[[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, [55466/1129, 839/1129]~, [111031/1129, 1480/1129]~, [179046
2/21451, 22844/21451]~, [3584116/21451, 39304/21451]~; 0, 1, 0, 0, 0, [-6071
0/1129, -512/1129]~, [-121528/1129, -808/1129]~, [4210657/21451, -12522/2145
1]~, [8428762/21451, -39940/21451]~; 0, 0, 1, 0, 0, [184604/1129, 1104/1129]
~, [369536/1129, 1552/1129]~, [-2435574/21451, 1771/21451]~, [-4875461/21451
, 12168/21451]~; 0, 0, 0, 1, 0, [96298/1129, 463/1129]~, [192767/1129, 584/1
129]~, [1767005/21451, 5405/21451]~, [3537145/21451, 4540/21451]~; 0, 0, 0, 
0, 1, [-216304/1129, -928/1129]~, [-432992/1129, -1088/1129]~, [-4319640/214
51, -5473/21451]~, [-8646937/21451, 4368/21451]~; 0, 0, 0, 0, 0, [-564/1129,
 -1/1129]~, -1, [9/21451, -18/21451]~, [18/21451, -36/21451]~; 0, 0, 0, 0, 0
, [1/1129, -2/1129]~, [2/1129, -4/1129]~, [7/21451, -14/21451]~, [14/21451, 
-28/21451]~; 0, 0, 0, 0, 0, 0, 0, [-10723/21451, -5/21451]~, [-21465/21451, 
28/21451]~; 0, 0, 0, 0, 0, 0, 0, [1/21451, -2/21451]~, [2/21451, -4/21451]~]
, [1, 1, 1, 1, 1, 1, 1, 1, [1, 0; 0, 1]], [1, 0; 0, 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, 0; 0,
 6487513772307278389925284499624661], 6487513772307278389925284499624661]
[[Mat(861), [1]], [480, [120, 2, 2], [334, 286, [-860]~]], [1, 0, 0; 0, 2, 0
; 0, 0, 2]]
[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
  ***   at top-level: rnfdedekind(nf,P,pr2
  ***                 ^--------------------
  *** rnfdedekind: sorry, Dedekind in the difficult case is not yet implemented.
1
  ***   at top-level: rnfdedekind(nf,P)
  ***                 ^-----------------
  *** rnfdedekind: sorry, Dedekind in the difficult case is not yet implemented.
  ***   at top-level: rnfdedekind(nf,P,[pr
  ***                 ^--------------------
  *** rnfdedekind: sorry, Dedekind in the difficult case is not yet implemented.
[[8, 2; 0, 1], [2, 0; 0, 1], [1, 0; 0, 1]]
1
1
1
1
  *** rnfisabelian: Warning: non-monic polynomial. Result of the form [nf,c].
0
  *** rnfisabelian: Warning: non-monic polynomial. Result of the form [nf,c].
1
[x, 1]
[(-78/43*y^2 - 14/43*y + 173/43)*x^2 + (60/43*y^2 + 24/43*y - 143/43)*x + (-
23/43*y^2 - 35/43*y + 110/43), 1]
[(-2*y^2 - 24/25*y + 139/25)*x^2 + (8/5*y^2 + 21/25*y - 4)*x + (-24/25*y^2 -
 27/25*y + 61/25), 1]
[x, -1]
  *** rnfisnorm: Warning: useless flag in rnfisnorm: the extension is Galois.
[1, 2]
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, -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]
[Mod(-1, y^3 - 21), -2]
[Mod(-y + 3, y^3 - 21), 1]
1:
[2, 0]~
Mod(2, x^2 + Mod(-y, y^3 - 21))
2
2
2
2
4
4
2:
[1/2, 0]~
Mod(1/2, x^2 + Mod(-y, y^3 - 21))
1/2
1/2
1/2
1/2
1
1/4
3:
[Mod(y^2 + y, y^3 - 21), Mod(1, y^3 - 21)]~
Mod(x + Mod(y, y^3 - 21), x^2 + Mod(-y, y^3 - 21))
error("incorrect type in rnfeltabstorel (t_POL).")
