Annotation of OpenXM_contrib/pari-2.2/src/test/64/nfields, Revision 1.1.1.1
1.1 noro 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: 2666710 E-76, 19.488486013650707197449403270536023970, 4.1504592246706085588
47: 902013976045703227; 10.000000000000000000000000000000000000, 2.0726804532226
48: 66710 E-76, 85.960217420851846480305133936577594605, -36.0342682914829798382
49: 67056239752434596, 53.576130452511107888183080361946556763; -5.0000000000000
50: 000000000000000000000000, 19.488486013650707197449403270536023970, -36.03426
51: 8291482979838267056239752434596, 60.916248374441986300937507618575151517, -1
52: 8.470101750219179344070032346246890434; 7.0000000000000000000000000000000000
53: 000, 4.1504592246706085588902013976045703227, 53.576130452511107888183080361
54: 946556763, -18.470101750219179344070032346246890434, 37.97015289284236734089
55: 7384258599214282], [5, 0, 10, -5, 7; 0, 10, 0, 10, -5; 10, 0, 30, -55, 20; -
56: 5, 10, -55, 45, -39; 7, -5, 20, -39, 9], [345, 0, 340, 167, 150; 0, 345, 110
57: , 220, 153; 0, 0, 5, 2, 1; 0, 0, 0, 1, 0; 0, 0, 0, 0, 1], [132825, -18975, -
58: 5175, 27600, 17250; -18975, 34500, 41400, 3450, -43125; -5175, 41400, -41400
59: , -15525, 51750; 27600, 3450, -15525, -3450, 0; 17250, -43125, 51750, 0, -86
60: 250], [595125, [-13800, 117300, 67275, 1725, 0]~]], [-2.42851749071941860689
61: 92069565359418364, 1.9647119211288133163138753392090569931 + 0.8097149241889
62: 7895128294082219556466857*I, -0.75045317576910401286427186094108607489 + 1.3
63: 101462685358123283560773619310445915*I], [1, x, x^2, 1/3*x^3 - 1/3*x^2 - 1/3
64: , 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,
65: 1, 1, -5; 0, 0, 0, 3, 0; 0, 0, 0, 0, 15], [1, 0, 0, 0, 0, 0, 0, 1, -2, -1, 0
66: , 1, -5, -5, -3, 0, -2, -5, 1, -4, 0, -1, -3, -4, -3; 0, 1, 0, 0, 0, 1, 0, 0
67: , -2, 0, 0, 0, -5, 0, -5, 0, -2, 0, -5, 0, 0, 0, -5, 0, -4; 0, 0, 1, 0, 0, 0
68: , 1, 1, -2, 1, 1, 1, -5, 3, -3, 0, -2, 3, -5, 1, 0, 1, -3, 1, -2; 0, 0, 0, 1
69: , 0, 0, 0, 3, -1, 2, 0, 3, 0, 5, 1, 1, -1, 5, -4, 3, 0, 2, 1, 3, 1; 0, 0, 0,
70: 0, 1, 0, 0, 0, 5, 0, 0, 0, 15, -5, 10, 0, 5, -5, 10, -2, 1, 0, 10, -2, 7]]
71: ? nf1=nfinit(nfpol,2)
72: [x^5 - 2*x^4 + 3*x^3 + 8*x^2 + 3*x + 2, [1, 2], 595125, 4, [[1, -1.089115145
73: 7205048250249527946671612684, 1.1861718006377964594796293860483989860, -0.59
74: 741050929194782733001765987770358483, 0.158944197453903762065494816710718942
75: 89; 1, -0.13838372073406036365047976417441696637 + 0.49181637657768643499753
76: 285514741525107*I, -0.22273329410580226599155701611419649154 - 0.13611876021
77: 752805221674918029071012580*I, -0.13167445871785818798769651537619416009 + 0
78: .13249517760521973840801462296650806543*I, -0.053650958656997725359297528357
79: 602608116 + 0.27622636814169107038138284681568361486*I; 1, 1.682941293594312
80: 7761629561615079976005 + 2.0500351226010726172974286983598602163*I, -1.37035
81: 26062130959637482576769100030014 + 6.9001775222880494773720769629846373016*I
82: , -8.0696202866361678983472946546849540475 + 8.87676767859710424508852843013
83: 48051602*I, -22.025821140069954155673449879997756863 - 8.4306586896999153544
84: 710860185447589664*I], [1, 2, 2; -1.0891151457205048250249527946671612684, -
85: 0.27676744146812072730095952834883393274 - 0.9836327531553728699950657102948
86: 3050214*I, 3.3658825871886255523259123230159952011 - 4.100070245202145234594
87: 8573967197204327*I; 1.1861718006377964594796293860483989860, -0.445466588211
88: 60453198311403222839298308 + 0.27223752043505610443349836058142025160*I, -2.
89: 7407052124261919274965153538200060029 - 13.800355044576098954744153925969274
90: 603*I; -0.59741050929194782733001765987770358483, -0.26334891743571637597539
91: 303075238832018 - 0.26499035521043947681602924593301613087*I, -16.1392405732
92: 72335796694589309369908095 - 17.753535357194208490177056860269610320*I; 0.15
93: 894419745390376206549481671071894289, -0.10730191731399545071859505671520521
94: 623 - 0.55245273628338214076276569363136722973*I, -44.0516422801399083113468
95: 99759995513726 + 16.861317379399830708942172037089517932*I], [5, 2.000000000
96: 0000000000000000000000000000, -2.0000000000000000000000000000000000000, -17.
97: 000000000000000000000000000000000000, -44.0000000000000000000000000000000000
98: 00; 2.0000000000000000000000000000000000000, 15.7781094086719980448363574712
99: 83695361, 22.314643349754061651916553814602769764, 10.0513952578314782754999
100: 32716306366248, -108.58917507620841447456569092094763671; -2.000000000000000
101: 0000000000000000000000, 22.314643349754061651916553814602769764, 100.5239126
102: 2388960975827806174040462368, 143.93295090847353519436673793501057176, -55.8
103: 42564718082452641322500190813370023; -17.00000000000000000000000000000000000
104: 0, 10.051395257831478275499932716306366248, 143.9329509084735351943667379350
105: 1057176, 288.25823756749944693139292174819167135, 205.7984003827766237572018
106: 0649465932302; -44.000000000000000000000000000000000000, -108.58917507620841
107: 447456569092094763671, -55.842564718082452641322500190813370023, 205.7984003
108: 8277662375720180649465932302, 1112.6092277946777707779250962522343036], [5,
109: 2, -2, -17, -44; 2, -2, -34, -63, -40; -2, -34, -90, -101, 177; -17, -63, -1
110: 01, -27, 505; -44, -40, 177, 505, 828], [345, 0, 160, 252, 156; 0, 345, 215,
111: 311, 306; 0, 0, 5, 3, 2; 0, 0, 0, 1, 0; 0, 0, 0, 0, 1], [163875, -388125, -
112: 296700, 234600, -89700; -388125, -1593900, -677925, 595125, -315675; -296700
113: , -677925, 17250, 58650, -87975; 234600, 595125, 58650, -100050, 89700; -897
114: 00, -315675, -87975, 89700, -55200], [595125, [-167325, -82800, 79350, 1725,
115: 0]~]], [-1.0891151457205048250249527946671612684, -0.1383837207340603636504
116: 7976417441696637 + 0.49181637657768643499753285514741525107*I, 1.68294129359
117: 43127761629561615079976005 + 2.0500351226010726172974286983598602163*I], [1,
118: 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,
119: 0, -1, -1; 0, 0, 1, -1, 0; 0, 0, 0, 2, 0; 0, 0, 0, 0, 2], [1, 0, 0, 0, 0, 0,
120: 0, 0, 0, -1, 0, 0, 0, -1, -2, 0, 0, -1, -2, -2, 0, -1, -2, -2, 5; 0, 1, 0,
121: 0, 0, 1, 0, -1, -1, -1, 0, -1, -1, -2, 2, 0, -1, -2, -1, 7, 0, -1, 2, 7, 14;
122: 0, 0, 1, 0, 0, 0, 1, -1, 0, -2, 1, -1, 0, -3, -3, 0, 0, -3, -4, -1, 0, -2,
123: -3, -1, 15; 0, 0, 0, 1, 0, 0, 0, 2, 1, -3, 0, 2, 0, -2, -13, 1, 1, -2, -9, -
124: 19, 0, -3, -13, -19, 7; 0, 0, 0, 0, 1, 0, 0, 0, 1, 2, 0, 0, 2, 3, 1, 0, 1, 3
125: , 4, -4, 1, 2, 1, -4, -21]]
126: ? nfinit(nfpol,3)
127: [[x^5 - 2*x^4 + 3*x^3 + 8*x^2 + 3*x + 2, [1, 2], 595125, 4, [[1, -1.08911514
128: 57205048250249527946671612684, 1.1861718006377964594796293860483989860, -0.5
129: 9741050929194782733001765987770358483, 0.15894419745390376206549481671071894
130: 289; 1, -0.13838372073406036365047976417441696637 + 0.4918163765776864349975
131: 3285514741525107*I, -0.22273329410580226599155701611419649154 - 0.1361187602
132: 1752805221674918029071012580*I, -0.13167445871785818798769651537619416009 +
133: 0.13249517760521973840801462296650806543*I, -0.05365095865699772535929752835
134: 7602608116 + 0.27622636814169107038138284681568361486*I; 1, 1.68294129359431
135: 27761629561615079976005 + 2.0500351226010726172974286983598602163*I, -1.3703
136: 526062130959637482576769100030014 + 6.9001775222880494773720769629846373016*
137: I, -8.0696202866361678983472946546849540475 + 8.8767676785971042450885284301
138: 348051602*I, -22.025821140069954155673449879997756863 - 8.430658689699915354
139: 4710860185447589664*I], [1, 2, 2; -1.0891151457205048250249527946671612684,
140: -0.27676744146812072730095952834883393274 - 0.983632753155372869995065710294
141: 83050214*I, 3.3658825871886255523259123230159952011 - 4.10007024520214523459
142: 48573967197204327*I; 1.1861718006377964594796293860483989860, -0.44546658821
143: 160453198311403222839298308 + 0.27223752043505610443349836058142025160*I, -2
144: .7407052124261919274965153538200060029 - 13.80035504457609895474415392596927
145: 4603*I; -0.59741050929194782733001765987770358483, -0.2633489174357163759753
146: 9303075238832018 - 0.26499035521043947681602924593301613087*I, -16.139240573
147: 272335796694589309369908095 - 17.753535357194208490177056860269610320*I; 0.1
148: 5894419745390376206549481671071894289, -0.1073019173139954507185950567152052
149: 1623 - 0.55245273628338214076276569363136722973*I, -44.051642280139908311346
150: 899759995513726 + 16.861317379399830708942172037089517932*I], [5, 2.00000000
151: 00000000000000000000000000000, -2.0000000000000000000000000000000000000, -17
152: .000000000000000000000000000000000000, -44.000000000000000000000000000000000
153: 000; 2.0000000000000000000000000000000000000, 15.778109408671998044836357471
154: 283695361, 22.314643349754061651916553814602769764, 10.051395257831478275499
155: 932716306366248, -108.58917507620841447456569092094763671; -2.00000000000000
156: 00000000000000000000000, 22.314643349754061651916553814602769764, 100.523912
157: 62388960975827806174040462368, 143.93295090847353519436673793501057176, -55.
158: 842564718082452641322500190813370023; -17.0000000000000000000000000000000000
159: 00, 10.051395257831478275499932716306366248, 143.932950908473535194366737935
160: 01057176, 288.25823756749944693139292174819167135, 205.798400382776623757201
161: 80649465932302; -44.000000000000000000000000000000000000, -108.5891750762084
162: 1447456569092094763671, -55.842564718082452641322500190813370023, 205.798400
163: 38277662375720180649465932302, 1112.6092277946777707779250962522343036], [5,
164: 2, -2, -17, -44; 2, -2, -34, -63, -40; -2, -34, -90, -101, 177; -17, -63, -
165: 101, -27, 505; -44, -40, 177, 505, 828], [345, 0, 160, 252, 156; 0, 345, 215
166: , 311, 306; 0, 0, 5, 3, 2; 0, 0, 0, 1, 0; 0, 0, 0, 0, 1], [163875, -388125,
167: -296700, 234600, -89700; -388125, -1593900, -677925, 595125, -315675; -29670
168: 0, -677925, 17250, 58650, -87975; 234600, 595125, 58650, -100050, 89700; -89
169: 700, -315675, -87975, 89700, -55200], [595125, [-167325, -82800, 79350, 1725
170: , 0]~]], [-1.0891151457205048250249527946671612684, -0.138383720734060363650
171: 47976417441696637 + 0.49181637657768643499753285514741525107*I, 1.6829412935
172: 943127761629561615079976005 + 2.0500351226010726172974286983598602163*I], [1
173: , 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,
174: 0, -1, -1; 0, 0, 1, -1, 0; 0, 0, 0, 2, 0; 0, 0, 0, 0, 2], [1, 0, 0, 0, 0, 0
175: , 0, 0, 0, -1, 0, 0, 0, -1, -2, 0, 0, -1, -2, -2, 0, -1, -2, -2, 5; 0, 1, 0,
176: 0, 0, 1, 0, -1, -1, -1, 0, -1, -1, -2, 2, 0, -1, -2, -1, 7, 0, -1, 2, 7, 14
177: ; 0, 0, 1, 0, 0, 0, 1, -1, 0, -2, 1, -1, 0, -3, -3, 0, 0, -3, -4, -1, 0, -2,
178: -3, -1, 15; 0, 0, 0, 1, 0, 0, 0, 2, 1, -3, 0, 2, 0, -2, -13, 1, 1, -2, -9,
179: -19, 0, -3, -13, -19, 7; 0, 0, 0, 0, 1, 0, 0, 0, 1, 2, 0, 0, 2, 3, 1, 0, 1,
180: 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^
181: 5 - 2*x^4 + 3*x^3 + 8*x^2 + 3*x + 2)]
182: ? nfinit(nfpol,4)
183: [x^5 - 2*x^4 + 3*x^3 + 8*x^2 + 3*x + 2, [1, 2], 595125, 4, [[1, -1.089115145
184: 7205048250249527946671612684, 1.1861718006377964594796293860483989860, -0.59
185: 741050929194782733001765987770358483, 0.158944197453903762065494816710718942
186: 89; 1, -0.13838372073406036365047976417441696637 + 0.49181637657768643499753
187: 285514741525107*I, -0.22273329410580226599155701611419649154 - 0.13611876021
188: 752805221674918029071012580*I, -0.13167445871785818798769651537619416009 + 0
189: .13249517760521973840801462296650806543*I, -0.053650958656997725359297528357
190: 602608116 + 0.27622636814169107038138284681568361486*I; 1, 1.682941293594312
191: 7761629561615079976005 + 2.0500351226010726172974286983598602163*I, -1.37035
192: 26062130959637482576769100030014 + 6.9001775222880494773720769629846373016*I
193: , -8.0696202866361678983472946546849540475 + 8.87676767859710424508852843013
194: 48051602*I, -22.025821140069954155673449879997756863 - 8.4306586896999153544
195: 710860185447589664*I], [1, 2, 2; -1.0891151457205048250249527946671612684, -
196: 0.27676744146812072730095952834883393274 - 0.9836327531553728699950657102948
197: 3050214*I, 3.3658825871886255523259123230159952011 - 4.100070245202145234594
198: 8573967197204327*I; 1.1861718006377964594796293860483989860, -0.445466588211
199: 60453198311403222839298308 + 0.27223752043505610443349836058142025160*I, -2.
