Annotation of OpenXM_contrib/pari-2.2/src/test/64/compat, Revision 1.1.1.1
1.1 noro 1: echo = 1 (on)
2: ? default(compatible,3)
3: compatible = 3 (use old functions, ignore case)
4: *** Warning: user functions re-initialized.
5: ? +3
6: 3
7: ? -5
8: -5
9: ? 5+3
10: 8
11: ? 5-3
12: 2
13: ? 5/3
14: 5/3
15: ? 5\3
16: 1
17: ? 5\/3
18: 2
19: ? 5%3
20: 2
21: ? 5^3
22: 125
23: ? \precision=57
24: realprecision = 57 significant digits
25: ? pi
26: 3.14159265358979323846264338327950288419716939937510582097
27: ? \precision=38
28: realprecision = 38 significant digits
29: ? o(x^12)
30: O(x^12)
31: ? padicno=(5/3)*127+o(127^5)
32: 44*127 + 42*127^2 + 42*127^3 + 42*127^4 + O(127^5)
33: ? initrect(0,500,500)
34: ? abs(-0.01)
35: 0.0099999999999999999999999999999999999999
36: ? acos(0.5)
37: 1.0471975511965977461542144610931676280
38: ? acosh(3)
39: 1.7627471740390860504652186499595846180
40: ? acurve=initell([0,0,1,-1,0])
41: [0, 0, 1, -1, 0, 0, -2, 1, -1, 48, -216, 37, 110592/37, [0.83756543528332303
42: 544481089907503024040, 0.26959443640544455826293795134926000404, -1.10715987
43: 16887675937077488504242902444]~, 2.9934586462319596298320099794525081778, 2.
44: 4513893819867900608542248318665252253*I, -0.47131927795681147588259389708033
45: 769964, -1.4354565186686843187232088566788165076*I, 7.3381327407895767390707
46: 210033323055881]
47: ? apoint=[2,2]
48: [2, 2]
49: ? isoncurve(acurve,apoint)
50: 1
51: ? addell(acurve,apoint,apoint)
52: [21/25, -56/125]
53: ? addprimes([nextprime(10^9),nextprime(10^10)])
54: [1000000007, 10000000019]
55: ? adj([1,2;3,4])
56:
57: [4 -2]
58:
59: [-3 1]
60:
61: ? agm(1,2)
62: 1.4567910310469068691864323832650819749
63: ? agm(1+o(7^5),8+o(7^5))
64: 1 + 4*7 + 6*7^2 + 5*7^3 + 2*7^4 + O(7^5)
65: ? algdep(2*cos(2*pi/13),6)
66: x^6 + x^5 - 5*x^4 - 4*x^3 + 6*x^2 + 3*x - 1
67: ? algdep2(2*cos(2*pi/13),6,15)
68: x^6 + x^5 - 5*x^4 - 4*x^3 + 6*x^2 + 3*x - 1
69: ? akell(acurve,1000000007)
70: 43800
71: ? nfpol=x^5-5*x^3+5*x+25
72: x^5 - 5*x^3 + 5*x + 25
73: ? nf=initalg(nfpol)
74: [x^5 - 5*x^3 + 5*x + 25, [1, 2], 595125, 45, [[1, -2.42851749071941860689920
75: 69565359418364, 5.8976972027301414394898806541072047941, -7.0734526715090929
76: 269887668671457811020, 3.8085820570096366144649278594400435257; 1, 1.9647119
77: 211288133163138753392090569931 + 0.80971492418897895128294082219556466857*I,
78: 3.2044546745713084269203768790545260356 + 3.1817131285400005341145852263331
79: 539899*I, -0.16163499313031744537610982231988834519 + 1.88804378620070569319
80: 06454476483475283*I, 2.0660709538372480632698971148801090692 + 2.68989675196
81: 23140991170523711857387388*I; 1, -0.75045317576910401286427186094108607489 +
82: 1.3101462685358123283560773619310445915*I, -1.15330327593637914666531720610
83: 81284327 - 1.9664068558894834311780119356739268309*I, 1.19836132888486390887
84: 04932558927788962 + 0.64370238076256988899570325671192132449*I, -0.470361982
85: 34206637050236104460013083212 + 0.083628266711589186119416762685933385421*I]
86: , [1, 2, 2; -2.4285174907194186068992069565359418364, 3.92942384225762663262
87: 77506784181139862 - 1.6194298483779579025658816443911293371*I, -1.5009063515
88: 382080257285437218821721497 - 2.6202925370716246567121547238620891831*I; 5.8
89: 976972027301414394898806541072047941, 6.408909349142616853840753758109052071
90: 2 - 6.3634262570800010682291704526663079798*I, -2.30660655187275829333063441
91: 22162568654 + 3.9328137117789668623560238713478536619*I; -7.0734526715090929
92: 269887668671457811020, -0.32326998626063489075221964463977669038 - 3.7760875
93: 724014113863812908952966950567*I, 2.3967226577697278177409865117855577924 -
94: 1.2874047615251397779914065134238426489*I; 3.8085820570096366144649278594400
95: 435257, 4.1321419076744961265397942297602181385 - 5.379793503924628198234104
96: 7423714774776*I, -0.94072396468413274100472208920026166424 - 0.1672565334231
97: 7837223883352537186677084*I], [5, 0.E-77, 10.0000000000000000000000000000000
98: 00000, -5.0000000000000000000000000000000000000, 7.0000000000000000000000000
99: 000000000000; 0.E-77, 19.488486013650707197449403270536023970, 2.07268045322
100: 2666710 E-76, 19.488486013650707197449403270536023970, 4.1504592246706085588
101: 902013976045703227; 10.000000000000000000000000000000000000, 2.0726804532226
102: 66710 E-76, 85.960217420851846480305133936577594605, -36.0342682914829798382
103: 67056239752434596, 53.576130452511107888183080361946556763; -5.0000000000000
104: 000000000000000000000000, 19.488486013650707197449403270536023970, -36.03426
105: 8291482979838267056239752434596, 60.916248374441986300937507618575151517, -1
106: 8.470101750219179344070032346246890434; 7.0000000000000000000000000000000000
107: 000, 4.1504592246706085588902013976045703227, 53.576130452511107888183080361
108: 946556763, -18.470101750219179344070032346246890434, 37.97015289284236734089
109: 7384258599214282], [5, 0, 10, -5, 7; 0, 10, 0, 10, -5; 10, 0, 30, -55, 20; -
110: 5, 10, -55, 45, -39; 7, -5, 20, -39, 9], [345, 0, 340, 167, 150; 0, 345, 110
111: , 220, 153; 0, 0, 5, 2, 1; 0, 0, 0, 1, 0; 0, 0, 0, 0, 1], [132825, -18975, -
112: 5175, 27600, 17250; -18975, 34500, 41400, 3450, -43125; -5175, 41400, -41400
113: , -15525, 51750; 27600, 3450, -15525, -3450, 0; 17250, -43125, 51750, 0, -86
114: 250], [595125, [-13800, 117300, 67275, 1725, 0]~]], [-2.42851749071941860689
115: 92069565359418364, 1.9647119211288133163138753392090569931 + 0.8097149241889
116: 7895128294082219556466857*I, -0.75045317576910401286427186094108607489 + 1.3
117: 101462685358123283560773619310445915*I], [1, x, x^2, 1/3*x^3 - 1/3*x^2 - 1/3
118: , 1/15*x^4 + 1/3*x^2 + 1/3*x + 1/3], [1, 0, 0, 1, -5; 0, 1, 0, 0, -5; 0, 0,
119: 1, 1, -5; 0, 0, 0, 3, 0; 0, 0, 0, 0, 15], [1, 0, 0, 0, 0, 0, 0, 1, -2, -1, 0
120: , 1, -5, -5, -3, 0, -2, -5, 1, -4, 0, -1, -3, -4, -3; 0, 1, 0, 0, 0, 1, 0, 0
121: , -2, 0, 0, 0, -5, 0, -5, 0, -2, 0, -5, 0, 0, 0, -5, 0, -4; 0, 0, 1, 0, 0, 0
122: , 1, 1, -2, 1, 1, 1, -5, 3, -3, 0, -2, 3, -5, 1, 0, 1, -3, 1, -2; 0, 0, 0, 1
123: , 0, 0, 0, 3, -1, 2, 0, 3, 0, 5, 1, 1, -1, 5, -4, 3, 0, 2, 1, 3, 1; 0, 0, 0,
124: 0, 1, 0, 0, 0, 5, 0, 0, 0, 15, -5, 10, 0, 5, -5, 10, -2, 1, 0, 10, -2, 7]]
125: ? ba=algtobasis(nf,mod(x^3+5,nfpol))
126: [6, 0, 1, 3, 0]~
127: ? anell(acurve,100)
128: [1, -2, -3, 2, -2, 6, -1, 0, 6, 4, -5, -6, -2, 2, 6, -4, 0, -12, 0, -4, 3, 1
129: 0, 2, 0, -1, 4, -9, -2, 6, -12, -4, 8, 15, 0, 2, 12, -1, 0, 6, 0, -9, -6, 2,
130: -10, -12, -4, -9, 12, -6, 2, 0, -4, 1, 18, 10, 0, 0, -12, 8, 12, -8, 8, -6,
131: -8, 4, -30, 8, 0, -6, -4, 9, 0, -1, 2, 3, 0, 5, -12, 4, 8, 9, 18, -15, 6, 0
132: , -4, -18, 0, 4, 24, 2, 4, 12, 18, 0, -24, 4, 12, -30, -2]
133: ? apell(acurve,10007)
134: 66
135: ? apell2(acurve,10007)
136: 66
137: ? apol=x^3+5*x+1
138: x^3 + 5*x + 1
139: ? apprpadic(apol,1+o(7^8))
140: [1 + 6*7 + 4*7^2 + 4*7^3 + 3*7^4 + 4*7^5 + 6*7^7 + O(7^8)]
141: ? apprpadic(x^3+5*x+1,mod(x*(1+o(7^8)),x^2+x-1))
142: [mod((1 + 3*7 + 3*7^2 + 4*7^3 + 4*7^4 + 4*7^5 + 2*7^6 + 3*7^7 + O(7^8))*x +
143: (2*7 + 6*7^2 + 6*7^3 + 3*7^4 + 3*7^5 + 4*7^6 + 5*7^7 + O(7^8)), x^2 + x - 1)
144: ]~
145: ? 4*arg(3+3*i)
146: 3.1415926535897932384626433832795028842
147: ? 3*asin(sqrt(3)/2)
148: 3.1415926535897932384626433832795028841
149: ? asinh(0.5)
150: 0.48121182505960344749775891342436842313
151: ? assmat(x^5-12*x^3+0.0005)
152:
153: [0 0 0 0 -0.00049999999999999999999999999999999999999]
154:
155: [1 0 0 0 0]
156:
157: [0 1 0 0 0]
158:
159: [0 0 1 0 12]
160:
161: [0 0 0 1 0]
162:
163: ? 3*atan(sqrt(3))
164: 3.1415926535897932384626433832795028841
165: ? atanh(0.5)
166: 0.54930614433405484569762261846126285232
167: ? basis(x^3+4*x+5)
168: [1, x, 1/7*x^2 - 1/7*x - 2/7]
169: ? basis2(x^3+4*x+5)
170: [1, x, 1/7*x^2 - 1/7*x - 2/7]
171: ? basistoalg(nf,ba)
172: mod(x^3 + 5, x^5 - 5*x^3 + 5*x + 25)
173: ? bernreal(12)
174: -0.25311355311355311355311355311355311354
175: ? bernvec(6)
176: [1, 1/6, -1/30, 1/42, -1/30, 5/66, -691/2730]
177: ? bestappr(pi,10000)
178: 355/113
179: ? bezout(123456789,987654321)
180: [-8, 1, 9]
181: ? bigomega(12345678987654321)
182: 8
183: ? mcurve=initell([0,0,0,-17,0])
184: [0, 0, 0, -17, 0, 0, -34, 0, -289, 816, 0, 314432, 1728, [4.1231056256176605
185: 498214098559740770251, 0.E-38, -4.1231056256176605498214098559740770251]~, 1
186: .2913084409290072207105564235857096009, 1.2913084409290072207105564235857096
187: 009*I, -1.2164377440798088266474269946818791934, -3.649313232239426479942280
188: 9840456375802*I, 1.6674774896145033307120230298772362381]
189: ? mpoints=[[-1,4],[-4,2]]~
190: [[-1, 4], [-4, 2]]~
191: ? mhbi=bilhell(mcurve,mpoints,[9,24])
192: [-0.72448571035980184146215805860545027438, 1.307328627832055544492943428892
193: 1943055]~
194: ? bin(1.1,5)
195: -0.0045457499999999999999999999999999999997
196: ? binary(65537)
197: [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1]
198: ? bittest(10^100,100)
199: 1
200: ? boundcf(pi,5)
201: [3, 7, 15, 1, 292]
202: ? boundfact(40!+1,100000)
203:
204: [41 1]
205:
206: [59 1]
207:
208: [277 1]
209:
210: [1217669507565553887239873369513188900554127 1]
211:
212: ? move(0,0,0);box(0,500,500)
213: ? setrand(1);buchimag(1-10^7,1,1)
214: *** Warning: not a fundamental discriminant in quadclassunit.
215: [2416, [1208, 2], [qfi(277, 55, 9028), qfi(1700, 1249, 1700)], 1, 0.99984980
216: 75377600233]
217: ? setrand(1);bnf=buchinitfu(x^2-x-57,0.2,0.2)
218: [mat(3), mat([1, 2, 1, 2, 1, 2, 1, 2, 1]), [-2.71246530518434397468087951060
219: 61300699 + 3.1415926535897932384626433832795028842*I; 2.71246530518434397468
220: 08795106061300699 - 6.2831853071795864769252867665590057684*I], [9.927737672
221: 2507613003718504524486100858 + 3.1415926535897932384626433832795028842*I, 1.
222: 2897619530652735025030086072395031017 + 0.E-57*I, -2.01097980249891575621226
223: 34098917610612 + 3.1415926535897932384626433832795028842*I, 24.4121877466590
224: 95772127915595455170629 + 6.2831853071795864769252867665590057684*I, 30.3376
225: 98160660239595315877930058147543 + 9.4247779607693797153879301498385086526*I
226: , -20.610866187462450639586440264933189691 + 9.42477796076937971538793014983
227: 85086526*I, 29.258282452818196217527894893424939793 + 9.42477796076937971538
228: 79301498385086526*I, -0.34328764427702709438988786673341921876 + 3.141592653
229: 5897932384626433832795028842*I, -14.550628376291080203941433635329724736 + 0
230: .E-56*I, 24.478366048541841504313284087778334822 + 3.14159265358979323846264
231: 33832795028842*I; -9.9277376722507613003718504524486100858 + 6.2831853071795
232: 864769252867665590057684*I, -1.2897619530652735025030086072395031017 + 9.424
233: 7779607693797153879301498385086526*I, 2.010979802498915756212263409891761061
234: 2 + 0.E-57*I, -24.412187746659095772127915595455170629 + 3.14159265358979323
235: 84626433832795028842*I, -30.337698160660239595315877930058147543 + 3.1415926
236: 535897932384626433832795028842*I, 20.610866187462450639586440264933189691 +
237: 3.1415926535897932384626433832795028842*I, -29.25828245281819621752789489342
238: 4939793 + 6.2831853071795864769252867665590057684*I, 0.343287644277027094389
239: 88786673341921876 + 0.E-57*I, 14.550628376291080203941433635329724736 + 3.14
240: 15926535897932384626433832795028842*I, -24.478366048541841504313284087778334
241: 822 + 3.1415926535897932384626433832795028842*I], [[3, [-1, 1]~, 1, 1, [0, 1
242: ]~], [3, [0, 1]~, 1, 1, [-1, 1]~], [5, [-2, 1]~, 1, 1, [1, 1]~], [5, [1, 1]~
243: , 1, 1, [-2, 1]~], [11, [-2, 1]~, 1, 1, [1, 1]~], [11, [1, 1]~, 1, 1, [-2, 1
244: ]~], [17, [-3, 1]~, 1, 1, [2, 1]~], [17, [2, 1]~, 1, 1, [-3, 1]~], [19, [-1,
245: 1]~, 1, 1, [0, 1]~], [19, [0, 1]~, 1, 1, [-1, 1]~]]~, [1, 3, 5, 2, 4, 6, 7,
246: 8, 10, 9], [x^2 - x - 57, [2, 0], 229, 1, [[1, -7.0663729752107779635959310
247: 246705326058; 1, 8.0663729752107779635959310246705326058], [1, 1; -7.0663729
248: 752107779635959310246705326058, 8.0663729752107779635959310246705326058], [2
249: , 1.0000000000000000000000000000000000000; 1.0000000000000000000000000000000
250: 000000, 115.00000000000000000000000000000000000], [2, 1; 1, 115], [229, 114;
251: 0, 1], [115, -1; -1, 2], [229, [114, 1]~]], [-7.066372975210777963595931024
252: 6705326058, 8.0663729752107779635959310246705326058], [1, x], [1, 0; 0, 1],
253: [1, 0, 0, 57; 0, 1, 1, 1]], [[3, [3], [[3, 2; 0, 1]]], 2.7124653051843439746
254: 808795106061300699, 0.8814422512654579369, [2, -1], [x + 7], 185], [mat(1),
255: [[0, 0]], [[9.9277376722507613003718504524486100858 + 3.14159265358979323846
256: 26433832795028842*I, -9.9277376722507613003718504524486100858 + 6.2831853071
257: 795864769252867665590057684*I]]], 0]
258: ? buchcertify(bnf)
259: 1
260: ? buchfu(bnf)
261: [[x + 7], 185]
262: ? setrand(1);buchinitforcefu(x^2-x-100000)
263: [mat(5), mat([3, 2, 1, 2, 0, 3, 2, 3, 0, 0, 1, 4, 3, 2, 2, 3, 3, 2]), [-129.
264: 82045011403975460991182396195022419 - 6.283185307179586476925286766559005768
265: 4*I; 129.82045011403975460991182396195022419 - 12.56637061435917295385057353
266: 3118011536*I], [-41.811264589129943393339502258694361489 + 8.121413879410077
267: 514 E-115*I, 9.2399004147902289816376260438840931575 + 3.1415926535897932384
268: 626433832795028842*I, -11.874609881075406725097315997431161032 + 9.424777960
269: 7693797153879301498385086526*I, 389.46135034211926382973547188585067257 + 12
270: .566370614359172953850573533118011536*I, -440.512515346039436204712600188429
271: 12722 + 0.E-113*I, -324.55112528509938652477955990487556047 + 6.283185307179
272: 5864769252867665590057684*I, 229.70424552002497255158146166263724792 + 3.141
273: 5926535897932384626433832795028842*I, -785.660451862534215720251179722755983
274: 25 + 6.2831853071795864769252867665590057684*I, -554.35531386699327377220656
275: 215544062014 + 6.2831853071795864769252867665590057684*I, -47.66831907156823
276: 3997332918482707687879 + 9.4247779607693797153879301498385086526*I, 177.4887
277: 6918560798860724474244465791207 + 6.497131103528062011 E-114*I, -875.6123693
278: 7168080069763246690606885226 + 2.598852441411224804 E-113*I, 54.878404098312
279: 329644822020875673145627 + 9.4247779607693797153879301498385086526*I, -404.4
280: 4153844676787690336623107514389175 + 0.E-113*I, 232.809823743598178900114904
281: 85449930607 + 6.2831853071795864769252867665590057684*I, -668.80899963671483
282: 856204802764462926790 + 9.4247779607693797153879301498385086526*I, 367.35683
283: 481950538594888487746203445802 + 12.566370614359172953850573533118011536*I,
284: -1214.0716092619656173892944003952818868 + 9.4247779607693797153879301498385
285: 086526*I, -125.94415646756187210316334148291471657 + 6.283185307179586476925
286: 2867665590057684*I; 41.811264589129943393339502258694361489 + 6.283185307179
287: 5864769252867665590057684*I, -9.2399004147902289816376260438840931575 + 12.5
288: 66370614359172953850573533118011536*I, 11.8746098810754067250973159974311610
289: 32 + 8.121413879410077514 E-115*I, -389.46135034211926382973547188585067257
290: + 6.2831853071795864769252867665590057684*I, 440.512515346039436204712600188
291: 42912722 + 3.1415926535897932384626433832795028842*I, 324.551125285099386524
292: 77955990487556047 + 9.4247779607693797153879301498385086526*I, -229.70424552
293: 002497255158146166263724792 + 6.2831853071795864769252867665590057684*I, 785
294: .66045186253421572025117972275598325 + 9.42477796076937971538793014983850865
295: 26*I, 554.35531386699327377220656215544062014 + 3.14159265358979323846264338
296: 32795028842*I, 47.668319071568233997332918482707687878 + 3.14159265358979323
297: 84626433832795028842*I, -177.48876918560798860724474244465791207 + 6.2831853
298: 071795864769252867665590057684*I, 875.61236937168080069763246690606885226 +
299: 6.497131103528062011 E-114*I, -54.878404098312329644822020875673145627 + 9.4
300: 247779607693797153879301498385086526*I, 404.44153844676787690336623107514389
301: 175 + 9.4247779607693797153879301498385086526*I, -232.8098237435981789001149
302: 0485449930607 + 3.1415926535897932384626433832795028842*I, 668.8089996367148
303: 3856204802764462926790 + 6.2831853071795864769252867665590057684*I, -367.356
304: 83481950538594888487746203445803 + 3.1415926535897932384626433832795028842*I
305: , 1214.0716092619656173892944003952818868 + 3.141592653589793238462643383279
306: 5028842*I, 125.94415646756187210316334148291471657 + 6.283185307179586476925
307: 2867665590057684*I], [[2, [1, 1]~, 1, 1, [0, 1]~], [2, [2, 1]~, 1, 1, [1, 1]
308: ~], [5, [4, 1]~, 1, 1, [0, 1]~], [5, [5, 1]~, 1, 1, [-1, 1]~], [7, [3, 1]~,
309: 2, 1, [3, 1]~], [13, [-6, 1]~, 1, 1, [5, 1]~], [13, [5, 1]~, 1, 1, [-6, 1]~]
310: , [17, [14, 1]~, 1, 1, [2, 1]~], [17, [19, 1]~, 1, 1, [-3, 1]~], [23, [-7, 1
311: ]~, 1, 1, [6, 1]~], [23, [6, 1]~, 1, 1, [-7, 1]~], [29, [-14, 1]~, 1, 1, [13
312: , 1]~], [29, [13, 1]~, 1, 1, [-14, 1]~], [31, [23, 1]~, 1, 1, [7, 1]~], [31,
313: [38, 1]~, 1, 1, [-8, 1]~], [41, [-7, 1]~, 1, 1, [6, 1]~], [41, [6, 1]~, 1,
314: 1, [-7, 1]~], [43, [-16, 1]~, 1, 1, [15, 1]~], [43, [15, 1]~, 1, 1, [-16, 1]
315: ~]]~, [1, 3, 6, 2, 4, 5, 7, 9, 8, 11, 10, 13, 12, 15, 14, 17, 16, 19, 18], [
316: x^2 - x - 100000, [2, 0], 400001, 1, [[1, -315.72816130129840161392089489603
317: 747004; 1, 316.72816130129840161392089489603747004], [1, 1; -315.72816130129
318: 840161392089489603747004, 316.72816130129840161392089489603747004], [2, 1.00
319: 00000000000000000000000000000000000; 1.0000000000000000000000000000000000000
320: , 200001.00000000000000000000000000000000], [2, 1; 1, 200001], [400001, 2000
321: 00; 0, 1], [200001, -1; -1, 2], [400001, [200000, 1]~]], [-315.7281613012984
322: 0161392089489603747004, 316.72816130129840161392089489603747004], [1, x], [1
323: , 0; 0, 1], [1, 0, 0, 100000; 0, 1, 1, 1]], [[5, [5], [[2, 1; 0, 1]]], 129.8
324: 2045011403975460991182396195022419, 0.9876536979069047239, [2, -1], [3795548
325: 84019013781006303254896369154068336082609238336*x + 119836165644250789990462
326: 835950022871665178127611316131167], 186], [mat(1), [[0, 0]], [[-41.811264589
327: 129943393339502258694361489 + 8.121413879410077514 E-115*I, 41.8112645891299
328: 43393339502258694361489 + 6.2831853071795864769252867665590057684*I]]], 0]
329: ? setrand(1);bnf=buchinitfu(x^2-x-57,0.2,0.2)
330: [mat(3), mat([1, 2, 1, 2, 1, 2, 1, 2, 1]), [-2.71246530518434397468087951060
331: 61300699 + 3.1415926535897932384626433832795028842*I; 2.71246530518434397468
332: 08795106061300699 - 6.2831853071795864769252867665590057684*I], [9.927737672
333: 2507613003718504524486100858 + 3.1415926535897932384626433832795028842*I, 1.
