Annotation of OpenXM_contrib/pari-2.2/src/test/64/compat, Revision 1.2
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)
1.2 ! noro 74: [x^5 - 5*x^3 + 5*x + 25, [1, 2], 595125, 45, [[1, -1.08911514572050482502495
! 75: 27946671612684, -2.4285174907194186068992069565359418364, 0.7194669112891317
! 76: 8943997506477288225733, -2.5558200350691694950646071159426779971; 1, -0.1383
! 77: 8372073406036365047976417441696637 - 0.4918163765776864349975328551474152510
! 78: 7*I, 1.9647119211288133163138753392090569931 + 0.809714924188978951282940822
! 79: 19556466857*I, -0.072312766896812300380582649294307897121 + 2.19808037538462
! 80: 76641195195160383234877*I, -0.98796319352507039803950539735452837194 + 1.570
! 81: 1452385894131769052374806001981108*I; 1, 1.682941293594312776162956161507997
! 82: 6005 + 2.0500351226010726172974286983598602163*I, -0.75045317576910401286427
! 83: 186094108607489 + 1.3101462685358123283560773619310445915*I, -0.787420688747
! 84: 75359433940488309213323154 + 2.1336633893126618034168454610457936017*I, 1.26
! 85: 58732110596551455718089553258673705 - 2.716479010374315056657802803578983483
! 86: 4*I], [1, -1.0891151457205048250249527946671612684, -2.428517490719418606899
! 87: 2069565359418364, 0.71946691128913178943997506477288225733, -2.5558200350691
! 88: 694950646071159426779971; 1.4142135623730950488016887242096980785, -0.195704
! 89: 13467375904264179382543977540673, 2.7785222450164664309920925654093065576, -
! 90: 0.10226569567819614506098907018896260035, -1.3971909474085893198147151262541
! 91: 540506; 0, -0.69553338995335755797766403996841143190, 1.14510982744395651299
! 92: 26149974389115722, 3.1085550780550843138423672171643499921, 2.22052069130868
! 93: 72788181483285734827868; 1.4142135623730950488016887242096980785, 2.38003840
! 94: 20787979181834702019470475018, -1.0613010590986270398182318786558994412, -1.
! 95: 1135810173202366904448352912286604470, 1.79021506332534372536778891648110361
! 96: 60; 0, 2.8991874737236275652408825679737171586, 1.85282662165584876344468105
! 97: 12816401036, 3.0174557027049114270734649132936867272, -3.8416814583731999185
! 98: 306312841432940661], 0, [5, 2, 0, -1, -2; 2, -2, -5, -10, 20; 0, -5, 10, -10
! 99: , 5; -1, -10, -10, -17, 1; -2, 20, 5, 1, -8], [345, 0, 200, 110, 177; 0, 345
! 100: , 95, 1, 145; 0, 0, 5, 4, 3; 0, 0, 0, 1, 0; 0, 0, 0, 0, 1], [108675, 5175, 0
! 101: , -10350, -15525; 5175, 13800, -8625, -1725, 27600; 0, -8625, 37950, -17250,
! 102: 0; -10350, -1725, -17250, -24150, -15525; -15525, 27600, 0, -15525, -3450],
! 103: [595125, [238050, -296700, 91425, 1725, 0]~]], [-2.428517490719418606899206
! 104: 9565359418364, 1.9647119211288133163138753392090569931 + 0.80971492418897895
! 105: 128294082219556466857*I, -0.75045317576910401286427186094108607489 + 1.31014
! 106: 62685358123283560773619310445915*I], [1, 1/15*x^4 - 2/3*x^2 + 1/3*x + 4/3, x
! 107: , 2/15*x^4 - 1/3*x^2 + 2/3*x - 1/3, -1/15*x^4 + 1/3*x^3 + 1/3*x^2 - 4/3*x -
! 108: 2/3], [1, 0, 3, 1, 10; 0, 0, -2, 1, -5; 0, 1, 0, 3, -5; 0, 0, 1, 1, 10; 0, 0
! 109: , 0, 3, 0], [1, 0, 0, 0, 0, 0, -1, -1, -2, 4, 0, -1, 3, -1, 1, 0, -2, -1, -3
! 110: , -1, 0, 4, 1, -1, -1; 0, 1, 0, 0, 0, 1, 1, -1, -1, 1, 0, -1, -2, -1, 1, 0,
! 111: -1, -1, -1, 3, 0, 1, 1, 3, -3; 0, 0, 1, 0, 0, 0, 0, 0, 1, -1, 1, 0, 0, 0, -2
! 112: , 0, 1, 0, -1, -1, 0, -1, -2, -1, -1; 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 1,
! 113: 1, 2, 1, 0, 1, 0, 0, 0, 0, 2, 0, -1; 0, 0, 0, 0, 1, 0, -1, -1, -1, 1, 0, -1
! 114: , 0, 1, 0, 0, -1, 1, 0, 0, 1, 1, 0, 0, -1]]
1.1 noro 115: ? ba=algtobasis(nf,mod(x^3+5,nfpol))
1.2 ! noro 116: [6, 1, 3, 1, 3]~
1.1 noro 117: ? anell(acurve,100)
118: [1, -2, -3, 2, -2, 6, -1, 0, 6, 4, -5, -6, -2, 2, 6, -4, 0, -12, 0, -4, 3, 1
119: 0, 2, 0, -1, 4, -9, -2, 6, -12, -4, 8, 15, 0, 2, 12, -1, 0, 6, 0, -9, -6, 2,
120: -10, -12, -4, -9, 12, -6, 2, 0, -4, 1, 18, 10, 0, 0, -12, 8, 12, -8, 8, -6,
121: -8, 4, -30, 8, 0, -6, -4, 9, 0, -1, 2, 3, 0, 5, -12, 4, 8, 9, 18, -15, 6, 0
122: , -4, -18, 0, 4, 24, 2, 4, 12, 18, 0, -24, 4, 12, -30, -2]
123: ? apell(acurve,10007)
124: 66
125: ? apell2(acurve,10007)
126: 66
127: ? apol=x^3+5*x+1
128: x^3 + 5*x + 1
129: ? apprpadic(apol,1+o(7^8))
130: [1 + 6*7 + 4*7^2 + 4*7^3 + 3*7^4 + 4*7^5 + 6*7^7 + O(7^8)]
131: ? apprpadic(x^3+5*x+1,mod(x*(1+o(7^8)),x^2+x-1))
132: [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 +
133: (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)
134: ]~
135: ? 4*arg(3+3*i)
136: 3.1415926535897932384626433832795028842
137: ? 3*asin(sqrt(3)/2)
138: 3.1415926535897932384626433832795028841
139: ? asinh(0.5)
140: 0.48121182505960344749775891342436842313
141: ? assmat(x^5-12*x^3+0.0005)
142:
143: [0 0 0 0 -0.00049999999999999999999999999999999999999]
144:
145: [1 0 0 0 0]
146:
147: [0 1 0 0 0]
148:
149: [0 0 1 0 12]
150:
151: [0 0 0 1 0]
152:
153: ? 3*atan(sqrt(3))
154: 3.1415926535897932384626433832795028841
155: ? atanh(0.5)
156: 0.54930614433405484569762261846126285232
157: ? basis(x^3+4*x+5)
158: [1, x, 1/7*x^2 - 1/7*x - 2/7]
159: ? basis2(x^3+4*x+5)
160: [1, x, 1/7*x^2 - 1/7*x - 2/7]
161: ? basistoalg(nf,ba)
162: mod(x^3 + 5, x^5 - 5*x^3 + 5*x + 25)
163: ? bernreal(12)
164: -0.25311355311355311355311355311355311354
165: ? bernvec(6)
166: [1, 1/6, -1/30, 1/42, -1/30, 5/66, -691/2730]
167: ? bestappr(pi,10000)
168: 355/113
169: ? bezout(123456789,987654321)
170: [-8, 1, 9]
171: ? bigomega(12345678987654321)
172: 8
173: ? mcurve=initell([0,0,0,-17,0])
174: [0, 0, 0, -17, 0, 0, -34, 0, -289, 816, 0, 314432, 1728, [4.1231056256176605
175: 498214098559740770251, 0.E-38, -4.1231056256176605498214098559740770251]~, 1
176: .2913084409290072207105564235857096009, 1.2913084409290072207105564235857096
177: 009*I, -1.2164377440798088266474269946818791934, -3.649313232239426479942280
178: 9840456375802*I, 1.6674774896145033307120230298772362381]
179: ? mpoints=[[-1,4],[-4,2]]~
180: [[-1, 4], [-4, 2]]~
181: ? mhbi=bilhell(mcurve,mpoints,[9,24])
182: [-0.72448571035980184146215805860545027438, 1.307328627832055544492943428892
183: 1943055]~
184: ? bin(1.1,5)
185: -0.0045457499999999999999999999999999999997
186: ? binary(65537)
187: [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1]
188: ? bittest(10^100,100)
189: 1
190: ? boundcf(pi,5)
191: [3, 7, 15, 1, 292]
192: ? boundfact(40!+1,100000)
193:
194: [41 1]
195:
196: [59 1]
197:
198: [277 1]
199:
200: [1217669507565553887239873369513188900554127 1]
201:
202: ? move(0,0,0);box(0,500,500)
203: ? setrand(1);buchimag(1-10^7,1,1)
204: *** Warning: not a fundamental discriminant in quadclassunit.
1.2 ! noro 205: [2416, [1208, 2], [qfi(277, 55, 9028), qfi(1700, 1249, 1700)], 1, 1.00257481
! 206: 6299307750]
1.1 noro 207: ? setrand(1);bnf=buchinitfu(x^2-x-57,0.2,0.2)
208: [mat(3), mat([1, 2, 1, 2, 1, 2, 1, 2, 1]), [-2.71246530518434397468087951060
1.2 ! noro 209: 61300698 + 3.1415926535897932384626433832795028842*I; 2.71246530518434397468
! 210: 08795106061300699], [1.7903417566977293763292119206302198761, 1.289761953065
! 211: 2735025030086072395031017 + 3.1415926535897932384626433832795028842*I, 0.701
! 212: 48550268542821846861610071436900868, 0.E-57, 0.50057980363245587382620331339
! 213: 071677436 + 3.1415926535897932384626433832795028842*I, 1.0888562540123011578
! 214: 605958199158508674, 1.7241634548149836441438434283070556826 + 3.141592653589
! 215: 7932384626433832795028842*I, -0.34328764427702709438988786673341921876 + 3.1
! 216: 415926535897932384626433832795028842*I, 2.1336294009747564707190997873636390
! 217: 948 + 3.1415926535897932384626433832795028842*I, 0.0661783018827457321853684
! 218: 92323164193433 + 3.1415926535897932384626433832795028842*I; -1.7903417566977
! 219: 293763292119206302198760, -1.2897619530652735025030086072395031017, -0.70148
! 220: 550268542821846861610071436900868, 0.E-57, -0.500579803632455873826203313390
! 221: 71677436, -1.0888562540123011578605958199158508674, -1.724163454814983644143
! 222: 8434283070556826, 0.34328764427702709438988786673341921876, -2.1336294009747
! 223: 564707190997873636390948, -0.066178301882745732185368492323164193433], [[3,
! 224: [0, 1]~, 1, 1, [1, 1]~], [5, [-1, 1]~, 1, 1, [2, 1]~], [11, [-1, 1]~, 1, 1,
! 225: [2, 1]~], [3, [1, 1]~, 1, 1, [0, 1]~], [5, [2, 1]~, 1, 1, [-1, 1]~], [11, [2
! 226: , 1]~, 1, 1, [-1, 1]~], [19, [1, 1]~, 1, 1, [0, 1]~], [17, [3, 1]~, 1, 1, [-
! 227: 2, 1]~], [17, [-2, 1]~, 1, 1, [3, 1]~], [19, [0, 1]~, 1, 1, [1, 1]~]], 0, [x
! 228: ^2 - x - 57, [2, 0], 229, 1, [[1, -8.0663729752107779635959310246705326058;
! 229: 1, 7.0663729752107779635959310246705326058], [1, -8.066372975210777963595931
! 230: 0246705326058; 1, 7.0663729752107779635959310246705326058], 0, [2, -1; -1, 1
! 231: 15], [229, 115; 0, 1], [115, 1; 1, 2], [229, [115, 1]~]], [-7.06637297521077
! 232: 79635959310246705326058, 8.0663729752107779635959310246705326058], [1, x - 1
! 233: ], [1, 1; 0, 1], [1, 0, 0, 57; 0, 1, 1, -1]], [[3, [3], [[3, 0; 0, 1]]], 2.7
! 234: 124653051843439746808795106061300699, 0.8814422512654579364, [2, -1], [x + 7
! 235: ], 187], [mat(1), [[0, 0]], [[1.7903417566977293763292119206302198761, -1.79
! 236: 03417566977293763292119206302198760]]], 0]
1.1 noro 237: ? buchcertify(bnf)
238: 1
239: ? buchfu(bnf)
1.2 ! noro 240: [[x + 7], 187]
1.1 noro 241: ? setrand(1);buchinitforcefu(x^2-x-100000)
1.2 ! noro 242: [mat(5), mat([3, 2, 1, 2, 0, 3, 0, 2, 2, 3, 1, 4, 3, 2, 2, 3, 3, 0]), [-129.
! 243: 82045011403975460991182396195022419 + 6.283185307179586476925286766559005768
! 244: 4*I; 129.82045011403975460991182396195022419], [-41.811264589129943393339502
! 245: 258694361489 + 6.2831853071795864769252867665590057684*I, 9.2399004147902289
! 246: 816376260438840931575 + 3.1415926535897932384626433832795028842*I, -11.87460
! 247: 9881075406725097315997431161032 + 3.1415926535897932384626433832795028842*I,
! 248: 0.E-115, -51.051165003920172374977128302578454646 + 3.141592653589793238462
! 249: 6433832795028842*I, -64.910225057019877304955911980975112095 + 3.14159265358
! 250: 97932384626433832795028842*I, -29.936654708054536668242186261263200456 + 3.1
! 251: 415926535897932384626433832795028842*I, -47.66831907156823399733291848270768
! 252: 7878 + 6.2831853071795864769252867665590057684*I, 3.876293646477882506748482
! 253: 4790355076166, -6.7377511782956880607802359510546381087 + 3.1415926535897932
! 254: 384626433832795028842*I, -35.073513410834255332559266307639723380 + 3.141592
! 255: 6535897932384626433832795028842*I, 33.130781426597481571750300827582717074 +
! 256: 2.030353469852519378 E-115*I, 54.878404098312329644822020875673145627 + 4.0
! 257: 60706939705038757 E-115*I, -14.980188104648613073630759189293219180 + 3.1415
! 258: 926535897932384626433832795028842*I, -26.83107648448133031970874306940114230
! 259: 8 + 3.1415926535897932384626433832795028842*I, -19.7067490665160655124889078
! 260: 34878146944 + 3.1415926535897932384626433832795028842*I, -22.104515522613877
! 261: 880850594423816214544 + 3.1415926535897932384626433832795028842*I, -45.68755
! 262: 8235607825900087984737729869105 + 6.2831853071795864769252867665590057684*I,
! 263: 47.668319071568233997332918482707687879 + 8.121413879410077514 E-115*I; 41.
! 264: 811264589129943393339502258694361489, -9.23990041479022898163762604388409315
! 265: 75, 11.874609881075406725097315997431161032, 0.E-115, 51.0511650039201723749
! 266: 77128302578454646, 64.910225057019877304955911980975112095, 29.9366547080545
! 267: 36668242186261263200456, 47.668319071568233997332918482707687879, -3.8762936
! 268: 464778825067484824790355076166, 6.7377511782956880607802359510546381087, 35.
! 269: 073513410834255332559266307639723380, -33.1307814265974815717503008275827170
! 270: 74, -54.878404098312329644822020875673145627, 14.980188104648613073630759189
! 271: 293219180, 26.831076484481330319708743069401142309, 19.706749066516065512488
! 272: 907834878146944, 22.104515522613877880850594423816214544, 45.687558235607825
! 273: 900087984737729869105, -47.668319071568233997332918482707687878], [[2, [2, 1
! 274: ]~, 1, 1, [1, 1]~], [5, [5, 1]~, 1, 1, [1, 1]~], [13, [-5, 1]~, 1, 1, [6, 1]
! 275: ~], [2, [3, 1]~, 1, 1, [0, 1]~], [5, [6, 1]~, 1, 1, [0, 1]~], [7, [4, 1]~, 2
! 276: , 1, [-3, 1]~], [13, [6, 1]~, 1, 1, [-5, 1]~], [23, [7, 1]~, 1, 1, [-6, 1]~]
! 277: , [43, [-15, 1]~, 1, 1, [16, 1]~], [17, [20, 1]~, 1, 1, [-2, 1]~], [17, [15,
! 278: 1]~, 1, 1, [3, 1]~], [29, [14, 1]~, 1, 1, [-13, 1]~], [29, [-13, 1]~, 1, 1,
! 279: [14, 1]~], [31, [39, 1]~, 1, 1, [-7, 1]~], [31, [24, 1]~, 1, 1, [8, 1]~], [
! 280: 41, [7, 1]~, 1, 1, [-6, 1]~], [41, [-6, 1]~, 1, 1, [7, 1]~], [43, [16, 1]~,
! 281: 1, 1, [-15, 1]~], [23, [-6, 1]~, 1, 1, [7, 1]~]], 0, [x^2 - x - 100000, [2,
! 282: 0], 400001, 1, [[1, -316.72816130129840161392089489603747004; 1, 315.7281613
! 283: 0129840161392089489603747004], [1, -316.72816130129840161392089489603747004;
! 284: 1, 315.72816130129840161392089489603747004], 0, [2, -1; -1, 200001], [40000
! 285: 1, 200001; 0, 1], [200001, 1; 1, 2], [400001, [200001, 1]~]], [-315.72816130
! 286: 129840161392089489603747004, 316.72816130129840161392089489603747004], [1, x
! 287: - 1], [1, 1; 0, 1], [1, 0, 0, 100000; 0, 1, 1, -1]], [[5, [5], [[2, 0; 0, 1
! 288: ]]], 129.82045011403975460991182396195022419, 0.9876536979069047228, [2, -1]
! 289: , [379554884019013781006303254896369154068336082609238336*x + 11983616564425
! 290: 0789990462835950022871665178127611316131167], 185], [mat(1), [[0, 0]], [[-41
! 291: .811264589129943393339502258694361489 + 6.2831853071795864769252867665590057
! 292: 684*I, 41.811264589129943393339502258694361489]]], 0]
1.1 noro 293: ? setrand(1);bnf=buchinitfu(x^2-x-57,0.2,0.2)
294: [mat(3), mat([1, 2, 1, 2, 1, 2, 1, 2, 1]), [-2.71246530518434397468087951060
1.2 ! noro 295: 61300698 + 3.1415926535897932384626433832795028842*I; 2.71246530518434397468
! 296: 08795106061300699], [1.7903417566977293763292119206302198761, 1.289761953065
! 297: 2735025030086072395031017 + 3.1415926535897932384626433832795028842*I, 0.701
! 298: 48550268542821846861610071436900868, 0.E-57, 0.50057980363245587382620331339
! 299: 071677436 + 3.1415926535897932384626433832795028842*I, 1.0888562540123011578
! 300: 605958199158508674, 1.7241634548149836441438434283070556826 + 3.141592653589
! 301: 7932384626433832795028842*I, -0.34328764427702709438988786673341921876 + 3.1
! 302: 415926535897932384626433832795028842*I, 2.1336294009747564707190997873636390
! 303: 948 + 3.1415926535897932384626433832795028842*I, 0.0661783018827457321853684
! 304: 92323164193433 + 3.1415926535897932384626433832795028842*I; -1.7903417566977
! 305: 293763292119206302198760, -1.2897619530652735025030086072395031017, -0.70148
! 306: 550268542821846861610071436900868, 0.E-57, -0.500579803632455873826203313390
! 307: 71677436, -1.0888562540123011578605958199158508674, -1.724163454814983644143
! 308: 8434283070556826, 0.34328764427702709438988786673341921876, -2.1336294009747
! 309: 564707190997873636390948, -0.066178301882745732185368492323164193433], [[3,
! 310: [0, 1]~, 1, 1, [1, 1]~], [5, [-1, 1]~, 1, 1, [2, 1]~], [11, [-1, 1]~, 1, 1,
! 311: [2, 1]~], [3, [1, 1]~, 1, 1, [0, 1]~], [5, [2, 1]~, 1, 1, [-1, 1]~], [11, [2
! 312: , 1]~, 1, 1, [-1, 1]~], [19, [1, 1]~, 1, 1, [0, 1]~], [17, [3, 1]~, 1, 1, [-
! 313: 2, 1]~], [17, [-2, 1]~, 1, 1, [3, 1]~], [19, [0, 1]~, 1, 1, [1, 1]~]], 0, [x
! 314: ^2 - x - 57, [2, 0], 229, 1, [[1, -8.0663729752107779635959310246705326058;
! 315: 1, 7.0663729752107779635959310246705326058], [1, -8.066372975210777963595931
! 316: 0246705326058; 1, 7.0663729752107779635959310246705326058], 0, [2, -1; -1, 1
! 317: 15], [229, 115; 0, 1], [115, 1; 1, 2], [229, [115, 1]~]], [-7.06637297521077
! 318: 79635959310246705326058, 8.0663729752107779635959310246705326058], [1, x - 1
! 319: ], [1, 1; 0, 1], [1, 0, 0, 57; 0, 1, 1, -1]], [[3, [3], [[3, 0; 0, 1]]], 2.7
! 320: 124653051843439746808795106061300699, 0.8814422512654579364, [2, -1], [x + 7
! 321: ], 187], [mat(1), [[0, 0]], [[1.7903417566977293763292119206302198761, -1.79
! 322: 03417566977293763292119206302198760]]], 0]
1.1 noro 323: ? setrand(1);buchreal(10^9-3,0,0.5,0.5)
324: [4, [4], [qfr(3, 1, -83333333, 0.E-57)], 2800.625251907016076486370621737074
1.2 ! noro 325: 5514, 0.9849577285369119736]
1.1 noro 326: ? setrand(1);buchgen(x^4-7,0.2,0.2)
327:
328: [x^4 - 7]
329:
330: [[2, 1]]
331:
332: [[-87808, 1]]
333:
334: [[1, x, x^2, x^3]]
335:
336: [[2, [2], [[3, 1, 2, 1; 0, 1, 0, 0; 0, 0, 1, 0; 0, 0, 0, 1]]]]
337:
338: [14.229975145405511722395637833443108790]
339:
340: [1.121117107152756229]
341:
342: ? setrand(1);buchgenfu(x^2-x-100000)
343: *** Warning: insufficient precision for fundamental units, not given.
