Annotation of OpenXM_contrib/pari-2.2/src/test/32/nfields, Revision 1.1.1.1
1.1 noro 1: realprecision = 38 significant digits
2: echo = 1 (on)
3: ? nfpol=x^5-5*x^3+5*x+25
4: x^5 - 5*x^3 + 5*x + 25
5: ? qpol=y^3-y-1;un=Mod(1,qpol);w=Mod(y,qpol);p=un*(x^5-5*x+w)
6: Mod(1, y^3 - y - 1)*x^5 + Mod(-5, y^3 - y - 1)*x + Mod(y, y^3 - y - 1)
7: ? p2=x^5+3021*x^4-786303*x^3-6826636057*x^2-546603588746*x+3853890514072057
8: x^5 + 3021*x^4 - 786303*x^3 - 6826636057*x^2 - 546603588746*x + 385389051407
9: 2057
10: ? fa=[11699,6;2392997,2;4987333019653,2]
11:
12: [11699 6]
13:
14: [2392997 2]
15:
16: [4987333019653 2]
17:
18: ? setrand(1);a=matrix(3,5,j,k,vectorv(5,l,random\10^8));
19: ? setrand(1);as=matrix(3,3,j,k,vectorv(5,l,random\10^8));
20: ? nf=nfinit(nfpol)
21: [x^5 - 5*x^3 + 5*x + 25, [1, 2], 595125, 45, [[1, -2.42851749071941860689920
22: 69565359418364, 5.8976972027301414394898806541072047941, -7.0734526715090929
23: 269887668671457811020, 3.8085820570096366144649278594400435257; 1, 1.9647119
24: 211288133163138753392090569931 + 0.80971492418897895128294082219556466857*I,
25: 3.2044546745713084269203768790545260356 + 3.1817131285400005341145852263331
26: 539899*I, -0.16163499313031744537610982231988834519 + 1.88804378620070569319
27: 06454476483475283*I, 2.0660709538372480632698971148801090692 + 2.68989675196
28: 23140991170523711857387388*I; 1, -0.75045317576910401286427186094108607489 +
29: 1.3101462685358123283560773619310445915*I, -1.15330327593637914666531720610
30: 81284327 - 1.9664068558894834311780119356739268309*I, 1.19836132888486390887
31: 04932558927788962 + 0.64370238076256988899570325671192132449*I, -0.470361982
32: 34206637050236104460013083212 + 0.083628266711589186119416762685933385421*I]
33: , [1, 2, 2; -2.4285174907194186068992069565359418364, 3.92942384225762663262
34: 77506784181139862 - 1.6194298483779579025658816443911293371*I, -1.5009063515
35: 382080257285437218821721497 - 2.6202925370716246567121547238620891831*I; 5.8
36: 976972027301414394898806541072047941, 6.408909349142616853840753758109052071
37: 2 - 6.3634262570800010682291704526663079798*I, -2.30660655187275829333063441
38: 22162568654 + 3.9328137117789668623560238713478536619*I; -7.0734526715090929
39: 269887668671457811020, -0.32326998626063489075221964463977669038 - 3.7760875
40: 724014113863812908952966950567*I, 2.3967226577697278177409865117855577924 -
41: 1.2874047615251397779914065134238426489*I; 3.8085820570096366144649278594400
42: 435257, 4.1321419076744961265397942297602181385 - 5.379793503924628198234104
43: 7423714774776*I, -0.94072396468413274100472208920026166424 - 0.1672565334231
44: 7837223883352537186677084*I], [5, 4.02152936 E-87, 10.0000000000000000000000
45: 00000000000000, -5.0000000000000000000000000000000000000, 7.0000000000000000
46: 000000000000000000000; 4.02152936 E-87, 19.488486013650707197449403270536023
47: 970, 8.04305873 E-86, 19.488486013650707197449403270536023970, 4.15045922467
48: 06085588902013976045703227; 10.000000000000000000000000000000000000, 8.04305
49: 873 E-86, 85.960217420851846480305133936577594605, -36.034268291482979838267
50: 056239752434596, 53.576130452511107888183080361946556763; -5.000000000000000
51: 0000000000000000000000, 19.488486013650707197449403270536023970, -36.0342682
52: 91482979838267056239752434596, 60.916248374441986300937507618575151517, -18.
53: 470101750219179344070032346246890434; 7.000000000000000000000000000000000000
54: 0, 4.1504592246706085588902013976045703227, 53.57613045251110788818308036194
55: 6556763, -18.470101750219179344070032346246890434, 37.9701528928423673408973
56: 84258599214282], [5, 0, 10, -5, 7; 0, 10, 0, 10, -5; 10, 0, 30, -55, 20; -5,
57: 10, -55, 45, -39; 7, -5, 20, -39, 9], [345, 0, 340, 167, 150; 0, 345, 110,
58: 220, 153; 0, 0, 5, 2, 1; 0, 0, 0, 1, 0; 0, 0, 0, 0, 1], [132825, -18975, -51
59: 75, 27600, 17250; -18975, 34500, 41400, 3450, -43125; -5175, 41400, -41400,
60: -15525, 51750; 27600, 3450, -15525, -3450, 0; 17250, -43125, 51750, 0, -8625
61: 0], [595125, [-13800, 117300, 67275, 1725, 0]~]], [-2.4285174907194186068992
62: 069565359418364, 1.9647119211288133163138753392090569931 + 0.809714924188978
63: 95128294082219556466857*I, -0.75045317576910401286427186094108607489 + 1.310
64: 1462685358123283560773619310445915*I], [1, x, x^2, 1/3*x^3 - 1/3*x^2 - 1/3,
65: 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, 1,
66: 1, -5; 0, 0, 0, 3, 0; 0, 0, 0, 0, 15], [1, 0, 0, 0, 0, 0, 0, 1, -2, -1, 0,
67: 1, -5, -5, -3, 0, -2, -5, 1, -4, 0, -1, -3, -4, -3; 0, 1, 0, 0, 0, 1, 0, 0,
68: -2, 0, 0, 0, -5, 0, -5, 0, -2, 0, -5, 0, 0, 0, -5, 0, -4; 0, 0, 1, 0, 0, 0,
69: 1, 1, -2, 1, 1, 1, -5, 3, -3, 0, -2, 3, -5, 1, 0, 1, -3, 1, -2; 0, 0, 0, 1,
70: 0, 0, 0, 3, -1, 2, 0, 3, 0, 5, 1, 1, -1, 5, -4, 3, 0, 2, 1, 3, 1; 0, 0, 0, 0
71: , 1, 0, 0, 0, 5, 0, 0, 0, 15, -5, 10, 0, 5, -5, 10, -2, 1, 0, 10, -2, 7]]
72: ? nf1=nfinit(nfpol,2)
73: [x^5 - 2*x^4 + 3*x^3 + 8*x^2 + 3*x + 2, [1, 2], 595125, 4, [[1, -1.089115145
74: 7205048250249527946671612684, 1.1861718006377964594796293860483989860, -0.59
75: 741050929194782733001765987770358483, 0.158944197453903762065494816710718942
76: 89; 1, -0.13838372073406036365047976417441696637 + 0.49181637657768643499753
77: 285514741525107*I, -0.22273329410580226599155701611419649154 - 0.13611876021
78: 752805221674918029071012580*I, -0.13167445871785818798769651537619416009 + 0
79: .13249517760521973840801462296650806543*I, -0.053650958656997725359297528357
80: 602608116 + 0.27622636814169107038138284681568361486*I; 1, 1.682941293594312
81: 7761629561615079976005 + 2.0500351226010726172974286983598602163*I, -1.37035
82: 26062130959637482576769100030014 + 6.9001775222880494773720769629846373016*I
83: , -8.0696202866361678983472946546849540475 + 8.87676767859710424508852843013
84: 48051602*I, -22.025821140069954155673449879997756863 - 8.4306586896999153544
85: 710860185447589664*I], [1, 2, 2; -1.0891151457205048250249527946671612684, -
86: 0.27676744146812072730095952834883393274 - 0.9836327531553728699950657102948
87: 3050214*I, 3.3658825871886255523259123230159952011 - 4.100070245202145234594
88: 8573967197204327*I; 1.1861718006377964594796293860483989860, -0.445466588211
89: 60453198311403222839298308 + 0.27223752043505610443349836058142025160*I, -2.
90: 7407052124261919274965153538200060029 - 13.800355044576098954744153925969274
91: 603*I; -0.59741050929194782733001765987770358483, -0.26334891743571637597539
92: 303075238832018 - 0.26499035521043947681602924593301613087*I, -16.1392405732
93: 72335796694589309369908095 - 17.753535357194208490177056860269610320*I; 0.15
94: 894419745390376206549481671071894289, -0.10730191731399545071859505671520521
95: 623 - 0.55245273628338214076276569363136722973*I, -44.0516422801399083113468
96: 99759995513726 + 16.861317379399830708942172037089517932*I], [5, 2.000000000
97: 0000000000000000000000000000, -2.0000000000000000000000000000000000000, -17.
98: 000000000000000000000000000000000000, -44.0000000000000000000000000000000000
99: 00; 2.0000000000000000000000000000000000000, 15.7781094086719980448363574712
100: 83695361, 22.314643349754061651916553814602769764, 10.0513952578314782754999
101: 32716306366248, -108.58917507620841447456569092094763671; -2.000000000000000
102: 0000000000000000000000, 22.314643349754061651916553814602769764, 100.5239126
103: 2388960975827806174040462368, 143.93295090847353519436673793501057176, -55.8
104: 42564718082452641322500190813370023; -17.00000000000000000000000000000000000
105: 0, 10.051395257831478275499932716306366248, 143.9329509084735351943667379350
106: 1057176, 288.25823756749944693139292174819167135, 205.7984003827766237572018
107: 0649465932302; -44.000000000000000000000000000000000000, -108.58917507620841
108: 447456569092094763671, -55.842564718082452641322500190813370023, 205.7984003
109: 8277662375720180649465932302, 1112.6092277946777707779250962522343036], [5,
110: 2, -2, -17, -44; 2, -2, -34, -63, -40; -2, -34, -90, -101, 177; -17, -63, -1
111: 01, -27, 505; -44, -40, 177, 505, 828], [345, 0, 160, 252, 156; 0, 345, 215,
112: 311, 306; 0, 0, 5, 3, 2; 0, 0, 0, 1, 0; 0, 0, 0, 0, 1], [163875, -388125, -
113: 296700, 234600, -89700; -388125, -1593900, -677925, 595125, -315675; -296700
114: , -677925, 17250, 58650, -87975; 234600, 595125, 58650, -100050, 89700; -897
115: 00, -315675, -87975, 89700, -55200], [595125, [-167325, -82800, 79350, 1725,
116: 0]~]], [-1.0891151457205048250249527946671612684, -0.1383837207340603636504
117: 7976417441696637 + 0.49181637657768643499753285514741525107*I, 1.68294129359
118: 43127761629561615079976005 + 2.0500351226010726172974286983598602163*I], [1,
119: 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,
120: 0, -1, -1; 0, 0, 1, -1, 0; 0, 0, 0, 2, 0; 0, 0, 0, 0, 2], [1, 0, 0, 0, 0, 0,
121: 0, 0, 0, -1, 0, 0, 0, -1, -2, 0, 0, -1, -2, -2, 0, -1, -2, -2, 5; 0, 1, 0,
122: 0, 0, 1, 0, -1, -1, -1, 0, -1, -1, -2, 2, 0, -1, -2, -1, 7, 0, -1, 2, 7, 14;
123: 0, 0, 1, 0, 0, 0, 1, -1, 0, -2, 1, -1, 0, -3, -3, 0, 0, -3, -4, -1, 0, -2,
124: -3, -1, 15; 0, 0, 0, 1, 0, 0, 0, 2, 1, -3, 0, 2, 0, -2, -13, 1, 1, -2, -9, -
125: 19, 0, -3, -13, -19, 7; 0, 0, 0, 0, 1, 0, 0, 0, 1, 2, 0, 0, 2, 3, 1, 0, 1, 3
126: , 4, -4, 1, 2, 1, -4, -21]]
127: ? nfinit(nfpol,3)
128: [[x^5 - 2*x^4 + 3*x^3 + 8*x^2 + 3*x + 2, [1, 2], 595125, 4, [[1, -1.08911514
129: 57205048250249527946671612684, 1.1861718006377964594796293860483989860, -0.5
130: 9741050929194782733001765987770358483, 0.15894419745390376206549481671071894
131: 289; 1, -0.13838372073406036365047976417441696637 + 0.4918163765776864349975
132: 3285514741525107*I, -0.22273329410580226599155701611419649154 - 0.1361187602
133: 1752805221674918029071012580*I, -0.13167445871785818798769651537619416009 +
134: 0.13249517760521973840801462296650806543*I, -0.05365095865699772535929752835
135: 7602608116 + 0.27622636814169107038138284681568361486*I; 1, 1.68294129359431
136: 27761629561615079976005 + 2.0500351226010726172974286983598602163*I, -1.3703
137: 526062130959637482576769100030014 + 6.9001775222880494773720769629846373016*
138: I, -8.0696202866361678983472946546849540475 + 8.8767676785971042450885284301
139: 348051602*I, -22.025821140069954155673449879997756863 - 8.430658689699915354
140: 4710860185447589664*I], [1, 2, 2; -1.0891151457205048250249527946671612684,
141: -0.27676744146812072730095952834883393274 - 0.983632753155372869995065710294
142: 83050214*I, 3.3658825871886255523259123230159952011 - 4.10007024520214523459
143: 48573967197204327*I; 1.1861718006377964594796293860483989860, -0.44546658821
144: 160453198311403222839298308 + 0.27223752043505610443349836058142025160*I, -2
145: .7407052124261919274965153538200060029 - 13.80035504457609895474415392596927
146: 4603*I; -0.59741050929194782733001765987770358483, -0.2633489174357163759753
147: 9303075238832018 - 0.26499035521043947681602924593301613087*I, -16.139240573
148: 272335796694589309369908095 - 17.753535357194208490177056860269610320*I; 0.1
149: 5894419745390376206549481671071894289, -0.1073019173139954507185950567152052
150: 1623 - 0.55245273628338214076276569363136722973*I, -44.051642280139908311346
151: 899759995513726 + 16.861317379399830708942172037089517932*I], [5, 2.00000000
152: 00000000000000000000000000000, -2.0000000000000000000000000000000000000, -17
153: .000000000000000000000000000000000000, -44.000000000000000000000000000000000
154: 000; 2.0000000000000000000000000000000000000, 15.778109408671998044836357471
155: 283695361, 22.314643349754061651916553814602769764, 10.051395257831478275499
156: 932716306366248, -108.58917507620841447456569092094763671; -2.00000000000000
157: 00000000000000000000000, 22.314643349754061651916553814602769764, 100.523912
158: 62388960975827806174040462368, 143.93295090847353519436673793501057176, -55.
