Problem l2313o24
Unknowns | Inequalities |
Equations |
Solution 1 |
Solution 2 |
Relevance |
Back to overview
Unknowns
All solutions for the following 79 unknowns have to be determined:
a1, ..., a13, b1, ..., b66
Inequalities
Each of the following lists represents one inequality which states
that not all unknowns in this list may vanish. These inequalities
filter out solutions which are trivial for the application.
{a1,a4,a9},
{a3,a4,a8,a7,a6,a5},
{a12,a11,a10},
{b1,b7,b34}
{b21,b14,b8,b15,b9,b22,b16,b10,b5,b6,b27,b23,b17,b11,b7,
b28,b24,b18,b12,b29,b25,b19,b33,b32,b31,b30,b26,b20,b13},
{b49,b40,b35,b41,b36,b50,b42,b37,b51,b43,b52,b44,b38,b53,
b45,b54,b46,b55,b47,b56,b65,b64,b63,b57,b48,b39}
Equations
All comma separated 276 expressions involving 2435 terms have to vanish.
All terms are products of one a- and one b-unknown.
a2*b38,
a2*b2,
a2*b4,
2*a10*b34 - a9*b38,
a1*b2 - 8*a2*b1,
a1*b3 - 18*a2*b1,
a1*b3 - 12*a2*b1,
a10*b4 - 2*a2*b39,
2*a11*b34 - a9*b44,
3*a10*b7 - a4*b35,
2*a12*b34 - a9*b52,
2*a11*b7 - a4*b40,
2*a13*b34 - a9*b58,
a12*b7 - a4*b49,
6*a13*b58 + a8*b52,
18*a10*b34 - 2*a9*b37 - 3*a9*b38,
12*a10*b34 - a9*b36 - a9*b37,
a10*b38 + a2*b37 - 2*a9*b39,
3*a1*b2 + 4*a1*b3 - 72*a2*b1,
7*a1*b4 - 2*a2*b2 - a2*b3,
6*a11*b34 - a9*b42 - a9*b44,
12*a11*b34 + 3*a4*b38 - 2*a9*b45,
2*a10*b44 + 2*a2*b44 + 3*a5*b38,
8*a11*b34 + a4*b37 - 2*a9*b47,
8*a11*b34 + a4*b36 - 2*a9*b47,
12*a12*b34 + a4*b44 - a9*b53,
12*a12*b34 - 2*a9*b52 - a9*b53,
16*a12*b34 + a4*b42 - 2*a9*b55,
8*a12*b34 + a4*b41 - a9*b55,
32*a12*b34 + a4*b43 - 4*a9*b55,
12*a12*b34 + a4*b47 - a9*b56,
36*a13*b34 + a4*b52 - 2*a9*b59,
18*a13*b34 - 3*a9*b58 - a9*b59,
24*a13*b34 + a4*b50 - 2*a9*b61,
48*a13*b34 - 2*a9*b59 - a9*b62,
96*a13*b34 + a4*b51 - 8*a9*b61,
72*a13*b34 + a4*b55 - 2*a9*b62,
a12*b33 - 6*a13*b66 - a8*b65,
3*a1*b38 + 18*a10*b34 - 2*a9*b37 - 3*a9*b38,
a1*b37 + 12*a10*b34 - 2*a9*b35 - a9*b37,
a1*b35 - 3*a10*b1 + 3*a10*b34 - a9*b35,
a1*b36 + 12*a10*b34 - 2*a9*b35 - a9*b36,
a1*b35 + 9*a10*b34 - a9*b35 - a9*b36,
a1*b36 + 36*a10*b34 - 2*a9*b35 - 5*a9*b36,
a1*b44 + 6*a11*b34 - a9*b42 - a9*b44,
12*a11*b34 - a9*b42 - 2*a9*b44 - a9*b45,
12*a11*b34 + 3*a3*b38 - 2*a9*b44 - 2*a9*b45,
a1*b42 + 8*a11*b34 - 2*a9*b40 - a9*b42,
a1*b40 - 2*a11*b1 + 2*a11*b34 - a9*b40,
a1*b41 + 4*a11*b34 - a9*b40 - a9*b41,
a1*b43 + 16*a11*b34 - 4*a9*b40 - a9*b43,
a1*b40 + 6*a11*b34 - a9*b40 - 2*a9*b41,
24*a11*b34 + a4*b36 - 2*a9*b43 - 2*a9*b47,
a1*b7 - a4*b1 + a4*b34 - a9*b7,
a10*b13 + a2*b13 - a5*b39 + 2*a5*b4,
a1*b52 + 6*a12*b34 - 2*a9*b50 - a9*b52,
24*a12*b34 - 4*a9*b50 - 4*a9*b52 - a9*b53,
12*a12*b34 + a3*b44 - 2*a9*b52 - a9*b53,
a1*b50 + 4*a12*b34 - 2*a9*b49 - a9*b50,
a1*b49 - a12*b1 + a12*b34 - a9*b49,
a1*b51 + 16*a12*b34 - 8*a9*b49 - a9*b51,
12*a12*b34 + a3*b46 - a9*b54 - a9*b56,
36*a13*b34 + a3*b52 - 6*a9*b58 - 2*a9*b59,
72*a13*b34 + a3*b54 - 4*a9*b60 - 2*a9*b62,
288*a13*b34 + a3*b56 - 8*a9*b60 - 10*a9*b62,
288*a13*b34 + a4*b56 - 8*a9*b61 - 8*a9*b62,
6*a12*b58 + 4*a13*b52 + a7*b52 + 2*a8*b44,
14*a13*b33 - a7*b33 + a8*b32 - 8*a8*b66,
a1*b37 + 36*a10*b34 - 2*a9*b35 - 2*a9*b36 - 3*a9*b37,
2*a1*b39 - a10*b2 + a10*b38 + 2*a2*b35 - 2*a9*b39,
a1*b42 + 24*a11*b34 - 2*a9*b40 - 4*a9*b41 - 3*a9*b42,
24*a11*b34 - 2*a9*b41 - 2*a9*b42 - a9*b43 - a9*b45,
24*a11*b34 + a4*b37 - a9*b43 - 2*a9*b45 - 2*a9*b47,
a10*b45 + 2*a11*b38 + a2*b45 + a5*b37 - 2*a9*b48,
a1*b43 + 48*a11*b34 - 4*a9*b40 - 8*a9*b41 - 3*a9*b43,
a1*b47 + 12*a11*b34 + a4*b35 - a9*b43 - a9*b47,
24*a11*b34 + a3*b36 - 2*a9*b41 - 2*a9*b43 - 2*a9*b46,
3*a10*b5 - 6*a11*b34 - 2*a3*b35 - a4*b35 + 2*a9*b46,
3*a10*b6 - 8*a11*b34 - 2*a3*b35 - 2*a4*b35 + 2*a9*b47,
3*a10*b12 - 2*a10*b47 - 2*a2*b47 - 6*a4*b39 - 2*a5*b35,
