Annotation of OpenXM_contrib/pari/src/test/64/nfields, Revision 1.1.1.1
1.1 maekawa 1: echo = 1 (on)
2: ? nfpol=x^5-5*x^3+5*x+25
3: x^5 - 5*x^3 + 5*x + 25
4: ? qpol=y^3-y-1;un=Mod(1,qpol);w=Mod(y,qpol);p=un*(x^5-5*x+w)
5: Mod(1, y^3 - y - 1)*x^5 + Mod(-5, y^3 - y - 1)*x + Mod(y, y^3 - y - 1)
6: ? p2=x^5+3021*x^4-786303*x^3-6826636057*x^2-546603588746*x+3853890514072057
7: x^5 + 3021*x^4 - 786303*x^3 - 6826636057*x^2 - 546603588746*x + 385389051407
8: 2057
9: ? fa=[11699,6;2392997,2;4987333019653,2]
10:
11: [11699 6]
12:
13: [2392997 2]
14:
15: [4987333019653 2]
16:
17: ? setrand(1);a=matrix(3,5,j,k,vectorv(5,l,random\10^8));
18: ? setrand(1);as=matrix(3,3,j,k,vectorv(5,l,random\10^8));
19: ? nf=nfinit(nfpol)
20: [x^5 - 5*x^3 + 5*x + 25, [1, 2], 595125, 45, [[1, -2.42851749071941860689920
21: 69565359418364, 5.8976972027301414394898806541072047941, -7.0734526715090929
22: 269887668671457811020, 3.8085820570096366144649278594400435257; 1, 1.9647119
23: 211288133163138753392090569931 + 0.80971492418897895128294082219556466857*I,
24: 3.2044546745713084269203768790545260356 + 3.1817131285400005341145852263331
25: 539899*I, -0.16163499313031744537610982231988834519 + 1.88804378620070569319
26: 06454476483475283*I, 2.0660709538372480632698971148801090692 + 2.68989675196
27: 23140991170523711857387388*I; 1, -0.75045317576910401286427186094108607489 +
28: 1.3101462685358123283560773619310445915*I, -1.15330327593637914666531720610
29: 81284327 - 1.9664068558894834311780119356739268309*I, 1.19836132888486390887
30: 04932558927788962 + 0.64370238076256988899570325671192132449*I, -0.470361982
31: 34206637050236104460013083212 + 0.083628266711589186119416762685933385421*I]
32: , [1, 2, 2; -2.4285174907194186068992069565359418364, 3.92942384225762663262
33: 77506784181139862 - 1.6194298483779579025658816443911293371*I, -1.5009063515
34: 382080257285437218821721497 - 2.6202925370716246567121547238620891831*I; 5.8
35: 976972027301414394898806541072047941, 6.408909349142616853840753758109052071
36: 2 - 6.3634262570800010682291704526663079798*I, -2.30660655187275829333063441
37: 22162568654 + 3.9328137117789668623560238713478536619*I; -7.0734526715090929
38: 269887668671457811020, -0.32326998626063489075221964463977669038 - 3.7760875
39: 724014113863812908952966950567*I, 2.3967226577697278177409865117855577924 -
40: 1.2874047615251397779914065134238426489*I; 3.8085820570096366144649278594400
41: 435257, 4.1321419076744961265397942297602181385 - 5.379793503924628198234104
42: 7423714774776*I, -0.94072396468413274100472208920026166424 - 0.1672565334231
43: 7837223883352537186677084*I], [5, 0.E-77, 10.0000000000000000000000000000000
44: 00000, -5.0000000000000000000000000000000000000, 7.0000000000000000000000000
45: 000000000000; 0.E-77, 19.488486013650707197449403270536023970, 2.07268045322
46: 26667100551498190000000000 E-76, 19.488486013650707197449403270536023970, 4.
47: 1504592246706085588902013976045703227; 10.0000000000000000000000000000000000
48: 00, 2.0726804532226667100551498190000000000 E-76, 85.96021742085184648030513
49: 3936577594605, -36.034268291482979838267056239752434596, 53.5761304525111078
50: 88183080361946556763; -5.0000000000000000000000000000000000000, 19.488486013
51: 650707197449403270536023970, -36.034268291482979838267056239752434596, 60.91
52: 6248374441986300937507618575151517, -18.470101750219179344070032346246890434
53: ; 7.0000000000000000000000000000000000000, 4.1504592246706085588902013976045
54: 703227, 53.576130452511107888183080361946556763, -18.47010175021917934407003
55: 2346246890434, 37.970152892842367340897384258599214282], [5, 0, 10, -5, 7; 0
56: , 10, 0, 10, -5; 10, 0, 30, -55, 20; -5, 10, -55, 45, -39; 7, -5, 20, -39, 9
57: ], [345, 0, 340, 167, 150; 0, 345, 110, 220, 153; 0, 0, 5, 2, 1; 0, 0, 0, 1,
58: 0; 0, 0, 0, 0, 1], [132825, -18975, -5175, 27600, 17250; -18975, 34500, 414
59: 00, 3450, -43125; -5175, 41400, -41400, -15525, 51750; 27600, 3450, -15525,
60: -3450, 0; 17250, -43125, 51750, 0, -86250], [595125, [-120750, 63825, 113850
61: , 0, 8625]~, 125439056256992431640625]], [-2.4285174907194186068992069565359
62: 418364, 1.9647119211288133163138753392090569931 + 0.809714924188978951282940
63: 82219556466857*I, -0.75045317576910401286427186094108607489 + 1.310146268535
64: 8123283560773619310445915*I], [1, x, x^2, 1/3*x^3 - 1/3*x^2 - 1/3, 1/15*x^4
65: + 1/3*x^2 + 1/3*x + 1/3], [1, 0, 0, 1, -5; 0, 1, 0, 0, -5; 0, 0, 1, 1, -5; 0
66: , 0, 0, 3, 0; 0, 0, 0, 0, 15], [1, 0, 0, 0, 0, 0, 0, 1, -2, -1, 0, 1, -5, -5
67: , -3, 0, -2, -5, 1, -4, 0, -1, -3, -4, -3; 0, 1, 0, 0, 0, 1, 0, 0, -2, 0, 0,
68: 0, -5, 0, -5, 0, -2, 0, -5, 0, 0, 0, -5, 0, -4; 0, 0, 1, 0, 0, 0, 1, 1, -2,
69: 1, 1, 1, -5, 3, -3, 0, -2, 3, -5, 1, 0, 1, -3, 1, -2; 0, 0, 0, 1, 0, 0, 0,
70: 3, -1, 2, 0, 3, 0, 5, 1, 1, -1, 5, -4, 3, 0, 2, 1, 3, 1; 0, 0, 0, 0, 1, 0, 0
71: , 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]~, 125439056256992431640625]], [-1.0891151457205048250249527946671612684,
117: -0.13838372073406036365047976417441696637 + 0.49181637657768643499753285514
118: 741525107*I, 1.6829412935943127761629561615079976005 + 2.0500351226010726172
119: 974286983598602163*I], [1, x, x^2, 1/2*x^3 + 1/2*x^2 + 1/2*x, 1/2*x^4 + 1/2*
120: x], [1, 0, 0, 0, 0; 0, 1, 0, -1, -1; 0, 0, 1, -1, 0; 0, 0, 0, 2, 0; 0, 0, 0,
121: 0, 2], [1, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, -1, -2, 0, 0, -1, -2, -2, 0
122: , -1, -2, -2, 5; 0, 1, 0, 0, 0, 1, 0, -1, -1, -1, 0, -1, -1, -2, 2, 0, -1, -
123: 2, -1, 7, 0, -1, 2, 7, 14; 0, 0, 1, 0, 0, 0, 1, -1, 0, -2, 1, -1, 0, -3, -3,
124: 0, 0, -3, -4, -1, 0, -2, -3, -1, 15; 0, 0, 0, 1, 0, 0, 0, 2, 1, -3, 0, 2, 0
125: , -2, -13, 1, 1, -2, -9, -19, 0, -3, -13, -19, 7; 0, 0, 0, 0, 1, 0, 0, 0, 1,
126: 2, 0, 0, 2, 3, 1, 0, 1, 3, 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]~, 125439056256992431640625]], [-1.0891151457205048250249527946671612684
172: , -0.13838372073406036365047976417441696637 + 0.4918163765776864349975328551
173: 4741525107*I, 1.6829412935943127761629561615079976005 + 2.050035122601072617
174: 2974286983598602163*I], [1, x, x^2, 1/2*x^3 + 1/2*x^2 + 1/2*x, 1/2*x^4 + 1/2
175: *x], [1, 0, 0, 0, 0; 0, 1, 0, -1, -1; 0, 0, 1, -1, 0; 0, 0, 0, 2, 0; 0, 0, 0
176: , 0, 2], [1, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, -1, -2, 0, 0, -1, -2, -2,
177: 0, -1, -2, -2, 5; 0, 1, 0, 0, 0, 1, 0, -1, -1, -1, 0, -1, -1, -2, 2, 0, -1,
178: -2, -1, 7, 0, -1, 2, 7, 14; 0, 0, 1, 0, 0, 0, 1, -1, 0, -2, 1, -1, 0, -3, -3
179: , 0, 0, -3, -4, -1, 0, -2, -3, -1, 15; 0, 0, 0, 1, 0, 0, 0, 2, 1, -3, 0, 2,
180: 0, -2, -13, 1, 1, -2, -9, -19, 0, -3, -13, -19, 7; 0, 0, 0, 0, 1, 0, 0, 0, 1
181: , 2, 0, 0, 2, 3, 1, 0, 1, 3, 4, -4, 1, 2, 1, -4, -21]], Mod(-1/2*x^4 + 3/2*x
182: ^3 - 5/2*x^2 - 2*x + 1, x^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]~, 125439056256992431640625]], [-1.0891151457205048250249527946671612684,
228: -0.13838372073406036365047976417441696637 + 0.49181637657768643499753285514
229: 741525107*I, 1.6829412935943127761629561615079976005 + 2.0500351226010726172
230: 974286983598602163*I], [1, x, x^2, 1/2*x^3 + 1/2*x^2 + 1/2*x, 1/2*x^4 + 1/2*
231: x], [1, 0, 0, 0, 0; 0, 1, 0, -1, -1; 0, 0, 1, -1, 0; 0, 0, 0, 2, 0; 0, 0, 0,
232: 0, 2], [1, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, -1, -2, 0, 0, -1, -2, -2, 0
233: , -1, -2, -2, 5; 0, 1, 0, 0, 0, 1, 0, -1, -1, -1, 0, -1, -1, -2, 2, 0, -1, -
234: 2, -1, 7, 0, -1, 2, 7, 14; 0, 0, 1, 0, 0, 0, 1, -1, 0, -2, 1, -1, 0, -3, -3,
235: 0, 0, -3, -4, -1, 0, -2, -3, -1, 15; 0, 0, 0, 1, 0, 0, 0, 2, 1, -3, 0, 2, 0
236: , -2, -13, 1, 1, -2, -9, -19, 0, -3, -13, -19, 7; 0, 0, 0, 0, 1, 0, 0, 0, 1,
237: 2, 0, 0, 2, 3, 1, 0, 1, 3, 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, -3.4544674220377778500919163650000000000 E-77, 10.
