Problem l1o35
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 |
Relevance |
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Unknowns
All solutions for the following 95 unknowns have to be determined:
a1, a2, ..., a20, a21, b1, b2, ..., b73, b74
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,a12},
{a8,a6,a7, a9,a11,a10},
{a13,15,a16,a15,a17,a21,a18},
{b1,b36},
{b1,b2,b3,b15,b5,b4,b6,b16,b21,b8,b7,
b22, b9,b17,b18,b23,b32,b26,b10,b12,
b13,b19,b29,b24,b14,b20,b30,b25,b31,
b33,b27,b35,b34,b28,b11},
{b37,b38,b42,b43,b39,b44,b61,b48,b45,
b49,b40,b46,b62,b50,b63,b68,b52,b36,
b41,b55,b47,b56,b64,b51,b57,b58,b65,
b72,b69,b53,b59,b66,b60,b67,b73,b70,
b74}
Equations
All comma separated 386 expressions involving 5000 terms have to vanish.
All terms are products of one a- and one b-unknown.
a5*b41,
a5*b47,
a5*b2,
a5*b5,
a5*b11,
a10*b41,
a11*b41,
3*a12*b41 - 5*a15*b36,
a15*b11 - 3*a5*b51,
a17*b11 - 2*a5*b53,
3*a1*b2 - 5*a2*b1,
a2*b11 - 3*a5*b8,
a4*b11 - 2*a5*b10,
3*a18*b11 - 5*a5*b54,
3*a12*b55 - 5*a19*b36,
a13*b14 - a7*b37,
a11*b64 - a15*b35,
a11*b74 - a21*b35,
3*a12*b47 - a15*b41 - 5*a17*b36,
3*a1*b5 - a2*b2 - 5*a4*b1,
a10*b47 + a18*b55,
a11*b47 + a21*b55,
2*a10*b11 - a10*b54 + a18*b28,
3*a12*b40 + 3*a12*b41 - 5*a14*b36 - 10*a15*b36,
3*a1*b2 + 3*a1*b3 - 10*a2*b1 - 10*a3*b1,
3*a1*b3 + 6*a1*b4 - 15*a2*b1 - 20*a3*b1,
9*a1*b8 + a2*b5 - 8*a4*b2 - 60*a5*b1,
5*a2*b11 + a3*b11 - a5* b9 - 2*a5*b8,
a12*b37 + a13*b1 - a13*b36 - a1*b37,
3*a12*b60 + a14*b14 - 5*a20*b36 - a7*b38,
a9*b37 - a13*b20 - a16*b14 + a7*b42,
a12*b14 - a1*b14 + a7*b1 - a7*b36,
4*a11*b37 - a13*b30 - a21*b14 + a7*b61,
a11*b69 - a17*b35 - a19*b74 + 2*a21*b72,
a10*b35 - a11*b34 + 2*a11*b74 - 3*a21*b35,
9*a12*b51 + a15*b47 - 7*a17*b41 - 15*a18*b36 - a4*b41,
3*a1*b6 - 4*a2*b2 + 2*a2*b4 - 6*a3*b2 - 20*a4*b1,
6*a1*b10 + 2*a2*b8 - 3*a4*b5 - 24*a5*b2 - 2*a5*b3,
3*a1*b6 + 6*a1*b7 - a2*b4 - 4*a3*b4 - 30*a4*b1,
90*a1*b11 + 8*a2*b10 - 4*a4*b8 - 36*a5*b5 - 5*a5*b6,
3*a12*b64 - 3*a15*b55 + a19*b41 - 5*a21*b36 - a8*b41,
6*a12*b55 + 3*a12*b56 - 20*a19*b36 - 5*a20*b36 - a6*b41,
6*a12*b55 + 3*a12*b56 - 20*a19*b36 - 5*a20*b36 - a7*b41,
3*a12*b56 + 3*a12*b58 - 20*a19*b36 - 10*a20*b36 - a7*b40,
3*a10*b51 - a15*b28 + 2*a18*b64 + a5*b64,
2*a11*b40 - 6*a12*b72 + 3*a19*b55 + a20*b55,
a10*b64 + 3*a11*b51 - a15*b34 + 2*a21*b64,
6*a12*b53 + 2*a15*b51 - 2*a17*b47 - 6*a18*b41 - a4*b47 - 2*a5*b40,
6*a1*b5 + 3*a1*b6 - 3*a2*b3 + a3*b2 - 30*a4*b1,
6*a1*b10 + a2* b9 - a3*b8 - 3*a4*b5 - 18*a5*b2 - 2*a5*b4,
a9*b41 - 6*a12*b64 - 4*a15*b55 + 8*a19*b41 + 10*a21*b36,
2*a10*b53 - a17*b28 + a18*b69 - a19*b54 + a5*b69,
a11*b2 - 4*a11*b37 + a13*b30 + a21*b14 - a7*b61,
4*a11*b62 + a11*b65 - 6*a14*b35 - 2*a19*b73 + 4*a20*b72,
4*a11*b61 + a11*b66 - 6*a13*b35 - a21*b29 + a6*b74,
4*a11*b61 + a11*b67 - 6*a13*b35 - a21*b30 + a7*b74,
a10*b74 + 3*a11*b71 - 3*a18*b35 - a21*b34 + 2*a21*b74,
3*a12*b37 + a12*b38 - 5*a13*b36 + a14*b1 - a14*b36 - a1*b38,
6*a1*b5 + 3*a1*b6 - 6*a2*b2 + 2*a2*b3 - 8*a3*b2 - 30*a4*b1,
7*a16*b11 + 5*a17*b54 + 3*a18*b10 - 3*a18*b53 - 5*a4*b54 - 7*a5*b52,
3*a12*b58 + 3*a12*b60 + a15*b14 - 10*a19*b36 - 10*a20*b36 - a7*b39,
3*a12*b59 + 2*a13*b12 + a13*b13 - 10*a20*b36 - 6*a6*b37 - 4*a7*b37,
3*a12*b60 + a13*b13 + 2*a13*b14 - 5*a20*b36 - 2*a6*b37 - 4*a7*b37,
a9*b42 + 2*a10*b37 - a13*b25 - a16*b20 - 3*a18*b14 + a7*b48,
5*a10*b54 - 3*a18*b28 + 2*a18*b71 - a21*b11 - 2*a21*b54 + 3*a5*b71,
a12*b13 - a1*b13 - 3*a1*b14 + 2*a6*b1 - 2*a6*b36 + 5*a7*b1,
8*a11*b39 - 24*a12*b72 - 6*a12*b73 - a15*b31 + 6*a19*b56 + 2*a20*b56,
8*a11*b61 + 4*a11*b63 - 24*a13*b35 + 2*a19*b73 - 4*a20*b72 - a21*b31,
a11*b21 - 4*a11*b61 + 6*a13*b35 + a21*b30 - a2*b35 - a7*b74,
a10*b74 - 2*a11*b28 + 2*a11*b71 - 3*a18*b35 - 2*a21*b34 + 2*a5*b35,
3*a12*b39 + 3*a12*b40 + a12*b41 - 5*a13*b36 - 10*a14*b36 - 10*a15*b36 - a1*b41,
3*a12*b46 + 6*a12*b47 + a14*b41 - 3*a15*b40 - 5*a16*b36 - 20*a17*b36 - a3*b41,
3*a12*b38 + 3*a12*b39 + a12*b40 - 10*a13*b36 - 10*a14*b36 - 5*a15*b36 - a1*b40,
15*a12*b54 + a15*b10 + 7*a15*b53 - a17*b51 - 9*a18*b47 - 3*a4*b51 - 5*a5*b46,
3*a1*b5 + 6*a1*b6 + 9*a1*b7 - 2*a2*b3 - 2*a2*b4 - 3*a3*b3 - 60*a4*b1,
6*a1* b9 + 9*a1*b8 - 3*a2*b5 + 2*a2*b6 - 6*a3*b5 - 20*a4*b2 - 120*a5*b1,
18*a1* b9 + 6*a1*b8 - 2*a2*b7 + a3*b6 - 12*a4*b3 - 4*a4*b4 - 240*a5*b1,
12*a1*b10 + a2* b9 + a3* b9 - a4*b6 - 2*a4*b7 - 12*a5*b2 - 12*a5*b3,
a9*b47 + a10*b40 - 3*a12*b69 - 2*a15*b64 + 3*a19*b47 + 4*a21*b41,
a9*b42 - a10*b2 + 2*a10*b37 - a13*b25 - a16*b20 - 3*a18*b14 + a7*b48,
