Problem l12o24
Unknowns |
Inequalities |
Equations |
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Unknowns
All solutions for the following 94 unknowns have to be determined:
a1, a2, ..., a15, b1, b2, ..., b79
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,a8},
{a4,a5,a6,a7},
{a9,a10,a11,a14},
{b1,b35},
{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}
Equations
All comma separated 313 expressions involving 3096 terms have to vanish.
All terms are products of one a- and one b-unknown.
a15*b79,
a3*b41,
a3*b45,
a3*b2,
a3*b5,
a3*b8,
a15*b49,
a15*b54,
a15*b9,
a15*b67,
a15*b70,
a15*b23,
2*a15*b34 - a7*b79,
2*a10*b35 - a8*b41,
a10*b8 - 3*a3*b47,
a1*b2 - 2*a2*b1,
a1*b3 - 10*a2*b1,
a2*b8 - 3*a3*b7,
a11*b8 - 2*a3*b48,
2*a12*b35 - a8*b49,
a11*b49 + a6*b41,
5*a13*b35 - a8*b53,
2*a13*b35 - a8*b54,
a5*b36 - a9*b14,
a1*b9 - 2*a4*b1,
a14*b49 + a7*b41,
a12*b79 - 3*a15*b76,
a13*b79 - 3*a15*b77,
3*a15*b31 - a4*b79,
a1*b2 + a1*b3 - 10*a2*b1,
4*a1*b5 - 3*a2*b2 - 40*a3*b1,
a1*b3 + 3*a1*b4 - 15*a2*b1,
a1*b6 - 3*a2*b2 - 30*a3*b1,
18*a1*b8 - 5*a3*b5 - 2*a3*b6,
6*a12*b35 + 2*a13*b35 - a8*b50,
4*a12*b35 + 3*a13*b35 - a8*b52,
a11*b59 + a3*b59 + 2*a6*b45,
2*a14*b67 + a15*b59 + a7*b59,
a15*b67 + a15*b70 - 2*a8*b79,
6*a10*b35 - a8*b40 - a8*b41 + 2*a9*b35,
2*a10*b41 + 8*a11*b35 + a2*b41 - 4*a8*b45,
6*a11*b41 + 2*a2*b45 + 3*a3*b40 - 6*a8*b47,
6*a1*b7 - 2*a2*b5 - 30*a3*b2 - 3*a3*b3,
3*a1*b6 - a2*b3 - 2*a2*b4 - 60*a3*b1,
a1*b36 - a8*b36 - a9*b1 + a9*b35,
6*a12*b35 + 2*a13*b35 - a8*b49 - a8*b50,
3*a12*b41 + 4*a14*b35 + a5*b41 - 2*a8*b59,
3*a12*b35 + 6*a13*b35 - a8*b51 - a8*b53,
a1*b10 + a1*b9 - 6*a4*b1 - 2*a5*b1,
a1*b14 - a5*b1 + a5*b35 - a8*b14,
a11*b22 + a3*b22 - a6*b48 + 3*a6*b8,
3*a12*b49 + a13*b49 + 8*a15*b35 - 4*a8*b67,
2*a11*b67 + a14*b59 + a6*b59 + 2*a7*b45,
a14*b34 - 3*a14*b79 - a15*b78 - a7*b78,
a1*b41 + 6*a10*b35 - a8*b40 - a8*b41 + 2*a9*b35,
a1*b40 + 8*a10*b35 - 2*a8*b38 - a8*b40 + 6*a9*b35,
2*a1*b5 + 2*a1*b6 - 2*a2*b2 - a2*b3 - 60*a3*b1,
a1*b37 - 2*a8*b36 - a8*b37 - a9*b1 + 5*a9*b35,
a1*b36 + a1*b37 - a8*b36 - 3*a8*b37 + 10*a9*b35,
24*a11*b35 + 2*a2*b37 - 2*a8*b43 + a9*b39 - a9*b4,
12*a12*b35 + 9*a13*b35 - a8*b50 - 2*a8*b51 - a8*b52,
6*a12*b41 + 3*a13*b41 + 12*a14*b35 + a5*b40 - 2*a8*b60,
4*a12*b35 + 8*a13*b35 - a8*b52 - a8*b53 - a8*b54,
2*a10*b14 - 3*a13*b41 - 8*a14*b35 - a5*b38 + 2*a8*b62,
a10*b22 - a11*b64 + a12*b48 - 2*a3*b64 - 3*a6*b47,
3*a13*b41 + 6*a14*b35 + 3*a5*b36 - 2*a8*b61 - a9*b13,
4*a11*b14 - 2*a11*b54 - a5*b42 - 2*a6*b36 + a9*b19,
a1*b10 + a1*b9 - 6*a4*b1 - 2*a5*b1 - a8*b9,
a1*b10 + 2*a1*b12 - 8*a4*b1 - 6*a5*b1 - a8*b10,
3*a1*b13 + a1*b14 - 10*a5*b1 - a8*b13 - a8*b14,
a1*b13 + 2*a1*b14 - 5*a5*b1 + a5*b35 - a8*b13,
6*a12*b49 + 3*a13*b49 + a13*b50 + 24*a15*b35 - 2*a8*b68,
3*a12*b50 + a13*b50 + 24*a15*b35 - 4*a8*b67 - 2*a8*b68,
2*a12*b54 - 3*a13*b49 - a13*b52 - 16*a15*b35 + 2*a8*b70,
3*a13*b49 - a13*b53 + 3*a13*b54 + 12*a15*b35 - 2*a8*b69,
3*a13*b49 - a13*b53 + 3*a13*b54 + 16*a15*b35 - 2*a8*b70,
a12*b53 + a13*b53 + 12*a15*b35 - a8*b69 - a8*b71,
2*a14*b14 - 2*a14*b54 - a5*b55 - 4*a7*b36 + a9*b26,
4*a1*b23 - a12*b9 - a13*b9 - 2*a4*b9 - 8*a7*b1,
2*a12*b67 + 2*a13*b67 + 6*a15*b49 + 3*a15*b50 - 6*a8*b76,
6*a1*b31 - 2*a12*b23 - 2*a13*b23 - 3*a15*b10 - 6*a7*b9,
a12*b77 - 3*a13*b76 - 4*a15*b67 - 4*a15*b68 + 8*a8*b79,
a10*b34 + a12*b78 - 3*a14*b76 - 2*a15*b73 - a7*b73,
a1*b40 + 24*a10*b35 - 2*a8*b38 - 4*a8*b39 - 3*a8*b40 + 18*a9*b35,
a1*b38 - 2*a10*b1 + 2*a10*b35 - 2*a8*b36 - a8*b38 + 4*a9*b35,
a1*b38 + 6*a10*b35 - 2*a8*b37 - a8*b38 - 2*a8*b39 + 12*a9*b35,
2*a10*b47 + a10*b7 - 4*a11*b45 - 3*a2*b47 - 4*a3*b44 + 8*a8*b48,
15*a1*b7 - a2*b5 - a2*b6 - 30*a3*b2 - 10*a3*b3 - 5*a3*b4,
4*a10*b48 - 2*a11*b47 + 2*a11*b7 - 4*a2*b48 - 5*a3*b46 + 5*a9*b8,
3*a10*b49 - a12*b41 + 4*a14*b35 + a4*b41 - 2*a8*b59 + a9*b49,
6*a12*b41 + 3*a13*b41 + 12*a14*b35 + a5*b40 - 2*a8*b59 - 2*a8*b60,
a11*b50 + 2*a12*b45 + 3*a14*b41 + 2*a5*b45 + a6*b40 - 2*a8*b64,
3*a13*b41 + 8*a14*b35 + 4*a5*b36 - 2*a8*b62 - a9*b13 - a9*b14,
4*a11*b19 - 2*a11*b62 - 2*a3*b62 - a5*b46 - 2*a6*b42 + a9*b21,
2*a11*b22 - a11*b66 + a14*b48 + a14*b8 - 3*a3*b66 - 4*a6*b48,
4*a11*b14 + 2*a11*b9 - a5*b42 + 2*a6*b2 - 2*a6*b36 + a9*b19,
2*a1*b16 - 6*a2*b9 + a5*b37 - 18*a6*b1 - a9*b10 - 3*a9*b14,
3*a1*b10 + 4*a1*b11 + 2*a1*b12 - 24*a4*b1 - 18*a5*b1 - a8*b10,
2*a1*b11 + a1*b12 + 2*a1*b13 - 6*a4*b1 - 12*a5*b1 - a8*b12,
a1*b12 + 2*a1*b14 - 2*a4*b1 + 2*a4*b35 - 4*a5*b1 - a8*b12,
6*a12*b49 + 3*a13*b49 + a13*b50 + 24*a15*b35 - 4*a8*b67 - 2*a8*b68,