248: 000000000000000000000000000000000000; -3.45446742203777785009191636500000000
249: 00 E-77, 20.000000000000000000000000000000000000, -12.0000000000000000000000
250: 00000000000000; 10.000000000000000000000000000000000000, -12.000000000000000
251: 000000000000000000000, 50.000000000000000000000000000000000000], [3, 0, 10;
252: 0, 20, -12; 10, -12, 50], [284, 168, 235; 0, 2, 0; 0, 0, 1], [856, -120, -20
253: 0; -120, 50, 36; -200, 36, 60], [568, [80, 14, -24]~, 322624]], [-3.50466435
254: 35880477051501085259043320579, 0.86464088669540302583112842266613688800, 2.6
255: 400234668926446793189801032381951699], [1, x, 1/2*x^2], [1, 0, 0; 0, 1, 0; 0
256: , 0, 2], [1, 0, 0, 0, 0, -4, 0, -4, 0; 0, 1, 0, 1, 0, 5, 0, 5, -2; 0, 0, 1,
257: 0, 2, 0, 1, 0, 5]]
258: ? setrand(1);bnf2=bnfinit(qpol);nf2=bnf2[7];
259: ? setrand(1);bnf=bnfinit(x^2-x-57,,[0.2,0.2])
260: [Mat(3), Mat([1, 2, 1, 2, 1, 2, 1, 2, 1]), [-2.71246530518434397468087951060
261: 61300699 - 9.4247779607693797153879301498385086526*I; 2.71246530518434397468
262: 08795106061300699 - 6.2831853071795864769252867665590057684*I], [23347.97922
263: 3478346319454659159707591731 + 6.2831853071795864769252867665590057684*I, 86
264: 6.56619430687100142570357249059499540 + 6.2831853071795864769252867665590057
265: 684*I, 2881.3396396084587293295626563644245032 + 3.1415926535897932384626433
266: 832795028842*I, 27379.624790530768080428797780058276925 + 2.0880974297595278
267: 484866027080000000000 E-52*I, 57933.334567930851067108050790839116749 + 3.54
268: 97656305911973423188043860000000000 E-52*I, -34585.5562501515577199980340439
269: 18848670 + 9.4247779607693797153879301498385086526*I, 23348.3225111226233465
270: 49049047574325150 + 3.1415926535897932384626433832795028842*I, -0.3432876442
271: 7702709438988786673341921876 + 3.1415926535897932384626433832795028842*I, -4
272: 031.7117453543045067063239888430083582 + 9.424777960769379715387930149838508
273: 6526*I, 27379.690968832650826160983148550600089 + 9.424777960769379715387930
274: 1498385086526*I; -23347.979223478346319454659159707591731 + 9.42477796076937
275: 97153879301498385086526*I, -866.56619430687100142570357249059499540 + 8.1566
276: 305849981556577374397490000000000 E-55*I, -2881.3396396084587293295626563644
277: 245032 + 9.4247779607693797153879301498385086526*I, -27379.62479053076808042
278: 8797780058276925 + 6.2831853071795864769252867665590057684*I, -57933.3345679
279: 30851067108050790839116749 + 3.1415926535897932384626433832795028842*I, 3458
280: 5.556250151557719998034043918848670 + 6.283185307179586476925286766559005768
281: 4*I, -23348.322511122623346549049047574325150 + 9.42477796076937971538793014
282: 98385086526*I, 0.34328764427702709438988786673341921876 + 0.E-57*I, 4031.711
283: 7453543045067063239888430083582 + 3.1415926535897932384626433832795028842*I,
284: -27379.690968832650826160983148550600089 + 6.283185307179586476925286766559
285: 0057684*I], [[3, [-1, 1]~, 1, 1, [0, 1]~], [3, [0, 1]~, 1, 1, [-1, 1]~], [5,
286: [-2, 1]~, 1, 1, [1, 1]~], [5, [1, 1]~, 1, 1, [-2, 1]~], [11, [-2, 1]~, 1, 1
287: , [1, 1]~], [11, [1, 1]~, 1, 1, [-2, 1]~], [17, [-3, 1]~, 1, 1, [2, 1]~], [1
288: 7, [2, 1]~, 1, 1, [-3, 1]~], [19, [-1, 1]~, 1, 1, [0, 1]~], [19, [0, 1]~, 1,
289: 1, [-1, 1]~]]~, [1, 3, 5, 2, 4, 6, 7, 8, 10, 9]~, [x^2 - x - 57, [2, 0], 22
290: 9, 1, [[1, -7.0663729752107779635959310246705326058; 1, 8.066372975210777963
291: 5959310246705326058], [1, 1; -7.0663729752107779635959310246705326058, 8.066
292: 3729752107779635959310246705326058], [2, 1.000000000000000000000000000000000
293: 0000; 1.0000000000000000000000000000000000000, 115.0000000000000000000000000
294: 0000000000], [2, 1; 1, 115], [229, 114; 0, 1], [115, -1; -1, 2], [229, [114,
295: 1]~, 229]], [-7.0663729752107779635959310246705326058, 8.066372975210777963
296: 5959310246705326058], [1, x], [1, 0; 0, 1], [1, 0, 0, 57; 0, 1, 1, 1]], [[3,
297: [3], [[3, 2; 0, 1]]], 2.7124653051843439746808795106061300699, 0.8814422512
298: 6545793690341704100000000000, [2, -1], [x + 7], 162], [Mat(1), Mat(1), [[[3,
299: 2; 0, 1], [0, 0]]]], 0]
300: ? setrand(1);bnfinit(x^2-x-100000,1)
301: [Mat(5), Mat([3, 2, 1, 2, 0, 3, 2, 3, 0, 0, 1, 4, 3, 2, 2, 3, 3, 2]), [-129.
302: 82045011403975460991182396195022419 + 6.283185307179586476925286766559005768
303: 4*I; 129.82045011403975460991182396195022419 + 5.348345931263972060504263694
304: 0000000000 E-115*I], [2093832.2286247580721598744691800364716 + 9.4247779607
305: 693797153879301498385086526*I, 463727.88770776479369558667281813008490 + 6.2
306: 831853071795864769252867665590057684*I, 229510.68119174121074359900744873056
307: 520 + 3.1415926535897932384626433832795028842*I, -13814064.27618485624828610
308: 7275967161406 + 6.2831853071795864769252867665590057684*I, 10975229.44237614
309: 5014058790444262893275 + 9.4247779607693797153879301498385086526*I, 12628868
310: .476868730308574917279106536834 + 6.2831853071795864769252867665590057684*I,
311: 2595210.6815750606798700790306370856686 + 3.1415926535897932384626433832795
312: 028842*I, 21463208.279603014333968661075393279510 + 6.2831853071795864769252
313: 867665590057684*I, 9340416.4917416354701732132629720490406 + 9.4247779607693
314: 797153879301498385086526*I, 224801.35127844528675036994618361508061 + 12.566
315: 370614359172953850573533118011536*I, -224801.3512784452867503699461836150806
316: 1 + 9.6067672535041710996049808843552935572 E-110*I, 40271115.67885724271600
317: 3879014241558828 + 6.2831853071795864769252867665590057684*I, -10066612.2847
318: 88886379386747743460630561 + 4.3018790993764137358012770550502916873 E-108*I
319: , 10267873.880681641662748682261863339788 + 12.56637061435917295385057353311
320: 8011536*I, -4435991.6114732228963510067335229085617 + 6.28318530717958647692
321: 52867665590057684*I, 8361196.2032957779193404684451855312611 + 9.42477796076
322: 93797153879301498385086526*I, -10272584.501589374356405593568879583106 + 9.4
323: 247779607693797153879301498385086526*I, 41648172.195327314227598351804544361
324: 493 + 9.4247779607693797153879301498385086526*I, -2117367.665066341919805155
325: 1003369291210 + 9.0483757581445359017535541005707614256 E-109*I; -2093832.22
326: 86247580721598744691800364716 + 3.1415926535897932384626433832795028842*I, -
327: 463727.88770776479369558667281813008490 + 9.42477796076937971538793014983850
328: 86526*I, -229510.68119174121074359900744873056520 + 12.566370614359172953850
329: 573533118011536*I, 13814064.276184856248286107275967161405 + 5.6909456906323
330: 670696834504660000000000 E-110*I, -10975229.442376145014058790444262893275 +
331: 12.566370614359172953850573533118011536*I, -12628868.4768687303085749172791
332: 06536834 + 3.1415926535897932384626433832795028842*I, -2595210.6815750606798
333: 700790306370856686 + 12.566370614359172953850573533118011536*I, -21463208.27
334: 9603014333968661075393279510 + 9.4247779607693797153879301498385086526*I, -9
335: 340416.4917416354701732132629720490406 + 6.283185307179586476925286766559005
336: 7684*I, -224801.35127844528675036994618361508061 + 12.5663706143591729538505
337: 73533118011536*I, 224801.35127844528675036994618361508061 + 9.26104300469294
338: 36195130014290000000000 E-112*I, -40271115.678857242716003879014241558828 +
339: 12.566370614359172953850573533118011536*I, 10066612.284788886379386747743460
340: 630561 + 4.1471150755962714546179470600000000000 E-110*I, -10267873.88068164
341: 1662748682261863339788 + 3.1415926535897932384626433832795028842*I, 4435991.
342: 6114732228963510067335229085617 + 9.4247779607693797153879301498385086526*I,
343: -8361196.2032957779193404684451855312611 + 12.56637061435917295385057353311
344: 8011536*I, 10272584.501589374356405593568879583106 + 4.231970404042868132057
345: 2257270000000000 E-110*I, -41648172.195327314227598351804544361493 + 3.14159
346: 26535897932384626433832795028842*I, 2117367.6650663419198051551003369291210
347: + 8.7228465941240376311377469060000000000 E-111*I], [[2, [1, 1]~, 1, 1, [0,
348: 1]~], [2, [2, 1]~, 1, 1, [1, 1]~], [5, [4, 1]~, 1, 1, [0, 1]~], [5, [5, 1]~,
349: 1, 1, [-1, 1]~], [7, [3, 1]~, 2, 1, [3, 1]~], [13, [-6, 1]~, 1, 1, [5, 1]~]
350: , [13, [5, 1]~, 1, 1, [-6, 1]~], [17, [14, 1]~, 1, 1, [2, 1]~], [17, [19, 1]
351: ~, 1, 1, [-3, 1]~], [23, [-7, 1]~, 1, 1, [6, 1]~], [23, [6, 1]~, 1, 1, [-7,
352: 1]~], [29, [-14, 1]~, 1, 1, [13, 1]~], [29, [13, 1]~, 1, 1, [-14, 1]~], [31,
353: [23, 1]~, 1, 1, [7, 1]~], [31, [38, 1]~, 1, 1, [-8, 1]~], [41, [-7, 1]~, 1,
354: 1, [6, 1]~], [41, [6, 1]~, 1, 1, [-7, 1]~], [43, [-16, 1]~, 1, 1, [15, 1]~]
355: , [43, [15, 1]~, 1, 1, [-16, 1]~]]~, [1, 3, 6, 2, 4, 5, 7, 9, 8, 11, 10, 13,
356: 12, 15, 14, 17, 16, 19, 18]~, [x^2 - x - 100000, [2, 0], 400001, 1, [[1, -3
357: 15.72816130129840161392089489603747004; 1, 316.72816130129840161392089489603
358: 747004], [1, 1; -315.72816130129840161392089489603747004, 316.72816130129840
359: 161392089489603747004], [2, 1.0000000000000000000000000000000000000; 1.00000
360: 00000000000000000000000000000000, 200001.00000000000000000000000000000000],
361: [2, 1; 1, 200001], [400001, 200000; 0, 1], [200001, -1; -1, 2], [400001, [20
362: 0000, 1]~, 400001]], [-315.72816130129840161392089489603747004, 316.72816130
363: 129840161392089489603747004], [1, x], [1, 0; 0, 1], [1, 0, 0, 100000; 0, 1,
364: 1, 1]], [[5, [5], [[2, 1; 0, 1]]], 129.82045011403975460991182396195022419,
365: 0.98765369790690472391212970100000000000, [2, -1], [379554884019013781006303
366: 254896369154068336082609238336*x + 11983616564425078999046283595002287166517
367: 8127611316131167], 185], [Mat(1), Mat(1), [[[2, 1; 0, 1], [0, 0]]]], 0]
368: ? \p19
369: realprecision = 19 significant digits
370: ? setrand(1);sbnf=bnfinit(x^3-x^2-14*x-1,3)
371: [x^3 - x^2 - 14*x - 1, 3, 10889, [1, x, x^2], [-3.233732695981516673, -0.071
372: 82350902743636344, 4.305556205008953036], [10889, 5698, 3794; 0, 1, 0; 0, 0,
373: 1], Mat(2), Mat([0, 1, 1, 1, 0, 1, 1, 1]), [9, 15, 16, 17, 10, 33, 69, 39,
374: 57], [2, [-1, 0, 0]~], [[0, 1, 0]~, [-4, 2, 1]~], [4, 3, 1, 2, 3, 1, 11, 1,
375: -7; -1, 1, -1, 1, 0, 1, 2, 4, -2; 0, 0, 0, 0, 0, 0, -1, 1, 0]]
376: ? \p38
377: realprecision = 38 significant digits
378: ? bnrinit(bnf,[[5,3;0,1],[1,0]],1)
379: [[Mat(3), Mat([1, 2, 1, 2, 1, 2, 1, 2, 1]), [-2.7124653051843439746808795106
380: 061300699 - 9.4247779607693797153879301498385086526*I; 2.7124653051843439746
381: 808795106061300699 - 6.2831853071795864769252867665590057684*I], [23347.9792
382: 23478346319454659159707591731 + 6.2831853071795864769252867665590057684*I, 8
383: 66.56619430687100142570357249059499540 + 6.283185307179586476925286766559005
384: 7684*I, 2881.3396396084587293295626563644245032 + 3.141592653589793238462643
385: 3832795028842*I, 27379.624790530768080428797780058276925 + 2.088097429759527
386: 8484866027080000000000 E-52*I, 57933.334567930851067108050790839116749 + 3.5
387: 497656305911973423188043860000000000 E-52*I, -34585.556250151557719998034043
388: 918848670 + 9.4247779607693797153879301498385086526*I, 23348.322511122623346