2*a12*b12 - 2*a1*b12 - 3*a1*b13 - 3*a1*b14 + 10*a6*b1 + 11*a7*b1 - a7*b36,
a10*b69 + 2*a11*b53 - a17*b34 + 2*a18*b72 - a19*b71 + a21*b69,
3*a10*b71 + 5*a11*b54 - 3*a18*b34 + 4*a18*b74 - a21*b28 + a5*b74,
3*a12*b46 + 6*a12*b47 - 4*a14*b41 + 2*a15*b40 - 5*a15*b41 - 5*a16*b36 - 20*a17*
b36 - a2*b41,
3*a14*b11 + 5*a15*b54 + a17*b10 + a17*b53 - 3*a18*b51 - 2*a4*b53 - 3*a5*b50,
6*a1* b9 + 9*a1*b8 + a2*b5 + a3*b5 - 10*a4*b2 - 4*a4*b3 - 120*a5*b1,
60*a1*b11 + 6*a2*b10 + 2*a3*b10 - a4* b9 - a4*b8 - 12*a5*b5 - 6*a5*b6 - 4*a5*b7
,
3*a12*b62 + 3*a12*b64 - 2*a13*b55 - 3*a14*b55 - 3*a15*b55 + a19*b40 - 10*a21*
b36 - a8*b40,
a9*b48 + 2*a10*b42 - a13*b27 - a16*b25 - 3*a18*b20 + 2*a18*b60 + a7*b52,
5* a9*b54 + 2*a10*b52 - 2*a16*b28 - 3*a18*b27 + 2*a18*b70 - 2*a20*b54 + 2*a5*
b70,
a9*b48 + 2*a10*b42 - 2*a10*b5 - a13*b27 - a16*b25 - 2*a18*b15 - 3*a18*b20 + a7
*b52,
a12*b13 + a12*b14 - 6*a1*b12 - 4*a1*b13 - a1*b14 + 20*a6*b1 + 15*a7*b1,
4*a11*b38 - 3*a12*b73 - a14*b30 - 2*a19*b60 + 3*a20*b55 + a20*b58 + a7*b62,
24*a11*b37 - 6*a12*b73 - 2*a13*b29 - 2*a13*b31 + 2*a19*b59 + 2*a20*b59 + a6*b66
,
a9*b61 + 4*a11*b42 - a13*b33 - a16*b30 - a21*b20 + 2*a21*b60 + a7*b68,
a9*b61 + 4*a11*b42 - 2*a11*b5 - a13*b33 - a16*b30 - 2*a21*b15 - a21*b20 + a7*
b68,
a10*b28 - a10*b71 + 3*a11*b11 - 2*a11*b54 + 2*a18*b34 + a21*b28 - a5*b34,
a9*b74 + 4*a11*b68 + 2*a11*b70 - 6*a16*b35 - 2*a20*b74 - a21*b33 + 4*a21*b73,
3*a12*b37 + 3*a12*b38 + a12*b39 - 10*a13*b36 - 5*a14*b36 + a15*b1 - a15*b36 -
a1*b39,
a12*b42 + a13*b2 - a13*b41 + a15*b37 + a16*b1 - a16*b36 - a1*b42 - a2*b37,
a10*b40 - 3*a12*b69 + a16*b55 + 3*a17*b55 - a19*b47 + 2*a21*b41 + a8*b47,
6*a12*b55 + 9*a12*b56 + 6*a12*b57 + 3*a12*b58 - 60*a19*b36 - 30*a20*b36 - 2*a6*
b40 - a7*b40,
a9*b38 - 3*a12*b67 - a14*b20 - 2*a15*b60 - 2*a17*b14 + 4*a20*b41 + 10*a21*b36
+ a7*b44,
a13*b13 + 4*a13*b14 + a14*b14 - 6*a1*b15 - 2*a6*b37 - 2*a7*b37 - a7*b38 + 10*a8
*b1,
10*a10*b1 + a13*b18 + 5*a16*b14 - 3*a1*b21 + 3*a2*b15 - 2*a7*b42 - a7*b43 - 2*
a8*b37,
a9*b1 - a9*b36 + a12*b20 + a15*b14 - a1*b20 - a2*b14 + a7*b2 - a7*b41,
5* a9*b11 - 2* a9*b54 + 2*a10*b10 - 2*a10*b53 + 2*a17*b28 + 2*a18*b27 - 2*a4*
b28 - a5*b27,
a11*b68 - a16*b35 - a19*b74 - a20*b74 - a21*b32 + a21*b72 + a21*b73 + a8*b74,
a9*b74 - 2*a11*b26 + 4*a11*b68 - 6*a16*b35 - 4*a21*b32 - a21*b33 + 2*a4*b35 +
2*a8*b74,
a9*b35 - 4*a11*b32 - a11*b33 + 4*a11*b72 + 4*a11*b73 - 6*a19*b35 - 6*a20*b35 +
6*a8*b35,
24*a1* b9 + 18*a1*b8 + a2*b6 + 6*a2*b7 - 2*a3*b6 - 30*a4*b2 - 6*a4*b3 - 10*a4*
b4 - 360*a5*b1,
72*a1*b10 + 7*a2* b9 + 6*a2*b8 + 3*a3*b8 - 12*a4*b5 - 6*a4*b6 - 144*a5*b2 - 36*
a5*b3 - 24*a5*b4,
a12*b42 + 3*a12*b43 - a13*b38 + a13*b3 + 2*a13*b4 - 10*a16*b36 - a1*b42 - 4*a2*
b37 - 6*a3*b37,
6*a12*b52 + 2*a13* b9 + a14*b49 - a16*b45 + a16*b7 - 6*a18*b40 - a3*b49 - 2*a4*
b43 - 24*a5*b37,
a9*b40 - 6*a12*b62 - 12*a12*b64 - 3*a12*b65 + 2*a15*b56 + 6*a19*b40 + 40*a21*
b36 + 2*a8*b40,
a9*b40 - 6*a12*b64 - 3*a12*b65 - 2*a15*b56 + 12*a19*b41 + 4*a20*b41 + 20*a21*
b36 + 2*a7*b47,
3* a9*b51 + 2*a10*b46 - 6*a12*b71 - a15*b27 - 4*a15*b69 + 2*a18*b56 + 4*a19*b51
+ 6*a21*b47,
4* a9*b53 + 2*a10*b50 - 2*a14*b28 - 4*a15*b71 - 2*a17*b27 + 2*a18*b65 + 4*a21*
b51 + a5*b65,
3*a12*b59 + 3*a12*b60 + 2*a13*b12 + 2*a13*b13 + a13*b14 - 15*a20*b36 - 8*a6*b37
- 7*a7*b37,
a9*b52 + 2*a10*b48 - 2*a13*b28 - a16*b27 - 3*a18*b25 + 2*a18*b67 + a5*b67 + 5*
a7*b54,
5* a9*b54 - 4*a10*b10 + 2*a10*b52 - 2*a16*b28 - 2*a18*b26 - 3*a18*b27 + 2*a4*
b28 - 2*a5*b26 + 2*a8*b54,
a11*b46 - 3*a12*b74 - a15*b32 + a15*b72 - a19*b64 + 3*a21*b55 + a21*b56 + a8*
b64,
4*a11*b39 - 12*a12*b72 - 3*a12*b73 - a15*b29 + 6*a19*b55 + 3*a20*b55 + a20*b56
+ a6*b64,
4*a11*b39 - 12*a12*b72 - 3*a12*b73 - a15*b30 + 6*a19*b55 + 3*a20*b55 + a20*b56
+ a7*b64,
a9*b31 - 8*a11*b16 + 48*a1*b35 - 4*a19*b31 - 4*a20*b31 + 4*a6*b73 + 8*a7*b72 +
4*a7*b73,
3*a12*b50 + 9*a12*b51 + a14*b47 + a15*b47 - 2*a16*b41 - 3*a17*b40 - 6*a17*b41 -
30*a18*b36 - a3*b47 - a4*b40,
a9*b40 - 6*a12*b64 - 3*a12*b65 - 2*a15*b55 - 2*a15*b56 + 12*a19*b41 + 4*a20*
b41 + 20*a21*b36 + 2*a6*b47,
3*a12*b56 + 6*a12*b57 + 3*a12*b58 + 3*a12*b59 + a15*b12 - 30*a19*b36 - 30*a20*
b36 - 2*a6*b39 - a7*b39,
a9*b39 - 3*a12*b65 - 3*a12*b67 - a15*b20 - 2*a15*b58 + 8*a19*b41 + 6*a20*b41 +
20*a21*b36 + a7*b46,
3*a12*b58 + 3*a12*b59 + 6*a12*b60 + a14*b13 + a14*b14 - 10*a19*b36 - 25*a20*b36
- 2*a6*b38 - 3*a7*b38,
a9*b44 + 2*a10*b38 - 3*a12*b70 - a14*b25 - 2*a15*b67 - 2*a17*b20 + 3*a20*b47 +