334: 2897619530652735025030086072395031017 + 0.E-57*I, -2.01097980249891575621226
335: 34098917610612 + 3.1415926535897932384626433832795028842*I, 24.4121877466590
336: 95772127915595455170629 + 6.2831853071795864769252867665590057684*I, 30.3376
337: 98160660239595315877930058147543 + 9.4247779607693797153879301498385086526*I
338: , -20.610866187462450639586440264933189691 + 9.42477796076937971538793014983
339: 85086526*I, 29.258282452818196217527894893424939793 + 9.42477796076937971538
340: 79301498385086526*I, -0.34328764427702709438988786673341921876 + 3.141592653
341: 5897932384626433832795028842*I, -14.550628376291080203941433635329724736 + 0
342: .E-56*I, 24.478366048541841504313284087778334822 + 3.14159265358979323846264
343: 33832795028842*I; -9.9277376722507613003718504524486100858 + 6.2831853071795
344: 864769252867665590057684*I, -1.2897619530652735025030086072395031017 + 9.424
345: 7779607693797153879301498385086526*I, 2.010979802498915756212263409891761061
346: 2 + 0.E-57*I, -24.412187746659095772127915595455170629 + 3.14159265358979323
347: 84626433832795028842*I, -30.337698160660239595315877930058147543 + 3.1415926
348: 535897932384626433832795028842*I, 20.610866187462450639586440264933189691 +
349: 3.1415926535897932384626433832795028842*I, -29.25828245281819621752789489342
350: 4939793 + 6.2831853071795864769252867665590057684*I, 0.343287644277027094389
351: 88786673341921876 + 0.E-57*I, 14.550628376291080203941433635329724736 + 3.14
352: 15926535897932384626433832795028842*I, -24.478366048541841504313284087778334
353: 822 + 3.1415926535897932384626433832795028842*I], [[3, [-1, 1]~, 1, 1, [0, 1
354: ]~], [3, [0, 1]~, 1, 1, [-1, 1]~], [5, [-2, 1]~, 1, 1, [1, 1]~], [5, [1, 1]~
355: , 1, 1, [-2, 1]~], [11, [-2, 1]~, 1, 1, [1, 1]~], [11, [1, 1]~, 1, 1, [-2, 1
356: ]~], [17, [-3, 1]~, 1, 1, [2, 1]~], [17, [2, 1]~, 1, 1, [-3, 1]~], [19, [-1,
357: 1]~, 1, 1, [0, 1]~], [19, [0, 1]~, 1, 1, [-1, 1]~]]~, [1, 3, 5, 2, 4, 6, 7,
358: 8, 10, 9], [x^2 - x - 57, [2, 0], 229, 1, [[1, -7.0663729752107779635959310
359: 246705326058; 1, 8.0663729752107779635959310246705326058], [1, 1; -7.0663729
360: 752107779635959310246705326058, 8.0663729752107779635959310246705326058], [2
361: , 1.0000000000000000000000000000000000000; 1.0000000000000000000000000000000
362: 000000, 115.00000000000000000000000000000000000], [2, 1; 1, 115], [229, 114;
363: 0, 1], [115, -1; -1, 2], [229, [114, 1]~]], [-7.066372975210777963595931024
364: 6705326058, 8.0663729752107779635959310246705326058], [1, x], [1, 0; 0, 1],
365: [1, 0, 0, 57; 0, 1, 1, 1]], [[3, [3], [[3, 2; 0, 1]]], 2.7124653051843439746
366: 808795106061300699, 0.8814422512654579369, [2, -1], [x + 7], 185], [mat(1),
367: [[0, 0]], [[9.9277376722507613003718504524486100858 + 3.14159265358979323846
368: 26433832795028842*I, -9.9277376722507613003718504524486100858 + 6.2831853071
369: 795864769252867665590057684*I]]], 0]
370: ? setrand(1);buchreal(10^9-3,0,0.5,0.5)
371: [4, [4], [qfr(3, 1, -83333333, 0.E-57)], 2800.625251907016076486370621737074
372: 5514, 0.9990369458964383232]
373: ? setrand(1);buchgen(x^4-7,0.2,0.2)
374:
375: [x^4 - 7]
376:
377: [[2, 1]]
378:
379: [[-87808, 1]]
380:
381: [[1, x, x^2, x^3]]
382:
383: [[2, [2], [[3, 1, 2, 1; 0, 1, 0, 0; 0, 0, 1, 0; 0, 0, 0, 1]]]]
384:
385: [14.229975145405511722395637833443108790]
386:
387: [1.121117107152756229]
388:
389: ? setrand(1);buchgenfu(x^2-x-100000)
390: *** Warning: insufficient precision for fundamental units, not given.
391:
392: [x^2 - x - 100000]
393:
394: [[2, 0]]
395:
396: [[400001, 1]]
397:
398: [[1, x]]
399:
400: [[5, [5], [[2, 1; 0, 1]]]]
401:
402: [129.82045011403975460991182396195022419]
403:
404: [0.9876536979069047239]
405:
406: [[2, -1]]
407:
408: [[;]]
409:
410: [0]
411:
412: ? setrand(1);buchgenforcefu(x^2-x-100000)
413:
414: [x^2 - x - 100000]
415:
416: [[2, 0]]
417:
418: [[400001, 1]]
419:
420: [[1, x]]
421:
422: [[5, [5], [[2, 1; 0, 1]]]]
423:
424: [129.82045011403975460991182396195022419]
425:
426: [0.9876536979069047239]
427:
428: [[2, -1]]
429:
430: [[379554884019013781006303254896369154068336082609238336*x + 119836165644250
431: 789990462835950022871665178127611316131167]]
432:
433: [186]
434:
435: ? setrand(1);buchgenfu(x^4+24*x^2+585*x+1791,0.1,0.1)
436:
437: [x^4 + 24*x^2 + 585*x + 1791]
438:
439: [[0, 2]]
440:
441: [[18981, 3087]]
442:
443: [[1, x, 1/3*x^2, 1/1029*x^3 + 33/343*x^2 - 155/343*x - 58/343]]
444:
445: [[4, [4], [[7, 6, 2, 4; 0, 1, 0, 0; 0, 0, 1, 0; 0, 0, 0, 1]]]]
446:
447: [3.7941269688216589341408274220859400302]
448:
449: [0.8826018286655581306]
450:
451: [[6, -10/1029*x^3 + 13/343*x^2 - 165/343*x - 1135/343]]
452:
453: [[1/147*x^3 + 1/147*x^2 - 8/49*x - 9/49]]
454:
455: [182]
456:
457: ? buchnarrow(bnf)
458: [3, [3], [[3, 2; 0, 1]]]
459: ? buchray(bnf,[[5,3;0,1],[1,0]])
460: [12, [12], [[3, 2; 0, 1]]]
461: ? bnr=buchrayinitgen(bnf,[[5,3;0,1],[1,0]])
462: [[mat(3), mat([1, 2, 1, 2, 1, 2, 1, 2, 1]), [-2.7124653051843439746808795106
463: 061300699 + 3.1415926535897932384626433832795028842*I; 2.7124653051843439746
464: 808795106061300699 - 6.2831853071795864769252867665590057684*I], [9.92773767
465: 22507613003718504524486100858 + 3.1415926535897932384626433832795028842*I, 1
466: .2897619530652735025030086072395031017 + 0.E-57*I, -2.0109798024989157562122
467: 634098917610612 + 3.1415926535897932384626433832795028842*I, 24.412187746659
468: 095772127915595455170629 + 6.2831853071795864769252867665590057684*I, 30.337
469: 698160660239595315877930058147543 + 9.4247779607693797153879301498385086526*
470: I, -20.610866187462450639586440264933189691 + 9.4247779607693797153879301498
471: 385086526*I, 29.258282452818196217527894893424939793 + 9.4247779607693797153
472: 879301498385086526*I, -0.34328764427702709438988786673341921876 + 3.14159265
473: 35897932384626433832795028842*I, -14.550628376291080203941433635329724736 +
474: 0.E-56*I, 24.478366048541841504313284087778334822 + 3.1415926535897932384626
475: 433832795028842*I; -9.9277376722507613003718504524486100858 + 6.283185307179
476: 5864769252867665590057684*I, -1.2897619530652735025030086072395031017 + 9.42
477: 47779607693797153879301498385086526*I, 2.01097980249891575621226340989176106
478: 12 + 0.E-57*I, -24.412187746659095772127915595455170629 + 3.1415926535897932
479: 384626433832795028842*I, -30.337698160660239595315877930058147543 + 3.141592
480: 6535897932384626433832795028842*I, 20.610866187462450639586440264933189691 +
481: 3.1415926535897932384626433832795028842*I, -29.2582824528181962175278948934
482: 24939793 + 6.2831853071795864769252867665590057684*I, 0.34328764427702709438
483: 988786673341921876 + 0.E-57*I, 14.550628376291080203941433635329724736 + 3.1
484: 415926535897932384626433832795028842*I, -24.47836604854184150431328408777833
485: 4822 + 3.1415926535897932384626433832795028842*I], [[3, [-1, 1]~, 1, 1, [0,
486: 1]~], [3, [0, 1]~, 1, 1, [-1, 1]~], [5, [-2, 1]~, 1, 1, [1, 1]~], [5, [1, 1]
487: ~, 1, 1, [-2, 1]~], [11, [-2, 1]~, 1, 1, [1, 1]~], [11, [1, 1]~, 1, 1, [-2,
488: 1]~], [17, [-3, 1]~, 1, 1, [2, 1]~], [17, [2, 1]~, 1, 1, [-3, 1]~], [19, [-1
489: , 1]~, 1, 1, [0, 1]~], [19, [0, 1]~, 1, 1, [-1, 1]~]]~, [1, 3, 5, 2, 4, 6, 7
490: , 8, 10, 9], [x^2 - x - 57, [2, 0], 229, 1, [[1, -7.066372975210777963595931
491: 0246705326058; 1, 8.0663729752107779635959310246705326058], [1, 1; -7.066372
492: 9752107779635959310246705326058, 8.0663729752107779635959310246705326058], [
493: 2, 1.0000000000000000000000000000000000000; 1.000000000000000000000000000000
494: 0000000, 115.00000000000000000000000000000000000], [2, 1; 1, 115], [229, 114
495: ; 0, 1], [115, -1; -1, 2], [229, [114, 1]~]], [-7.06637297521077796359593102
496: 46705326058, 8.0663729752107779635959310246705326058], [1, x], [1, 0; 0, 1],
497: [1, 0, 0, 57; 0, 1, 1, 1]], [[3, [3], [[3, 2; 0, 1]]], 2.712465305184343974
498: 6808795106061300699, 0.8814422512654579369, [2, -1], [x + 7], 185], [mat(1),
499: [[0, 0]], [[9.9277376722507613003718504524486100858 + 3.1415926535897932384
500: 626433832795028842*I, -9.9277376722507613003718504524486100858 + 6.283185307
501: 1795864769252867665590057684*I]]], [0, [mat([[5, 1]~, 1])]]], [[[5, 3; 0, 1]
502: , [1, 0]], [8, [4, 2], [[2, 0]~, [-1, 1]~]], mat([[5, [-2, 1]~, 1, 1, [1, 1]
503: ~], 1]), [[[[4], [[2, 0]~], [[2, 0]~], [[mod(0, 2)]~], 1]], [[2], [[-1, 1]~]
504: , mat(1)]], [1, 0; 0, 1]], [1], [1, -3, -6; 0, 0, 1; 0, 1, 0], [12, [12], [[
505: 3, 2; 0, 1]]], [[1/2, 0; 0, 0], [1, -1; 1, 1]]]
506: ? bnr2=buchrayinitgen(bnf,[[25,13;0,1],[1,1]])
507: [[mat(3), mat([1, 2, 1, 2, 1, 2, 1, 2, 1]), [-2.7124653051843439746808795106
508: 061300699 + 3.1415926535897932384626433832795028842*I; 2.7124653051843439746
509: 808795106061300699 - 6.2831853071795864769252867665590057684*I], [9.92773767
510: 22507613003718504524486100858 + 3.1415926535897932384626433832795028842*I, 1
511: .2897619530652735025030086072395031017 + 0.E-57*I, -2.0109798024989157562122
512: 634098917610612 + 3.1415926535897932384626433832795028842*I, 24.412187746659
513: 095772127915595455170629 + 6.2831853071795864769252867665590057684*I, 30.337
514: 698160660239595315877930058147543 + 9.4247779607693797153879301498385086526*
515: I, -20.610866187462450639586440264933189691 + 9.4247779607693797153879301498
516: 385086526*I, 29.258282452818196217527894893424939793 + 9.4247779607693797153
517: 879301498385086526*I, -0.34328764427702709438988786673341921876 + 3.14159265
518: 35897932384626433832795028842*I, -14.550628376291080203941433635329724736 +
519: 0.E-56*I, 24.478366048541841504313284087778334822 + 3.1415926535897932384626
520: 433832795028842*I; -9.9277376722507613003718504524486100858 + 6.283185307179
521: 5864769252867665590057684*I, -1.2897619530652735025030086072395031017 + 9.42
522: 47779607693797153879301498385086526*I, 2.01097980249891575621226340989176106
523: 12 + 0.E-57*I, -24.412187746659095772127915595455170629 + 3.1415926535897932
524: 384626433832795028842*I, -30.337698160660239595315877930058147543 + 3.141592
525: 6535897932384626433832795028842*I, 20.610866187462450639586440264933189691 +
526: 3.1415926535897932384626433832795028842*I, -29.2582824528181962175278948934
527: 24939793 + 6.2831853071795864769252867665590057684*I, 0.34328764427702709438
528: 988786673341921876 + 0.E-57*I, 14.550628376291080203941433635329724736 + 3.1
529: 415926535897932384626433832795028842*I, -24.47836604854184150431328408777833
530: 4822 + 3.1415926535897932384626433832795028842*I], [[3, [-1, 1]~, 1, 1, [0,
531: 1]~], [3, [0, 1]~, 1, 1, [-1, 1]~], [5, [-2, 1]~, 1, 1, [1, 1]~], [5, [1, 1]
532: ~, 1, 1, [-2, 1]~], [11, [-2, 1]~, 1, 1, [1, 1]~], [11, [1, 1]~, 1, 1, [-2,
533: 1]~], [17, [-3, 1]~, 1, 1, [2, 1]~], [17, [2, 1]~, 1, 1, [-3, 1]~], [19, [-1
534: , 1]~, 1, 1, [0, 1]~], [19, [0, 1]~, 1, 1, [-1, 1]~]]~, [1, 3, 5, 2, 4, 6, 7
535: , 8, 10, 9], [x^2 - x - 57, [2, 0], 229, 1, [[1, -7.066372975210777963595931
536: 0246705326058; 1, 8.0663729752107779635959310246705326058], [1, 1; -7.066372
537: 9752107779635959310246705326058, 8.0663729752107779635959310246705326058], [
538: 2, 1.0000000000000000000000000000000000000; 1.000000000000000000000000000000
539: 0000000, 115.00000000000000000000000000000000000], [2, 1; 1, 115], [229, 114
540: ; 0, 1], [115, -1; -1, 2], [229, [114, 1]~]], [-7.06637297521077796359593102
541: 46705326058, 8.0663729752107779635959310246705326058], [1, x], [1, 0; 0, 1],
542: [1, 0, 0, 57; 0, 1, 1, 1]], [[3, [3], [[3, 2; 0, 1]]], 2.712465305184343974
543: 6808795106061300699, 0.8814422512654579369, [2, -1], [x + 7], 185], [mat(1),
544: [[0, 0]], [[9.9277376722507613003718504524486100858 + 3.1415926535897932384
545: 626433832795028842*I, -9.9277376722507613003718504524486100858 + 6.283185307
546: 1795864769252867665590057684*I]]], [0, [mat([[5, 1]~, 1])]]], [[[25, 13; 0,
547: 1], [1, 1]], [80, [20, 2, 2], [[2, 0]~, [0, -2]~, [2, 2]~]], mat([[5, [-2, 1
548: ]~, 1, 1, [1, 1]~], 2]), [[[[4], [[2, 0]~], [[2, 0]~], [[mod(0, 2), mod(0, 2
549: )]~], 1], [[5], [[6, 0]~], [[6, 0]~], [[mod(0, 2), mod(0, 2)]~], mat([1/5, -
550: 13/5])]], [[2, 2], [[0, -2]~, [2, 2]~], [0, 1; 1, 0]]], [1, -12, 0, 0; 0, 0,
551: 1, 0; 0, 0, 0, 1]], [1], [1, -3, 0, -6; 0, 0, 1, 0; 0, 0, 0, 1; 0, 1, 0, 0]
552: , [12, [12], [[3, 2; 0, 1]]], [[1, 9, -18; -1/2, -5, 10], [-2, 0; 0, 10]]]
553: ? bytesize(%)
554: 14120
555: ? ceil(-2.5)
556: -2
557: ? centerlift(mod(456,555))
558: -99
559: ? cf(pi)
560: [3, 7, 15, 1, 292, 1, 1, 1, 2, 1, 3, 1, 14, 2, 1, 1, 2, 2, 2, 2, 1, 84, 2, 1
561: , 1, 15, 3, 13, 1, 4, 2, 6, 6]
562: ? cf2([1,3,5,7,9],(exp(1)-1)/(exp(1)+1))
563: [0, 6, 10, 42, 30]
564: ? changevar(x+y,[z,t])
565: y + z
566: ? char([1,2;3,4],z)
567: z^2 - 5*z - 2
568: ? char(mod(x^2+x+1,x^3+5*x+1),z)
569: z^3 + 7*z^2 + 16*z - 19
570: ? char1([1,2;3,4],z)
571: z^2 - 5*z - 2
572: ? char2(mod(1,8191)*[1,2;3,4],z)
573: z^2 + mod(8186, 8191)*z + mod(8189, 8191)
574: ? acurve=chell(acurve,[-1,1,2,3])
575: [-4, -1, -7, -12, -12, 12, 4, 1, -1, 48, -216, 37, 110592/37, [-0.1624345647
576: 1667696455518910092496975959, -0.73040556359455544173706204865073999595, -2.
