1, -2, -3]
! 2607: ? shiftmul([3,4,-11,-12],-2)
! 2608: [3/4, 1, -11/4, -3]
! 2609: ? sigma(100)
! 2610: 217
! 2611: ? sigmak(2,100)
! 2612: 13671
! 2613: ? sigmak(-3,100)
! 2614: 1149823/1000000
! 2615: ? sign(-1)
! 2616: -1
! 2617: ? sign(0)
! 2618: 0
! 2619: ? sign(0.)
! 2620: 0
! 2621: ? signat(hilbert(5)-0.11*idmat(5))
! 2622: [2, 3]
! 2623: ? signunit(bnf)
! 2624:
! 2625: [-1]
! 2626:
! 2627: [1]
! 2628:
! 2629: ? simplefactmod(x^11+1,7)
! 2630:
! 2631: [1 1]
! 2632:
! 2633: [10 1]
! 2634:
! 2635: ? simplify(((x+i+1)^2-x^2-2*x*(i+1))^2)
! 2636: -4
! 2637: ? sin(pi/6)
! 2638: 0.5000000000000000000000000000
! 2639: ? sinh(1)
! 2640: 1.175201193643801456882381850
! 2641: ? size([1.3*10^5,2*i*pi*exp(4*pi)])
! 2642: 7
! 2643: ? smallbasis(x^3+4*x+12)
! 2644: [1, x, 1/2*x^2]
! 2645: ? smalldiscf(x^3+4*x+12)
! 2646: -1036
! 2647: ? smallfact(100!+1)
! 2648:
! 2649: [101 1]
! 2650:
! 2651: [14303 1]
! 2652:
! 2653: [149239 1]
! 2654:
! 2655: [432885273849892962613071800918658949059679308685024481795740765527568493010
! 2656: 727023757461397498800981521440877813288657839195622497225621499427628453 1]
! 2657:
! 2658: ? smallinitell([0,0,0,-17,0])
! 2659: [0, 0, 0, -17, 0, 0, -34, 0, -289, 816, 0, 314432, 1728]
! 2660: ? smallpolred(x^4+576)
! 2661: [x - 1, x^2 - x + 1, x^2 + 1, x^4 - x^2 + 1]
! 2662: ? smallpolred2(x^4+576)
! 2663:
! 2664: [1 x - 1]
! 2665:
! 2666: [1/192*x^3 + 1/8*x + 1/2 x^2 - x + 1]
! 2667:
! 2668: [-1/24*x^2 x^2 + 1]
! 2669:
! 2670: [-1/192*x^3 + 1/48*x^2 + 1/8*x x^4 - x^2 + 1]
! 2671:
! 2672: ? smith(matrix(5,5,j,k,random()))
! 2673: [1442459322553825252071178240, 2147483648, 2147483648, 1, 1]
! 2674: ? smith(1/hilbert(6))
! 2675: [27720, 2520, 2520, 840, 210, 6]
! 2676: ? smithpol(x*idmat(5)-matrix(5,5,j,k,1))
! 2677: [x^2 - 5*x, x, x, x, 1]
! 2678: ? solve(x=1,4,sin(x))
! 2679: 3.141592653589793238462643383
! 2680: ? sort(vector(17,x,5*x%17))
! 2681: [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16]
! 2682: ? sqr(1+o(2))
! 2683: 1 + O(2^3)
! 2684: ? sqred(hilbert(5))
! 2685:
! 2686: [1 1/2 1/3 1/4 1/5]
! 2687:
! 2688: [0 1/12 1 9/10 4/5]
! 2689:
! 2690: [0 0 1/180 3/2 12/7]
! 2691:
! 2692: [0 0 0 1/2800 2]
! 2693:
! 2694: [0 0 0 0 1/44100]
! 2695:
! 2696: ? sqrt(13+o(127^12))
! 2697: 34 + 125*127 + 83*127^2 + 107*127^3 + 53*127^4 + 42*127^5 + 22*127^6 + 98*12
! 2698: 7^7 + 127^8 + 23*127^9 + 122*127^10 + 79*127^11 + O(127^12)
! 2699: ? srgcd(x^10-1,x^15-1)
! 2700: x^5 - 1
! 2701: ? move(0,100,100);string(0,pi)
! 2702: ? move(0,200,200);string(0,"(0,0)")
! 2703: ? postdraw([0,10,10])
! 2704: ? apol=0.3+legendre(10)
! 2705: 46189/256*x^10 - 109395/256*x^8 + 45045/128*x^6 - 15015/128*x^4 + 3465/256*x
! 2706: ^2 + 0.05390625000000000000000000000
! 2707: ? sturm(apol)
! 2708: 4
! 2709: ? sturmpart(apol,0.91,1)