6*a12*b54 - a13*b50 + a13*b53 + 3*a13*b54 + 24*a15*b35 - 2*a8*b71,
2*a14*b14 + 2*a14*b9 - a5*b55 + 2*a7*b2 - 4*a7*b36 + a9*b26,
4*a1*b23 + 2*a1*b24 - a12*b10 - a13*b10 - 2*a4*b10 - 24*a7*b1,
2*a11*b30 + a14*b22 + 2*a6*b22 - a6*b66 - 2*a7*b48 + 4*a7*b8,
2*a12*b70 - 2*a13*b67 - a13*b68 - 12*a15*b49 - 6*a15*b52 + 2*a8*b77,
2*a11*b34 - 4*a11*b79 + a14*b33 - 2*a14*b78 - a6*b78 - 2*a7*b75,
4*a14*b34 + 3*a15*b33 - a6*b34 - a6*b79 + a7*b33 - 2*a7*b78,
a10*b40 + 2*a10*b41 + 24*a11*b35 + a2*b40 - 2*a8*b44 - 4*a8*b45 + a9*b41,
a1*b39 + 4*a10*b35 - a8*b36 - a8*b37 - a8*b38 - a8*b39 + 8*a9*b35,
2*a10*b19 - 2*a11*b52 - 2*a13*b45 - 6*a14*b41 - a5*b44 - 2*a6*b38 + 2*a8*b65,
a10*b21 - a11*b60 - 2*a14*b45 - a3*b60 - 3*a5*b47 - a6*b44 + 2*a8*b66,
2*a11*b21 - a11*b65 + a13*b48 - 2*a3*b65 - 4*a5*b48 - a6*b46 + a9*b22,
2*a1*b15 + 4*a1*b16 - 12*a2*b9 + 2*a4*b37 - 36*a6*b1 - a9*b10 - 3*a9*b12,
2*a11*b15 + 4*a11*b19 + 2*a3*b15 - a5*b46 - 2*a6*b42 + 4*a6*b5 + a9*b21,
a1*b11 + a1*b12 + a1*b13 + a1*b14 - 4*a4*b1 - 8*a5*b1 - a8*b11,
2*a1*b18 + a1*b19 - a10*b13 + a2*b13 - 3*a5*b2 - 6*a6*b1 - a8*b19,
a10*b22 + a11*b21 - a2*b22 - a5*b48 + 4*a5*b8 - a6*b47 + a6*b7,
a10*b30 - 2*a11*b73 + a12*b66 - a14*b64 - a3*b73 - 2*a6*b64 - 3*a7*b47,
8*a12*b54 - 2*a13*b49 - a13*b52 + a13*b53 + 3*a13*b54 + 32*a15*b35 - 4*a8*b70,
2*a11*b30 - 2*a11*b75 + a14*b22 + 2*a15*b48 - 2*a3*b75 - 3*a6*b66 - 4*a7*b48,
2*a1*b28 - 2*a14*b12 - 2*a2*b23 + 2*a4*b56 - 6*a6*b9 - 2*a7*b4 - a9*b24,
2*a1*b25 + 2*a1*b27 - 2*a12*b13 - 2*a13*b13 - a5*b11 + a5*b51 - 24*a7*b1,
a10*b33 - 3*a11*b76 + a12*b75 - 2*a14*b73 - a15*b64 - a6*b73 - 2*a7*b64,
a13*b67 - a13*b69 + a13*b70 + 6*a15*b49 - a15*b53 + 6*a15*b54 - a8*b77,
2*a14*b26 - 4*a14*b70 - 2*a15*b62 - a5*b72 - 4*a7*b55 - 2*a7*b62 + a9*b32,
2*a12*b71 - a13*b68 + a13*b71 + 4*a15*b50 + 4*a15*b53 + 12*a15*b54 - 4*a8*b77,
4*a14*b23 + 2*a14*b26 + 2*a15*b15 - a5*b72 + 2*a7*b15 - 4*a7*b55 + a9*b32,
a12*b77 - 3*a13*b76 + 4*a15*b67 + 4*a15*b69 + 8*a15*b70 + 4*a15*b71 - 24*a8*b79
,
4*a11*b34 + 3*a14*b33 + 2*a15*b30 - 2*a3*b34 - a6*b78 + 2*a7*b30 - 2*a7*b75,
4*a1*b45 - a10*b40 + 6*a10*b41 + 24*a11*b35 + a2*b40 - 2*a8*b44 - 4*a8*b45 + 3*
a9*b41,
a1*b42 - a10*b36 - 4*a11*b1 + 4*a11*b35 + a2*b36 - a8*b42 - a9*b2 + a9*b41,
6*a10*b49 - a12*b40 + 12*a14*b35 + a4*b40 - 2*a8*b57 - 2*a8*b59 + 3*a9*b49 + a9
*b50,
2*a10*b13 - 6*a12*b41 - 9*a13*b41 - 24*a14*b35 - 3*a5*b38 + 2*a8*b60 + 4*a8*b61
+ 2*a8*b62,
4*a11*b18 - 2*a11*b61 - 2*a14*b45 - 2*a3*b61 - a5*b46 - 2*a6*b42 + 2*a8*b66 +
a9*b21,
2*a1*b22 - a10*b21 - 2*a11*b18 + a2*b21 + 2*a3*b18 + a5*b47 - a5*b7 - 2*a6*b5,
a1*b19 - a10*b14 + a2*b14 - a5*b2 + a5*b41 - 2*a6*b1 + 2*a6*b35 - a8*b19,
2*a10*b67 - a12*b59 + 3*a14*b49 + a14*b50 + a4*b59 + a7*b40 - 2*a8*b73 + 2*a9*
b67,
2*a12*b59 + a13*b59 + 3*a14*b49 + 2*a14*b50 + 6*a15*b41 + a5*b59 + 2*a7*b40 - 4
*a8*b73,
6*a12*b49 - 2*a12*b53 + 9*a13*b49 + 3*a13*b52 + 48*a15*b35 - 2*a8*b68 - 4*a8*
b69 - 2*a8*b70,
3*a12*b52 + a13*b50 + a13*b51 + 2*a13*b52 + 48*a15*b35 - 2*a8*b68 - 2*a8*b70 -
2*a8*b71,
2*a12*b53 + 6*a12*b54 - a13*b50 + 3*a13*b53 + 3*a13*b54 + 48*a15*b35 - 2*a8*b70
- 4*a8*b71,
4*a1*b23 + 2*a1*b24 - a12*b10 - a13*b10 + a4*b10 - 6*a4*b9 - 3*a5*b9 - 24*a7*b1
,
2*a11*b33 - 3*a11*b78 + a14*b30 - a14*b75 + a15*b66 - a3*b78 - 2*a6*b75 - 3*a7*
b66,
4*a1*b32 - 2*a12*b27 - 2*a13*b27 - 4*a15*b13 - 12*a15*b14 + a5*b68 + a5*b71 - 4
*a7*b10,
3*a11*b33 + 2*a14*b30 + a15*b22 - a3*b33 + a6*b30 - a6*b75 + 3*a7*b22 - 2*a7*
b66,
a13*b78 + a14*b32 - 3*a14*b77 - 2*a15*b74 - a5*b78 - 2*a7*b72 - a7*b74 + 4*a9*
b34,
8*a1*b34 - 3*a12*b31 - 3*a13*b31 - 4*a15*b24 + 2*a4*b31 + a4*b76 + a4*b77 - 4*
a7*b23,
4*a12*b34 + 4*a13*b34 + 5*a15*b32 - 4*a4*b34 - 5*a5*b79 + 2*a7*b31 - 2*a7*b76 -
2*a7*b77,
a1*b44 - 2*a10*b2 - a10*b38 + 2*a10*b41 + 16*a11*b35 + a2*b38 - 2*a8*b42 - a8*
b44 + 3*a9*b41,
a10*b39 - a10*b4 + a10*b40 + 48*a11*b35 + a2*b38 + 2*a2*b39 - 2*a8*b43 - 3*a8*
b44 + a9*b40,
a1*b46 - a10*b42 - 4*a11*b2 + 4*a11*b41 + a2*b42 + 6*a3*b36 - a8*b46 + a9*b45 -
a9*b5,
8*a1*b48 - a10*b46 + 4*a11*b45 - 4*a11*b5 + a2*b46 + 8*a3*b42 - 8*a8*b48 + a9*
b47 - a9*b7,
2*a1*b59 + 6*a10*b49 - a12*b40 + 12*a14*b35 + a4*b40 - 2*a8*b57 - 2*a8*b59 + 3*
a9*b49 + a9*b50,
3*a10*b50 + 2*a12*b40 + 24*a14*b35 + a4*b40 + a5*b40 - 2*a8*b57 - 4*a8*b59 - 2*
a8*b60 + a9*b50,
2*a10*b18 - 2*a11*b51 - 2*a12*b45 - 2*a13*b45 - 6*a14*b41 - a5*b44 - 2*a6*b38 +
2*a8*b64 + 2*a8*b65,
a1*b55 - a12*b37 - a13*b37 + 6*a14*b35 + a4*b37 - a8*b55 - 2*a8*b56 + 3*a9*b49
+ 3*a9*b54,