159: 842564718082452641322500190813370023; -17.0000000000000000000000000000000000
160: 00, 10.051395257831478275499932716306366248, 143.932950908473535194366737935
161: 01057176, 288.25823756749944693139292174819167135, 205.798400382776623757201
162: 80649465932302; -44.000000000000000000000000000000000000, -108.5891750762084
163: 1447456569092094763671, -55.842564718082452641322500190813370023, 205.798400
164: 38277662375720180649465932302, 1112.6092277946777707779250962522343036], [5,
165: 2, -2, -17, -44; 2, -2, -34, -63, -40; -2, -34, -90, -101, 177; -17, -63, -
166: 101, -27, 505; -44, -40, 177, 505, 828], [345, 0, 160, 252, 156; 0, 345, 215
167: , 311, 306; 0, 0, 5, 3, 2; 0, 0, 0, 1, 0; 0, 0, 0, 0, 1], [163875, -388125,
168: -296700, 234600, -89700; -388125, -1593900, -677925, 595125, -315675; -29670
169: 0, -677925, 17250, 58650, -87975; 234600, 595125, 58650, -100050, 89700; -89
170: 700, -315675, -87975, 89700, -55200], [595125, [-167325, -82800, 79350, 1725
171: , 0]~]], [-1.0891151457205048250249527946671612684, -0.138383720734060363650
172: 47976417441696637 + 0.49181637657768643499753285514741525107*I, 1.6829412935
173: 943127761629561615079976005 + 2.0500351226010726172974286983598602163*I], [1
174: , 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,
175: 0, -1, -1; 0, 0, 1, -1, 0; 0, 0, 0, 2, 0; 0, 0, 0, 0, 2], [1, 0, 0, 0, 0, 0
176: , 0, 0, 0, -1, 0, 0, 0, -1, -2, 0, 0, -1, -2, -2, 0, -1, -2, -2, 5; 0, 1, 0,
177: 0, 0, 1, 0, -1, -1, -1, 0, -1, -1, -2, 2, 0, -1, -2, -1, 7, 0, -1, 2, 7, 14
178: ; 0, 0, 1, 0, 0, 0, 1, -1, 0, -2, 1, -1, 0, -3, -3, 0, 0, -3, -4, -1, 0, -2,
179: -3, -1, 15; 0, 0, 0, 1, 0, 0, 0, 2, 1, -3, 0, 2, 0, -2, -13, 1, 1, -2, -9,
180: -19, 0, -3, -13, -19, 7; 0, 0, 0, 0, 1, 0, 0, 0, 1, 2, 0, 0, 2, 3, 1, 0, 1,
181: 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^
182: 5 - 2*x^4 + 3*x^3 + 8*x^2 + 3*x + 2)]
183: ? nfinit(nfpol,4)
184: [x^5 - 2*x^4 + 3*x^3 + 8*x^2 + 3*x + 2, [1, 2], 595125, 4, [[1, -1.089115145
185: 7205048250249527946671612684, 1.1861718006377964594796293860483989860, -0.59
186: 741050929194782733001765987770358483, 0.158944197453903762065494816710718942
187: 89; 1, -0.13838372073406036365047976417441696637 + 0.49181637657768643499753
188: 285514741525107*I, -0.22273329410580226599155701611419649154 - 0.13611876021
189: 752805221674918029071012580*I, -0.13167445871785818798769651537619416009 + 0
190: .13249517760521973840801462296650806543*I, -0.053650958656997725359297528357
191: 602608116 + 0.27622636814169107038138284681568361486*I; 1, 1.682941293594312
192: 7761629561615079976005 + 2.0500351226010726172974286983598602163*I, -1.37035
193: 26062130959637482576769100030014 + 6.9001775222880494773720769629846373016*I
194: , -8.0696202866361678983472946546849540475 + 8.87676767859710424508852843013
195: 48051602*I, -22.025821140069954155673449879997756863 - 8.4306586896999153544
196: 710860185447589664*I], [1, 2, 2; -1.0891151457205048250249527946671612684, -
197: 0.27676744146812072730095952834883393274 - 0.9836327531553728699950657102948
198: 3050214*I, 3.3658825871886255523259123230159952011 - 4.100070245202145234594
199: 8573967197204327*I; 1.1861718006377964594796293860483989860, -0.445466588211
200: 60453198311403222839298308 + 0.27223752043505610443349836058142025160*I, -2.
201: 7407052124261919274965153538200060029 - 13.800355044576098954744153925969274
202: 603*I; -0.59741050929194782733001765987770358483, -0.26334891743571637597539
203: 303075238832018 - 0.26499035521043947681602924593301613087*I, -16.1392405732
204: 72335796694589309369908095 - 17.753535357194208490177056860269610320*I; 0.15
205: 894419745390376206549481671071894289, -0.10730191731399545071859505671520521
206: 623 - 0.55245273628338214076276569363136722973*I, -44.0516422801399083113468
207: 99759995513726 + 16.861317379399830708942172037089517932*I], [5, 2.000000000
208: 0000000000000000000000000000, -2.0000000000000000000000000000000000000, -17.
209: 000000000000000000000000000000000000, -44.0000000000000000000000000000000000
210: 00; 2.0000000000000000000000000000000000000, 15.7781094086719980448363574712
211: 83695361, 22.314643349754061651916553814602769764, 10.0513952578314782754999
212: 32716306366248, -108.58917507620841447456569092094763671; -2.000000000000000
213: 0000000000000000000000, 22.314643349754061651916553814602769764, 100.5239126
214: 2388960975827806174040462368, 143.93295090847353519436673793501057176, -55.8
215: 42564718082452641322500190813370023; -17.00000000000000000000000000000000000
216: 0, 10.051395257831478275499932716306366248, 143.9329509084735351943667379350
217: 1057176, 288.25823756749944693139292174819167135, 205.7984003827766237572018
218: 0649465932302; -44.000000000000000000000000000000000000, -108.58917507620841
219: 447456569092094763671, -55.842564718082452641322500190813370023, 205.7984003
220: 8277662375720180649465932302, 1112.6092277946777707779250962522343036], [5,
221: 2, -2, -17, -44; 2, -2, -34, -63, -40; -2, -34, -90, -101, 177; -17, -63, -1
222: 01, -27, 505; -44, -40, 177, 505, 828], [345, 0, 160, 252, 156; 0, 345, 215,
223: 311, 306; 0, 0, 5, 3, 2; 0, 0, 0, 1, 0; 0, 0, 0, 0, 1], [163875, -388125, -
224: 296700, 234600, -89700; -388125, -1593900, -677925, 595125, -315675; -296700
225: , -677925, 17250, 58650, -87975; 234600, 595125, 58650, -100050, 89700; -897
226: 00, -315675, -87975, 89700, -55200], [595125, [-167325, -82800, 79350, 1725,
227: 0]~]], [-1.0891151457205048250249527946671612684, -0.1383837207340603636504
228: 7976417441696637 + 0.49181637657768643499753285514741525107*I, 1.68294129359
229: 43127761629561615079976005 + 2.0500351226010726172974286983598602163*I], [1,
230: 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,
231: 0, -1, -1; 0, 0, 1, -1, 0; 0, 0, 0, 2, 0; 0, 0, 0, 0, 2], [1, 0, 0, 0, 0, 0,
232: 0, 0, 0, -1, 0, 0, 0, -1, -2, 0, 0, -1, -2, -2, 0, -1, -2, -2, 5; 0, 1, 0,
233: 0, 0, 1, 0, -1, -1, -1, 0, -1, -1, -2, 2, 0, -1, -2, -1, 7, 0, -1, 2, 7, 14;
234: 0, 0, 1, 0, 0, 0, 1, -1, 0, -2, 1, -1, 0, -3, -3, 0, 0, -3, -4, -1, 0, -2,
235: -3, -1, 15; 0, 0, 0, 1, 0, 0, 0, 2, 1, -3, 0, 2, 0, -2, -13, 1, 1, -2, -9, -
236: 19, 0, -3, -13, -19, 7; 0, 0, 0, 0, 1, 0, 0, 0, 1, 2, 0, 0, 2, 3, 1, 0, 1, 3
237: , 4, -4, 1, 2, 1, -4, -21]]
238: ? nf3=nfinit(x^6+108);
239: ? nf4=nfinit(x^3-10*x+8)
240: [x^3 - 10*x + 8, [3, 0], 568, 2, [[1, -3.50466435358804770515010852590433205
241: 79, 6.1413361156553641347759399165844441383; 1, 0.86464088669540302583112842
242: 266613688800, 0.37380193147270638662350044992137561317; 1, 2.640023466892644
243: 6793189801032381951699, 3.4848619528719294786005596334941802484], [1, 1, 1;
244: -3.5046643535880477051501085259043320579, 0.86464088669540302583112842266613
245: 688800, 2.6400234668926446793189801032381951699; 6.1413361156553641347759399
246: 165844441383, 0.37380193147270638662350044992137561317, 3.484861952871929478
247: 6005596334941802484], [3, -3.45446742 E-77, 10.00000000000000000000000000000
248: 0000000; -3.45446742 E-77, 20.000000000000000000000000000000000000, -12.0000
249: 00000000000000000000000000000000; 10.000000000000000000000000000000000000, -
250: 12.000000000000000000000000000000000000, 50.00000000000000000000000000000000
251: 0000], [3, 0, 10; 0, 20, -12; 10, -12, 50], [284, 168, 235; 0, 2, 0; 0, 0, 1
252: ], [856, -120, -200; -120, 50, 36; -200, 36, 60], [568, [-216, 90, 8]~]], [-
253: 3.5046643535880477051501085259043320579, 0.864640886695403025831128422666136
254: 88800, 2.6400234668926446793189801032381951699], [1, x, 1/2*x^2], [1, 0, 0;
255: 0, 1, 0; 0, 0, 2], [1, 0, 0, 0, 0, -4, 0, -4, 0; 0, 1, 0, 1, 0, 5, 0, 5, -2;
256: 0, 0, 1, 0, 2, 0, 1, 0, 5]]
257: ? setrand(1);bnf2=bnfinit(qpol);nf2=bnf2[7];
258: ? setrand(1);bnf=bnfinit(x^2-x-57,,[0.2,0.2])
259: [Mat(3), Mat([1, 2, 1, 2, 1, 2, 1, 2, 1]), [-2.71246530518434397468087951060
260: 61300699 + 3.1415926535897932384626433832795028842*I; 2.71246530518434397468
261: 08795106061300699 - 6.2831853071795864769252867665590057684*I], [9.927737672
262: 2507613003718504524486100858 + 3.1415926535897932384626433832795028842*I, 1.
263: 2897619530652735025030086072395031017 + 0.E-47*I, -2.01097980249891575621226
264: 34098917610612 + 3.1415926535897932384626433832795028842*I, 24.4121877466590
265: 95772127915595455170629 + 6.2831853071795864769252867665590057684*I, 30.3376
266: 98160660239595315877930058147543 + 9.4247779607693797153879301498385086526*I
267: , -20.610866187462450639586440264933189691 + 9.42477796076937971538793014983
268: 85086526*I, 29.258282452818196217527894893424939793 + 9.42477796076937971538
269: 79301498385086526*I, -0.34328764427702709438988786673341921876 + 3.141592653
270: 5897932384626433832795028842*I, -14.550628376291080203941433635329724736 + 0
271: .E-47*I, 24.478366048541841504313284087778334822 + 3.14159265358979323846264
272: 33832795028842*I; -9.9277376722507613003718504524486100858 + 6.2831853071795
273: 864769252867665590057684*I, -1.2897619530652735025030086072395031017 + 9.424
274: 7779607693797153879301498385086526*I, 2.010979802498915756212263409891761061
275: 2 + 0.E-47*I, -24.412187746659095772127915595455170629 + 3.14159265358979323
276: 84626433832795028842*I, -30.337698160660239595315877930058147543 + 3.1415926
277: 535897932384626433832795028842*I, 20.610866187462450639586440264933189691 +
278: 3.1415926535897932384626433832795028842*I, -29.25828245281819621752789489342
279: 4939793 + 6.2831853071795864769252867665590057684*I, 0.343287644277027094389
280: 88786673341921876 + 0.E-48*I, 14.550628376291080203941433635329724736 + 3.14
281: 15926535897932384626433832795028842*I, -24.478366048541841504313284087778334
282: 822 + 3.1415926535897932384626433832795028842*I], [[3, [-1, 1]~, 1, 1, [0, 1
283: ]~], [3, [0, 1]~, 1, 1, [-1, 1]~], [5, [-2, 1]~, 1, 1, [1, 1]~], [5, [1, 1]~
284: , 1, 1, [-2, 1]~], [11, [-2, 1]~, 1, 1, [1, 1]~], [11, [1, 1]~, 1, 1, [-2, 1
285: ]~], [17, [-3, 1]~, 1, 1, [2, 1]~], [17, [2, 1]~, 1, 1, [-3, 1]~], [19, [-1,
286: 1]~, 1, 1, [0, 1]~], [19, [0, 1]~, 1, 1, [-1, 1]~]]~, [1, 3, 5, 2, 4, 6, 7,
287: 8, 10, 9], [x^2 - x - 57, [2, 0], 229, 1, [[1, -7.0663729752107779635959310
288: 246705326058; 1, 8.0663729752107779635959310246705326058], [1, 1; -7.0663729
289: 752107779635959310246705326058, 8.0663729752107779635959310246705326058], [2
290: , 1.0000000000000000000000000000000000000; 1.0000000000000000000000000000000
291: 000000, 115.00000000000000000000000000000000000], [2, 1; 1, 115], [229, 114;
292: 0, 1], [115, -1; -1, 2], [229, [114, 1]~]], [-7.066372975210777963595931024
293: 6705326058, 8.0663729752107779635959310246705326058], [1, x], [1, 0; 0, 1],
294: [1, 0, 0, 57; 0, 1, 1, 1]], [[3, [3], [[3, 2; 0, 1]]], 2.7124653051843439746
295: 808795106061300699, 0.8814422512654579369, [2, -1], [x + 7], 153], [Mat(1),
296: [[0, 0]], [[9.9277376722507613003718504524486100858 + 3.14159265358979323846
297: 26433832795028842*I, -9.9277376722507613003718504524486100858 + 6.2831853071
298: 795864769252867665590057684*I]]], 0]
299: ? setrand(1);bnfinit(x^2-x-100000,1)
300: [Mat(5), Mat([3, 2, 1, 2, 0, 3, 2, 3, 0, 0, 1, 4, 3, 2, 2, 3, 3, 2]), [-129.
