*** Warning: new stack size = 60000000 (57.220 Mbytes).
[85997496, [42998748, 2], [[408188227, 99620635; 0, 1], [2, 1; 0, 1]]]
12.340047278667903334059769086970462209
4.1894250945222025884896456921310573069
*** bnfinit: Warning: non-monic polynomial in bnfinit, using polredbest.
[1, [], []]
*** bnfinit: Warning: non-monic polynomial in bnfinit, using polredbest.
[1, [], []]
[2, -1]
20915648110955829231381594293324156411897455346679838307589120000
571459344155975480004612560667633185714077696
[54898, [54898], [[17, 15; 0, 1]]]
[26, [26], [[19, 15, 18, 5; 0, 1, 0, 0; 0, 0, 1, 0; 0, 0, 0, 1]]]
[1, [], []]
[3, 3]
20/3
-5
13
0
5/2
-1
1024/243
-1
31
-11
1/32
15853839
1736217747
Mod(4/3, y^5 - 4*y^3 + 2*y + 11)
Mod(-1, y^5 - 4*y^3 + 2*y + 11)
Mod(y^2 + y + 1, y^5 - 4*y^3 + 2*y + 11)
Mod(y, y^5 - 4*y^3 + 2*y + 11)
Mod(1/2, y^5 - 4*y^3 + 2*y + 11)
Mod(5*y^4 + 4*y^3 - 12*y^2 - y - 5, y^5 - 4*y^3 + 2*y + 11)
[4/3, 0, 0, 0, 0]~
[-1, 0, 0, 0, 0]~
[3, 1, 1, 0, 0]~
[0, 1, 0, 0, 0]~
[1/2, 0, 0, 0, 0]~
[1, 2, 3, 4, 5]~
(f)->for(i=1,#v,for(j=1,#v,print(f(nf,v[i],v[j]))))
8/3
1/3
[13/3, 1, 1, 0, 0]~
[4/3, 1, 0, 0, 0]~
11/6
[7/3, 2, 3, 4, 5]~
1/3
-2
[2, 1, 1, 0, 0]~
[-1, 1, 0, 0, 0]~
-1/2
[0, 2, 3, 4, 5]~
[13/3, 1, 1, 0, 0]~
[2, 1, 1, 0, 0]~
[6, 2, 2, 0, 0]~
[3, 2, 1, 0, 0]~
[7/2, 1, 1, 0, 0]~
[4, 3, 4, 4, 5]~
[4/3, 1, 0, 0, 0]~
[-1, 1, 0, 0, 0]~
[3, 2, 1, 0, 0]~
[0, 2, 0, 0, 0]~
[1/2, 1, 0, 0, 0]~
[1, 3, 3, 4, 5]~
11/6
-1/2
[7/2, 1, 1, 0, 0]~
[1/2, 1, 0, 0, 0]~
1
[3/2, 2, 3, 4, 5]~
[7/3, 2, 3, 4, 5]~
[0, 2, 3, 4, 5]~
[4, 3, 4, 4, 5]~
[1, 3, 3, 4, 5]~
[3/2, 2, 3, 4, 5]~
[2, 4, 6, 8, 10]~
1
-4/3
[-64/93, 16/31, 16/93, -8/31, 4/93]~
[0, 4/33, 4/33, 0, -4/33]~
8/3
[1587988/47561517, -165136/5284613, 41300/5284613, -212540/47561517, -78712/
47561517]~
-3/4
1
[16/31, -12/31, -4/31, 6/31, -1/31]~
[0, -1/11, -1/11, 0, 1/11]~
-2
[-396997/15853839, 123852/5284613, -30975/5284613, 53135/15853839, 19678/158
53839]~
[9/4, 3/4, 3/4, 0, 0]~
[-3, -1, -1, 0, 0]~
[1, 0, 0, 0, 0]~
[1, 12/11, 1/11, 0, -1/11]~
[6, 2, 2, 0, 0]~
[1249690/15853839, -222317/5284613, 39600/5284613, -477392/15853839, 434/158
53839]~
[0, 3/4, 0, 0, 0]~
[0, -1, 0, 0, 0]~
[3/31, -10/31, 7/31, 5/31, -6/31]~
[1, 0, 0, 0, 0]~
[0, 2, 0, 0, 0]~
[-672280/15853839, 150044/5284613, -148123/5284613, 73247/15853839, -53135/1
5853839]~
3/8
-1/2
[-8/31, 6/31, 2/31, -3/31, 1/62]~
[0, 1/22, 1/22, 0, -1/22]~
1
[396997/31707678, -61926/5284613, 30975/10569226, -53135/31707678, -9839/158
53839]~
[3/4, 3/2, 9/4, 3, 15/4]~
[-1, -2, -3, -4, -5]~
[-314/31, -59/31, 311/31, 14/31, -85/31]~
[7, -27/11, 39/11, 5, 5/11]~
[2, 4, 6, 8, 10]~
[1, 0, 0, 0, 0]~
1
-1
[-1, 1, 0, 0, 0]~
[0, 0, 0, 0, 0]~
3
[0, 0, 0, 0, 0]~
-1
1
[1, 0, 0, 0, 0]~
[0, 0, 0, 0, 0]~
-2
[0, 0, 0, 0, 0]~
[2, 1, 1, 0, 0]~
[-3, -1, -1, 0, 0]~
[1, 0, 0, 0, 0]~
[1, 1, 0, 0, 0]~
[6, 2, 2, 0, 0]~
[0, 0, 0, 0, 0]~
[0, 1, 0, 0, 0]~