577: 1071598716887675937077488504242902444]~, -2.99345864623195962983200997945250
578: 81778, -2.4513893819867900608542248318665252253*I, 0.47131927795681147588259
579: 389708033769964, 1.4354565186686843187232088566788165076*I, 7.33813274078957
580: 67390707210033323055881]
581: ? chinese(mod(7,15),mod(13,21))
582: mod(97, 105)
583: ? apoint=chptell(apoint,[-1,1,2,3])
584: [1, 3]
585: ? isoncurve(acurve,apoint)
586: 1
587: ? classno(-12391)
588: 63
589: ? classno(1345)
590: 6
591: ? classno2(-12391)
592: 63
593: ? classno2(1345)
594: 6
595: ? coeff(sin(x),7)
596: -1/5040
597: ? compimag(qfi(2,1,3),qfi(2,1,3))
598: qfi(2, -1, 3)
599: ? compo(1+o(7^4),3)
600: 1
601: ? compositum(x^4-4*x+2,x^3-x-1)
602: [x^12 - 4*x^10 + 8*x^9 + 12*x^8 + 12*x^7 + 138*x^6 + 132*x^5 - 43*x^4 + 58*x
603: ^2 - 128*x - 5]
604: ? compositum2(x^4-4*x+2,x^3-x-1)
605: [[x^12 - 4*x^10 + 8*x^9 + 12*x^8 + 12*x^7 + 138*x^6 + 132*x^5 - 43*x^4 + 58*
606: x^2 - 128*x - 5, mod(-279140305176/29063006931199*x^11 + 129916611552/290630
607: 06931199*x^10 + 1272919322296/29063006931199*x^9 - 2813750209005/29063006931
608: 199*x^8 - 2859411937992/29063006931199*x^7 - 414533880536/29063006931199*x^6
609: - 35713977492936/29063006931199*x^5 - 17432607267590/29063006931199*x^4 + 4
610: 9785595543672/29063006931199*x^3 + 9423768373204/29063006931199*x^2 - 427797
611: 76146743/29063006931199*x + 37962587857138/29063006931199, x^12 - 4*x^10 + 8
612: *x^9 + 12*x^8 + 12*x^7 + 138*x^6 + 132*x^5 - 43*x^4 + 58*x^2 - 128*x - 5), m
613: od(-279140305176/29063006931199*x^11 + 129916611552/29063006931199*x^10 + 12
614: 72919322296/29063006931199*x^9 - 2813750209005/29063006931199*x^8 - 28594119
615: 37992/29063006931199*x^7 - 414533880536/29063006931199*x^6 - 35713977492936/
616: 29063006931199*x^5 - 17432607267590/29063006931199*x^4 + 49785595543672/2906
617: 3006931199*x^3 + 9423768373204/29063006931199*x^2 - 13716769215544/290630069
618: 31199*x + 37962587857138/29063006931199, x^12 - 4*x^10 + 8*x^9 + 12*x^8 + 12
619: *x^7 + 138*x^6 + 132*x^5 - 43*x^4 + 58*x^2 - 128*x - 5), -1]]
620: ? comprealraw(qfr(5,3,-1,0.),qfr(7,1,-1,0.))
621: qfr(35, 43, 13, 0.E-38)
622: ? concat([1,2],[3,4])
623: [1, 2, 3, 4]
624: ? conductor(bnf,[[25,13;0,1],[1,1]])
625: [[[5, 3; 0, 1], [1, 0]], [12, [12], [[3, 2; 0, 1]]], mat(12)]
626: ? conductorofchar(bnr,[2])
627: [[5, 3; 0, 1], [0, 0]]
628: ? conj(1+i)
629: 1 - I
630: ? conjvec(mod(x^2+x+1,x^3-x-1))
631: [4.0795956234914387860104177508366260325, 0.46020218825428060699479112458168
632: 698369 + 0.18258225455744299269398828369501930573*I, 0.460202188254280606994
633: 79112458168698369 - 0.18258225455744299269398828369501930573*I]~
634: ? content([123,456,789,234])
635: 3
636: ? convol(sin(x),x*cos(x))
637: x + 1/12*x^3 + 1/2880*x^5 + 1/3628800*x^7 + 1/14631321600*x^9 + 1/1448500838
638: 40000*x^11 + 1/2982752926433280000*x^13 + 1/114000816848279961600000*x^15 +
639: O(x^16)
640: ? core(54713282649239)
641: 5471
642: ? core2(54713282649239)
643: [5471, 100003]
644: ? coredisc(54713282649239)
645: 21884
646: ? coredisc2(54713282649239)
647: [21884, 100003/2]
648: ? cos(1)
649: 0.54030230586813971740093660744297660373
650: ? cosh(1)
651: 1.5430806348152437784779056207570616825
652: ? move(0,200,150)
653: ? cursor(0)
654: ? cvtoi(1.7)
655: 1
656: ? cyclo(105)
657: x^48 + x^47 + x^46 - x^43 - x^42 - 2*x^41 - x^40 - x^39 + x^36 + x^35 + x^34
658: + x^33 + x^32 + x^31 - x^28 - x^26 - x^24 - x^22 - x^20 + x^17 + x^16 + x^1
659: 5 + x^14 + x^13 + x^12 - x^9 - x^8 - 2*x^7 - x^6 - x^5 + x^2 + x + 1
660: ? degree(x^3/(x-1))
661: 2
662: ? denom(12345/54321)
663: 18107
664: ? deplin(mod(1,7)*[2,-1;1,3])
665: [mod(6, 7), mod(5, 7)]~
666: ? deriv((x+y)^5,y)
667: 5*x^4 + 20*y*x^3 + 30*y^2*x^2 + 20*y^3*x + 5*y^4
668: ? ((x+y)^5)'
669: 5*x^4 + 20*y*x^3 + 30*y^2*x^2 + 20*y^3*x + 5*y^4
670: ? det([1,2,3;1,5,6;9,8,7])
671: -30
672: ? det2([1,2,3;1,5,6;9,8,7])
673: -30
674: ? detint([1,2,3;4,5,6])
675: 3
676: ? diagonal([2,4,6])
677:
678: [2 0 0]
679:
680: [0 4 0]
681:
682: [0 0 6]
683:
684: ? dilog(0.5)
685: 0.58224052646501250590265632015968010858
686: ? dz=vector(30,k,1);dd=vector(30,k,k==1);dm=dirdiv(dd,dz)
687: [1, -1, -1, 0, -1, 1, -1, 0, 0, 1, -1, 0, -1, 1, 1, 0, -1, 0, -1, 0, 1, 1, -
688: 1, 0, 0, 1, 0, 0, -1, -1]
689: ? deu=direuler(p=2,100,1/(1-apell(acurve,p)*x+if(acurve[12]%p,p,0)*x^2))
690: [1, -2, -3, 2, -2, 6, -1, 0, 6, 4, -5, -6, -2, 2, 6, -4, 0, -12, 0, -4, 3, 1
691: 0, 2, 0, -1, 4, -9, -2, 6, -12, -4, 8, 15, 0, 2, 12, -1, 0, 6, 0, -9, -6, 2,
692: -10, -12, -4, -9, 12, -6, 2, 0, -4, 1, 18, 10, 0, 0, -12, 8, 12, -8, 8, -6,
693: -8, 4, -30, 8, 0, -6, -4, 9, 0, -1, 2, 3, 0, 5, -12, 4, 8, 9, 18, -15, 6, 0
694: , -4, -18, 0, 4, 24, 2, 4, 12, 18, 0, -24, 4, 12, -30, -2]
695: ? anell(acurve,100)==deu
696: 1
697: ? dirmul(abs(dm),dz)
698: [1, 2, 2, 2, 2, 4, 2, 2, 2, 4, 2, 4, 2, 4, 4, 2, 2, 4, 2, 4, 4, 4, 2, 4, 2,
699: 4, 2, 4, 2, 8]
700: ? dirzetak(initalg(x^3-10*x+8),30)
701: [1, 2, 0, 3, 1, 0, 0, 4, 0, 2, 1, 0, 0, 0, 0, 5, 1, 0, 0, 3, 0, 2, 0, 0, 2,
702: 0, 1, 0, 1, 0]
703: ? disc(x^3+4*x+12)
704: -4144
705: ? discf(x^3+4*x+12)
706: -1036
707: ? discrayabs(bnr,mat(6))
708: [12, 12, 18026977100265125]
709: ? discrayabs(bnr)
710: [24, 12, 40621487921685401825918161408203125]
711: ? discrayabscond(bnr2)
712: 0
713: ? lu=ideallistunitgen(bnf,55);discrayabslist(bnf,lu)
714: [[[6, 6, mat([229, 3])]], [], [[], []], [[]], [[12, 12, [5, 3; 229, 6]], [12
715: , 12, [5, 3; 229, 6]]], [], [], [], [[], [], []], [], [[], []], [[], []], []
716: , [], [[24, 24, [3, 6; 5, 9; 229, 12]], [], [], [24, 24, [3, 6; 5, 9; 229, 1
717: 2]]], [[]], [[], []], [], [[18, 18, [19, 6; 229, 9]], [18, 18, [19, 6; 229,
718: 9]]], [[], []], [], [], [], [], [[], [24, 24, [5, 12; 229, 12]], []], [], [[
719: ], [], [], []], [], [], [], [], [], [[], [12, 12, [3, 3; 11, 3; 229, 6]], [1
720: 2, 12, [3, 3; 11, 3; 229, 6]], []], [], [], [[18, 18, [2, 12; 3, 12; 229, 9]
721: ], [], [18, 18, [2, 12; 3, 12; 229, 9]]], [[12, 12, [37, 3; 229, 6]], [12, 1
722: 2, [37, 3; 229, 6]]], [], [], [], [], [], [[], []], [[], []], [[], [], [], [
723: ], [], []], [], [], [[12, 12, [2, 12; 3, 3; 229, 6]], [12, 12, [2, 12; 3, 3;
724: 229, 6]]], [[18, 18, [7, 12; 229, 9]]], [], [[], [], [], []], [], [[], []],
725: [], [[], [24, 24, [5, 9; 11, 6; 229, 12]], [24, 24, [5, 9; 11, 6; 229, 12]]
726: , []]]
727: ? discrayabslistlong(bnf,20)
728: [[[[matrix(0,2,j,k,0), 6, 6, mat([229, 3])]], [], [[mat([12, 1]), 0, 0, 0],
729: [mat([13, 1]), 0, 0, 0]], [[mat([10, 1]), 0, 0, 0]], [[mat([20, 1]), 12, 12,
730: [5, 3; 229, 6]], [mat([21, 1]), 12, 12, [5, 3; 229, 6]]], [], [], [], [[mat
731: ([12, 2]), 0, 0, 0], [[12, 1; 13, 1], 0, 0, 0], [mat([13, 2]), 0, 0, 0]], []
732: , [[mat([44, 1]), 0, 0, 0], [mat([45, 1]), 0, 0, 0]], [[[10, 1; 12, 1], 0, 0
733: , 0], [[10, 1; 13, 1], 0, 0, 0]], [], [], [[[12, 1; 20, 1], 24, 24, [3, 6; 5
734: , 9; 229, 12]], [[13, 1; 20, 1], 0, 0, 0], [[12, 1; 21, 1], 0, 0, 0], [[13,
735: 1; 21, 1], 24, 24, [3, 6; 5, 9; 229, 12]]], [[mat([10, 2]), 0, 0, 0]], [[mat
736: ([68, 1]), 0, 0, 0], [mat([69, 1]), 0, 0, 0]], [], [[mat([76, 1]), 18, 18, [
737: 19, 6; 229, 9]], [mat([77, 1]), 18, 18, [19, 6; 229, 9]]], [[[10, 1; 20, 1],
738: 0, 0, 0], [[10, 1; 21, 1], 0, 0, 0]]]]
739: ? discrayrel(bnr,mat(6))
740: [6, 2, [125, 13; 0, 1]]
741: ? discrayrel(bnr)
742: [12, 1, [1953125, 1160888; 0, 1]]
743: ? discrayrelcond(bnr2)
744: 0
745: ? divisors(8!)
746: [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 14, 15, 16, 18, 20, 21, 24, 28, 30, 32,
747: 35, 36, 40, 42, 45, 48, 56, 60, 63, 64, 70, 72, 80, 84, 90, 96, 105, 112, 12
748: 0, 126, 128, 140, 144, 160, 168, 180, 192, 210, 224, 240, 252, 280, 288, 315
749: , 320, 336, 360, 384, 420, 448, 480, 504, 560, 576, 630, 640, 672, 720, 840,
750: 896, 960, 1008, 1120, 1152, 1260, 1344, 1440, 1680, 1920, 2016, 2240, 2520,
751: 2688, 2880, 3360, 4032, 4480, 5040, 5760, 6720, 8064, 10080, 13440, 20160,
752: 40320]
753: ? divres(345,123)
754: [2, 99]~
755: ? divres(x^7-1,x^5+1)
756: [x^2, -x^2 - 1]~
757: ? divsum(8!,x,x)
758: 159120
759: ? postdraw([0,0,0])
760: ? eigen([1,2,3;4,5,6;7,8,9])
761:
762: [-1.2833494518006402717978106547571267252 1 0.283349451800640271797810654757
763: 12672521]
764:
765: [-0.14167472590032013589890532737856336260 -2 0.6416747259003201358989053273
766: 7856336260]
767:
768: [1 1 1]
769:
770: ? eint1(2)
771: 0.048900510708061119567239835228049522206
772: ? erfc(2)
773: 0.0046777349810472658379307436327470713891
774: ? eta(q)
775: 1 - q - q^2 + q^5 + q^7 - q^12 - q^15 + O(q^16)
776: ? euler
777: 0.57721566490153286060651209008240243104
778: ? z=y;y=x;eval(z)
779: x
780: ? exp(1)
781: 2.7182818284590452353602874713526624977
782: ? extract([1,2,3,4,5,6,7,8,9,10],1000)
783: [4, 6, 7, 8, 9, 10]
784: ? 10!
785: 3628800
786: ? fact(10)
787: 3628800.0000000000000000000000000000000
788: ? factcantor(x^11+1,7)
789:
790: [mod(1, 7)*x + mod(1, 7) 1]
791:
792: [mod(1, 7)*x^10 + mod(6, 7)*x^9 + mod(1, 7)*x^8 + mod(6, 7)*x^7 + mod(1, 7)*
793: x^6 + mod(6, 7)*x^5 + mod(1, 7)*x^4 + mod(6, 7)*x^3 + mod(1, 7)*x^2 + mod(6,
794: 7)*x + mod(1, 7) 1]
795:
796: ? centerlift(lift(factfq(x^3+x^2+x-1,3,t^3+t^2+t-1)))
797:
798: [x - t 1]
799:
800: [x + (t^2 + t - 1) 1]
801:
802: [x + (-t^2 - 1) 1]
803:
804: ? factmod(x^11+1,7)
805:
806: [mod(1, 7)*x + mod(1, 7) 1]
807:
808: [mod(1, 7)*x^10 + mod(6, 7)*x^9 + mod(1, 7)*x^8 + mod(6, 7)*x^7 + mod(1, 7)*
809: x^6 + mod(6, 7)*x^5 + mod(1, 7)*x^4 + mod(6, 7)*x^3 + mod(1, 7)*x^2 + mod(6,
810: 7)*x + mod(1, 7) 1]
811:
812: ? factor(17!+1)
813:
814: [661 1]
815:
816: [537913 1]
817:
818: [1000357 1]
819:
820: ? p=x^5+3021*x^4-786303*x^3-6826636057*x^2-546603588746*x+3853890514072057
821: x^5 + 3021*x^4 - 786303*x^3 - 6826636057*x^2 - 546603588746*x + 385389051407
822: 2057
823: ? fa=[11699,6;2392997,2;4987333019653,2]
824:
825: [11699 6]
826:
827: [2392997 2]
828:
829: [4987333019653 2]
830:
831: ? factoredbasis(p,fa)
832: [1, x, x^2, 1/11699*x^3 + 1847/11699*x^2 - 132/11699*x - 2641/11699, 1/13962
833: 3738889203638909659*x^4 - 1552451622081122020/139623738889203638909659*x^3 +
834: 418509858130821123141/139623738889203638909659*x^2 - 6810913798507599407313
835: 4/139623738889203638909659*x - 13185339461968406/58346808996920447]
836: ? factoreddiscf(p,fa)
837: 136866601
838: ? factoredpolred(p,fa)
839: [x - 1, x^5 - 2*x^4 - 62*x^3 + 85*x^2 + 818*x + 1, x^5 - 2*x^4 - 53*x^3 - 46
840: *x^2 + 508*x + 913, x^5 - 2*x^4 - 13*x^3 + 37*x^2 - 21*x - 1, x^5 - x^4 - 52
841: *x^3 - 197*x^2 - 273*x - 127]
842: ? factoredpolred2(p,fa)
843:
844: [1 x - 1]
845:
846: [320031469790/139623738889203638909659*x^4 + 525154323698149/139623738889203
847: 638909659*x^3 + 68805502220272624/139623738889203638909659*x^2 + 11626197624
848: 4907072724/139623738889203638909659*x - 265513916545157609/58346808996920447
849: x^5 - 2*x^4 - 62*x^3 + 85*x^2 + 818*x + 1]
850:
851: [-649489679500/139623738889203638909659*x^4 - 1004850936416946/1396237388892
852: 03638909659*x^3 + 1850137668999773331/139623738889203638909659*x^2 + 1162464
853: 435118744503168/139623738889203638909659*x - 744221404070129897/583468089969
854: 20447 x^5 - 2*x^4 - 53*x^3 - 46*x^2 + 508*x + 913]
855:
856: [404377049971/139623738889203638909659*x^4 + 1028343729806593/13962373888920
857: 3638909659*x^3 - 220760129739668913/139623738889203638909659*x^2 - 139192454
858: 3479498840309/139623738889203638909659*x - 21580477171925514/583468089969204
859: 47 x^5 - 2*x^4 - 13*x^3 + 37*x^2 - 21*x - 1]
860:
861: [160329790087/139623738889203638909659*x^4 + 1043812506369034/13962373888920
862: 3638909659*x^3 + 1517006779298914407/139623738889203638909659*x^2 - 52234888
863: 8528537141362/139623738889203638909659*x - 677624890046649103/58346808996920
864: 447 x^5 - x^4 - 52*x^3 - 197*x^2 - 273*x - 127]
865:
866: ? factornf(x^3+x^2-2*x-1,t^3+t^2-2*t-1)
867:
868: [mod(1, t^3 + t^2 - 2*t - 1)*x + mod(-t, t^3 + t^2 - 2*t - 1) 1]
869:
870: [mod(1, t^3 + t^2 - 2*t - 1)*x + mod(-t^2 + 2, t^3 + t^2 - 2*t - 1) 1]
871:
872: [mod(1, t^3 + t^2 - 2*t - 1)*x + mod(t^2 + t - 1, t^3 + t^2 - 2*t - 1) 1]
873:
874: ? factorpadic(apol,7,8)
875:
876: [(1 + O(7^8))*x + (6 + 2*7^2 + 2*7^3 + 3*7^4 + 2*7^5 + 6*7^6 + O(7^8)) 1]
877:
878: [(1 + O(7^8))*x^2 + (1 + 6*7 + 4*7^2 + 4*7^3 + 3*7^4 + 4*7^5 + 6*7^7 + O(7^8
879: ))*x + (6 + 5*7 + 3*7^2 + 6*7^3 + 7^4 + 3*7^5 + 2*7^6 + 5*7^7 + O(7^8)) 1]
880:
881: ? factorpadic2(apol,7,8)
882:
883: [(1 + O(7^8))*x + (6 + 2*7^2 + 2*7^3 + 3*7^4 + 2*7^5 + 6*7^6 + O(7^8)) 1]
884:
885: [(1 + O(7^8))*x^2 + (1 + 6*7 + 4*7^2 + 4*7^3 + 3*7^4 + 4*7^5 + 6*7^7 + O(7^8
886: ))*x + (6 + 5*7 + 3*7^2 + 6*7^3 + 7^4 + 3*7^5 + 2*7^6 + 5*7^7 + O(7^8)) 1]
887:
888: ? factpol(x^15-1,3,1)
889:
890: [x - 1 1]
891:
892: [x^2 + x + 1 1]
893:
894: [x^4 + x^3 + x^2 + x + 1 1]
895:
896: [x^8 - x^7 + x^5 - x^4 + x^3 - x + 1 1]
897:
898: ? factpol(x^15-1,0,1)
899:
900: [x - 1 1]
901:
902: [x^2 + x + 1 1]
903:
904: [x^4 + x^3 + x^2 + x + 1 1]
905:
906: [x^8 - x^7 + x^5 - x^4 + x^3 - x + 1 1]
907:
908: ? factpol2(x^15-1,0)
909: *** this function has been suppressed.
910: ? fibo(100)
911: 354224848179261915075
912: ? floor(-1/2)
913: -1
914: ? floor(-2.5)
915: -3
916: ? for(x=1,5,print(x!))
