Annotation of OpenXM_contrib/pari/src/test/32/compat, Revision 1.1.1.1
1.1 maekawa 1: echo = 1 (on)
2: ? default(compatible,3)
3: compatible = 3 (use old functions, ignore case)
4: *** Warning: user functions re-initialized.
5: ? +3
6: 3
7: ? -5
8: -5
9: ? 5+3
10: 8
11: ? 5-3
12: 2
13: ? 5/3
14: 5/3
15: ? 5\3
16: 1
17: ? 5\/3
18: 2
19: ? 5%3
20: 2
21: ? 5^3
22: 125
23: ? \precision=57
24: realprecision = 57 significant digits
25: ? pi
26: 3.14159265358979323846264338327950288419716939937510582097
27: ? \precision=38
28: realprecision = 38 significant digits
29: ? o(x^12)
30: O(x^12)
31: ? padicno=(5/3)*127+O(127^5)
32: 44*127 + 42*127^2 + 42*127^3 + 42*127^4 + O(127^5)
33: ? initrect(0,500,500)
34: ? abs(-0.01)
35: 0.0099999999999999999999999999999999999999
36: ? acos(0.5)
37: 1.0471975511965977461542144610931676280
38: ? acosh(3)
39: 1.7627471740390860504652186499595846180
40: ? acurve=initell([0,0,1,-1,0])
41: [0, 0, 1, -1, 0, 0, -2, 1, -1, 48, -216, 37, 110592/37, [0.83756543528332303
42: 544481089907503024040, 0.26959443640544455826293795134926000404, -1.10715987
43: 16887675937077488504242902444]~, 2.9934586462319596298320099794525081778, 2.
44: 4513893819867900608542248318665252253*I, -0.47131927795681147588259389708033
45: 769964, -1.4354565186686843187232088566788165076*I, 7.3381327407895767390707
46: 210033323055881]
47: ? apoint=[2,2]
48: [2, 2]
49: ? isoncurve(acurve,apoint)
50: 1
51: ? addell(acurve,apoint,apoint)
52: [21/25, -56/125]
53: ? addprimes([nextprime(10^9),nextprime(10^10)])
54: [1000000007, 10000000019]
55: ? adj([1,2;3,4])
56:
57: [4 -2]
58:
59: [-3 1]
60:
61: ? agm(1,2)
62: 1.4567910310469068691864323832650819749
63: ? agm(1+o(7^5),8+o(7^5))
64: 1 + 4*7 + 6*7^2 + 5*7^3 + 2*7^4 + O(7^5)
65: ? algdep(2*cos(2*pi/13),6)
66: x^6 + x^5 - 5*x^4 - 4*x^3 + 6*x^2 + 3*x - 1
67: ? algdep2(2*cos(2*pi/13),6,15)
68: x^6 + x^5 - 5*x^4 - 4*x^3 + 6*x^2 + 3*x - 1
69: ? akell(acurve,1000000007)
70: 43800
71: ? nfpol=x^5-5*x^3+5*x+25
72: x^5 - 5*x^3 + 5*x + 25
73: ? nf=initalg(nfpol)
74: [x^5 - 5*x^3 + 5*x + 25, [1, 2], 595125, 45, [[1, -2.42851749071941860689920
75: 69565359418364, 5.8976972027301414394898806541072047941, -7.0734526715090929
76: 269887668671457811020, 3.8085820570096366144649278594400435257; 1, 1.9647119
77: 211288133163138753392090569931 + 0.80971492418897895128294082219556466857*I,
78: 3.2044546745713084269203768790545260356 + 3.1817131285400005341145852263331
79: 539899*I, -0.16163499313031744537610982231988834519 + 1.88804378620070569319
80: 06454476483475283*I, 2.0660709538372480632698971148801090692 + 2.68989675196
81: 23140991170523711857387388*I; 1, -0.75045317576910401286427186094108607489 +
82: 1.3101462685358123283560773619310445915*I, -1.15330327593637914666531720610
83: 81284327 - 1.9664068558894834311780119356739268309*I, 1.19836132888486390887
84: 04932558927788962 + 0.64370238076256988899570325671192132449*I, -0.470361982
85: 34206637050236104460013083212 + 0.083628266711589186119416762685933385421*I]
86: , [1, 2, 2; -2.4285174907194186068992069565359418364, 3.92942384225762663262
87: 77506784181139862 - 1.6194298483779579025658816443911293371*I, -1.5009063515
88: 382080257285437218821721497 - 2.6202925370716246567121547238620891831*I; 5.8
89: 976972027301414394898806541072047941, 6.408909349142616853840753758109052071
90: 2 - 6.3634262570800010682291704526663079798*I, -2.30660655187275829333063441
91: 22162568654 + 3.9328137117789668623560238713478536619*I; -7.0734526715090929
92: 269887668671457811020, -0.32326998626063489075221964463977669038 - 3.7760875
93: 724014113863812908952966950567*I, 2.3967226577697278177409865117855577924 -
94: 1.2874047615251397779914065134238426489*I; 3.8085820570096366144649278594400
95: 435257, 4.1321419076744961265397942297602181385 - 5.379793503924628198234104
96: 7423714774776*I, -0.94072396468413274100472208920026166424 - 0.1672565334231
97: 7837223883352537186677084*I], [5, 4.0215293653309345240000000000000000000 E-
98: 87, 10.000000000000000000000000000000000000, -5.0000000000000000000000000000
99: 000000000, 7.0000000000000000000000000000000000000; 4.0215293653309345240000
100: 000000000000000 E-87, 19.488486013650707197449403270536023970, 8.04305873066
101: 18690490000000000000000000 E-86, 19.488486013650707197449403270536023970, 4.
102: 1504592246706085588902013976045703227; 10.0000000000000000000000000000000000
103: 00, 8.0430587306618690490000000000000000000 E-86, 85.96021742085184648030513
104: 3936577594605, -36.034268291482979838267056239752434596, 53.5761304525111078
105: 88183080361946556763; -5.0000000000000000000000000000000000000, 19.488486013
106: 650707197449403270536023970, -36.034268291482979838267056239752434596, 60.91
107: 6248374441986300937507618575151517, -18.470101750219179344070032346246890434
108: ; 7.0000000000000000000000000000000000000, 4.1504592246706085588902013976045
109: 703227, 53.576130452511107888183080361946556763, -18.47010175021917934407003
110: 2346246890434, 37.970152892842367340897384258599214282], [5, 0, 10, -5, 7; 0
111: , 10, 0, 10, -5; 10, 0, 30, -55, 20; -5, 10, -55, 45, -39; 7, -5, 20, -39, 9
112: ], [345, 0, 340, 167, 150; 0, 345, 110, 220, 153; 0, 0, 5, 2, 1; 0, 0, 0, 1,
113: 0; 0, 0, 0, 0, 1], [132825, -18975, -5175, 27600, 17250; -18975, 34500, 414
114: 00, 3450, -43125; -5175, 41400, -41400, -15525, 51750; 27600, 3450, -15525,
115: -3450, 0; 17250, -43125, 51750, 0, -86250], [595125, [-120750, 63825, 113850
116: , 0, 8625]~, 125439056256992431640625]], [-2.4285174907194186068992069565359
117: 418364, 1.9647119211288133163138753392090569931 + 0.809714924188978951282940
118: 82219556466857*I, -0.75045317576910401286427186094108607489 + 1.310146268535
119: 8123283560773619310445915*I], [1, x, x^2, 1/3*x^3 - 1/3*x^2 - 1/3, 1/15*x^4
120: + 1/3*x^2 + 1/3*x + 1/3], [1, 0, 0, 1, -5; 0, 1, 0, 0, -5; 0, 0, 1, 1, -5; 0
121: , 0, 0, 3, 0; 0, 0, 0, 0, 15], [1, 0, 0, 0, 0, 0, 0, 1, -2, -1, 0, 1, -5, -5
122: , -3, 0, -2, -5, 1, -4, 0, -1, -3, -4, -3; 0, 1, 0, 0, 0, 1, 0, 0, -2, 0, 0,
123: 0, -5, 0, -5, 0, -2, 0, -5, 0, 0, 0, -5, 0, -4; 0, 0, 1, 0, 0, 0, 1, 1, -2,
124: 1, 1, 1, -5, 3, -3, 0, -2, 3, -5, 1, 0, 1, -3, 1, -2; 0, 0, 0, 1, 0, 0, 0,
125: 3, -1, 2, 0, 3, 0, 5, 1, 1, -1, 5, -4, 3, 0, 2, 1, 3, 1; 0, 0, 0, 0, 1, 0, 0
126: , 0, 5, 0, 0, 0, 15, -5, 10, 0, 5, -5, 10, -2, 1, 0, 10, -2, 7]]
127: ? ba=algtobasis(nf,mod(x^3+5,nfpol))
128: [6, 0, 1, 3, 0]~
129: ? anell(acurve,100)
130: [1, -2, -3, 2, -2, 6, -1, 0, 6, 4, -5, -6, -2, 2, 6, -4, 0, -12, 0, -4, 3, 1
131: 0, 2, 0, -1, 4, -9, -2, 6, -12, -4, 8, 15, 0, 2, 12, -1, 0, 6, 0, -9, -6, 2,
132: -10, -12, -4, -9, 12, -6, 2, 0, -4, 1, 18, 10, 0, 0, -12, 8, 12, -8, 8, -6,
133: -8, 4, -30, 8, 0, -6, -4, 9, 0, -1, 2, 3, 0, 5, -12, 4, 8, 9, 18, -15, 6, 0
134: , -4, -18, 0, 4, 24, 2, 4, 12, 18, 0, -24, 4, 12, -30, -2]
135: ? apell(acurve,10007)
136: 66
137: ? apell2(acurve,10007)
138: 66
139: ? apol=x^3+5*x+1
140: x^3 + 5*x + 1
141: ? apprpadic(apol,1+O(7^8))
142: [1 + 6*7 + 4*7^2 + 4*7^3 + 3*7^4 + 4*7^5 + 6*7^7 + O(7^8)]
143: ? apprpadic(x^3+5*x+1,mod(x*(1+O(7^8)),x^2+x-1))
144: [mod((1 + 3*7 + 3*7^2 + 4*7^3 + 4*7^4 + 4*7^5 + 2*7^6 + 3*7^7 + O(7^8))*x +
145: (2*7 + 6*7^2 + 6*7^3 + 3*7^4 + 3*7^5 + 4*7^6 + 5*7^7 + O(7^8)), x^2 + x - 1)
146: ]~
147: ? 4*arg(3+3*i)
148: 3.1415926535897932384626433832795028842
149: ? 3*asin(sqrt(3)/2)
150: 3.1415926535897932384626433832795028841
151: ? asinh(0.5)
152: 0.48121182505960344749775891342436842313
153: ? assmat(x^5-12*x^3+0.0005)
154:
155: [0 0 0 0 -0.00049999999999999999999999999999999999999]
156:
157: [1 0 0 0 0]
158:
159: [0 1 0 0 0]
160:
161: [0 0 1 0 12]
162:
163: [0 0 0 1 0]
164:
165: ? 3*atan(sqrt(3))
166: 3.1415926535897932384626433832795028841
167: ? atanh(0.5)
168: 0.54930614433405484569762261846126285232
169: ? basis(x^3+4*x+5)
170: [1, x, 1/7*x^2 - 1/7*x - 2/7]
171: ? basis2(x^3+4*x+5)
172: [1, x, 1/7*x^2 - 1/7*x - 2/7]
173: ? basistoalg(nf,ba)
174: mod(x^3 + 5, x^5 - 5*x^3 + 5*x + 25)
175: ? bernreal(12)
176: -0.25311355311355311355311355311355311354
177: ? bernvec(6)
178: [1, 1/6, -1/30, 1/42, -1/30, 5/66, -691/2730]
179: ? bestappr(pi,10000)
180: 355/113
181: ? bezout(123456789,987654321)
182: [-8, 1, 9]
183: ? bigomega(12345678987654321)
184: 8
185: ? mcurve=initell([0,0,0,-17,0])
186: [0, 0, 0, -17, 0, 0, -34, 0, -289, 816, 0, 314432, 1728, [4.1231056256176605
187: 498214098559740770251, 0.E-38, -4.1231056256176605498214098559740770251]~, 1
188: .2913084409290072207105564235857096009, 1.2913084409290072207105564235857096
189: 009*I, -1.2164377440798088266474269946818791934, -3.649313232239426479942280
190: 9840456375802*I, 1.6674774896145033307120230298772362381]
191: ? mpoints=[[-1,4],[-4,2]]~
192: [[-1, 4], [-4, 2]]~
193: ? mhbi=bilhell(mcurve,mpoints,[9,24])
194: [-0.72448571035980184146215805860545027439, 1.307328627832055544492943428892
195: 1943055]~
196: ? bin(1.1,5)
197: -0.0045457499999999999999999999999999999997
198: ? binary(65537)
199: [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1]
200: ? bittest(10^100,100)
201: 1
202: ? boundcf(pi,5)
203: [3, 7, 15, 1, 292]
204: ? boundfact(40!+1,100000)
205:
206: [41 1]
207:
208: [59 1]
209:
210: [277 1]
211:
212: [1217669507565553887239873369513188900554127 1]
213:
214: ? move(0,0,0);box(0,500,500)
215: ? setrand(1);buchimag(1-10^7,1,1)
216: *** Warning: not a fundamental discriminant in quadclassunit.
217: [2416, [1208, 2], [qfi(277, 55, 9028), qfi(1700, 1249, 1700)], 1, 0.99984980
218: 753776002339750644800000000000]
219: ? setrand(1);bnf=buchinitfu(x^2-x-57,0.2,0.2)
220: [mat(3), mat([1, 2, 1, 2, 1, 2, 1, 2, 1]), [-2.71246530518434397468087951060
221: 61300699 + 3.1415926535897932384626433832795028842*I; 2.71246530518434397468
222: 08795106061300699 - 6.2831853071795864769252867665590057684*I], [23347.97922
223: 3478346319454659159707591731 + 6.2831853071795864769252867665590057684*I, 86
224: 6.56619430687100142570357249059499540 + 6.2831853071795864769252867665590057
225: 684*I, 2881.3396396084587293295626563644245032 + 3.1415926535897932384626433
226: 832795028842*I, 27379.624790530768080428797780058276925 + 1.9281866867095232
227: 000000000000000000000 E-42*I, 57933.334567930851067108050790839116749 + 2.69
228: 04930509626865380000000000000000000 E-42*I, -34585.5562501515577199980340439
229: 18848670 + 9.4247779607693797153879301498385086526*I, 23348.3225111226233465
230: 49049047574325150 + 3.1415926535897932384626433832795028842*I, -0.3432876442
231: 7702709438988786673341921876 + 3.1415926535897932384626433832795028842*I, -4
232: 031.7117453543045067063239888430083582 + 9.424777960769379715387930149838508
233: 6526*I, 27379.690968832650826160983148550600089 + 9.424777960769379715387930
234: 1498385086526*I; -23347.979223478346319454659159707591731 + 9.42477796076937
235: 97153879301498385086526*I, -866.56619430687100142570357249059499540 + 2.1019
236: 476959481835360000000000000000000 E-45*I, -2881.3396396084587293295626563644
237: 245032 + 9.4247779607693797153879301498385086526*I, -27379.62479053076808042
238: 8797780058276925 + 6.2831853071795864769252867665590057684*I, -57933.3345679
239: 30851067108050790839116749 + 3.1415926535897932384626433832795028842*I, 3458
240: 5.556250151557719998034043918848670 + 6.283185307179586476925286766559005768
241: 4*I, -23348.322511122623346549049047574325150 + 9.42477796076937971538793014
242: 98385086526*I, 0.34328764427702709438988786673341921876 + 0.E-48*I, 4031.711
243: 7453543045067063239888430083582 + 3.1415926535897932384626433832795028842*I,
244: -27379.690968832650826160983148550600089 + 6.283185307179586476925286766559
245: 0057684*I], [[3, [-1, 1]~, 1, 1, [0, 1]~], [3, [0, 1]~, 1, 1, [-1, 1]~], [5,
246: [-2, 1]~, 1, 1, [1, 1]~], [5, [1, 1]~, 1, 1, [-2, 1]~], [11, [-2, 1]~, 1, 1
247: , [1, 1]~], [11, [1, 1]~, 1, 1, [-2, 1]~], [17, [-3, 1]~, 1, 1, [2, 1]~], [1
248: 7, [2, 1]~, 1, 1, [-3, 1]~], [19, [-1, 1]~, 1, 1, [0, 1]~], [19, [0, 1]~, 1,
249: 1, [-1, 1]~]]~, [1, 3, 5, 2, 4, 6, 7, 8, 10, 9]~, [x^2 - x - 57, [2, 0], 22
250: 9, 1, [[1, -7.0663729752107779635959310246705326058; 1, 8.066372975210777963
251: 5959310246705326058], [1, 1; -7.0663729752107779635959310246705326058, 8.066
252: 3729752107779635959310246705326058], [2, 1.000000000000000000000000000000000
253: 0000; 1.0000000000000000000000000000000000000, 115.0000000000000000000000000
254: 0000000000], [2, 1; 1, 115], [229, 114; 0, 1], [115, -1; -1, 2], [229, [114,
255: 1]~, 229]], [-7.0663729752107779635959310246705326058, 8.066372975210777963
256: 5959310246705326058], [1, x], [1, 0; 0, 1], [1, 0, 0, 57; 0, 1, 1, 1]], [[3,
257: [3], [[3, 2; 0, 1]]], 2.7124653051843439746808795106061300699, 0.8814422512
258: 6545793690341704100000000000, [2, -1], [x + 7], 130], [mat(1), mat(1), [[[3,
259: 2; 0, 1], [0, 0]]]], 0]
260: ? buchcertify(bnf)
261: 1
262: ? buchfu(bnf)
263: [[x + 7], 130]
264: ? setrand(1);buchinitforcefu(x^2-x-100000)
265: [mat(5), mat([3, 2, 1, 2, 0, 3, 2, 3, 0, 0, 1, 4, 3, 2, 2, 3, 3, 2]), [-129.
266: 82045011403975460991182396195022419 + 6.283185307179586476925286766559005768
267: 4*I; 129.82045011403975460991182396195022419 + 4.907207226380705833000000000
268: 0000000000 E-95*I], [2093832.2286247580721598744691800364716 + 9.42477796076
269: 93797153879301498385086526*I, 463727.88770776479369558667281813008490 + 6.28
270: 31853071795864769252867665590057684*I, 229510.681191741210743599007448730565
271: 20 + 3.1415926535897932384626433832795028842*I, -13814064.276184856248286107
272: 275967161406 + 6.2831853071795864769252867665590057684*I, 10975229.442376145
273: 014058790444262893275 + 9.4247779607693797153879301498385086526*I, 12628868.