4*a11*b13 - 2*a11*b53 - 2*a13*b45 - 6*a14*b41 - 3*a5*b42 - 6*a6*b36 + 2*a8*b65
+ 2*a9*b18 + a9*b19,
4*a1*b15 - 6*a2*b9 + 2*a4*b36 + a5*b36 + a5*b37 - 24*a6*b1 - a9*b12 - 4*a9*b14
- 2*a9*b9,
a11*b20 + 2*a11*b21 - a2*b22 + 2*a3*b20 - a4*b48 - 4*a5*b48 - a6*b46 + 3*a6*b7
+ a9*b22,
4*a11*b26 - 4*a11*b70 + 2*a14*b19 - 2*a14*b62 - a5*b63 - 2*a6*b55 - 2*a6*b62 -
4*a7*b42 + a9*b29,
4*a1*b23 + 2*a1*b24 - a12*b10 - a13*b10 + a4*b10 - 6*a4*b9 - 3*a5*b9 - 24*a7*b1
- 4*a8*b23,
2*a1*b25 + a1*b26 - a12*b13 - 3*a13*b14 + a4*b13 + a5*b53 - 3*a5*b9 - 12*a7*b1
- a8*b26,
2*a12*b67 - 2*a12*b69 + 2*a13*b67 + a13*b68 + 12*a15*b49 + 2*a15*b51 + 4*a15*
b52 - 6*a8*b76 - 2*a8*b77,
a12*b68 - a12*b71 + 2*a13*b68 + 12*a15*b49 + 4*a15*b50 + 4*a15*b51 + 8*a15*b52
- 12*a8*b76 - 4*a8*b77,
6*a12*b70 - 4*a13*b67 - a13*b68 + 2*a13*b69 + 2*a13*b70 + 24*a15*b49 + 8*a15*
b53 + 48*a15*b54 - 8*a8*b77,
a12*b78 + a13*b78 + a14*b31 - a14*b76 - a14*b77 - a4*b78 - a7*b72 + a9*b34 - 4*
a9*b79,
3*a14*b31 + a14*b32 + 2*a15*b28 - a2*b34 - a4*b78 - a5*b78 + a7*b28 - 2*a7*b72
+ 4*a9*b34,
6*a1*b47 - a10*b44 + 2*a10*b45 - 2*a10*b5 + 12*a11*b41 + a2*b44 + 6*a3*b38 - 2*
a8*b46 - 6*a8*b47 + 2*a9*b45,
3*a1*b42 - a10*b37 + 36*a11*b35 + 6*a2*b36 + a2*b37 - 3*a8*b42 - 2*a8*b43 - a9*
b3 + a9*b38 + 3*a9*b41,
5*a10*b46 - 4*a11*b44 - 12*a11*b45 + 4*a11*b6 - 7*a2*b46 - 20*a3*b42 - 12*a3*
b43 + 56*a8*b48 - a9*b47 + 7*a9*b7,
a10*b59 + 6*a11*b49 + 2*a11*b50 - 2*a12*b45 + 3*a14*b41 + a2*b59 + 2*a4*b45 + 2
*a6*b40 - 4*a8*b64 + a9*b59,
a1*b55 - a12*b36 - a13*b36 - 2*a14*b1 + 2*a14*b35 + a4*b36 - a8*b55 + a9*b49 +
a9*b54 - a9*b9,
2*a10*b53 + 24*a14*b35 + 2*a4*b37 + 2*a5*b37 - 2*a8*b56 - 2*a8*b58 - 2*a8*b61 -
a9*b11 + a9*b51 + 2*a9*b53,
6*a10*b54 - 2*a13*b41 + 16*a14*b35 + 2*a4*b36 + 3*a5*b36 + a5*b37 - 4*a8*b62 -
a9*b12 - 2*a9*b14 + 2*a9*b54,
2*a1*b16 + a1*b17 - a10*b12 - a2*b10 + a4*b39 - 3*a4*b4 - a5*b4 - 24*a6*b1 - a9
*b11 - a9*b12,
2*a1*b18 + 2*a1*b19 - a10*b13 - a10*b14 + a2*b13 + a2*b14 - 4*a5*b2 + a5*b41 -
8*a6*b1 - 2*a8*b18,
a1*b21 - a10*b19 - 2*a11*b14 + a2*b19 + 4*a3*b14 + a5*b45 - a5*b5 - 2*a6*b2 + 2
*a6*b41 - a8*b21,
2*a1*b22 - a10*b21 - 2*a11*b19 + a2*b21 + 2*a3*b19 + a5*b47 - a5*b7 + 2*a6*b45
- 2*a6*b5 - 2*a8*b22,
a12*b50 + 2*a12*b51 + a12*b52 + a13*b50 + 2*a13*b51 + a13*b52 + 48*a15*b35 - 3*
a8*b68 - 2*a8*b69 - 2*a8*b71,
2*a10*b26 + 2*a12*b62 - 2*a13*b59 - a13*b60 - 6*a14*b49 - 4*a14*b52 - 12*a15*
b41 - a5*b57 - 4*a7*b38 + 2*a8*b74,
4*a11*b23 + 4*a11*b26 + 2*a14*b15 + 2*a14*b19 - a5*b63 + 2*a6*b15 - 2*a6*b55 -
4*a7*b42 + 4*a7*b5 + a9*b29,
a1*b26 - a12*b14 - a13*b14 + a4*b14 + a5*b49 + a5*b54 - a5*b9 - 4*a7*b1 + 4*a7*
b35 - a8*b26,
2*a1*b26 + 2*a1*b27 - 6*a12*b14 - a13*b13 - 3*a13*b14 - a5*b12 + a5*b50 + a5*
b52 - 24*a7*b1 - 2*a8*b26,
4*a12*b69 + 2*a12*b70 - a13*b68 + 2*a13*b69 + 2*a13*b70 + 24*a15*b49 + 4*a15*
b50 + 12*a15*b53 + 36*a15*b54 - 12*a8*b77,
12*a1*b31 + 4*a1*b32 - 2*a12*b24 - 2*a13*b24 - 4*a15*b11 - 8*a15*b12 + a4*b68 +
a4*b71 - 4*a7*b10 - 12*a7*b9,
a10*b44 - 2*a10*b45 + 2*a10*b6 - 8*a11*b40 - 36*a11*b41 - 5*a2*b44 - 20*a3*b38
- 10*a3*b39 + 10*a8*b46 + 30*a8*b47 - 2*a9*b45,
2*a1*b43 + 144*a11*b35 + 12*a2*b36 + 8*a2*b37 - 6*a8*b42 - 10*a8*b43 - 2*a9*b3
+ a9*b38 + a9*b39 - 3*a9*b4 + 3*a9*b40,
a1*b57 + 2*a10*b49 - 2*a10*b9 - 2*a12*b36 - a12*b38 + 8*a14*b35 + a4*b38 - 2*a8
*b55 - a8*b57 + 3*a9*b49 + a9*b52,
a10*b12 - 3*a10*b52 - a13*b40 - 24*a14*b35 - a4*b38 - a5*b38 - a5*b39 + a8*b58
+ 2*a8*b60 + 2*a8*b62 - a9*b52,
6*a10*b54 - a13*b40 + 24*a14*b35 + 2*a4*b37 + 2*a5*b37 - 2*a8*b58 - 2*a8*b62 -
a9*b12 + a9*b52 + a9*b53 + 3*a9*b54,
4*a1*b15 - 2*a10*b14 - 2*a10*b9 + 2*a2*b9 - 6*a4*b2 - 2*a5*b2 + 2*a5*b36 + a5*
b38 - 24*a6*b1 - a9*b13 - 3*a9*b14,
2*a1*b15 + 2*a1*b17 - a10*b10 - 2*a10*b13 + a2*b10 - 6*a4*b2 - 3*a5*b2 - a5*b3
+ a5*b38 - 36*a6*b1 - 2*a9*b13,
3*a1*b21 - 2*a10*b18 - a10*b19 - 2*a11*b13 + 2*a2*b18 + a2*b19 + 4*a3*b13 + a5*
b45 - 3*a5*b5 - 6*a6*b2 - a8*b21,
2*a10*b67 - 2*a12*b56 - a12*b57 + 6*a14*b49 + 2*a14*b52 + a4*b57 + 2*a7*b39 - 2
*a8*b72 - 2*a8*b73 + 2*a9*b67 + a9*b68,
a10*b27 - a12*b60 - a13*b60 - 2*a14*b50 - 2*a14*b51 - 2*a14*b52 - 12*a15*b41 -
a5*b60 - 4*a7*b38 + 4*a8*b73 + 2*a8*b74,
6*a12*b53 + 6*a12*b54 + 2*a13*b50 - 2*a13*b51 - a13*b52 + 3*a13*b53 + 9*a13*b54
+ 96*a15*b35 - 8*a8*b69 - 4*a8*b70 - 4*a8*b71,
2*a11*b29 - 2*a11*b74 + a13*b66 + a14*b21 - a14*b65 - a3*b74 - 3*a5*b66 - a6*
b63 - 2*a6*b65 - 2*a7*b46 + 2*a9*b30,
a1*b24 + 2*a1*b26 - a12*b12 - a13*b12 + a4*b12 + 2*a4*b49 + 2*a4*b54 - 2*a4*b9
- 3*a5*b9 - 16*a7*b1 - a8*b24,