[0, -1, 0, 0, 0]~
[0, 0, 0, 0, 0]~
[1, 0, 0, 0, 0]~
[0, 2, 0, 0, 0]~
[0, 0, 0, 0, 0]~
0
0
[0, 0, 0, 0, 0]~
[0, 0, 0, 0, 0]~
1
[0, 0, 0, 0, 0]~
[1, 2, 2, 3, 4]~
[-1, -2, -3, -4, -5]~
[-10, -2, 10, 0, -3]~
[7, -2, 4, 5, 0]~
[2, 4, 6, 8, 10]~
[1, 0, 0, 0, 0]~
[1, 0]
[-1, 1/3]
[[-1, 1, 0, 0, 0]~, [7/3, -2, 0, -1, 0]~]
[[0, 0, 0, 0, 0]~, 4/3]
[3, -1/6]
[[0, 0, 0, 0, 0]~, 4/3]
[-1, 1/3]
[1, 0]
[[1, 0, 0, 0, 0]~, [-4, -1, -1, 0, 0]~]
[[0, 0, 0, 0, 0]~, -1]
[-2, 0]
[[0, 0, 0, 0, 0]~, -1]
[[2, 1, 1, 0, 0]~, [1/3, -1/3, -1/3, 0, 0]~]
[[-3, -1, -1, 0, 0]~, [0, 0, 0, 0, 0]~]
[[1, 0, 0, 0, 0]~, [0, 0, 0, 0, 0]~]
[[1, 1, 0, 0, 0]~, [1, 0, 0, 0, 0]~]
[[6, 2, 2, 0, 0]~, [0, 0, 0, 0, 0]~]
[[0, 0, 0, 0, 0]~, [3, 1, 1, 0, 0]~]
[[0, 1, 0, 0, 0]~, [0, -1/3, 0, 0, 0]~]
[[0, -1, 0, 0, 0]~, [0, 0, 0, 0, 0]~]
[[0, 0, 0, 0, 0]~, [0, 1, 0, 0, 0]~]
[[1, 0, 0, 0, 0]~, [0, 0, 0, 0, 0]~]
[[0, 2, 0, 0, 0]~, [0, 0, 0, 0, 0]~]
[[0, 0, 0, 0, 0]~, [0, 1, 0, 0, 0]~]
[0, 1/2]
[0, 1/2]
[[0, 0, 0, 0, 0]~, 1/2]
[[0, 0, 0, 0, 0]~, 1/2]
[1, 0]
[[0, 0, 0, 0, 0]~, 1/2]
[[1, 2, 2, 3, 4]~, [-1/3, -2/3, 1/3, 0, -1/3]~]
[[-1, -2, -3, -4, -5]~, [0, 0, 0, 0, 0]~]
[[-10, -2, 10, 0, -3]~, [-6, -2, 1, 2, 1]~]
[[7, -2, 4, 5, 0]~, [-5, 0, 0, 0, 0]~]
[[2, 4, 6, 8, 10]~, [0, 0, 0, 0, 0]~]
[[1, 0, 0, 0, 0]~, [0, 0, 0, 0, 0]~]
0
1/3
[7/3, -2, 0, -1, 0]~
4/3
-1/6
4/3
1/3
0
[-4, -1, -1, 0, 0]~
-1
0
-1
[1/3, -1/3, -1/3, 0, 0]~
[0, 0, 0, 0, 0]~
[0, 0, 0, 0, 0]~
[1, 0, 0, 0, 0]~
[0, 0, 0, 0, 0]~
[3, 1, 1, 0, 0]~
[0, -1/3, 0, 0, 0]~
[0, 0, 0, 0, 0]~
[0, 1, 0, 0, 0]~
[0, 0, 0, 0, 0]~
[0, 0, 0, 0, 0]~
[0, 1, 0, 0, 0]~
1/2
1/2
1/2
1/2
0
1/2
[-1/3, -2/3, 1/3, 0, -1/3]~
[0, 0, 0, 0, 0]~
[-6, -2, 1, 2, 1]~
[-5, 0, 0, 0, 0]~
[0, 0, 0, 0, 0]~
[0, 0, 0, 0, 0]~
16/9
-4/3
[4, 4/3, 4/3, 0, 0]~
[0, 4/3, 0, 0, 0]~
2/3
[4/3, 8/3, 4, 16/3, 20/3]~
-4/3
1
[-3, -1, -1, 0, 0]~
[0, -1, 0, 0, 0]~
-1/2
[-1, -2, -3, -4, -5]~
[4, 4/3, 4/3, 0, 0]~
[-3, -1, -1, 0, 0]~
[13, 5, 6, 2, 1]~
[2, 3, 1, 1, 0]~
[3/2, 1/2, 1/2, 0, 0]~
[-58, -42, 23, 27, 17]~
[0, 4/3, 0, 0, 0]~
[0, -1, 0, 0, 0]~
[2, 3, 1, 1, 0]~
[2, 0, 1, 0, 0]~
[0, 1/2, 0, 0, 0]~
[-33, -3, 11, 8, 4]~
2/3
-1/2
[3/2, 1/2, 1/2, 0, 0]~
[0, 1/2, 0, 0, 0]~
1/4
[1/2, 1, 3/2, 2, 5/2]~
[4/3, 8/3, 4, 16/3, 20/3]~
[-1, -2, -3, -4, -5]~
[-58, -42, 23, 27, 17]~
[-33, -3, 11, 8, 4]~
[1/2, 1, 3/2, 2, 5/2]~
[-1071, -384, -251, -155, 20]~
[1]
[1, 1/2*x - 1/2]
[2, Mod(0, 2)]~
[x^2 + x + 1, [0, 1], -3, 1, [Mat([1, -0.50000000000000000000000000000000000
000 + 0.86602540378443864676372317075293618347*I]), [1, 0.366025403784438646
76372317075293618347; 1, -1.3660254037844386467637231707529361835], [1, 0; 1
, -1], [2, -1; -1, -1], [3, 2; 0, 1], [1, -1; -1, -2], [3, [2, -1; 1, 1]], [
3]~], [-0.50000000000000000000000000000000000000 + 0.86602540378443864676372
317075293618347*I], [1, x], [1, 0; 0, 1], [1, 0, 0, -1; 0, 1, 1, -1]]
2
[0, Mod(0, 2), 1, 0, 0, 0, 0]~
