Problem l112o24
Unknowns | Inequalities |
Equations |
Solution 1 |
Solution 2 |
Solution 3 |
Solution 4 |
Solution 5 |
Solution 6 |
Solution 7 |
Solution 8 |
Solution 9 |
Solution 10 |
Solution 11 |
Solution 12 |
Solution 13 |
Solution 14 |
Solution 15 |
Solution 16 |
Solution 17 |
Solution 18 |
Solution 19 |
Solution 20 |
Solution 21 |
Solution 22 |
Solution 23 |
Solution 24 |
Solution 25 |
Solution 26 |
Solution 27 |
Solution 28 |
Solution 29 |
Solution 30 |
Solution 31 |
Solution 32 |
Solution 33 |
Solution 34 |
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Unknowns
All solutions for the following 106 unknowns have to be determined:
a1, ..., a19, b1, ..., b87
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,a5,a12},
{a6,a4,a5,a9,a7,a11,a10,a8},
{a13,a14,a18,a15},
{b1,b10,b46},
{b1,b2,b3,b4,b5,b6,b7,b8,b9,b10,b11,b12,b13,b14,b15,b16,b17,
b18,b19,b20,b21,b22,b23,b24,b25,b26,b27,b28,b29,b30,b31,b32,
b33,b34,b35,b36,b37,b38,b39,b40,b41,b42,b43,b44,b45},
{b46,b47,b48,b49,b50,b51,b52,b53,b54,b55,b56,b57,b58,b59,b60,
b61,b62,b63,b64,b65,b66,b67,b68,b69,b70,b71,b72,b73,b74,b75,
b76,b77,b78,b79,b80,b81,b82,b83,b84,b85,b86,b87}
Equations
All comma separated 322 expressions involving 4355 terms have to vanish.
All terms are products of one a- and one b-unknown.
a11*b67 + 4*a19*b75,
6*a11*b47 - a13*b38 - a18*b27 + 2*a19*b63 + a5*b80 + a9*b64,
a11*b2 - 6*a11*b47 + a13*b38 + a18*b27 + 2*a19*b11 - a5*b80 - a9*b64,
3*a10*b74 + 4*a11*b57 - 2*a15*b42 + 6*a15*b86 - a18*b36 + 2*a18*b83 - 2*a19*b74
+ a3*b86 + 2*a8*b83,
3*a10*b24 - 4*a10*b74 - 6*a11*b57 + 5*a11*b7 + 6*a15*b42 + 4*a18*b36 + 2*a19*
b24 - a3*b42 + a8*b36 - 2*a8*b83,
24*a11*b47 - 4*a12*b85 - a13*b39 + 2*a16*b79 - a17*b76 + a17*b79 + 4*a19*b59 +
4*a19*b62 + 12*a19*b63 + a9*b66,
4*a10*b64 + a10*b70 + 6*a11*b51 - a13*b41 - 2*a15*b38 - a18*b32 + 4*a18*b78 + 2
*a19*b70 + 2*a5*b83 + a7*b80 + a9*b71,
2*a1*b42 - a10*b18 - a11*b5 + 6*a11*b52 - 6*a13*b40 - 2*a15*b38 - a18*b30 - 2*
a19*b18 + 2*a5*b83 + 2*a6*b80 - 2*a8*b29 + a9*b71,
a10*b17 - 4*a10*b64 + 2*a11*b4 - 6*a11*b51 + a13*b41 + 2*a15*b38 + 4*a18*b29 +
a18*b32 + 2*a19*b17 - 2*a5*b83 - a7*b80 - a9*b71,
4*a10*b71 + 2*a10*b73 + 6*a11*b55 - 6*a13*b42 - 2*a15*b41 + 6*a15*b85 - 2*a17*
b83 - a18*b35 + 4*a18*b82 + 2*a19*b73 + 2*a7*b83 + 2*a8*b80 + a8*b82 + 3*a9*b74
,
18*a11*b47 - 2*a12*b85 - 2*a13*b37 - a13*b38 + 2*a17*b75 - 2*a17*b77 + 2*a17*
b78 - a18*b25 + 12*a19*b58 - 2*a19*b62 + 12*a19*b63 + 2*a4*b80 + a5*b80 + 3*a9*
b64,
a1*b86 + a10*b64 + a11*b51 - a12*b86 - a13*b40 + a13*b84 + a13*b85 - a16*b80 -
a17*b80 - a18*b29 + a18*b75 + a18*b78 - 2*a19*b64 + a6*b80,
a1*b38 + a10*b10 - 6*a11*b1 + 6*a11*b46 - a12*b38 - a16*b27 - a17*b27 - 6*a19*
b10 - a5*b29 + a5*b75 + a5*b78 + a6*b27 - a9*b11 + a9*b58 + a9*b63,
2*a10*b22 - 4*a10*b71 - 6*a11*b55 + 3*a11*b6 + 6*a13*b42 + 6*a15*b40 + 2*a15*
b41 + 4*a18*b34 + a18*b35 + 2*a19*b22 - a2*b42 - 2*a6*b83 - 2*a7*b83 + a8*b34 -
2*a8*b80 - 3*a9*b74,
4*a10*b64 + a10*b69 + 6*a11*b51 - 6*a12*b86 - a13*b41 - 2*a15*b37 - a18*b31 + 2
*a18*b75 + 2*a18*b77 + 2*a18*b78 + 4*a19*b67 - 2*a19*b69 + 4*a19*b70 + 2*a4*b83
+ a7*b80 + a9*b71,
2*a1*b37 + a1*b38 + a10*b8 - 18*a11*b1 - a12*b38 - a16*b25 - 3*a17*b27 - 12*a19
*b10 - 2*a19*b8 - 2*a4*b29 - a5*b29 + a5*b75 + 2*a5*b77 + a5*b78 + a6*b25 - 3*
a9*b11 + a9*b62,
72*a11*b47 - 8*a12*b85 - 4*a13*b38 - 2*a13*b39 + 6*a16*b78 - 4*a17*b75 - a17*
b76 + 2*a17*b77 + 2*a17*b78 - a18*b28 + 24*a19*b58 + 8*a19*b62 + 48*a19*b63 +
a5*b82 + 6*a9*b64 + a9*b66 + a9*b70,
4*a1*b41 - 4*a10*b12 - 24*a11*b2 - a14*b39 - 2*a16*b33 - 2*a17*b33 - 2*a18*b26
- 2*a18*b28 - 4*a19*b15 - 12*a19*b16 + a2*b39 + 2*a4*b82 + 4*a5*b81 + 2*a5*b82
+ a7*b76 + a7*b79 - a9*b19 + a9*b68,
4*a1*b37 + 2*a1*b39 - 72*a11*b1 - 2*a16*b25 - a16*b26 - 2*a17*b25 - a17*b26 -
24*a19*b10 - 12*a19*b9 - a4*b31 + 2*a4*b76 + 2*a4*b77 + 2*a5*b77 + 2*a5*b79 +
a6*b26 - 6*a9*b11 - a9*b13 + a9*b60,
8*a10*b64 + 4*a10*b66 + 24*a11*b51 - 24*a12*b86 - 4*a13*b41 - 2*a15*b39 + 2*a16
*b82 - 4*a17*b81 - a18*b33 + 4*a18*b77 + 4*a18*b78 + 6*a18*b79 + 8*a19*b67 + 8*
a19*b69 + 16*a19*b70 + a7*b82 + 2*a9*b71 + 2*a9*b73,
72*a11*b47 - 12*a12*b85 - 4*a13*b37 - 2*a13*b39 + 4*a16*b77 + 2*a16*b78 - a17*
b76 + 2*a17*b77 + 2*a17*b78 - a18*b26 + 24*a19*b58 + 4*a19*b59 + 12*a19*b62 +
36*a19*b63 + a4*b82 + 6*a9*b64 + a9*b66 + a9*b69,
2*a10*b71 + 2*a11*b55 - 2*a13*b42 + 6*a13*b86 - a14*b86 - 2*a15*b40 + 2*a15*b84
+ 2*a15*b85 - 2*a16*b83 - 2*a17*b83 - a18*b34 + 2*a18*b80 + a18*b81 + a18*b82
- 2*a19*b71 + a2*b86 + 2*a6*b83 + 2*a8*b80,
8*a1*b37 + 10*a1*b39 - 288*a11*b1 - 6*a16*b26 - 2*a16*b28 - 6*a17*b26 - 2*a17*
b28 - 96*a19*b10 - 48*a19*b9 - a4*b33 + 4*a4*b76 + 4*a4*b77 + 6*a4*b79 + 6*a5*
b76 + 4*a5*b77 + 4*a5*b79 + a7*b26 - 6*a9*b12 - 2*a9*b13 + 2*a9*b60,
4*a1*b38 + 2*a1*b39 - 72*a11*b1 - 4*a12*b38 - 6*a16*b27 - a16*b28 - a17*b25 - 3
*a17*b27 - a17*b28 - 48*a19*b10 - 8*a19*b8 - a5*b32 + 4*a5*b75 + 2*a5*b76 + 4*
a5*b78 + 2*a5*b79 + a6*b28 - 6*a9*b11 - a9*b14 + a9*b59 + a9*b61,
2*a1*b37 + 2*a1*b38 + a10*b9 - 24*a11*b1 - 2*a12*b37 - a16*b25 - a16*b27 - 4*
a17*b27 - 16*a19*b10 - 2*a19*b9 - 2*a4*b29 + 2*a4*b75 - 2*a5*b29 + 2*a5*b77 + 2
*a5*b78 + a6*b25 + a6*b27 - 4*a9*b11 + a9*b58 + a9*b62 + a9*b63,
2*a10*b22 + a10*b23 - 2*a10*b72 - 2*a10*b73 - 3*a11*b56 + 3*a11*b6 + 3*a14*b42
+ 3*a15*b41 + 2*a16*b36 + 2*a17*b36 + 3*a18*b35 + 3*a19*b23 - 3*a2*b42 - a3*b41
- 2*a6*b36 + a7*b36 - 3*a7*b83 + a8*b34 - a8*b81 - a8*b82 + 2*a9*b24 - 3*a9*
b74,
8*a1*b38 + 10*a1*b39 - 288*a11*b1 - 2*a12*b39 - 8*a16*b28 - 2*a17*b26 - 6*a17*
b28 - 144*a19*b10 - 16*a19*b8 - 24*a19*b9 + 4*a4*b78 + 4*a4*b79 - a5*b33 + 8*a5
*b75 + 10*a5*b76 + 4*a5*b78 + 6*a5*b79 + a7*b28 - 6*a9*b12 - 2*a9*b14 + 2*a9*
b59 + 2*a9*b61,
12*a1*b40 - 12*a10*b11 - 6*a11*b3 + 6*a11*b48 - 2*a13*b37 - 2*a13*b38 - 2*a13*