917: 1
918: 2
919: 6
920: 24
921: 120
922: ? fordiv(10,x,print(x))
923: 1
924: 2
925: 5
926: 10
927: ? forprime(p=1,30,print(p))
928: 2
929: 3
930: 5
931: 7
932: 11
933: 13
934: 17
935: 19
936: 23
937: 29
938: ? forstep(x=0,pi,pi/12,print(sin(x)))
939: 0.E-38
940: 0.25881904510252076234889883762404832834
941: 0.49999999999999999999999999999999999999
942: 0.70710678118654752440084436210484903928
943: 0.86602540378443864676372317075293618346
944: 0.96592582628906828674974319972889736763
945: 1.0000000000000000000000000000000000000
946: 0.96592582628906828674974319972889736764
947: 0.86602540378443864676372317075293618348
948: 0.70710678118654752440084436210484903930
949: 0.50000000000000000000000000000000000002
950: 0.25881904510252076234889883762404832838
951: 4.7019774032891500318749461488889827112 E-38
952: ? forvec(x=[[1,3],[-2,2]],print1([x[1],x[2]]," "));print(" ");
953: [1, -2] [1, -1] [1, 0] [1, 1] [1, 2] [2, -2] [2, -1] [2, 0] [2, 1] [2, 2] [3
954: , -2] [3, -1] [3, 0] [3, 1] [3, 2]
955: ? frac(-2.7)
956: 0.30000000000000000000000000000000000000
957: ? galois(x^6-3*x^2-1)
958: [12, 1, 1]
959: ? nf3=initalg(x^6+108);galoisconj(nf3)
960: [-x, x, -1/12*x^4 - 1/2*x, -1/12*x^4 + 1/2*x, 1/12*x^4 - 1/2*x, 1/12*x^4 + 1
961: /2*x]~
962: ? aut=%[2];galoisapply(nf3,aut,mod(x^5,x^6+108))
963: mod(x^5, x^6 + 108)
964: ? gamh(10)
965: 1133278.3889487855673345741655888924755
966: ? gamma(10.5)
967: 1133278.3889487855673345741655888924755
968: ? gauss(hilbert(10),[1,2,3,4,5,6,7,8,9,0]~)
969: [9236800, -831303990, 18288515520, -170691240720, 832112321040, -23298940665
970: 00, 3883123564320, -3803844432960, 2020775945760, -449057772020]~
971: ? gaussmodulo([2,3;5,4],[7,11],[1,4]~)
972: [-5, -1]~
973: ? gaussmodulo2([2,3;5,4],[7,11],[1,4]~)
974: [[-5, -1]~, [-77, 723; 0, 1]]
975: ? gcd(12345678,87654321)
976: 9
977: ? getheap()
978: [214, 46166]
979: ? getrand()
980: 1939683225
981: ? getstack()
982: 0
983: ? globalred(acurve)
984: [37, [1, -1, 2, 2], 1]
985: ? getstack()
986: 0
987: ? hclassno(2000003)
988: 357
989: ? hell(acurve,apoint)
990: 0.40889126591975072188708879805553617287
991: ? hell2(acurve,apoint)
992: 0.40889126591975072188708879805553617296
993: ? hermite(amat=1/hilbert(7))
994:
995: [420 0 0 0 210 168 175]
996:
997: [0 840 0 0 0 0 504]
998:
999: [0 0 2520 0 0 0 1260]
1000:
1001: [0 0 0 2520 0 0 840]
1002:
1003: [0 0 0 0 13860 0 6930]
1004:
1005: [0 0 0 0 0 5544 0]
1006:
1007: [0 0 0 0 0 0 12012]
1008:
1009: ? hermite2(amat)
1010: [[420, 0, 0, 0, 210, 168, 175; 0, 840, 0, 0, 0, 0, 504; 0, 0, 2520, 0, 0, 0,
1011: 1260; 0, 0, 0, 2520, 0, 0, 840; 0, 0, 0, 0, 13860, 0, 6930; 0, 0, 0, 0, 0,
1012: 5544, 0; 0, 0, 0, 0, 0, 0, 12012], [420, 420, 840, 630, 2982, 1092, 4159; 21
1013: 0, 280, 630, 504, 2415, 876, 3395; 140, 210, 504, 420, 2050, 749, 2901; 105,
1014: 168, 420, 360, 1785, 658, 2542; 84, 140, 360, 315, 1582, 588, 2266; 70, 120
1015: , 315, 280, 1421, 532, 2046; 60, 105, 280, 252, 1290, 486, 1866]]
1016: ? hermitehavas(amat)
1017: *** this function has been suppressed.
1018: ? hermitemod(amat,detint(amat))
1019:
1020: [420 0 0 0 210 168 175]
1021:
1022: [0 840 0 0 0 0 504]
1023:
1024: [0 0 2520 0 0 0 1260]
1025:
1026: [0 0 0 2520 0 0 840]
1027:
1028: [0 0 0 0 13860 0 6930]
1029:
1030: [0 0 0 0 0 5544 0]
1031:
1032: [0 0 0 0 0 0 12012]
1033:
1034: ? hermiteperm(amat)
1035: [[360360, 0, 0, 0, 0, 144144, 300300; 0, 27720, 0, 0, 0, 0, 22176; 0, 0, 277
1036: 20, 0, 0, 0, 6930; 0, 0, 0, 2520, 0, 0, 840; 0, 0, 0, 0, 2520, 0, 1260; 0, 0
1037: , 0, 0, 0, 168, 0; 0, 0, 0, 0, 0, 0, 7], [51480, 4620, 5544, 630, 840, 20676
1038: , 48619; 45045, 3960, 4620, 504, 630, 18074, 42347; 40040, 3465, 3960, 420,
1039: 504, 16058, 37523; 36036, 3080, 3465, 360, 420, 14448, 33692; 32760, 2772, 3
1040: 080, 315, 360, 13132, 30574; 30030, 2520, 2772, 280, 315, 12036, 27986; 2772
1041: 0, 2310, 2520, 252, 280, 11109, 25803], [7, 6, 5, 4, 3, 2, 1]]
1042: ? hess(hilbert(7))
1043:
1044: [1 90281/58800 -1919947/4344340 4858466341/1095033030 -77651417539/819678732
1045: 6 3386888964/106615355 1/2]
1046:
1047: [1/3 43/48 38789/5585580 268214641/109503303 -581330123627/126464718744 4365
1048: 450643/274153770 1/4]
1049:
1050: [0 217/2880 442223/7447440 53953931/292008808 -32242849453/168619624992 1475
1051: 457901/1827691800 1/80]
1052:
1053: [0 0 1604444/264539275 24208141/149362505292 847880210129/47916076768560 -45
1054: 44407141/103873817300 -29/40920]
1055:
1056: [0 0 0 9773092581/35395807550620 -24363634138919/107305824577186620 72118203
1057: 606917/60481351061158500 55899/3088554700]
1058:
1059: [0 0 0 0 67201501179065/8543442888354179988 -9970556426629/74082861999267660
1060: 0 -3229/13661312210]
1061:
1062: [0 0 0 0 0 -258198800769/9279048099409000 -13183/38381527800]
1063:
1064: ? hilb(2/3,3/4,5)
1065: 1
1066: ? hilbert(5)
1067:
1068: [1 1/2 1/3 1/4 1/5]
1069:
1070: [1/2 1/3 1/4 1/5 1/6]
1071:
1072: [1/3 1/4 1/5 1/6 1/7]
1073:
1074: [1/4 1/5 1/6 1/7 1/8]
1075:
1076: [1/5 1/6 1/7 1/8 1/9]
1077:
1078: ? hilbp(mod(5,7),mod(6,7))
1079: 1
1080: ? hvector(10,x,1/x)
1081: [1, 1/2, 1/3, 1/4, 1/5, 1/6, 1/7, 1/8, 1/9, 1/10]
1082: ? hyperu(1,1,1)
1083: 0.59634736232319407434107849936927937488
1084: ? i^2
1085: -1
1086: ? nf1=initalgred(nfpol)
1087: [x^5 - 2*x^4 + 3*x^3 + 8*x^2 + 3*x + 2, [1, 2], 595125, 4, [[1, -1.089115145
1088: 7205048250249527946671612684, 1.1861718006377964594796293860483989860, -0.59
1089: 741050929194782733001765987770358483, 0.158944197453903762065494816710718942
1090: 89; 1, -0.13838372073406036365047976417441696637 + 0.49181637657768643499753
1091: 285514741525107*I, -0.22273329410580226599155701611419649154 - 0.13611876021
1092: 752805221674918029071012580*I, -0.13167445871785818798769651537619416009 + 0
1093: .13249517760521973840801462296650806543*I, -0.053650958656997725359297528357
1094: 602608116 + 0.27622636814169107038138284681568361486*I; 1, 1.682941293594312
1095: 7761629561615079976005 + 2.0500351226010726172974286983598602163*I, -1.37035
1096: 26062130959637482576769100030014 + 6.9001775222880494773720769629846373016*I
1097: , -8.0696202866361678983472946546849540475 + 8.87676767859710424508852843013
1098: 48051602*I, -22.025821140069954155673449879997756863 - 8.4306586896999153544
1099: 710860185447589664*I], [1, 2, 2; -1.0891151457205048250249527946671612684, -
1100: 0.27676744146812072730095952834883393274 - 0.9836327531553728699950657102948
1101: 3050214*I, 3.3658825871886255523259123230159952011 - 4.100070245202145234594
1102: 8573967197204327*I; 1.1861718006377964594796293860483989860, -0.445466588211
1103: 60453198311403222839298308 + 0.27223752043505610443349836058142025160*I, -2.
1104: 7407052124261919274965153538200060029 - 13.800355044576098954744153925969274
1105: 603*I; -0.59741050929194782733001765987770358483, -0.26334891743571637597539
1106: 303075238832018 - 0.26499035521043947681602924593301613087*I, -16.1392405732
1107: 72335796694589309369908095 - 17.753535357194208490177056860269610320*I; 0.15
1108: 894419745390376206549481671071894289, -0.10730191731399545071859505671520521
1109: 623 - 0.55245273628338214076276569363136722973*I, -44.0516422801399083113468
1110: 99759995513726 + 16.861317379399830708942172037089517932*I], [5, 2.000000000
1111: 0000000000000000000000000000, -2.0000000000000000000000000000000000000, -17.
1112: 000000000000000000000000000000000000, -44.0000000000000000000000000000000000
1113: 00; 2.0000000000000000000000000000000000000, 15.7781094086719980448363574712
1114: 83695361, 22.314643349754061651916553814602769764, 10.0513952578314782754999
1115: 32716306366248, -108.58917507620841447456569092094763671; -2.000000000000000
1116: 0000000000000000000000, 22.314643349754061651916553814602769764, 100.5239126
1117: 2388960975827806174040462368, 143.93295090847353519436673793501057176, -55.8
1118: 42564718082452641322500190813370023; -17.00000000000000000000000000000000000
1119: 0, 10.051395257831478275499932716306366248, 143.9329509084735351943667379350
1120: 1057176, 288.25823756749944693139292174819167135, 205.7984003827766237572018
1121: 0649465932302; -44.000000000000000000000000000000000000, -108.58917507620841
1122: 447456569092094763671, -55.842564718082452641322500190813370023, 205.7984003
1123: 8277662375720180649465932302, 1112.6092277946777707779250962522343036], [5,
1124: 2, -2, -17, -44; 2, -2, -34, -63, -40; -2, -34, -90, -101, 177; -17, -63, -1
1125: 01, -27, 505; -44, -40, 177, 505, 828], [345, 0, 160, 252, 156; 0, 345, 215,
1126: 311, 306; 0, 0, 5, 3, 2; 0, 0, 0, 1, 0; 0, 0, 0, 0, 1], [163875, -388125, -
1127: 296700, 234600, -89700; -388125, -1593900, -677925, 595125, -315675; -296700
1128: , -677925, 17250, 58650, -87975; 234600, 595125, 58650, -100050, 89700; -897
1129: 00, -315675, -87975, 89700, -55200], [595125, [-167325, -82800, 79350, 1725,
1130: 0]~]], [-1.0891151457205048250249527946671612684, -0.1383837207340603636504
1131: 7976417441696637 + 0.49181637657768643499753285514741525107*I, 1.68294129359
1132: 43127761629561615079976005 + 2.0500351226010726172974286983598602163*I], [1,
1133: x, x^2, 1/2*x^3 + 1/2*x^2 + 1/2*x, 1/2*x^4 + 1/2*x], [1, 0, 0, 0, 0; 0, 1,
1134: 0, -1, -1; 0, 0, 1, -1, 0; 0, 0, 0, 2, 0; 0, 0, 0, 0, 2], [1, 0, 0, 0, 0, 0,
1135: 0, 0, 0, -1, 0, 0, 0, -1, -2, 0, 0, -1, -2, -2, 0, -1, -2, -2, 5; 0, 1, 0,
1136: 0, 0, 1, 0, -1, -1, -1, 0, -1, -1, -2, 2, 0, -1, -2, -1, 7, 0, -1, 2, 7, 14;
1137: 0, 0, 1, 0, 0, 0, 1, -1, 0, -2, 1, -1, 0, -3, -3, 0, 0, -3, -4, -1, 0, -2,
1138: -3, -1, 15; 0, 0, 0, 1, 0, 0, 0, 2, 1, -3, 0, 2, 0, -2, -13, 1, 1, -2, -9, -
1139: 19, 0, -3, -13, -19, 7; 0, 0, 0, 0, 1, 0, 0, 0, 1, 2, 0, 0, 2, 3, 1, 0, 1, 3
1140: , 4, -4, 1, 2, 1, -4, -21]]
1141: ? initalgred2(nfpol)
1142: [[x^5 - 2*x^4 + 3*x^3 + 8*x^2 + 3*x + 2, [1, 2], 595125, 4, [[1, -1.08911514
1143: 57205048250249527946671612684, 1.1861718006377964594796293860483989860, -0.5
1144: 9741050929194782733001765987770358483, 0.15894419745390376206549481671071894
1145: 289; 1, -0.13838372073406036365047976417441696637 + 0.4918163765776864349975
1146: 3285514741525107*I, -0.22273329410580226599155701611419649154 - 0.1361187602
1147: 1752805221674918029071012580*I, -0.13167445871785818798769651537619416009 +
1148: 0.13249517760521973840801462296650806543*I, -0.05365095865699772535929752835
1149: 7602608116 + 0.27622636814169107038138284681568361486*I; 1, 1.68294129359431
1150: 27761629561615079976005 + 2.0500351226010726172974286983598602163*I, -1.3703
1151: 526062130959637482576769100030014 + 6.9001775222880494773720769629846373016*
1152: I, -8.0696202866361678983472946546849540475 + 8.8767676785971042450885284301
1153: 348051602*I, -22.025821140069954155673449879997756863 - 8.430658689699915354
1154: 4710860185447589664*I], [1, 2, 2; -1.0891151457205048250249527946671612684,
1155: -0.27676744146812072730095952834883393274 - 0.983632753155372869995065710294
1156: 83050214*I, 3.3658825871886255523259123230159952011 - 4.10007024520214523459
1157: 48573967197204327*I; 1.1861718006377964594796293860483989860, -0.44546658821
1158: 160453198311403222839298308 + 0.27223752043505610443349836058142025160*I, -2
1159: .7407052124261919274965153538200060029 - 13.80035504457609895474415392596927
1160: 4603*I; -0.59741050929194782733001765987770358483, -0.2633489174357163759753
1161: 9303075238832018 - 0.26499035521043947681602924593301613087*I, -16.139240573
1162: 272335796694589309369908095 - 17.753535357194208490177056860269610320*I; 0.1
1163: 5894419745390376206549481671071894289, -0.1073019173139954507185950567152052
1164: 1623 - 0.55245273628338214076276569363136722973*I, -44.051642280139908311346
1165: 899759995513726 + 16.861317379399830708942172037089517932*I], [5, 2.00000000
1166: 00000000000000000000000000000, -2.0000000000000000000000000000000000000, -17
1167: .000000000000000000000000000000000000, -44.000000000000000000000000000000000
1168: 000; 2.0000000000000000000000000000000000000, 15.778109408671998044836357471
1169: 283695361, 22.314643349754061651916553814602769764, 10.051395257831478275499
1170: 932716306366248, -108.58917507620841447456569092094763671; -2.00000000000000
1171: 00000000000000000000000, 22.314643349754061651916553814602769764, 100.523912
1172: 62388960975827806174040462368, 143.93295090847353519436673793501057176, -55.