301: 82045011403975460991182396195022419 - 6.283185307179586476925286766559005768
302: 4*I; 129.82045011403975460991182396195022419 - 7.12167580 E-66*I], [-41.8112
303: 64589129943393339502258694361489 + 0.E-66*I, 9.23990041479022898163762604388
304: 40931575 + 3.1415926535897932384626433832795028842*I, -11.874609881075406725
305: 097315997431161032 + 9.4247779607693797153879301498385086526*I, 389.46135034
306: 211926382973547188585067257 + 12.566370614359172953850573533118011536*I, -44
307: 0.51251534603943620471260018842912722 + 0.E-65*I, -324.551125285099386524779
308: 55990487556047 + 6.2831853071795864769252867665590057684*I, 229.704245520024
309: 97255158146166263724792 + 3.1415926535897932384626433832795028842*I, -785.66
310: 045186253421572025117972275598325 + 6.2831853071795864769252867665590057684*
311: I, -554.35531386699327377220656215544062014 + 6.2831853071795864769252867665
312: 590057684*I, -47.668319071568233997332918482707687879 + 9.424777960769379715
313: 3879301498385086526*I, 177.48876918560798860724474244465791207 + 9.49556774
314: E-66*I, -875.61236937168080069763246690606885226 - 3.79822709 E-65*I, 54.878
315: 404098312329644822020875673145627 + 9.4247779607693797153879301498385086526*
316: I, -404.44153844676787690336623107514389175 - 9.49556774 E-66*I, 232.8098237
317: 4359817890011490485449930607 + 6.2831853071795864769252867665590057684*I, -6
318: 68.80899963671483856204802764462926790 + 9.424777960769379715387930149838508
319: 6526*I, 367.35683481950538594888487746203445802 + 9.49556774 E-66*I, -1214.0
320: 716092619656173892944003952818868 + 9.4247779607693797153879301498385086526*
321: I, -125.94415646756187210316334148291471657 + 6.2831853071795864769252867665
322: 590057684*I; 41.811264589129943393339502258694361489 + 6.2831853071795864769
323: 252867665590057684*I, -9.2399004147902289816376260438840931575 + 0.E-66*I, 1
324: 1.874609881075406725097315997431161032 + 0.E-66*I, -389.46135034211926382973
325: 547188585067257 + 6.2831853071795864769252867665590057684*I, 440.51251534603
326: 943620471260018842912722 + 3.1415926535897932384626433832795028842*I, 324.55
327: 112528509938652477955990487556047 + 9.4247779607693797153879301498385086526*
328: I, -229.70424552002497255158146166263724792 + 6.2831853071795864769252867665
329: 590057684*I, 785.66045186253421572025117972275598325 + 9.4247779607693797153
330: 879301498385086526*I, 554.35531386699327377220656215544062014 + 3.1415926535
331: 897932384626433832795028842*I, 47.668319071568233997332918482707687878 + 3.1
332: 415926535897932384626433832795028842*I, -177.4887691856079886072447424446579
333: 1207 + 6.2831853071795864769252867665590057684*I, 875.6123693716808006976324
334: 6690606885226 + 2.84867032 E-65*I, -54.878404098312329644822020875673145627
335: + 9.4247779607693797153879301498385086526*I, 404.441538446767876903366231075
336: 14389175 + 9.4247779607693797153879301498385086526*I, -232.80982374359817890
337: 011490485449930607 + 3.1415926535897932384626433832795028842*I, 668.80899963
338: 671483856204802764462926790 + 6.2831853071795864769252867665590057684*I, -36
339: 7.35683481950538594888487746203445803 + 3.1415926535897932384626433832795028
340: 842*I, 1214.0716092619656173892944003952818868 + 3.1415926535897932384626433
341: 832795028842*I, 125.94415646756187210316334148291471657 + 6.2831853071795864
342: 769252867665590057684*I], [[2, [1, 1]~, 1, 1, [0, 1]~], [2, [2, 1]~, 1, 1, [
343: 1, 1]~], [5, [4, 1]~, 1, 1, [0, 1]~], [5, [5, 1]~, 1, 1, [-1, 1]~], [7, [3,
344: 1]~, 2, 1, [3, 1]~], [13, [-6, 1]~, 1, 1, [5, 1]~], [13, [5, 1]~, 1, 1, [-6,
345: 1]~], [17, [14, 1]~, 1, 1, [2, 1]~], [17, [19, 1]~, 1, 1, [-3, 1]~], [23, [
346: -7, 1]~, 1, 1, [6, 1]~], [23, [6, 1]~, 1, 1, [-7, 1]~], [29, [-14, 1]~, 1, 1
347: , [13, 1]~], [29, [13, 1]~, 1, 1, [-14, 1]~], [31, [23, 1]~, 1, 1, [7, 1]~],
348: [31, [38, 1]~, 1, 1, [-8, 1]~], [41, [-7, 1]~, 1, 1, [6, 1]~], [41, [6, 1]~
349: , 1, 1, [-7, 1]~], [43, [-16, 1]~, 1, 1, [15, 1]~], [43, [15, 1]~, 1, 1, [-1
350: 6, 1]~]]~, [1, 3, 6, 2, 4, 5, 7, 9, 8, 11, 10, 13, 12, 15, 14, 17, 16, 19, 1
351: 8], [x^2 - x - 100000, [2, 0], 400001, 1, [[1, -315.728161301298401613920894
352: 89603747004; 1, 316.72816130129840161392089489603747004], [1, 1; -315.728161
353: 30129840161392089489603747004, 316.72816130129840161392089489603747004], [2,
354: 1.0000000000000000000000000000000000000; 1.00000000000000000000000000000000
355: 00000, 200001.00000000000000000000000000000000], [2, 1; 1, 200001], [400001,
356: 200000; 0, 1], [200001, -1; -1, 2], [400001, [200000, 1]~]], [-315.72816130
357: 129840161392089489603747004, 316.72816130129840161392089489603747004], [1, x
358: ], [1, 0; 0, 1], [1, 0, 0, 100000; 0, 1, 1, 1]], [[5, [5], [[2, 1; 0, 1]]],
359: 129.82045011403975460991182396195022419, 0.9876536979069047239, [2, -1], [37
360: 9554884019013781006303254896369154068336082609238336*x + 1198361656442507899
361: 90462835950022871665178127611316131167], 26], [Mat(1), [[0, 0]], [[-41.81126
362: 4589129943393339502258694361489 + 0.E-66*I, 41.81126458912994339333950225869
363: 4361489 + 6.2831853071795864769252867665590057684*I]]], 0]
364: ? \p19
365: realprecision = 19 significant digits
366: ? setrand(1);sbnf=bnfinit(x^3-x^2-14*x-1,3)
367: [x^3 - x^2 - 14*x - 1, 3, 10889, [1, x, x^2], [-3.233732695981516673, -0.071
368: 82350902743636344, 4.305556205008953036], [10889, 5698, 3794; 0, 1, 0; 0, 0,
369: 1], Mat(2), Mat([0, 1, 1, 1, 1, 0, 1, 1]), [9, 15, 16, 17, 10, 69, 33, 39,
370: 57], [2, [-1, 0, 0]~], [[0, 1, 0]~, [-4, 2, 1]~], [-4, 3, -1, 2, 3, 11, 1, -
371: 1, -7; 1, 1, 1, 1, 0, 2, 1, -4, -2; 0, 0, 0, 0, 0, -1, 0, -1, 0]]
372: ? \p38
373: realprecision = 38 significant digits
374: ? bnrinit(bnf,[[5,3;0,1],[1,0]],1)
375: [[Mat(3), Mat([1, 2, 1, 2, 1, 2, 1, 2, 1]), [-2.7124653051843439746808795106
376: 061300699 + 3.1415926535897932384626433832795028842*I; 2.7124653051843439746
377: 808795106061300699 - 6.2831853071795864769252867665590057684*I], [9.92773767
378: 22507613003718504524486100858 + 3.1415926535897932384626433832795028842*I, 1
379: .2897619530652735025030086072395031017 + 0.E-47*I, -2.0109798024989157562122
380: 634098917610612 + 3.1415926535897932384626433832795028842*I, 24.412187746659
381: 095772127915595455170629 + 6.2831853071795864769252867665590057684*I, 30.337
382: 698160660239595315877930058147543 + 9.4247779607693797153879301498385086526*
383: I, -20.610866187462450639586440264933189691 + 9.4247779607693797153879301498
384: 385086526*I, 29.258282452818196217527894893424939793 + 9.4247779607693797153
385: 879301498385086526*I, -0.34328764427702709438988786673341921876 + 3.14159265
386: 35897932384626433832795028842*I, -14.550628376291080203941433635329724736 +
387: 0.E-47*I, 24.478366048541841504313284087778334822 + 3.1415926535897932384626
388: 433832795028842*I; -9.9277376722507613003718504524486100858 + 6.283185307179
389: 5864769252867665590057684*I, -1.2897619530652735025030086072395031017 + 9.42
390: 47779607693797153879301498385086526*I, 2.01097980249891575621226340989176106
391: 12 + 0.E-47*I, -24.412187746659095772127915595455170629 + 3.1415926535897932
392: 384626433832795028842*I, -30.337698160660239595315877930058147543 + 3.141592
393: 6535897932384626433832795028842*I, 20.610866187462450639586440264933189691 +
394: 3.1415926535897932384626433832795028842*I, -29.2582824528181962175278948934
395: 24939793 + 6.2831853071795864769252867665590057684*I, 0.34328764427702709438
396: 988786673341921876 + 0.E-48*I, 14.550628376291080203941433635329724736 + 3.1
397: 415926535897932384626433832795028842*I, -24.47836604854184150431328408777833
398: 4822 + 3.1415926535897932384626433832795028842*I], [[3, [-1, 1]~, 1, 1, [0,
399: 1]~], [3, [0, 1]~, 1, 1, [-1, 1]~], [5, [-2, 1]~, 1, 1, [1, 1]~], [5, [1, 1]
400: ~, 1, 1, [-2, 1]~], [11, [-2, 1]~, 1, 1, [1, 1]~], [11, [1, 1]~, 1, 1, [-2,
401: 1]~], [17, [-3, 1]~, 1, 1, [2, 1]~], [17, [2, 1]~, 1, 1, [-3, 1]~], [19, [-1
402: , 1]~, 1, 1, [0, 1]~], [19, [0, 1]~, 1, 1, [-1, 1]~]]~, [1, 3, 5, 2, 4, 6, 7
403: , 8, 10, 9], [x^2 - x - 57, [2, 0], 229, 1, [[1, -7.066372975210777963595931
404: 0246705326058; 1, 8.0663729752107779635959310246705326058], [1, 1; -7.066372
405: 9752107779635959310246705326058, 8.0663729752107779635959310246705326058], [
406: 2, 1.0000000000000000000000000000000000000; 1.000000000000000000000000000000
407: 0000000, 115.00000000000000000000000000000000000], [2, 1; 1, 115], [229, 114
408: ; 0, 1], [115, -1; -1, 2], [229, [114, 1]~]], [-7.06637297521077796359593102
409: 46705326058, 8.0663729752107779635959310246705326058], [1, x], [1, 0; 0, 1],
410: [1, 0, 0, 57; 0, 1, 1, 1]], [[3, [3], [[3, 2; 0, 1]]], 2.712465305184343974
411: 6808795106061300699, 0.8814422512654579369, [2, -1], [x + 7], 153], [Mat(1),
412: [[0, 0]], [[9.9277376722507613003718504524486100858 + 3.1415926535897932384
413: 626433832795028842*I, -9.9277376722507613003718504524486100858 + 6.283185307
414: 1795864769252867665590057684*I]]], [0, [Mat([[5, 1]~, 1])]]], [[[5, 3; 0, 1]
415: , [1, 0]], [8, [4, 2], [[2, 0]~, [-1, 1]~]], Mat([[5, [-2, 1]~, 1, 1, [1, 1]
416: ~], 1]), [[[[4], [[2, 0]~], [[2, 0]~], [[Mod(0, 2)]~], 1]], [[2], [[-1, 1]~]
417: , Mat(1)]], [1, 0; 0, 1]], [1], [1, -3, -6; 0, 0, 1; 0, 1, 0], [12, [12], [[
418: 3, 2; 0, 1]]], [[1/2, 0; 0, 0], [1, -1; 1, 1]]]
419: ? bnr=bnrclass(bnf,[[5,3;0,1],[1,0]],2)
420: [[Mat(3), Mat([1, 2, 1, 2, 1, 2, 1, 2, 1]), [-2.7124653051843439746808795106
421: 061300699 + 3.1415926535897932384626433832795028842*I; 2.7124653051843439746
422: 808795106061300699 - 6.2831853071795864769252867665590057684*I], [9.92773767
423: 22507613003718504524486100858 + 3.1415926535897932384626433832795028842*I, 1
424: .2897619530652735025030086072395031017 + 0.E-47*I, -2.0109798024989157562122
425: 634098917610612 + 3.1415926535897932384626433832795028842*I, 24.412187746659
426: 095772127915595455170629 + 6.2831853071795864769252867665590057684*I, 30.337
427: 698160660239595315877930058147543 + 9.4247779607693797153879301498385086526*
428: I, -20.610866187462450639586440264933189691 + 9.4247779607693797153879301498
429: 385086526*I, 29.258282452818196217527894893424939793 + 9.4247779607693797153
430: 879301498385086526*I, -0.34328764427702709438988786673341921876 + 3.14159265
431: 35897932384626433832795028842*I, -14.550628376291080203941433635329724736 +
432: 0.E-47*I, 24.478366048541841504313284087778334822 + 3.1415926535897932384626
433: 433832795028842*I; -9.9277376722507613003718504524486100858 + 6.283185307179
434: 5864769252867665590057684*I, -1.2897619530652735025030086072395031017 + 9.42
435: 47779607693797153879301498385086526*I, 2.01097980249891575621226340989176106
436: 12 + 0.E-47*I, -24.412187746659095772127915595455170629 + 3.1415926535897932
437: 384626433832795028842*I, -30.337698160660239595315877930058147543 + 3.141592