b39 - a14*b38 - 4*a16*b29 - 4*a17*b29 - a18*b25 - 9*a18*b27 - a18*b28 - 6*a19*
b12 + 2*a4*b80 + 10*a5*b80 + a5*b81 + a5*b82 - a9*b17 + 6*a9*b64 + a9*b65 + a9*
b66,
8*a10*b64 + a10*b66 + 12*a11*b52 - 12*a12*b86 - 6*a13*b40 - a13*b41 + 6*a13*b85
+ a14*b85 - a16*b82 - 2*a17*b80 - a17*b81 - a17*b82 - a18*b30 + 4*a18*b75 +
a18*b76 + 2*a18*b77 + 6*a18*b78 + 2*a18*b79 + 2*a19*b66 + 2*a6*b80 + a6*b82 +
a7*b80 + a9*b71,
a1*b41 - 4*a10*b11 + 4*a10*b58 + 4*a10*b63 - 6*a11*b2 + 6*a11*b50 - a12*b41 -
a14*b38 - a16*b32 - a17*b32 - 6*a18*b27 - 6*a19*b16 + a2*b38 - a5*b34 + a5*b81
+ a5*b82 + a6*b32 - a7*b29 + a7*b75 + a7*b78 + 2*a8*b27 - a9*b17 + a9*b67 + a9*
b70,
8*a1*b38 + 2*a1*b39 - 96*a11*b1 - 2*a12*b39 - 10*a16*b27 - a16*b28 - a17*b25 -
7*a17*b27 - a17*b28 - 64*a19*b10 - 8*a19*b9 + 2*a4*b78 - a5*b30 + 8*a5*b75 + 2*
a5*b76 + 6*a5*b78 + 2*a5*b79 + 2*a6*b27 + a6*b28 + a7*b27 - 8*a9*b11 - a9*b12 -
a9*b16 + 4*a9*b58 + a9*b59 + a9*b61 + 4*a9*b63,
6*a1*b40 + 2*a1*b41 - 12*a10*b11 - 6*a11*b3 - 6*a13*b37 - 2*a14*b37 - a16*b30 -
a17*b30 - 2*a18*b25 - a18*b26 - 6*a18*b27 - 2*a19*b13 - 4*a19*b14 + a2*b37 -
a4*b34 + 2*a4*b80 + 2*a4*b81 + 4*a5*b80 + 2*a5*b82 - 2*a6*b29 + a6*b30 + 2*a6*
b77 - 2*a7*b29 - 2*a9*b18 + a9*b65 + a9*b66 + a9*b69,
6*a1*b42 - 4*a10*b17 - a10*b20 + 4*a10*b69 - 6*a11*b4 - a14*b41 - 6*a15*b37 -
a16*b35 - a17*b35 - 4*a18*b31 - 2*a18*b32 - 2*a19*b20 - 4*a19*b21 + a2*b41 + 3*
a3*b37 - 3*a4*b36 + 2*a4*b83 + 4*a5*b83 + a6*b35 - a7*b34 + a7*b81 + a7*b82 - 2
*a8*b29 + a8*b31 + 2*a8*b77 - a9*b22 + a9*b72 + a9*b73,
24*a1*b40 + 8*a1*b41 - 24*a10*b11 - 8*a10*b12 - 24*a11*b3 - 6*a13*b39 - 2*a14*
b39 - 4*a16*b30 - 4*a17*b30 - 4*a18*b25 - 2*a18*b26 - 12*a18*b27 - 6*a18*b28 -
8*a19*b13 - 16*a19*b14 + a2*b39 + 8*a4*b80 + 2*a4*b82 + 16*a5*b80 + 8*a5*b81 +
6*a5*b82 + 2*a6*b76 + 2*a6*b79 - 4*a9*b18 - a9*b19 + 4*a9*b65 + 4*a9*b66 + a9*
b68,
6*a1*b42 - 4*a10*b17 - a10*b21 + 4*a10*b67 + 4*a10*b70 - 6*a11*b4 + 6*a11*b54 -
6*a12*b42 - a14*b41 - 6*a15*b38 - a16*b35 - a17*b35 - 6*a18*b32 - 6*a19*b21 +
a2*b41 + 3*a3*b38 - 3*a5*b36 + 6*a5*b83 + a6*b35 - a7*b34 + a7*b81 + a7*b82 - 2
*a8*b29 + a8*b32 + 2*a8*b75 + 2*a8*b78 - a9*b22 + a9*b72 + a9*b73,
6*a1*b40 + 2*a1*b41 - 12*a10*b11 - 6*a11*b3 + 6*a11*b49 - 6*a12*b40 - 6*a13*b38
- 2*a14*b38 - a16*b30 - a17*b30 - a18*b25 - 9*a18*b27 - a18*b28 - 6*a19*b14 +
a2*b38 - a5*b34 + 6*a5*b80 + 2*a5*b81 + 2*a5*b82 - 2*a6*b29 + a6*b30 + 2*a6*b75
+ 2*a6*b78 - 2*a7*b29 - 2*a9*b18 + a9*b65 + a9*b66 + a9*b67 + a9*b70,
24*a1*b42 - 8*a10*b17 - 4*a10*b19 + 4*a10*b68 - 24*a11*b4 - 4*a14*b41 - 6*a15*
b39 - 4*a16*b35 - 4*a17*b35 - 4*a18*b31 - 4*a18*b32 - 8*a18*b33 - 8*a19*b20 -
16*a19*b21 + 4*a2*b41 + 3*a3*b39 + 8*a4*b83 + 16*a5*b83 + 2*a6*b35 - a7*b35 + 4
*a7*b81 + 4*a7*b82 - 2*a8*b30 + a8*b33 + 2*a8*b76 + 2*a8*b79 - 2*a9*b22 - 3*a9*
b23 + 4*a9*b72 + 4*a9*b73,
3*a1*b41 - 12*a10*b11 + 4*a10*b62 - 18*a11*b2 - a12*b41 - 2*a14*b37 - a14*b38 -
2*a16*b31 - a16*b32 - 3*a17*b32 - 4*a18*b25 - 6*a18*b27 - 2*a19*b15 - 12*a19*
b16 + 2*a2*b37 + a2*b38 - 2*a4*b34 + 2*a4*b81 - a5*b34 + a5*b81 + 3*a5*b82 + 2*
a6*b31 + a6*b32 - 3*a7*b29 + a7*b75 + 2*a7*b77 + a7*b78 + 2*a8*b25 - 3*a9*b17 +
a9*b67 + 2*a9*b69 + a9*b70,
4*a1*b37 + 4*a1*b38 + 4*a1*b39 - 144*a11*b1 - 4*a12*b37 - 2*a16*b25 - a16*b26 -
6*a16*b27 - a16*b28 - 3*a17*b25 - a17*b26 - 3*a17*b27 - a17*b28 - 72*a19*b10 -
8*a19*b8 - 12*a19*b9 - a4*b32 + 2*a4*b76 + 2*a4*b78 - a5*b31 + 4*a5*b75 + 2*a5
*b76 + 4*a5*b77 + 2*a5*b78 + 4*a5*b79 + a6*b26 + a6*b28 - 12*a9*b11 - a9*b13 -
a9*b14 + a9*b59 + a9*b60 + a9*b61,
16*a1*b37 + 8*a1*b38 + 6*a1*b39 - 288*a11*b1 - 2*a12*b39 - 8*a16*b25 - 2*a16*
b26 - 6*a16*b27 - a16*b28 - 7*a17*b25 - 9*a17*b27 - 3*a17*b28 - 144*a19*b10 -
16*a19*b8 - 24*a19*b9 - 2*a4*b30 + 8*a4*b75 + 2*a4*b76 + 4*a4*b77 + 2*a4*b78 -
a5*b30 + 4*a5*b76 + 12*a5*b77 + 6*a5*b78 + 6*a5*b79 + 2*a6*b25 + 2*a6*b26 + a6*
b28 + a7*b25 - 24*a9*b11 - 3*a9*b12 - a9*b15 + a9*b59 + 2*a9*b60 + a9*b61 + 4*
a9*b62,
24*a1*b42 - 8*a10*b17 - 8*a10*b18 - a10*b19 + 4*a10*b65 + 4*a10*b66 - 12*a11*b5
+ 6*a11*b53 - 6*a13*b41 - 6*a14*b40 - a14*b41 - 4*a15*b37 - 4*a15*b38 - 4*a15*
b39 - 4*a16*b34 - 4*a17*b34 - 6*a18*b30 - 2*a18*b31 - 6*a18*b32 - 2*a18*b33 - 6
*a19*b19 + 6*a2*b40 + a2*b41 + 4*a4*b83 + 20*a5*b83 + 2*a6*b34 + 2*a6*b81 + 2*
a6*b82 - a7*b34 + 6*a7*b80 + a7*b81 + a7*b82 - 8*a8*b29 - 2*a9*b22 + 6*a9*b71 +
2*a9*b72 + 2*a9*b73,
12*a1*b41 - 24*a10*b11 - 4*a10*b12 - 4*a10*b13 + 4*a10*b60 - 72*a11*b2 - 4*a14*
b37 - 2*a14*b39 - 6*a16*b31 - 2*a16*b32 - 2*a16*b33 - 6*a17*b31 - 2*a17*b32 - 2
*a17*b33 - 6*a18*b25 - 6*a18*b26 - 6*a18*b27 - 2*a18*b28 - 12*a19*b15 - 36*a19*
b16 + 4*a2*b37 + 2*a2*b39 - 2*a4*b35 + 8*a4*b81 + 4*a4*b82 + 4*a5*b81 + 8*a5*
b82 + 2*a6*b31 + 2*a6*b33 - a7*b30 + 2*a7*b76 + 4*a7*b77 + 2*a7*b79 + 2*a8*b26
- 6*a9*b17 - a9*b19 - 2*a9*b20 + 2*a9*b68 + 4*a9*b69,
12*a1*b41 - 24*a10*b11 - 4*a10*b12 - 4*a10*b14 + 4*a10*b59 + 4*a10*b61 - 72*a11
*b2 - 4*a12*b41 - 4*a14*b38 - 2*a14*b39 - 8*a16*b32 - 2*a16*b33 - 2*a17*b31 - 6
*a17*b32 - 2*a17*b33 - 4*a18*b25 - 12*a18*b27 - 8*a18*b28 - 8*a19*b15 - 48*a19*
b16 + 4*a2*b38 + 2*a2*b39 + 2*a4*b82 - 2*a5*b35 + 12*a5*b81 + 10*a5*b82 + 2*a6*
b32 + 2*a6*b33 - a7*b30 + 4*a7*b75 + 2*a7*b76 + 4*a7*b78 + 2*a7*b79 + 2*a8*b28
- 6*a9*b17 - a9*b19 - 2*a9*b21 + 4*a9*b67 + 2*a9*b68 + 4*a9*b70,
2*a10*b72 + 3*a11*b56 - a14*b42 + 6*a15*b84 - 2*a16*b83 + 4*a18*b81 + 2*a19*b72
+ a8*b81,
6*a11*b48 - 2*a12*b85 - a14*b38 - 2*a16*b78 + 2*a17*b75 + a17*b76 + 12*a19*b58
+ 6*a19*b61 + a5*b81 + a9*b65,
a10*b65 + a11*b53 - 2*a12*b86 + 6*a13*b84 - a14*b40 + a14*b84 - 2*a16*b80 - a16
*b81 + 2*a18*b75 + a18*b76 + 2*a19*b65 + a6*b81,
4*a10*b65 + a10*b68 + 6*a11*b53 - 12*a12*b86 - a14*b41 - 2*a16*b82 + 4*a17*b81
