[[1, 0, 0, 0; 0, 1, 0, 0; 0, 0, 1, 0; 0, 0, 0, 1], [6, 6, 6, 6]]
[[1, 0, 0, 0; 0, 1, 0, 0; 0, 0, 1, 0; 0, 0, 0, 1], [6, 6, 6, 6]]
[]
[[1, 0, 0, 0, 0, [-361894/1129, 99/1129]~, [-724429/1129, 1480/1129]~, [-929
3266/21451, 168/1129]~, [-18602992/21451, 39304/21451]~; 0, 1, 0, 0, 0, [167
146/1129, -108/1129]~, [334588/1129, -808/1129]~, [15473737/21451, 392/1129]
~, [30974892/21451, -39940/21451]~; 0, 0, 1, 0, 0, [-253060/1129, 328/1129]~
, [-506568/1129, 1552/1129]~, [-5866950/21451, -227/1129]~, [-11744297/21451
, 12168/21451]~; 0, 0, 0, 1, 0, [-68390/1129, 171/1129]~, [-136901/1129, 584
/1129]~, [486725/21451, 165/1129]~, [974315/21451, 4540/21451]~; 0, 0, 0, 0,
 1, [90512/1129, -384/1129]~, [181184/1129, -1088/1129]~, [-5551416/21451, -
403/1129]~, [-11112673/21451, 4368/21451]~; 0, 0, 0, 0, 0, [-564/1129, -1/11
29]~, -1, 9/19, [20340/21451, -36/21451]~; 0, 0, 0, 0, 0, 1, [2260/1129, -4/
1129]~, 7/19, [15820/21451, -28/21451]~; 0, 0, 0, 0, 0, 0, 0, [-18619/21451,
 -1/1129]~, [-37271/21451, 28/21451]~; 0, 0, 0, 0, 0, 0, 0, 1/19, [2260/2145
1, -4/21451]~], [1, 1, 1, 1, 1, 1, 1, 1, [1, 0; 0, 1]], 1, 1]
[[[1, 0, 0; 0, 1, 0; 0, 0, 1], [1, 1, 1]], [1, 0, 0; 0, 1, 0; 0, 0, 1]]
[[1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0; 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0; 0, 0, 1,
 0, 0, 0, 0, 0, -1, 0, 1; 0, 0, 0, 1, 0, 0, 0, 0, -1, -1, 1; 0, 0, 0, 0, 1, 
0, 0, 0, 1, -1, 1; 0, 0, 0, 0, 0, 1, 0, 0, -1, 1, 0; 0, 0, 0, 0, 0, 0, 1, 0,
 1, -1, 0; 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, -1; 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0
; 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0; 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1], [1, 1, 
1, 1, 1, 1, 1, 1, 1/3, 1/3, 1/3], 6487513772307278389925284499624661, 648751
3772307278389925284499624661]
[[1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0; 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0; 0, 0, 1,
 0, 0, 0, 0, 0, -1, 0, 1; 0, 0, 0, 1, 0, 0, 0, 0, -1, -1, 1; 0, 0, 0, 0, 1, 
0, 0, 0, 1, -1, 1; 0, 0, 0, 0, 0, 1, 0, 0, -1, 1, 0; 0, 0, 0, 0, 0, 0, 1, 0,
 1, -1, 0; 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, -1; 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0
; 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0; 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1], [1, 1, 
1, 1, 1, 1, 1, 1, 1/3, 1/3, 1/3], 6487513772307278389925284499624661, 648751
3772307278389925284499624661]
[[1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0; 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0; 0, 0, 1,
 0, 0, 0, 0, 0, -1, 0, 1; 0, 0, 0, 1, 0, 0, 0, 0, -1, -1, 1; 0, 0, 0, 0, 1, 
0, 0, 0, 1, -1, 1; 0, 0, 0, 0, 0, 1, 0, 0, -1, 1, 0; 0, 0, 0, 0, 0, 0, 1, 0,
 1, -1, 0; 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, -1; 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0
; 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0; 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1], [1, 1, 
1, 1, 1, 1, 1, 1, 1/3, 1/3, 1/3], 6487513772307278389925284499624661, 648751
3772307278389925284499624661]
[[1, -2018006054; 0, 1], [1, [1/1009003027, 3/4036012108; 0, 1/4036012108]],
 [4036, 3027; 0, 1009], [0, -1009]~]
[[1, -2018006054; 0, 1], [1, [1/1009003027, 3/4036012108; 0, 1/4036012108]],
 [4036, 3027; 0, 1009], [0, -1009]~]
[[1, -2018006054; 0, 1], [1, [1/1009003027, 3/4036012108; 0, 1/4036012108]],
 [4036, 3027; 0, 1009], [0, -1009]~]
[[1, -2018006054; 0, 1], [1, [1/1009003027, 3/4036012108; 0, 1/4036012108]],
 [4036, 3027; 0, 1009], [0, -1009]~]
[[4036, 3027; 0, 1009], [0, -1009]~]
[[4, 3; 0, 1], [0, -1009]~]
[[4036, 3027; 0, 1009], [0, -1009]~]
[[1, -2018006054; 0, 1], [1, [1/1009003027, 3/4036012108; 0, 1/4036012108]],
 [4036, 3027; 0, 1009], [0, -1009]~]
[[1, -2018006054; 0, 1], [1, [1/1009003027, 3/4036012108; 0, 1/4036012108]],
 [4036, 3027; 0, 1009], [0, -1009]~]
[[Mat(861), [1]], [[[;], [;], [;], [;], []~, 0, [y, [1, 0], 1, 1, [Mat(1), M
at(1), Mat(16), Mat(1), 1, Mat(1), [1, 0], []], [0.E-38], [1], Mat(1), Mat(1
)], [[1, [], []], 1, 1, [2, -1], []], [[;], [;], [;], [], [;], [;]], [0, 0, 
0]], [[Mat(861), [1]], [960, [120, 2, 2, 2], [808, 286, 575, [-860]~]], [[[3
, [3]~, 1, 1, 1], 1; [7, [7]~, 1, 1, 1], 1; [41, [41]~, 1, 1, 1], 1], [[3, [
3]~, 1, 1, 1], 1; [7, [7]~, 1, 1, 1], 1; [41, [41]~, 1, 1, 1], 1]], [[[[2], 
[-286], Mat(3), [[1, [1], [3, [3]~, 1, 1, 1]]~, 2, [2, Mat([2, 1])]]], [[6],
 [493], Mat(7), [[1, [1], [7, [7]~, 1, 1, 1]]~, 3, [6, [2, 1; 3, 1]]]], [[40
], [211], Mat(41), [[1, [1], [41, [41]~, 1, 1, 1]]~, 6, [40, [2, 3; 5, 1]]]]
], [[2], Vecsmall([1]), Mat(1/861), 861861/2000, Mat(861)]], [[0; 0; 1; 0], 
[-20; 1; 0; 0], [3; -1; 0; 0], [0; 0; 0; 1]]], [], [[;], [1, 0, 0, 0; 0, 1, 
0, -1; 0, 0, 1, -1], [1, 0, 0; 0, -1, 0; 0, 0, -1; 0, 0, 0]], [480, [120, 2,
 2], [808, 286, 575]], [Mat([0, 0, 0, 1]), Mat(-2), 1]], [1, 0, 0; 0, 2, 0; 
0, 0, 2]]
[[Mat(861), [1]], [[[;], [;], [;], [;], []~, 0, [y, [1, 0], 1, 1, [Mat(1), M
at(1), Mat(16), Mat(1), 1, Mat(1), [1, 0], []], [0.E-38], [1], Mat(1), Mat(1
)], [[1, [], []], 1, 1, [2, -1], []], [[;], [;], [;], [], [;], [;]], [0, 0, 
0]], [[Mat(861), [1]], [960, [120, 2, 2, 2], [808, 286, 575, [-860]~]], [[[3
, [3]~, 1, 1, 1], 1; [7, [7]~, 1, 1, 1], 1; [41, [41]~, 1, 1, 1], 1], [[3, [
3]~, 1, 1, 1], 1; [7, [7]~, 1, 1, 1], 1; [41, [41]~, 1, 1, 1], 1]], [[[[2], 
[-286], Mat(3), [[1, [1], [3, [3]~, 1, 1, 1]]~, 2, [2, Mat([2, 1])]]], [[6],
 [493], Mat(7), [[1, [1], [7, [7]~, 1, 1, 1]]~, 3, [6, [2, 1; 3, 1]]]], [[40
], [211], Mat(41), [[1, [1], [41, [41]~, 1, 1, 1]]~, 6, [40, [2, 3; 5, 1]]]]
], [[2], Vecsmall([1]), Mat(1/861), 861861/2000, Mat(861)]], [[0; 0; 1; 0], 
[-20; 1; 0; 0], [3; -1; 0; 0], [0; 0; 0; 1]]], [], [[;], [1, 0, 0, 0; 0, 1, 
0, -1; 0, 0, 1, -1], [1, 0, 0; 0, -1, 0; 0, 0, -1; 0, 0, 0]], [480, [120, 2,
 2], [808, 286, 575]], [Mat([0, 0, 0, 1]), Mat(-2), 1]], [1, 0, 0; 0, 2, 0; 
0, 0, 2]]
[[Mat(861), [1]], [[[;], [;], [;], [;], []~, 0, [y, [1, 0], 1, 1, [Mat(1), M
at(1), Mat(16), Mat(1), 1, Mat(1), [1, 0], []], [0.E-38], [1], Mat(1), Mat(1
)], [[1, [], []], 1, 1, [2, -1], []], [[;], [;], [;], [], [;], [;]], [0, 0, 
0]], [[Mat(861), [1]], [960, [120, 2, 2, 2], [808, 286, 575, [-860]~]], [[[3
, [3]~, 1, 1, 1], 1; [7, [7]~, 1, 1, 1], 1; [41, [41]~, 1, 1, 1], 1], [[3, [
3]~, 1, 1, 1], 1; [7, [7]~, 1, 1, 1], 1; [41, [41]~, 1, 1, 1], 1]], [[[[2], 
[-286], Mat(3), [[1, [1], [3, [3]~, 1, 1, 1]]~, 2, [2, Mat([2, 1])]]], [[6],
 [493], Mat(7), [[1, [1], [7, [7]~, 1, 1, 1]]~, 3, [6, [2, 1; 3, 1]]]], [[40
], [211], Mat(41), [[1, [1], [41, [41]~, 1, 1, 1]]~, 6, [40, [2, 3; 5, 1]]]]
], [[2], Vecsmall([1]), Mat(1/861), 861861/2000, Mat(861)]], [[0; 0; 1; 0], 
[-20; 1; 0; 0], [3; -1; 0; 0], [0; 0; 0; 1]]], [], [[;], [1, 0, 0, 0; 0, 1, 
0, -1; 0, 0, 1, -1], [1, 0, 0; 0, -1, 0; 0, 0, -1; 0, 0, 0]], [480, [120, 2,
 2], [808, 286, 575]], [Mat([0, 0, 0, 1]), Mat(-2), 1]], [1, 0, 0; 0, 2, 0; 
0, 0, 2]]
[Mat(117), [0]]