! 2710: 1
! 2711: ? subcyclo(31,5)
! 2712: x^5 + x^4 - 12*x^3 - 21*x^2 + x + 5
! 2713: ? subell(initell([0,0,0,-17,0]),[-1,4],[-4,2])
! 2714: [9, -24]
! 2715: ? subst(sin(x),x,y)
! 2716: y - 1/6*y^3 + 1/120*y^5 - 1/5040*y^7 + 1/362880*y^9 - 1/39916800*y^11 + O(y^
! 2717: 12)
! 2718: ? subst(sin(x),x,x+x^2)
! 2719: 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
! 2720: ^8 + 13609/362880*x^9 + 19/13440*x^10 - 273241/39916800*x^11 + O(x^12)
! 2721: ? sum(0,k=1,10,2^-k)
! 2722: 1023/1024
! 2723: ? sum(0.,k=1,10,2^-k)
! 2724: 0.9990234375000000000000000000
! 2725: ? sylvestermatrix(a2*x^2+a1*x+a0,b1*x+b0)
! 2726:
! 2727: [a2 b1 0]
! 2728:
! 2729: [a1 b0 b1]
! 2730:
! 2731: [a0 0 b0]
! 2732:
! 2733: ? \precision=38
! 2734: realprecision = 38 significant digits
! 2735: ? 4*sumalt(n=0,(-1)^n/(2*n+1))
! 2736: 3.1415926535897932384626433832795028841
! 2737: ? 4*sumalt2(n=0,(-1)^n/(2*n+1))
! 2738: 3.1415926535897932384626433832795028842
! 2739: ? suminf(n=1,2.^-n)
! 2740: 0.99999999999999999999999999999999999999
! 2741: ? 6/pi^2*sumpos(n=1,n^-2)
! 2742: 0.99999999999999999999999999999999999999
! 2743: ? supplement([1,3;2,4;3,6])
! 2744:
! 2745: [1 3 0]
! 2746:
! 2747: [2 4 0]
! 2748:
! 2749: [3 6 1]
! 2750:
! 2751: ? sqr(tan(pi/3))
! 2752: 2.9999999999999999999999999999999999999
! 2753: ? tanh(1)
! 2754: 0.76159415595576488811945828260479359041
! 2755: ? taniyama(bcurve)
! 2756: [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
! 2757: )]
! 2758: ? taylor(y/(x-y),y)
! 2759: (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
! 2760: ^7*x^4 + y^8*x^3 + y^9*x^2 + y^10*x + y^11)/x^11
! 2761: ? tchebi(10)
! 2762: 512*x^10 - 1280*x^8 + 1120*x^6 - 400*x^4 + 50*x^2 - 1
! 2763: ? teich(7+o(127^12))
! 2764: 7 + 57*127 + 58*127^2 + 83*127^3 + 52*127^4 + 109*127^5 + 74*127^6 + 16*127^
! 2765: 7 + 60*127^8 + 47*127^9 + 65*127^10 + 5*127^11 + O(127^12)
! 2766: ? texprint((x+y)^3/(x-y)^2)
! 2767: {{x^{3} + {{3}y}x^{2} + {{3}y^{2}}x + {y^{3}}}\over{x^{2} - {{2}y}x + {y^{2}
! 2768: }}}
! 2769: ? theta(0.5,3)
! 2770: 0.080806418251894691299871683210466298535
! 2771: ? thetanullk(0.5,7)
! 2772: -804.63037320243369422783730584965684022
! 2773: ? torsell(tcurve)
! 2774: [12, [6, 2], [[-2, 8], [3, -2]]]
! 2775: ? trace(1+i)
! 2776: 2
! 2777: ? trace(mod(x+5,x^3+x+1))
! 2778: 15
! 2779: ? trans(vector(2,x,x))
! 2780: [1, 2]~
! 2781: ? %*%~
! 2782:
! 2783: [1 2]
! 2784:
! 2785: [2 4]
! 2786:
! 2787: ? trunc(-2.7)
! 2788: -2
! 2789: ? trunc(sin(x^2))
! 2790: 1/120*x^10 - 1/6*x^6 + x^2
! 2791: ? tschirnhaus(x^5-x-1)
! 2792: x^5 - 18*x^3 - 12*x^2 + 785*x + 457
! 2793: ? type(mod(x,x^2+1))
! 2794: 9
! 2795: ? unit(17)
! 2796: 3 + 2*w
! 2797: ? n=33;until(n==1,print1(n," ");if(n%2,n=3*n+1,n=n/2));print(1)
! 2798: 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
