[[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-57], [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]], [Mat([0, 0, 0, 1]), Mat(-2), 1]], [1, 0, 0; 0, 2, 0; 0, 0, 2]]
[[Mat(861), [1]], [[3, [3]~, 1, 1, 1], 1; [7, [7]~, 1, 1, 1], 1; [41, [41]~,
 1, 1, 1], 1]]
[[Mat(861), [1]], [[3, [3]~, 1, 1, 1], 1; [7, [7]~, 1, 1, 1], 1; [41, [41]~,
 1, 1, 1], 1]]
[[Mat(861), [1]], [[3, [3]~, 1, 1, 1], 1; [7, [7]~, 1, 1, 1], 1; [41, [41]~,
 1, 1, 1], 1]]
[[Mat(117), [0]], [[3, [3]~, 1, 1, 1], 2; [13, [13]~, 1, 1, 1], 1]]
[Mat(3), Mat(1)]
[[Mat(3), Mat(1)], [0, -1; 1, 1], [1, 1; -1/3, 0]]
[Mat(4), Mat(4)]
[[Mat(4), Mat(4)], [1, 0; 0, 1], [1/2, 0; 0, 1/2]]

[3 1]

[0 1]

[[8, 2; 0, 1], [2, 0; 0, 1], [1, 0; 0, 1]]
1
1
1
0
1
1
[1, y]
[1, 2]
[1, 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]]

[[-7299, -3342, -2170]~ [28944, 9855, -18888]~ [-403109721, -130243536, 3134
63442]~ [14327960067, -6668848710, -6564138180]~]

[[-8931, -7002, -4889]~ [1757, 2965, 3850]~ [37941889, 4175158, -24594320]~ 
[-6449565004, 4002663648, -4747437435]~]

[[1582, 287, -979]~ [-22620, -7713, 17845]~ [345203944, 119358263, -27416790
8]~ [-12604280171, -1376229454, 7984127400]~]

[[16328, 10812, 8737]~ [-12774, -6624, -161]~ [81698859, 24909626, -61460862
]~ [2425192175, 6514839743, 3707931485]~]


[0 1 0 0]

[0 0 1 0]

[0 0 0 1]

[[2148564093, 1880231385, 101485359; 0, 87, 9; 0, 0, 3], [1, 0, 0; 0, 1, 0; 
0, 0, 1], [1, 0, 0; 0, 1, 0; 0, 0, 1]]

[1 [-1335, -25, 865]~ [15231, -65250, -69787]~]

[0                  1      [-389, -202, -196]~]

[0                  0                        1]


[[122218751/716188031, 92116373/716188031, -100209652/716188031]~ [358, 179,
 -331]~ 0]

[[-51524140/716188031, -1828617/716188031, 31588281/716188031]~ [-169, -40, 
121]~ [-2, -11, 6]~]

[[-4650644/24696139, -2252334/24696139, 2933316/24696139]~ [-377, -145, 319]
~ [4, 0, 7]~]