[3 1]

[0 1]

[[8, 2; 0, 1], [2, 0; 0, 1], [1, 0; 0, 1]]
1
1
1
1
  *** rnfisabelian: Warning: nonmonic polynomial. Result of the form [nf,c].
  *** rnfisabelian: Warning: nonmonic polynomial. Result of the form [nf,c].
0
  *** rnfisabelian: Warning: nonmonic polynomial. Result of the form [nf,c].
1
1
[(9*y^2 + 6*y - 12)*x^2 + 10*x + (6*y^2 + 6*y - 6), 1]
2
2
[x, -1]
[1, 2]
-28124/93*x^3 + 14062/31*x^2 + 562480/93*x + 166769/31
Mod(x^5 + x^2 + 2, x^6 + x^5 + x^4 + x^3 + x^2 + x + 1)
Mod(z^2, z^3 + z^2 - 2*z - 1)
[[1, 0, 0; 0, 1, 0; 0, 0, 1], [1, 1, 1]]

[[-9843, 391, -3472]~ [5826, -17043, -23934]~ [-183013449, -53300400, -56068
6734]~ [-4831228968, -2610454140, -9159229488]~]

[[3393, 2719, 1883]~ [3799, -2741, -7311]~ [44971153, -74830626, -108534066]
~ [2330522034, 204707177, -1049209305]~]

[[3690, -3485, 1185]~ [-7214, 11969, 18952]~ [135688819, 52627092, 452330447
]~ [1633778037, 574919842, 6646910401]~]

[[4169, 4338, 229]~ [722, 8865, 13444]~ [-106537503, 134281548, 137000286]~ 
[1060748979, 4131422295, 3026338070]~]


[0 1 0 0]

[0 0 1 0]

[0 0 0 1]

[[6017899359, 5241880500, 2055449334; 0, 87, 12; 0, 0, 3], [1, 0, 0; 0, 1, 0
; 0, 0, 1], [1, 0, 0; 0, 1, 0; 0, 0, 1]]

[1 [-8073, 4800, -5591]~ [-315011, 112392, -182676]~]

[0                     1          [-87, -173, -155]~]

[0                     0                           1]


[[165073371/2005966453, -120336277/2005966453, -220005359/2005966453]~ [436,
 -266, 285]~ 0]

[[-36888191/2005966453, 61195737/2005966453, 56154718/2005966453]~ [-321, 17
8, -216]~ [-4, -4, -5]~]

[[-137636147/2005966453, 99618172/2005966453, 248701141/2005966453]~ [-20, 3
7, 3]~ [7, 1, -3]~]


[1 0 0]

[0 1 0]

[0 0 1]