a10*b31 - a10*b76 + a12*b72 + a12*b73 - 2*a14*b67 - a14*b68 - a15*b57 - a4*b73
- a7*b57 + 2*a8*b78 - 3*a9*b76,
a10*b32 + a12*b74 - 2*a13*b73 - 2*a14*b67 - 3*a14*b68 - 4*a15*b59 - 3*a15*b60 -
a5*b73 - 2*a7*b57 - a7*b60 + 6*a8*b78,
a12*b72 + a13*b72 - 2*a14*b67 - 2*a14*b70 + 2*a15*b56 - a4*b72 - 2*a7*b56 + 2*
a8*b78 + a9*b31 - a9*b76 - a9*b77,
6*a1*b33 - 2*a14*b24 - 2*a14*b26 - 2*a15*b16 + 2*a4*b72 + a5*b72 - 6*a6*b23 - 2
*a7*b16 + 4*a7*b56 - 6*a9*b31 - a9*b32,
6*a1*b31 + 2*a1*b32 - a12*b24 - a13*b24 - 2*a15*b11 - 4*a15*b12 - 2*a4*b23 + a4
*b24 + 2*a4*b69 - 2*a5*b23 - 12*a7*b9,
8*a1*b34 - a12*b32 - a13*b32 - 4*a15*b25 - 4*a15*b26 + a4*b32 - a5*b31 + a5*b76
+ a5*b77 - 4*a7*b23 + 4*a7*b69,
2*a1*b43 - a10*b36 - a10*b37 + 48*a11*b35 + 9*a2*b36 + a2*b37 - 6*a8*b42 - 2*a8
*b43 - 3*a9*b2 - a9*b3 + a9*b40 + 4*a9*b41,
2*a10*b43 - 4*a11*b39 + 4*a11*b4 - 12*a11*b40 - 24*a11*b41 - 2*a2*b42 - 6*a2*
b43 - 60*a3*b36 - 20*a3*b37 + 20*a8*b46 - a9*b44 + 4*a9*b6,
a10*b50 + a10*b52 + 24*a14*b35 + 2*a4*b39 + a5*b39 - 2*a8*b56 - 2*a8*b57 - a8*
b58 - a8*b60 + a9*b50 + a9*b51 + a9*b52,
2*a1*b16 + 4*a1*b17 + 6*a1*b18 - 4*a10*b11 - 2*a10*b13 - 2*a4*b3 - 2*a5*b3 + a5
*b39 - 3*a5*b4 - 72*a6*b1 - 2*a9*b11 - 2*a9*b13,
a10*b29 - 2*a11*b68 + a12*b65 - a13*b64 - 2*a14*b59 - 2*a14*b60 - 4*a15*b45 - 2
*a5*b64 - a6*b57 - a6*b60 - 2*a7*b44 + 4*a8*b75,
2*a13*b59 - 2*a13*b61 + 2*a13*b62 - 2*a14*b13 + 6*a14*b49 + 6*a14*b54 + 12*a15*
b41 + 3*a5*b55 + 12*a7*b36 - 2*a8*b74 - 2*a9*b25 - a9*b26,
4*a11*b25 - 4*a11*b69 + 2*a14*b18 - 2*a14*b59 - 2*a14*b62 - 4*a15*b45 - a5*b63
- 2*a6*b55 - 2*a6*b61 - 4*a7*b42 + 4*a8*b75 + a9*b29,
2*a11*b27 - 2*a11*b71 - a12*b65 + a13*b64 - 2*a14*b61 - 2*a14*b62 - 4*a15*b45 -
2*a5*b65 - a6*b58 - 4*a7*b42 + 4*a8*b75 + a9*b29,
3*a1*b24 + 2*a1*b25 + 2*a1*b27 - 2*a12*b11 - a12*b12 - 2*a13*b11 - a13*b12 - a4
*b10 - a4*b11 + a4*b51 - a5*b10 - 48*a7*b1,
4*a1*b26 + 2*a1*b27 - 8*a12*b14 - a13*b13 - 5*a13*b14 - a5*b10 + 2*a5*b49 + a5*
b50 + a5*b52 + 2*a5*b54 - 32*a7*b1 - 2*a8*b27,
2*a14*b25 - 2*a14*b67 - 2*a14*b69 - 2*a14*b70 - 4*a15*b59 + 2*a15*b61 - 4*a15*
b62 - a5*b72 - 4*a7*b55 - 2*a7*b61 + 6*a8*b78 + a9*b32,
2*a11*b32 - 3*a11*b77 + a13*b75 + a14*b29 - 2*a14*b74 - a15*b65 - 2*a5*b75 - a6
*b72 - a6*b74 - 2*a7*b63 - 2*a7*b65 + 3*a9*b33,
6*a1*b31 + 2*a1*b32 - a12*b24 - a13*b24 - 6*a15*b12 - 2*a4*b23 + a4*b24 + 2*a4*
b67 + 2*a4*b70 - 2*a5*b23 - 12*a7*b9 - 6*a8*b31,
a1*b32 - a12*b26 - a13*b26 - 6*a15*b14 + a4*b26 - a5*b23 + a5*b67 + a5*b70 + 4*
a7*b49 + 4*a7*b54 - 4*a7*b9 - a8*b32,
8*a1*b34 - a12*b32 - a13*b32 - 8*a15*b26 + a4*b32 - a5*b31 + a5*b76 + a5*b77 -
4*a7*b23 + 4*a7*b67 + 4*a7*b70 - 8*a8*b34,
a1*b57 + 6*a10*b49 - 2*a12*b37 - a12*b38 - 2*a12*b39 + 24*a14*b35 + a4*b38 + 2*
a4*b39 - 2*a8*b55 - 4*a8*b56 - 3*a8*b57 + 9*a9*b49 + 3*a9*b52,
a10*b11 - 3*a10*b51 - a12*b40 - a13*b40 - 24*a14*b35 - a4*b38 - a5*b38 - a5*b39
+ a8*b57 + a8*b58 + 2*a8*b60 + 2*a8*b61 - a9*b51,
2*a1*b56 - a12*b36 - a12*b37 - a13*b36 - a13*b37 + 8*a14*b35 + a4*b36 + a4*b37
- 2*a8*b55 - 2*a8*b56 + 4*a9*b49 + 4*a9*b54 - a9*b9,
2*a1*b61 + 2*a10*b53 + 24*a14*b35 + 6*a4*b36 + 3*a5*b36 + a5*b37 - 2*a8*b55 - 2
*a8*b58 - 2*a8*b61 - a9*b10 - a9*b11 + a9*b51 + 2*a9*b53,
6*a10*b53 + 2*a13*b40 + 48*a14*b35 + 6*a4*b36 + 9*a5*b36 + 3*a5*b37 - 2*a8*b58
- 8*a8*b61 - 4*a8*b62 - 2*a9*b11 - a9*b12 - 2*a9*b13 + 2*a9*b53,
12*a1*b20 - 12*a11*b12 - 24*a11*b14 - 2*a2*b15 - 2*a2*b16 - 60*a3*b9 + 2*a4*b43
+ 2*a5*b43 - 6*a6*b2 - 6*a6*b3 - 6*a6*b4 - 2*a9*b16 - a9*b17,
42*a1*b22 - 2*a11*b16 - 4*a11*b17 - 12*a11*b19 - 20*a3*b15 - 6*a3*b16 + 2*a4*
b46 + 5*a5*b46 + 2*a6*b43 - 6*a6*b5 - 6*a6*b6 - 2*a9*b20 - a9*b21,
2*a1*b73 - 2*a10*b23 + 2*a10*b67 - 2*a12*b55 - a12*b57 + 6*a14*b49 + 2*a14*b52
+ a4*b57 + 2*a7*b38 - 2*a8*b72 - 2*a8*b73 + 2*a9*b67 + a9*b68,
2*a10*b25 - 2*a12*b59 + 2*a12*b61 - 2*a13*b59 - a13*b60 - 6*a14*b49 - 2*a14*b51
- 2*a14*b52 - 12*a15*b41 - a5*b57 - 4*a7*b38 + 4*a8*b73 + 2*a8*b74,
a1*b72 - a12*b55 - a13*b55 + 2*a14*b49 + 2*a14*b54 - 2*a14*b9 - 4*a15*b36 + a4*
b55 + 2*a7*b36 - a8*b72 - a9*b23 + a9*b67 + a9*b70,
3*a1*b24 + 4*a1*b25 + 2*a1*b26 - 2*a12*b11 - a12*b12 - 3*a13*b12 + 2*a4*b11 +
a4*b12 + 2*a4*b53 - 6*a4*b9 - 9*a5*b9 - 48*a7*b1 - a8*b24,
3*a1*b24 + 2*a1*b26 + 2*a1*b27 - 3*a12*b12 - a13*b11 - 2*a13*b12 - a4*b10 - a4*
b12 + a4*b50 + a4*b52 - a5*b10 - 48*a7*b1 - a8*b24,
2*a11*b28 + 2*a11*b29 + a14*b20 + a14*b21 - a2*b30 + a3*b28 - a4*b66 - 3*a5*b66
+ 2*a6*b20 - a6*b63 - 2*a7*b46 + 3*a7*b7 + 2*a9*b30,
2*a1*b25 + 2*a1*b26 - a12*b13 - a12*b14 - 4*a13*b14 + a4*b13 + a4*b14 + a5*b49