[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]
[Mod(-224*y^2 - 618*y - 1705, y^3 - 21), -2]
[Mod(54*y^2 + 149*y + 411, y^3 - 21), 1]
rnfalgtobasis(L,2): [2, 0]~
rnfalgtobasis(M,2): [2]~
rnfbasistoalg(L,2): Mod(2, x^2 + Mod(-y, y^3 - 21))
rnfbasistoalg(M,2): Mod(2, x)
rnfeltabstorel(L,2): 2
rnfeltabstorel(M,2): 2
rnfeltreltoabs(L,2): 2
rnfeltreltoabs(M,2): 2
rnfeltup(L,2): 2
rnfeltup(M,2): 2
rnfeltdown(L,2): 2
rnfeltdown(M,2): 2
rnfelttrace(L,2): 4
rnfelttrace(M,2): 2
rnfeltnorm(L,2): 4
rnfeltnorm(M,2): 2
rnfalgtobasis(L,1/2): [1/2, 0]~
rnfalgtobasis(M,1/2): [1/2]~
rnfbasistoalg(L,1/2): Mod(1/2, x^2 + Mod(-y, y^3 - 21))
rnfbasistoalg(M,1/2): Mod(1/2, x)
rnfeltabstorel(L,1/2): 1/2
rnfeltabstorel(M,1/2): 1/2
rnfeltreltoabs(L,1/2): 1/2
rnfeltreltoabs(M,1/2): 1/2
rnfeltup(L,1/2): 1/2
rnfeltup(M,1/2): 1/2
rnfeltdown(L,1/2): 1/2
rnfeltdown(M,1/2): 1/2
rnfelttrace(L,1/2): 1
rnfelttrace(M,1/2): 1/2
rnfeltnorm(L,1/2): 1/4
rnfeltnorm(M,1/2): 1/2
rnfalgtobasis(L,x + y): [Mod(y^2 + y, y^3 - 21), Mod(1, y^3 - 21)]~
rnfalgtobasis(M,x + y): [Mod(y, y^3 - 21)]~
rnfbasistoalg(L,x + y): Mod(x + Mod(y, y^3 - 21), x^2 + Mod(-y, y^3 - 21))
rnfbasistoalg(M,x + y): Mod(Mod(y, y^3 - 21), x)
rnfeltabstorel(L,x + y): error("incorrect type in rnfeltabstorel [not in Q[X
]] (t_POL).")
rnfeltabstorel(M,x + y): error("incorrect type in rnfeltabstorel [not in Q[X
]] (t_POL).")
rnfeltreltoabs(L,x + y): Mod(x^2 + x, x^6 - 21)
rnfeltreltoabs(M,x + y): Mod(-x, x^3 + 21)
rnfeltup(L,x + y): error("inconsistent variables in nf_to_scalar_or_basis, x
 != y.")
rnfeltup(M,x + y): error("inconsistent variables in nf_to_scalar_or_basis, x
 != y.")
rnfeltdown(L,x + y): error("incorrect type in rnfeltabstorel [not in Q[X]] (
t_POL).")
rnfeltdown(M,x + y): error("incorrect type in rnfeltabstorel [not in Q[X]] (
t_POL).")
rnfelttrace(L,x + y): Mod(2*y, y^3 - 21)
rnfelttrace(M,x + y): Mod(y, y^3 - 21)
rnfeltnorm(L,x + y): Mod(y^2 - y, y^3 - 21)
rnfeltnorm(M,x + y): Mod(y, y^3 - 21)
rnfalgtobasis(L,Mod(1, y^3 - 21)): [1, 0]~
rnfalgtobasis(M,Mod(1, y^3 - 21)): [1]~
rnfbasistoalg(L,Mod(1, y^3 - 21)): Mod(1, x^2 + Mod(-y, y^3 - 21))
rnfbasistoalg(M,Mod(1, y^3 - 21)): Mod(1, x)
rnfeltabstorel(L,Mod(1, y^3 - 21)): Mod(1, x^2 + Mod(-y, y^3 - 21))
rnfeltabstorel(M,Mod(1, y^3 - 21)): Mod(1, x)
rnfeltreltoabs(L,Mod(1, y^3 - 21)): Mod(1, x^6 - 21)
rnfeltreltoabs(M,Mod(1, y^3 - 21)): Mod(1, x^3 + 21)
rnfeltup(L,Mod(1, y^3 - 21)): 1
rnfeltup(M,Mod(1, y^3 - 21)): 1
rnfeltdown(L,Mod(1, y^3 - 21)): 1
rnfeltdown(M,Mod(1, y^3 - 21)): 1
rnfelttrace(L,Mod(1, y^3 - 21)): 2
rnfelttrace(M,Mod(1, y^3 - 21)): 1
rnfeltnorm(L,Mod(1, y^3 - 21)): 1
rnfeltnorm(M,Mod(1, y^3 - 21)): 1
rnfalgtobasis(L,Mod(1/2, y^3 - 21)): [1/2, 0]~
rnfalgtobasis(M,Mod(1/2, y^3 - 21)): [1/2]~
rnfbasistoalg(L,Mod(1/2, y^3 - 21)): Mod(1/2, x^2 + Mod(-y, y^3 - 21))
rnfbasistoalg(M,Mod(1/2, y^3 - 21)): Mod(1/2, x)
rnfeltabstorel(L,Mod(1/2, y^3 - 21)): Mod(1/2, x^2 + Mod(-y, y^3 - 21))
rnfeltabstorel(M,Mod(1/2, y^3 - 21)): Mod(1/2, x)
rnfeltreltoabs(L,Mod(1/2, y^3 - 21)): Mod(1/2, x^6 - 21)
rnfeltreltoabs(M,Mod(1/2, y^3 - 21)): Mod(1/2, x^3 + 21)
rnfeltup(L,Mod(1/2, y^3 - 21)): 1/2
rnfeltup(M,Mod(1/2, y^3 - 21)): 1/2
rnfeltdown(L,Mod(1/2, y^3 - 21)): 1/2
rnfeltdown(M,Mod(1/2, y^3 - 21)): 1/2
rnfelttrace(L,Mod(1/2, y^3 - 21)): 1
rnfelttrace(M,Mod(1/2, y^3 - 21)): 1/2
rnfeltnorm(L,Mod(1/2, y^3 - 21)): 1/4
rnfeltnorm(M,Mod(1/2, y^3 - 21)): 1/2
rnfalgtobasis(L,Mod(y, y^3 - 21)): [Mod(y, y^3 - 21), 0]~
rnfalgtobasis(M,Mod(y, y^3 - 21)): [Mod(y, y^3 - 21)]~
rnfbasistoalg(L,Mod(y, y^3 - 21)): Mod(Mod(y, y^3 - 21), x^2 + Mod(-y, y^3 -
 21))
rnfbasistoalg(M,Mod(y, y^3 - 21)): Mod(Mod(y, y^3 - 21), x)
rnfeltabstorel(L,Mod(y, y^3 - 21)): Mod(Mod(y, y^3 - 21), x^2 + Mod(-y, y^3 
- 21))
rnfeltabstorel(M,Mod(y, y^3 - 21)): Mod(Mod(y, y^3 - 21), x)
rnfeltreltoabs(L,Mod(y, y^3 - 21)): Mod(x^2, x^6 - 21)
rnfeltreltoabs(M,Mod(y, y^3 - 21)): Mod(-x, x^3 + 21)
rnfeltup(L,Mod(y, y^3 - 21)): Mod(x^2, x^6 - 21)
rnfeltup(M,Mod(y, y^3 - 21)): Mod(-x, x^3 + 21)
rnfeltdown(L,Mod(y, y^3 - 21)): Mod(y, y^3 - 21)
rnfeltdown(M,Mod(y, y^3 - 21)): Mod(y, y^3 - 21)
rnfelttrace(L,Mod(y, y^3 - 21)): Mod(2*y, y^3 - 21)
rnfelttrace(M,Mod(y, y^3 - 21)): Mod(y, y^3 - 21)
rnfeltnorm(L,Mod(y, y^3 - 21)): Mod(y^2, y^3 - 21)
rnfeltnorm(M,Mod(y, y^3 - 21)): Mod(y, y^3 - 21)
rnfalgtobasis(L,Mod(1, x^6 - 21)): error("inconsistent moduli in rnfalgtobas
is: x^6 - 21 != y^3 - 21")
rnfalgtobasis(M,Mod(1, x^6 - 21)): error("inconsistent moduli in rnfalgtobas
is: x^6 - 21 != y^3 - 21")
rnfbasistoalg(L,Mod(1, x^6 - 21)): error("inconsistent moduli in rnfbasistoa
lg: x^6 - 21 != y^3 - 21")
rnfbasistoalg(M,Mod(1, x^6 - 21)): error("inconsistent moduli in rnfbasistoa
lg: x^6 - 21 != y^3 - 21")
rnfeltabstorel(L,Mod(1, x^6 - 21)): 1
rnfeltabstorel(M,Mod(1, x^6 - 21)): error("inconsistent moduli in rnfeltabst
orel: x^6 - 21 != x^3 + 21")
rnfeltreltoabs(L,Mod(1, x^6 - 21)): Mod(1, x^6 - 21)
rnfeltreltoabs(M,Mod(1, x^6 - 21)): error("inconsistent moduli in rnfeltrelt
oabs: x^6 - 21 != y^3 - 21")
rnfeltup(L,Mod(1, x^6 - 21)): Mod(1, x^6 - 21)
rnfeltup(M,Mod(1, x^6 - 21)): error("inconsistent moduli in nf_to_scalar_or_
basis: x^6 - 21 != y^3 - 21")
rnfeltdown(L,Mod(1, x^6 - 21)): 1
rnfeltdown(M,Mod(1, x^6 - 21)): error("inconsistent moduli in rnfeltdown: x^