8*a21*b41 + a7*b50,
5* a9*b1 + 3*a13*b13 + a14*b13 - 6*a1*b15 - 3*a1*b16 + a6*b2 - 2*a6*b37 - 2*a6*
b38 + 20*a8*b1,
a9*b52 + 2*a10*b48 - 3*a10*b8 - 2*a13*b28 - a16*b27 - 2*a18*b21 - 3*a18*b25 +
a2*b28 - a5*b21 + 5*a7*b54,
10* a9*b1 + a12*b20 + a15*b13 - 3*a1*b19 - a1*b20 - 2*a2*b12 - a2*b13 + 6*a6*b2
+ 4*a7*b2,
24*a11*b37 - 6*a12*b73 - 2*a13*b30 - 2*a13*b31 + 6*a19*b60 - a20*b56 + a20*b59
+ 3*a20*b60 + a7*b67,
3*a12*b44 + 6*a12*b45 + 9*a12*b46 + 6*a12*b47 - 2*a14*b40 - 2*a15*b39 - 3*a15*
b40 - 30*a16*b36 - 60*a17*b36 - a2*b40 - 2*a3*b40,
3*a12*b50 + 9*a12*b51 - 3*a14*b47 + 2*a15*b46 - a15*b47 - 4*a16*b41 + a17*b40 -
12*a17*b41 - 30*a18*b36 - 2*a2*b47 - a4*b40,
3*a12*b42 + 4*a12*b43 + a13*b2 + 2*a13*b3 - a13*b39 + 2*a13*b4 - 15*a16*b36 -
a1*b43 - 7*a2*b37 - 8*a3*b37,
6*a13*b11 + 5*a15*b54 + a16*b10 - a16*b53 + a17*b52 - 3*a18*b51 + 3*a18*b8 - 5*
a2*b54 - a4*b52 - 6*a5*b48,
a12*b61 + a13*b15 - a13*b55 - a13*b60 - a1*b61 + a19*b37 + a20*b37 + a21*b1 -
a21*b36 - a8*b37,
4* a9*b37 - 3*a12*b67 - a13*b18 - 2*a13*b20 + 3*a15*b60 - a16*b14 - a20*b41 +
10*a21*b36 + a7*b43 + 2*a8*b37,
a9*b10 - a9*b53 + 2*a10*b8 + a17*b27 + 2*a18*b24 - 2*a2*b28 - a4*b27 - 2*a5*
b24 + 6*a6*b11 - 2*a6*b54,
a9*b64 + 4*a11*b46 - 12*a12*b74 - a15*b33 - 8*a15*b72 + 4*a19*b64 + 2*a20*b64
+ 6*a21*b55 + 4*a21*b56,
12*a11*b37 - 3*a12*b73 - 2*a13*b29 - a13*b30 + 3*a20*b55 - a20*b59 + 3*a20*b60
- a21*b12 + 2*a6*b61 + a7*b61,
16*a11*b37 - 3*a12*b73 - 2*a13*b29 - 2*a13*b30 + 3*a20*b55 - a20*b59 + 3*a20*
b60 - a21*b13 + 2*a6*b61 + 2*a7*b61,
32*a11*b37 - 6*a12*b73 - 4*a13*b30 - 2*a13*b31 + 8*a19*b60 - 2*a20*b55 - a20*
b58 + a20*b59 + 3*a20*b60 + a7*b63,
4*a11*b1 - 4*a11*b36 + a12*b30 - a1*b30 + a19*b14 + a20*b14 + a7*b15 - a7*b55 -
a7*b60 - a8*b14,
3*a12*b43 + 3*a12*b44 + 6*a12*b45 + 3*a12*b46 - 2*a14*b39 - a15*b39 + a15*b4 -
30*a16*b36 - 30*a17*b36 - a2*b39 - 2*a3*b39,
3*a12*b49 + 6*a12*b50 + 6*a12*b51 + a14*b46 - a15*b45 + a15*b7 - 3*a16*b40 - 6*
a17*b40 - 60*a18*b36 - a3*b46 - 2*a4*b39,
3*a12*b56 + 6*a12*b57 + 6*a12*b58 + 3*a12*b59 + 3*a12*b60 + a15*b13 - 40*a19*
b36 - 40*a20*b36 - 2*a6*b39 - 2*a7*b39,
a9*b46 + 2*a10*b39 - 6*a12*b69 - 3*a12*b70 - a15*b25 - 2*a15*b65 + 6*a19*b47 +
3*a20*b47 + 12*a21*b41 + 3*a7*b51,
3*a12*b61 + a12*b62 - 3*a13*b55 - a13*b58 + a14*b15 - a14*b55 - a1*b62 + 2*a19*
b37 + a19*b38 - 5*a21*b36 - a8*b38,
6*a12*b57 + 3*a12*b58 + 9*a12*b59 + 3*a12*b60 + 2*a14*b12 + a14*b13 - 20*a19*
b36 - 50*a20*b36 - 6*a6*b38 - 4*a7*b38,
a9*b50 + 2*a10*b44 - 6*a12*b71 - a14*b27 - 2*a15*b70 - 2*a17*b25 + 2*a18*b58 +
2*a20*b51 + 6*a21*b47 + 4*a7*b53,
5* a9*b37 - 3*a12*b67 - a13*b19 - 2*a13*b20 - 2*a15*b60 - a16*b13 - a16*b14 + 4
*a20*b41 + 10*a21*b36 + 2*a6*b42 + 3*a7*b42,
a9*b52 + 2*a10*b48 - 2*a13*b28 - 2*a15*b71 - a16*b27 - 3*a18*b24 + 2*a18*b66 +
2*a21*b51 + a5*b66 + 5*a6*b54,
20*a10*b1 + 2*a13*b15 + a13*b16 + 10*a16*b14 - 3*a1*b21 - 6*a1*b22 + 3*a2*b15 +
6*a3*b15 - a7*b42 - 3*a7*b43,
6* a9*b1 - a9*b36 + a12*b19 + a15*b13 - a1*b19 - 3*a1*b20 - a2*b13 - 2*a2*b14
+ 2*a6*b2 - 2*a6*b41 + 4*a7*b2,
a11*b44 - 3*a12*b74 + 4*a13*b72 - a14*b32 + a14*b72 - 2*a19*b61 - a19*b62 + 3*
a21*b55 + a21*b58 + a8*b62,
24*a11*b38 - 24*a12*b72 - 18*a12*b73 - 2*a14*b30 - 2*a14*b31 + 6*a19*b58 + 2*
a20*b56 + 2*a20*b57 + 4*a20*b58 + a7*b65,
a9*b68 + 2*a10*b61 + a10*b67 + 4*a11*b48 - 4*a13*b34 - a16*b33 - 3*a18*b30 -
a21*b25 + 2*a21*b67 + 3*a7*b71,
3* a9*b71 + 2*a10*b68 + 2*a10*b70 + 4*a11*b52 - 4*a16*b34 - 3*a18*b33 + 4*a18*
b73 - 2*a20*b71 - a21*b27 + 2*a21*b70,
6*a10*b15 - 4*a11*b43 + a11*b6 + 4*a13*b32 + 3*a16*b30 - 6*a1*b34 + a21*b16 +
a21*b18 - 3*a7*b68 - 2*a8*b61,
3*a12*b44 + 3*a12*b46 + 2*a12*b47 - 4*a13*b41 - 6*a14*b41 + 2*a15*b39 + a15*b40
- 4*a15*b41 - 10*a16*b36 - 20*a17*b36 - 2*a1*b47 - a2*b40,
3*a12*b42 + a12*b43 + 2*a13*b2 + a13*b3 - a13*b40 + a14*b37 + a16*b1 - 6*a16*
b36 - a1*b43 - 4*a2*b37 - 2*a3*b37,
3*a12*b61 + 3*a12*b62 + a12*b64 - 3*a13*b55 - a13*b56 - 3*a14*b55 + a15*b15 -
a15*b55 - a1*b64 + a19*b39 - 10*a21*b36 - a8*b39,
a9*b46 + 2*a10*b39 - 6*a12*b69 - 3*a12*b70 - a15*b24 - 2*a15*b64 - 2*a15*b65 +
6*a19*b47 + 3*a20*b47 + 12*a21*b41 + 3*a6*b51,
3* a9*b38 - 3*a12*b63 - 3*a12*b65 - 6*a12*b67 - a14*b18 - a14*b20 + 2*a15*b58 +
3*a20*b40 + 40*a21*b36 + 2*a7*b45 + 2*a8*b38,
10* a9*b37 - 6*a12*b66 - 3*a12*b67 - 3*a13*b19 - a13*b20 - 2*a15*b59 - 2*a16*
b12 - a16*b13 + 10*a20*b41 + 20*a21*b36 + 6*a6*b42 + 4*a7*b42,
12*a11*b38 - 12*a12*b72 - 9*a12*b73 - 2*a14*b29 - a14*b30 + 6*a19*b55 - 2*a19*