389: 549049047574325150 + 3.1415926535897932384626433832795028842*I, -0.343287644
390: 27702709438988786673341921876 + 3.1415926535897932384626433832795028842*I, -
391: 4031.7117453543045067063239888430083582 + 9.42477796076937971538793014983850
392: 86526*I, 27379.690968832650826160983148550600089 + 9.42477796076937971538793
393: 01498385086526*I; -23347.979223478346319454659159707591731 + 9.4247779607693
394: 797153879301498385086526*I, -866.56619430687100142570357249059499540 + 8.156
395: 6305849981556577374397490000000000 E-55*I, -2881.339639608458729329562656364
396: 4245032 + 9.4247779607693797153879301498385086526*I, -27379.6247905307680804
397: 28797780058276925 + 6.2831853071795864769252867665590057684*I, -57933.334567
398: 930851067108050790839116749 + 3.1415926535897932384626433832795028842*I, 345
399: 85.556250151557719998034043918848670 + 6.28318530717958647692528676655900576
400: 84*I, -23348.322511122623346549049047574325150 + 9.4247779607693797153879301
401: 498385086526*I, 0.34328764427702709438988786673341921876 + 0.E-57*I, 4031.71
402: 17453543045067063239888430083582 + 3.1415926535897932384626433832795028842*I
403: , -27379.690968832650826160983148550600089 + 6.28318530717958647692528676655
404: 90057684*I], [[3, [-1, 1]~, 1, 1, [0, 1]~], [3, [0, 1]~, 1, 1, [-1, 1]~], [5
405: , [-2, 1]~, 1, 1, [1, 1]~], [5, [1, 1]~, 1, 1, [-2, 1]~], [11, [-2, 1]~, 1,
406: 1, [1, 1]~], [11, [1, 1]~, 1, 1, [-2, 1]~], [17, [-3, 1]~, 1, 1, [2, 1]~], [
407: 17, [2, 1]~, 1, 1, [-3, 1]~], [19, [-1, 1]~, 1, 1, [0, 1]~], [19, [0, 1]~, 1
408: , 1, [-1, 1]~]]~, [1, 3, 5, 2, 4, 6, 7, 8, 10, 9]~, [x^2 - x - 57, [2, 0], 2
409: 29, 1, [[1, -7.0663729752107779635959310246705326058; 1, 8.06637297521077796
410: 35959310246705326058], [1, 1; -7.0663729752107779635959310246705326058, 8.06
411: 63729752107779635959310246705326058], [2, 1.00000000000000000000000000000000
412: 00000; 1.0000000000000000000000000000000000000, 115.000000000000000000000000
413: 00000000000], [2, 1; 1, 115], [229, 114; 0, 1], [115, -1; -1, 2], [229, [114
414: , 1]~, 229]], [-7.0663729752107779635959310246705326058, 8.06637297521077796
415: 35959310246705326058], [1, x], [1, 0; 0, 1], [1, 0, 0, 57; 0, 1, 1, 1]], [[3
416: , [3], [[3, 2; 0, 1]]], 2.7124653051843439746808795106061300699, 0.881442251
417: 26545793690341704100000000000, [2, -1], [x + 7], 162], [Mat(1), Mat(1), [[[3
418: , 2; 0, 1], [0, 0]]]], 0], [[[5, 3; 0, 1], [1, 0]], [8, [4, 2], [[2, 0]~, [-
419: 1, 1]~]], Mat([[5, [-2, 1]~, 1, 1, [1, 1]~], 1]), [[[[4], [[2, 0]~], [[2, 0]
420: ~], [[Mod(0, 2)]~], 1]], [[2], [[-1, 1]~], Mat(1)]], [1, 0; 0, 1]], [[1, 0]~
421: ], [1, -3, -6; 0, 0, 1; 0, 1, 0], [12, [12], [[3, 2; 0, 1]]], [[0, 0; 0, 1],
422: [1, -1; 1, 1]]]
423: ? bnr=bnrclass(bnf,[[5,3;0,1],[1,0]],2)
424: [[Mat(3), Mat([1, 2, 1, 2, 1, 2, 1, 2, 1]), [-2.7124653051843439746808795106
425: 061300699 - 9.4247779607693797153879301498385086526*I; 2.7124653051843439746
426: 808795106061300699 - 6.2831853071795864769252867665590057684*I], [23347.9792
427: 23478346319454659159707591731 + 6.2831853071795864769252867665590057684*I, 8
428: 66.56619430687100142570357249059499540 + 6.283185307179586476925286766559005
429: 7684*I, 2881.3396396084587293295626563644245032 + 3.141592653589793238462643
430: 3832795028842*I, 27379.624790530768080428797780058276925 + 2.088097429759527
431: 8484866027080000000000 E-52*I, 57933.334567930851067108050790839116749 + 3.5
432: 497656305911973423188043860000000000 E-52*I, -34585.556250151557719998034043
433: 918848670 + 9.4247779607693797153879301498385086526*I, 23348.322511122623346
434: 549049047574325150 + 3.1415926535897932384626433832795028842*I, -0.343287644
435: 27702709438988786673341921876 + 3.1415926535897932384626433832795028842*I, -
436: 4031.7117453543045067063239888430083582 + 9.42477796076937971538793014983850
437: 86526*I, 27379.690968832650826160983148550600089 + 9.42477796076937971538793
438: 01498385086526*I; -23347.979223478346319454659159707591731 + 9.4247779607693
439: 797153879301498385086526*I, -866.56619430687100142570357249059499540 + 8.156
440: 6305849981556577374397490000000000 E-55*I, -2881.339639608458729329562656364
441: 4245032 + 9.4247779607693797153879301498385086526*I, -27379.6247905307680804
442: 28797780058276925 + 6.2831853071795864769252867665590057684*I, -57933.334567
443: 930851067108050790839116749 + 3.1415926535897932384626433832795028842*I, 345
444: 85.556250151557719998034043918848670 + 6.28318530717958647692528676655900576
445: 84*I, -23348.322511122623346549049047574325150 + 9.4247779607693797153879301
446: 498385086526*I, 0.34328764427702709438988786673341921876 + 0.E-57*I, 4031.71
447: 17453543045067063239888430083582 + 3.1415926535897932384626433832795028842*I
448: , -27379.690968832650826160983148550600089 + 6.28318530717958647692528676655
449: 90057684*I], [[3, [-1, 1]~, 1, 1, [0, 1]~], [3, [0, 1]~, 1, 1, [-1, 1]~], [5
450: , [-2, 1]~, 1, 1, [1, 1]~], [5, [1, 1]~, 1, 1, [-2, 1]~], [11, [-2, 1]~, 1,
451: 1, [1, 1]~], [11, [1, 1]~, 1, 1, [-2, 1]~], [17, [-3, 1]~, 1, 1, [2, 1]~], [
452: 17, [2, 1]~, 1, 1, [-3, 1]~], [19, [-1, 1]~, 1, 1, [0, 1]~], [19, [0, 1]~, 1
453: , 1, [-1, 1]~]]~, [1, 3, 5, 2, 4, 6, 7, 8, 10, 9]~, [x^2 - x - 57, [2, 0], 2
454: 29, 1, [[1, -7.0663729752107779635959310246705326058; 1, 8.06637297521077796
455: 35959310246705326058], [1, 1; -7.0663729752107779635959310246705326058, 8.06
456: 63729752107779635959310246705326058], [2, 1.00000000000000000000000000000000
457: 00000; 1.0000000000000000000000000000000000000, 115.000000000000000000000000
458: 00000000000], [2, 1; 1, 115], [229, 114; 0, 1], [115, -1; -1, 2], [229, [114
459: , 1]~, 229]], [-7.0663729752107779635959310246705326058, 8.06637297521077796
460: 35959310246705326058], [1, x], [1, 0; 0, 1], [1, 0, 0, 57; 0, 1, 1, 1]], [[3
461: , [3], [[3, 2; 0, 1]]], 2.7124653051843439746808795106061300699, 0.881442251
462: 26545793690341704100000000000, [2, -1], [x + 7], 162], [Mat(1), Mat(1), [[[3
463: , 2; 0, 1], [0, 0]]]], 0], [[[5, 3; 0, 1], [1, 0]], [8, [4, 2], [[2, 0]~, [-
464: 1, 1]~]], Mat([[5, [-2, 1]~, 1, 1, [1, 1]~], 1]), [[[[4], [[2, 0]~], [[2, 0]
465: ~], [[Mod(0, 2)]~], 1]], [[2], [[-1, 1]~], Mat(1)]], [1, 0; 0, 1]], [[1, 0]~
466: ], [1, -3, -6; 0, 0, 1; 0, 1, 0], [12, [12], [[3, 2; 0, 1]]], [[0, 0; 0, 1],
467: [1, -1; 1, 1]]]
468: ? rnfinit(nf2,x^5-x-2)
469: [x^5 - x - 2, [[1, 2], [0, 5]], [[49744, 0, 0; 0, 49744, 0; 0, 0, 49744], [3
470: 109, 0, 0]~], [1, 0, 0; 0, 1, 0; 0, 0, 1], [[[1, 1.2671683045421243172528914
471: 279776896412, 1.6057155120361619195949075151301679393, 2.0347118029638523119
472: 874445717108994866, 2.5783223055935536544757871909285592749; 1, 0.2609638803
473: 8645528500256735072673484811 + 1.1772261533941944394700286585617926513*I, -1
474: .3177592693689352747870763902256347904 + 0.614427010164338838041906608641467
475: 31824*I, -1.0672071180669977537495893497477340535 - 1.3909574189920019216524
476: 673160314582604*I, 1.3589689411882615753626439480614001936 - 1.6193337759893
477: 970298359887428575174472*I; 1, -0.89454803265751744362901306471557966872 + 0
478: .53414854617473272670874609150394379949*I, 0.5149015133508543149896226326605
479: 5082078 - 0.95564306225496055080453352211847466685*I, 0.04985121658507159775
480: 5867063892284310224 + 1.1299025160425089918993024639913611785*I, -0.64813009
481: 398503840260053754352567983115 - 0.98412411795664774269323431620030610541*I]
482: , [1, 1.2671683045421243172528914279776896412 + 0.E-38*I, 1.6057155120361619
483: 195949075151301679393 + 0.E-38*I, 2.0347118029638523119874445717108994866 +
484: 0.E-37*I, 2.5783223055935536544757871909285592749 + 0.E-37*I; 1, 0.260963880
485: 38645528500256735072673484811 - 1.1772261533941944394700286585617926513*I, -
486: 1.3177592693689352747870763902256347904 - 0.61442701016433883804190660864146
487: 731824*I, -1.0672071180669977537495893497477340535 + 1.390957418992001921652
488: 4673160314582604*I, 1.3589689411882615753626439480614001936 + 1.619333775989
489: 3970298359887428575174472*I; 1, 0.26096388038645528500256735072673484811 + 1
490: .1772261533941944394700286585617926513*I, -1.3177592693689352747870763902256
491: 347904 + 0.61442701016433883804190660864146731824*I, -1.06720711806699775374
492: 95893497477340535 - 1.3909574189920019216524673160314582604*I, 1.35896894118
493: 82615753626439480614001936 - 1.6193337759893970298359887428575174472*I; 1, -
494: 0.89454803265751744362901306471557966872 - 0.5341485461747327267087460915039
495: 4379949*I, 0.51490151335085431498962263266055082078 + 0.95564306225496055080
496: 453352211847466685*I, 0.049851216585071597755867063892284310224 - 1.12990251
497: 60425089918993024639913611785*I, -0.64813009398503840260053754352567983115 +
498: 0.98412411795664774269323431620030610541*I; 1, -0.8945480326575174436290130
499: 6471557966872 + 0.53414854617473272670874609150394379949*I, 0.51490151335085
500: 431498962263266055082078 - 0.95564306225496055080453352211847466685*I, 0.049
501: 851216585071597755867063892284310224 + 1.12990251604250899189930246399136117
502: 85*I, -0.64813009398503840260053754352567983115 - 0.984124117956647742693234
503: 31620030610541*I]], [[1, 2, 2; 1.2671683045421243172528914279776896412, 0.52
504: 192776077291057000513470145346969622 - 2.35445230678838887894005731712358530
505: 26*I, -1.7890960653150348872580261294311593374 - 1.0682970923494654534174921
506: 830078875989*I; 1.6057155120361619195949075151301679393, -2.6355185387378705
507: 495741527804512695809 - 1.2288540203286776760838132172829346364*I, 1.0298030
508: 267017086299792452653211016415 + 1.9112861245099211016090670442369493337*I;
509: 2.0347118029638523119874445717108994866, -2.13441423613399550749917869949546
510: 81070 + 2.7819148379840038433049346320629165208*I, 0.09970243317014319551173
511: 4127784568620449 - 2.2598050320850179837986049279827223571*I; 2.578322305593
512: 5536544757871909285592749, 2.7179378823765231507252878961228003872 + 3.23866
513: 75519787940596719774857150348944*I, -1.2962601879700768052010750870513596623
514: + 1.9682482359132954853864686324006122108*I], [1, 1, 1, 1, 1; 1.26716830454
515: 21243172528914279776896412 + 0.E-38*I, 0.26096388038645528500256735072673484
516: 811 + 1.1772261533941944394700286585617926513*I, 0.2609638803864552850025673
517: 5072673484811 - 1.1772261533941944394700286585617926513*I, -0.89454803265751
518: 744362901306471557966872 + 0.53414854617473272670874609150394379949*I, -0.89
519: 454803265751744362901306471557966872 - 0.53414854617473272670874609150394379
520: 949*I; 1.6057155120361619195949075151301679393 + 0.E-38*I, -1.31775926936893
521: 52747870763902256347904 + 0.61442701016433883804190660864146731824*I, -1.317
522: 7592693689352747870763902256347904 - 0.6144270101643388380419066086414673182
523: 4*I, 0.51490151335085431498962263266055082078 - 0.95564306225496055080453352
524: 211847466685*I, 0.51490151335085431498962263266055082078 + 0.955643062254960
525: 55080453352211847466685*I; 2.0347118029638523119874445717108994866 + 0.E-37*
