x^2 + 10*x + 27
x^2 + 10/3*x + 3
x^2 + 10/a*x + 27/a^2
x^2 + 10*a*x + 27*a^2
[2, 1]
[X^2 + 10*X + 27, X^2 + 10*X + 27, 1, 1]
x^2 - 2*a*x + (a^2 - d^2)
3
2
0
2
3
3
1
3
4
2
3
1
0
2
2
2
2
2
(M)->my([F,B]=matfrobenius(M,2));if(M!=B^-1*F*B,error("matfrobenius:",M));F
Mat(1)
[0, -1; 1, 2]
[0, 0, 1; 1, 0, -3; 0, 1, 3]
[0, 0, 0, -1; 1, 0, 0, 4; 0, 1, 0, -6; 0, 0, 1, 4]
[0, 0, 0, 0, 1; 1, 0, 0, 0, -5; 0, 1, 0, 0, 10; 0, 0, 1, 0, -10; 0, 0, 0, 1,
 5]
[0, 0, 0, 0, 0, -1; 1, 0, 0, 0, 0, 6; 0, 1, 0, 0, 0, -15; 0, 0, 1, 0, 0, 20;
 0, 0, 0, 1, 0, -15; 0, 0, 0, 0, 1, 6]
[0, 0, 0, 0, 0, 0, 1; 1, 0, 0, 0, 0, 0, -7; 0, 1, 0, 0, 0, 0, 21; 0, 0, 1, 0
, 0, 0, -35; 0, 0, 0, 1, 0, 0, 35; 0, 0, 0, 0, 1, 0, -21; 0, 0, 0, 0, 0, 1, 
7]
[0, 0, 0, 0, 0, 0, 0, -1; 1, 0, 0, 0, 0, 0, 0, 8; 0, 1, 0, 0, 0, 0, 0, -28; 
0, 0, 1, 0, 0, 0, 0, 56; 0, 0, 0, 1, 0, 0, 0, -70; 0, 0, 0, 0, 1, 0, 0, 56; 
0, 0, 0, 0, 0, 1, 0, -28; 0, 0, 0, 0, 0, 0, 1, 8]
[0, 0, 0, 0, 0, 0, 0, 0, 1; 1, 0, 0, 0, 0, 0, 0, 0, -9; 0, 1, 0, 0, 0, 0, 0,
 0, 36; 0, 0, 1, 0, 0, 0, 0, 0, -84; 0, 0, 0, 1, 0, 0, 0, 0, 126; 0, 0, 0, 0
, 1, 0, 0, 0, -126; 0, 0, 0, 0, 0, 1, 0, 0, 84; 0, 0, 0, 0, 0, 0, 1, 0, -36;
 0, 0, 0, 0, 0, 0, 0, 1, 9]
[0, 0, 0, 0, 0, 0, 0, 0, 0, -1; 1, 0, 0, 0, 0, 0, 0, 0, 0, 10; 0, 1, 0, 0, 0
, 0, 0, 0, 0, -45; 0, 0, 1, 0, 0, 0, 0, 0, 0, 120; 0, 0, 0, 1, 0, 0, 0, 0, 0
, -210; 0, 0, 0, 0, 1, 0, 0, 0, 0, 252; 0, 0, 0, 0, 0, 1, 0, 0, 0, -210; 0, 
0, 0, 0, 0, 0, 1, 0, 0, 120; 0, 0, 0, 0, 0, 0, 0, 1, 0, -45; 0, 0, 0, 0, 0, 
0, 0, 0, 1, 10]
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1; 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, -11; 0, 1, 0
, 0, 0, 0, 0, 0, 0, 0, 55; 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, -165; 0, 0, 0, 1, 0
, 0, 0, 0, 0, 0, 330; 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, -462; 0, 0, 0, 0, 0, 1, 
0, 0, 0, 0, 462; 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, -330; 0, 0, 0, 0, 0, 0, 0, 1,
 0, 0, 165; 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, -55; 0, 0, 0, 0, 0, 0, 0, 0, 0, 1,
 11]
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1; 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 12; 0
, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, -66; 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 220; 0
, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, -495; 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 792; 
0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, -924; 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 792;
 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, -495; 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 220
; 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, -66; 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 12]
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1; 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 
-13; 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 78; 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0
, 0, -286; 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 715; 0, 0, 0, 0, 1, 0, 0, 0, 
0, 0, 0, 0, -1287; 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1716; 0, 0, 0, 0, 0, 
0, 1, 0, 0, 0, 0, 0, -1716; 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1287; 0, 0, 
0, 0, 0, 0, 0, 0, 1, 0, 0, 0, -715; 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 286;
 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, -78; 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1
, 13]
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1; 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
 0, 0, 14; 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -91; 0, 0, 1, 0, 0, 0, 0, 
0, 0, 0, 0, 0, 0, 364; 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1001; 0, 0, 0
, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 2002; 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0,
 -3003; 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 3432; 0, 0, 0, 0, 0, 0, 0, 1,
 0, 0, 0, 0, 0, -3003; 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 2002; 0, 0, 0,
 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, -1001; 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0,