b59 + 9*a20*b55 + 3*a20*b58 + 2*a6*b62 + a7*b62,
2* a9*b70 + 2*a10*b63 + 8*a11*b48 - 8*a13*b34 - 8*a15*b74 - 2*a16*b33 - 3*a18*
b31 + 2*a19*b70 - 2*a20*b69 + 4*a21*b66 + 4*a21*b67,
a9*b68 - a10*b21 + 2*a10*b61 + 4*a11*b48 - 3*a11*b8 - 4*a13*b34 - a16*b33 - 3*
a18*b30 - 2*a21*b21 - a21*b25 + a2*b34 + 3*a7*b71,
3* a9*b71 - 2*a10*b26 + 2*a10*b68 - 4*a11*b10 + 4*a11*b52 - 4*a16*b34 - 4*a18*
b32 - 3*a18*b33 - 2*a21*b26 - a21*b27 + 2*a4*b34 + 2*a8*b71,
3*a12*b42 + a12*b44 - 4*a13*b41 + a14*b2 - a14*b41 + 2*a15*b37 + a15*b38 - 5*
a16*b36 + 2*a17*b1 - 2*a17*b36 - a1*b44 - a2*b38,
a12*b48 - a13*b47 + a13*b5 + a15*b42 + a16*b2 - a16*b41 + a17*b37 + 3*a18*b1 -
3*a18*b36 - a1*b48 - a2*b42 - a4*b37,
6*a12*b48 + 12*a12*b49 + 3*a13*b6 + 6*a13*b7 + a14*b43 - 3*a16*b39 - 3*a16*b40
+ a16*b4 - 90*a18*b36 - 2*a2*b43 - 4*a3*b43 - 30*a4*b37,
3* a9*b42 + 6*a10*b37 - 3*a12*b70 - 2*a13*b24 - a13*b25 - 2*a15*b66 - a16*b19 -
3*a18*b12 + 3*a20*b47 + 6*a21*b41 + 2*a6*b48 + a7*b48,
a9*b43 - 6*a10*b2 - 2*a10*b4 - 2*a13*b21 - a16*b16 - 3*a16*b20 - 18*a18*b14 +
6*a1*b26 + 2*a2*b22 - 2*a3*b21 - 6*a4*b15 + 2*a7*b48 + 2*a7*b49,
5* a9*b1 + a12*b18 + a14*b14 + 4*a15*b14 - a1*b18 - 3*a1*b20 - 2*a3*b14 + a7*b3
- a7*b40 - 2*a7*b41 + 2*a8*b1 - 2*a8*b36,
15* a9*b1 + a12*b19 + 2*a15*b12 + a15*b14 - 4*a1*b19 - 3*a1*b20 - 2*a2*b12 - 2*
a2*b13 - a2*b14 + 8*a6*b2 + 7*a7*b2 - a7*b41,
a9*b2 - a9*b41 + 2*a10*b1 - 2*a10*b36 + a12*b25 + a15*b20 + a17*b14 - a1*b25
- a2*b20 - a4*b14 - a7*b47 + a7*b5,
a9*b10 - a9*b53 - 2*a10*b51 + 2*a10*b8 + 2*a15*b28 + a17*b27 + 2*a18*b25 - 2*
a2*b28 - a4*b27 - 2*a5*b25 + 6*a7*b11 - 2*a7*b54,
2* a9*b69 + 2*a10*b62 + a10*b65 + 4*a11*b50 - 4*a14*b34 - 8*a15*b74 - 2*a17*b33
- 2*a19*b70 + 2*a20*b69 + 4*a21*b64 + 4*a21*b65,
a9*b17 - a9*b57 + 24*a11*b2 - 6*a1*b33 + 2*a19*b19 + 2*a20*b19 + 6*a21*b13 -
2*a2*b29 - 2*a2*b31 + 2*a6*b24 - 2*a6*b65 - 2*a6*b66,
4*a11*b15 + a11*b20 - 4*a11*b55 - 4*a11*b60 + 6*a12*b35 - 6*a1*b35 + a19*b30 +
a20*b30 + a7*b32 - a7*b72 - a7*b73 - a8*b30,
3*a12*b42 + 3*a12*b44 + a12*b46 - 6*a13*b41 - 4*a14*b41 + a15*b2 + 2*a15*b38 +
a15*b39 - a15*b41 - 10*a16*b36 - 10*a17*b36 - a1*b46 - a2*b39,
3*a12*b52 + 12*a12*b53 - 2*a14*b51 + 2*a15*b50 + 2*a15*b51 + a15*b8 - 3*a16*b47
+ a17*b46 - 6*a17*b47 - 18*a18*b41 - 3*a2*b51 - a4*b46 - 4*a5*b39,
15*a12*b54 + a14*b10 - a14*b53 + 2*a15*b52 + 4*a15*b53 - 2*a16*b51 + a17*b50 -
2*a17*b51 + 2*a17*b8 - 9*a18*b47 - 4*a2*b53 - a4*b50 - 5*a5*b44,
a12*b52 - a13*b51 + a13*b8 + a15*b48 - a16*b47 + a16*b5 + a17*b42 + 3*a18*b2 -
3*a18*b41 - a1*b52 - a2*b48 - a4*b42 - 4*a5*b37,
5*a12*b54 + a13*b10 - a13*b53 + a15*b52 - a16*b51 + a16*b8 + a17*b48 - 3*a18*
b47 + 3*a18*b5 - 5*a1*b54 - a2*b52 - a4*b48 - 5*a5*b42,
30*a13*b11 + 5*a14*b54 + 20*a15*b54 + 5*a16*b10 - a16*b53 + 3*a17*b52 + 3*a18*
b9 - 3*a18*b50 - 6*a18*b51 - 5*a3*b54 - 5*a4*b52 - 12*a5*b48 - 9*a5*b49,
3* a9*b38 - 3*a12*b65 - 6*a12*b66 - 3*a12*b67 - a14*b19 - 2*a15*b57 - 2*a15*b59
- 2*a17*b12 + 6*a19*b41 + 12*a20*b41 + 30*a21*b36 + 2*a6*b44 + a7*b44,
a9*b50 + 2*a10*b44 - 6*a12*b71 - a14*b27 - 2*a15*b69 - 2*a15*b70 - 2*a17*b24 +
2*a18*b57 + 2*a19*b51 + 2*a20*b51 + 6*a21*b47 + 4*a6*b53,
4* a9*b42 + 8*a10*b37 - 3*a12*b70 - 2*a13*b24 - 2*a13*b25 - 2*a15*b67 - a16*b19
- a16*b20 - 3*a18*b13 + 3*a20*b47 + 8*a21*b41 + 2*a6*b48 + 2*a7*b48,
5* a9*b1 + 2*a13*b12 + 6*a13*b14 + 4*a14*b14 + a15*b14 - 6*a1*b15 - 3*a1*b16 +
a7*b2 - 2*a7*b37 - 2*a7*b38 - a7*b39 + 20*a8*b1,
a9*b62 + 4*a11*b44 - 12*a12*b74 - a14*b33 - 2*a15*b73 - 2*a17*b30 - 2*a19*b67
+ 2*a20*b64 + a20*b65 + 6*a21*b55 + 4*a21*b58 + 2*a7*b69,
a9*b65 + 8*a11*b44 - 24*a12*b74 - 2*a14*b33 - 8*a15*b72 - 4*a15*b73 - 2*a17*
b31 + 2*a19*b65 + 2*a20*b65 + 4*a21*b56 + 4*a21*b57 + 4*a21*b58,
a11*b42 - a12*b74 - a13*b32 + a13*b72 + a13*b73 + a1*b74 - a19*b61 - a20*b61 -
a21*b15 + a21*b55 + a21*b60 + a8*b61,
48*a11*b37 - 12*a12*b73 - 2*a13*b29 - 2*a13*b30 - 4*a13*b31 + 2*a19*b59 + 6*a19
*b60 - a20*b56 + 3*a20*b59 + 3*a20*b60 + a6*b67 + a7*b66,
a9*b68 + 2*a10*b61 + a10*b66 + 4*a11*b48 - 4*a13*b34 - 4*a15*b74 - a16*b33 - 3
*a18*b29 - a21*b24 + 2*a21*b64 + 2*a21*b67 + 3*a6*b71,
9*a12*b52 + 36*a12*b53 + 3*a14*b51 + a15* b9 + 3*a15*b50 + 6*a15*b51 - 3*a16*
b47 - 3*a17*b46 - 6*a17*b47 - 9*a18*b40 - 36*a18*b41 - 3*a3*b51 - 3*a4*b46 - 12
*a5*b39,
3*a12*b42 + 9*a12*b43 + 4*a12*b44 + 6*a12*b45 - 2*a13*b39 - a14*b38 + a14*b3 -
a14*b39 + 2*a14*b4 - 50*a16*b36 - 20*a17*b36 - a1*b44 - 4*a2*b38 - 6*a3*b38,