1173: 842564718082452641322500190813370023; -17.0000000000000000000000000000000000
1174: 00, 10.051395257831478275499932716306366248, 143.932950908473535194366737935
1175: 01057176, 288.25823756749944693139292174819167135, 205.798400382776623757201
1176: 80649465932302; -44.000000000000000000000000000000000000, -108.5891750762084
1177: 1447456569092094763671, -55.842564718082452641322500190813370023, 205.798400
1178: 38277662375720180649465932302, 1112.6092277946777707779250962522343036], [5,
1179: 2, -2, -17, -44; 2, -2, -34, -63, -40; -2, -34, -90, -101, 177; -17, -63, -
1180: 101, -27, 505; -44, -40, 177, 505, 828], [345, 0, 160, 252, 156; 0, 345, 215
1181: , 311, 306; 0, 0, 5, 3, 2; 0, 0, 0, 1, 0; 0, 0, 0, 0, 1], [163875, -388125,
1182: -296700, 234600, -89700; -388125, -1593900, -677925, 595125, -315675; -29670
1183: 0, -677925, 17250, 58650, -87975; 234600, 595125, 58650, -100050, 89700; -89
1184: 700, -315675, -87975, 89700, -55200], [595125, [-167325, -82800, 79350, 1725
1185: , 0]~]], [-1.0891151457205048250249527946671612684, -0.138383720734060363650
1186: 47976417441696637 + 0.49181637657768643499753285514741525107*I, 1.6829412935
1187: 943127761629561615079976005 + 2.0500351226010726172974286983598602163*I], [1
1188: , x, x^2, 1/2*x^3 + 1/2*x^2 + 1/2*x, 1/2*x^4 + 1/2*x], [1, 0, 0, 0, 0; 0, 1,
1189: 0, -1, -1; 0, 0, 1, -1, 0; 0, 0, 0, 2, 0; 0, 0, 0, 0, 2], [1, 0, 0, 0, 0, 0
1190: , 0, 0, 0, -1, 0, 0, 0, -1, -2, 0, 0, -1, -2, -2, 0, -1, -2, -2, 5; 0, 1, 0,
1191: 0, 0, 1, 0, -1, -1, -1, 0, -1, -1, -2, 2, 0, -1, -2, -1, 7, 0, -1, 2, 7, 14
1192: ; 0, 0, 1, 0, 0, 0, 1, -1, 0, -2, 1, -1, 0, -3, -3, 0, 0, -3, -4, -1, 0, -2,
1193: -3, -1, 15; 0, 0, 0, 1, 0, 0, 0, 2, 1, -3, 0, 2, 0, -2, -13, 1, 1, -2, -9,
1194: -19, 0, -3, -13, -19, 7; 0, 0, 0, 0, 1, 0, 0, 0, 1, 2, 0, 0, 2, 3, 1, 0, 1,
1195: 3, 4, -4, 1, 2, 1, -4, -21]], mod(-1/2*x^4 + 3/2*x^3 - 5/2*x^2 - 2*x + 1, x^
1196: 5 - 2*x^4 + 3*x^3 + 8*x^2 + 3*x + 2)]
1197: ? vp=primedec(nf,3)[1]
1198: [3, [1, 1, 0, 0, 0]~, 1, 1, [1, -1, -1, 0, 0]~]
1199: ? idx=idealmul(nf,idmat(5),vp)
1200:
1201: [3 1 2 2 2]
1202:
1203: [0 1 0 0 0]
1204:
1205: [0 0 1 0 0]
1206:
1207: [0 0 0 1 0]
1208:
1209: [0 0 0 0 1]
1210:
1211: ? idealinv(nf,idx)
1212:
1213: [1 0 2/3 0 0]
1214:
1215: [0 1 1/3 0 0]
1216:
1217: [0 0 1/3 0 0]
1218:
1219: [0 0 0 1 0]
1220:
1221: [0 0 0 0 1]
1222:
1223: ? idy=ideallllred(nf,idx,[1,5,6])
1224:
1225: [5 0 0 2 0]
1226:
1227: [0 5 0 0 0]
1228:
1229: [0 0 5 2 0]
1230:
1231: [0 0 0 1 0]
1232:
1233: [0 0 0 0 5]
1234:
1235: ? idealadd(nf,idx,idy)
1236:
1237: [1 0 0 0 0]
1238:
1239: [0 1 0 0 0]
1240:
1241: [0 0 1 0 0]
1242:
1243: [0 0 0 1 0]
1244:
1245: [0 0 0 0 1]
1246:
1247: ? idealaddone(nf,idx,idy)
1248: [[3, 0, 2, 1, 0]~, [-2, 0, -2, -1, 0]~]
1249: ? idealaddmultone(nf,[idy,idx])
1250: [[-5, 0, 0, 0, 0]~, [6, 0, 0, 0, 0]~]
1251: ? idealappr(nf,idy)
1252: [-2, 0, -2, 4, 0]~
1253: ? idealapprfact(nf,idealfactor(nf,idy))
1254: [-2, 0, -2, 4, 0]~
1255: ? idealcoprime(nf,idx,idx)
1256: [-2/3, 2/3, -1/3, 0, 0]~
1257: ? idz=idealintersect(nf,idx,idy)
1258:
1259: [15 5 10 12 10]
1260:
1261: [0 5 0 0 0]
1262:
1263: [0 0 5 2 0]
1264:
1265: [0 0 0 1 0]
1266:
1267: [0 0 0 0 5]
1268:
1269: ? idealfactor(nf,idz)
1270:
1271: [[3, [1, 1, 0, 0, 0]~, 1, 1, [1, -1, -1, 0, 0]~] 1]
1272:
1273: [[5, [-2, 0, 0, 0, 1]~, 1, 1, [2, 2, 1, 1, 4]~] 1]
1274:
1275: [[5, [0, 0, -1, 0, 1]~, 4, 1, [4, 5, 4, 2, 0]~] 3]
1276:
1277: ? ideallist(bnf,20)
1278: [[[1, 0; 0, 1]], [], [[3, 2; 0, 1], [3, 0; 0, 1]], [[2, 0; 0, 2]], [[5, 3; 0
1279: , 1], [5, 1; 0, 1]], [], [], [], [[9, 5; 0, 1], [3, 0; 0, 3], [9, 3; 0, 1]],
1280: [], [[11, 9; 0, 1], [11, 1; 0, 1]], [[6, 4; 0, 2], [6, 0; 0, 2]], [], [], [
1281: [15, 8; 0, 1], [15, 3; 0, 1], [15, 11; 0, 1], [15, 6; 0, 1]], [[4, 0; 0, 4]]
1282: , [[17, 14; 0, 1], [17, 2; 0, 1]], [], [[19, 18; 0, 1], [19, 0; 0, 1]], [[10
1283: , 6; 0, 2], [10, 2; 0, 2]]]
1284: ? idx2=idealmul(nf,idx,idx)
1285:
1286: [9 7 5 8 2]
1287:
1288: [0 1 0 0 0]
1289:
1290: [0 0 1 0 0]
1291:
1292: [0 0 0 1 0]
1293:
1294: [0 0 0 0 1]
1295:
1296: ? idt=idealmulred(nf,idx,idx)
1297:
1298: [2 0 0 0 1]
1299:
1300: [0 2 0 0 1]
1301:
1302: [0 0 2 0 0]
1303:
1304: [0 0 0 2 1]
1305:
1306: [0 0 0 0 1]
1307:
1308: ? idealdiv(nf,idy,idt)
1309:
1310: [5 5/2 5/2 7/2 0]
1311:
1312: [0 5/2 0 0 0]
1313:
1314: [0 0 5/2 1 0]
1315:
1316: [0 0 0 1/2 0]
1317:
1318: [0 0 0 0 5/2]
1319:
1320: ? idealdivexact(nf,idx2,idx)
1321:
1322: [3 1 2 2 2]
1323:
1324: [0 1 0 0 0]
1325:
1326: [0 0 1 0 0]
1327:
1328: [0 0 0 1 0]
1329:
1330: [0 0 0 0 1]
1331:
1332: ? idealhermite(nf,vp)
1333:
1334: [3 1 2 2 2]
1335:
1336: [0 1 0 0 0]
1337:
1338: [0 0 1 0 0]
1339:
1340: [0 0 0 1 0]
1341:
1342: [0 0 0 0 1]
1343:
1344: ? idealhermite2(nf,vp[2],3)
1345:
1346: [3 1 2 2 2]
1347:
1348: [0 1 0 0 0]
1349:
1350: [0 0 1 0 0]
1351:
1352: [0 0 0 1 0]
1353:
1354: [0 0 0 0 1]
1355:
1356: ? idealnorm(nf,idt)
1357: 16
1358: ? idp=idealpow(nf,idx,7)
1359:
1360: [2187 1807 2129 692 1379]
1361:
1362: [0 1 0 0 0]
1363:
1364: [0 0 1 0 0]
1365:
1366: [0 0 0 1 0]
1367:
1368: [0 0 0 0 1]
1369:
1370: ? idealpowred(nf,idx,7)
1371:
1372: [5 0 0 2 0]
1373:
1374: [0 5 0 0 0]
1375:
1376: [0 0 5 2 0]
1377:
1378: [0 0 0 1 0]
1379:
1380: [0 0 0 0 5]
1381:
1382: ? idealtwoelt(nf,idy)
1383: [5, [2, 0, 2, 1, 0]~]
1384: ? idealtwoelt2(nf,idy,10)
1385: [-2, 0, -2, -1, 0]~
1386: ? idealval(nf,idp,vp)
1387: 7
1388: ? idmat(5)
1389:
1390: [1 0 0 0 0]
1391:
1392: [0 1 0 0 0]
1393:
1394: [0 0 1 0 0]
1395:
1396: [0 0 0 1 0]
1397:
1398: [0 0 0 0 1]
1399:
1400: ? if(3<2,print("bof"),print("ok"));
1401: ok
1402: ? imag(2+3*i)
1403: 3
1404: ? image([1,3,5;2,4,6;3,5,7])
1405:
1406: [1 3]
1407:
1408: [2 4]
1409:
1410: [3 5]
1411:
1412: ? image(pi*[1,3,5;2,4,6;3,5,7])
1413:
1414: [9.4247779607693797153879301498385086525 15.70796326794896619231321691639751
1415: 4420]
1416:
1417: [12.566370614359172953850573533118011536 18.84955592153875943077586029967701
1418: 7305]
1419:
1420: [15.707963267948966192313216916397514420 21.99114857512855266923850368295652
1421: 0189]
1422:
1423: ? incgam(2,1)
1424: 0.73575888234288464319104754032292173491
1425: ? incgam1(2,1)
1426: -0.26424111765711535680895245967678075578
1427: ? incgam2(2,1)
1428: 0.73575888234288464319104754032292173489
1429: ? incgam3(2,1)
1430: 0.26424111765711535680895245967707826508
1431: ? incgam4(4,1,6)
1432: 5.8860710587430771455283803225833738791
1433: ? indexrank([1,1,1;1,1,1;1,1,2])
1434: [[1, 3], [1, 3]]
1435: ? indsort([8,7,6,5])
1436: [4, 3, 2, 1]
1437: ? initell([0,0,0,-1,0])
1438: [0, 0, 0, -1, 0, 0, -2, 0, -1, 48, 0, 64, 1728, [1.0000000000000000000000000
1439: 000000000000, 0.E-38, -1.0000000000000000000000000000000000000]~, 2.62205755
1440: 42921198104648395898911194136, 2.6220575542921198104648395898911194136*I, -0
1441: .59907011736779610371996124614016193910, -1.79721035210338831115988373842048
1442: 58173*I, 6.8751858180203728274900957798105571979]
1443: ? initrect(1,700,700)
1444: ? nfz=initzeta(x^2-2);
1445: ? integ(sin(x),x)
1446: 1/2*x^2 - 1/24*x^4 + 1/720*x^6 - 1/40320*x^8 + 1/3628800*x^10 - 1/479001600*
1447: x^12 + 1/87178291200*x^14 - 1/20922789888000*x^16 + O(x^17)
1448: ? integ((-x^2-2*a*x+8*a)/(x^4-14*x^3+(2*a+49)*x^2-14*a*x+a^2),x)
1449: (x + a)/(x^2 - 7*x + a)
1450: ? intersect([1,2;3,4;5,6],[2,3;7,8;8,9])
1451:
1452: [-1]
1453:
1454: [-1]
1455:
1456: [-1]
1457:
1458: ? \precision=19
1459: realprecision = 19 significant digits
1460: ? intgen(x=0,pi,sin(x))
1461: 2.000000000000000017
1462: ? sqr(2*intgen(x=0,4,exp(-x^2)))
1463: 3.141592556720305685
1464: ? 4*intinf(x=1,10^20,1/(1+x^2))
1465: 3.141592653589793208
1466: ? intnum(x=-0.5,0.5,1/sqrt(1-x^2))
1467: 1.047197551196597747
1468: ? 2*intopen(x=0,100,sin(x)/x)
1469: 3.124450933778112629
1470: ? \precision=38
1471: realprecision = 38 significant digits
1472: ? inverseimage([1,1;2,3;5,7],[2,2,6]~)
1473: [4, -2]~
1474: ? isdiagonal([1,0,0;0,5,0;0,0,0])
1475: 1
1476: ? isfund(12345)
1477: 1
1478: ? isideal(bnf[7],[5,1;0,1])
1479: 1
1480: ? isincl(x^2+1,x^4+1)
1481: [-x^2, x^2]
1482: ? isinclfast(initalg(x^2+1),initalg(x^4+1))
1483: [-x^2, x^2]
1484: ? isirreducible(x^5+3*x^3+5*x^2+15)
1485: 0
1486: ? isisom(x^3+x^2-2*x-1,x^3+x^2-2*x-1)
1487: [x, -x^2 - x + 1, x^2 - 2]
1488: ? isisomfast(initalg(x^3-2),initalg(x^3-6*x^2-6*x-30))
1489: [-1/25*x^2 + 13/25*x - 2/5]
1490: ? isprime(12345678901234567)
1491: 0
1492: ? isprincipal(bnf,[5,1;0,1])
1493: [1]~
1494: ? isprincipalgen(bnf,[5,1;0,1])
1495: [[1]~, [-2, -1/3]~, 181]
1496: ? isprincipalraygen(bnr,primedec(bnf,7)[1])
1497: [[9]~, [-2170/6561, -931/19683]~, 256]
1498: ? ispsp(73!+1)
1499: 1
1500: ? isqrt(10!^2+1)
1501: 3628800
1502: ? isset([-3,5,7,7])
1503: 0
1504: ? issqfree(123456789876543219)
1505: 0
1506: ? issquare(12345678987654321)
1507: 1
1508: ? isunit(bnf,mod(3405*x-27466,x^2-x-57))
1509: [-4, mod(1, 2)]~
1510: ? jacobi(hilbert(6))
1511: [[1.6188998589243390969705881471257800712, 0.2423608705752095521357284158507
1512: 0114077, 0.000012570757122625194922982397996498755027, 0.0000001082799484565
1513: 5497685388772372251711485, 0.016321521319875822124345079564191505890, 0.0006
1514: 1574835418265769764919938428527140264]~, [0.74871921887909485900280109200517
1515: 845109, -0.61454482829258676899320019644273870645, 0.01114432093072471053067
1516: 8340374220998541, -0.0012481940840821751169398163046387834473, 0.24032536934
1517: 252330399154228873240534568, -0.062226588150197681775152126611810492910; 0.4
1518: 4071750324351206127160083580231701801, 0.21108248167867048675227675845247769
1519: 095, -0.17973275724076003758776897803740640964, 0.03560664294428763526612284
1520: 8131812048466, -0.69765137527737012296208335046678265583, 0.4908392097109243
1521: 6297498316169060044997; 0.32069686982225190106359024326699463106, 0.36589360
1522: 730302614149086554211117169622, 0.60421220675295973004426567844103062241, -0
1523: .24067907958842295837736719558855679285, -0.23138937333290388042251363554209
1524: 048309, -0.53547692162107486593474491750949545456; 0.25431138634047419251788
1525: 312792590944672, 0.39470677609501756783094636145991581708, -0.44357471627623
1526: 954554460416705180105301, 0.62546038654922724457753441039459331059, 0.132863
1527: 15850933553530333839628101576050, -0.41703769221897886840494514780771076439;
1528: 0.21153084007896524664213667673977991959, 0.3881904338738864286311144882599
1529: 2418973, -0.44153664101228966222143649752977203423, -0.689807199293836684198
1530: 01738006926829419, 0.36271492146487147525299457604461742111, 0.0470340189331
1531: 15649705614518466541243873; 0.18144297664876947372217005457727093715, 0.3706
1532: 9590776736280861775501084807394603, 0.45911481681642960284551392793050866602
1533: , 0.27160545336631286930015536176213647001, 0.502762866757515384892605663686
1534: 47786272, 0.54068156310385293880022293448123782121]]
1535: ? jbesselh(1,1)
1536: 0.24029783912342701089584304474193368045
1537: ? jell(i)
1538: 1728.0000000000000000000000000000000000 + 0.E-54*I
1539: ? kbessel(1+i,1)
1540: 0.32545977186584141085464640324923711863 + 0.2894280370259921276345671592415
1541: 2302704*I
1542: ? kbessel2(1+i,1)
1543: 0.32545977186584141085464640324923711863 + 0.2894280370259921276345671592415
1544: 2302704*I
1545: ? x
1546: x
1547: ? y
1548: x
1549: ? ker(matrix(4,4,x,y,x/y))
1550:
1551: [-1/2 -1/3 -1/4]
1552:
1553: [1 0 0]
1554:
1555: [0 1 0]
1556:
1557: [0 0 1]
1558:
1559: ? ker(matrix(4,4,x,y,sin(x+y)))
1560:
1561: [0.72968694572192883282306463453582002359]
1562:
1563: [0.2114969213291234874]
1564:
1565: [-0.3509176660143506019]
1566:
1567: [1]
1568:
1569: ? keri(matrix(4,4,x,y,x+y))
1570:
1571: [1 2]
1572:
1573: [-2 -3]
1574:
1575: [1 0]
1576:
1577: [0 1]
1578:
1579: ? kerint(matrix(4,4,x,y,x*y))
1580:
1581: [-1 -1 -1]
1582:
1583: [-1 0 1]
1584:
1585: [1 -1 1]
1586:
1587: [0 1 -1]
1588:
1589: ? kerint1(matrix(4,4,x,y,x*y))
1590:
1591: [-1 -1 -1]
1592:
1593: [-1 0 1]
1594:
1595: [1 -1 1]
1596:
1597: [0 1 -1]
1598:
1599: ? kerint2(matrix(4,6,x,y,2520/(x+y)))
1600:
1601: [3 1]
1602:
1603: [-30 -15]
1604:
1605: [70 70]
1606:
1607: [0 -140]
1608:
1609: [-126 126]
1610:
1611: [84 -42]
1612:
1613: ? f(u)=u+1;
1614: ? print(f(5));kill(f);
1615: 6
1616: ? f=12
1617: 12
1618: ? killrect(1)
1619: ? kro(5,7)
1620: -1
1621: ? kro(3,18)
1622: 0
1623: ? laplace(x*exp(x*y)/(exp(x)-1))
1624: 1 - 1/2*x + 13/6*x^2 - 3*x^3 + 419/30*x^4 - 30*x^5 + 6259/42*x^6 - 420*x^7 +
1625: 22133/10*x^8 - 7560*x^9 + 2775767/66*x^10 - 166320*x^11 + 2655339269/2730*x
1626: ^12 - 4324320*x^13 + 264873251/10*x^14 + O(x^15)
1627: ? lcm(15,-21)
1628: 105
1629: ? length(divisors(1000))
1630: 16
1631: ? legendre(10)
1632: 46189/256*x^10 - 109395/256*x^8 + 45045/128*x^6 - 15015/128*x^4 + 3465/256*x
1633: ^2 - 63/256
1634: ? lex([1,3],[1,3,5])
1635: -1
1636: ? lexsort([[1,5],[2,4],[1,5,1],[1,4,2]])
1637: [[1, 4, 2], [1, 5], [1, 5, 1], [2, 4]]
1638: ? lift(chinese(mod(7,15),mod(4,21)))
1639: 67
1640: ? lindep([(1-3*sqrt(2))/(3-2*sqrt(3)),1,sqrt(2),sqrt(3),sqrt(6)])
1641: [-3, -3, 9, -2, 6]
1642: ? lindep2([(1-3*sqrt(2))/(3-2*sqrt(3)),1,sqrt(2),sqrt(3),sqrt(6)],14)
1643: [-3, -3, 9, -2, 6]
1644: ? move(0,0,900);line(0,900,0)
1645: ? lines(0,vector(5,k,50*k),vector(5,k,10*k*k))
1646: ? m=1/hilbert(7)
1647:
1648: [49 -1176 8820 -29400 48510 -38808 12012]
1649:
1650: [-1176 37632 -317520 1128960 -1940400 1596672 -504504]
1651:
1652: [8820 -317520 2857680 -10584000 18711000 -15717240 5045040]
1653:
1654: [-29400 1128960 -10584000 40320000 -72765000 62092800 -20180160]
1655:
1656: [48510 -1940400 18711000 -72765000 133402500 -115259760 37837800]
1657:
1658: [-38808 1596672 -15717240 62092800 -115259760 100590336 -33297264]
1659:
1660: [12012 -504504 5045040 -20180160 37837800 -33297264 11099088]
1661:
1662: ? mp=concat(m,idmat(7))
1663:
1664: [49 -1176 8820 -29400 48510 -38808 12012 1 0 0 0 0 0 0]
1665:
1666: [-1176 37632 -317520 1128960 -1940400 1596672 -504504 0 1 0 0 0 0 0]
1667:
1668: [8820 -317520 2857680 -10584000 18711000 -15717240 5045040 0 0 1 0 0 0 0]
1669:
1670: [-29400 1128960 -10584000 40320000 -72765000 62092800 -20180160 0 0 0 1 0 0
1671: 0]
1672:
1673: [48510 -1940400 18711000 -72765000 133402500 -115259760 37837800 0 0 0 0 1 0
1674: 0]
1675:
1676: [-38808 1596672 -15717240 62092800 -115259760 100590336 -33297264 0 0 0 0 0
1677: 1 0]
1678:
1679: [12012 -504504 5045040 -20180160 37837800 -33297264 11099088 0 0 0 0 0 0 1]
1680:
1681: ? lll(m)
1682:
1683: [-420 -420 840 630 -1092 -83 2562]
1684:
1685: [-210 -280 630 504 -876 70 2205]
1686:
1687: [-140 -210 504 420 -749 137 1910]
1688:
1689: [-105 -168 420 360 -658 169 1680]
1690:
1691: [-84 -140 360 315 -588 184 1498]
1692:
1693: [-70 -120 315 280 -532 190 1351]
1694:
1695: [-60 -105 280 252 -486 191 1230]
1696:
1697: ? lll1(m)
1698:
1699: [-420 -420 840 630 -1092 -83 2562]
1700:
1701: [-210 -280 630 504 -876 70 2205]
1702:
1703: [-140 -210 504 420 -749 137 1910]
1704:
1705: [-105 -168 420 360 -658 169 1680]
1706:
1707: [-84 -140 360 315 -588 184 1498]
1708:
1709: [-70 -120 315 280 -532 190 1351]
1710:
1711: [-60 -105 280 252 -486 191 1230]
1712:
1713: ? lllgram(m)
1714:
1715: [1 1 27 -27 69 0 141]
1716:
1717: [0 1 4 -22 34 -24 49]
1718:
1719: [0 1 3 -21 18 -24 23]
1720:
1721: [0 1 3 -20 10 -19 13]
1722:
1723: [0 1 3 -19 6 -14 8]
1724:
1725: [0 1 3 -18 4 -10 5]
1726:
1727: [0 1 3 -17 3 -7 3]
1728:
1729: ? lllgram1(m)
1730:
1731: [1 1 27 -27 69 0 141]
1732:
1733: [0 1 4 -22 34 -24 49]
1734:
1735: [0 1 3 -21 18 -24 23]
1736:
1737: [0 1 3 -20 10 -19 13]
1738:
1739: [0 1 3 -19 6 -14 8]
1740:
1741: [0 1 3 -18 4 -10 5]
1742:
1743: [0 1 3 -17 3 -7 3]
1744:
1745: ? lllgramint(m)
1746:
1747: [1 1 27 -27 69 0 141]
1748:
1749: [0 1 4 -23 34 -24 91]
1750:
1751: [0 1 3 -22 18 -24 65]
1752:
1753: [0 1 3 -21 10 -19 49]
1754:
1755: [0 1 3 -20 6 -14 38]
1756:
1757: [0 1 3 -19 4 -10 30]
1758:
1759: [0 1 3 -18 3 -7 24]
1760:
1761: ? lllgramkerim(mp~*mp)
1762: [[-420, -420, 840, 630, 2982, -1092, -83; -210, -280, 630, 504, 2415, -876,
1763: 70; -140, -210, 504, 420, 2050, -749, 137; -105, -168, 420, 360, 1785, -658,
1764: 169; -84, -140, 360, 315, 1582, -588, 184; -70, -120, 315, 280, 1421, -532,
1765: 190; -60, -105, 280, 252, 1290, -486, 191; 420, 0, 0, 0, -210, 168, 35; 0,
1766: 840, 0, 0, 0, 0, 336; 0, 0, -2520, 0, 0, 0, 1260; 0, 0, 0, -2520, 0, 0, -840
1767: ; 0, 0, 0, 0, -13860, 0, 6930; 0, 0, 0, 0, 0, 5544, 0; 0, 0, 0, 0, 0, 0, -12
1768: 012], [0, 0, 0, 0, 0, 0, 0; 0, 0, 0, 0, 0, 0, 0; 0, 0, 0, 0, 0, 0, 0; 0, 0,
1769: 0, 0, 0, 0, 0; 0, 0, 0, 0, 0, 0, 0; 0, 0, 0, 0, 0, 0, 0; 0, 0, 0, 0, 0, 0, 0
1770: ; 1, 0, 0, 0, 0, 0, 0; 0, 1, 0, 0, 0, 0, 0; 0, 0, 1, 0, 0, 0, 0; 0, 0, 0, 1,
1771: 0, 0, 0; 0, 0, 0, 0, 1, 0, 0; 0, 0, 0, 0, 0, 1, 0; 0, 0, 0, 0, 0, 0, 1]]
1772: ? lllint(m)
1773:
1774: [-420 -420 840 630 -1092 -83 2982]
1775:
1776: [-210 -280 630 504 -876 70 2415]
1777:
1778: [-140 -210 504 420 -749 137 2050]
1779:
1780: [-105 -168 420 360 -658 169 1785]
1781:
1782: [-84 -140 360 315 -588 184 1582]
1783:
1784: [-70 -120 315 280 -532 190 1421]
1785:
1786: [-60 -105 280 252 -486 191 1290]
1787:
1788: ? lllintpartial(m)
1789:
1790: [-420 -420 -630 840 1092 2982 -83]
1791:
1792: [-210 -280 -504 630 876 2415 70]
1793:
1794: [-140 -210 -420 504 749 2050 137]
1795:
1796: [-105 -168 -360 420 658 1785 169]
1797:
1798: [-84 -140 -315 360 588 1582 184]
1799:
1800: [-70 -120 -280 315 532 1421 190]
1801:
1802: [-60 -105 -252 280 486 1290 191]
1803:
1804: ? lllkerim(mp)
1805: [[-420, -420, 840, 630, 2982, -1092, -83; -210, -280, 630, 504, 2415, -876,
1806: 70; -140, -210, 504, 420, 2050, -749, 137; -105, -168, 420, 360, 1785, -658,
1807: 169; -84, -140, 360, 315, 1582, -588, 184; -70, -120, 315, 280, 1421, -532,
1808: 190; -60, -105, 280, 252, 1290, -486, 191; 420, 0, 0, 0, -210, 168, 35; 0,
1809: 840, 0, 0, 0, 0, 336; 0, 0, -2520, 0, 0, 0, 1260; 0, 0, 0, -2520, 0, 0, -840
1810: ; 0, 0, 0, 0, -13860, 0, 6930; 0, 0, 0, 0, 0, 5544, 0; 0, 0, 0, 0, 0, 0, -12
1811: 012], [0, 0, 0, 0, 0, 0, 0; 0, 0, 0, 0, 0, 0, 0; 0, 0, 0, 0, 0, 0, 0; 0, 0,
1812: 0, 0, 0, 0, 0; 0, 0, 0, 0, 0, 0, 0; 0, 0, 0, 0, 0, 0, 0; 0, 0, 0, 0, 0, 0, 0
1813: ; 1, 0, 0, 0, 0, 0, 0; 0, 1, 0, 0, 0, 0, 0; 0, 0, 1, 0, 0, 0, 0; 0, 0, 0, 1,
1814: 0, 0, 0; 0, 0, 0, 0, 1, 0, 0; 0, 0, 0, 0, 0, 1, 0; 0, 0, 0, 0, 0, 0, 1]]
1815: ? lllrat(m)
1816:
1817: [-420 -420 840 630 -1092 -83 2982]
1818:
1819: [-210 -280 630 504 -876 70 2415]
1820:
1821: [-140 -210 504 420 -749 137 2050]
1822:
1823: [-105 -168 420 360 -658 169 1785]
1824:
1825: [-84 -140 360 315 -588 184 1582]
1826:
1827: [-70 -120 315 280 -532 190 1421]
1828:
1829: [-60 -105 280 252 -486 191 1290]
1830:
1831: ? \precision=96
1832: realprecision = 96 significant digits
1833: ? ln(2)
1834: 0.69314718055994530941723212145817656807550013436025525412068000949339362196
1835: 9694715605863326996418
1836: ? lngamma(10^50*i)
1837: -157079632679489661923132169163975144209858469968811.93673753887608474948977
1838: 0941153418951907406847 - 2.5258126069288717421377720813802613884088088474975
1839: 8842763772207531866369674037379004058787354391*I
1840: ? \precision=2000
1841: realprecision = 2003 significant digits (2000 digits displayed)
1842: ? log(2)
1843: 0.69314718055994530941723212145817656807550013436025525412068000949339362196
1844: 9694715605863326996418687542001481020570685733685520235758130557032670751635
1845: 0759619307275708283714351903070386238916734711233501153644979552391204751726
1846: 8157493206515552473413952588295045300709532636664265410423915781495204374043
1847: 0385500801944170641671518644712839968171784546957026271631064546150257207402
1848: 4816377733896385506952606683411372738737229289564935470257626520988596932019
1849: 6505855476470330679365443254763274495125040606943814710468994650622016772042
1850: 4524529612687946546193165174681392672504103802546259656869144192871608293803
1851: 1727143677826548775664850856740776484514644399404614226031930967354025744460
1852: 7030809608504748663852313818167675143866747664789088143714198549423151997354
1853: 8803751658612753529166100071053558249879414729509293113897155998205654392871
1854: 7000721808576102523688921324497138932037843935308877482597017155910708823683
1855: 6275898425891853530243634214367061189236789192372314672321720534016492568727
1856: 4778234453534764811494186423867767744060695626573796008670762571991847340226
1857: 5146283790488306203306114463007371948900274364396500258093651944304119115060
1858: 8094879306786515887090060520346842973619384128965255653968602219412292420757
1859: 4321757489097706752687115817051137009158942665478595964890653058460258668382
1860: 9400228330053820740056770530467870018416240441883323279838634900156312188956
1861: 0650553151272199398332030751408426091479001265168243443893572472788205486271
1862: 5527418772430024897945401961872339808608316648114909306675193393128904316413
1863: 7068139777649817697486890388778999129650361927071088926410523092478391737350
1864: 1229842420499568935992206602204654941510613918788574424557751020683703086661
1865: 9480896412186807790208181588580001688115973056186676199187395200766719214592
1866: 2367206025395954365416553112951759899400560003665135675690512459268257439464
1867: 8316833262490180382424082423145230614096380570070255138770268178516306902551
1868: 3703234053802145019015374029509942262995779647427138157363801729873940704242
1869: 17997226696297993931270693
1870: ? logagm(2)
1871: 0.69314718055994530941723212145817656807550013436025525412068000949339362196
1872: 9694715605863326996418687542001481020570685733685520235758130557032670751635
1873: 0759619307275708283714351903070386238916734711233501153644979552391204751726
1874: 8157493206515552473413952588295045300709532636664265410423915781495204374043
1875: 0385500801944170641671518644712839968171784546957026271631064546150257207402
1876: 4816377733896385506952606683411372738737229289564935470257626520988596932019
1877: 6505855476470330679365443254763274495125040606943814710468994650622016772042
1878: 4524529612687946546193165174681392672504103802546259656869144192871608293803
1879: 1727143677826548775664850856740776484514644399404614226031930967354025744460
1880: 7030809608504748663852313818167675143866747664789088143714198549423151997354
1881: 8803751658612753529166100071053558249879414729509293113897155998205654392871
1882: 7000721808576102523688921324497138932037843935308877482597017155910708823683
1883: 6275898425891853530243634214367061189236789192372314672321720534016492568727
1884: 4778234453534764811494186423867767744060695626573796008670762571991847340226
1885: 5146283790488306203306114463007371948900274364396500258093651944304119115060
1886: 8094879306786515887090060520346842973619384128965255653968602219412292420757
1887: 4321757489097706752687115817051137009158942665478595964890653058460258668382
1888: 9400228330053820740056770530467870018416240441883323279838634900156312188956
1889: 0650553151272199398332030751408426091479001265168243443893572472788205486271
1890: 5527418772430024897945401961872339808608316648114909306675193393128904316413
1891: 7068139777649817697486890388778999129650361927071088926410523092478391737350
1892: 1229842420499568935992206602204654941510613918788574424557751020683703086661
1893: 9480896412186807790208181588580001688115973056186676199187395200766719214592
1894: 2367206025395954365416553112951759899400560003665135675690512459268257439464
1895: 8316833262490180382424082423145230614096380570070255138770268178516306902551
1896: 3703234053802145019015374029509942262995779647427138157363801729873940704242
1897: 17997226696297993931270693
1898: ? \precision=19
1899: realprecision = 19 significant digits
1900: ? bcurve=initell([0,0,0,-3,0])
1901: [0, 0, 0, -3, 0, 0, -6, 0, -9, 144, 0, 1728, 1728, [1.732050807568877293, 0.
1902: E-19, -1.732050807568877293]~, 1.992332899583490707, 1.992332899583490708*I,
1903: -0.7884206134041560682, -2.365261840212468204*I, 3.969390382762759668]
1904: ? localred(bcurve,2)
1905: [6, 2, [1, 1, 1, 0], 1]
1906: ? ccurve=initell([0,0,-1,-1,0])
1907: [0, 0, -1, -1, 0, 0, -2, 1, -1, 48, -216, 37, 110592/37, [0.8375654352833230
1908: 353, 0.2695944364054445582, -1.107159871688767593]~, 2.993458646231959630, 2
1909: .451389381986790061*I, -0.4713192779568114757, -1.435456518668684318*I, 7.33
1910: 8132740789576742]
1911: ? l=lseriesell(ccurve,2,-37,1)
1912: 0.3815754082607112111
1913: ? lseriesell(ccurve,2,-37,1.2)-l
1914: -1.084202172485504434 E-19
1915: ? sbnf=smallbuchinit(x^3-x^2-14*x-1)
1916: [x^3 - x^2 - 14*x - 1, 3, 10889, [1, x, x^2], [-3.233732695981516673, -0.071
1917: 82350902743636344, 4.305556205008953036], [10889, 5698, 3794; 0, 1, 0; 0, 0,
1918: 1], mat(2), mat([0, 1, 1, 1, 1, 0, 1, 1]), [9, 15, 16, 17, 10, 69, 33, 39,
1919: 57], [2, [-1, 0, 0]~], [[0, 1, 0]~, [-4, 2, 1]~], [-4, 3, -1, 2, -3, 11, 1,
1920: -1, -7; 1, 1, 1, 1, 0, 2, 1, -4, -2; 0, 0, 0, 0, 0, -1, 0, -1, 0]]
1921: ? makebigbnf(sbnf)
1922: [mat(2), mat([0, 1, 1, 1, 1, 0, 1, 1]), [1.173637103435061715 + 3.1415926535
1923: 89793238*I, -4.562279014988837901 + 3.141592653589793238*I; -2.6335434327389
1924: 76049 + 3.141592653589793238*I, 1.420330600779487357 + 3.141592653589793238*
1925: I; 1.459906329303914334, 3.141948414209350543], [1.246346989334819161 + 3.14
1926: 1592653589793238*I, -1.990056445584799713 + 3.141592653589793238*I, 0.540400
1927: 6376129469727 + 3.141592653589793238*I, -0.6926391142471042845 + 3.141592653
1928: 589793238*I, 0.E-96 + 3.141592653589793238*I, 0.3677262014027817705 + 3.1415
1929: 92653589793238*I, 0.004375616572659815402 + 3.141592653589793238*I, -0.83056
1930: 25946607188639, -1.977791147836553953 + 3.141592653589793238*I; 0.6716827432
1931: 867392935 + 3.141592653589793238*I, 0.5379005671092853266, -0.83332198837424
1932: 04172 + 3.141592653589793238*I, -0.2461086674077943078, 0.E-96 + 3.141592653
1933: 589793238*I, 0.9729063188316092378, -0.8738318043071131265, -1.5526615498687
1934: 75853 + 3.141592653589793238*I, 0.5774919091398324092 + 3.141592653589793238
1935: *I; -1.918029732621558454, 1.452155878475514386, 0.2929213507612934444, 0.93
1936: 87477816548985923, 0.E-96 + 3.141592653589793238*I, -1.340632520234391008, 0
1937: .8694561877344533111, 2.383224144529494717 + 3.141592653589793238*I, 1.40029
1938: 9238696721544 + 3.141592653589793238*I], [[3, [-1, 1, 0]~, 1, 1, [1, 0, 1]~]
1939: , [5, [3, 1, 0]~, 1, 1, [-2, 1, 1]~], [5, [-1, 1, 0]~, 1, 1, [1, 0, 1]~], [5
1940: , [2, 1, 0]~, 1, 1, [2, 2, 1]~], [3, [1, 0, 1]~, 1, 2, [-1, 1, 0]~], [23, [-
1941: 10, 1, 0]~, 1, 1, [7, 9, 1]~], [11, [1, 1, 0]~, 1, 1, [-1, -2, 1]~], [13, [1
1942: 9, 1, 0]~, 1, 1, [2, 6, 1]~], [19, [-6, 1, 0]~, 1, 1, [-3, 5, 1]~]]~, [1, 2,
1943: 3, 4, 5, 6, 7, 8, 9]~, [x^3 - x^2 - 14*x - 1, [3, 0], 10889, 1, [[1, -3.233
1944: 732695981516673, 10.45702714905988813; 1, -0.07182350902743636344, 0.0051586
1945: 16449014232794; 1, 4.305556205008953036, 18.53781423449109762], [1, 1, 1; -3
1946: .233732695981516673, -0.07182350902743636344, 4.305556205008953036; 10.45702
1947: 714905988813, 0.005158616449014232794, 18.53781423449109762], [3, 1.00000000
1948: 0000000000, 29.00000000000000000; 1.000000000000000000, 29.00000000000000000
1949: , 46.00000000000000000; 29.00000000000000000, 46.00000000000000000, 453.0000
1950: 000000000000], [3, 1, 29; 1, 29, 46; 29, 46, 453], [10889, 5698, 3794; 0, 1,
1951: 0; 0, 0, 1], [11021, 881, -795; 881, 518, -109; -795, -109, 86], [10889, [1
1952: 890, 5190, 1]~]], [-3.233732695981516673, -0.07182350902743636344, 4.3055562
1953: 05008953036], [1, x, x^2], [1, 0, 0; 0, 1, 0; 0, 0, 1], [1, 0, 0, 0, 0, 1, 0
1954: , 1, 1; 0, 1, 0, 1, 0, 14, 0, 14, 15; 0, 0, 1, 0, 1, 1, 1, 1, 15]], [[2, [2]
1955: , [[3, 2, 2; 0, 1, 0; 0, 0, 1]]], 10.34800724602767998, 1.000000000000000000
1956: , [2, -1], [x, x^2 + 2*x - 4], 1000], [mat(1), [[0, 0, 0]], [[1.246346989334
1957: 819161 + 3.141592653589793238*I, 0.6716827432867392935 + 3.14159265358979323
1958: 8*I, -1.918029732621558454]]], [-4, 3, -1, 2, -3, 11, 1, -1, -7; 1, 1, 1, 1,
1959: 0, 2, 1, -4, -2; 0, 0, 0, 0, 0, -1, 0, -1, 0]]
1960: ? concat(mat(vector(4,x,x)~),vector(4,x,10+x)~)
1961:
1962: [1 11]
1963:
1964: [2 12]
1965:
1966: [3 13]
1967:
1968: [4 14]
1969:
1970: ? matextract(matrix(15,15,x,y,x+y),vector(5,x,3*x),vector(3,y,3*y))
1971:
1972: [6 9 12]
1973:
1974: [9 12 15]
1975:
1976: [12 15 18]
1977:
1978: [15 18 21]
1979:
1980: [18 21 24]
1981:
1982: ? ma=mathell(mcurve,mpoints)
1983:
1984: [1.172183098700697010 0.4476973883408951692]
1985:
1986: [0.4476973883408951692 1.755026016172950713]
1987:
1988: ? gauss(ma,mhbi)
1989: [-1.000000000000000000, 1.000000000000000000]~
1990: ? (1.*hilbert(7))^(-1)
1991:
1992: [48.99999999999354616 -1175.999999999759026 8819.999999997789586 -29399.9999
1993: 9999171836 48509.99999998526254 -38807.99999998756766 12011.99999999599856]
1994:
1995: [-1175.999999999756499 37631.99999999093860 -317519.9999999170483 1128959.99
1996: 9999689868 -1940399.999999448886 1596671.999999535762 -504503.9999998507690]
1997:
1998: [8819.999999997745604 -317519.9999999163090 2857679.999999235184 -10583999.9
1999: 9999714478 18710999.99999493212 -15717239.99999573533 5045039.999998630382]
2000:
2001: [-29399.99999999149442 1128959.999999684822 -10583999.99999712372 40319999.9
2002: 9998927448 -72764999.99998098063 62092799.99998400783 -20180159.99999486766]
2003:
2004: [48509.99999998476962 -1940399.999999436456 18710999.99999486299 -72764999.9
2005: 9998086196 133402499.9999660890 -115259759.9999715052 37837799.99999086044]
2006:
2007: [-38807.99999998708779 1596671.999999522805 -15717239.99999565420 62092799.9
2008: 9998382209 -115259759.9999713525 100590335.9999759413 -33297263.99999228701]
2009:
2010: [12011.99999999582671 -504503.9999998459239 5045039.999998597949 -20180159.9
2011: 9999478405 37837799.99999076882 -33297263.99999225112 11099087.99999751679]
2012:
2013: ? matsize([1,2;3,4;5,6])
2014: [3, 2]
2015: ? matrix(5,5,x,y,gcd(x,y))
2016:
2017: [1 1 1 1 1]
2018:
2019: [1 2 1 2 1]
2020:
2021: [1 1 3 1 1]
2022:
2023: [1 2 1 4 1]
2024:
2025: [1 1 1 1 5]
2026:
2027: ? matrixqz([1,3;3,5;5,7],0)
2028:
2029: [1 1]
2030:
2031: [3 2]
2032:
2033: [5 3]
2034:
2035: ? matrixqz2([1/3,1/4,1/6;1/2,1/4,-1/4;1/3,1,0])
2036:
2037: [19 12 2]
2038:
2039: [0 1 0]
2040:
2041: [0 0 1]
2042:
2043: ? matrixqz3([1,3;3,5;5,7])
2044:
2045: [2 -1]
2046:
2047: [1 0]
2048:
2049: [0 1]
2050:
2051: ? max(2,3)
2052: 3
2053: ? min(2,3)
2054: 2
2055: ? minim([2,1;1,2],4,6)
2056: [6, 2, [0, -1, 1; 1, 1, 0]]
2057: ? mod(-12,7)
2058: mod(2, 7)
2059: ? modp(-12,7)
2060: mod(2, 7)
2061: ? mod(10873,49649)^-1
2062: *** impossible inverse modulo: mod(131, 49649).