Mod(x^2 + x, x^6 - 21)
error("inconsistent variables in nf_to_scalar_or_basis, x != y.")
error("incorrect type in rnfeltabstorel (t_POL).")
error("incorrect type in rnfeltabstorel (t_POL).")
error("incorrect type in rnfeltabstorel (t_POL).")
4:
[1, 0]~
Mod(1, x^2 + Mod(-y, y^3 - 21))
Mod(1, x^2 + Mod(-y, y^3 - 21))
Mod(1, x^6 - 21)
1
1
2
1
5:
[1/2, 0]~
Mod(1/2, x^2 + Mod(-y, y^3 - 21))
Mod(1/2, x^2 + Mod(-y, y^3 - 21))
Mod(1/2, x^6 - 21)
1/2
1/2
1
1/4
6:
[Mod(y, y^3 - 21), 0]~
Mod(Mod(y, y^3 - 21), x^2 + Mod(-y, y^3 - 21))
Mod(Mod(y, y^3 - 21), x^2 + Mod(-y, y^3 - 21))
Mod(x^2, x^6 - 21)
Mod(x^2, x^6 - 21)
Mod(y, y^3 - 21)
Mod(2*y, y^3 - 21)
Mod(y^2, y^3 - 21)
7:
error("inconsistent moduli in rnfalgtobasis: x^6 - 21 != y^3 - 21")
error("inconsistent moduli in rnfbasistoalg: x^6 - 21 != y^3 - 21")
1
Mod(1, x^6 - 21)
Mod(1, x^6 - 21)
1
2
1
8:
error("inconsistent moduli in rnfalgtobasis: x^6 - 21 != y^3 - 21")
error("inconsistent moduli in rnfbasistoalg: x^6 - 21 != y^3 - 21")
1/2
Mod(1/2, x^6 - 21)
Mod(1/2, x^6 - 21)
1/2
1
1/4
9:
error("inconsistent moduli in rnfalgtobasis: x^6 - 21 != y^3 - 21")
error("inconsistent moduli in rnfbasistoalg: x^6 - 21 != y^3 - 21")
Mod(x, x^2 + Mod(-y, y^3 - 21))
Mod(x, x^6 - 21)
Mod(x, x^6 - 21)
error("domain error in rnfeltdown: element not in the base field")
0
Mod(-y, y^3 - 21)
10:
[Mod(y^2 + 1/2*y, y^3 - 21), Mod(1, y^3 - 21)]~
Mod(x + Mod(1/2*y, y^3 - 21), x^2 + Mod(-y, y^3 - 21))
Mod(x + Mod(1/2*y, y^3 - 21), x^2 - y)
Mod(1/2*x^2 + x, x^6 - 21)
error("inconsistent moduli in nf_to_scalar_or_basis: x^2 - y != y^3 - 21")
error("domain error in rnfeltdown: element not in the base field")
Mod(y, y^3 - 21)
Mod(1/4*y^2 - y, y^3 - 21)
11:
[Mod(y, y^3 - 21), 0]~
Mod(Mod(y, y^3 - 21), x^2 + Mod(-y, y^3 - 21))
Mod(Mod(y, y^3 - 21), x^2 + Mod(-y, y^3 - 21))
Mod(x^2, x^6 - 21)
Mod(x^2, x^6 - 21)
Mod(y, y^3 - 21)
Mod(2*y, y^3 - 21)
Mod(y^2, y^3 - 21)
12:
error("incorrect priority in rnfalgtobasis: variable z >= y")
error("inconsistent variables in rnfbasistoalg, z != x.")
error("inconsistent variables in rnfeltabstorel, z != x.")
error("inconsistent variables in eltreltoabs, z != y.")
error("inconsistent variables in nf_to_scalar_or_basis, z != y.")
error("inconsistent variables in rnfeltabstorel, z != x.")
error("inconsistent variables in rnfeltabstorel, z != x.")
error("inconsistent variables in rnfeltabstorel, z != x.")