30*a12*b54 + 2*a14*b10 + 2*a14*b53 + 3*a15*b52 + 6*a15*b53 - a16*b51 + a17* b9
- a17*b51 - 3*a18*b46 - 9*a18*b47 - 2*a3*b53 - 2*a4*b50 - 6*a5*b44 - 4*a5*b45,
a9*b39 - 6*a12*b61 - 12*a12*b62 - 3*a12*b63 - 6*a12*b64 - 3*a12*b65 + 2*a13*
b56 + 3*a14*b56 - a15*b16 + a15*b56 + 4*a19*b39 + 60*a21*b36 + 4*a8*b39,
2* a9*b39 - 6*a12*b62 - 3*a12*b63 - 6*a12*b64 - 6*a12*b65 - 3*a12*b66 - a15*b17
+ a15*b57 + 6*a19*b40 + 3*a20*b40 + 60*a21*b36 + a6*b46 + 2*a8*b39,
3*a10*b46 - 9*a12*b71 - a15*b26 - 3*a15*b69 + 2*a16*b64 + 3*a17*b64 + 9*a18*b55
+ 3*a18*b56 - 3*a19*b51 + 3*a21*b47 + a4*b64 + 3*a8*b51,
3* a9*b39 - 6*a12*b64 - 9*a12*b65 - 6*a12*b66 - 3*a12*b67 - a15*b19 - 2*a15*b56
- 4*a15*b57 - 2*a15*b58 + 24*a19*b41 + 18*a20*b41 + 60*a21*b36 + 2*a6*b46 + a7
*b46,
6* a9*b37 - 3*a12*b63 - 3*a12*b67 - a13*b16 - 2*a13*b18 - a13*b20 + 2*a13*b60 +
3*a14*b60 + 3*a15*b60 - a20*b40 + 20*a21*b36 + a7*b43 + 8*a8*b37,
3* a9*b48 + 6*a10*b42 - 6*a12*b71 - 3*a13*b27 - 2*a15*b70 - 2*a16*b24 - a16*b25
- 3*a18*b19 + 2*a18*b59 + 2*a20*b51 + 6*a21*b47 + 2*a6*b52 + a7*b52,
a9*b42 + a9*b43 - 8*a10*b2 - 2*a10*b3 - a13*b23 - 2*a16*b15 - a16*b18 - 4*a16
*b20 - 24*a18*b14 + 6*a1*b26 - 6*a4*b15 + 4*a7*b48 + 2*a7*b49 + 2*a8*b42,
30* a9*b1 + 2*a13*b12 + 4*a14*b12 + 2*a15*b12 - 3*a1*b16 - 6*a1*b17 - 3*a1*b18
- 3*a1*b19 - a2*b12 + 4*a6*b4 - a7*b39 + 2*a7*b4 + 30*a8*b1,
3* a9*b5 + 6*a10*b2 + a15*b25 + a17*b19 + 2*a18*b12 - 3*a1*b27 - 2*a2*b24 - a2*
b25 - a4*b19 - 4*a5*b12 + 2*a6*b8 - a7*b51 + a7*b8,
24*a11*b38 - 24*a12*b72 - 18*a12*b73 - 2*a14*b29 - 2*a14*b31 + 2*a19*b56 + 4*
a19*b57 + 2*a19*b58 + 2*a20*b56 + 4*a20*b57 + 2*a20*b58 + a6*b65,
a9*b63 + 8*a11*b43 - 24*a12*b74 - 8*a13*b32 - 4*a13*b33 - a16*b31 + 2*a19*b63
- 2*a20*b62 - a20*b65 + 4*a21*b56 + 4*a21*b59 + 12*a21*b60 + 2*a8*b63,
a9*b68 - 2*a10*b21 - 2*a10*b22 - 2*a11* b9 + 4*a11*b49 - 4*a16*b32 - a16*b33 -
6*a18*b30 - 2*a21*b22 - a21*b23 + 2*a2*b34 + 2*a3*b34 + 6*a7*b71 + 2*a8*b68,
6*a12*b42 + 3*a12*b43 + 3*a12*b44 + 2*a12*b45 - 3*a13*b40 + a14*b2 + a14*b38 +
a14*b3 - a14*b40 - 25*a16*b36 - 10*a17*b36 - 2*a1*b45 - 3*a2*b38 - 2*a3*b38,
2*a10*b39 - 3*a12*b68 - 6*a12*b69 - a14*b64 - a15*b22 + a15*b62 + 3*a16*b55 +
a16*b56 + 6*a17*b55 - a19*b46 + 3*a21*b40 + a3*b64 + a8*b46,
4* a9*b38 - 3*a12*b65 - 6*a12*b66 - 6*a12*b67 - a14*b19 - a14*b20 - 2*a15*b58 -
2*a15*b59 - 2*a15*b60 - 2*a17*b13 + 8*a19*b41 + 16*a20*b41 + 40*a21*b36 + 2*a6
*b44 + 2*a7*b44,
12* a9*b37 - 3*a12*b63 - 6*a12*b66 - 3*a12*b67 - 2*a13*b17 - a13*b18 - 2*a13*
b19 + a15*b59 - a16*b12 + 3*a20*b40 + 30*a21*b36 + 2*a6*b43 + a7*b43 + 6*a8*b37
,
6*a10*b3 + 4*a10*b4 + 2*a13*b22 + a16*b16 + 3*a16*b18 + 36*a18*b14 - 12*a1*b26
+ a2*b22 - a3*b21 + 12*a4*b15 - 2*a7*b48 - 5*a7*b49 - 2*a8*b43,
10* a9*b1 + a12*b16 + 2*a13*b14 + 4*a14*b14 + 6*a15*b14 - a1*b16 - 3*a1*b18 - 3
*a1*b20 - a2*b14 - a7*b39 - 2*a7*b40 - a7*b41 + 2*a7*b4 + 10*a8*b1,
a9*b49 - 2*a10*b6 - 4*a10*b7 - 2*a16*b22 - a16*b23 - 6*a18*b18 - 6*a18*b20 +
24*a1*b28 + 2*a2*b26 + 2*a3*b26 - 2*a4*b21 - 2*a4*b22 - 24*a5*b15 + 6*a7*b52 +
2*a8*b49,
3* a9*b52 - 4*a10* b9 + 2*a10*b49 - 2*a10*b8 - 2*a16*b26 - a16*b27 - 2*a18*b22
- 3*a18*b23 - 6*a18*b25 + 12*a2*b28 + 4*a3*b28 - 12*a5*b21 - 4*a5*b22 + 20*a7*
b54 + 2*a8*b52,
a9*b47 - a9*b5 - 2*a10*b2 + 2*a10*b41 - a12*b27 - a15*b25 - a17*b20 - 2*a18*
b14 + a1*b27 + a2*b25 + a4*b20 + 4*a5*b14 + a7*b51 - a7*b8,
a9*b51 - a9*b8 + 2*a10*b47 - 2*a10*b5 - 2*a12*b28 - a15*b27 - a17*b25 - 2*a18
*b20 + 2*a1*b28 + a2*b27 + a4*b25 + 3*a5*b20 - a7*b10 + a7*b53,
2*a10*b62 + 2*a11*b50 - 2*a14*b34 - 2*a15*b74 + 4*a16*b72 - 2*a17*b32 + 2*a17*
b72 - 2*a19*b68 - 2*a19*b69 + 2*a21*b62 + 2*a21*b64 + a21*b65 + 2*a8*b69,
40*a11*b1 + a12*b30 - 6*a1*b29 - 4*a1*b30 + 2*a19*b12 + a19*b13 + 10*a20*b14 +
6*a6*b15 + 4*a7*b15 - a7*b55 - 3*a7*b59 - a7*b60 - 2*a8*b12 - a8*b13,
20*a11*b1 + 2*a12*b29 - 2*a1*b29 - 3*a1*b30 + a19*b13 + a19*b14 + 5*a20*b14 + 2
*a6*b15 - 2*a6*b55 + 3*a7*b15 - a7*b59 - 2*a7*b60 - a8*b13 - a8*b14,
12*a11*b15 + a11*b19 - 4*a11*b59 - 18*a1*b35 + 2*a19*b29 + a19*b30 + 3*a20*b30
+ 2*a6*b32 - 2*a6*b72 + a7*b32 - a7*b72 - 3*a7*b73 - 2*a8*b29 - a8*b30,
3*a12*b48 + a12*b50 - 3*a13*b47 - a14*b47 + a14*b5 + 2*a15*b42 + a15*b44 - 4*
a16*b41 + 2*a17*b2 + a17*b38 - 2*a17*b41 - 15*a18*b36 - a1*b50 - a2*b44 - a4*
b38,
2* a9*b39 - 6*a12*b62 - 3*a12*b63 - 6*a12*b64 - 6*a12*b65 - 3*a12*b67 - a15*b18
+ a15*b56 + a15*b58 + 6*a19*b40 + 3*a20*b40 + 60*a21*b36 + a7*b46 + 2*a8*b39,
3* a9*b44 + 6*a10*b38 - 6*a12*b69 - 9*a12*b70 - 2*a14*b24 - a14*b25 - 2*a15*b65