6 - 21 != y^3 - 21")
rnfelttrace(L,Mod(1, x^6 - 21)): 2
rnfelttrace(M,Mod(1, x^6 - 21)): error("inconsistent moduli in rnfeltabstore
l: x^6 - 21 != x^3 + 21")
rnfeltnorm(L,Mod(1, x^6 - 21)): 1
rnfeltnorm(M,Mod(1, x^6 - 21)): error("inconsistent moduli in rnfeltabstorel
: x^6 - 21 != x^3 + 21")
rnfalgtobasis(L,Mod(1/2, x^6 - 21)): error("inconsistent moduli in rnfalgtob
asis: x^6 - 21 != y^3 - 21")
rnfalgtobasis(M,Mod(1/2, x^6 - 21)): error("inconsistent moduli in rnfalgtob
asis: x^6 - 21 != y^3 - 21")
rnfbasistoalg(L,Mod(1/2, x^6 - 21)): error("inconsistent moduli in rnfbasist
oalg: x^6 - 21 != y^3 - 21")
rnfbasistoalg(M,Mod(1/2, x^6 - 21)): error("inconsistent moduli in rnfbasist
oalg: x^6 - 21 != y^3 - 21")
rnfeltabstorel(L,Mod(1/2, x^6 - 21)): 1/2
rnfeltabstorel(M,Mod(1/2, x^6 - 21)): error("inconsistent moduli in rnfeltab
storel: x^6 - 21 != x^3 + 21")
rnfeltreltoabs(L,Mod(1/2, x^6 - 21)): Mod(1/2, x^6 - 21)
rnfeltreltoabs(M,Mod(1/2, x^6 - 21)): error("inconsistent moduli in rnfeltre
ltoabs: x^6 - 21 != y^3 - 21")
rnfeltup(L,Mod(1/2, x^6 - 21)): Mod(1/2, x^6 - 21)
rnfeltup(M,Mod(1/2, x^6 - 21)): error("inconsistent moduli in nf_to_scalar_o
r_basis: x^6 - 21 != y^3 - 21")
rnfeltdown(L,Mod(1/2, x^6 - 21)): 1/2
rnfeltdown(M,Mod(1/2, x^6 - 21)): error("inconsistent moduli in rnfeltdown: 
x^6 - 21 != y^3 - 21")
rnfelttrace(L,Mod(1/2, x^6 - 21)): 1
rnfelttrace(M,Mod(1/2, x^6 - 21)): error("inconsistent moduli in rnfeltabsto
rel: x^6 - 21 != x^3 + 21")
rnfeltnorm(L,Mod(1/2, x^6 - 21)): 1/4
rnfeltnorm(M,Mod(1/2, x^6 - 21)): error("inconsistent moduli in rnfeltabstor
el: x^6 - 21 != x^3 + 21")
rnfalgtobasis(L,Mod(x, x^6 - 21)): error("inconsistent moduli in rnfalgtobas
is: x^6 - 21 != y^3 - 21")
rnfalgtobasis(M,Mod(x, x^6 - 21)): error("inconsistent moduli in rnfalgtobas
is: x^6 - 21 != y^3 - 21")
rnfbasistoalg(L,Mod(x, x^6 - 21)): error("inconsistent moduli in rnfbasistoa
lg: x^6 - 21 != y^3 - 21")
rnfbasistoalg(M,Mod(x, x^6 - 21)): error("inconsistent moduli in rnfbasistoa
lg: x^6 - 21 != y^3 - 21")
rnfeltabstorel(L,Mod(x, x^6 - 21)): Mod(x, x^2 + Mod(-y, y^3 - 21))
rnfeltabstorel(M,Mod(x, x^6 - 21)): error("inconsistent moduli in rnfeltabst
orel: x^6 - 21 != x^3 + 21")
rnfeltreltoabs(L,Mod(x, x^6 - 21)): Mod(x, x^6 - 21)
rnfeltreltoabs(M,Mod(x, x^6 - 21)): error("inconsistent moduli in rnfeltrelt
oabs: x^6 - 21 != y^3 - 21")
rnfeltup(L,Mod(x, x^6 - 21)): Mod(x, x^6 - 21)
rnfeltup(M,Mod(x, x^6 - 21)): error("inconsistent moduli in nf_to_scalar_or_
basis: x^6 - 21 != y^3 - 21")
rnfeltdown(L,Mod(x, x^6 - 21)): error("domain error in rnfeltdown: element n
ot in the base field")
rnfeltdown(M,Mod(x, x^6 - 21)): error("inconsistent moduli in rnfeltdown: x^
6 - 21 != y^3 - 21")
rnfelttrace(L,Mod(x, x^6 - 21)): 0
rnfelttrace(M,Mod(x, x^6 - 21)): error("inconsistent moduli in rnfeltabstore
l: x^6 - 21 != x^3 + 21")
rnfeltnorm(L,Mod(x, x^6 - 21)): Mod(-y, y^3 - 21)
rnfeltnorm(M,Mod(x, x^6 - 21)): error("inconsistent moduli in rnfeltabstorel
: x^6 - 21 != x^3 + 21")
rnfalgtobasis(L,Mod(x + 1/2*y, x^2 - y)): [Mod(y^2 + 1/2*y, y^3 - 21), Mod(1
, y^3 - 21)]~
rnfalgtobasis(M,Mod(x + 1/2*y, x^2 - y)): error("inconsistent moduli in rnfa
lgtobasis: x^2 - y != y^3 - 21")
rnfbasistoalg(L,Mod(x + 1/2*y, x^2 - y)): Mod(x + Mod(1/2*y, y^3 - 21), x^2 
+ Mod(-y, y^3 - 21))
rnfbasistoalg(M,Mod(x + 1/2*y, x^2 - y)): error("inconsistent moduli in rnfb
asistoalg: x^2 - y != y^3 - 21")
rnfeltabstorel(L,Mod(x + 1/2*y, x^2 - y)): Mod(x + Mod(1/2*y, y^3 - 21), x^2
 + Mod(-y, y^3 - 21))
rnfeltabstorel(M,Mod(x + 1/2*y, x^2 - y)): error("inconsistent moduli in rnf
eltabstorel: x^2 - y != x^3 + 21")
rnfeltreltoabs(L,Mod(x + 1/2*y, x^2 - y)): Mod(1/2*x^2 + x, x^6 - 21)
rnfeltreltoabs(M,Mod(x + 1/2*y, x^2 - y)): error("inconsistent moduli in rnf
eltreltoabs: x^2 - y != y^3 - 21")
rnfeltup(L,Mod(x + 1/2*y, x^2 - y)): error("inconsistent moduli in nf_to_sca
lar_or_basis: x^2 - y != y^3 - 21")
rnfeltup(M,Mod(x + 1/2*y, x^2 - y)): error("inconsistent moduli in nf_to_sca
lar_or_basis: x^2 - y != y^3 - 21")
rnfeltdown(L,Mod(x + 1/2*y, x^2 - y)): error("domain error in rnfeltdown: el
ement not in the base field")
rnfeltdown(M,Mod(x + 1/2*y, x^2 - y)): error("inconsistent moduli in rnfeltd
own: x^2 - y != y^3 - 21")
rnfelttrace(L,Mod(x + 1/2*y, x^2 - y)): Mod(y, y^3 - 21)
rnfelttrace(M,Mod(x + 1/2*y, x^2 - y)): error("inconsistent moduli in rnfelt
abstorel: x^2 - y != x^3 + 21")
rnfeltnorm(L,Mod(x + 1/2*y, x^2 - y)): Mod(1/4*y^2 - y, y^3 - 21)
rnfeltnorm(M,Mod(x + 1/2*y, x^2 - y)): error("inconsistent moduli in rnfelta
bstorel: x^2 - y != x^3 + 21")
rnfalgtobasis(L,y): [Mod(y, y^3 - 21), 0]~
rnfalgtobasis(M,y): [Mod(y, y^3 - 21)]~
rnfbasistoalg(L,y): Mod(Mod(y, y^3 - 21), x^2 + Mod(-y, y^3 - 21))
rnfbasistoalg(M,y): Mod(Mod(y, y^3 - 21), x)
rnfeltabstorel(L,y): Mod(Mod(y, y^3 - 21), x^2 + Mod(-y, y^3 - 21))
rnfeltabstorel(M,y): Mod(Mod(y, y^3 - 21), x)
rnfeltreltoabs(L,y): Mod(x^2, x^6 - 21)
rnfeltreltoabs(M,y): Mod(-x, x^3 + 21)
rnfeltup(L,y): Mod(x^2, x^6 - 21)
rnfeltup(M,y): Mod(-x, x^3 + 21)
rnfeltdown(L,y): Mod(y, y^3 - 21)
rnfeltdown(M,y): Mod(y, y^3 - 21)
rnfelttrace(L,y): Mod(2*y, y^3 - 21)
rnfelttrace(M,y): Mod(y, y^3 - 21)
rnfeltnorm(L,y): Mod(y^2, y^3 - 21)
rnfeltnorm(M,y): Mod(y, y^3 - 21)