[0, Mod(1, 2), 1, 0, 1, 0, 0]~
[]~
[]~
388
[2 0]
[0 1]
*** bnfisprincipal: Warning: precision too low for generators, not given.
[[]~, [-16275043782306513717209797591668600538906793729160424387141562023303
069241961, -3992515767463859376807521115314587378342597458337773390379448027
181914746015, 40263088752008514039400780199135662260965092541683607359784818
2049497266399, 3875196415920480829978279850511752676499384722019721458357455
29259111353576, 524613164482816169908873750526849574668376660999341089640759
880949016596504]~]
[[[[[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], Vecsmall([1])], [2, [2]], [matrix(0,2), matrix(0,2)], [[], [[2], Vecsma
ll([1]), Mat(1), 20.85619222793697806338436677312547069840936189148609965738
5606105759553686957605190193844727221233577865144297166021560180960373224372
600900514567409428535493879667818173119, [1; 0; 0; 0; 0]]], [Mat(1)]]], [[[[
2, 0, 0, 0, 0; 0, 1, 0, 0, 0; 0, 0, 1, 0, 0; 0, 0, 0, 1, 0; 0, 0, 0, 0, 1],
Vecsmall([1])], [2, [2]], [Mat([[2, [0, 0, 1, -1, 0]~, 3, 1, [0, -80, 60, -1
0, -60; 0, 0, -100, 0, -20; 0, 0, 0, -10, -100; 0, 2, -2, 0, 2; 1, 0, 0, -10
, 0]], 1]), matrix(0,2)], [[], [[2], Vecsmall([1]), Mat(1/2), 21.35619222793
6978063384366773125470698409361891486099657385606105759553686957605190193844
7272212335778651442971660215601809603732243726009005145674094285354938796678
18173119, [2; 0; 0; 0; 0]]], [Mat(1)]]], [], [[[[2, 0, 0, 0, 0; 0, 1, 0, 0,
0; 0, 0, 1, 0, 0; 0, 0, 0, 2, 0; 0, 0, 0, 0, 1], Vecsmall([1])], [4, [2, 2]]
, [Mat([[2, [0, 0, 1, -1, 0]~, 3, 1, [0, -80, 60, -10, -60; 0, 0, -100, 0, -
20; 0, 0, 0, -10, -100; 0, 2, -2, 0, 2; 1, 0, 0, -10, 0]], 2]), Mat([[2, [0,
0, 1, -1, 0]~, 3, 1, [0, -80, 60, -10, -60; 0, 0, -100, 0, -20; 0, 0, 0, -1
0, -100; 0, 2, -2, 0, 2; 1, 0, 0, -10, 0]], 2])], [[[[2], [[-1, 0, 0, -1, 0]
~], [2, 0, 0, 0, 0; 0, 1, 0, 0, 0; 0, 0, 1, 0, 0; 0, 0, 0, 2, 0; 0, 0, 0, 0,
1], [[[1, 0, -1, 0, 0]~, [1, 0, 0, 0, 0], [2, [0, 0, 1, -1, 0]~, 3, 1, [0,
-80, 60, -10, -60; 0, 0, -100, 0, -20; 0, 0, 0, -10, -100; 0, 2, -2, 0, 2; 1
, 0, 0, -10, 0]]]~, 1, [1, matrix(0,2)]], [1, 1, [[[2], [[1, 0, 0, 1, 0]~],
Mat([0, 0, 0, 2, 0]), 2]]], [[0]~, Mat(1)]]], [[2], Vecsmall([1]), Mat(1/2),
41.368578564704732409417461169787335389425015098066066992052113922491767356
2518479971386990773198806459616749645245612672289886701908980504482902220220
62722979243788174152853, [2; 0; 0; 0; 0]]], [[1; 0], [0; 1]]], [[[2, 0, 1, 0
, 0; 0, 2, 0, 0, 0; 0, 0, 1, 0, 0; 0, 0, 0, 1, 0; 0, 0, 0, 0, 1], Vecsmall([
1])], [6, [6]], [Mat([[2, [1, 2, 1, 0, 0]~, 1, 2, [0, -80, -20, 0, 0; 0, -1,
-100, -10, -120; 1, 0, -1, -20, -100; 0, 2, 0, 0, 0; 1, 1, -1, -10, 0]], 1]
), Mat([[2, [1, 2, 1, 0, 0]~, 1, 2, [0, -80, -20, 0, 0; 0, -1, -100, -10, -1
20; 1, 0, -1, -20, -100; 0, 2, 0, 0, 0; 1, 1, -1, -10, 0]], 1])], [[[[3], [[