[[1, -1/2; 0, 1], [1, 1]]
[Mod(-1/6*y + 2/3, y^2 - 40), -3]
[Mod(1/2*y - 4, y^2 - 40), 1]
[1, 2]
[Mod(-y + 3, y^3 - 21), 1]
[1, 1]: [2, 0]~
[1, 2]: Mod(2, x^2 + Mod(-y, y^3 - 21))
[1, 3]: 2
[1, 4]: 2
[1, 5]: 2
[1, 6]: 2
[1, 7]: 4
[1, 8]: 4
[2, 1]: [1/2, 0]~
[2, 2]: Mod(1/2, x^2 + Mod(-y, y^3 - 21))
[2, 3]: 1/2
[2, 4]: 1/2
[2, 5]: 1/2
[2, 6]: 1/2
[2, 7]: 1
[2, 8]: 1/4
[3, 1]: [Mod(y^2 + y, y^3 - 21), Mod(1, y^3 - 21)]~
[3, 2]: Mod(x + Mod(y, y^3 - 21), x^2 + Mod(-y, y^3 - 21))
[3, 3]: error("incorrect type in rnfeltabstorel [not in Q[X]] (t_POL).")
[3, 4]: Mod(x^2 + x, x^6 - 21)
[3, 5]: error("inconsistent variables in nf_to_scalar_or_basis, x != y.")
[3, 6]: error("incorrect type in rnfeltabstorel [not in Q[X]] (t_POL).")
[3, 7]: error("incorrect type in rnfeltabstorel [not in Q[X]] (t_POL).")
[3, 8]: error("incorrect type in rnfeltabstorel [not in Q[X]] (t_POL).")
[4, 1]: [1, 0]~
[4, 2]: Mod(1, x^2 + Mod(-y, y^3 - 21))
[4, 3]: Mod(1, x^2 + Mod(-y, y^3 - 21))
[4, 4]: Mod(1, x^6 - 21)
[4, 5]: 1
[4, 6]: 1
[4, 7]: 2
[4, 8]: 1
[5, 1]: [1/2, 0]~
[5, 2]: Mod(1/2, x^2 + Mod(-y, y^3 - 21))
[5, 3]: Mod(1/2, x^2 + Mod(-y, y^3 - 21))
[5, 4]: Mod(1/2, x^6 - 21)
[5, 5]: 1/2
[5, 6]: 1/2
[5, 7]: 1
[5, 8]: 1/4
[6, 1]: [Mod(y, y^3 - 21), 0]~
[6, 2]: Mod(Mod(y, y^3 - 21), x^2 + Mod(-y, y^3 - 21))
[6, 3]: Mod(Mod(y, y^3 - 21), x^2 + Mod(-y, y^3 - 21))
[6, 4]: Mod(x^2, x^6 - 21)
[6, 5]: Mod(x^2, x^6 - 21)
[6, 6]: Mod(y, y^3 - 21)
[6, 7]: Mod(2*y, y^3 - 21)
[6, 8]: Mod(y^2, y^3 - 21)
[7, 1]: error("inconsistent moduli in rnfalgtobasis: x^6 - 21 != y^3 - 21")
[7, 2]: error("inconsistent moduli in rnfbasistoalg: x^6 - 21 != y^3 - 21")
[7, 3]: 1
[7, 4]: Mod(1, x^6 - 21)
[7, 5]: Mod(1, x^6 - 21)
[7, 6]: 1
[7, 7]: 2
[7, 8]: 1
[8, 1]: error("inconsistent moduli in rnfalgtobasis: x^6 - 21 != y^3 - 21")
[8, 2]: error("inconsistent moduli in rnfbasistoalg: x^6 - 21 != y^3 - 21")
[8, 3]: 1/2
[8, 4]: Mod(1/2, x^6 - 21)
[8, 5]: Mod(1/2, x^6 - 21)
[8, 6]: 1/2
[8, 7]: 1
[8, 8]: 1/4
[9, 1]: error("inconsistent moduli in rnfalgtobasis: x^6 - 21 != y^3 - 21")
[9, 2]: error("inconsistent moduli in rnfbasistoalg: x^6 - 21 != y^3 - 21")
[9, 3]: Mod(x, x^2 + Mod(-y, y^3 - 21))
[9, 4]: Mod(x, x^6 - 21)
[9, 5]: Mod(x, x^6 - 21)
[9, 6]: error("domain error in rnfeltdown: element not in the base field")
[9, 7]: 0
[9, 8]: Mod(-y, y^3 - 21)
[10, 1]: [Mod(y^2 + 1/2*y, y^3 - 21), Mod(1, y^3 - 21)]~
[10, 2]: Mod(x + Mod(1/2*y, y^3 - 21), x^2 + Mod(-y, y^3 - 21))
[10, 3]: Mod(x + Mod(1/2*y, y^3 - 21), x^2 + Mod(-y, y^3 - 21))
[10, 4]: Mod(1/2*x^2 + x, x^6 - 21)
[10, 5]: error("inconsistent moduli in nf_to_scalar_or_basis: x^2 - y != y^3
 - 21")
[10, 6]: error("domain error in rnfeltdown: element not in the base field")
[10, 7]: Mod(y, y^3 - 21)
[10, 8]: Mod(1/4*y^2 - y, y^3 - 21)
[11, 1]: [Mod(y, y^3 - 21), 0]~
[11, 2]: Mod(Mod(y, y^3 - 21), x^2 + Mod(-y, y^3 - 21))
[11, 3]: Mod(Mod(y, y^3 - 21), x^2 + Mod(-y, y^3 - 21))
[11, 4]: Mod(x^2, x^6 - 21)
[11, 5]: Mod(x^2, x^6 - 21)
[11, 6]: Mod(y, y^3 - 21)
[11, 7]: Mod(2*y, y^3 - 21)
[11, 8]: Mod(y^2, y^3 - 21)
[12, 1]: error("incorrect priority in rnfalgtobasis: variable z >= y")
[12, 2]: error("inconsistent variables in rnfbasistoalg, z != x.")
[12, 3]: error("inconsistent variables in rnfeltabstorel, z != x.")
[12, 4]: error("inconsistent variables in eltreltoabs, z != y.")
[12, 5]: error("inconsistent variables in nf_to_scalar_or_basis, z != y.")
[12, 6]: error("inconsistent variables in rnfeltabstorel, z != x.")
[12, 7]: error("inconsistent variables in rnfeltabstorel, z != x.")
[12, 8]: error("inconsistent variables in rnfeltabstorel, z != x.")
[13, 1]: error("inconsistent moduli in rnfalgtobasis: y^2 + 1 != y^3 - 21")
[13, 2]: error("inconsistent moduli in rnfbasistoalg: y^2 + 1 != y^3 - 21")
[13, 3]: error("inconsistent moduli in rnfeltabstorel: y^2 + 1 != x^6 - 21")
[13, 4]: error("inconsistent moduli in rnfeltreltoabs: y^2 + 1 != y^3 - 21")
[13, 5]: error("inconsistent moduli in nf_to_scalar_or_basis: y^2 + 1 != y^3
 - 21")
[13, 6]: error("inconsistent moduli in rnfeltdown: y^2 + 1 != y^3 - 21")
[13, 7]: error("inconsistent moduli in rnfeltabstorel: y^2 + 1 != x^6 - 21")
[13, 8]: error("inconsistent moduli in rnfeltabstorel: y^2 + 1 != x^6 - 21")
[14, 1]: error("inconsistent dimensions in rnfalgtobasis.")