438: 6535897932384626433832795028842*I, 20.610866187462450639586440264933189691 +
439: 3.1415926535897932384626433832795028842*I, -29.2582824528181962175278948934
440: 24939793 + 6.2831853071795864769252867665590057684*I, 0.34328764427702709438
441: 988786673341921876 + 0.E-48*I, 14.550628376291080203941433635329724736 + 3.1
442: 415926535897932384626433832795028842*I, -24.47836604854184150431328408777833
443: 4822 + 3.1415926535897932384626433832795028842*I], [[3, [-1, 1]~, 1, 1, [0,
444: 1]~], [3, [0, 1]~, 1, 1, [-1, 1]~], [5, [-2, 1]~, 1, 1, [1, 1]~], [5, [1, 1]
445: ~, 1, 1, [-2, 1]~], [11, [-2, 1]~, 1, 1, [1, 1]~], [11, [1, 1]~, 1, 1, [-2,
446: 1]~], [17, [-3, 1]~, 1, 1, [2, 1]~], [17, [2, 1]~, 1, 1, [-3, 1]~], [19, [-1
447: , 1]~, 1, 1, [0, 1]~], [19, [0, 1]~, 1, 1, [-1, 1]~]]~, [1, 3, 5, 2, 4, 6, 7
448: , 8, 10, 9], [x^2 - x - 57, [2, 0], 229, 1, [[1, -7.066372975210777963595931
449: 0246705326058; 1, 8.0663729752107779635959310246705326058], [1, 1; -7.066372
450: 9752107779635959310246705326058, 8.0663729752107779635959310246705326058], [
451: 2, 1.0000000000000000000000000000000000000; 1.000000000000000000000000000000
452: 0000000, 115.00000000000000000000000000000000000], [2, 1; 1, 115], [229, 114
453: ; 0, 1], [115, -1; -1, 2], [229, [114, 1]~]], [-7.06637297521077796359593102
454: 46705326058, 8.0663729752107779635959310246705326058], [1, x], [1, 0; 0, 1],
455: [1, 0, 0, 57; 0, 1, 1, 1]], [[3, [3], [[3, 2; 0, 1]]], 2.712465305184343974
456: 6808795106061300699, 0.8814422512654579369, [2, -1], [x + 7], 153], [Mat(1),
457: [[0, 0]], [[9.9277376722507613003718504524486100858 + 3.1415926535897932384
458: 626433832795028842*I, -9.9277376722507613003718504524486100858 + 6.283185307
459: 1795864769252867665590057684*I]]], [0, [Mat([[5, 1]~, 1])]]], [[[5, 3; 0, 1]
460: , [1, 0]], [8, [4, 2], [[2, 0]~, [-1, 1]~]], Mat([[5, [-2, 1]~, 1, 1, [1, 1]
461: ~], 1]), [[[[4], [[2, 0]~], [[2, 0]~], [[Mod(0, 2)]~], 1]], [[2], [[-1, 1]~]
462: , Mat(1)]], [1, 0; 0, 1]], [1], [1, -3, -6; 0, 0, 1; 0, 1, 0], [12, [12], [[
463: 3, 2; 0, 1]]], [[1/2, 0; 0, 0], [1, -1; 1, 1]]]
464: ? rnfinit(nf2,x^5-x-2)
465: [x^5 - x - 2, [[1, 2], [0, 5]], [[49744, 0, 0; 0, 49744, 0; 0, 0, 49744], [3
466: 109, 0, 0]~], [1, 0, 0; 0, 1, 0; 0, 0, 1], [[[1, 1.2671683045421243172528914
467: 279776896412, 1.6057155120361619195949075151301679393, 2.0347118029638523119
468: 874445717108994866, 2.5783223055935536544757871909285592749; 1, 0.2609638803
469: 8645528500256735072673484811 + 1.1772261533941944394700286585617926513*I, -1
470: .3177592693689352747870763902256347904 + 0.614427010164338838041906608641467
471: 31824*I, -1.0672071180669977537495893497477340535 - 1.3909574189920019216524
472: 673160314582604*I, 1.3589689411882615753626439480614001936 - 1.6193337759893
473: 970298359887428575174472*I; 1, -0.89454803265751744362901306471557966872 + 0
474: .53414854617473272670874609150394379949*I, 0.5149015133508543149896226326605
475: 5082078 - 0.95564306225496055080453352211847466685*I, 0.04985121658507159775
476: 5867063892284310224 + 1.1299025160425089918993024639913611785*I, -0.64813009
477: 398503840260053754352567983115 - 0.98412411795664774269323431620030610541*I]
478: , [1, 1.2671683045421243172528914279776896412 + 0.E-38*I, 1.6057155120361619
479: 195949075151301679393 + 0.E-38*I, 2.0347118029638523119874445717108994866 +
480: 0.E-37*I, 2.5783223055935536544757871909285592749 + 0.E-37*I; 1, 0.260963880
481: 38645528500256735072673484811 - 1.1772261533941944394700286585617926513*I, -
482: 1.3177592693689352747870763902256347904 - 0.61442701016433883804190660864146
483: 731824*I, -1.0672071180669977537495893497477340535 + 1.390957418992001921652
484: 4673160314582604*I, 1.3589689411882615753626439480614001936 + 1.619333775989
485: 3970298359887428575174472*I; 1, 0.26096388038645528500256735072673484811 + 1
486: .1772261533941944394700286585617926513*I, -1.3177592693689352747870763902256
487: 347904 + 0.61442701016433883804190660864146731824*I, -1.06720711806699775374
488: 95893497477340535 - 1.3909574189920019216524673160314582604*I, 1.35896894118
489: 82615753626439480614001936 - 1.6193337759893970298359887428575174472*I; 1, -
490: 0.89454803265751744362901306471557966872 - 0.5341485461747327267087460915039
491: 4379949*I, 0.51490151335085431498962263266055082078 + 0.95564306225496055080
492: 453352211847466685*I, 0.049851216585071597755867063892284310224 - 1.12990251
493: 60425089918993024639913611785*I, -0.64813009398503840260053754352567983115 +
494: 0.98412411795664774269323431620030610541*I; 1, -0.8945480326575174436290130
495: 6471557966872 + 0.53414854617473272670874609150394379949*I, 0.51490151335085
496: 431498962263266055082078 - 0.95564306225496055080453352211847466685*I, 0.049
497: 851216585071597755867063892284310224 + 1.12990251604250899189930246399136117
498: 85*I, -0.64813009398503840260053754352567983115 - 0.984124117956647742693234
499: 31620030610541*I]], [[1, 2, 2; 1.2671683045421243172528914279776896412, 0.52
500: 192776077291057000513470145346969622 - 2.35445230678838887894005731712358530
501: 26*I, -1.7890960653150348872580261294311593374 - 1.0682970923494654534174921
502: 830078875989*I; 1.6057155120361619195949075151301679393, -2.6355185387378705
503: 495741527804512695809 - 1.2288540203286776760838132172829346364*I, 1.0298030
504: 267017086299792452653211016415 + 1.9112861245099211016090670442369493337*I;
505: 2.0347118029638523119874445717108994866, -2.13441423613399550749917869949546
506: 81070 + 2.7819148379840038433049346320629165208*I, 0.09970243317014319551173
507: 4127784568620449 - 2.2598050320850179837986049279827223571*I; 2.578322305593
508: 5536544757871909285592749, 2.7179378823765231507252878961228003872 + 3.23866
509: 75519787940596719774857150348944*I, -1.2962601879700768052010750870513596623
510: + 1.9682482359132954853864686324006122108*I], [1, 1, 1, 1, 1; 1.26716830454
511: 21243172528914279776896412 + 0.E-38*I, 0.26096388038645528500256735072673484
512: 811 + 1.1772261533941944394700286585617926513*I, 0.2609638803864552850025673
513: 5072673484811 - 1.1772261533941944394700286585617926513*I, -0.89454803265751
514: 744362901306471557966872 + 0.53414854617473272670874609150394379949*I, -0.89
515: 454803265751744362901306471557966872 - 0.53414854617473272670874609150394379
516: 949*I; 1.6057155120361619195949075151301679393 + 0.E-38*I, -1.31775926936893
517: 52747870763902256347904 + 0.61442701016433883804190660864146731824*I, -1.317
518: 7592693689352747870763902256347904 - 0.6144270101643388380419066086414673182
519: 4*I, 0.51490151335085431498962263266055082078 - 0.95564306225496055080453352
520: 211847466685*I, 0.51490151335085431498962263266055082078 + 0.955643062254960
521: 55080453352211847466685*I; 2.0347118029638523119874445717108994866 + 0.E-37*
522: I, -1.0672071180669977537495893497477340535 - 1.3909574189920019216524673160
523: 314582604*I, -1.0672071180669977537495893497477340535 + 1.390957418992001921
524: 6524673160314582604*I, 0.049851216585071597755867063892284310224 + 1.1299025
525: 160425089918993024639913611785*I, 0.049851216585071597755867063892284310224
526: - 1.1299025160425089918993024639913611785*I; 2.57832230559355365447578719092
527: 85592749 + 0.E-37*I, 1.3589689411882615753626439480614001936 - 1.61933377598
528: 93970298359887428575174472*I, 1.3589689411882615753626439480614001936 + 1.61
529: 93337759893970298359887428575174472*I, -0.6481300939850384026005375435256798
530: 3115 - 0.98412411795664774269323431620030610541*I, -0.6481300939850384026005
531: 3754352567983115 + 0.98412411795664774269323431620030610541*I]], [[5, -5.877
532: 47175 E-39 + 3.4227493991378543323575495001314729016*I, 2.35098870 E-38 - 0.
533: 68243210418124342552525382695401469720*I, -2.35098870 E-38 - 0.5221098058989
534: 8585950632970408019416371*I, 3.9999999999999999999999999999999999999 - 5.206
535: 9157878920895450584461181156471052*I; -5.87747175 E-39 - 3.42274939913785433
536: 23575495001314729016*I, 6.6847043424634879841147654217963674264 - 5.87747175
537: E-39*I, 0.85145677340721376574333983502938573598 + 4.5829573180978430291541
538: 592600601794652*I, -0.13574266252716976137461193821267520737 - 0.28805108544
539: 025772361738936467682050391*I, 0.27203784387468568916539788233281013320 - 1.
540: 5917147279942947718965650859986677247*I; 2.35098870 E-38 + 0.682432104181243
541: 42552525382695401469720*I, 0.85145677340721376574333983502938573598 - 4.5829
542: 573180978430291541592600601794652*I, 9.1630968530221077951281598310681467898
543: + 0.E-38*I, 2.2622987652095629453403849736225691490 + 6.2361927913558506765
544: 724047063180706869*I, -0.21796409886496632254445901043974770643 + 0.34559368
545: 931063215686158939748833975810*I; -2.35098870 E-38 + 0.522109805898985859506
546: 32970408019416371*I, -0.13574266252716976137461193821267520737 + 0.288051085
547: 44025772361738936467682050392*I, 2.2622987652095629453403849736225691490 - 6
548: .2361927913558506765724047063180706869*I, 12.8457689488323355118826969393806
549: 96155 + 1.17549435 E-38*I, 4.5618400502378124720913214622468855074 + 8.60339
550: 30051068500425218923146793019614*I; 3.9999999999999999999999999999999999999
551: + 5.2069157878920895450584461181156471052*I, 0.27203784387468568916539788233
552: 281013320 + 1.5917147279942947718965650859986677247*I, -0.217964098864966322
553: 54445901043974770643 - 0.34559368931063215686158939748833975810*I, 4.5618400
554: 502378124720913214622468855074 - 8.6033930051068500425218923146793019615*I,
555: 18.362968630416114402425299186062892646 + 5.87747175 E-39*I], [5, -1.1754943
556: 5 E-38 + 0.E-38*I, 2.35098870 E-38 + 0.E-38*I, -1.76324152 E-38 + 0.E-38*I,
557: 3.9999999999999999999999999999999999998 + 0.E-38*I; -1.17549435 E-38 + 0.E-3
558: 8*I, 6.6847043424634879841147654217963674264 - 5.87747175 E-39*I, 0.85145677
559: 340721376574333983502938573597 + 5.87747175 E-39*I, -0.135742662527169761374
560: 61193821267520737 + 5.87747175 E-39*I, 0.27203784387468568916539788233281013
561: 314 - 5.87747175 E-39*I; 2.35098870 E-38 + 0.E-38*I, 0.851456773407213765743
562: 33983502938573597 + 5.87747175 E-39*I, 9.16309685302210779512815983106814678
563: 98 + 0.E-38*I, 2.2622987652095629453403849736225691490 + 2.35098870 E-38*I,
564: -0.21796409886496632254445901043974770651 + 0.E-38*I; -1.76324152 E-38 + 0.E
565: -38*I, -0.13574266252716976137461193821267520737 + 5.87747175 E-39*I, 2.2622
566: 987652095629453403849736225691490 + 2.35098870 E-38*I, 12.845768948832335511
567: 882696939380696155 + 0.E-37*I, 4.5618400502378124720913214622468855073 - 3.5
568: 2648305 E-38*I; 3.9999999999999999999999999999999999998 + 0.E-38*I, 0.272037
569: 84387468568916539788233281013314 - 5.87747175 E-39*I, -0.2179640988649663225
570: 4445901043974770651 + 0.E-38*I, 4.5618400502378124720913214622468855073 - 3.