1, 1, 0, 0, 0]~], [2, 0, 1, 0, 0; 0, 2, 0, 0, 0; 0, 0, 1, 0, 0; 0, 0, 0, 1,
0; 0, 0, 0, 0, 1], [[[0, 0, -1, 0, -1]~, [1, 0, 1, 0, 0; 0, 1, 0, 0, 0], [2,
[1, 2, 1, 0, 0]~, 1, 2, [0, -80, -20, 0, 0; 0, -1, -100, -10, -120; 1, 0, -
1, -20, -100; 0, 2, 0, 0, 0; 1, 1, -1, -10, 0]], x^2 + x + 1, [1, 0; 0, 1; 0
, 0; 0, 0; 0, 0]]~, x + 1, [3, Mat([3, 1])]]]], [[2], Vecsmall([1]), Mat(1/2
), 21.9561427071251651311029092693376679934648273587965202418363934409277005
5508085947230952445471265103162532611846023078065155339896128119468225362650
5116814177943190107524899, [2; 0; 0; 0; 0]]], [Mat(-2), Mat(-3)]]]]
[[[[[[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], Vecsmall([1])], [2, [2], [[-21, 0, 0, 0, 0]~]], [matrix(0,2), matrix(0
,2)], [[], [[2], Vecsmall([1]), Mat(1), 20.856192227936978063384366773125470
6984093618914860996573856061057595536869576051901938447272212335778651442971
66021560180960373224372600900514567409428535493879667818173119, [1; 0; 0; 0;
0]]], [Mat(1)]], [Mat([1, 1, 1])]]], [[[[[2, 0, 0, 0, 0; 0, 1, 0, 0, 0; 0,
0, 1, 0, 0; 0, 0, 0, 1, 0; 0, 0, 0, 0, 1], Vecsmall([1])], [2, [2], [[-21, 0
, 0, 0, 0]~]], [Mat([[2, [0, 0, 1, -1, 0]~, 3, 1, [0, -80, 60, -10, -60; 0,
0, -100, 0, -20; 0, 0, 0, -10, -100; 0, 2, -2, 0, 2; 1, 0, 0, -10, 0]], 1]),
matrix(0,2)], [[], [[2], Vecsmall([1]), Mat(1/2), 21.3561922279369780633843
6677312547069840936189148609965738560610575955368695760519019384472722123357
7865144297166021560180960373224372600900514567409428535493879667818173119, [
2; 0; 0; 0; 0]]], [Mat(1)]], [[], Mat([1, 1, 1])]]], [], [[[[[2, 0, 0, 0, 0;
0, 1, 0, 0, 0; 0, 0, 1, 0, 0; 0, 0, 0, 2, 0; 0, 0, 0, 0, 1], Vecsmall([1])]
, [4, [2, 2], [[81, 0, 0, -1, 0]~, [-41, 0, 0, 0, 0]~]], [Mat([[2, [0, 0, 1,
-1, 0]~, 3, 1, [0, -80, 60, -10, -60; 0, 0, -100, 0, -20; 0, 0, 0, -10, -10
0; 0, 2, -2, 0, 2; 1, 0, 0, -10, 0]], 2]), Mat([[2, [0, 0, 1, -1, 0]~, 3, 1,
[0, -80, 60, -10, -60; 0, 0, -100, 0, -20; 0, 0, 0, -10, -100; 0, 2, -2, 0,
2; 1, 0, 0, -10, 0]], 2])], [[[[2], [[-1, 0, 0, -1, 0]~], [2, 0, 0, 0, 0; 0
, 1, 0, 0, 0; 0, 0, 1, 0, 0; 0, 0, 0, 2, 0; 0, 0, 0, 0, 1], [[[1, 0, -1, 0,
0]~, [1, 0, 0, 0, 0], [2, [0, 0, 1, -1, 0]~, 3, 1, [0, -80, 60, -10, -60; 0,
0, -100, 0, -20; 0, 0, 0, -10, -100; 0, 2, -2, 0, 2; 1, 0, 0, -10, 0]]]~, 1
, [1, matrix(0,2)]], [1, 1, [[[2], [[1, 0, 0, 1, 0]~], Mat([0, 0, 0, 2, 0]),
2]]], [[0]~, Mat(1)]]], [[2], Vecsmall([1]), Mat(1/2), 41.36857856470473240
9417461169787335389425015098066066992052113922491767356251847997138699077319
8806459616749645245612672289886701908980504482902220220627229792437881741528
53, [2; 0; 0; 0; 0]]], [[1; 0], [0; 1]]], [Mat([0, 0, 0]), Mat([1, 1, 1])]],
[[[[2, 0, 1, 0, 0; 0, 2, 0, 0, 0; 0, 0, 1, 0, 0; 0, 0, 0, 1, 0; 0, 0, 0, 0,
1], Vecsmall([1])], [6, [6], [[-21, 1, 0, 0, 0]~]], [Mat([[2, [1, 2, 1, 0,
0]~, 1, 2, [0, -80, -20, 0, 0; 0, -1, -100, -10, -120; 1, 0, -1, -20, -100;