526: I, -1.0672071180669977537495893497477340535 - 1.3909574189920019216524673160
527: 314582604*I, -1.0672071180669977537495893497477340535 + 1.390957418992001921
528: 6524673160314582604*I, 0.049851216585071597755867063892284310224 + 1.1299025
529: 160425089918993024639913611785*I, 0.049851216585071597755867063892284310224
530: - 1.1299025160425089918993024639913611785*I; 2.57832230559355365447578719092
531: 85592749 + 0.E-37*I, 1.3589689411882615753626439480614001936 - 1.61933377598
532: 93970298359887428575174472*I, 1.3589689411882615753626439480614001936 + 1.61
533: 93337759893970298359887428575174472*I, -0.6481300939850384026005375435256798
534: 3115 - 0.98412411795664774269323431620030610541*I, -0.6481300939850384026005
535: 3754352567983115 + 0.98412411795664774269323431620030610541*I]], [[5, -5.877
536: 4717541114375398032809710000000000 E-39 + 3.42274939913785433235754950013147
537: 29016*I, 2.3509887016445750159213123880000000000 E-38 - 0.682432104181243425
538: 52525382695401469720*I, -2.3509887016445750159213123880000000000 E-38 - 0.52
539: 210980589898585950632970408019416371*I, 3.9999999999999999999999999999999999
540: 999 - 5.2069157878920895450584461181156471052*I; -5.877471754111437539803280
541: 9710000000000 E-39 - 3.4227493991378543323575495001314729016*I, 6.6847043424
542: 634879841147654217963674264 - 5.8774717541114375398032809710000000000 E-39*I
543: , 0.85145677340721376574333983502938573598 + 4.58295731809784302915415926006
544: 01794652*I, -0.13574266252716976137461193821267520737 - 0.288051085440257723
545: 61738936467682050391*I, 0.27203784387468568916539788233281013320 - 1.5917147
546: 279942947718965650859986677247*I; 2.3509887016445750159213123880000000000 E-
547: 38 + 0.68243210418124342552525382695401469720*I, 0.8514567734072137657433398
548: 3502938573598 - 4.5829573180978430291541592600601794652*I, 9.163096853022107
549: 7951281598310681467898 + 0.E-38*I, 2.2622987652095629453403849736225691490 +
550: 6.2361927913558506765724047063180706869*I, -0.21796409886496632254445901043
551: 974770643 + 0.34559368931063215686158939748833975810*I; -2.35098870164457501
552: 59213123880000000000 E-38 + 0.52210980589898585950632970408019416371*I, -0.1
553: 3574266252716976137461193821267520737 + 0.2880510854402577236173893646768205
554: 0392*I, 2.2622987652095629453403849736225691490 - 6.236192791355850676572404
555: 7063180706869*I, 12.845768948832335511882696939380696155 + 1.175494350822287
556: 5079606561940000000000 E-38*I, 4.5618400502378124720913214622468855074 + 8.6
557: 033930051068500425218923146793019614*I; 3.9999999999999999999999999999999999
558: 999 + 5.2069157878920895450584461181156471052*I, 0.2720378438746856891653978
559: 8233281013320 + 1.5917147279942947718965650859986677247*I, -0.21796409886496
560: 632254445901043974770643 - 0.34559368931063215686158939748833975810*I, 4.561
561: 8400502378124720913214622468855074 - 8.6033930051068500425218923146793019615
562: *I, 18.362968630416114402425299186062892646 + 5.8774717541114375398032809710
563: 000000000 E-39*I], [5, -1.1754943508222875079606561940000000000 E-38 + 0.E-3
564: 8*I, 2.3509887016445750159213123880000000000 E-38 + 0.E-38*I, -1.76324152623
565: 34312619409842910000000000 E-38 + 0.E-38*I, 3.999999999999999999999999999999
566: 9999998 + 0.E-38*I; -1.1754943508222875079606561940000000000 E-38 + 0.E-38*I
567: , 6.6847043424634879841147654217963674264 - 5.877471754111437539803280971000
568: 0000000 E-39*I, 0.85145677340721376574333983502938573597 + 5.877471754111437
569: 5398032809710000000000 E-39*I, -0.13574266252716976137461193821267520737 + 5
570: .8774717541114375398032809710000000000 E-39*I, 0.272037843874685689165397882
571: 33281013314 - 5.8774717541114375398032809710000000000 E-39*I; 2.350988701644
572: 5750159213123880000000000 E-38 + 0.E-38*I, 0.8514567734072137657433398350293
573: 8573597 + 5.8774717541114375398032809710000000000 E-39*I, 9.1630968530221077
574: 951281598310681467898 + 0.E-38*I, 2.2622987652095629453403849736225691490 +
575: 2.3509887016445750159213123880000000000 E-38*I, -0.2179640988649663225444590
576: 1043974770651 + 0.E-38*I; -1.7632415262334312619409842910000000000 E-38 + 0.
577: E-38*I, -0.13574266252716976137461193821267520737 + 5.8774717541114375398032
578: 809710000000000 E-39*I, 2.2622987652095629453403849736225691490 + 2.35098870
579: 16445750159213123880000000000 E-38*I, 12.84576894883233551188269693938069615
580: 5 + 0.E-37*I, 4.5618400502378124720913214622468855073 - 3.526483052466862523
581: 8819685820000000000 E-38*I; 3.9999999999999999999999999999999999998 + 0.E-38
582: *I, 0.27203784387468568916539788233281013314 - 5.877471754111437539803280971
583: 0000000000 E-39*I, -0.21796409886496632254445901043974770651 + 0.E-38*I, 4.5
584: 618400502378124720913214622468855073 - 3.52648305246686252388196858200000000
585: 00 E-38*I, 18.362968630416114402425299186062892646 + 0.E-37*I]], [Mod(5, y^3
586: - y - 1), 0, 0, 0, Mod(4, y^3 - y - 1); 0, 0, 0, Mod(4, y^3 - y - 1), Mod(1
587: 0, y^3 - y - 1); 0, 0, Mod(4, y^3 - y - 1), Mod(10, y^3 - y - 1), 0; 0, Mod(
588: 4, y^3 - y - 1), Mod(10, y^3 - y - 1), 0, 0; Mod(4, y^3 - y - 1), Mod(10, y^
589: 3 - y - 1), 0, 0, Mod(4, y^3 - y - 1)], [;], [;], [;]], [[1.2671683045421243
590: 172528914279776896412, 0.26096388038645528500256735072673484811 + 1.17722615
591: 33941944394700286585617926513*I, -0.89454803265751744362901306471557966872 +
592: 0.53414854617473272670874609150394379949*I], [1.267168304542124317252891427
593: 9776896412 + 0.E-38*I, 0.26096388038645528500256735072673484811 - 1.17722615
594: 33941944394700286585617926513*I, 0.26096388038645528500256735072673484811 +
595: 1.1772261533941944394700286585617926513*I, -0.894548032657517443629013064715
596: 57966872 - 0.53414854617473272670874609150394379949*I, -0.894548032657517443
597: 62901306471557966872 + 0.53414854617473272670874609150394379949*I]~], [[Mod(
598: 1, y^3 - y - 1), Mod(1, y^3 - y - 1)*x, Mod(1, y^3 - y - 1)*x^2, Mod(1, y^3
599: - y - 1)*x^3, Mod(1, y^3 - y - 1)*x^4], [[1, 0, 0; 0, 1, 0; 0, 0, 1], [1, 0,
600: 0; 0, 1, 0; 0, 0, 1], [1, 0, 0; 0, 1, 0; 0, 0, 1], [1, 0, 0; 0, 1, 0; 0, 0,
601: 1], [1, 0, 0; 0, 1, 0; 0, 0, 1]]], [Mod(1, y^3 - y - 1), 0, 0, 0, 0; 0, Mod
602: (1, y^3 - y - 1), 0, 0, 0; 0, 0, Mod(1, y^3 - y - 1), 0, 0; 0, 0, 0, Mod(1,
603: y^3 - y - 1), 0; 0, 0, 0, 0, Mod(1, y^3 - y - 1)], [], [y^3 - y - 1, [1, 1],
604: -23, 1, [[1, 1.3247179572447460259609088544780973407, 1.7548776662466927600
605: 495088963585286918; 1, -0.66235897862237301298045442723904867036 + 0.5622795
606: 1206230124389918214490937306149*I, 0.12256116687665361997524555182073565405
607: - 0.74486176661974423659317042860439236724*I], [1, 2; 1.32471795724474602596
608: 09088544780973407, -1.3247179572447460259609088544780973407 - 1.124559024124
609: 6024877983642898187461229*I; 1.7548776662466927600495088963585286918, 0.2451
610: 2233375330723995049110364147130810 + 1.4897235332394884731863408572087847344
611: *I], [3, 0.E-96, 2.0000000000000000000000000000000000000; 0.E-96, 3.26463299
612: 87400782801485266890755860756, 1.3247179572447460259609088544780973407; 2.00
613: 00000000000000000000000000000000000, 1.3247179572447460259609088544780973407
614: , 4.2192762054875453178332176670757633303], [3, 0, 2; 0, 2, 3; 2, 3, 2], [23
615: , 13, 15; 0, 1, 0; 0, 0, 1], [-5, 6, -4; 6, 2, -9; -4, -9, 6], [23, [7, 10,
616: 1]~, 529]], [1.3247179572447460259609088544780973407, -0.6623589786223730129
617: 8045442723904867036 + 0.56227951206230124389918214490937306149*I], [1, y, y^
618: 2], [1, 0, 0; 0, 1, 0; 0, 0, 1], [1, 0, 0, 0, 0, 1, 0, 1, 0; 0, 1, 0, 1, 0,
619: 1, 0, 1, 1; 0, 0, 1, 0, 1, 0, 1, 0, 1]], [x^15 - 5*x^13 + 5*x^12 + 7*x^11 -
620: 26*x^10 - 5*x^9 + 45*x^8 + 158*x^7 - 98*x^6 + 110*x^5 - 190*x^4 + 189*x^3 +
621: 144*x^2 + 25*x + 1, Mod(39516536165538345/83718587879473471*x^14 - 650051247
622: 6832995/83718587879473471*x^13 - 196215472046117185/83718587879473471*x^12 +
623: 229902227480108910/83718587879473471*x^11 + 237380704030959181/837185878794
624: 73471*x^10 - 1064931988160773805/83718587879473471*x^9 - 20657086671714300/8
625: 3718587879473471*x^8 + 1772885205999206010/83718587879473471*x^7 + 595203321
626: 7241102348/83718587879473471*x^6 - 4838840187320655696/83718587879473471*x^5
627: + 5180390720553188700/83718587879473471*x^4 - 8374015687535120430/837185878
628: 79473471*x^3 + 8907744727915040221/83718587879473471*x^2 + 41559766641234343
629: 81/83718587879473471*x + 318920215718580450/83718587879473471, x^15 - 5*x^13
630: + 5*x^12 + 7*x^11 - 26*x^10 - 5*x^9 + 45*x^8 + 158*x^7 - 98*x^6 + 110*x^5 -
631: 190*x^4 + 189*x^3 + 144*x^2 + 25*x + 1), -1, [1, x, x^2, x^3, x^4, x^5, x^6
632: , x^7, x^8, x^9, x^10, x^11, x^12, x^13, 1/83718587879473471*x^14 - 20528463
633: 024680133/83718587879473471*x^13 - 4742392948888610/83718587879473471*x^12 -
634: 9983523646123358/83718587879473471*x^11 + 40898955597139011/837185878794734
635: 71*x^10 + 29412692423971937/83718587879473471*x^9 - 5017479463612351/8371858
636: 7879473471*x^8 + 41014993230075066/83718587879473471*x^7 - 2712810874903165/
637: 83718587879473471*x^6 + 20152905879672878/83718587879473471*x^5 + 9591643151
638: 927789/83718587879473471*x^4 - 8471905745957397/83718587879473471*x^3 - 1339
639: 5753879413605/83718587879473471*x^2 + 27623037732247492/83718587879473471*x
640: + 26306699661480593/83718587879473471], [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
641: 0, 0, -26306699661480593; 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -276230
642: 37732247492; 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 13395753879413605; 0,
643: 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8471905745957397; 0, 0, 0, 0, 1, 0,
644: 0, 0, 0, 0, 0, 0, 0, 0, -9591643151927789; 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0,
645: 0, 0, 0, -20152905879672878; 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 27128
646: 10874903165; 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, -41014993230075066; 0
647: , 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 5017479463612351; 0, 0, 0, 0, 0, 0,
648: 0, 0, 0, 1, 0, 0, 0, 0, -29412692423971937; 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1
649: , 0, 0, 0, -40898955597139011; 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 998
650: 3523646123358; 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 4742392948888610; 0
651: , 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 20528463024680133; 0, 0, 0, 0, 0, 0
652: , 0, 0, 0, 0, 0, 0, 0, 0, 83718587879473471]]]
653: ? bnfcertify(bnf)
654: 1
655: ? setrand(1);bnfclassunit(x^4-7,2,[0.2,0.2])
656:
657: [x^4 - 7]
658:
659: [[2, 1]]
660:
661: [[-87808, 1]]
662:
663: [[1, x, x^2, x^3]]
664:
665: [[2, [2], [[2, 1, 1, 1; 0, 1, 0, 0; 0, 0, 1, 0; 0, 0, 0, 1]]]]
666:
667: [14.229975145405511722395637833443108790]
668:
669: [1.1211171071527562299744232290000000000]
670:
671: ? setrand(1);bnfclassunit(x^2-x-100000)
672: *** Warning: fundamental units too large, not given.