[14, 2]: error("inconsistent operation 'RgV_RgC_mul' t_VEC (2 elts) , t_COL 
(1 elts).")
[14, 3]: error("incorrect type in rnfeltabstorel, apply nfinit(rnf) (t_COL).
")
[14, 4]: error("incorrect type in rnfeltreltoabs (t_COL).")
[14, 5]: error("incorrect type in nf_to_scalar_or_basis (t_COL).")
[14, 6]: error("incorrect type in rnfeltdown (t_COL).")
[14, 7]: error("incorrect type in rnfeltabstorel, apply nfinit(rnf) (t_COL).
")
[14, 8]: error("incorrect type in rnfeltabstorel, apply nfinit(rnf) (t_COL).
")
[15, 1]: [1, 2]~
[15, 2]: Mod(2*x + Mod(-2*y^2 + 1, y^3 - 21), x^2 + Mod(-y, y^3 - 21))
[15, 3]: error("incorrect type in rnfeltabstorel, apply nfinit(rnf) (t_COL).
")
[15, 4]: error("incorrect type in rnfeltreltoabs (t_COL).")
[15, 5]: error("incorrect type in nf_to_scalar_or_basis (t_COL).")
[15, 6]: error("incorrect type in rnfeltdown (t_COL).")
[15, 7]: error("incorrect type in rnfeltabstorel, apply nfinit(rnf) (t_COL).
")
[15, 8]: error("incorrect type in rnfeltabstorel, apply nfinit(rnf) (t_COL).
")
[16, 1]: [1, Mod(y, y^3 - 21)]~
[16, 2]: Mod(Mod(y, y^3 - 21)*x - 20, x^2 + Mod(-y, y^3 - 21))
[16, 3]: error("incorrect type in rnfeltabstorel, apply nfinit(rnf) (t_COL).
")
[16, 4]: error("incorrect type in rnfeltreltoabs (t_COL).")
[16, 5]: error("incorrect type in nf_to_scalar_or_basis (t_COL).")
[16, 6]: error("incorrect type in rnfeltdown (t_COL).")
[16, 7]: error("incorrect type in rnfeltabstorel, apply nfinit(rnf) (t_COL).
")
[16, 8]: error("incorrect type in rnfeltabstorel, apply nfinit(rnf) (t_COL).
")
[17, 1]: error("incorrect type in rnfalgtobasis (t_COMPLEX).")
[17, 2]: error("incorrect type in nf_to_scalar_or_alg (t_COMPLEX).")
[17, 3]: error("incorrect type in rnfeltabstorel, apply nfinit(rnf) (t_COL).
")
[17, 4]: error("incorrect type in rnfeltreltoabs (t_COL).")
[17, 5]: error("incorrect type in nf_to_scalar_or_basis (t_COL).")
[17, 6]: error("incorrect type in rnfeltdown (t_COL).")
[17, 7]: error("incorrect type in rnfeltabstorel, apply nfinit(rnf) (t_COL).
")
[17, 8]: error("incorrect type in rnfeltabstorel, apply nfinit(rnf) (t_COL).
")
[18, 1]: error("incorrect type in rnfalgtobasis [not in Q[X]] (t_POL).")
[18, 2]: error("incorrect type in rnfbasistoalg [not in Q[X]] (t_POL).")
[18, 3]: error("incorrect type in rnfeltabstorel [not in Q[X]] (t_POL).")
[18, 4]: error("incorrect type in poltobasis (t_POL).")
[18, 5]: error("incorrect type in poltobasis (t_POL).")
[18, 6]: error("incorrect type in rnfeltdown [not in Q[X]] (t_POL).")
[18, 7]: error("incorrect type in rnfeltabstorel [not in Q[X]] (t_POL).")
[18, 8]: error("incorrect type in rnfeltabstorel [not in Q[X]] (t_POL).")
[19, 1]: [y, 0]~
[19, 2]: Mod(Mod(y, y^3 - 21), x^2 + Mod(-y, y^3 - 21))
[19, 3]: Mod(Mod(y, y^3 - 21), x^2 + Mod(-y, y^3 - 21))
[19, 4]: Mod(x^2, x^6 - 21)
[19, 5]: error("inconsistent variables in nf_to_scalar_or_basis, x != y.")
[19, 6]: Mod(y, y^3 - 21)
[19, 7]: Mod(2*y, y^3 - 21)
[19, 8]: Mod(y^2, y^3 - 21)
1: x^2 - 4*x + 4
2: x^2 - x + 1/4
3: x^2 + Mod(-2*y, y^3 - 21)*x + Mod(y^2 - y, y^3 - 21)
4: x^2 - 2*x + 1
5: x^2 - x + 1/4
6: Mod(1, y^3 - 21)*x^2 + Mod(-2*y, y^3 - 21)*x + Mod(y^2, y^3 - 21)
7: error("inconsistent moduli in rnfcharpoly: x^6 - 21 != y^3 - 21")
8: error("inconsistent moduli in rnfcharpoly: x^6 - 21 != y^3 - 21")
9: error("inconsistent moduli in rnfcharpoly: x^6 - 21 != y^3 - 21")
10: x^2 + Mod(-y, y^3 - 21)*x + Mod(1/4*y^2 - y, y^3 - 21)
11: Mod(1, y^3 - 21)*x^2 + Mod(-2*y, y^3 - 21)*x + Mod(y^2, y^3 - 21)
12: error("incorrect priority in rnfcharpoly: variable z >= y")
13: error("inconsistent moduli in rnfcharpoly: y^2 + 1 != y^3 - 21")
14: error("incorrect type in rnfcharpoly (t_COL).")
15: error("incorrect type in rnfcharpoly (t_COL).")
16: error("incorrect type in rnfcharpoly (t_COL).")
17: error("incorrect type in rnfcharpoly (t_COL).")
18: error("incorrect type in rnfcharpoly [not in Q[X]] (t_POL).")
19: x^2 + Mod(-2*y, y^3 - 21)*x + Mod(y^2, y^3 - 21)
[1, 1]: [2, 0]~
[1, 2]: Mod(2, x^2 + 1)
[1, 3]: 2
[1, 4]: 2
[1, 5]: 2
[1, 6]: 2
[1, 7]: 4
[1, 8]: 4
[2, 1]: [1/2, 0]~
[2, 2]: Mod(1/2, x^2 + 1)
[2, 3]: 1/2
[2, 4]: 1/2
[2, 5]: 1/2
[2, 6]: 1/2
[2, 7]: 1
[2, 8]: 1/4
[3, 1]: [-1, 1]~
[3, 2]: Mod(x - 1, x^2 + 1)
[3, 3]: error("incorrect type in rnfeltabstorel [not in Q[X]] (t_POL).")
[3, 4]: Mod(x - 1, x^2 + 1)
[3, 5]: error("inconsistent variables in nf_to_scalar_or_basis, x != y.")