344:
345: [x^2 - x - 100000]
346:
347: [[2, 0]]
348:
349: [[400001, 1]]
350:
1.2 ! noro 351: [[1, x - 1]]
1.1 noro 352:
1.2 ! noro 353: [[5, [5], [[2, 0; 0, 1]]]]
1.1 noro 354:
355: [129.82045011403975460991182396195022419]
356:
1.2 ! noro 357: [0.9876536979069047228]
1.1 noro 358:
359: [[2, -1]]
360:
361: [[;]]
362:
363: [0]
364:
365: ? setrand(1);buchgenforcefu(x^2-x-100000)
366:
367: [x^2 - x - 100000]
368:
369: [[2, 0]]
370:
371: [[400001, 1]]
372:
1.2 ! noro 373: [[1, x - 1]]
1.1 noro 374:
1.2 ! noro 375: [[5, [5], [[2, 0; 0, 1]]]]
1.1 noro 376:
377: [129.82045011403975460991182396195022419]
378:
1.2 ! noro 379: [0.9876536979069047228]
1.1 noro 380:
381: [[2, -1]]
382:
383: [[379554884019013781006303254896369154068336082609238336*x + 119836165644250
384: 789990462835950022871665178127611316131167]]
385:
1.2 ! noro 386: [185]
1.1 noro 387:
388: ? setrand(1);buchgenfu(x^4+24*x^2+585*x+1791,0.1,0.1)
389:
390: [x^4 + 24*x^2 + 585*x + 1791]
391:
392: [[0, 2]]
393:
394: [[18981, 3087]]
395:
1.2 ! noro 396: [[1, -10/1029*x^3 + 13/343*x^2 - 165/343*x - 1135/343, 17/1029*x^3 - 32/1029
! 397: *x^2 + 109/343*x + 2444/343, -11/343*x^3 + 163/1029*x^2 - 373/343*x - 4260/3
! 398: 43]]
1.1 noro 399:
1.2 ! noro 400: [[4, [4], [[7, 2, 4, 0; 0, 1, 0, 0; 0, 0, 1, 0; 0, 0, 0, 1]]]]
1.1 noro 401:
402: [3.7941269688216589341408274220859400302]
403:
1.2 ! noro 404: [0.8826018286655581299]
1.1 noro 405:
1.2 ! noro 406: [[6, 10/1029*x^3 - 13/343*x^2 + 165/343*x + 1478/343]]
1.1 noro 407:
408: [[1/147*x^3 + 1/147*x^2 - 8/49*x - 9/49]]
409:
1.2 ! noro 410: [365]
1.1 noro 411:
412: ? buchnarrow(bnf)
1.2 ! noro 413: [3, [3], [[3, 0; 0, 1]]]
! 414: ? buchray(bnf,[[5,4;0,1],[1,0]])
! 415: [12, [12], [[3, 0; 0, 1]]]
! 416: ? bnr=buchrayinitgen(bnf,[[5,4;0,1],[1,0]])
1.1 noro 417: [[mat(3), mat([1, 2, 1, 2, 1, 2, 1, 2, 1]), [-2.7124653051843439746808795106
1.2 ! noro 418: 061300698 + 3.1415926535897932384626433832795028842*I; 2.7124653051843439746
! 419: 808795106061300699], [1.7903417566977293763292119206302198761, 1.28976195306
! 420: 52735025030086072395031017 + 3.1415926535897932384626433832795028842*I, 0.70
! 421: 148550268542821846861610071436900868, 0.E-57, 0.5005798036324558738262033133
! 422: 9071677436 + 3.1415926535897932384626433832795028842*I, 1.088856254012301157
! 423: 8605958199158508674, 1.7241634548149836441438434283070556826 + 3.14159265358
! 424: 97932384626433832795028842*I, -0.34328764427702709438988786673341921876 + 3.
! 425: 1415926535897932384626433832795028842*I, 2.133629400974756470719099787363639
! 426: 0948 + 3.1415926535897932384626433832795028842*I, 0.066178301882745732185368
! 427: 492323164193433 + 3.1415926535897932384626433832795028842*I; -1.790341756697
! 428: 7293763292119206302198760, -1.2897619530652735025030086072395031017, -0.7014
! 429: 8550268542821846861610071436900868, 0.E-57, -0.50057980363245587382620331339
! 430: 071677436, -1.0888562540123011578605958199158508674, -1.72416345481498364414
! 431: 38434283070556826, 0.34328764427702709438988786673341921876, -2.133629400974
! 432: 7564707190997873636390948, -0.066178301882745732185368492323164193433], [[3,
! 433: [0, 1]~, 1, 1, [1, 1]~], [5, [-1, 1]~, 1, 1, [2, 1]~], [11, [-1, 1]~, 1, 1,
! 434: [2, 1]~], [3, [1, 1]~, 1, 1, [0, 1]~], [5, [2, 1]~, 1, 1, [-1, 1]~], [11, [
! 435: 2, 1]~, 1, 1, [-1, 1]~], [19, [1, 1]~, 1, 1, [0, 1]~], [17, [3, 1]~, 1, 1, [
! 436: -2, 1]~], [17, [-2, 1]~, 1, 1, [3, 1]~], [19, [0, 1]~, 1, 1, [1, 1]~]], 0, [
! 437: x^2 - x - 57, [2, 0], 229, 1, [[1, -8.0663729752107779635959310246705326058;
! 438: 1, 7.0663729752107779635959310246705326058], [1, -8.06637297521077796359593
! 439: 10246705326058; 1, 7.0663729752107779635959310246705326058], 0, [2, -1; -1,
! 440: 115], [229, 115; 0, 1], [115, 1; 1, 2], [229, [115, 1]~]], [-7.0663729752107
! 441: 779635959310246705326058, 8.0663729752107779635959310246705326058], [1, x -
! 442: 1], [1, 1; 0, 1], [1, 0, 0, 57; 0, 1, 1, -1]], [[3, [3], [[3, 0; 0, 1]]], 2.
! 443: 7124653051843439746808795106061300699, 0.8814422512654579364, [2, -1], [x +
! 444: 7], 187], [mat(1), [[0, 0]], [[1.7903417566977293763292119206302198761, -1.7
! 445: 903417566977293763292119206302198760]]], [0, [mat([[6, 1]~, 1])]]], [[[5, 4;
! 446: 0, 1], [1, 0]], [8, [4, 2], [[2, 0]~, [0, 1]~]], mat([[5, [-1, 1]~, 1, 1, [
! 447: 2, 1]~], 1]), [[[[4], [[2, 0]~], [[2, 0]~], [[mod(0, 2)]~], 1]], [[2], [[0,
! 448: 1]~], mat(1)]], [1, 0; 0, 1]], [1], mat([1, -3, -6]), [12, [12], [[3, 0; 0,
! 449: 1]]], [[1/2, 0; 0, 0], [1, -1; 1, 1]]]
! 450: ? bnr2=buchrayinitgen(bnf,[[25,14;0,1],[1,1]])
1.1 noro 451: [[mat(3), mat([1, 2, 1, 2, 1, 2, 1, 2, 1]), [-2.7124653051843439746808795106
1.2 ! noro 452: 061300698 + 3.1415926535897932384626433832795028842*I; 2.7124653051843439746
! 453: 808795106061300699], [1.7903417566977293763292119206302198761, 1.28976195306
! 454: 52735025030086072395031017 + 3.1415926535897932384626433832795028842*I, 0.70
! 455: 148550268542821846861610071436900868, 0.E-57, 0.5005798036324558738262033133
! 456: 9071677436 + 3.1415926535897932384626433832795028842*I, 1.088856254012301157
! 457: 8605958199158508674, 1.7241634548149836441438434283070556826 + 3.14159265358
! 458: 97932384626433832795028842*I, -0.34328764427702709438988786673341921876 + 3.
! 459: 1415926535897932384626433832795028842*I, 2.133629400974756470719099787363639
! 460: 0948 + 3.1415926535897932384626433832795028842*I, 0.066178301882745732185368
! 461: 492323164193433 + 3.1415926535897932384626433832795028842*I; -1.790341756697
! 462: 7293763292119206302198760, -1.2897619530652735025030086072395031017, -0.7014
! 463: 8550268542821846861610071436900868, 0.E-57, -0.50057980363245587382620331339
! 464: 071677436, -1.0888562540123011578605958199158508674, -1.72416345481498364414
! 465: 38434283070556826, 0.34328764427702709438988786673341921876, -2.133629400974
! 466: 7564707190997873636390948, -0.066178301882745732185368492323164193433], [[3,
! 467: [0, 1]~, 1, 1, [1, 1]~], [5, [-1, 1]~, 1, 1, [2, 1]~], [11, [-1, 1]~, 1, 1,
! 468: [2, 1]~], [3, [1, 1]~, 1, 1, [0, 1]~], [5, [2, 1]~, 1, 1, [-1, 1]~], [11, [
! 469: 2, 1]~, 1, 1, [-1, 1]~], [19, [1, 1]~, 1, 1, [0, 1]~], [17, [3, 1]~, 1, 1, [
! 470: -2, 1]~], [17, [-2, 1]~, 1, 1, [3, 1]~], [19, [0, 1]~, 1, 1, [1, 1]~]], 0, [
! 471: x^2 - x - 57, [2, 0], 229, 1, [[1, -8.0663729752107779635959310246705326058;
! 472: 1, 7.0663729752107779635959310246705326058], [1, -8.06637297521077796359593
! 473: 10246705326058; 1, 7.0663729752107779635959310246705326058], 0, [2, -1; -1,
! 474: 115], [229, 115; 0, 1], [115, 1; 1, 2], [229, [115, 1]~]], [-7.0663729752107
! 475: 779635959310246705326058, 8.0663729752107779635959310246705326058], [1, x -
! 476: 1], [1, 1; 0, 1], [1, 0, 0, 57; 0, 1, 1, -1]], [[3, [3], [[3, 0; 0, 1]]], 2.
! 477: 7124653051843439746808795106061300699, 0.8814422512654579364, [2, -1], [x +
! 478: 7], 187], [mat(1), [[0, 0]], [[1.7903417566977293763292119206302198761, -1.7
! 479: 903417566977293763292119206302198760]]], [0, [mat([[6, 1]~, 1])]]], [[[25, 1
! 480: 4; 0, 1], [1, 1]], [80, [20, 2, 2], [[2, 0]~, [4, 2]~, [-2, -2]~]], mat([[5,
! 481: [-1, 1]~, 1, 1, [2, 1]~], 2]), [[[[4], [[2, 0]~], [[2, 0]~], [[mod(0, 2), m
! 482: od(0, 2)]~], 1], [[5], [[6, 0]~], [[6, 0]~], [[mod(0, 2), mod(0, 2)]~], mat(
! 483: [1/5, -14/5])]], [[2, 2], [[4, 2]~, [-2, -2]~], [1, 0; 0, 1]]], [1, -12, 0,
! 484: 0; 0, 0, 1, 0; 0, 0, 0, 1]], [1], mat([1, -3, -6, 0]), [12, [12], [[3, 0; 0,
! 485: 1]]], [[1, -18, 9; -1/2, 10, -5], [-2, 0; 0, -10]]]
1.1 noro 486: ? bytesize(%)
1.2 ! noro 487: 12096
1.1 noro 488: ? ceil(-2.5)
489: -2
490: ? centerlift(mod(456,555))
491: -99
492: ? cf(pi)
493: [3, 7, 15, 1, 292, 1, 1, 1, 2, 1, 3, 1, 14, 2, 1, 1, 2, 2, 2, 2, 1, 84, 2, 1
494: , 1, 15, 3, 13, 1, 4, 2, 6, 6]
495: ? cf2([1,3,5,7,9],(exp(1)-1)/(exp(1)+1))
496: [0, 6, 10, 42, 30]
497: ? changevar(x+y,[z,t])
498: y + z
499: ? char([1,2;3,4],z)
500: z^2 - 5*z - 2
501: ? char(mod(x^2+x+1,x^3+5*x+1),z)
502: z^3 + 7*z^2 + 16*z - 19
503: ? char1([1,2;3,4],z)
504: z^2 - 5*z - 2
505: ? char2(mod(1,8191)*[1,2;3,4],z)
506: z^2 + mod(8186, 8191)*z + mod(8189, 8191)
507: ? acurve=chell(acurve,[-1,1,2,3])
508: [-4, -1, -7, -12, -12, 12, 4, 1, -1, 48, -216, 37, 110592/37, [-0.1624345647
1.2 ! noro 509: 1667696455518910092496975959, -0.73040556359455544173706204865073999594, -2.
1.1 noro 510: 1071598716887675937077488504242902444]~, -2.99345864623195962983200997945250
511: 81778, -2.4513893819867900608542248318665252253*I, 0.47131927795681147588259
512: 389708033769964, 1.4354565186686843187232088566788165076*I, 7.33813274078957
513: 67390707210033323055881]
514: ? chinese(mod(7,15),mod(13,21))
515: mod(97, 105)
516: ? apoint=chptell(apoint,[-1,1,2,3])
517: [1, 3]
518: ? isoncurve(acurve,apoint)
519: 1
520: ? classno(-12391)
521: 63
522: ? classno(1345)
523: 6
524: ? classno2(-12391)
525: 63
526: ? classno2(1345)
527: 6
528: ? coeff(sin(x),7)
529: -1/5040
530: ? compimag(qfi(2,1,3),qfi(2,1,3))
531: qfi(2, -1, 3)
532: ? compo(1+o(7^4),3)
533: 1
534: ? compositum(x^4-4*x+2,x^3-x-1)
535: [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
536: ^2 - 128*x - 5]
537: ? compositum2(x^4-4*x+2,x^3-x-1)
538: [[x^12 - 4*x^10 + 8*x^9 + 12*x^8 + 12*x^7 + 138*x^6 + 132*x^5 - 43*x^4 + 58*
539: x^2 - 128*x - 5, mod(-279140305176/29063006931199*x^11 + 129916611552/290630
540: 06931199*x^10 + 1272919322296/29063006931199*x^9 - 2813750209005/29063006931
541: 199*x^8 - 2859411937992/29063006931199*x^7 - 414533880536/29063006931199*x^6
542: - 35713977492936/29063006931199*x^5 - 17432607267590/29063006931199*x^4 + 4
543: 9785595543672/29063006931199*x^3 + 9423768373204/29063006931199*x^2 - 427797
544: 76146743/29063006931199*x + 37962587857138/29063006931199, x^12 - 4*x^10 + 8
545: *x^9 + 12*x^8 + 12*x^7 + 138*x^6 + 132*x^5 - 43*x^4 + 58*x^2 - 128*x - 5), m
546: od(-279140305176/29063006931199*x^11 + 129916611552/29063006931199*x^10 + 12
547: 72919322296/29063006931199*x^9 - 2813750209005/29063006931199*x^8 - 28594119
548: 37992/29063006931199*x^7 - 414533880536/29063006931199*x^6 - 35713977492936/
549: 29063006931199*x^5 - 17432607267590/29063006931199*x^4 + 49785595543672/2906
550: 3006931199*x^3 + 9423768373204/29063006931199*x^2 - 13716769215544/290630069
551: 31199*x + 37962587857138/29063006931199, x^12 - 4*x^10 + 8*x^9 + 12*x^8 + 12
552: *x^7 + 138*x^6 + 132*x^5 - 43*x^4 + 58*x^2 - 128*x - 5), -1]]
553: ? comprealraw(qfr(5,3,-1,0.),qfr(7,1,-1,0.))