673:
674: [x^2 - x - 100000]
675:
676: [[2, 0]]
677:
678: [[400001, 1]]
679:
680: [[1, x]]
681:
682: [[5, [5], [[2, 1; 0, 1]]]]
683:
684: [129.82045011403975460991182396195022419]
685:
686: [0.98765369790690472391212970100000000000]
687:
688: [[2, -1]]
689:
690: [[;]]
691:
692: [0]
693:
694: ? setrand(1);bnfclassunit(x^2-x-100000,1)
695:
696: [x^2 - x - 100000]
697:
698: [[2, 0]]
699:
700: [[400001, 1]]
701:
702: [[1, x]]
703:
704: [[5, [5], [[2, 1; 0, 1]]]]
705:
706: [129.82045011403975460991182396195022419]
707:
708: [0.98765369790690472391212970100000000000]
709:
710: [[2, -1]]
711:
712: [[379554884019013781006303254896369154068336082609238336*x + 119836165644250
713: 789990462835950022871665178127611316131167]]
714:
715: [185]
716:
717: ? setrand(1);bnfclassunit(x^4+24*x^2+585*x+1791,,[0.1,0.1])
718:
719: [x^4 + 24*x^2 + 585*x + 1791]
720:
721: [[0, 2]]
722:
723: [[18981, 3087]]
724:
725: [[1, x, 1/3*x^2, 1/1029*x^3 + 33/343*x^2 - 155/343*x - 58/343]]
726:
727: [[4, [4], [[7, 6, 2, 4; 0, 1, 0, 0; 0, 0, 1, 0; 0, 0, 0, 1]]]]
728:
729: [3.7941269688216589341408274220859400302]
730:
731: [0.88260182866555813061644128400000000000]
732:
733: [[6, -10/1029*x^3 + 13/343*x^2 - 165/343*x - 1135/343]]
734:
735: [[4/1029*x^3 + 53/1029*x^2 + 66/343*x + 111/343]]
736:
737: [140]
738:
739: ? setrand(1);bnfclgp(17)
740: [1, [], []]
741: ? setrand(1);bnfclgp(-31)
742: [3, [3], [Qfb(2, 1, 4)]]
743: ? setrand(1);bnfclgp(x^4+24*x^2+585*x+1791)
744: [4, [4], [[7, 5, 1, 0; 0, 1, 0, 0; 0, 0, 1, 0; 0, 0, 0, 1]]]
745: ? bnrconductor(bnf,[[25,13;0,1],[1,1]])
746: [[5, 3; 0, 1], [1, 0]]
747: ? bnrconductorofchar(bnr,[2])
748: [[5, 3; 0, 1], [0, 0]]
749: ? bnfisprincipal(bnf,[5,1;0,1],0)
750: [1]~
751: ? bnfisprincipal(bnf,[5,1;0,1])
752: [[1]~, [2, 1/3]~, 151]
753: ? bnfisunit(bnf,Mod(3405*x-27466,x^2-x-57))
754: [-4, Mod(1, 2)]~
755: ? \p19
756: realprecision = 19 significant digits
757: ? bnfmake(sbnf)
758: [Mat(2), Mat([0, 1, 1, 1, 0, 1, 1, 1]), [1.173637103435061715 + 3.1415926535
759: 89793238*I, -4.562279014988837901 + 3.141592653589793238*I; -2.6335434327389
760: 76049 + 3.141592653589793238*I, 1.420330600779487358 + 3.141592653589793238*
761: I; 1.459906329303914334, 3.141948414209350543], [1.246346989334819161, -1.99
762: 0056445584799713 + 3.141592653589793238*I, 0.5404006376129469727, -0.6926391
763: 142471042845 + 3.141592653589793238*I, 0.E-96, 0.004375616572659815402 + 3.1
764: 41592653589793238*I, 0.3677262014027817705 + 3.141592653589793238*I, -0.8305
765: 625946607188639 + 3.141592653589793238*I, -1.977791147836553953 + 3.14159265
766: 3589793238*I; 0.6716827432867392935, 0.5379005671092853266, -0.8333219883742
767: 404172, -0.2461086674077943078, 0.E-96, -0.8738318043071131265, 0.9729063188
768: 316092378, -1.552661549868775853, 0.5774919091398324092 + 3.1415926535897932
769: 38*I; -1.918029732621558454 + 3.141592653589793238*I, 1.452155878475514386,
770: 0.2929213507612934444 + 3.141592653589793238*I, 0.9387477816548985923, 0.E-9
771: 6, 0.8694561877344533111, -1.340632520234391008, 2.383224144529494717, 1.400
772: 299238696721544 + 3.141592653589793238*I], [[3, [-1, 1, 0]~, 1, 1, [1, 0, 1]
773: ~], [5, [3, 1, 0]~, 1, 1, [-2, 1, 1]~], [5, [-1, 1, 0]~, 1, 1, [1, 0, 1]~],
774: [5, [2, 1, 0]~, 1, 1, [2, 2, 1]~], [3, [1, 0, 1]~, 1, 2, [-1, 1, 0]~], [11,
775: [1, 1, 0]~, 1, 1, [-1, -2, 1]~], [23, [-10, 1, 0]~, 1, 1, [7, 9, 1]~], [13,
776: [19, 1, 0]~, 1, 1, [2, 6, 1]~], [19, [-6, 1, 0]~, 1, 1, [-3, 5, 1]~]]~, [1,
777: 2, 3, 4, 5, 6, 7, 8, 9]~, [x^3 - x^2 - 14*x - 1, [3, 0], 10889, 1, [[1, -3.2
778: 33732695981516673, 10.45702714905988813; 1, -0.07182350902743636344, 0.00515
779: 8616449014232794; 1, 4.305556205008953036, 18.53781423449109762], [1, 1, 1;
780: -3.233732695981516673, -0.07182350902743636344, 4.305556205008953036; 10.457
781: 02714905988813, 0.005158616449014232794, 18.53781423449109762], [3, 1.000000
782: 000000000000, 29.00000000000000000; 1.000000000000000000, 29.000000000000000
783: 00, 46.00000000000000000; 29.00000000000000000, 46.00000000000000000, 453.00
784: 00000000000000], [3, 1, 29; 1, 29, 46; 29, 46, 453], [10889, 5698, 3794; 0,
785: 1, 0; 0, 0, 1], [11021, 881, -795; 881, 518, -109; -795, -109, 86], [10889,
786: [1890, 5190, 1]~, 118570321]], [-3.233732695981516673, -0.071823509027436363
787: 44, 4.305556205008953036], [1, x, x^2], [1, 0, 0; 0, 1, 0; 0, 0, 1], [1, 0,
788: 0, 0, 0, 1, 0, 1, 1; 0, 1, 0, 1, 0, 14, 0, 14, 15; 0, 0, 1, 0, 1, 1, 1, 1, 1
789: 5]], [[2, [2], [[3, 2, 2; 0, 1, 0; 0, 0, 1]]], 10.34800724602767998, 1.00000
790: 0000000000000, [2, -1], [x, x^2 + 2*x - 4], 1000], [Mat(1), Mat(1), [[[3, 2,
791: 2; 0, 1, 0; 0, 0, 1], [0, 0, 0]]]], 0]
792: ? \p38
793: realprecision = 38 significant digits
794: ? bnfnarrow(bnf)
795: [3, [3], [[3, 2; 0, 1]]]
796: ? bnfreg(x^2-x-57)
797: 2.7124653051843439746808795106061300699
798: ? bnfsignunit(bnf)
799:
800: [-1]
801:
802: [1]
803:
804: ? bnfunit(bnf)
805: [[x + 7], 162]
806: ? bnrclass(bnf,[[5,3;0,1],[1,0]])
807: [12, [12], [[3, 2; 0, 1]]]
808: ? bnr2=bnrclass(bnf,[[25,13;0,1],[1,1]],2)
809: [[Mat(3), Mat([1, 2, 1, 2, 1, 2, 1, 2, 1]), [-2.7124653051843439746808795106
810: 061300699 - 9.4247779607693797153879301498385086526*I; 2.7124653051843439746
811: 808795106061300699 - 6.2831853071795864769252867665590057684*I], [23347.9792
812: 23478346319454659159707591731 + 6.2831853071795864769252867665590057684*I, 8
813: 66.56619430687100142570357249059499540 + 6.283185307179586476925286766559005
814: 7684*I, 2881.3396396084587293295626563644245032 + 3.141592653589793238462643
815: 3832795028842*I, 27379.624790530768080428797780058276925 + 2.088097429759527
816: 8484866027080000000000 E-52*I, 57933.334567930851067108050790839116749 + 3.5
817: 497656305911973423188043860000000000 E-52*I, -34585.556250151557719998034043
818: 918848670 + 9.4247779607693797153879301498385086526*I, 23348.322511122623346
819: 549049047574325150 + 3.1415926535897932384626433832795028842*I, -0.343287644
820: 27702709438988786673341921876 + 3.1415926535897932384626433832795028842*I, -
821: 4031.7117453543045067063239888430083582 + 9.42477796076937971538793014983850
822: 86526*I, 27379.690968832650826160983148550600089 + 9.42477796076937971538793
823: 01498385086526*I; -23347.979223478346319454659159707591731 + 9.4247779607693
824: 797153879301498385086526*I, -866.56619430687100142570357249059499540 + 8.156
825: 6305849981556577374397490000000000 E-55*I, -2881.339639608458729329562656364
826: 4245032 + 9.4247779607693797153879301498385086526*I, -27379.6247905307680804
827: 28797780058276925 + 6.2831853071795864769252867665590057684*I, -57933.334567
828: 930851067108050790839116749 + 3.1415926535897932384626433832795028842*I, 345
829: 85.556250151557719998034043918848670 + 6.28318530717958647692528676655900576
830: 84*I, -23348.322511122623346549049047574325150 + 9.4247779607693797153879301
831: 498385086526*I, 0.34328764427702709438988786673341921876 + 0.E-57*I, 4031.71
832: 17453543045067063239888430083582 + 3.1415926535897932384626433832795028842*I
833: , -27379.690968832650826160983148550600089 + 6.28318530717958647692528676655
834: 90057684*I], [[3, [-1, 1]~, 1, 1, [0, 1]~], [3, [0, 1]~, 1, 1, [-1, 1]~], [5
835: , [-2, 1]~, 1, 1, [1, 1]~], [5, [1, 1]~, 1, 1, [-2, 1]~], [11, [-2, 1]~, 1,
836: 1, [1, 1]~], [11, [1, 1]~, 1, 1, [-2, 1]~], [17, [-3, 1]~, 1, 1, [2, 1]~], [
837: 17, [2, 1]~, 1, 1, [-3, 1]~], [19, [-1, 1]~, 1, 1, [0, 1]~], [19, [0, 1]~, 1
838: , 1, [-1, 1]~]]~, [1, 3, 5, 2, 4, 6, 7, 8, 10, 9]~, [x^2 - x - 57, [2, 0], 2
839: 29, 1, [[1, -7.0663729752107779635959310246705326058; 1, 8.06637297521077796
840: 35959310246705326058], [1, 1; -7.0663729752107779635959310246705326058, 8.06
841: 63729752107779635959310246705326058], [2, 1.00000000000000000000000000000000