 364; 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, -91; 0, 0, 0, 0, 0, 0, 0, 0, 0,
 0, 0, 0, 1, 14]
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1; 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 
0, 0, 0, 0, -15; 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 105; 0, 0, 1, 0, 
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -455; 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0
, 1365; 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3003; 0, 0, 0, 0, 0, 1, 0
, 0, 0, 0, 0, 0, 0, 0, 5005; 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, -6435
; 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 6435; 0, 0, 0, 0, 0, 0, 0, 0, 1,
 0, 0, 0, 0, 0, -5005; 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 3003; 0, 0,
 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, -1365; 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
 1, 0, 0, 455; 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, -105; 0, 0, 0, 0, 0
, 0, 0, 0, 0, 0, 0, 0, 0, 1, 15]
[0, -1; 1, 2]
[0, 0, 1; 1, 0, -3; 0, 1, 3]
[0, 0, 0, -1; 1, 0, 0, 4; 0, 1, 0, -6; 0, 0, 1, 4]
[0, 0, 0, 0, 1; 1, 0, 0, 0, -5; 0, 1, 0, 0, 10; 0, 0, 1, 0, -10; 0, 0, 0, 1,
 5]
[0, 0, 0, 0, 0, -1; 1, 0, 0, 0, 0, 6; 0, 1, 0, 0, 0, -15; 0, 0, 1, 0, 0, 20;
 0, 0, 0, 1, 0, -15; 0, 0, 0, 0, 1, 6]
[0, 0, 0, 0, 0, 0, 1; 1, 0, 0, 0, 0, 0, -7; 0, 1, 0, 0, 0, 0, 21; 0, 0, 1, 0
, 0, 0, -35; 0, 0, 0, 1, 0, 0, 35; 0, 0, 0, 0, 1, 0, -21; 0, 0, 0, 0, 0, 1, 
7]
[0, 0, 0, 0, 0, 0, 0, -1; 1, 0, 0, 0, 0, 0, 0, 8; 0, 1, 0, 0, 0, 0, 0, -28; 
0, 0, 1, 0, 0, 0, 0, 56; 0, 0, 0, 1, 0, 0, 0, -70; 0, 0, 0, 0, 1, 0, 0, 56; 
0, 0, 0, 0, 0, 1, 0, -28; 0, 0, 0, 0, 0, 0, 1, 8]
[0, 0, 0, 0, 0, 0, 0, 0, 1; 1, 0, 0, 0, 0, 0, 0, 0, -9; 0, 1, 0, 0, 0, 0, 0,
 0, 36; 0, 0, 1, 0, 0, 0, 0, 0, -84; 0, 0, 0, 1, 0, 0, 0, 0, 126; 0, 0, 0, 0
, 1, 0, 0, 0, -126; 0, 0, 0, 0, 0, 1, 0, 0, 84; 0, 0, 0, 0, 0, 0, 1, 0, -36;
 0, 0, 0, 0, 0, 0, 0, 1, 9]
[0, 0, 0, 0, 0, 0, 0, 0, 0, -1; 1, 0, 0, 0, 0, 0, 0, 0, 0, 10; 0, 1, 0, 0, 0
, 0, 0, 0, 0, -45; 0, 0, 1, 0, 0, 0, 0, 0, 0, 120; 0, 0, 0, 1, 0, 0, 0, 0, 0
, -210; 0, 0, 0, 0, 1, 0, 0, 0, 0, 252; 0, 0, 0, 0, 0, 1, 0, 0, 0, -210; 0, 
0, 0, 0, 0, 0, 1, 0, 0, 120; 0, 0, 0, 0, 0, 0, 0, 1, 0, -45; 0, 0, 0, 0, 0, 
0, 0, 0, 1, 10]
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1; 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, -11; 0, 1, 0
, 0, 0, 0, 0, 0, 0, 0, 55; 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, -165; 0, 0, 0, 1, 0
, 0, 0, 0, 0, 0, 330; 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, -462; 0, 0, 0, 0, 0, 1, 
0, 0, 0, 0, 462; 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, -330; 0, 0, 0, 0, 0, 0, 0, 1,
 0, 0, 165; 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, -55; 0, 0, 0, 0, 0, 0, 0, 0, 0, 1,
 11]
Mat(1)
[0, -1/12; 1, 4/3]
[0, 0, 1/2160; 1, 0, -127/720; 0, 1, 23/15]
[0, 0, 0, -1/6048000; 1, 0, 0, 41/23625; 0, 1, 0, -3341/12600; 0, 0, 1, 176/
105]
[0, 0, 0, 0, 1/266716800000; 1, 0, 0, 0, -61501/53343360000; 0, 1, 0, 0, 852
401/222264000; 0, 0, 1, 0, -735781/2116800; 0, 0, 0, 1, 563/315]
[0, 0, 0, 0, 0, -1/186313420339200000; 1, 0, 0, 0, 0, 3529/70573265280000; 0
, 1, 0, 0, 0, -10828423/2688505344000; 0, 0, 1, 0, 0, 18344719/2750517000; 0
, 0, 0, 1, 0, -14806217/34927200; 0, 0, 0, 0, 1, 6508/3465]
[0, 0, 0, 0, 0, 0, 1/2067909047925770649600000; 1, 0, 0, 0, 0, 0, -8237351/5
9083115655022018560000; 0, 1, 0, 0, 0, 0, 509709971/1758426061161369600; 0, 
0, 1, 0, 0, 0, -126867217979/12687056718336000; 0, 0, 0, 1, 0, 0, 2804123885
/276900047424; 0, 0, 0, 0, 1, 0, -197708437/399567168; 0, 0, 0, 0, 0, 1, 880
69/45045]
[0, 0, 0, 0, 0, 0, 0, -1/365356847125734485878112256000000; 1, 0, 0, 0, 0, 0
, 0, 442037/17839689801061254193267200000; 0, 1, 0, 0, 0, 0, 0, -12581527408
69/906142974022158943150080000; 0, 0, 1, 0, 0, 0, 0, 725120398661/6688626213
66980040000; 0, 0, 0, 1, 0, 0, 0, -3571285252517/176488178798131200; 0, 0, 0
, 0, 1, 0, 0, 85934726089/6093243231075; 0, 0, 0, 0, 0, 1, 0, -6070382321/10
821610800; 0, 0, 0, 0, 0, 0, 1, 91072/45045]
[0, x, x]
[0, x^2 + x, 1]
[0, 0]
[[1, 0, 0; 0, -2, 1], [;], [;]]
[]
[matrix(0,1), [1, 0; 0, -2; 0, 1], matrix(0,2)]
[Mod(1, 3)*x^4 + Mod(2, 3)*x + Mod(2, 3), 1, 1]