200: 7407052124261919274965153538200060029 - 13.800355044576098954744153925969274
201: 603*I; -0.59741050929194782733001765987770358483, -0.26334891743571637597539
202: 303075238832018 - 0.26499035521043947681602924593301613087*I, -16.1392405732
203: 72335796694589309369908095 - 17.753535357194208490177056860269610320*I; 0.15
204: 894419745390376206549481671071894289, -0.10730191731399545071859505671520521
205: 623 - 0.55245273628338214076276569363136722973*I, -44.0516422801399083113468
206: 99759995513726 + 16.861317379399830708942172037089517932*I], [5, 2.000000000
207: 0000000000000000000000000000, -2.0000000000000000000000000000000000000, -17.
208: 000000000000000000000000000000000000, -44.0000000000000000000000000000000000
209: 00; 2.0000000000000000000000000000000000000, 15.7781094086719980448363574712
210: 83695361, 22.314643349754061651916553814602769764, 10.0513952578314782754999
211: 32716306366248, -108.58917507620841447456569092094763671; -2.000000000000000
212: 0000000000000000000000, 22.314643349754061651916553814602769764, 100.5239126
213: 2388960975827806174040462368, 143.93295090847353519436673793501057176, -55.8
214: 42564718082452641322500190813370023; -17.00000000000000000000000000000000000
215: 0, 10.051395257831478275499932716306366248, 143.9329509084735351943667379350
216: 1057176, 288.25823756749944693139292174819167135, 205.7984003827766237572018
217: 0649465932302; -44.000000000000000000000000000000000000, -108.58917507620841
218: 447456569092094763671, -55.842564718082452641322500190813370023, 205.7984003
219: 8277662375720180649465932302, 1112.6092277946777707779250962522343036], [5,
220: 2, -2, -17, -44; 2, -2, -34, -63, -40; -2, -34, -90, -101, 177; -17, -63, -1
221: 01, -27, 505; -44, -40, 177, 505, 828], [345, 0, 160, 252, 156; 0, 345, 215,
222: 311, 306; 0, 0, 5, 3, 2; 0, 0, 0, 1, 0; 0, 0, 0, 0, 1], [163875, -388125, -
223: 296700, 234600, -89700; -388125, -1593900, -677925, 595125, -315675; -296700
224: , -677925, 17250, 58650, -87975; 234600, 595125, 58650, -100050, 89700; -897
225: 00, -315675, -87975, 89700, -55200], [595125, [-167325, -82800, 79350, 1725,
226: 0]~]], [-1.0891151457205048250249527946671612684, -0.1383837207340603636504
227: 7976417441696637 + 0.49181637657768643499753285514741525107*I, 1.68294129359
228: 43127761629561615079976005 + 2.0500351226010726172974286983598602163*I], [1,
229: 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,
230: 0, -1, -1; 0, 0, 1, -1, 0; 0, 0, 0, 2, 0; 0, 0, 0, 0, 2], [1, 0, 0, 0, 0, 0,
231: 0, 0, 0, -1, 0, 0, 0, -1, -2, 0, 0, -1, -2, -2, 0, -1, -2, -2, 5; 0, 1, 0,
232: 0, 0, 1, 0, -1, -1, -1, 0, -1, -1, -2, 2, 0, -1, -2, -1, 7, 0, -1, 2, 7, 14;
233: 0, 0, 1, 0, 0, 0, 1, -1, 0, -2, 1, -1, 0, -3, -3, 0, 0, -3, -4, -1, 0, -2,
234: -3, -1, 15; 0, 0, 0, 1, 0, 0, 0, 2, 1, -3, 0, 2, 0, -2, -13, 1, 1, -2, -9, -
235: 19, 0, -3, -13, -19, 7; 0, 0, 0, 0, 1, 0, 0, 0, 1, 2, 0, 0, 2, 3, 1, 0, 1, 3
236: , 4, -4, 1, 2, 1, -4, -21]]
237: ? nf3=nfinit(x^6+108);
238: ? nf4=nfinit(x^3-10*x+8)
239: [x^3 - 10*x + 8, [3, 0], 568, 2, [[1, -3.50466435358804770515010852590433205
240: 79, 6.1413361156553641347759399165844441383; 1, 0.86464088669540302583112842
241: 266613688800, 0.37380193147270638662350044992137561317; 1, 2.640023466892644
242: 6793189801032381951699, 3.4848619528719294786005596334941802484], [1, 1, 1;
243: -3.5046643535880477051501085259043320579, 0.86464088669540302583112842266613
244: 688800, 2.6400234668926446793189801032381951699; 6.1413361156553641347759399
245: 165844441383, 0.37380193147270638662350044992137561317, 3.484861952871929478
246: 6005596334941802484], [3, -3.454467422037777850 E-77, 10.0000000000000000000
247: 00000000000000000; -3.454467422037777850 E-77, 20.00000000000000000000000000
248: 0000000000, -12.000000000000000000000000000000000000; 10.0000000000000000000
249: 00000000000000000, -12.000000000000000000000000000000000000, 50.000000000000
250: 000000000000000000000000], [3, 0, 10; 0, 20, -12; 10, -12, 50], [284, 168, 2
251: 35; 0, 2, 0; 0, 0, 1], [856, -120, -200; -120, 50, 36; -200, 36, 60], [568,
252: [-216, 90, 8]~]], [-3.5046643535880477051501085259043320579, 0.8646408866954
253: 0302583112842266613688800, 2.6400234668926446793189801032381951699], [1, x,
254: 1/2*x^2], [1, 0, 0; 0, 1, 0; 0, 0, 2], [1, 0, 0, 0, 0, -4, 0, -4, 0; 0, 1, 0
255: , 1, 0, 5, 0, 5, -2; 0, 0, 1, 0, 2, 0, 1, 0, 5]]
256: ? setrand(1);bnf2=bnfinit(qpol);nf2=bnf2[7];
257: ? setrand(1);bnf=bnfinit(x^2-x-57,,[0.2,0.2])
258: [Mat(3), Mat([1, 2, 1, 2, 1, 2, 1, 2, 1]), [-2.71246530518434397468087951060
259: 61300699 + 3.1415926535897932384626433832795028842*I; 2.71246530518434397468
260: 08795106061300699 - 6.2831853071795864769252867665590057684*I], [9.927737672
261: 2507613003718504524486100858 + 3.1415926535897932384626433832795028842*I, 1.
262: 2897619530652735025030086072395031017 + 0.E-57*I, -2.01097980249891575621226
263: 34098917610612 + 3.1415926535897932384626433832795028842*I, 24.4121877466590
264: 95772127915595455170629 + 6.2831853071795864769252867665590057684*I, 30.3376
265: 98160660239595315877930058147543 + 9.4247779607693797153879301498385086526*I
266: , -20.610866187462450639586440264933189691 + 9.42477796076937971538793014983
267: 85086526*I, 29.258282452818196217527894893424939793 + 9.42477796076937971538
268: 79301498385086526*I, -0.34328764427702709438988786673341921876 + 3.141592653
269: 5897932384626433832795028842*I, -14.550628376291080203941433635329724736 + 0
270: .E-56*I, 24.478366048541841504313284087778334822 + 3.14159265358979323846264
271: 33832795028842*I; -9.9277376722507613003718504524486100858 + 6.2831853071795
272: 864769252867665590057684*I, -1.2897619530652735025030086072395031017 + 9.424
273: 7779607693797153879301498385086526*I, 2.010979802498915756212263409891761061
274: 2 + 0.E-57*I, -24.412187746659095772127915595455170629 + 3.14159265358979323
275: 84626433832795028842*I, -30.337698160660239595315877930058147543 + 3.1415926
276: 535897932384626433832795028842*I, 20.610866187462450639586440264933189691 +
277: 3.1415926535897932384626433832795028842*I, -29.25828245281819621752789489342
278: 4939793 + 6.2831853071795864769252867665590057684*I, 0.343287644277027094389
279: 88786673341921876 + 0.E-57*I, 14.550628376291080203941433635329724736 + 3.14
280: 15926535897932384626433832795028842*I, -24.478366048541841504313284087778334
281: 822 + 3.1415926535897932384626433832795028842*I], [[3, [-1, 1]~, 1, 1, [0, 1
282: ]~], [3, [0, 1]~, 1, 1, [-1, 1]~], [5, [-2, 1]~, 1, 1, [1, 1]~], [5, [1, 1]~
283: , 1, 1, [-2, 1]~], [11, [-2, 1]~, 1, 1, [1, 1]~], [11, [1, 1]~, 1, 1, [-2, 1
284: ]~], [17, [-3, 1]~, 1, 1, [2, 1]~], [17, [2, 1]~, 1, 1, [-3, 1]~], [19, [-1,
285: 1]~, 1, 1, [0, 1]~], [19, [0, 1]~, 1, 1, [-1, 1]~]]~, [1, 3, 5, 2, 4, 6, 7,
286: 8, 10, 9], [x^2 - x - 57, [2, 0], 229, 1, [[1, -7.0663729752107779635959310
287: 246705326058; 1, 8.0663729752107779635959310246705326058], [1, 1; -7.0663729
288: 752107779635959310246705326058, 8.0663729752107779635959310246705326058], [2
289: , 1.0000000000000000000000000000000000000; 1.0000000000000000000000000000000
290: 000000, 115.00000000000000000000000000000000000], [2, 1; 1, 115], [229, 114;
291: 0, 1], [115, -1; -1, 2], [229, [114, 1]~]], [-7.066372975210777963595931024
292: 6705326058, 8.0663729752107779635959310246705326058], [1, x], [1, 0; 0, 1],
293: [1, 0, 0, 57; 0, 1, 1, 1]], [[3, [3], [[3, 2; 0, 1]]], 2.7124653051843439746
294: 808795106061300699, 0.8814422512654579369, [2, -1], [x + 7], 185], [Mat(1),
295: [[0, 0]], [[9.9277376722507613003718504524486100858 + 3.14159265358979323846
296: 26433832795028842*I, -9.9277376722507613003718504524486100858 + 6.2831853071
297: 795864769252867665590057684*I]]], 0]
298: ? setrand(1);bnfinit(x^2-x-100000,1)
299: [Mat(5), Mat([3, 2, 1, 2, 0, 3, 2, 3, 0, 0, 1, 4, 3, 2, 2, 3, 3, 2]), [-129.