842: 00000; 1.0000000000000000000000000000000000000, 115.000000000000000000000000
843: 00000000000], [2, 1; 1, 115], [229, 114; 0, 1], [115, -1; -1, 2], [229, [114
844: , 1]~, 229]], [-7.0663729752107779635959310246705326058, 8.06637297521077796
845: 35959310246705326058], [1, x], [1, 0; 0, 1], [1, 0, 0, 57; 0, 1, 1, 1]], [[3
846: , [3], [[3, 2; 0, 1]]], 2.7124653051843439746808795106061300699, 0.881442251
847: 26545793690341704100000000000, [2, -1], [x + 7], 162], [Mat(1), Mat(1), [[[3
848: , 2; 0, 1], [0, 0]]]], 0], [[[25, 13; 0, 1], [1, 1]], [80, [20, 2, 2], [[2,
849: 0]~, [0, -2]~, [2, 2]~]], Mat([[5, [-2, 1]~, 1, 1, [1, 1]~], 2]), [[[[4], [[
850: 2, 0]~], [[2, 0]~], [[Mod(0, 2), Mod(0, 2)]~], 1], [[5], [[6, 0]~], [[6, 0]~
851: ], [[Mod(0, 2), Mod(0, 2)]~], Mat([1/5, -13/5])]], [[2, 2], [[0, -2]~, [2, 2
852: ]~], [0, 1; 1, 0]]], [1, -12, 0, 0; 0, 0, 1, 0; 0, 0, 0, 1]], [[1, 0]~], [1,
853: -3, 0, -6; 0, 0, 1, 0; 0, 0, 0, 1; 0, 1, 0, 0], [12, [12], [[3, 2; 0, 1]]],
854: [[1/2, 5, -9; -1/2, -5, 10], [-2, 0; 0, 10]]]
855: ? bnrclassno(bnf,[[5,3;0,1],[1,0]])
856: 12
857: ? lu=ideallist(bnf,55,3);
858: ? bnrclassnolist(bnf,lu)
859: [[3], [], [3, 3], [3], [6, 6], [], [], [], [3, 3, 3], [], [3, 3], [3, 3], []
860: , [], [12, 6, 6, 12], [3], [3, 3], [], [9, 9], [6, 6], [], [], [], [], [6, 1
861: 2, 6], [], [3, 3, 3, 3], [], [], [], [], [], [3, 6, 6, 3], [], [], [9, 3, 9]
862: , [6, 6], [], [], [], [], [], [3, 3], [3, 3], [12, 12, 6, 6, 12, 12], [], []
863: , [6, 6], [9], [], [3, 3, 3, 3], [], [3, 3], [], [6, 12, 12, 6]]
864: ? bnrdisc(bnr,Mat(6))
865: [12, 12, 18026977100265125]
866: ? bnrdisc(bnr)
867: [24, 12, 40621487921685401825918161408203125]
868: ? bnrdisc(bnr2,,,2)
869: 0
870: ? bnrdisc(bnr,Mat(6),,1)
871: [6, 2, [125, 13; 0, 1]]
872: ? bnrdisc(bnr,,,1)
873: [12, 1, [1953125, 1160888; 0, 1]]
874: ? bnrdisc(bnr2,,,3)
875: 0
876: ? bnrdisclist(bnf,lu)
877: [[[6, 6, Mat([229, 3])]], [], [[], []], [[]], [[12, 12, [5, 3; 229, 6]], [12
878: , 12, [5, 3; 229, 6]]], [], [], [], [[], [], []], [], [[], []], [[], []], []
879: , [], [[24, 24, [3, 6; 5, 9; 229, 12]], [], [], [24, 24, [3, 6; 5, 9; 229, 1
880: 2]]], [[]], [[], []], [], [[18, 18, [19, 6; 229, 9]], [18, 18, [19, 6; 229,
881: 9]]], [[], []], [], [], [], [], [[], [24, 24, [5, 12; 229, 12]], []], [], [[
882: ], [], [], []], [], [], [], [], [], [[], [12, 12, [3, 3; 11, 3; 229, 6]], [1
883: 2, 12, [3, 3; 11, 3; 229, 6]], []], [], [], [[18, 18, [2, 12; 3, 12; 229, 9]
884: ], [], [18, 18, [2, 12; 3, 12; 229, 9]]], [[12, 12, [37, 3; 229, 6]], [12, 1
885: 2, [37, 3; 229, 6]]], [], [], [], [], [], [[], []], [[], []], [[], [], [], [
886: ], [], []], [], [], [[12, 12, [2, 12; 3, 3; 229, 6]], [12, 12, [2, 12; 3, 3;
887: 229, 6]]], [[18, 18, [7, 12; 229, 9]]], [], [[], [], [], []], [], [[], []],
888: [], [[], [24, 24, [5, 9; 11, 6; 229, 12]], [24, 24, [5, 9; 11, 6; 229, 12]]
889: , []]]
890: ? bnrdisclist(bnf,20,,1)
891: [[[[matrix(0,2), [[6, 6, Mat([229, 3])], [0, 0, 0], [0, 0, 0], [0, 0, 0]]]],
892: [], [[Mat([12, 1]), [[0, 0, 0], [0, 0, 0], [0, 0, 0], [12, 0, [3, 3; 229, 6
893: ]]]], [Mat([13, 1]), [[0, 0, 0], [0, 0, 0], [12, 6, [-1, 1; 3, 3; 229, 6]],
894: [0, 0, 0]]]], [[Mat([10, 1]), [[0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0]]]]
895: , [[Mat([20, 1]), [[12, 12, [5, 3; 229, 6]], [0, 0, 0], [0, 0, 0], [24, 0, [
896: 5, 9; 229, 12]]]], [Mat([21, 1]), [[12, 12, [5, 3; 229, 6]], [0, 0, 0], [24,
897: 12, [5, 9; 229, 12]], [0, 0, 0]]]], [], [], [], [[Mat([12, 2]), [[0, 0, 0],
898: [0, 0, 0], [0, 0, 0], [0, 0, 0]]], [[12, 1; 13, 1], [[0, 0, 0], [12, 6, [-1
899: , 1; 3, 6; 229, 6]], [0, 0, 0], [24, 0, [3, 12; 229, 12]]]], [Mat([13, 2]),
900: [[0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0]]]], [], [[Mat([44, 1]), [[0, 0,
901: 0], [0, 0, 0], [12, 6, [-1, 1; 11, 3; 229, 6]], [0, 0, 0]]], [Mat([45, 1]),
902: [[0, 0, 0], [0, 0, 0], [0, 0, 0], [12, 0, [11, 3; 229, 6]]]]], [[[10, 1; 12,
903: 1], [[0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0]]], [[10, 1; 13, 1], [[0, 0,
904: 0], [0, 0, 0], [0, 0, 0], [0, 0, 0]]]], [], [], [[[12, 1; 20, 1], [[24, 24,
905: [3, 6; 5, 9; 229, 12]], [0, 0, 0], [0, 0, 0], [48, 0, [3, 12; 5, 18; 229, 2
906: 4]]]], [[13, 1; 20, 1], [[0, 0, 0], [24, 12, [3, 6; 5, 9; 229, 12]], [24, 12
907: , [3, 6; 5, 6; 229, 12]], [48, 0, [3, 12; 5, 18; 229, 24]]]], [[12, 1; 21, 1
908: ], [[0, 0, 0], [24, 12, [3, 6; 5, 9; 229, 12]], [0, 0, 0], [48, 0, [3, 12; 5
909: , 18; 229, 24]]]], [[13, 1; 21, 1], [[24, 24, [3, 6; 5, 9; 229, 12]], [0, 0,
910: 0], [48, 24, [3, 12; 5, 18; 229, 24]], [0, 0, 0]]]], [[Mat([10, 2]), [[0, 0
911: , 0], [12, 6, [-1, 1; 2, 12; 229, 6]], [12, 6, [-1, 1; 2, 12; 229, 6]], [24,
912: 0, [2, 36; 229, 12]]]]], [[Mat([68, 1]), [[0, 0, 0], [12, 6, [-1, 1; 17, 3;
913: 229, 6]], [0, 0, 0], [0, 0, 0]]], [Mat([69, 1]), [[0, 0, 0], [12, 6, [-1, 1
914: ; 17, 3; 229, 6]], [0, 0, 0], [0, 0, 0]]]], [], [[Mat([76, 1]), [[18, 18, [1
915: 9, 6; 229, 9]], [0, 0, 0], [0, 0, 0], [36, 0, [19, 15; 229, 18]]]], [Mat([77
916: , 1]), [[18, 18, [19, 6; 229, 9]], [0, 0, 0], [36, 18, [-1, 1; 19, 15; 229,
917: 18]], [0, 0, 0]]]], [[[10, 1; 20, 1], [[0, 0, 0], [0, 0, 0], [0, 0, 0], [0,
918: 0, 0]]], [[10, 1; 21, 1], [[0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0]]]]]]
919: ? bnrisprincipal(bnr,idealprimedec(bnf,7)[1])
920: [[9]~, [-2170/6561, -931/19683]~, 148]
921: ? dirzetak(nf4,30)
922: [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,
923: 0, 1, 0, 1, 0]
924: ? factornf(x^3+x^2-2*x-1,t^3+t^2-2*t-1)
925:
926: [Mod(1, t^3 + t^2 - 2*t - 1)*x + Mod(-t, t^3 + t^2 - 2*t - 1) 1]
927:
928: [Mod(1, t^3 + t^2 - 2*t - 1)*x + Mod(-t^2 + 2, t^3 + t^2 - 2*t - 1) 1]
929:
930: [Mod(1, t^3 + t^2 - 2*t - 1)*x + Mod(t^2 + t - 1, t^3 + t^2 - 2*t - 1) 1]
931:
932: ? vp=idealprimedec(nf,3)[1]
933: [3, [1, 1, 0, 0, 0]~, 1, 1, [1, -1, -1, 0, 0]~]
934: ? idx=idealmul(nf,matid(5),vp)
935:
936: [3 1 2 2 2]
937:
938: [0 1 0 0 0]
939:
940: [0 0 1 0 0]
941:
942: [0 0 0 1 0]
943:
944: [0 0 0 0 1]
945:
946: ? idealinv(nf,idx)
947:
948: [1 0 2/3 0 0]
949:
950: [0 1 1/3 0 0]
951:
952: [0 0 1/3 0 0]
953:
954: [0 0 0 1 0]
955:
956: [0 0 0 0 1]
957:
958: ? idy=idealred(nf,idx,[1,5,6])
959:
960: [5 0 0 2 0]
961:
962: [0 5 0 0 0]
963:
964: [0 0 5 2 0]
965:
966: [0 0 0 1 0]
967:
968: [0 0 0 0 5]
969:
970: ? idx2=idealmul(nf,idx,idx)
971:
972: [9 7 5 8 2]
973:
974: [0 1 0 0 0]
975:
976: [0 0 1 0 0]
977:
978: [0 0 0 1 0]
979:
980: [0 0 0 0 1]
981:
982: ? idt=idealmul(nf,idx,idx,1)
983:
984: [2 0 0 0 1]
985:
986: [0 2 0 0 1]
987:
988: [0 0 2 0 0]
989:
990: [0 0 0 2 1]
991:
992: [0 0 0 0 1]
993:
994: ? idz=idealintersect(nf,idx,idy)
995:
996: [15 5 10 12 10]
997:
998: [0 5 0 0 0]
999:
1000: [0 0 5 2 0]
1001:
1002: [0 0 0 1 0]
1003:
1004: [0 0 0 0 5]
1005:
1006: ? aid=[idx,idy,idz,matid(5),idx]
1007: [[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]
1008: , [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
1009: ], [15, 5, 10, 12, 10; 0, 5, 0, 0, 0; 0, 0, 5, 2, 0; 0, 0, 0, 1, 0; 0, 0, 0,
1010: 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
1011: , 0, 1], [3, 1, 2, 2, 2; 0, 1, 0, 0, 0; 0, 0, 1, 0, 0; 0, 0, 0, 1, 0; 0, 0,
1012: 0, 0, 1]]
1013: ? bid=idealstar(nf2,54,1)
1014: [[[54, 0, 0; 0, 54, 0; 0, 0, 54], [0]], [132678, [1638, 9, 9]], [[2, [2, 0,
1015: 0]~, 1, 3, [1, 0, 0]~], 1; [3, [3, 0, 0]~, 1, 3, [1, 0, 0]~], 3], [[[[7], [[
1016: 0, 1, 0]~], [[-26, -27, 0]~], [[]~], 1]], [[[26], [[0, 2, 0]~], [[-27, 2, 0]
1017: ~], [[]~], 1], [[3, 3, 3], [[1, 3, 0]~, [1, 0, 3]~, [4, 0, 0]~], [[1, -24, 0
1018: ]~, [1, 0, -24]~, [-23, 0, 0]~], [[]~, []~, []~], [0, 1/3, 0; 0, 0, 1/3; 1/3
1019: , 0, 0]], [[3, 3, 3], [[1, 9, 0]~, [1, 0, 9]~, [10, 0, 0]~], [[1, -18, 0]~,
1020: [1, 0, -18]~, [-17, 0, 0]~], [[]~, []~, []~], [0, 1/9, 0; 0, 0, 1/9; 1/9, 0,