2*a1*b8 - 12*a10*b7 + 2*a4*b35 + a4*b36 - 12*a5*b1,
a1*b9 - 9*a10*b7 + a4*b35 + a4*b36 - 9*a5*b1,
2*a1*b5 + a1*b6 - 6*a3*b1 - 4*a4*b1 - a9*b6,
4*a10*b52 + 2*a11*b44 + a2*b52 + 2*a5*b44 + 3*a6*b38,
48*a12*b34 + a4*b42 - 2*a9*b51 - 2*a9*b53 - 2*a9*b55,
48*a12*b34 - 4*a9*b50 - 2*a9*b51 - 2*a9*b53 - a9*b56,
48*a12*b34 + a3*b45 - 3*a9*b53 - 2*a9*b54 - 2*a9*b56,
48*a12*b34 + a4*b45 - 2*a9*b53 - 2*a9*b55 - 2*a9*b56,
a1*b55 + 24*a12*b34 + a4*b40 - 2*a9*b51 - a9*b55,
a1*b56 + 48*a12*b34 - 8*a9*b49 - 4*a9*b51 - a9*b56,
96*a12*b34 + a3*b43 - 6*a9*b51 - 4*a9*b54 - 4*a9*b56,
96*a12*b34 + a4*b43 - 4*a9*b51 - 4*a9*b55 - 4*a9*b56,
2*a11*b5 - 12*a12*b34 - 2*a3*b40 - a4*b40 + 2*a9*b54,
a11*b6 - 8*a12*b34 - a3*b40 - a4*b40 + a9*b55,
24*a12*b34 + a3*b47 + a4*b46 - a9*b55 - 2*a9*b56,
a1*b14 - 4*a11*b7 + a4*b40 + a4*b41 - 4*a6*b1,
2*a1*b15 - 6*a11*b7 + a4*b40 + 2*a4*b41 - 6*a6*b1,
288*a13*b34 + a3*b53 - 12*a9*b59 - 8*a9*b60 - 4*a9*b62,
288*a13*b34 + a4*b53 - 8*a9*b59 - 8*a9*b61 - 4*a9*b62,
a12*b5 - 18*a13*b34 - 2*a3*b49 - a4*b49 + 2*a9*b60,
a12*b6 - 24*a13*b34 - 2*a3*b49 - 2*a4*b49 + 2*a9*b61,
144*a13*b34 + a3*b55 + a4*b54 - 4*a9*b61 - 4*a9*b62,
12*a13*b58 + 12*a13*b59 + 8*a8*b50 + a8*b53 - 24*a9*b66,
a12*b28 - 6*a13*b61 - a4*b65 - 8*a8*b49 - a8*b55,
a12*b28 + 6*a13*b21 - a4*b65 + a8*b14 - 8*a8*b49,
a10*b3 - a10*b37 - 2*a10*b38 - 4*a2*b35 - 3*a2*b36 + 10*a9*b39,
a1*b45 + 24*a11*b34 - 2*a9*b40 - 2*a9*b42 - a9*b43 - a9*b45,
24*a11*b34 + a3*b37 - a9*b42 - a9*b43 - 2*a9*b45 - 2*a9*b46,
24*a11*b34 + 2*a3*b37 + a4*b37 - 2*a9*b45 - 4*a9*b46 - 2*a9*b47,
a1*b46 + 12*a11*b34 + a3*b35 - a9*b40 - a9*b43 - a9*b46,
24*a11*b34 + 2*a3*b36 + a4*b36 - a9*b43 - 4*a9*b46 - 2*a9*b47,
3*a10*b13 - 2*a10*b48 + 2*a11*b39 + 2*a11*b4 - 5*a2*b48 - 6*a5*b39,
2*a1*b8 + 4*a1*b9 - 36*a10*b7 + 2*a4*b35 + 5*a4*b36 - 36*a5*b1,
3*a10*b12 + 2*a10*b8 + 2*a2*b8 - 6*a4*b39 + 3*a5*b2 - 2*a5*b35,
a1*b6 + 2*a1*b7 - 2*a3*b1 + 2*a3*b34 - 4*a4*b1 - a9*b6,
2*a1*b13 - 2*a10*b11 + a2*b11 + 2*a3*b39 - 7*a3*b4 - 2*a5*b2,
a1*b53 + 48*a12*b34 - 8*a9*b49 - 8*a9*b50 - 2*a9*b51 - a9*b53,
48*a12*b34 + a3*b42 - 4*a9*b50 - 2*a9*b51 - 2*a9*b53 - 2*a9*b54,
48*a12*b34 + 2*a3*b42 + a4*b42 - 2*a9*b53 - 4*a9*b54 - 2*a9*b55,
a1*b54 + 24*a12*b34 + a3*b40 - 4*a9*b49 - 2*a9*b51 - a9*b54,
24*a12*b34 + 2*a3*b41 + a4*b41 - a9*b51 - 2*a9*b54 - a9*b55,
96*a12*b34 + 2*a3*b43 + a4*b43 - 8*a9*b54 - 4*a9*b55 - 4*a9*b56,
6*a10*b58 + 4*a11*b52 + 2*a12*b44 + a5*b52 + 2*a6*b44 + 3*a7*b38,
72*a13*b34 + 2*a3*b50 + a4*b50 - 2*a9*b59 - 4*a9*b60 - 2*a9*b61,
288*a13*b34 + 2*a3*b51 + a4*b51 - 16*a9*b60 - 8*a9*b61 - 4*a9*b62,
6*a11*b58 + 4*a12*b52 + 2*a13*b44 + a6*b52 + 2*a7*b44 + 3*a8*b38,
2*a12*b58 + a12*b59 + 4*a13*b50 + a7*b50 + a8*b42 - 2*a9*b65,
2*a11*b33 + a12*b32 - 8*a12*b66 - 4*a13*b65 - a7*b65 - 2*a8*b64,
7*a12*b33 + 6*a13*b32 - a6*b33 - 3*a7*b66 + a8*b31 - 4*a8*b65,
2*a10*b42 + 6*a10*b44 + 3*a10*b45 + 4*a11*b38 + 5*a2*b42 + 5*a5*b37 - 10*a9*b48
,
3*a10*b11 - 2*a10*b46 - 2*a11*b38 - 2*a2*b46 - 6*a3*b39 - 2*a5*b35 + 2*a9*b48,
4*a1*b8 - 3*a10*b6 - 12*a10*b7 + 2*a3*b35 + 2*a4*b35 + a4*b37 - 24*a5*b1,
2*a1*b10 + 2*a1*b8 - 9*a10*b6 - 3*a3*b2 + 2*a3*b35 + 2*a3*b37 - 36*a5*b1,
2*a1*b17 + 2*a1*b19 - 6*a11*b6 - 3*a3*b11 + 2*a3*b45 + 2*a3*b46 - 24*a6*b1,
4*a10*b20 + 2*a11*b13 + a2*b20 + 3*a5*b13 - 2*a5*b48 - 4*a6*b39 + 5*a6*b4,
2*a1*b29 - 12*a13*b6 - 48*a13*b7 + a3*b62 + 2*a4*b59 + a4*b62 - 96*a8*b1,
a12*b27 - 6*a13*b58 - 6*a13*b61 - a3*b65 - 8*a8*b49 - a8*b54 + 12*a9*b66,
a1*b10 + 2*a1*b9 - 3*a10*b6 - 12*a10*b7 + a3*b36 + a4*b36 + a4*b37 - 24*a5*b1,
2*a1*b10 + 3*a1*b11 + a1*b9 - 9*a10*b6 - a3*b3 + a3*b36 + 2*a3*b37 - 36*a5*b1,
2*a1*b5 + 2*a1*b6 + a1*b7 - 8*a3*b1 - 7*a4*b1 + a4*b34 - 2*a9*b5 - a9*b7,