554: qfr(35, 43, 13, 0.E-38)
555: ? concat([1,2],[3,4])
556: [1, 2, 3, 4]
1.2 ! noro 557: ? conductor(bnf,[[25,14;0,1],[1,1]])
! 558: [[[5, 4; 0, 1], [1, 0]], [12, [12], [[3, 0; 0, 1]]], mat(12)]
1.1 noro 559: ? conductorofchar(bnr,[2])
1.2 ! noro 560: [[5, 4; 0, 1], [0, 0]]
1.1 noro 561: ? conj(1+i)
562: 1 - I
563: ? conjvec(mod(x^2+x+1,x^3-x-1))
564: [4.0795956234914387860104177508366260325, 0.46020218825428060699479112458168
565: 698369 + 0.18258225455744299269398828369501930573*I, 0.460202188254280606994
566: 79112458168698369 - 0.18258225455744299269398828369501930573*I]~
567: ? content([123,456,789,234])
568: 3
569: ? convol(sin(x),x*cos(x))
570: x + 1/12*x^3 + 1/2880*x^5 + 1/3628800*x^7 + 1/14631321600*x^9 + 1/1448500838
571: 40000*x^11 + 1/2982752926433280000*x^13 + 1/114000816848279961600000*x^15 +
572: O(x^16)
573: ? core(54713282649239)
574: 5471
575: ? core2(54713282649239)
576: [5471, 100003]
577: ? coredisc(54713282649239)
578: 21884
579: ? coredisc2(54713282649239)
580: [21884, 100003/2]
581: ? cos(1)
582: 0.54030230586813971740093660744297660373
583: ? cosh(1)
584: 1.5430806348152437784779056207570616825
585: ? move(0,200,150)
586: ? cursor(0)
587: ? cvtoi(1.7)
588: 1
589: ? cyclo(105)
590: x^48 + x^47 + x^46 - x^43 - x^42 - 2*x^41 - x^40 - x^39 + x^36 + x^35 + x^34
591: + x^33 + x^32 + x^31 - x^28 - x^26 - x^24 - x^22 - x^20 + x^17 + x^16 + x^1
592: 5 + x^14 + x^13 + x^12 - x^9 - x^8 - 2*x^7 - x^6 - x^5 + x^2 + x + 1
593: ? degree(x^3/(x-1))
594: 2
595: ? denom(12345/54321)
596: 18107
597: ? deplin(mod(1,7)*[2,-1;1,3])
598: [mod(6, 7), mod(5, 7)]~
599: ? deriv((x+y)^5,y)
600: 5*x^4 + 20*y*x^3 + 30*y^2*x^2 + 20*y^3*x + 5*y^4
601: ? ((x+y)^5)'
602: 5*x^4 + 20*y*x^3 + 30*y^2*x^2 + 20*y^3*x + 5*y^4
603: ? det([1,2,3;1,5,6;9,8,7])
604: -30
605: ? det2([1,2,3;1,5,6;9,8,7])
606: -30
607: ? detint([1,2,3;4,5,6])
608: 3
609: ? diagonal([2,4,6])
610:
611: [2 0 0]
612:
613: [0 4 0]
614:
615: [0 0 6]
616:
617: ? dilog(0.5)
618: 0.58224052646501250590265632015968010858
619: ? dz=vector(30,k,1);dd=vector(30,k,k==1);dm=dirdiv(dd,dz)
620: [1, -1, -1, 0, -1, 1, -1, 0, 0, 1, -1, 0, -1, 1, 1, 0, -1, 0, -1, 0, 1, 1, -
621: 1, 0, 0, 1, 0, 0, -1, -1]
622: ? deu=direuler(p=2,100,1/(1-apell(acurve,p)*x+if(acurve[12]%p,p,0)*x^2))
623: [1, -2, -3, 2, -2, 6, -1, 0, 6, 4, -5, -6, -2, 2, 6, -4, 0, -12, 0, -4, 3, 1
624: 0, 2, 0, -1, 4, -9, -2, 6, -12, -4, 8, 15, 0, 2, 12, -1, 0, 6, 0, -9, -6, 2,
625: -10, -12, -4, -9, 12, -6, 2, 0, -4, 1, 18, 10, 0, 0, -12, 8, 12, -8, 8, -6,
626: -8, 4, -30, 8, 0, -6, -4, 9, 0, -1, 2, 3, 0, 5, -12, 4, 8, 9, 18, -15, 6, 0
627: , -4, -18, 0, 4, 24, 2, 4, 12, 18, 0, -24, 4, 12, -30, -2]
628: ? anell(acurve,100)==deu
629: 1
630: ? dirmul(abs(dm),dz)
631: [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,
632: 4, 2, 4, 2, 8]
633: ? dirzetak(initalg(x^3-10*x+8),30)
634: [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,
635: 0, 1, 0, 1, 0]
636: ? disc(x^3+4*x+12)
637: -4144
638: ? discf(x^3+4*x+12)
639: -1036
640: ? discrayabs(bnr,mat(6))
641: [12, 12, 18026977100265125]
642: ? discrayabs(bnr)
643: [24, 12, 40621487921685401825918161408203125]
644: ? discrayabscond(bnr2)
645: 0
646: ? lu=ideallistunitgen(bnf,55);discrayabslist(bnf,lu)
647: [[[6, 6, mat([229, 3])]], [], [[], []], [[]], [[12, 12, [5, 3; 229, 6]], [12
648: , 12, [5, 3; 229, 6]]], [], [], [], [[], [], []], [], [[], []], [[], []], []
649: , [], [[24, 24, [3, 6; 5, 9; 229, 12]], [], [], [24, 24, [3, 6; 5, 9; 229, 1
650: 2]]], [[]], [[], []], [], [[18, 18, [19, 6; 229, 9]], [18, 18, [19, 6; 229,
651: 9]]], [[], []], [], [], [], [], [[], [24, 24, [5, 12; 229, 12]], []], [], [[
652: ], [], [], []], [], [], [], [], [], [[], [12, 12, [3, 3; 11, 3; 229, 6]], [1
653: 2, 12, [3, 3; 11, 3; 229, 6]], []], [], [], [[18, 18, [2, 12; 3, 12; 229, 9]
654: ], [], [18, 18, [2, 12; 3, 12; 229, 9]]], [[12, 12, [37, 3; 229, 6]], [12, 1
655: 2, [37, 3; 229, 6]]], [], [], [], [], [], [[], []], [[], []], [[], [], [], [
656: ], [], []], [], [], [[12, 12, [2, 12; 3, 3; 229, 6]], [12, 12, [2, 12; 3, 3;
657: 229, 6]]], [[18, 18, [7, 12; 229, 9]]], [], [[], [], [], []], [], [[], []],
658: [], [[], [24, 24, [5, 9; 11, 6; 229, 12]], [24, 24, [5, 9; 11, 6; 229, 12]]
659: , []]]
660: ? discrayabslistlong(bnf,20)
661: [[[[matrix(0,2,j,k,0), 6, 6, mat([229, 3])]], [], [[mat([12, 1]), 0, 0, 0],
662: [mat([13, 1]), 0, 0, 0]], [[mat([10, 1]), 0, 0, 0]], [[mat([20, 1]), 12, 12,
663: [5, 3; 229, 6]], [mat([21, 1]), 12, 12, [5, 3; 229, 6]]], [], [], [], [[mat
664: ([12, 2]), 0, 0, 0], [[12, 1; 13, 1], 0, 0, 0], [mat([13, 2]), 0, 0, 0]], []
665: , [[mat([44, 1]), 0, 0, 0], [mat([45, 1]), 0, 0, 0]], [[[10, 1; 12, 1], 0, 0
666: , 0], [[10, 1; 13, 1], 0, 0, 0]], [], [], [[[12, 1; 20, 1], 24, 24, [3, 6; 5
667: , 9; 229, 12]], [[13, 1; 20, 1], 0, 0, 0], [[12, 1; 21, 1], 0, 0, 0], [[13,
668: 1; 21, 1], 24, 24, [3, 6; 5, 9; 229, 12]]], [[mat([10, 2]), 0, 0, 0]], [[mat
669: ([68, 1]), 0, 0, 0], [mat([69, 1]), 0, 0, 0]], [], [[mat([76, 1]), 18, 18, [
670: 19, 6; 229, 9]], [mat([77, 1]), 18, 18, [19, 6; 229, 9]]], [[[10, 1; 20, 1],
671: 0, 0, 0], [[10, 1; 21, 1], 0, 0, 0]]]]
672: ? discrayrel(bnr,mat(6))
1.2 ! noro 673: [6, 2, [125, 14; 0, 1]]
1.1 noro 674: ? discrayrel(bnr)
1.2 ! noro 675: [12, 1, [1953125, 1160889; 0, 1]]
1.1 noro 676: ? discrayrelcond(bnr2)
677: 0
678: ? divisors(8!)
679: [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 14, 15, 16, 18, 20, 21, 24, 28, 30, 32,
680: 35, 36, 40, 42, 45, 48, 56, 60, 63, 64, 70, 72, 80, 84, 90, 96, 105, 112, 12
681: 0, 126, 128, 140, 144, 160, 168, 180, 192, 210, 224, 240, 252, 280, 288, 315
682: , 320, 336, 360, 384, 420, 448, 480, 504, 560, 576, 630, 640, 672, 720, 840,
683: 896, 960, 1008, 1120, 1152, 1260, 1344, 1440, 1680, 1920, 2016, 2240, 2520,
684: 2688, 2880, 3360, 4032, 4480, 5040, 5760, 6720, 8064, 10080, 13440, 20160,
685: 40320]
686: ? divres(345,123)
687: [2, 99]~
688: ? divres(x^7-1,x^5+1)
689: [x^2, -x^2 - 1]~
690: ? divsum(8!,x,x)
691: 159120
692: ? postdraw([0,0,0])
693: ? eigen([1,2,3;4,5,6;7,8,9])
694:
695: [-1.2833494518006402717978106547571267252 1 0.283349451800640271797810654757
696: 12672521]
697:
698: [-0.14167472590032013589890532737856336260 -2 0.6416747259003201358989053273
699: 7856336260]
700:
701: [1 1 1]
702:
703: ? eint1(2)
704: 0.048900510708061119567239835228049522206
705: ? erfc(2)
706: 0.0046777349810472658379307436327470713891
707: ? eta(q)
708: 1 - q - q^2 + q^5 + q^7 - q^12 - q^15 + O(q^16)
709: ? euler
710: 0.57721566490153286060651209008240243104
711: ? z=y;y=x;eval(z)
712: x
713: ? exp(1)
714: 2.7182818284590452353602874713526624977
715: ? extract([1,2,3,4,5,6,7,8,9,10],1000)
716: [4, 6, 7, 8, 9, 10]
717: ? 10!
718: 3628800
719: ? fact(10)
720: 3628800.0000000000000000000000000000000
721: ? factcantor(x^11+1,7)
722:
723: [mod(1, 7)*x + mod(1, 7) 1]
724:
725: [mod(1, 7)*x^10 + mod(6, 7)*x^9 + mod(1, 7)*x^8 + mod(6, 7)*x^7 + mod(1, 7)*
726: x^6 + mod(6, 7)*x^5 + mod(1, 7)*x^4 + mod(6, 7)*x^3 + mod(1, 7)*x^2 + mod(6,
727: 7)*x + mod(1, 7) 1]
728:
729: ? centerlift(lift(factfq(x^3+x^2+x-1,3,t^3+t^2+t-1)))
730:
731: [x - t 1]
732:
733: [x + (t^2 + t - 1) 1]
734:
735: [x + (-t^2 - 1) 1]
736:
737: ? factmod(x^11+1,7)
738:
739: [mod(1, 7)*x + mod(1, 7) 1]
740:
741: [mod(1, 7)*x^10 + mod(6, 7)*x^9 + mod(1, 7)*x^8 + mod(6, 7)*x^7 + mod(1, 7)*
742: x^6 + mod(6, 7)*x^5 + mod(1, 7)*x^4 + mod(6, 7)*x^3 + mod(1, 7)*x^2 + mod(6,
743: 7)*x + mod(1, 7) 1]
744:
745: ? factor(17!+1)
746:
747: [661 1]
748:
749: [537913 1]
750:
751: [1000357 1]
752:
753: ? p=x^5+3021*x^4-786303*x^3-6826636057*x^2-546603588746*x+3853890514072057
754: x^5 + 3021*x^4 - 786303*x^3 - 6826636057*x^2 - 546603588746*x + 385389051407
755: 2057
756: ? fa=[11699,6;2392997,2;4987333019653,2]
757:
758: [11699 6]
759:
760: [2392997 2]
761:
762: [4987333019653 2]
763:
764: ? factoredbasis(p,fa)
765: [1, x, x^2, 1/11699*x^3 + 1847/11699*x^2 - 132/11699*x - 2641/11699, 1/13962
766: 3738889203638909659*x^4 - 1552451622081122020/139623738889203638909659*x^3 +
767: 418509858130821123141/139623738889203638909659*x^2 - 6810913798507599407313
768: 4/139623738889203638909659*x - 13185339461968406/58346808996920447]
769: ? factoreddiscf(p,fa)
770: 136866601
771: ? factoredpolred(p,fa)
772: [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
773: *x^2 + 508*x + 913, x^5 - 2*x^4 - 13*x^3 + 37*x^2 - 21*x - 1, x^5 - x^4 - 52
774: *x^3 - 197*x^2 - 273*x - 127]
775: ? factoredpolred2(p,fa)
1.2 ! noro 776: [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
! 777: *x^2 + 508*x + 913, x^5 - 2*x^4 - 13*x^3 + 37*x^2 - 21*x - 1, x^5 - x^4 - 52
! 778: *x^3 - 197*x^2 - 273*x - 127]
1.1 noro 779: ? factornf(x^3+x^2-2*x-1,t^3+t^2-2*t-1)
780:
781: [mod(1, t^3 + t^2 - 2*t - 1)*x + mod(-t, t^3 + t^2 - 2*t - 1) 1]
782:
783: [mod(1, t^3 + t^2 - 2*t - 1)*x + mod(-t^2 + 2, t^3 + t^2 - 2*t - 1) 1]
784:
785: [mod(1, t^3 + t^2 - 2*t - 1)*x + mod(t^2 + t - 1, t^3 + t^2 - 2*t - 1) 1]
786:
787: ? factorpadic(apol,7,8)
788:
789: [(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]
790:
791: [(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
792: ))*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]
793:
794: ? factorpadic2(apol,7,8)
795:
796: [(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]
797:
798: [(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
799: ))*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]
800:
801: ? factpol(x^15-1,3,1)
802:
803: [x - 1 1]
804:
805: [x^2 + x + 1 1]
806:
807: [x^4 + x^3 + x^2 + x + 1 1]
808:
809: [x^8 - x^7 + x^5 - x^4 + x^3 - x + 1 1]
810:
811: ? factpol(x^15-1,0,1)
812:
813: [x - 1 1]
814:
815: [x^2 + x + 1 1]
816:
817: [x^4 + x^3 + x^2 + x + 1 1]
818:
819: [x^8 - x^7 + x^5 - x^4 + x^3 - x + 1 1]
820:
821: ? factpol2(x^15-1,0)
822: *** this function has been suppressed.
823: ? fibo(100)
824: 354224848179261915075
825: ? floor(-1/2)
826: -1
827: ? floor(-2.5)
828: -3
829: ? for(x=1,5,print(x!))
830: 1
831: 2
832: 6
833: 24
834: 120
835: ? fordiv(10,x,print(x))
836: 1
837: 2
838: 5
839: 10
840: ? forprime(p=1,30,print(p))
841: 2
842: 3
843: 5
844: 7
845: 11
846: 13
847: 17
848: 19
849: 23
850: 29
851: ? forstep(x=0,pi,pi/12,print(sin(x)))
852: 0.E-38
853: 0.25881904510252076234889883762404832834
854: 0.49999999999999999999999999999999999999
855: 0.70710678118654752440084436210484903928
1.2 ! noro 856: 0.86602540378443864676372317075293618347
1.1 noro 857: 0.96592582628906828674974319972889736763
858: 1.0000000000000000000000000000000000000
859: 0.96592582628906828674974319972889736764
860: 0.86602540378443864676372317075293618348
861: 0.70710678118654752440084436210484903930
862: 0.50000000000000000000000000000000000002
863: 0.25881904510252076234889883762404832838
864: 4.7019774032891500318749461488889827112 E-38
865: ? forvec(x=[[1,3],[-2,2]],print1([x[1],x[2]]," "));print(" ");
866: [1, -2] [1, -1] [1, 0] [1, 1] [1, 2] [2, -2] [2, -1] [2, 0] [2, 1] [2, 2] [3
867: , -2] [3, -1] [3, 0] [3, 1] [3, 2]
868: ? frac(-2.7)
869: 0.30000000000000000000000000000000000000
870: ? galois(x^6-3*x^2-1)
871: [12, 1, 1]
872: ? nf3=initalg(x^6+108);galoisconj(nf3)
873: [-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
874: /2*x]~
875: ? aut=%[2];galoisapply(nf3,aut,mod(x^5,x^6+108))
876: mod(x^5, x^6 + 108)
877: ? gamh(10)
878: 1133278.3889487855673345741655888924755
879: ? gamma(10.5)
880: 1133278.3889487855673345741655888924755
881: ? gauss(hilbert(10),[1,2,3,4,5,6,7,8,9,0]~)
882: [9236800, -831303990, 18288515520, -170691240720, 832112321040, -23298940665
883: 00, 3883123564320, -3803844432960, 2020775945760, -449057772020]~
884: ? gaussmodulo([2,3;5,4],[7,11],[1,4]~)
885: [-5, -1]~
886: ? gaussmodulo2([2,3;5,4],[7,11],[1,4]~)
887: [[-5, -1]~, [-77, 723; 0, 1]]
888: ? gcd(12345678,87654321)
889: 9
890: ? getheap()
1.2 ! noro 891: [215, 43452]
1.1 noro 892: ? getrand()
1.2 ! noro 893: 419462396
1.1 noro 894: ? getstack()
895: 0
896: ? globalred(acurve)
897: [37, [1, -1, 2, 2], 1]
898: ? getstack()
899: 0
900: ? hclassno(2000003)
901: 357
902: ? hell(acurve,apoint)
903: 0.40889126591975072188708879805553617287
904: ? hell2(acurve,apoint)
905: 0.40889126591975072188708879805553617296
906: ? hermite(amat=1/hilbert(7))
907:
908: [420 0 0 0 210 168 175]
909:
910: [0 840 0 0 0 0 504]
911:
912: [0 0 2520 0 0 0 1260]
913:
914: [0 0 0 2520 0 0 840]
915:
916: [0 0 0 0 13860 0 6930]
917:
918: [0 0 0 0 0 5544 0]
919:
920: [0 0 0 0 0 0 12012]
921:
922: ? hermite2(amat)
923: [[420, 0, 0, 0, 210, 168, 175; 0, 840, 0, 0, 0, 0, 504; 0, 0, 2520, 0, 0, 0,
924: 1260; 0, 0, 0, 2520, 0, 0, 840; 0, 0, 0, 0, 13860, 0, 6930; 0, 0, 0, 0, 0,
925: 5544, 0; 0, 0, 0, 0, 0, 0, 12012], [420, 420, 840, 630, 2982, 1092, 4159; 21
926: 0, 280, 630, 504, 2415, 876, 3395; 140, 210, 504, 420, 2050, 749, 2901; 105,
927: 168, 420, 360, 1785, 658, 2542; 84, 140, 360, 315, 1582, 588, 2266; 70, 120
928: , 315, 280, 1421, 532, 2046; 60, 105, 280, 252, 1290, 486, 1866]]
929: ? hermitehavas(amat)
930: *** this function has been suppressed.