rnfalgtobasis(L,z): error("incorrect priority in rnfalgtobasis: variable z >
= y")
rnfalgtobasis(M,z): error("incorrect priority in rnfalgtobasis: variable z >
= y")
rnfbasistoalg(L,z): error("inconsistent variables in rnfbasistoalg, z != x."
)
rnfbasistoalg(M,z): error("inconsistent variables in rnfbasistoalg, z != x."
)
rnfeltabstorel(L,z): error("inconsistent variables in rnfeltabstorel, z != x
.")
rnfeltabstorel(M,z): error("inconsistent variables in rnfeltabstorel, z != x
.")
rnfeltreltoabs(L,z): error("inconsistent variables in eltreltoabs, z != y.")
rnfeltreltoabs(M,z): error("inconsistent variables in eltreltoabs, z != y.")
rnfeltup(L,z): error("inconsistent variables in nf_to_scalar_or_basis, z != 
y.")
rnfeltup(M,z): error("inconsistent variables in nf_to_scalar_or_basis, z != 
y.")
rnfeltdown(L,z): error("inconsistent variables in rnfeltabstorel, z != x.")
rnfeltdown(M,z): error("inconsistent variables in rnfeltabstorel, z != x.")
rnfelttrace(L,z): error("inconsistent variables in rnfeltabstorel, z != x.")
rnfelttrace(M,z): error("inconsistent variables in rnfeltabstorel, z != x.")
rnfeltnorm(L,z): error("inconsistent variables in rnfeltabstorel, z != x.")
rnfeltnorm(M,z): error("inconsistent variables in rnfeltabstorel, z != x.")
rnfalgtobasis(L,Mod(y + 1/2, y^2 + 1)): error("inconsistent moduli in rnfalg
tobasis: y^2 + 1 != y^3 - 21")
rnfalgtobasis(M,Mod(y + 1/2, y^2 + 1)): error("inconsistent moduli in rnfalg
tobasis: y^2 + 1 != y^3 - 21")
rnfbasistoalg(L,Mod(y + 1/2, y^2 + 1)): error("inconsistent moduli in rnfbas
istoalg: y^2 + 1 != y^3 - 21")
rnfbasistoalg(M,Mod(y + 1/2, y^2 + 1)): error("inconsistent moduli in rnfbas
istoalg: y^2 + 1 != y^3 - 21")
rnfeltabstorel(L,Mod(y + 1/2, y^2 + 1)): error("inconsistent moduli in rnfel
tabstorel: y^2 + 1 != x^6 - 21")
rnfeltabstorel(M,Mod(y + 1/2, y^2 + 1)): error("inconsistent moduli in rnfel
tabstorel: y^2 + 1 != x^3 + 21")
rnfeltreltoabs(L,Mod(y + 1/2, y^2 + 1)): error("inconsistent moduli in rnfel
treltoabs: y^2 + 1 != y^3 - 21")
rnfeltreltoabs(M,Mod(y + 1/2, y^2 + 1)): error("inconsistent moduli in rnfel
treltoabs: y^2 + 1 != y^3 - 21")
rnfeltup(L,Mod(y + 1/2, y^2 + 1)): error("inconsistent moduli in nf_to_scala
r_or_basis: y^2 + 1 != y^3 - 21")
rnfeltup(M,Mod(y + 1/2, y^2 + 1)): error("inconsistent moduli in nf_to_scala
r_or_basis: y^2 + 1 != y^3 - 21")
rnfeltdown(L,Mod(y + 1/2, y^2 + 1)): error("inconsistent moduli in rnfeltdow
n: y^2 + 1 != y^3 - 21")
rnfeltdown(M,Mod(y + 1/2, y^2 + 1)): error("inconsistent moduli in rnfeltdow
n: y^2 + 1 != y^3 - 21")
rnfelttrace(L,Mod(y + 1/2, y^2 + 1)): error("inconsistent moduli in rnfeltab
storel: y^2 + 1 != x^6 - 21")
rnfelttrace(M,Mod(y + 1/2, y^2 + 1)): error("inconsistent moduli in rnfeltab
storel: y^2 + 1 != x^3 + 21")
rnfeltnorm(L,Mod(y + 1/2, y^2 + 1)): error("inconsistent moduli in rnfeltabs
torel: y^2 + 1 != x^6 - 21")
rnfeltnorm(M,Mod(y + 1/2, y^2 + 1)): error("inconsistent moduli in rnfeltabs
torel: y^2 + 1 != x^3 + 21")
rnfalgtobasis(L,[1]~): error("inconsistent dimensions in rnfalgtobasis.")
rnfalgtobasis(M,[1]~): [1]~
rnfbasistoalg(L,[1]~): error("inconsistent operation 'RgV_RgC_mul' t_VEC (2 
elts) , t_COL (1 elts).")
rnfbasistoalg(M,[1]~): Mod(1, x)
rnfeltabstorel(L,[1]~): error("incorrect type in rnfeltabstorel, apply nfini
t(rnf) (t_COL).")
rnfeltabstorel(M,[1]~): error("incorrect type in rnfeltabstorel, apply nfini
t(rnf) (t_COL).")
rnfeltreltoabs(L,[1]~): error("incorrect type in rnfeltreltoabs (t_COL).")
rnfeltreltoabs(M,[1]~): error("incorrect type in rnfeltreltoabs (t_COL).")
rnfeltup(L,[1]~): error("incorrect type in nf_to_scalar_or_basis (t_COL).")
rnfeltup(M,[1]~): error("incorrect type in nf_to_scalar_or_basis (t_COL).")
rnfeltdown(L,[1]~): error("incorrect type in rnfeltdown (t_COL).")
rnfeltdown(M,[1]~): error("incorrect type in rnfeltdown (t_COL).")
rnfelttrace(L,[1]~): error("incorrect type in rnfeltabstorel, apply nfinit(r
nf) (t_COL).")
rnfelttrace(M,[1]~): error("incorrect type in rnfeltabstorel, apply nfinit(r
nf) (t_COL).")
rnfeltnorm(L,[1]~): error("incorrect type in rnfeltabstorel, apply nfinit(rn
f) (t_COL).")
rnfeltnorm(M,[1]~): error("incorrect type in rnfeltabstorel, apply nfinit(rn
f) (t_COL).")
rnfalgtobasis(L,[1, 2]~): [1, 2]~
rnfalgtobasis(M,[1, 2]~): error("inconsistent dimensions in rnfalgtobasis.")
rnfbasistoalg(L,[1, 2]~): Mod(2*x + Mod(-2*y^2 + 1, y^3 - 21), x^2 + Mod(-y,
 y^3 - 21))
rnfbasistoalg(M,[1, 2]~): error("inconsistent operation 'RgV_RgC_mul' t_VEC 
(1 elts) , t_COL (2 elts).")
rnfeltabstorel(L,[1, 2]~): error("incorrect type in rnfeltabstorel, apply nf
init(rnf) (t_COL).")
rnfeltabstorel(M,[1, 2]~): error("incorrect type in rnfeltabstorel, apply nf
init(rnf) (t_COL).")
rnfeltreltoabs(L,[1, 2]~): error("incorrect type in rnfeltreltoabs (t_COL)."
)
rnfeltreltoabs(M,[1, 2]~): error("incorrect type in rnfeltreltoabs (t_COL)."
)
rnfeltup(L,[1, 2]~): error("incorrect type in nf_to_scalar_or_basis (t_COL).
")
rnfeltup(M,[1, 2]~): error("incorrect type in nf_to_scalar_or_basis (t_COL).
")
rnfeltdown(L,[1, 2]~): error("incorrect type in rnfeltdown (t_COL).")
rnfeltdown(M,[1, 2]~): error("incorrect type in rnfeltdown (t_COL).")
rnfelttrace(L,[1, 2]~): error("incorrect type in rnfeltabstorel, apply nfini