571: 52648305 E-38*I, 18.362968630416114402425299186062892646 + 0.E-37*I]], [Mod(
572: 5, y^3 - y - 1), 0, 0, 0, Mod(4, y^3 - y - 1); 0, 0, 0, Mod(4, y^3 - y - 1),
573: Mod(10, y^3 - y - 1); 0, 0, Mod(4, y^3 - y - 1), Mod(10, y^3 - y - 1), 0; 0
574: , Mod(4, y^3 - y - 1), Mod(10, y^3 - y - 1), 0, 0; Mod(4, y^3 - y - 1), Mod(
575: 10, y^3 - y - 1), 0, 0, Mod(4, y^3 - y - 1)], [;], [;], [;]], [[1.2671683045
576: 421243172528914279776896412, 0.26096388038645528500256735072673484811 + 1.17
577: 72261533941944394700286585617926513*I, -0.8945480326575174436290130647155796
578: 6872 + 0.53414854617473272670874609150394379949*I], [1.267168304542124317252
579: 8914279776896412 + 0.E-38*I, 0.26096388038645528500256735072673484811 - 1.17
580: 72261533941944394700286585617926513*I, 0.26096388038645528500256735072673484
581: 811 + 1.1772261533941944394700286585617926513*I, -0.894548032657517443629013
582: 06471557966872 - 0.53414854617473272670874609150394379949*I, -0.894548032657
583: 51744362901306471557966872 + 0.53414854617473272670874609150394379949*I]~],
584: [[Mod(1, y^3 - y - 1), Mod(1, y^3 - y - 1)*x, Mod(1, y^3 - y - 1)*x^2, Mod(1
585: , y^3 - y - 1)*x^3, Mod(1, y^3 - y - 1)*x^4], [[1, 0, 0; 0, 1, 0; 0, 0, 1],
586: [1, 0, 0; 0, 1, 0; 0, 0, 1], [1, 0, 0; 0, 1, 0; 0, 0, 1], [1, 0, 0; 0, 1, 0;
587: 0, 0, 1], [1, 0, 0; 0, 1, 0; 0, 0, 1]]], [Mod(1, y^3 - y - 1), 0, 0, 0, 0;
588: 0, Mod(1, y^3 - y - 1), 0, 0, 0; 0, 0, Mod(1, y^3 - y - 1), 0, 0; 0, 0, 0, M
589: od(1, y^3 - y - 1), 0; 0, 0, 0, 0, Mod(1, y^3 - y - 1)], [], [y^3 - y - 1, [
590: 1, 1], -23, 1, [[1, 1.3247179572447460259609088544780973407, 1.7548776662466
591: 927600495088963585286918; 1, -0.66235897862237301298045442723904867036 + 0.5
592: 6227951206230124389918214490937306149*I, 0.122561166876653619975245551820735
593: 65405 - 0.74486176661974423659317042860439236724*I], [1, 2; 1.32471795724474
594: 60259609088544780973407, -1.3247179572447460259609088544780973407 - 1.124559
595: 0241246024877983642898187461229*I; 1.7548776662466927600495088963585286918,
596: 0.24512233375330723995049110364147130810 + 1.4897235332394884731863408572087
597: 847344*I], [3, 0.E-96, 2.0000000000000000000000000000000000000; 0.E-96, 3.26
598: 46329987400782801485266890755860756, 1.3247179572447460259609088544780973407
599: ; 2.0000000000000000000000000000000000000, 1.3247179572447460259609088544780
600: 973407, 4.2192762054875453178332176670757633303], [3, 0, 2; 0, 2, 3; 2, 3, 2
601: ], [23, 13, 15; 0, 1, 0; 0, 0, 1], [-5, 6, -4; 6, 2, -9; -4, -9, 6], [23, [7
602: , 10, 1]~]], [1.3247179572447460259609088544780973407, -0.662358978622373012
603: 98045442723904867036 + 0.56227951206230124389918214490937306149*I], [1, y, y
604: ^2], [1, 0, 0; 0, 1, 0; 0, 0, 1], [1, 0, 0, 0, 0, 1, 0, 1, 0; 0, 1, 0, 1, 0,
605: 1, 0, 1, 1; 0, 0, 1, 0, 1, 0, 1, 0, 1]], [x^15 - 5*x^13 + 5*x^12 + 7*x^11 -
606: 26*x^10 - 5*x^9 + 45*x^8 + 158*x^7 - 98*x^6 + 110*x^5 - 190*x^4 + 189*x^3 +
607: 144*x^2 + 25*x + 1, Mod(39516536165538345/83718587879473471*x^14 - 65005124
608: 76832995/83718587879473471*x^13 - 196215472046117185/83718587879473471*x^12
609: + 229902227480108910/83718587879473471*x^11 + 237380704030959181/83718587879
610: 473471*x^10 - 1064931988160773805/83718587879473471*x^9 - 20657086671714300/
611: 83718587879473471*x^8 + 1772885205999206010/83718587879473471*x^7 + 59520332
612: 17241102348/83718587879473471*x^6 - 4838840187320655696/83718587879473471*x^
613: 5 + 5180390720553188700/83718587879473471*x^4 - 8374015687535120430/83718587
614: 879473471*x^3 + 8907744727915040221/83718587879473471*x^2 + 4155976664123434
615: 381/83718587879473471*x + 318920215718580450/83718587879473471, x^15 - 5*x^1
616: 3 + 5*x^12 + 7*x^11 - 26*x^10 - 5*x^9 + 45*x^8 + 158*x^7 - 98*x^6 + 110*x^5
617: - 190*x^4 + 189*x^3 + 144*x^2 + 25*x + 1), -1, [1, x, x^2, x^3, x^4, x^5, x^
618: 6, x^7, x^8, x^9, x^10, x^11, x^12, x^13, 1/83718587879473471*x^14 - 2052846
619: 3024680133/83718587879473471*x^13 - 4742392948888610/83718587879473471*x^12
620: - 9983523646123358/83718587879473471*x^11 + 40898955597139011/83718587879473
621: 471*x^10 + 29412692423971937/83718587879473471*x^9 - 5017479463612351/837185
622: 87879473471*x^8 + 41014993230075066/83718587879473471*x^7 - 2712810874903165
623: /83718587879473471*x^6 + 20152905879672878/83718587879473471*x^5 + 959164315
624: 1927789/83718587879473471*x^4 - 8471905745957397/83718587879473471*x^3 - 133
625: 95753879413605/83718587879473471*x^2 + 27623037732247492/83718587879473471*x
626: + 26306699661480593/83718587879473471], [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0
627: , 0, 0, -26306699661480593; 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -27623
628: 037732247492; 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 13395753879413605; 0
629: , 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8471905745957397; 0, 0, 0, 0, 1, 0,
630: 0, 0, 0, 0, 0, 0, 0, 0, -9591643151927789; 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0,
631: 0, 0, 0, -20152905879672878; 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 2712
632: 810874903165; 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, -41014993230075066;
633: 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 5017479463612351; 0, 0, 0, 0, 0, 0
634: , 0, 0, 0, 1, 0, 0, 0, 0, -29412692423971937; 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
635: 1, 0, 0, 0, -40898955597139011; 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 99
636: 83523646123358; 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 4742392948888610;
637: 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 20528463024680133; 0, 0, 0, 0, 0,
638: 0, 0, 0, 0, 0, 0, 0, 0, 0, 83718587879473471]]]
639: ? bnfcertify(bnf)
640: 1
641: ? setrand(1);bnfclassunit(x^4-7,2,[0.2,0.2])
642:
643: [x^4 - 7]
644:
645: [[2, 1]]
646:
647: [[-87808, 1]]
648:
649: [[1, x, x^2, x^3]]
650:
651: [[2, [2], [[3, 1, 2, 1; 0, 1, 0, 0; 0, 0, 1, 0; 0, 0, 0, 1]]]]
652:
653: [14.229975145405511722395637833443108790]
654:
655: [1.121117107152756229]
656:
657: ? setrand(1);bnfclassunit(x^2-x-100000)
658: *** Warning: insufficient precision for fundamental units, not given.
659:
660: [x^2 - x - 100000]
661:
662: [[2, 0]]
663:
664: [[400001, 1]]
665:
666: [[1, x]]
667:
668: [[5, [5], [[2, 1; 0, 1]]]]
669:
670: [129.82045011403975460991182396195022419]
671:
672: [0.9876536979069047239]
673:
674: [[2, -1]]
675:
676: [[;]]
677:
678: [-27]
679:
680: ? setrand(1);bnfclassunit(x^2-x-100000,1)
681:
682: [x^2 - x - 100000]
683:
684: [[2, 0]]
685:
686: [[400001, 1]]
687:
688: [[1, x]]
689:
690: [[5, [5], [[2, 1; 0, 1]]]]
691:
692: [129.82045011403975460991182396195022419]
693:
694: [0.9876536979069047239]
695:
696: [[2, -1]]
697:
698: [[379554884019013781006303254896369154068336082609238336*x + 119836165644250
699: 789990462835950022871665178127611316131167]]
700:
701: [26]
702:
703: ? setrand(1);bnfclassunit(x^4+24*x^2+585*x+1791,,[0.1,0.1])
704:
705: [x^4 + 24*x^2 + 585*x + 1791]
706:
707: [[0, 2]]
708:
709: [[18981, 3087]]
710:
711: [[1, x, 1/3*x^2, 1/1029*x^3 + 33/343*x^2 - 155/343*x - 58/343]]
712:
713: [[4, [4], [[7, 6, 2, 4; 0, 1, 0, 0; 0, 0, 1, 0; 0, 0, 0, 1]]]]
714:
715: [3.7941269688216589341408274220859400302]
716:
717: [0.8826018286655581306]
718:
719: [[6, 10/1029*x^3 - 13/343*x^2 + 165/343*x + 1478/343]]
720:
721: [[4/1029*x^3 + 53/1029*x^2 + 66/343*x + 111/343]]
722:
723: [151]
724:
725: ? setrand(1);bnfclgp(17)
726: [1, [], []]
727: ? setrand(1);bnfclgp(-31)
728: [3, [3], [Qfb(2, 1, 4)]]
729: ? setrand(1);bnfclgp(x^4+24*x^2+585*x+1791)
730: [4, [4], [[7, 5, 1, 0; 0, 1, 0, 0; 0, 0, 1, 0; 0, 0, 0, 1]]]
731: ? bnrconductor(bnf,[[25,13;0,1],[1,1]])
732: [[5, 3; 0, 1], [1, 0]]
733: ? bnrconductorofchar(bnr,[2])
734: [[5, 3; 0, 1], [0, 0]]
735: ? bnfisprincipal(bnf,[5,1;0,1],0)
736: [1]~
737: ? bnfisprincipal(bnf,[5,1;0,1])
738: [[1]~, [-2, -1/3]~, 151]
739: ? bnfisunit(bnf,Mod(3405*x-27466,x^2-x-57))
740: [-4, Mod(1, 2)]~
741: ? \p19
742: realprecision = 19 significant digits
743: ? bnfmake(sbnf)
744: [Mat(2), Mat([0, 1, 1, 1, 1, 0, 1, 1]), [1.173637103435061715 + 3.1415926535
745: 89793238*I, -4.562279014988837901 + 3.141592653589793238*I; -2.6335434327389
746: 76049 + 3.141592653589793238*I, 1.420330600779487357 + 3.141592653589793238*
747: I; 1.459906329303914334, 3.141948414209350543], [1.246346989334819161 + 3.14
748: 1592653589793238*I, -1.990056445584799713 + 3.141592653589793238*I, 0.540400
749: 6376129469727 + 3.141592653589793238*I, -0.6926391142471042845 + 3.141592653
750: 589793238*I, 0.E-96, 0.3677262014027817705 + 3.141592653589793238*I, 0.00437
751: 5616572659815402 + 3.141592653589793238*I, -0.8305625946607188639, -1.977791
752: 147836553953 + 3.141592653589793238*I; 0.6716827432867392935 + 3.14159265358
753: 9793238*I, 0.5379005671092853266, -0.8333219883742404172 + 3.141592653589793
754: 238*I, -0.2461086674077943078, 0.E-96, 0.9729063188316092378, -0.87383180430
755: 71131265, -1.552661549868775853 + 3.141592653589793238*I, 0.5774919091398324
756: 092 + 3.141592653589793238*I; -1.918029732621558454, 1.452155878475514386, 0
757: .2929213507612934444, 0.9387477816548985923, 0.E-96, -1.340632520234391008,
758: 0.8694561877344533111, 2.383224144529494717 + 3.141592653589793238*I, 1.4002
759: 99238696721544 + 3.141592653589793238*I], [[3, [-1, 1, 0]~, 1, 1, [1, 0, 1]~