+ 4*a18*b75 + 6*a18*b76 + 8*a19*b67 + 6*a19*b68 + a7*b81 + 2*a9*b72,
24*a11*b48 - 24*a12*b84 - 8*a12*b85 - a14*b39 + 2*a16*b76 - 2*a16*b79 + 4*a17*
b76 + 24*a19*b58 + 8*a19*b59 + 8*a19*b60 + 16*a19*b61 + 2*a9*b65 + a9*b68,
6*a11*b48 - 6*a12*b84 - 2*a12*b85 - a14*b37 + 2*a16*b75 - 2*a16*b77 + 2*a17*b75
+ a17*b76 + 12*a19*b58 + 2*a19*b60 + 4*a19*b61 + a4*b81 + a9*b65,
a10*b67 + 2*a11*b54 + 4*a18*b75 + 2*a19*b67,
6*a11*b49 - 12*a12*b84 + 4*a16*b75 + 4*a17*b75 + 12*a19*b58 + 6*a19*b59 + a9*
b67,
a11*b50 + 2*a19*b58,
a13*b27 + a18*b10 - a5*b64 - a9*b47,
2*a10*b57 - 2*a10*b7 - 2*a15*b36 - a18*b24 - a8*b24 + a8*b74,
4*a10*b57 - 2*a15*b36 + 4*a15*b83 - a18*b24 - 4*a19*b57 + 2*a3*b83 + 3*a8*b74,
4*a10*b47 - a13*b32 - 2*a15*b27 - a18*b16 + 2*a18*b63 + a5*b71 + a7*b64 + a9*
b51,
2*a12*b77 + 2*a12*b79 + a13*b26 - 2*a16*b62 - 2*a17*b62 - 24*a19*b46 - a4*b69 -
6*a9*b47,
a10*b2 - 4*a10*b47 + a13*b32 + 2*a15*b27 + 2*a18*b11 + a18*b16 - a5*b71 - a7*
b64 - a9*b51,
2*a12*b79 + a13*b28 - 6*a16*b63 + a17*b59 - a17*b62 - 3*a17*b63 - 24*a19*b46 -
a5*b70 - 6*a9*b47,
a1*b27 - a12*b27 - a16*b10 - a17*b10 - a5*b11 + a5*b58 + a5*b63 + a6*b10 - a9*
b1 + a9*b46,
2*a12*b77 + a13*b25 - 3*a17*b58 + a17*b62 - 3*a17*b63 + a18*b8 - 12*a19*b46 - 2
*a4*b64 - a5*b64 - 3*a9*b47,
4*a10*b51 - a13*b35 - 2*a15*b32 + 4*a15*b78 - a18*b21 + 2*a18*b70 + 3*a5*b74 +
a7*b71 + 2*a8*b64 + a8*b70 + a9*b55,
4*a12*b78 + 2*a13*b27 + a13*b28 - 8*a16*b63 + 2*a17*b58 + a17*b61 - a17*b62 - 3
*a17*b63 - 32*a19*b46 - a5*b66 - 8*a9*b47,
2*a12*b78 + a13*b25 + a13*b27 - 3*a17*b58 + a17*b62 - 3*a17*b63 + a18*b9 - 16*
a19*b46 - 2*a4*b64 - 2*a5*b64 - 4*a9*b47,
2*a10*b4 - 4*a10*b51 + a13*b35 + 4*a15*b29 + 2*a15*b32 + 2*a18*b17 + a18*b21 -
3*a5*b74 - a7*b71 + a8*b17 - 2*a8*b64 - a9*b55,
4*a10*b55 - 4*a13*b36 - 2*a15*b35 + 4*a15*b82 - 2*a17*b74 - a18*b23 + 2*a18*b73
+ a3*b82 + 3*a7*b74 + 2*a8*b71 + 2*a8*b73 + 4*a9*b57,
2*a1*b34 - a10*b3 - 4*a13*b29 - a13*b30 - 6*a15*b27 - a18*b12 - a18*b14 - 2*a2*
b29 + 3*a5*b71 + 2*a6*b64 - 6*a8*b11 + a9*b51 + 2*a9*b52,
4*a10*b51 - 4*a12*b83 - a13*b35 - a15*b33 + 2*a15*b79 + a16*b73 - a17*b72 + 2*
a18*b69 + 2*a18*b70 + 4*a19*b54 + a7*b73 + a8*b66 + a9*b55,
2*a12*b78 + 4*a12*b79 + a13*b26 + a13*b28 - 2*a16*b62 - 6*a16*b63 + a17*b59 - 3
*a17*b62 - 3*a17*b63 - 48*a19*b46 - a4*b70 - a5*b69 - 12*a9*b47,
a1*b80 + a10*b47 - a12*b80 - a13*b29 + a13*b75 + a13*b78 - a16*b64 - a17*b64 -
a18*b11 + a18*b58 + a18*b63 - 4*a19*b47 + a6*b64,
2*a1*b31 + 2*a1*b33 - 24*a10*b1 - a14*b26 - 2*a16*b15 - 2*a17*b15 - 6*a18*b9 +
a2*b26 - 2*a4*b20 + 2*a4*b68 + 2*a4*b69 - a7*b13 + a7*b60 - 6*a9*b2,
4*a10*b55 - 3*a10*b6 - 4*a13*b36 - 4*a15*b34 - 2*a15*b35 - 2*a18*b22 - a18*b23
+ a2*b36 - a3*b34 + 2*a6*b74 + 3*a7*b74 - 2*a8*b22 + 2*a8*b71 + 4*a9*b57,
4*a10*b51 - 4*a12*b83 - a13*b35 - 2*a15*b31 + 4*a15*b77 - a18*b20 + 2*a18*b67 +
2*a18*b70 + 4*a19*b54 + 3*a4*b74 + a7*b71 + 2*a8*b64 + a8*b69 + a9*b55,
2*a1*b27 + 3*a1*b28 - 2*a12*b27 - a12*b28 - 20*a16*b10 - 10*a17*b10 - 2*a17*b8
- a17*b9 - a5*b14 - a5*b16 + 2*a5*b58 + 3*a5*b59 + 3*a5*b61 + 2*a5*b63 - 20*a9*
b1,
4*a1*b27 + a1*b28 - a12*b28 - 10*a16*b10 - 6*a17*b10 - a17*b9 + 2*a4*b63 - a5*
b12 + 4*a5*b58 + a5*b59 + a5*b61 + 2*a5*b63 + a7*b10 - 10*a9*b1 + 2*a9*b46,
a1*b25 + 2*a1*b27 - a12*b25 - a16*b10 - a16*b9 - 5*a17*b10 - 2*a4*b11 + 2*a4*
b58 - 3*a5*b11 + a5*b62 + 2*a5*b63 + a6*b10 + a6*b9 - 5*a9*b1 + a9*b46,
3*a1*b25 + a1*b27 - a12*b25 - a12*b27 - 2*a16*b8 - a16*b9 - 10*a17*b10 - 6*a4*
b11 - 4*a5*b11 + a5*b58 + 3*a5*b62 + a5*b63 + 2*a6*b8 + a6*b9 - 10*a9*b1,
6*a1*b36 - 2*a10*b5 + 4*a10*b52 - 4*a13*b34 - 2*a15*b30 - 2*a15*b32 - 2*a18*b18
- a18*b19 - 6*a3*b29 + 6*a5*b74 + 2*a6*b71 + a7*b71 - 2*a8*b17 - 2*a8*b18 + 2*
a9*b55,
2*a10*b52 - 2*a12*b83 - a13*b34 + 4*a13*b80 + 2*a15*b75 + 2*a15*b78 - a16*b71 -
a17*b71 - a18*b18 + a18*b65 + a18*b66 - 4*a19*b52 + a2*b80 + a6*b71 + 2*a8*b64
,
a1*b26 + 2*a1*b27 + 2*a1*b28 - a12*b26 - 12*a16*b10 - 2*a16*b9 - 4*a17*b10 - 4*
a17*b9 - a4*b16 + 2*a4*b61 + 2*a4*b63 - a5*b13 + 2*a5*b58 + 2*a5*b59 + a5*b60 -
20*a9*b1,
12*a10*b47 - 2*a12*b82 - 2*a13*b31 - a13*b32 - 2*a15*b25 + 2*a17*b67 - 2*a17*
b69 + 2*a17*b70 - a18*b15 + 6*a18*b58 + 6*a18*b63 + 12*a19*b50 + 2*a4*b71 + a5*
b71 + 3*a7*b64 + 3*a9*b51,
2*a1*b25 + 7*a1*b26 + 2*a1*b28 - a12*b26 - 4*a16*b8 - 12*a16*b9 - 4*a17*b8 - 12
*a17*b9 - 2*a4*b13 - a4*b15 + 2*a4*b59 + 6*a4*b60 + 2*a4*b61 + 2*a4*b62 - a5*
b13 + a5*b60 - 60*a9*b1,
24*a10*b47 - 4*a12*b82 - 2*a13*b32 - 2*a13*b33 - 2*a15*b28 + 6*a16*b70 - 2*a17*
b67 - a17*b68 + 2*a17*b69 + 2*a17*b70 + 4*a18*b62 + 12*a18*b63 + 24*a19*b50 + 2
*a5*b73 + a7*b66 + a7*b70 + 6*a9*b51,
8*a12*b77 + 4*a12*b78 + 4*a12*b79 + 2*a13*b25 + 2*a13*b26 + a13*b28 - 6*a16*b62
- 6*a16*b63 - 2*a17*b59 + 2*a17*b60 + a17*b61 - 3*a17*b62 - 9*a17*b63 - 96*a19
*b46 - 2*a4*b66 - a5*b66 - 24*a9*b47,
24*a10*b47 - 8*a12*b80 - 4*a12*b82 - 2*a13*b30 - a13*b33 + 4*a13*b79 + 2*a14*
b79 + 2*a16*b66 - 2*a17*b65 - a17*b68 + 4*a18*b59 + 4*a18*b62 + 12*a18*b63 + 8*
a19*b49 + 2*a6*b66 + a7*b66 + 4*a9*b52,
4*a10*b56 - 4*a10*b6 - 4*a14*b36 - 4*a15*b35 - 2*a16*b24 - 2*a17*b24 - 4*a18*
b23 + 4*a2*b36 + a3*b35 + 2*a6*b24 - 3*a7*b24 + 4*a7*b74 - 2*a8*b22 - a8*b23 +
2*a8*b72 + 2*a8*b73 + 4*a9*b57 - 5*a9*b7,
4*a1*b25 + 2*a1*b26 + a1*b28 - a12*b28 - 6*a16*b10 - 8*a16*b8 - 12*a17*b10 - 2*
a17*b8 - 3*a17*b9 - 2*a4*b12 + 2*a4*b62 - a5*b12 + a5*b59 + 2*a5*b60 + a5*b61 +
2*a5*b62 + a7*b8 - 30*a9*b1,
8*a1*b29 - 16*a10*b1 - a13*b25 - 3*a13*b27 - a13*b28 - a14*b27 - 2*a16*b11 - 2*
a17*b11 - 12*a18*b10 - a18*b9 + 2*a4*b64 + 6*a5*b64 + a5*b65 + a5*b66 - 4*a6*
b11 - a9*b2 + 4*a9*b47 + a9*b48,
24*a10*b47 - 6*a12*b82 - 2*a13*b31 - 2*a13*b33 - 2*a15*b26 + 4*a16*b69 + 2*a16*
b70 - a17*b68 + 2*a17*b69 + 2*a17*b70 + 2*a18*b59 + 6*a18*b62 + 6*a18*b63 + 24*