a1*b12 - 2*a10*b7 + 4*a2*b7 - a4*b2 + a4*b38 - 2*a5*b1 + 2*a5*b34 - a9*b12,
2*a1*b13 - 2*a10*b12 + a2*b12 + 2*a4*b39 - 7*a4*b4 - 2*a5*b2 + 2*a5*b38 - 2*a9*
b13,
3*a10*b20 - 4*a10*b57 + 2*a11*b13 + 4*a12*b39 + a12*b4 - 4*a2*b57 - 5*a5*b48 -
6*a6*b39,
8*a1*b14 - 2*a11*b6 - 24*a11*b7 + 2*a3*b40 + 6*a4*b40 + a4*b42 + a4*b43 - 32*a6
*b1,
12*a1*b21 - a12*b6 - 20*a12*b7 + 2*a3*b49 + 10*a4*b49 + a4*b50 + a4*b51 - 24*a7
*b1,
a1*b65 - a12*b21 + a12*b58 + a12*b61 - 2*a13*b49 + a7*b49 + a8*b40 - a9*b65,
a1*b10 + 6*a1*b12 - 3*a10*b6 - 12*a10*b7 - 2*a4*b3 + a4*b37 + 6*a4*b38 - 24*a5*
b1 - a9*b10,
2*a1*b11 + a1*b12 - 2*a10*b5 + 4*a2*b5 - 2*a3*b2 - a4*b2 + a4*b38 - 6*a5*b1 -
a9*b12,
a1*b11 + a1*b12 - a10*b6 + 2*a2*b6 - a3*b2 + a3*b38 - a4*b2 - 4*a5*b1 - a9*b11,
4*a10*b53 + 4*a11*b44 + 4*a11*b45 + 8*a12*b38 + a2*b53 + 2*a5*b42 + 2*a5*b45 +
4*a6*b37 - 8*a9*b57,
3*a10*b18 - 4*a10*b55 + 2*a11*b12 - 2*a11*b47 - a2*b55 - 5*a4*b48 - 2*a5*b40 -
2*a5*b47 - 4*a6*b35,
3*a10*b19 - 4*a10*b56 - 4*a11*b46 - 4*a11*b47 - 8*a12*b38 - a2*b56 - 2*a5*b43 -
8*a6*b35 + 8*a9*b57,
a1*b18 - 4*a11*b7 + a4*b44 + a4*b47 - a4*b8 + 3*a5*b7 - 4*a6*b1 + 4*a6*b34 - a9
*b18,
a1*b24 - 6*a12*b7 - a4*b14 + a4*b52 + a4*b55 + 2*a6*b7 - 6*a7*b1 + 6*a7*b34 -
a9*b24,
3*a10*b26 + 2*a11*b20 + a12*b13 + a5*b20 - a5*b57 + 2*a6*b13 - 2*a6*b48 - 3*a7*
b39 + 3*a7*b4,
a1*b28 - 8*a13*b7 - a4*b21 + a4*b58 + a4*b61 + a7*b7 - 8*a8*b1 + 8*a8*b34 - a9*
b28,
8*a12*b58 + 10*a12*b59 + 12*a13*b52 + 10*a13*b53 + 6*a7*b50 + a7*b53 + 8*a8*b42
+ 2*a8*b45 - 20*a9*b65,
2*a11*b28 + a12*b24 - 6*a12*b61 - 4*a13*b55 - 2*a4*b64 - 6*a7*b49 - a7*b55 - 8*
a8*b40 - 2*a8*b47,
2*a11*b28 + 6*a12*b21 + a12*b24 + 4*a13*b14 - 2*a4*b64 + a7*b14 - 6*a7*b49 - 8*
a8*b40 + 2*a8*b8,
2*a1*b31 - 2*a11*b28 - a12*b22 - 4*a13*b15 + 2*a4*b64 - 2*a6*b21 - a7*b15 + 8*
a8*b41 - a8*b9,
a12*b29 - 24*a13*b58 - 12*a13*b60 - 36*a13*b61 - 12*a13*b62 - 48*a8*b49 - 8*a8*
b51 - a8*b56 + 120*a9*b66,
3*a10*b33 + 2*a11*b32 - 10*a11*b66 + a12*b31 - 6*a12*b65 - 2*a13*b64 - a6*b65 -
2*a7*b64 - 3*a8*b63,
3*a10*b10 - 2*a10*b43 - 3*a10*b45 - 6*a10*b46 - 6*a10*b47 - 8*a11*b38 - 5*a2*
b43 - 12*a5*b35 - 4*a5*b36 + 20*a9*b48,
2*a1*b10 + 2*a1*b8 - 6*a10*b5 - 18*a10*b7 - 3*a4*b2 + 2*a4*b35 + 2*a4*b37 + 3*
a4*b38 - 36*a5*b1 - 2*a9*b8,
30*a1*b13 - 3*a10*b10 - 6*a10*b12 - 2*a10*b9 - 12*a2*b8 - 5*a2*b9 + 30*a4*b39 -
6*a5*b2 - 5*a5*b3 + 2*a5*b36,
12*a1*b13 - a10*b10 - 3*a10*b11 - 3*a10*b12 - a2*b10 + 6*a3*b39 + 6*a4*b39 - 6*
a5*b2 - 2*a5*b3 + a5*b37,
4*a10*b14 + 3*a10*b18 + 2*a11*b12 + 2*a11*b8 + a2*b14 - 5*a4*b48 - 2*a5*b40 + 2
*a5*b8 + 3*a6*b2 - 4*a6*b35,
2*a1*b18 + 2*a1*b19 - 4*a11*b5 - 12*a11*b7 - 3*a4*b12 + 2*a4*b44 + 2*a4*b45 + 2
*a4*b47 - 24*a6*b1 - 2*a9*b18,
4*a1*b20 - 2*a10*b19 - 2*a11*b11 - 2*a11*b12 + a2*b19 + 2*a3*b48 + 2*a4*b48 -
a5*b10 + a5*b45 - 4*a6*b2,
2*a1*b23 + a1*b25 - 6*a12*b6 - 12*a12*b7 - a3*b17 + a3*b53 + a3*b54 + a4*b54 +
a4*b56 - 36*a7*b1,
4*a11*b58 + 2*a11*b59 + 4*a12*b50 + 2*a12*b52 + a12*b53 + 2*a13*b42 + 2*a6*b50
+ 2*a7*b42 + 2*a8*b37 - 4*a9*b64,
2*a11*b58 + 2*a11*b61 - a12*b15 + a12*b50 + a12*b51 - 4*a13*b41 + 2*a6*b49 + 2*
a7*b41 + a8*b36 - 2*a9*b64,
6*a1*b27 + 2*a1*b29 - 18*a13*b6 - 72*a13*b7 - a3*b23 + 2*a3*b59 + 2*a3*b60 + 4*
a4*b60 + 2*a4*b62 - 144*a8*b1,
3*a10*b32 - 12*a10*b66 + 2*a11*b31 - 8*a11*b65 + a12*b30 - 4*a12*b64 - a5*b65 -
2*a6*b64 - 3*a7*b63 - 4*a8*b57,
14*a1*b33 - 8*a13*b27 - 6*a13*b28 - a3*b32 + 2*a3*b66 + 12*a4*b66 + a7*b27 - 8*
a8*b21 - a8*b23 + 8*a8*b60,
14*a1*b33 - 14*a13*b28 - a4*b32 + 14*a4*b66 + a7*b28 - 8*a8*b21 - a8*b24 + 8*a8
*b58 + 8*a8*b61 - 14*a9*b33,
14*a11*b33 + 12*a12*b32 + 10*a13*b31 - 3*a5*b33 - a6*b32 - 4*a6*b66 + a7*b31 -
6*a7*b65 + 3*a8*b30 - 8*a8*b64,