300: 82045011403975460991182396195022419 - 6.283185307179586476925286766559005768
301: 4*I; 129.82045011403975460991182396195022419 - 12.56637061435917295385057353
302: 3118011536*I], [-41.811264589129943393339502258694361489 + 8.121413879410077
303: 514 E-115*I, 9.2399004147902289816376260438840931575 + 3.1415926535897932384
304: 626433832795028842*I, -11.874609881075406725097315997431161032 + 9.424777960
305: 7693797153879301498385086526*I, 389.46135034211926382973547188585067257 + 12
306: .566370614359172953850573533118011536*I, -440.512515346039436204712600188429
307: 12722 + 0.E-113*I, -324.55112528509938652477955990487556047 + 6.283185307179
308: 5864769252867665590057684*I, 229.70424552002497255158146166263724792 + 3.141
309: 5926535897932384626433832795028842*I, -785.660451862534215720251179722755983
310: 25 + 6.2831853071795864769252867665590057684*I, -554.35531386699327377220656
311: 215544062014 + 6.2831853071795864769252867665590057684*I, -47.66831907156823
312: 3997332918482707687879 + 9.4247779607693797153879301498385086526*I, 177.4887
313: 6918560798860724474244465791207 + 6.497131103528062011 E-114*I, -875.6123693
314: 7168080069763246690606885226 + 2.598852441411224804 E-113*I, 54.878404098312
315: 329644822020875673145627 + 9.4247779607693797153879301498385086526*I, -404.4
316: 4153844676787690336623107514389175 + 0.E-113*I, 232.809823743598178900114904
317: 85449930607 + 6.2831853071795864769252867665590057684*I, -668.80899963671483
318: 856204802764462926790 + 9.4247779607693797153879301498385086526*I, 367.35683
319: 481950538594888487746203445802 + 12.566370614359172953850573533118011536*I,
320: -1214.0716092619656173892944003952818868 + 9.4247779607693797153879301498385
321: 086526*I, -125.94415646756187210316334148291471657 + 6.283185307179586476925
322: 2867665590057684*I; 41.811264589129943393339502258694361489 + 6.283185307179
323: 5864769252867665590057684*I, -9.2399004147902289816376260438840931575 + 12.5
324: 66370614359172953850573533118011536*I, 11.8746098810754067250973159974311610
325: 32 + 8.121413879410077514 E-115*I, -389.46135034211926382973547188585067257
326: + 6.2831853071795864769252867665590057684*I, 440.512515346039436204712600188
327: 42912722 + 3.1415926535897932384626433832795028842*I, 324.551125285099386524
328: 77955990487556047 + 9.4247779607693797153879301498385086526*I, -229.70424552
329: 002497255158146166263724792 + 6.2831853071795864769252867665590057684*I, 785
330: .66045186253421572025117972275598325 + 9.42477796076937971538793014983850865
331: 26*I, 554.35531386699327377220656215544062014 + 3.14159265358979323846264338
332: 32795028842*I, 47.668319071568233997332918482707687878 + 3.14159265358979323
333: 84626433832795028842*I, -177.48876918560798860724474244465791207 + 6.2831853
334: 071795864769252867665590057684*I, 875.61236937168080069763246690606885226 +
335: 6.497131103528062011 E-114*I, -54.878404098312329644822020875673145627 + 9.4
336: 247779607693797153879301498385086526*I, 404.44153844676787690336623107514389
337: 175 + 9.4247779607693797153879301498385086526*I, -232.8098237435981789001149
338: 0485449930607 + 3.1415926535897932384626433832795028842*I, 668.8089996367148
339: 3856204802764462926790 + 6.2831853071795864769252867665590057684*I, -367.356
340: 83481950538594888487746203445803 + 3.1415926535897932384626433832795028842*I
341: , 1214.0716092619656173892944003952818868 + 3.141592653589793238462643383279
342: 5028842*I, 125.94415646756187210316334148291471657 + 6.283185307179586476925
343: 2867665590057684*I], [[2, [1, 1]~, 1, 1, [0, 1]~], [2, [2, 1]~, 1, 1, [1, 1]
344: ~], [5, [4, 1]~, 1, 1, [0, 1]~], [5, [5, 1]~, 1, 1, [-1, 1]~], [7, [3, 1]~,
345: 2, 1, [3, 1]~], [13, [-6, 1]~, 1, 1, [5, 1]~], [13, [5, 1]~, 1, 1, [-6, 1]~]
346: , [17, [14, 1]~, 1, 1, [2, 1]~], [17, [19, 1]~, 1, 1, [-3, 1]~], [23, [-7, 1
347: ]~, 1, 1, [6, 1]~], [23, [6, 1]~, 1, 1, [-7, 1]~], [29, [-14, 1]~, 1, 1, [13
348: , 1]~], [29, [13, 1]~, 1, 1, [-14, 1]~], [31, [23, 1]~, 1, 1, [7, 1]~], [31,
349: [38, 1]~, 1, 1, [-8, 1]~], [41, [-7, 1]~, 1, 1, [6, 1]~], [41, [6, 1]~, 1,
350: 1, [-7, 1]~], [43, [-16, 1]~, 1, 1, [15, 1]~], [43, [15, 1]~, 1, 1, [-16, 1]
351: ~]]~, [1, 3, 6, 2, 4, 5, 7, 9, 8, 11, 10, 13, 12, 15, 14, 17, 16, 19, 18], [
352: x^2 - x - 100000, [2, 0], 400001, 1, [[1, -315.72816130129840161392089489603
353: 747004; 1, 316.72816130129840161392089489603747004], [1, 1; -315.72816130129
354: 840161392089489603747004, 316.72816130129840161392089489603747004], [2, 1.00
355: 00000000000000000000000000000000000; 1.0000000000000000000000000000000000000
356: , 200001.00000000000000000000000000000000], [2, 1; 1, 200001], [400001, 2000
357: 00; 0, 1], [200001, -1; -1, 2], [400001, [200000, 1]~]], [-315.7281613012984
358: 0161392089489603747004, 316.72816130129840161392089489603747004], [1, x], [1
359: , 0; 0, 1], [1, 0, 0, 100000; 0, 1, 1, 1]], [[5, [5], [[2, 1; 0, 1]]], 129.8
360: 2045011403975460991182396195022419, 0.9876536979069047239, [2, -1], [3795548
361: 84019013781006303254896369154068336082609238336*x + 119836165644250789990462
362: 835950022871665178127611316131167], 186], [Mat(1), [[0, 0]], [[-41.811264589
363: 129943393339502258694361489 + 8.121413879410077514 E-115*I, 41.8112645891299
364: 43393339502258694361489 + 6.2831853071795864769252867665590057684*I]]], 0]
365: ? \p19
366: realprecision = 19 significant digits
367: ? setrand(1);sbnf=bnfinit(x^3-x^2-14*x-1,3)
368: [x^3 - x^2 - 14*x - 1, 3, 10889, [1, x, x^2], [-3.233732695981516673, -0.071
369: 82350902743636344, 4.305556205008953036], [10889, 5698, 3794; 0, 1, 0; 0, 0,
370: 1], Mat(2), Mat([0, 1, 1, 1, 1, 0, 1, 1]), [9, 15, 16, 17, 10, 69, 33, 39,
371: 57], [2, [-1, 0, 0]~], [[0, 1, 0]~, [-4, 2, 1]~], [-4, 3, -1, 2, 3, 11, 1, -
372: 1, -7; 1, 1, 1, 1, 0, 2, 1, -4, -2; 0, 0, 0, 0, 0, -1, 0, -1, 0]]
373: ? \p38
374: realprecision = 38 significant digits
375: ? bnrinit(bnf,[[5,3;0,1],[1,0]],1)
376: [[Mat(3), Mat([1, 2, 1, 2, 1, 2, 1, 2, 1]), [-2.7124653051843439746808795106
377: 061300699 + 3.1415926535897932384626433832795028842*I; 2.7124653051843439746
378: 808795106061300699 - 6.2831853071795864769252867665590057684*I], [9.92773767
379: 22507613003718504524486100858 + 3.1415926535897932384626433832795028842*I, 1
380: .2897619530652735025030086072395031017 + 0.E-57*I, -2.0109798024989157562122
381: 634098917610612 + 3.1415926535897932384626433832795028842*I, 24.412187746659
382: 095772127915595455170629 + 6.2831853071795864769252867665590057684*I, 30.337
383: 698160660239595315877930058147543 + 9.4247779607693797153879301498385086526*
384: I, -20.610866187462450639586440264933189691 + 9.4247779607693797153879301498
385: 385086526*I, 29.258282452818196217527894893424939793 + 9.4247779607693797153
386: 879301498385086526*I, -0.34328764427702709438988786673341921876 + 3.14159265
387: 35897932384626433832795028842*I, -14.550628376291080203941433635329724736 +
388: 0.E-56*I, 24.478366048541841504313284087778334822 + 3.1415926535897932384626
389: 433832795028842*I; -9.9277376722507613003718504524486100858 + 6.283185307179
390: 5864769252867665590057684*I, -1.2897619530652735025030086072395031017 + 9.42
391: 47779607693797153879301498385086526*I, 2.01097980249891575621226340989176106
392: 12 + 0.E-57*I, -24.412187746659095772127915595455170629 + 3.1415926535897932
393: 384626433832795028842*I, -30.337698160660239595315877930058147543 + 3.141592
394: 6535897932384626433832795028842*I, 20.610866187462450639586440264933189691 +
395: 3.1415926535897932384626433832795028842*I, -29.2582824528181962175278948934
396: 24939793 + 6.2831853071795864769252867665590057684*I, 0.34328764427702709438
397: 988786673341921876 + 0.E-57*I, 14.550628376291080203941433635329724736 + 3.1
398: 415926535897932384626433832795028842*I, -24.47836604854184150431328408777833
399: 4822 + 3.1415926535897932384626433832795028842*I], [[3, [-1, 1]~, 1, 1, [0,
400: 1]~], [3, [0, 1]~, 1, 1, [-1, 1]~], [5, [-2, 1]~, 1, 1, [1, 1]~], [5, [1, 1]
401: ~, 1, 1, [-2, 1]~], [11, [-2, 1]~, 1, 1, [1, 1]~], [11, [1, 1]~, 1, 1, [-2,
402: 1]~], [17, [-3, 1]~, 1, 1, [2, 1]~], [17, [2, 1]~, 1, 1, [-3, 1]~], [19, [-1
403: , 1]~, 1, 1, [0, 1]~], [19, [0, 1]~, 1, 1, [-1, 1]~]]~, [1, 3, 5, 2, 4, 6, 7
404: , 8, 10, 9], [x^2 - x - 57, [2, 0], 229, 1, [[1, -7.066372975210777963595931
405: 0246705326058; 1, 8.0663729752107779635959310246705326058], [1, 1; -7.066372
406: 9752107779635959310246705326058, 8.0663729752107779635959310246705326058], [
407: 2, 1.0000000000000000000000000000000000000; 1.000000000000000000000000000000
408: 0000000, 115.00000000000000000000000000000000000], [2, 1; 1, 115], [229, 114
409: ; 0, 1], [115, -1; -1, 2], [229, [114, 1]~]], [-7.06637297521077796359593102
410: 46705326058, 8.0663729752107779635959310246705326058], [1, x], [1, 0; 0, 1],
411: [1, 0, 0, 57; 0, 1, 1, 1]], [[3, [3], [[3, 2; 0, 1]]], 2.712465305184343974
412: 6808795106061300699, 0.8814422512654579369, [2, -1], [x + 7], 185], [Mat(1),
413: [[0, 0]], [[9.9277376722507613003718504524486100858 + 3.1415926535897932384
414: 626433832795028842*I, -9.9277376722507613003718504524486100858 + 6.283185307
415: 1795864769252867665590057684*I]]], [0, [Mat([[5, 1]~, 1])]]], [[[5, 3; 0, 1]
416: , [1, 0]], [8, [4, 2], [[2, 0]~, [-1, 1]~]], Mat([[5, [-2, 1]~, 1, 1, [1, 1]
417: ~], 1]), [[[[4], [[2, 0]~], [[2, 0]~], [[Mod(0, 2)]~], 1]], [[2], [[-1, 1]~]
418: , Mat(1)]], [1, 0; 0, 1]], [1], [1, -3, -6; 0, 0, 1; 0, 1, 0], [12, [12], [[
419: 3, 2; 0, 1]]], [[1/2, 0; 0, 0], [1, -1; 1, 1]]]
420: ? bnr=bnrclass(bnf,[[5,3;0,1],[1,0]],2)
421: [[Mat(3), Mat([1, 2, 1, 2, 1, 2, 1, 2, 1]), [-2.7124653051843439746808795106
422: 061300699 + 3.1415926535897932384626433832795028842*I; 2.7124653051843439746
423: 808795106061300699 - 6.2831853071795864769252867665590057684*I], [9.92773767
424: 22507613003718504524486100858 + 3.1415926535897932384626433832795028842*I, 1
425: .2897619530652735025030086072395031017 + 0.E-57*I, -2.0109798024989157562122