0, 2, 0, 0, 0; 1, 1, -1, -10, 0]], 1]), Mat([[2, [1, 2, 1, 0, 0]~, 1, 2, [0,
-80, -20, 0, 0; 0, -1, -100, -10, -120; 1, 0, -1, -20, -100; 0, 2, 0, 0, 0;
1, 1, -1, -10, 0]], 1])], [[[[3], [[1, 1, 0, 0, 0]~], [2, 0, 1, 0, 0; 0, 2,
0, 0, 0; 0, 0, 1, 0, 0; 0, 0, 0, 1, 0; 0, 0, 0, 0, 1], [[[0, 0, -1, 0, -1]~
, [1, 0, 1, 0, 0; 0, 1, 0, 0, 0], [2, [1, 2, 1, 0, 0]~, 1, 2, [0, -80, -20,
0, 0; 0, -1, -100, -10, -120; 1, 0, -1, -20, -100; 0, 2, 0, 0, 0; 1, 1, -1,
-10, 0]], x^2 + x + 1, [1, 0; 0, 1; 0, 0; 0, 0; 0, 0]]~, x + 1, [3, Mat([3,
1])]]]], [[2], Vecsmall([1]), Mat(1/2), 21.956142707125165131102909269337667
9934648273587965202418363934409277005550808594723095244547126510316253261184
60230780651553398961281194682253626505116814177943190107524899, [2; 0; 0; 0;
0]]], [Mat(-2), Mat(-3)]], [Mat([0, 1, 0]), Mat([1, 1, 1])]]]]
[[[5, 1, [2, 2; 5, 2; 39821, 1; 161141, 1]]], [[]], [], [[10, 2, [2, 6; 5, 4
; 39821, 2; 161141, 2]], []]]
[[[0, 0, 0]], [[10, 0, [-1, 1; 2, 5; 5, 4; 39821, 2; 161141, 2]]], [], [[],
[]]]
[[[[Vecsmall([]), Vecsmall([])], 0, 0, 0]], [[[Vecsmall([50]), Vecsmall([1])
], 0, 0, 0]], [], [[[Vecsmall([50]), Vecsmall([2])], 0, 0, 0], [[Vecsmall([5
6]), Vecsmall([1])], 0, 0, 0]]]
2
[6416795761]
[x^7 - x^6 + x^5 - x^4 - x^3 - x^2, x^9 + x^8 + x^7 + x^6 + 2*x^4 + 2*x^3 +
x^2 + x + 1, x^10 + x^9 - x^8 - x^3 - x^2 - x, x^10 + x^9 + 2*x^7 + x^6 + x^
5 + x^4 + 2*x^2 + x + 1, -x^11 - 2*x^10 - x^8 - 2*x^7 - x^6 - x^5 - 2*x^4 -
x^3 - 2*x^2 - x - 1, -x^11 - x^10 - 2*x^9 - x^8 - 2*x^7 - x^6 - 2*x^5 - x^4
- x^2 - 2*x - 1, -x^11 - x^10 - x^9 + x^8 - x^7 + x^6, -x^11 - x^9 - x^6 + x
^4 - x^3 + x, x^11 - x^10 + x^6 - x^5 - x^2 - x, x^11 - x^8 - x^7 + x^5 - x^
4 - x, x^11 + x^10 + 2*x^8 + x^7 + x^4 + x^3 + 2*x^2 + x + 1, x^11 + 2*x^10
+ x^9 + x^7 + x^5 + x^3 + x^2 + 2*x + 1]
[-x^2, x^2]
[-x^2, x^2]
[-x^2, x^2]
0
[35952239140236636613554193911666/20990466712995598590763903143048989*x^20 +
219201047314343953199542006623468/20990466712995598590763903143048989*x^19
- 544094474369607287844071682948984/20990466712995598590763903143048989*x^18
- 1301738076793130194798253391725406/20990466712995598590763903143048989*x^
17 + 4323784229146831865769550863399188/20990466712995598590763903143048989*
x^16 + 1180785226777964111519743237847228/2099046671299559859076390314304898
9*x^15 - 16009478553791306868545675624906176/2099046671299559859076390314304
8989*x^14 + 11661369832298820433335186698644800/2099046671299559859076390314
3048989*x^13 + 24577904562406269454374516161861844/2099046671299559859076390
3143048989*x^12 - 2841411922644145137800873408789776/12347333360585646229861
11949591117*x^11 + 40513760532585028733891495151094508/209904667129955985907
63903143048989*x^10 + 77137274588135205291798303592401638/209904667129955985
90763903143048989*x^9 - 9612104031689093945033225402487055/12347333360585646