2063: ? modreverse(mod(x^2+1,x^3-x-1))
2064: mod(x^2 - 3*x + 2, x^3 - 5*x^2 + 8*x - 5)
2065: ? move(0,243,583);cursor(0)
2066: ? mu(3*5*7*11*13)
2067: -1
2068: ? newtonpoly(x^4+3*x^3+27*x^2+9*x+81,3)
2069: [2, 2/3, 2/3, 2/3]
2070: ? nextprime(100000000000000000000000)
2071: 100000000000000000000117
2072: ? setrand(1);a=matrix(3,5,j,k,vvector(5,l,random()\10^8))
2073:
2074: [[10, 7, 8, 7, 18]~ [17, 0, 9, 20, 10]~ [5, 4, 7, 18, 20]~ [0, 16, 4, 2, 0]~
2075: [17, 19, 17, 1, 14]~]
2076:
2077: [[17, 16, 6, 3, 6]~ [17, 13, 9, 19, 6]~ [1, 14, 12, 20, 8]~ [6, 1, 8, 17, 21
2078: ]~ [18, 17, 9, 10, 13]~]
2079:
2080: [[4, 13, 3, 17, 14]~ [14, 16, 11, 5, 4]~ [9, 11, 13, 7, 15]~ [19, 21, 2, 4,
2081: 5]~ [14, 16, 6, 20, 14]~]
2082:
2083: ? aid=[idx,idy,idz,idmat(5),idx]
2084: [[3, 1, 2, 2, 2; 0, 1, 0, 0, 0; 0, 0, 1, 0, 0; 0, 0, 0, 1, 0; 0, 0, 0, 0, 1]
2085: , [5, 0, 0, 2, 0; 0, 5, 0, 0, 0; 0, 0, 5, 2, 0; 0, 0, 0, 1, 0; 0, 0, 0, 0, 5
2086: ], [15, 5, 10, 12, 10; 0, 5, 0, 0, 0; 0, 0, 5, 2, 0; 0, 0, 0, 1, 0; 0, 0, 0,
2087: 0, 5], [1, 0, 0, 0, 0; 0, 1, 0, 0, 0; 0, 0, 1, 0, 0; 0, 0, 0, 1, 0; 0, 0, 0
2088: , 0, 1], [3, 1, 2, 2, 2; 0, 1, 0, 0, 0; 0, 0, 1, 0, 0; 0, 0, 0, 1, 0; 0, 0,
2089: 0, 0, 1]]
2090: ? bb=algtobasis(nf,mod(x^3+x,nfpol))
2091: [1, 1, 1, 3, 0]~
2092: ? da=nfdetint(nf,[a,aid])
2093:
2094: [30 5 25 27 10]
2095:
2096: [0 5 0 0 0]
2097:
2098: [0 0 5 2 0]
2099:
2100: [0 0 0 1 0]
2101:
2102: [0 0 0 0 5]
2103:
2104: ? nfdiv(nf,ba,bb)
2105: [755/373, -152/373, 159/373, 120/373, -264/373]~
2106: ? nfdiveuc(nf,ba,bb)
2107: [2, 0, 0, 0, -1]~
2108: ? nfdivres(nf,ba,bb)
2109: [[2, 0, 0, 0, -1]~, [-12, -7, 0, 9, 5]~]
2110: ? nfhermite(nf,[a,aid])
2111: [[[1, 0, 0, 0, 0]~, [0, 0, 0, 0, 0]~, [0, 0, 0, 0, 0]~; [0, 0, 0, 0, 0]~, [1
2112: , 0, 0, 0, 0]~, [0, 0, 0, 0, 0]~; [0, 0, 0, 0, 0]~, [0, 0, 0, 0, 0]~, [1, 0,
2113: 0, 0, 0]~], [[2, 1, 1, 1, 0; 0, 1, 0, 0, 0; 0, 0, 1, 0, 0; 0, 0, 0, 1, 0; 0
2114: , 0, 0, 0, 1], [1, 0, 0, 0, 0; 0, 1, 0, 0, 0; 0, 0, 1, 0, 0; 0, 0, 0, 1, 0;
2115: 0, 0, 0, 0, 1], [3, 1, 2, 2, 2; 0, 1, 0, 0, 0; 0, 0, 1, 0, 0; 0, 0, 0, 1, 0;
2116: 0, 0, 0, 0, 1]]]
2117: ? nfhermitemod(nf,[a,aid],da)
2118: [[[1, 0, 0, 0, 0]~, [0, 0, 0, 0, 0]~, [0, 0, 0, 0, 0]~; [0, 0, 0, 0, 0]~, [1
2119: , 0, 0, 0, 0]~, [0, 0, 0, 0, 0]~; [0, 0, 0, 0, 0]~, [0, 0, 0, 0, 0]~, [1, 0,
2120: 0, 0, 0]~], [[2, 1, 1, 1, 0; 0, 1, 0, 0, 0; 0, 0, 1, 0, 0; 0, 0, 0, 1, 0; 0
2121: , 0, 0, 0, 1], [1, 0, 0, 0, 0; 0, 1, 0, 0, 0; 0, 0, 1, 0, 0; 0, 0, 0, 1, 0;
2122: 0, 0, 0, 0, 1], [3, 1, 2, 2, 2; 0, 1, 0, 0, 0; 0, 0, 1, 0, 0; 0, 0, 0, 1, 0;
2123: 0, 0, 0, 0, 1]]]
2124: ? nfmod(nf,ba,bb)
2125: [-12, -7, 0, 9, 5]~
2126: ? nfmul(nf,ba,bb)
2127: [-25, -50, -30, 15, 90]~
2128: ? nfpow(nf,bb,5)
2129: [23455, 156370, 115855, 74190, -294375]~
2130: ? nfreduce(nf,ba,idx)
2131: [1, 0, 0, 0, 0]~
2132: ? setrand(1);as=matrix(3,3,j,k,vvector(5,l,random()\10^8))
2133:
2134: [[10, 7, 8, 7, 18]~ [17, 0, 9, 20, 10]~ [5, 4, 7, 18, 20]~]
2135:
2136: [[17, 16, 6, 3, 6]~ [17, 13, 9, 19, 6]~ [1, 14, 12, 20, 8]~]
2137:
2138: [[4, 13, 3, 17, 14]~ [14, 16, 11, 5, 4]~ [9, 11, 13, 7, 15]~]
2139:
2140: ? vaid=[idx,idy,idmat(5)]
2141: [[3, 1, 2, 2, 2; 0, 1, 0, 0, 0; 0, 0, 1, 0, 0; 0, 0, 0, 1, 0; 0, 0, 0, 0, 1]
2142: , [5, 0, 0, 2, 0; 0, 5, 0, 0, 0; 0, 0, 5, 2, 0; 0, 0, 0, 1, 0; 0, 0, 0, 0, 5
2143: ], [1, 0, 0, 0, 0; 0, 1, 0, 0, 0; 0, 0, 1, 0, 0; 0, 0, 0, 1, 0; 0, 0, 0, 0,
2144: 1]]
2145: ? haid=[idmat(5),idmat(5),idmat(5)]
2146: [[1, 0, 0, 0, 0; 0, 1, 0, 0, 0; 0, 0, 1, 0, 0; 0, 0, 0, 1, 0; 0, 0, 0, 0, 1]
2147: , [1, 0, 0, 0, 0; 0, 1, 0, 0, 0; 0, 0, 1, 0, 0; 0, 0, 0, 1, 0; 0, 0, 0, 0, 1
2148: ], [1, 0, 0, 0, 0; 0, 1, 0, 0, 0; 0, 0, 1, 0, 0; 0, 0, 0, 1, 0; 0, 0, 0, 0,
2149: 1]]
2150: ? nfsmith(nf,[as,haid,vaid])
2151: [[10951073973332888246310, 5442457637639729109215, 2693780223637146570055, 3
2152: 910837124677073032737, 3754666252923836621170; 0, 5, 0, 0, 0; 0, 0, 5, 2, 0;
2153: 0, 0, 0, 1, 0; 0, 0, 0, 0, 5], [1, 0, 0, 0, 0; 0, 1, 0, 0, 0; 0, 0, 1, 0, 0
2154: ; 0, 0, 0, 1, 0; 0, 0, 0, 0, 1], [1, 0, 0, 0, 0; 0, 1, 0, 0, 0; 0, 0, 1, 0,
2155: 0; 0, 0, 0, 1, 0; 0, 0, 0, 0, 1]]
2156: ? nfval(nf,ba,vp)
2157: 0
2158: ? norm(1+i)
2159: 2
2160: ? norm(mod(x+5,x^3+x+1))
2161: 129
2162: ? norml2(vector(10,x,x))
2163: 385
2164: ? nucomp(qfi(2,1,9),qfi(4,3,5),3)
2165: qfi(2, -1, 9)
2166: ? form=qfi(2,1,9);nucomp(form,form,3)
2167: qfi(4, -3, 5)
2168: ? numdiv(2^99*3^49)
2169: 5000
2170: ? numer((x+1)/(x-1))
2171: x + 1
2172: ? nupow(form,111)
2173: qfi(2, -1, 9)
2174: ? 1/(1+x)+o(x^20)
2175: 1 - x + x^2 - x^3 + x^4 - x^5 + x^6 - x^7 + x^8 - x^9 + x^10 - x^11 + x^12 -
2176: x^13 + x^14 - x^15 + x^16 - x^17 + x^18 - x^19 + O(x^20)
2177: ? omega(100!)
2178: 25
2179: ? ordell(acurve,1)
2180: [8, 3]
2181: ? order(mod(33,2^16+1))
2182: 2048
2183: ? tcurve=initell([1,0,1,-19,26]);
2184: ? orderell(tcurve,[1,2])
2185: 6
2186: ? ordred(x^3-12*x+45*x-1)
2187: [x - 1, x^3 - 363*x - 2663, x^3 + 33*x - 1]
2188: ? padicprec(padicno,127)
2189: 5
2190: ? pascal(8)
2191:
2192: [1 0 0 0 0 0 0 0 0]
2193:
2194: [1 1 0 0 0 0 0 0 0]
2195:
2196: [1 2 1 0 0 0 0 0 0]
2197:
2198: [1 3 3 1 0 0 0 0 0]
2199:
2200: [1 4 6 4 1 0 0 0 0]
2201:
2202: [1 5 10 10 5 1 0 0 0]
2203:
2204: [1 6 15 20 15 6 1 0 0]
2205:
2206: [1 7 21 35 35 21 7 1 0]
2207:
2208: [1 8 28 56 70 56 28 8 1]
2209:
2210: ? perf([2,0,1;0,2,1;1,1,2])
2211: 6
2212: ? permutation(7,1035)
2213: [4, 7, 1, 6, 3, 5, 2]
2214: ? permutation2num([4,7,1,6,3,5,2])
2215: 1035
2216: ? pf(-44,3)
2217: qfi(3, 2, 4)
2218: ? phi(257^2)
2219: 65792
2220: ? pi
2221: 3.141592653589793238
2222: ? plot(x=-5,5,sin(x))
2223:
2224: 0.9995545 x""x_''''''''''''''''''''''''''''''''''_x""x'''''''''''''''''''|
2225: | x _ "_ |
2226: | x _ _ |
2227: | x _ |
2228: | _ " |
2229: | " x |
2230: | x _ |
2231: | " |
2232: | " x _ |
2233: | _ |
2234: | " x |
2235: ````````````x``````````````````_````````````````````````````````
2236: | " |
2237: | " x _ |
2238: | _ |
2239: | " x |
2240: | x _ |
2241: | _ " |
2242: | " x |
2243: | " " x |
2244: | "_ " x |
2245: -0.999555 |...................x__x".................................."x__x
2246: -5 5
2247: ? pnqn([2,6,10,14,18,22,26])
2248:
2249: [19318376 741721]
2250:
2251: [8927353 342762]
2252:
2253: ? pnqn([1,1,1,1,1,1,1,1;1,1,1,1,1,1,1,1])
2254:
2255: [34 21]
2256:
2257: [21 13]
2258:
2259: ? point(0,225,334)
2260: ? points(0,vector(10,k,10*k),vector(10,k,5*k*k))
2261: ? pointell(acurve,zell(acurve,apoint))
2262: [0.9999999999999999986 + 0.E-19*I, 2.999999999999999998 + 0.E-18*I]
2263: ? polint([0,2,3],[0,4,9],5)
2264: 25
2265: ? polred(x^5-2*x^4-4*x^3-96*x^2-352*x-568)
2266: [x - 1, x^5 - x^4 - 6*x^3 + 6*x^2 + 13*x - 5, x^5 - x^4 + 2*x^3 - 4*x^2 + x
2267: - 1, x^5 - x^4 + 4*x^3 - 2*x^2 + x - 1, x^5 + 4*x^3 - 4*x^2 + 8*x - 8]
2268: ? polred2(x^4-28*x^3-458*x^2+9156*x-25321)
2269:
2270: [1 x - 1]
2271:
2272: [1/115*x^2 - 14/115*x - 327/115 x^2 - 10]
2273:
2274: [3/1495*x^3 - 63/1495*x^2 - 1607/1495*x + 13307/1495 x^4 - 32*x^2 + 216]
2275:
2276: [1/4485*x^3 - 7/1495*x^2 - 1034/4485*x + 7924/4485 x^4 - 8*x^2 + 6]
2277:
2278: ? polredabs(x^5-2*x^4-4*x^3-96*x^2-352*x-568)
2279: x^5 - x^4 + 2*x^3 - 4*x^2 + x - 1
2280: ? polredabs2(x^5-2*x^4-4*x^3-96*x^2-352*x-568)
2281: [x^5 - x^4 + 2*x^3 - 4*x^2 + x - 1, mod(2*x^4 - x^3 + 3*x^2 - 3*x - 1, x^5 -
2282: x^4 + 2*x^3 - 4*x^2 + x - 1)]
2283: ? polsym(x^17-1,17)
2284: [17, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 17]~
2285: ? polvar(name^4-other)
2286: name
2287: ? poly(sin(x),x)
2288: -1/1307674368000*x^15 + 1/6227020800*x^13 - 1/39916800*x^11 + 1/362880*x^9 -
2289: 1/5040*x^7 + 1/120*x^5 - 1/6*x^3 + x
2290: ? polylog(5,0.5)
2291: 0.5084005792422687065
2292: ? polylog(-4,t)
2293: (t^4 + 11*t^3 + 11*t^2 + t)/(-t^5 + 5*t^4 - 10*t^3 + 10*t^2 - 5*t + 1)
2294: ? polylogd(5,0.5)
2295: 1.033792745541689061
2296: ? polylogdold(5,0.5)
2297: 1.034459423449010483
2298: ? polylogp(5,0.5)
2299: 0.9495693489964922581
2300: ? poly([1,2,3,4,5],x)
2301: x^4 + 2*x^3 + 3*x^2 + 4*x + 5
2302: ? polyrev([1,2,3,4,5],x)
2303: 5*x^4 + 4*x^3 + 3*x^2 + 2*x + 1
2304: ? polzag(6,3)
2305: 4608*x^6 - 13824*x^5 + 46144/3*x^4 - 23168/3*x^3 + 5032/3*x^2 - 120*x + 1
2306: ? postdraw([0,20,20])
2307: ? postploth(x=-5,5,sin(x))
2308: [-5.000000000000000000, 5.000000000000000000, -0.9999964107564721649, 0.9999
2309: 964107564721649]
2310: ? postploth2(t=0,2*pi,[sin(5*t),sin(7*t)])
2311: [-0.9999994509568810308, 0.9999994509568810308, -0.9999994509568810308, 0.99
2312: 99994509568810308]
2313: ? postplothraw(vector(100,k,k),vector(100,k,k*k/100))
2314: [1.000000000000000000, 100.0000000000000000, 0.01000000000000000020, 100.000
2315: 0000000000000]
2316: ? powell(acurve,apoint,10)
2317: [-28919032218753260057646013785951999/292736325329248127651484680640160000,
2318: 478051489392386968218136375373985436596569736643531551/158385319626308443937
2319: 475969221994173751192384064000000]
2320: ? cmcurve=initell([0,-3/4,0,-2,-1])
2321: [0, -3/4, 0, -2, -1, -3, -4, -4, -1, 105, 1323, -343, -3375, [2.000000000000
2322: 000000, -0.6249999999999999999 + 0.3307189138830738238*I, -0.624999999999999
2323: 9999 - 0.3307189138830738238*I]~, 1.933311705616811546, 0.966655852808405773
2324: 3 + 2.557530989916099474*I, -0.8558486330998558525 - 4.598829819117624524 E-
2325: 20*I, -0.4279243165499279261 - 2.757161217166147204*I, 4.944504600282546727]
2326: ? powell(cmcurve,[x,y],quadgen(-7))
2327: [((-2 + 3*w)*x^2 + (6 - w))/((-2 - 5*w)*x + (-4 - 2*w)), ((34 - 11*w)*x^3 +
2328: (40 - 28*w)*x^2 + (22 + 23*w)*x)/((-90 - w)*x^2 + (-136 + 44*w)*x + (-40 + 2
2329: 8*w))]
2330: ? powrealraw(qfr(5,3,-1,0.),3)
2331: qfr(125, 23, 1, 0.E-18)
2332: ? pprint((x-12*y)/(y+13*x));
2333: (-(11 /14))
2334: ? pprint([1,2;3,4])
2335:
2336: [1 2]
2337:
2338: [3 4]
2339:
2340: ? pprint1(x+y);pprint(x+y);
2341: (2 x)(2 x)
2342: ? \precision=96
2343: realprecision = 96 significant digits
2344: ? pi
2345: 3.14159265358979323846264338327950288419716939937510582097494459230781640628
2346: 620899862803482534211
2347: ? prec(pi,20)
2348: 3.1415926535897932384626433832795028841
2349: ? precision(cmcurve)
2350: 19
2351: ? \precision=38
2352: realprecision = 38 significant digits
2353: ? prime(100)
2354: 541
2355: ? primedec(nf,2)
2356: [[2, [3, 1, 0, 0, 0]~, 1, 1, [1, 1, 0, 1, 1]~], [2, [-3, -5, -4, 3, 15]~, 1,
2357: 4, [1, 1, 0, 0, 0]~]]
2358: ? primedec(nf,3)
2359: [[3, [1, 1, 0, 0, 0]~, 1, 1, [1, -1, -1, 0, 0]~], [3, [-1, 1, -1, 0, 1]~, 2,
2360: 2, [1, 2, 3, 1, 0]~]]
2361: ? primedec(nf,11)
2362: [[11, [11, 0, 0, 0, 0]~, 1, 5, [1, 0, 0, 0, 0]~]]
2363: ? primes(100)
2364: [2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71,
2365: 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151,
2366: 157, 163, 167, 173, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229, 233, 2
2367: 39, 241, 251, 257, 263, 269, 271, 277, 281, 283, 293, 307, 311, 313, 317, 33
2368: 1, 337, 347, 349, 353, 359, 367, 373, 379, 383, 389, 397, 401, 409, 419, 421
2369: , 431, 433, 439, 443, 449, 457, 461, 463, 467, 479, 487, 491, 499, 503, 509,
2370: 521, 523, 541]
2371: ? forprime(p=2,100,print(p," ",lift(primroot(p))))
2372: 2 1
2373: 3 2
2374: 5 2
2375: 7 3
2376: 11 2
2377: 13 2
2378: 17 3
2379: 19 2
2380: 23 5
2381: 29 2
2382: 31 3
2383: 37 2
2384: 41 6
2385: 43 3
2386: 47 5
2387: 53 2
2388: 59 2
2389: 61 2
2390: 67 2
2391: 71 7
2392: 73 5
2393: 79 3
2394: 83 2
2395: 89 3
2396: 97 5
2397: ? principalideal(nf,mod(x^3+5,nfpol))
2398:
2399: [6]
2400:
2401: [0]
2402:
2403: [1]
2404:
2405: [3]
2406:
2407: [0]
2408:
2409: ? principalidele(nf,mod(x^3+5,nfpol))
2410: [[6; 0; 1; 3; 0], [2.2324480827796254080981385584384939684 + 3.1415926535897
2411: 932384626433832795028842*I, 5.0387659675158716386435353106610489968 + 1.5851
2412: 760343512250049897278861965702423*I, 4.2664040272651028743625910797589683173
2413: - 0.0083630478144368246110910258645462996191*I]]
2414: ? print((x-12*y)/(y+13*x));
2415: -11/14
2416: ? print([1,2;3,4])
2417: [1, 2; 3, 4]
2418: ? print1(x+y);print1(" equals ");print(x+y);
2419: 2*x equals 2*x
2420: ? prod(1,k=1,10,1+1/k!)
2421: 3335784368058308553334783/905932868585678438400000
2422: ? prod(1.,k=1,10,1+1/k!)
2423: 3.6821540356142043935732308433185262945
2424: ? pi^2/6*prodeuler(p=2,10000,1-p^-2)
2425: 1.0000098157493066238697591433298145174
2426: ? prodinf(n=0,(1+2^-n)/(1+2^(-n+1)))
2427: 0.33333333333333333333333333333333333320
2428: ? prodinf1(n=0,-2^-n/(1+2^(-n+1)))
2429: 0.33333333333333333333333333333333333320
2430: ? psi(1)
2431: -0.57721566490153286060651209008240243102
2432: ? quaddisc(-252)
2433: -7
2434: ? quadgen(-11)
2435: w
2436: ? quadpoly(-11)
2437: x^2 - x + 3
2438: ? rank(matrix(5,5,x,y,x+y))
2439: 2
2440: ? rayclassno(bnf,[[5,3;0,1],[1,0]])
2441: 12
2442: ? rayclassnolist(bnf,lu)
2443: [[3], [], [3, 3], [3], [6, 6], [], [], [], [3, 3, 3], [], [3, 3], [3, 3], []
2444: , [], [12, 6, 6, 12], [3], [3, 3], [], [9, 9], [6, 6], [], [], [], [], [6, 1
2445: 2, 6], [], [3, 3, 3, 3], [], [], [], [], [], [3, 6, 6, 3], [], [], [9, 3, 9]
2446: , [6, 6], [], [], [], [], [], [3, 3], [3, 3], [12, 12, 6, 6, 12, 12], [], []
2447: , [6, 6], [9], [], [3, 3, 3, 3], [], [3, 3], [], [6, 12, 12, 6]]
2448: ? move(0,50,50);rbox(0,50,50)
2449: ? print1("give a value for s? ");s=read();print(1/s)
2450: give a value for s? 37.
2451: 0.027027027027027027027027027027027027026
2452: ? real(5-7*i)
2453: 5
2454: ? recip(3*x^7-5*x^3+6*x-9)
2455: -9*x^7 + 6*x^6 - 5*x^4 + 3
2456: ? redimag(qfi(3,10,12))
2457: qfi(3, -2, 4)
2458: ? redreal(qfr(3,10,-20,1.5))
2459: qfr(3, 16, -7, 1.5000000000000000000000000000000000000)
2460: ? redrealnod(qfr(3,10,-20,1.5),18)
2461: qfr(3, 16, -7, 1.5000000000000000000000000000000000000)
2462: ? reduceddisc(x^3+4*x+12)
2463: [1036, 4, 1]
2464: ? regula(17)
2465: 2.0947125472611012942448228460655286534
2466: ? kill(y);print(x+y);reorder([x,y]);print(x+y);
2467: x + y
2468: x + y
2469: ? resultant(x^3-1,x^3+1)
2470: 8
2471: ? resultant2(x^3-1.,x^3+1.)