931: ? hermitemod(amat,detint(amat))
932:
933: [420 0 0 0 210 168 175]
934:
935: [0 840 0 0 0 0 504]
936:
937: [0 0 2520 0 0 0 1260]
938:
939: [0 0 0 2520 0 0 840]
940:
941: [0 0 0 0 13860 0 6930]
942:
943: [0 0 0 0 0 5544 0]
944:
945: [0 0 0 0 0 0 12012]
946:
947: ? hermiteperm(amat)
948: [[360360, 0, 0, 0, 0, 144144, 300300; 0, 27720, 0, 0, 0, 0, 22176; 0, 0, 277
949: 20, 0, 0, 0, 6930; 0, 0, 0, 2520, 0, 0, 840; 0, 0, 0, 0, 2520, 0, 1260; 0, 0
950: , 0, 0, 0, 168, 0; 0, 0, 0, 0, 0, 0, 7], [51480, 4620, 5544, 630, 840, 20676
951: , 48619; 45045, 3960, 4620, 504, 630, 18074, 42347; 40040, 3465, 3960, 420,
952: 504, 16058, 37523; 36036, 3080, 3465, 360, 420, 14448, 33692; 32760, 2772, 3
953: 080, 315, 360, 13132, 30574; 30030, 2520, 2772, 280, 315, 12036, 27986; 2772
954: 0, 2310, 2520, 252, 280, 11109, 25803], [7, 6, 5, 4, 3, 2, 1]]
955: ? hess(hilbert(7))
956:
957: [1 90281/58800 -1919947/4344340 4858466341/1095033030 -77651417539/819678732
958: 6 3386888964/106615355 1/2]
959:
960: [1/3 43/48 38789/5585580 268214641/109503303 -581330123627/126464718744 4365
961: 450643/274153770 1/4]
962:
963: [0 217/2880 442223/7447440 53953931/292008808 -32242849453/168619624992 1475
964: 457901/1827691800 1/80]
965:
966: [0 0 1604444/264539275 24208141/149362505292 847880210129/47916076768560 -45
967: 44407141/103873817300 -29/40920]
968:
969: [0 0 0 9773092581/35395807550620 -24363634138919/107305824577186620 72118203
970: 606917/60481351061158500 55899/3088554700]
971:
972: [0 0 0 0 67201501179065/8543442888354179988 -9970556426629/74082861999267660
973: 0 -3229/13661312210]
974:
975: [0 0 0 0 0 -258198800769/9279048099409000 -13183/38381527800]
976:
977: ? hilb(2/3,3/4,5)
978: 1
979: ? hilbert(5)
980:
981: [1 1/2 1/3 1/4 1/5]
982:
983: [1/2 1/3 1/4 1/5 1/6]
984:
985: [1/3 1/4 1/5 1/6 1/7]
986:
987: [1/4 1/5 1/6 1/7 1/8]
988:
989: [1/5 1/6 1/7 1/8 1/9]
990:
991: ? hilbp(mod(5,7),mod(6,7))
992: 1
993: ? hvector(10,x,1/x)
994: [1, 1/2, 1/3, 1/4, 1/5, 1/6, 1/7, 1/8, 1/9, 1/10]
995: ? hyperu(1,1,1)
996: 0.59634736232319407434107849936927937488
997: ? i^2
998: -1
999: ? nf1=initalgred(nfpol)
1000: [x^5 - 2*x^4 + 3*x^3 + 8*x^2 + 3*x + 2, [1, 2], 595125, 4, [[1, -1.089115145
1.2 ! noro 1001: 7205048250249527946671612684, 2.4285174907194186068992069565359418364, -0.71
! 1002: 946691128913178943997506477288225733, 2.555820035069169495064607115942677997
! 1003: 1; 1, -0.13838372073406036365047976417441696637 + 0.491816376577686434997532
! 1004: 85514741525107*I, -1.9647119211288133163138753392090569931 + 0.8097149241889
! 1005: 7895128294082219556466856*I, 0.072312766896812300380582649294307897121 + 2.1
! 1006: 980803753846276641195195160383234877*I, 0.9879631935250703980395053973545283
! 1007: 7194 + 1.5701452385894131769052374806001981108*I; 1, 1.682941293594312776162
! 1008: 9561615079976005 + 2.0500351226010726172974286983598602163*I, 0.750453175769
! 1009: 10401286427186094108607489 - 1.3101462685358123283560773619310445915*I, 0.78
! 1010: 742068874775359433940488309213323154 - 2.13366338931266180341684546104579360
! 1011: 17*I, -1.2658732110596551455718089553258673705 + 2.7164790103743150566578028
! 1012: 035789834834*I], [1, -1.0891151457205048250249527946671612684, 2.42851749071
! 1013: 94186068992069565359418364, -0.71946691128913178943997506477288225733, 2.555
! 1014: 8200350691694950646071159426779971; 1.4142135623730950488016887242096980785,
! 1015: -0.19570413467375904264179382543977540674, -2.77852224501646643099209256540
! 1016: 93065576, 0.10226569567819614506098907018896260035, 1.3971909474085893198147
! 1017: 151262541540506; 0, 0.69553338995335755797766403996841143190, 1.145109827443
! 1018: 9565129926149974389115722, 3.1085550780550843138423672171643499922, 2.220520
! 1019: 6913086872788181483285734827868; 1.4142135623730950488016887242096980785, 2.
! 1020: 3800384020787979181834702019470475018, 1.06130105909862703981823187865589944
! 1021: 12, 1.1135810173202366904448352912286604470, -1.7902150633253437253677889164
! 1022: 811036160; 0, 2.8991874737236275652408825679737171587, -1.852826621655848763
! 1023: 4446810512816401036, -3.0174557027049114270734649132936867272, 3.84168145837
! 1024: 31999185306312841432940661], 0, [5, 2, 0, 1, 2; 2, -2, 5, 10, -20; 0, 5, 10,
! 1025: -10, 5; 1, 10, -10, -17, 1; 2, -20, 5, 1, -8], [345, 0, 145, 235, 168; 0, 3
! 1026: 45, 250, 344, 200; 0, 0, 5, 4, 3; 0, 0, 0, 1, 0; 0, 0, 0, 0, 1], [108675, 51
! 1027: 75, 0, 10350, 15525; 5175, 13800, 8625, 1725, -27600; 0, 8625, 37950, -17250
! 1028: , 0; 10350, 1725, -17250, -24150, -15525; 15525, -27600, 0, -15525, -3450],
! 1029: [595125, [-238050, 296700, 91425, 1725, 0]~]], [-1.0891151457205048250249527
! 1030: 946671612684, -0.13838372073406036365047976417441696637 + 0.4918163765776864
! 1031: 3499753285514741525107*I, 1.6829412935943127761629561615079976005 + 2.050035
! 1032: 1226010726172974286983598602163*I], [1, x, 1/2*x^4 - 3/2*x^3 + 5/2*x^2 + 2*x
! 1033: - 1, 1/2*x^4 - x^3 + x^2 + 9/2*x + 1, 1/2*x^4 - x^3 + 2*x^2 + 7/2*x + 2], [
! 1034: 1, 0, -1, -7, -14; 0, 1, 1, -2, -15; 0, 0, 0, -2, -4; 0, 0, -1, -1, 2; 0, 0,
! 1035: 1, 3, 4], [1, 0, 0, 0, 0, 0, -1, 1, 2, -4, 0, 1, 3, -1, 1, 0, 2, -1, -3, -1
! 1036: , 0, -4, 1, -1, -1; 0, 1, 0, 0, 0, 1, 1, 1, 1, -1, 0, 1, -2, -1, 1, 0, 1, -1
! 1037: , -1, 3, 0, -1, 1, 3, -3; 0, 0, 1, 0, 0, 0, 0, 0, 1, -1, 1, 0, 0, 0, 2, 0, 1
! 1038: , 0, 1, 1, 0, -1, 2, 1, 1; 0, 0, 0, 1, 0, 0, -1, 0, 0, 0, 0, 0, -1, -1, -2,
! 1039: 1, 0, -1, 0, 0, 0, 0, -2, 0, 1; 0, 0, 0, 0, 1, 0, 1, -1, -1, 1, 0, -1, 0, -1
! 1040: , 0, 0, -1, -1, 0, 0, 1, 1, 0, 0, 1]]
1.1 noro 1041: ? initalgred2(nfpol)
1042: [[x^5 - 2*x^4 + 3*x^3 + 8*x^2 + 3*x + 2, [1, 2], 595125, 4, [[1, -1.08911514
1.2 ! noro 1043: 57205048250249527946671612684, 2.4285174907194186068992069565359418364, -0.7
! 1044: 1946691128913178943997506477288225733, 2.55582003506916949506460711594267799
! 1045: 71; 1, -0.13838372073406036365047976417441696637 + 0.49181637657768643499753
! 1046: 285514741525107*I, -1.9647119211288133163138753392090569931 + 0.809714924188
! 1047: 97895128294082219556466856*I, 0.072312766896812300380582649294307897121 + 2.
! 1048: 1980803753846276641195195160383234877*I, 0.987963193525070398039505397354528
! 1049: 37194 + 1.5701452385894131769052374806001981108*I; 1, 1.68294129359431277616
! 1050: 29561615079976005 + 2.0500351226010726172974286983598602163*I, 0.75045317576
! 1051: 910401286427186094108607489 - 1.3101462685358123283560773619310445915*I, 0.7
! 1052: 8742068874775359433940488309213323154 - 2.1336633893126618034168454610457936
! 1053: 017*I, -1.2658732110596551455718089553258673705 + 2.716479010374315056657802
! 1054: 8035789834834*I], [1, -1.0891151457205048250249527946671612684, 2.4285174907
! 1055: 194186068992069565359418364, -0.71946691128913178943997506477288225733, 2.55
! 1056: 58200350691694950646071159426779971; 1.4142135623730950488016887242096980785
! 1057: , -0.19570413467375904264179382543977540674, -2.7785222450164664309920925654
! 1058: 093065576, 0.10226569567819614506098907018896260035, 1.397190947408589319814
! 1059: 7151262541540506; 0, 0.69553338995335755797766403996841143190, 1.14510982744
! 1060: 39565129926149974389115722, 3.1085550780550843138423672171643499922, 2.22052
! 1061: 06913086872788181483285734827868; 1.4142135623730950488016887242096980785, 2
! 1062: .3800384020787979181834702019470475018, 1.0613010590986270398182318786558994
! 1063: 412, 1.1135810173202366904448352912286604470, -1.790215063325343725367788916
! 1064: 4811036160; 0, 2.8991874737236275652408825679737171587, -1.85282662165584876
! 1065: 34446810512816401036, -3.0174557027049114270734649132936867272, 3.8416814583
! 1066: 731999185306312841432940661], 0, [5, 2, 0, 1, 2; 2, -2, 5, 10, -20; 0, 5, 10
! 1067: , -10, 5; 1, 10, -10, -17, 1; 2, -20, 5, 1, -8], [345, 0, 145, 235, 168; 0,
! 1068: 345, 250, 344, 200; 0, 0, 5, 4, 3; 0, 0, 0, 1, 0; 0, 0, 0, 0, 1], [108675, 5
! 1069: 175, 0, 10350, 15525; 5175, 13800, 8625, 1725, -27600; 0, 8625, 37950, -1725
! 1070: 0, 0; 10350, 1725, -17250, -24150, -15525; 15525, -27600, 0, -15525, -3450],
! 1071: [595125, [-238050, 296700, 91425, 1725, 0]~]], [-1.089115145720504825024952
! 1072: 7946671612684, -0.13838372073406036365047976417441696637 + 0.491816376577686
! 1073: 43499753285514741525107*I, 1.6829412935943127761629561615079976005 + 2.05003
! 1074: 51226010726172974286983598602163*I], [1, x, 1/2*x^4 - 3/2*x^3 + 5/2*x^2 + 2*
! 1075: x - 1, 1/2*x^4 - x^3 + x^2 + 9/2*x + 1, 1/2*x^4 - x^3 + 2*x^2 + 7/2*x + 2],
! 1076: [1, 0, -1, -7, -14; 0, 1, 1, -2, -15; 0, 0, 0, -2, -4; 0, 0, -1, -1, 2; 0, 0
! 1077: , 1, 3, 4], [1, 0, 0, 0, 0, 0, -1, 1, 2, -4, 0, 1, 3, -1, 1, 0, 2, -1, -3, -
! 1078: 1, 0, -4, 1, -1, -1; 0, 1, 0, 0, 0, 1, 1, 1, 1, -1, 0, 1, -2, -1, 1, 0, 1, -
! 1079: 1, -1, 3, 0, -1, 1, 3, -3; 0, 0, 1, 0, 0, 0, 0, 0, 1, -1, 1, 0, 0, 0, 2, 0,
! 1080: 1, 0, 1, 1, 0, -1, 2, 1, 1; 0, 0, 0, 1, 0, 0, -1, 0, 0, 0, 0, 0, -1, -1, -2,
! 1081: 1, 0, -1, 0, 0, 0, 0, -2, 0, 1; 0, 0, 0, 0, 1, 0, 1, -1, -1, 1, 0, -1, 0, -
! 1082: 1, 0, 0, -1, -1, 0, 0, 1, 1, 0, 0, 1]], mod(-1/2*x^4 + 3/2*x^3 - 5/2*x^2 - 2
! 1083: *x + 1, x^5 - 2*x^4 + 3*x^3 + 8*x^2 + 3*x + 2)]
1.1 noro 1084: ? vp=primedec(nf,3)[1]
1.2 ! noro 1085: [3, [1, 0, 1, 0, 0]~, 1, 1, [1, -1, -1, -1, 0]~]
1.1 noro 1086: ? idx=idealmul(nf,idmat(5),vp)
1087:
1.2 ! noro 1088: [3 2 1 0 1]
1.1 noro 1089:
1090: [0 1 0 0 0]
1091:
1092: [0 0 1 0 0]
1093:
1094: [0 0 0 1 0]
1095:
1096: [0 0 0 0 1]
1097:
1098: ? idealinv(nf,idx)
1099:
1.2 ! noro 1100: [1 0 0 2/3 0]
1.1 noro 1101:
1.2 ! noro 1102: [0 1 0 1/3 0]
1.1 noro 1103:
1.2 ! noro 1104: [0 0 1 1/3 0]
1.1 noro 1105:
1.2 ! noro 1106: [0 0 0 1/3 0]
1.1 noro 1107:
1108: [0 0 0 0 1]
1109:
1110: ? idy=ideallllred(nf,idx,[1,5,6])
1111:
1.2 ! noro 1112: [5 0 0 0 2]
1.1 noro 1113:
1.2 ! noro 1114: [0 5 0 0 2]
1.1 noro 1115:
1.2 ! noro 1116: [0 0 5 0 1]
1.1 noro 1117:
1.2 ! noro 1118: [0 0 0 5 2]
1.1 noro 1119:
1.2 ! noro 1120: [0 0 0 0 1]
1.1 noro 1121:
1122: ? idealadd(nf,idx,idy)
1123:
1124: [1 0 0 0 0]
1125:
1126: [0 1 0 0 0]
1127:
1128: [0 0 1 0 0]
1129:
1130: [0 0 0 1 0]
1131:
1132: [0 0 0 0 1]
1133:
1134: ? idealaddone(nf,idx,idy)
1.2 ! noro 1135: [[3, 2, 1, 2, 1]~, [-2, -2, -1, -2, -1]~]
1.1 noro 1136: ? idealaddmultone(nf,[idy,idx])
1137: [[-5, 0, 0, 0, 0]~, [6, 0, 0, 0, 0]~]
1138: ? idealappr(nf,idy)
1.2 ! noro 1139: [-2, -2, -1, -2, -1]~
1.1 noro 1140: ? idealapprfact(nf,idealfactor(nf,idy))
1.2 ! noro 1141: [-2, -2, -1, -2, -1]~
1.1 noro 1142: ? idealcoprime(nf,idx,idx)
1.2 ! noro 1143: [1/3, -1/3, -1/3, -1/3, 0]~
1.1 noro 1144: ? idz=idealintersect(nf,idx,idy)
1145:
1.2 ! noro 1146: [15 10 5 0 12]
1.1 noro 1147:
1.2 ! noro 1148: [0 5 0 0 2]
1.1 noro 1149:
1.2 ! noro 1150: [0 0 5 0 1]
1.1 noro 1151:
1.2 ! noro 1152: [0 0 0 5 2]
1.1 noro 1153:
1.2 ! noro 1154: [0 0 0 0 1]
1.1 noro 1155:
1156: ? idealfactor(nf,idz)
1157:
1.2 ! noro 1158: [[3, [1, 0, 1, 0, 0]~, 1, 1, [1, -1, -1, -1, 0]~] 1]
1.1 noro 1159:
1.2 ! noro 1160: [[5, [-1, 0, 0, 0, 1]~, 1, 1, [2, 0, 3, 0, 1]~] 1]
1.1 noro 1161:
1.2 ! noro 1162: [[5, [2, 0, 0, 0, 1]~, 4, 1, [2, 2, 1, 2, 1]~] 3]
1.1 noro 1163:
1164: ? ideallist(bnf,20)
1.2 ! noro 1165: [[[1, 0; 0, 1]], [], [[3, 0; 0, 1], [3, 1; 0, 1]], [[2, 0; 0, 2]], [[5, 4; 0
! 1166: , 1], [5, 2; 0, 1]], [], [], [], [[9, 6; 0, 1], [3, 0; 0, 3], [9, 4; 0, 1]],
! 1167: [], [[11, 10; 0, 1], [11, 2; 0, 1]], [[6, 0; 0, 2], [6, 2; 0, 2]], [], [],
! 1168: [[15, 9; 0, 1], [15, 4; 0, 1], [15, 12; 0, 1], [15, 7; 0, 1]], [[4, 0; 0, 4]
! 1169: ], [[17, 15; 0, 1], [17, 3; 0, 1]], [], [[19, 0; 0, 1], [19, 1; 0, 1]], [[10
! 1170: , 8; 0, 2], [10, 4; 0, 2]]]
1.1 noro 1171: ? idx2=idealmul(nf,idx,idx)
1172:
1.2 ! noro 1173: [9 5 7 0 4]
1.1 noro 1174:
1175: [0 1 0 0 0]
1176:
1177: [0 0 1 0 0]
1178:
1179: [0 0 0 1 0]
1180:
1181: [0 0 0 0 1]
1182:
1183: ? idt=idealmulred(nf,idx,idx)
1184:
1.2 ! noro 1185: [2 0 0 0 0]
1.1 noro 1186:
1.2 ! noro 1187: [0 2 0 0 0]
1.1 noro 1188:
1189: [0 0 2 0 0]
1190:
1191: [0 0 0 2 1]
1192:
1193: [0 0 0 0 1]
1194:
1195: ? idealdiv(nf,idy,idt)
1196:
1.2 ! noro 1197: [5 0 5/2 0 1]
1.1 noro 1198:
1.2 ! noro 1199: [0 5/2 0 0 1]
1.1 noro 1200:
1.2 ! noro 1201: [0 0 5/2 0 1/2]
1.1 noro 1202:
1.2 ! noro 1203: [0 0 0 5/2 1]
1.1 noro 1204:
1.2 ! noro 1205: [0 0 0 0 1/2]
1.1 noro 1206:
1207: ? idealdivexact(nf,idx2,idx)
1208:
1.2 ! noro 1209: [3 2 1 0 1]
1.1 noro 1210:
1211: [0 1 0 0 0]
1212:
1213: [0 0 1 0 0]
1214:
1215: [0 0 0 1 0]
1216:
1217: [0 0 0 0 1]
1218:
1219: ? idealhermite(nf,vp)
1220:
1.2 ! noro 1221: [3 2 1 0 1]
1.1 noro 1222:
1223: [0 1 0 0 0]
1224:
1225: [0 0 1 0 0]
1226:
1227: [0 0 0 1 0]
1228:
1229: [0 0 0 0 1]
1230:
1231: ? idealhermite2(nf,vp[2],3)
1232:
1.2 ! noro 1233: [3 2 1 0 1]
1.1 noro 1234:
1235: [0 1 0 0 0]
1236:
1237: [0 0 1 0 0]
1238:
1239: [0 0 0 1 0]
1240:
1241: [0 0 0 0 1]
1242:
1243: ? idealnorm(nf,idt)
1244: 16
1245: ? idp=idealpow(nf,idx,7)
1246:
1.2 ! noro 1247: [2187 1436 1807 630 1822]
1.1 noro 1248:
1249: [0 1 0 0 0]
1250:
1251: [0 0 1 0 0]
1252:
1253: [0 0 0 1 0]
1254:
1255: [0 0 0 0 1]
1256:
1257: ? idealpowred(nf,idx,7)
1258:
1.2 ! noro 1259: [2 0 0 0 0]
1.1 noro 1260:
1.2 ! noro 1261: [0 2 0 0 0]
1.1 noro 1262:
1.2 ! noro 1263: [0 0 2 0 0]
1.1 noro 1264:
1.2 ! noro 1265: [0 0 0 2 1]
1.1 noro 1266:
1.2 ! noro 1267: [0 0 0 0 1]
1.1 noro 1268:
1269: ? idealtwoelt(nf,idy)
1.2 ! noro 1270: [5, [2, 2, 1, 2, 1]~]
1.1 noro 1271: ? idealtwoelt2(nf,idy,10)
1.2 ! noro 1272: [-2, -2, -1, -2, -1]~
1.1 noro 1273: ? idealval(nf,idp,vp)
1274: 7
1275: ? idmat(5)
1276:
1277: [1 0 0 0 0]
1278:
1279: [0 1 0 0 0]
1280:
1281: [0 0 1 0 0]
1282:
1283: [0 0 0 1 0]
1284:
1285: [0 0 0 0 1]
1286:
1287: ? if(3<2,print("bof"),print("ok"));
1288: ok
1289: ? imag(2+3*i)
1290: 3
1291: ? image([1,3,5;2,4,6;3,5,7])
1292:
1293: [1 3]
1294:
1295: [2 4]
1296:
1297: [3 5]
1298:
1299: ? image(pi*[1,3,5;2,4,6;3,5,7])
1300:
1301: [9.4247779607693797153879301498385086525 15.70796326794896619231321691639751
1302: 4420]
1303:
1304: [12.566370614359172953850573533118011536 18.84955592153875943077586029967701
1305: 7305]
1306:
1307: [15.707963267948966192313216916397514420 21.99114857512855266923850368295652
1308: 0189]
1309:
1310: ? incgam(2,1)
1311: 0.73575888234288464319104754032292173491
1312: ? incgam1(2,1)
1313: -0.26424111765711535680895245967678075578
1314: ? incgam2(2,1)
1315: 0.73575888234288464319104754032292173489
1316: ? incgam3(2,1)
1317: 0.26424111765711535680895245967707826508
1318: ? incgam4(4,1,6)
1319: 5.8860710587430771455283803225833738791
1320: ? indexrank([1,1,1;1,1,1;1,1,2])
1321: [[1, 3], [1, 3]]
1322: ? indsort([8,7,6,5])
1323: [4, 3, 2, 1]
1324: ? initell([0,0,0,-1,0])
1325: [0, 0, 0, -1, 0, 0, -2, 0, -1, 48, 0, 64, 1728, [1.0000000000000000000000000
1326: 000000000000, 0.E-38, -1.0000000000000000000000000000000000000]~, 2.62205755
1327: 42921198104648395898911194136, 2.6220575542921198104648395898911194136*I, -0
1328: .59907011736779610371996124614016193910, -1.79721035210338831115988373842048
1329: 58173*I, 6.8751858180203728274900957798105571979]
1330: ? initrect(1,700,700)
1331: ? nfz=initzeta(x^2-2);
1332: ? integ(sin(x),x)
1333: 1/2*x^2 - 1/24*x^4 + 1/720*x^6 - 1/40320*x^8 + 1/3628800*x^10 - 1/479001600*
1334: x^12 + 1/87178291200*x^14 - 1/20922789888000*x^16 + O(x^17)
1335: ? integ((-x^2-2*a*x+8*a)/(x^4-14*x^3+(2*a+49)*x^2-14*a*x+a^2),x)
1336: (x + a)/(x^2 - 7*x + a)
1337: ? intersect([1,2;3,4;5,6],[2,3;7,8;8,9])
1338:
1339: [-1]
1340:
1341: [-1]
1342:
1343: [-1]
1344:
1345: ? \precision=19
1346: realprecision = 19 significant digits
1347: ? intgen(x=0,pi,sin(x))
1348: 2.000000000000000017
1349: ? sqr(2*intgen(x=0,4,exp(-x^2)))
1350: 3.141592556720305685
1351: ? 4*intinf(x=1,10^20,1/(1+x^2))
1352: 3.141592653589793208
1353: ? intnum(x=-0.5,0.5,1/sqrt(1-x^2))
1354: 1.047197551196597747
1355: ? 2*intopen(x=0,100,sin(x)/x)
1356: 3.124450933778112629
1357: ? \precision=38
1358: realprecision = 38 significant digits
1359: ? inverseimage([1,1;2,3;5,7],[2,2,6]~)
1360: [4, -2]~
1361: ? isdiagonal([1,0,0;0,5,0;0,0,0])
1362: 1
1363: ? isfund(12345)
1364: 1
1.2 ! noro 1365: ? isideal(bnf[7],[5,2;0,1])
1.1 noro 1366: 1
1367: ? isincl(x^2+1,x^4+1)
1368: [-x^2, x^2]
1369: ? isinclfast(initalg(x^2+1),initalg(x^4+1))
1370: [-x^2, x^2]
1371: ? isirreducible(x^5+3*x^3+5*x^2+15)
1372: 0
1373: ? isisom(x^3+x^2-2*x-1,x^3+x^2-2*x-1)
1374: [x, -x^2 - x + 1, x^2 - 2]
1375: ? isisomfast(initalg(x^3-2),initalg(x^3-6*x^2-6*x-30))
1376: [-1/25*x^2 + 13/25*x - 2/5]
1377: ? isprime(12345678901234567)
1378: 0
1.2 ! noro 1379: ? isprincipal(bnf,[5,2;0,1])
1.1 noro 1380: [1]~
1.2 ! noro 1381: ? isprincipalgen(bnf,[5,2;0,1])
! 1382: [[1]~, [7/3, 1/3]~, 187]
1.1 noro 1383: ? isprincipalraygen(bnr,primedec(bnf,7)[1])
1.2 ! noro 1384: [[9]~, [112595/19683, 13958/19683]~, 256]
1.1 noro 1385: ? ispsp(73!+1)
1386: 1
1387: ? isqrt(10!^2+1)
1388: 3628800
1389: ? isset([-3,5,7,7])
1390: 0
1391: ? issqfree(123456789876543219)
1392: 0
1393: ? issquare(12345678987654321)
1394: 1
1395: ? isunit(bnf,mod(3405*x-27466,x^2-x-57))
1396: [-4, mod(1, 2)]~
1397: ? jacobi(hilbert(6))
1398: [[1.6188998589243390969705881471257800712, 0.2423608705752095521357284158507
1399: 0114077, 0.000012570757122625194922982397996498755027, 0.0000001082799484565
1400: 5497685388772372251711485, 0.016321521319875822124345079564191505890, 0.0006
1401: 1574835418265769764919938428527140264]~, [0.74871921887909485900280109200517
1402: 845109, -0.61454482829258676899320019644273870645, 0.01114432093072471053067
1403: 8340374220998541, -0.0012481940840821751169398163046387834473, 0.24032536934
1404: 252330399154228873240534568, -0.062226588150197681775152126611810492910; 0.4
1405: 4071750324351206127160083580231701801, 0.21108248167867048675227675845247769
1406: 095, -0.17973275724076003758776897803740640964, 0.03560664294428763526612284
1407: 8131812048466, -0.69765137527737012296208335046678265583, 0.4908392097109243
1408: 6297498316169060044997; 0.32069686982225190106359024326699463106, 0.36589360
1409: 730302614149086554211117169622, 0.60421220675295973004426567844103062241, -0
1410: .24067907958842295837736719558855679285, -0.23138937333290388042251363554209
1411: 048309, -0.53547692162107486593474491750949545456; 0.25431138634047419251788
1412: 312792590944672, 0.39470677609501756783094636145991581708, -0.44357471627623
1413: 954554460416705180105301, 0.62546038654922724457753441039459331059, 0.132863
1414: 15850933553530333839628101576050, -0.41703769221897886840494514780771076439;
1415: 0.21153084007896524664213667673977991959, 0.3881904338738864286311144882599
1416: 2418973, -0.44153664101228966222143649752977203423, -0.689807199293836684198
1417: 01738006926829419, 0.36271492146487147525299457604461742111, 0.0470340189331
1418: 15649705614518466541243873; 0.18144297664876947372217005457727093715, 0.3706
1419: 9590776736280861775501084807394603, 0.45911481681642960284551392793050866602
1420: , 0.27160545336631286930015536176213647001, 0.502762866757515384892605663686
1421: 47786272, 0.54068156310385293880022293448123782121]]
1422: ? jbesselh(1,1)
1423: 0.24029783912342701089584304474193368045
1424: ? jell(i)
1425: 1728.0000000000000000000000000000000000 + 0.E-54*I
1426: ? kbessel(1+i,1)
1427: 0.32545977186584141085464640324923711863 + 0.2894280370259921276345671592415
1428: 2302704*I
1429: ? kbessel2(1+i,1)
1430: 0.32545977186584141085464640324923711863 + 0.2894280370259921276345671592415
1431: 2302704*I
1432: ? x
1433: x
1434: ? y
1435: x
1436: ? ker(matrix(4,4,x,y,x/y))
1437:
1438: [-1/2 -1/3 -1/4]
1439:
1440: [1 0 0]
1441:
1442: [0 1 0]
1443:
1444: [0 0 1]
1445:
1446: ? ker(matrix(4,4,x,y,sin(x+y)))
1447:
1448: [0.72968694572192883282306463453582002359]
1449:
1450: [0.2114969213291234874]
1451:
1452: [-0.3509176660143506019]
1453:
1454: [1]
1455:
1456: ? keri(matrix(4,4,x,y,x+y))
1457:
1458: [1 2]
1459:
1460: [-2 -3]
1461:
1462: [1 0]
1463:
1464: [0 1]
1465:
1466: ? kerint(matrix(4,4,x,y,x*y))
1467:
1468: [-1 -1 -1]
1469:
1470: [-1 0 1]
1471:
1472: [1 -1 1]
1473:
1474: [0 1 -1]
1475:
1476: ? kerint1(matrix(4,4,x,y,x*y))
1477:
1478: [-1 -1 -1]
1479:
1480: [-1 0 1]
1481:
1482: [1 -1 1]
1483:
1484: [0 1 -1]
1485:
1486: ? kerint2(matrix(4,6,x,y,2520/(x+y)))
1.2 ! noro 1487: *** this function has been suppressed.
1.1 noro 1488: ? f(u)=u+1;
1489: ? print(f(5));kill(f);
1490: 6
1491: ? f=12
1492: 12
1493: ? killrect(1)
1494: ? kro(5,7)
1495: -1
1496: ? kro(3,18)
1497: 0
1498: ? laplace(x*exp(x*y)/(exp(x)-1))
1499: 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 +
1500: 22133/10*x^8 - 7560*x^9 + 2775767/66*x^10 - 166320*x^11 + 2655339269/2730*x
1501: ^12 - 4324320*x^13 + 264873251/10*x^14 + O(x^15)
1502: ? lcm(15,-21)
1503: 105
1504: ? length(divisors(1000))
1505: 16
1506: ? legendre(10)
1507: 46189/256*x^10 - 109395/256*x^8 + 45045/128*x^6 - 15015/128*x^4 + 3465/256*x
1508: ^2 - 63/256
1509: ? lex([1,3],[1,3,5])
1510: -1
1511: ? lexsort([[1,5],[2,4],[1,5,1],[1,4,2]])
1512: [[1, 4, 2], [1, 5], [1, 5, 1], [2, 4]]
1513: ? lift(chinese(mod(7,15),mod(4,21)))
1514: 67
1515: ? lindep([(1-3*sqrt(2))/(3-2*sqrt(3)),1,sqrt(2),sqrt(3),sqrt(6)])
1516: [-3, -3, 9, -2, 6]
1517: ? lindep2([(1-3*sqrt(2))/(3-2*sqrt(3)),1,sqrt(2),sqrt(3),sqrt(6)],14)
1518: [-3, -3, 9, -2, 6]
1519: ? move(0,0,900);line(0,900,0)
1520: ? lines(0,vector(5,k,50*k),vector(5,k,10*k*k))
1521: ? m=1/hilbert(7)
1522:
1523: [49 -1176 8820 -29400 48510 -38808 12012]
1524:
1525: [-1176 37632 -317520 1128960 -1940400 1596672 -504504]
1526:
1527: [8820 -317520 2857680 -10584000 18711000 -15717240 5045040]
1528:
1529: [-29400 1128960 -10584000 40320000 -72765000 62092800 -20180160]
1530:
1531: [48510 -1940400 18711000 -72765000 133402500 -115259760 37837800]
1532:
1533: [-38808 1596672 -15717240 62092800 -115259760 100590336 -33297264]
1534:
1535: [12012 -504504 5045040 -20180160 37837800 -33297264 11099088]
1536:
1537: ? mp=concat(m,idmat(7))
1538:
1539: [49 -1176 8820 -29400 48510 -38808 12012 1 0 0 0 0 0 0]
1540:
1541: [-1176 37632 -317520 1128960 -1940400 1596672 -504504 0 1 0 0 0 0 0]
1542:
1543: [8820 -317520 2857680 -10584000 18711000 -15717240 5045040 0 0 1 0 0 0 0]
1544:
1545: [-29400 1128960 -10584000 40320000 -72765000 62092800 -20180160 0 0 0 1 0 0
1546: 0]
1547:
1548: [48510 -1940400 18711000 -72765000 133402500 -115259760 37837800 0 0 0 0 1 0
1549: 0]
1550:
1551: [-38808 1596672 -15717240 62092800 -115259760 100590336 -33297264 0 0 0 0 0
1552: 1 0]
1553:
1554: [12012 -504504 5045040 -20180160 37837800 -33297264 11099088 0 0 0 0 0 0 1]
1555:
1556: ? lll(m)
1557:
1.2 ! noro 1558: [-420 -420 840 630 -1092 -83 2982]
1.1 noro 1559:
1.2 ! noro 1560: [-210 -280 630 504 -876 70 2415]
1.1 noro 1561:
1.2 ! noro 1562: [-140 -210 504 420 -749 137 2050]
1.1 noro 1563:
1.2 ! noro 1564: [-105 -168 420 360 -658 169 1785]
1.1 noro 1565:
1.2 ! noro 1566: [-84 -140 360 315 -588 184 1582]
1.1 noro 1567:
1.2 ! noro 1568: [-70 -120 315 280 -532 190 1421]
1.1 noro 1569:
1.2 ! noro 1570: [-60 -105 280 252 -486 191 1290]
1.1 noro 1571:
1572: ? lll1(m)
1.2 ! noro 1573: *** this function has been suppressed.
1.1 noro 1574: ? lllgram(m)
1575:
1576: [1 1 27 -27 69 0 141]
1577:
1578: [0 1 4 -22 34 -24 49]
1579:
1580: [0 1 3 -21 18 -24 23]
1581:
1582: [0 1 3 -20 10 -19 13]
1583:
1584: [0 1 3 -19 6 -14 8]
1585:
1586: [0 1 3 -18 4 -10 5]
1587:
1588: [0 1 3 -17 3 -7 3]
1589:
1590: ? lllgram1(m)
1.2 ! noro 1591: *** this function has been suppressed.
1.1 noro 1592: ? lllgramint(m)
1593:
1594: [1 1 27 -27 69 0 141]
1595:
1596: [0 1 4 -23 34 -24 91]
1597:
1598: [0 1 3 -22 18 -24 65]
1599:
1600: [0 1 3 -21 10 -19 49]
1601:
1602: [0 1 3 -20 6 -14 38]
1603:
1604: [0 1 3 -19 4 -10 30]
1605:
1606: [0 1 3 -18 3 -7 24]
1607:
1608: ? lllgramkerim(mp~*mp)
1609: [[-420, -420, 840, 630, 2982, -1092, -83; -210, -280, 630, 504, 2415, -876,
1610: 70; -140, -210, 504, 420, 2050, -749, 137; -105, -168, 420, 360, 1785, -658,
1611: 169; -84, -140, 360, 315, 1582, -588, 184; -70, -120, 315, 280, 1421, -532,
1612: 190; -60, -105, 280, 252, 1290, -486, 191; 420, 0, 0, 0, -210, 168, 35; 0,
1613: 840, 0, 0, 0, 0, 336; 0, 0, -2520, 0, 0, 0, 1260; 0, 0, 0, -2520, 0, 0, -840
1614: ; 0, 0, 0, 0, -13860, 0, 6930; 0, 0, 0, 0, 0, 5544, 0; 0, 0, 0, 0, 0, 0, -12
1615: 012], [0, 0, 0, 0, 0, 0, 0; 0, 0, 0, 0, 0, 0, 0; 0, 0, 0, 0, 0, 0, 0; 0, 0,
1616: 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
1617: ; 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,
1618: 0, 0, 0; 0, 0, 0, 0, 1, 0, 0; 0, 0, 0, 0, 0, 1, 0; 0, 0, 0, 0, 0, 0, 1]]
1619: ? lllint(m)
1620:
1621: [-420 -420 840 630 -1092 -83 2982]
1622:
1623: [-210 -280 630 504 -876 70 2415]
1624:
1625: [-140 -210 504 420 -749 137 2050]
1626:
1627: [-105 -168 420 360 -658 169 1785]
1628:
1629: [-84 -140 360 315 -588 184 1582]
1630:
1631: [-70 -120 315 280 -532 190 1421]
1632:
1633: [-60 -105 280 252 -486 191 1290]
1634:
1635: ? lllintpartial(m)
1636:
1637: [-420 -420 -630 840 1092 2982 -83]
1638:
1639: [-210 -280 -504 630 876 2415 70]
1640:
1641: [-140 -210 -420 504 749 2050 137]
1642:
1643: [-105 -168 -360 420 658 1785 169]
1644:
1645: [-84 -140 -315 360 588 1582 184]
1646:
1647: [-70 -120 -280 315 532 1421 190]
1648:
1649: [-60 -105 -252 280 486 1290 191]
1650:
1651: ? lllkerim(mp)
1652: [[-420, -420, 840, 630, 2982, -1092, -83; -210, -280, 630, 504, 2415, -876,
1653: 70; -140, -210, 504, 420, 2050, -749, 137; -105, -168, 420, 360, 1785, -658,
1654: 169; -84, -140, 360, 315, 1582, -588, 184; -70, -120, 315, 280, 1421, -532,
1655: 190; -60, -105, 280, 252, 1290, -486, 191; 420, 0, 0, 0, -210, 168, 35; 0,
1656: 840, 0, 0, 0, 0, 336; 0, 0, -2520, 0, 0, 0, 1260; 0, 0, 0, -2520, 0, 0, -840
1657: ; 0, 0, 0, 0, -13860, 0, 6930; 0, 0, 0, 0, 0, 5544, 0; 0, 0, 0, 0, 0, 0, -12
1658: 012], [0, 0, 0, 0, 0, 0, 0; 0, 0, 0, 0, 0, 0, 0; 0, 0, 0, 0, 0, 0, 0; 0, 0,
1659: 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
1660: ; 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,
1661: 0, 0, 0; 0, 0, 0, 0, 1, 0, 0; 0, 0, 0, 0, 0, 1, 0; 0, 0, 0, 0, 0, 0, 1]]
1662: ? lllrat(m)
1.2 ! noro 1663: *** this function has been suppressed.