760: ], [5, [3, 1, 0]~, 1, 1, [-2, 1, 1]~], [5, [-1, 1, 0]~, 1, 1, [1, 0, 1]~], [
761: 5, [2, 1, 0]~, 1, 1, [2, 2, 1]~], [3, [1, 0, 1]~, 1, 2, [-1, 1, 0]~], [23, [
762: -10, 1, 0]~, 1, 1, [7, 9, 1]~], [11, [1, 1, 0]~, 1, 1, [-1, -2, 1]~], [13, [
763: 19, 1, 0]~, 1, 1, [2, 6, 1]~], [19, [-6, 1, 0]~, 1, 1, [-3, 5, 1]~]]~, [1, 2
764: , 3, 4, 5, 6, 7, 8, 9]~, [x^3 - x^2 - 14*x - 1, [3, 0], 10889, 1, [[1, -3.23
765: 3732695981516673, 10.45702714905988813; 1, -0.07182350902743636344, 0.005158
766: 616449014232794; 1, 4.305556205008953036, 18.53781423449109762], [1, 1, 1; -
767: 3.233732695981516673, -0.07182350902743636344, 4.305556205008953036; 10.4570
768: 2714905988813, 0.005158616449014232794, 18.53781423449109762], [3, 1.0000000
769: 00000000000, 29.00000000000000000; 1.000000000000000000, 29.0000000000000000
770: 0, 46.00000000000000000; 29.00000000000000000, 46.00000000000000000, 453.000
771: 0000000000000], [3, 1, 29; 1, 29, 46; 29, 46, 453], [10889, 5698, 3794; 0, 1
772: , 0; 0, 0, 1], [11021, 881, -795; 881, 518, -109; -795, -109, 86], [10889, [
773: 1890, 5190, 1]~]], [-3.233732695981516673, -0.07182350902743636344, 4.305556
774: 205008953036], [1, x, x^2], [1, 0, 0; 0, 1, 0; 0, 0, 1], [1, 0, 0, 0, 0, 1,
775: 0, 1, 1; 0, 1, 0, 1, 0, 14, 0, 14, 15; 0, 0, 1, 0, 1, 1, 1, 1, 15]], [[2, [2
776: ], [[3, 2, 2; 0, 1, 0; 0, 0, 1]]], 10.34800724602767998, 1.00000000000000000
777: 0, [2, -1], [x, x^2 + 2*x - 4], 1000], [Mat(1), [[0, 0, 0]], [[1.24634698933
778: 4819161 + 3.141592653589793238*I, 0.6716827432867392935 + 3.1415926535897932
779: 38*I, -1.918029732621558454]]], [-4, 3, -1, 2, 3, 11, 1, -1, -7; 1, 1, 1, 1,
780: 0, 2, 1, -4, -2; 0, 0, 0, 0, 0, -1, 0, -1, 0]]
781: ? \p38
782: realprecision = 38 significant digits
783: ? bnfnarrow(bnf)
784: [3, [3], [[3, 2; 0, 1]]]
785: ? bnfreg(x^2-x-57)
786: 2.7124653051843439746808795106061300699
787: ? bnfsignunit(bnf)
788:
789: [-1]
790:
791: [1]
792:
793: ? bnfunit(bnf)
794: [[x + 7], 153]
795: ? bnrclass(bnf,[[5,3;0,1],[1,0]])
796: [12, [12], [[3, 2; 0, 1]]]
797: ? bnr2=bnrclass(bnf,[[25,13;0,1],[1,1]],2)
798: [[Mat(3), Mat([1, 2, 1, 2, 1, 2, 1, 2, 1]), [-2.7124653051843439746808795106
799: 061300699 + 3.1415926535897932384626433832795028842*I; 2.7124653051843439746
800: 808795106061300699 - 6.2831853071795864769252867665590057684*I], [9.92773767
801: 22507613003718504524486100858 + 3.1415926535897932384626433832795028842*I, 1
802: .2897619530652735025030086072395031017 + 0.E-47*I, -2.0109798024989157562122
803: 634098917610612 + 3.1415926535897932384626433832795028842*I, 24.412187746659
804: 095772127915595455170629 + 6.2831853071795864769252867665590057684*I, 30.337
805: 698160660239595315877930058147543 + 9.4247779607693797153879301498385086526*
806: I, -20.610866187462450639586440264933189691 + 9.4247779607693797153879301498
807: 385086526*I, 29.258282452818196217527894893424939793 + 9.4247779607693797153
808: 879301498385086526*I, -0.34328764427702709438988786673341921876 + 3.14159265
809: 35897932384626433832795028842*I, -14.550628376291080203941433635329724736 +
810: 0.E-47*I, 24.478366048541841504313284087778334822 + 3.1415926535897932384626
811: 433832795028842*I; -9.9277376722507613003718504524486100858 + 6.283185307179
812: 5864769252867665590057684*I, -1.2897619530652735025030086072395031017 + 9.42
813: 47779607693797153879301498385086526*I, 2.01097980249891575621226340989176106
814: 12 + 0.E-47*I, -24.412187746659095772127915595455170629 + 3.1415926535897932
815: 384626433832795028842*I, -30.337698160660239595315877930058147543 + 3.141592
816: 6535897932384626433832795028842*I, 20.610866187462450639586440264933189691 +
817: 3.1415926535897932384626433832795028842*I, -29.2582824528181962175278948934
818: 24939793 + 6.2831853071795864769252867665590057684*I, 0.34328764427702709438
819: 988786673341921876 + 0.E-48*I, 14.550628376291080203941433635329724736 + 3.1
820: 415926535897932384626433832795028842*I, -24.47836604854184150431328408777833
821: 4822 + 3.1415926535897932384626433832795028842*I], [[3, [-1, 1]~, 1, 1, [0,
822: 1]~], [3, [0, 1]~, 1, 1, [-1, 1]~], [5, [-2, 1]~, 1, 1, [1, 1]~], [5, [1, 1]
823: ~, 1, 1, [-2, 1]~], [11, [-2, 1]~, 1, 1, [1, 1]~], [11, [1, 1]~, 1, 1, [-2,
824: 1]~], [17, [-3, 1]~, 1, 1, [2, 1]~], [17, [2, 1]~, 1, 1, [-3, 1]~], [19, [-1
825: , 1]~, 1, 1, [0, 1]~], [19, [0, 1]~, 1, 1, [-1, 1]~]]~, [1, 3, 5, 2, 4, 6, 7
826: , 8, 10, 9], [x^2 - x - 57, [2, 0], 229, 1, [[1, -7.066372975210777963595931
827: 0246705326058; 1, 8.0663729752107779635959310246705326058], [1, 1; -7.066372
828: 9752107779635959310246705326058, 8.0663729752107779635959310246705326058], [
829: 2, 1.0000000000000000000000000000000000000; 1.000000000000000000000000000000
830: 0000000, 115.00000000000000000000000000000000000], [2, 1; 1, 115], [229, 114
831: ; 0, 1], [115, -1; -1, 2], [229, [114, 1]~]], [-7.06637297521077796359593102
832: 46705326058, 8.0663729752107779635959310246705326058], [1, x], [1, 0; 0, 1],
833: [1, 0, 0, 57; 0, 1, 1, 1]], [[3, [3], [[3, 2; 0, 1]]], 2.712465305184343974
834: 6808795106061300699, 0.8814422512654579369, [2, -1], [x + 7], 153], [Mat(1),
835: [[0, 0]], [[9.9277376722507613003718504524486100858 + 3.1415926535897932384
836: 626433832795028842*I, -9.9277376722507613003718504524486100858 + 6.283185307
837: 1795864769252867665590057684*I]]], [0, [Mat([[5, 1]~, 1])]]], [[[25, 13; 0,
838: 1], [1, 1]], [80, [20, 2, 2], [[2, 0]~, [0, -2]~, [2, 2]~]], Mat([[5, [-2, 1
839: ]~, 1, 1, [1, 1]~], 2]), [[[[4], [[2, 0]~], [[2, 0]~], [[Mod(0, 2), Mod(0, 2
840: )]~], 1], [[5], [[6, 0]~], [[6, 0]~], [[Mod(0, 2), Mod(0, 2)]~], Mat([1/5, -
841: 13/5])]], [[2, 2], [[0, -2]~, [2, 2]~], [0, 1; 1, 0]]], [1, -12, 0, 0; 0, 0,
842: 1, 0; 0, 0, 0, 1]], [1], [1, -3, 0, -6; 0, 0, 1, 0; 0, 0, 0, 1; 0, 1, 0, 0]
843: , [12, [12], [[3, 2; 0, 1]]], [[1, 9, -18; -1/2, -5, 10], [-2, 0; 0, 10]]]
844: ? bnrclassno(bnf,[[5,3;0,1],[1,0]])
845: 12
846: ? lu=ideallist(bnf,55,3);
847: ? bnrclassnolist(bnf,lu)
848: [[3], [], [3, 3], [3], [6, 6], [], [], [], [3, 3, 3], [], [3, 3], [3, 3], []
849: , [], [12, 6, 6, 12], [3], [3, 3], [], [9, 9], [6, 6], [], [], [], [], [6, 1
850: 2, 6], [], [3, 3, 3, 3], [], [], [], [], [], [3, 6, 6, 3], [], [], [9, 3, 9]
851: , [6, 6], [], [], [], [], [], [3, 3], [3, 3], [12, 12, 6, 6, 12, 12], [], []
852: , [6, 6], [9], [], [3, 3, 3, 3], [], [3, 3], [], [6, 12, 12, 6]]
853: ? bnrdisc(bnr,Mat(6))
854: [12, 12, 18026977100265125]
855: ? bnrdisc(bnr)
856: [24, 12, 40621487921685401825918161408203125]
857: ? bnrdisc(bnr2,,,2)
858: 0
859: ? bnrdisc(bnr,Mat(6),,1)
860: [6, 2, [125, 13; 0, 1]]
861: ? bnrdisc(bnr,,,1)
862: [12, 1, [1953125, 1160888; 0, 1]]
863: ? bnrdisc(bnr2,,,3)
864: 0
865: ? bnrdisclist(bnf,lu)
866: [[[6, 6, Mat([229, 3])]], [], [[], []], [[]], [[12, 12, [5, 3; 229, 6]], [12
867: , 12, [5, 3; 229, 6]]], [], [], [], [[], [], []], [], [[], []], [[], []], []
868: , [], [[24, 24, [3, 6; 5, 9; 229, 12]], [], [], [24, 24, [3, 6; 5, 9; 229, 1
869: 2]]], [[]], [[], []], [], [[18, 18, [19, 6; 229, 9]], [18, 18, [19, 6; 229,
870: 9]]], [[], []], [], [], [], [], [[], [24, 24, [5, 12; 229, 12]], []], [], [[
871: ], [], [], []], [], [], [], [], [], [[], [12, 12, [3, 3; 11, 3; 229, 6]], [1
872: 2, 12, [3, 3; 11, 3; 229, 6]], []], [], [], [[18, 18, [2, 12; 3, 12; 229, 9]
873: ], [], [18, 18, [2, 12; 3, 12; 229, 9]]], [[12, 12, [37, 3; 229, 6]], [12, 1
874: 2, [37, 3; 229, 6]]], [], [], [], [], [], [[], []], [[], []], [[], [], [], [
875: ], [], []], [], [], [[12, 12, [2, 12; 3, 3; 229, 6]], [12, 12, [2, 12; 3, 3;
876: 229, 6]]], [[18, 18, [7, 12; 229, 9]]], [], [[], [], [], []], [], [[], []],
877: [], [[], [24, 24, [5, 9; 11, 6; 229, 12]], [24, 24, [5, 9; 11, 6; 229, 12]]
878: , []]]
879: ? bnrdisclist(bnf,20,,1)
880: [[[[matrix(0,2), [[6, 6, Mat([229, 3])], [0, 0, 0], [0, 0, 0], [0, 0, 0]]]],
881: [], [[Mat([12, 1]), [[0, 0, 0], [0, 0, 0], [0, 0, 0], [12, 0, [3, 3; 229, 6
882: ]]]], [Mat([13, 1]), [[0, 0, 0], [0, 0, 0], [12, 6, [-1, 1; 3, 3; 229, 6]],
883: [0, 0, 0]]]], [[Mat([10, 1]), [[0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0]]]]
884: , [[Mat([20, 1]), [[12, 12, [5, 3; 229, 6]], [0, 0, 0], [0, 0, 0], [24, 0, [
885: 5, 9; 229, 12]]]], [Mat([21, 1]), [[12, 12, [5, 3; 229, 6]], [0, 0, 0], [24,
886: 12, [5, 9; 229, 12]], [0, 0, 0]]]], [], [], [], [[Mat([12, 2]), [[0, 0, 0],
887: [0, 0, 0], [0, 0, 0], [0, 0, 0]]], [[12, 1; 13, 1], [[0, 0, 0], [12, 6, [-1
888: , 1; 3, 6; 229, 6]], [0, 0, 0], [24, 0, [3, 12; 229, 12]]]], [Mat([13, 2]),
889: [[0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0]]]], [], [[Mat([44, 1]), [[0, 0,
890: 0], [0, 0, 0], [12, 6, [-1, 1; 11, 3; 229, 6]], [0, 0, 0]]], [Mat([45, 1]),
891: [[0, 0, 0], [0, 0, 0], [0, 0, 0], [12, 0, [11, 3; 229, 6]]]]], [[[10, 1; 12,
892: 1], [[0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0]]], [[10, 1; 13, 1], [[0, 0,
893: 0], [0, 0, 0], [0, 0, 0], [0, 0, 0]]]], [], [], [[[12, 1; 20, 1], [[24, 24,
894: [3, 6; 5, 9; 229, 12]], [0, 0, 0], [0, 0, 0], [48, 0, [3, 12; 5, 18; 229, 2
895: 4]]]], [[13, 1; 20, 1], [[0, 0, 0], [24, 12, [3, 6; 5, 9; 229, 12]], [24, 12
896: , [3, 6; 5, 6; 229, 12]], [48, 0, [3, 12; 5, 18; 229, 24]]]], [[12, 1; 21, 1
897: ], [[0, 0, 0], [24, 12, [3, 6; 5, 9; 229, 12]], [0, 0, 0], [48, 0, [3, 12; 5
898: , 18; 229, 24]]]], [[13, 1; 21, 1], [[24, 24, [3, 6; 5, 9; 229, 12]], [0, 0,
899: 0], [48, 24, [3, 12; 5, 18; 229, 24]], [0, 0, 0]]]], [[Mat([10, 2]), [[0, 0
