
#0
  4,   1,   1,   1
  1,   5,   3,  -1
 -1,  -2,   1,  -1
 -1,  -1,  -1,   2

extention = []
  3,   1,   0,   0
  0,   3,   1,   0
  0,   0,   3,   1
  0,   0,   0,   3

P =
112/25, 32/25, 16/5,   0
64/25, 16/25, 48/25,   0
32/25,   0, 16/25,   0
16/25,   0,   0, 16/25

P^-1 =
25/16, -25/8, 25/16,   0
25/8, -75/16, -25/16,   0
-25/8, 25/4, -25/16,   0
-25/16, 25/8, -25/16, 25/16


#0
  4,   1,   1,   1
  1,   5,   3,  -1
 -1,  -2,   1,  -1
 -1,  -1,  -1,   2

[1, 1, 1, x^4 - 12x^3 + 54x^2 - 108x + 81]

  1,   0,   0,   0
  0,   1,   0,   0
  0,   0,   1,   0
  0,   0,   0, x^4 - 12x^3 + 54x^2 - 108x + 81

[(x - 3)^4, [3, 3, 3, 3], []]
  3,   1,   0,   0
  0,   3,   1,   0
  0,   0,   3,   1
  0,   0,   0,   3

#1
 -3,  -3,   4,   2
  5,   1,  -4,  -6
  4,  -1,  -2,  -5
 -5,  -3,   4,   4

[1, 1, 1, x^4 - 8x^2 + 16]

  1,   0,   0,   0
  0,   1,   0,   0
  0,   0,   1,   0
  0,   0,   0, x^4 - 8x^2 + 16

[(x - 2)^2(x + 2)^2, [2, 2, -2, -2], []]
  2,   1,   0,   0
  0,   2,   0,   0
  0,   0,  -2,   1
  0,   0,   0,  -2

#2
  3,  -1,   3
 -1,   3,   3
  1,  -1,   5

[1, 1, x^3 - 11x^2 + 38x - 40]

  1,   0,   0
  0,   1,   0
  0,   0, x^3 - 11x^2 + 38x - 40

[(x - 5)(x - 4)(x - 2), [5, 4, 2], []]
  5,   0,   0
  0,   4,   0
  0,   0,   2

#3
 -1,   1,   2,  -1
 -5,   3,   4,  -2
  3,  -1,   0,   1
  5,  -2,  -2,   3

[1, 1, 1, x^4 - 5x^3 + 9x^2 - 7x + 2]

  1,   0,   0,   0
  0,   1,   0,   0
  0,   0,   1,   0
  0,   0,   0, x^4 - 5x^3 + 9x^2 - 7x + 2

[(x - 2)(x - 1)^3, [2, 1, 1, 1], []]
  2,   0,   0,   0
  0,   1,   1,   0
  0,   0,   1,   1
  0,   0,   0,   1

#4
  1,   2,   0,   0
  0,   1,   2,   0
  0,   0,   1,   2
  0,   0,   0,   1

[1, 1, 1, x^4 - 4x^3 + 6x^2 - 4x + 1]

  1,   0,   0,   0
  0,   1,   0,   0
  0,   0,   1,   0
  0,   0,   0, x^4 - 4x^3 + 6x^2 - 4x + 1

[(x - 1)^4, [1, 1, 1, 1], []]
  1,   1,   0,   0
  0,   1,   1,   0
  0,   0,   1,   1
  0,   0,   0,   1

#5
  3,   0,   2,   1
  0,   3,   0,   2
  0,   0,   3,   0
  0,   0,   0,   3

[1, 1, x^2 - 6x + 9, x^2 - 6x + 9]

  1,   0,   0,   0
  0,   1,   0,   0
  0,   0, x^2 - 6x + 9,   0
  0,   0,   0, x^2 - 6x + 9

[(x - 3)^2, [3, 3], []]
  3,   1,   0,   0
  0,   3,   0,   0
  0,   0,   3,   1
  0,   0,   0,   3

#6
  1,   0,   0,   0
  2,   1,   0,   0
  0,   2,   1,   0
  0,   0,   2,   1

[1, 1, 1, x^4 - 4x^3 + 6x^2 - 4x + 1]

  1,   0,   0,   0
  0,   1,   0,   0
  0,   0,   1,   0
  0,   0,   0, x^4 - 4x^3 + 6x^2 - 4x + 1

[(x - 1)^4, [1, 1, 1, 1], []]
  1,   1,   0,   0
  0,   1,   1,   0
  0,   0,   1,   1
  0,   0,   0,   1

#7
  2,   0,   0,   0
  0,   2,   0,   0
  0,   0,   2,   0
  5,   0,   0,   2

[1, x - 2, x - 2, x^2 - 4x + 4]

  1,   0,   0,   0
  0, x - 2,   0,   0
  0,   0, x - 2,   0
  0,   0,   0, x^2 - 4x + 4

[(x - 2)^2, [2, 2], []]
  2,   0,   0,   0
  0,   2,   0,   0
  0,   0,   2,   1
  0,   0,   0,   2

#8
  0,   0,   8
  1,   0,   4
  0,   1,  -2

[1, 1, x^3 + 2x^2 - 4x - 8]

  1,   0,   0
  0,   1,   0
  0,   0, x^3 + 2x^2 - 4x - 8

[(x - 2)(x + 2)^2, [2, -2, -2], []]
  2,   0,   0
  0,  -2,   1
  0,   0,  -2

#9
  1,   1,   0
  1,   1,   1
  0,   1,   1

[1, 1, x^3 - 3x^2 + x + 1]

  1,   0,   0
  0,   1,   0
  0,   0, x^3 - 3x^2 + x + 1

[(x - 1)(x - a)(x + a - 2), [1, a, -a + 2], [a]]
  1,   0,   0
  0,   a,   0
  0,   0, -a + 2

#10
  1,   0,   8
  1,   1,   4
  0,   1,  -2

[1, 1, x^3 - 7x - 2]

  1,   0,   0
  0,   1,   0
  0,   0, x^3 - 7x - 2

[(x - a)(x - b)(x + b + a), [a, b, -b - a], [a, b]]
  a,   0,   0
  0,   b,   0
  0,   0, -b - a

#11
  0,   0,   1,   0
  1,   1,   1,   1
  1,   1,   1,   1
  0,   1,   1,   1

[1, 1, 1, x^4 - 3x^3 - x^2 + x]

  1,   0,   0,   0
  0,   1,   0,   0
  0,   0,   1,   0
  0,   0,   0, x^4 - 3x^3 - x^2 + x

[(x)(x - a)(x - b)(x + b + a - 3), [0, a, b, -b - a + 3], [a, b]]
  0,   0,   0,   0
  0,   a,   0,   0
  0,   0,   b,   0
  0,   0,   0, -b - a + 3