+ a5*b53 + a5*b54 - 4*a5*b9 - 16*a7*b1 - 2*a8*b25,
2*a1*b78 - a12*b72 - a13*b72 - 2*a14*b23 + 2*a14*b67 + 2*a14*b70 - 2*a15*b55 +
a4*b72 + 2*a7*b55 - 2*a8*b78 - a9*b31 + a9*b76 + a9*b77,
3*a11*b31 + 2*a11*b32 + 2*a14*b28 + a14*b29 + a15*b20 - a2*b33 - a4*b75 - 2*a5*
b75 + a6*b28 - a6*b72 + 2*a7*b20 - 2*a7*b63 + 3*a9*b33,
24*a1*b34 - 3*a12*b32 - 3*a13*b32 - 4*a15*b25 - 8*a15*b26 - 6*a15*b27 + 2*a4*
b32 + 3*a5*b76 + 3*a5*b77 - 4*a7*b23 - 2*a7*b24 + 2*a7*b68 + 2*a7*b71,
3*a1*b44 - 2*a10*b3 + a10*b38 - 2*a10*b39 + 2*a10*b40 + 6*a10*b41 + 144*a11*b35
+ 7*a2*b38 + 2*a2*b39 - 6*a8*b42 - 4*a8*b43 - 9*a8*b44 + 2*a9*b40 + 9*a9*b41,
a1*b60 - a10*b10 + a10*b50 + a10*b52 + 24*a14*b35 + 2*a4*b38 + a5*b38 - 2*a8*
b55 - 2*a8*b57 - a8*b58 - a8*b60 + a9*b50 + a9*b51 + a9*b52,
a10*b20 + a10*b64 - a11*b57 - 4*a11*b59 - 2*a11*b60 + a12*b46 + 3*a12*b47 - 2*
a14*b45 - 2*a2*b64 - 3*a3*b57 - 3*a4*b47 - 3*a6*b44 + 6*a8*b66 - a9*b64,
a1*b58 + 2*a10*b54 - 2*a13*b36 - a13*b38 + 16*a14*b35 + 6*a4*b36 + 2*a5*b36 - 4
*a8*b55 - a8*b58 - a9*b10 + a9*b50 + a9*b53 + 3*a9*b54 - 2*a9*b9,
2*a1*b62 + 6*a10*b54 - a13*b40 + 24*a14*b35 + 6*a4*b36 + 3*a5*b36 + a5*b37 - 2*
a8*b58 - 2*a8*b62 - a9*b10 - a9*b12 + a9*b52 + a9*b53 + 3*a9*b54,
2*a1*b15 + 2*a1*b17 - a10*b10 - 6*a10*b14 + a2*b10 - 6*a4*b2 - 3*a5*b2 - a5*b3
+ a5*b38 + a5*b40 - 36*a6*b1 - 2*a8*b15 - a9*b13 - 3*a9*b14,
a10*b28 - 4*a11*b67 - 2*a11*b68 + a12*b63 + 2*a12*b64 - a14*b57 - 2*a14*b59 -
a14*b60 - a2*b73 - 2*a4*b64 - 2*a6*b57 - 2*a7*b44 + 4*a8*b75 - 2*a9*b73,
6*a12*b62 - 2*a13*b59 - a13*b60 + 2*a13*b61 + 2*a13*b62 + 4*a14*b53 + 12*a14*
b54 + 24*a15*b41 + a5*b58 + 2*a5*b62 + 24*a7*b36 - 4*a8*b74 - 2*a9*b26 - 2*a9*
b27,
4*a1*b28 - 2*a14*b10 - 2*a14*b12 - 6*a14*b14 - 4*a2*b23 + 2*a4*b55 + a5*b55 + 2
*a5*b56 - 18*a6*b9 - 2*a7*b3 + 4*a7*b37 - 4*a9*b23 - a9*b24 - 3*a9*b26,
8*a1*b25 + 4*a1*b26 + 6*a1*b27 - 6*a12*b13 - 6*a12*b14 - 5*a13*b13 - 9*a13*b14
- 3*a5*b10 + a5*b50 + 2*a5*b51 + a5*b52 + 2*a5*b53 - 96*a7*b1 - 2*a8*b27,
2*a1*b25 + 2*a1*b26 + 4*a1*b27 - 2*a12*b13 - 6*a12*b14 - 3*a13*b13 - 3*a13*b14
- a5*b11 - a5*b12 + a5*b50 + a5*b51 + a5*b52 - 48*a7*b1 - 2*a8*b25,
a12*b74 - 2*a13*b73 - a14*b27 + 2*a14*b69 + 2*a14*b70 + 3*a14*b71 + 4*a15*b59 +
4*a15*b61 + 8*a15*b62 + a5*b74 + 4*a7*b55 + 2*a7*b58 - 12*a8*b78 - 2*a9*b32,
a1*b58 + 6*a10*b54 - 2*a13*b37 - a13*b38 - 2*a13*b39 + 48*a14*b35 + 6*a4*b37 +
2*a5*b37 - 4*a8*b55 - 8*a8*b56 - 3*a8*b58 - a9*b10 + 3*a9*b50 + 3*a9*b53 + 9*a9
*b54,
8*a1*b20 - 4*a11*b10 - 4*a11*b12 - 36*a11*b14 - 4*a2*b15 - 60*a3*b9 + 2*a4*b42
+ 3*a5*b42 + 2*a5*b43 - 18*a6*b2 - 4*a6*b3 + 2*a6*b37 - 2*a9*b15 - a9*b17 - 3*
a9*b19,
2*a1*b20 + 10*a1*b21 - a10*b17 - 4*a10*b18 - 2*a11*b11 - 8*a11*b13 + a2*b17 + 2
*a2*b18 - 2*a4*b5 + a5*b44 - 2*a5*b5 - 2*a5*b6 - 18*a6*b2 - 2*a6*b3 - 2*a9*b18,
a1*b17 + 6*a1*b19 - a10*b12 - 6*a10*b14 + a2*b12 + 2*a2*b14 - 2*a4*b2 + 2*a4*
b41 - 3*a5*b2 - a5*b3 + a5*b40 + 2*a5*b41 - 24*a6*b1 - a8*b17 - 2*a9*b14,
a1*b72 - a12*b55 - 2*a12*b56 - a13*b55 - 2*a13*b56 + 6*a14*b49 + 6*a14*b54 - 4*
a15*b37 + a4*b55 + 2*a4*b56 + 2*a7*b37 - 3*a8*b72 - a9*b23 + 3*a9*b67 + 3*a9*
b70,
4*a12*b61 + 2*a12*b62 - a13*b60 + 2*a13*b61 + 2*a13*b62 + 2*a14*b50 + 6*a14*b53
+ 6*a14*b54 + 24*a15*b41 + a5*b58 + 2*a5*b61 + 24*a7*b36 - 6*a8*b74 - 2*a9*b25
- 2*a9*b27,
4*a1*b30 - a10*b29 - 2*a11*b27 - a12*b21 - a13*b21 - 2*a14*b18 - 2*a14*b19 + a2
*b29 + 2*a3*b27 - 2*a5*b21 + a5*b64 + a5*b65 - a6*b17 + a6*b60 - 4*a7*b5,
3*a1*b32 - 2*a12*b25 - a12*b26 - 3*a13*b26 - 2*a15*b13 - 12*a15*b14 + 2*a4*b25
+ a4*b26 - 3*a5*b23 + a5*b67 + 2*a5*b69 + a5*b70 + 4*a7*b53 - 12*a7*b9 - a8*b32
,
5*a1*b46 - 3*a10*b42 - 2*a10*b43 - 4*a11*b3 + 4*a11*b38 + 4*a11*b40 + 36*a11*
b41 + 9*a2*b42 + 2*a2*b43 + 60*a3*b36 + 10*a3*b37 - 15*a8*b46 + a9*b44 + 3*a9*
b45 - 5*a9*b5 - 2*a9*b6,
4*a1*b64 - 2*a10*b15 - a10*b57 + 2*a10*b59 + 12*a11*b49 + 4*a11*b52 - 2*a12*b42
- a12*b44 + 6*a14*b41 + a2*b57 + a4*b44 + 4*a6*b38 - 2*a8*b63 - 4*a8*b64 + 2*
a9*b59 + a9*b60,
a10*b17 - a10*b60 - 4*a11*b50 - 4*a11*b51 - 4*a11*b52 - 2*a14*b40 - 12*a14*b41
- a2*b60 - a4*b44 - 2*a5*b44 - 6*a6*b38 - 2*a6*b39 + 2*a8*b63 + 8*a8*b64 + 4*a8
*b65 - a9*b60,
3*a10*b66 + 2*a11*b20 - a11*b63 - 2*a11*b64 - 2*a11*b65 + 4*a12*b48 + 4*a13*b48
+ a14*b46 - a14*b47 + a14*b7 - 3*a2*b66 - 4*a3*b63 - 4*a4*b48 - 4*a6*b46 + 4*
a9*b22 - a9*b66,
4*a1*b20 - 2*a10*b15 - 2*a10*b19 - 2*a11*b10 - 4*a11*b13 - 12*a11*b14 + 2*a2*
b15 - 4*a4*b5 + 2*a5*b42 + a5*b44 - 4*a5*b5 - 18*a6*b2 - 2*a6*b3 + 2*a6*b38 - 2