t(rnf) (t_COL).")
rnfelttrace(M,[1, 2]~): error("incorrect type in rnfeltabstorel, apply nfini
t(rnf) (t_COL).")
rnfeltnorm(L,[1, 2]~): error("incorrect type in rnfeltabstorel, apply nfinit
(rnf) (t_COL).")
rnfeltnorm(M,[1, 2]~): error("incorrect type in rnfeltabstorel, apply nfinit
(rnf) (t_COL).")
rnfalgtobasis(L,[1, y]~): [1, Mod(y, y^3 - 21)]~
rnfalgtobasis(M,[1, y]~): error("inconsistent dimensions in rnfalgtobasis.")
rnfbasistoalg(L,[1, y]~): Mod(Mod(y, y^3 - 21)*x - 20, x^2 + Mod(-y, y^3 - 2
1))
rnfbasistoalg(M,[1, y]~): error("inconsistent operation 'RgV_RgC_mul' t_VEC 
(1 elts) , t_COL (2 elts).")
rnfeltabstorel(L,[1, y]~): error("incorrect type in rnfeltabstorel, apply nf
init(rnf) (t_COL).")
rnfeltabstorel(M,[1, y]~): error("incorrect type in rnfeltabstorel, apply nf
init(rnf) (t_COL).")
rnfeltreltoabs(L,[1, y]~): error("incorrect type in rnfeltreltoabs (t_COL)."
)
rnfeltreltoabs(M,[1, y]~): error("incorrect type in rnfeltreltoabs (t_COL)."
)
rnfeltup(L,[1, y]~): error("incorrect type in nf_to_scalar_or_basis (t_COL).
")
rnfeltup(M,[1, y]~): error("incorrect type in nf_to_scalar_or_basis (t_COL).
")
rnfeltdown(L,[1, y]~): error("incorrect type in rnfeltdown (t_COL).")
rnfeltdown(M,[1, y]~): error("incorrect type in rnfeltdown (t_COL).")
rnfelttrace(L,[1, y]~): error("incorrect type in rnfeltabstorel, apply nfini
t(rnf) (t_COL).")
rnfelttrace(M,[1, y]~): error("incorrect type in rnfeltabstorel, apply nfini
t(rnf) (t_COL).")
rnfeltnorm(L,[1, y]~): error("incorrect type in rnfeltabstorel, apply nfinit
(rnf) (t_COL).")
rnfeltnorm(M,[1, y]~): error("incorrect type in rnfeltabstorel, apply nfinit
(rnf) (t_COL).")
rnfalgtobasis(L,[1, I]~): error("incorrect type in rnfalgtobasis (t_COMPLEX)
.")
rnfalgtobasis(M,[1, I]~): error("inconsistent dimensions in rnfalgtobasis.")
rnfbasistoalg(L,[1, I]~): error("incorrect type in nf_to_scalar_or_alg (t_CO
MPLEX).")
rnfbasistoalg(M,[1, I]~): error("incorrect type in nf_to_scalar_or_alg (t_CO
MPLEX).")
rnfeltabstorel(L,[1, I]~): error("incorrect type in rnfeltabstorel, apply nf
init(rnf) (t_COL).")
rnfeltabstorel(M,[1, I]~): error("incorrect type in rnfeltabstorel, apply nf
init(rnf) (t_COL).")
rnfeltreltoabs(L,[1, I]~): error("incorrect type in rnfeltreltoabs (t_COL)."
)
rnfeltreltoabs(M,[1, I]~): error("incorrect type in rnfeltreltoabs (t_COL)."
)
rnfeltup(L,[1, I]~): error("incorrect type in nf_to_scalar_or_basis (t_COL).
")
rnfeltup(M,[1, I]~): error("incorrect type in nf_to_scalar_or_basis (t_COL).
")
rnfeltdown(L,[1, I]~): error("incorrect type in rnfeltdown (t_COL).")
rnfeltdown(M,[1, I]~): error("incorrect type in rnfeltdown (t_COL).")
rnfelttrace(L,[1, I]~): error("incorrect type in rnfeltabstorel, apply nfini
t(rnf) (t_COL).")
rnfelttrace(M,[1, I]~): error("incorrect type in rnfeltabstorel, apply nfini
t(rnf) (t_COL).")
rnfeltnorm(L,[1, I]~): error("incorrect type in rnfeltabstorel, apply nfinit
(rnf) (t_COL).")
rnfeltnorm(M,[1, I]~): error("incorrect type in rnfeltabstorel, apply nfinit
(rnf) (t_COL).")
rnfalgtobasis(L,y + I): error("incorrect type in rnfalgtobasis [not in Q[X]]
 (t_POL).")
rnfalgtobasis(M,y + I): error("incorrect type in rnfalgtobasis [not in Q[X]]
 (t_POL).")
rnfbasistoalg(L,y + I): error("incorrect type in rnfbasistoalg [not in Q[X]]
 (t_POL).")
rnfbasistoalg(M,y + I): error("incorrect type in rnfbasistoalg [not in Q[X]]
 (t_POL).")
rnfeltabstorel(L,y + I): error("incorrect type in rnfeltabstorel [not in Q[X
]] (t_POL).")
rnfeltabstorel(M,y + I): error("incorrect type in rnfeltabstorel [not in Q[X
]] (t_POL).")
rnfeltreltoabs(L,y + I): error("incorrect type in poltobasis (t_POL).")
rnfeltreltoabs(M,y + I): error("incorrect type in poltobasis (t_POL).")
rnfeltup(L,y + I): error("incorrect type in poltobasis (t_POL).")
rnfeltup(M,y + I): error("incorrect type in poltobasis (t_POL).")
rnfeltdown(L,y + I): error("incorrect type in rnfeltdown [not in Q[X]] (t_PO
L).")
rnfeltdown(M,y + I): error("incorrect type in rnfeltdown [not in Q[X]] (t_PO
L).")
rnfelttrace(L,y + I): error("incorrect type in rnfeltabstorel [not in Q[X]] 
(t_POL).")
rnfelttrace(M,y + I): error("incorrect type in rnfeltabstorel [not in Q[X]] 
(t_POL).")
rnfeltnorm(L,y + I): error("incorrect type in rnfeltabstorel [not in Q[X]] (
t_POL).")
rnfeltnorm(M,y + I): error("incorrect type in rnfeltabstorel [not in Q[X]] (
t_POL).")
rnfalgtobasis(L,x^2): [y, 0]~
rnfalgtobasis(M,x^2): [0]~
rnfbasistoalg(L,x^2): Mod(Mod(y, y^3 - 21), x^2 + Mod(-y, y^3 - 21))
rnfbasistoalg(M,x^2): Mod(0, x)
rnfeltabstorel(L,x^2): Mod(Mod(y, y^3 - 21), x^2 + Mod(-y, y^3 - 21))
rnfeltabstorel(M,x^2): Mod(Mod(y^2, y^3 - 21), x)
rnfeltreltoabs(L,x^2): Mod(x^2, x^6 - 21)
rnfeltreltoabs(M,x^2): Mod(0, x^3 + 21)
rnfeltup(L,x^2): error("inconsistent variables in nf_to_scalar_or_basis, x !
= y.")
rnfeltup(M,x^2): error("inconsistent variables in nf_to_scalar_or_basis, x !
= y.")
rnfeltdown(L,x^2): Mod(y, y^3 - 21)
rnfeltdown(M,x^2): Mod(y^2, y^3 - 21)
rnfelttrace(L,x^2): Mod(2*y, y^3 - 21)
rnfelttrace(M,x^2): 0
rnfeltnorm(L,x^2): Mod(y^2, y^3 - 21)
rnfeltnorm(M,x^2): 0
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)
rnfalgtobasis(L,2): [2, 0]~
rnfalgtobasis(M,2): [2]~
rnfbasistoalg(L,2): Mod(2, x^2 + 1)
rnfbasistoalg(M,2): Mod(2, x)
rnfeltabstorel(L,2): 2
rnfeltabstorel(M,2): 2