1.1 noro 1664: ? \precision=96
1665: realprecision = 96 significant digits
1666: ? ln(2)
1667: 0.69314718055994530941723212145817656807550013436025525412068000949339362196
1668: 9694715605863326996418
1669: ? lngamma(10^50*i)
1670: -157079632679489661923132169163975144209858469968811.93673753887608474948977
1671: 0941153418951907406847 - 2.5258126069288717421377720813802613884088088474975
1672: 8842763772207531866369674037379004058787354391*I
1673: ? \precision=2000
1674: realprecision = 2003 significant digits (2000 digits displayed)
1675: ? log(2)
1676: 0.69314718055994530941723212145817656807550013436025525412068000949339362196
1677: 9694715605863326996418687542001481020570685733685520235758130557032670751635
1678: 0759619307275708283714351903070386238916734711233501153644979552391204751726
1679: 8157493206515552473413952588295045300709532636664265410423915781495204374043
1680: 0385500801944170641671518644712839968171784546957026271631064546150257207402
1681: 4816377733896385506952606683411372738737229289564935470257626520988596932019
1682: 6505855476470330679365443254763274495125040606943814710468994650622016772042
1683: 4524529612687946546193165174681392672504103802546259656869144192871608293803
1684: 1727143677826548775664850856740776484514644399404614226031930967354025744460
1685: 7030809608504748663852313818167675143866747664789088143714198549423151997354
1686: 8803751658612753529166100071053558249879414729509293113897155998205654392871
1687: 7000721808576102523688921324497138932037843935308877482597017155910708823683
1688: 6275898425891853530243634214367061189236789192372314672321720534016492568727
1689: 4778234453534764811494186423867767744060695626573796008670762571991847340226
1690: 5146283790488306203306114463007371948900274364396500258093651944304119115060
1691: 8094879306786515887090060520346842973619384128965255653968602219412292420757
1692: 4321757489097706752687115817051137009158942665478595964890653058460258668382
1693: 9400228330053820740056770530467870018416240441883323279838634900156312188956
1694: 0650553151272199398332030751408426091479001265168243443893572472788205486271
1695: 5527418772430024897945401961872339808608316648114909306675193393128904316413
1696: 7068139777649817697486890388778999129650361927071088926410523092478391737350
1697: 1229842420499568935992206602204654941510613918788574424557751020683703086661
1698: 9480896412186807790208181588580001688115973056186676199187395200766719214592
1699: 2367206025395954365416553112951759899400560003665135675690512459268257439464
1700: 8316833262490180382424082423145230614096380570070255138770268178516306902551
1701: 3703234053802145019015374029509942262995779647427138157363801729873940704242
1702: 17997226696297993931270693
1703: ? logagm(2)
1704: 0.69314718055994530941723212145817656807550013436025525412068000949339362196
1705: 9694715605863326996418687542001481020570685733685520235758130557032670751635
1706: 0759619307275708283714351903070386238916734711233501153644979552391204751726
1707: 8157493206515552473413952588295045300709532636664265410423915781495204374043
1708: 0385500801944170641671518644712839968171784546957026271631064546150257207402
1709: 4816377733896385506952606683411372738737229289564935470257626520988596932019
1710: 6505855476470330679365443254763274495125040606943814710468994650622016772042
1711: 4524529612687946546193165174681392672504103802546259656869144192871608293803
1712: 1727143677826548775664850856740776484514644399404614226031930967354025744460
1713: 7030809608504748663852313818167675143866747664789088143714198549423151997354
1714: 8803751658612753529166100071053558249879414729509293113897155998205654392871
1715: 7000721808576102523688921324497138932037843935308877482597017155910708823683
1716: 6275898425891853530243634214367061189236789192372314672321720534016492568727
1717: 4778234453534764811494186423867767744060695626573796008670762571991847340226
1718: 5146283790488306203306114463007371948900274364396500258093651944304119115060
1719: 8094879306786515887090060520346842973619384128965255653968602219412292420757
1720: 4321757489097706752687115817051137009158942665478595964890653058460258668382
1721: 9400228330053820740056770530467870018416240441883323279838634900156312188956
1722: 0650553151272199398332030751408426091479001265168243443893572472788205486271
1723: 5527418772430024897945401961872339808608316648114909306675193393128904316413
1724: 7068139777649817697486890388778999129650361927071088926410523092478391737350
1725: 1229842420499568935992206602204654941510613918788574424557751020683703086661
1726: 9480896412186807790208181588580001688115973056186676199187395200766719214592
1727: 2367206025395954365416553112951759899400560003665135675690512459268257439464
1728: 8316833262490180382424082423145230614096380570070255138770268178516306902551
1729: 3703234053802145019015374029509942262995779647427138157363801729873940704242
1730: 17997226696297993931270693
1731: ? \precision=19
1732: realprecision = 19 significant digits
1733: ? bcurve=initell([0,0,0,-3,0])
1734: [0, 0, 0, -3, 0, 0, -6, 0, -9, 144, 0, 1728, 1728, [1.732050807568877293, 0.
1735: E-19, -1.732050807568877293]~, 1.992332899583490707, 1.992332899583490708*I,
1736: -0.7884206134041560682, -2.365261840212468204*I, 3.969390382762759668]
1737: ? localred(bcurve,2)
1738: [6, 2, [1, 1, 1, 0], 1]
1739: ? ccurve=initell([0,0,-1,-1,0])
1740: [0, 0, -1, -1, 0, 0, -2, 1, -1, 48, -216, 37, 110592/37, [0.8375654352833230
1741: 353, 0.2695944364054445582, -1.107159871688767593]~, 2.993458646231959630, 2
1742: .451389381986790061*I, -0.4713192779568114757, -1.435456518668684318*I, 7.33
1743: 8132740789576742]
1744: ? l=lseriesell(ccurve,2,-37,1)
1745: 0.3815754082607112111
1746: ? lseriesell(ccurve,2,-37,1.2)-l
1747: -1.084202172485504434 E-19
1748: ? sbnf=smallbuchinit(x^3-x^2-14*x-1)
1.2 ! noro 1749: [x^3 - x^2 - 14*x - 1, 3, 10889, [1, x, x^2 - x - 9], [-3.233732695981516672
! 1750: , -0.07182350902743636344, 4.305556205008953036], [10889, 5698, 8994; 0, 1,
! 1751: 0; 0, 0, 1], mat(2), mat([1, 1, 0, 1, 1, 0, 1, 1]), [9, 15, 16, 17, 39, 10,
! 1752: 33, 57, 69], [2, [-1, 0, 0]~], [[0, 1, 0]~, [5, 3, 1]~], [-4, -1, 2, 3, 10,
! 1753: 3, 1, 7, 2; 1, 1, 1, 1, 5, 0, 1, 2, 1; 0, 0, 0, 0, 1, 0, 0, 0, -1]]
1.1 noro 1754: ? makebigbnf(sbnf)
1.2 ! noro 1755: [mat(2), mat([1, 1, 0, 1, 1, 0, 1, 1]), [1.173637103435061715 + 3.1415926535
! 1756: 89793238*I, -4.562279014988837952 + 3.141592653589793238*I; -2.6335434327389
1.1 noro 1757: 76049 + 3.141592653589793238*I, 1.420330600779487357 + 3.141592653589793238*
1758: I; 1.459906329303914334, 3.141948414209350543], [1.246346989334819161 + 3.14
1.2 ! noro 1759: 1592653589793238*I, 0.5404006376129469727 + 3.141592653589793238*I, -0.69263
! 1760: 91142471042844 + 3.141592653589793238*I, -1.990056445584799713 + 3.141592653
! 1761: 589793238*I, -0.8305625946607188643 + 3.141592653589793238*I, 0.E-57, 0.0043
! 1762: 75616572659815433 + 3.141592653589793238*I, -1.977791147836553953, 0.3677262
! 1763: 014027817708 + 3.141592653589793238*I; 0.6716827432867392938 + 3.14159265358
! 1764: 9793238*I, -0.8333219883742404170 + 3.141592653589793238*I, -0.2461086674077
! 1765: 943076, 0.5379005671092853269, -1.552661549868775853, 0.E-57, -0.87383180430
! 1766: 71131263, 0.5774919091398324092, 0.9729063188316092380; -1.91802973262155845
! 1767: 5, 0.2929213507612934444, 0.9387477816548985923, 1.452155878475514386, 2.383
! 1768: 224144529494717, 0.E-57, 0.8694561877344533111, 1.400299238696721544, -1.340
! 1769: 632520234391008], [[3, [-1, 1, 0]~, 1, 1, [1, 1, 1]~], [5, [-1, 1, 0]~, 1, 1
! 1770: , [0, 1, 1]~], [5, [2, 1, 0]~, 1, 1, [1, -2, 1]~], [5, [3, 1, 0]~, 1, 1, [2,
! 1771: 2, 1]~], [13, [19, 1, 0]~, 1, 1, [-2, -6, 1]~], [3, [10, 1, 1]~, 1, 2, [-1,
! 1772: 1, 0]~], [11, [1, 1, 0]~, 1, 1, [-3, -1, 1]~], [19, [-6, 1, 0]~, 1, 1, [6,
! 1773: 6, 1]~], [23, [-10, 1, 0]~, 1, 1, [-7, 10, 1]~]]~, 0, [x^3 - x^2 - 14*x - 1,
! 1774: [3, 0], 10889, 1, [[1, -3.233732695981516672, 4.690759845041404811; 1, -0.0
! 1775: 7182350902743636344, -8.923017874523549402; 1, 4.305556205008953036, 5.23225
! 1776: 8029482144592], [1, -3.233732695981516672, 4.690759845041404811; 1, -0.07182
! 1777: 350902743636344, -8.923017874523549402; 1, 4.305556205008953036, 5.232258029
! 1778: 482144592], 0, [3, 1, 1; 1, 29, 8; 1, 8, 129], [10889, 5698, 8994; 0, 1, 0;
! 1779: 0, 0, 1], [3677, -121, -21; -121, 386, -23; -21, -23, 86], [10889, [1899, 51
! 1780: 91, 1]~]], [-3.233732695981516672, -0.07182350902743636344, 4.30555620500895
! 1781: 3036], [1, x, x^2 - x - 9], [1, 0, 9; 0, 1, 1; 0, 0, 1], [1, 0, 0, 0, 9, 1,
! 1782: 0, 1, 44; 0, 1, 0, 1, 1, 5, 0, 5, 1; 0, 0, 1, 0, 1, 0, 1, 0, -4]], [[2, [2],
! 1783: [[3, 2, 0; 0, 1, 0; 0, 0, 1]]], 10.34800724602768011, 1.000000000000000000,
! 1784: [2, -1], [x, x^2 + 2*x - 4], 1000], [mat(1), [[0.E-57, 0.E-57, 0.E-57]], [[
! 1785: 1.246346989334819161 + 3.141592653589793238*I, 0.6716827432867392938 + 3.141
! 1786: 592653589793238*I, -1.918029732621558455]]], [-4, -1, 2, 3, 10, 3, 1, 7, 2;
! 1787: 1, 1, 1, 1, 5, 0, 1, 2, 1; 0, 0, 0, 0, 1, 0, 0, 0, -1]]
1.1 noro 1788: ? concat(mat(vector(4,x,x)~),vector(4,x,10+x)~)
1789:
1790: [1 11]
1791:
1792: [2 12]
1793:
1794: [3 13]
1795:
1796: [4 14]
1797:
1798: ? matextract(matrix(15,15,x,y,x+y),vector(5,x,3*x),vector(3,y,3*y))
1799:
1800: [6 9 12]
1801:
1802: [9 12 15]
1803:
1804: [12 15 18]
1805:
1806: [15 18 21]
1807:
1808: [18 21 24]
1809:
1810: ? ma=mathell(mcurve,mpoints)
1811:
1812: [1.172183098700697010 0.4476973883408951692]
1813:
1814: [0.4476973883408951692 1.755026016172950713]
1815:
1816: ? gauss(ma,mhbi)
1817: [-1.000000000000000000, 1.000000000000000000]~
1818: ? (1.*hilbert(7))^(-1)
1819:
1820: [48.99999999999354616 -1175.999999999759026 8819.999999997789586 -29399.9999
1821: 9999171836 48509.99999998526254 -38807.99999998756766 12011.99999999599856]
1822:
1823: [-1175.999999999756499 37631.99999999093860 -317519.9999999170483 1128959.99
1824: 9999689868 -1940399.999999448886 1596671.999999535762 -504503.9999998507690]
1825:
1826: [8819.999999997745604 -317519.9999999163090 2857679.999999235184 -10583999.9
1827: 9999714478 18710999.99999493212 -15717239.99999573533 5045039.999998630382]
1828:
1829: [-29399.99999999149442 1128959.999999684822 -10583999.99999712372 40319999.9
1830: 9998927448 -72764999.99998098063 62092799.99998400783 -20180159.99999486766]
1831:
1832: [48509.99999998476962 -1940399.999999436456 18710999.99999486299 -72764999.9
1833: 9998086196 133402499.9999660890 -115259759.9999715052 37837799.99999086044]
1834:
1835: [-38807.99999998708779 1596671.999999522805 -15717239.99999565420 62092799.9
1836: 9998382209 -115259759.9999713525 100590335.9999759413 -33297263.99999228701]
1837:
1838: [12011.99999999582671 -504503.9999998459239 5045039.999998597949 -20180159.9
1839: 9999478405 37837799.99999076882 -33297263.99999225112 11099087.99999751679]
1840:
1841: ? matsize([1,2;3,4;5,6])
1842: [3, 2]
1843: ? matrix(5,5,x,y,gcd(x,y))
1844:
1845: [1 1 1 1 1]
1846:
1847: [1 2 1 2 1]
1848:
1849: [1 1 3 1 1]
1850:
1851: [1 2 1 4 1]
1852:
1853: [1 1 1 1 5]
1854:
1855: ? matrixqz([1,3;3,5;5,7],0)
1856:
1857: [1 1]
1858:
1859: [3 2]
1860:
1861: [5 3]
1862:
1863: ? matrixqz2([1/3,1/4,1/6;1/2,1/4,-1/4;1/3,1,0])
1864:
1865: [19 12 2]
1866:
1867: [0 1 0]
1868:
1869: [0 0 1]
1870:
1871: ? matrixqz3([1,3;3,5;5,7])
1872:
1873: [2 -1]
1874:
1875: [1 0]
1876:
1877: [0 1]
1878:
1879: ? max(2,3)
1880: 3
1881: ? min(2,3)
1882: 2
1883: ? minim([2,1;1,2],4,6)
1884: [6, 2, [0, -1, 1; 1, 1, 0]]
1885: ? mod(-12,7)
1886: mod(2, 7)
1887: ? modp(-12,7)
1888: mod(2, 7)
1889: ? mod(10873,49649)^-1
1890: *** impossible inverse modulo: mod(131, 49649).
1891: ? modreverse(mod(x^2+1,x^3-x-1))
1892: mod(x^2 - 3*x + 2, x^3 - 5*x^2 + 8*x - 5)
1893: ? move(0,243,583);cursor(0)
1894: ? mu(3*5*7*11*13)
1895: -1
1896: ? newtonpoly(x^4+3*x^3+27*x^2+9*x+81,3)
1897: [2, 2/3, 2/3, 2/3]
1898: ? nextprime(100000000000000000000000)
1899: 100000000000000000000117
1900: ? setrand(1);a=matrix(3,5,j,k,vvector(5,l,random()\10^8))
1901:
1902: [[10, 7, 8, 7, 18]~ [17, 0, 9, 20, 10]~ [5, 4, 7, 18, 20]~ [0, 16, 4, 2, 0]~
1903: [17, 19, 17, 1, 14]~]
1904:
1905: [[17, 16, 6, 3, 6]~ [17, 13, 9, 19, 6]~ [1, 14, 12, 20, 8]~ [6, 1, 8, 17, 21
1906: ]~ [18, 17, 9, 10, 13]~]
1907:
1908: [[4, 13, 3, 17, 14]~ [14, 16, 11, 5, 4]~ [9, 11, 13, 7, 15]~ [19, 21, 2, 4,
1909: 5]~ [14, 16, 6, 20, 14]~]
1910:
1911: ? aid=[idx,idy,idz,idmat(5),idx]
1.2 ! noro 1912: [[3, 2, 1, 0, 1; 0, 1, 0, 0, 0; 0, 0, 1, 0, 0; 0, 0, 0, 1, 0; 0, 0, 0, 0, 1]
! 1913: , [5, 0, 0, 0, 2; 0, 5, 0, 0, 2; 0, 0, 5, 0, 1; 0, 0, 0, 5, 2; 0, 0, 0, 0, 1
! 1914: ], [15, 10, 5, 0, 12; 0, 5, 0, 0, 2; 0, 0, 5, 0, 1; 0, 0, 0, 5, 2; 0, 0, 0,
! 1915: 0, 1], [1, 0, 0, 0, 0; 0, 1, 0, 0, 0; 0, 0, 1, 0, 0; 0, 0, 0, 1, 0; 0, 0, 0,
! 1916: 0, 1], [3, 2, 1, 0, 1; 0, 1, 0, 0, 0; 0, 0, 1, 0, 0; 0, 0, 0, 1, 0; 0, 0, 0
! 1917: , 0, 1]]
1.1 noro 1918: ? bb=algtobasis(nf,mod(x^3+x,nfpol))
1.2 ! noro 1919: [1, 1, 4, 1, 3]~
1.1 noro 1920: ? da=nfdetint(nf,[a,aid])
1921:
1.2 ! noro 1922: [90 70 35 0 65]
1.1 noro 1923:
1924: [0 5 0 0 0]
1925:
1.2 ! noro 1926: [0 0 5 0 0]
1.1 noro 1927:
1.2 ! noro 1928: [0 0 0 5 0]
1.1 noro 1929:
1930: [0 0 0 0 5]
1931:
1932: ? nfdiv(nf,ba,bb)
1.2 ! noro 1933: [584/373, 66/373, -32/373, -105/373, 120/373]~
1.1 noro 1934: ? nfdiveuc(nf,ba,bb)
1.2 ! noro 1935: [2, 0, 0, 0, 0]~
1.1 noro 1936: ? nfdivres(nf,ba,bb)
1.2 ! noro 1937: [[2, 0, 0, 0, 0]~, [4, -1, -5, -1, -3]~]
1.1 noro 1938: ? nfhermite(nf,[a,aid])
1.2 ! noro 1939: [[[1, 0, 0, 0, 0]~, [-2, 0, 0, 0, 0]~, [0, 0, 0, 0, 0]~; [0, 0, 0, 0, 0]~, [
! 1940: 1, 0, 0, 0, 0]~, [0, 0, 0, 0, 0]~; [0, 0, 0, 0, 0]~, [0, 0, 0, 0, 0]~, [1, 0
! 1941: , 0, 0, 0]~], [[10, 4, 5, 6, 7; 0, 1, 0, 0, 0; 0, 0, 1, 0, 0; 0, 0, 0, 1, 0;
! 1942: 0, 0, 0, 0, 1], [1, 0, 0, 0, 0; 0, 1, 0, 0, 0; 0, 0, 1, 0, 0; 0, 0, 0, 1, 0
! 1943: ; 0, 0, 0, 0, 1], [3, 2, 1, 0, 1; 0, 1, 0, 0, 0; 0, 0, 1, 0, 0; 0, 0, 0, 1,
! 1944: 0; 0, 0, 0, 0, 1]]]
1.1 noro 1945: ? nfhermitemod(nf,[a,aid],da)
1.2 ! noro 1946: [[[1, 0, 0, 0, 0]~, [-2, 0, 0, 0, 0]~, [0, 0, 0, 0, 0]~; [0, 0, 0, 0, 0]~, [
! 1947: 1, 0, 0, 0, 0]~, [0, 0, 0, 0, 0]~; [0, 0, 0, 0, 0]~, [0, 0, 0, 0, 0]~, [1, 0
! 1948: , 0, 0, 0]~], [[10, 4, 5, 6, 7; 0, 1, 0, 0, 0; 0, 0, 1, 0, 0; 0, 0, 0, 1, 0;
! 1949: 0, 0, 0, 0, 1], [1, 0, 0, 0, 0; 0, 1, 0, 0, 0; 0, 0, 1, 0, 0; 0, 0, 0, 1, 0
! 1950: ; 0, 0, 0, 0, 1], [3, 2, 1, 0, 1; 0, 1, 0, 0, 0; 0, 0, 1, 0, 0; 0, 0, 0, 1,
! 1951: 0; 0, 0, 0, 0, 1]]]
1.1 noro 1952: ? nfmod(nf,ba,bb)
1.2 ! noro 1953: [4, -1, -5, -1, -3]~
1.1 noro 1954: ? nfmul(nf,ba,bb)
1.2 ! noro 1955: [50, -15, -35, 60, 15]~
1.1 noro 1956: ? nfpow(nf,bb,5)
1.2 ! noro 1957: [-291920, 136855, 230560, -178520, 74190]~
1.1 noro 1958: ? nfreduce(nf,ba,idx)
1959: [1, 0, 0, 0, 0]~
1960: ? setrand(1);as=matrix(3,3,j,k,vvector(5,l,random()\10^8))
1961:
1962: [[10, 7, 8, 7, 18]~ [17, 0, 9, 20, 10]~ [5, 4, 7, 18, 20]~]
1963:
1964: [[17, 16, 6, 3, 6]~ [17, 13, 9, 19, 6]~ [1, 14, 12, 20, 8]~]
1965:
1966: [[4, 13, 3, 17, 14]~ [14, 16, 11, 5, 4]~ [9, 11, 13, 7, 15]~]
1967:
1968: ? vaid=[idx,idy,idmat(5)]
1.2 ! noro 1969: [[3, 2, 1, 0, 1; 0, 1, 0, 0, 0; 0, 0, 1, 0, 0; 0, 0, 0, 1, 0; 0, 0, 0, 0, 1]
! 1970: , [5, 0, 0, 0, 2; 0, 5, 0, 0, 2; 0, 0, 5, 0, 1; 0, 0, 0, 5, 2; 0, 0, 0, 0, 1
1.1 noro 1971: ], [1, 0, 0, 0, 0; 0, 1, 0, 0, 0; 0, 0, 1, 0, 0; 0, 0, 0, 1, 0; 0, 0, 0, 0,
1972: 1]]
1973: ? haid=[idmat(5),idmat(5),idmat(5)]
1974: [[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]
1975: , [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
1976: ], [1, 0, 0, 0, 0; 0, 1, 0, 0, 0; 0, 0, 1, 0, 0; 0, 0, 0, 1, 0; 0, 0, 0, 0,
1977: 1]]
1978: ? nfsmith(nf,[as,haid,vaid])
1.2 ! noro 1979: [[2562748315629757085585610, 436545976069778274371140, 123799938628701108220
! 1980: 1405, 2356446991473627724963350, 801407102592194537169612; 0, 5, 0, 0, 2; 0,
! 1981: 0, 5, 0, 1; 0, 0, 0, 5, 2; 0, 0, 0, 0, 1], [1, 0, 0, 0, 0; 0, 1, 0, 0, 0; 0
! 1982: , 0, 1, 0, 0; 0, 0, 0, 1, 0; 0, 0, 0, 0, 1], [1, 0, 0, 0, 0; 0, 1, 0, 0, 0;
! 1983: 0, 0, 1, 0, 0; 0, 0, 0, 1, 0; 0, 0, 0, 0, 1]]
1.1 noro 1984: ? nfval(nf,ba,vp)
1985: 0
1986: ? norm(1+i)
1987: 2
1988: ? norm(mod(x+5,x^3+x+1))
1989: 129
1990: ? norml2(vector(10,x,x))
1991: 385
1992: ? nucomp(qfi(2,1,9),qfi(4,3,5),3)
1993: qfi(2, -1, 9)
1994: ? form=qfi(2,1,9);nucomp(form,form,3)
1995: qfi(4, -3, 5)
1996: ? numdiv(2^99*3^49)
1997: 5000
1998: ? numer((x+1)/(x-1))
1999: x + 1
2000: ? nupow(form,111)
2001: qfi(2, -1, 9)
2002: ? 1/(1+x)+o(x^20)
2003: 1 - x + x^2 - x^3 + x^4 - x^5 + x^6 - x^7 + x^8 - x^9 + x^10 - x^11 + x^12 -
2004: x^13 + x^14 - x^15 + x^16 - x^17 + x^18 - x^19 + O(x^20)
2005: ? omega(100!)