900: , 0], [12, 6, [-1, 1; 2, 12; 229, 6]], [12, 6, [-1, 1; 2, 12; 229, 6]], [24,
901: 0, [2, 36; 229, 12]]]]], [[Mat([68, 1]), [[0, 0, 0], [12, 6, [-1, 1; 17, 3;
902: 229, 6]], [0, 0, 0], [0, 0, 0]]], [Mat([69, 1]), [[0, 0, 0], [12, 6, [-1, 1
903: ; 17, 3; 229, 6]], [0, 0, 0], [0, 0, 0]]]], [], [[Mat([76, 1]), [[18, 18, [1
904: 9, 6; 229, 9]], [0, 0, 0], [0, 0, 0], [36, 0, [19, 15; 229, 18]]]], [Mat([77
905: , 1]), [[18, 18, [19, 6; 229, 9]], [0, 0, 0], [36, 18, [-1, 1; 19, 15; 229,
906: 18]], [0, 0, 0]]]], [[[10, 1; 20, 1], [[0, 0, 0], [0, 0, 0], [0, 0, 0], [0,
907: 0, 0]]], [[10, 1; 21, 1], [[0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0]]]]]]
908: ? bnrisprincipal(bnr,idealprimedec(bnf,7)[1])
909: [[9]~, [-2170/6561, -931/19683]~, 192]
910: ? dirzetak(nf4,30)
911: [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,
912: 0, 1, 0, 1, 0]
913: ? factornf(x^3+x^2-2*x-1,t^3+t^2-2*t-1)
914:
915: [Mod(1, t^3 + t^2 - 2*t - 1)*x + Mod(-t, t^3 + t^2 - 2*t - 1) 1]
916:
917: [Mod(1, t^3 + t^2 - 2*t - 1)*x + Mod(-t^2 + 2, t^3 + t^2 - 2*t - 1) 1]
918:
919: [Mod(1, t^3 + t^2 - 2*t - 1)*x + Mod(t^2 + t - 1, t^3 + t^2 - 2*t - 1) 1]
920:
921: ? vp=idealprimedec(nf,3)[1]
922: [3, [1, 1, 0, 0, 0]~, 1, 1, [1, -1, -1, 0, 0]~]
923: ? idx=idealmul(nf,matid(5),vp)
924:
925: [3 1 2 2 2]
926:
927: [0 1 0 0 0]
928:
929: [0 0 1 0 0]
930:
931: [0 0 0 1 0]
932:
933: [0 0 0 0 1]
934:
935: ? idealinv(nf,idx)
936:
937: [1 0 2/3 0 0]
938:
939: [0 1 1/3 0 0]
940:
941: [0 0 1/3 0 0]
942:
943: [0 0 0 1 0]
944:
945: [0 0 0 0 1]
946:
947: ? idy=idealred(nf,idx,[1,5,6])
948:
949: [5 0 0 2 0]
950:
951: [0 5 0 0 0]
952:
953: [0 0 5 2 0]
954:
955: [0 0 0 1 0]
956:
957: [0 0 0 0 5]
958:
959: ? idx2=idealmul(nf,idx,idx)
960:
961: [9 7 5 8 2]
962:
963: [0 1 0 0 0]
964:
965: [0 0 1 0 0]
966:
967: [0 0 0 1 0]
968:
969: [0 0 0 0 1]
970:
971: ? idt=idealmul(nf,idx,idx,1)
972:
973: [2 0 0 0 1]
974:
975: [0 2 0 0 1]
976:
977: [0 0 2 0 0]
978:
979: [0 0 0 2 1]
980:
981: [0 0 0 0 1]
982:
983: ? idz=idealintersect(nf,idx,idy)
984:
985: [15 5 10 12 10]
986:
987: [0 5 0 0 0]
988:
989: [0 0 5 2 0]
990:
991: [0 0 0 1 0]
992:
993: [0 0 0 0 5]
994:
995: ? aid=[idx,idy,idz,matid(5),idx]
996: [[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]
997: , [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
998: ], [15, 5, 10, 12, 10; 0, 5, 0, 0, 0; 0, 0, 5, 2, 0; 0, 0, 0, 1, 0; 0, 0, 0,
999: 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
1000: , 0, 1], [3, 1, 2, 2, 2; 0, 1, 0, 0, 0; 0, 0, 1, 0, 0; 0, 0, 0, 1, 0; 0, 0,
1001: 0, 0, 1]]
1002: ? bid=idealstar(nf2,54,1)
1003: [[[54, 0, 0; 0, 54, 0; 0, 0, 54], [0]], [132678, [1638, 9, 9]], [[2, [2, 0,
1004: 0]~, 1, 3, [1, 0, 0]~], 1; [3, [3, 0, 0]~, 1, 3, [1, 0, 0]~], 3], [[[[7], [[
1005: 0, 1, 0]~], [[-26, -27, 0]~], [[]~], 1]], [[[26], [[0, 2, 0]~], [[-27, 2, 0]
1006: ~], [[]~], 1], [[3, 3, 3], [[1, 3, 0]~, [1, 0, 3]~, [4, 0, 0]~], [[1, -24, 0
1007: ]~, [1, 0, -24]~, [-23, 0, 0]~], [[]~, []~, []~], [0, 1/3, 0; 0, 0, 1/3; 1/3
1008: , 0, 0]], [[3, 3, 3], [[1, 9, 0]~, [1, 0, 9]~, [10, 0, 0]~], [[1, -18, 0]~,
1009: [1, 0, -18]~, [-17, 0, 0]~], [[]~, []~, []~], [0, 1/9, 0; 0, 0, 1/9; 1/9, 0,
1010: 0]]], [[], [], [;]]], [468, 469, 0, 0, -48776, 0, 0, -36582; 0, 0, 1, 0, -7
1011: , -6, 0, -3; 0, 0, 0, 1, -3, 0, -6, 0]]
1012: ? vaid=[idx,idy,matid(5)]
1013: [[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]
1014: , [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
1015: ], [1, 0, 0, 0, 0; 0, 1, 0, 0, 0; 0, 0, 1, 0, 0; 0, 0, 0, 1, 0; 0, 0, 0, 0,
1016: 1]]
1017: ? haid=[matid(5),matid(5),matid(5)]
1018: [[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]
1019: , [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
1020: ], [1, 0, 0, 0, 0; 0, 1, 0, 0, 0; 0, 0, 1, 0, 0; 0, 0, 0, 1, 0; 0, 0, 0, 0,
1021: 1]]
1022: ? idealadd(nf,idx,idy)
1023:
1024: [1 0 0 0 0]
1025:
1026: [0 1 0 0 0]
1027:
1028: [0 0 1 0 0]
1029:
1030: [0 0 0 1 0]
1031:
1032: [0 0 0 0 1]
1033:
1034: ? idealaddtoone(nf,idx,idy)
1035: [[3, 0, 2, 1, 0]~, [-2, 0, -2, -1, 0]~]
1036: ? idealaddtoone(nf,[idy,idx])
1037: [[-5, 0, 0, 0, 0]~, [6, 0, 0, 0, 0]~]
1038: ? idealappr(nf,idy)
1039: [-2, 0, -2, 4, 0]~
1040: ? idealappr(nf,idealfactor(nf,idy),1)
1041: [-2, 0, -2, 4, 0]~
1042: ? idealcoprime(nf,idx,idx)
1043: [-2/3, 2/3, -1/3, 0, 0]~
1044: ? idealdiv(nf,idy,idt)
1045:
1046: [5 5/2 5/2 7/2 0]
1047:
1048: [0 5/2 0 0 0]
1049:
1050: [0 0 5/2 1 0]
1051:
1052: [0 0 0 1/2 0]
1053:
1054: [0 0 0 0 5/2]
1055:
1056: ? idealdiv(nf,idx2,idx,1)
1057:
1058: [3 1 2 2 2]
1059:
1060: [0 1 0 0 0]
1061:
1062: [0 0 1 0 0]
1063:
1064: [0 0 0 1 0]
1065:
1066: [0 0 0 0 1]
1067:
1068: ? idf=idealfactor(nf,idz)
1069:
1070: [[3, [1, 1, 0, 0, 0]~, 1, 1, [1, -1, -1, 0, 0]~] 1]
1071:
1072: [[5, [-2, 0, 0, 0, 1]~, 1, 1, [2, 2, 1, 1, 4]~] 1]
1073:
1074: [[5, [0, 0, -1, 0, 1]~, 4, 1, [4, 5, 4, 2, 0]~] 3]
1075:
1076: ? idealhnf(nf,vp)
1077:
1078: [3 1 2 2 2]
1079:
1080: [0 1 0 0 0]
1081:
1082: [0 0 1 0 0]
1083:
1084: [0 0 0 1 0]
1085:
1086: [0 0 0 0 1]
1087:
1088: ? idealhnf(nf,vp[2],3)
1089:
1090: [3 1 2 2 2]
1091:
1092: [0 1 0 0 0]
1093:
1094: [0 0 1 0 0]
1095:
1096: [0 0 0 1 0]
1097:
1098: [0 0 0 0 1]
1099:
1100: ? ideallist(bnf,20)
1101: [[[1, 0; 0, 1]], [], [[3, 2; 0, 1], [3, 0; 0, 1]], [[2, 0; 0, 2]], [[5, 3; 0
1102: , 1], [5, 1; 0, 1]], [], [], [], [[9, 5; 0, 1], [3, 0; 0, 3], [9, 3; 0, 1]],
1103: [], [[11, 9; 0, 1], [11, 1; 0, 1]], [[6, 4; 0, 2], [6, 0; 0, 2]], [], [], [
1104: [15, 8; 0, 1], [15, 3; 0, 1], [15, 11; 0, 1], [15, 6; 0, 1]], [[4, 0; 0, 4]]
1105: , [[17, 14; 0, 1], [17, 2; 0, 1]], [], [[19, 18; 0, 1], [19, 0; 0, 1]], [[10
1106: , 6; 0, 2], [10, 2; 0, 2]]]
1107: ? ideallog(nf2,w,bid)
1108: [1574, 8, 6]~
1109: ? idealmin(nf,idx,[1,2,3])
1110: [[-1; 0; 0; 1; 0], [2.0885812311199768913287869744681966008 + 3.141592653589
1111: 7932384626433832795028842*I, 1.5921096812520196555597562531657929785 + 4.244
1112: 7196639216499665715751642189271112*I, -0.79031915447583185468082063233076160
1113: 203 + 2.5437460822678889883600220330800078854*I]]
1114: ? idealnorm(nf,idt)
1115: 16
1116: ? idp=idealpow(nf,idx,7)
1117:
1118: [2187 1807 2129 692 1379]
1119:
1120: [0 1 0 0 0]
1121:
1122: [0 0 1 0 0]
1123:
1124: [0 0 0 1 0]
1125:
1126: [0 0 0 0 1]
1127:
1128: ? idealpow(nf,idx,7,1)
1129:
1130: [5 0 0 2 0]
1131:
1132: [0 5 0 0 0]
1133:
1134: [0 0 5 2 0]
1135:
1136: [0 0 0 1 0]
1137:
1138: [0 0 0 0 5]
1139:
1140: ? idealprimedec(nf,2)
1141: [[2, [3, 1, 0, 0, 0]~, 1, 1, [1, 1, 0, 1, 1]~], [2, [-3, -5, -4, 3, 15]~, 1,
1142: 4, [1, 1, 0, 0, 0]~]]
1143: ? idealprimedec(nf,3)
1144: [[3, [1, 1, 0, 0, 0]~, 1, 1, [1, -1, -1, 0, 0]~], [3, [-1, 1, -1, 0, 1]~, 2,
1145: 2, [1, 2, 3, 1, 0]~]]
1146: ? idealprimedec(nf,11)
1147: [[11, [11, 0, 0, 0, 0]~, 1, 5, [1, 0, 0, 0, 0]~]]
1148: ? idealprincipal(nf,Mod(x^3+5,nfpol))
1149:
1150: [6]
1151:
1152: [0]
1153:
1154: [1]
1155:
1156: [3]
1157:
1158: [0]
1159:
1160: ? idealtwoelt(nf,idy)
1161: [5, [2, 0, 2, 1, 0]~]
1162: ? idealtwoelt(nf,idy,10)
1163: [-2, 0, -2, -1, 0]~
1164: ? idealstar(nf2,54)
1165: [[[54, 0, 0; 0, 54, 0; 0, 0, 54], [0]], [132678, [1638, 9, 9]], [[2, [2, 0,
1166: 0]~, 1, 3, [1, 0, 0]~], 1; [3, [3, 0, 0]~, 1, 3, [1, 0, 0]~], 3], [[[[7], [[
1167: 0, 1, 0]~], [[-26, -27, 0]~], [[]~], 1]], [[[26], [[0, 2, 0]~], [[-27, 2, 0]
1168: ~], [[]~], 1], [[3, 3, 3], [[1, 3, 0]~, [1, 0, 3]~, [4, 0, 0]~], [[1, -24, 0
1169: ]~, [1, 0, -24]~, [-23, 0, 0]~], [[]~, []~, []~], [0, 1/3, 0; 0, 0, 1/3; 1/3
1170: , 0, 0]], [[3, 3, 3], [[1, 9, 0]~, [1, 0, 9]~, [10, 0, 0]~], [[1, -18, 0]~,
1171: [1, 0, -18]~, [-17, 0, 0]~], [[]~, []~, []~], [0, 1/9, 0; 0, 0, 1/9; 1/9, 0,
1172: 0]]], [[], [], [;]]], [468, 469, 0, 0, -48776, 0, 0, -36582; 0, 0, 1, 0, -7
1173: , -6, 0, -3; 0, 0, 0, 1, -3, 0, -6, 0]]
1174: ? idealval(nf,idp,vp)
1175: 7
1176: ? ideleprincipal(nf,Mod(x^3+5,nfpol))
1177: [[6; 0; 1; 3; 0], [2.2324480827796254080981385584384939684 + 3.1415926535897
1178: 932384626433832795028842*I, 5.0387659675158716386435353106610489968 + 1.5851
1179: 760343512250049897278861965702423*I, 4.2664040272651028743625910797589683173
1180: - 0.0083630478144368246110910258645462996191*I]]
1181: ? ba=nfalgtobasis(nf,Mod(x^3+5,nfpol))
1182: [6, 0, 1, 3, 0]~
1183: ? bb=nfalgtobasis(nf,Mod(x^3+x,nfpol))
1184: [1, 1, 1, 3, 0]~
1185: ? bc=matalgtobasis(nf,[Mod(x^2+x,nfpol);Mod(x^2+1,nfpol)])
1186:
1187: [[0, 1, 1, 0, 0]~]
1188:
1189: [[1, 0, 1, 0, 0]~]
1190:
1191: ? matbasistoalg(nf,bc)
1192:
1193: [Mod(x^2 + x, x^5 - 5*x^3 + 5*x + 25)]
1194:
1195: [Mod(x^2 + 1, x^5 - 5*x^3 + 5*x + 25)]
1196:
1197: ? nfbasis(x^3+4*x+5)
1198: [1, x, 1/7*x^2 - 1/7*x - 2/7]
1199: ? nfbasis(x^3+4*x+5,2)
1200: [1, x, 1/7*x^2 - 1/7*x - 2/7]
1201: ? nfbasis(x^3+4*x+12,1)
1202: [1, x, 1/2*x^2]
1203: ? nfbasistoalg(nf,ba)
1204: Mod(x^3 + 5, x^5 - 5*x^3 + 5*x + 25)
1205: ? nfbasis(p2,0,fa)
1206: [1, x, x^2, 1/11699*x^3 + 1847/11699*x^2 - 132/11699*x - 2641/11699, 1/13962
1207: 3738889203638909659*x^4 - 1552451622081122020/139623738889203638909659*x^3 +
1208: 418509858130821123141/139623738889203638909659*x^2 - 6810913798507599407313
1209: 4/139623738889203638909659*x - 13185339461968406/58346808996920447]
1210: ? da=nfdetint(nf,[a,aid])
1211:
1212: [30 5 25 27 10]
1213:
1214: [0 5 0 0 0]
1215:
1216: [0 0 5 2 0]
1217:
1218: [0 0 0 1 0]
1219:
1220: [0 0 0 0 5]
1221:
1222: ? nfdisc(x^3+4*x+12)
1223: -1036
1224: ? nfdisc(x^3+4*x+12,1)
1225: -1036