13:
error("inconsistent moduli in rnfalgtobasis: y^2 + 1 != y^3 - 21")
error("inconsistent moduli in rnfbasistoalg: y^2 + 1 != y^3 - 21")
error("inconsistent moduli in rnfeltabstorel: y^2 + 1 != x^6 - 21")
error("inconsistent moduli in rnfeltreltoabs: 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 rnfeltdown: y^2 + 1 != y^3 - 21")
error("inconsistent moduli in rnfeltabstorel: y^2 + 1 != x^6 - 21")
error("inconsistent moduli in rnfeltabstorel: y^2 + 1 != x^6 - 21")
14:
error("inconsistent dimensions in rnfalgtobasis.")
error("inconsistent operation 'RgV_RgC_mul' t_VEC (2 elts) , t_COL (1 elts).
")
error("incorrect type in rnfeltabstorel (t_COL).")
error("incorrect type in rnfeltreltoabs (t_COL).")
error("incorrect type in nf_to_scalar_or_basis (t_COL).")
error("incorrect type in rnfeltabstorel (t_COL).")
error("incorrect type in rnfeltabstorel (t_COL).")
error("incorrect type in rnfeltabstorel (t_COL).")
15:
[1, 2]~
Mod(2*x + Mod(-2*y^2 + 1, y^3 - 21), x^2 + Mod(-y, y^3 - 21))
error("incorrect type in rnfeltabstorel (t_COL).")
error("incorrect type in rnfeltreltoabs (t_COL).")
error("incorrect type in nf_to_scalar_or_basis (t_COL).")
error("incorrect type in rnfeltabstorel (t_COL).")
error("incorrect type in rnfeltabstorel (t_COL).")
error("incorrect type in rnfeltabstorel (t_COL).")
16:
[1, Mod(y, y^3 - 21)]~
Mod(Mod(y, y^3 - 21)*x + Mod(-20, y^3 - 21), x^2 + Mod(-y, y^3 - 21))
error("incorrect type in rnfeltabstorel (t_COL).")
error("incorrect type in rnfeltreltoabs (t_COL).")
error("incorrect type in nf_to_scalar_or_basis (t_COL).")
error("incorrect type in rnfeltabstorel (t_COL).")
error("incorrect type in rnfeltabstorel (t_COL).")
error("incorrect type in rnfeltabstorel (t_COL).")
17:
error("incorrect type in rnfalgtobasis (t_COMPLEX).")
error("incorrect type in nf_to_scalar_or_alg (t_COMPLEX).")
error("incorrect type in rnfeltabstorel (t_COL).")
error("incorrect type in rnfeltreltoabs (t_COL).")
error("incorrect type in nf_to_scalar_or_basis (t_COL).")
error("incorrect type in rnfeltabstorel (t_COL).")
error("incorrect type in rnfeltabstorel (t_COL).")
error("incorrect type in rnfeltabstorel (t_COL).")
18:
error("incorrect type in rnfalgtobasis (t_POL).")
error("incorrect type in rnfbasistoalg (t_POL).")
error("incorrect type in rnfeltabstorel (t_POL).")
error("incorrect type in rnfeltup (t_COL).")
error("incorrect type in rnfeltup (t_COL).")
error("incorrect type in rnfeltdown (t_POL).")
error("incorrect type in rnfeltabstorel (t_POL).")
error("incorrect type in rnfeltabstorel (t_POL).")
19:
[y, 0]~
Mod(Mod(y, y^3 - 21), x^2 + Mod(-y, y^3 - 21))
Mod(Mod(y, y^3 - 21), x^2 + Mod(-y, y^3 - 21))
Mod(x^2, x^6 - 21)
error("inconsistent variables in nf_to_scalar_or_basis, x != y.")