- 4*a15*b66 - 2*a15*b67 - 2*a17*b19 + 6*a19*b47 + 9*a20*b47 + 24*a21*b41 + 2*
a6*b50 + a7*b50,
a9*b37 - 6*a12*b61 - a12*b63 - 4*a13*b15 - a13*b16 + a13*b56 + a13*b59 + 3*a13
*b60 + a14*b60 + a1*b63 - 2*a20*b37 - a20*b38 + 10*a21*b36 + 8*a8*b37,
4* a9*b37 - 6*a12*b61 - 3*a12*b63 - a12*b66 - 2*a13*b15 - 2*a13*b16 - a13*b17 +
a13*b57 + 2*a13*b59 + a14*b59 + a1*b66 + 20*a21*b36 + a6*b42 + 12*a8*b37,
6*a10*b37 - 3*a12*b68 - a13*b21 - 2*a13*b22 + 2*a13*b61 + 3*a16*b55 + 3*a16*b60
- a19*b43 - a20*b43 + a21*b39 - a21*b4 + a2*b61 + 2*a3*b61 + a8*b43,
16* a9*b37 - 3*a12*b63 - 6*a12*b66 - 6*a12*b67 - 2*a13*b17 - 2*a13*b18 - 2*a13*
b19 - 2*a13*b20 + 2*a15*b59 - a16*b13 + 3*a20*b40 + 40*a21*b36 + 2*a6*b43 + 2*
a7*b43 + 8*a8*b37,
3* a9*b42 + a9*b43 + 16*a10*b37 - 6*a12*b70 - a13*b23 - 4*a13*b25 - a16*b18 -
2*a16*b20 + 2*a16*b60 + 6*a17*b60 - 2*a20*b47 + 8*a21*b41 + 2*a7*b49 + 2*a8*b42
,
10* a9*b1 + 2*a12*b15 + a13*b13 + 4*a13*b14 + 6*a14*b14 + 4*a15*b14 - 2*a1*b15
- 3*a1*b16 - 3*a1*b18 - a7*b38 + a7*b3 - 2*a7*b39 - a7*b40 + 20*a8*b1,
2*a10*b61 + a11*b49 - 2*a13*b34 - a14*b74 - a16*b32 + a16*b72 + a16*b73 - a19*
b68 - a20*b68 - a21*b22 + a21*b62 + a21*b63 + a3*b74 + a8*b68,
96*a11*b37 - 24*a12*b73 - 8*a13*b29 - 4*a13*b30 - 6*a13*b31 + 6*a19*b59 + 6*a19
*b60 + 2*a20*b56 - 2*a20*b57 - a20*b58 + 3*a20*b59 + 9*a20*b60 + 2*a6*b63 + a7*
b63,
4*a11*b38 - 4*a11*b3 - 2*a13*b29 - 2*a13*b30 - 2*a13*b31 - a14*b30 + 12*a1*b32
- 2*a19*b15 - 2*a20*b15 - a21*b13 - 12*a21*b14 + 2*a6*b61 + 6*a7*b61 + a7*b62 +
a7*b63 - 4*a8*b15,
a9*b14 - 40*a11*b1 - 2*a12*b31 + 6*a1*b30 + 2*a1*b31 - 10*a19*b14 - a20*b13 -
6*a20*b14 + 2*a6*b60 - a7*b16 + 4*a7*b55 + a7*b56 + a7*b58 + 2*a7*b60,
80*a11*b1 + 2*a12*b30 - 8*a1*b30 - 6*a1*b31 + 20*a19*b14 + 2*a20*b12 + a20*b13
+ 10*a20*b14 + a7*b18 + a7*b20 - 2*a7*b55 - 3*a7*b56 - 3*a7*b58 - 2*a7*b60,
3*a12*b42 + 3*a12*b43 + 6*a12*b44 + 6*a12*b45 + 4*a12*b46 - 3*a13*b40 + a14*b39
- 3*a14*b40 - a15*b38 + a15*b3 - a15*b40 - 40*a16*b36 - 40*a17*b36 - a1*b46 -
2*a2*b39 - 2*a3*b39,
3*a12*b48 + 3*a12*b50 + 3*a12*b51 - 3*a13*b47 - 3*a14*b47 + 2*a15*b44 + a15*b46
- a15*b47 + a15*b5 - 6*a16*b41 + a17*b39 - 8*a17*b41 - 30*a18*b36 - 3*a1*b51 -
a2*b46 - a4*b39,
3*a12*b52 + 4*a12*b53 - 2*a13*b51 - a14*b51 + a14*b8 + 2*a15*b48 + a15*b50 - 3*
a16*b47 + a17*b44 - 2*a17*b47 + 2*a17*b5 - 12*a18*b41 - 4*a1*b53 - a2*b50 - a4*
b44 - 4*a5*b38,
6*a12*b48 + 15*a12*b49 + 12*a12*b50 + a14*b44 + a14*b45 + a14*b6 + 3*a14*b7 - 2
*a16*b39 - 9*a16*b40 - 2*a17*b39 - 6*a17*b40 - 180*a18*b36 - 2*a2*b45 - a3*b44
- 4*a3*b45 - 12*a4*b38,
9*a12*b52 + 12*a12*b53 + a14* b9 + a14*b50 + a15*b49 + a15*b50 - a16*b46 - a17*
b45 - a17*b46 + a17*b7 - 9*a18*b40 - 12*a18*b41 - a3*b50 - a4*b44 - 2*a4*b45 -
12*a5*b38,
60*a12*b54 + 12*a13*b10 + 3*a14*b52 + 6*a15*b52 + 3*a16* b9 - a16*b50 + a17*b49
- 3*a18*b45 - 6*a18*b46 - 6*a18*b47 + 3*a18*b7 - 3*a3*b52 - 2*a4*b48 - 5*a4*
b49 - 24*a5*b42 - 12*a5*b43,
2*a10*b39 - 3*a12*b68 - 6*a12*b69 + 2*a13*b64 + 2*a14*b64 - a15*b21 - 2*a15*b62
+ 3*a16*b55 + a16*b56 + 6*a17*b55 - a19*b46 + 6*a21*b41 + a2*b64 + a8*b46,
2* a9*b46 + 8*a10*b39 - 6*a12*b68 - 24*a12*b69 - 6*a12*b70 - a15*b23 - 4*a15*
b62 - 4*a15*b64 - a15*b65 + 2*a16*b56 + 6*a17*b56 + 4*a19*b46 + 6*a21*b40 + 24*
a21*b41 + 2*a8*b46,
3* a9*b38 - 6*a12*b61 - 6*a12*b62 - 6*a12*b63 - 3*a12*b65 - 3*a12*b66 + 2*a13*
b57 - a14*b16 - a14*b17 + 3*a14*b57 + 2*a19*b39 + 2*a20*b39 + 60*a21*b36 + a6*
b44 + 6*a8*b38,
3* a9*b38 - 6*a12*b61 - 6*a12*b62 - 6*a12*b63 - 3*a12*b65 - 3*a12*b67 + 2*a13*
b58 - a14*b16 - a14*b18 + 3*a14*b58 + a15*b58 + 2*a20*b39 + 60*a21*b36 + a7*b44
+ 6*a8*b38,
4*a10*b50 - 4*a14*b28 - 6*a15*b71 + 2*a16*b69 - 2*a17*b26 + 2*a18*b62 + 6*a18*
b64 + 3*a18*b65 - 2*a19*b52 - 4*a19*b53 + 2*a21*b51 + 2*a4*b69 + 4*a5*b62 + 4*
a8*b53,
a9*b62 + 8*a11*b45 - 24*a12*b74 - 4*a14*b32 - a14*b33 - 2*a19*b63 - a19*b65 +
2*a20*b62 + 12*a21*b55 + 2*a21*b56 + 2*a21*b57 + 6*a21*b58 + 2*a8*b62 + a8*b65,
3* a9*b61 + 12*a11*b42 - 12*a12*b74 - 3*a13*b33 - 2*a15*b73 - 2*a16*b29 - a16*
b30 + 2*a20*b64 - 2*a20*b66 + 2*a20*b67 - a21*b19 + 6*a21*b55 + 6*a21*b60 + 2*
a6*b68 + a7*b68,
2* a9*b72 + 2* a9*b73 + a10*b31 - 4*a11*b21 - 2*a11*b23 + 2*a11*b65 - 2*a19*b33
- 2*a20*b33 - 2*a21*b29 - 2*a21*b30 - 4*a21*b31 + 12*a2*b35 + 4*a6*b74 + 8*a7*
b74 + a8*b33,
a9*b38 - 12*a12*b61 - 6*a12*b62 - 3*a12*b63 - a12*b65 + 2*a13*b56 + 2*a13*b57
+ 2*a13*b58 - 2*a14*b15 - a14*b16 + a14*b56 + a14*b58 + a1*b65 + 40*a21*b36 + 6