a19*b50 + 2*a4*b73 + a7*b66 + a7*b69 + 6*a9*b51,
3*a10*b55 - 3*a13*b36 + 4*a13*b83 - 2*a14*b83 - 2*a15*b34 + 4*a15*b80 + 2*a15*
b81 + 2*a15*b82 - 3*a16*b74 - 3*a17*b74 - a18*b22 + a18*b72 + a18*b73 - 4*a19*
b55 + 2*a2*b83 + 3*a3*b80 + 3*a6*b74 + 3*a8*b71,
4*a1*b36 - 4*a10*b4 - a14*b35 - 2*a15*b33 - a16*b23 - a17*b23 - 2*a18*b20 - 2*
a18*b21 + a2*b35 + a3*b33 + 2*a4*b74 + 2*a5*b74 - a7*b23 + a7*b72 + a7*b73 - a8
*b19 + a8*b68 + a9*b56 - a9*b6,
2*a1*b32 + 2*a1*b33 - 24*a10*b1 - 2*a12*b32 - a14*b28 - 6*a16*b16 - a17*b15 - 3
*a17*b16 - 12*a18*b10 - 4*a18*b8 + a2*b28 - 2*a5*b21 + 2*a5*b67 + 2*a5*b68 + 2*
a5*b70 - a7*b14 + a7*b59 + a7*b61 - 6*a9*b2,
a1*b32 - 4*a10*b1 + 4*a10*b46 - a12*b32 - a14*b27 - a16*b16 - a17*b16 - 4*a18*
b10 + a2*b27 - a5*b17 + a5*b67 + a5*b70 + a6*b16 - a7*b11 + a7*b58 + a7*b63 + 2
*a8*b10 - a9*b2 + a9*b50,
8*a1*b29 + 4*a1*b30 - 48*a10*b1 - 2*a13*b26 - 2*a13*b28 - a14*b28 - 2*a16*b12 -
2*a17*b12 - 24*a18*b10 - 6*a18*b9 + 4*a4*b64 + 2*a4*b66 + 4*a5*b64 + 4*a5*b65
+ 2*a5*b66 + a5*b68 - 4*a6*b12 - 2*a9*b3 + 2*a9*b48,
12*a10*b47 - 2*a12*b82 - a13*b30 - a13*b32 + 4*a13*b78 + 2*a14*b78 - a16*b70 -
a17*b67 - a17*b70 - a18*b14 + 6*a18*b58 + a18*b61 + a18*b62 + 9*a18*b63 + a5*
b71 + 2*a6*b64 + a6*b70 + 2*a7*b64 + 2*a9*b52,
2*a1*b83 + 2*a10*b51 - 2*a12*b83 - a13*b34 + a13*b81 + a13*b82 - a14*b80 - 2*
a15*b29 + 2*a15*b75 + 2*a15*b78 - a16*b71 - a17*b71 - a18*b17 + a18*b67 + a18*
b70 - 4*a19*b51 + a2*b80 + a6*b71 + 2*a8*b64,
2*a1*b31 + a1*b32 - 12*a10*b1 - a12*b32 - a14*b25 - a16*b15 - 3*a17*b16 - 6*a18
*b10 - 2*a18*b8 + a2*b25 - 2*a4*b17 - a5*b17 + a5*b67 + 2*a5*b69 + a5*b70 + a6*
b15 - 3*a7*b11 + a7*b62 + 2*a8*b8 - 3*a9*b2,
12*a10*b47 - 4*a12*b80 - 2*a12*b82 - a13*b30 - a13*b31 + 4*a13*b77 + 2*a14*b77
- a16*b69 - a17*b69 - a18*b13 + 6*a18*b58 + a18*b60 + 2*a18*b62 + 6*a18*b63 + 4
*a19*b49 + a4*b71 + 2*a6*b64 + a6*b69 + 2*a7*b64 + 2*a9*b52,
4*a1*b36 - 4*a10*b4 - a14*b35 - 4*a15*b31 - a16*b23 - a17*b23 - 2*a18*b20 - 2*
a18*b21 + a2*b35 + 2*a3*b31 - 4*a4*b24 + 2*a4*b74 + 2*a5*b74 + a6*b23 - a7*b22
+ a7*b72 + a7*b73 - 2*a8*b17 + 2*a8*b69 + a9*b56 - a9*b6,
2*a1*b25 + 4*a1*b26 + 5*a1*b28 - 2*a12*b25 - a12*b28 - 24*a16*b10 - 4*a16*b8 -
6*a16*b9 - 18*a17*b10 - 10*a17*b8 - 3*a17*b9 - 2*a4*b14 + 2*a4*b59 + 2*a4*b61 -
a5*b14 - a5*b15 + 3*a5*b59 + 4*a5*b60 + 3*a5*b61 + 2*a5*b62 - 60*a9*b1,
4*a1*b25 + 2*a1*b26 + 4*a1*b27 + 2*a1*b28 - 2*a12*b26 - 8*a16*b10 - 8*a16*b9 -
16*a17*b10 - 6*a17*b9 - 2*a4*b12 + 4*a4*b58 + 2*a4*b59 + 2*a4*b62 + 2*a4*b63 -
2*a5*b12 + 2*a5*b60 + 2*a5*b61 + 2*a5*b62 + 2*a5*b63 + a7*b9 - 40*a9*b1,
4*a1*b29 + 2*a1*b30 - 24*a10*b1 - 2*a13*b25 - a13*b26 - a14*b25 - a16*b12 - a17
*b12 - 12*a18*b10 - 3*a18*b9 - a4*b17 + 2*a4*b64 + 2*a4*b65 + 2*a5*b64 + 2*a5*
b66 + a5*b69 - 6*a6*b11 + a6*b12 - 3*a7*b11 - a9*b3 + a9*b48,
4*a1*b36 - 4*a10*b4 + 4*a10*b54 - 4*a12*b36 - a14*b35 - 4*a15*b32 - a16*b23 -
a17*b23 - 4*a18*b21 + a2*b35 + 2*a3*b32 - 4*a5*b24 + 4*a5*b74 + a6*b23 - a7*b22
+ a7*b72 + a7*b73 - 2*a8*b17 + 2*a8*b67 + 2*a8*b70 + a9*b56 - a9*b6,
a1*b35 - 4*a10*b2 + 4*a10*b50 - a12*b35 - a14*b32 - 4*a15*b27 - a16*b21 - a17*
b21 - 4*a18*b16 + a2*b32 + 3*a3*b27 - a5*b22 + a5*b72 + a5*b73 + a6*b21 - a7*
b17 + a7*b67 + a7*b70 - 2*a8*b11 + a8*b16 + 2*a8*b58 + 2*a8*b63 - a9*b4 + a9*
b54,
a1*b30 + 2*a1*b32 - 16*a10*b1 - a12*b30 - 4*a13*b27 - 3*a14*b27 - a16*b14 - a17
*b14 - 12*a18*b10 - a18*b9 + a2*b27 - 2*a5*b18 + a5*b65 + a5*b66 + 2*a5*b67 + 2
*a5*b70 - 2*a6*b11 + a6*b14 + 2*a6*b58 + 2*a6*b63 - 3*a7*b11 - a9*b3 + a9*b49 +
a9*b50,
4*a1*b29 + 2*a1*b30 - 24*a10*b1 - 4*a12*b29 - a13*b25 - 3*a13*b27 - a13*b28 - 3
*a14*b27 - a16*b12 - a17*b12 - 18*a18*b10 - 2*a18*b8 - a5*b17 + 4*a5*b64 + 2*a5
*b65 + 2*a5*b66 + a5*b67 + a5*b70 - 6*a6*b11 + a6*b12 - 3*a7*b11 - a9*b3 + a9*
b48 + a9*b49,
a1*b82 + 12*a10*b47 - 8*a12*b80 - a12*b82 - 4*a13*b29 - a13*b30 + a13*b76 + 2*
a13*b77 + 2*a13*b78 + 2*a13*b79 + a14*b78 - a16*b66 - 2*a17*b64 - a17*b65 - a17
*b66 - a18*b12 + 6*a18*b58 + a18*b59 + a18*b62 + 9*a18*b63 + 4*a6*b64 + a6*b66
+ a7*b64 + a9*b51,
4*a1*b32 + 2*a1*b33 - 32*a10*b1 - 2*a12*b33 - 2*a14*b27 - a14*b28 - 8*a16*b16 -
a17*b15 - 5*a17*b16 - 16*a18*b10 - 4*a18*b9 + 2*a2*b27 + a2*b28 + 2*a4*b70 -
a5*b19 + 4*a5*b67 + 2*a5*b68 + 2*a5*b70 - a7*b12 + 2*a7*b58 + a7*b59 + a7*b61 +
2*a7*b63 - 8*a9*b2 + 2*a9*b50,
8*a1*b34 + 2*a1*b35 - 8*a10*b3 - 4*a13*b30 - a14*b30 - 2*a15*b25 - 6*a15*b27 -
2*a15*b28 - 2*a16*b18 - 2*a17*b18 - 2*a18*b13 - 6*a18*b14 + 2*a4*b71 + 6*a5*b71
+ 2*a5*b72 + 2*a5*b73 - 2*a6*b18 + 2*a6*b65 + 2*a6*b66 - a7*b18 - 12*a8*b11 -
2*a8*b12 - a9*b5 + 4*a9*b52 + a9*b53,
6*a1*b35 - 24*a10*b2 - 2*a14*b31 - 2*a14*b33 - 4*a15*b26 - 4*a16*b20 - 2*a16*
b21 - 4*a17*b20 - 2*a17*b21 - 6*a18*b15 - 6*a18*b16 + 2*a2*b31 + 2*a2*b33 + 3*
a3*b26 - 3*a4*b23 + 4*a4*b72 + 4*a4*b73 + 2*a5*b72 + 2*a5*b73 - a7*b19 - a7*b20
+ 2*a7*b68 + 2*a7*b69 - 2*a8*b12 - 2*a8*b13 + 2*a8*b60 - 6*a9*b4,
2*a1*b31 + 2*a1*b32 - 16*a10*b1 - 2*a12*b31 - a14*b25 - a14*b27 - a16*b15 - a16
*b16 - 4*a17*b16 - 8*a18*b10 - 2*a18*b9 + a2*b25 + a2*b27 - 2*a4*b17 + 2*a4*b67
- 2*a5*b17 + 2*a5*b69 + 2*a5*b70 + a6*b15 + a6*b16 - 4*a7*b11 + a7*b58 + a7*
b62 + a7*b63 + 2*a8*b9 - 4*a9*b2 + a9*b50,
6*a1*b30 + 4*a1*b31 + 4*a1*b33 - 96*a10*b1 - 4*a13*b26 - 3*a14*b26 - 4*a16*b13
- 2*a16*b14 - 4*a17*b13 - 2*a17*b14 - 24*a18*b10 - 18*a18*b9 + a2*b26 - a4*b19
+ 4*a4*b65 + 4*a4*b66 + 2*a4*b68 + 2*a4*b69 + 2*a5*b65 + 2*a5*b66 + 2*a5*b68 +
2*a5*b69 - 2*a6*b12 - 2*a6*b13 + 2*a6*b60 - 2*a7*b12 - 6*a9*b3,
8*a10*b51 + 8*a10*b52 - 16*a12*b83 - 4*a13*b34 - 2*a13*b35 + 4*a13*b82 - 2*a15*
b30 + 2*a15*b76 + 4*a15*b77 + 4*a15*b78 + 4*a15*b79 - 2*a16*b73 - 2*a17*b71 - 2
*a17*b72 - 2*a17*b73 - a18*b19 + 2*a18*b66 + 4*a18*b67 + a18*b68 + 2*a18*b69 +
6*a18*b70 + a2*b82 + 2*a6*b71 + 2*a6*b73 + 2*a7*b71 + 8*a8*b64 + 2*a8*b66 + 2*