! 2799: ? valuation(6^10000-1,5)
! 2800: 5
! 2801: ? vec(sin(x))
! 2802: [1, 0, -1/6, 0, 1/120, 0, -1/5040, 0, 1/362880, 0, -1/39916800]
! 2803: ? vecmax([-3,7,-2,11])
! 2804: 11
! 2805: ? vecmin([-3,7,-2,11])
! 2806: -3
! 2807: ? vecsort([[1,8,5],[2,5,8],[3,6,-6],[4,8,6]],2)
! 2808: [[2, 5, 8], [3, 6, -6], [4, 8, 6], [1, 8, 5]]
! 2809: ? vecsort([[1,8,5],[2,5,8],[3,6,-6],[4,8,6]],[2,1])
! 2810: [[2, 5, 8], [3, 6, -6], [1, 8, 5], [4, 8, 6]]
! 2811: ? weipell(acurve)
! 2812: x^-2 + 1/5*x^2 - 1/28*x^4 + 1/75*x^6 - 3/1540*x^8 + 1943/3822000*x^10 - 1/11
! 2813: 550*x^12 + 193/10510500*x^14 - 1269/392392000*x^16 + 21859/34684650000*x^18
! 2814: - 1087/9669660000*x^20 + O(x^22)
! 2815: ? wf(i)
! 2816: 1.1892071150027210667174999705604759152 - 1.175494350822287507 E-38*I
! 2817: ? wf2(i)
! 2818: 1.0905077326652576592070106557607079789 + 0.E-58*I
! 2819: ? m=5;while(m<20,print1(m," ");m=m+1);print()
! 2820: 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19
! 2821: ? zell(acurve,apoint)
! 2822: 0.72491221490962306778878739838332384646 + 0.E-77*I
! 2823: ? zeta(3)
! 2824: 1.2020569031595942853997381615114499907
! 2825: ? zeta(0.5+14.1347251*i)
! 2826: 0.0000000052043097453468479398562848599419244606 - 0.00000003269063986978698
! 2827: 2176409251733800562856*I
! 2828: ? zetak(nfz,-3)
! 2829: 0.091666666666666666666666666666666666666
! 2830: ? zetak(nfz,1.5+3*i)
! 2831: 0.88324345992059326405525724366416928890 - 0.2067536250233895222724230899142
! 2832: 7938845*I
! 2833: ? zidealstar(nf2,54)
! 2834: [132678, [1638, 9, 9], [[-27, 2, -27]~, [1, -24, 0]~, [1, 0, -24]~]]
! 2835: ? bid=zidealstarinit(nf2,54)
! 2836: [[[54, 0, 0; 0, 54, 0; 0, 0, 54], [0]], [132678, [1638, 9, 9]], [[2, [2, 0,
! 2837: 0]~, 1, 3, [1, 0, 0]~], 1; [3, [3, 0, 0]~, 1, 3, [1, 0, 0]~], 3], [[[[7], [[
! 2838: 0, 1, 0]~], [[-26, -27, 0]~], [[]~], 1]], [[[26], [[0, 2, 0]~], [[-27, 2, 0]
! 2839: ~], [[]~], 1], [[3, 3, 3], [[1, 3, 0]~, [1, 0, 3]~, [4, 0, 0]~], [[1, -24, 0
! 2840: ]~, [1, 0, -24]~, [-23, 0, 0]~], [[]~, []~, []~], [0, 1/3, 0; 0, 0, 1/3; 1/3
! 2841: , 0, 0]], [[3, 3, 3], [[1, 9, 0]~, [1, 0, 9]~, [10, 0, 0]~], [[1, -18, 0]~,
! 2842: [1, 0, -18]~, [-17, 0, 0]~], [[]~, []~, []~], [0, 1/9, 0; 0, 0, 1/9; 1/9, 0,
! 2843: 0]]], [[], [], [;]]], [468, 469, 0, 0, -48776, 0, 0, -36582; 0, 0, 1, 0, -7
! 2844: , -6, 0, -3; 0, 0, 0, 1, -3, 0, -6, 0]]
! 2845: ? zideallog(nf2,w,bid)
! 2846: [1574, 8, 6]~
! 2847: ? znstar(3120)
! 2848: [768, [12, 4, 4, 2, 2], [mod(67, 3120), mod(2341, 3120), mod(1847, 3120), mo
! 2849: d(391, 3120), mod(2081, 3120)]]
! 2850: ? getstack()
! 2851: 0
! 2852: ? getheap()
! 2853: [624, 111936]
! 2854: ? print("Total time spent: ",gettime());
! 2855: Total time spent: 6865
! 2856: ? \q
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