1021: 0]]], [[], [], [;]]], [468, 469, 0, 0, -48776, 0, 0, -36582; 0, 0, 1, 0, -7
1022: , -6, 0, -3; 0, 0, 0, 1, -3, 0, -6, 0]]
1023: ? vaid=[idx,idy,matid(5)]
1024: [[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]
1025: , [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
1026: ], [1, 0, 0, 0, 0; 0, 1, 0, 0, 0; 0, 0, 1, 0, 0; 0, 0, 0, 1, 0; 0, 0, 0, 0,
1027: 1]]
1028: ? haid=[matid(5),matid(5),matid(5)]
1029: [[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]
1030: , [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
1031: ], [1, 0, 0, 0, 0; 0, 1, 0, 0, 0; 0, 0, 1, 0, 0; 0, 0, 0, 1, 0; 0, 0, 0, 0,
1032: 1]]
1033: ? idealadd(nf,idx,idy)
1034:
1035: [1 0 0 0 0]
1036:
1037: [0 1 0 0 0]
1038:
1039: [0 0 1 0 0]
1040:
1041: [0 0 0 1 0]
1042:
1043: [0 0 0 0 1]
1044:
1045: ? idealaddtoone(nf,idx,idy)
1046: [[3, 0, 2, 1, 0]~, [-2, 0, -2, -1, 0]~]
1047: ? idealaddtoone(nf,[idy,idx])
1048: [[-5, 0, 0, 0, 0]~, [6, 0, 0, 0, 0]~]
1049: ? idealappr(nf,idy)
1050: [-2, 0, -2, 4, 0]~
1051: ? idealappr(nf,idealfactor(nf,idy),1)
1052: [-2, 0, -2, 4, 0]~
1053: ? idealcoprime(nf,idx,idx)
1054: [-2/3, 2/3, -1/3, 0, 0]~
1055: ? idealdiv(nf,idy,idt)
1056:
1057: [5 5/2 5/2 7/2 0]
1058:
1059: [0 5/2 0 0 0]
1060:
1061: [0 0 5/2 1 0]
1062:
1063: [0 0 0 1/2 0]
1064:
1065: [0 0 0 0 5/2]
1066:
1067: ? idealdiv(nf,idx2,idx,1)
1068:
1069: [3 1 2 2 2]
1070:
1071: [0 1 0 0 0]
1072:
1073: [0 0 1 0 0]
1074:
1075: [0 0 0 1 0]
1076:
1077: [0 0 0 0 1]
1078:
1079: ? idf=idealfactor(nf,idz)
1080:
1081: [[3, [1, 1, 0, 0, 0]~, 1, 1, [1, -1, -1, 0, 0]~] 1]
1082:
1083: [[5, [-2, 0, 0, 0, 1]~, 1, 1, [2, 2, 1, 1, 4]~] 1]
1084:
1085: [[5, [0, 0, -1, 0, 1]~, 4, 1, [4, 5, 4, 2, 0]~] 3]
1086:
1087: ? idealhnf(nf,vp)
1088:
1089: [3 1 2 2 2]
1090:
1091: [0 1 0 0 0]
1092:
1093: [0 0 1 0 0]
1094:
1095: [0 0 0 1 0]
1096:
1097: [0 0 0 0 1]
1098:
1099: ? idealhnf(nf,vp[2],3)
1100:
1101: [3 1 2 2 2]
1102:
1103: [0 1 0 0 0]
1104:
1105: [0 0 1 0 0]
1106:
1107: [0 0 0 1 0]
1108:
1109: [0 0 0 0 1]
1110:
1111: ? ideallist(bnf,20)
1112: [[[1, 0; 0, 1]], [], [[3, 2; 0, 1], [3, 0; 0, 1]], [[2, 0; 0, 2]], [[5, 3; 0
1113: , 1], [5, 1; 0, 1]], [], [], [], [[9, 5; 0, 1], [3, 0; 0, 3], [9, 3; 0, 1]],
1114: [], [[11, 9; 0, 1], [11, 1; 0, 1]], [[6, 4; 0, 2], [6, 0; 0, 2]], [], [], [
1115: [15, 8; 0, 1], [15, 3; 0, 1], [15, 11; 0, 1], [15, 6; 0, 1]], [[4, 0; 0, 4]]
1116: , [[17, 14; 0, 1], [17, 2; 0, 1]], [], [[19, 18; 0, 1], [19, 0; 0, 1]], [[10
1117: , 6; 0, 2], [10, 2; 0, 2]]]
1118: ? ideallog(nf2,w,bid)
1119: [1574, 8, 6]~
1120: ? idealmin(nf,idx,[1,2,3,4,5])
1121: [[-1; 0; 0; 1; 0], [2.0885812311199768913287869744681966008 + 3.141592653589
1122: 7932384626433832795028842*I, 1.5921096812520196555597562531657929785 + 4.244
1123: 7196639216499665715751642189271112*I, -0.79031915447583185468082063233076160
1124: 203 + 2.5437460822678889883600220330800078854*I]]
1125: ? idealnorm(nf,idt)
1126: 16
1127: ? idp=idealpow(nf,idx,7)
1128:
1129: [2187 1807 2129 692 1379]
1130:
1131: [0 1 0 0 0]
1132:
1133: [0 0 1 0 0]
1134:
1135: [0 0 0 1 0]
1136:
1137: [0 0 0 0 1]
1138:
1139: ? idealpow(nf,idx,7,1)
1140:
1141: [2 0 0 0 1]
1142:
1143: [0 2 0 0 1]
1144:
1145: [0 0 2 0 0]
1146:
1147: [0 0 0 2 1]
1148:
1149: [0 0 0 0 1]
1150:
1151: ? idealprimedec(nf,2)
1152: [[2, [3, 1, 0, 0, 0]~, 1, 1, [1, 1, 0, 1, 1]~], [2, [-3, -5, -4, 3, 15]~, 1,
1153: 4, [1, 1, 0, 0, 0]~]]
1154: ? idealprimedec(nf,3)
1155: [[3, [1, 1, 0, 0, 0]~, 1, 1, [1, -1, -1, 0, 0]~], [3, [-1, 1, -1, 0, 1]~, 2,
1156: 2, [1, 2, 3, 1, 0]~]]
1157: ? idealprimedec(nf,11)
1158: [[11, [11, 0, 0, 0, 0]~, 1, 5, [1, 0, 0, 0, 0]~]]
1159: ? idealprincipal(nf,Mod(x^3+5,nfpol))
1160:
1161: [6]
1162:
1163: [0]
1164:
1165: [1]
1166:
1167: [3]
1168:
1169: [0]
1170:
1171: ? idealtwoelt(nf,idy)
1172: [5, [2, 0, 2, 1, 0]~]
1173: ? idealtwoelt(nf,idy,10)
1174: [-2, 0, -2, -1, 0]~
1175: ? idealstar(nf2,54)
1176: [[[54, 0, 0; 0, 54, 0; 0, 0, 54], [0]], [132678, [1638, 9, 9]], [[2, [2, 0,
1177: 0]~, 1, 3, [1, 0, 0]~], 1; [3, [3, 0, 0]~, 1, 3, [1, 0, 0]~], 3], [[[[7], [[
1178: 0, 1, 0]~], [[-26, -27, 0]~], [[]~], 1]], [[[26], [[0, 2, 0]~], [[-27, 2, 0]
1179: ~], [[]~], 1], [[3, 3, 3], [[1, 3, 0]~, [1, 0, 3]~, [4, 0, 0]~], [[1, -24, 0
1180: ]~, [1, 0, -24]~, [-23, 0, 0]~], [[]~, []~, []~], [0, 1/3, 0; 0, 0, 1/3; 1/3
1181: , 0, 0]], [[3, 3, 3], [[1, 9, 0]~, [1, 0, 9]~, [10, 0, 0]~], [[1, -18, 0]~,
1182: [1, 0, -18]~, [-17, 0, 0]~], [[]~, []~, []~], [0, 1/9, 0; 0, 0, 1/9; 1/9, 0,
1183: 0]]], [[], [], [;]]], [468, 469, 0, 0, -48776, 0, 0, -36582; 0, 0, 1, 0, -7
1184: , -6, 0, -3; 0, 0, 0, 1, -3, 0, -6, 0]]
1185: ? idealval(nf,idp,vp)
1186: 7
1187: ? ideleprincipal(nf,Mod(x^3+5,nfpol))
1188: [[6; 0; 1; 3; 0], [2.2324480827796254080981385584384939684 + 3.1415926535897
1189: 932384626433832795028842*I, 5.0387659675158716386435353106610489968 + 1.5851
1190: 760343512250049897278861965702423*I, 4.2664040272651028743625910797589683173
1191: - 0.0083630478144368246110910258645462996191*I]]
1192: ? ba=nfalgtobasis(nf,Mod(x^3+5,nfpol))
1193: [6, 0, 1, 3, 0]~
1194: ? bb=nfalgtobasis(nf,Mod(x^3+x,nfpol))
1195: [1, 1, 1, 3, 0]~
1196: ? bc=matalgtobasis(nf,[Mod(x^2+x,nfpol);Mod(x^2+1,nfpol)])
1197:
1198: [[0, 1, 1, 0, 0]~]
1199:
1200: [[1, 0, 1, 0, 0]~]
1201:
1202: ? matbasistoalg(nf,bc)
1203:
1204: [Mod(x^2 + x, x^5 - 5*x^3 + 5*x + 25)]
1205:
1206: [Mod(x^2 + 1, x^5 - 5*x^3 + 5*x + 25)]
1207:
1208: ? nfbasis(x^3+4*x+5)
1209: [1, x, 1/7*x^2 - 1/7*x - 2/7]
1210: ? nfbasis(x^3+4*x+5,2)
1211: [1, x, 1/7*x^2 - 1/7*x - 2/7]
1212: ? nfbasis(x^3+4*x+12,1)
1213: [1, x, 1/2*x^2]
1214: ? nfbasistoalg(nf,ba)
1215: Mod(x^3 + 5, x^5 - 5*x^3 + 5*x + 25)
1216: ? nfbasis(p2,0,fa)
1217: [1, x, x^2, 1/11699*x^3 + 1847/11699*x^2 - 132/11699*x - 2641/11699, 1/13962
1218: 3738889203638909659*x^4 - 1552451622081122020/139623738889203638909659*x^3 +
1219: 418509858130821123141/139623738889203638909659*x^2 - 6810913798507599407313
1220: 4/139623738889203638909659*x - 13185339461968406/58346808996920447]
1221: ? da=nfdetint(nf,[a,aid])
1222:
1223: [30 5 25 27 10]
1224:
1225: [0 5 0 0 0]
1226:
1227: [0 0 5 2 0]
1228:
1229: [0 0 0 1 0]
1230:
1231: [0 0 0 0 5]
1232:
1233: ? nfdisc(x^3+4*x+12)
1234: -1036
1235: ? nfdisc(x^3+4*x+12,1)
1236: -1036
1237: ? nfdisc(p2,0,fa)
1238: 136866601
1239: ? nfeltdiv(nf,ba,bb)
1240: [755/373, -152/373, 159/373, 120/373, -264/373]~
1241: ? nfeltdiveuc(nf,ba,bb)
1242: [2, 0, 0, 0, -1]~
1243: ? nfeltdivrem(nf,ba,bb)
1244: [[2, 0, 0, 0, -1]~, [-12, -7, 0, 9, 5]~]
1245: ? nfeltmod(nf,ba,bb)
1246: [-12, -7, 0, 9, 5]~
1247: ? nfeltmul(nf,ba,bb)
1248: [-25, -50, -30, 15, 90]~
1249: ? nfeltpow(nf,bb,5)
1250: [23455, 156370, 115855, 74190, -294375]~
1251: ? nfeltreduce(nf,ba,idx)
1252: [1, 0, 0, 0, 0]~
1253: ? nfeltval(nf,ba,vp)
1254: 0
1255: ? nffactor(nf2,x^3+x)
1256:
1257: [Mod(1, y^3 - y - 1)*x 1]
1258:
1259: [Mod(1, y^3 - y - 1)*x^2 + Mod(1, y^3 - y - 1) 1]
1260:
1261: ? aut=nfgaloisconj(nf3)
1262: [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
1263: , -x]~
1264: ? nfgaloisapply(nf3,aut[5],Mod(x^5,x^6+108))
1265: Mod(1/2*x^5 - 9*x^2, x^6 + 108)
1266: ? nfhilbert(nf,3,5)
1267: -1
1268: ? nfhilbert(nf,3,5,idf[1,1])
1269: -1
1270: ? nfhnf(nf,[a,aid])
1271: [[[1, 0, 0, 0, 0]~, [0, 0, 0, 0, 0]~, [0, 0, 0, 0, 0]~; [0, 0, 0, 0, 0]~, [1
1272: , 0, 0, 0, 0]~, [0, 0, 0, 0, 0]~; [0, 0, 0, 0, 0]~, [0, 0, 0, 0, 0]~, [1, 0,
1273: 0, 0, 0]~], [[2, 1, 1, 1, 0; 0, 1, 0, 0, 0; 0, 0, 1, 0, 0; 0, 0, 0, 1, 0; 0
1274: , 0, 0, 0, 1], [1, 0, 0, 0, 0; 0, 1, 0, 0, 0; 0, 0, 1, 0, 0; 0, 0, 0, 1, 0;
1275: 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;
1276: 0, 0, 0, 0, 1]]]
1277: ? nfhnfmod(nf,[a,aid],da)
1278: [[[1, 0, 0, 0, 0]~, [0, 0, 0, 0, 0]~, [0, 0, 0, 0, 0]~; [0, 0, 0, 0, 0]~, [1
1279: , 0, 0, 0, 0]~, [0, 0, 0, 0, 0]~; [0, 0, 0, 0, 0]~, [0, 0, 0, 0, 0]~, [1, 0,
1280: 0, 0, 0]~], [[2, 1, 1, 1, 0; 0, 1, 0, 0, 0; 0, 0, 1, 0, 0; 0, 0, 0, 1, 0; 0