*a9*b18 - 2*a9*b19,
2*a1*b16 + 4*a1*b17 + 6*a1*b19 - 4*a10*b12 - 6*a10*b14 - 2*a4*b3 + 2*a4*b40 - 2
*a5*b3 + a5*b39 - 3*a5*b4 + a5*b40 - 72*a6*b1 - 2*a8*b16 - 2*a9*b12 - a9*b13 -
3*a9*b14,
3*a1*b17 + 12*a1*b18 + 6*a1*b19 - 2*a10*b11 - a10*b12 - 6*a10*b13 + 2*a2*b11 +
a2*b12 + 2*a2*b13 - 6*a4*b2 - 9*a5*b2 - 3*a5*b3 + a5*b40 - 72*a6*b1 - a8*b17 -
2*a9*b13,
20*a1*b30 - 4*a11*b24 - 12*a11*b26 - 2*a14*b16 - 2*a14*b17 - 2*a14*b19 - 20*a3*
b23 + 2*a4*b63 + 3*a5*b63 - 6*a6*b15 - 4*a6*b16 + 2*a6*b56 + 4*a7*b43 - 4*a7*b6
- 4*a9*b28 - a9*b29,
4*a1*b30 - a10*b29 - 4*a11*b25 - a12*b21 - a13*b21 - 2*a14*b18 - 2*a14*b19 + a2
*b29 + 4*a3*b25 + a4*b21 - a5*b20 + a5*b64 + a5*b65 - 2*a6*b15 + 2*a6*b61 - 4*
a7*b5,
2*a10*b30 + 2*a11*b29 + a12*b22 + a13*b22 + 2*a14*b21 - 2*a2*b30 - a3*b29 - a4*
b22 + 3*a5*b22 - 2*a5*b66 + a6*b20 + a6*b21 - a6*b64 - a6*b65 - 2*a7*b47 + 2*a7
*b7,
a1*b63 - a10*b55 + 4*a11*b49 + 4*a11*b54 - 4*a11*b9 - a12*b42 - a13*b42 - 2*a14
*b2 - 2*a14*b36 + 2*a14*b41 + a2*b55 + a4*b42 + 4*a6*b36 - a8*b63 - a9*b15 + a9
*b59 + a9*b62,
24*a11*b49 + 24*a11*b54 - 2*a12*b43 - 2*a13*b43 + 2*a14*b39 - 2*a14*b4 + 2*a14*
b40 + 2*a2*b55 + 4*a2*b56 + 2*a4*b43 + 6*a6*b36 + 6*a6*b37 - 6*a8*b63 - 2*a9*
b16 + 2*a9*b56 + a9*b57 + a9*b58,
2*a10*b61 - 4*a11*b11 + 4*a11*b51 + 8*a11*b53 + 2*a14*b40 + 12*a14*b41 + 2*a2*
b61 + 2*a4*b42 + 2*a5*b42 + 2*a5*b43 + 18*a6*b36 + 2*a6*b37 - 2*a8*b63 - 8*a8*
b65 - a9*b17 - 4*a9*b18 + 2*a9*b61,
2*a10*b62 - 4*a11*b12 + 4*a11*b52 + 4*a11*b53 + 12*a11*b54 - 4*a13*b45 + 12*a14
*b41 + 2*a2*b62 + 2*a4*b42 + 2*a5*b42 + 2*a5*b43 + 18*a6*b36 + 2*a6*b37 - 8*a8*
b65 - a9*b17 - 4*a9*b19 + 2*a9*b62,
2*a10*b71 + a12*b58 - a13*b57 - a13*b60 + 4*a14*b50 + 4*a14*b53 + 12*a14*b54 +
4*a15*b40 + a4*b58 + a5*b58 + 12*a7*b36 + 4*a7*b37 - 4*a8*b72 - 4*a8*b74 - a9*
b24 - a9*b27 + 2*a9*b71,
a1*b29 - a10*b26 - a12*b19 - a13*b19 - 4*a14*b14 + a2*b26 + a4*b19 - a5*b15 +
a5*b59 + a5*b62 + 2*a6*b14 + 2*a6*b49 + 2*a6*b54 - 2*a6*b9 - 4*a7*b2 + 4*a7*b41
- a8*b29,
a10*b78 + 2*a11*b31 - 2*a11*b76 - 2*a11*b77 + 2*a12*b75 + 2*a13*b75 + a14*b28 -
a14*b72 - a14*b73 - a14*b74 + a15*b63 - a2*b78 - 2*a4*b75 - 2*a6*b72 - 2*a7*
b63 + 2*a9*b33 - 3*a9*b78,
4*a10*b34 + 3*a12*b33 + 3*a13*b33 + 4*a14*b32 + 4*a15*b29 - 4*a2*b34 - 3*a4*b33
+ a5*b33 - 4*a5*b78 + a6*b31 - a6*b32 - a6*b76 - a6*b77 + 2*a7*b28 + a7*b29 -
2*a7*b73 - 2*a7*b74,
2*a10*b16 - a10*b57 - 2*a10*b59 - 36*a11*b49 - 12*a11*b52 + 2*a12*b43 + 3*a12*
b44 - 4*a14*b40 - 6*a14*b41 - 3*a2*b57 - 3*a4*b44 - 6*a6*b38 - 6*a6*b39 + 6*a8*
b63 + 12*a8*b64 - 2*a9*b57 - 2*a9*b59 - a9*b60,
14*a1*b22 - a10*b20 - a10*b21 - a11*b17 - 4*a11*b18 - 4*a11*b19 + a2*b20 + a2*
b21 - a3*b17 + a4*b47 - a4*b7 + a5*b46 + 3*a5*b47 - 3*a5*b7 + a6*b44 - 6*a6*b5
- 2*a6*b6 - a9*b21,
2*a10*b75 + 2*a11*b28 - 2*a11*b72 - 2*a11*b73 - 2*a11*b74 + 3*a12*b66 + 3*a13*
b66 + a14*b20 - a14*b64 - a14*b65 + 2*a15*b46 - 2*a2*b75 - 3*a3*b72 - 3*a4*b66
- 3*a6*b63 - 3*a7*b46 + 3*a9*b30 - 2*a9*b75,
4*a1*b30 - a10*b29 - 4*a11*b26 - a12*b21 - a13*b21 - 4*a14*b19 + a2*b29 + 4*a3*
b26 + a4*b21 - a5*b20 + a5*b64 + a5*b65 - 2*a6*b15 + 2*a6*b59 + 2*a6*b62 + 4*a7
*b45 - 4*a7*b5 - 4*a8*b30,
3*a10*b33 + 3*a11*b32 + 2*a12*b30 + 2*a13*b30 + 3*a14*b29 + 3*a15*b21 - 3*a2*
b33 - 2*a3*b32 - 2*a4*b30 + 2*a5*b30 - 3*a5*b75 + a6*b28 - a6*b73 - a6*b74 + 2*
a7*b20 + 2*a7*b21 - 2*a7*b64 - 2*a7*b65,
6*a1*b66 - a10*b63 - 4*a11*b15 + 2*a11*b55 + 4*a11*b59 + 4*a11*b62 - a12*b46 -
a13*b46 - 2*a14*b42 + 2*a14*b45 - 2*a14*b5 + a2*b63 + 6*a3*b55 + a4*b46 + 6*a6*
b42 - 6*a8*b66 - a9*b20 + a9*b64 + a9*b65,
a10*b65 + 2*a11*b17 - a11*b58 - 2*a11*b60 - 4*a11*b61 - 4*a11*b62 + a13*b46 + 3
*a13*b47 - 4*a14*b45 - 2*a2*b65 - 3*a3*b58 - a4*b46 - 3*a5*b46 - 6*a6*b42 - 2*
a6*b43 + 12*a8*b66 + a9*b20 + 3*a9*b21 - a9*b65,
8*a1*b15 + 8*a1*b16 + 4*a1*b17 - 2*a10*b10 - 2*a10*b12 - 6*a10*b14 - 4*a2*b10 -
6*a4*b3 + 2*a4*b38 - 2*a5*b3 + 2*a5*b37 + a5*b38 + 2*a5*b39 - 144*a6*b1 - 2*a9
*b10 - 2*a9*b11 - 2*a9*b12 - 3*a9*b13 - 9*a9*b14,
a10*b24 - 2*a10*b68 + a12*b58 + a12*b60 - a13*b57 - 12*a14*b49 - 2*a14*b50 - 2*
a14*b51 - 6*a14*b52 - 4*a15*b40 - a4*b57 - a4*b60 - a5*b57 - 4*a7*b38 - 4*a7*
b39 + 4*a8*b72 + 8*a8*b73 + 2*a8*b74 - 2*a9*b68,
4*a1*b75 - a10*b72 - 4*a11*b23 + 4*a11*b67 + 4*a11*b70 - a12*b63 - a13*b63 - 2*
a14*b15 + 2*a14*b59 + 2*a14*b62 - 4*a15*b42 + a2*b72 + a4*b63 + 4*a6*b55 + 4*a7
*b42 - 4*a8*b75 - a9*b28 + a9*b73 + a9*b74,
4*a10*b70 - 2*a12*b62 - 2*a13*b59 - 2*a13*b62 - 2*a14*b12 + 12*a14*b49 + 2*a14*