2006: 25
2007: ? ordell(acurve,1)
2008: [8, 3]
2009: ? order(mod(33,2^16+1))
2010: 2048
2011: ? tcurve=initell([1,0,1,-19,26]);
2012: ? orderell(tcurve,[1,2])
2013: 6
2014: ? ordred(x^3-12*x+45*x-1)
2015: [x - 1, x^3 - 363*x - 2663, x^3 + 33*x - 1]
2016: ? padicprec(padicno,127)
2017: 5
2018: ? pascal(8)
2019:
2020: [1 0 0 0 0 0 0 0 0]
2021:
2022: [1 1 0 0 0 0 0 0 0]
2023:
2024: [1 2 1 0 0 0 0 0 0]
2025:
2026: [1 3 3 1 0 0 0 0 0]
2027:
2028: [1 4 6 4 1 0 0 0 0]
2029:
2030: [1 5 10 10 5 1 0 0 0]
2031:
2032: [1 6 15 20 15 6 1 0 0]
2033:
2034: [1 7 21 35 35 21 7 1 0]
2035:
2036: [1 8 28 56 70 56 28 8 1]
2037:
2038: ? perf([2,0,1;0,2,1;1,1,2])
2039: 6
2040: ? permutation(7,1035)
2041: [4, 7, 1, 6, 3, 5, 2]
2042: ? permutation2num([4,7,1,6,3,5,2])
2043: 1035
2044: ? pf(-44,3)
2045: qfi(3, 2, 4)
2046: ? phi(257^2)
2047: 65792
2048: ? pi
2049: 3.141592653589793238
2050: ? plot(x=-5,5,sin(x))
2051:
2052: 0.9995545 x""x_''''''''''''''''''''''''''''''''''_x""x'''''''''''''''''''|
2053: | x _ "_ |
2054: | x _ _ |
2055: | x _ |
2056: | _ " |
2057: | " x |
2058: | x _ |
2059: | " |
2060: | " x _ |
2061: | _ |
2062: | " x |
2063: ````````````x``````````````````_````````````````````````````````
2064: | " |
2065: | " x _ |
2066: | _ |
2067: | " x |
2068: | x _ |
2069: | _ " |
2070: | " x |
2071: | " " x |
2072: | "_ " x |
2073: -0.999555 |...................x__x".................................."x__x
2074: -5 5
2075: ? pnqn([2,6,10,14,18,22,26])
2076:
2077: [19318376 741721]
2078:
2079: [8927353 342762]
2080:
2081: ? pnqn([1,1,1,1,1,1,1,1;1,1,1,1,1,1,1,1])
2082:
2083: [34 21]
2084:
2085: [21 13]
2086:
2087: ? point(0,225,334)
2088: ? points(0,vector(10,k,10*k),vector(10,k,5*k*k))
2089: ? pointell(acurve,zell(acurve,apoint))
2090: [0.9999999999999999986 + 0.E-19*I, 2.999999999999999998 + 0.E-18*I]
2091: ? polint([0,2,3],[0,4,9],5)
2092: 25
2093: ? polred(x^5-2*x^4-4*x^3-96*x^2-352*x-568)
2094: [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
2095: - 1, x^5 - x^4 + 4*x^3 - 2*x^2 + x - 1, x^5 + 4*x^3 - 4*x^2 + 8*x - 8]
2096: ? polred2(x^4-28*x^3-458*x^2+9156*x-25321)
2097:
2098: [1 x - 1]
2099:
2100: [1/115*x^2 - 14/115*x - 327/115 x^2 - 10]
2101:
2102: [3/1495*x^3 - 63/1495*x^2 - 1607/1495*x + 13307/1495 x^4 - 32*x^2 + 216]
2103:
2104: [1/4485*x^3 - 7/1495*x^2 - 1034/4485*x + 7924/4485 x^4 - 8*x^2 + 6]
2105:
2106: ? polredabs(x^5-2*x^4-4*x^3-96*x^2-352*x-568)
2107: x^5 - x^4 + 2*x^3 - 4*x^2 + x - 1
2108: ? polredabs2(x^5-2*x^4-4*x^3-96*x^2-352*x-568)
2109: [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 -
2110: x^4 + 2*x^3 - 4*x^2 + x - 1)]
2111: ? polsym(x^17-1,17)
2112: [17, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 17]~
2113: ? polvar(name^4-other)
2114: name
2115: ? poly(sin(x),x)
2116: -1/1307674368000*x^15 + 1/6227020800*x^13 - 1/39916800*x^11 + 1/362880*x^9 -
2117: 1/5040*x^7 + 1/120*x^5 - 1/6*x^3 + x
2118: ? polylog(5,0.5)
2119: 0.5084005792422687065
2120: ? polylog(-4,t)
2121: (t^4 + 11*t^3 + 11*t^2 + t)/(-t^5 + 5*t^4 - 10*t^3 + 10*t^2 - 5*t + 1)
2122: ? polylogd(5,0.5)
2123: 1.033792745541689061
2124: ? polylogdold(5,0.5)
2125: 1.034459423449010483
2126: ? polylogp(5,0.5)
2127: 0.9495693489964922581
2128: ? poly([1,2,3,4,5],x)
2129: x^4 + 2*x^3 + 3*x^2 + 4*x + 5
2130: ? polyrev([1,2,3,4,5],x)
2131: 5*x^4 + 4*x^3 + 3*x^2 + 2*x + 1
2132: ? polzag(6,3)
2133: 4608*x^6 - 13824*x^5 + 46144/3*x^4 - 23168/3*x^3 + 5032/3*x^2 - 120*x + 1
2134: ? postdraw([0,20,20])
2135: ? postploth(x=-5,5,sin(x))
2136: [-5.000000000000000000, 5.000000000000000000, -0.9999964107564721649, 0.9999
2137: 964107564721649]
2138: ? postploth2(t=0,2*pi,[sin(5*t),sin(7*t)])
2139: [-0.9999994509568810308, 0.9999994509568810308, -0.9999994509568810308, 0.99
2140: 99994509568810308]
2141: ? postplothraw(vector(100,k,k),vector(100,k,k*k/100))
2142: [1.000000000000000000, 100.0000000000000000, 0.01000000000000000020, 100.000
2143: 0000000000000]
2144: ? powell(acurve,apoint,10)
2145: [-28919032218753260057646013785951999/292736325329248127651484680640160000,
2146: 478051489392386968218136375373985436596569736643531551/158385319626308443937
2147: 475969221994173751192384064000000]
2148: ? cmcurve=initell([0,-3/4,0,-2,-1])
2149: [0, -3/4, 0, -2, -1, -3, -4, -4, -1, 105, 1323, -343, -3375, [2.000000000000
2150: 000000, -0.6249999999999999999 + 0.3307189138830738238*I, -0.624999999999999
2151: 9999 - 0.3307189138830738238*I]~, 1.933311705616811546, 0.966655852808405773
2152: 3 + 2.557530989916099474*I, -0.8558486330998558525 - 4.598829819117624524 E-
2153: 20*I, -0.4279243165499279261 - 2.757161217166147204*I, 4.944504600282546727]
2154: ? powell(cmcurve,[x,y],quadgen(-7))
2155: [((-2 + 3*w)*x^2 + (6 - w))/((-2 - 5*w)*x + (-4 - 2*w)), ((34 - 11*w)*x^3 +
2156: (40 - 28*w)*x^2 + (22 + 23*w)*x)/((-90 - w)*x^2 + (-136 + 44*w)*x + (-40 + 2
2157: 8*w))]
2158: ? powrealraw(qfr(5,3,-1,0.),3)
2159: qfr(125, 23, 1, 0.E-18)
2160: ? pprint((x-12*y)/(y+13*x));
2161: (-(11 /14))
2162: ? pprint([1,2;3,4])
2163:
2164: [1 2]
2165:
2166: [3 4]
2167:
2168: ? pprint1(x+y);pprint(x+y);
2169: (2 x)(2 x)
2170: ? \precision=96
2171: realprecision = 96 significant digits
2172: ? pi
2173: 3.14159265358979323846264338327950288419716939937510582097494459230781640628
2174: 620899862803482534211
2175: ? prec(pi,20)
2176: 3.1415926535897932384626433832795028841
2177: ? precision(cmcurve)
2178: 19
2179: ? \precision=38
2180: realprecision = 38 significant digits
2181: ? prime(100)
2182: 541
2183: ? primedec(nf,2)
1.2 ! noro 2184: [[2, [3, 0, 1, 0, 0]~, 1, 1, [0, 0, 0, 1, 1]~], [2, [12, -4, -2, 11, 3]~, 1,
! 2185: 4, [1, 0, 1, 0, 0]~]]
1.1 noro 2186: ? primedec(nf,3)
1.2 ! noro 2187: [[3, [1, 0, 1, 0, 0]~, 1, 1, [1, -1, -1, -1, 0]~], [3, [-1, -1, -1, 0, 0]~,
! 2188: 2, 2, [0, 2, 2, 1, 0]~]]
1.1 noro 2189: ? primedec(nf,11)
2190: [[11, [11, 0, 0, 0, 0]~, 1, 5, [1, 0, 0, 0, 0]~]]
2191: ? primes(100)
2192: [2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71,
2193: 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151,
2194: 157, 163, 167, 173, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229, 233, 2
2195: 39, 241, 251, 257, 263, 269, 271, 277, 281, 283, 293, 307, 311, 313, 317, 33
2196: 1, 337, 347, 349, 353, 359, 367, 373, 379, 383, 389, 397, 401, 409, 419, 421
2197: , 431, 433, 439, 443, 449, 457, 461, 463, 467, 479, 487, 491, 499, 503, 509,
2198: 521, 523, 541]
2199: ? forprime(p=2,100,print(p," ",lift(primroot(p))))
2200: 2 1
2201: 3 2
2202: 5 2
2203: 7 3
2204: 11 2
2205: 13 2
2206: 17 3
2207: 19 2
2208: 23 5
2209: 29 2
2210: 31 3
2211: 37 2
2212: 41 6
2213: 43 3
2214: 47 5
2215: 53 2
2216: 59 2
2217: 61 2
2218: 67 2
2219: 71 7
2220: 73 5
2221: 79 3
2222: 83 2
2223: 89 3
2224: 97 5
2225: ? principalideal(nf,mod(x^3+5,nfpol))
2226:
2227: [6]
2228:
1.2 ! noro 2229: [1]
! 2230:
! 2231: [3]
1.1 noro 2232:
2233: [1]
2234:
2235: [3]
2236:
2237: ? principalidele(nf,mod(x^3+5,nfpol))
1.2 ! noro 2238: [[6; 1; 3; 1; 3], [2.2324480827796254080981385584384939684 + 3.1415926535897
! 2239: 932384626433832795028841*I, 5.0387659675158716386435353106610489968 + 1.5851
1.1 noro 2240: 760343512250049897278861965702423*I, 4.2664040272651028743625910797589683173
1.2 ! noro 2241: - 0.0083630478144368246110910258645462996225*I]]
1.1 noro 2242: ? print((x-12*y)/(y+13*x));
2243: -11/14
2244: ? print([1,2;3,4])
2245: [1, 2; 3, 4]
2246: ? print1(x+y);print1(" equals ");print(x+y);
2247: 2*x equals 2*x
2248: ? prod(1,k=1,10,1+1/k!)
2249: 3335784368058308553334783/905932868585678438400000
2250: ? prod(1.,k=1,10,1+1/k!)
2251: 3.6821540356142043935732308433185262945
2252: ? pi^2/6*prodeuler(p=2,10000,1-p^-2)
1.2 ! noro 2253: 1.0000098157493066238697591433298145166
1.1 noro 2254: ? prodinf(n=0,(1+2^-n)/(1+2^(-n+1)))
1.2 ! noro 2255: 0.33333333333333333333333333333333333313
1.1 noro 2256: ? prodinf1(n=0,-2^-n/(1+2^(-n+1)))
1.2 ! noro 2257: 0.33333333333333333333333333333333333313
1.1 noro 2258: ? psi(1)
1.2 ! noro 2259: -0.57721566490153286060651209008240243104
1.1 noro 2260: ? quaddisc(-252)
2261: -7
2262: ? quadgen(-11)
2263: w
2264: ? quadpoly(-11)
2265: x^2 - x + 3
2266: ? rank(matrix(5,5,x,y,x+y))
2267: 2
1.2 ! noro 2268: ? rayclassno(bnf,[[5,4;0,1],[1,0]])
1.1 noro 2269: 12
2270: ? rayclassnolist(bnf,lu)
2271: [[3], [], [3, 3], [3], [6, 6], [], [], [], [3, 3, 3], [], [3, 3], [3, 3], []
2272: , [], [12, 6, 6, 12], [3], [3, 3], [], [9, 9], [6, 6], [], [], [], [], [6, 1
2273: 2, 6], [], [3, 3, 3, 3], [], [], [], [], [], [3, 6, 6, 3], [], [], [9, 3, 9]
2274: , [6, 6], [], [], [], [], [], [3, 3], [3, 3], [12, 12, 6, 6, 12, 12], [], []
2275: , [6, 6], [9], [], [3, 3, 3, 3], [], [3, 3], [], [6, 12, 12, 6]]
2276: ? move(0,50,50);rbox(0,50,50)
2277: ? print1("give a value for s? ");s=read();print(1/s)
2278: give a value for s? 37.
2279: 0.027027027027027027027027027027027027026
2280: ? real(5-7*i)
2281: 5
2282: ? recip(3*x^7-5*x^3+6*x-9)
2283: -9*x^7 + 6*x^6 - 5*x^4 + 3
2284: ? redimag(qfi(3,10,12))
2285: qfi(3, -2, 4)
2286: ? redreal(qfr(3,10,-20,1.5))
2287: qfr(3, 16, -7, 1.5000000000000000000000000000000000000)
2288: ? redrealnod(qfr(3,10,-20,1.5),18)
2289: qfr(3, 16, -7, 1.5000000000000000000000000000000000000)
2290: ? reduceddisc(x^3+4*x+12)
2291: [1036, 4, 1]
2292: ? regula(17)
2293: 2.0947125472611012942448228460655286534
2294: ? kill(y);print(x+y);reorder([x,y]);print(x+y);
2295: x + y
2296: x + y
2297: ? resultant(x^3-1,x^3+1)
2298: 8
2299: ? resultant2(x^3-1.,x^3+1.)