22986111949591117*x^8 + 844775560812208284237807638227260/209904667129955985
90763903143048989*x^7 - 153457335161602039094310022600574514/209904667129955
98590763903143048989*x^6 + 454725983158981264651921915989314030/209904667129
95598590763903143048989*x^5 - 247595736314170743760908290075787460/209904667
12995598590763903143048989*x^4 + 246411488365177430998635983532374564/209904
66712995598590763903143048989*x^3 - 300616800198203967230858561992730353/209
90466712995598590763903143048989*x^2 + 62128367926034523995700779963870389/2
0990466712995598590763903143048989*x + 73920020404088609656492594951950857/2
0990466712995598590763903143048989]
0
[-z^2, z^2]
0
[-1/2*x, 1/2*x]
[-2*x, 2*x]
[-z, z]
x^2 + 1
1
[x^10 + Mod(-5/2*y + 5/2, y^2 - 5)*x^9 + Mod(-5*y + 20, y^2 - 5)*x^8 + Mod(-
20*y + 30, y^2 - 5)*x^7 + Mod(-45/2*y + 145/2, y^2 - 5)*x^6 + Mod(-71/2*y +
121/2, y^2 - 5)*x^5 + Mod(-20*y + 60, y^2 - 5)*x^4 + Mod(-25*y + 5, y^2 - 5)
*x^3 + 45*x^2 + Mod(-5*y + 15, y^2 - 5)*x + Mod(-2*y + 6, y^2 - 5), x^10 + M
od(5/2*y + 5/2, y^2 - 5)*x^9 + Mod(5*y + 20, y^2 - 5)*x^8 + Mod(20*y + 30, y
^2 - 5)*x^7 + Mod(45/2*y + 145/2, y^2 - 5)*x^6 + Mod(79/2*y + 121/2, y^2 - 5
)*x^5 + Mod(25*y + 85, y^2 - 5)*x^4 + Mod(15*y + 55, y^2 - 5)*x^3 + Mod(10*y
- 5, y^2 - 5)*x^2 - 10*x + Mod(-2*y + 6, y^2 - 5)]
[x^10 + Mod(-5/2*y + 5/2, y^2 - 5)*x^9 + Mod(-5*y + 20, y^2 - 5)*x^8 + Mod(-
20*y + 30, y^2 - 5)*x^7 + Mod(-45/2*y + 145/2, y^2 - 5)*x^6 + Mod(-71/2*y +
121/2, y^2 - 5)*x^5 + Mod(-20*y + 60, y^2 - 5)*x^4 + Mod(-25*y + 5, y^2 - 5)
*x^3 + 45*x^2 + Mod(-5*y + 15, y^2 - 5)*x + Mod(-2*y + 6, y^2 - 5), Mod(Mod(
26/2945*y - 653/5890, y^2 - 5)*x^9 + Mod(1633/5890*y - 869/2945, y^2 - 5)*x^
8 + Mod(2951/5890*y - 5939/2945, y^2 - 5)*x^7 + Mod(21757/11780*y - 29451/11
780, y^2 - 5)*x^6 + Mod(18733/11780*y - 69587/11780, y^2 - 5)*x^5 + Mod(1445
/589*y - 9436/2945, y^2 - 5)*x^4 + Mod(7893/11780*y - 34679/11780, y^2 - 5)*
x^3 + Mod(9461/5890*y + 3919/2945, y^2 - 5)*x^2 + Mod(-8383/11780*y - 54699/
11780, y^2 - 5)*x + Mod(261/589*y - 2467/2945, y^2 - 5), x^10 + Mod(-5/2*y +
5/2, y^2 - 5)*x^9 + Mod(-5*y + 20, y^2 - 5)*x^8 + Mod(-20*y + 30, y^2 - 5)*
x^7 + Mod(-45/2*y + 145/2, y^2 - 5)*x^6 + Mod(-71/2*y + 121/2, y^2 - 5)*x^5
+ Mod(-20*y + 60, y^2 - 5)*x^4 + Mod(-25*y + 5, y^2 - 5)*x^3 + 45*x^2 + Mod(
-5*y + 15, y^2 - 5)*x + Mod(-2*y + 6, y^2 - 5)), Mod(Mod(26/2945*y - 653/589
0, y^2 - 5)*x^9 + Mod(1633/5890*y - 869/2945, y^2 - 5)*x^8 + Mod(2951/5890*y
- 5939/2945, y^2 - 5)*x^7 + Mod(21757/11780*y - 29451/11780, y^2 - 5)*x^6 +
Mod(18733/11780*y - 69587/11780, y^2 - 5)*x^5 + Mod(1445/589*y - 9436/2945,
y^2 - 5)*x^4 + Mod(7893/11780*y - 34679/11780, y^2 - 5)*x^3 + Mod(9461/5890
*y + 3919/2945, y^2 - 5)*x^2 + Mod(-8383/11780*y - 42919/11780, y^2 - 5)*x +
Mod(261/589*y - 2467/2945, y^2 - 5), x^10 + Mod(-5/2*y + 5/2, y^2 - 5)*x^9