rnfeltreltoabs(L,2): 2
rnfeltreltoabs(M,2): 2
rnfeltup(L,2): 2
rnfeltup(M,2): 2
rnfeltdown(L,2): 2
rnfeltdown(M,2): 2
rnfelttrace(L,2): 4
rnfelttrace(M,2): 2
rnfeltnorm(L,2): 4
rnfeltnorm(M,2): 2
rnfalgtobasis(L,1/2): [1/2, 0]~
rnfalgtobasis(M,1/2): [1/2]~
rnfbasistoalg(L,1/2): Mod(1/2, x^2 + 1)
rnfbasistoalg(M,1/2): Mod(1/2, x)
rnfeltabstorel(L,1/2): 1/2
rnfeltabstorel(M,1/2): 1/2
rnfeltreltoabs(L,1/2): 1/2
rnfeltreltoabs(M,1/2): 1/2
rnfeltup(L,1/2): 1/2
rnfeltup(M,1/2): 1/2
rnfeltdown(L,1/2): 1/2
rnfeltdown(M,1/2): 1/2
rnfelttrace(L,1/2): 1
rnfelttrace(M,1/2): 1/2
rnfeltnorm(L,1/2): 1/4
rnfeltnorm(M,1/2): 1/2
rnfalgtobasis(L,x + y): [-1, 1]~
rnfalgtobasis(M,x + y): [Mod(y, y^3 - 21)]~
rnfbasistoalg(L,x + y): Mod(x - 1, x^2 + 1)
rnfbasistoalg(M,x + y): Mod(Mod(y, y^3 - 21), x)
rnfeltabstorel(L,x + y): error("incorrect type in rnfeltabstorel [not in Q[X
]] (t_POL).")
rnfeltabstorel(M,x + y): error("incorrect type in rnfeltabstorel [not in Q[X
]] (t_POL).")
rnfeltreltoabs(L,x + y): Mod(x - 1, x^2 + 1)
rnfeltreltoabs(M,x + y): Mod(-x, x^3 + 21)
rnfeltup(L,x + y): error("inconsistent variables in nf_to_scalar_or_basis, x
 != y.")
rnfeltup(M,x + y): error("inconsistent variables in nf_to_scalar_or_basis, x
 != y.")
rnfeltdown(L,x + y): error("incorrect type in rnfeltabstorel [not in Q[X]] (
t_POL).")
rnfeltdown(M,x + y): error("incorrect type in rnfeltabstorel [not in Q[X]] (
t_POL).")
rnfelttrace(L,x + y): -2
rnfelttrace(M,x + y): Mod(y, y^3 - 21)
rnfeltnorm(L,x + y): 2
rnfeltnorm(M,x + y): Mod(y, y^3 - 21)
rnfalgtobasis(L,Mod(1/2, y + 1)): [1/2, 0]~
rnfalgtobasis(M,Mod(1/2, y + 1)): error("inconsistent moduli in rnfalgtobasi
s: y + 1 != y^3 - 21")
rnfbasistoalg(L,Mod(1/2, y + 1)): Mod(1/2, x^2 + 1)
rnfbasistoalg(M,Mod(1/2, y + 1)): error("inconsistent moduli in rnfbasistoal
g: y + 1 != y^3 - 21")
rnfeltabstorel(L,Mod(1/2, y + 1)): Mod(1/2, x^2 + 1)
rnfeltabstorel(M,Mod(1/2, y + 1)): error("inconsistent moduli in rnfeltabsto
rel: y + 1 != x^3 + 21")
rnfeltreltoabs(L,Mod(1/2, y + 1)): Mod(1/2, x^2 + 1)
rnfeltreltoabs(M,Mod(1/2, y + 1)): error("inconsistent moduli in rnfeltrelto
abs: y + 1 != y^3 - 21")
rnfeltup(L,Mod(1/2, y + 1)): 1/2
rnfeltup(M,Mod(1/2, y + 1)): error("inconsistent moduli in nf_to_scalar_or_b
asis: y + 1 != y^3 - 21")
rnfeltdown(L,Mod(1/2, y + 1)): 1/2
rnfeltdown(M,Mod(1/2, y + 1)): error("inconsistent moduli in rnfeltdown: y +
 1 != y^3 - 21")
rnfelttrace(L,Mod(1/2, y + 1)): 1
rnfelttrace(M,Mod(1/2, y + 1)): error("inconsistent moduli in rnfeltabstorel
: y + 1 != x^3 + 21")
rnfeltnorm(L,Mod(1/2, y + 1)): 1/4
rnfeltnorm(M,Mod(1/2, y + 1)): error("inconsistent moduli in rnfeltabstorel:
 y + 1 != x^3 + 21")
rnfalgtobasis(L,y): [Mod(-1, y + 1), 0]~
rnfalgtobasis(M,y): [Mod(y, y^3 - 21)]~
rnfbasistoalg(L,y): Mod(Mod(-1, y + 1), x^2 + 1)
rnfbasistoalg(M,y): Mod(Mod(y, y^3 - 21), x)
rnfeltabstorel(L,y): Mod(-1, x^2 + 1)
rnfeltabstorel(M,y): Mod(Mod(y, y^3 - 21), x)
rnfeltreltoabs(L,y): -1
rnfeltreltoabs(M,y): Mod(-x, x^3 + 21)
rnfeltup(L,y): -1
rnfeltup(M,y): Mod(-x, x^3 + 21)
rnfeltdown(L,y): -1
rnfeltdown(M,y): Mod(y, y^3 - 21)
rnfelttrace(L,y): -2
rnfelttrace(M,y): Mod(y, y^3 - 21)
rnfeltnorm(L,y): 1
rnfeltnorm(M,y): Mod(y, y^3 - 21)
rnfalgtobasis(L,Mod(1/2*x + 1, x^2 + 1)): [1, 1/2]~
rnfalgtobasis(M,Mod(1/2*x + 1, x^2 + 1)): error("inconsistent moduli in rnfa
lgtobasis: x^2 + 1 != y^3 - 21")
rnfbasistoalg(L,Mod(1/2*x + 1, x^2 + 1)): Mod(1/2*x + 1, x^2 + 1)
rnfbasistoalg(M,Mod(1/2*x + 1, x^2 + 1)): error("inconsistent moduli in rnfb
asistoalg: x^2 + 1 != y^3 - 21")
rnfeltabstorel(L,Mod(1/2*x + 1, x^2 + 1)): Mod(1/2*x + 1, x^2 + 1)
rnfeltabstorel(M,Mod(1/2*x + 1, x^2 + 1)): error("inconsistent moduli in rnf
eltabstorel: x^2 + 1 != x^3 + 21")
rnfeltreltoabs(L,Mod(1/2*x + 1, x^2 + 1)): Mod(1/2*x + 1, x^2 + 1)
rnfeltreltoabs(M,Mod(1/2*x + 1, x^2 + 1)): error("inconsistent moduli in rnf
eltreltoabs: x^2 + 1 != y^3 - 21")
rnfeltup(L,Mod(1/2*x + 1, x^2 + 1)): Mod(1/2*x + 1, x^2 + 1)
rnfeltup(M,Mod(1/2*x + 1, x^2 + 1)): error("inconsistent moduli in nf_to_sca
lar_or_basis: x^2 + 1 != y^3 - 21")
rnfeltdown(L,Mod(1/2*x + 1, x^2 + 1)): error("domain error in rnfeltdown: el
ement not in the base field")
rnfeltdown(M,Mod(1/2*x + 1, x^2 + 1)): error("inconsistent moduli in rnfeltd
own: x^2 + 1 != y^3 - 21")
rnfelttrace(L,Mod(1/2*x + 1, x^2 + 1)): 2
rnfelttrace(M,Mod(1/2*x + 1, x^2 + 1)): error("inconsistent moduli in rnfelt
abstorel: x^2 + 1 != x^3 + 21")
rnfeltnorm(L,Mod(1/2*x + 1, x^2 + 1)): 5/4
rnfeltnorm(M,Mod(1/2*x + 1, x^2 + 1)): error("inconsistent moduli in rnfelta
bstorel: x^2 + 1 != x^3 + 21")
rnfalgtobasis(L,Mod(x, x^2 + 1)): [0, 1]~
rnfalgtobasis(M,Mod(x, x^2 + 1)): error("inconsistent moduli in rnfalgtobasi
s: x^2 + 1 != y^3 - 21")
rnfbasistoalg(L,Mod(x, x^2 + 1)): Mod(x, x^2 + 1)
rnfbasistoalg(M,Mod(x, x^2 + 1)): error("inconsistent moduli in rnfbasistoal
g: x^2 + 1 != y^3 - 21")
rnfeltabstorel(L,Mod(x, x^2 + 1)): Mod(x, x^2 + 1)
rnfeltabstorel(M,Mod(x, x^2 + 1)): error("inconsistent moduli in rnfeltabsto
rel: x^2 + 1 != x^3 + 21")
rnfeltreltoabs(L,Mod(x, x^2 + 1)): Mod(x, x^2 + 1)
rnfeltreltoabs(M,Mod(x, x^2 + 1)): error("inconsistent moduli in rnfeltrelto
abs: x^2 + 1 != y^3 - 21")
rnfeltup(L,Mod(x, x^2 + 1)): Mod(x, x^2 + 1)