1226: ? nfdisc(p2,0,fa)
1227: 136866601
1228: ? nfeltdiv(nf,ba,bb)
1229: [755/373, -152/373, 159/373, 120/373, -264/373]~
1230: ? nfeltdiveuc(nf,ba,bb)
1231: [2, 0, 0, 0, -1]~
1232: ? nfeltdivrem(nf,ba,bb)
1233: [[2, 0, 0, 0, -1]~, [-12, -7, 0, 9, 5]~]
1234: ? nfeltmod(nf,ba,bb)
1235: [-12, -7, 0, 9, 5]~
1236: ? nfeltmul(nf,ba,bb)
1237: [-25, -50, -30, 15, 90]~
1238: ? nfeltpow(nf,bb,5)
1239: [23455, 156370, 115855, 74190, -294375]~
1240: ? nfeltreduce(nf,ba,idx)
1241: [1, 0, 0, 0, 0]~
1242: ? nfeltval(nf,ba,vp)
1243: 0
1244: ? nffactor(nf2,x^3+x)
1245:
1246: [Mod(1, y^3 - y - 1)*x 1]
1247:
1248: [Mod(1, y^3 - y - 1)*x^2 + Mod(1, y^3 - y - 1) 1]
1249:
1250: ? aut=nfgaloisconj(nf3)
1251: [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 + 1/2*x
1252: , -x]~
1253: ? nfgaloisapply(nf3,aut[5],Mod(x^5,x^6+108))
1254: Mod(1/2*x^5 - 9*x^2, x^6 + 108)
1255: ? nfhilbert(nf,3,5)
1256: -1
1257: ? nfhilbert(nf,3,5,idf[1,1])
1258: -1
1259: ? nfhnf(nf,[a,aid])
1260: [[[1, 0, 0, 0, 0]~, [0, 0, 0, 0, 0]~, [0, 0, 0, 0, 0]~; [0, 0, 0, 0, 0]~, [1
1261: , 0, 0, 0, 0]~, [0, 0, 0, 0, 0]~; [0, 0, 0, 0, 0]~, [0, 0, 0, 0, 0]~, [1, 0,
1262: 0, 0, 0]~], [[2, 1, 1, 1, 0; 0, 1, 0, 0, 0; 0, 0, 1, 0, 0; 0, 0, 0, 1, 0; 0
1263: , 0, 0, 0, 1], [1, 0, 0, 0, 0; 0, 1, 0, 0, 0; 0, 0, 1, 0, 0; 0, 0, 0, 1, 0;
1264: 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;
1265: 0, 0, 0, 0, 1]]]
1266: ? nfhnfmod(nf,[a,aid],da)
1267: [[[1, 0, 0, 0, 0]~, [0, 0, 0, 0, 0]~, [0, 0, 0, 0, 0]~; [0, 0, 0, 0, 0]~, [1
1268: , 0, 0, 0, 0]~, [0, 0, 0, 0, 0]~; [0, 0, 0, 0, 0]~, [0, 0, 0, 0, 0]~, [1, 0,
1269: 0, 0, 0]~], [[2, 1, 1, 1, 0; 0, 1, 0, 0, 0; 0, 0, 1, 0, 0; 0, 0, 0, 1, 0; 0
1270: , 0, 0, 0, 1], [1, 0, 0, 0, 0; 0, 1, 0, 0, 0; 0, 0, 1, 0, 0; 0, 0, 0, 1, 0;
1271: 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;
1272: 0, 0, 0, 0, 1]]]
1273: ? nfisideal(bnf[7],[5,1;0,1])
1274: 1
1275: ? nfisincl(x^2+1,x^4+1)
1276: [-x^2, x^2]
1277: ? nfisincl(x^2+1,nfinit(x^4+1))
1278: [-x^2, x^2]
1279: ? nfisisom(x^3+x^2-2*x-1,x^3+x^2-2*x-1)
1280: [x, -x^2 - x + 1, x^2 - 2]
1281: ? nfisisom(x^3-2,nfinit(x^3-6*x^2-6*x-30))
1282: [-1/25*x^2 + 13/25*x - 2/5]
1283: ? nfroots(nf2,x+2)
1284: [Mod(-2, y^3 - y - 1)]
1285: ? nfrootsof1(nf)
1286: [2, [-1, 0, 0, 0, 0]~]
1287: ? nfsnf(nf,[as,haid,vaid])
1288: [[10951073973332888246310, 5442457637639729109215, 2693780223637146570055, 3
1289: 910837124677073032737, 3754666252923836621170; 0, 5, 0, 0, 0; 0, 0, 5, 2, 0;
1290: 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
1291: ; 0, 0, 0, 1, 0; 0, 0, 0, 0, 1], [1, 0, 0, 0, 0; 0, 1, 0, 0, 0; 0, 0, 1, 0,
1292: 0; 0, 0, 0, 1, 0; 0, 0, 0, 0, 1]]
1293: ? nfsubfields(nf)
1294: [[x^5 - 5*x^3 + 5*x + 25, x], [x, x^5 - 5*x^3 + 5*x + 25]]
1295: ? polcompositum(x^4-4*x+2,x^3-x-1)
1296: [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
1297: ^2 - 128*x - 5]
1298: ? polcompositum(x^4-4*x+2,x^3-x-1,1)
1299: [[x^12 - 4*x^10 + 8*x^9 + 12*x^8 + 12*x^7 + 138*x^6 + 132*x^5 - 43*x^4 + 58*
1300: x^2 - 128*x - 5, Mod(-279140305176/29063006931199*x^11 + 129916611552/290630
1301: 06931199*x^10 + 1272919322296/29063006931199*x^9 - 2813750209005/29063006931
1302: 199*x^8 - 2859411937992/29063006931199*x^7 - 414533880536/29063006931199*x^6
1303: - 35713977492936/29063006931199*x^5 - 17432607267590/29063006931199*x^4 + 4
1304: 9785595543672/29063006931199*x^3 + 9423768373204/29063006931199*x^2 - 427797
1305: 76146743/29063006931199*x + 37962587857138/29063006931199, x^12 - 4*x^10 + 8
1306: *x^9 + 12*x^8 + 12*x^7 + 138*x^6 + 132*x^5 - 43*x^4 + 58*x^2 - 128*x - 5), M
1307: od(-279140305176/29063006931199*x^11 + 129916611552/29063006931199*x^10 + 12
1308: 72919322296/29063006931199*x^9 - 2813750209005/29063006931199*x^8 - 28594119
1309: 37992/29063006931199*x^7 - 414533880536/29063006931199*x^6 - 35713977492936/
1310: 29063006931199*x^5 - 17432607267590/29063006931199*x^4 + 49785595543672/2906
1311: 3006931199*x^3 + 9423768373204/29063006931199*x^2 - 13716769215544/290630069
1312: 31199*x + 37962587857138/29063006931199, x^12 - 4*x^10 + 8*x^9 + 12*x^8 + 12
1313: *x^7 + 138*x^6 + 132*x^5 - 43*x^4 + 58*x^2 - 128*x - 5), -1]]
1314: ? polgalois(x^6-3*x^2-1)
1315: [12, 1, 1]
1316: ? polred(x^5-2*x^4-4*x^3-96*x^2-352*x-568)
1317: [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
1318: - 1, x^5 - x^4 + 4*x^3 - 2*x^2 + x - 1, x^5 + 4*x^3 - 4*x^2 + 8*x - 8]
1319: ? polred(x^4-28*x^3-458*x^2+9156*x-25321,3)
1320:
1321: [1 x - 1]
1322:
1323: [1/115*x^2 - 14/115*x - 327/115 x^2 - 10]
1324:
1325: [3/1495*x^3 - 63/1495*x^2 - 1607/1495*x + 13307/1495 x^4 - 32*x^2 + 216]
1326:
1327: [1/4485*x^3 - 7/1495*x^2 - 1034/4485*x + 7924/4485 x^4 - 8*x^2 + 6]
1328:
1329: ? polred(x^4+576,1)
1330: [x - 1, x^2 - x + 1, x^2 + 1, x^4 - x^2 + 1]
1331: ? polred(x^4+576,3)
1332:
1333: [1 x - 1]
1334:
1335: [1/192*x^3 + 1/8*x + 1/2 x^2 - x + 1]
1336:
1337: [-1/24*x^2 x^2 + 1]
1338:
1339: [-1/192*x^3 + 1/48*x^2 + 1/8*x x^4 - x^2 + 1]
1340:
1341: ? polred(p2,0,fa)
1342: [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
1343: *x^2 + 508*x + 913, x^5 - 2*x^4 - 13*x^3 + 37*x^2 - 21*x - 1, x^5 - x^4 - 52
1344: *x^3 - 197*x^2 - 273*x - 127]
1345: ? polred(p2,1,fa)
1346: [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
1347: *x^2 + 508*x + 913, x^5 - 2*x^4 - 13*x^3 + 37*x^2 - 21*x - 1, x^5 - x^4 - 52
1348: *x^3 - 197*x^2 - 273*x - 127]
1349: ? polredabs(x^5-2*x^4-4*x^3-96*x^2-352*x-568)
1350: x^5 - x^4 + 2*x^3 - 4*x^2 + x - 1
1351: ? polredabs(x^5-2*x^4-4*x^3-96*x^2-352*x-568,1)
1352: [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 -
1353: x^4 + 2*x^3 - 4*x^2 + x - 1)]
1354: ? polredord(x^3-12*x+45*x-1)
1355: [x - 1, x^3 - 363*x - 2663, x^3 + 33*x - 1]
1356: ? polsubcyclo(31,5)
1357: x^5 + x^4 - 12*x^3 - 21*x^2 + x + 5
1358: ? setrand(1);poltschirnhaus(x^5-x-1)
1359: x^5 - 15*x^4 + 88*x^3 - 278*x^2 + 452*x - 289
1360: ? aa=rnfpseudobasis(nf2,p)
1361: [[[1, 0, 0]~, [0, 0, 0]~, [0, 0, 0]~, [-2, 0, 0]~, [11, 0, 0]~; [0, 0, 0]~,
1362: [1, 0, 0]~, [0, 0, 0]~, [2, 0, 0]~, [-8, 0, 0]~; [0, 0, 0]~, [0, 0, 0]~, [1,
1363: 0, 0]~, [1, 0, 0]~, [4, 0, 0]~; [0, 0, 0]~, [0, 0, 0]~, [0, 0, 0]~, [1, 0,
1364: 0]~, [-2, 0, 0]~; [0, 0, 0]~, [0, 0, 0]~, [0, 0, 0]~, [0, 0, 0]~, [1, 0, 0]~
1365: ], [[1, 0, 0; 0, 1, 0; 0, 0, 1], [1, 0, 0; 0, 1, 0; 0, 0, 1], [1, 0, 0; 0, 1
1366: , 0; 0, 0, 1], [1, 0, 3/5; 0, 1, 2/5; 0, 0, 1/5], [1, 0, 8/25; 0, 1, 22/25;
1367: 0, 0, 1/25]], [416134375, 212940625, 388649575; 0, 3125, 550; 0, 0, 25], [-1
1368: 280, 5, 5]~]
1369: ? rnfbasis(bnf2,aa)
1370:
1371: [[1, 0, 0]~ [0, 0, 0]~ [0, 0, 0]~ [38/25, -33/25, 11/25]~ [-11, -4, 9]~]
1372:
1373: [[0, 0, 0]~ [1, 0, 0]~ [0, 0, 0]~ [-14/25, 24/25, -8/25]~ [28/5, 2/5, -24/5]
1374: ~]
1375:
1376: [[0, 0, 0]~ [0, 0, 0]~ [1, 0, 0]~ [57/25, -12/25, 4/25]~ [-58/5, -47/5, 44/5
1377: ]~]
1378:
1379: [[0, 0, 0]~ [0, 0, 0]~ [0, 0, 0]~ [9/25, 6/25, -2/25]~ [-4/5, -11/5, 2/5]~]
1380:
1381: [[0, 0, 0]~ [0, 0, 0]~ [0, 0, 0]~ [8/25, -3/25, 1/25]~ [-9/5, -6/5, 7/5]~]
1382:
1383: ? rnfdisc(nf2,p)
1384: [[416134375, 212940625, 388649575; 0, 3125, 550; 0, 0, 25], [-1280, 5, 5]~]
1385: ? rnfequation(nf2,p)
1386: x^15 - 15*x^11 + 75*x^7 - x^5 - 125*x^3 + 5*x + 1
1387: ? rnfequation(nf2,p,1)
1388: [x^15 - 15*x^11 + 75*x^7 - x^5 - 125*x^3 + 5*x + 1, Mod(-x^5 + 5*x, x^15 - 1
1389: 5*x^11 + 75*x^7 - x^5 - 125*x^3 + 5*x + 1), 0]
1390: ? rnfhnfbasis(bnf2,aa)
1391:
1392: [[1, 0, 0]~ [0, 0, 0]~ [0, 0, 0]~ [-2/5, 2/5, -4/5]~ [11/25, 99/25, -33/25]~
1393: ]
1394:
1395: [[0, 0, 0]~ [1, 0, 0]~ [0, 0, 0]~ [2/5, -2/5, 4/5]~ [-8/25, -72/25, 24/25]~]
1396:
1397: [[0, 0, 0]~ [0, 0, 0]~ [1, 0, 0]~ [1/5, -1/5, 2/5]~ [4/25, 36/25, -12/25]~]
1398:
1399: [[0, 0, 0]~ [0, 0, 0]~ [0, 0, 0]~ [1/5, -1/5, 2/5]~ [-2/25, -18/25, 6/25]~]
1400:
1401: [[0, 0, 0]~ [0, 0, 0]~ [0, 0, 0]~ [0, 0, 0]~ [1/25, 9/25, -3/25]~]
1402:
1403: ? rnfisfree(bnf2,aa)
1404: 1
1405: ? rnfsteinitz(nf2,aa)
1406: [[[1, 0, 0]~, [0, 0, 0]~, [0, 0, 0]~, [38/25, -33/25, 11/25]~, [-27/125, 33/
1407: 125, -11/125]~; [0, 0, 0]~, [1, 0, 0]~, [0, 0, 0]~, [-14/25, 24/25, -8/25]~,
1408: [6/125, -24/125, 8/125]~; [0, 0, 0]~, [0, 0, 0]~, [1, 0, 0]~, [57/25, -12/2
1409: 5, 4/25]~, [-53/125, 12/125, -4/125]~; [0, 0, 0]~, [0, 0, 0]~, [0, 0, 0]~, [
1410: 9/25, 6/25, -2/25]~, [-11/125, -6/125, 2/125]~; [0, 0, 0]~, [0, 0, 0]~, [0,
1411: 0, 0]~, [8/25, -3/25, 1/25]~, [-7/125, 3/125, -1/125]~], [[1, 0, 0; 0, 1, 0;
1412: 0, 0, 1], [1, 0, 0; 0, 1, 0; 0, 0, 1], [1, 0, 0; 0, 1, 0; 0, 0, 1], [1, 0,
1413: 0; 0, 1, 0; 0, 0, 1], [125, 0, 108; 0, 125, 22; 0, 0, 1]], [416134375, 21294
1414: 0625, 388649575; 0, 3125, 550; 0, 0, 25], [-1280, 5, 5]~]
1415: ? nfz=zetakinit(x^2-2);
1416: ? zetak(nfz,-3)
1417: 0.091666666666666666666666666666666666666
1418: ? zetak(nfz,1.5+3*I)
1419: 0.88324345992059326405525724366416928890 - 0.2067536250233895222724230899142
1420: 7938845*I
1421: ? setrand(1);quadclassunit(1-10^7,,[1,1])
1422: *** Warning: not a fundamental discriminant in quadclassunit.
1423: [2416, [1208, 2], [Qfb(277, 55, 9028), Qfb(1700, 1249, 1700)], 1, 0.99984980
1424: 75377600233]
1425: ? setrand(1);quadclassunit(10^9-3,,[0.5,0.5])
1426: [4, [4], [Qfb(3, 1, -83333333, 0.E-48)], 2800.625251907016076486370621737074
1427: 5514, 0.9990369458964383232]
1428: ? sizebyte(%)
1429: 176
1430: ? getheap
1431: [198, 134908]
1432: ? print("Total time spent: ",gettime);
1433: Total time spent: 4200
1434: ? \q
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