426: 634098917610612 + 3.1415926535897932384626433832795028842*I, 24.412187746659
427: 095772127915595455170629 + 6.2831853071795864769252867665590057684*I, 30.337
428: 698160660239595315877930058147543 + 9.4247779607693797153879301498385086526*
429: I, -20.610866187462450639586440264933189691 + 9.4247779607693797153879301498
430: 385086526*I, 29.258282452818196217527894893424939793 + 9.4247779607693797153
431: 879301498385086526*I, -0.34328764427702709438988786673341921876 + 3.14159265
432: 35897932384626433832795028842*I, -14.550628376291080203941433635329724736 +
433: 0.E-56*I, 24.478366048541841504313284087778334822 + 3.1415926535897932384626
434: 433832795028842*I; -9.9277376722507613003718504524486100858 + 6.283185307179
435: 5864769252867665590057684*I, -1.2897619530652735025030086072395031017 + 9.42
436: 47779607693797153879301498385086526*I, 2.01097980249891575621226340989176106
437: 12 + 0.E-57*I, -24.412187746659095772127915595455170629 + 3.1415926535897932
438: 384626433832795028842*I, -30.337698160660239595315877930058147543 + 3.141592
439: 6535897932384626433832795028842*I, 20.610866187462450639586440264933189691 +
440: 3.1415926535897932384626433832795028842*I, -29.2582824528181962175278948934
441: 24939793 + 6.2831853071795864769252867665590057684*I, 0.34328764427702709438
442: 988786673341921876 + 0.E-57*I, 14.550628376291080203941433635329724736 + 3.1
443: 415926535897932384626433832795028842*I, -24.47836604854184150431328408777833
444: 4822 + 3.1415926535897932384626433832795028842*I], [[3, [-1, 1]~, 1, 1, [0,
445: 1]~], [3, [0, 1]~, 1, 1, [-1, 1]~], [5, [-2, 1]~, 1, 1, [1, 1]~], [5, [1, 1]
446: ~, 1, 1, [-2, 1]~], [11, [-2, 1]~, 1, 1, [1, 1]~], [11, [1, 1]~, 1, 1, [-2,
447: 1]~], [17, [-3, 1]~, 1, 1, [2, 1]~], [17, [2, 1]~, 1, 1, [-3, 1]~], [19, [-1
448: , 1]~, 1, 1, [0, 1]~], [19, [0, 1]~, 1, 1, [-1, 1]~]]~, [1, 3, 5, 2, 4, 6, 7
449: , 8, 10, 9], [x^2 - x - 57, [2, 0], 229, 1, [[1, -7.066372975210777963595931
450: 0246705326058; 1, 8.0663729752107779635959310246705326058], [1, 1; -7.066372
451: 9752107779635959310246705326058, 8.0663729752107779635959310246705326058], [
452: 2, 1.0000000000000000000000000000000000000; 1.000000000000000000000000000000
453: 0000000, 115.00000000000000000000000000000000000], [2, 1; 1, 115], [229, 114
454: ; 0, 1], [115, -1; -1, 2], [229, [114, 1]~]], [-7.06637297521077796359593102
455: 46705326058, 8.0663729752107779635959310246705326058], [1, x], [1, 0; 0, 1],
456: [1, 0, 0, 57; 0, 1, 1, 1]], [[3, [3], [[3, 2; 0, 1]]], 2.712465305184343974
457: 6808795106061300699, 0.8814422512654579369, [2, -1], [x + 7], 185], [Mat(1),
458: [[0, 0]], [[9.9277376722507613003718504524486100858 + 3.1415926535897932384
459: 626433832795028842*I, -9.9277376722507613003718504524486100858 + 6.283185307
460: 1795864769252867665590057684*I]]], [0, [Mat([[5, 1]~, 1])]]], [[[5, 3; 0, 1]
461: , [1, 0]], [8, [4, 2], [[2, 0]~, [-1, 1]~]], Mat([[5, [-2, 1]~, 1, 1, [1, 1]
462: ~], 1]), [[[[4], [[2, 0]~], [[2, 0]~], [[Mod(0, 2)]~], 1]], [[2], [[-1, 1]~]
463: , Mat(1)]], [1, 0; 0, 1]], [1], [1, -3, -6; 0, 0, 1; 0, 1, 0], [12, [12], [[
464: 3, 2; 0, 1]]], [[1/2, 0; 0, 0], [1, -1; 1, 1]]]
465: ? rnfinit(nf2,x^5-x-2)
466: [x^5 - x - 2, [[1, 2], [0, 5]], [[49744, 0, 0; 0, 49744, 0; 0, 0, 49744], [3
467: 109, 0, 0]~], [1, 0, 0; 0, 1, 0; 0, 0, 1], [[[1, 1.2671683045421243172528914
468: 279776896412, 1.6057155120361619195949075151301679393, 2.0347118029638523119
469: 874445717108994866, 2.5783223055935536544757871909285592749; 1, 0.2609638803
470: 8645528500256735072673484811 + 1.1772261533941944394700286585617926513*I, -1
471: .3177592693689352747870763902256347904 + 0.614427010164338838041906608641467
472: 31824*I, -1.0672071180669977537495893497477340535 - 1.3909574189920019216524
473: 673160314582604*I, 1.3589689411882615753626439480614001936 - 1.6193337759893
474: 970298359887428575174472*I; 1, -0.89454803265751744362901306471557966872 + 0
475: .53414854617473272670874609150394379949*I, 0.5149015133508543149896226326605
476: 5082078 - 0.95564306225496055080453352211847466685*I, 0.04985121658507159775
477: 5867063892284310224 + 1.1299025160425089918993024639913611785*I, -0.64813009
478: 398503840260053754352567983115 - 0.98412411795664774269323431620030610541*I]
479: , [1, 1.2671683045421243172528914279776896412 + 0.E-38*I, 1.6057155120361619
480: 195949075151301679393 + 0.E-38*I, 2.0347118029638523119874445717108994866 +
481: 0.E-37*I, 2.5783223055935536544757871909285592749 + 0.E-37*I; 1, 0.260963880
482: 38645528500256735072673484811 - 1.1772261533941944394700286585617926513*I, -
483: 1.3177592693689352747870763902256347904 - 0.61442701016433883804190660864146
484: 731824*I, -1.0672071180669977537495893497477340535 + 1.390957418992001921652
485: 4673160314582604*I, 1.3589689411882615753626439480614001936 + 1.619333775989
486: 3970298359887428575174472*I; 1, 0.26096388038645528500256735072673484811 + 1
487: .1772261533941944394700286585617926513*I, -1.3177592693689352747870763902256
488: 347904 + 0.61442701016433883804190660864146731824*I, -1.06720711806699775374
489: 95893497477340535 - 1.3909574189920019216524673160314582604*I, 1.35896894118
490: 82615753626439480614001936 - 1.6193337759893970298359887428575174472*I; 1, -
491: 0.89454803265751744362901306471557966872 - 0.5341485461747327267087460915039
492: 4379949*I, 0.51490151335085431498962263266055082078 + 0.95564306225496055080
493: 453352211847466685*I, 0.049851216585071597755867063892284310224 - 1.12990251
494: 60425089918993024639913611785*I, -0.64813009398503840260053754352567983115 +
495: 0.98412411795664774269323431620030610541*I; 1, -0.8945480326575174436290130
496: 6471557966872 + 0.53414854617473272670874609150394379949*I, 0.51490151335085
497: 431498962263266055082078 - 0.95564306225496055080453352211847466685*I, 0.049
498: 851216585071597755867063892284310224 + 1.12990251604250899189930246399136117
499: 85*I, -0.64813009398503840260053754352567983115 - 0.984124117956647742693234
500: 31620030610541*I]], [[1, 2, 2; 1.2671683045421243172528914279776896412, 0.52
501: 192776077291057000513470145346969622 - 2.35445230678838887894005731712358530
502: 26*I, -1.7890960653150348872580261294311593374 - 1.0682970923494654534174921
503: 830078875989*I; 1.6057155120361619195949075151301679393, -2.6355185387378705
504: 495741527804512695809 - 1.2288540203286776760838132172829346364*I, 1.0298030
505: 267017086299792452653211016415 + 1.9112861245099211016090670442369493337*I;
506: 2.0347118029638523119874445717108994866, -2.13441423613399550749917869949546
507: 81070 + 2.7819148379840038433049346320629165208*I, 0.09970243317014319551173
508: 4127784568620449 - 2.2598050320850179837986049279827223571*I; 2.578322305593
509: 5536544757871909285592749, 2.7179378823765231507252878961228003872 + 3.23866
510: 75519787940596719774857150348944*I, -1.2962601879700768052010750870513596623
511: + 1.9682482359132954853864686324006122108*I], [1, 1, 1, 1, 1; 1.26716830454
512: 21243172528914279776896412 + 0.E-38*I, 0.26096388038645528500256735072673484
513: 811 + 1.1772261533941944394700286585617926513*I, 0.2609638803864552850025673
514: 5072673484811 - 1.1772261533941944394700286585617926513*I, -0.89454803265751
515: 744362901306471557966872 + 0.53414854617473272670874609150394379949*I, -0.89
516: 454803265751744362901306471557966872 - 0.53414854617473272670874609150394379
517: 949*I; 1.6057155120361619195949075151301679393 + 0.E-38*I, -1.31775926936893
518: 52747870763902256347904 + 0.61442701016433883804190660864146731824*I, -1.317
519: 7592693689352747870763902256347904 - 0.6144270101643388380419066086414673182
520: 4*I, 0.51490151335085431498962263266055082078 - 0.95564306225496055080453352
521: 211847466685*I, 0.51490151335085431498962263266055082078 + 0.955643062254960
522: 55080453352211847466685*I; 2.0347118029638523119874445717108994866 + 0.E-37*
523: I, -1.0672071180669977537495893497477340535 - 1.3909574189920019216524673160
524: 314582604*I, -1.0672071180669977537495893497477340535 + 1.390957418992001921
525: 6524673160314582604*I, 0.049851216585071597755867063892284310224 + 1.1299025
526: 160425089918993024639913611785*I, 0.049851216585071597755867063892284310224
527: - 1.1299025160425089918993024639913611785*I; 2.57832230559355365447578719092
528: 85592749 + 0.E-37*I, 1.3589689411882615753626439480614001936 - 1.61933377598
529: 93970298359887428575174472*I, 1.3589689411882615753626439480614001936 + 1.61
530: 93337759893970298359887428575174472*I, -0.6481300939850384026005375435256798
531: 3115 - 0.98412411795664774269323431620030610541*I, -0.6481300939850384026005
532: 3754352567983115 + 0.98412411795664774269323431620030610541*I]], [[5, -5.877
533: 471754111437539 E-39 + 3.4227493991378543323575495001314729016*I, 2.35098870
534: 1644575015 E-38 - 0.68243210418124342552525382695401469720*I, -2.35098870164
535: 4575015 E-38 - 0.52210980589898585950632970408019416371*I, 3.999999999999999
536: 9999999999999999999999 - 5.2069157878920895450584461181156471052*I; -5.87747
537: 1754111437539 E-39 - 3.4227493991378543323575495001314729016*I, 6.6847043424
538: 634879841147654217963674264 - 5.877471754111437539 E-39*I, 0.851456773407213
539: 76574333983502938573598 + 4.5829573180978430291541592600601794652*I, -0.1357
540: 4266252716976137461193821267520737 - 0.2880510854402577236173893646768205039
541: 1*I, 0.27203784387468568916539788233281013320 - 1.59171472799429477189656508
542: 59986677247*I; 2.350988701644575015 E-38 + 0.6824321041812434255252538269540
543: 1469720*I, 0.85145677340721376574333983502938573598 - 4.58295731809784302915
544: 41592600601794652*I, 9.1630968530221077951281598310681467898 + 0.E-38*I, 2.2
545: 622987652095629453403849736225691490 + 6.23619279135585067657240470631807068
546: 69*I, -0.21796409886496632254445901043974770643 + 0.345593689310632156861589
547: 39748833975810*I; -2.350988701644575015 E-38 + 0.522109805898985859506329704