2300: 8.0000000000000000000000000000000000000
2301: ? reverse(tan(x))
2302: 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
2303: 5 + O(x^16)
2304: ? rhoreal(qfr(3,10,-20,1.5))
2305: qfr(-20, -10, 3, 2.1074451073987839947135880252731470615)
2306: ? rhorealnod(qfr(3,10,-20,1.5),18)
2307: qfr(-20, -10, 3, 1.5000000000000000000000000000000000000)
2308: ? rline(0,200,150)
2309: ? cursor(0)
2310: ? rmove(0,5,5);cursor(0)
2311: ? rndtoi(prod(1,k=1,17,x-exp(2*i*pi*k/17)))
2312: x^17 - 1
2313: ? qpol=y^3-y-1;setrand(1);bnf2=buchinit(qpol);nf2=bnf2[7];
2314: ? un=mod(1,qpol);w=mod(y,qpol);p=un*(x^5-5*x+w)
2315: mod(1, y^3 - y - 1)*x^5 + mod(-5, y^3 - y - 1)*x + mod(y, y^3 - y - 1)
2316: ? aa=rnfpseudobasis(nf2,p)
2317: [[[1, 0, 0]~, [0, 0, 0]~, [0, 0, 0]~, [-2, 0, 0]~, [11, 0, 0]~; [0, 0, 0]~,
2318: [1, 0, 0]~, [0, 0, 0]~, [2, 0, 0]~, [-8, 0, 0]~; [0, 0, 0]~, [0, 0, 0]~, [1,
2319: 0, 0]~, [1, 0, 0]~, [4, 0, 0]~; [0, 0, 0]~, [0, 0, 0]~, [0, 0, 0]~, [1, 0,
2320: 0]~, [-2, 0, 0]~; [0, 0, 0]~, [0, 0, 0]~, [0, 0, 0]~, [0, 0, 0]~, [1, 0, 0]~
2321: ], [[1, 0, 0; 0, 1, 0; 0, 0, 1], [1, 0, 0; 0, 1, 0; 0, 0, 1], [1, 0, 0; 0, 1
1.2 ! noro 2322: , 0; 0, 0, 1], [1, 0, 2/5; 0, 1, 3/5; 0, 0, 1/5], [1, 0, 22/25; 0, 1, 8/25;
! 2323: 0, 0, 1/25]], [416134375, 202396875, 60056800; 0, 3125, 2700; 0, 0, 25], [-1
! 2324: 275, 5, 5]~]
1.1 noro 2325: ? rnfbasis(bnf2,aa)
2326:
1.2 ! noro 2327: [[1, 0, 0]~ [0, 0, 0]~ [0, 0, 0]~ [-6/25, 66/25, 77/25]~ [-391/25, -699/25,
! 2328: 197/25]~]
1.1 noro 2329:
1.2 ! noro 2330: [[0, 0, 0]~ [1, 0, 0]~ [0, 0, 0]~ [18/25, -48/25, -56/25]~ [268/25, 552/25,
! 2331: -206/25]~]
1.1 noro 2332:
1.2 ! noro 2333: [[0, 0, 0]~ [0, 0, 0]~ [1, 0, 0]~ [41/25, 24/25, 28/25]~ [-194/25, -116/25,
! 2334: -127/25]~]
1.1 noro 2335:
1.2 ! noro 2336: [[0, 0, 0]~ [0, 0, 0]~ [0, 0, 0]~ [17/25, -12/25, -14/25]~ [52/25, 178/25, -
! 2337: 109/25]~]
1.1 noro 2338:
1.2 ! noro 2339: [[0, 0, 0]~ [0, 0, 0]~ [0, 0, 0]~ [4/25, 6/25, 7/25]~ [-41/25, -49/25, -3/25
! 2340: ]~]
1.1 noro 2341:
2342: ? rnfdiscf(nf2,p)
1.2 ! noro 2343: [[416134375, 202396875, 60056800; 0, 3125, 2700; 0, 0, 25], [-1275, 5, 5]~]
1.1 noro 2344: ? rnfequation(nf2,p)
2345: x^15 - 15*x^11 + 75*x^7 - x^5 - 125*x^3 + 5*x + 1
2346: ? rnfequation2(nf2,p)
2347: [x^15 - 15*x^11 + 75*x^7 - x^5 - 125*x^3 + 5*x + 1, mod(-x^5 + 5*x, x^15 - 1
2348: 5*x^11 + 75*x^7 - x^5 - 125*x^3 + 5*x + 1), 0]
2349: ? rnfhermitebasis(bnf2,aa)
2350:
1.2 ! noro 2351: [[1, 0, 0]~ [0, 0, 0]~ [0, 0, 0]~ [6/5, 4/5, -2/5]~ [-22/25, -33/25, 99/25]~
1.1 noro 2352: ]
2353:
1.2 ! noro 2354: [[0, 0, 0]~ [1, 0, 0]~ [0, 0, 0]~ [-6/5, -4/5, 2/5]~ [16/25, 24/25, -72/25]~
! 2355: ]
1.1 noro 2356:
1.2 ! noro 2357: [[0, 0, 0]~ [0, 0, 0]~ [1, 0, 0]~ [-3/5, -2/5, 1/5]~ [-8/25, -12/25, 36/25]~
! 2358: ]
1.1 noro 2359:
1.2 ! noro 2360: [[0, 0, 0]~ [0, 0, 0]~ [0, 0, 0]~ [-3/5, -2/5, 1/5]~ [4/25, 6/25, -18/25]~]
1.1 noro 2361:
1.2 ! noro 2362: [[0, 0, 0]~ [0, 0, 0]~ [0, 0, 0]~ [0, 0, 0]~ [-2/25, -3/25, 9/25]~]
1.1 noro 2363:
2364: ? rnfisfree(bnf2,aa)
2365: 1
2366: ? rnfsteinitz(nf2,aa)
1.2 ! noro 2367: [[[1, 0, 0]~, [0, 0, 0]~, [0, 0, 0]~, [-6/25, 66/25, 77/25]~, [17/125, -66/1
! 2368: 25, -77/125]~; [0, 0, 0]~, [1, 0, 0]~, [0, 0, 0]~, [18/25, -48/25, -56/25]~,
! 2369: [-26/125, 48/125, 56/125]~; [0, 0, 0]~, [0, 0, 0]~, [1, 0, 0]~, [41/25, 24/
! 2370: 25, 28/25]~, [-37/125, -24/125, -28/125]~; [0, 0, 0]~, [0, 0, 0]~, [0, 0, 0]
! 2371: ~, [17/25, -12/25, -14/25]~, [-19/125, 12/125, 14/125]~; [0, 0, 0]~, [0, 0,
! 2372: 0]~, [0, 0, 0]~, [4/25, 6/25, 7/25]~, [-3/125, -6/125, -7/125]~], [[1, 0, 0;
! 2373: 0, 1, 0; 0, 0, 1], [1, 0, 0; 0, 1, 0; 0, 0, 1], [1, 0, 0; 0, 1, 0; 0, 0, 1]
! 2374: , [1, 0, 0; 0, 1, 0; 0, 0, 1], [125, 0, 22; 0, 125, 108; 0, 0, 1]], [4161343
! 2375: 75, 202396875, 60056800; 0, 3125, 2700; 0, 0, 25], [-1275, 5, 5]~]
1.1 noro 2376: ? rootmod(x^16-1,41)
2377: [mod(1, 41), mod(3, 41), mod(9, 41), mod(14, 41), mod(27, 41), mod(32, 41),
2378: mod(38, 41), mod(40, 41)]~
2379: ? rootpadic(x^4+1,41,6)
2380: [3 + 22*41 + 27*41^2 + 15*41^3 + 27*41^4 + 33*41^5 + O(41^6), 14 + 20*41 + 2
2381: 5*41^2 + 24*41^3 + 4*41^4 + 18*41^5 + O(41^6), 27 + 20*41 + 15*41^2 + 16*41^
2382: 3 + 36*41^4 + 22*41^5 + O(41^6), 38 + 18*41 + 13*41^2 + 25*41^3 + 13*41^4 +
2383: 7*41^5 + O(41^6)]~
2384: ? roots(x^5-5*x^2-5*x-5)
2385: [2.0509134529831982130058170163696514536 + 0.E-38*I, -0.67063790319207539268
2386: 663382582902335603 + 0.84813118358634026680538906224199030917*I, -0.67063790
2387: 319207539268663382582902335603 - 0.84813118358634026680538906224199030917*I,
2388: -0.35481882329952371381627468235580237077 + 1.39980287391035466982975228340
2389: 62081964*I, -0.35481882329952371381627468235580237077 - 1.399802873910354669
2390: 8297522834062081964*I]~
2391: ? rootsold(x^4-1000000000000000000000)
2392: [-177827.94100389228012254211951926848447 + 0.E-38*I, 177827.941003892280122
1.2 ! noro 2393: 54211951926848447 + 0.E-38*I, 3.3589380537835443758954827944751135647 E-139
! 2394: + 177827.94100389228012254211951926848447*I, 3.35893805378354437589548279447
! 2395: 51135647 E-139 - 177827.94100389228012254211951926848447*I]~
1.1 noro 2396: ? round(prod(1,k=1,17,x-exp(2*i*pi*k/17)))
2397: x^17 - 1
2398: ? rounderror(prod(1,k=1,17,x-exp(2*i*pi*k/17)))
2399: -35
2400: ? rpoint(0,20,20)
2401: ? initrect(3,600,600);scale(3,-7,7,-2,2);cursor(3)
2402: ? q*series(anell(acurve,100),q)
2403: 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 -
2404: 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*
2405: 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
2406: + 8*q^32 + 15*q^33 + 2*q^35 + 12*q^36 - q^37 + 6*q^39 - 9*q^41 - 6*q^42 + 2*
2407: 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
2408: ^52 + q^53 + 18*q^54 + 10*q^55 - 12*q^58 + 8*q^59 + 12*q^60 - 8*q^61 + 8*q^6
2409: 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 -
2410: 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
2411: ^82 - 15*q^83 + 6*q^84 - 4*q^86 - 18*q^87 + 4*q^89 + 24*q^90 + 2*q^91 + 4*q^
2412: 92 + 12*q^93 + 18*q^94 - 24*q^96 + 4*q^97 + 12*q^98 - 30*q^99 - 2*q^100 + O(
2413: q^101)
2414: ? aset=set([5,-2,7,3,5,1])
2415: ["-2", "1", "3", "5", "7"]
2416: ? bset=set([7,5,-5,7,2])
2417: ["-5", "2", "5", "7"]
2418: ? setintersect(aset,bset)
2419: ["5", "7"]
2420: ? setminus(aset,bset)
2421: ["-2", "1", "3"]
2422: ? setprecision(28)
2423: 38
2424: ? setrand(10)
2425: 10
2426: ? setsearch(aset,3)
2427: 3
2428: ? setsearch(bset,3)
2429: 0
2430: ? setserieslength(12)
2431: 16
2432: ? setunion(aset,bset)
2433: ["-2", "-5", "1", "2", "3", "5", "7"]
2434: ? arat=(x^3+x+1)/x^3;settype(arat,14)
2435: (x^3 + x + 1)/x^3
2436: ? shift(1,50)
2437: 1125899906842624
2438: ? shift([3,4,-11,-12],-2)
2439: [0, 1, -2, -3]
2440: ? shiftmul([3,4,-11,-12],-2)
2441: [3/4, 1, -11/4, -3]
2442: ? sigma(100)
2443: 217
2444: ? sigmak(2,100)
2445: 13671
2446: ? sigmak(-3,100)
2447: 1149823/1000000
2448: ? sign(-1)
2449: -1
2450: ? sign(0)
2451: 0
2452: ? sign(0.)
2453: 0
2454: ? signat(hilbert(5)-0.11*idmat(5))
2455: [2, 3]
2456: ? signunit(bnf)
2457:
2458: [-1]
2459:
2460: [1]
2461:
2462: ? simplefactmod(x^11+1,7)
2463:
2464: [1 1]
2465:
2466: [10 1]
2467:
2468: ? simplify(((x+i+1)^2-x^2-2*x*(i+1))^2)
2469: -4
2470: ? sin(pi/6)
2471: 0.5000000000000000000000000000
2472: ? sinh(1)
2473: 1.175201193643801456882381850
2474: ? size([1.3*10^5,2*i*pi*exp(4*pi)])
2475: 7
2476: ? smallbasis(x^3+4*x+12)
2477: [1, x, 1/2*x^2]
2478: ? smalldiscf(x^3+4*x+12)
2479: -1036
2480: ? smallfact(100!+1)
2481:
2482: [101 1]
2483:
2484: [14303 1]
2485:
2486: [149239 1]
2487:
2488: [432885273849892962613071800918658949059679308685024481795740765527568493010
2489: 727023757461397498800981521440877813288657839195622497225621499427628453 1]
2490:
2491: ? smallinitell([0,0,0,-17,0])
2492: [0, 0, 0, -17, 0, 0, -34, 0, -289, 816, 0, 314432, 1728]
2493: ? smallpolred(x^4+576)
2494: [x - 1, x^2 - x + 1, x^2 + 1, x^4 - x^2 + 1]
2495: ? smallpolred2(x^4+576)
2496:
2497: [1 x - 1]
2498:
2499: [1/192*x^3 + 1/8*x + 1/2 x^2 - x + 1]
2500:
2501: [-1/24*x^2 x^2 + 1]
2502:
2503: [-1/192*x^3 + 1/48*x^2 + 1/8*x x^4 - x^2 + 1]
2504:
2505: ? smith(matrix(5,5,j,k,random()))
1.2 ! noro 2506: [239509529380671174817611776, 2147483648, 2147483648, 1, 1]
1.1 noro 2507: ? smith(1/hilbert(6))
2508: [27720, 2520, 2520, 840, 210, 6]
2509: ? smithpol(x*idmat(5)-matrix(5,5,j,k,1))
2510: [x^2 - 5*x, x, x, x, 1]
2511: ? solve(x=1,4,sin(x))
2512: 3.141592653589793238462643383
2513: ? sort(vector(17,x,5*x%17))
2514: [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16]
2515: ? sqr(1+o(2))
2516: 1 + O(2^3)
2517: ? sqred(hilbert(5))
2518:
2519: [1 1/2 1/3 1/4 1/5]
2520:
2521: [0 1/12 1 9/10 4/5]
2522:
2523: [0 0 1/180 3/2 12/7]
2524:
2525: [0 0 0 1/2800 2]
2526:
2527: [0 0 0 0 1/44100]
2528:
2529: ? sqrt(13+o(127^12))
2530: 34 + 125*127 + 83*127^2 + 107*127^3 + 53*127^4 + 42*127^5 + 22*127^6 + 98*12
2531: 7^7 + 127^8 + 23*127^9 + 122*127^10 + 79*127^11 + O(127^12)
2532: ? srgcd(x^10-1,x^15-1)
2533: x^5 - 1
2534: ? move(0,100,100);string(0,pi)
2535: ? move(0,200,200);string(0,"(0,0)")
2536: ? postdraw([0,10,10])
2537: ? apol=0.3+legendre(10)
2538: 46189/256*x^10 - 109395/256*x^8 + 45045/128*x^6 - 15015/128*x^4 + 3465/256*x
2539: ^2 + 0.05390625000000000000000000000
2540: ? sturm(apol)
2541: 4
2542: ? sturmpart(apol,0.91,1)
2543: 1
2544: ? subcyclo(31,5)
2545: x^5 + x^4 - 12*x^3 - 21*x^2 + x + 5
2546: ? subell(initell([0,0,0,-17,0]),[-1,4],[-4,2])
2547: [9, -24]
2548: ? subst(sin(x),x,y)
2549: y - 1/6*y^3 + 1/120*y^5 - 1/5040*y^7 + 1/362880*y^9 - 1/39916800*y^11 + O(y^
2550: 12)
2551: ? subst(sin(x),x,x+x^2)
2552: 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
2553: ^8 + 13609/362880*x^9 + 19/13440*x^10 - 273241/39916800*x^11 + O(x^12)
2554: ? sum(0,k=1,10,2^-k)
2555: 1023/1024
2556: ? sum(0.,k=1,10,2^-k)
2557: 0.9990234375000000000000000000
2558: ? sylvestermatrix(a2*x^2+a1*x+a0,b1*x+b0)
2559:
2560: [a2 b1 0]
2561:
2562: [a1 b0 b1]
2563:
2564: [a0 0 b0]
2565:
2566: ? \precision=38
2567: realprecision = 38 significant digits
2568: ? 4*sumalt(n=0,(-1)^n/(2*n+1))
2569: 3.1415926535897932384626433832795028841
2570: ? 4*sumalt2(n=0,(-1)^n/(2*n+1))
2571: 3.1415926535897932384626433832795028842
2572: ? suminf(n=1,2.^-n)
2573: 0.99999999999999999999999999999999999999
2574: ? 6/pi^2*sumpos(n=1,n^-2)
2575: 0.99999999999999999999999999999999999999
2576: ? supplement([1,3;2,4;3,6])
2577:
2578: [1 3 0]
2579:
2580: [2 4 0]
2581:
2582: [3 6 1]
2583:
2584: ? sqr(tan(pi/3))
2585: 2.9999999999999999999999999999999999999
2586: ? tanh(1)
2587: 0.76159415595576488811945828260479359041
2588: ? taniyama(bcurve)
2589: [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
2590: )]
2591: ? taylor(y/(x-y),y)
2592: (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
2593: ^7*x^4 + y^8*x^3 + y^9*x^2 + y^10*x + y^11)/x^11
2594: ? tchebi(10)
2595: 512*x^10 - 1280*x^8 + 1120*x^6 - 400*x^4 + 50*x^2 - 1
2596: ? teich(7+o(127^12))
2597: 7 + 57*127 + 58*127^2 + 83*127^3 + 52*127^4 + 109*127^5 + 74*127^6 + 16*127^
2598: 7 + 60*127^8 + 47*127^9 + 65*127^10 + 5*127^11 + O(127^12)
2599: ? texprint((x+y)^3/(x-y)^2)
2600: {{x^{3} + {{3}y}x^{2} + {{3}y^{2}}x + {y^{3}}}\over{x^{2} - {{2}y}x + {y^{2}
2601: }}}
2602: ? theta(0.5,3)
2603: 0.080806418251894691299871683210466298535
2604: ? thetanullk(0.5,7)
2605: -804.63037320243369422783730584965684022
2606: ? torsell(tcurve)
2607: [12, [6, 2], [[-2, 8], [3, -2]]]
2608: ? trace(1+i)
2609: 2
2610: ? trace(mod(x+5,x^3+x+1))
2611: 15
2612: ? trans(vector(2,x,x))
2613: [1, 2]~
2614: ? %*%~
2615:
2616: [1 2]
2617:
2618: [2 4]
2619:
2620: ? trunc(-2.7)
2621: -2
2622: ? trunc(sin(x^2))
2623: 1/120*x^10 - 1/6*x^6 + x^2
2624: ? tschirnhaus(x^5-x-1)
1.2 ! noro 2625: x^5 + 20*x^4 + 158*x^3 + 616*x^2 + 1185*x + 899
1.1 noro 2626: ? type(mod(x,x^2+1))
2627: 9
2628: ? unit(17)
2629: 3 + 2*w
2630: ? n=33;until(n==1,print1(n," ");if(n%2,n=3*n+1,n=n/2));print(1)
2631: 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
2632: ? valuation(6^10000-1,5)
2633: 5
2634: ? vec(sin(x))
2635: [1, 0, -1/6, 0, 1/120, 0, -1/5040, 0, 1/362880, 0, -1/39916800]
2636: ? vecmax([-3,7,-2,11])
2637: 11
2638: ? vecmin([-3,7,-2,11])
2639: -3
2640: ? vecsort([[1,8,5],[2,5,8],[3,6,-6],[4,8,6]],2)
2641: [[2, 5, 8], [3, 6, -6], [4, 8, 6], [1, 8, 5]]
2642: ? vecsort([[1,8,5],[2,5,8],[3,6,-6],[4,8,6]],[2,1])
2643: [[2, 5, 8], [3, 6, -6], [1, 8, 5], [4, 8, 6]]
2644: ? weipell(acurve)
2645: x^-2 + 1/5*x^2 - 1/28*x^4 + 1/75*x^6 - 3/1540*x^8 + 1943/3822000*x^10 - 1/11
2646: 550*x^12 + 193/10510500*x^14 - 1269/392392000*x^16 + 21859/34684650000*x^18
2647: - 1087/9669660000*x^20 + O(x^22)
2648: ? wf(i)
2649: 1.1892071150027210667174999705604759152 - 1.175494350822287507 E-38*I
2650: ? wf2(i)
2651: 1.0905077326652576592070106557607079789 + 0.E-58*I
2652: ? m=5;while(m<20,print1(m," ");m=m+1);print()
2653: 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19
2654: ? zell(acurve,apoint)
2655: 0.72491221490962306778878739838332384646 + 0.E-77*I
2656: ? zeta(3)
2657: 1.2020569031595942853997381615114499907
2658: ? zeta(0.5+14.1347251*i)
2659: 0.0000000052043097453468479398562848599419244606 - 0.00000003269063986978698
2660: 2176409251733800562856*I
2661: ? zetak(nfz,-3)
2662: 0.091666666666666666666666666666666666666
2663: ? zetak(nfz,1.5+3*i)
2664: 0.88324345992059326405525724366416928890 - 0.2067536250233895222724230899142
2665: 7938845*I
2666: ? zidealstar(nf2,54)
1.2 ! noro 2667: [132678, [1638, 9, 9], [[3, 1, 2]~, [-23, 0, 0]~, [1, 0, -24]~]]
1.1 noro 2668: ? bid=zidealstarinit(nf2,54)
2669: [[[54, 0, 0; 0, 54, 0; 0, 0, 54], [0]], [132678, [1638, 9, 9]], [[2, [2, 0,
2670: 0]~, 1, 3, [1, 0, 0]~], 1; [3, [3, 0, 0]~, 1, 3, [1, 0, 0]~], 3], [[[[7], [[
1.2 ! noro 2671: 2, 1, 0]~], [[-26, -27, 0]~], [[]~], 1]], [[[26], [[2, 1, 0]~], [[-25, -26,
! 2672: 0]~], [[]~], 1], [[3, 3, 3], [[1, 3, 0]~, [1, 0, 3]~, [4, 0, 0]~], [[1, -24,
! 2673: 0]~, [1, 0, -24]~, [-23, 0, 0]~], [[]~, []~, []~], [0, 1/3, 0; 0, 0, 1/3; 1
! 2674: /3, 0, 0]], [[3, 3, 3], [[1, 9, 0]~, [1, 0, 9]~, [10, 0, 0]~], [[1, -18, 0]~
! 2675: , [1, 0, -18]~, [-17, 0, 0]~], [[]~, []~, []~], [0, 1/9, 0; 0, 0, 1/9; 1/9,
! 2676: 0, 0]]], [[], [], [;]]], [2106, -77, 10556, 0, -4368, 12012, 0, -13104; 0, 0
! 2677: , 0, 1, -2, 0, -6, -6; -27, 1, -136, 0, 56, -156, 0, 168]]
1.1 noro 2678: ? zideallog(nf2,w,bid)
1.2 ! noro 2679: [1422, 3, 7]~
1.1 noro 2680: ? znstar(3120)
2681: [768, [12, 4, 4, 2, 2], [mod(67, 3120), mod(2341, 3120), mod(1847, 3120), mo
2682: d(391, 3120), mod(2081, 3120)]]
2683: ? getstack()
2684: 0
2685: ? getheap()
1.2 ! noro 2686: [620, 106879]
1.1 noro 2687: ? print("Total time spent: ",gettime());
1.2 ! noro 2688: Total time spent: 7184
1.1 noro 2689: ? \q
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