2472: 8.0000000000000000000000000000000000000
2473: ? reverse(tan(x))
2474: x - 1/3*x^3 + 1/5*x^5 - 1/7*x^7 + 1/9*x^9 - 1/11*x^11 + 1/13*x^13 - 1/15*x^1
2475: 5 + O(x^16)
2476: ? rhoreal(qfr(3,10,-20,1.5))
2477: qfr(-20, -10, 3, 2.1074451073987839947135880252731470615)
2478: ? rhorealnod(qfr(3,10,-20,1.5),18)
2479: qfr(-20, -10, 3, 1.5000000000000000000000000000000000000)
2480: ? rline(0,200,150)
2481: ? cursor(0)
2482: ? rmove(0,5,5);cursor(0)
2483: ? rndtoi(prod(1,k=1,17,x-exp(2*i*pi*k/17)))
2484: x^17 - 1
2485: ? qpol=y^3-y-1;setrand(1);bnf2=buchinit(qpol);nf2=bnf2[7];
2486: ? un=mod(1,qpol);w=mod(y,qpol);p=un*(x^5-5*x+w)
2487: mod(1, y^3 - y - 1)*x^5 + mod(-5, y^3 - y - 1)*x + mod(y, y^3 - y - 1)
2488: ? aa=rnfpseudobasis(nf2,p)
2489: [[[1, 0, 0]~, [0, 0, 0]~, [0, 0, 0]~, [-2, 0, 0]~, [11, 0, 0]~; [0, 0, 0]~,
2490: [1, 0, 0]~, [0, 0, 0]~, [2, 0, 0]~, [-8, 0, 0]~; [0, 0, 0]~, [0, 0, 0]~, [1,
2491: 0, 0]~, [1, 0, 0]~, [4, 0, 0]~; [0, 0, 0]~, [0, 0, 0]~, [0, 0, 0]~, [1, 0,
2492: 0]~, [-2, 0, 0]~; [0, 0, 0]~, [0, 0, 0]~, [0, 0, 0]~, [0, 0, 0]~, [1, 0, 0]~
2493: ], [[1, 0, 0; 0, 1, 0; 0, 0, 1], [1, 0, 0; 0, 1, 0; 0, 0, 1], [1, 0, 0; 0, 1
2494: , 0; 0, 0, 1], [1, 0, 3/5; 0, 1, 2/5; 0, 0, 1/5], [1, 0, 8/25; 0, 1, 22/25;
2495: 0, 0, 1/25]], [416134375, 212940625, 388649575; 0, 3125, 550; 0, 0, 25], [-1
2496: 280, 5, 5]~]
2497: ? rnfbasis(bnf2,aa)
2498:
2499: [[1, 0, 0]~ [0, 0, 0]~ [0, 0, 0]~ [38/25, -33/25, 11/25]~ [-11, -4, 9]~]
2500:
2501: [[0, 0, 0]~ [1, 0, 0]~ [0, 0, 0]~ [-14/25, 24/25, -8/25]~ [28/5, 2/5, -24/5]
2502: ~]
2503:
2504: [[0, 0, 0]~ [0, 0, 0]~ [1, 0, 0]~ [57/25, -12/25, 4/25]~ [-58/5, -47/5, 44/5
2505: ]~]
2506:
2507: [[0, 0, 0]~ [0, 0, 0]~ [0, 0, 0]~ [9/25, 6/25, -2/25]~ [-4/5, -11/5, 2/5]~]
2508:
2509: [[0, 0, 0]~ [0, 0, 0]~ [0, 0, 0]~ [8/25, -3/25, 1/25]~ [-9/5, -6/5, 7/5]~]
2510:
2511: ? rnfdiscf(nf2,p)
2512: [[416134375, 212940625, 388649575; 0, 3125, 550; 0, 0, 25], [-1280, 5, 5]~]
2513: ? rnfequation(nf2,p)
2514: x^15 - 15*x^11 + 75*x^7 - x^5 - 125*x^3 + 5*x + 1
2515: ? rnfequation2(nf2,p)
2516: [x^15 - 15*x^11 + 75*x^7 - x^5 - 125*x^3 + 5*x + 1, mod(-x^5 + 5*x, x^15 - 1
2517: 5*x^11 + 75*x^7 - x^5 - 125*x^3 + 5*x + 1), 0]
2518: ? rnfhermitebasis(bnf2,aa)
2519:
2520: [[1, 0, 0]~ [0, 0, 0]~ [0, 0, 0]~ [-2/5, 2/5, -4/5]~ [11/25, 99/25, -33/25]~
2521: ]
2522:
2523: [[0, 0, 0]~ [1, 0, 0]~ [0, 0, 0]~ [2/5, -2/5, 4/5]~ [-8/25, -72/25, 24/25]~]
2524:
2525: [[0, 0, 0]~ [0, 0, 0]~ [1, 0, 0]~ [1/5, -1/5, 2/5]~ [4/25, 36/25, -12/25]~]
2526:
2527: [[0, 0, 0]~ [0, 0, 0]~ [0, 0, 0]~ [1/5, -1/5, 2/5]~ [-2/25, -18/25, 6/25]~]
2528:
2529: [[0, 0, 0]~ [0, 0, 0]~ [0, 0, 0]~ [0, 0, 0]~ [1/25, 9/25, -3/25]~]
2530:
2531: ? rnfisfree(bnf2,aa)
2532: 1
2533: ? rnfsteinitz(nf2,aa)
2534: [[[1, 0, 0]~, [0, 0, 0]~, [0, 0, 0]~, [38/25, -33/25, 11/25]~, [-27/125, 33/
2535: 125, -11/125]~; [0, 0, 0]~, [1, 0, 0]~, [0, 0, 0]~, [-14/25, 24/25, -8/25]~,
2536: [6/125, -24/125, 8/125]~; [0, 0, 0]~, [0, 0, 0]~, [1, 0, 0]~, [57/25, -12/2
2537: 5, 4/25]~, [-53/125, 12/125, -4/125]~; [0, 0, 0]~, [0, 0, 0]~, [0, 0, 0]~, [
2538: 9/25, 6/25, -2/25]~, [-11/125, -6/125, 2/125]~; [0, 0, 0]~, [0, 0, 0]~, [0,
2539: 0, 0]~, [8/25, -3/25, 1/25]~, [-7/125, 3/125, -1/125]~], [[1, 0, 0; 0, 1, 0;
2540: 0, 0, 1], [1, 0, 0; 0, 1, 0; 0, 0, 1], [1, 0, 0; 0, 1, 0; 0, 0, 1], [1, 0,
2541: 0; 0, 1, 0; 0, 0, 1], [125, 0, 108; 0, 125, 22; 0, 0, 1]], [416134375, 21294
2542: 0625, 388649575; 0, 3125, 550; 0, 0, 25], [-1280, 5, 5]~]
2543: ? rootmod(x^16-1,41)
2544: [mod(1, 41), mod(3, 41), mod(9, 41), mod(14, 41), mod(27, 41), mod(32, 41),
2545: mod(38, 41), mod(40, 41)]~
2546: ? rootpadic(x^4+1,41,6)
2547: [3 + 22*41 + 27*41^2 + 15*41^3 + 27*41^4 + 33*41^5 + O(41^6), 14 + 20*41 + 2
2548: 5*41^2 + 24*41^3 + 4*41^4 + 18*41^5 + O(41^6), 27 + 20*41 + 15*41^2 + 16*41^
2549: 3 + 36*41^4 + 22*41^5 + O(41^6), 38 + 18*41 + 13*41^2 + 25*41^3 + 13*41^4 +
2550: 7*41^5 + O(41^6)]~
2551: ? roots(x^5-5*x^2-5*x-5)
2552: [2.0509134529831982130058170163696514536 + 0.E-38*I, -0.67063790319207539268
2553: 663382582902335603 + 0.84813118358634026680538906224199030917*I, -0.67063790
2554: 319207539268663382582902335603 - 0.84813118358634026680538906224199030917*I,
2555: -0.35481882329952371381627468235580237077 + 1.39980287391035466982975228340
2556: 62081964*I, -0.35481882329952371381627468235580237077 - 1.399802873910354669
2557: 8297522834062081964*I]~
2558: ? rootsold(x^4-1000000000000000000000)
2559: [-177827.94100389228012254211951926848447 + 0.E-38*I, 177827.941003892280122
2560: 54211951926848447 + 0.E-38*I, 6.7178761075670887517909655889502271295 E-139
2561: + 177827.94100389228012254211951926848447*I, 6.71787610756708875179096558895
2562: 02271295 E-139 - 177827.94100389228012254211951926848447*I]~
2563: ? round(prod(1,k=1,17,x-exp(2*i*pi*k/17)))
2564: x^17 - 1
2565: ? rounderror(prod(1,k=1,17,x-exp(2*i*pi*k/17)))
2566: -35
2567: ? rpoint(0,20,20)
2568: ? initrect(3,600,600);scale(3,-7,7,-2,2);cursor(3)
2569: ? q*series(anell(acurve,100),q)
2570: q - 2*q^2 - 3*q^3 + 2*q^4 - 2*q^5 + 6*q^6 - q^7 + 6*q^9 + 4*q^10 - 5*q^11 -
2571: 6*q^12 - 2*q^13 + 2*q^14 + 6*q^15 - 4*q^16 - 12*q^18 - 4*q^20 + 3*q^21 + 10*
2572: q^22 + 2*q^23 - q^25 + 4*q^26 - 9*q^27 - 2*q^28 + 6*q^29 - 12*q^30 - 4*q^31
2573: + 8*q^32 + 15*q^33 + 2*q^35 + 12*q^36 - q^37 + 6*q^39 - 9*q^41 - 6*q^42 + 2*
2574: q^43 - 10*q^44 - 12*q^45 - 4*q^46 - 9*q^47 + 12*q^48 - 6*q^49 + 2*q^50 - 4*q
2575: ^52 + q^53 + 18*q^54 + 10*q^55 - 12*q^58 + 8*q^59 + 12*q^60 - 8*q^61 + 8*q^6
2576: 2 - 6*q^63 - 8*q^64 + 4*q^65 - 30*q^66 + 8*q^67 - 6*q^69 - 4*q^70 + 9*q^71 -
2577: q^73 + 2*q^74 + 3*q^75 + 5*q^77 - 12*q^78 + 4*q^79 + 8*q^80 + 9*q^81 + 18*q
2578: ^82 - 15*q^83 + 6*q^84 - 4*q^86 - 18*q^87 + 4*q^89 + 24*q^90 + 2*q^91 + 4*q^
2579: 92 + 12*q^93 + 18*q^94 - 24*q^96 + 4*q^97 + 12*q^98 - 30*q^99 - 2*q^100 + O(
2580: q^101)
2581: ? aset=set([5,-2,7,3,5,1])
2582: ["-2", "1", "3", "5", "7"]
2583: ? bset=set([7,5,-5,7,2])
2584: ["-5", "2", "5", "7"]
2585: ? setintersect(aset,bset)
2586: ["5", "7"]
2587: ? setminus(aset,bset)
2588: ["-2", "1", "3"]
2589: ? setprecision(28)
2590: 38
2591: ? setrand(10)
2592: 10
2593: ? setsearch(aset,3)
2594: 3
2595: ? setsearch(bset,3)
2596: 0
2597: ? setserieslength(12)
2598: 16
2599: ? setunion(aset,bset)
2600: ["-2", "-5", "1", "2", "3", "5", "7"]
2601: ? arat=(x^3+x+1)/x^3;settype(arat,14)
2602: (x^3 + x + 1)/x^3
2603: ? shift(1,50)
2604: 1125899906842624
2605: ? shift([3,4,-11,-12],-2)
2606: [0, 1, -2, -3]
2607: ? shiftmul([3,4,-11,-12],-2)
2608: [3/4, 1, -11/4, -3]
2609: ? sigma(100)
2610: 217
2611: ? sigmak(2,100)
2612: 13671
2613: ? sigmak(-3,100)
2614: 1149823/1000000
2615: ? sign(-1)
2616: -1
2617: ? sign(0)
2618: 0
2619: ? sign(0.)
2620: 0
2621: ? signat(hilbert(5)-0.11*idmat(5))
2622: [2, 3]
2623: ? signunit(bnf)
2624:
2625: [-1]
2626:
2627: [1]
2628:
2629: ? simplefactmod(x^11+1,7)
2630:
2631: [1 1]
2632:
2633: [10 1]
2634:
2635: ? simplify(((x+i+1)^2-x^2-2*x*(i+1))^2)
2636: -4
2637: ? sin(pi/6)
2638: 0.5000000000000000000000000000
2639: ? sinh(1)
2640: 1.175201193643801456882381850
2641: ? size([1.3*10^5,2*i*pi*exp(4*pi)])
2642: 7
2643: ? smallbasis(x^3+4*x+12)
2644: [1, x, 1/2*x^2]
2645: ? smalldiscf(x^3+4*x+12)
2646: -1036
2647: ? smallfact(100!+1)
2648:
2649: [101 1]
2650:
2651: [14303 1]
2652:
2653: [149239 1]
2654:
2655: [432885273849892962613071800918658949059679308685024481795740765527568493010
2656: 727023757461397498800981521440877813288657839195622497225621499427628453 1]
2657:
2658: ? smallinitell([0,0,0,-17,0])
2659: [0, 0, 0, -17, 0, 0, -34, 0, -289, 816, 0, 314432, 1728]
2660: ? smallpolred(x^4+576)
2661: [x - 1, x^2 - x + 1, x^2 + 1, x^4 - x^2 + 1]
2662: ? smallpolred2(x^4+576)
2663:
2664: [1 x - 1]
2665:
2666: [1/192*x^3 + 1/8*x + 1/2 x^2 - x + 1]
2667:
2668: [-1/24*x^2 x^2 + 1]
2669:
2670: [-1/192*x^3 + 1/48*x^2 + 1/8*x x^4 - x^2 + 1]
2671:
2672: ? smith(matrix(5,5,j,k,random()))
2673: [1442459322553825252071178240, 2147483648, 2147483648, 1, 1]
2674: ? smith(1/hilbert(6))
2675: [27720, 2520, 2520, 840, 210, 6]
2676: ? smithpol(x*idmat(5)-matrix(5,5,j,k,1))
2677: [x^2 - 5*x, x, x, x, 1]
2678: ? solve(x=1,4,sin(x))
2679: 3.141592653589793238462643383
2680: ? sort(vector(17,x,5*x%17))
2681: [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16]
2682: ? sqr(1+o(2))
2683: 1 + O(2^3)
2684: ? sqred(hilbert(5))
2685:
2686: [1 1/2 1/3 1/4 1/5]
2687:
2688: [0 1/12 1 9/10 4/5]
2689:
2690: [0 0 1/180 3/2 12/7]
2691:
2692: [0 0 0 1/2800 2]
2693:
2694: [0 0 0 0 1/44100]
2695:
2696: ? sqrt(13+o(127^12))
2697: 34 + 125*127 + 83*127^2 + 107*127^3 + 53*127^4 + 42*127^5 + 22*127^6 + 98*12
2698: 7^7 + 127^8 + 23*127^9 + 122*127^10 + 79*127^11 + O(127^12)
2699: ? srgcd(x^10-1,x^15-1)
2700: x^5 - 1
2701: ? move(0,100,100);string(0,pi)
2702: ? move(0,200,200);string(0,"(0,0)")
2703: ? postdraw([0,10,10])
2704: ? apol=0.3+legendre(10)
2705: 46189/256*x^10 - 109395/256*x^8 + 45045/128*x^6 - 15015/128*x^4 + 3465/256*x
2706: ^2 + 0.05390625000000000000000000000
2707: ? sturm(apol)
2708: 4
2709: ? sturmpart(apol,0.91,1)
2710: 1
2711: ? subcyclo(31,5)
2712: x^5 + x^4 - 12*x^3 - 21*x^2 + x + 5
2713: ? subell(initell([0,0,0,-17,0]),[-1,4],[-4,2])
2714: [9, -24]
2715: ? subst(sin(x),x,y)
2716: y - 1/6*y^3 + 1/120*y^5 - 1/5040*y^7 + 1/362880*y^9 - 1/39916800*y^11 + O(y^
2717: 12)
2718: ? subst(sin(x),x,x+x^2)
2719: x + x^2 - 1/6*x^3 - 1/2*x^4 - 59/120*x^5 - 1/8*x^6 + 419/5040*x^7 + 59/720*x
2720: ^8 + 13609/362880*x^9 + 19/13440*x^10 - 273241/39916800*x^11 + O(x^12)
2721: ? sum(0,k=1,10,2^-k)
2722: 1023/1024
2723: ? sum(0.,k=1,10,2^-k)
2724: 0.9990234375000000000000000000
2725: ? sylvestermatrix(a2*x^2+a1*x+a0,b1*x+b0)
2726:
2727: [a2 b1 0]
2728:
2729: [a1 b0 b1]
2730:
2731: [a0 0 b0]
2732:
2733: ? \precision=38
2734: realprecision = 38 significant digits
2735: ? 4*sumalt(n=0,(-1)^n/(2*n+1))
2736: 3.1415926535897932384626433832795028841
2737: ? 4*sumalt2(n=0,(-1)^n/(2*n+1))
2738: 3.1415926535897932384626433832795028842
2739: ? suminf(n=1,2.^-n)
2740: 0.99999999999999999999999999999999999999
2741: ? 6/pi^2*sumpos(n=1,n^-2)
2742: 0.99999999999999999999999999999999999999
2743: ? supplement([1,3;2,4;3,6])
2744:
2745: [1 3 0]
2746:
2747: [2 4 0]
2748:
2749: [3 6 1]
2750:
2751: ? sqr(tan(pi/3))
2752: 2.9999999999999999999999999999999999999
2753: ? tanh(1)
2754: 0.76159415595576488811945828260479359041
2755: ? taniyama(bcurve)
2756: [x^-2 - x^2 + 3*x^6 - 2*x^10 + O(x^11), -x^-3 + 3*x - 3*x^5 + 8*x^9 + O(x^10
2757: )]
2758: ? taylor(y/(x-y),y)
2759: (O(y^12)*x^11 + y*x^10 + y^2*x^9 + y^3*x^8 + y^4*x^7 + y^5*x^6 + y^6*x^5 + y
2760: ^7*x^4 + y^8*x^3 + y^9*x^2 + y^10*x + y^11)/x^11
2761: ? tchebi(10)
2762: 512*x^10 - 1280*x^8 + 1120*x^6 - 400*x^4 + 50*x^2 - 1
2763: ? teich(7+o(127^12))
2764: 7 + 57*127 + 58*127^2 + 83*127^3 + 52*127^4 + 109*127^5 + 74*127^6 + 16*127^
2765: 7 + 60*127^8 + 47*127^9 + 65*127^10 + 5*127^11 + O(127^12)
2766: ? texprint((x+y)^3/(x-y)^2)
2767: {{x^{3} + {{3}y}x^{2} + {{3}y^{2}}x + {y^{3}}}\over{x^{2} - {{2}y}x + {y^{2}
2768: }}}
2769: ? theta(0.5,3)
2770: 0.080806418251894691299871683210466298535
2771: ? thetanullk(0.5,7)
2772: -804.63037320243369422783730584965684022
2773: ? torsell(tcurve)
2774: [12, [6, 2], [[-2, 8], [3, -2]]]
2775: ? trace(1+i)
2776: 2
2777: ? trace(mod(x+5,x^3+x+1))
2778: 15
2779: ? trans(vector(2,x,x))
2780: [1, 2]~
2781: ? %*%~
2782:
2783: [1 2]
2784:
2785: [2 4]
2786:
2787: ? trunc(-2.7)
2788: -2
2789: ? trunc(sin(x^2))
2790: 1/120*x^10 - 1/6*x^6 + x^2
2791: ? tschirnhaus(x^5-x-1)
2792: x^5 - 18*x^3 - 12*x^2 + 785*x + 457
2793: ? type(mod(x,x^2+1))
2794: 9
2795: ? unit(17)
2796: 3 + 2*w
2797: ? n=33;until(n==1,print1(n," ");if(n%2,n=3*n+1,n=n/2));print(1)
2798: 33 100 50 25 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1
2799: ? valuation(6^10000-1,5)
2800: 5
2801: ? vec(sin(x))
2802: [1, 0, -1/6, 0, 1/120, 0, -1/5040, 0, 1/362880, 0, -1/39916800]
2803: ? vecmax([-3,7,-2,11])
2804: 11
2805: ? vecmin([-3,7,-2,11])
2806: -3
2807: ? vecsort([[1,8,5],[2,5,8],[3,6,-6],[4,8,6]],2)
2808: [[2, 5, 8], [3, 6, -6], [4, 8, 6], [1, 8, 5]]
2809: ? vecsort([[1,8,5],[2,5,8],[3,6,-6],[4,8,6]],[2,1])
2810: [[2, 5, 8], [3, 6, -6], [1, 8, 5], [4, 8, 6]]
2811: ? weipell(acurve)
2812: x^-2 + 1/5*x^2 - 1/28*x^4 + 1/75*x^6 - 3/1540*x^8 + 1943/3822000*x^10 - 1/11
2813: 550*x^12 + 193/10510500*x^14 - 1269/392392000*x^16 + 21859/34684650000*x^18
2814: - 1087/9669660000*x^20 + O(x^22)
2815: ? wf(i)
2816: 1.1892071150027210667174999705604759152 - 1.175494350822287507 E-38*I
2817: ? wf2(i)
2818: 1.0905077326652576592070106557607079789 + 0.E-58*I
2819: ? m=5;while(m<20,print1(m," ");m=m+1);print()
2820: 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19
2821: ? zell(acurve,apoint)
2822: 0.72491221490962306778878739838332384646 + 0.E-77*I
2823: ? zeta(3)
2824: 1.2020569031595942853997381615114499907
2825: ? zeta(0.5+14.1347251*i)
2826: 0.0000000052043097453468479398562848599419244606 - 0.00000003269063986978698
2827: 2176409251733800562856*I
2828: ? zetak(nfz,-3)
2829: 0.091666666666666666666666666666666666666
2830: ? zetak(nfz,1.5+3*i)
2831: 0.88324345992059326405525724366416928890 - 0.2067536250233895222724230899142
2832: 7938845*I
2833: ? zidealstar(nf2,54)
2834: [132678, [1638, 9, 9], [[-27, 2, -27]~, [1, -24, 0]~, [1, 0, -24]~]]
2835: ? bid=zidealstarinit(nf2,54)
2836: [[[54, 0, 0; 0, 54, 0; 0, 0, 54], [0]], [132678, [1638, 9, 9]], [[2, [2, 0,
2837: 0]~, 1, 3, [1, 0, 0]~], 1; [3, [3, 0, 0]~, 1, 3, [1, 0, 0]~], 3], [[[[7], [[
2838: 0, 1, 0]~], [[-26, -27, 0]~], [[]~], 1]], [[[26], [[0, 2, 0]~], [[-27, 2, 0]
2839: ~], [[]~], 1], [[3, 3, 3], [[1, 3, 0]~, [1, 0, 3]~, [4, 0, 0]~], [[1, -24, 0
2840: ]~, [1, 0, -24]~, [-23, 0, 0]~], [[]~, []~, []~], [0, 1/3, 0; 0, 0, 1/3; 1/3
2841: , 0, 0]], [[3, 3, 3], [[1, 9, 0]~, [1, 0, 9]~, [10, 0, 0]~], [[1, -18, 0]~,
2842: [1, 0, -18]~, [-17, 0, 0]~], [[]~, []~, []~], [0, 1/9, 0; 0, 0, 1/9; 1/9, 0,
2843: 0]]], [[], [], [;]]], [468, 469, 0, 0, -48776, 0, 0, -36582; 0, 0, 1, 0, -7
2844: , -6, 0, -3; 0, 0, 0, 1, -3, 0, -6, 0]]
2845: ? zideallog(nf2,w,bid)
2846: [1574, 8, 6]~
2847: ? znstar(3120)
2848: [768, [12, 4, 4, 2, 2], [mod(67, 3120), mod(2341, 3120), mod(1847, 3120), mo
2849: d(391, 3120), mod(2081, 3120)]]
2850: ? getstack()
2851: 0
2852: ? getheap()
2853: [624, 111936]
2854: ? print("Total time spent: ",gettime());
2855: Total time spent: 6865
2856: ? \q
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