a9*b55,
6*a1*b35 - 24*a10*b2 - 2*a12*b35 - 2*a14*b32 - 2*a14*b33 - 4*a15*b28 - 6*a16*
b21 - 2*a17*b20 - 4*a17*b21 - 4*a18*b15 - 12*a18*b16 + 2*a2*b32 + 2*a2*b33 + 3*
a3*b28 + 2*a4*b73 - 3*a5*b23 + 6*a5*b72 + 4*a5*b73 - a7*b19 - a7*b21 + 2*a7*b67
+ 2*a7*b68 + 2*a7*b70 - 2*a8*b12 - 2*a8*b14 + 2*a8*b59 + 2*a8*b61 - 6*a9*b4 +
2*a9*b54,
2*a1*b31 + 2*a1*b32 + 4*a1*b33 - 48*a10*b1 - 2*a12*b31 - a14*b26 - a14*b28 - 2*
a16*b15 - 6*a16*b16 - 3*a17*b15 - 3*a17*b16 - 12*a18*b10 - 4*a18*b8 - 6*a18*b9
+ a2*b26 + a2*b28 - 2*a4*b21 + 2*a4*b68 + 2*a4*b70 - 2*a5*b20 + 2*a5*b67 + 2*a5
*b68 + 2*a5*b69 - a7*b13 - a7*b14 + a7*b59 + a7*b60 + a7*b61 - 12*a9*b2,
6*a1*b30 + 4*a1*b32 + 4*a1*b33 - 96*a10*b1 - 2*a12*b30 - 4*a13*b28 - 3*a14*b28
- 6*a16*b14 - 2*a17*b13 - 4*a17*b14 - 48*a18*b10 - 8*a18*b8 - 6*a18*b9 + a2*b28
+ 2*a4*b66 + 2*a4*b70 - a5*b19 + 6*a5*b65 + 4*a5*b66 + 4*a5*b67 + 4*a5*b68 + 2
*a5*b70 - 2*a6*b12 - 2*a6*b14 + 2*a6*b59 + 2*a6*b61 - 2*a7*b12 - 6*a9*b3 + 2*a9
*b49,
3*a1*b30 + 4*a1*b31 + 2*a1*b32 - 48*a10*b1 - a12*b30 - 4*a13*b25 - 3*a14*b25 -
2*a16*b13 - a16*b14 - 3*a17*b14 - 24*a18*b10 - 4*a18*b8 - 3*a18*b9 + a2*b25 - 4
*a4*b18 + 2*a4*b65 + 2*a4*b67 - 2*a5*b18 + a5*b65 + 3*a5*b66 + 4*a5*b69 + 2*a5*
b70 - 6*a6*b11 + 2*a6*b13 + a6*b14 + 2*a6*b62 - 9*a7*b11 - 3*a9*b3 + a9*b49,
3*a1*b35 - 12*a10*b2 - a12*b35 - 2*a14*b31 - a14*b32 - 4*a15*b25 - 2*a16*b20 -
a16*b21 - 3*a17*b21 - 2*a18*b15 - 6*a18*b16 + 2*a2*b31 + a2*b32 + 3*a3*b25 - 2*
a4*b22 + 2*a4*b72 - a5*b22 + a5*b72 + 3*a5*b73 + 2*a6*b20 + a6*b21 - 3*a7*b17 +
a7*b67 + 2*a7*b69 + a7*b70 - 6*a8*b11 + a8*b15 + 2*a8*b62 - 3*a9*b4 + a9*b54,
8*a1*b34 + 8*a1*b35 - 24*a10*b2 - 8*a10*b3 - 4*a13*b33 - 2*a14*b30 - 2*a14*b33
- 4*a15*b26 - 4*a15*b28 - 2*a16*b19 - 2*a17*b19 - 4*a18*b13 - 4*a18*b14 - 4*a18
*b15 - 12*a18*b16 + 2*a2*b30 + a2*b33 + 4*a4*b71 + 4*a4*b73 + 4*a5*b71 + 8*a5*
b72 + 4*a5*b73 - 2*a6*b19 + 2*a6*b68 - a7*b19 + 2*a7*b65 + 2*a7*b66 + a7*b68 -
8*a8*b12 - 4*a9*b5 + 2*a9*b53,
8*a1*b34 - 12*a10*b2 - 4*a10*b3 + 4*a10*b48 - 2*a13*b31 - 2*a13*b32 - 2*a13*b33
- 4*a14*b29 - a14*b32 - 2*a15*b25 - 6*a15*b27 - 2*a15*b28 - 2*a16*b17 - 2*a17*
b17 - 4*a18*b12 - a18*b15 - 9*a18*b16 + 4*a2*b29 + 2*a4*b71 + 6*a5*b71 + 2*a5*
b72 + 2*a5*b73 - 2*a6*b17 - a7*b17 + 4*a7*b64 + a7*b65 + a7*b66 - 12*a8*b11 - 2
*a9*b4 + 4*a9*b51 + a9*b53,
8*a1*b31 + 4*a1*b32 + 6*a1*b33 - 96*a10*b1 - 2*a12*b33 - 2*a14*b25 - 2*a14*b26
- a14*b28 - 6*a16*b15 - 6*a16*b16 - 5*a17*b15 - 9*a17*b16 - 24*a18*b10 - 8*a18*
b8 - 12*a18*b9 + 2*a2*b25 + 2*a2*b26 + a2*b28 - 2*a4*b19 + 4*a4*b67 + 2*a4*b68
+ 4*a4*b69 + 2*a4*b70 - a5*b19 + 4*a5*b68 + 4*a5*b69 + 2*a5*b70 - 3*a7*b12 + a7
*b59 + 2*a7*b60 + a7*b61 + 2*a7*b62 - 24*a9*b2,
4*a1*b34 + 4*a1*b35 - 12*a10*b2 - 4*a10*b3 - 4*a13*b31 - a14*b30 - 2*a14*b31 -
4*a15*b25 - 2*a15*b26 - a16*b19 - a17*b19 - 2*a18*b13 - 2*a18*b14 - 2*a18*b15 -
6*a18*b16 + a2*b30 + a2*b31 - 2*a4*b22 + 2*a4*b71 + 4*a4*b72 + 2*a5*b71 + 4*a5
*b73 - 2*a6*b17 + a6*b19 + 2*a6*b69 - 2*a7*b17 - 2*a7*b18 + a7*b65 + a7*b66 +
a7*b69 - 12*a8*b11 - 2*a9*b5 + a9*b53,
24*a1*b36 - 8*a10*b4 - 8*a10*b5 + 4*a10*b53 - 4*a13*b35 - 4*a14*b34 - a14*b35 -
4*a15*b30 - 4*a15*b31 - 4*a15*b32 - 4*a15*b33 - 2*a16*b22 - 2*a17*b22 - 4*a18*
b19 - 2*a18*b20 - 6*a18*b21 + 4*a2*b34 + a2*b35 + 6*a4*b74 + 18*a5*b74 + 2*a6*
b72 + 2*a6*b73 - 2*a7*b22 + 4*a7*b71 + 2*a7*b72 + 2*a7*b73 - 8*a8*b17 - 4*a8*
b18 - a8*b19 + 2*a8*b65 + 2*a8*b66 + 4*a9*b55 + 3*a9*b56 - 3*a9*b6,
4*a1*b34 + 4*a1*b35 - 12*a10*b2 - 4*a10*b3 + 4*a10*b49 - 4*a12*b34 - 4*a13*b32
- a14*b30 - 2*a14*b32 - 2*a15*b25 - 6*a15*b27 - 2*a15*b28 - a16*b19 - a17*b19 -
4*a18*b14 - a18*b15 - 9*a18*b16 + a2*b30 + a2*b32 - 2*a5*b22 + 4*a5*b71 + 4*a5
*b72 + 4*a5*b73 - 2*a6*b17 + a6*b19 + 2*a6*b67 + 2*a6*b70 - 2*a7*b17 - 2*a7*b18
+ a7*b65 + a7*b66 + a7*b67 + a7*b70 - 12*a8*b11 - 2*a9*b5 + a9*b53 + 2*a9*b54,
3*a10*b56 - a14*b36 + 4*a15*b81 - 2*a16*b74 + 2*a18*b72 + a3*b81 + 2*a8*b72,
2*a12*b78 + a14*b27 + 2*a16*b63 - 3*a17*b58 - a17*b61 - 16*a19*b46 - a5*b65 -
a9*b48,
4*a12*b76 + 4*a12*b78 + 4*a12*b79 + a14*b28 - 6*a16*b61 - 2*a17*b59 - 2*a17*b60
- 4*a17*b61 - 96*a19*b46 - a5*b68 - 6*a9*b48,
8*a10*b48 - 8*a12*b81 - 4*a12*b82 - a14*b33 + 2*a16*b68 + 2*a17*b68 + 4*a18*b59
+ 4*a18*b60 + 4*a18*b61 + 24*a19*b50 + a7*b68 + 2*a9*b53,
4*a10*b48 - 2*a12*b82 - a14*b32 - 2*a16*b70 + 2*a17*b67 + a17*b68 + 6*a18*b58 +
4*a18*b61 + 12*a19*b50 + 2*a5*b72 + a7*b65 + a9*b53,
2*a12*b76 + 4*a12*b77 + 2*a12*b78 + a14*b25 - 6*a16*b58 + 2*a16*b62 - 9*a17*b58
- 3*a17*b61 - 48*a19*b46 - 2*a4*b65 - a5*b65 - 3*a9*b48,
4*a10*b53 - 8*a12*b83 - a14*b35 + 4*a15*b76 - 2*a16*b73 + 2*a17*b72 + 4*a18*b67
+ 4*a18*b68 + 8*a19*b54 + 2*a7*b72 + 2*a8*b65 + a8*b68 + 3*a9*b56,
6*a12*b76 + 4*a12*b77 + 4*a12*b79 + a14*b26 - 2*a16*b59 - 4*a16*b60 - 2*a16*b61
- 2*a17*b59 - 4*a17*b60 - 2*a17*b61 - 96*a19*b46 - a4*b68 - 6*a9*b48,
a1*b81 + a10*b48 - 2*a12*b80 - a12*b81 + 2*a13*b75 + a13*b76 - a14*b29 + a14*
b75 - 2*a16*b64 - a16*b65 + 3*a18*b58 + a18*b61 + a6*b65,
2*a10*b53 - 4*a12*b83 + 4*a13*b81 - a14*b34 + 4*a15*b75 + 2*a15*b76 - 2*a16*b71
- 2*a16*b72 + 2*a18*b65 + 2*a18*b67 + a18*b68 + a2*b81 + 2*a6*b72 + 2*a8*b65,
4*a10*b48 - 4*a12*b81 - 2*a12*b82 - a14*b31 + 2*a16*b67 - 2*a16*b69 + 2*a17*b67
+ a17*b68 + 6*a18*b58 + 2*a18*b60 + 2*a18*b61 + 12*a19*b50 + 2*a4*b72 + a7*b65
+ a9*b53,
8*a10*b48 - 8*a12*b80 - 8*a12*b81 - 2*a12*b82 + 4*a13*b76 - a14*b30 + 2*a14*b76
- 2*a16*b66 - a16*b68 + 2*a17*b65 + 12*a18*b58 + 2*a18*b59 + 2*a18*b60 + 6*a18
*b61 + 8*a19*b49 + 2*a6*b65 + a6*b68 + a7*b65 + a9*b53,
2*a10*b54 + 4*a15*b75 + 2*a18*b67 + a8*b67,
4*a12*b75 + 2*a12*b76 - 3*a16*b59 - a17*b59 - 24*a19*b46 - a9*b49,
2*a12*b76 - 6*a16*b58 - 3*a17*b58 - a17*b59 - 24*a19*b46 - a5*b67 - a9*b49,