548: 08019416371*I, -0.13574266252716976137461193821267520737 + 0.288051085440257
549: 72361738936467682050392*I, 2.2622987652095629453403849736225691490 - 6.23619
550: 27913558506765724047063180706869*I, 12.845768948832335511882696939380696155
551: + 1.175494350822287507 E-38*I, 4.5618400502378124720913214622468855074 + 8.6
552: 033930051068500425218923146793019614*I; 3.9999999999999999999999999999999999
553: 999 + 5.2069157878920895450584461181156471052*I, 0.2720378438746856891653978
554: 8233281013320 + 1.5917147279942947718965650859986677247*I, -0.21796409886496
555: 632254445901043974770643 - 0.34559368931063215686158939748833975810*I, 4.561
556: 8400502378124720913214622468855074 - 8.6033930051068500425218923146793019615
557: *I, 18.362968630416114402425299186062892646 + 5.877471754111437539 E-39*I],
558: [5, -1.175494350822287507 E-38 + 0.E-38*I, 2.350988701644575015 E-38 + 0.E-3
559: 8*I, -1.763241526233431261 E-38 + 0.E-38*I, 3.999999999999999999999999999999
560: 9999998 + 0.E-38*I; -1.175494350822287507 E-38 + 0.E-38*I, 6.684704342463487
561: 9841147654217963674264 - 5.877471754111437539 E-39*I, 0.85145677340721376574
562: 333983502938573597 + 5.877471754111437539 E-39*I, -0.13574266252716976137461
563: 193821267520737 + 5.877471754111437539 E-39*I, 0.272037843874685689165397882
564: 33281013314 - 5.877471754111437539 E-39*I; 2.350988701644575015 E-38 + 0.E-3
565: 8*I, 0.85145677340721376574333983502938573597 + 5.877471754111437539 E-39*I,
566: 9.1630968530221077951281598310681467898 + 0.E-38*I, 2.262298765209562945340
567: 3849736225691490 + 2.350988701644575015 E-38*I, -0.2179640988649663225444590
568: 1043974770651 + 0.E-38*I; -1.763241526233431261 E-38 + 0.E-38*I, -0.13574266
569: 252716976137461193821267520737 + 5.877471754111437539 E-39*I, 2.262298765209
570: 5629453403849736225691490 + 2.350988701644575015 E-38*I, 12.8457689488323355
571: 11882696939380696155 + 0.E-37*I, 4.5618400502378124720913214622468855073 - 3
572: .526483052466862523 E-38*I; 3.9999999999999999999999999999999999998 + 0.E-38
573: *I, 0.27203784387468568916539788233281013314 - 5.877471754111437539 E-39*I,
574: -0.21796409886496632254445901043974770651 + 0.E-38*I, 4.56184005023781247209
575: 13214622468855073 - 3.526483052466862523 E-38*I, 18.362968630416114402425299
576: 186062892646 + 0.E-37*I]], [Mod(5, y^3 - y - 1), 0, 0, 0, Mod(4, y^3 - y - 1
577: ); 0, 0, 0, Mod(4, y^3 - y - 1), Mod(10, y^3 - y - 1); 0, 0, Mod(4, y^3 - y
578: - 1), Mod(10, y^3 - y - 1), 0; 0, Mod(4, y^3 - y - 1), Mod(10, y^3 - y - 1),
579: 0, 0; Mod(4, y^3 - y - 1), Mod(10, y^3 - y - 1), 0, 0, Mod(4, y^3 - y - 1)]
580: , [;], [;], [;]], [[1.2671683045421243172528914279776896412, 0.2609638803864
581: 5528500256735072673484811 + 1.1772261533941944394700286585617926513*I, -0.89
582: 454803265751744362901306471557966872 + 0.53414854617473272670874609150394379
583: 949*I], [1.2671683045421243172528914279776896412 + 0.E-38*I, 0.2609638803864
584: 5528500256735072673484811 - 1.1772261533941944394700286585617926513*I, 0.260
585: 96388038645528500256735072673484811 + 1.177226153394194439470028658561792651
586: 3*I, -0.89454803265751744362901306471557966872 - 0.5341485461747327267087460
587: 9150394379949*I, -0.89454803265751744362901306471557966872 + 0.5341485461747
588: 3272670874609150394379949*I]~], [[Mod(1, y^3 - y - 1), Mod(1, y^3 - y - 1)*x
589: , Mod(1, y^3 - y - 1)*x^2, Mod(1, y^3 - y - 1)*x^3, Mod(1, y^3 - y - 1)*x^4]
590: , [[1, 0, 0; 0, 1, 0; 0, 0, 1], [1, 0, 0; 0, 1, 0; 0, 0, 1], [1, 0, 0; 0, 1,
591: 0; 0, 0, 1], [1, 0, 0; 0, 1, 0; 0, 0, 1], [1, 0, 0; 0, 1, 0; 0, 0, 1]]], [M
592: od(1, y^3 - y - 1), 0, 0, 0, 0; 0, Mod(1, y^3 - y - 1), 0, 0, 0; 0, 0, Mod(1
593: , y^3 - y - 1), 0, 0; 0, 0, 0, Mod(1, y^3 - y - 1), 0; 0, 0, 0, 0, Mod(1, y^
594: 3 - y - 1)], [], [y^3 - y - 1, [1, 1], -23, 1, [[1, 1.3247179572447460259609
595: 088544780973407, 1.7548776662466927600495088963585286918; 1, -0.662358978622
596: 37301298045442723904867036 + 0.56227951206230124389918214490937306149*I, 0.1
597: 2256116687665361997524555182073565405 - 0.7448617666197442365931704286043923
598: 6724*I], [1, 2; 1.3247179572447460259609088544780973407, -1.3247179572447460
599: 259609088544780973407 - 1.1245590241246024877983642898187461229*I; 1.7548776
600: 662466927600495088963585286918, 0.24512233375330723995049110364147130810 + 1
601: .4897235332394884731863408572087847344*I], [3, 0.E-96, 2.0000000000000000000
602: 000000000000000000; 0.E-96, 3.2646329987400782801485266890755860756, 1.32471
603: 79572447460259609088544780973407; 2.0000000000000000000000000000000000000, 1
604: .3247179572447460259609088544780973407, 4.2192762054875453178332176670757633
605: 303], [3, 0, 2; 0, 2, 3; 2, 3, 2], [23, 13, 15; 0, 1, 0; 0, 0, 1], [-5, 6, -
606: 4; 6, 2, -9; -4, -9, 6], [23, [7, 10, 1]~]], [1.3247179572447460259609088544
607: 780973407, -0.66235897862237301298045442723904867036 + 0.5622795120623012438
608: 9918214490937306149*I], [1, y, y^2], [1, 0, 0; 0, 1, 0; 0, 0, 1], [1, 0, 0,
609: 0, 0, 1, 0, 1, 0; 0, 1, 0, 1, 0, 1, 0, 1, 1; 0, 0, 1, 0, 1, 0, 1, 0, 1]], [x
610: ^15 - 5*x^13 + 5*x^12 + 7*x^11 - 26*x^10 - 5*x^9 + 45*x^8 + 158*x^7 - 98*x^6
611: + 110*x^5 - 190*x^4 + 189*x^3 + 144*x^2 + 25*x + 1, Mod(39516536165538345/8
612: 3718587879473471*x^14 - 6500512476832995/83718587879473471*x^13 - 1962154720
613: 46117185/83718587879473471*x^12 + 229902227480108910/83718587879473471*x^11
614: + 237380704030959181/83718587879473471*x^10 - 1064931988160773805/8371858787
615: 9473471*x^9 - 20657086671714300/83718587879473471*x^8 + 1772885205999206010/
616: 83718587879473471*x^7 + 5952033217241102348/83718587879473471*x^6 - 48388401
617: 87320655696/83718587879473471*x^5 + 5180390720553188700/83718587879473471*x^
618: 4 - 8374015687535120430/83718587879473471*x^3 + 8907744727915040221/83718587
619: 879473471*x^2 + 4155976664123434381/83718587879473471*x + 318920215718580450
620: /83718587879473471, x^15 - 5*x^13 + 5*x^12 + 7*x^11 - 26*x^10 - 5*x^9 + 45*x
621: ^8 + 158*x^7 - 98*x^6 + 110*x^5 - 190*x^4 + 189*x^3 + 144*x^2 + 25*x + 1), -
622: 1, [1, x, x^2, x^3, x^4, x^5, x^6, x^7, x^8, x^9, x^10, x^11, x^12, x^13, 1/
623: 83718587879473471*x^14 - 20528463024680133/83718587879473471*x^13 - 47423929
624: 48888610/83718587879473471*x^12 - 9983523646123358/83718587879473471*x^11 +
625: 40898955597139011/83718587879473471*x^10 + 29412692423971937/837185878794734
626: 71*x^9 - 5017479463612351/83718587879473471*x^8 + 41014993230075066/83718587
627: 879473471*x^7 - 2712810874903165/83718587879473471*x^6 + 20152905879672878/8
628: 3718587879473471*x^5 + 9591643151927789/83718587879473471*x^4 - 847190574595
629: 7397/83718587879473471*x^3 - 13395753879413605/83718587879473471*x^2 + 27623
630: 037732247492/83718587879473471*x + 26306699661480593/83718587879473471], [1,
631: 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -26306699661480593; 0, 1, 0, 0, 0, 0
632: , 0, 0, 0, 0, 0, 0, 0, 0, -27623037732247492; 0, 0, 1, 0, 0, 0, 0, 0, 0, 0,
633: 0, 0, 0, 0, 13395753879413605; 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 847
634: 1905745957397; 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, -9591643151927789;
635: 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, -20152905879672878; 0, 0, 0, 0, 0,
636: 0, 1, 0, 0, 0, 0, 0, 0, 0, 2712810874903165; 0, 0, 0, 0, 0, 0, 0, 1, 0, 0,
637: 0, 0, 0, 0, -41014993230075066; 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 50
638: 17479463612351; 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, -29412692423971937
639: ; 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, -40898955597139011; 0, 0, 0, 0,
640: 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 9983523646123358; 0, 0, 0, 0, 0, 0, 0, 0, 0, 0
641: , 0, 0, 1, 0, 4742392948888610; 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 20
642: 528463024680133; 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 83718587879473471
643: ]]]
644: ? bnfcertify(bnf)
645: 1
646: ? setrand(1);bnfclassunit(x^4-7,2,[0.2,0.2])
647:
648: [x^4 - 7]
649:
650: [[2, 1]]
651:
652: [[-87808, 1]]
653:
654: [[1, x, x^2, x^3]]
655:
656: [[2, [2], [[3, 1, 2, 1; 0, 1, 0, 0; 0, 0, 1, 0; 0, 0, 0, 1]]]]
657:
658: [14.229975145405511722395637833443108790]
659:
660: [1.121117107152756229]
661:
662: ? setrand(1);bnfclassunit(x^2-x-100000)
663: *** Warning: insufficient precision for fundamental units, not given.
664:
665: [x^2 - x - 100000]
666:
667: [[2, 0]]
668:
669: [[400001, 1]]
670:
671: [[1, x]]
672:
673: [[5, [5], [[2, 1; 0, 1]]]]
674:
675: [129.82045011403975460991182396195022419]
676:
677: [0.9876536979069047239]
678:
679: [[2, -1]]
680:
681: [[;]]
682:
683: [0]
684:
685: ? setrand(1);bnfclassunit(x^2-x-100000,1)
686:
687: [x^2 - x - 100000]
688:
689: [[2, 0]]
690:
691: [[400001, 1]]
692:
693: [[1, x]]
694:
695: [[5, [5], [[2, 1; 0, 1]]]]
696:
697: [129.82045011403975460991182396195022419]
698:
699: [0.9876536979069047239]
700:
701: [[2, -1]]
702:
703: [[379554884019013781006303254896369154068336082609238336*x + 119836165644250
704: 789990462835950022871665178127611316131167]]
705:
706: [186]
707:
708: ? setrand(1);bnfclassunit(x^4+24*x^2+585*x+1791,,[0.1,0.1])
709:
710: [x^4 + 24*x^2 + 585*x + 1791]
711:
712: [[0, 2]]
713:
714: [[18981, 3087]]
715:
716: [[1, x, 1/3*x^2, 1/1029*x^3 + 33/343*x^2 - 155/343*x - 58/343]]
717:
718: [[4, [4], [[7, 6, 2, 4; 0, 1, 0, 0; 0, 0, 1, 0; 0, 0, 0, 1]]]]
719:
720: [3.7941269688216589341408274220859400302]
721:
722: [0.8826018286655581306]
723:
724: [[6, -10/1029*x^3 + 13/343*x^2 - 165/343*x - 1135/343]]
725:
726: [[1/147*x^3 + 1/147*x^2 - 8/49*x - 9/49]]
727:
728: [182]
729:
730: ? setrand(1);bnfclgp(17)
731: [1, [], []]
732: ? setrand(1);bnfclgp(-31)
733: [3, [3], [Qfb(2, 1, 4)]]
734: ? setrand(1);bnfclgp(x^4+24*x^2+585*x+1791)
735: [4, [4], [[7, 5, 1, 0; 0, 1, 0, 0; 0, 0, 1, 0; 0, 0, 0, 1]]]
736: ? bnrconductor(bnf,[[25,13;0,1],[1,1]])