5*a1*b48 + 2*a10*b40 + 3*a10*b44 + 3*a10*b47 - 3*a10*b8 - 2*a11*b2 - 2*a11*b35
+ 2*a11*b38 + 5*a2*b40 + 5*a5*b35 - 5*a9*b48,
2*a1*b10 + 4*a1*b8 + 4*a1*b9 - 9*a10*b6 - 36*a10*b7 + 2*a3*b35 + 2*a3*b36 + 2*
a4*b35 + 2*a4*b36 + 3*a4*b37 - 72*a5*b1,
2*a1*b10 + 3*a1*b12 + a1*b9 - 6*a10*b5 - 18*a10*b7 - a4*b3 + a4*b36 + 2*a4*b37
+ 3*a4*b38 - 36*a5*b1 - a9*b9,
4*a10*b50 + 6*a10*b52 + 3*a10*b53 + 2*a11*b42 + 4*a11*b44 + 2*a11*b45 + 2*a12*
b38 + 4*a2*b50 + 4*a5*b42 + 4*a6*b37 - 8*a9*b57,
2*a1*b14 + a1*b16 - 3*a11*b6 - 12*a11*b7 + a3*b40 + a3*b42 - a3*b8 + a4*b40 +
a4*b43 + a4*b46 - 24*a6*b1,
4*a1*b14 + 2*a1*b16 - 6*a11*b6 - 24*a11*b7 + 2*a3*b40 + a3*b43 + 2*a4*b40 + 2*
a4*b42 + a4*b43 + a4*b45 - 48*a6*b1,
a1*b16 + 4*a1*b18 - 2*a11*b6 - 24*a11*b7 + a4*b42 + a4*b43 + 4*a4*b44 + 4*a4*
b47 - 2*a4*b9 - 32*a6*b1 - a9*b16,
2*a1*b20 - 2*a10*b17 - a11*b11 - a11*b12 + a2*b17 - 3*a3*b13 + a3*b48 + a4*b48
+ a5*b46 - a5*b8 - 2*a6*b2,
4*a1*b18 + 2*a1*b19 - 4*a11*b6 - 16*a11*b7 + 2*a3*b47 - a4*b10 + 4*a4*b44 + 2*
a4*b45 + 2*a4*b47 - 32*a6*b1 - 2*a9*b19,
3*a10*b26 - 6*a10*b63 + 2*a11*b20 - 2*a11*b57 + a12*b13 + 2*a12*b48 + 6*a13*b39
- 3*a2*b63 - 4*a5*b57 - 5*a6*b48 - 6*a7*b39,
6*a1*b21 + 2*a1*b22 - 3*a12*b6 - 24*a12*b7 - a3*b14 + 2*a3*b49 + 2*a3*b50 + 4*
a4*b49 + 2*a4*b51 + a4*b54 - 36*a7*b1,
a1*b22 + 2*a1*b24 - a12*b6 - 20*a12*b7 - 2*a4*b15 + a4*b50 + a4*b51 + 2*a4*b52
+ 2*a4*b55 - 24*a7*b1 - a9*b22,
4*a1*b22 + 2*a1*b25 - 12*a12*b6 - 48*a12*b7 + 2*a3*b51 + a3*b56 + 4*a4*b50 + 2*
a4*b51 + 2*a4*b53 + a4*b56 - 96*a7*b1,
2*a1*b24 + a1*b25 - 4*a12*b5 - 24*a12*b7 - a4*b18 + 2*a4*b52 + a4*b53 + 2*a4*
b55 + a4*b56 - 36*a7*b1 - 2*a9*b24,
3*a10*b30 - 8*a10*b64 + 2*a11*b26 - 4*a11*b63 + a12*b20 + 4*a13*b48 - 2*a2*b64
- 3*a5*b63 - 4*a6*b57 - 5*a7*b48 - 6*a8*b39,
6*a1*b28 + 2*a1*b29 - 12*a13*b5 - 108*a13*b7 - a4*b24 + 6*a4*b58 + 2*a4*b59 + 6
*a4*b61 + 2*a4*b62 - 144*a8*b1 - 6*a9*b28,
3*a1*b10 + 12*a1*b11 + 6*a1*b12 - 12*a10*b5 - 9*a10*b6 - 4*a3*b3 + 2*a3*b37 + 6
*a3*b38 - 2*a4*b3 + a4*b37 - 72*a5*b1 - a9*b10,
3*a10*b17 - 4*a10*b54 + 2*a11*b11 - 2*a11*b44 - 2*a11*b47 - 4*a12*b38 - a2*b54
- 5*a3*b48 - 2*a5*b40 - 2*a5*b46 - 4*a6*b35 + 4*a9*b57,
8*a1*b14 + 16*a1*b15 + 2*a1*b16 - 6*a11*b6 - 72*a11*b7 + 2*a3*b40 + 4*a3*b41 +
6*a4*b40 + 12*a4*b41 + 3*a4*b42 + 3*a4*b43 - 96*a6*b1,
2*a1*b14 + a1*b16 - 2*a11*b5 - 18*a11*b7 + 2*a4*b40 + a4*b42 + a4*b43 + a4*b44
+ a4*b47 - a4*b8 - 24*a6*b1 - 2*a9*b14,
4*a1*b15 + 2*a1*b16 + 2*a1*b17 - 6*a11*b6 - 24*a11*b7 + 2*a3*b41 + 2*a3*b42 -
a3*b9 + 2*a4*b41 + 2*a4*b43 + 2*a4*b46 - 48*a6*b1,
4*a1*b15 + 2*a1*b16 + a1*b19 - 6*a11*b6 - 24*a11*b7 + 2*a3*b41 + a3*b43 + 2*a4*
b41 + 2*a4*b42 + a4*b43 + a4*b45 - 48*a6*b1,
2*a1*b17 + a1*b18 - 2*a11*b5 - 6*a11*b7 - 2*a3*b8 + a4*b44 + 2*a4*b46 + a4*b47
- a4*b8 + 3*a5*b5 - 12*a6*b1 - a9*b18,
2*a1*b17 + 2*a1*b18 - 2*a11*b6 - 8*a11*b7 + 2*a3*b44 - 2*a3*b8 + 2*a4*b46 + 2*
a4*b47 - 2*a4*b8 + 3*a5*b6 - 16*a6*b1 - 2*a9*b17,
2*a1*b20 - 2*a10*b18 - 2*a11*b12 + a2*b18 - 3*a4*b13 + 2*a4*b48 + a5*b44 + a5*
b47 - a5*b8 - 2*a6*b2 + 2*a6*b38 - 2*a9*b20,
6*a10*b58 + 3*a10*b59 + 4*a11*b50 + 4*a11*b52 + 2*a11*b53 + 2*a12*b42 + 2*a12*
b44 + a12*b45 + 3*a5*b50 + 3*a6*b42 + 3*a7*b37 - 6*a9*b63,
6*a10*b59 + 4*a11*b52 + 6*a11*b53 + 8*a12*b44 + 6*a12*b45 + 12*a13*b38 + 2*a5*
b50 + a5*b53 + 4*a6*b42 + 2*a6*b45 + 6*a7*b37 - 12*a9*b63,
3*a10*b24 - 6*a10*b61 + 2*a11*b18 - 4*a11*b55 + a12*b12 - 2*a12*b47 - 4*a4*b57
- 2*a5*b49 - a5*b55 - 4*a6*b40 - 2*a6*b47 - 6*a7*b35,
6*a1*b21 + 2*a1*b22 - 2*a12*b5 - 30*a12*b7 - a4*b14 + 6*a4*b49 + 2*a4*b50 + 2*
a4*b51 + a4*b52 + a4*b55 - 36*a7*b1 - 6*a9*b21,
24*a1*b21 + 8*a1*b22 - 12*a12*b6 - 96*a12*b7 + 8*a3*b49 + 2*a3*b51 + 16*a4*b49
+ 8*a4*b50 + 6*a4*b51 + a4*b53 + a4*b56 - 144*a7*b1,