*a8*b38,
9* a9*b38 - 6*a12*b62 - 9*a12*b63 - 9*a12*b65 - 12*a12*b66 - 6*a12*b67 - 2*a14*
b17 - a14*b18 - a14*b19 + 2*a15*b57 + 6*a19*b40 + 9*a20*b40 + 120*a21*b36 + 4*
a6*b45 + 2*a7*b45 + 6*a8*b38,
40* a9*b1 + a12*b16 + 2*a13*b13 + 4*a14*b13 + 3*a15*b13 - 4*a1*b16 - 6*a1*b17 -
6*a1*b18 - 3*a1*b19 - 3*a1*b20 - a2*b13 - 2*a6*b39 - 2*a6*b40 + 4*a6*b4 + 4*a7
*b4 + 40*a8*b1,
25* a9*b1 + 2*a12*b17 + a14*b13 + a14*b14 + 3*a15*b13 - 2*a1*b17 - 3*a1*b18 - 3
*a1*b19 - 6*a1*b20 - 2*a3*b13 - 2*a3*b14 + 2*a6*b3 - 2*a6*b40 - 2*a6*b41 + 3*a7
*b3 + 10*a8*b1,
5* a9*b2 - a9*b41 + 10*a10*b1 + 2*a12*b24 + a15*b19 + a17*b13 + a17*b14 - 2*a1
*b24 - 3*a1*b25 - a2*b19 - 2*a2*b20 - a4*b13 - a4*b14 - 2*a6*b47 + 2*a6*b5 + 3*
a7*b5,
a9*b51 - 3* a9*b8 - 6*a10*b5 - a15*b27 - 2*a17*b24 - a17*b25 - 2*a18*b19 + 6*
a1*b28 + 3*a2*b27 + 2*a4*b24 + a4*b25 + 3*a5*b19 - 2*a6*b10 + 2*a6*b53 - a7*b10
+ a7*b53,
a9*b62 + 4*a11*b44 - 12*a12*b74 - a14*b33 - 4*a15*b72 - 2*a15*b73 - 2*a17*b29
+ 2*a19*b64 - 2*a19*b66 + 2*a20*b64 + a20*b65 + 6*a21*b55 + 2*a21*b57 + 2*a21*
b58 + 2*a6*b69,
2*a10*b61 + 2*a11*b48 - 2*a13*b34 + 4*a13*b74 - a15*b74 - a16*b32 + a16*b72 +
a16*b73 - a19*b68 - a20*b68 - a21*b21 + a21*b64 + a21*b67 + a2*b74 + a8*b68,
3*a10*b68 + 3*a11*b52 - 3*a16*b34 + 4*a16*b74 - a17*b74 - 3*a18*b32 + 3*a18*b72
+ 3*a18*b73 - 3*a19*b71 - 3*a20*b71 - a21*b26 + a21*b69 + a21*b70 + a4*b74 + 3
*a8*b71,
240*a11*b1 - 18*a1*b29 - 6*a1*b30 - 18*a1*b31 + 4*a19*b12 + 12*a19*b13 + 4*a20*
b12 + 12*a20*b13 + 2*a6*b17 + a6*b19 - 2*a6*b56 - 6*a6*b57 - 2*a6*b58 - 2*a6*
b59 + a7*b17 - a7*b57,
80*a11*b1 + 2*a12*b29 - 2*a1*b29 - 6*a1*b30 - 6*a1*b31 + 2*a19*b13 + 12*a19*b14
+ 4*a20*b13 + 4*a20*b14 + a6*b20 - 2*a6*b58 - 2*a6*b60 + a7*b17 - 2*a7*b55 - 2
*a7*b56 - a7*b57,
8*a11*b22 + a11*b23 - 4*a11*b62 - 4*a11*b63 + 6*a14*b35 + 4*a19*b32 + 4*a20*b32
+ 2*a21*b29 + 6*a21*b30 + 2*a21*b31 - 12*a3*b35 - 2*a6*b74 - 10*a7*b74 - 2*a8*
b32 - 2*a8*b72 - 2*a8*b73,
a9*b32 - a9*b72 - a9*b73 - 2*a10*b29 + 4*a11*b21 + 2*a11*b24 - 4*a11*b66 +
a19*b33 + a20*b33 + 4*a21*b29 + 2*a21*b30 - 6*a2*b35 + 2*a6*b34 - 2*a6*b74 - 4*
a7*b74 - a8*b33,
a9*b32 - a9*b72 - a9*b73 - 2*a10*b30 + 4*a11*b21 + 2*a11*b25 - 4*a11*b64 - 4
*a11*b67 + 6*a15*b35 + a19*b33 + a20*b33 + 6*a21*b30 - 6*a2*b35 + 2*a7*b34 - 6*
a7*b74 - a8*b33,
a9*b34 - 6* a9*b74 + 2*a10*b32 - a10*b33 - 2*a10*b72 - 2*a10*b73 + 4*a11*b26 +
3*a11*b27 - 4*a11*b69 - 4*a11*b70 + 6*a17*b35 + 4*a19*b34 + 4*a20*b34 + 6*a21*
b33 - 6*a4*b35 - 4*a8*b34,
6*a12*b48 + 6*a12*b49 + 6*a12*b50 - a14*b44 + a14*b6 + 2*a15*b43 + a15*b44 + 2*
a15*b45 - 2*a16*b39 - 12*a16*b41 - 2*a17*b39 - 6*a17*b41 + 2*a17*b4 - 90*a18*
b36 - 2*a2*b44 - 2*a3*b44 - 6*a4*b38,
6*a12*b48 + 7*a12*b49 - a13*b45 + 2*a13*b5 + 2*a13*b6 + 3*a13*b7 + a14*b42 +
a14*b43 - a16*b38 + a16*b3 - 4*a16*b40 - 60*a18*b36 - a1*b49 - 2*a2*b43 - a3*
b42 - 2*a3*b43 - 20*a4*b37,
9*a12*b52 + 2*a13* b9 + 3*a13*b8 + 2*a15*b48 + 2*a15*b49 - a16*b44 - 3*a16*b47
+ a16*b6 + a17*b43 - 3*a18*b39 - 18*a18*b41 + 3*a18*b4 - 3*a2*b48 - 2*a3*b48 -
6*a4*b42 - a4*b43 - 36*a5*b37,
2*a10*b43 - 6*a12*b71 - 2*a13*b26 - a14*b68 - a16*b22 + a16*b62 + a16*b63 + 6*
a18*b55 + 6*a18*b60 - a19*b49 - a20*b49 + a21*b45 - a21*b7 + a3*b68 + 2*a4*b61
+ a8*b49,
2* a9*b43 + 24*a10*b37 - 6*a12*b68 - 6*a12*b70 - 2*a13*b22 - 2*a13*b23 - 2*a13*
b24 - a14*b66 - a16*b17 + a16*b57 + 2*a16*b59 + 2*a17*b59 + 6*a21*b40 + a3*b66
+ a6*b49 + 2*a8*b43,
5*a10*b52 - 5*a16*b28 + 2*a16*b71 - 3*a17*b71 - 3*a18*b26 + 2*a18*b68 + 3*a18*
b69 + 3*a18*b70 - 5*a19*b54 - 5*a20*b54 - a21*b10 - 2*a21*b52 + a21*b53 + 3*a4*
b71 + 5*a5*b68 + 5*a8*b54,
a9*b2 - 2* a9*b37 - a9*b38 + 20*a10*b1 + a13*b19 + 3*a13*b20 + a14*b20 + a16*
b13 + 4*a16*b14 + 2*a17*b14 - 6*a1*b21 - 4*a2*b15 - 2*a6*b42 - 2*a7*b42 - a7*
b44 + 8*a8*b2,
30* a9*b1 + 4*a13*b12 + 3*a13*b13 + 2*a14*b12 + 3*a14*b13 + a15*b13 - 6*a1*b15
- 9*a1*b16 - 6*a1*b17 - 3*a1*b18 - 2*a6*b38 + 2*a6*b3 - 2*a6*b39 - a7*b38 + a7*
b3 + 60*a8*b1,
4* a9*b2 - a9*b38 + a9*b3 + 40*a10*b1 + 2*a13*b19 + a14*b19 + 3*a16*b13 + 2*
a17*b13 - 6*a1*b21 - 3*a1*b23 - 2*a2*b15 - 2*a2*b16 - 2*a6*b42 - 2*a6*b44 + 2*
a6*b5 + 12*a8*b2,
a9*b4 + 60*a10*b1 + 2*a13*b16 + a14*b16 + 3*a16*b13 + 12*a16*b14 + 6*a17*b14 -
6*a1*b21 - 12*a1*b22 - 3*a1*b23 + 2*a3*b16 - 2*a6*b43 - 2*a7*b43 - a7*b44 - 2*
a7*b45 + 8*a8*b4,
2* a9*b48 + 2* a9*b49 + 2*a10*b43 - 6*a10*b5 - 3*a10*b6 - 2*a13*b26 - 2*a16*b21
- a16*b23 - 3*a16*b25 - 3*a18*b16 - 3*a18*b18 - 18*a18*b20 + 36*a1*b28 + 4*a2*