274: 476868730308574917279106536834 + 6.2831853071795864769252867665590057684*I,
275: 2595210.6815750606798700790306370856686 + 3.14159265358979323846264338327950
276: 28842*I, 21463208.279603014333968661075393279510 + 6.28318530717958647692528
277: 67665590057684*I, 9340416.4917416354701732132629720490406 + 9.42477796076937
278: 97153879301498385086526*I, 224801.35127844528675036994618361508061 + 12.5663
279: 70614359172953850573533118011536*I, -224801.35127844528675036994618361508061
280: + 2.1125754163178543118626478980000000000 E-90*I, 40271115.6788572427160038
281: 79014241558828 + 6.2831853071795864769252867665590057684*I, -10066612.284788
282: 886379386747743460630561 + 9.4600667685469491310218392850000000000 E-89*I, 1
283: 0267873.880681641662748682261863339788 + 12.56637061435917295385057353311801
284: 1536*I, -4435991.6114732228963510067335229085617 + 6.28318530717958647692528
285: 67665590057684*I, 8361196.2032957779193404684451855312611 + 9.42477796076937
286: 97153879301498385086526*I, -10272584.501589374356405593568879583106 + 9.4247
287: 779607693797153879301498385086526*I, 41648172.195327314227598351804544361493
288: + 9.4247779607693797153879301498385086526*I, -2117367.665066341919805155100
289: 3369291210 + 1.9897854874556092437572207830000000000 E-89*I; -2093832.228624
290: 7580721598744691800364716 + 3.1415926535897932384626433832795028842*I, -4637
291: 27.88770776479369558667281813008490 + 9.424777960769379715387930149838508652
292: 6*I, -229510.68119174121074359900744873056520 + 12.5663706143591729538505735
293: 33118011536*I, 13814064.276184856248286107275967161405 + 5.22154890000820159
294: 90000000000000000000 E-90*I, -10975229.442376145014058790444262893275 + 12.5
295: 66370614359172953850573533118011536*I, -12628868.476868730308574917279106536
296: 834 + 3.1415926535897932384626433832795028842*I, -2595210.681575060679870079
297: 0306370856686 + 12.566370614359172953850573533118011536*I, -21463208.2796030
298: 14333968661075393279510 + 9.4247779607693797153879301498385086526*I, -934041
299: 6.4917416354701732132629720490406 + 6.2831853071795864769252867665590057684*
300: I, -224801.35127844528675036994618361508061 + 12.566370614359172953850573533
301: 118011536*I, 224801.35127844528675036994618361508061 + 8.4971798285841941830
302: 000000000000000000 E-92*I, -40271115.678857242716003879014241558828 + 12.566
303: 370614359172953850573533118011536*I, 10066612.284788886379386747743460630561
304: + 3.8050554944202303880000000000000000000 E-90*I, -10267873.880681641662748
305: 682261863339788 + 3.1415926535897932384626433832795028842*I, 4435991.6114732
306: 228963510067335229085617 + 9.4247779607693797153879301498385086526*I, -83611
307: 96.2032957779193404684451855312611 + 12.566370614359172953850573533118011536
308: *I, 10272584.501589374356405593568879583106 + 3.8829118423163890830000000000
309: 000000000 E-90*I, -41648172.195327314227598351804544361493 + 3.1415926535897
310: 932384626433832795028842*I, 2117367.6650663419198051551003369291210 + 8.0033
311: 745765686035150000000000000000000 E-91*I], [[2, [1, 1]~, 1, 1, [0, 1]~], [2,
312: [2, 1]~, 1, 1, [1, 1]~], [5, [4, 1]~, 1, 1, [0, 1]~], [5, [5, 1]~, 1, 1, [-
313: 1, 1]~], [7, [3, 1]~, 2, 1, [3, 1]~], [13, [-6, 1]~, 1, 1, [5, 1]~], [13, [5
314: , 1]~, 1, 1, [-6, 1]~], [17, [14, 1]~, 1, 1, [2, 1]~], [17, [19, 1]~, 1, 1,
315: [-3, 1]~], [23, [-7, 1]~, 1, 1, [6, 1]~], [23, [6, 1]~, 1, 1, [-7, 1]~], [29
316: , [-14, 1]~, 1, 1, [13, 1]~], [29, [13, 1]~, 1, 1, [-14, 1]~], [31, [23, 1]~
317: , 1, 1, [7, 1]~], [31, [38, 1]~, 1, 1, [-8, 1]~], [41, [-7, 1]~, 1, 1, [6, 1
318: ]~], [41, [6, 1]~, 1, 1, [-7, 1]~], [43, [-16, 1]~, 1, 1, [15, 1]~], [43, [1
319: 5, 1]~, 1, 1, [-16, 1]~]]~, [1, 3, 6, 2, 4, 5, 7, 9, 8, 11, 10, 13, 12, 15,
320: 14, 17, 16, 19, 18]~, [x^2 - x - 100000, [2, 0], 400001, 1, [[1, -315.728161
321: 30129840161392089489603747004; 1, 316.72816130129840161392089489603747004],
322: [1, 1; -315.72816130129840161392089489603747004, 316.72816130129840161392089
323: 489603747004], [2, 1.0000000000000000000000000000000000000; 1.00000000000000
324: 00000000000000000000000, 200001.00000000000000000000000000000000], [2, 1; 1,
325: 200001], [400001, 200000; 0, 1], [200001, -1; -1, 2], [400001, [200000, 1]~
326: , 400001]], [-315.72816130129840161392089489603747004, 316.72816130129840161
327: 392089489603747004], [1, x], [1, 0; 0, 1], [1, 0, 0, 100000; 0, 1, 1, 1]], [
328: [5, [5], [[2, 1; 0, 1]]], 129.82045011403975460991182396195022419, 0.9876536
329: 9790690472391212970100000000000, [2, -1], [379554884019013781006303254896369
330: 154068336082609238336*x + 11983616564425078999046283595002287166517812761131
331: 6131167], 124], [mat(1), mat(1), [[[2, 1; 0, 1], [0, 0]]]], 0]
332: ? setrand(1);bnf=buchinitfu(x^2-x-57,0.2,0.2)
333: [mat(3), mat([1, 2, 1, 2, 1, 2, 1, 2, 1]), [-2.71246530518434397468087951060
334: 61300699 + 3.1415926535897932384626433832795028842*I; 2.71246530518434397468
335: 08795106061300699 - 6.2831853071795864769252867665590057684*I], [23347.97922
336: 3478346319454659159707591731 + 6.2831853071795864769252867665590057684*I, 86
337: 6.56619430687100142570357249059499540 + 6.2831853071795864769252867665590057
338: 684*I, 2881.3396396084587293295626563644245032 + 3.1415926535897932384626433
339: 832795028842*I, 27379.624790530768080428797780058276925 + 1.9281866867095232
340: 000000000000000000000 E-42*I, 57933.334567930851067108050790839116749 + 2.69
341: 04930509626865380000000000000000000 E-42*I, -34585.5562501515577199980340439
342: 18848670 + 9.4247779607693797153879301498385086526*I, 23348.3225111226233465
343: 49049047574325150 + 3.1415926535897932384626433832795028842*I, -0.3432876442
344: 7702709438988786673341921876 + 3.1415926535897932384626433832795028842*I, -4
345: 031.7117453543045067063239888430083582 + 9.424777960769379715387930149838508
346: 6526*I, 27379.690968832650826160983148550600089 + 9.424777960769379715387930
347: 1498385086526*I; -23347.979223478346319454659159707591731 + 9.42477796076937
348: 97153879301498385086526*I, -866.56619430687100142570357249059499540 + 2.1019
349: 476959481835360000000000000000000 E-45*I, -2881.3396396084587293295626563644
350: 245032 + 9.4247779607693797153879301498385086526*I, -27379.62479053076808042
351: 8797780058276925 + 6.2831853071795864769252867665590057684*I, -57933.3345679
352: 30851067108050790839116749 + 3.1415926535897932384626433832795028842*I, 3458
353: 5.556250151557719998034043918848670 + 6.283185307179586476925286766559005768
354: 4*I, -23348.322511122623346549049047574325150 + 9.42477796076937971538793014
355: 98385086526*I, 0.34328764427702709438988786673341921876 + 0.E-48*I, 4031.711
356: 7453543045067063239888430083582 + 3.1415926535897932384626433832795028842*I,
357: -27379.690968832650826160983148550600089 + 6.283185307179586476925286766559
358: 0057684*I], [[3, [-1, 1]~, 1, 1, [0, 1]~], [3, [0, 1]~, 1, 1, [-1, 1]~], [5,
359: [-2, 1]~, 1, 1, [1, 1]~], [5, [1, 1]~, 1, 1, [-2, 1]~], [11, [-2, 1]~, 1, 1
360: , [1, 1]~], [11, [1, 1]~, 1, 1, [-2, 1]~], [17, [-3, 1]~, 1, 1, [2, 1]~], [1
361: 7, [2, 1]~, 1, 1, [-3, 1]~], [19, [-1, 1]~, 1, 1, [0, 1]~], [19, [0, 1]~, 1,
362: 1, [-1, 1]~]]~, [1, 3, 5, 2, 4, 6, 7, 8, 10, 9]~, [x^2 - x - 57, [2, 0], 22
363: 9, 1, [[1, -7.0663729752107779635959310246705326058; 1, 8.066372975210777963
364: 5959310246705326058], [1, 1; -7.0663729752107779635959310246705326058, 8.066
365: 3729752107779635959310246705326058], [2, 1.000000000000000000000000000000000
366: 0000; 1.0000000000000000000000000000000000000, 115.0000000000000000000000000
367: 0000000000], [2, 1; 1, 115], [229, 114; 0, 1], [115, -1; -1, 2], [229, [114,
368: 1]~, 229]], [-7.0663729752107779635959310246705326058, 8.066372975210777963
369: 5959310246705326058], [1, x], [1, 0; 0, 1], [1, 0, 0, 57; 0, 1, 1, 1]], [[3,
370: [3], [[3, 2; 0, 1]]], 2.7124653051843439746808795106061300699, 0.8814422512
371: 6545793690341704100000000000, [2, -1], [x + 7], 130], [mat(1), mat(1), [[[3,
372: 2; 0, 1], [0, 0]]]], 0]
373: ? setrand(1);buchreal(10^9-3,0,0.5,0.5)
374: [4, [4], [qfr(3, 1, -83333333, 0.E-48)], 2800.625251907016076486370621737074
375: 5513, 0.99903694589643832327024650000000000000]
376: ? setrand(1);buchgen(x^4-7,0.2,0.2)
377:
378: [x^4 - 7]
379:
380: [[2, 1]]
381:
382: [[-87808, 1]]
383:
384: [[1, x, x^2, x^3]]
385:
386: [[2, [2], [[2, 1, 1, 1; 0, 1, 0, 0; 0, 0, 1, 0; 0, 0, 0, 1]]]]
387:
388: [14.229975145405511722395637833443108790]
389:
390: [1.1211171071527562299744232290000000000]
391:
392: ? setrand(1);buchgenfu(x^2-x-100000)
393: *** Warning: insufficient precision for fundamental units, not given.
394:
395: [x^2 - x - 100000]
396:
397: [[2, 0]]
398:
399: [[400001, 1]]
400:
401: [[1, x]]
402:
403: [[5, [5], [[2, 1; 0, 1]]]]
404:
405: [129.82045011403975460991182396195022419]
406:
407: [0.98765369790690472391212970100000000000]
408:
409: [[2, -1]]
410:
411: [[;]]
412:
413: [0]
414:
415: ? setrand(1);buchgenforcefu(x^2-x-100000)
416:
417: [x^2 - x - 100000]
418:
419: [[2, 0]]
420:
421: [[400001, 1]]
422:
423: [[1, x]]
424:
425: [[5, [5], [[2, 1; 0, 1]]]]
426:
427: [129.82045011403975460991182396195022419]
428:
429: [0.98765369790690472391212970100000000000]
430:
431: [[2, -1]]
432:
433: [[379554884019013781006303254896369154068336082609238336*x + 119836165644250
434: 789990462835950022871665178127611316131167]]
435:
436: [124]
437:
438: ? setrand(1);buchgenfu(x^4+24*x^2+585*x+1791,0.1,0.1)
439:
440: [x^4 + 24*x^2 + 585*x + 1791]
441:
442: [[0, 2]]
443:
444: [[18981, 3087]]
445:
446: [[1, x, 1/3*x^2, 1/1029*x^3 + 33/343*x^2 - 155/343*x - 58/343]]
447:
448: [[4, [4], [[7, 6, 2, 4; 0, 1, 0, 0; 0, 0, 1, 0; 0, 0, 0, 1]]]]
449:
450: [3.7941269688216589341408274220859400302]
451:
452: [0.88260182866555813061644128400000000000]
453:
454: [[6, 10/1029*x^3 - 13/343*x^2 + 165/343*x + 1478/343]]
455:
456: [[4/1029*x^3 + 53/1029*x^2 + 66/343*x + 111/343]]
457:
458: [103]
459:
460: ? buchnarrow(bnf)
461: [3, [3], [[3, 2; 0, 1]]]
462: ? buchray(bnf,[[5,3;0,1],[1,0]])
463: [12, [12], [[3, 2; 0, 1]]]
464: ? bnr=buchrayinitgen(bnf,[[5,3;0,1],[1,0]])
465: [[mat(3), mat([1, 2, 1, 2, 1, 2, 1, 2, 1]), [-2.7124653051843439746808795106
466: 061300699 + 3.1415926535897932384626433832795028842*I; 2.7124653051843439746
467: 808795106061300699 - 6.2831853071795864769252867665590057684*I], [23347.9792
468: 23478346319454659159707591731 + 6.2831853071795864769252867665590057684*I, 8
469: 66.56619430687100142570357249059499540 + 6.283185307179586476925286766559005
470: 7684*I, 2881.3396396084587293295626563644245032 + 3.141592653589793238462643
471: 3832795028842*I, 27379.624790530768080428797780058276925 + 1.928186686709523
472: 2000000000000000000000 E-42*I, 57933.334567930851067108050790839116749 + 2.6
473: 904930509626865380000000000000000000 E-42*I, -34585.556250151557719998034043
474: 918848670 + 9.4247779607693797153879301498385086526*I, 23348.322511122623346
475: 549049047574325150 + 3.1415926535897932384626433832795028842*I, -0.343287644
476: 27702709438988786673341921876 + 3.1415926535897932384626433832795028842*I, -
477: 4031.7117453543045067063239888430083582 + 9.42477796076937971538793014983850
478: 86526*I, 27379.690968832650826160983148550600089 + 9.42477796076937971538793
479: 01498385086526*I; -23347.979223478346319454659159707591731 + 9.4247779607693
480: 797153879301498385086526*I, -866.56619430687100142570357249059499540 + 2.101
481: 9476959481835360000000000000000000 E-45*I, -2881.339639608458729329562656364
482: 4245032 + 9.4247779607693797153879301498385086526*I, -27379.6247905307680804
483: 28797780058276925 + 6.2831853071795864769252867665590057684*I, -57933.334567
484: 930851067108050790839116749 + 3.1415926535897932384626433832795028842*I, 345
485: 85.556250151557719998034043918848670 + 6.28318530717958647692528676655900576
486: 84*I, -23348.322511122623346549049047574325150 + 9.4247779607693797153879301
487: 498385086526*I, 0.34328764427702709438988786673341921876 + 0.E-48*I, 4031.71
488: 17453543045067063239888430083582 + 3.1415926535897932384626433832795028842*I
489: , -27379.690968832650826160983148550600089 + 6.28318530717958647692528676655
490: 90057684*I], [[3, [-1, 1]~, 1, 1, [0, 1]~], [3, [0, 1]~, 1, 1, [-1, 1]~], [5
491: , [-2, 1]~, 1, 1, [1, 1]~], [5, [1, 1]~, 1, 1, [-2, 1]~], [11, [-2, 1]~, 1,
492: 1, [1, 1]~], [11, [1, 1]~, 1, 1, [-2, 1]~], [17, [-3, 1]~, 1, 1, [2, 1]~], [
493: 17, [2, 1]~, 1, 1, [-3, 1]~], [19, [-1, 1]~, 1, 1, [0, 1]~], [19, [0, 1]~, 1
494: , 1, [-1, 1]~]]~, [1, 3, 5, 2, 4, 6, 7, 8, 10, 9]~, [x^2 - x - 57, [2, 0], 2
495: 29, 1, [[1, -7.0663729752107779635959310246705326058; 1, 8.06637297521077796
496: 35959310246705326058], [1, 1; -7.0663729752107779635959310246705326058, 8.06
497: 63729752107779635959310246705326058], [2, 1.00000000000000000000000000000000
498: 00000; 1.0000000000000000000000000000000000000, 115.000000000000000000000000
499: 00000000000], [2, 1; 1, 115], [229, 114; 0, 1], [115, -1; -1, 2], [229, [114
500: , 1]~, 229]], [-7.0663729752107779635959310246705326058, 8.06637297521077796
501: 35959310246705326058], [1, x], [1, 0; 0, 1], [1, 0, 0, 57; 0, 1, 1, 1]], [[3
502: , [3], [[3, 2; 0, 1]]], 2.7124653051843439746808795106061300699, 0.881442251
503: 26545793690341704100000000000, [2, -1], [x + 7], 130], [mat(1), mat(1), [[[3
504: , 2; 0, 1], [0, 0]]]], 0], [[[5, 3; 0, 1], [1, 0]], [8, [4, 2], [[2, 0]~, [-
505: 1, 1]~]], mat([[5, [-2, 1]~, 1, 1, [1, 1]~], 1]), [[[[4], [[2, 0]~], [[2, 0]
506: ~], [[mod(0, 2)]~], 1]], [[2], [[-1, 1]~], mat(1)]], [1, 0; 0, 1]], [[1, 0]~
507: ], [1, -3, -6; 0, 0, 1; 0, 1, 0], [12, [12], [[3, 2; 0, 1]]], [[0, 0; 0, 1],
508: [1, -1; 1, 1]]]
509: ? bnr2=buchrayinitgen(bnf,[[25,13;0,1],[1,1]])
510: [[mat(3), mat([1, 2, 1, 2, 1, 2, 1, 2, 1]), [-2.7124653051843439746808795106
511: 061300699 + 3.1415926535897932384626433832795028842*I; 2.7124653051843439746
512: 808795106061300699 - 6.2831853071795864769252867665590057684*I], [23347.9792
513: 23478346319454659159707591731 + 6.2831853071795864769252867665590057684*I, 8
514: 66.56619430687100142570357249059499540 + 6.283185307179586476925286766559005
515: 7684*I, 2881.3396396084587293295626563644245032 + 3.141592653589793238462643
516: 3832795028842*I, 27379.624790530768080428797780058276925 + 1.928186686709523
517: 2000000000000000000000 E-42*I, 57933.334567930851067108050790839116749 + 2.6
518: 904930509626865380000000000000000000 E-42*I, -34585.556250151557719998034043
519: 918848670 + 9.4247779607693797153879301498385086526*I, 23348.322511122623346
520: 549049047574325150 + 3.1415926535897932384626433832795028842*I, -0.343287644
521: 27702709438988786673341921876 + 3.1415926535897932384626433832795028842*I, -
522: 4031.7117453543045067063239888430083582 + 9.42477796076937971538793014983850
523: 86526*I, 27379.690968832650826160983148550600089 + 9.42477796076937971538793
524: 01498385086526*I; -23347.979223478346319454659159707591731 + 9.4247779607693
525: 797153879301498385086526*I, -866.56619430687100142570357249059499540 + 2.101
526: 9476959481835360000000000000000000 E-45*I, -2881.339639608458729329562656364
527: 4245032 + 9.4247779607693797153879301498385086526*I, -27379.6247905307680804
528: 28797780058276925 + 6.2831853071795864769252867665590057684*I, -57933.334567
529: 930851067108050790839116749 + 3.1415926535897932384626433832795028842*I, 345
530: 85.556250151557719998034043918848670 + 6.28318530717958647692528676655900576
531: 84*I, -23348.322511122623346549049047574325150 + 9.4247779607693797153879301
532: 498385086526*I, 0.34328764427702709438988786673341921876 + 0.E-48*I, 4031.71
533: 17453543045067063239888430083582 + 3.1415926535897932384626433832795028842*I
534: , -27379.690968832650826160983148550600089 + 6.28318530717958647692528676655
535: 90057684*I], [[3, [-1, 1]~, 1, 1, [0, 1]~], [3, [0, 1]~, 1, 1, [-1, 1]~], [5
536: , [-2, 1]~, 1, 1, [1, 1]~], [5, [1, 1]~, 1, 1, [-2, 1]~], [11, [-2, 1]~, 1,
537: 1, [1, 1]~], [11, [1, 1]~, 1, 1, [-2, 1]~], [17, [-3, 1]~, 1, 1, [2, 1]~], [
538: 17, [2, 1]~, 1, 1, [-3, 1]~], [19, [-1, 1]~, 1, 1, [0, 1]~], [19, [0, 1]~, 1
539: , 1, [-1, 1]~]]~, [1, 3, 5, 2, 4, 6, 7, 8, 10, 9]~, [x^2 - x - 57, [2, 0], 2
540: 29, 1, [[1, -7.0663729752107779635959310246705326058; 1, 8.06637297521077796
541: 35959310246705326058], [1, 1; -7.0663729752107779635959310246705326058, 8.06
542: 63729752107779635959310246705326058], [2, 1.00000000000000000000000000000000
543: 00000; 1.0000000000000000000000000000000000000, 115.000000000000000000000000
544: 00000000000], [2, 1; 1, 115], [229, 114; 0, 1], [115, -1; -1, 2], [229, [114
545: , 1]~, 229]], [-7.0663729752107779635959310246705326058, 8.06637297521077796
546: 35959310246705326058], [1, x], [1, 0; 0, 1], [1, 0, 0, 57; 0, 1, 1, 1]], [[3
547: , [3], [[3, 2; 0, 1]]], 2.7124653051843439746808795106061300699, 0.881442251
548: 26545793690341704100000000000, [2, -1], [x + 7], 130], [mat(1), mat(1), [[[3
549: , 2; 0, 1], [0, 0]]]], 0], [[[25, 13; 0, 1], [1, 1]], [80, [20, 2, 2], [[2,
550: 0]~, [0, -2]~, [2, 2]~]], mat([[5, [-2, 1]~, 1, 1, [1, 1]~], 2]), [[[[4], [[
551: 2, 0]~], [[2, 0]~], [[mod(0, 2), mod(0, 2)]~], 1], [[5], [[6, 0]~], [[6, 0]~
552: ], [[mod(0, 2), mod(0, 2)]~], mat([1/5, -13/5])]], [[2, 2], [[0, -2]~, [2, 2
553: ]~], [0, 1; 1, 0]]], [1, -12, 0, 0; 0, 0, 1, 0; 0, 0, 0, 1]], [[1, 0]~], [1,
554: -3, 0, -6; 0, 0, 1, 0; 0, 0, 0, 1; 0, 1, 0, 0], [12, [12], [[3, 2; 0, 1]]],
555: [[1/2, 5, -9; -1/2, -5, 10], [-2, 0; 0, 10]]]
556: ? bytesize(%)
557: 7532
558: ? ceil(-2.5)
559: -2
560: ? centerlift(mod(456,555))
561: -99
562: ? cf(pi)
563: [3, 7, 15, 1, 292, 1, 1, 1, 2, 1, 3, 1, 14, 2, 1, 1, 2, 2, 2, 2, 1, 84, 2, 1
564: , 1, 15, 3, 13, 1, 4, 2, 6, 6]
565: ? cf2([1,3,5,7,9],(exp(1)-1)/(exp(1)+1))
566: [0, 6, 10, 42, 30]
567: ? changevar(x+y,[z,t])
568: y + z
569: ? char([1,2;3,4],z)
570: z^2 - 5*z - 2
571: ? char(mod(x^2+x+1,x^3+5*x+1),z)
572: z^3 + 7*z^2 + 16*z - 19
573: ? char1([1,2;3,4],z)
574: z^2 - 5*z - 2
575: ? char2(mod(1,8191)*[1,2;3,4],z)
576: mod(1, 8191)*z^2 + mod(8186, 8191)*z + mod(8189, 8191)
577: ? acurve=chell(acurve,[-1,1,2,3])
578: [-4, -1, -7, -12, -12, 12, 4, 1, -1, 48, -216, 37, 110592/37, [-0.1624345647
579: 1667696455518910092496975959, -0.73040556359455544173706204865073999595, -2.