Mod(y, y^3 - 21)
Mod(2*y, y^3 - 21)
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:
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:
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 (t_POL).")
19:
x^2 + Mod(-2*y, y^3 - 21)*x + Mod(y^2, y^3 - 21)
1:
[2, 0]~
Mod(2, x^2 + 1)
2
2
2
2
4
4
2:
[1/2, 0]~
Mod(1/2, x^2 + 1)
1/2
1/2
1/2
1/2
1
1/4
3:
[-1, 1]~
Mod(x - 1, x^2 + 1)
error("incorrect type in rnfeltabstorel (t_POL).")
Mod(x - 2, x^2 - 2*x + 2)
error("inconsistent variables in nf_to_scalar_or_basis, x != y.")
error("incorrect type in rnfeltabstorel (t_POL).")
error("incorrect type in rnfeltabstorel (t_POL).")
error("incorrect type in rnfeltabstorel (t_POL).")
4:
[1/2, 0]~
Mod(1/2, x^2 + 1)
Mod(1/2, x^2 + 1)
Mod(1/2, x^2 - 2*x + 2)
1/2
1/2
1
1/4
5:
[Mod(y, y + 1), 0]~
Mod(Mod(-1, y + 1), x^2 + 1)
Mod(-1, x^2 + 1)
-1
-1
-1
-2
1
6:
[1, 1/2]~
Mod(1/2*x + 1, x^2 + 1)
Mod(1/2*x + 1, x^2 + 1)
Mod(1/2*x + 1/2, x^2 - 2*x + 2)
error("inconsistent moduli in nf_to_scalar_or_basis: x^2 + 1 != y + 1")
error("domain error in rnfeltdown: element not in the base field")
2
5/4
7:
[0, 1]~
Mod(x, x^2 + 1)
Mod(x, x^2 + 1)
Mod(x - 1, x^2 - 2*x + 2)
error("inconsistent moduli in nf_to_scalar_or_basis: x^2 + 1 != y + 1")
error("domain error in rnfeltdown: element not in the base field")
0
1
8:
error("inconsistent moduli in rnfalgtobasis: x^2 - 2*x + 2 != y + 1")
error("inconsistent moduli in rnfbasistoalg: x^2 - 2*x + 2 != y + 1")
Mod(x + 1, x^2 + 1)
Mod(x, x^2 - 2*x + 2)
Mod(x, x^2 - 2*x + 2)
error("domain error in rnfeltdown: element not in the base field")
2
2
9:
error("inconsistent moduli in rnfalgtobasis: x^2 - y != y + 1")
error("inconsistent moduli in rnfbasistoalg: x^2 - y != y + 1")
error("inconsistent moduli in rnfeltabstorel: x^2 - y != x^2 - 2*x + 2")
error("inconsistent moduli in rnfeltreltoabs: x^2 - y != y + 1")
error("inconsistent moduli in nf_to_scalar_or_basis: x^2 - y != y + 1")
error("inconsistent moduli in rnfeltdown: x^2 - y != y + 1")
error("inconsistent moduli in rnfeltabstorel: x^2 - y != x^2 - 2*x + 2")
error("inconsistent moduli in rnfeltabstorel: x^2 - y != x^2 - 2*x + 2")
10:
[0, 1]~
Mod(x, x^2 + 1)
Mod(x + 1, x^2 + 1)
Mod(x - 1, x^2 - 2*x + 2)
error("inconsistent variables in nf_to_scalar_or_basis, x != y.")
error("domain error in rnfeltdown: element not in the base field")
2
2
11:
error("inconsistent dimensions in rnfalgtobasis.")
error("inconsistent operation 'RgV_RgC_mul' t_VEC (2 elts) , t_COL (1 elts).