[0 0 0 0 0 0 0 0  0]

[1 0 0 0 0 0 0 0 -8]

[0 1 0 0 0 0 0 0  2]

[0 0 1 0 0 0 0 0  4]

[0 0 0 1 0 0 0 0  5]

[0 0 0 0 1 0 0 0  4]

[0 0 0 0 0 1 0 0 13]

[0 0 0 0 0 0 1 0  5]

[0 0 0 0 0 0 0 1  2]

x^9 - 2*x^8 - 5*x^7 - 13*x^6 - 4*x^5 - 5*x^4 - 4*x^3 - 2*x^2 + 8*x
[[0, 0, 0, 1; 1, 9, -27, 0; 0, 1, 0, 0], [-1; 1], [0; 0; 3]]
3
[[0, 0, 0, 1; 1, 9, -27, 0; 0, 1, 0, 0; 0, 0, 1, 0], [-1, 1; 1, 0], [0, 0; 0
, 0; 3, 0; 0, 1]]
3
[64, 32, 32, 32, 32, 16, 16, 16, 16, 16, 16, 16, 16, 8, 8, 8, 8, 8, 8, 8, 8,
 8, 8, 8, 8, 8, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 2, 2, 1, 1, 
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1
, 1, 1, 1, 1, 1, 1]
  ***   Warning: new stack size = 88000000 (83.923 Mbytes).
1
Total time spent: 14194