580: 1071598716887675937077488504242902444]~, -2.99345864623195962983200997945250
581: 81778, -2.4513893819867900608542248318665252253*I, 0.47131927795681147588259
582: 389708033769964, 1.4354565186686843187232088566788165076*I, 7.33813274078957
583: 67390707210033323055881]
584: ? chinese(mod(7,15),mod(13,21))
585: mod(97, 105)
586: ? apoint=chptell(apoint,[-1,1,2,3])
587: [1, 3]
588: ? isoncurve(acurve,apoint)
589: 1
590: ? classno(-12391)
591: 63
592: ? classno(1345)
593: 6
594: ? classno2(-12391)
595: 63
596: ? classno2(1345)
597: 6
598: ? coeff(sin(x),7)
599: -1/5040
600: ? compimag(qfi(2,1,3),qfi(2,1,3))
601: qfi(2, -1, 3)
602: ? compo(1+o(7^4),3)
603: 1
604: ? compositum(x^4-4*x+2,x^3-x-1)
605: [x^12 - 4*x^10 + 8*x^9 + 12*x^8 + 12*x^7 + 138*x^6 + 132*x^5 - 43*x^4 + 58*x
606: ^2 - 128*x - 5]~
607: ? compositum2(x^4-4*x+2,x^3-x-1)
608: [[x^12 - 4*x^10 + 8*x^9 + 12*x^8 + 12*x^7 + 138*x^6 + 132*x^5 - 43*x^4 + 58*
609: x^2 - 128*x - 5, mod(-279140305176/29063006931199*x^11 + 129916611552/290630
610: 06931199*x^10 + 1272919322296/29063006931199*x^9 - 2813750209005/29063006931
611: 199*x^8 - 2859411937992/29063006931199*x^7 - 414533880536/29063006931199*x^6
612: - 35713977492936/29063006931199*x^5 - 17432607267590/29063006931199*x^4 + 4
613: 9785595543672/29063006931199*x^3 + 9423768373204/29063006931199*x^2 - 427797
614: 76146743/29063006931199*x + 37962587857138/29063006931199, x^12 - 4*x^10 + 8
615: *x^9 + 12*x^8 + 12*x^7 + 138*x^6 + 132*x^5 - 43*x^4 + 58*x^2 - 128*x - 5), m
616: od(-279140305176/29063006931199*x^11 + 129916611552/29063006931199*x^10 + 12
617: 72919322296/29063006931199*x^9 - 2813750209005/29063006931199*x^8 - 28594119
618: 37992/29063006931199*x^7 - 414533880536/29063006931199*x^6 - 35713977492936/
619: 29063006931199*x^5 - 17432607267590/29063006931199*x^4 + 49785595543672/2906
620: 3006931199*x^3 + 9423768373204/29063006931199*x^2 - 13716769215544/290630069
621: 31199*x + 37962587857138/29063006931199, x^12 - 4*x^10 + 8*x^9 + 12*x^8 + 12
622: *x^7 + 138*x^6 + 132*x^5 - 43*x^4 + 58*x^2 - 128*x - 5), -1]]
623: ? comprealraw(qfr(5,3,-1,0.),qfr(7,1,-1,0.))
624: qfr(35, 43, 13, 0.E-38)
625: ? concat([1,2],[3,4])
626: [1, 2, 3, 4]
627: ? conductor(bnf,[[25,13;0,1],[1,1]])
628: [[[5, 3; 0, 1], [1, 0]], [12, [12], [[3, 2; 0, 1]]], mat(12)]
629: ? conductorofchar(bnr,[2])
630: [[5, 3; 0, 1], [0, 0]]
631: ? conj(1+i)
632: 1 - I
633: ? conjvec(mod(x^2+x+1,x^3-x-1))
634: [4.0795956234914387860104177508366260325, 0.46020218825428060699479112458168
635: 698369 + 0.18258225455744299269398828369501930573*I, 0.460202188254280606994
636: 79112458168698369 - 0.18258225455744299269398828369501930573*I]~
637: ? content([123,456,789,234])
638: 3
639: ? convol(sin(x),x*cos(x))
640: x + 1/12*x^3 + 1/2880*x^5 + 1/3628800*x^7 + 1/14631321600*x^9 + 1/1448500838
641: 40000*x^11 + 1/2982752926433280000*x^13 + 1/114000816848279961600000*x^15 +
642: O(x^16)
643: ? core(54713282649239)
644: 5471
645: ? core2(54713282649239)
646: [5471, 100003]
647: ? coredisc(54713282649239)
648: 21884
649: ? coredisc2(54713282649239)
650: [21884, 100003/2]
651: ? cos(1)
652: 0.54030230586813971740093660744297660373
653: ? cosh(1)
654: 1.5430806348152437784779056207570616825
655: ? move(0,200,150)
656: ? cursor(0)
657: ? cvtoi(1.7)
658: 1
659: ? cyclo(105)
660: x^48 + x^47 + x^46 - x^43 - x^42 - 2*x^41 - x^40 - x^39 + x^36 + x^35 + x^34
661: + x^33 + x^32 + x^31 - x^28 - x^26 - x^24 - x^22 - x^20 + x^17 + x^16 + x^1
662: 5 + x^14 + x^13 + x^12 - x^9 - x^8 - 2*x^7 - x^6 - x^5 + x^2 + x + 1
663: ? degree(x^3/(x-1))
664: 2
665: ? denom(12345/54321)
666: 18107
667: ? deplin(mod(1,7)*[2,-1;1,3])
668: [mod(6, 7), mod(5, 7)]~
669: ? deriv((x+y)^5,y)
670: 5*x^4 + 20*y*x^3 + 30*y^2*x^2 + 20*y^3*x + 5*y^4
671: ? ((x+y)^5)'
672: 5*x^4 + 20*y*x^3 + 30*y^2*x^2 + 20*y^3*x + 5*y^4
673: ? det([1,2,3;1,5,6;9,8,7])
674: -30
675: ? det2([1,2,3;1,5,6;9,8,7])
676: -30
677: ? detint([1,2,3;4,5,6])
678: 3
679: ? diagonal([2,4,6])
680:
681: [2 0 0]
682:
683: [0 4 0]
684:
685: [0 0 6]
686:
687: ? dilog(0.5)
688: 0.58224052646501250590265632015968010858
689: ? dz=vector(30,k,1);dd=vector(30,k,k==1);dm=dirdiv(dd,dz)
690: [1, -1, -1, 0, -1, 1, -1, 0, 0, 1, -1, 0, -1, 1, 1, 0, -1, 0, -1, 0, 1, 1, -
691: 1, 0, 0, 1, 0, 0, -1, -1]
692: ? deu=direuler(p=2,100,1/(1-apell(acurve,p)*x+if(acurve[12]%p,p,0)*x^2))
693: [1, -2, -3, 2, -2, 6, -1, 0, 6, 4, -5, -6, -2, 2, 6, -4, 0, -12, 0, -4, 3, 1
694: 0, 2, 0, -1, 4, -9, -2, 6, -12, -4, 8, 15, 0, 2, 12, -1, 0, 6, 0, -9, -6, 2,
695: -10, -12, -4, -9, 12, -6, 2, 0, -4, 1, 18, 10, 0, 0, -12, 8, 12, -8, 8, -6,
696: -8, 4, -30, 8, 0, -6, -4, 9, 0, -1, 2, 3, 0, 5, -12, 4, 8, 9, 18, -15, 6, 0
697: , -4, -18, 0, 4, 24, 2, 4, 12, 18, 0, -24, 4, 12, -30, -2]
698: ? anell(acurve,100)==deu
699: 1
700: ? dirmul(abs(dm),dz)
701: [1, 2, 2, 2, 2, 4, 2, 2, 2, 4, 2, 4, 2, 4, 4, 2, 2, 4, 2, 4, 4, 4, 2, 4, 2,
702: 4, 2, 4, 2, 8]
703: ? dirzetak(initalg(x^3-10*x+8),30)
704: [1, 2, 0, 3, 1, 0, 0, 4, 0, 2, 1, 0, 0, 0, 0, 5, 1, 0, 0, 3, 0, 2, 0, 0, 2,
705: 0, 1, 0, 1, 0]
706: ? disc(x^3+4*x+12)
707: -4144
708: ? discf(x^3+4*x+12)
709: -1036
710: ? discrayabs(bnr,mat(6))
711: [12, 12, 18026977100265125]
712: ? discrayabs(bnr)
713: [24, 12, 40621487921685401825918161408203125]
714: ? discrayabscond(bnr2)
715: 0
716: ? lu=ideallistunitgen(bnf,55);discrayabslist(bnf,lu)
717: [[[6, 6, mat([229, 3])]], [], [[], []], [[]], [[12, 12, [5, 3; 229, 6]], [12
718: , 12, [5, 3; 229, 6]]], [], [], [], [[], [], []], [], [[], []], [[], []], []
719: , [], [[24, 24, [3, 6; 5, 9; 229, 12]], [], [], [24, 24, [3, 6; 5, 9; 229, 1
720: 2]]], [[]], [[], []], [], [[18, 18, [19, 6; 229, 9]], [18, 18, [19, 6; 229,
721: 9]]], [[], []], [], [], [], [], [[], [24, 24, [5, 12; 229, 12]], []], [], [[
722: ], [], [], []], [], [], [], [], [], [[], [12, 12, [3, 3; 11, 3; 229, 6]], [1
723: 2, 12, [3, 3; 11, 3; 229, 6]], []], [], [], [[18, 18, [2, 12; 3, 12; 229, 9]
724: ], [], [18, 18, [2, 12; 3, 12; 229, 9]]], [[12, 12, [37, 3; 229, 6]], [12, 1
725: 2, [37, 3; 229, 6]]], [], [], [], [], [], [[], []], [[], []], [[], [], [], [
726: ], [], []], [], [], [[12, 12, [2, 12; 3, 3; 229, 6]], [12, 12, [2, 12; 3, 3;
727: 229, 6]]], [[18, 18, [7, 12; 229, 9]]], [], [[], [], [], []], [], [[], []],
728: [], [[], [24, 24, [5, 9; 11, 6; 229, 12]], [24, 24, [5, 9; 11, 6; 229, 12]]
729: , []]]
730: ? discrayabslistlong(bnf,20)
731: [[[[matrix(0,2,j,k,0), 6, 6, mat([229, 3])]], [], [[mat([12, 1]), 0, 0, 0],
732: [mat([13, 1]), 0, 0, 0]], [[mat([10, 1]), 0, 0, 0]], [[mat([20, 1]), 12, 12,
733: [5, 3; 229, 6]], [mat([21, 1]), 12, 12, [5, 3; 229, 6]]], [], [], [], [[mat
734: ([12, 2]), 0, 0, 0], [[12, 1; 13, 1], 0, 0, 0], [mat([13, 2]), 0, 0, 0]], []
735: , [[mat([44, 1]), 0, 0, 0], [mat([45, 1]), 0, 0, 0]], [[[10, 1; 12, 1], 0, 0
736: , 0], [[10, 1; 13, 1], 0, 0, 0]], [], [], [[[12, 1; 20, 1], 24, 24, [3, 6; 5
737: , 9; 229, 12]], [[13, 1; 20, 1], 0, 0, 0], [[12, 1; 21, 1], 0, 0, 0], [[13,
738: 1; 21, 1], 24, 24, [3, 6; 5, 9; 229, 12]]], [[mat([10, 2]), 0, 0, 0]], [[mat
739: ([68, 1]), 0, 0, 0], [mat([69, 1]), 0, 0, 0]], [], [[mat([76, 1]), 18, 18, [
740: 19, 6; 229, 9]], [mat([77, 1]), 18, 18, [19, 6; 229, 9]]], [[[10, 1; 20, 1],
741: 0, 0, 0], [[10, 1; 21, 1], 0, 0, 0]]]]
742: ? discrayrel(bnr,mat(6))
743: [6, 2, [125, 13; 0, 1]]
744: ? discrayrel(bnr)
745: [12, 1, [1953125, 1160888; 0, 1]]
746: ? discrayrelcond(bnr2)
747: 0
748: ? divisors(8!)
749: [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 14, 15, 16, 18, 20, 21, 24, 28, 30, 32,
750: 35, 36, 40, 42, 45, 48, 56, 60, 63, 64, 70, 72, 80, 84, 90, 96, 105, 112, 12
751: 0, 126, 128, 140, 144, 160, 168, 180, 192, 210, 224, 240, 252, 280, 288, 315
752: , 320, 336, 360, 384, 420, 448, 480, 504, 560, 576, 630, 640, 672, 720, 840,
753: 896, 960, 1008, 1120, 1152, 1260, 1344, 1440, 1680, 1920, 2016, 2240, 2520,
754: 2688, 2880, 3360, 4032, 4480, 5040, 5760, 6720, 8064, 10080, 13440, 20160,
755: 40320]
756: ? divres(345,123)
757: [2, 99]~
758: ? divres(x^7-1,x^5+1)
759: [x^2, -x^2 - 1]~
760: ? divsum(8!,x,x)
761: 159120
762: ? postdraw([0,0,0])
763: ? eigen([1,2,3;4,5,6;7,8,9])
764:
765: [-1.2833494518006402717978106547571267252 1 0.283349451800640271797810654757
766: 12672521]
767:
768: [-0.14167472590032013589890532737856336261 -2 0.6416747259003201358989053273
769: 7856336260]
770:
771: [1 1 1]
772:
773: ? eint1(2)
774: 0.048900510708061119567239835228049522206
775: ? erfc(2)
776: 0.0046777349810472658379307436327470713891
777: ? eta(q)
778: 1 - q - q^2 + q^5 + q^7 - q^12 - q^15 + O(q^16)
779: ? euler
780: 0.57721566490153286060651209008240243104
781: ? z=y;y=x;eval(z)
782: x
783: ? exp(1)
784: 2.7182818284590452353602874713526624977
785: ? extract([1,2,3,4,5,6,7,8,9,10],1000)
786: [4, 6, 7, 8, 9, 10]
787: ? 10!
788: 3628800
789: ? fact(10)
790: 3628800.0000000000000000000000000000000
791: ? factcantor(x^11+1,7)
792:
793: [mod(1, 7)*x + mod(1, 7) 1]
794:
795: [mod(1, 7)*x^10 + mod(6, 7)*x^9 + mod(1, 7)*x^8 + mod(6, 7)*x^7 + mod(1, 7)*
796: x^6 + mod(6, 7)*x^5 + mod(1, 7)*x^4 + mod(6, 7)*x^3 + mod(1, 7)*x^2 + mod(6,
797: 7)*x + mod(1, 7) 1]
798:
799: ? centerlift(lift(factfq(x^3+x^2+x-1,3,t^3+t^2+t-1)))
800:
801: [x - t 1]
802:
803: [x + (t^2 + t - 1) 1]
804:
805: [x + (-t^2 - 1) 1]
806:
807: ? factmod(x^11+1,7)
808:
809: [mod(1, 7)*x + mod(1, 7) 1]
810:
811: [mod(1, 7)*x^10 + mod(6, 7)*x^9 + mod(1, 7)*x^8 + mod(6, 7)*x^7 + mod(1, 7)*
812: x^6 + mod(6, 7)*x^5 + mod(1, 7)*x^4 + mod(6, 7)*x^3 + mod(1, 7)*x^2 + mod(6,
813: 7)*x + mod(1, 7) 1]
814:
815: ? factor(17!+1)
816:
817: [661 1]
818:
819: [537913 1]
820:
821: [1000357 1]
822:
823: ? p=x^5+3021*x^4-786303*x^3-6826636057*x^2-546603588746*x+3853890514072057
824: x^5 + 3021*x^4 - 786303*x^3 - 6826636057*x^2 - 546603588746*x + 385389051407
825: 2057
826: ? fa=[11699,6;2392997,2;4987333019653,2]
827:
828: [11699 6]
829:
830: [2392997 2]
831:
832: [4987333019653 2]
833:
834: ? factoredbasis(p,fa)
835: [1, x, x^2, 1/11699*x^3 + 1847/11699*x^2 - 132/11699*x - 2641/11699, 1/13962
836: 3738889203638909659*x^4 - 1552451622081122020/139623738889203638909659*x^3 +
837: 418509858130821123141/139623738889203638909659*x^2 - 6810913798507599407313
838: 4/139623738889203638909659*x - 13185339461968406/58346808996920447]
839: ? factoreddiscf(p,fa)
840: 136866601
841: ? factoredpolred(p,fa)
842: [x - 1, x^5 - 2*x^4 - 62*x^3 + 85*x^2 + 818*x + 1, x^5 - 2*x^4 - 53*x^3 - 46
843: *x^2 + 508*x + 913, x^5 - 2*x^4 - 13*x^3 + 37*x^2 - 21*x - 1, x^5 - x^4 - 52
844: *x^3 - 197*x^2 - 273*x - 127]
845: ? factoredpolred2(p,fa)
846:
847: [1 x - 1]
848:
849: [320031469790/139623738889203638909659*x^4 + 525154323698149/139623738889203
850: 638909659*x^3 + 68805502220272624/139623738889203638909659*x^2 + 11626197624
851: 4907072724/139623738889203638909659*x - 265513916545157609/58346808996920447
852: x^5 - 2*x^4 - 62*x^3 + 85*x^2 + 818*x + 1]
853:
854: [-649489679500/139623738889203638909659*x^4 - 1004850936416946/1396237388892
855: 03638909659*x^3 + 1850137668999773331/139623738889203638909659*x^2 + 1162464
856: 435118744503168/139623738889203638909659*x - 744221404070129897/583468089969
857: 20447 x^5 - 2*x^4 - 53*x^3 - 46*x^2 + 508*x + 913]
858:
859: [404377049971/139623738889203638909659*x^4 + 1028343729806593/13962373888920
860: 3638909659*x^3 - 220760129739668913/139623738889203638909659*x^2 - 139192454
861: 3479498840309/139623738889203638909659*x - 21580477171925514/583468089969204
862: 47 x^5 - 2*x^4 - 13*x^3 + 37*x^2 - 21*x - 1]
863:
864: [160329790087/139623738889203638909659*x^4 + 1043812506369034/13962373888920
865: 3638909659*x^3 + 1517006779298914407/139623738889203638909659*x^2 - 52234888
866: 8528537141362/139623738889203638909659*x - 677624890046649103/58346808996920
867: 447 x^5 - x^4 - 52*x^3 - 197*x^2 - 273*x - 127]
868:
869: ? factornf(x^3+x^2-2*x-1,t^3+t^2-2*t-1)
870:
871: [mod(1, t^3 + t^2 - 2*t - 1)*x + mod(-t, t^3 + t^2 - 2*t - 1) 1]
872:
873: [mod(1, t^3 + t^2 - 2*t - 1)*x + mod(-t^2 + 2, t^3 + t^2 - 2*t - 1) 1]
874:
875: [mod(1, t^3 + t^2 - 2*t - 1)*x + mod(t^2 + t - 1, t^3 + t^2 - 2*t - 1) 1]
876:
877: ? factorpadic(apol,7,8)
878:
879: [(1 + O(7^8))*x + (6 + 2*7^2 + 2*7^3 + 3*7^4 + 2*7^5 + 6*7^6 + O(7^8)) 1]
880:
881: [(1 + O(7^8))*x^2 + (1 + 6*7 + 4*7^2 + 4*7^3 + 3*7^4 + 4*7^5 + 6*7^7 + O(7^8
882: ))*x + (6 + 5*7 + 3*7^2 + 6*7^3 + 7^4 + 3*7^5 + 2*7^6 + 5*7^7 + O(7^8)) 1]
883:
884: ? factorpadic2(apol,7,8)
885:
886: [(1 + O(7^8))*x + (6 + 2*7^2 + 2*7^3 + 3*7^4 + 2*7^5 + 6*7^6 + O(7^8)) 1]
887:
888: [(1 + O(7^8))*x^2 + (1 + 6*7 + 4*7^2 + 4*7^3 + 3*7^4 + 4*7^5 + 6*7^7 + O(7^8
889: ))*x + (6 + 5*7 + 3*7^2 + 6*7^3 + 7^4 + 3*7^5 + 2*7^6 + 5*7^7 + O(7^8)) 1]
890:
891: ? factpol(x^15-1,3,1)
892:
893: [x - 1 1]
894:
895: [x^2 + x + 1 1]
896:
897: [x^12 + x^9 + x^6 + x^3 + 1 1]
898:
899: ? factpol(x^15-1,0,1)
900:
901: [x - 1 1]
902:
903: [x^2 + x + 1 1]
904:
905: [x^4 + x^3 + x^2 + x + 1 1]
906:
907: [x^8 - x^7 + x^5 - x^4 + x^3 - x + 1 1]
908:
909: ? factpol2(x^15-1,0)
910:
911: [x - 1 1]
912:
913: [x^2 + x + 1 1]
914:
915: [x^4 + x^3 + x^2 + x + 1 1]
916:
917: [x^8 - x^7 + x^5 - x^4 + x^3 - x + 1 1]
918:
919: ? fibo(100)
920: 354224848179261915075
921: ? floor(-1/2)
922: -1
923: ? floor(-2.5)
924: -3
925: ? for(x=1,5,print(x!))