737: [[5, 3; 0, 1], [1, 0]]
738: ? bnrconductorofchar(bnr,[2])
739: [[5, 3; 0, 1], [0, 0]]
740: ? bnfisprincipal(bnf,[5,1;0,1],0)
741: [1]~
742: ? bnfisprincipal(bnf,[5,1;0,1])
743: [[1]~, [-2, -1/3]~, 181]
744: ? bnfisunit(bnf,Mod(3405*x-27466,x^2-x-57))
745: [-4, Mod(1, 2)]~
746: ? \p19
747: realprecision = 19 significant digits
748: ? bnfmake(sbnf)
749: [Mat(2), Mat([0, 1, 1, 1, 1, 0, 1, 1]), [1.173637103435061715 + 3.1415926535
750: 89793238*I, -4.562279014988837901 + 3.141592653589793238*I; -2.6335434327389
751: 76049 + 3.141592653589793238*I, 1.420330600779487357 + 3.141592653589793238*
752: I; 1.459906329303914334, 3.141948414209350543], [1.246346989334819161 + 3.14
753: 1592653589793238*I, -1.990056445584799713 + 3.141592653589793238*I, 0.540400
754: 6376129469727 + 3.141592653589793238*I, -0.6926391142471042845 + 3.141592653
755: 589793238*I, 0.E-96, 0.3677262014027817705 + 3.141592653589793238*I, 0.00437
756: 5616572659815402 + 3.141592653589793238*I, -0.8305625946607188639, -1.977791
757: 147836553953 + 3.141592653589793238*I; 0.6716827432867392935 + 3.14159265358
758: 9793238*I, 0.5379005671092853266, -0.8333219883742404172 + 3.141592653589793
759: 238*I, -0.2461086674077943078, 0.E-96, 0.9729063188316092378, -0.87383180430
760: 71131265, -1.552661549868775853 + 3.141592653589793238*I, 0.5774919091398324
761: 092 + 3.141592653589793238*I; -1.918029732621558454, 1.452155878475514386, 0
762: .2929213507612934444, 0.9387477816548985923, 0.E-96, -1.340632520234391008,
763: 0.8694561877344533111, 2.383224144529494717 + 3.141592653589793238*I, 1.4002
764: 99238696721544 + 3.141592653589793238*I], [[3, [-1, 1, 0]~, 1, 1, [1, 0, 1]~
765: ], [5, [3, 1, 0]~, 1, 1, [-2, 1, 1]~], [5, [-1, 1, 0]~, 1, 1, [1, 0, 1]~], [
766: 5, [2, 1, 0]~, 1, 1, [2, 2, 1]~], [3, [1, 0, 1]~, 1, 2, [-1, 1, 0]~], [23, [
767: -10, 1, 0]~, 1, 1, [7, 9, 1]~], [11, [1, 1, 0]~, 1, 1, [-1, -2, 1]~], [13, [
768: 19, 1, 0]~, 1, 1, [2, 6, 1]~], [19, [-6, 1, 0]~, 1, 1, [-3, 5, 1]~]]~, [1, 2
769: , 3, 4, 5, 6, 7, 8, 9]~, [x^3 - x^2 - 14*x - 1, [3, 0], 10889, 1, [[1, -3.23
770: 3732695981516673, 10.45702714905988813; 1, -0.07182350902743636344, 0.005158
771: 616449014232794; 1, 4.305556205008953036, 18.53781423449109762], [1, 1, 1; -
772: 3.233732695981516673, -0.07182350902743636344, 4.305556205008953036; 10.4570
773: 2714905988813, 0.005158616449014232794, 18.53781423449109762], [3, 1.0000000
774: 00000000000, 29.00000000000000000; 1.000000000000000000, 29.0000000000000000
775: 0, 46.00000000000000000; 29.00000000000000000, 46.00000000000000000, 453.000
776: 0000000000000], [3, 1, 29; 1, 29, 46; 29, 46, 453], [10889, 5698, 3794; 0, 1
777: , 0; 0, 0, 1], [11021, 881, -795; 881, 518, -109; -795, -109, 86], [10889, [
778: 1890, 5190, 1]~]], [-3.233732695981516673, -0.07182350902743636344, 4.305556
779: 205008953036], [1, x, x^2], [1, 0, 0; 0, 1, 0; 0, 0, 1], [1, 0, 0, 0, 0, 1,
780: 0, 1, 1; 0, 1, 0, 1, 0, 14, 0, 14, 15; 0, 0, 1, 0, 1, 1, 1, 1, 15]], [[2, [2
781: ], [[3, 2, 2; 0, 1, 0; 0, 0, 1]]], 10.34800724602767998, 1.00000000000000000
782: 0, [2, -1], [x, x^2 + 2*x - 4], 1000], [Mat(1), [[0, 0, 0]], [[1.24634698933
783: 4819161 + 3.141592653589793238*I, 0.6716827432867392935 + 3.1415926535897932
784: 38*I, -1.918029732621558454]]], [-4, 3, -1, 2, 3, 11, 1, -1, -7; 1, 1, 1, 1,
785: 0, 2, 1, -4, -2; 0, 0, 0, 0, 0, -1, 0, -1, 0]]
786: ? \p38
787: realprecision = 38 significant digits
788: ? bnfnarrow(bnf)
789: [3, [3], [[3, 2; 0, 1]]]
790: ? bnfreg(x^2-x-57)
791: 2.7124653051843439746808795106061300699
792: ? bnfsignunit(bnf)
793:
794: [-1]
795:
796: [1]
797:
798: ? bnfunit(bnf)
799: [[x + 7], 185]
800: ? bnrclass(bnf,[[5,3;0,1],[1,0]])
801: [12, [12], [[3, 2; 0, 1]]]
802: ? bnr2=bnrclass(bnf,[[25,13;0,1],[1,1]],2)
803: [[Mat(3), Mat([1, 2, 1, 2, 1, 2, 1, 2, 1]), [-2.7124653051843439746808795106
804: 061300699 + 3.1415926535897932384626433832795028842*I; 2.7124653051843439746
805: 808795106061300699 - 6.2831853071795864769252867665590057684*I], [9.92773767
806: 22507613003718504524486100858 + 3.1415926535897932384626433832795028842*I, 1
807: .2897619530652735025030086072395031017 + 0.E-57*I, -2.0109798024989157562122
808: 634098917610612 + 3.1415926535897932384626433832795028842*I, 24.412187746659
809: 095772127915595455170629 + 6.2831853071795864769252867665590057684*I, 30.337
810: 698160660239595315877930058147543 + 9.4247779607693797153879301498385086526*
811: I, -20.610866187462450639586440264933189691 + 9.4247779607693797153879301498
812: 385086526*I, 29.258282452818196217527894893424939793 + 9.4247779607693797153
813: 879301498385086526*I, -0.34328764427702709438988786673341921876 + 3.14159265
814: 35897932384626433832795028842*I, -14.550628376291080203941433635329724736 +
815: 0.E-56*I, 24.478366048541841504313284087778334822 + 3.1415926535897932384626
816: 433832795028842*I; -9.9277376722507613003718504524486100858 + 6.283185307179
817: 5864769252867665590057684*I, -1.2897619530652735025030086072395031017 + 9.42
818: 47779607693797153879301498385086526*I, 2.01097980249891575621226340989176106
819: 12 + 0.E-57*I, -24.412187746659095772127915595455170629 + 3.1415926535897932
820: 384626433832795028842*I, -30.337698160660239595315877930058147543 + 3.141592
821: 6535897932384626433832795028842*I, 20.610866187462450639586440264933189691 +
822: 3.1415926535897932384626433832795028842*I, -29.2582824528181962175278948934
823: 24939793 + 6.2831853071795864769252867665590057684*I, 0.34328764427702709438
824: 988786673341921876 + 0.E-57*I, 14.550628376291080203941433635329724736 + 3.1
825: 415926535897932384626433832795028842*I, -24.47836604854184150431328408777833
826: 4822 + 3.1415926535897932384626433832795028842*I], [[3, [-1, 1]~, 1, 1, [0,
827: 1]~], [3, [0, 1]~, 1, 1, [-1, 1]~], [5, [-2, 1]~, 1, 1, [1, 1]~], [5, [1, 1]
828: ~, 1, 1, [-2, 1]~], [11, [-2, 1]~, 1, 1, [1, 1]~], [11, [1, 1]~, 1, 1, [-2,
829: 1]~], [17, [-3, 1]~, 1, 1, [2, 1]~], [17, [2, 1]~, 1, 1, [-3, 1]~], [19, [-1
830: , 1]~, 1, 1, [0, 1]~], [19, [0, 1]~, 1, 1, [-1, 1]~]]~, [1, 3, 5, 2, 4, 6, 7
831: , 8, 10, 9], [x^2 - x - 57, [2, 0], 229, 1, [[1, -7.066372975210777963595931
832: 0246705326058; 1, 8.0663729752107779635959310246705326058], [1, 1; -7.066372
833: 9752107779635959310246705326058, 8.0663729752107779635959310246705326058], [
834: 2, 1.0000000000000000000000000000000000000; 1.000000000000000000000000000000
835: 0000000, 115.00000000000000000000000000000000000], [2, 1; 1, 115], [229, 114
836: ; 0, 1], [115, -1; -1, 2], [229, [114, 1]~]], [-7.06637297521077796359593102
837: 46705326058, 8.0663729752107779635959310246705326058], [1, x], [1, 0; 0, 1],
838: [1, 0, 0, 57; 0, 1, 1, 1]], [[3, [3], [[3, 2; 0, 1]]], 2.712465305184343974
839: 6808795106061300699, 0.8814422512654579369, [2, -1], [x + 7], 185], [Mat(1),
840: [[0, 0]], [[9.9277376722507613003718504524486100858 + 3.1415926535897932384
841: 626433832795028842*I, -9.9277376722507613003718504524486100858 + 6.283185307
842: 1795864769252867665590057684*I]]], [0, [Mat([[5, 1]~, 1])]]], [[[25, 13; 0,
843: 1], [1, 1]], [80, [20, 2, 2], [[2, 0]~, [0, -2]~, [2, 2]~]], Mat([[5, [-2, 1
844: ]~, 1, 1, [1, 1]~], 2]), [[[[4], [[2, 0]~], [[2, 0]~], [[Mod(0, 2), Mod(0, 2
845: )]~], 1], [[5], [[6, 0]~], [[6, 0]~], [[Mod(0, 2), Mod(0, 2)]~], Mat([1/5, -
846: 13/5])]], [[2, 2], [[0, -2]~, [2, 2]~], [0, 1; 1, 0]]], [1, -12, 0, 0; 0, 0,
847: 1, 0; 0, 0, 0, 1]], [1], [1, -3, 0, -6; 0, 0, 1, 0; 0, 0, 0, 1; 0, 1, 0, 0]
848: , [12, [12], [[3, 2; 0, 1]]], [[1, 9, -18; -1/2, -5, 10], [-2, 0; 0, 10]]]
849: ? bnrclassno(bnf,[[5,3;0,1],[1,0]])
850: 12
851: ? lu=ideallist(bnf,55,3);
852: ? bnrclassnolist(bnf,lu)
853: [[3], [], [3, 3], [3], [6, 6], [], [], [], [3, 3, 3], [], [3, 3], [3, 3], []
854: , [], [12, 6, 6, 12], [3], [3, 3], [], [9, 9], [6, 6], [], [], [], [], [6, 1
855: 2, 6], [], [3, 3, 3, 3], [], [], [], [], [], [3, 6, 6, 3], [], [], [9, 3, 9]
856: , [6, 6], [], [], [], [], [], [3, 3], [3, 3], [12, 12, 6, 6, 12, 12], [], []
857: , [6, 6], [9], [], [3, 3, 3, 3], [], [3, 3], [], [6, 12, 12, 6]]
858: ? bnrdisc(bnr,Mat(6))
859: [12, 12, 18026977100265125]
860: ? bnrdisc(bnr)
861: [24, 12, 40621487921685401825918161408203125]
862: ? bnrdisc(bnr2,,,2)
863: 0
864: ? bnrdisc(bnr,Mat(6),,1)
865: [6, 2, [125, 13; 0, 1]]
866: ? bnrdisc(bnr,,,1)
867: [12, 1, [1953125, 1160888; 0, 1]]
868: ? bnrdisc(bnr2,,,3)
869: 0
870: ? bnrdisclist(bnf,lu)
871: [[[6, 6, Mat([229, 3])]], [], [[], []], [[]], [[12, 12, [5, 3; 229, 6]], [12
872: , 12, [5, 3; 229, 6]]], [], [], [], [[], [], []], [], [[], []], [[], []], []
873: , [], [[24, 24, [3, 6; 5, 9; 229, 12]], [], [], [24, 24, [3, 6; 5, 9; 229, 1
874: 2]]], [[]], [[], []], [], [[18, 18, [19, 6; 229, 9]], [18, 18, [19, 6; 229,
875: 9]]], [[], []], [], [], [], [], [[], [24, 24, [5, 12; 229, 12]], []], [], [[
876: ], [], [], []], [], [], [], [], [], [[], [12, 12, [3, 3; 11, 3; 229, 6]], [1
877: 2, 12, [3, 3; 11, 3; 229, 6]], []], [], [], [[18, 18, [2, 12; 3, 12; 229, 9]
878: ], [], [18, 18, [2, 12; 3, 12; 229, 9]]], [[12, 12, [37, 3; 229, 6]], [12, 1
879: 2, [37, 3; 229, 6]]], [], [], [], [], [], [[], []], [[], []], [[], [], [], [
880: ], [], []], [], [], [[12, 12, [2, 12; 3, 3; 229, 6]], [12, 12, [2, 12; 3, 3;
881: 229, 6]]], [[18, 18, [7, 12; 229, 9]]], [], [[], [], [], []], [], [[], []],
882: [], [[], [24, 24, [5, 9; 11, 6; 229, 12]], [24, 24, [5, 9; 11, 6; 229, 12]]
883: , []]]
884: ? bnrdisclist(bnf,20,,1)
885: [[[[matrix(0,2), [[6, 6, Mat([229, 3])], [0, 0, 0], [0, 0, 0], [0, 0, 0]]]],
886: [], [[Mat([12, 1]), [[0, 0, 0], [0, 0, 0], [0, 0, 0], [12, 0, [3, 3; 229, 6
887: ]]]], [Mat([13, 1]), [[0, 0, 0], [0, 0, 0], [12, 6, [-1, 1; 3, 3; 229, 6]],
888: [0, 0, 0]]]], [[Mat([10, 1]), [[0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0]]]]
889: , [[Mat([20, 1]), [[12, 12, [5, 3; 229, 6]], [0, 0, 0], [0, 0, 0], [24, 0, [
890: 5, 9; 229, 12]]]], [Mat([21, 1]), [[12, 12, [5, 3; 229, 6]], [0, 0, 0], [24,