")
error("incorrect type in rnfeltabstorel (t_COL).")
error("incorrect type in rnfeltreltoabs (t_COL).")
1
error("incorrect type in rnfeltabstorel (t_COL).")
error("incorrect type in rnfeltabstorel (t_COL).")
error("incorrect type in rnfeltabstorel (t_COL).")
12:
[1, 2]~
Mod(2*x + 1, x^2 + 1)
error("incorrect type in rnfeltabstorel (t_COL).")
error("incorrect type in rnfeltreltoabs (t_COL).")
error("incorrect type in nf_to_scalar_or_basis (t_COL).")
error("incorrect type in rnfeltabstorel (t_COL).")
error("incorrect type in rnfeltabstorel (t_COL).")
error("incorrect type in rnfeltabstorel (t_COL).")
13:
error("inconsistent dimensions in rnfalgtobasis.")
error("inconsistent operation 'RgV_RgC_mul' t_VEC (2 elts) , t_COL (1 elts).
")
error("incorrect type in rnfeltabstorel (t_COL).")
error("incorrect type in rnfeltreltoabs (t_COL).")
Mod(y, x^2 - 2*x + 2)
error("incorrect type in rnfeltabstorel (t_COL).")
error("incorrect type in rnfeltabstorel (t_COL).")
error("incorrect type in rnfeltabstorel (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:
error("inconsistent moduli in rnfcharpoly: x^2 - 2*x + 2 != y + 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]]]
[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
[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

[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, 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 (t_POL).")
error("incorrect type in rnfbasistoalg (t_POL).")
error("incorrect type in rnfidealabstorel (t_POL).")
error("incorrect type in rnfbasistoalg (t_POL).")
error("incorrect type in idealhnf [integer vector] (t_COL).")
error("incorrect type in rnfbasistoalg (t_POL).")
error("incorrect type in rnfbasistoalg (t_POL).")
error("incorrect type in rnfbasistoalg (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:
error("incorrect type in rnfidealhnf (t_MAT).")
error("incorrect type in rnfidealhnf (t_MAT).")
error("incorrect type in rnfidealabstorel (t_MAT).")
error("incorrect type in rnfidealhnf (t_MAT).")
[]
error("incorrect type in rnfidealhnf (t_MAT).")
error("incorrect type in rnfidealhnf (t_MAT).")
error("incorrect type in rnfidealhnf (t_MAT).")
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("incorrect type in rnfidealhnf (t_MAT).")
error("incorrect type in rnfidealhnf (t_MAT).")
error("incorrect type in rnfidealabstorel (t_MAT).")
error("incorrect type in rnfidealhnf (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("incorrect type in rnfidealhnf (t_MAT).")
error("incorrect type in rnfidealhnf (t_MAT).")
error("incorrect type in rnfidealhnf (t_MAT).")
26:
error("incorrect type in rnfidealhnf (t_MAT).")
error("incorrect type in rnfidealhnf (t_MAT).")
error("incorrect type in rnfidealabstorel (t_MAT).")
error("incorrect type in rnfidealhnf (t_MAT).")
error("inconsistent operation 'RgV_RgC_mul' t_VEC (3 elts) , t_COL (6 elts).
")
error("incorrect type in rnfidealhnf (t_MAT).")
error("incorrect type in rnfidealhnf (t_MAT).")
error("incorrect type in rnfidealhnf (t_MAT).")
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 operation 'RgV_RgC_mul' t_VEC (3 elts) , t_COL (2 elts).
")
[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]]]
  ***   at top-level: rnfdet(L,[[;],[]])
  ***                 ^------------------
  *** rnfdet: incorrect type in checknf [please apply nfinit()] (t_VEC).

[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
  ***   at top-level: rnfidealtwoelt(L,[[1
  ***                 ^--------------------
  *** rnfidealtwoelt: incorrect type in idealtyp [non-square t_MAT] (t_MAT).
Total time spent: 380
