]>
gitweb.michael.orlitzky.com - sage.d.git/blob - mjo/eja/eja_cache.py
84983211c47a95222e39bf988094d1ca176c71ee
2 Cached characteristic polynomial coefficients for a few of the
3 example algebras. These take a long time to compute, so it makes more
4 sense to cache them and then only test that the cached values are
5 correct every once in a while.
7 The function used to turn SageMath's output into the appropriate input
8 can be found in the eja_utils module.
11 def quaternion_hermitian_eja_coeffs(J
):
12 X
= J
.coordinate_polynomial_ring().gens()
14 if J
.dimension() == 1: # n == 1
18 elif J
.dimension() == 6: # n == 2
19 a0
= -X
[1]**2 - X
[2]**2 - X
[3]**2 - X
[4]**2 + X
[0]*X
[5]
23 elif J
.dimension() == 15: # n == 3
24 a0
= ( X
[5]*X
[6]**2 + X
[5]*X
[7]**2 + X
[5]*X
[8]**2 + X
[5]*X
[9]**2 -
25 2*X
[1]*X
[6]*X
[10] - 2*X
[2]*X
[7]*X
[10] - 2*X
[3]*X
[8]*X
[10] -
26 2*X
[4]*X
[9]*X
[10] + X
[0]*X
[10]**2 + 2*X
[2]*X
[6]*X
[11] -
27 2*X
[1]*X
[7]*X
[11] + 2*X
[4]*X
[8]*X
[11] - 2*X
[3]*X
[9]*X
[11] +
28 X
[0]*X
[11]**2 + 2*X
[3]*X
[6]*X
[12] - 2*X
[4]*X
[7]*X
[12] -
29 2*X
[1]*X
[8]*X
[12] + 2*X
[2]*X
[9]*X
[12] + X
[0]*X
[12]**2 +
30 2*X
[4]*X
[6]*X
[13] + 2*X
[3]*X
[7]*X
[13] - 2*X
[2]*X
[8]*X
[13] -
31 2*X
[1]*X
[9]*X
[13] + X
[0]*X
[13]**2 + X
[1]**2*X
[14] +
32 X
[2]**2*X
[14] + X
[3]**2*X
[14] + X
[4]**2*X
[14] -
34 a1
= ( -X
[1]**2 - X
[2]**2 - X
[3]**2 - X
[4]**2 + X
[0]*X
[5] -
35 X
[6]**2 - X
[7]**2 - X
[8]**2 - X
[9]**2 - X
[10]**2 -
36 X
[11]**2 - X
[12]**2 - X
[13]**2 + X
[0]*X
[14] + X
[5]*X
[14] )
38 a2
= -X
[0] - X
[5] - X
[14]
45 def octonion_hermitian_eja_coeffs(J
):
46 X
= J
.coordinate_polynomial_ring().gens()
48 if J
.dimension() == 1: # n == 1
52 elif J
.dimension() == 10: # n == 2
53 a0
= ( -X
[1]**2 - X
[2]**2 - X
[3]**2 - X
[4]**2 - X
[5]**2 -
54 X
[6]**2 - X
[7]**2 - X
[8]**2 + X
[0]*X
[9] )
58 elif J
.dimension() == 27: # n == 3
59 a0
= ( X
[9]*X
[10]**2 + X
[9]*X
[11]**2 + X
[9]*X
[12]**2 + X
[9]*X
[13]**2 +
60 X
[9]*X
[14]**2 + X
[9]*X
[15]**2 + X
[9]*X
[16]**2 + X
[9]*X
[17]**2 -
61 2*X
[1]*X
[10]*X
[18] - 2*X
[2]*X
[11]*X
[18] - 2*X
[3]*X
[12]*X
[18] -
62 2*X
[4]*X
[13]*X
[18] - 2*X