891: 12, [5, 9; 229, 12]], [0, 0, 0]]]], [], [], [], [[Mat([12, 2]), [[0, 0, 0],
892: [0, 0, 0], [0, 0, 0], [0, 0, 0]]], [[12, 1; 13, 1], [[0, 0, 0], [12, 6, [-1
893: , 1; 3, 6; 229, 6]], [0, 0, 0], [24, 0, [3, 12; 229, 12]]]], [Mat([13, 2]),
894: [[0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0]]]], [], [[Mat([44, 1]), [[0, 0,
895: 0], [0, 0, 0], [12, 6, [-1, 1; 11, 3; 229, 6]], [0, 0, 0]]], [Mat([45, 1]),
896: [[0, 0, 0], [0, 0, 0], [0, 0, 0], [12, 0, [11, 3; 229, 6]]]]], [[[10, 1; 12,
897: 1], [[0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0]]], [[10, 1; 13, 1], [[0, 0,
898: 0], [0, 0, 0], [0, 0, 0], [0, 0, 0]]]], [], [], [[[12, 1; 20, 1], [[24, 24,
899: [3, 6; 5, 9; 229, 12]], [0, 0, 0], [0, 0, 0], [48, 0, [3, 12; 5, 18; 229, 2
900: 4]]]], [[13, 1; 20, 1], [[0, 0, 0], [24, 12, [3, 6; 5, 9; 229, 12]], [24, 12
901: , [3, 6; 5, 6; 229, 12]], [48, 0, [3, 12; 5, 18; 229, 24]]]], [[12, 1; 21, 1
902: ], [[0, 0, 0], [24, 12, [3, 6; 5, 9; 229, 12]], [0, 0, 0], [48, 0, [3, 12; 5
903: , 18; 229, 24]]]], [[13, 1; 21, 1], [[24, 24, [3, 6; 5, 9; 229, 12]], [0, 0,
904: 0], [48, 24, [3, 12; 5, 18; 229, 24]], [0, 0, 0]]]], [[Mat([10, 2]), [[0, 0
905: , 0], [12, 6, [-1, 1; 2, 12; 229, 6]], [12, 6, [-1, 1; 2, 12; 229, 6]], [24,
906: 0, [2, 36; 229, 12]]]]], [[Mat([68, 1]), [[0, 0, 0], [12, 6, [-1, 1; 17, 3;
907: 229, 6]], [0, 0, 0], [0, 0, 0]]], [Mat([69, 1]), [[0, 0, 0], [12, 6, [-1, 1
908: ; 17, 3; 229, 6]], [0, 0, 0], [0, 0, 0]]]], [], [[Mat([76, 1]), [[18, 18, [1
909: 9, 6; 229, 9]], [0, 0, 0], [0, 0, 0], [36, 0, [19, 15; 229, 18]]]], [Mat([77
910: , 1]), [[18, 18, [19, 6; 229, 9]], [0, 0, 0], [36, 18, [-1, 1; 19, 15; 229,
911: 18]], [0, 0, 0]]]], [[[10, 1; 20, 1], [[0, 0, 0], [0, 0, 0], [0, 0, 0], [0,
912: 0, 0]]], [[10, 1; 21, 1], [[0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0]]]]]]
913: ? bnrisprincipal(bnr,idealprimedec(bnf,7)[1])
914: [[9]~, [-2170/6561, -931/19683]~, 256]
915: ? dirzetak(nf4,30)
916: [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,
917: 0, 1, 0, 1, 0]
918: ? factornf(x^3+x^2-2*x-1,t^3+t^2-2*t-1)
919:
920: [Mod(1, t^3 + t^2 - 2*t - 1)*x + Mod(-t, t^3 + t^2 - 2*t - 1) 1]
921:
922: [Mod(1, t^3 + t^2 - 2*t - 1)*x + Mod(-t^2 + 2, t^3 + t^2 - 2*t - 1) 1]
923:
924: [Mod(1, t^3 + t^2 - 2*t - 1)*x + Mod(t^2 + t - 1, t^3 + t^2 - 2*t - 1) 1]
925:
926: ? vp=idealprimedec(nf,3)[1]
927: [3, [1, 1, 0, 0, 0]~, 1, 1, [1, -1, -1, 0, 0]~]
928: ? idx=idealmul(nf,matid(5),vp)
929:
930: [3 1 2 2 2]
931:
932: [0 1 0 0 0]
933:
934: [0 0 1 0 0]
935:
936: [0 0 0 1 0]
937:
938: [0 0 0 0 1]
939:
940: ? idealinv(nf,idx)
941:
942: [1 0 2/3 0 0]
943:
944: [0 1 1/3 0 0]
945:
946: [0 0 1/3 0 0]
947:
948: [0 0 0 1 0]
949:
950: [0 0 0 0 1]
951:
952: ? idy=idealred(nf,idx,[1,5,6])
953:
954: [5 0 0 2 0]
955:
956: [0 5 0 0 0]
957:
958: [0 0 5 2 0]
959:
960: [0 0 0 1 0]
961:
962: [0 0 0 0 5]
963:
964: ? idx2=idealmul(nf,idx,idx)
965:
966: [9 7 5 8 2]
967:
968: [0 1 0 0 0]
969:
970: [0 0 1 0 0]
971:
972: [0 0 0 1 0]
973:
974: [0 0 0 0 1]
975:
976: ? idt=idealmul(nf,idx,idx,1)
977:
978: [2 0 0 0 1]
979:
980: [0 2 0 0 1]
981:
982: [0 0 2 0 0]
983:
984: [0 0 0 2 1]
985:
986: [0 0 0 0 1]
987:
988: ? idz=idealintersect(nf,idx,idy)
989:
990: [15 5 10 12 10]
991:
992: [0 5 0 0 0]
993:
994: [0 0 5 2 0]
995:
996: [0 0 0 1 0]
997:
998: [0 0 0 0 5]
999:
1000: ? aid=[idx,idy,idz,matid(5),idx]
1001: [[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]
1002: , [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
1003: ], [15, 5, 10, 12, 10; 0, 5, 0, 0, 0; 0, 0, 5, 2, 0; 0, 0, 0, 1, 0; 0, 0, 0,
1004: 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
1005: , 0, 1], [3, 1, 2, 2, 2; 0, 1, 0, 0, 0; 0, 0, 1, 0, 0; 0, 0, 0, 1, 0; 0, 0,
1006: 0, 0, 1]]
1007: ? bid=idealstar(nf2,54,1)
1008: [[[54, 0, 0; 0, 54, 0; 0, 0, 54], [0]], [132678, [1638, 9, 9]], [[2, [2, 0,
1009: 0]~, 1, 3, [1, 0, 0]~], 1; [3, [3, 0, 0]~, 1, 3, [1, 0, 0]~], 3], [[[[7], [[
1010: 0, 1, 0]~], [[-26, -27, 0]~], [[]~], 1]], [[[26], [[0, 2, 0]~], [[-27, 2, 0]
1011: ~], [[]~], 1], [[3, 3, 3], [[1, 3, 0]~, [1, 0, 3]~, [4, 0, 0]~], [[1, -24, 0
1012: ]~, [1, 0, -24]~, [-23, 0, 0]~], [[]~, []~, []~], [0, 1/3, 0; 0, 0, 1/3; 1/3
1013: , 0, 0]], [[3, 3, 3], [[1, 9, 0]~, [1, 0, 9]~, [10, 0, 0]~], [[1, -18, 0]~,
1014: [1, 0, -18]~, [-17, 0, 0]~], [[]~, []~, []~], [0, 1/9, 0; 0, 0, 1/9; 1/9, 0,
1015: 0]]], [[], [], [;]]], [468, 469, 0, 0, -48776, 0, 0, -36582; 0, 0, 1, 0, -7
1016: , -6, 0, -3; 0, 0, 0, 1, -3, 0, -6, 0]]
1017: ? vaid=[idx,idy,matid(5)]
1018: [[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]
1019: , [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
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: ? haid=[matid(5),matid(5),matid(5)]
1023: [[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]
1024: , [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
1025: ], [1, 0, 0, 0, 0; 0, 1, 0, 0, 0; 0, 0, 1, 0, 0; 0, 0, 0, 1, 0; 0, 0, 0, 0,
1026: 1]]
1027: ? idealadd(nf,idx,idy)
1028:
1029: [1 0 0 0 0]
1030:
1031: [0 1 0 0 0]
1032:
1033: [0 0 1 0 0]
1034:
1035: [0 0 0 1 0]
1036:
1037: [0 0 0 0 1]
1038:
1039: ? idealaddtoone(nf,idx,idy)
1040: [[3, 0, 2, 1, 0]~, [-2, 0, -2, -1, 0]~]
1041: ? idealaddtoone(nf,[idy,idx])
1042: [[-5, 0, 0, 0, 0]~, [6, 0, 0, 0, 0]~]
1043: ? idealappr(nf,idy)
1044: [-2, 0, -2, 4, 0]~
1045: ? idealappr(nf,idealfactor(nf,idy),1)
1046: [-2, 0, -2, 4, 0]~
1047: ? idealcoprime(nf,idx,idx)
1048: [-2/3, 2/3, -1/3, 0, 0]~
1049: ? idealdiv(nf,idy,idt)
1050:
1051: [5 5/2 5/2 7/2 0]
1052:
1053: [0 5/2 0 0 0]
1054:
1055: [0 0 5/2 1 0]
1056:
1057: [0 0 0 1/2 0]
1058:
1059: [0 0 0 0 5/2]
1060:
1061: ? idealdiv(nf,idx2,idx,1)
1062:
1063: [3 1 2 2 2]
1064:
1065: [0 1 0 0 0]
1066:
1067: [0 0 1 0 0]
1068:
1069: [0 0 0 1 0]
1070:
1071: [0 0 0 0 1]
1072:
1073: ? idf=idealfactor(nf,idz)
1074:
1075: [[3, [1, 1, 0, 0, 0]~, 1, 1, [1, -1, -1, 0, 0]~] 1]
1076:
1077: [[5, [-2, 0, 0, 0, 1]~, 1, 1, [2, 2, 1, 1, 4]~] 1]
1078:
1079: [[5, [0, 0, -1, 0, 1]~, 4, 1, [4, 5, 4, 2, 0]~] 3]
1080:
1081: ? idealhnf(nf,vp)
1082:
1083: [3 1 2 2 2]
1084:
1085: [0 1 0 0 0]
1086:
1087: [0 0 1 0 0]
1088:
1089: [0 0 0 1 0]
1090:
1091: [0 0 0 0 1]
1092:
1093: ? idealhnf(nf,vp[2],3)
1094:
1095: [3 1 2 2 2]
1096:
1097: [0 1 0 0 0]
1098:
1099: [0 0 1 0 0]
1100:
1101: [0 0 0 1 0]
1102:
1103: [0 0 0 0 1]
1104:
1105: ? ideallist(bnf,20)
1106: [[[1, 0; 0, 1]], [], [[3, 2; 0, 1], [3, 0; 0, 1]], [[2, 0; 0, 2]], [[5, 3; 0
1107: , 1], [5, 1; 0, 1]], [], [], [], [[9, 5; 0, 1], [3, 0; 0, 3], [9, 3; 0, 1]],
1108: [], [[11, 9; 0, 1], [11, 1; 0, 1]], [[6, 4; 0, 2], [6, 0; 0, 2]], [], [], [
1109: [15, 8; 0, 1], [15, 3; 0, 1], [15, 11; 0, 1], [15, 6; 0, 1]], [[4, 0; 0, 4]]
1110: , [[17, 14; 0, 1], [17, 2; 0, 1]], [], [[19, 18; 0, 1], [19, 0; 0, 1]], [[10
1111: , 6; 0, 2], [10, 2; 0, 2]]]
1112: ? ideallog(nf2,w,bid)
1113: [1574, 8, 6]~
1114: ? idealmin(nf,idx,[1,2,3])
1115: [[-1; 0; 0; 1; 0], [2.0885812311199768913287869744681966008 + 3.141592653589
1116: 7932384626433832795028842*I, 1.5921096812520196555597562531657929785 + 4.244
1117: 7196639216499665715751642189271112*I, -0.79031915447583185468082063233076160
1118: 203 + 2.5437460822678889883600220330800078854*I]]
1119: ? idealnorm(nf,idt)
1120: 16
1121: ? idp=idealpow(nf,idx,7)
1122:
1123: [2187 1807 2129 692 1379]
1124:
1125: [0 1 0 0 0]
1126:
1127: [0 0 1 0 0]
1128:
1129: [0 0 0 1 0]
1130:
1131: [0 0 0 0 1]
1132:
1133: ? idealpow(nf,idx,7,1)
1134:
1135: [5 0 0 2 0]
1136:
1137: [0 5 0 0 0]
1138:
1139: [0 0 5 2 0]
1140:
1141: [0 0 0 1 0]
1142:
1143: [0 0 0 0 5]
1144:
1145: ? idealprimedec(nf,2)
1146: [[2, [3, 1, 0, 0, 0]~, 1, 1, [1, 1, 0, 1, 1]~], [2, [-3, -5, -4, 3, 15]~, 1,
1147: 4, [1, 1, 0, 0, 0]~]]
1148: ? idealprimedec(nf,3)
1149: [[3, [1, 1, 0, 0, 0]~, 1, 1, [1, -1, -1, 0, 0]~], [3, [-1, 1, -1, 0, 1]~, 2,
1150: 2, [1, 2, 3, 1, 0]~]]
1151: ? idealprimedec(nf,11)
1152: [[11, [11, 0, 0, 0, 0]~, 1, 5, [1, 0, 0, 0, 0]~]]
1153: ? idealprincipal(nf,Mod(x^3+5,nfpol))
1154:
1155: [6]
1156:
1157: [0]
1158:
1159: [1]
1160:
1161: [3]
1162:
1163: [0]
1164:
1165: ? idealtwoelt(nf,idy)
1166: [5, [2, 0, 2, 1, 0]~]
1167: ? idealtwoelt(nf,idy,10)
1168: [-2, 0, -2, -1, 0]~
1169: ? idealstar(nf2,54)
1170: [[[54, 0, 0; 0, 54, 0; 0, 0, 54], [0]], [132678, [1638, 9, 9]], [[2, [2, 0,
1171: 0]~, 1, 3, [1, 0, 0]~], 1; [3, [3, 0, 0]~, 1, 3, [1, 0, 0]~], 3], [[[[7], [[
1172: 0, 1, 0]~], [[-26, -27, 0]~], [[]~], 1]], [[[26], [[0, 2, 0]~], [[-27, 2, 0]
1173: ~], [[]~], 1], [[3, 3, 3], [[1, 3, 0]~, [1, 0, 3]~, [4, 0, 0]~], [[1, -24, 0
1174: ]~, [1, 0, -24]~, [-23, 0, 0]~], [[]~, []~, []~], [0, 1/3, 0; 0, 0, 1/3; 1/3
1175: , 0, 0]], [[3, 3, 3], [[1, 9, 0]~, [1, 0, 9]~, [10, 0, 0]~], [[1, -18, 0]~,
1176: [1, 0, -18]~, [-17, 0, 0]~], [[]~, []~, []~], [0, 1/9, 0; 0, 0, 1/9; 1/9, 0,
1177: 0]]], [[], [], [;]]], [468, 469, 0, 0, -48776, 0, 0, -36582; 0, 0, 1, 0, -7
1178: , -6, 0, -3; 0, 0, 0, 1, -3, 0, -6, 0]]
1179: ? idealval(nf,idp,vp)
1180: 7
1181: ? ideleprincipal(nf,Mod(x^3+5,nfpol))
1182: [[6; 0; 1; 3; 0], [2.2324480827796254080981385584384939684 + 3.1415926535897
1183: 932384626433832795028842*I, 5.0387659675158716386435353106610489968 + 1.5851
1184: 760343512250049897278861965702423*I, 4.2664040272651028743625910797589683173
1185: - 0.0083630478144368246110910258645462996191*I]]
1186: ? ba=nfalgtobasis(nf,Mod(x^3+5,nfpol))
1187: [6, 0, 1, 3, 0]~
1188: ? bb=nfalgtobasis(nf,Mod(x^3+x,nfpol))
1189: [1, 1, 1, 3, 0]~
1190: ? bc=matalgtobasis(nf,[Mod(x^2+x,nfpol);Mod(x^2+1,nfpol)])
1191:
1192: [[0, 1, 1, 0, 0]~]
1193:
1194: [[1, 0, 1, 0, 0]~]
1195:
1196: ? matbasistoalg(nf,bc)
1197:
1198: [Mod(x^2 + x, x^5 - 5*x^3 + 5*x + 25)]
1199:
1200: [Mod(x^2 + 1, x^5 - 5*x^3 + 5*x + 25)]
1201:
1202: ? nfbasis(x^3+4*x+5)
1203: [1, x, 1/7*x^2 - 1/7*x - 2/7]
1204: ? nfbasis(x^3+4*x+5,2)
1205: [1, x, 1/7*x^2 - 1/7*x - 2/7]
1206: ? nfbasis(x^3+4*x+12,1)
1207: [1, x, 1/2*x^2]
1208: ? nfbasistoalg(nf,ba)
1209: Mod(x^3 + 5, x^5 - 5*x^3 + 5*x + 25)
1210: ? nfbasis(p2,0,fa)