+ Mod(-5*y + 20, y^2 - 5)*x^8 + Mod(-20*y + 30, y^2 - 5)*x^7 + Mod(-45/2*y +
145/2, y^2 - 5)*x^6 + Mod(-71/2*y + 121/2, y^2 - 5)*x^5 + Mod(-20*y + 60, y
^2 - 5)*x^4 + Mod(-25*y + 5, y^2 - 5)*x^3 + 45*x^2 + Mod(-5*y + 15, y^2 - 5)
*x + Mod(-2*y + 6, y^2 - 5)), -1]
Mod(0, x^10 + Mod(-5/2*y + 5/2, y^2 - 5)*x^9 + Mod(-5*y + 20, y^2 - 5)*x^8 +
Mod(-20*y + 30, y^2 - 5)*x^7 + Mod(-45/2*y + 145/2, y^2 - 5)*x^6 + Mod(-71/
2*y + 121/2, y^2 - 5)*x^5 + Mod(-20*y + 60, y^2 - 5)*x^4 + Mod(-25*y + 5, y^
2 - 5)*x^3 + 45*x^2 + Mod(-5*y + 15, y^2 - 5)*x + Mod(-2*y + 6, y^2 - 5))
1
[Mod(1, y^2 - 5)*x^5 + Mod(y, y^2 - 5), x^10 + Mod(77*y - 275, y^2 - 5)*x^5
+ Mod(-41525*y + 96630, y^2 - 5), x^10 + Mod(77*y + 275, y^2 - 5)*x^5 + Mod(
41525*y + 96630, y^2 - 5)]
x^10 + 5*x^9 + 15*x^8 + 30*x^7 + 45*x^6 + Mod(2*y + 51, y^2 - 5)*x^5 + Mod(5
*y + 45, y^2 - 5)*x^4 + Mod(-10*y + 30, y^2 - 5)*x^3 + Mod(-20*y + 15, y^2 -
5)*x^2 + Mod(-5*y + 5, y^2 - 5)*x + Mod(y + 6, y^2 - 5)
[x^10 + 5*x^9 + 15*x^8 + 30*x^7 + 45*x^6 + Mod(2*y + 51, y^2 - 5)*x^5 + Mod(
5*y + 45, y^2 - 5)*x^4 + Mod(-10*y + 30, y^2 - 5)*x^3 + Mod(-20*y + 15, y^2
- 5)*x^2 + Mod(-5*y + 5, y^2 - 5)*x + Mod(y + 6, y^2 - 5), Mod(-32280/622201
*x^9 + Mod(22275/622201*y - 145260/622201, y^2 - 5)*x^8 + Mod(89100/622201*y
- 397350/622201, y^2 - 5)*x^7 + Mod(244100/622201*y - 22995/20071, y^2 - 5)
*x^6 + Mod(420450/622201*y - 918351/622201, y^2 - 5)*x^5 + Mod(510720/622201
*y - 852705/622201, y^2 - 5)*x^4 + Mod(424640/622201*y - 238275/622201, y^2
- 5)*x^3 + Mod(871950/622201*y + 235710/622201, y^2 - 5)*x^2 + Mod(714855/62
2201*y - 1610346/622201, y^2 - 5)*x + Mod(-62626/622201*y - 860751/622201, y
^2 - 5), x^10 + 5*x^9 + 15*x^8 + 30*x^7 + 45*x^6 + Mod(2*y + 51, y^2 - 5)*x^
5 + Mod(5*y + 45, y^2 - 5)*x^4 + Mod(-10*y + 30, y^2 - 5)*x^3 + Mod(-20*y +
15, y^2 - 5)*x^2 + Mod(-5*y + 5, y^2 - 5)*x + Mod(y + 6, y^2 - 5)), Mod(-322
80/622201*x^9 + Mod(22275/622201*y - 145260/622201, y^2 - 5)*x^8 + Mod(89100
/622201*y - 397350/622201, y^2 - 5)*x^7 + Mod(244100/622201*y - 22995/20071,
y^2 - 5)*x^6 + Mod(420450/622201*y - 918351/622201, y^2 - 5)*x^5 + Mod(5107
20/622201*y - 852705/622201, y^2 - 5)*x^4 + Mod(424640/622201*y - 238275/622
201, y^2 - 5)*x^3 + Mod(871950/622201*y + 235710/622201, y^2 - 5)*x^2 + Mod(
714855/622201*y - 988145/622201, y^2 - 5)*x + Mod(-62626/622201*y - 860751/6
22201, y^2 - 5), x^10 + 5*x^9 + 15*x^8 + 30*x^7 + 45*x^6 + Mod(2*y + 51, y^2
- 5)*x^5 + Mod(5*y + 45, y^2 - 5)*x^4 + Mod(-10*y + 30, y^2 - 5)*x^3 + Mod(
-20*y + 15, y^2 - 5)*x^2 + Mod(-5*y + 5, y^2 - 5)*x + Mod(y + 6, y^2 - 5)),
-1]
[x^2 + x + 1, Mod(0, x^2 + x + 1), Mod(x, x^2 + x + 1), -1]
[25339, [10960, 0, 0, -3420]~]
[x^3 - 3*x^2 + 3*x + 1, x^6 + 3*x^5 + 6*x^4 + 11*x^3 + 12*x^2 - 3*x + 1]
[x^3 - 3*x^2 + 3*x + 1, x^6 + 3*x^5 + 6*x^4 + 11*x^3 + 12*x^2 - 3*x + 1]
[[4]~, [33/343, 2/2401]~]
Mod(1/2*x - 1/2, x^2 + 23)
[1, 2]~