[5]*X
[14]*X
[18] - 2*X
[6]*X
[15]*X
[18] -
63 2*X
[7]*X
[16]*X
[18] - 2*X
[8]*X
[17]*X
[18] + X
[0]*X
[18]**2 +
64 2*X
[2]*X
[10]*X
[19] - 2*X
[1]*X
[11]*X
[19] + 2*X
[4]*X
[12]*X
[19] -
65 2*X
[3]*X
[13]*X
[19] + 2*X
[6]*X
[14]*X
[19] - 2*X
[5]*X
[15]*X
[19] -
66 2*X
[8]*X
[16]*X
[19] + 2*X
[7]*X
[17]*X
[19] + X
[0]*X
[19]**2 +
67 2*X
[3]*X
[10]*X
[20] - 2*X
[4]*X
[11]*X
[20] - 2*X
[1]*X
[12]*X
[20] +
68 2*X
[2]*X
[13]*X
[20] + 2*X
[7]*X
[14]*X
[20] + 2*X
[8]*X
[15]*X
[20] -
69 2*X
[5]*X
[16]*X
[20] - 2*X
[6]*X
[17]*X
[20] + X
[0]*X
[20]**2 +
70 2*X
[4]*X
[10]*X
[21] + 2*X
[3]*X
[11]*X
[21] - 2*X
[2]*X
[12]*X
[21] -
71 2*X
[1]*X
[13]*X
[21] + 2*X
[8]*X
[14]*X
[21] - 2*X
[7]*X
[15]*X
[21] +
72 2*X
[6]*X
[16]*X
[21] - 2*X
[5]*X
[17]*X
[21] + X
[0]*X
[21]**2 +
73 2*X
[5]*X
[10]*X
[22] - 2*X
[6]*X
[11]*X
[22] - 2*X
[7]*X
[12]*X
[22] -
74 2*X
[8]*X
[13]*X
[22] - 2*X
[1]*X
[14]*X
[22] + 2*X
[2]*X
[15]*X
[22] +
75 2*X
[3]*X
[16]*X
[22] + 2*X
[4]*X
[17]*X
[22] + X
[0]*X
[22]**2 +
76 2*X
[6]*X
[10]*X
[23] + 2*X
[5]*X
[11]*X
[23] - 2*X
[8]*X
[12]*X
[23] +
77 2*X
[7]*X
[13]*X
[23] - 2*X
[2]*X
[14]*X
[23] - 2*X
[1]*X
[15]*X
[23] -
78 2*X
[4]*X
[16]*X
[23] + 2*X
[3]*X
[17]*X
[23] + X
[0]*X
[23]**2 +
79 2*X
[7]*X
[10]*X
[24] + 2*X
[8]*X
[11]*X
[24] + 2*X
[5]*X
[12]*X
[24] -
80 2*X
[6]*X
[13]*X
[24] - 2*X
[3]*X
[14]*X
[24] + 2*X
[4]*X
[15]*X
[24] -
81 2*X
[1]*X
[16]*X
[24] - 2*X
[2]*X
[17]*X
[24] + X
[0]*X
[24]**2 +
82 2*X
[8]*X
[10]*X
[25] - 2*X
[7]*X
[11]*X
[25] + 2*X
[6]*X
[12]*X
[25] +
83 2*X
[5]*X
[13]*X
[25] - 2*X
[4]*X
[14]*X
[25] - 2*X
[3]*X
[15]*X
[25] +
84 2*X
[2]*X
[16]*X
[25] - 2*X
[1]*X
[17]*X
[25] + X
[0]*X
[25]**2 +
85 X
[1]**2*X
[26] + X
[2]**2*X
[26] + X
[3]**2*X
[26] + X
[4]**2*X
[26] +
86 X
[5]**2*X
[26] + X
[6]**2*X
[26] + X
[7]**2*X
[26] + X
[8]**2*X
[26] -
89 a1
= ( -X
[1]**2 - X
[2]**2 - X
[3]**2 - X
[4]**2 - X
[5]**2 - X
[6]**2 -
90 X
[7]**2 - X
[8]**2 + X
[0]*X
[9] - X
[10]**2 - X
[11]**2 -
91 X
[12]**2 - X
[13]**2 - X
[14]**2 - X
[15]**2 - X
[16]**2 -
92 X
[17]**2 - X
[18]**2 - X
[19]**2 - X
[20]**2 - X
[21]**2 -
93 X
[22]**2 - X
[23]**2 - X
[24]**2 - X
[25]**2 + X
[0]*X
[26] +
96 a2
= -X
[0] - X
[9] - X
[26]