[3, 6]: error("incorrect type in rnfeltabstorel [not in Q[X]] (t_POL).")
[3, 7]: error("incorrect type in rnfeltabstorel [not in Q[X]] (t_POL).")
[3, 8]: error("incorrect type in rnfeltabstorel [not in Q[X]] (t_POL).")
[4, 1]: [1/2, 0]~
[4, 2]: Mod(1/2, x^2 + 1)
[4, 3]: Mod(1/2, x^2 + 1)
[4, 4]: Mod(1/2, x^2 + 1)
[4, 5]: 1/2
[4, 6]: 1/2
[4, 7]: 1
[4, 8]: 1/4
[5, 1]: [Mod(-1, y + 1), 0]~
[5, 2]: Mod(Mod(-1, y + 1), x^2 + 1)
[5, 3]: Mod(-1, x^2 + 1)
[5, 4]: -1
[5, 5]: -1
[5, 6]: -1
[5, 7]: -2
[5, 8]: 1
[6, 1]: [1, 1/2]~
[6, 2]: Mod(1/2*x + 1, x^2 + 1)
[6, 3]: Mod(1/2*x + 1, x^2 + 1)
[6, 4]: Mod(1/2*x + 1, x^2 + 1)
[6, 5]: Mod(1/2*x + 1, x^2 + 1)
[6, 6]: error("domain error in rnfeltdown: element not in the base field")
[6, 7]: 2
[6, 8]: 5/4
[7, 1]: [0, 1]~
[7, 2]: Mod(x, x^2 + 1)
[7, 3]: Mod(x, x^2 + 1)
[7, 4]: Mod(x, x^2 + 1)
[7, 5]: Mod(x, x^2 + 1)
[7, 6]: error("domain error in rnfeltdown: element not in the base field")
[7, 7]: 0
[7, 8]: 1
[8, 1]: [0, 1]~
[8, 2]: Mod(x, x^2 + 1)
[8, 3]: Mod(x, x^2 + 1)
[8, 4]: Mod(x, x^2 + 1)
[8, 5]: Mod(x, x^2 + 1)
[8, 6]: error("domain error in rnfeltdown: element not in the base field")
[8, 7]: 0
[8, 8]: 1
[9, 1]: error("inconsistent moduli in rnfalgtobasis: x^2 - y != y + 1")
[9, 2]: error("inconsistent moduli in rnfbasistoalg: x^2 - y != y + 1")
[9, 3]: error("inconsistent moduli in rnfeltabstorel: x^2 - y != x^2 + 1")
[9, 4]: error("inconsistent moduli in rnfeltreltoabs: x^2 - y != y + 1")
[9, 5]: error("inconsistent moduli in nf_to_scalar_or_basis: x^2 - y != y + 
1")
[9, 6]: error("inconsistent moduli in rnfeltdown: x^2 - y != y + 1")
[9, 7]: error("inconsistent moduli in rnfeltabstorel: x^2 - y != x^2 + 1")
[9, 8]: error("inconsistent moduli in rnfeltabstorel: x^2 - y != x^2 + 1")
[10, 1]: [0, 1]~
[10, 2]: Mod(x, x^2 + 1)
[10, 3]: Mod(x, x^2 + 1)
[10, 4]: Mod(x, x^2 + 1)
[10, 5]: error("inconsistent variables in nf_to_scalar_or_basis, x != y.")
[10, 6]: error("domain error in rnfeltdown: element not in the base field")
[10, 7]: 0
[10, 8]: 1
[11, 1]: error("inconsistent dimensions in rnfalgtobasis.")
[11, 2]: error("inconsistent operation 'RgV_RgC_mul' t_VEC (2 elts) , t_COL 
(1 elts).")
[11, 3]: error("incorrect type in rnfeltabstorel, apply nfinit(rnf) (t_COL).
")
[11, 4]: error("incorrect type in rnfeltreltoabs (t_COL).")
[11, 5]: 1
[11, 6]: 1
[11, 7]: error("incorrect type in rnfeltabstorel, apply nfinit(rnf) (t_COL).
")
[11, 8]: error("incorrect type in rnfeltabstorel, apply nfinit(rnf) (t_COL).
")
[12, 1]: [1, 2]~
[12, 2]: Mod(2*x + 1, x^2 + 1)
[12, 3]: error("incorrect type in rnfeltabstorel, apply nfinit(rnf) (t_COL).
")
[12, 4]: error("incorrect type in rnfeltreltoabs (t_COL).")
[12, 5]: error("incorrect type in nf_to_scalar_or_basis (t_COL).")
[12, 6]: error("incorrect type in rnfeltdown (t_COL).")
[12, 7]: error("incorrect type in rnfeltabstorel, apply nfinit(rnf) (t_COL).
")
[12, 8]: error("incorrect type in rnfeltabstorel, apply nfinit(rnf) (t_COL).
")
[13, 1]: error("inconsistent dimensions in rnfalgtobasis.")
[13, 2]: error("inconsistent operation 'RgV_RgC_mul' t_VEC (2 elts) , t_COL 
(1 elts).")
[13, 3]: error("incorrect type in rnfeltabstorel, apply nfinit(rnf) (t_COL).
")
[13, 4]: error("incorrect type in rnfeltreltoabs (t_COL).")
[13, 5]: Mod(y, x^2 + 1)
[13, 6]: error("incorrect type in rnfeltdown (t_COL).")
[13, 7]: error("incorrect type in rnfeltabstorel, apply nfinit(rnf) (t_COL).
")
[13, 8]: error("incorrect type in rnfeltabstorel, apply nfinit(rnf) (t_COL).
")
1: x^2 - 4*x + 4
2: x^2 - x + 1/4
3: x^2 + 2*x + 2
4: x^2 - x + 1/4
5: x^2 + 2*x + 1
6: x^2 - 2*x + 5/4
7: x^2 + 1
8: x^2 + 1
9: error("inconsistent moduli in rnfcharpoly: x^2 - y != y + 1")
10: x^2 + 1
11: error("incorrect type in rnfcharpoly (t_COL).")
12: error("incorrect type in rnfcharpoly (t_COL).")
13: error("incorrect type in rnfcharpoly (t_COL).")
Mod(1, x^2 - 2)
0
[[1, -66328; 0, 1], [[280970, 12259, 35869; 0, 1, 0; 0, 0, 1], [1, 1/2, 1/2;
 0, 1/2, 0; 0, 0, 1/2]]]
1
[280970, x^2 + 12259, x^4 + 35869, -x^4 + x - 66328, -1/2*x^4 + 1/2*x^3 - 33
164*x^2 + 1/2*x - 66349/2, 1/2*x^5 - 66329/2*x^4 - 21/2*x^2 + 1/2*x - 33164]
1
[[3, [0, 1, 0, 0, 0, 0]~, 6, 1]]
[[[7, [0, 1, 0]~, 3, 1]], [[7, [0, 1, 0, 0, 0, 0]~, 6, 1]]]
[[89, [-21, 1, 0]~, 1, 1, [17, 1, 22; 21, -4, 1; 1, 21, 17]]]