1281: , 0, 0, 0, 1], [1, 0, 0, 0, 0; 0, 1, 0, 0, 0; 0, 0, 1, 0, 0; 0, 0, 0, 1, 0;
1282: 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;
1283: 0, 0, 0, 0, 1]]]
1284: ? nfisideal(bnf[7],[5,1;0,1])
1285: 1
1286: ? nfisincl(x^2+1,x^4+1)
1287: [-x^2, x^2]
1288: ? nfisincl(x^2+1,nfinit(x^4+1))
1289: [-x^2, x^2]
1290: ? nfisisom(x^3+x^2-2*x-1,x^3+x^2-2*x-1)
1291: [x, -x^2 - x + 1, x^2 - 2]
1292: ? nfisisom(x^3-2,nfinit(x^3-6*x^2-6*x-30))
1293: [-1/25*x^2 + 13/25*x - 2/5]
1294: ? nfroots(nf2,x+2)
1295: [Mod(-2, y^3 - y - 1)]
1296: ? nfrootsof1(nf)
1297: [2, [-1, 0, 0, 0, 0]~]
1298: ? nfsnf(nf,[as,haid,vaid])
1299: [[10951073973332888246310, 5442457637639729109215, 2693780223637146570055, 3
1300: 910837124677073032737, 3754666252923836621170; 0, 5, 0, 0, 0; 0, 0, 5, 2, 0;
1301: 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
1302: ; 0, 0, 0, 1, 0; 0, 0, 0, 0, 1], [1, 0, 0, 0, 0; 0, 1, 0, 0, 0; 0, 0, 1, 0,
1303: 0; 0, 0, 0, 1, 0; 0, 0, 0, 0, 1]]
1304: ? nfsubfields(nf)
1305: [[x^5 - 5*x^3 + 5*x + 25, x], [x, x^5 - 5*x^3 + 5*x + 25]]
1306: ? polcompositum(x^4-4*x+2,x^3-x-1)
1307: [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
1308: ^2 - 128*x - 5]~
1309: ? polcompositum(x^4-4*x+2,x^3-x-1,1)
1310: [[x^12 - 4*x^10 + 8*x^9 + 12*x^8 + 12*x^7 + 138*x^6 + 132*x^5 - 43*x^4 + 58*
1311: x^2 - 128*x - 5, Mod(-279140305176/29063006931199*x^11 + 129916611552/290630
1312: 06931199*x^10 + 1272919322296/29063006931199*x^9 - 2813750209005/29063006931
1313: 199*x^8 - 2859411937992/29063006931199*x^7 - 414533880536/29063006931199*x^6
1314: - 35713977492936/29063006931199*x^5 - 17432607267590/29063006931199*x^4 + 4
1315: 9785595543672/29063006931199*x^3 + 9423768373204/29063006931199*x^2 - 427797
1316: 76146743/29063006931199*x + 37962587857138/29063006931199, x^12 - 4*x^10 + 8
1317: *x^9 + 12*x^8 + 12*x^7 + 138*x^6 + 132*x^5 - 43*x^4 + 58*x^2 - 128*x - 5), M
1318: od(-279140305176/29063006931199*x^11 + 129916611552/29063006931199*x^10 + 12
1319: 72919322296/29063006931199*x^9 - 2813750209005/29063006931199*x^8 - 28594119
1320: 37992/29063006931199*x^7 - 414533880536/29063006931199*x^6 - 35713977492936/
1321: 29063006931199*x^5 - 17432607267590/29063006931199*x^4 + 49785595543672/2906
1322: 3006931199*x^3 + 9423768373204/29063006931199*x^2 - 13716769215544/290630069
1323: 31199*x + 37962587857138/29063006931199, x^12 - 4*x^10 + 8*x^9 + 12*x^8 + 12
1324: *x^7 + 138*x^6 + 132*x^5 - 43*x^4 + 58*x^2 - 128*x - 5), -1]]
1325: ? polgalois(x^6-3*x^2-1)
1326: [12, 1, 1]
1327: ? polred(x^5-2*x^4-4*x^3-96*x^2-352*x-568)
1328: [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
1329: - 1, x^5 - x^4 + 4*x^3 - 2*x^2 + x - 1, x^5 + 4*x^3 - 4*x^2 + 8*x - 8]
1330: ? polred(x^4-28*x^3-458*x^2+9156*x-25321,3)
1331:
1332: [1 x - 1]
1333:
1334: [1/115*x^2 - 14/115*x - 327/115 x^2 - 10]
1335:
1336: [3/1495*x^3 - 63/1495*x^2 - 1607/1495*x + 13307/1495 x^4 - 32*x^2 + 216]
1337:
1338: [1/4485*x^3 - 7/1495*x^2 - 1034/4485*x + 7924/4485 x^4 - 8*x^2 + 6]
1339:
1340: ? polred(x^4+576,1)
1341: [x - 1, x^2 - x + 1, x^2 + 1, x^4 - x^2 + 1]
1342: ? polred(x^4+576,3)
1343:
1344: [1 x - 1]
1345:
1346: [1/192*x^3 + 1/8*x + 1/2 x^2 - x + 1]
1347:
1348: [-1/24*x^2 x^2 + 1]
1349:
1350: [-1/192*x^3 + 1/48*x^2 + 1/8*x x^4 - x^2 + 1]
1351:
1352: ? polred(p2,0,fa)
1353: [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
1354: *x^2 + 508*x + 913, x^5 - 2*x^4 - 13*x^3 + 37*x^2 - 21*x - 1, x^5 - x^4 - 52
1355: *x^3 - 197*x^2 - 273*x - 127]
1356: ? polred(p2,1,fa)
1357: [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
1358: *x^2 + 508*x + 913, x^5 - 2*x^4 - 13*x^3 + 37*x^2 - 21*x - 1, x^5 - x^4 - 52
1359: *x^3 - 197*x^2 - 273*x - 127]
1360: ? polredabs(x^5-2*x^4-4*x^3-96*x^2-352*x-568)
1361: x^5 - x^4 + 2*x^3 - 4*x^2 + x - 1
1362: ? polredabs(x^5-2*x^4-4*x^3-96*x^2-352*x-568,1)
1363: [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 -
1364: x^4 + 2*x^3 - 4*x^2 + x - 1)]
1365: ? polredord(x^3-12*x+45*x-1)
1366: [x - 1, x^3 - 363*x - 2663, x^3 + 33*x - 1]
1367: ? polsubcyclo(31,5)
1368: x^5 + x^4 - 12*x^3 - 21*x^2 + x + 5
1369: ? setrand(1);poltschirnhaus(x^5-x-1)
1370: x^5 - 15*x^4 + 88*x^3 - 278*x^2 + 452*x - 289
1371: ? aa=rnfpseudobasis(nf2,p)
1372: [[[1, 0, 0]~, [0, 0, 0]~, [0, 0, 0]~, [-2, 0, 0]~, [11, 0, 0]~; [0, 0, 0]~,
1373: [1, 0, 0]~, [0, 0, 0]~, [2, 0, 0]~, [-8, 0, 0]~; [0, 0, 0]~, [0, 0, 0]~, [1,
1374: 0, 0]~, [1, 0, 0]~, [4, 0, 0]~; [0, 0, 0]~, [0, 0, 0]~, [0, 0, 0]~, [1, 0,
1375: 0]~, [-2, 0, 0]~; [0, 0, 0]~, [0, 0, 0]~, [0, 0, 0]~, [0, 0, 0]~, [1, 0, 0]~
1376: ], [[1, 0, 0; 0, 1, 0; 0, 0, 1], [1, 0, 0; 0, 1, 0; 0, 0, 1], [1, 0, 0; 0, 1
1377: , 0; 0, 0, 1], [1, 0, 3/5; 0, 1, 2/5; 0, 0, 1/5], [1, 0, 8/25; 0, 1, 22/25;
1378: 0, 0, 1/25]], [416134375, 212940625, 388649575; 0, 3125, 550; 0, 0, 25], [-1
1379: 280, 5, 5]~]
1380: ? rnfbasis(bnf2,aa)
1381:
1382: [[1, 0, 0]~ [0, 0, 0]~ [0, 0, 0]~ [4/5, -4/5, -2/5]~ [187/25, 208/25, -61/25
1383: ]~]
1384:
1385: [[0, 0, 0]~ [1, 0, 0]~ [0, 0, 0]~ [-4/5, 4/5, 2/5]~ [-196/25, -214/25, 88/25
1386: ]~]
1387:
1388: [[0, 0, 0]~ [0, 0, 0]~ [1, 0, 0]~ [-2/5, 2/5, 1/5]~ [-122/25, -123/25, 116/2
1389: 5]~]
1390:
1391: [[0, 0, 0]~ [0, 0, 0]~ [0, 0, 0]~ [-2/5, 2/5, 1/5]~ [-104/25, -111/25, 62/25
1392: ]~]
1393:
1394: [[0, 0, 0]~ [0, 0, 0]~ [0, 0, 0]~ [0, 0, 0]~ [-3/25, -2/25, 9/25]~]
1395:
1396: ? rnfdisc(nf2,p)
1397: [[416134375, 212940625, 388649575; 0, 3125, 550; 0, 0, 25], [-1280, 5, 5]~]
1398: ? rnfequation(nf2,p)
1399: x^15 - 15*x^11 + 75*x^7 - x^5 - 125*x^3 + 5*x + 1
1400: ? rnfequation(nf2,p,1)
1401: [x^15 - 15*x^11 + 75*x^7 - x^5 - 125*x^3 + 5*x + 1, Mod(-x^5 + 5*x, x^15 - 1
1402: 5*x^11 + 75*x^7 - x^5 - 125*x^3 + 5*x + 1), 0]
1403: ? rnfhnfbasis(bnf2,aa)
1404:
1405: [[1, 0, 0]~ [0, 0, 0]~ [0, 0, 0]~ [-2/5, 2/5, -4/5]~ [11/25, 99/25, -33/25]~
1406: ]
1407:
1408: [[0, 0, 0]~ [1, 0, 0]~ [0, 0, 0]~ [2/5, -2/5, 4/5]~ [-8/25, -72/25, 24/25]~]
1409:
1410: [[0, 0, 0]~ [0, 0, 0]~ [1, 0, 0]~ [1/5, -1/5, 2/5]~ [4/25, 36/25, -12/25]~]
1411:
1412: [[0, 0, 0]~ [0, 0, 0]~ [0, 0, 0]~ [1/5, -1/5, 2/5]~ [-2/25, -18/25, 6/25]~]
1413:
1414: [[0, 0, 0]~ [0, 0, 0]~ [0, 0, 0]~ [0, 0, 0]~ [1/25, 9/25, -3/25]~]
1415:
1416: ? rnfisfree(bnf2,aa)
1417: 1
1418: ? rnfsteinitz(nf2,aa)
1419: [[[1, 0, 0]~, [0, 0, 0]~, [0, 0, 0]~, [4/5, -4/5, -2/5]~, [39/125, 11/125, 1
1420: 1/125]~; [0, 0, 0]~, [1, 0, 0]~, [0, 0, 0]~, [-4/5, 4/5, 2/5]~, [-42/125, -8
1421: /125, -8/125]~; [0, 0, 0]~, [0, 0, 0]~, [1, 0, 0]~, [-2/5, 2/5, 1/5]~, [-29/
1422: 125, 4/125, 4/125]~; [0, 0, 0]~, [0, 0, 0]~, [0, 0, 0]~, [-2/5, 2/5, 1/5]~,
1423: [-23/125, -2/125, -2/125]~; [0, 0, 0]~, [0, 0, 0]~, [0, 0, 0]~, [0, 0, 0]~,
1424: [-1/125, 1/125, 1/125]~], [[1, 0, 0; 0, 1, 0; 0, 0, 1], [1, 0, 0; 0, 1, 0; 0
1425: , 0, 1], [1, 0, 0; 0, 1, 0; 0, 0, 1], [1, 0, 0; 0, 1, 0; 0, 0, 1], [125, 0,
1426: 108; 0, 125, 22; 0, 0, 1]], [416134375, 212940625, 388649575; 0, 3125, 550;
1427: 0, 0, 25], [-1280, 5, 5]~]
1428: ? nfz=zetakinit(x^2-2);
1429: ? zetak(nfz,-3)
1430: 0.091666666666666666666666666666666666666
1431: ? zetak(nfz,1.5+3*I)
1432: 0.88324345992059326405525724366416928890 - 0.2067536250233895222724230899142
1433: 7938845*I
1434: ? setrand(1);quadclassunit(1-10^7,,[1,1])
1435: *** Warning: not a fundamental discriminant in quadclassunit.
1436: [2416, [1208, 2], [Qfb(277, 55, 9028), Qfb(1700, 1249, 1700)], 1, 0.99984980
1437: 753776002339750644800000000000]
1438: ? setrand(1);quadclassunit(10^9-3,,[0.5,0.5])
1439: [4, [4], [Qfb(3, 1, -83333333, 0.E-57)], 2800.625251907016076486370621737074
1440: 5514, 0.99903694589643832327024650000000000000]
1441: ? sizebyte(%)
1442: 328
1443: ? getheap
1444: [197, 120501]
1445: ? print("Total time spent: ",gettime);
1446: Total time spent: 6424
1447: ? \q
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