2*a1*b23 + a1*b24 - 2*a12*b5 - 12*a12*b7 - 2*a3*b14 - a4*b14 + a4*b52 + 2*a4*
b54 + a4*b55 + 2*a6*b5 - 18*a7*b1 - a9*b24,
a1*b23 + a1*b24 - a12*b6 - 8*a12*b7 - a3*b14 + a3*b52 - a4*b14 + a4*b54 + a4*
b55 + a6*b6 - 12*a7*b1 - a9*b23,
4*a1*b23 + 5*a1*b25 - 24*a12*b6 - 48*a12*b7 - a3*b19 + 2*a3*b53 + 2*a3*b54 + 3*
a3*b56 + 3*a4*b53 + 2*a4*b54 + 2*a4*b56 - 144*a7*b1,
8*a1*b24 + 2*a1*b25 - 8*a12*b6 - 64*a12*b7 + 2*a3*b55 - a4*b16 + 8*a4*b52 + 2*
a4*b53 + 6*a4*b55 + 2*a4*b56 - 96*a7*b1 - 2*a9*b25,
4*a11*b58 + 8*a11*b59 + 8*a12*b52 + 8*a12*b53 + 12*a13*b44 + 8*a13*b45 + 4*a6*
b50 + a6*b53 + 6*a7*b42 + 2*a7*b45 + 8*a8*b37 - 16*a9*b64,
2*a1*b64 - 2*a11*b21 + 2*a11*b58 + 2*a11*b61 - a12*b14 + a12*b52 + a12*b55 - 4*
a13*b40 + 2*a6*b49 + 2*a7*b40 + 2*a8*b35 - 2*a9*b64,
3*a10*b28 + 2*a11*b24 - 6*a11*b61 + a12*b18 - 4*a12*b55 - 2*a13*b47 - 3*a4*b63
- 4*a6*b49 - a6*b55 - 6*a7*b40 - 2*a7*b47 - 8*a8*b35,
2*a1*b27 + a1*b28 - 2*a13*b5 - 18*a13*b7 - 2*a3*b21 - a4*b21 + a4*b58 + 2*a4*
b60 + a4*b61 + a7*b5 - 24*a8*b1 - a9*b28,
2*a1*b27 + 2*a1*b28 - 2*a13*b6 - 24*a13*b7 - 2*a3*b21 + 2*a3*b58 - 2*a4*b21 + 2
*a4*b60 + 2*a4*b61 + a7*b6 - 32*a8*b1 - 2*a9*b27,
24*a1*b27 + 20*a1*b29 - 144*a13*b6 - 576*a13*b7 - a3*b25 + 8*a3*b59 + 8*a3*b60
+ 6*a3*b62 + 12*a4*b59 + 16*a4*b60 + 14*a4*b62 - 1152*a8*b1,
12*a1*b28 + 2*a1*b29 - 12*a13*b6 - 144*a13*b7 + 2*a3*b61 - a4*b22 + 12*a4*b58 +
2*a4*b59 + 10*a4*b61 + 2*a4*b62 - 192*a8*b1 - 2*a9*b29,
a12*b22 - 8*a12*b58 - a12*b59 - 2*a12*b60 - 10*a12*b61 - 2*a12*b62 - 4*a13*b51
- 12*a7*b49 - a7*b51 - 16*a8*b41 - a8*b43 + 20*a9*b65,
3*a10*b31 - 10*a10*b65 + 2*a11*b30 - 6*a11*b64 + a12*b26 - 2*a12*b63 + 2*a13*
b57 - a2*b65 - 2*a5*b64 - 3*a6*b63 - 4*a7*b57 - 5*a8*b48,
5*a10*b31 + 4*a11*b30 + 3*a12*b26 + 2*a13*b20 - a2*b31 - a5*b64 + a6*b26 - 2*a6
*b63 + 2*a7*b20 - 3*a7*b57 + 3*a8*b13 - 4*a8*b48,
24*a1*b32 - 2*a12*b27 - 10*a12*b28 - 2*a12*b29 - 12*a13*b22 + 2*a3*b65 + 22*a4*
b65 - 12*a7*b21 - 16*a8*b15 - a8*b16 + 8*a8*b50 + 8*a8*b51,
168*a1*b33 - 12*a13*b27 - 36*a13*b28 - 20*a13*b29 + 24*a3*b66 + 144*a4*b66 + a7
*b29 - 48*a8*b21 - 8*a8*b22 - a8*b25 + 8*a8*b59 + 8*a8*b62,
7*a10*b33 + 6*a11*b32 + 5*a12*b31 + 4*a13*b30 - 2*a2*b33 - a5*b32 - a5*b66 - 2*
a6*b65 + a7*b30 - 3*a7*b64 + 2*a8*b26 - 4*a8*b63,
4*a1*b15 + 2*a1*b16 + 2*a1*b18 - 4*a11*b5 - 36*a11*b7 + 4*a4*b41 + 2*a4*b42 + 2
*a4*b43 + 2*a4*b44 + 2*a4*b47 - a4*b9 - 48*a6*b1 - 4*a9*b15,
6*a10*b21 + 3*a10*b24 + 4*a11*b14 + 2*a11*b18 + a12*b12 + 2*a12*b8 - 4*a4*b57 +
a5*b14 - 2*a5*b49 - 4*a6*b40 + 2*a6*b8 + 3*a7*b2 - 6*a7*b35,
3*a10*b28 + 6*a11*b21 + 2*a11*b24 + 4*a12*b14 + a12*b18 + 2*a13*b8 - 3*a4*b63 +
a6*b14 - 4*a6*b49 - 6*a7*b40 + 2*a7*b8 + 3*a8*b2 - 8*a8*b35,
8*a10*b30 + 6*a11*b26 + 4*a12*b20 + 2*a13*b13 - a2*b30 + a5*b26 - 2*a5*b63 + 3*
a6*b20 - 4*a6*b57 + 5*a7*b13 - 6*a7*b48 - 8*a8*b39 + 7*a8*b4,
12*a10*b32 + 10*a11*b31 + 8*a12*b30 + 6*a13*b26 - 3*a2*b32 - a5*b31 - 2*a5*b65
+ a6*b30 - 4*a6*b64 + 3*a7*b26 - 6*a7*b63 + 5*a8*b20 - 8*a8*b57,
4*a1*b24 + 5*a1*b25 - 8*a12*b5 - 12*a12*b6 - 72*a12*b7 + 2*a3*b55 + 2*a3*b56 -
a4*b19 + 4*a4*b52 + 5*a4*b53 + 2*a4*b55 + 3*a4*b56 - 144*a7*b1 - a9*b25,
24*a1*b28 + 20*a1*b29 - 48*a13*b5 - 72*a13*b6 - 720*a13*b7 + 8*a3*b61 + 4*a3*
b62 - a4*b25 + 24*a4*b58 + 20*a4*b59 + 16*a4*b61 + 16*a4*b62 - 1152*a8*b1 - 4*
a9*b29,
2*a11*b27 + a12*b23 - 4*a12*b58 - 2*a12*b60 - 4*a12*b61 - 6*a13*b52 + 2*a13*b54
- 6*a13*b55 - 2*a3*b64 - 6*a7*b49 - a7*b54 - 8*a8*b40 - 2*a8*b46 + 10*a9*b65,
6*a1*b32 - 4*a12*b27 - 2*a12*b28 - 3*a13*b23 - 3*a13*b24 - a3*b31 + a3*b65 + 5*
a4*b65 + a6*b27 - 3*a7*b21 + 3*a7*b60 - 4*a8*b14 - a8*b17 + 4*a8*b54,
6*a1*b32 - 6*a12*b28 - 6*a13*b24 - a4*b31 + 6*a4*b65 + a6*b28 - 3*a7*b21 + 3*a7