4*a12*b75 + 2*a12*b76 - 6*a16*b58 - 3*a17*b58 - a17*b59 - 24*a19*b46 - a4*b67 -
a9*b49,
a10*b49 - 2*a12*b81 + 4*a13*b75 + 2*a14*b75 - a16*b67 + 3*a18*b58 + a18*b59 +
a6*b67,
4*a10*b49 - 8*a12*b81 + 4*a16*b67 + 2*a17*b67 + 6*a18*b58 + 4*a18*b59 + 12*a19*
b50 + a7*b67 + 2*a9*b54,
a10*b50 + 2*a18*b58,
8*a12*b75 - 6*a16*b58 - 2*a17*b58 - 16*a19*b46 - a9*b50,
a13*b10 - a5*b47,
2*a15*b24 + a3*b24 - 2*a8*b57 + 3*a8*b7,
a1*b10 - a12*b10 - a5*b1 + a5*b46,
a13*b16 + 2*a15*b10 - a5*b51 - a7*b47,
2*a1*b8 + a1*b9 - a12*b9 - 6*a4*b1 - 4*a5*b1,
2*a1*b10 + a1*b9 - a12*b9 - 2*a4*b1 + 2*a4*b46 - 4*a5*b1,
2*a15*b24 - 2*a15*b74 + 2*a18*b57 + a18*b7 - 3*a3*b74 - 4*a8*b57,
a13*b21 + 2*a15*b16 - 2*a15*b63 - a5*b55 - a7*b51 - 2*a8*b47,
2*a12*b63 + a13*b10 + a13*b9 - 4*a17*b46 - 2*a4*b47 - 3*a5*b47,
2*a12*b62 + 2*a13*b8 + a13*b9 - 10*a17*b46 - 6*a4*b47 - 4*a5*b47,
a14*b24 + a15*b23 - a2*b24 - a7*b57 + 2*a7*b7 - a8*b56 + a8*b6,
2*a1*b18 - a13*b12 - 6*a15*b10 - 3*a2*b11 + a5*b51 + 2*a5*b52 - 6*a8*b1,
a13*b21 + 2*a15*b11 + 2*a15*b16 - a5*b55 - a7*b51 + a8*b2 - 2*a8*b47,
a13*b24 + a15*b23 - a15*b73 + a17*b57 - a3*b73 - 2*a7*b57 - a8*b55,
a13*b23 + 2*a15*b21 - 2*a15*b70 - a3*b70 - 4*a5*b57 - a7*b55 - 2*a8*b51,
a1*b16 - a12*b16 - a14*b10 + a2*b10 - a5*b2 + a5*b50 - a7*b1 + a7*b46,
a1*b10 + 2*a1*b8 + 2*a1*b9 - a12*b10 - 2*a12*b8 - 8*a4*b1 - 7*a5*b1 + a5*b46,
2*a1*b22 - 2*a13*b18 - 2*a15*b14 - a2*b18 - 6*a3*b11 + 2*a5*b55 + 2*a6*b52 - 2*
a8*b3,
a13*b23 + 2*a15*b17 + 2*a15*b21 + a3*b17 - 4*a5*b57 - a7*b55 + 2*a8*b4 - 2*a8*
b51,
4*a1*b11 - 4*a13*b10 - a13*b9 - a14*b10 + 2*a4*b47 + 2*a5*b47 + a5*b48 - 8*a6*
b1,
2*a12*b69 + a13*b15 + 2*a15*b8 - 3*a17*b50 - 6*a18*b46 - 2*a4*b51 - a5*b51 - 3*
a7*b47,
2*a13*b24 + 2*a15*b22 + 2*a15*b23 - a2*b24 + 2*a3*b22 - 2*a6*b57 - 4*a7*b57 - 2
*a8*b55 + 3*a8*b6,
2*a1*b11 + 2*a1*b12 - 3*a13*b9 - a14*b9 - a4*b2 + 2*a4*b47 + 2*a4*b48 - 12*a6*
b1 - 4*a7*b1,
2*a1*b17 - 2*a13*b11 - a13*b14 - 8*a15*b10 - 3*a2*b11 + 2*a5*b51 + 2*a5*b52 + 2
*a6*b47 - 8*a8*b1,
2*a12*b74 + a13*b23 + 2*a15*b20 - 2*a15*b69 - 2*a18*b54 - a3*b69 - 4*a4*b57 -
a7*b55 - 2*a8*b51,
2*a12*b70 + a13*b15 + a13*b16 + 2*a15*b9 - 3*a17*b50 - 8*a18*b46 - 2*a4*b51 - 2
*a5*b51 - 4*a7*b47,
2*a1*b24 - a14*b23 - 2*a15*b20 + a2*b23 + a3*b20 + 2*a4*b57 - 5*a4*b7 + a7*b56
- a7*b6 - 2*a8*b4,
2*a12*b70 + a13*b14 + a13*b16 - 2*a13*b63 - 3*a14*b63 + a17*b50 - 8*a18*b46 - 2
*a5*b52 - 2*a6*b47 - 3*a7*b47,
a1*b64 - a12*b64 - a13*b11 + a13*b58 + a13*b63 - a16*b47 - a17*b47 - a18*b1 +
a18*b46 + a6*b47,
2*a12*b73 + 2*a13*b20 + a13*b21 + 2*a15*b15 - 2*a15*b62 - 2*a17*b54 - 6*a18*b50
- 2*a4*b55 - a5*b55 - 3*a7*b51 - 6*a8*b47,
2*a1*b24 - 2*a12*b24 - a14*b23 - 2*a15*b21 + a2*b23 + a3*b21 + 2*a5*b57 - 5*a5*
b7 + a7*b56 - a7*b6 - 2*a8*b4 + 2*a8*b54,
a1*b23 - a12*b23 - a14*b21 - 2*a15*b16 + a2*b21 + 2*a3*b16 + a5*b56 - a5*b6 -
a7*b4 + a7*b54 - 2*a8*b2 + 2*a8*b50,
a1*b21 - a12*b21 - a14*b16 - 2*a15*b10 + a2*b16 + 3*a3*b10 - a5*b4 + a5*b54 -
a7*b2 + a7*b50 - 2*a8*b1 + 2*a8*b46,
a1*b15 + 2*a1*b16 - a12*b15 - a14*b10 - a14*b9 + a2*b10 + a2*b9 - 2*a4*b2 + 2*
a4*b50 - 3*a5*b2 - 5*a7*b1 + a7*b46,
2*a1*b20 + a1*b21 - a12*b21 - a14*b15 - 2*a15*b8 + a2*b15 + 3*a3*b8 - 2*a4*b4 -
a5*b4 + a5*b54 - 3*a7*b2 - 6*a8*b1,
3*a1*b15 + a1*b16 - a12*b15 - a12*b16 - 2*a14*b8 - a14*b9 + 2*a2*b8 + a2*b9 - 6
*a4*b2 - 4*a5*b2 + a5*b50 - 10*a7*b1,
a1*b14 + 2*a1*b16 - a12*b14 - 2*a13*b10 - 4*a14*b10 + a2*b10 - a5*b3 + a5*b49 +
2*a5*b50 - 2*a6*b1 + 2*a6*b46 - 4*a7*b1,
2*a1*b13 + a1*b14 + 2*a1*b15 - a12*b14 - 2*a13*b8 - 4*a14*b8 + a2*b8 - 2*a4*b3
- a5*b3 + a5*b49 - 6*a6*b1 - 12*a7*b1,
2*a1*b18 + 2*a1*b19 + 2*a1*b20 - 2*a13*b13 - 2*a14*b13 - 6*a15*b9 - a4*b5 + 2*
a4*b52 + 2*a4*b53 - 2*a6*b3 - 2*a7*b3 - 24*a8*b1,
a1*b12 + 2*a1*b14 - a12*b12 - 4*a13*b10 - a13*b9 - 6*a14*b10 - a5*b3 + a5*b48 +
2*a5*b49 + a5*b50 - 8*a6*b1 - 6*a7*b1,
2*a1*b11 + 2*a1*b12 - 2*a12*b11 - 6*a13*b10 - 2*a13*b8 - 4*a14*b10 - a5*b2 + 2*
a5*b47 + 2*a5*b48 + a5*b49 - 12*a6*b1 - 4*a7*b1,
12*a1*b24 - 2*a13*b22 - 2*a15*b18 - 2*a15*b19 - 2*a15*b21 - 6*a3*b17 - 3*a3*b18
+ 12*a5*b57 + 2*a6*b55 + 2*a7*b55 - 2*a8*b4 - 3*a8*b5 + 2*a8*b52,
a1*b69 - 2*a12*b64 - 2*a12*b66 - a12*b69 - a13*b12 - a13*b13 + a13*b60 + 2*a13*
b62 + a14*b62 + 12*a18*b46 + a4*b51 + 6*a6*b47 + 3*a7*b47,
2*a1*b13 + 2*a1*b14 + 2*a1*b15 + 2*a1*b16 - 2*a12*b13 - 2*a13*b9 - 4*a14*b9 +
a2*b9 - 2*a4*b3 + 2*a4*b49 + 2*a4*b50 - 2*a5*b3 - 8*a6*b1 - 16*a7*b1,
4*a1*b22 - 2*a13*b17 - a13*b19 - 2*a15*b12 - 2*a15*b14 - 6*a15*b16 - 2*a2*b17 -
18*a3*b11 + 6*a5*b55 + 2*a6*b51 + a7*b51 + 2*a7*b52 - 6*a8*b2 - 2*a8*b3,
2*a12*b66 + 4*a12*b69 + 2*a12*b70 + 2*a13*b13 + a13*b14 + a13*b15 - 2*a13*b62 -
3*a14*b62 - 2*a17*b49 - 24*a18*b46 - 4*a4*b52 - 2*a5*b52 - 6*a6*b47 - 9*a7*b47
,
a1*b70 - 2*a12*b66 - a12*b70 - a13*b12 - a13*b14 + a13*b61 + a13*b62 + 3*a13*
b63 + 3*a14*b63 - a17*b49 + 12*a18*b46 + a5*b51 + 6*a6*b47 + 3*a7*b47,
a1*b66 - 4*a12*b64 - a12*b66 - 2*a13*b11 - a13*b12 + a13*b59 + a13*b62 + 3*a13*
b63 + a14*b63 - 2*a17*b47 - a17*b48 + 8*a18*b46 + 6*a6*b47 + a7*b47,
3*a1*b23 - a12*b23 - 2*a14*b20 - a14*b21 - 2*a15*b15 + 2*a2*b20 + a2*b21 + 2*a3
*b15 + 2*a4*b56 - 2*a4*b6 + a5*b56 - a5*b6 - 3*a7*b4 + a7*b54 - 6*a8*b2,
2*a1*b20 + 2*a1*b21 - 2*a12*b20 - a14*b15 - a14*b16 - 2*a15*b9 + a2*b15 + a2*
b16 + 3*a3*b9 - 2*a4*b4 + 2*a4*b54 - 2*a5*b4 - 4*a7*b2 + a7*b50 - 8*a8*b1,
2*a1*b17 + 2*a1*b19 - 2*a13*b15 - a14*b12 - a14*b15 - 6*a15*b9 + a2*b12 - 2*a4*
b4 + 2*a4*b51 + 2*a4*b53 - 6*a6*b2 - 3*a7*b2 - a7*b3 + a7*b48 - 24*a8*b1,
3*a1*b12 + 4*a1*b13 + 2*a1*b14 - a12*b12 - 4*a13*b8 - 3*a13*b9 - 2*a14*b8 - 3*
a14*b9 - 2*a4*b3 + 2*a4*b48 + 2*a4*b49 - a5*b3 + a5*b48 - 24*a6*b1 - 18*a7*b1,
2*a1*b18 + 2*a1*b19 + 2*a1*b21 - 2*a12*b18 - 2*a13*b14 - 2*a14*b14 - 12*a15*b10
- 4*a15*b8 - a5*b5 + 2*a5*b52 + 2*a5*b53 + 2*a5*b54 - 2*a6*b3 + 2*a6*b49 - 2*