926: 1
927: 2
928: 6
929: 24
930: 120
931: ? fordiv(10,x,print(x))
932: 1
933: 2
934: 5
935: 10
936: ? forprime(p=1,30,print(p))
937: 2
938: 3
939: 5
940: 7
941: 11
942: 13
943: 17
944: 19
945: 23
946: 29
947: ? forstep(x=0,pi,pi/12,print(sin(x)))
948: 0.E-38
949: 0.25881904510252076234889883762404832834
950: 0.49999999999999999999999999999999999999
951: 0.70710678118654752440084436210484903928
952: 0.86602540378443864676372317075293618346
953: 0.96592582628906828674974319972889736763
954: 1.0000000000000000000000000000000000000
955: 0.96592582628906828674974319972889736764
956: 0.86602540378443864676372317075293618348
957: 0.70710678118654752440084436210484903930
958: 0.50000000000000000000000000000000000002
959: 0.25881904510252076234889883762404832838
960: 4.7019774032891500318749461488889827112 E-38
961: ? forvec(x=[[1,3],[-2,2]],print1([x[1],x[2]]," "));print(" ");
962: [1, -2] [1, -1] [1, 0] [1, 1] [1, 2] [2, -2] [2, -1] [2, 0] [2, 1] [2, 2] [3
963: , -2] [3, -1] [3, 0] [3, 1] [3, 2]
964: ? frac(-2.7)
965: 0.30000000000000000000000000000000000000
966: ? galois(x^6-3*x^2-1)
967: [12, 1, 1]
968: ? nf3=initalg(x^6+108);galoisconj(nf3)
969: [-x, x, -1/12*x^4 - 1/2*x, -1/12*x^4 + 1/2*x, 1/12*x^4 - 1/2*x, 1/12*x^4 + 1
970: /2*x]~
971: ? galoisconjforce(nf3)
972: *** this function has been suppressed.
973:
974: ? aut=%[2];galoisapply(nf3,aut,mod(x^5,x^6+108))
975: mod(x^5, x^6 + 108)
976: ? gamh(10)
977: 1133278.3889487855673345741655888924755
978: ? gamma(10.5)
979: 1133278.3889487855673345741655888924755
980: ? gauss(hilbert(10),[1,2,3,4,5,6,7,8,9,0]~)
981: [9236800, -831303990, 18288515520, -170691240720, 832112321040, -23298940665
982: 00, 3883123564320, -3803844432960, 2020775945760, -449057772020]~
983: ? gaussmodulo([2,3;5,4],[7,11],[1,4]~)
984: [-5, -1]~
985: ? gaussmodulo2([2,3;5,4],[7,11],[1,4]~)
986: [[-5, -1]~, [-77, 723; 0, 1]]
987: ? gcd(12345678,87654321)
988: 9
989: ? getheap()
990: [214, 48887]
991: ? getrand()
992: 1285582432
993: ? getstack()
994: 0
995: ? globalred(acurve)
996: [37, [1, -1, 2, 2], 1]
997: ? getstack()
998: 0
999: ? hclassno(2000003)
1000: 357
1001: ? hell(acurve,apoint)
1002: 0.40889126591975072188708879805553617287
1003: ? hell2(acurve,apoint)
1004: 0.40889126591975072188708879805553617296
1005: ? hermite(amat=1/hilbert(7))
1006:
1007: [420 0 0 0 210 168 175]
1008:
1009: [0 840 0 0 0 0 504]
1010:
1011: [0 0 2520 0 0 0 1260]
1012:
1013: [0 0 0 2520 0 0 840]
1014:
1015: [0 0 0 0 13860 0 6930]
1016:
1017: [0 0 0 0 0 5544 0]
1018:
1019: [0 0 0 0 0 0 12012]
1020:
1021: ? hermite2(amat)
1022: [[420, 0, 0, 0, 210, 168, 175; 0, 840, 0, 0, 0, 0, 504; 0, 0, 2520, 0, 0, 0,
1023: 1260; 0, 0, 0, 2520, 0, 0, 840; 0, 0, 0, 0, 13860, 0, 6930; 0, 0, 0, 0, 0,
1024: 5544, 0; 0, 0, 0, 0, 0, 0, 12012], [420, 420, 840, 630, 2982, 1092, 4159; 21
1025: 0, 280, 630, 504, 2415, 876, 3395; 140, 210, 504, 420, 2050, 749, 2901; 105,
1026: 168, 420, 360, 1785, 658, 2542; 84, 140, 360, 315, 1582, 588, 2266; 70, 120
1027: , 315, 280, 1421, 532, 2046; 60, 105, 280, 252, 1290, 486, 1866]]
1028: ? hermitehavas(amat)
1029: [[360360, 0, 0, 0, 0, 144144, 300300; 0, 27720, 0, 0, 0, 0, 22176; 0, 0, 277
1030: 20, 0, 0, 0, 6930; 0, 0, 0, 2520, 0, 0, 840; 0, 0, 0, 0, 2520, 0, 1260; 0, 0
1031: , 0, 0, 0, 168, 0; 0, 0, 0, 0, 0, 0, 7], [51480, 4620, 5544, 630, 840, 20676
1032: , 48619; 45045, 3960, 4620, 504, 630, 18074, 42347; 40040, 3465, 3960, 420,
1033: 504, 16058, 37523; 36036, 3080, 3465, 360, 420, 14448, 33692; 32760, 2772, 3
1034: 080, 315, 360, 13132, 30574; 30030, 2520, 2772, 280, 315, 12036, 27986; 2772
1035: 0, 2310, 2520, 252, 280, 11109, 25803], [7, 6, 5, 4, 3, 2, 1]]
1036: ? hermitemod(amat,detint(amat))
1037:
1038: [420 0 0 0 210 168 175]
1039:
1040: [0 840 0 0 0 0 504]
1041:
1042: [0 0 2520 0 0 0 1260]
1043:
1044: [0 0 0 2520 0 0 840]
1045:
1046: [0 0 0 0 13860 0 6930]
1047:
1048: [0 0 0 0 0 5544 0]
1049:
1050: [0 0 0 0 0 0 12012]
1051:
1052: ? hermiteperm(amat)
1053: [[360360, 0, 0, 0, 0, 144144, 300300; 0, 27720, 0, 0, 0, 0, 22176; 0, 0, 277
1054: 20, 0, 0, 0, 6930; 0, 0, 0, 2520, 0, 0, 840; 0, 0, 0, 0, 2520, 0, 1260; 0, 0
1055: , 0, 0, 0, 168, 0; 0, 0, 0, 0, 0, 0, 7], [51480, 4620, 5544, 630, 840, 20676
1056: , 48619; 45045, 3960, 4620, 504, 630, 18074, 42347; 40040, 3465, 3960, 420,
1057: 504, 16058, 37523; 36036, 3080, 3465, 360, 420, 14448, 33692; 32760, 2772, 3
1058: 080, 315, 360, 13132, 30574; 30030, 2520, 2772, 280, 315, 12036, 27986; 2772
1059: 0, 2310, 2520, 252, 280, 11109, 25803], [7, 6, 5, 4, 3, 2, 1]]
1060: ? hess(hilbert(7))
1061:
1062: [1 90281/58800 -1919947/4344340 4858466341/1095033030 -77651417539/819678732
1063: 6 3386888964/106615355 1/2]
1064:
1065: [1/3 43/48 38789/5585580 268214641/109503303 -581330123627/126464718744 4365
1066: 450643/274153770 1/4]
1067:
1068: [0 217/2880 442223/7447440 53953931/292008808 -32242849453/168619624992 1475
1069: 457901/1827691800 1/80]
1070:
1071: [0 0 1604444/264539275 24208141/149362505292 847880210129/47916076768560 -45
1072: 44407141/103873817300 -29/40920]
1073:
1074: [0 0 0 9773092581/35395807550620 -24363634138919/107305824577186620 72118203
1075: 606917/60481351061158500 55899/3088554700]
1076:
1077: [0 0 0 0 67201501179065/8543442888354179988 -9970556426629/74082861999267660
1078: 0 -3229/13661312210]
1079:
1080: [0 0 0 0 0 -258198800769/9279048099409000 -13183/38381527800]
1081:
1082: ? hilb(2/3,3/4,5)
1083: 1
1084: ? hilbert(5)
1085:
1086: [1 1/2 1/3 1/4 1/5]
1087:
1088: [1/2 1/3 1/4 1/5 1/6]
1089:
1090: [1/3 1/4 1/5 1/6 1/7]
1091:
1092: [1/4 1/5 1/6 1/7 1/8]
1093:
1094: [1/5 1/6 1/7 1/8 1/9]
1095:
1096: ? hilbp(mod(5,7),mod(6,7))
1097: 1
1098: ? hvector(10,x,1/x)
1099: [1, 1/2, 1/3, 1/4, 1/5, 1/6, 1/7, 1/8, 1/9, 1/10]
1100: ? hyperu(1,1,1)
1101: 0.59634736232319407434107849936927937488
1102: ? i^2
1103: -1
1104: ? nf1=initalgred(nfpol)
1105: [x^5 - 2*x^4 + 3*x^3 + 8*x^2 + 3*x + 2, [1, 2], 595125, 4, [[1, -1.089115145
1106: 7205048250249527946671612684, 1.1861718006377964594796293860483989860, -0.59
1107: 741050929194782733001765987770358483, 0.158944197453903762065494816710718942
1108: 89; 1, -0.13838372073406036365047976417441696637 + 0.49181637657768643499753
1109: 285514741525107*I, -0.22273329410580226599155701611419649154 - 0.13611876021
1110: 752805221674918029071012580*I, -0.13167445871785818798769651537619416009 + 0
1111: .13249517760521973840801462296650806543*I, -0.053650958656997725359297528357
1112: 602608116 + 0.27622636814169107038138284681568361486*I; 1, 1.682941293594312
1113: 7761629561615079976005 + 2.0500351226010726172974286983598602163*I, -1.37035
1114: 26062130959637482576769100030014 + 6.9001775222880494773720769629846373016*I
1115: , -8.0696202866361678983472946546849540475 + 8.87676767859710424508852843013
1116: 48051602*I, -22.025821140069954155673449879997756863 - 8.4306586896999153544
1117: 710860185447589664*I], [1, 2, 2; -1.0891151457205048250249527946671612684, -
1118: 0.27676744146812072730095952834883393274 - 0.9836327531553728699950657102948
1119: 3050214*I, 3.3658825871886255523259123230159952011 - 4.100070245202145234594
1120: 8573967197204327*I; 1.1861718006377964594796293860483989860, -0.445466588211
1121: 60453198311403222839298308 + 0.27223752043505610443349836058142025160*I, -2.
1122: 7407052124261919274965153538200060029 - 13.800355044576098954744153925969274
1123: 603*I; -0.59741050929194782733001765987770358483, -0.26334891743571637597539
1124: 303075238832018 - 0.26499035521043947681602924593301613087*I, -16.1392405732
1125: 72335796694589309369908095 - 17.753535357194208490177056860269610320*I; 0.15
1126: 894419745390376206549481671071894289, -0.10730191731399545071859505671520521
1127: 623 - 0.55245273628338214076276569363136722973*I, -44.0516422801399083113468
1128: 99759995513726 + 16.861317379399830708942172037089517932*I], [5, 2.000000000
1129: 0000000000000000000000000000, -2.0000000000000000000000000000000000000, -17.
1130: 000000000000000000000000000000000000, -44.0000000000000000000000000000000000
1131: 00; 2.0000000000000000000000000000000000000, 15.7781094086719980448363574712
1132: 83695361, 22.314643349754061651916553814602769764, 10.0513952578314782754999
1133: 32716306366248, -108.58917507620841447456569092094763671; -2.000000000000000
1134: 0000000000000000000000, 22.314643349754061651916553814602769764, 100.5239126
1135: 2388960975827806174040462368, 143.93295090847353519436673793501057176, -55.8
1136: 42564718082452641322500190813370023; -17.00000000000000000000000000000000000
1137: 0, 10.051395257831478275499932716306366248, 143.9329509084735351943667379350
1138: 1057176, 288.25823756749944693139292174819167135, 205.7984003827766237572018
1139: 0649465932302; -44.000000000000000000000000000000000000, -108.58917507620841
1140: 447456569092094763671, -55.842564718082452641322500190813370023, 205.7984003
1141: 8277662375720180649465932302, 1112.6092277946777707779250962522343036], [5,
1142: 2, -2, -17, -44; 2, -2, -34, -63, -40; -2, -34, -90, -101, 177; -17, -63, -1
1143: 01, -27, 505; -44, -40, 177, 505, 828], [345, 0, 160, 252, 156; 0, 345, 215,
1144: 311, 306; 0, 0, 5, 3, 2; 0, 0, 0, 1, 0; 0, 0, 0, 0, 1], [163875, -388125, -
1145: 296700, 234600, -89700; -388125, -1593900, -677925, 595125, -315675; -296700
1146: , -677925, 17250, 58650, -87975; 234600, 595125, 58650, -100050, 89700; -897
1147: 00, -315675, -87975, 89700, -55200], [595125, [-167325, -82800, 79350, 1725,
1148: 0]~, 125439056256992431640625]], [-1.0891151457205048250249527946671612684,
1149: -0.13838372073406036365047976417441696637 + 0.49181637657768643499753285514
1150: 741525107*I, 1.6829412935943127761629561615079976005 + 2.0500351226010726172
1151: 974286983598602163*I], [1, x, x^2, 1/2*x^3 + 1/2*x^2 + 1/2*x, 1/2*x^4 + 1/2*
1152: x], [1, 0, 0, 0, 0; 0, 1, 0, -1, -1; 0, 0, 1, -1, 0; 0, 0, 0, 2, 0; 0, 0, 0,
1153: 0, 2], [1, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, -1, -2, 0, 0, -1, -2, -2, 0
1154: , -1, -2, -2, 5; 0, 1, 0, 0, 0, 1, 0, -1, -1, -1, 0, -1, -1, -2, 2, 0, -1, -
1155: 2, -1, 7, 0, -1, 2, 7, 14; 0, 0, 1, 0, 0, 0, 1, -1, 0, -2, 1, -1, 0, -3, -3,
1156: 0, 0, -3, -4, -1, 0, -2, -3, -1, 15; 0, 0, 0, 1, 0, 0, 0, 2, 1, -3, 0, 2, 0
1157: , -2, -13, 1, 1, -2, -9, -19, 0, -3, -13, -19, 7; 0, 0, 0, 0, 1, 0, 0, 0, 1,
1158: 2, 0, 0, 2, 3, 1, 0, 1, 3, 4, -4, 1, 2, 1, -4, -21]]
1159: ? initalgred2(nfpol)
1160: [[x^5 - 2*x^4 + 3*x^3 + 8*x^2 + 3*x + 2, [1, 2], 595125, 4, [[1, -1.08911514
1161: 57205048250249527946671612684, 1.1861718006377964594796293860483989860, -0.5
1162: 9741050929194782733001765987770358483, 0.15894419745390376206549481671071894
1163: 289; 1, -0.13838372073406036365047976417441696637 + 0.4918163765776864349975
1164: 3285514741525107*I, -0.22273329410580226599155701611419649154 - 0.1361187602
1165: 1752805221674918029071012580*I, -0.13167445871785818798769651537619416009 +
1166: 0.13249517760521973840801462296650806543*I, -0.05365095865699772535929752835
1167: 7602608116 + 0.27622636814169107038138284681568361486*I; 1, 1.68294129359431
1168: 27761629561615079976005 + 2.0500351226010726172974286983598602163*I, -1.3703
1169: 526062130959637482576769100030014 + 6.9001775222880494773720769629846373016*
1170: I, -8.0696202866361678983472946546849540475 + 8.8767676785971042450885284301
1171: 348051602*I, -22.025821140069954155673449879997756863 - 8.430658689699915354
1172: 4710860185447589664*I], [1, 2, 2; -1.0891151457205048250249527946671612684,
1173: -0.27676744146812072730095952834883393274 - 0.983632753155372869995065710294
1174: 83050214*I, 3.3658825871886255523259123230159952011 - 4.10007024520214523459
1175: 48573967197204327*I; 1.1861718006377964594796293860483989860, -0.44546658821
1176: 160453198311403222839298308 + 0.27223752043505610443349836058142025160*I, -2
1177: .7407052124261919274965153538200060029 - 13.80035504457609895474415392596927
1178: 4603*I; -0.59741050929194782733001765987770358483, -0.2633489174357163759753
1179: 9303075238832018 - 0.26499035521043947681602924593301613087*I, -16.139240573
1180: 272335796694589309369908095 - 17.753535357194208490177056860269610320*I; 0.1
1181: 5894419745390376206549481671071894289, -0.1073019173139954507185950567152052
1182: 1623 - 0.55245273628338214076276569363136722973*I, -44.051642280139908311346
1183: 899759995513726 + 16.861317379399830708942172037089517932*I], [5, 2.00000000
1184: 00000000000000000000000000000, -2.0000000000000000000000000000000000000, -17
1185: .000000000000000000000000000000000000, -44.000000000000000000000000000000000
1186: 000; 2.0000000000000000000000000000000000000, 15.778109408671998044836357471
1187: 283695361, 22.314643349754061651916553814602769764, 10.051395257831478275499
1188: 932716306366248, -108.58917507620841447456569092094763671; -2.00000000000000
1189: 00000000000000000000000, 22.314643349754061651916553814602769764, 100.523912
1190: 62388960975827806174040462368, 143.93295090847353519436673793501057176, -55.