b52 + 2*a14*b53 + 18*a14*b54 + 2*a4*b55 + 2*a4*b62 + 2*a5*b55 + 2*a5*b56 + 12*
a7*b36 + 4*a7*b37 - 4*a8*b74 - a9*b24 - 2*a9*b26 + 4*a9*b70,
6*a1*b29 - 2*a10*b25 - 2*a10*b27 - 4*a12*b18 - 2*a12*b19 - 4*a13*b18 - 2*a13*
b19 - 6*a14*b13 - 6*a14*b14 + 2*a2*b25 + 2*a2*b27 - a5*b17 - 2*a5*b18 + 2*a5*
b60 + 2*a5*b61 - 2*a6*b10 - 2*a6*b11 + 2*a6*b51 - 24*a7*b2,
12*a1*b32 - 6*a12*b25 - 2*a12*b26 - 2*a12*b27 - 6*a13*b25 - 2*a13*b26 - 2*a13*
b27 - 12*a15*b13 - 36*a15*b14 + 2*a4*b25 + 2*a4*b27 - a5*b24 + 2*a5*b68 + 4*a5*
b69 + 2*a5*b71 - 4*a7*b10 - 4*a7*b11 + 4*a7*b51 - 24*a7*b9,
6*a1*b33 - a10*b32 - a12*b29 - a13*b29 - 4*a14*b25 - 2*a14*b26 - 2*a15*b18 - 4*
a15*b19 + a2*b32 + a4*b29 - a5*b28 + a5*b73 + a5*b74 - 2*a6*b23 + 2*a6*b25 + 2*
a6*b69 - 4*a7*b15 - 2*a7*b18 + 4*a7*b61,
2*a1*b20 + 10*a1*b21 - a10*b17 - 4*a10*b19 - 2*a11*b12 - 4*a11*b13 - 12*a11*b14
+ a2*b17 + 2*a2*b19 + 2*a4*b45 - 2*a4*b5 + a5*b44 + 4*a5*b45 - 2*a5*b5 - 2*a5*
b6 - 18*a6*b2 - 2*a6*b3 + 2*a6*b40 - 2*a8*b20 - 2*a9*b19,
2*a10*b70 - a12*b58 - 2*a13*b56 - a13*b57 - a13*b58 + 12*a14*b49 + 2*a14*b50 +
2*a14*b53 + 18*a14*b54 + 4*a4*b56 + a4*b58 + 2*a5*b56 + 8*a7*b37 - 8*a8*b72 - 2
*a8*b74 - a9*b24 + a9*b68 + 2*a9*b69 + 2*a9*b70 + 2*a9*b71,
4*a10*b69 - 2*a12*b61 - 2*a13*b61 - 2*a14*b11 + 12*a14*b49 + 2*a14*b51 + 4*a14*
b53 + 12*a14*b54 + 4*a15*b40 + 2*a4*b55 + 2*a4*b61 + 2*a5*b55 + 2*a5*b56 + 12*
a7*b36 + 4*a7*b37 - 4*a8*b72 - 4*a8*b74 - a9*b24 - 2*a9*b25 + 4*a9*b69,
6*a1*b33 - a10*b32 - a12*b29 - a13*b29 - 6*a14*b26 - 6*a15*b19 + a2*b32 + a4*
b29 - a5*b28 + a5*b73 + a5*b74 - 2*a6*b23 + 2*a6*b26 + 2*a6*b67 + 2*a6*b70 - 4*
a7*b15 - 2*a7*b19 + 4*a7*b59 + 4*a7*b62 - 6*a8*b33,
a10*b72 - 12*a11*b67 - 12*a11*b70 + 3*a12*b63 + 3*a13*b63 + 2*a14*b16 - 2*a14*
b57 - 2*a14*b58 - 2*a14*b59 - 2*a14*b62 + 4*a15*b43 - 3*a2*b72 - 3*a4*b63 - 6*
a6*b55 - 6*a6*b56 - 4*a7*b43 + 12*a8*b75 + 3*a9*b28 - 4*a9*b72 - a9*b73 - a9*
b74,
8*a1*b28 - 4*a10*b23 - 2*a10*b26 - 2*a12*b15 - 2*a13*b15 - 4*a14*b10 - 2*a14*
b13 - 18*a14*b14 + 4*a2*b23 - 2*a4*b15 - 2*a5*b15 + 4*a5*b55 + a5*b57 + a5*b58
- 18*a6*b9 - 12*a7*b2 - 4*a7*b3 + 4*a7*b38 - 2*a9*b25 - 2*a9*b26 - 2*a9*b27,
3*a1*b29 - 2*a10*b25 - a10*b26 - 2*a12*b18 - a12*b19 - 3*a13*b19 - 2*a14*b13 -
6*a14*b14 + 2*a2*b25 + a2*b26 + 2*a4*b18 + a4*b19 - 3*a5*b15 + a5*b59 + 2*a5*
b61 + a5*b62 + 2*a6*b13 + 2*a6*b53 - 6*a6*b9 - 12*a7*b2 - a8*b29,
6*a1*b29 - 2*a10*b26 - 2*a10*b27 - 6*a12*b19 - 2*a13*b18 - 4*a13*b19 - 4*a14*
b13 - 12*a14*b14 + 2*a2*b26 + 2*a2*b27 - a5*b17 - 2*a5*b19 + 2*a5*b59 + 2*a5*
b60 + 2*a5*b62 - 2*a6*b10 - 2*a6*b12 + 2*a6*b50 + 2*a6*b52 - 24*a7*b2 - 2*a8*
b29,
12*a1*b32 - 8*a12*b26 - 2*a12*b27 - 2*a13*b25 - 6*a13*b26 - 2*a13*b27 - 8*a15*
b13 - 48*a15*b14 + 2*a4*b26 + 2*a4*b27 - a5*b24 + 4*a5*b67 + 2*a5*b68 + 4*a5*
b70 + 2*a5*b71 - 4*a7*b10 - 4*a7*b12 + 4*a7*b50 + 4*a7*b52 - 24*a7*b9 - 4*a8*
b32,
12*a1*b33 - 2*a10*b32 - 2*a12*b29 - 2*a13*b29 - 2*a14*b25 - 2*a14*b26 - 4*a14*
b27 - 4*a15*b18 - 8*a15*b19 + 2*a2*b32 + a4*b29 - a5*b29 + 2*a5*b73 + 2*a5*b74
- a6*b24 + a6*b27 + a6*b68 + a6*b71 - 4*a7*b15 - 2*a7*b17 + 2*a7*b60,
4*a1*b65 - a10*b58 + 2*a10*b62 - 4*a11*b10 + 4*a11*b50 + 4*a11*b53 + 12*a11*b54
- 2*a13*b42 - a13*b44 + 12*a14*b41 + a2*b58 + 4*a4*b42 + 4*a5*b42 + 18*a6*b36
+ 2*a6*b37 - 4*a8*b63 - 4*a8*b65 - 2*a9*b15 - a9*b17 + a9*b60 + 2*a9*b61 + 2*a9
*b62,
a10*b58 + 2*a10*b62 + 12*a11*b50 + 12*a11*b53 + 36*a11*b54 - 2*a13*b43 - 3*a13*
b44 + 8*a14*b40 + 12*a14*b41 + 3*a2*b58 + 4*a4*b43 + 4*a5*b43 + 36*a6*b36 + 12*
a6*b37 - 12*a8*b63 - 12*a8*b65 - 2*a9*b16 - 3*a9*b17 + 2*a9*b58 + a9*b60 + 2*a9
*b61 + 2*a9*b62,
4*a1*b28 + 6*a1*b29 - a10*b24 - 2*a10*b27 - a12*b17 - a13*b17 - 2*a14*b11 - 2*
a14*b12 - 4*a14*b13 - 12*a14*b14 + a2*b24 + a2*b27 - a4*b17 + a4*b60 - a5*b17 +
a5*b57 + a5*b58 + a5*b60 - 6*a6*b10 - 12*a7*b2 - 4*a7*b3 - 2*a9*b27,
a10*b77 - a12*b74 - a13*b72 - a13*b73 - a13*b74 - a14*b24 + 4*a14*b67 + a14*b68
+ 2*a14*b69 + 6*a14*b70 + 2*a14*b71 + a15*b58 + a4*b72 + a4*b74 + a5*b72 + 4*
a7*b55 + 4*a7*b56 + a7*b58 - 12*a8*b78 - 3*a9*b31 - a9*b32 + 3*a9*b77,
16*a1*b20 + 20*a1*b21 - 2*a10*b16 - 2*a10*b17 - 2*a10*b19 - 8*a11*b11 - 8*a11*
b12 - 12*a11*b13 - 36*a11*b14 + 2*a2*b16 - 20*a3*b10 + 2*a4*b44 - 4*a4*b6 + 2*
a5*b43 + 3*a5*b44 - 4*a5*b6 - 36*a6*b2 - 12*a6*b3 + 2*a6*b39 - 6*a6*b4 - 2*a9*
b17 - 2*a9*b18 - 2*a9*b19,
3*a10*b63 + 4*a11*b16 - 2*a11*b56 - 4*a11*b57 - 4*a11*b58 - 12*a11*b59 - 12*a11
*b62 + 5*a12*b46 + 5*a13*b46 + 2*a14*b43 - 2*a14*b44 - 2*a14*b45 + 2*a14*b6 - 5
*a2*b63 - 20*a3*b55 - 10*a3*b56 - 5*a4*b46 - 6*a6*b42 - 8*a6*b43 + 30*a8*b66 +