1211: [1, x, x^2, 1/11699*x^3 + 1847/11699*x^2 - 132/11699*x - 2641/11699, 1/13962
1212: 3738889203638909659*x^4 - 1552451622081122020/139623738889203638909659*x^3 +
1213: 418509858130821123141/139623738889203638909659*x^2 - 6810913798507599407313
1214: 4/139623738889203638909659*x - 13185339461968406/58346808996920447]
1215: ? da=nfdetint(nf,[a,aid])
1216:
1217: [30 5 25 27 10]
1218:
1219: [0 5 0 0 0]
1220:
1221: [0 0 5 2 0]
1222:
1223: [0 0 0 1 0]
1224:
1225: [0 0 0 0 5]
1226:
1227: ? nfdisc(x^3+4*x+12)
1228: -1036
1229: ? nfdisc(x^3+4*x+12,1)
1230: -1036
1231: ? nfdisc(p2,0,fa)
1232: 136866601
1233: ? nfeltdiv(nf,ba,bb)
1234: [755/373, -152/373, 159/373, 120/373, -264/373]~
1235: ? nfeltdiveuc(nf,ba,bb)
1236: [2, 0, 0, 0, -1]~
1237: ? nfeltdivrem(nf,ba,bb)
1238: [[2, 0, 0, 0, -1]~, [-12, -7, 0, 9, 5]~]
1239: ? nfeltmod(nf,ba,bb)
1240: [-12, -7, 0, 9, 5]~
1241: ? nfeltmul(nf,ba,bb)
1242: [-25, -50, -30, 15, 90]~
1243: ? nfeltpow(nf,bb,5)
1244: [23455, 156370, 115855, 74190, -294375]~
1245: ? nfeltreduce(nf,ba,idx)
1246: [1, 0, 0, 0, 0]~
1247: ? nfeltval(nf,ba,vp)
1248: 0
1249: ? nffactor(nf2,x^3+x)
1250:
1251: [Mod(1, y^3 - y - 1)*x 1]
1252:
1253: [Mod(1, y^3 - y - 1)*x^2 + Mod(1, y^3 - y - 1) 1]
1254:
1255: ? aut=nfgaloisconj(nf3)
1256: [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
1257: , -x]~
1258: ? nfgaloisapply(nf3,aut[5],Mod(x^5,x^6+108))
1259: Mod(1/2*x^5 - 9*x^2, x^6 + 108)
1260: ? nfhilbert(nf,3,5)
1261: -1
1262: ? nfhilbert(nf,3,5,idf[1,1])
1263: -1
1264: ? nfhnf(nf,[a,aid])
1265: [[[1, 0, 0, 0, 0]~, [0, 0, 0, 0, 0]~, [0, 0, 0, 0, 0]~; [0, 0, 0, 0, 0]~, [1
1266: , 0, 0, 0, 0]~, [0, 0, 0, 0, 0]~; [0, 0, 0, 0, 0]~, [0, 0, 0, 0, 0]~, [1, 0,
1267: 0, 0, 0]~], [[2, 1, 1, 1, 0; 0, 1, 0, 0, 0; 0, 0, 1, 0, 0; 0, 0, 0, 1, 0; 0
1268: , 0, 0, 0, 1], [1, 0, 0, 0, 0; 0, 1, 0, 0, 0; 0, 0, 1, 0, 0; 0, 0, 0, 1, 0;
1269: 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;
1270: 0, 0, 0, 0, 1]]]
1271: ? nfhnfmod(nf,[a,aid],da)
1272: [[[1, 0, 0, 0, 0]~, [0, 0, 0, 0, 0]~, [0, 0, 0, 0, 0]~; [0, 0, 0, 0, 0]~, [1
1273: , 0, 0, 0, 0]~, [0, 0, 0, 0, 0]~; [0, 0, 0, 0, 0]~, [0, 0, 0, 0, 0]~, [1, 0,
1274: 0, 0, 0]~], [[2, 1, 1, 1, 0; 0, 1, 0, 0, 0; 0, 0, 1, 0, 0; 0, 0, 0, 1, 0; 0
1275: , 0, 0, 0, 1], [1, 0, 0, 0, 0; 0, 1, 0, 0, 0; 0, 0, 1, 0, 0; 0, 0, 0, 1, 0;
1276: 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;
1277: 0, 0, 0, 0, 1]]]
1278: ? nfisideal(bnf[7],[5,1;0,1])
1279: 1
1280: ? nfisincl(x^2+1,x^4+1)
1281: [-x^2, x^2]
1282: ? nfisincl(x^2+1,nfinit(x^4+1))
1283: [-x^2, x^2]
1284: ? nfisisom(x^3+x^2-2*x-1,x^3+x^2-2*x-1)
1285: [x, -x^2 - x + 1, x^2 - 2]
1286: ? nfisisom(x^3-2,nfinit(x^3-6*x^2-6*x-30))
1287: [-1/25*x^2 + 13/25*x - 2/5]
1288: ? nfroots(nf2,x+2)
1289: [Mod(-2, y^3 - y - 1)]
1290: ? nfrootsof1(nf)
1291: [2, [-1, 0, 0, 0, 0]~]
1292: ? nfsnf(nf,[as,haid,vaid])
1293: [[10951073973332888246310, 5442457637639729109215, 2693780223637146570055, 3
1294: 910837124677073032737, 3754666252923836621170; 0, 5, 0, 0, 0; 0, 0, 5, 2, 0;
1295: 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
1296: ; 0, 0, 0, 1, 0; 0, 0, 0, 0, 1], [1, 0, 0, 0, 0; 0, 1, 0, 0, 0; 0, 0, 1, 0,
1297: 0; 0, 0, 0, 1, 0; 0, 0, 0, 0, 1]]
1298: ? nfsubfields(nf)
1299: [[x^5 - 5*x^3 + 5*x + 25, x], [x, x^5 - 5*x^3 + 5*x + 25]]
1300: ? polcompositum(x^4-4*x+2,x^3-x-1)
1301: [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
1302: ^2 - 128*x - 5]
1303: ? polcompositum(x^4-4*x+2,x^3-x-1,1)
1304: [[x^12 - 4*x^10 + 8*x^9 + 12*x^8 + 12*x^7 + 138*x^6 + 132*x^5 - 43*x^4 + 58*
1305: x^2 - 128*x - 5, Mod(-279140305176/29063006931199*x^11 + 129916611552/290630
1306: 06931199*x^10 + 1272919322296/29063006931199*x^9 - 2813750209005/29063006931
1307: 199*x^8 - 2859411937992/29063006931199*x^7 - 414533880536/29063006931199*x^6
1308: - 35713977492936/29063006931199*x^5 - 17432607267590/29063006931199*x^4 + 4
1309: 9785595543672/29063006931199*x^3 + 9423768373204/29063006931199*x^2 - 427797
1310: 76146743/29063006931199*x + 37962587857138/29063006931199, x^12 - 4*x^10 + 8
1311: *x^9 + 12*x^8 + 12*x^7 + 138*x^6 + 132*x^5 - 43*x^4 + 58*x^2 - 128*x - 5), M
1312: od(-279140305176/29063006931199*x^11 + 129916611552/29063006931199*x^10 + 12
1313: 72919322296/29063006931199*x^9 - 2813750209005/29063006931199*x^8 - 28594119
1314: 37992/29063006931199*x^7 - 414533880536/29063006931199*x^6 - 35713977492936/
1315: 29063006931199*x^5 - 17432607267590/29063006931199*x^4 + 49785595543672/2906
1316: 3006931199*x^3 + 9423768373204/29063006931199*x^2 - 13716769215544/290630069
1317: 31199*x + 37962587857138/29063006931199, x^12 - 4*x^10 + 8*x^9 + 12*x^8 + 12
1318: *x^7 + 138*x^6 + 132*x^5 - 43*x^4 + 58*x^2 - 128*x - 5), -1]]
1319: ? polgalois(x^6-3*x^2-1)
1320: [12, 1, 1]
1321: ? polred(x^5-2*x^4-4*x^3-96*x^2-352*x-568)
1322: [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
1323: - 1, x^5 - x^4 + 4*x^3 - 2*x^2 + x - 1, x^5 + 4*x^3 - 4*x^2 + 8*x - 8]
1324: ? polred(x^4-28*x^3-458*x^2+9156*x-25321,3)
1325:
1326: [1 x - 1]
1327:
1328: [1/115*x^2 - 14/115*x - 327/115 x^2 - 10]
1329:
1330: [3/1495*x^3 - 63/1495*x^2 - 1607/1495*x + 13307/1495 x^4 - 32*x^2 + 216]
1331:
1332: [1/4485*x^3 - 7/1495*x^2 - 1034/4485*x + 7924/4485 x^4 - 8*x^2 + 6]
1333:
1334: ? polred(x^4+576,1)
1335: [x - 1, x^2 - x + 1, x^2 + 1, x^4 - x^2 + 1]
1336: ? polred(x^4+576,3)
1337:
1338: [1 x - 1]
1339:
1340: [1/192*x^3 + 1/8*x + 1/2 x^2 - x + 1]
1341:
1342: [-1/24*x^2 x^2 + 1]
1343:
1344: [-1/192*x^3 + 1/48*x^2 + 1/8*x x^4 - x^2 + 1]
1345:
1346: ? polred(p2,0,fa)
1347: [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
1348: *x^2 + 508*x + 913, x^5 - 2*x^4 - 13*x^3 + 37*x^2 - 21*x - 1, x^5 - x^4 - 52
1349: *x^3 - 197*x^2 - 273*x - 127]
1350: ? polred(p2,1,fa)
1351: [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
1352: *x^2 + 508*x + 913, x^5 - 2*x^4 - 13*x^3 + 37*x^2 - 21*x - 1, x^5 - x^4 - 52
1353: *x^3 - 197*x^2 - 273*x - 127]
1354: ? polredabs(x^5-2*x^4-4*x^3-96*x^2-352*x-568)
1355: x^5 - x^4 + 2*x^3 - 4*x^2 + x - 1
1356: ? polredabs(x^5-2*x^4-4*x^3-96*x^2-352*x-568,1)
1357: [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 -
1358: x^4 + 2*x^3 - 4*x^2 + x - 1)]
1359: ? polredord(x^3-12*x+45*x-1)
1360: [x - 1, x^3 - 363*x - 2663, x^3 + 33*x - 1]
1361: ? polsubcyclo(31,5)
1362: x^5 + x^4 - 12*x^3 - 21*x^2 + x + 5
1363: ? setrand(1);poltschirnhaus(x^5-x-1)
1364: x^5 - 15*x^4 + 88*x^3 - 278*x^2 + 452*x - 289
1365: ? aa=rnfpseudobasis(nf2,p)
1366: [[[1, 0, 0]~, [0, 0, 0]~, [0, 0, 0]~, [-2, 0, 0]~, [11, 0, 0]~; [0, 0, 0]~,
1367: [1, 0, 0]~, [0, 0, 0]~, [2, 0, 0]~, [-8, 0, 0]~; [0, 0, 0]~, [0, 0, 0]~, [1,
1368: 0, 0]~, [1, 0, 0]~, [4, 0, 0]~; [0, 0, 0]~, [0, 0, 0]~, [0, 0, 0]~, [1, 0,
1369: 0]~, [-2, 0, 0]~; [0, 0, 0]~, [0, 0, 0]~, [0, 0, 0]~, [0, 0, 0]~, [1, 0, 0]~
1370: ], [[1, 0, 0; 0, 1, 0; 0, 0, 1], [1, 0, 0; 0, 1, 0; 0, 0, 1], [1, 0, 0; 0, 1
1371: , 0; 0, 0, 1], [1, 0, 3/5; 0, 1, 2/5; 0, 0, 1/5], [1, 0, 8/25; 0, 1, 22/25;
1372: 0, 0, 1/25]], [416134375, 212940625, 388649575; 0, 3125, 550; 0, 0, 25], [-1
1373: 280, 5, 5]~]
1374: ? rnfbasis(bnf2,aa)
1375:
1376: [[1, 0, 0]~ [0, 0, 0]~ [0, 0, 0]~ [38/25, -33/25, 11/25]~ [-11, -4, 9]~]
1377:
1378: [[0, 0, 0]~ [1, 0, 0]~ [0, 0, 0]~ [-14/25, 24/25, -8/25]~ [28/5, 2/5, -24/5]
1379: ~]
1380:
1381: [[0, 0, 0]~ [0, 0, 0]~ [1, 0, 0]~ [57/25, -12/25, 4/25]~ [-58/5, -47/5, 44/5
1382: ]~]
1383:
1384: [[0, 0, 0]~ [0, 0, 0]~ [0, 0, 0]~ [9/25, 6/25, -2/25]~ [-4/5, -11/5, 2/5]~]
1385:
1386: [[0, 0, 0]~ [0, 0, 0]~ [0, 0, 0]~ [8/25, -3/25, 1/25]~ [-9/5, -6/5, 7/5]~]
1387:
1388: ? rnfdisc(nf2,p)
1389: [[416134375, 212940625, 388649575; 0, 3125, 550; 0, 0, 25], [-1280, 5, 5]~]
1390: ? rnfequation(nf2,p)
1391: x^15 - 15*x^11 + 75*x^7 - x^5 - 125*x^3 + 5*x + 1
1392: ? rnfequation(nf2,p,1)
1393: [x^15 - 15*x^11 + 75*x^7 - x^5 - 125*x^3 + 5*x + 1, Mod(-x^5 + 5*x, x^15 - 1
1394: 5*x^11 + 75*x^7 - x^5 - 125*x^3 + 5*x + 1), 0]
1395: ? rnfhnfbasis(bnf2,aa)
1396:
1397: [[1, 0, 0]~ [0, 0, 0]~ [0, 0, 0]~ [-2/5, 2/5, -4/5]~ [11/25, 99/25, -33/25]~
1398: ]
1399:
1400: [[0, 0, 0]~ [1, 0, 0]~ [0, 0, 0]~ [2/5, -2/5, 4/5]~ [-8/25, -72/25, 24/25]~]
1401:
1402: [[0, 0, 0]~ [0, 0, 0]~ [1, 0, 0]~ [1/5, -1/5, 2/5]~ [4/25, 36/25, -12/25]~]
1403:
1404: [[0, 0, 0]~ [0, 0, 0]~ [0, 0, 0]~ [1/5, -1/5, 2/5]~ [-2/25, -18/25, 6/25]~]
1405:
1406: [[0, 0, 0]~ [0, 0, 0]~ [0, 0, 0]~ [0, 0, 0]~ [1/25, 9/25, -3/25]~]
1407:
1408: ? rnfisfree(bnf2,aa)
1409: 1
1410: ? rnfsteinitz(nf2,aa)
1411: [[[1, 0, 0]~, [0, 0, 0]~, [0, 0, 0]~, [38/25, -33/25, 11/25]~, [-27/125, 33/
1412: 125, -11/125]~; [0, 0, 0]~, [1, 0, 0]~, [0, 0, 0]~, [-14/25, 24/25, -8/25]~,
1413: [6/125, -24/125, 8/125]~; [0, 0, 0]~, [0, 0, 0]~, [1, 0, 0]~, [57/25, -12/2
1414: 5, 4/25]~, [-53/125, 12/125, -4/125]~; [0, 0, 0]~, [0, 0, 0]~, [0, 0, 0]~, [
1415: 9/25, 6/25, -2/25]~, [-11/125, -6/125, 2/125]~; [0, 0, 0]~, [0, 0, 0]~, [0,
1416: 0, 0]~, [8/25, -3/25, 1/25]~, [-7/125, 3/125, -1/125]~], [[1, 0, 0; 0, 1, 0;
1417: 0, 0, 1], [1, 0, 0; 0, 1, 0; 0, 0, 1], [1, 0, 0; 0, 1, 0; 0, 0, 1], [1, 0,
1418: 0; 0, 1, 0; 0, 0, 1], [125, 0, 108; 0, 125, 22; 0, 0, 1]], [416134375, 21294
1419: 0625, 388649575; 0, 3125, 550; 0, 0, 25], [-1280, 5, 5]~]
1420: ? nfz=zetakinit(x^2-2);
1421: ? zetak(nfz,-3)
1422: 0.091666666666666666666666666666666666666
1423: ? zetak(nfz,1.5+3*I)
1424: 0.88324345992059326405525724366416928890 - 0.2067536250233895222724230899142
1425: 7938845*I
1426: ? setrand(1);quadclassunit(1-10^7,,[1,1])
1427: *** Warning: not a fundamental discriminant in quadclassunit.
1428: [2416, [1208, 2], [Qfb(277, 55, 9028), Qfb(1700, 1249, 1700)], 1, 0.99984980
1429: 75377600233]
1430: ? setrand(1);quadclassunit(10^9-3,,[0.5,0.5])
1431: [4, [4], [Qfb(3, 1, -83333333, 0.E-57)], 2800.625251907016076486370621737074
1432: 5514, 0.9990369458964383232]
1433: ? sizebyte(%)
1434: 328
1435: ? getheap
1436: [198, 120613]
1437: ? print("Total time spent: ",gettime);
1438: Total time spent: 4836
1439: ? \q
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