[[7, [0, 1, 0, 0, 0, 0]~, 6, 1] 6]


[[3, [0, 1, 0, 0, 0, 0]~, 6, 1] 1]

[[7, [0, 1, 0, 0, 0, 0]~, 6, 1] 1]


[[3, [0, 1, 0, 0, 0, 0]~, 6, 1] 2]

[[7, [0, 1, 0, 0, 0, 0]~, 6, 1] 2]

1
[18416, x^2 + 6979, x^4 + 3879, -9208*x^4 + 9208*x, -6979/2*x^4 + 1/2*x^3 + 
6979/2*x - 21/2, 1/2*x^5 - 3879/2*x^4 - 21/2*x^2 + 3879/2*x]
1
1
1

[280970 12259 35869]

[     0     1     0]

[     0     0     1]

[280970, x^2 + 12259, x^4 + 35869, -140485*x^4 + 140485*x, -12259/2*x^4 + 1/
2*x^3 + 12259/2*x - 21/2, 1/2*x^5 - 35869/2*x^4 - 21/2*x^2 + 35869/2*x]
1
1:
[[1, 0; 0, 1], [2, 1]]
[2, 2*x^2, 2*x^4, -x^4 + x, x^3 - 21, x^5 - 21*x^2]
error("incorrect type in rnfidealabstorel (t_INT).")
2
[2, 2*x^2, 2*x^4, -x^4 + x, x^3 - 21, x^5 - 21*x^2]
[4, 0, 0; 0, 4, 0; 0, 0, 4]
64
[2, 0]
2:
[[1, 0; 0, 1], [1/2, 1/4]]
[1/2, 1/2*x^2, 1/2*x^4, -1/4*x^4 + 1/4*x, 1/4*x^3 - 21/4, 1/4*x^5 - 21/4*x^2
]
error("incorrect type in rnfidealabstorel (t_FRAC).")
1/2
[1/2, 1/2*x^2, 1/2*x^4, -1/4*x^4 + 1/4*x, 1/4*x^3 - 21/4, 1/4*x^5 - 21/4*x^2
]
[1/4, 0, 0; 0, 1/4, 0; 0, 0, 1/4]
1/64
[1/2, 0]
3:
[[1, 42; 0, 1], [[210, 189, 189; 0, 1, 0; 0, 0, 1], [1, 1/2, 1/2; 0, 1/2, 0;
 0, 0, 1/2]]]
[210, x^2 + 189, x^4 + 189, -x^4 + x + 42, -1/2*x^4 + 1/2*x^3 + 21*x^2 + 1/2
*x + 21/2, 1/2*x^5 + 41/2*x^4 - 21/2*x^2 + 1/2*x + 21]
error("incorrect type in rnfidealabstorel (t_POL).")
[210, 189, 189; 0, 1, 0; 0, 0, 1]
error("inconsistent variables in nf_to_scalar_or_basis, x != y.")
[420, 399, 399; 0, 1, 0; 0, 0, 1]
420
[210, Mod(x + Mod(105*y - 84, y^3 - 21), x^2 + Mod(-y, y^3 - 21))]
4:
[[1, 0; 0, 1], [1, 1/2]]
[1, x^2, x^4, -1/2*x^4 + 1/2*x, 1/2*x^3 - 21/2, 1/2*x^5 - 21/2*x^2]
error("incorrect type in rnfidealabstorel (t_POLMOD).")
1
[1, x^2, x^4, -1/2*x^4 + 1/2*x, 1/2*x^3 - 21/2, 1/2*x^5 - 21/2*x^2]
[1, 0, 0; 0, 1, 0; 0, 0, 1]
1
[1, 0]
5:
[[1, 0; 0, 1], [1/2, 1/4]]
[1/2, 1/2*x^2, 1/2*x^4, -1/4*x^4 + 1/4*x, 1/4*x^3 - 21/4, 1/4*x^5 - 21/4*x^2
]
error("incorrect type in rnfidealabstorel (t_POLMOD).")
1/2
[1/2, 1/2*x^2, 1/2*x^4, -1/4*x^4 + 1/4*x, 1/4*x^3 - 21/4, 1/4*x^5 - 21/4*x^2
]
[1/4, 0, 0; 0, 1/4, 0; 0, 0, 1/4]
1/64
[1/2, 0]
6:
[[1, 0; 0, 1], [[21, 0, 0; 0, 1, 0; 0, 0, 1], [21/2, 0, 0; 0, 1/2, 0; 0, 0, 
1/2]]]
[21, x^2, x^4, -21/2*x^4 + 21/2*x, 1/2*x^3 - 21/2, 1/2*x^5 - 21/2*x^2]
error("incorrect type in rnfidealabstorel (t_POLMOD).")
[21, 0, 0; 0, 1, 0; 0, 0, 1]
[21, x^2, x^4, -21/2*x^4 + 21/2*x, 1/2*x^3 - 21/2, 1/2*x^5 - 21/2*x^2]
[21, 0, 0; 0, 21, 0; 0, 0, 1]
441
[21, Mod(Mod(y, y^3 - 21), x^2 + Mod(-y, y^3 - 21))]
7:
error("inconsistent moduli in rnfbasistoalg: x^6 - 21 != y^3 - 21")
error("inconsistent moduli in rnfbasistoalg: x^6 - 21 != y^3 - 21")
error("incorrect type in rnfidealabstorel (t_POLMOD).")
error("inconsistent moduli in rnfbasistoalg: x^6 - 21 != y^3 - 21")
error("inconsistent moduli in nf_to_scalar_or_basis: x^6 - 21 != y^3 - 21")
error("inconsistent moduli in rnfbasistoalg: x^6 - 21 != y^3 - 21")
error("inconsistent moduli in rnfbasistoalg: x^6 - 21 != y^3 - 21")
error("inconsistent moduli in rnfbasistoalg: x^6 - 21 != y^3 - 21")
8:
error("inconsistent moduli in rnfbasistoalg: x^6 - 21 != y^3 - 21")
error("inconsistent moduli in rnfbasistoalg: x^6 - 21 != y^3 - 21")
error("incorrect type in rnfidealabstorel (t_POLMOD).")
error("inconsistent moduli in rnfbasistoalg: x^6 - 21 != y^3 - 21")
error("inconsistent moduli in nf_to_scalar_or_basis: x^6 - 21 != y^3 - 21")
error("inconsistent moduli in rnfbasistoalg: x^6 - 21 != y^3 - 21")
error("inconsistent moduli in rnfbasistoalg: x^6 - 21 != y^3 - 21")
error("inconsistent moduli in rnfbasistoalg: x^6 - 21 != y^3 - 21")
9:
error("inconsistent moduli in rnfbasistoalg: x^6 - 21 != y^3 - 21")
error("inconsistent moduli in rnfbasistoalg: x^6 - 21 != y^3 - 21")
error("incorrect type in rnfidealabstorel (t_POLMOD).")
error("inconsistent moduli in rnfbasistoalg: x^6 - 21 != y^3 - 21")
error("inconsistent moduli in nf_to_scalar_or_basis: x^6 - 21 != y^3 - 21")
error("inconsistent moduli in rnfbasistoalg: x^6 - 21 != y^3 - 21")
error("inconsistent moduli in rnfbasistoalg: x^6 - 21 != y^3 - 21")
error("inconsistent moduli in rnfbasistoalg: x^6 - 21 != y^3 - 21")
10:
[[1, -756; 0, 1], [[903/2, 84, 336; 0, 1/2, 0; 0, 0, 1/2], 1/4]]
[903/2, 1/2*x^2 + 84, 1/2*x^4 + 336, -1/4*x^4 + 1/4*x - 189, 1/4*x^3 - 189*x
^2 - 21/4, 1/4*x^5 - 189*x^4 - 21/4*x^2]
error("incorrect type in rnfidealabstorel (t_POLMOD).")
[903/2, 84, 336; 0, 1/2, 0; 0, 0, 1/2]
error("inconsistent moduli in nf_to_scalar_or_basis: x^2 - y != y^3 - 21")
[903/4, 42, 168; 0, 1/4, 0; 0, 0, 1/4]
903/64
[903/2, Mod(1/2*x - 42, x^2 + Mod(-y, y^3 - 21))]
11:
[[1, 0; 0, 1], [[21, 0, 0; 0, 1, 0; 0, 0, 1], [21/2, 0, 0; 0, 1/2, 0; 0, 0, 
1/2]]]
[21, x^2, x^4, -21/2*x^4 + 21/2*x, 1/2*x^3 - 21/2, 1/2*x^5 - 21/2*x^2]
error("incorrect type in rnfidealabstorel (t_POL).")
[21, 0, 0; 0, 1, 0; 0, 0, 1]
[21, x^2, x^4, -21/2*x^4 + 21/2*x, 1/2*x^3 - 21/2, 1/2*x^5 - 21/2*x^2]
[21, 0, 0; 0, 21, 0; 0, 0, 1]
441
[21, Mod(Mod(y, y^3 - 21), x^2 + Mod(-y, y^3 - 21))]
12:
error("inconsistent variables in rnfbasistoalg, z != x.")
error("inconsistent variables in rnfbasistoalg, z != x.")
error("incorrect type in rnfidealabstorel (t_POL).")
error("inconsistent variables in rnfbasistoalg, z != x.")
error("inconsistent variables in nf_to_scalar_or_basis, z != y.")
error("inconsistent variables in rnfbasistoalg, z != x.")
error("inconsistent variables in rnfbasistoalg, z != x.")
error("inconsistent variables in rnfbasistoalg, z != x.")
13:
error("inconsistent moduli in rnfbasistoalg: y^2 + 1 != y^3 - 21")
error("inconsistent moduli in rnfbasistoalg: y^2 + 1 != y^3 - 21")
error("incorrect type in rnfidealabstorel (t_POLMOD).")
error("inconsistent moduli in rnfbasistoalg: y^2 + 1 != y^3 - 21")
error("inconsistent moduli in nf_to_scalar_or_basis: y^2 + 1 != y^3 - 21")
error("inconsistent moduli in rnfbasistoalg: y^2 + 1 != y^3 - 21")
error("inconsistent moduli in rnfbasistoalg: y^2 + 1 != y^3 - 21")
error("inconsistent moduli in rnfbasistoalg: y^2 + 1 != y^3 - 21")
14:
error("inconsistent operation 'RgV_RgC_mul' t_VEC (2 elts) , t_COL (1 elts).
")