*b58 + 3*a7*b61 - 4*a8*b14 - a8*b18 + 4*a8*b52 + 4*a8*b55 - 6*a9*b32,
2*a10*b41 + 3*a10*b42 + 3*a10*b43 + 6*a10*b44 + 6*a10*b47 - 3*a10*b9 - 2*a11*b3
- 2*a11*b36 + 2*a11*b37 + 2*a11*b38 + 12*a2*b40 + 8*a2*b41 + 6*a5*b35 + 7*a5*
b36 - 20*a9*b48,
4*a1*b57 - 3*a10*b14 + 4*a10*b49 + 3*a10*b52 + 3*a10*b55 + 2*a11*b44 + 2*a11*
b47 - 2*a11*b8 - a12*b2 - 4*a12*b35 + a12*b38 + 4*a2*b49 + 4*a5*b40 + 4*a6*b35
- 4*a9*b57,
3*a1*b16 + 4*a1*b17 + 4*a1*b19 - 18*a11*b6 - 24*a11*b7 - a3*b10 + 2*a3*b42 + 2*
a3*b43 + 2*a3*b45 + 2*a3*b46 + a4*b42 + a4*b43 + 2*a4*b45 + 2*a4*b46 - 96*a6*b1
,
2*a1*b17 + 2*a1*b18 + 4*a1*b19 - 4*a11*b5 - 6*a11*b6 - 12*a11*b7 - 3*a3*b12 + 2
*a3*b45 + 2*a3*b47 - 3*a4*b11 + 2*a4*b44 + 2*a4*b45 + 2*a4*b46 - 48*a6*b1 - 2*
a9*b17,
6*a1*b30 - 6*a10*b28 - 2*a11*b22 - 2*a11*b24 - 4*a12*b15 - a12*b16 - 2*a13*b9 +
6*a4*b63 - 6*a5*b21 - 2*a6*b14 - 2*a6*b15 + 6*a7*b41 - 2*a7*b9 - 2*a8*b3 + 8*
a8*b36,
20*a1*b20 - 4*a10*b15 - 3*a10*b16 - 6*a10*b18 - 2*a11*b10 - 2*a11*b12 - 2*a11*
b9 - 12*a2*b14 - 4*a2*b15 + 20*a4*b48 + 2*a5*b41 - 6*a5*b8 - 4*a5*b9 - 2*a6*b2
- 4*a6*b3 + 4*a6*b36,
3*a1*b16 + 8*a1*b17 + 4*a1*b18 - 8*a11*b5 - 6*a11*b6 - 48*a11*b7 + 2*a3*b42 + 4
*a3*b44 - 4*a3*b9 + a4*b42 + 3*a4*b43 + 8*a4*b46 + 4*a4*b47 - 2*a4*b9 - 96*a6*
b1 - a9*b16,
3*a1*b16 + 4*a1*b18 + 4*a1*b19 - 8*a11*b5 - 6*a11*b6 - 48*a11*b7 + a3*b43 + 2*
a3*b47 - a4*b10 + 3*a4*b42 + 2*a4*b43 + 4*a4*b44 + 4*a4*b45 + 2*a4*b47 - 96*a6*
b1 - a9*b16,
3*a10*b25 - 6*a10*b62 + 2*a11*b19 - 4*a11*b54 - 4*a11*b55 - 6*a11*b56 - 8*a12*
b44 - 8*a12*b46 - 16*a12*b47 - 24*a13*b38 - 2*a5*b51 - a5*b56 - 8*a6*b40 - 4*a6
*b43 - 24*a7*b35 + 24*a9*b63,
3*a1*b22 + 4*a1*b23 + 2*a1*b24 - 4*a12*b5 - 3*a12*b6 - 48*a12*b7 - 4*a3*b15 + 2
*a3*b50 + 2*a3*b52 - 2*a4*b15 + a4*b50 + 3*a4*b51 + 4*a4*b54 + 2*a4*b55 - 72*a7
*b1 - a9*b22,
12*a1*b22 + 8*a1*b23 + 4*a1*b25 - 36*a12*b6 - 144*a12*b7 - a3*b16 + 8*a3*b50 +
4*a3*b51 + 2*a3*b53 + 2*a3*b54 + 4*a4*b50 + 8*a4*b51 + 2*a4*b53 + 6*a4*b54 + 4*
a4*b56 - 288*a7*b1,
2*a11*b29 + a12*b25 - 8*a12*b58 - 8*a12*b60 - 16*a12*b61 - 10*a12*b62 - 24*a13*
b52 - 12*a13*b54 - 36*a13*b55 - 10*a13*b56 - 24*a7*b49 - 6*a7*b51 - a7*b56 - 48
*a8*b40 - 8*a8*b43 + 80*a9*b65,
8*a1*b17 + 4*a1*b18 + 6*a1*b19 - 8*a11*b5 - 12*a11*b6 - 24*a11*b7 - 2*a3*b10 +
4*a3*b44 + 2*a3*b45 + 4*a3*b46 + 2*a3*b47 - a4*b10 + 4*a4*b45 + 4*a4*b46 + 2*a4
*b47 - 96*a6*b1 - 2*a9*b19,
3*a1*b63 - 3*a10*b21 + 3*a10*b58 + 3*a10*b61 - 2*a11*b14 + 2*a11*b49 + 2*a11*
b52 + 2*a11*b55 - 2*a12*b40 + a12*b44 + a12*b47 - a12*b8 - 6*a13*b35 + 3*a5*b49
+ 3*a6*b40 + 3*a7*b35 - 3*a9*b63,
6*a10*b58 + 6*a10*b61 - 2*a11*b15 + 2*a11*b50 + 2*a11*b51 + 2*a11*b52 + 2*a11*
b55 - 2*a12*b41 + a12*b42 + a12*b43 - a12*b9 - 6*a13*b36 + 6*a5*b49 + 2*a6*b40
+ 4*a6*b41 + 3*a7*b36 - 6*a9*b63,
12*a1*b26 - 3*a10*b22 - 6*a10*b24 - 4*a11*b15 - 2*a11*b16 - 2*a11*b18 - a12*b10
- 2*a12*b9 - 12*a2*b21 + 12*a4*b57 - 6*a5*b14 - 3*a5*b15 + 4*a6*b41 - 2*a6*b8
- 3*a6*b9 - 3*a7*b3 + 6*a7*b36,
12*a1*b22 + 8*a1*b24 + 4*a1*b25 - 16*a12*b5 - 12*a12*b6 - 192*a12*b7 + 2*a3*b51
+ 2*a3*b55 - a4*b16 + 12*a4*b50 + 10*a4*b51 + 8*a4*b52 + 4*a4*b53 + 6*a4*b55 +
4*a4*b56 - 288*a7*b1 - 4*a9*b22,
2*a1*b23 + 2*a1*b24 + 2*a1*b25 - 4*a12*b5 - 6*a12*b6 - 36*a12*b7 - a3*b18 + a3*
b53 + a3*b55 - a4*b17 + 2*a4*b52 + a4*b53 + 2*a4*b54 + a4*b55 + 2*a4*b56 - 72*
a7*b1 - 2*a9*b23,
6*a1*b26 - 6*a10*b23 - 4*a11*b17 - 2*a11*b18 - 2*a12*b11 - 4*a12*b12 + 3*a2*b23
- 5*a3*b20 + 2*a3*b57 + 4*a4*b57 - 2*a5*b14 + a5*b17 + 2*a5*b54 - a6*b11 + 4*
a6*b46 - 4*a6*b8 - 6*a7*b2,
6*a1*b27 + 6*a1*b28 + 4*a1*b29 - 12*a13*b5 - 18*a13*b6 - 180*a13*b7 - a3*b24 +
2*a3*b59 + 2*a3*b61 - a4*b23 + 6*a4*b58 + 2*a4*b59 + 6*a4*b60 + 4*a4*b61 + 4*a4