rnfeltup(M,Mod(x, x^2 + 1)): error("inconsistent moduli in nf_to_scalar_or_b
asis: x^2 + 1 != y^3 - 21")
rnfeltdown(L,Mod(x, x^2 + 1)): error("domain error in rnfeltdown: element no
t in the base field")
rnfeltdown(M,Mod(x, x^2 + 1)): error("inconsistent moduli in rnfeltdown: x^2
 + 1 != y^3 - 21")
rnfelttrace(L,Mod(x, x^2 + 1)): 0
rnfelttrace(M,Mod(x, x^2 + 1)): error("inconsistent moduli in rnfeltabstorel
: x^2 + 1 != x^3 + 21")
rnfeltnorm(L,Mod(x, x^2 + 1)): 1
rnfeltnorm(M,Mod(x, x^2 + 1)): error("inconsistent moduli in rnfeltabstorel:
 x^2 + 1 != x^3 + 21")
rnfalgtobasis(L,Mod(x, x^2 + 1)): [0, 1]~
rnfalgtobasis(M,Mod(x, x^2 + 1)): error("inconsistent moduli in rnfalgtobasi
s: x^2 + 1 != y^3 - 21")
rnfbasistoalg(L,Mod(x, x^2 + 1)): Mod(x, x^2 + 1)
rnfbasistoalg(M,Mod(x, x^2 + 1)): error("inconsistent moduli in rnfbasistoal
g: x^2 + 1 != y^3 - 21")
rnfeltabstorel(L,Mod(x, x^2 + 1)): Mod(x, x^2 + 1)
rnfeltabstorel(M,Mod(x, x^2 + 1)): error("inconsistent moduli in rnfeltabsto
rel: x^2 + 1 != x^3 + 21")
rnfeltreltoabs(L,Mod(x, x^2 + 1)): Mod(x, x^2 + 1)
rnfeltreltoabs(M,Mod(x, x^2 + 1)): error("inconsistent moduli in rnfeltrelto
abs: x^2 + 1 != y^3 - 21")
rnfeltup(L,Mod(x, x^2 + 1)): Mod(x, x^2 + 1)
rnfeltup(M,Mod(x, x^2 + 1)): error("inconsistent moduli in nf_to_scalar_or_b
asis: x^2 + 1 != y^3 - 21")
rnfeltdown(L,Mod(x, x^2 + 1)): error("domain error in rnfeltdown: element no
t in the base field")
rnfeltdown(M,Mod(x, x^2 + 1)): error("inconsistent moduli in rnfeltdown: x^2
 + 1 != y^3 - 21")
rnfelttrace(L,Mod(x, x^2 + 1)): 0
rnfelttrace(M,Mod(x, x^2 + 1)): error("inconsistent moduli in rnfeltabstorel
: x^2 + 1 != x^3 + 21")
rnfeltnorm(L,Mod(x, x^2 + 1)): 1
rnfeltnorm(M,Mod(x, x^2 + 1)): error("inconsistent moduli in rnfeltabstorel:
 x^2 + 1 != x^3 + 21")
rnfalgtobasis(L,Mod(x + 1/2*y, x^2 - y)): error("inconsistent moduli in rnfa
lgtobasis: x^2 - y != y + 1")
rnfalgtobasis(M,Mod(x + 1/2*y, x^2 - y)): error("inconsistent moduli in rnfa
lgtobasis: x^2 - y != y^3 - 21")
rnfbasistoalg(L,Mod(x + 1/2*y, x^2 - y)): error("inconsistent moduli in rnfb
asistoalg: x^2 - y != y + 1")
rnfbasistoalg(M,Mod(x + 1/2*y, x^2 - y)): error("inconsistent moduli in rnfb
asistoalg: x^2 - y != y^3 - 21")
rnfeltabstorel(L,Mod(x + 1/2*y, x^2 - y)): error("inconsistent moduli in rnf
eltabstorel: x^2 - y != x^2 + 1")
rnfeltabstorel(M,Mod(x + 1/2*y, x^2 - y)): error("inconsistent moduli in rnf
eltabstorel: x^2 - y != x^3 + 21")
rnfeltreltoabs(L,Mod(x + 1/2*y, x^2 - y)): error("inconsistent moduli in rnf
eltreltoabs: x^2 - y != y + 1")
rnfeltreltoabs(M,Mod(x + 1/2*y, x^2 - y)): error("inconsistent moduli in rnf
eltreltoabs: x^2 - y != y^3 - 21")
rnfeltup(L,Mod(x + 1/2*y, x^2 - y)): error("inconsistent moduli in nf_to_sca
lar_or_basis: x^2 - y != y + 1")
rnfeltup(M,Mod(x + 1/2*y, x^2 - y)): error("inconsistent moduli in nf_to_sca
lar_or_basis: x^2 - y != y^3 - 21")
rnfeltdown(L,Mod(x + 1/2*y, x^2 - y)): error("inconsistent moduli in rnfeltd
own: x^2 - y != y + 1")
rnfeltdown(M,Mod(x + 1/2*y, x^2 - y)): error("inconsistent moduli in rnfeltd
own: x^2 - y != y^3 - 21")
rnfelttrace(L,Mod(x + 1/2*y, x^2 - y)): error("inconsistent moduli in rnfelt
abstorel: x^2 - y != x^2 + 1")
rnfelttrace(M,Mod(x + 1/2*y, x^2 - y)): error("inconsistent moduli in rnfelt
abstorel: x^2 - y != x^3 + 21")
rnfeltnorm(L,Mod(x + 1/2*y, x^2 - y)): error("inconsistent moduli in rnfelta
bstorel: x^2 - y != x^2 + 1")
rnfeltnorm(M,Mod(x + 1/2*y, x^2 - y)): error("inconsistent moduli in rnfelta
bstorel: x^2 - y != x^3 + 21")
rnfalgtobasis(L,x): [0, 1]~
rnfalgtobasis(M,x): [0]~
rnfbasistoalg(L,x): Mod(x, x^2 + 1)
rnfbasistoalg(M,x): Mod(0, x)
rnfeltabstorel(L,x): Mod(x, x^2 + 1)
rnfeltabstorel(M,x): Mod(Mod(-y, y^3 - 21), x)
rnfeltreltoabs(L,x): Mod(x, x^2 + 1)
rnfeltreltoabs(M,x): Mod(0, x^3 + 21)
rnfeltup(L,x): error("inconsistent variables in nf_to_scalar_or_basis, x != 
y.")
rnfeltup(M,x): error("inconsistent variables in nf_to_scalar_or_basis, x != 
y.")
rnfeltdown(L,x): error("domain error in rnfeltdown: element not in the base 
field")
rnfeltdown(M,x): Mod(-y, y^3 - 21)
rnfelttrace(L,x): 0
rnfelttrace(M,x): 0
rnfeltnorm(L,x): 1
rnfeltnorm(M,x): 0
rnfalgtobasis(L,[1]~): error("inconsistent dimensions in rnfalgtobasis.")
rnfalgtobasis(M,[1]~): [1]~
rnfbasistoalg(L,[1]~): error("inconsistent operation 'RgV_RgC_mul' t_VEC (2 
elts) , t_COL (1 elts).")
rnfbasistoalg(M,[1]~): Mod(1, x)
rnfeltabstorel(L,[1]~): error("incorrect type in rnfeltabstorel, apply nfini
t(rnf) (t_COL).")
rnfeltabstorel(M,[1]~): error("incorrect type in rnfeltabstorel, apply nfini
t(rnf) (t_COL).")
rnfeltreltoabs(L,[1]~): error("incorrect type in rnfeltreltoabs (t_COL).")
rnfeltreltoabs(M,[1]~): error("incorrect type in rnfeltreltoabs (t_COL).")
rnfeltup(L,[1]~): 1
rnfeltup(M,[1]~): error("incorrect type in nf_to_scalar_or_basis (t_COL).")
rnfeltdown(L,[1]~): 1
rnfeltdown(M,[1]~): error("incorrect type in rnfeltdown (t_COL).")
rnfelttrace(L,[1]~): error("incorrect type in rnfeltabstorel, apply nfinit(r
nf) (t_COL).")
rnfelttrace(M,[1]~): error("incorrect type in rnfeltabstorel, apply nfinit(r
nf) (t_COL).")
rnfeltnorm(L,[1]~): error("incorrect type in rnfeltabstorel, apply nfinit(rn
f) (t_COL).")
rnfeltnorm(M,[1]~): error("incorrect type in rnfeltabstorel, apply nfinit(rn
f) (t_COL).")