error("inconsistent operation 'RgV_RgC_mul' t_VEC (2 elts) , t_COL (1 elts).
")
error("incorrect type in rnfidealabstorel (t_COL).")
error("inconsistent operation 'RgV_RgC_mul' t_VEC (2 elts) , t_COL (1 elts).
")
error("incorrect type in nf_to_scalar_or_basis (t_COL).")
error("inconsistent operation 'RgV_RgC_mul' t_VEC (2 elts) , t_COL (1 elts).
")
error("inconsistent operation 'RgV_RgC_mul' t_VEC (2 elts) , t_COL (1 elts).
")
error("inconsistent operation 'RgV_RgC_mul' t_VEC (2 elts) , t_COL (1 elts).
")
15:
[[1, -5371968; 0, 1], [[10743937, 8099895, 3524829; 0, 1, 0; 0, 0, 1], 1/2]]
[10743937, x^2 + 8099895, x^4 + 3524829, -1/2*x^4 + 1/2*x - 2685984, 1/2*x^3
 - 2685984*x^2 - 21/2, 1/2*x^5 - 2685984*x^4 - 21/2*x^2]
error("incorrect type in rnfidealabstorel (t_COL).")
[10743937, 8099895, 3524829; 0, 1, 0; 0, 0, 1]
error("incorrect type in nf_to_scalar_or_basis (t_COL).")
[10743937, 8099895, 3524829; 0, 1, 0; 0, 0, 1]
10743937
[10743937, Mod(x - 1847139, x^2 + Mod(-y, y^3 - 21))]
16:
[[1, [0, 0, -18]~; 0, 1], [379, 1/2]]
[379, 379*x^2, 379*x^4, -19/2*x^4 + 1/2*x, 1/2*x^3 - 399/2, 1/2*x^5 - 399/2*
x^2]
error("incorrect type in rnfidealabstorel (t_COL).")
379
error("incorrect type in nf_to_scalar_or_basis (t_COL).")
[379, 0, 0; 0, 379, 0; 0, 0, 379]
54439939
[379, Mod(Mod(1/2*y, y^3 - 21)*x + 359/2, x^2 + Mod(-y, y^3 - 21))]
17:
error("incorrect type in nf_to_scalar_or_alg (t_COMPLEX).")
error("incorrect type in nf_to_scalar_or_alg (t_COMPLEX).")
error("incorrect type in rnfidealabstorel (t_COL).")
error("incorrect type in nf_to_scalar_or_alg (t_COMPLEX).")
error("incorrect type in nf_to_scalar_or_basis (t_COL).")
error("incorrect type in nf_to_scalar_or_alg (t_COMPLEX).")
error("incorrect type in nf_to_scalar_or_alg (t_COMPLEX).")
error("incorrect type in nf_to_scalar_or_alg (t_COMPLEX).")
18:
error("incorrect type in rnfbasistoalg [not in Q[X]] (t_POL).")
error("incorrect type in rnfbasistoalg [not in Q[X]] (t_POL).")
error("incorrect type in rnfidealabstorel (t_POL).")
error("incorrect type in rnfbasistoalg [not in Q[X]] (t_POL).")
error("incorrect type in poltobasis (t_POL).")
error("incorrect type in rnfbasistoalg [not in Q[X]] (t_POL).")
error("incorrect type in rnfbasistoalg [not in Q[X]] (t_POL).")
error("incorrect type in rnfbasistoalg [not in Q[X]] (t_POL).")
19:
[[1, 0; 0, 1], [[21, 0, 0; 0, 1, 0; 0, 0, 1], [21/2, 0, 0; 0, 1/2, 0; 0, 0, 
1/2]]]
[21, x^2, x^4, -21/2*x^4 + 21/2*x, 1/2*x^3 - 21/2, 1/2*x^5 - 21/2*x^2]
error("incorrect type in rnfidealabstorel (t_POL).")
[21, 0, 0; 0, 1, 0; 0, 0, 1]
error("inconsistent variables in nf_to_scalar_or_basis, x != y.")
[21, 0, 0; 0, 21, 0; 0, 0, 1]
441
[21, Mod(Mod(y, y^3 - 21), x^2 + Mod(-y, y^3 - 21))]
20:
[[;], []]
[]
[[;], []]
[;]
[]
[;]
0
[0, 0]
21:
[[;], []]
[]
[[;], []]
[;]
error("incorrect type in idealtyp (t_VEC).")
[;]
0
[0, 0]
22:
[[;], []]
[]
error("incorrect type in rnfidealabstorel (t_INT).")
[;]
[]
[;]
0
[0, 0]
23:
[[;], []]
[]
error("inconsistent dimensions in rnfidealabstorel.")
[;]
[]
[;]
0
[0, 0]
24:
error("inconsistent dimensions in rnfidealabstorel.")
error("inconsistent dimensions in rnfidealabstorel.")
error("inconsistent dimensions in rnfidealabstorel.")
error("inconsistent dimensions in rnfidealabstorel.")
[2, x^2 + 1, x^4 + 1, -x^4 + x, -1/2*x^4 + 1/2*x^3 + 1/2*x - 21/2, 1/2*x^5 -
 1/2*x^4 - 21/2*x^2 + 1/2*x]
error("inconsistent dimensions in rnfidealabstorel.")
error("inconsistent dimensions in rnfidealabstorel.")
error("inconsistent dimensions in rnfidealabstorel.")
25:
error("inconsistent dimensions in rnfidealabstorel.")
error("inconsistent dimensions in rnfidealabstorel.")
error("inconsistent dimensions in rnfidealabstorel.")
error("incorrect type in idealhnf [wrong dimension] (t_MAT).")
[18416, x^2 + 6979, x^4 + 3879, -9208*x^4 + 9208*x, -6979/2*x^4 + 1/2*x^3 + 
6979/2*x - 21/2, 1/2*x^5 - 3879/2*x^4 - 21/2*x^2 + 3879/2*x]
error("inconsistent dimensions in rnfidealabstorel.")
error("inconsistent dimensions in rnfidealabstorel.")
error("inconsistent dimensions in rnfidealabstorel.")
26:
[[1, -66328; 0, 1], [[280970, 12259, 35869; 0, 1, 0; 0, 0, 1], [1, 1/2, 1/2;
 0, 1/2, 0; 0, 0, 1/2]]]
[280970, x^2 + 12259, x^4 + 35869, -x^4 + x - 66328, -1/2*x^4 + 1/2*x^3 - 33
164*x^2 + 1/2*x - 66349/2, 1/2*x^5 - 66329/2*x^4 - 21/2*x^2 + 1/2*x - 33164]
[[1, -66328; 0, 1], [[280970, 12259, 35869; 0, 1, 0; 0, 0, 1], [1, 1/2, 1/2;
 0, 1/2, 0; 0, 0, 1/2]]]
[280970, 12259, 35869; 0, 1, 0; 0, 0, 1]
error("inconsistent dimensions in idealtwoelt.")
[561940, 12259, 316839; 0, 1, 0; 0, 0, 1]
561940
[280970, Mod(x + Mod(-140485*y + 110026, y^3 - 21), x^2 + Mod(-y, y^3 - 21))
]
27:
[[1, -66328; 0, 1], [[280970, 12259, 35869; 0, 1, 0; 0, 0, 1], [1, 1/2, 1/2;
 0, 1/2, 0; 0, 0, 1/2]]]
[280970, x^2 + 12259, x^4 + 35869, -x^4 + x - 66328, -1/2*x^4 + 1/2*x^3 - 33
164*x^2 + 1/2*x - 66349/2, 1/2*x^5 - 66329/2*x^4 - 21/2*x^2 + 1/2*x - 33164]
[[1, -66328; 0, 1], [[280970, 12259, 35869; 0, 1, 0; 0, 0, 1], [1, 1/2, 1/2;
 0, 1/2, 0; 0, 0, 1/2]]]
[280970, 12259, 35869; 0, 1, 0; 0, 0, 1]
error("incorrect type in idealtyp (t_VEC).")
[561940, 12259, 316839; 0, 1, 0; 0, 0, 1]
561940
[280970, Mod(x + Mod(-140485*y + 110026, y^3 - 21), x^2 + Mod(-y, y^3 - 21))
]
28:
[[1, -66328; 0, 1], [[280970, 12259, 35869; 0, 1, 0; 0, 0, 1], [1, 1/2, 1/2;
 0, 1/2, 0; 0, 0, 1/2]]]
[280970, x^2 + 12259, x^4 + 35869, -x^4 + x - 66328, -1/2*x^4 + 1/2*x^3 - 33
164*x^2 + 1/2*x - 66349/2, 1/2*x^5 - 66329/2*x^4 - 21/2*x^2 + 1/2*x - 33164]
error("inconsistent dimensions in rnfidealabstorel.")
[280970, 12259, 35869; 0, 1, 0; 0, 0, 1]
error("inconsistent dimensions in idealtwoelt.")
[561940, 12259, 316839; 0, 1, 0; 0, 0, 1]
561940
[280970, Mod(x + Mod(-140485*y + 110026, y^3 - 21), x^2 + Mod(-y, y^3 - 21))
]
[[;], []]
[[;], []]
[[1, 0; 0, 1], [[21, 0, 0; 0, 21, 0; 0, 0, 1], [21/2, 0, 0; 0, 1/2, 0; 0, 0,
 1/2]]]
[[1, 0; 0, 1], [[21, 0, 0; 0, 21, 0; 0, 0, 1], [21/2, 0, 0; 0, 1/2, 0; 0, 0,
 1/2]]]
[[1, -347298; 0, 1], [[5900370, 2821959, 5374299; 0, 1, 0; 0, 0, 1], [1, 1/2
, 1/2; 0, 1/2, 0; 0, 0, 1/2]]]
[[1, -347298; 0, 1], [[5900370, 2821959, 5374299; 0, 1, 0; 0, 0, 1], [1, 1/2
, 1/2; 0, 1/2, 0; 0, 0, 1/2]]]