5*a9*b20 - 2*a9*b63 - a9*b64 - a9*b65,
2*a1*b74 + 2*a10*b70 - a12*b58 - 2*a13*b55 - a13*b57 - a13*b58 - 2*a14*b10 + 12
*a14*b49 + 2*a14*b50 + 2*a14*b53 + 18*a14*b54 + 4*a4*b55 + a4*b58 + 2*a5*b55 +
12*a7*b36 + 4*a7*b37 - 8*a8*b72 - 2*a8*b74 - 4*a9*b23 - a9*b24 + a9*b68 + 2*a9*
b69 + 2*a9*b70 + 2*a9*b71,
4*a1*b28 + 6*a1*b29 - a10*b24 - 4*a10*b25 - a12*b17 - a13*b17 - 2*a14*b11 - 2*
a14*b12 - 4*a14*b13 - 12*a14*b14 + a2*b24 + 2*a2*b25 - 2*a4*b15 + a4*b17 + 2*a4
*b61 - 2*a5*b15 - 2*a5*b16 + a5*b57 + a5*b58 + 2*a5*b61 - 18*a6*b9 - 12*a7*b2 -
4*a7*b3 - 4*a9*b25,
16*a1*b28 + 6*a1*b29 - 2*a10*b24 - 2*a10*b26 - 2*a12*b16 - 2*a13*b16 - 4*a14*
b11 - 12*a14*b12 - 2*a14*b13 - 18*a14*b14 - 2*a4*b16 + 2*a4*b57 + 2*a4*b58 - 2*
a5*b16 + 4*a5*b56 + a5*b57 + a5*b58 - 6*a6*b10 - 36*a6*b9 - 8*a7*b3 + 4*a7*b39
- 12*a7*b4 - 4*a9*b24 - 2*a9*b25 - 2*a9*b26 - 2*a9*b27,
18*a1*b33 - 3*a10*b31 - a10*b32 - 2*a12*b28 - 2*a13*b28 - 3*a14*b24 - 2*a14*b25
- 6*a14*b26 - 2*a14*b27 - 3*a15*b17 + 3*a2*b31 + a2*b32 + a4*b28 + a4*b73 + a4
*b74 - a5*b28 + 3*a5*b72 + a5*b73 + a5*b74 - 6*a6*b23 - 4*a7*b15 - 4*a7*b16 -
a7*b17 + 2*a7*b57 + 2*a7*b58 - 3*a9*b32,
4*a1*b28 + 6*a1*b29 - a10*b24 - 4*a10*b26 - a12*b17 - a13*b17 - 4*a14*b12 - 2*
a14*b13 - 18*a14*b14 + a2*b24 + 2*a2*b26 - 2*a4*b15 + a4*b17 + 2*a4*b59 + 2*a4*
b62 - 2*a5*b15 - 2*a5*b16 + a5*b57 + a5*b58 + 2*a5*b59 + 2*a5*b62 - 18*a6*b9 -
12*a7*b2 - 4*a7*b3 + 4*a7*b40 - 4*a8*b28 - 4*a9*b26,
3*a1*b63 - a10*b55 - 2*a10*b56 + 36*a11*b49 + 36*a11*b54 - 3*a12*b42 - 2*a12*
b43 - 3*a13*b42 - 2*a13*b43 - 2*a14*b3 - 2*a14*b37 + 2*a14*b38 + 2*a14*b40 + 6*
a14*b41 + 7*a2*b55 + 2*a2*b56 + 3*a4*b42 + 2*a4*b43 + 18*a6*b36 + 6*a6*b37 - 9*
a8*b63 - 3*a9*b15 - 2*a9*b16 + 2*a9*b55 + a9*b57 + a9*b58 + 3*a9*b59 + 3*a9*b62
,
2*a11*b24 - 2*a11*b68 - 4*a11*b69 - 4*a11*b70 - 4*a11*b71 + 2*a12*b65 + a13*b63
+ 2*a13*b64 + 2*a13*b65 + a14*b17 - a14*b58 - 4*a14*b59 - a14*b60 - 2*a14*b61
- 6*a14*b62 - a2*b74 - a4*b63 - 2*a4*b65 - 2*a5*b63 - 6*a6*b55 - 2*a6*b56 - 2*
a6*b58 - 4*a7*b42 - 4*a7*b43 + 16*a8*b75 + 2*a9*b28 + 2*a9*b29 - 2*a9*b74,
20*a1*b30 - 2*a10*b28 - a10*b29 - 2*a11*b24 - 4*a11*b25 - 4*a11*b26 - 4*a11*b27
- a12*b20 - a13*b20 - 2*a14*b17 - 2*a14*b18 - 6*a14*b19 + 2*a2*b28 + a2*b29 +
a4*b64 + a4*b65 - 2*a5*b20 + 2*a5*b63 + 2*a5*b64 + 2*a5*b65 - 6*a6*b15 - 2*a6*
b16 - a6*b17 + a6*b57 + a6*b58 + 2*a7*b44 - 4*a7*b5 - 4*a7*b6 - 2*a9*b29
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.
2 2
u = u *a1 + u *f(v,v)*a4 + u *a2*u + f(v,v )*a5*u + f(v,v) *a7*u
t 2x x x x
3 5
+ f(v,v)*a6*u + a3*u
2
v = u *a9*u*v + v *a8 + v *f(v,v)*a12 + v *a10*u + f(v,v )*a13*v
t x 2x x x x
2 2 4
+ f(v,v) *a15*v + f(v,v)*a14*u *v + a11*u *v
For any solution of the above algebraic conditions for the
a's and b's this system has the following symmetry:
2
u = u *b1 + u *f(v,v)*b9 + u *b2*u + u *u *b3*u + u *f(v,v )*b10
t 4x 3x 3x 2x x 2x x
2 2 4 3
+ u *f(v,v) *b23 + u *f(v,v)*b15*u + u *b5*u + u *b4
2x 2x 2x x
2 2 3
+ u *f(v,v)*b16*u + u *b6*u + u *f(v ,v )*b11 + u *f(v,v )*b12
x x x x x x 2x
2 3
+ u *f(v,v )*f(v,v)*b24 + u *f(v,v )*b17*u + u *f(v,v) *b31
x x x x x
2 2 4 6
+ u *f(v,v) *b28*u + u *f(v,v)*b20*u + u *b7*u + f(v ,v )*b13*u
x x x x 2x
3
+ f(v ,v )*f(v,v)*b25*u + f(v ,v )*b18*u + f(v,v )*b14*u
x x x x 3x
3 2
+ f(v,v )*f(v,v)*b26*u + f(v,v )*b19*u + f(v,v ) *b27*u
2x 2x x
2 3 5
+ f(v,v )*f(v,v) *b32*u + f(v,v )*f(v,v)*b29*u + f(v,v )*b21*u
x x x
4 3 3 2 5 7
+ f(v,v) *b34*u + f(v,v) *b33*u + f(v,v) *b30*u + f(v,v)*b22*u
9
+ b8*u
v = u *b36*u*v + u *u *b37*v + u *v *b38*u + u *f(v,v)*b55*u*v
t 3x 2x x 2x x 2x
3 2 2 2 2
+ u *b42*u *v + u *v *b39 + u *f(v,v)*b56*v + u *b43*u *v
2x x x x x
3
+ u *v *b40*u + u *v *f(v,v)*b57*u + u *v *b44*u + u *f(v,v )*b58*u*v
x 2x x x x x x x
2 3 5
+ u *f(v,v) *b72*u*v + u *f(v,v)*b63*u *v + u *b46*u *v + v *b35
x x x 4x
2 2
+ v *f(v,v)*b49 + v *b41*u + v *f(v,v )*b50 + v *f(v,v) *b67
3x 3x 2x x 2x
2 4
+ v *f(v,v)*b59*u + v *b45*u + v *f(v ,v )*b51 + v *f(v,v )*b52
2x 2x x x x x 2x
2 3
+ v *f(v,v )*f(v,v)*b68 + v *f(v,v )*b60*u + v *f(v,v) *b76
x x x x x
2 2 4 6
+ v *f(v,v) *b73*u + v *f(v,v)*b64*u + v *b47*u + f(v ,v )*b53*v
x x x x 2x
2
+ f(v ,v )*f(v,v)*b69*v + f(v ,v )*b61*u *v + f(v,v )*b54*v
x x x x 3x
2 2
+ f(v,v )*f(v,v)*b70*v + f(v,v )*b62*u *v + f(v,v ) *b71*v
2x 2x x
2 2 4
+ f(v,v )*f(v,v) *b77*v + f(v,v )*f(v,v)*b74*u *v + f(v,v )*b65*u *v
x x x
4 3 2 2 4 6
+ f(v,v) *b79*v + f(v,v) *b78*u *v + f(v,v) *b75*u *v + f(v,v)*b66*u *v
8
+ b48*u *v