a7*b3 - 24*a8*b1,
4*a1*b17 - a13*b15 - 3*a13*b16 - 2*a14*b11 - a14*b16 - 8*a15*b10 - 2*a15*b9 + 2
*a2*b11 + 2*a4*b51 + 2*a5*b51 + a5*b53 - 6*a6*b2 - a7*b2 + 2*a7*b47 + a7*b48 -
16*a8*b1,
4*a13*b24 - 2*a13*b74 + 3*a14*b74 + 2*a15*b22 - 2*a15*b71 - 2*a15*b72 - 2*a15*
b73 + 4*a16*b57 + 4*a17*b57 + 2*a18*b55 - a18*b56 + a18*b6 - 3*a2*b74 - 4*a3*
b71 - 4*a6*b57 - 4*a8*b55,
4*a12*b71 + 2*a12*b73 + 2*a13*b18 + a13*b19 - 2*a13*b66 - a14*b66 - 2*a15*b59 -
2*a15*b62 - 6*a15*b63 + 2*a17*b52 + a17*b53 - 4*a18*b49 - a2*b66 - 4*a6*b52 -
2*a7*b52 - 12*a8*b47,
4*a12*b73 + a13*b19 + 2*a13*b21 - 2*a13*b70 - a14*b70 + 2*a15*b14 - 2*a15*b61 -
2*a15*b62 - 6*a15*b63 + 2*a17*b54 - 6*a18*b50 - a2*b70 - 2*a5*b55 - 2*a6*b51 -
2*a7*b51 - 2*a7*b52 - 12*a8*b47,
2*a12*b71 + 4*a12*b73 + a13*b19 + 2*a13*b20 - 2*a13*b69 - a14*b69 + 2*a15*b13 -
2*a15*b60 - 4*a15*b62 - 2*a18*b49 - 6*a18*b50 - a2*b69 - 2*a4*b55 - 2*a6*b51 -
2*a7*b51 - 2*a7*b52 - 12*a8*b47,
a1*b71 - a12*b71 - a13*b17 + a13*b67 + a13*b70 - a14*b64 - 2*a15*b11 + 2*a15*
b58 + 2*a15*b63 - a16*b51 - a17*b51 - a18*b2 - 2*a18*b47 + a18*b50 + a2*b64 +
a6*b51 + 2*a8*b47,
2*a1*b22 + 6*a1*b23 - 2*a13*b20 - a14*b19 - 2*a14*b20 - 2*a15*b13 - 4*a15*b15 +
a2*b19 + a2*b20 + 2*a4*b55 + 6*a4*b56 - 3*a4*b6 - 2*a6*b4 - 2*a7*b4 - 2*a7*b5
+ a7*b53 - 12*a8*b2 - 2*a8*b3,
4*a1*b22 - 2*a13*b20 - 2*a13*b21 - 2*a14*b17 - a14*b21 - 2*a15*b12 - 2*a15*b15
- 6*a15*b16 + 2*a2*b17 + 2*a4*b55 + 2*a5*b55 + 3*a5*b56 - 4*a6*b4 - 2*a7*b4 + 2
*a7*b51 + a7*b53 - 12*a8*b2 - 2*a8*b3 + 2*a8*b48,
12*a12*b74 + 2*a13*b22 + 3*a13*b23 - 2*a13*b73 + a14*b73 + 2*a15*b19 - 2*a15*
b66 - 2*a15*b68 - 4*a15*b69 - 4*a15*b70 + 2*a17*b55 + 3*a17*b56 - 4*a18*b54 - 2
*a2*b73 - 3*a3*b66 - 2*a6*b55 - 3*a7*b55 - 8*a8*b51 - 4*a8*b52,
6*a12*b74 + 2*a13*b22 - 2*a13*b71 + a14*b71 + 2*a15*b18 - 2*a15*b65 - 2*a15*b66
- 2*a15*b67 - 2*a15*b70 + 2*a16*b55 + 2*a17*b55 + a18*b5 + 2*a18*b52 - a18*b53
- 2*a2*b71 - 6*a3*b64 - 2*a6*b55 - 2*a8*b51 - 4*a8*b52,
3*a1*b74 - 3*a12*b74 - a13*b22 + a13*b72 + a13*b73 - a14*b71 - 2*a15*b17 + 2*
a15*b64 + 2*a15*b67 + 2*a15*b70 - a16*b55 - a17*b55 - a18*b4 - 2*a18*b51 + a18*
b54 + a2*b71 + 3*a3*b64 + a6*b55 + 3*a8*b51,
16*a1*b24 - 2*a13*b23 - 2*a14*b22 - a14*b23 - 2*a15*b19 - 4*a15*b20 - 4*a15*b21
+ 2*a2*b22 + a2*b23 - a3*b19 + 8*a4*b57 + 8*a5*b57 + 2*a6*b56 - 2*a6*b6 + 2*a7
*b55 + 3*a7*b56 - 3*a7*b6 - 8*a8*b4 - 4*a8*b5 + 2*a8*b53,
a1*b19 + 4*a1*b21 - a12*b19 - 2*a13*b16 - a14*b14 - 3*a14*b16 - 8*a15*b10 - 2*
a15*b9 + a2*b14 + a2*b16 - 2*a5*b5 + a5*b53 + 4*a5*b54 - 2*a6*b2 + 2*a6*b50 - 3
*a7*b2 - a7*b3 + a7*b49 + a7*b50 - 16*a8*b1,
2*a1*b17 + 2*a1*b19 - 2*a12*b17 - a13*b15 - 3*a13*b16 - a14*b12 - 3*a14*b16 -
12*a15*b10 - 4*a15*b8 + a2*b12 - 2*a5*b4 + 2*a5*b51 + 2*a5*b53 + 2*a5*b54 - 6*
a6*b2 - 3*a7*b2 - a7*b3 + a7*b48 + a7*b49 - 24*a8*b1,
4*a1*b17 + 8*a1*b18 + 2*a1*b19 - 2*a13*b12 - 2*a13*b13 - 2*a13*b14 - a14*b12 -
a14*b14 - 24*a15*b10 - 6*a15*b9 - 2*a2*b12 + 2*a4*b51 + 4*a4*b52 + 2*a5*b51 + 4
*a5*b52 + 3*a5*b53 - 6*a6*b3 + 2*a6*b48 - a7*b3 - 48*a8*b1,
a1*b71 - 3*a12*b71 - a13*b17 - 2*a13*b18 + 2*a13*b64 + a13*b65 + a13*b66 + 6*
a15*b58 + 6*a15*b63 - a16*b51 - 2*a16*b52 - a17*b51 - 2*a17*b52 - a18*b3 + a18*
b48 + a18*b49 + 3*a2*b64 + a6*b51 + 2*a6*b52 + 6*a8*b47,
8*a1*b22 + 6*a1*b23 - 2*a13*b19 - 2*a14*b18 - a14*b19 - 4*a15*b13 - 4*a15*b14 -
2*a15*b15 - 6*a15*b16 + 2*a2*b18 - 6*a3*b12 + 4*a4*b55 + 4*a5*b55 + 6*a5*b56 -
4*a6*b5 + 2*a6*b53 - 2*a7*b5 + 2*a7*b52 + a7*b53 - 12*a8*b2 - 8*a8*b3,
2*a1*b73 - 4*a12*b71 - 2*a12*b73 - 2*a13*b17 - a13*b19 + a13*b68 + 2*a13*b69 +
2*a13*b70 - a14*b66 + a14*b70 - 2*a15*b12 + 2*a15*b59 + 2*a15*b62 + 6*a15*b63 -
2*a17*b51 - a17*b53 + 6*a18*b50 + a2*b66 + 4*a6*b51 + 2*a7*b51 + 12*a8*b47,
2*a1*b22 + 6*a1*b23 - 2*a12*b22 - 2*a13*b21 - a14*b19 - 2*a14*b21 - 2*a15*b14 -
2*a15*b15 - 6*a15*b16 + a2*b19 + a2*b21 + 2*a5*b55 + 6*a5*b56 - 3*a5*b6 - 2*a6
*b4 + 2*a6*b54 - 2*a7*b4 - 2*a7*b5 + a7*b53 + 2*a7*b54 - 12*a8*b2 - 2*a8*b3 + 2
*a8*b49,
3*a1*b19 + 8*a1*b20 + 4*a1*b21 - a12*b19 - 2*a13*b15 - 2*a14*b13 - a14*b14 - 3*
a14*b15 - 8*a15*b8 - 6*a15*b9 + 2*a2*b13 + a2*b14 + a2*b15 - 4*a4*b5 + 2*a4*b53
+ 4*a4*b54 - 2*a5*b5 + a5*b53 - 6*a6*b2 - 9*a7*b2 - 3*a7*b3 + a7*b49 - 48*a8*
b1,
2*a12*b63 + a14*b10 - 4*a17*b46 - a5*b48,
a14*b24 - 2*a15*b72 + 2*a16*b57 - 2*a3*b72 - 3*a8*b56,
2*a12*b70 + a14*b16 - 3*a17*b50 - 8*a18*b46 - a5*b53 - a7*b48,
4*a12*b74 + a14*b23 - 2*a15*b68 - 4*a18*b54 - a3*b68 - 3*a7*b56 - 2*a8*b53,
2*a12*b60 + 2*a12*b62 + a14*b8 - 6*a16*b46 - 12*a17*b46 - 2*a4*b48 - a5*b48,
2*a12*b73 + a14*b21 - 2*a15*b61 - 2*a17*b54 - 6*a18*b50 - 3*a5*b56 - a7*b53 - 2
*a8*b48,
2*a12*b61 + 2*a12*b62 + 2*a12*b63 + a14*b9 - 8*a16*b46 - 16*a17*b46 - 2*a4*b48
- 2*a5*b48,
2*a12*b72 + 2*a12*b73 + a14*b20 - 2*a15*b60 - 2*a16*b54 - 2*a17*b54 - 6*a18*b50
- 3*a4*b56 - a7*b53 - 2*a8*b48,
2*a12*b68 + 4*a12*b69 + 2*a12*b70 + a14*b15 - 6*a16*b50 - 9*a17*b50 - 24*a18*
b46 - 2*a4*b53 - a5*b53 - 3*a7*b48,
2*a12*b66 + 2*a12*b68 + 2*a12*b70 - 2*a13*b61 + a14*b14 - 3*a14*b61 - 2*a17*b49
- 24*a18*b46 - a5*b53 - 2*a6*b48 - 2*a7*b48,
a1*b65 - 2*a12*b64 - a12*b65 + 3*a13*b58 + a13*b61 - a14*b11 + a14*b58 - 2*a16*
b47 - a16*b48 + 4*a18*b46 + a6*b48,
2*a12*b65 + 2*a12*b66 + 2*a12*b68 + 2*a12*b69 - 2*a13*b60 + a14*b13 - 3*a14*b60
- 2*a16*b49 - 2*a17*b49 - 24*a18*b46 - a4*b53 - 2*a6*b48 - 2*a7*b48,
2*a12*b71 + 2*a12*b72 - 2*a13*b65 + a14*b18 - a14*b65 - 6*a15*b58 - 2*a15*b61 +
2*a16*b52 + a16*b53 - 2*a18*b49 - a2*b65 - a6*b53 - 2*a8*b48,
6*a12*b74 - 2*a13*b72 + a14*b22 + a14*b72 - 2*a15*b65 - 4*a15*b67 - 2*a15*b68 +
2*a16*b55 + 3*a16*b56 - 2*a18*b54 - 2*a2*b72 - 3*a3*b65 - 3*a6*b56 - 3*a8*b53,
a1*b68 - 4*a12*b64 - 4*a12*b65 - 2*a12*b66 - a12*b68 + 2*a13*b59 + 2*a13*b60 +