1191: 842564718082452641322500190813370023; -17.0000000000000000000000000000000000
1192: 00, 10.051395257831478275499932716306366248, 143.932950908473535194366737935
1193: 01057176, 288.25823756749944693139292174819167135, 205.798400382776623757201
1194: 80649465932302; -44.000000000000000000000000000000000000, -108.5891750762084
1195: 1447456569092094763671, -55.842564718082452641322500190813370023, 205.798400
1196: 38277662375720180649465932302, 1112.6092277946777707779250962522343036], [5,
1197: 2, -2, -17, -44; 2, -2, -34, -63, -40; -2, -34, -90, -101, 177; -17, -63, -
1198: 101, -27, 505; -44, -40, 177, 505, 828], [345, 0, 160, 252, 156; 0, 345, 215
1199: , 311, 306; 0, 0, 5, 3, 2; 0, 0, 0, 1, 0; 0, 0, 0, 0, 1], [163875, -388125,
1200: -296700, 234600, -89700; -388125, -1593900, -677925, 595125, -315675; -29670
1201: 0, -677925, 17250, 58650, -87975; 234600, 595125, 58650, -100050, 89700; -89
1202: 700, -315675, -87975, 89700, -55200], [595125, [-167325, -82800, 79350, 1725
1203: , 0]~, 125439056256992431640625]], [-1.0891151457205048250249527946671612684
1204: , -0.13838372073406036365047976417441696637 + 0.4918163765776864349975328551
1205: 4741525107*I, 1.6829412935943127761629561615079976005 + 2.050035122601072617
1206: 2974286983598602163*I], [1, x, x^2, 1/2*x^3 + 1/2*x^2 + 1/2*x, 1/2*x^4 + 1/2
1207: *x], [1, 0, 0, 0, 0; 0, 1, 0, -1, -1; 0, 0, 1, -1, 0; 0, 0, 0, 2, 0; 0, 0, 0
1208: , 0, 2], [1, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, -1, -2, 0, 0, -1, -2, -2,
1209: 0, -1, -2, -2, 5; 0, 1, 0, 0, 0, 1, 0, -1, -1, -1, 0, -1, -1, -2, 2, 0, -1,
1210: -2, -1, 7, 0, -1, 2, 7, 14; 0, 0, 1, 0, 0, 0, 1, -1, 0, -2, 1, -1, 0, -3, -3
1211: , 0, 0, -3, -4, -1, 0, -2, -3, -1, 15; 0, 0, 0, 1, 0, 0, 0, 2, 1, -3, 0, 2,
1212: 0, -2, -13, 1, 1, -2, -9, -19, 0, -3, -13, -19, 7; 0, 0, 0, 0, 1, 0, 0, 0, 1
1213: , 2, 0, 0, 2, 3, 1, 0, 1, 3, 4, -4, 1, 2, 1, -4, -21]], mod(-1/2*x^4 + 3/2*x
1214: ^3 - 5/2*x^2 - 2*x + 1, x^5 - 2*x^4 + 3*x^3 + 8*x^2 + 3*x + 2)]
1215: ? vp=primedec(nf,3)[1]
1216: [3, [1, 1, 0, 0, 0]~, 1, 1, [1, -1, -1, 0, 0]~]
1217: ? idx=idealmul(nf,idmat(5),vp)
1218:
1219: [3 1 2 2 2]
1220:
1221: [0 1 0 0 0]
1222:
1223: [0 0 1 0 0]
1224:
1225: [0 0 0 1 0]
1226:
1227: [0 0 0 0 1]
1228:
1229: ? idealinv(nf,idx)
1230:
1231: [1 0 2/3 0 0]
1232:
1233: [0 1 1/3 0 0]
1234:
1235: [0 0 1/3 0 0]
1236:
1237: [0 0 0 1 0]
1238:
1239: [0 0 0 0 1]
1240:
1241: ? idy=ideallllred(nf,idx,[1,5,6])
1242:
1243: [5 0 0 2 0]
1244:
1245: [0 5 0 0 0]
1246:
1247: [0 0 5 2 0]
1248:
1249: [0 0 0 1 0]
1250:
1251: [0 0 0 0 5]
1252:
1253: ? idealadd(nf,idx,idy)
1254:
1255: [1 0 0 0 0]
1256:
1257: [0 1 0 0 0]
1258:
1259: [0 0 1 0 0]
1260:
1261: [0 0 0 1 0]
1262:
1263: [0 0 0 0 1]
1264:
1265: ? idealaddone(nf,idx,idy)
1266: [[3, 0, 2, 1, 0]~, [-2, 0, -2, -1, 0]~]
1267: ? idealaddmultone(nf,[idy,idx])
1268: [[-5, 0, 0, 0, 0]~, [6, 0, 0, 0, 0]~]
1269: ? idealappr(nf,idy)
1270: [-2, 0, -2, 4, 0]~
1271: ? idealapprfact(nf,idealfactor(nf,idy))
1272: [-2, 0, -2, 4, 0]~
1273: ? idealcoprime(nf,idx,idx)
1274: [-2/3, 2/3, -1/3, 0, 0]~
1275: ? idz=idealintersect(nf,idx,idy)
1276:
1277: [15 5 10 12 10]
1278:
1279: [0 5 0 0 0]
1280:
1281: [0 0 5 2 0]
1282:
1283: [0 0 0 1 0]
1284:
1285: [0 0 0 0 5]
1286:
1287: ? idealfactor(nf,idz)
1288:
1289: [[3, [1, 1, 0, 0, 0]~, 1, 1, [1, -1, -1, 0, 0]~] 1]
1290:
1291: [[5, [-2, 0, 0, 0, 1]~, 1, 1, [2, 2, 1, 1, 4]~] 1]
1292:
1293: [[5, [0, 0, -1, 0, 1]~, 4, 1, [4, 5, 4, 2, 0]~] 3]
1294:
1295: ? ideallist(bnf,20)
1296: [[[1, 0; 0, 1]], [], [[3, 2; 0, 1], [3, 0; 0, 1]], [[2, 0; 0, 2]], [[5, 3; 0
1297: , 1], [5, 1; 0, 1]], [], [], [], [[9, 5; 0, 1], [3, 0; 0, 3], [9, 3; 0, 1]],
1298: [], [[11, 9; 0, 1], [11, 1; 0, 1]], [[6, 4; 0, 2], [6, 0; 0, 2]], [], [], [
1299: [15, 8; 0, 1], [15, 3; 0, 1], [15, 11; 0, 1], [15, 6; 0, 1]], [[4, 0; 0, 4]]
1300: , [[17, 14; 0, 1], [17, 2; 0, 1]], [], [[19, 18; 0, 1], [19, 0; 0, 1]], [[10
1301: , 6; 0, 2], [10, 2; 0, 2]]]
1302: ? idx2=idealmul(nf,idx,idx)
1303:
1304: [9 7 5 8 2]
1305:
1306: [0 1 0 0 0]
1307:
1308: [0 0 1 0 0]
1309:
1310: [0 0 0 1 0]
1311:
1312: [0 0 0 0 1]
1313:
1314: ? idt=idealmulred(nf,idx,idx)
1315:
1316: [2 0 0 0 1]
1317:
1318: [0 2 0 0 1]
1319:
1320: [0 0 2 0 0]
1321:
1322: [0 0 0 2 1]
1323:
1324: [0 0 0 0 1]
1325:
1326: ? idealdiv(nf,idy,idt)
1327:
1328: [5 5/2 5/2 7/2 0]
1329:
1330: [0 5/2 0 0 0]
1331:
1332: [0 0 5/2 1 0]
1333:
1334: [0 0 0 1/2 0]
1335:
1336: [0 0 0 0 5/2]
1337:
1338: ? idealdivexact(nf,idx2,idx)
1339:
1340: [3 1 2 2 2]
1341:
1342: [0 1 0 0 0]
1343:
1344: [0 0 1 0 0]
1345:
1346: [0 0 0 1 0]
1347:
1348: [0 0 0 0 1]
1349:
1350: ? idealhermite(nf,vp)
1351:
1352: [3 1 2 2 2]
1353:
1354: [0 1 0 0 0]
1355:
1356: [0 0 1 0 0]
1357:
1358: [0 0 0 1 0]
1359:
1360: [0 0 0 0 1]
1361:
1362: ? idealhermite2(nf,vp[2],3)
1363:
1364: [3 1 2 2 2]
1365:
1366: [0 1 0 0 0]
1367:
1368: [0 0 1 0 0]
1369:
1370: [0 0 0 1 0]
1371:
1372: [0 0 0 0 1]
1373:
1374: ? idealnorm(nf,idt)
1375: 16
1376: ? idp=idealpow(nf,idx,7)
1377:
1378: [2187 1807 2129 692 1379]
1379:
1380: [0 1 0 0 0]
1381:
1382: [0 0 1 0 0]
1383:
1384: [0 0 0 1 0]
1385:
1386: [0 0 0 0 1]
1387:
1388: ? idealpowred(nf,idx,7)
1389:
1390: [2 0 0 0 1]
1391:
1392: [0 2 0 0 1]
1393:
1394: [0 0 2 0 0]
1395:
1396: [0 0 0 2 1]
1397:
1398: [0 0 0 0 1]
1399:
1400: ? idealtwoelt(nf,idy)
1401: [5, [2, 0, 2, 1, 0]~]
1402: ? idealtwoelt2(nf,idy,10)
1403: [-2, 0, -2, -1, 0]~
1404: ? idealval(nf,idp,vp)
1405: 7
1406: ? idmat(5)
1407:
1408: [1 0 0 0 0]
1409:
1410: [0 1 0 0 0]
1411:
1412: [0 0 1 0 0]
1413:
1414: [0 0 0 1 0]
1415:
1416: [0 0 0 0 1]
1417:
1418: ? if(3<2,print("bof"),print("ok"));
1419: ok
1420: ? imag(2+3*i)
1421: 3
1422: ? image([1,3,5;2,4,6;3,5,7])
1423:
1424: [1 3]
1425:
1426: [2 4]
1427:
1428: [3 5]
1429:
1430: ? image(pi*[1,3,5;2,4,6;3,5,7])
1431:
1432: [3.1415926535897932384626433832795028841 9.424777960769379715387930149838508
1433: 6525]
1434:
1435: [6.2831853071795864769252867665590057683 12.56637061435917295385057353311801
1436: 1536]
1437:
1438: [9.4247779607693797153879301498385086525 15.70796326794896619231321691639751
1439: 4420]
1440:
1441: ? incgam(2,1)
1442: 0.73575888234288464319104754032292173491
1443: ? incgam1(2,1)
1444: -0.26424111765711535680895245967678075578
1445: ? incgam2(2,1)
1446: 0.73575888234288464319104754032292173489
1447: ? incgam3(2,1)
1448: 0.26424111765711535680895245967707826508
1449: ? incgam4(4,1,6)
1450: 5.8860710587430771455283803225833738791
1451: ? indexrank([1,1,1;1,1,1;1,1,2])
1452: [[1, 3], [1, 3]]
1453: ? indsort([8,7,6,5])
1454: [4, 3, 2, 1]
1455: ? initell([0,0,0,-1,0])
1456: [0, 0, 0, -1, 0, 0, -2, 0, -1, 48, 0, 64, 1728, [1.0000000000000000000000000
1457: 000000000000, 0.E-38, -1.0000000000000000000000000000000000000]~, 2.62205755
1458: 42921198104648395898911194136, 2.6220575542921198104648395898911194136*I, -0
1459: .59907011736779610371996124614016193910, -1.79721035210338831115988373842048
1460: 58173*I, 6.8751858180203728274900957798105571979]
1461: ? initrect(1,700,700)
1462: ? nfz=initzeta(x^2-2);
1463: ? integ(sin(x),x)
1464: 1/2*x^2 - 1/24*x^4 + 1/720*x^6 - 1/40320*x^8 + 1/3628800*x^10 - 1/479001600*
1465: x^12 + 1/87178291200*x^14 - 1/20922789888000*x^16 + O(x^17)
1466: ? integ((-x^2-2*a*x+8*a)/(x^4-14*x^3+(2*a+49)*x^2-14*a*x+a^2),x)
1467: (x + a)/(x^2 - 7*x + a)
1468: ? intersect([1,2;3,4;5,6],[2,3;7,8;8,9])
1469:
1470: [-1]
1471:
1472: [-1]
1473:
1474: [-1]
1475:
1476: ? \precision=19
1477: realprecision = 19 significant digits
1478: ? intgen(x=0,pi,sin(x))
1479: 2.000000000000000017
1480: ? sqr(2*intgen(x=0,4,exp(-x^2)))
1481: 3.141592556720305685
1482: ? 4*intinf(x=1,10^20,1/(1+x^2))
1483: 3.141592653589793208
1484: ? intnum(x=-0.5,0.5,1/sqrt(1-x^2))
1485: 1.047197551196597747
1486: ? 2*intopen(x=0,100,sin(x)/x)
1487: 3.124450933778112629
1488: ? \precision=38
1489: realprecision = 38 significant digits
1490: ? inverseimage([1,1;2,3;5,7],[2,2,6]~)
1491: [4, -2]~
1492: ? isdiagonal([1,0,0;0,5,0;0,0,0])
1493: 1
1494: ? isfund(12345)
1495: 1
1496: ? isideal(bnf[7],[5,1;0,1])
1497: 1
1498: ? isincl(x^2+1,x^4+1)
1499: [-x^2, x^2]
1500: ? isinclfast(initalg(x^2+1),initalg(x^4+1))
1501: [-x^2, x^2]
1502: ? isirreducible(x^5+3*x^3+5*x^2+15)
1503: 0
1504: ? isisom(x^3+x^2-2*x-1,x^3+x^2-2*x-1)
1505: [x, -x^2 - x + 1, x^2 - 2]
1506: ? isisomfast(initalg(x^3-2),initalg(x^3-6*x^2-6*x-30))
1507: [-1/25*x^2 + 13/25*x - 2/5]
1508: ? isprime(12345678901234567)
1509: 0
1510: ? isprincipal(bnf,[5,1;0,1])
1511: [1]~
1512: ? isprincipalgen(bnf,[5,1;0,1])
1513: [[1]~, [2, 1/3]~, 117]
1514: ? isprincipalraygen(bnr,primedec(bnf,7)[1])
1515: [[9]~, [-2170/6561, -931/19683]~, 113]
1516: ? ispsp(73!+1)
1517: 1
1518: ? isqrt(10!^2+1)
1519: 3628800
1520: ? isset([-3,5,7,7])
1521: 0
1522: ? issqfree(123456789876543219)
1523: 0
1524: ? issquare(12345678987654321)
1525: 1
1526: ? isunit(bnf,mod(3405*x-27466,x^2-x-57))
1527: [-4, mod(1, 2)]~
1528: ? jacobi(hilbert(6))
1529: [[1.6188998589243390969705881471257800712, 0.2423608705752095521357284158507
1530: 0114077, 0.000012570757122625194922982397996498755027, 0.0000001082799484565
1531: 5497685388772372251711485, 0.016321521319875822124345079564191505890, 0.0006
1532: 1574835418265769764919938428527140264]~, [0.74871921887909485900280109200517
1533: 845109, -0.61454482829258676899320019644273870645, 0.01114432093072471053067
1534: 8340374220998541, -0.0012481940840821751169398163046387834473, 0.24032536934
1535: 252330399154228873240534568, -0.062226588150197681775152126611810492910; 0.4
1536: 4071750324351206127160083580231701801, 0.21108248167867048675227675845247769
1537: 095, -0.17973275724076003758776897803740640964, 0.03560664294428763526612284
1538: 8131812048466, -0.69765137527737012296208335046678265583, 0.4908392097109243
1539: 6297498316169060044997; 0.32069686982225190106359024326699463106, 0.36589360
1540: 730302614149086554211117169622, 0.60421220675295973004426567844103062241, -0
1541: .24067907958842295837736719558855679285, -0.23138937333290388042251363554209
1542: 048309, -0.53547692162107486593474491750949545456; 0.25431138634047419251788
1543: 312792590944672, 0.39470677609501756783094636145991581708, -0.44357471627623
1544: 954554460416705180105301, 0.62546038654922724457753441039459331059, 0.132863
1545: 15850933553530333839628101576050, -0.41703769221897886840494514780771076439;
1546: 0.21153084007896524664213667673977991959, 0.3881904338738864286311144882599
1547: 2418973, -0.44153664101228966222143649752977203423, -0.689807199293836684198
1548: 01738006926829419, 0.36271492146487147525299457604461742111, 0.0470340189331
1549: 15649705614518466541243873; 0.18144297664876947372217005457727093715, 0.3706
1550: 9590776736280861775501084807394603, 0.45911481681642960284551392793050866602
1551: , 0.27160545336631286930015536176213647001, 0.502762866757515384892605663686
1552: 47786272, 0.54068156310385293880022293448123782121]]
1553: ? jbesselh(1,1)
1554: 0.24029783912342701089584304474193368045
1555: ? jell(i)
1556: 1728.0000000000000000000000000000000000 + 0.E-45*I
1557: ? kbessel(1+i,1)
1558: 0.32545977186584141085464640324923711863 + 0.2894280370259921276345671592415
1559: 2302704*I
1560: ? kbessel2(1+i,1)
1561: 0.32545977186584141085464640324923711863 + 0.2894280370259921276345671592415
1562: 2302704*I
1563: ? x
1564: x
1565: ? y
1566: x
1567: ? ker(matrix(4,4,x,y,x/y))
1568:
1569: [-1/2 -1/3 -1/4]
1570:
1571: [1 0 0]
1572:
1573: [0 1 0]
1574:
1575: [0 0 1]
1576:
1577: ? ker(matrix(4,4,x,y,sin(x+y)))
1578:
1579: [1.0000000000000000000000000000000000000 1.080604611736279434801873214885953
1580: 2074]
1581:
1582: [-1.0806046117362794348018732148859532074 -0.1677063269057152260048635409984
1583: 7562046]
1584:
1585: [1 0]
1586:
1587: [0 1]
1588:
1589: ? keri(matrix(4,4,x,y,x+y))
1590:
1591: [1 2]
1592:
1593: [-2 -3]
1594:
1595: [1 0]
1596:
1597: [0 1]
1598:
1599: ? kerint(matrix(4,4,x,y,x*y))
1600:
1601: [-1 -1 -1]
1602:
1603: [-1 0 1]
1604:
1605: [1 -1 1]
1606:
1607: [0 1 -1]
1608:
1609: ? kerint1(matrix(4,4,x,y,x*y))
1610:
1611: [-1 -1 -1]
1612:
1613: [-1 0 1]
1614:
1615: [1 -1 1]
1616:
1617: [0 1 -1]
1618:
1619: ? kerint2(matrix(4,6,x,y,2520/(x+y)))
1620:
1621: [3 1]
1622:
1623: [-30 -15]
1624:
1625: [70 70]
1626:
1627: [0 -140]
1628:
1629: [-126 126]
1630:
1631: [84 -42]
1632:
1633: ? f(u)=u+1;
1634: ? print(f(5));kill(f);
1635: 6
1636: ? f=12
1637: 12
1638: ? killrect(1)
1639: ? kro(5,7)
1640: -1
1641: ? kro(3,18)
1642: 0
1643: ? laplace(x*exp(x*y)/(exp(x)-1))
1644: 1 - 1/2*x + 13/6*x^2 - 3*x^3 + 419/30*x^4 - 30*x^5 + 6259/42*x^6 - 420*x^7 +
1645: 22133/10*x^8 - 7560*x^9 + 2775767/66*x^10 - 166320*x^11 + 2655339269/2730*x
1646: ^12 - 4324320*x^13 + 264873251/10*x^14 + O(x^15)
1647: ? lcm(15,-21)
1648: 105
1649: ? length(divisors(1000))
1650: 16
1651: ? legendre(10)
1652: 46189/256*x^10 - 109395/256*x^8 + 45045/128*x^6 - 15015/128*x^4 + 3465/256*x
1653: ^2 - 63/256
1654: ? lex([1,3],[1,3,5])
1655: -1
1656: ? lexsort([[1,5],[2,4],[1,5,1],[1,4,2]])
1657: [[1, 4, 2], [1, 5], [1, 5, 1], [2, 4]]
1658: ? lift(chinese(mod(7,15),mod(4,21)))
1659: 67
1660: ? lindep([(1-3*sqrt(2))/(3-2*sqrt(3)),1,sqrt(2),sqrt(3),sqrt(6)])
1661: [-3, -3, 9, -2, 6]
1662: ? lindep2([(1-3*sqrt(2))/(3-2*sqrt(3)),1,sqrt(2),sqrt(3),sqrt(6)],14)
1663: [-3, -3, 9, -2, 6]
1664: ? move(0,0,900);line(0,900,0)
1665: ? lines(0,vector(5,k,50*k),vector(5,k,10*k*k))
1666: ? m=1/hilbert(7)
1667:
1668: [49 -1176 8820 -29400 48510 -38808 12012]
1669:
1670: [-1176 37632 -317520 1128960 -1940400 1596672 -504504]
1671:
1672: [8820 -317520 2857680 -10584000 18711000 -15717240 5045040]
1673:
1674: [-29400 1128960 -10584000 40320000 -72765000 62092800 -20180160]
1675:
1676: [48510 -1940400 18711000 -72765000 133402500 -115259760 37837800]
1677:
1678: [-38808 1596672 -15717240 62092800 -115259760 100590336 -33297264]
1679:
1680: [12012 -504504 5045040 -20180160 37837800 -33297264 11099088]
1681:
1682: ? mp=concat(m,idmat(7))
1683:
1684: [49 -1176 8820 -29400 48510 -38808 12012 1 0 0 0 0 0 0]
1685:
1686: [-1176 37632 -317520 1128960 -1940400 1596672 -504504 0 1 0 0 0 0 0]
1687:
1688: [8820 -317520 2857680 -10584000 18711000 -15717240 5045040 0 0 1 0 0 0 0]
1689:
1690: [-29400 1128960 -10584000 40320000 -72765000 62092800 -20180160 0 0 0 1 0 0
1691: 0]
1692:
1693: [48510 -1940400 18711000 -72765000 133402500 -115259760 37837800 0 0 0 0 1 0
1694: 0]
1695:
1696: [-38808 1596672 -15717240 62092800 -115259760 100590336 -33297264 0 0 0 0 0
1697: 1 0]
1698:
1699: [12012 -504504 5045040 -20180160 37837800 -33297264 11099088 0 0 0 0 0 0 1]
1700:
1701: ? lll(m)
1702:
1703: [-420 -420 840 630 -1092 757 2982]
1704:
1705: [-210 -280 630 504 -876 700 2415]
1706:
1707: [-140 -210 504 420 -749 641 2050]
1708:
1709: [-105 -168 420 360 -658 589 1785]
1710:
1711: [-84 -140 360 315 -588 544 1582]
1712:
1713: [-70 -120 315 280 -532 505 1421]
1714:
1715: [-60 -105 280 252 -486 471 1290]
1716:
1717: ? lll1(m)
1718:
1719: [-420 -420 840 630 -1092 757 2982]
1720:
1721: [-210 -280 630 504 -876 700 2415]
1722:
1723: [-140 -210 504 420 -749 641 2050]
1724:
1725: [-105 -168 420 360 -658 589 1785]
1726:
1727: [-84 -140 360 315 -588 544 1582]
1728:
1729: [-70 -120 315 280 -532 505 1421]
1730:
1731: [-60 -105 280 252 -486 471 1290]
1732:
1733: ? lllgram(m)
1734:
1735: [1 1 27 -27 69 0 141]
1736:
1737: [0 1 4 -22 34 -24 49]
1738:
1739: [0 1 3 -21 18 -24 23]
1740:
1741: [0 1 3 -20 10 -19 13]
1742:
1743: [0 1 3 -19 6 -14 8]
1744:
1745: [0 1 3 -18 4 -10 5]
1746:
1747: [0 1 3 -17 3 -7 3]
1748:
1749: ? lllgram1(m)
1750:
1751: [1 1 27 -27 69 0 141]
1752:
1753: [0 1 4 -22 34 -24 49]
1754:
1755: [0 1 3 -21 18 -24 23]
1756:
1757: [0 1 3 -20 10 -19 13]
1758:
1759: [0 1 3 -19 6 -14 8]
1760:
1761: [0 1 3 -18 4 -10 5]
1762:
1763: [0 1 3 -17 3 -7 3]
1764:
1765: ? lllgramint(m)
1766:
1767: [1 1 27 -27 69 0 141]
1768:
1769: [0 1 4 -23 34 -24 91]
1770:
1771: [0 1 3 -22 18 -24 65]
1772:
1773: [0 1 3 -21 10 -19 49]
1774:
1775: [0 1 3 -20 6 -14 38]
1776:
1777: [0 1 3 -19 4 -10 30]
1778:
1779: [0 1 3 -18 3 -7 24]
1780:
1781: ? lllgramkerim(mp~*mp)
1782: [[-420, -420, 840, 630, 2982, -1092, -83; -210, -280, 630, 504, 2415, -876,
1783: 70; -140, -210, 504, 420, 2050, -749, 137; -105, -168, 420, 360, 1785, -658,
1784: 169; -84, -140, 360, 315, 1582, -588, 184; -70, -120, 315, 280, 1421, -532,
1785: 190; -60, -105, 280, 252, 1290, -486, 191; 420, 0, 0, 0, -210, 168, 35; 0,
1786: 840, 0, 0, 0, 0, 336; 0, 0, -2520, 0, 0, 0, 1260; 0, 0, 0, -2520, 0, 0, -840
1787: ; 0, 0, 0, 0, -13860, 0, 6930; 0, 0, 0, 0, 0, 5544, 0; 0, 0, 0, 0, 0, 0, -12
1788: 012], [0, 0, 0, 0, 0, 0, 0; 0, 0, 0, 0, 0, 0, 0; 0, 0, 0, 0, 0, 0, 0; 0, 0,
1789: 0, 0, 0, 0, 0; 0, 0, 0, 0, 0, 0, 0; 0, 0, 0, 0, 0, 0, 0; 0, 0, 0, 0, 0, 0, 0
1790: ; 1, 0, 0, 0, 0, 0, 0; 0, 1, 0, 0, 0, 0, 0; 0, 0, 1, 0, 0, 0, 0; 0, 0, 0, 1,
1791: 0, 0, 0; 0, 0, 0, 0, 1, 0, 0; 0, 0, 0, 0, 0, 1, 0; 0, 0, 0, 0, 0, 0, 1]]
1792: ? lllint(m)
1793:
1794: [-420 -420 840 630 -1092 -83 2982]
1795:
1796: [-210 -280 630 504 -876 70 2415]
1797:
1798: [-140 -210 504 420 -749 137 2050]
1799:
1800: [-105 -168 420 360 -658 169 1785]
1801:
1802: [-84 -140 360 315 -588 184 1582]
1803:
1804: [-70 -120 315 280 -532 190 1421]
1805:
1806: [-60 -105 280 252 -486 191 1290]
1807:
1808: ? lllintpartial(m)
1809:
1810: [-420 -420 -630 840 1092 2982 -83]
1811:
1812: [-210 -280 -504 630 876 2415 70]
1813:
1814: [-140 -210 -420 504 749 2050 137]
1815:
1816: [-105 -168 -360 420 658 1785 169]
1817:
1818: [-84 -140 -315 360 588 1582 184]
1819:
1820: [-70 -120 -280 315 532 1421 190]
1821:
1822: [-60 -105 -252 280 486 1290 191]
1823:
1824: ? lllkerim(mp)
1825: [[-420, -420, 840, 630, 2982, -1092, -83; -210, -280, 630, 504, 2415, -876,
1826: 70; -140, -210, 504, 420, 2050, -749, 137; -105, -168, 420, 360, 1785, -658,
1827: 169; -84, -140, 360, 315, 1582, -588, 184; -70, -120, 315, 280, 1421, -532,
1828: 190; -60, -105, 280, 252, 1290, -486, 191; 420, 0, 0, 0, -210, 168, 35; 0,
1829: 840, 0, 0, 0, 0, 336; 0, 0, -2520, 0, 0, 0, 1260; 0, 0, 0, -2520, 0, 0, -840
1830: ; 0, 0, 0, 0, -13860, 0, 6930; 0, 0, 0, 0, 0, 5544, 0; 0, 0, 0, 0, 0, 0, -12
1831: 012], [0, 0, 0, 0, 0, 0, 0; 0, 0, 0, 0, 0, 0, 0; 0, 0, 0, 0, 0, 0, 0; 0, 0,
1832: 0, 0, 0, 0, 0; 0, 0, 0, 0, 0, 0, 0; 0, 0, 0, 0, 0, 0, 0; 0, 0, 0, 0, 0, 0, 0
1833: ; 1, 0, 0, 0, 0, 0, 0; 0, 1, 0, 0, 0, 0, 0; 0, 0, 1, 0, 0, 0, 0; 0, 0, 0, 1,
1834: 0, 0, 0; 0, 0, 0, 0, 1, 0, 0; 0, 0, 0, 0, 0, 1, 0; 0, 0, 0, 0, 0, 0, 1]]
1835: ? lllrat(m)
1836:
1837: [-420 -420 840 630 -1092 -83 2982]
1838:
1839: [-210 -280 630 504 -876 70 2415]
1840:
1841: [-140 -210 504 420 -749 137 2050]
1842:
1843: [-105 -168 420 360 -658 169 1785]
1844:
1845: [-84 -140 360 315 -588 184 1582]
1846:
1847: [-70 -120 315 280 -532 190 1421]
1848:
1849: [-60 -105 280 252 -486 191 1290]
1850:
1851: ? \precision=96
1852: realprecision = 96 significant digits
1853: ? ln(2)
1854: 0.69314718055994530941723212145817656807550013436025525412068000949339362196
1855: 9694715605863326996418
1856: ? lngamma(10^50*i)
1857: -157079632679489661923132169163975144209858469968811.93673753887608474948977
1858: 0941153418951907406847 - 2.5258126069288717421377720813802613884088088474975
1859: 8842685248040385012601916745265645208759475328*I
1860: ? \precision=2000
1861: realprecision = 2003 significant digits (2000 digits displayed)
1862: ? log(2)
1863: 0.69314718055994530941723212145817656807550013436025525412068000949339362196
1864: 9694715605863326996418687542001481020570685733685520235758130557032670751635
1865: 0759619307275708283714351903070386238916734711233501153644979552391204751726
1866: 8157493206515552473413952588295045300709532636664265410423915781495204374043
1867: 0385500801944170641671518644712839968171784546957026271631064546150257207402
1868: 4816377733896385506952606683411372738737229289564935470257626520988596932019
1869: 6505855476470330679365443254763274495125040606943814710468994650622016772042
1870: 4524529612687946546193165174681392672504103802546259656869144192871608293803
1871: 1727143677826548775664850856740776484514644399404614226031930967354025744460
1872: 7030809608504748663852313818167675143866747664789088143714198549423151997354
1873: 8803751658612753529166100071053558249879414729509293113897155998205654392871
1874: 7000721808576102523688921324497138932037843935308877482597017155910708823683
1875: 6275898425891853530243634214367061189236789192372314672321720534016492568727
1876: 4778234453534764811494186423867767744060695626573796008670762571991847340226
1877: 5146283790488306203306114463007371948900274364396500258093651944304119115060
1878: 8094879306786515887090060520346842973619384128965255653968602219412292420757
1879: 4321757489097706752687115817051137009158942665478595964890653058460258668382
1880: 9400228330053820740056770530467870018416240441883323279838634900156312188956
1881: 0650553151272199398332030751408426091479001265168243443893572472788205486271
1882: 5527418772430024897945401961872339808608316648114909306675193393128904316413
1883: 7068139777649817697486890388778999129650361927071088926410523092478391737350
1884: 1229842420499568935992206602204654941510613918788574424557751020683703086661
1885: 9480896412186807790208181588580001688115973056186676199187395200766719214592
1886: 2367206025395954365416553112951759899400560003665135675690512459268257439464
1887: 8316833262490180382424082423145230614096380570070255138770268178516306902551
1888: 3703234053802145019015374029509942262995779647427138157363801729873940704242
1889: 17997226696297993931270693
1890: ? logagm(2)
1891: 0.69314718055994530941723212145817656807550013436025525412068000949339362196
1892: 9694715605863326996418687542001481020570685733685520235758130557032670751635
1893: 0759619307275708283714351903070386238916734711233501153644979552391204751726
1894: 8157493206515552473413952588295045300709532636664265410423915781495204374043
1895: 0385500801944170641671518644712839968171784546957026271631064546150257207402
1896: 4816377733896385506952606683411372738737229289564935470257626520988596932019
1897: 6505855476470330679365443254763274495125040606943814710468994650622016772042
1898: 4524529612687946546193165174681392672504103802546259656869144192871608293803
1899: 1727143677826548775664850856740776484514644399404614226031930967354025744460
1900: 7030809608504748663852313818167675143866747664789088143714198549423151997354
1901: 8803751658612753529166100071053558249879414729509293113897155998205654392871
1902: 7000721808576102523688921324497138932037843935308877482597017155910708823683
1903: 6275898425891853530243634214367061189236789192372314672321720534016492568727
1904: 4778234453534764811494186423867767744060695626573796008670762571991847340226
1905: 5146283790488306203306114463007371948900274364396500258093651944304119115060
1906: 8094879306786515887090060520346842973619384128965255653968602219412292420757
1907: 4321757489097706752687115817051137009158942665478595964890653058460258668382
1908: 9400228330053820740056770530467870018416240441883323279838634900156312188956
1909: 0650553151272199398332030751408426091479001265168243443893572472788205486271
1910: 5527418772430024897945401961872339808608316648114909306675193393128904316413
1911: 7068139777649817697486890388778999129650361927071088926410523092478391737350
1912: 1229842420499568935992206602204654941510613918788574424557751020683703086661
1913: 9480896412186807790208181588580001688115973056186676199187395200766719214592
1914: 2367206025395954365416553112951759899400560003665135675690512459268257439464
1915: 8316833262490180382424082423145230614096380570070255138770268178516306902551
1916: 3703234053802145019015374029509942262995779647427138157363801729873940704242
1917: 17997226696297993931270693
1918: ? \precision=19
1919: realprecision = 19 significant digits
1920: ? bcurve=initell([0,0,0,-3,0])
1921: [0, 0, 0, -3, 0, 0, -6, 0, -9, 144, 0, 1728, 1728, [1.732050807568877293, 0.
1922: E-19, -1.732050807568877293]~, 1.992332899583490707, 1.992332899583490708*I,
1923: -0.7884206134041560682, -2.365261840212468204*I, 3.969390382762759668]
1924: ? localred(bcurve,2)
1925: [6, 2, [1, 1, 1, 0], 1]
1926: ? ccurve=initell([0,0,-1,-1,0])
1927: [0, 0, -1, -1, 0, 0, -2, 1, -1, 48, -216, 37, 110592/37, [0.8375654352833230
1928: 353, 0.2695944364054445582, -1.107159871688767593]~, 2.993458646231959630, 2
1929: .451389381986790061*I, -0.4713192779568114757, -1.435456518668684318*I, 7.33
1930: 8132740789576742]
1931: ? l=lseriesell(ccurve,2,-37,1)
1932: 0.3815754082607112111
1933: ? lseriesell(ccurve,2,-37,1.2)-l
1934: -1.084202172234654426 E-19
1935: ? sbnf=smallbuchinit(x^3-x^2-14*x-1)
1936: [x^3 - x^2 - 14*x - 1, 3, 10889, [1, x, x^2], [-3.233732695981516673, -0.071
1937: 82350902743636344, 4.305556205008953036], [10889, 5698, 3794; 0, 1, 0; 0, 0,
1938: 1], mat(2), mat([0, 1, 1, 1, 0, 1, 1, 1]), [9, 15, 16, 17, 10, 33, 69, 39,
1939: 57], [2, [-1, 0, 0]~], [[0, 1, 0]~, [-4, 2, 1]~], [-4, -3, -1, 2, 3, 1, 11,
1940: -1, -7; 1, -1, 1, 1, 0, 1, 2, -4, -2; 0, 0, 0, 0, 0, 0, -1, -1, 0]]
1941: ? makebigbnf(sbnf)
1942: [mat(2), mat([0, 1, 1, 1, 0, 1, 1, 1]), [1.173637103435061715 + 3.1415926535
1943: 89793238*I, -4.562279014988837901 + 3.141592653589793238*I; -2.6335434327389
1944: 76049 + 3.141592653589793238*I, 1.420330600779487358 + 3.141592653589793238*
1945: I; 1.459906329303914334, 3.141948414209350543], [1.246346989334819161 + 3.14
1946: 1592653589793238*I, -1.990056445584799713, 0.5404006376129469727 + 3.1415926
1947: 53589793238*I, -0.6926391142471042845 + 3.141592653589793238*I, 0.E-96, 0.00
1948: 4375616572659815402 + 3.141592653589793238*I, 0.3677262014027817705 + 3.1415
1949: 92653589793238*I, -0.8305625946607188639, -1.977791147836553953 + 3.14159265
1950: 3589793238*I; 0.6716827432867392935 + 3.141592653589793238*I, 0.537900567109
1951: 2853266 + 3.141592653589793238*I, -0.8333219883742404172 + 3.141592653589793
1952: 238*I, -0.2461086674077943078, 0.E-96, -0.8738318043071131265, 0.97290631883
1953: 16092378, -1.552661549868775853 + 3.141592653589793238*I, 0.5774919091398324
1954: 092 + 3.141592653589793238*I; -1.918029732621558454, 1.452155878475514386 +
1955: 3.141592653589793238*I, 0.2929213507612934444, 0.9387477816548985923, 0.E-96
1956: , 0.8694561877344533111, -1.340632520234391008, 2.383224144529494717 + 3.141
1957: 592653589793238*I, 1.400299238696721544 + 3.141592653589793238*I], [[3, [-1,
1958: 1, 0]~, 1, 1, [1, 0, 1]~], [5, [3, 1, 0]~, 1, 1, [-2, 1, 1]~], [5, [-1, 1,
1959: 0]~, 1, 1, [1, 0, 1]~], [5, [2, 1, 0]~, 1, 1, [2, 2, 1]~], [3, [1, 0, 1]~, 1
1960: , 2, [-1, 1, 0]~], [11, [1, 1, 0]~, 1, 1, [-1, -2, 1]~], [23, [-10, 1, 0]~,
1961: 1, 1, [7, 9, 1]~], [13, [19, 1, 0]~, 1, 1, [2, 6, 1]~], [19, [-6, 1, 0]~, 1,
1962: 1, [-3, 5, 1]~]]~, [1, 2, 3, 4, 5, 6, 7, 8, 9]~, [x^3 - x^2 - 14*x - 1, [3,
1963: 0], 10889, 1, [[1, -3.233732695981516673, 10.45702714905988813; 1, -0.07182
1964: 350902743636344, 0.005158616449014232794; 1, 4.305556205008953036, 18.537814
1965: 23449109762], [1, 1, 1; -3.233732695981516673, -0.07182350902743636344, 4.30
1966: 5556205008953036; 10.45702714905988813, 0.005158616449014232794, 18.53781423
1967: 449109762], [3, 1.000000000000000000, 29.00000000000000000; 1.00000000000000
1968: 0000, 29.00000000000000000, 46.00000000000000000; 29.00000000000000000, 46.0
1969: 0000000000000000, 453.0000000000000000], [3, 1, 29; 1, 29, 46; 29, 46, 453],
1970: [10889, 5698, 3794; 0, 1, 0; 0, 0, 1], [11021, 881, -795; 881, 518, -109; -
1971: 795, -109, 86], [10889, [1890, 5190, 1]~, 118570321]], [-3.23373269598151667
1972: 3, -0.07182350902743636344, 4.305556205008953036], [1, x, x^2], [1, 0, 0; 0,
1973: 1, 0; 0, 0, 1], [1, 0, 0, 0, 0, 1, 0, 1, 1; 0, 1, 0, 1, 0, 14, 0, 14, 15; 0
1974: , 0, 1, 0, 1, 1, 1, 1, 15]], [[2, [2], [[3, 2, 2; 0, 1, 0; 0, 0, 1]]], 10.34
1975: 800724602767998, 1.000000000000000000, [2, -1], [x, x^2 + 2*x - 4], 1000], [
1976: mat(1), mat(1), [[[3, 2, 2; 0, 1, 0; 0, 0, 1], [0, 0, 0]]]], 0]
1977: ? concat(mat(vector(4,x,x)~),vector(4,x,10+x)~)
1978:
1979: [1 11]
1980:
1981: [2 12]
1982:
1983: [3 13]
1984:
1985: [4 14]
1986:
1987: ? matextract(matrix(15,15,x,y,x+y),vector(5,x,3*x),vector(3,y,3*y))
1988:
1989: [6 9 12]
1990:
1991: [9 12 15]
1992:
1993: [12 15 18]
1994:
1995: [15 18 21]
1996:
1997: [18 21 24]
1998:
1999: ? ma=mathell(mcurve,mpoints)
2000:
2001: [1.172183098700697010 0.4476973883408951692]
2002:
2003: [0.4476973883408951692 1.755026016172950713]
2004:
2005: ? gauss(ma,mhbi)
2006: [-1.000000000000000000, 1.000000000000000000]~
2007: ? (1.*hilbert(7))^(-1)
2008:
2009: [48.99999999999354616 -1175.999999999759026 8819.999999997789586 -29399.9999
2010: 9999171836 48509.99999998526254 -38807.99999998756766 12011.99999999599856]
2011:
2012: [-1175.999999999756499 37631.99999999093860 -317519.9999999170483 1128959.99
2013: 9999689868 -1940399.999999448886 1596671.999999535762 -504503.9999998507690]
2014:
2015: [8819.999999997745604 -317519.9999999163090 2857679.999999235184 -10583999.9
2016: 9999714478 18710999.99999493212 -15717239.99999573533 5045039.999998630382]
2017:
2018: [-29399.99999999149442 1128959.999999684822 -10583999.99999712372 40319999.9
2019: 9998927448 -72764999.99998098063 62092799.99998400783 -20180159.99999486766]
2020:
2021: [48509.99999998476962 -1940399.999999436456 18710999.99999486299 -72764999.9
2022: 9998086196 133402499.9999660890 -115259759.9999715052 37837799.99999086044]
2023:
2024: [-38807.99999998708779 1596671.999999522805 -15717239.99999565420 62092799.9
2025: 9998382209 -115259759.9999713525 100590335.9999759413 -33297263.99999228701]
2026:
2027: [12011.99999999582671 -504503.9999998459239 5045039.999998597949 -20180159.9
2028: 9999478405 37837799.99999076882 -33297263.99999225112 11099087.99999751679]
2029:
2030: ? matsize([1,2;3,4;5,6])
2031: [3, 2]
2032: ? matrix(5,5,x,y,gcd(x,y))
2033:
2034: [1 1 1 1 1]
2035:
2036: [1 2 1 2 1]
2037:
2038: [1 1 3 1 1]
2039:
2040: [1 2 1 4 1]
2041:
2042: [1 1 1 1 5]
2043:
2044: ? matrixqz([1,3;3,5;5,7],0)
2045:
2046: [1 1]
2047:
2048: [3 2]
2049:
2050: [5 3]
2051:
2052: ? matrixqz2([1/3,1/4,1/6;1/2,1/4,-1/4;1/3,1,0])
2053:
2054: [19 12 2]
2055:
2056: [0 1 0]
2057:
2058: [0 0 1]
2059:
2060: ? matrixqz3([1,3;3,5;5,7])
2061:
2062: [2 -1]
2063:
2064: [1 0]
2065:
2066: [0 1]
2067:
2068: ? max(2,3)
2069: 3
2070: ? min(2,3)
2071: 2
2072: ? minim([2,1;1,2],4,6)
2073: [6, 2, [0, -1, 1; 1, 1, 0]]
2074: ? mod(-12,7)
2075: mod(2, 7)
2076: ? modp(-12,7)
2077: mod(2, 7)
2078: ? mod(10873,49649)^-1
2079: *** impossible inverse modulo: mod(131, 49649).