*b62 - 288*a8*b1 - 6*a9*b27,
3*a10*b23 - 6*a10*b60 + 2*a11*b17 - 2*a11*b52 - 2*a11*b54 - 2*a11*b55 + a12*b11
- 4*a12*b44 + 2*a12*b46 - 4*a12*b47 - 6*a13*b38 - 4*a3*b57 - 2*a5*b49 - a5*b54
- 4*a6*b40 - 2*a6*b46 - 6*a7*b35 + 6*a9*b63,
16*a1*b23 + 8*a1*b24 + 6*a1*b25 - 16*a12*b5 - 24*a12*b6 - 144*a12*b7 - 2*a3*b16
+ 8*a3*b52 + 2*a3*b53 + 4*a3*b54 + 2*a3*b55 - a4*b16 + 4*a4*b53 + 12*a4*b54 +
6*a4*b55 + 6*a4*b56 - 288*a7*b1 - 2*a9*b25,
6*a1*b26 - 6*a10*b24 - 6*a11*b18 - 6*a12*b12 + 3*a2*b24 - 5*a4*b20 + 6*a4*b57 -
2*a5*b14 + a5*b18 + 2*a5*b52 + 2*a5*b55 - a6*b12 + 4*a6*b44 + 4*a6*b47 - 4*a6*
b8 - 6*a7*b2 + 6*a7*b38 - 6*a9*b26,
24*a1*b26 - 6*a10*b25 - 4*a11*b17 - 4*a11*b18 - 8*a11*b19 - 8*a12*b11 - 16*a12*
b12 + 3*a2*b25 + 8*a3*b57 + 16*a4*b57 - 2*a5*b16 + a5*b19 + 2*a5*b53 + 2*a5*b56
- 4*a6*b10 + 4*a6*b45 - 8*a6*b8 - 24*a7*b2,
3*a10*b27 + 2*a11*b23 - 2*a11*b58 - 4*a11*b60 - 2*a11*b61 + a12*b17 - 4*a12*b52
- 4*a12*b55 - 6*a13*b44 + 4*a13*b46 - 6*a13*b47 - 3*a3*b63 - 4*a6*b49 - a6*b54
- 6*a7*b40 - 2*a7*b46 - 8*a8*b35 + 8*a9*b64,
24*a1*b27 + 12*a1*b28 + 6*a1*b29 - 24*a13*b5 - 36*a13*b6 - 360*a13*b7 - 2*a3*
b22 + 12*a3*b58 + 2*a3*b59 + 4*a3*b60 + 2*a3*b61 - a4*b22 + 4*a4*b59 + 20*a4*
b60 + 10*a4*b61 + 6*a4*b62 - 576*a8*b1 - 2*a9*b29,
3*a10*b15 - 3*a10*b50 - 3*a10*b51 - 6*a10*b52 - 6*a10*b55 - 2*a11*b42 - 2*a11*
b43 - 2*a11*b44 - 2*a11*b47 + 2*a11*b9 + a12*b3 + 4*a12*b36 - a12*b37 - 12*a2*
b49 - 6*a5*b40 - 6*a5*b41 - 2*a6*b35 - 5*a6*b36 + 12*a9*b57,
40*a1*b20 - 4*a10*b16 - 6*a10*b17 - 6*a10*b18 - 6*a10*b19 - 4*a11*b10 - 4*a11*
b11 - 12*a11*b12 - a2*b16 + 10*a3*b48 + 30*a4*b48 - 2*a5*b10 + 2*a5*b42 + 2*a5*
b43 - 12*a5*b8 - 4*a5*b9 - 16*a6*b2 - 8*a6*b3 + 4*a6*b37,
60*a1*b32 - 4*a12*b27 - 8*a12*b28 - 8*a12*b29 - 6*a13*b23 - 18*a13*b24 - 9*a13*
b25 + 10*a3*b65 + 50*a4*b65 + a6*b29 - 12*a7*b21 - 3*a7*b22 + 3*a7*b59 + 3*a7*
b62 - 24*a8*b14 - 4*a8*b16 - a8*b19 + 4*a8*b53 + 4*a8*b56,
3*a10*b16 - 4*a10*b51 - 3*a10*b53 - 6*a10*b54 - 6*a10*b55 - 6*a10*b56 + 2*a11*
b10 - 2*a11*b43 - 8*a11*b44 - 2*a11*b45 - 4*a11*b46 - 12*a11*b47 - 8*a12*b38 -
4*a2*b51 - 12*a5*b40 - 4*a5*b41 - 4*a5*b43 - 16*a6*b35 - 8*a6*b36 + 32*a9*b57,
3*a10*b29 + 2*a11*b25 - 4*a11*b60 - 4*a11*b61 - 8*a11*b62 + a12*b19 - 8*a12*b52
- 8*a12*b54 - 16*a12*b55 - 8*a12*b56 - 24*a13*b44 - 12*a13*b46 - 36*a13*b47 -
8*a6*b49 - 4*a6*b51 - a6*b56 - 24*a7*b40 - 6*a7*b43 - 48*a8*b35 + 48*a9*b64,
10*a1*b31 - 8*a11*b27 - 2*a11*b28 - 6*a12*b23 - 4*a12*b24 - 4*a13*b17 - 6*a13*
b18 - 3*a3*b30 + 2*a3*b64 + 8*a4*b64 + 3*a5*b27 - 4*a6*b21 + a6*b23 + 4*a6*b60
- 6*a7*b14 - a7*b17 + 6*a7*b54 - 3*a8*b11 + 8*a8*b46 - 8*a8*b8,
10*a1*b31 - 10*a11*b28 - 10*a12*b24 - 10*a13*b18 - 3*a4*b30 + 10*a4*b64 + 3*a5*
b28 - 4*a6*b21 + a6*b24 + 4*a6*b58 + 4*a6*b61 - 6*a7*b14 - a7*b18 + 6*a7*b52 +
6*a7*b55 - 3*a8*b12 + 8*a8*b44 + 8*a8*b47 - 8*a8*b8 - 10*a9*b31,
2*a11*b22 - 8*a11*b58 - 2*a11*b59 - 4*a11*b60 - 12*a11*b61 - 4*a11*b62 + a12*
b16 - 4*a12*b51 - 8*a12*b52 - a12*b53 - 2*a12*b54 - 10*a12*b55 - 2*a12*b56 - 2*
a13*b43 - 16*a6*b49 - 2*a6*b51 - 12*a7*b40 - 12*a7*b41 - 2*a7*b43 - 16*a8*b36 +
32*a9*b64,
4*a1*b30 - 4*a10*b27 - 3*a11*b23 - a11*b24 - 2*a12*b17 - 2*a12*b18 - a13*b11 -
3*a13*b12 + 2*a2*b27 - 2*a3*b26 + a3*b63 + 3*a4*b63 - a5*b21 + a5*b23 + a5*b60
- 2*a6*b14 + 2*a6*b54 - a7*b11 + 3*a7*b46 - 3*a7*b8 - 4*a8*b2,
40*a1*b31 - 4*a11*b27 - 12*a11*b28 - 4*a11*b29 - 10*a12*b22 - 2*a12*b23 - 10*
a12*b24 - 2*a12*b25 - 10*a13*b16 + 4*a3*b64 + 36*a4*b64 - 16*a6*b21 - 12*a7*b14
- 12*a7*b15 - a7*b16 + 6*a7*b50 + 6*a7*b51 - 2*a8*b10 + 8*a8*b42 + 8*a8*b43 -
16*a8*b9,
4*a1*b30 - 4*a10*b28 - 4*a11*b24 - 4*a12*b18 - 4*a13*b12 + 2*a2*b28 - 2*a4*b26
+ 4*a4*b63 - a5*b21 + a5*b24 + a5*b58 + a5*b61 - 2*a6*b14 + 2*a6*b52 + 2*a6*b55