2*a13*b61 - a14*b12 + a14*b59 + a14*b61 + 24*a18*b46 + 4*a6*b48 + a7*b48,
4*a12*b71 + 8*a12*b72 + 4*a12*b73 - 2*a13*b68 + a14*b19 - a14*b68 - 4*a15*b59 -
4*a15*b60 - 4*a15*b61 - 4*a18*b49 - 12*a18*b50 - a2*b68 - 2*a6*b53 - 2*a7*b53
- 8*a8*b48,
2*a1*b72 - 2*a12*b71 - 2*a12*b72 + 2*a13*b67 + a13*b68 - a14*b17 - a14*b65 +
a14*b67 + 6*a15*b58 + 2*a15*b61 - 2*a16*b51 - a16*b53 + 3*a18*b50 + a2*b65 + a6
*b53 + 2*a8*b48,
2*a15*b67 + a3*b67 + 2*a8*b54,
2*a12*b61 - 8*a16*b46 - 6*a17*b46 - a5*b49,
2*a12*b72 - a15*b59 - 2*a16*b54 - 3*a18*b50 - a7*b54 - a8*b49,
2*a12*b68 - 6*a16*b50 - 3*a17*b50 - 12*a18*b46 - 2*a5*b54 - a7*b49,
2*a12*b67 + 2*a12*b68 - 6*a16*b50 - 3*a17*b50 - 12*a18*b46 - 2*a4*b54 - a7*b49,
2*a12*b59 + 4*a12*b60 + 2*a12*b61 - 24*a16*b46 - 18*a17*b46 - 2*a4*b49 - a5*b49
,
4*a12*b65 + 4*a12*b67 + 2*a12*b68 - 2*a13*b59 - 3*a14*b59 - 4*a16*b49 - 24*a18*
b46 - 2*a6*b49 - a7*b49,
a1*b67 - 2*a12*b65 - a12*b67 + 3*a13*b58 + a13*b59 + 3*a14*b58 - a16*b49 + 6*
a18*b46 + a6*b49,
4*a12*b72 - 2*a13*b67 - a14*b67 - 6*a15*b58 - 2*a15*b59 + 2*a16*b54 - 3*a18*b50
- a2*b67 - 2*a6*b54 - 2*a8*b49,
2*a15*b58 + a8*b50,
4*a12*b67 - 6*a16*b50 - 8*a18*b46 - a7*b50,
2*a12*b59 - 12*a16*b46 - 4*a17*b46 - a5*b50,
2*a12*b58 + 2*a12*b59 - 12*a16*b46 - 4*a17*b46 - a4*b50,
2*a12*b67 - 2*a13*b58 - 3*a14*b58 + a16*b50 - 4*a18*b46 - a6*b50,
a12*b58 - 2*a16*b46,
a3*b7,
a3*b4,
a3*b2,
a15*b7 - 2*a3*b57,
a2*b7 - 3*a3*b6,
a1*b3 - 5*a2*b1,
a1*b2 - 2*a2*b1,
10*a1*b7 - 3*a3*b4 - 2*a3*b5,
2*a1*b5 - 3*a2*b2 - 18*a3*b1,
4*a1*b4 - 3*a2*b2 - 24*a3*b1,
a1*b47 - a12*b47 - a13*b1 + a13*b46,
6*a1*b6 - a2*b5 - 6*a3*b2 - 6*a3*b3,
6*a1*b6 - 2*a2*b4 - 18*a3*b2 - 3*a3*b3,
2*a1*b4 + 4*a1*b5 - 3*a2*b3 - 36*a3*b1,
2*a12*b55 + a13*b5 - 2*a15*b49 - 2*a2*b52 - 6*a3*b47,
5*a13*b7 + 4*a14*b57 - 2*a15*b56 + 2*a15*b6 - 4*a2*b57 - 5*a3*b55,
a1*b51 - a12*b51 - 2*a12*b52 - a13*b3 + a13*b48 + 6*a15*b46 + 3*a2*b47,
2*a1*b52 - 2*a12*b51 - 2*a12*b52 - a13*b2 - a13*b3 + a13*b49 + 8*a15*b46 + 4*a2
*b47,
a1*b51 - a12*b51 - a13*b2 + a13*b50 - a14*b47 - 2*a15*b1 + 2*a15*b46 + a2*b47,
12*a12*b57 + 3*a13*b6 + 2*a14*b55 + 2*a15*b5 - 2*a15*b53 - 2*a15*b54 - 3*a2*b55
- 6*a3*b51 - 6*a3*b52,
4*a1*b57 - 4*a12*b57 + a13*b56 - a13*b6 - a14*b55 - 2*a15*b4 + 2*a15*b54 + a2*
b55 + 4*a3*b51,
a1*b55 - a12*b55 - a13*b4 + a13*b54 - a14*b51 - 2*a15*b2 + 2*a15*b50 + a2*b51 +
3*a3*b47,
2*a1*b55 - 6*a12*b55 - 2*a13*b4 - 2*a13*b5 + a13*b53 - a14*b51 - 2*a14*b52 - 2*
a15*b3 + 2*a15*b48 + 2*a15*b49 + 6*a15*b50 + 4*a2*b51 + 2*a2*b52 + 18*a3*b47,
a14*b7 - 3*a3*b56,
8*a12*b57 + 2*a14*b56 + a14*b6 - 4*a15*b54 - 3*a2*b56 - 4*a3*b53,
a1*b48 - 2*a12*b47 - a12*b48 + 4*a13*b46 - a14*b1 + a14*b46,
4*a12*b55 + 6*a12*b56 + a14*b5 - 4*a15*b49 - 6*a15*b50 - 2*a2*b53 - 6*a3*b48,
a1*b53 - 2*a12*b51 - a12*b53 + 3*a13*b50 - a14*b2 - a14*b48 + a14*b50 + 8*a15*
b46 + a2*b48,
3*a1*b56 - 2*a12*b55 - 3*a12*b56 + 2*a13*b54 - a14*b4 - a14*b53 + a14*b54 + 6*
a15*b50 + a2*b53 + 3*a3*b48,
a1*b53 - 2*a12*b51 - 4*a12*b52 - 3*a12*b53 + 2*a13*b49 - a14*b3 + a14*b48 + a14
*b49 + 24*a15*b46 + 3*a2*b48,
a3*b54,
6*a12*b56 - 6*a15*b50 - 2*a2*b54 - 3*a3*b49,
2*a12*b53 + 2*a12*b54 - 2*a14*b49 - 12*a15*b46 - a2*b49,
a1*b49 - 2*a12*b48 - a12*b49 + 6*a13*b46 + 4*a14*b46,
2*a1*b54 - 2*a12*b53 - 2*a12*b54 + 3*a13*b50 - a14*b49 + 3*a14*b50 + 12*a15*b46
+ a2*b49,
a3*b50,
4*a12*b54 - 2*a14*b50 - 8*a15*b46 - a2*b50,
a1*b50 - 2*a12*b49 - a12*b50 + 4*a13*b46 + 6*a14*b46,
a12*b50 - 2*a14*b46
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.
u = u *a1 + u *f(v,v)*a6 + u *a2*u + f(v ,v )*a4 + f(v,v )*a5
t 2x x x x x 2x
3 2
+ f(v,v )*f(v,v)*a9 + f(v,v )*a7*u + f(v,v) *a11 + f(v,v) *a10*u
x x
2 3
+ f(v,v)*a8*u + a3*u ,
v = u *a13*v + v *a12 + v *f(v,v)*a16 + v *a14*u + f(v,v )*a17*v
t x 2x x x x
2 2
+ f(v,v) *a19*v + f(v,v)*a18*u*v + a15*u *v
For any solution of the above algebraic conditions for the
a's and b's this system has the following symmetry:
u = u *b1 + u *f(v,v)*b11 + u *b2*u + u *u *b3 + u *f(v,v )*b12
s 4x 3x 3x 2x x 2x x
2 2 2
+ u *f(v,v) *b29 + u *f(v,v)*b17*u + u *b4*u + u *f(v,v)*b18
2x 2x 2x x
2
+ u *b5*u + u *f(v ,v )*b13 + u *f(v,v )*b14 + u *f(v,v )*f(v,v)*b30
x x x x x 2x x x
3 2
+ u *f(v,v )*b19*u + u *f(v,v) *b40 + u *f(v,v) *b34*u
x x x x
2 3
+ u *f(v,v)*b22*u + u *b6*u + f(v ,v )*b8 + f(v ,v )*b9
x x 2x 2x x 3x
+ f(v ,v )*f(v,v)*b25 + f(v ,v )*b15*u + f(v ,v )*f(v,v )*b26
x 2x x 2x x x x
2 2
+ f(v ,v )*f(v,v) *b37 + f(v ,v )*f(v,v)*b31*u + f(v ,v )*b20*u
x x x x x x
+ f(v,v )*b10 + f(v,v )*f(v,v)*b27 + f(v,v )*b16*u
4x 3x 3x
2
+ f(v,v )*f(v,v )*b28 + f(v,v )*f(v,v) *b38 + f(v,v )*f(v,v)*b32*u
2x x 2x 2x
2 2 2
+ f(v,v )*b21*u + f(v,v ) *f(v,v)*b39 + f(v,v ) *b33*u
2x x x
3 2 2
+ f(v,v )*f(v,v) *b43 + f(v,v )*f(v,v) *b41*u + f(v,v )*f(v,v)*b35*u
x x x
3 5 4 3 2
+ f(v,v )*b23*u + f(v,v) *b45 + f(v,v) *b44*u + f(v,v) *b42*u
x
2 3 4 5
+ f(v,v) *b36*u + f(v,v)*b24*u + b7*u ,
2
v = u *b47*v + u *v *b48 + u *f(v,v)*b64*v + u *b51*u*v + u *b52*v
s 3x 2x x 2x 2x x
+ u *v *b49 + u *v *f(v,v)*b65 + u *v *b53*u + u *f(v,v )*b66*v
x 2x x x x x x x
2 2
+ u *f(v,v) *b80*v + u *f(v,v)*b71*u*v + u *b55*u *v + v *b46
x x x 4x
2
+ v *f(v,v)*b58 + v *b50*u + v *f(v,v )*b59 + v *f(v,v) *b75
3x 3x 2x x 2x
2
+ v *f(v,v)*b67*u + v *b54*u + v *f(v ,v )*b60 + v *f(v,v )*b61
2x 2x x x x x 2x
3
+ v *f(v,v )*f(v,v)*b76 + v *f(v,v )*b68*u + v *f(v,v) *b84
x x x x x
2 2 3
+ v *f(v,v) *b81*u + v *f(v,v)*b72*u + v *b56*u + f(v ,v )*b62*v
x x x x 2x
+ f(v ,v )*f(v,v)*b77*v + f(v ,v )*b69*u*v + f(v,v )*b63*v
x x x x 3x
2
+ f(v,v )*f(v,v)*b78*v + f(v,v )*b70*u*v + f(v,v ) *b79*v
2x 2x x
2 2
+ f(v,v )*f(v,v) *b85*v + f(v,v )*f(v,v)*b82*u*v + f(v,v )*b73*u *v
x x x
4 3 2 2 3
+ f(v,v) *b87*v + f(v,v) *b86*u*v + f(v,v) *b83*u *v + f(v,v)*b74*u *v
4
+ b57*u *v