[1, 1/2*x - 1/2]
Mod(0, x)
Mod(-6/5, x)
*** at top-level: nfinit([y^3+2,[1,x]])
*** ^---------------------
*** nfinit: incorrect type in nfbasic_init (t_VEC).
*** at top-level: nfinit([y^3+2,[1,x,x^2]])
*** ^-------------------------
*** nfinit: incorrect type in nfbasic_init (t_VEC).
*** at top-level: nfinit([y^3+2,[1,y^5,y]])
*** ^-------------------------
*** nfinit: incorrect type in nfbasic_init (t_VEC).
*** at top-level: nfdisc([y^2+2,matid(3)])
*** ^------------------------
*** nfdisc: incorrect type in nfmaxord (t_MAT).
*** at top-level: nfdisc([2*y^2+1,matid(3)])
*** ^--------------------------
*** nfdisc: incorrect type in nfbasis [factorization expected] (t_MAT).
*** at top-level: nfdisc([y^2+2,""])
*** ^------------------
*** nfdisc: incorrect type in nfmaxord (t_STR).
*** at top-level: nfnewprec(x)
*** ^------------
*** nfnewprec: incorrect type in nfnewprec (t_POL).
*** at top-level: nfnewprec(quadgen(5))
*** ^---------------------
*** nfnewprec: incorrect type in nfnewprec (t_QUAD).
*** at top-level: nfnewprec(vector(5))
*** ^--------------------
*** nfnewprec: incorrect type in nfnewprec (t_VEC).
*** at top-level: nfnewprec(vector(6))
*** ^--------------------
*** nfnewprec: incorrect type in nfnewprec (t_VEC).
*** at top-level: nfnewprec(vector(8))
*** ^--------------------
*** nfnewprec: incorrect type in nfnewprec (t_VEC).
*** at top-level: nfnewprec(vector(9))
*** ^--------------------
*** nfnewprec: incorrect type in nfnewprec (t_VEC).
*** at top-level: nfnewprec(vector(16))
*** ^---------------------
*** nfnewprec: incorrect type in nfnewprec (t_VEC).
*** at top-level: nfcompositum(nfinit(x-1),x^3-2,x^3-1)
*** ^-------------------------------------
*** nfcompositum: incorrect priority in polcompositum: variable x >= x
*** at top-level: nfcompositum(nfinit(x^2+1),x^3-2,x^3-1)
*** ^---------------------------------------
*** nfcompositum: incorrect priority in polcompositum: variable x >= x
*** at top-level: nfcompositum(nfinit(x-1),y^3-2,y^3-1)
*** ^-------------------------------------
*** nfcompositum: incorrect priority in polcompositum: variable x >= y
*** at top-level: nfcompositum(bnfinit(x),x^3-2,x^3-1)
*** ^------------------------------------
*** nfcompositum: incorrect priority in polcompositum: variable x >= x
*** at top-level: nfisincl(y^2+1,z^4+z^2+1)
*** ^-------------------------
*** nfisincl: not an irreducible polynomial in nfisincl: z^4 + z^2 + 1.
*** at top-level: nfisisom(x,x^0)
*** ^---------------
*** nfisisom: not an irreducible polynomial in nfisincl: 1.
*** at top-level: idealhnf(nf,3,('a^2+1)*Mod(1,3))
*** ^--------------------------------
*** idealhnf: incorrect type in nf_to_scalar_or_basis (t_INTMOD).
*** at top-level: nfalgtobasis(nf,['a,'a]~)
*** ^-------------------------
*** nfalgtobasis: incorrect type in nfalgtobasis (t_COL).
Total time spent: 13920