2080:
2081: ? modreverse(mod(x^2+1,x^3-x-1))
2082: mod(x^2 - 3*x + 2, x^3 - 5*x^2 + 8*x - 5)
2083: ? move(0,243,583);cursor(0)
2084: ? mu(3*5*7*11*13)
2085: -1
2086: ? newtonpoly(x^4+3*x^3+27*x^2+9*x+81,3)
2087: [2, 2/3, 2/3, 2/3]
2088: ? nextprime(100000000000000000000000)
2089: 100000000000000000000117
2090: ? setrand(1);a=matrix(3,5,j,k,vvector(5,l,random()\10^8))
2091:
2092: [[10, 7, 8, 7, 18]~ [17, 0, 9, 20, 10]~ [5, 4, 7, 18, 20]~ [0, 16, 4, 2, 0]~
2093: [17, 19, 17, 1, 14]~]
2094:
2095: [[17, 16, 6, 3, 6]~ [17, 13, 9, 19, 6]~ [1, 14, 12, 20, 8]~ [6, 1, 8, 17, 21
2096: ]~ [18, 17, 9, 10, 13]~]
2097:
2098: [[4, 13, 3, 17, 14]~ [14, 16, 11, 5, 4]~ [9, 11, 13, 7, 15]~ [19, 21, 2, 4,
2099: 5]~ [14, 16, 6, 20, 14]~]
2100:
2101: ? aid=[idx,idy,idz,idmat(5),idx]
2102: [[3, 1, 2, 2, 2; 0, 1, 0, 0, 0; 0, 0, 1, 0, 0; 0, 0, 0, 1, 0; 0, 0, 0, 0, 1]
2103: , [5, 0, 0, 2, 0; 0, 5, 0, 0, 0; 0, 0, 5, 2, 0; 0, 0, 0, 1, 0; 0, 0, 0, 0, 5
2104: ], [15, 5, 10, 12, 10; 0, 5, 0, 0, 0; 0, 0, 5, 2, 0; 0, 0, 0, 1, 0; 0, 0, 0,
2105: 0, 5], [1, 0, 0, 0, 0; 0, 1, 0, 0, 0; 0, 0, 1, 0, 0; 0, 0, 0, 1, 0; 0, 0, 0
2106: , 0, 1], [3, 1, 2, 2, 2; 0, 1, 0, 0, 0; 0, 0, 1, 0, 0; 0, 0, 0, 1, 0; 0, 0,
2107: 0, 0, 1]]
2108: ? bb=algtobasis(nf,mod(x^3+x,nfpol))
2109: [1, 1, 1, 3, 0]~
2110: ? da=nfdetint(nf,[a,aid])
2111:
2112: [30 5 25 27 10]
2113:
2114: [0 5 0 0 0]
2115:
2116: [0 0 5 2 0]
2117:
2118: [0 0 0 1 0]
2119:
2120: [0 0 0 0 5]
2121:
2122: ? nfdiv(nf,ba,bb)
2123: [755/373, -152/373, 159/373, 120/373, -264/373]~
2124: ? nfdiveuc(nf,ba,bb)
2125: [2, 0, 0, 0, -1]~
2126: ? nfdivres(nf,ba,bb)
2127: [[2, 0, 0, 0, -1]~, [-12, -7, 0, 9, 5]~]
2128: ? nfhermite(nf,[a,aid])
2129: [[[1, 0, 0, 0, 0]~, [0, 0, 0, 0, 0]~, [0, 0, 0, 0, 0]~; [0, 0, 0, 0, 0]~, [1
2130: , 0, 0, 0, 0]~, [0, 0, 0, 0, 0]~; [0, 0, 0, 0, 0]~, [0, 0, 0, 0, 0]~, [1, 0,
2131: 0, 0, 0]~], [[2, 1, 1, 1, 0; 0, 1, 0, 0, 0; 0, 0, 1, 0, 0; 0, 0, 0, 1, 0; 0
2132: , 0, 0, 0, 1], [1, 0, 0, 0, 0; 0, 1, 0, 0, 0; 0, 0, 1, 0, 0; 0, 0, 0, 1, 0;
2133: 0, 0, 0, 0, 1], [3, 1, 2, 2, 2; 0, 1, 0, 0, 0; 0, 0, 1, 0, 0; 0, 0, 0, 1, 0;
2134: 0, 0, 0, 0, 1]]]
2135: ? nfhermitemod(nf,[a,aid],da)
2136: [[[1, 0, 0, 0, 0]~, [0, 0, 0, 0, 0]~, [0, 0, 0, 0, 0]~; [0, 0, 0, 0, 0]~, [1
2137: , 0, 0, 0, 0]~, [0, 0, 0, 0, 0]~; [0, 0, 0, 0, 0]~, [0, 0, 0, 0, 0]~, [1, 0,
2138: 0, 0, 0]~], [[2, 1, 1, 1, 0; 0, 1, 0, 0, 0; 0, 0, 1, 0, 0; 0, 0, 0, 1, 0; 0
2139: , 0, 0, 0, 1], [1, 0, 0, 0, 0; 0, 1, 0, 0, 0; 0, 0, 1, 0, 0; 0, 0, 0, 1, 0;
2140: 0, 0, 0, 0, 1], [3, 1, 2, 2, 2; 0, 1, 0, 0, 0; 0, 0, 1, 0, 0; 0, 0, 0, 1, 0;
2141: 0, 0, 0, 0, 1]]]
2142: ? nfmod(nf,ba,bb)
2143: [-12, -7, 0, 9, 5]~
2144: ? nfmul(nf,ba,bb)
2145: [-25, -50, -30, 15, 90]~
2146: ? nfpow(nf,bb,5)
2147: [23455, 156370, 115855, 74190, -294375]~
2148: ? nfreduce(nf,ba,idx)
2149: [1, 0, 0, 0, 0]~
2150: ? setrand(1);as=matrix(3,3,j,k,vvector(5,l,random()\10^8))
2151:
2152: [[10, 7, 8, 7, 18]~ [17, 0, 9, 20, 10]~ [5, 4, 7, 18, 20]~]
2153:
2154: [[17, 16, 6, 3, 6]~ [17, 13, 9, 19, 6]~ [1, 14, 12, 20, 8]~]
2155:
2156: [[4, 13, 3, 17, 14]~ [14, 16, 11, 5, 4]~ [9, 11, 13, 7, 15]~]
2157:
2158: ? vaid=[idx,idy,idmat(5)]
2159: [[3, 1, 2, 2, 2; 0, 1, 0, 0, 0; 0, 0, 1, 0, 0; 0, 0, 0, 1, 0; 0, 0, 0, 0, 1]
2160: , [5, 0, 0, 2, 0; 0, 5, 0, 0, 0; 0, 0, 5, 2, 0; 0, 0, 0, 1, 0; 0, 0, 0, 0, 5
2161: ], [1, 0, 0, 0, 0; 0, 1, 0, 0, 0; 0, 0, 1, 0, 0; 0, 0, 0, 1, 0; 0, 0, 0, 0,
2162: 1]]
2163: ? haid=[idmat(5),idmat(5),idmat(5)]
2164: [[1, 0, 0, 0, 0; 0, 1, 0, 0, 0; 0, 0, 1, 0, 0; 0, 0, 0, 1, 0; 0, 0, 0, 0, 1]
2165: , [1, 0, 0, 0, 0; 0, 1, 0, 0, 0; 0, 0, 1, 0, 0; 0, 0, 0, 1, 0; 0, 0, 0, 0, 1
2166: ], [1, 0, 0, 0, 0; 0, 1, 0, 0, 0; 0, 0, 1, 0, 0; 0, 0, 0, 1, 0; 0, 0, 0, 0,
2167: 1]]
2168: ? nfsmith(nf,[as,haid,vaid])
2169: [[10951073973332888246310, 5442457637639729109215, 2693780223637146570055, 3
2170: 910837124677073032737, 3754666252923836621170; 0, 5, 0, 0, 0; 0, 0, 5, 2, 0;
2171: 0, 0, 0, 1, 0; 0, 0, 0, 0, 5], [1, 0, 0, 0, 0; 0, 1, 0, 0, 0; 0, 0, 1, 0, 0
2172: ; 0, 0, 0, 1, 0; 0, 0, 0, 0, 1], [1, 0, 0, 0, 0; 0, 1, 0, 0, 0; 0, 0, 1, 0,
2173: 0; 0, 0, 0, 1, 0; 0, 0, 0, 0, 1]]
2174: ? nfval(nf,ba,vp)
2175: 0
2176: ? norm(1+i)
2177: 2
2178: ? norm(mod(x+5,x^3+x+1))
2179: 129
2180: ? norml2(vector(10,x,x))
2181: 385
2182: ? nucomp(qfi(2,1,9),qfi(4,3,5),3)
2183: qfi(2, -1, 9)
2184: ? form=qfi(2,1,9);nucomp(form,form,3)
2185: qfi(4, -3, 5)
2186: ? numdiv(2^99*3^49)
2187: 5000
2188: ? numer((x+1)/(x-1))
2189: x + 1
2190: ? nupow(form,111)
2191: qfi(2, -1, 9)
2192: ? 1/(1+x)+o(x^20)
2193: 1 - x + x^2 - x^3 + x^4 - x^5 + x^6 - x^7 + x^8 - x^9 + x^10 - x^11 + x^12 -
2194: x^13 + x^14 - x^15 + x^16 - x^17 + x^18 - x^19 + O(x^20)
2195: ? omega(100!)
2196: 25
2197: ? ordell(acurve,1)
2198: [8, 3]
2199: ? order(mod(33,2^16+1))
2200: 2048
2201: ? tcurve=initell([1,0,1,-19,26]);
2202: ? orderell(tcurve,[1,2])
2203: 6
2204: ? ordred(x^3-12*x+45*x-1)
2205: [x - 1, x^3 - 363*x - 2663, x^3 + 33*x - 1]
2206: ? padicprec(padicno,127)
2207: 5
2208: ? pascal(8)
2209:
2210: [1 0 0 0 0 0 0 0 0]
2211:
2212: [1 1 0 0 0 0 0 0 0]
2213:
2214: [1 2 1 0 0 0 0 0 0]
2215:
2216: [1 3 3 1 0 0 0 0 0]
2217:
2218: [1 4 6 4 1 0 0 0 0]
2219:
2220: [1 5 10 10 5 1 0 0 0]
2221:
2222: [1 6 15 20 15 6 1 0 0]
2223:
2224: [1 7 21 35 35 21 7 1 0]
2225:
2226: [1 8 28 56 70 56 28 8 1]
2227:
2228: ? perf([2,0,1;0,2,1;1,1,2])
2229: 6
2230: ? permutation(7,1035)
2231: [4, 7, 1, 6, 3, 5, 2]
2232: ? permutation2num([4,7,1,6,3,5,2])
2233: 1035
2234: ? pf(-44,3)
2235: qfi(3, 2, 4)
2236: ? phi(257^2)
2237: 65792
2238: ? pi
2239: 3.141592653589793238
2240: ? plot(x=-5,5,sin(x))
2241:
2242: 0.9995545 x""x_''''''''''''''''''''''''''''''''''_x""x'''''''''''''''''''|
2243: | x _ "_ |
2244: | x _ _ |
2245: | x _ |
2246: | _ " |
2247: | " x |
2248: | x _ |
2249: | " |
2250: | " x _ |
2251: | _ |
2252: | " x |
2253: ````````````x``````````````````_````````````````````````````````
2254: | " |
2255: | " x _ |
2256: | _ |
2257: | " x |
2258: | x _ |
2259: | _ " |
2260: | " x |
2261: | " " x |
2262: | "_ " x |
2263: -0.999555 |...................x__x".................................."x__x
2264: -5 5
2265: ? pnqn([2,6,10,14,18,22,26])
2266:
2267: [19318376 741721]
2268:
2269: [8927353 342762]
2270:
2271: ? pnqn([1,1,1,1,1,1,1,1;1,1,1,1,1,1,1,1])
2272:
2273: [34 21]
2274:
2275: [21 13]
2276:
2277: ? point(0,225,334)
2278: ? points(0,vector(10,k,10*k),vector(10,k,5*k*k))
2279: ? pointell(acurve,zell(acurve,apoint))
2280: [0.9999999999999999986 + 0.E-19*I, 2.999999999999999998 + 0.E-18*I]
2281: ? polint([0,2,3],[0,4,9],5)
2282: 25
2283: ? polred(x^5-2*x^4-4*x^3-96*x^2-352*x-568)
2284: [x - 1, x^5 - x^4 - 6*x^3 + 6*x^2 + 13*x - 5, x^5 - x^4 + 2*x^3 - 4*x^2 + x
2285: - 1, x^5 - x^4 + 4*x^3 - 2*x^2 + x - 1, x^5 + 4*x^3 - 4*x^2 + 8*x - 8]
2286: ? polred2(x^4-28*x^3-458*x^2+9156*x-25321)
2287:
2288: [1 x - 1]
2289:
2290: [1/115*x^2 - 14/115*x - 327/115 x^2 - 10]
2291:
2292: [3/1495*x^3 - 63/1495*x^2 - 1607/1495*x + 13307/1495 x^4 - 32*x^2 + 216]
2293:
2294: [1/4485*x^3 - 7/1495*x^2 - 1034/4485*x + 7924/4485 x^4 - 8*x^2 + 6]
2295:
2296: ? polredabs(x^5-2*x^4-4*x^3-96*x^2-352*x-568)
2297: x^5 - x^4 + 2*x^3 - 4*x^2 + x - 1
2298: ? polredabs2(x^5-2*x^4-4*x^3-96*x^2-352*x-568)
2299: [x^5 - x^4 + 2*x^3 - 4*x^2 + x - 1, mod(2*x^4 - x^3 + 3*x^2 - 3*x - 1, x^5 -
2300: x^4 + 2*x^3 - 4*x^2 + x - 1)]
2301: ? polsym(x^17-1,17)
2302: [17, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 17]~
2303: ? polvar(name^4-other)
2304: name
2305: ? poly(sin(x),x)
2306: -1/1307674368000*x^15 + 1/6227020800*x^13 - 1/39916800*x^11 + 1/362880*x^9 -
2307: 1/5040*x^7 + 1/120*x^5 - 1/6*x^3 + x
2308: ? polylog(5,0.5)
2309: 0.5084005792422687065
2310: ? polylog(-4,t)
2311: (t^4 + 11*t^3 + 11*t^2 + t)/(-t^5 + 5*t^4 - 10*t^3 + 10*t^2 - 5*t + 1)
2312: ? polylogd(5,0.5)
2313: 1.033792745541689061
2314: ? polylogdold(5,0.5)
2315: 1.034459423449010483
2316: ? polylogp(5,0.5)
2317: 0.9495693489964922581
2318: ? poly([1,2,3,4,5],x)
2319: x^4 + 2*x^3 + 3*x^2 + 4*x + 5
2320: ? polyrev([1,2,3,4,5],x)
2321: 5*x^4 + 4*x^3 + 3*x^2 + 2*x + 1
2322: ? polzag(6,3)
2323: 4608*x^6 - 13824*x^5 + 46144/3*x^4 - 23168/3*x^3 + 5032/3*x^2 - 120*x + 1
2324: ? postdraw([0,20,20])
2325: ? postploth(x=-5,5,sin(x))
2326: [-5.000000000000000000, 5.000000000000000000, -0.9999964107564721649, 0.9999
2327: 964107564721649]
2328: ? postploth2(t=0,2*pi,[sin(5*t),sin(7*t)])
2329: [-0.9999994509568810308, 0.9999994509568810308, -0.9999994509568810308, 0.99
2330: 99994509568810308]
2331: ? postplothraw(vector(100,k,k),vector(100,k,k*k/100))
2332: [1.000000000000000000, 100.0000000000000000, 0.01000000000000000020, 100.000
2333: 0000000000000]
2334: ? powell(acurve,apoint,10)
2335: [-28919032218753260057646013785951999/292736325329248127651484680640160000,
2336: 478051489392386968218136375373985436596569736643531551/158385319626308443937
2337: 475969221994173751192384064000000]
2338: ? cmcurve=initell([0,-3/4,0,-2,-1])
2339: [0, -3/4, 0, -2, -1, -3, -4, -4, -1, 105, 1323, -343, -3375, [1.999999999999
2340: 999999, -0.6250000000000000000 + 0.3307189138830738238*I, -0.625000000000000
2341: 0000 - 0.3307189138830738238*I]~, 1.933311705616811546, 0.966655852808405773
2342: 4 + 2.557530989916099474*I, -0.8558486330998558523 - 4.598829817026853561 E-
2343: 20*I, -0.4279243165499279261 - 2.757161217166147204*I, 4.944504600282546729]
2344: ? powell(cmcurve,[x,y],quadgen(-7))
2345: [((-2 + 3*w)*x^2 + (6 - w))/((-2 - 5*w)*x + (-4 - 2*w)), ((34 - 11*w)*x^3 +
2346: (40 - 28*w)*x^2 + (22 + 23*w)*x)/((-90 - w)*x^2 + (-136 + 44*w)*x + (-40 + 2
2347: 8*w))]
2348: ? powrealraw(qfr(5,3,-1,0.),3)
2349: qfr(125, 23, 1, 0.E-18)
2350: ? pprint((x-12*y)/(y+13*x));
2351: (-(11 /14))
2352: ? pprint([1,2;3,4])
2353:
2354: [1 2]
2355:
2356: [3 4]
2357:
2358: ? pprint1(x+y);pprint(x+y);
2359: (2 x)(2 x)
2360: ? \precision=96
2361: realprecision = 96 significant digits
2362: ? pi
2363: 3.14159265358979323846264338327950288419716939937510582097494459230781640628
2364: 620899862803482534211
2365: ? prec(pi,20)
2366: 3.14159265358979323846264338325408976600000000000000000000000000000000000000
2367: 000000000000000000000
2368: ? precision(cmcurve)
2369: 19
2370: ? \precision=38
2371: realprecision = 38 significant digits
2372: ? prime(100)
2373: 541
2374: ? primedec(nf,2)
2375: [[2, [3, 1, 0, 0, 0]~, 1, 1, [1, 1, 0, 1, 1]~], [2, [-3, -5, -4, 3, 15]~, 1,
2376: 4, [1, 1, 0, 0, 0]~]]
2377: ? primedec(nf,3)
2378: [[3, [1, 1, 0, 0, 0]~, 1, 1, [1, -1, -1, 0, 0]~], [3, [-1, 1, -1, 0, 1]~, 2,
2379: 2, [1, 2, 3, 1, 0]~]]
2380: ? primedec(nf,11)
2381: [[11, [11, 0, 0, 0, 0]~, 1, 5, [1, 0, 0, 0, 0]~]]
2382: ? primes(100)
2383: [2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71,
2384: 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151,
2385: 157, 163, 167, 173, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229, 233, 2
2386: 39, 241, 251, 257, 263, 269, 271, 277, 281, 283, 293, 307, 311, 313, 317, 33
2387: 1, 337, 347, 349, 353, 359, 367, 373, 379, 383, 389, 397, 401, 409, 419, 421
2388: , 431, 433, 439, 443, 449, 457, 461, 463, 467, 479, 487, 491, 499, 503, 509,
2389: 521, 523, 541]
2390: ? forprime(p=2,100,print(p," ",lift(primroot(p))))
2391: 2 1
2392: 3 2
2393: 5 2
2394: 7 3
2395: 11 2
2396: 13 2
2397: 17 3
2398: 19 2
2399: 23 5
2400: 29 2
2401: 31 3
2402: 37 2
2403: 41 6
2404: 43 3
2405: 47 5
2406: 53 2
2407: 59 2
2408: 61 2
2409: 67 2
2410: 71 7
2411: 73 5
2412: 79 3
2413: 83 2
2414: 89 3
2415: 97 5
2416: ? principalideal(nf,mod(x^3+5,nfpol))
2417:
2418: [6]
2419:
2420: [0]
2421:
2422: [1]
2423:
2424: [3]
2425:
2426: [0]
2427:
2428: ? principalidele(nf,mod(x^3+5,nfpol))
2429: [[6; 0; 1; 3; 0], [2.2324480827796254080981385584384939684 + 3.1415926535897
2430: 932384626433832795028842*I, 5.0387659675158716386435353106610489968 + 1.5851
2431: 760343512250049897278861965702423*I, 4.2664040272651028743625910797589683173
2432: - 0.0083630478144368246110910258645462996191*I]]
2433: ? print((x-12*y)/(y+13*x));
2434: -11/14
2435: ? print([1,2;3,4])
2436: [1, 2; 3, 4]
2437: ? print1(x+y);print1(" equals ");print(x+y);
2438: 2*x equals 2*x
2439: ? prod(1,k=1,10,1+1/k!)
2440: 3335784368058308553334783/905932868585678438400000
2441: ? prod(1.,k=1,10,1+1/k!)
2442: 3.6821540356142043935732308433185262945
2443: ? pi^2/6*prodeuler(p=2,10000,1-p^-2)
2444: 1.0000098157493066238697591433298145174
2445: ? prodinf(n=0,(1+2^-n)/(1+2^(-n+1)))
2446: 0.33333333333333333333333333333333333322
2447: ? prodinf1(n=0,-2^-n/(1+2^(-n+1)))
2448: 0.33333333333333333333333333333333333322
2449: ? psi(1)
2450: -0.57721566490153286060651209008240243102
2451: ? quaddisc(-252)
2452: -7
2453: ? quadgen(-11)
2454: w
2455: ? quadpoly(-11)
2456: x^2 - x + 3
2457: ? rank(matrix(5,5,x,y,x+y))
2458: 2
2459: ? rayclassno(bnf,[[5,3;0,1],[1,0]])
2460: 12
2461: ? rayclassnolist(bnf,lu)
2462: [[3], [], [3, 3], [3], [6, 6], [], [], [], [3, 3, 3], [], [3, 3], [3, 3], []
2463: , [], [12, 6, 6, 12], [3], [3, 3], [], [9, 9], [6, 6], [], [], [], [], [6, 1
2464: 2, 6], [], [3, 3, 3, 3], [], [], [], [], [], [3, 6, 6, 3], [], [], [9, 3, 9]
2465: , [6, 6], [], [], [], [], [], [3, 3], [3, 3], [12, 12, 6, 6, 12, 12], [], []
2466: , [6, 6], [9], [], [3, 3, 3, 3], [], [3, 3], [], [6, 12, 12, 6]]
2467: ? move(0,50,50);rbox(0,50,50)
2468: ? print1("give a value for s? ");s=read();print(1/s)
2469: give a value for s? 37.
2470: 0.027027027027027027027027027027027027026
2471: ? real(5-7*i)
2472: 5
2473: ? recip(3*x^7-5*x^3+6*x-9)
2474: -9*x^7 + 6*x^6 - 5*x^4 + 3
2475: ? redimag(qfi(3,10,12))
2476: qfi(3, -2, 4)
2477: ? redreal(qfr(3,10,-20,1.5))
2478: qfr(3, 16, -7, 1.5000000000000000000000000000000000000)
2479: ? redrealnod(qfr(3,10,-20,1.5),18)
2480: qfr(3, 16, -7, 1.5000000000000000000000000000000000000)
2481: ? reduceddisc(x^3+4*x+12)
2482: [1036, 4, 1]
2483: ? regula(17)
2484: 2.0947125472611012942448228460655286534
2485: ? kill(y);print(x+y);reorder([x,y]);print(x+y);
2486: x + y
2487: x + y
2488: ? resultant(x^3-1,x^3+1)
2489: 8
2490: ? resultant2(x^3-1.,x^3+1.)