[1 0 0]

[0 1 0]

[0 0 1]


[280970 12259/2 316839/2]

[     0     1/2        0]

[     0       0      1/2]


[1 -1 [-1/2, -1/2]~]

[0  1   [1/2, 1/2]~]

1
[1/2, -1/12*x^3 - 1/12*x, -1/12*x^3 + 5/12*x, -1/24*x^3 - 1/8*x^2 + 5/24*x +
 1/8]
0
[[[205009, 37462, 90172; 0, 1, 0; 0, 0, 1], [0, 0, 0]], Mat(3)]
[[[1163, 141, 1055; 0, 1, 0; 0, 0, 1], [1, 0, 0]], Mat(2)]
[[1, 0, 0, 0; 0, 1, 0, 0; 0, 0, 1, 0; 0, 0, 0, 1], []]
0
1
1
1
[0, [[1, 0, -1; 0, 1, [0, -1]~; 0, 0, 1], [1, 1, 1/3]], 5]
[0, [[1, 0, 0; 0, 1, 0; 0, 0, 1], [1, 1, [1, 1/2; 0, 1/2]]], 2]
[1, [[1, 0, 0; 0, 1, 0; 0, 0, 1], [1, 1, 1]], 8]
0
1
0
0
1
[[433, 322, 318, 1318/17; 0, 1, 0, 12/17; 0, 0, 1, 5/17; 0, 0, 0, 1/17], [25
/17, -12/17, 12/17, 16/17]~]
[1, -1]
[[12, 0, 0, 0; 0, 12, 8, 0; 0, 0, 4, 0; 0, 0, 0, 4], [6, 1, 5, 2]~]
  ***   Warning: new stack size = 16000000 (15.259 Mbytes).
[1, [-1, 0, -5, 0, 4, 0, 2, 0, -2, 0, -3, 0, 3, 0, 1, 0, -2, 0, -2, 0, 4, 0,
 3, 0, -7, 0, 4, 0, -1, 0, 5, 0, -8, 2, 5, 1, -4, -1, 5, 0, -4, -1, 5, -2, -
3, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]~]
  ***   at top-level: rnfdedekind(nf,P,pr2,1)
  ***                 ^-----------------------
  *** rnfdedekind: sorry, Dedekind in the difficult case is not yet implemented.
  ***   at top-level: rnfdedekind(nf,P)
  ***                 ^-----------------
  *** rnfdedekind: sorry, Dedekind in the difficult case is not yet implemented.
  ***   at top-level: rnfdedekind(nf,P,[pr2,pr3])
  ***                 ^---------------------------
  *** rnfdedekind: sorry, Dedekind in the difficult case is not yet implemented.
  ***   at top-level: rnfpseudobasis(nf,x^2/2+1)
  ***                 ^--------------------------
  *** rnfpseudobasis: sorry, nonmonic relative polynomials in rnfallbase is not yet implemented.
  ***   at top-level: rnfpseudobasis(nf,x^2+1/2)
  ***                 ^--------------------------
  *** rnfpseudobasis: impossible inverse in Fl_inv: Mod(0, 2).
  ***   at top-level: rnfislocalcyclo(rnfinit(K,x^6-y+1))
  ***                 ^-----------------------------------
  *** rnfislocalcyclo: sorry, rnfislocalcyclo for non-l-extensions is not yet implemented.
  ***   at top-level: rnfidealtwoelt(L,[[1;0],[1/104]])
  ***                 ^---------------------------------
  *** rnfidealtwoelt: incorrect type in idealtyp [nonsquare t_MAT] (t_MAT).
  ***   at top-level: bnfinit(rnf)
  ***                 ^------------
  *** bnfinit: incorrect type in checknf [please apply nfinit()] (t_VEC).
Total time spent: 2116