- a7*b12 + 3*a7*b44 + 3*a7*b47 - 3*a7*b8 - 4*a8*b2 + 4*a8*b38 - 4*a9*b30,
24*a1*b30 - 4*a10*b29 - 2*a11*b23 - 2*a11*b24 - 5*a11*b25 - 4*a12*b17 - 8*a12*
b18 - 6*a12*b19 - 6*a13*b11 - 18*a13*b12 + 2*a2*b29 + 6*a3*b63 + 18*a4*b63 - a5
*b22 + a5*b25 + a5*b59 + a5*b62 - 4*a6*b14 - 2*a6*b16 + 2*a6*b53 + 2*a6*b56 - 3
*a7*b10 + 3*a7*b45 - 12*a7*b8 - 24*a8*b2,
3*a10*b22 - 3*a10*b59 - 6*a10*b60 - 6*a10*b61 - 6*a10*b62 + 2*a11*b16 - 4*a11*
b51 - 8*a11*b52 - 2*a11*b53 - 4*a11*b54 - 12*a11*b55 - 4*a11*b56 + a12*b10 - 2*
a12*b43 - 8*a12*b44 - a12*b45 - 2*a12*b46 - 10*a12*b47 - 12*a5*b49 - 3*a5*b51 -
16*a6*b40 - 8*a6*b41 - 3*a6*b43 - 12*a7*b35 - 12*a7*b36 + 36*a9*b63,
80*a1*b31 - 4*a11*b27 - 4*a11*b28 - 12*a11*b29 - 8*a12*b23 - 16*a12*b24 - 14*
a12*b25 - 12*a13*b17 - 36*a13*b18 - 16*a13*b19 + 16*a3*b64 + 64*a4*b64 + 3*a5*
b29 - 8*a6*b21 - 4*a6*b22 + a6*b25 + 4*a6*b59 + 4*a6*b62 - 24*a7*b14 - 6*a7*b16
- a7*b19 + 6*a7*b53 + 6*a7*b56 - 8*a8*b10 + 8*a8*b45 - 48*a8*b8,
48*a1*b26 - 6*a10*b22 - 6*a10*b23 - 6*a10*b24 - 6*a10*b25 - 6*a11*b16 - 4*a11*
b17 - 12*a11*b18 - 4*a11*b19 - 6*a12*b10 - 2*a12*b11 - 10*a12*b12 + 8*a3*b57 +
40*a4*b57 - 12*a5*b14 - 4*a5*b15 - a5*b16 + 2*a5*b50 + 2*a5*b51 - 2*a6*b10 + 4*
a6*b42 + 4*a6*b43 - 16*a6*b8 - 8*a6*b9 - 12*a7*b2 - 12*a7*b3 + 6*a7*b37,
48*a1*b30 - 6*a10*b27 - 6*a10*b28 - 6*a10*b29 - 8*a11*b22 - 4*a11*b23 - 12*a11*
b24 - 4*a11*b25 - 8*a12*b16 - 2*a12*b17 - 10*a12*b18 - 2*a12*b19 - 8*a13*b10 +
6*a3*b63 + 42*a4*b63 - 12*a5*b21 - 16*a6*b14 - 8*a6*b15 - a6*b16 + 4*a6*b50 + 4
*a6*b51 - 2*a7*b10 + 6*a7*b42 + 6*a7*b43 - 12*a7*b8 - 12*a7*b9 - 16*a8*b3 + 8*
a8*b37
Relevance
In the following evolutionary system u=u(t,x) is a scalar function,
v=v(t,x) is a vector function and f(..,..) stands for the scalar
product of both vector arguments of f.
4 3
u = u *a1 + f(v ,v )*a3 + f(v,v )*a4 + f(v,v) *a8 + f(v,v) *a7*u
t 2x x x 2x
2 2 3 4
+ f(v,v) *a6*u + f(v,v)*a5*u + a2*u
3 2 2 3
v = v *a9 + f(v,v) *a13*v + f(v,v) *a12*u*v + f(v,v)*a11*u *v + a10*u *v
t 2x
For any solution of the above algebraic conditions for the
a's and b's this system has the following symmetry:
3 2 2
u = u *b1 + u *f(v,v) *b21 + u *f(v,v) *b14*u + u *f(v,v)*b8*u
t 4x 2x 2x 2x
3 2 2 2 2 2
+ u *b2*u + u *f(v,v) *b15 + u *f(v,v)*b9*u + u *b3*u
2x x x x
2 2
+ u *f(v,v )*f(v,v) *b22 + u *f(v,v )*f(v,v)*b16*u + u *f(v,v )*b10*u
x x x x x x
3
+ f(v ,v )*b5 + f(v ,v )*b6 + f(v ,v )*f(v,v) *b27
2x 2x x 3x x x
2 2 3
+ f(v ,v )*f(v,v) *b23*u + f(v ,v )*f(v,v)*b17*u + f(v ,v )*b11*u
x x x x x x
3 2
+ f(v,v )*b7 + f(v,v )*f(v,v) *b28 + f(v,v )*f(v,v) *b24*u
4x 2x 2x
2 3 2 2
+ f(v,v )*f(v,v)*b18*u + f(v,v )*b12*u + f(v,v ) *f(v,v) *b29
2x 2x x
2 2 2 7 6
+ f(v,v ) *f(v,v)*b25*u + f(v,v ) *b19*u + f(v,v) *b33 + f(v,v) *b32*u
x x
5 2 4 3 3 4 2 5
+ f(v,v) *b31*u + f(v,v) *b30*u + f(v,v) *b26*u + f(v,v) *b20*u
6 7
+ f(v,v)*b13*u + b4*u
2 2 2
v = u *f(v,v) *b49*v + u *f(v,v)*b40*u*v + u *b35*u *v + u *f(v,v)*b41*v
t 2x 2x 2x x
2 2 2
+ u *b36*u*v + u *v *f(v,v) *b50 + u *v *f(v,v)*b42*u + u *v *b37*u
x x x x x x x
+ u *f(v,v )*f(v,v)*b51*v + u *f(v,v )*b43*u*v + v *b34
x x x x 4x
3 2 2 3
+ v *f(v,v) *b58 + v *f(v,v) *b52*u + v *f(v,v)*b44*u + v *b38*u
2x 2x 2x 2x
2 2
+ v *f(v,v )*f(v,v) *b59 + v *f(v,v )*f(v,v)*b53*u + v *f(v,v )*b45*u
x x x x x x
2 2
+ f(v ,v )*f(v,v) *b60*v + f(v ,v )*f(v,v)*b54*u*v + f(v ,v )*b46*u *v
x x x x x x
2 2
+ f(v,v )*f(v,v) *b61*v + f(v,v )*f(v,v)*b55*u*v + f(v,v )*b47*u *v
2x 2x 2x
2 2 6
+ f(v,v ) *f(v,v)*b62*v + f(v,v ) *b56*u*v + f(v,v) *b66*v
x x
5 4 2 3 3
+ f(v,v) *b65*u*v + f(v,v) *b64*u *v + f(v,v) *b63*u *v
2 4 5 6
+ f(v,v) *b57*u *v + f(v,v)*b48*u *v + b39*u *v
.