rnfalgtobasis(L,[1, 2]~): [1, 2]~
rnfalgtobasis(M,[1, 2]~): error("inconsistent dimensions in rnfalgtobasis.")
rnfbasistoalg(L,[1, 2]~): Mod(2*x + 1, x^2 + 1)
rnfbasistoalg(M,[1, 2]~): error("inconsistent operation 'RgV_RgC_mul' t_VEC 
(1 elts) , t_COL (2 elts).")
rnfeltabstorel(L,[1, 2]~): error("incorrect type in rnfeltabstorel, apply nf
init(rnf) (t_COL).")
rnfeltabstorel(M,[1, 2]~): error("incorrect type in rnfeltabstorel, apply nf
init(rnf) (t_COL).")
rnfeltreltoabs(L,[1, 2]~): error("incorrect type in rnfeltreltoabs (t_COL)."
)
rnfeltreltoabs(M,[1, 2]~): error("incorrect type in rnfeltreltoabs (t_COL)."
)
rnfeltup(L,[1, 2]~): error("incorrect type in nf_to_scalar_or_basis (t_COL).
")
rnfeltup(M,[1, 2]~): error("incorrect type in nf_to_scalar_or_basis (t_COL).
")
rnfeltdown(L,[1, 2]~): error("incorrect type in rnfeltdown (t_COL).")
rnfeltdown(M,[1, 2]~): error("incorrect type in rnfeltdown (t_COL).")
rnfelttrace(L,[1, 2]~): error("incorrect type in rnfeltabstorel, apply nfini
t(rnf) (t_COL).")
rnfelttrace(M,[1, 2]~): error("incorrect type in rnfeltabstorel, apply nfini
t(rnf) (t_COL).")
rnfeltnorm(L,[1, 2]~): error("incorrect type in rnfeltabstorel, apply nfinit
(rnf) (t_COL).")
rnfeltnorm(M,[1, 2]~): error("incorrect type in rnfeltabstorel, apply nfinit
(rnf) (t_COL).")
rnfalgtobasis(L,[y]~): error("inconsistent dimensions in rnfalgtobasis.")
rnfalgtobasis(M,[y]~): [Mod(y, y^3 - 21)]~
rnfbasistoalg(L,[y]~): error("inconsistent operation 'RgV_RgC_mul' t_VEC (2 
elts) , t_COL (1 elts).")
rnfbasistoalg(M,[y]~): Mod(Mod(y, y^3 - 21), x)
rnfeltabstorel(L,[y]~): error("incorrect type in rnfeltabstorel, apply nfini
t(rnf) (t_COL).")
rnfeltabstorel(M,[y]~): error("incorrect type in rnfeltabstorel, apply nfini
t(rnf) (t_COL).")
rnfeltreltoabs(L,[y]~): error("incorrect type in rnfeltreltoabs (t_COL).")
rnfeltreltoabs(M,[y]~): error("incorrect type in rnfeltreltoabs (t_COL).")
rnfeltup(L,[y]~): Mod(y, x^2 + 1)
rnfeltup(M,[y]~): error("incorrect type in nf_to_scalar_or_basis (t_COL).")
rnfeltdown(L,[y]~): error("incorrect type in rnfeltdown (t_COL).")
rnfeltdown(M,[y]~): error("incorrect type in rnfeltdown (t_COL).")
rnfelttrace(L,[y]~): error("incorrect type in rnfeltabstorel, apply nfinit(r
nf) (t_COL).")
rnfelttrace(M,[y]~): error("incorrect type in rnfeltabstorel, apply nfinit(r
nf) (t_COL).")
rnfeltnorm(L,[y]~): error("incorrect type in rnfeltabstorel, apply nfinit(rn
f) (t_COL).")
rnfeltnorm(M,[y]~): error("incorrect type in rnfeltabstorel, apply nfinit(rn
f) (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 [fake prime ideal] (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 [fake prime ideal] (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, 127633; 0, 1, 0; 0, 0, 1], [0, 0, 0]], Mat(3)]
[[[1163, 141, 32; 0, 1, 0; 0, 0, 1], [1, 0, 0]], Mat(2)]
0
[[1, 0, 0, 0; 0, 1, 0, 0; 0, 0, 1, 0; 0, 0, 0, 1], []]
[[[36, 0; 0, 36], []], [[2, [2, 0]~, 1, 2, 1], 2; [3, [-1, 1]~, 2, 1, [-1, -
1; 1, -2]], 4]]
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, 318, 322, 1318/17; 0, 1, 0, 5/17; 0, 0, 1, 12/17; 0, 0, 0, 1/17], [25
/17, 12/17, -12/17, 16/17]~]
[1, -1]
[[12, 0, 0, 0; 0, 12, 4, 0; 0, 0, 4, 0; 0, 0, 0, 4], [6, 5, -1, 2]~]
  ***   Warning: new stack size = 12000000 (11.444 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: rnfdedekind(nf,x^2)
  ***                 ^-------------------
  *** rnfdedekind: domain error in rnfdedekind: issquarefree(pol) = 0
  ***   at top-level: rnfinit(nf,x^2-y/3)
  ***                 ^-------------------
  *** rnfinit: sorry, non integral polynomial in rnfallbase is not yet implemented.
  ***   at top-level: rnfconductor(nf,x^2)
  ***                 ^--------------------
  *** rnfconductor: incorrect type in checkbnf [please apply bnfinit()] (t_VEC).
  ***   at top-level: rnfconductor(nf,[x^2,1])
  ***                 ^------------------------
  *** rnfconductor: incorrect type in checkbnf [please apply bnfinit()] (t_VEC).
  ***   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: sorry, non integral polynomial in rnfallbase is not yet implemented.
  ***   at top-level: rnfpseudobasis(nf,x^2)
  ***                 ^----------------------
  *** rnfpseudobasis: domain error in rnfpseudobasis: issquarefree(pol) = 0
  ***   at top-level: rnfeltnorm(x,x)
  ***                 ^---------------
  *** rnfeltnorm: incorrect type in checkrnf (t_POL).
  ***   at top-level: rnfelttrace(x,x)
  ***                 ^----------------
  *** rnfelttrace: incorrect type in checkrnf (t_POL).
  ***   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).
[[13752104408392050085222299912837424016744346918215907754003059659430226886
5203518397679148347720654316386840367785157190137487454547848, 2959570140384
0008752126889275684782087998403235378132669994230963941569723600340025047099
92462649028358180476038782378726113404321956; 0, 371584220729649394547077712
6096031739262741319686634426034412234116662922714846511467163377330801518008
56981442689032724], [-177846162678347392861779010175300647931976968103167121
4616746896704286594334662045803530653683643332613227600515985901534558021, -
1756839977043712272060233380581107042236141123409211618384398509656714409036
54196479376831010271529801027728469404407277067209]~]
Total time spent: 1565