2491: 8.0000000000000000000000000000000000000
2492: ? reverse(tan(x))
2493: x - 1/3*x^3 + 1/5*x^5 - 1/7*x^7 + 1/9*x^9 - 1/11*x^11 + 1/13*x^13 - 1/15*x^1
2494: 5 + O(x^16)
2495: ? rhoreal(qfr(3,10,-20,1.5))
2496: qfr(-20, -10, 3, 2.1074451073987839947135880252731470615)
2497: ? rhorealnod(qfr(3,10,-20,1.5),18)
2498: qfr(-20, -10, 3, 1.5000000000000000000000000000000000000)
2499: ? rline(0,200,150)
2500: ? cursor(0)
2501: ? rmove(0,5,5);cursor(0)
2502: ? rndtoi(prod(1,k=1,17,x-exp(2*i*pi*k/17)))
2503: x^17 - 1
2504: ? qpol=y^3-y-1;setrand(1);bnf2=buchinit(qpol);nf2=bnf2[7];
2505: ? un=mod(1,qpol);w=mod(y,qpol);p=un*(x^5-5*x+w)
2506: mod(1, y^3 - y - 1)*x^5 + mod(-5, y^3 - y - 1)*x + mod(y, y^3 - y - 1)
2507: ? aa=rnfpseudobasis(nf2,p)
2508: [[[1, 0, 0]~, [0, 0, 0]~, [0, 0, 0]~, [-2, 0, 0]~, [11, 0, 0]~; [0, 0, 0]~,
2509: [1, 0, 0]~, [0, 0, 0]~, [2, 0, 0]~, [-8, 0, 0]~; [0, 0, 0]~, [0, 0, 0]~, [1,
2510: 0, 0]~, [1, 0, 0]~, [4, 0, 0]~; [0, 0, 0]~, [0, 0, 0]~, [0, 0, 0]~, [1, 0,
2511: 0]~, [-2, 0, 0]~; [0, 0, 0]~, [0, 0, 0]~, [0, 0, 0]~, [0, 0, 0]~, [1, 0, 0]~
2512: ], [[1, 0, 0; 0, 1, 0; 0, 0, 1], [1, 0, 0; 0, 1, 0; 0, 0, 1], [1, 0, 0; 0, 1
2513: , 0; 0, 0, 1], [1, 0, 3/5; 0, 1, 2/5; 0, 0, 1/5], [1, 0, 8/25; 0, 1, 22/25;
2514: 0, 0, 1/25]], [416134375, 212940625, 388649575; 0, 3125, 550; 0, 0, 25], [-1
2515: 280, 5, 5]~]
2516: ? rnfbasis(bnf2,aa)
2517:
2518: [[1, 0, 0]~ [0, 0, 0]~ [0, 0, 0]~ [4/5, -4/5, -2/5]~ [187/25, 208/25, -61/25
2519: ]~]
2520:
2521: [[0, 0, 0]~ [1, 0, 0]~ [0, 0, 0]~ [-4/5, 4/5, 2/5]~ [-196/25, -214/25, 88/25
2522: ]~]
2523:
2524: [[0, 0, 0]~ [0, 0, 0]~ [1, 0, 0]~ [-2/5, 2/5, 1/5]~ [-122/25, -123/25, 116/2
2525: 5]~]
2526:
2527: [[0, 0, 0]~ [0, 0, 0]~ [0, 0, 0]~ [-2/5, 2/5, 1/5]~ [-104/25, -111/25, 62/25
2528: ]~]
2529:
2530: [[0, 0, 0]~ [0, 0, 0]~ [0, 0, 0]~ [0, 0, 0]~ [-3/25, -2/25, 9/25]~]
2531:
2532: ? rnfdiscf(nf2,p)
2533: [[416134375, 212940625, 388649575; 0, 3125, 550; 0, 0, 25], [-1280, 5, 5]~]
2534: ? rnfequation(nf2,p)
2535: x^15 - 15*x^11 + 75*x^7 - x^5 - 125*x^3 + 5*x + 1
2536: ? rnfequation2(nf2,p)
2537: [x^15 - 15*x^11 + 75*x^7 - x^5 - 125*x^3 + 5*x + 1, mod(-x^5 + 5*x, x^15 - 1
2538: 5*x^11 + 75*x^7 - x^5 - 125*x^3 + 5*x + 1), 0]
2539: ? rnfhermitebasis(bnf2,aa)
2540:
2541: [[1, 0, 0]~ [0, 0, 0]~ [0, 0, 0]~ [-2/5, 2/5, -4/5]~ [11/25, 99/25, -33/25]~
2542: ]
2543:
2544: [[0, 0, 0]~ [1, 0, 0]~ [0, 0, 0]~ [2/5, -2/5, 4/5]~ [-8/25, -72/25, 24/25]~]
2545:
2546: [[0, 0, 0]~ [0, 0, 0]~ [1, 0, 0]~ [1/5, -1/5, 2/5]~ [4/25, 36/25, -12/25]~]
2547:
2548: [[0, 0, 0]~ [0, 0, 0]~ [0, 0, 0]~ [1/5, -1/5, 2/5]~ [-2/25, -18/25, 6/25]~]
2549:
2550: [[0, 0, 0]~ [0, 0, 0]~ [0, 0, 0]~ [0, 0, 0]~ [1/25, 9/25, -3/25]~]
2551:
2552: ? rnfisfree(bnf2,aa)
2553: 1
2554: ? rnfsteinitz(nf2,aa)
2555: [[[1, 0, 0]~, [0, 0, 0]~, [0, 0, 0]~, [4/5, -4/5, -2/5]~, [39/125, 11/125, 1
2556: 1/125]~; [0, 0, 0]~, [1, 0, 0]~, [0, 0, 0]~, [-4/5, 4/5, 2/5]~, [-42/125, -8
2557: /125, -8/125]~; [0, 0, 0]~, [0, 0, 0]~, [1, 0, 0]~, [-2/5, 2/5, 1/5]~, [-29/
2558: 125, 4/125, 4/125]~; [0, 0, 0]~, [0, 0, 0]~, [0, 0, 0]~, [-2/5, 2/5, 1/5]~,
2559: [-23/125, -2/125, -2/125]~; [0, 0, 0]~, [0, 0, 0]~, [0, 0, 0]~, [0, 0, 0]~,
2560: [-1/125, 1/125, 1/125]~], [[1, 0, 0; 0, 1, 0; 0, 0, 1], [1, 0, 0; 0, 1, 0; 0
2561: , 0, 1], [1, 0, 0; 0, 1, 0; 0, 0, 1], [1, 0, 0; 0, 1, 0; 0, 0, 1], [125, 0,
2562: 108; 0, 125, 22; 0, 0, 1]], [416134375, 212940625, 388649575; 0, 3125, 550;
2563: 0, 0, 25], [-1280, 5, 5]~]
2564: ? rootmod(x^16-1,41)
2565: [mod(1, 41), mod(3, 41), mod(9, 41), mod(14, 41), mod(27, 41), mod(32, 41),
2566: mod(38, 41), mod(40, 41)]~
2567: ? rootpadic(x^4+1,41,6)
2568: [3 + 22*41 + 27*41^2 + 15*41^3 + 27*41^4 + 33*41^5 + O(41^6), 14 + 20*41 + 2
2569: 5*41^2 + 24*41^3 + 4*41^4 + 18*41^5 + O(41^6), 27 + 20*41 + 15*41^2 + 16*41^
2570: 3 + 36*41^4 + 22*41^5 + O(41^6), 38 + 18*41 + 13*41^2 + 25*41^3 + 13*41^4 +
2571: 7*41^5 + O(41^6)]~
2572: ? roots(x^5-5*x^2-5*x-5)
2573: [2.0509134529831982130058170163696514536 + 0.E-38*I, -0.67063790319207539268
2574: 663382582902335603 + 0.84813118358634026680538906224199030917*I, -0.67063790
2575: 319207539268663382582902335603 - 0.84813118358634026680538906224199030917*I,
2576: -0.35481882329952371381627468235580237077 + 1.39980287391035466982975228340
2577: 62081964*I, -0.35481882329952371381627468235580237077 - 1.399802873910354669
2578: 8297522834062081964*I]~
2579: ? rootsold(x^4-1000000000000000000000)
2580: [-177827.94100389228012254211951926848447 + 0.E-38*I, 177827.941003892280122
2581: 54211951926848447 + 0.E-38*I, 6.6530622500127354998594589316364200753 E-111
2582: + 177827.94100389228012254211951926848447*I, 6.65306225001273549985945893163
2583: 64200753 E-111 - 177827.94100389228012254211951926848447*I]~
2584: ? round(prod(1,k=1,17,x-exp(2*i*pi*k/17)))
2585: x^17 - 1
2586: ? rounderror(prod(1,k=1,17,x-exp(2*i*pi*k/17)))
2587: -35
2588: ? rpoint(0,20,20)
2589: ? initrect(3,600,600);scale(3,-7,7,-2,2);cursor(3)
2590: ? q*series(anell(acurve,100),q)
2591: q - 2*q^2 - 3*q^3 + 2*q^4 - 2*q^5 + 6*q^6 - q^7 + 6*q^9 + 4*q^10 - 5*q^11 -
2592: 6*q^12 - 2*q^13 + 2*q^14 + 6*q^15 - 4*q^16 - 12*q^18 - 4*q^20 + 3*q^21 + 10*
2593: q^22 + 2*q^23 - q^25 + 4*q^26 - 9*q^27 - 2*q^28 + 6*q^29 - 12*q^30 - 4*q^31
2594: + 8*q^32 + 15*q^33 + 2*q^35 + 12*q^36 - q^37 + 6*q^39 - 9*q^41 - 6*q^42 + 2*
2595: q^43 - 10*q^44 - 12*q^45 - 4*q^46 - 9*q^47 + 12*q^48 - 6*q^49 + 2*q^50 - 4*q
2596: ^52 + q^53 + 18*q^54 + 10*q^55 - 12*q^58 + 8*q^59 + 12*q^60 - 8*q^61 + 8*q^6
2597: 2 - 6*q^63 - 8*q^64 + 4*q^65 - 30*q^66 + 8*q^67 - 6*q^69 - 4*q^70 + 9*q^71 -
2598: q^73 + 2*q^74 + 3*q^75 + 5*q^77 - 12*q^78 + 4*q^79 + 8*q^80 + 9*q^81 + 18*q
2599: ^82 - 15*q^83 + 6*q^84 - 4*q^86 - 18*q^87 + 4*q^89 + 24*q^90 + 2*q^91 + 4*q^
2600: 92 + 12*q^93 + 18*q^94 - 24*q^96 + 4*q^97 + 12*q^98 - 30*q^99 - 2*q^100 + O(
2601: q^101)
2602: ? aset=set([5,-2,7,3,5,1])
2603: ["-2", "1", "3", "5", "7"]
2604: ? bset=set([7,5,-5,7,2])
2605: ["-5", "2", "5", "7"]
2606: ? setintersect(aset,bset)
2607: ["5", "7"]
2608: ? setminus(aset,bset)
2609: ["-2", "1", "3"]
2610: ? setprecision(28)
2611: 38
2612: ? setrand(10)
2613: 10
2614: ? setsearch(aset,3)
2615: 3
2616: ? setsearch(bset,3)
2617: 0
2618: ? setserieslength(12)
2619: 16
2620: ? setunion(aset,bset)
2621: ["-2", "-5", "1", "2", "3", "5", "7"]
2622: ? arat=(x^3+x+1)/x^3;settype(arat,14)
2623: (x^3 + x + 1)/x^3
2624: ? shift(1,50)
2625: 1125899906842624
2626: ? shift([3,4,-11,-12],-2)
2627: [0, 1, -2, -3]
2628: ? shiftmul([3,4,-11,-12],-2)
2629: [3/4, 1, -11/4, -3]
2630: ? sigma(100)
2631: 217
2632: ? sigmak(2,100)
2633: 13671
2634: ? sigmak(-3,100)
2635: 1149823/1000000
2636: ? sign(-1)
2637: -1
2638: ? sign(0)
2639: 0
2640: ? sign(0.)
2641: 0
2642: ? signat(hilbert(5)-0.11*idmat(5))
2643: [2, 3]
2644: ? signunit(bnf)
2645:
2646: [-1]
2647:
2648: [1]
2649:
2650: ? simplefactmod(x^11+1,7)
2651:
2652: [1 1]
2653:
2654: [10 1]
2655:
2656: ? simplify(((x+i+1)^2-x^2-2*x*(i+1))^2)
2657: -4
2658: ? sin(pi/6)
2659: 0.4999999999999999999999999999
2660: ? sinh(1)
2661: 1.175201193643801456882381850
2662: ? size([1.3*10^5,2*i*pi*exp(4*pi)])
2663: 7
2664: ? smallbasis(x^3+4*x+12)
2665: [1, x, 1/2*x^2]
2666: ? smalldiscf(x^3+4*x+12)
2667: -1036
2668: ? smallfact(100!+1)
2669:
2670: [101 1]
2671:
2672: [14303 1]
2673:
2674: [149239 1]
2675:
2676: [432885273849892962613071800918658949059679308685024481795740765527568493010
2677: 727023757461397498800981521440877813288657839195622497225621499427628453 1]
2678:
2679: ? smallinitell([0,0,0,-17,0])
2680: [0, 0, 0, -17, 0, 0, -34, 0, -289, 816, 0, 314432, 1728]
2681: ? smallpolred(x^4+576)
2682: [x - 1, x^2 - x + 1, x^2 + 1, x^4 - x^2 + 1]
2683: ? smallpolred2(x^4+576)
2684:
2685: [1 x - 1]
2686:
2687: [-1/192*x^3 - 1/8*x + 1/2 x^2 - x + 1]
2688:
2689: [-1/24*x^2 x^2 + 1]
2690:
2691: [-1/192*x^3 + 1/48*x^2 + 1/8*x x^4 - x^2 + 1]
2692:
2693: ? smith(matrix(5,5,j,k,random()))
2694: [434644616238830047700451328, 2147483648, 2147483648, 1, 1]
2695: ? smith(1/hilbert(6))
2696: [27720, 2520, 2520, 840, 210, 6]
2697: ? smithpol(x*idmat(5)-matrix(5,5,j,k,1))
2698: [x^2 - 5*x, x, x, x, 1]
2699: ? solve(x=1,4,sin(x))
2700: 3.141592653589793238462643383
2701: ? sort(vector(17,x,5*x%17))
2702: [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16]
2703: ? sqr(1+o(2))
2704: 1 + O(2^3)
2705: ? sqred(hilbert(5))
2706:
2707: [1 1/2 1/3 1/4 1/5]
2708:
2709: [0 1/12 1 9/10 4/5]
2710:
2711: [0 0 1/180 3/2 12/7]
2712:
2713: [0 0 0 1/2800 2]
2714:
2715: [0 0 0 0 1/44100]
2716:
2717: ? sqrt(13+o(127^12))
2718: 34 + 125*127 + 83*127^2 + 107*127^3 + 53*127^4 + 42*127^5 + 22*127^6 + 98*12
2719: 7^7 + 127^8 + 23*127^9 + 122*127^10 + 79*127^11 + O(127^12)
2720: ? srgcd(x^10-1,x^15-1)
2721: x^5 - 1
2722: ? move(0,100,100);string(0,pi)
2723: ? move(0,200,200);string(0,"(0,0)")
2724: ? postdraw([0,10,10])
2725: ? apol=0.3+legendre(10)
2726: 46189/256*x^10 - 109395/256*x^8 + 45045/128*x^6 - 15015/128*x^4 + 3465/256*x
2727: ^2 + 0.05390624999999999999999999999
2728: ? sturm(apol)
2729: 4
2730: ? sturmpart(apol,0.91,1)
2731: 1
2732: ? subcyclo(31,5)
2733: x^5 + x^4 - 12*x^3 - 21*x^2 + x + 5
2734: ? subell(initell([0,0,0,-17,0]),[-1,4],[-4,2])
2735: [9, -24]
2736: ? subst(sin(x),x,y)
2737: y - 1/6*y^3 + 1/120*y^5 - 1/5040*y^7 + 1/362880*y^9 - 1/39916800*y^11 + O(y^
2738: 12)
2739: ? subst(sin(x),x,x+x^2)
2740: x + x^2 - 1/6*x^3 - 1/2*x^4 - 59/120*x^5 - 1/8*x^6 + 419/5040*x^7 + 59/720*x
2741: ^8 + 13609/362880*x^9 + 19/13440*x^10 - 273241/39916800*x^11 + O(x^12)
2742: ? sum(0,k=1,10,2^-k)
2743: 1023/1024
2744: ? sum(0.,k=1,10,2^-k)
2745: 0.9990234375000000000000000000
2746: ? sylvestermatrix(a2*x^2+a1*x+a0,b1*x+b0)
2747:
2748: [a2 b1 0]
2749:
2750: [a1 b0 b1]
2751:
2752: [a0 0 b0]
2753:
2754: ? \precision=38
2755: realprecision = 38 significant digits
2756: ? 4*sumalt(n=0,(-1)^n/(2*n+1))
2757: 3.1415926535897932384626433832795028841
2758: ? 4*sumalt2(n=0,(-1)^n/(2*n+1))
2759: 3.1415926535897932384626433832795028842
2760: ? suminf(n=1,2.^-n)
2761: 0.99999999999999999999999999999999999999
2762: ? 6/pi^2*sumpos(n=1,n^-2)
2763: 0.99999999999999999999999999999999999999
2764: ? supplement([1,3;2,4;3,6])
2765:
2766: [1 3 0]
2767:
2768: [2 4 0]
2769:
2770: [3 6 1]
2771:
2772: ? sqr(tan(pi/3))
2773: 2.9999999999999999999999999999999999999
2774: ? tanh(1)
2775: 0.76159415595576488811945828260479359041
2776: ? taniyama(bcurve)
2777: [x^-2 - x^2 + 3*x^6 - 2*x^10 + O(x^11), -x^-3 + 3*x - 3*x^5 + 8*x^9 + O(x^10
2778: )]
2779: ? taylor(y/(x-y),y)
2780: (O(y^12)*x^11 + y*x^10 + y^2*x^9 + y^3*x^8 + y^4*x^7 + y^5*x^6 + y^6*x^5 + y
2781: ^7*x^4 + y^8*x^3 + y^9*x^2 + y^10*x + y^11)/x^11
2782: ? tchebi(10)
2783: 512*x^10 - 1280*x^8 + 1120*x^6 - 400*x^4 + 50*x^2 - 1
2784: ? teich(7+o(127^12))
2785: 7 + 57*127 + 58*127^2 + 83*127^3 + 52*127^4 + 109*127^5 + 74*127^6 + 16*127^
2786: 7 + 60*127^8 + 47*127^9 + 65*127^10 + 5*127^11 + O(127^12)
2787: ? texprint((x+y)^3/(x-y)^2)
2788: {{x^{3} + {{3}y}x^{2} + {{3}y^{2}}x + {y^{3}}}\over{x^{2} - {{2}y}x + {y^{2}
2789: }}}
2790: ? theta(0.5,3)
2791: 0.080806418251894691299871683210466298535
2792: ? thetanullk(0.5,7)
2793: -804.63037320243369422783730584965684022
2794: ? torsell(tcurve)
2795: [12, [6, 2], [[-2, 8], [3, -2]]]
2796: ? trace(1+i)
2797: 2
2798: ? trace(mod(x+5,x^3+x+1))
2799: 15
2800: ? trans(vector(2,x,x))
2801: [1, 2]~
2802: ? %*%~
2803:
2804: [1 2]
2805:
2806: [2 4]
2807:
2808: ? trunc(-2.7)
2809: -2
2810: ? trunc(sin(x^2))
2811: 1/120*x^10 - 1/6*x^6 + x^2
2812: ? tschirnhaus(x^5-x-1)
2813: x^5 - 8*x^3 + 16*x - 32
2814: ? type(mod(x,x^2+1))
2815: 9
2816: ? unit(17)
2817: 3 + 2*w
2818: ? n=33;until(n==1,print1(n," ");if(n%2,n=3*n+1,n=n/2));print(1)
2819: 33 100 50 25 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1
2820: ? valuation(6^10000-1,5)
2821: 5
2822: ? vec(sin(x))
2823: [1, 0, -1/6, 0, 1/120, 0, -1/5040, 0, 1/362880, 0, -1/39916800]
2824: ? vecmax([-3,7,-2,11])
2825: 11
2826: ? vecmin([-3,7,-2,11])
2827: -3
2828: ? vecsort([[1,8,5],[2,5,8],[3,6,-6],[4,8,6]],2)
2829: [[2, 5, 8], [3, 6, -6], [4, 8, 6], [1, 8, 5]]
2830: ? vecsort([[1,8,5],[2,5,8],[3,6,-6],[4,8,6]],[2,1])
2831: [[2, 5, 8], [3, 6, -6], [1, 8, 5], [4, 8, 6]]
2832: ? weipell(acurve)
2833: x^-2 + 1/5*x^2 - 1/28*x^4 + 1/75*x^6 - 3/1540*x^8 + 1943/3822000*x^10 - 1/11
2834: 550*x^12 + 193/10510500*x^14 - 1269/392392000*x^16 + 21859/34684650000*x^18
2835: - 1087/9669660000*x^20 + O(x^22)
2836: ? wf(i)
2837: 1.1892071150027210667174999705604759152 - 1.17549435049295425400000000000000
2838: 00000 E-38*I
2839: ? wf2(i)
2840: 1.0905077326652576592070106557607079789 + 0.E-48*I
2841: ? m=5;while(m<20,print1(m," ");m=m+1);print()
2842: 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19
2843: ? zell(acurve,apoint)
2844: 0.72491221490962306778878739838332384646 + 0.E-58*I
2845: ? zeta(3)
2846: 1.2020569031595942853997381615114499907
2847: ? zeta(0.5+14.1347251*i)
2848: 0.0000000052043097453468479398562848599419244554 - 0.00000003269063986978698
2849: 2176409251733800562846*I
2850: ? zetak(nfz,-3)
2851: 0.091666666666666666666666666666666666666
2852: ? zetak(nfz,1.5+3*i)
2853: 0.88324345992059326405525724366416928890 - 0.2067536250233895222724230899142
2854: 7938845*I
2855: ? zidealstar(nf2,54)
2856: [132678, [1638, 9, 9], [[-27, 2, -27]~, [1, -24, 0]~, [1, 0, -24]~]]
2857: ? bid=zidealstarinit(nf2,54)
2858: [[[54, 0, 0; 0, 54, 0; 0, 0, 54], [0]], [132678, [1638, 9, 9]], [[2, [2, 0,
2859: 0]~, 1, 3, [1, 0, 0]~], 1; [3, [3, 0, 0]~, 1, 3, [1, 0, 0]~], 3], [[[[7], [[
2860: 0, 1, 0]~], [[-26, -27, 0]~], [[]~], 1]], [[[26], [[0, 2, 0]~], [[-27, 2, 0]
2861: ~], [[]~], 1], [[3, 3, 3], [[1, 3, 0]~, [1, 0, 3]~, [4, 0, 0]~], [[1, -24, 0
2862: ]~, [1, 0, -24]~, [-23, 0, 0]~], [[]~, []~, []~], [0, 1/3, 0; 0, 0, 1/3; 1/3
2863: , 0, 0]], [[3, 3, 3], [[1, 9, 0]~, [1, 0, 9]~, [10, 0, 0]~], [[1, -18, 0]~,
2864: [1, 0, -18]~, [-17, 0, 0]~], [[]~, []~, []~], [0, 1/9, 0; 0, 0, 1/9; 1/9, 0,
2865: 0]]], [[], [], [;]]], [468, 469, 0, 0, -48776, 0, 0, -36582; 0, 0, 1, 0, -7
2866: , -6, 0, -3; 0, 0, 0, 1, -3, 0, -6, 0]]
2867: ? zideallog(nf2,w,bid)
2868: [1574, 8, 6]~
2869: ? znstar(3120)
2870: [768, [12, 4, 4, 2, 2], [mod(67, 3120), mod(2341, 3120), mod(1847, 3120), mo
2871: d(391, 3120), mod(2081, 3120)]]
2872: ? getstack()
2873: 0
2874: ? getheap()
2875: [625, 126641]
2876: ? print("Total time spent: ",gettime());
2877: Total time spent: 19852
2878: ? \q
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