b26 - 4*a4*b21 - 36*a5*b15 + 9*a7*b52 + 2*a8*b48,
50* a9*b1 + a12*b18 + 2*a14*b12 + a14*b13 + 4*a15*b12 + a15*b13 - 6*a1*b17 - 4*
a1*b18 - 9*a1*b19 - 3*a1*b20 - 4*a3*b12 - 2*a3*b13 + 6*a6*b3 + 4*a7*b3 - a7*b40
+ 20*a8*b1,
10* a9*b2 + 20*a10*b1 + a12*b25 + a15*b19 + a15*b20 + 2*a17*b12 + a17*b13 - 6*
a1*b24 - 4*a1*b25 - 3*a2*b19 - a2*b20 - 2*a4*b12 - a4*b13 + 6*a6*b5 - a7*b47 +
4*a7*b5,
a9*b47 - 4* a9*b5 - 8*a10*b2 - a12*b27 - 2*a15*b24 - a17*b19 - a17*b20 - 2*a18
*b13 + 4*a1*b27 + 2*a2*b24 + 2*a2*b25 + a4*b19 + a4*b20 + 4*a5*b13 + 2*a6*b51 -
2*a6*b8 - 2*a7*b8,
2* a9*b61 + 4*a11*b43 - 12*a12*b74 - 4*a13*b32 - 2*a13*b33 - a16*b29 - a19*b66
- a20*b66 - a21*b17 + 6*a21*b55 + a21*b57 + 2*a21*b59 + 6*a21*b60 + a6*b68 + 2*
a8*b61 + a8*b66,
a9*b63 + a9*b67 + 24*a11*b42 - 24*a12*b74 - 6*a13*b33 - 4*a15*b73 - 2*a16*b30
- 2*a16*b31 + 6*a19*b67 - 2*a20*b64 - a20*b65 + 2*a20*b66 + 2*a20*b67 + 4*a21*
b59 + 12*a21*b60 + 2*a7*b70,
16*a11*b4 + 4*a13*b31 + 2*a14*b31 - 24*a1*b32 - 6*a1*b33 + 2*a19*b16 + 2*a20*
b16 + 6*a21*b13 + 24*a21*b14 - a2*b31 - 4*a6*b61 - 2*a6*b63 - 4*a7*b61 - 4*a7*
b62 - 2*a7*b63 - a7*b65 + 4*a8*b16,
a9*b15 - a9*b55 - a9*b60 - 2*a10*b14 + 4*a11*b2 - 4*a11*b41 + a12*b33 + a15*
b30 - a1*b33 + a19*b20 + a20*b20 + 4*a21*b14 - a2*b30 + a7*b21 - a7*b64 - a7*
b67 - a8*b20,
3* a9*b28 - 4* a9*b71 + 2*a10*b26 + a10*b27 - 2*a10*b69 - 2*a10*b70 + 4*a11*b10
- 4*a11*b53 + 4*a17*b34 + 4*a18*b33 + 2*a19*b28 + 2*a20*b28 + 4*a21*b27 - 4*a4
*b34 - 3*a5*b33 - 2*a8*b28,
6*a12*b48 + 6*a12*b49 + 18*a12*b50 + 18*a12*b51 - a14*b46 + a15*b44 + 4*a15*b45
+ 2*a15*b46 + a15*b6 - 3*a16*b40 - 18*a16*b41 - 4*a17*b39 - 6*a17*b40 - 24*a17
*b41 - 180*a18*b36 - 2*a2*b46 - 2*a3*b46 - 6*a4*b39,
8*a12*b48 + 6*a12*b49 - a13*b44 + 2*a13*b5 + 3*a13*b6 + a15*b42 + 3*a15*b43 -
a16*b38 + a16*b3 - a16*b39 - 10*a16*b41 + 2*a16*b4 - 60*a18*b36 - 2*a1*b48 - 5*
a2*b42 - a2*b43 - 6*a3*b42 - 20*a4*b37,
2* a9*b45 + 12*a10*b38 - 12*a12*b68 - 12*a12*b69 - 6*a12*b70 - 2*a14*b22 - a14*
b23 - a14*b65 + 2*a16*b56 + 2*a16*b57 + 2*a16*b58 + 2*a17*b56 + 2*a17*b58 + 12*
a21*b40 + a3*b65 + 4*a8*b45,
2*a10*b37 - a12*b68 - a13*b21 + a13*b64 + a13*b67 - a15*b61 - a16*b15 + a16*b55
+ a16*b60 + a1*b68 - a19*b42 - a20*b42 - a21*b2 - 2*a21*b37 + a21*b41 + a2*b61
+ a8*b42,
18* a9*b37 - 6*a12*b61 - 9*a12*b63 - 6*a12*b66 - 3*a12*b67 - 3*a13*b16 - 4*a13*
b17 - 2*a13*b18 - a13*b19 + 2*a13*b59 + 3*a14*b59 + a15*b59 + 2*a20*b39 + 60*
a21*b36 + 2*a6*b43 + a7*b43 + 24*a8*b37,
a9*b12 - 120*a11*b1 + 12*a1*b29 + 6*a1*b30 + 6*a1*b31 - 8*a19*b12 - 6*a19*b14
- 2*a20*b12 - 3*a20*b13 - 12*a20*b14 - 2*a6*b16 + 2*a6*b59 - a7*b16 + a7*b56 +
2*a7*b57 + a7*b58 + 2*a7*b59,
a9*b18 - a9*b56 - a9*b58 + 24*a11*b2 + 2*a15*b30 - 6*a1*b33 + 6*a19*b20 +
a20*b19 + 3*a20*b20 + 4*a21*b12 + 12*a21*b14 - 2*a2*b30 - 2*a2*b31 + 2*a7*b25 -
2*a7*b64 - 2*a7*b65 - 2*a7*b67,
a9*b27 - a9*b69 - a9*b70 + a10*b23 - a10*b65 + 4*a11*b8 + a17*b33 + 2*a18*
b31 + a19*b27 + a20*b27 + 2*a21*b24 + 2*a21*b25 - 4*a2*b34 - a4*b33 - 2*a5*b31
- 2*a6*b71 - 2*a7*b71,
6*a12*b48 + 2*a12*b49 - a13*b46 + 4*a13*b5 + a13*b6 + a14*b42 + 2*a15*b42 + a15
*b43 + 2*a16*b2 + a16*b3 - a16*b40 - 5*a16*b41 - 30*a18*b36 - 2*a1*b49 - 3*a2*
b42 - a2*b43 - 2*a3*b42 - 10*a4*b37,
4* a9*b37 - 6*a12*b61 - 3*a12*b63 - a12*b67 - 2*a13*b15 - 2*a13*b16 - a13*b18 +
a13*b58 + a13*b59 + 3*a13*b60 + 3*a14*b60 + a15*b60 + a1*b67 - a20*b39 + 20*
a21*b36 + a7*b42 + 12*a8*b37,
3* a9*b15 - a9*b59 - 2*a10*b12 + 12*a11*b2 + a15*b30 - 3*a1*b33 + a19*b19 + 3*
a20*b20 + 2*a21*b12 + 6*a21*b14 - 2*a2*b29 - a2*b30 + 2*a6*b21 + a7*b21 - a7*
b64 - 2*a7*b66 - a7*b67 - a8*b19,
a9*b30 - 24*a11*b15 - 4*a11*b16 - 4*a11*b18 + 4*a11*b56 + 4*a11*b58 + 72*a1*
b35 - 8*a19*b30 - 2*a19*b31 - 2*a20*b29 - 6*a20*b30 - 2*a20*b31 + 2*a6*b73 - a7
*b33 + 12*a7*b72 + 10*a7*b73 + 2*a8*b30 + 2*a8*b31,
2* a9*b7 + 12*a10*b3 + 2*a14*b22 + 2*a16*b17 + 2*a16*b18 + 2*a17*b18 + 6*a18*
b13 + 24*a18*b14 - 12*a1*b26 - 6*a1*b27 - 4*a3*b22 - a3*b23 + 2*a4*b16 - 2*a6*
b49 - 2*a7*b49 - 2*a7*b50 - 2*a8*b45 + 6*a8*b7,
a9*b61 + 4*a11*b43 - 12*a12*b74 - 8*a13*b32 - a13*b33 + 4*a13*b73 + a14*b73 -
a19*b63 - 2*a20*b61 - a20*b62 - a20*b63 - a21*b16 + 6*a21*b55 + a21*b56 + a21*
b59 + 9*a21*b60 + 4*a8*b61 + a8*b63,
2* a9*b61 + 4*a11*b43 - 12*a12*b74 - 4*a13*b32 - 2*a13*b33 + a15*b73 - a16*b30
- a19*b67 - a20*b64 - a20*b67 - a21*b18 + 6*a21*b55 + a21*b58 + a21*b59 + 9*a21
*b60 + a7*b68 + 2*a8*b61 + a8*b67,
a9*b63 + a9*b66 + 24*a11*b42 - 24*a12*b74 - 6*a13*b33 - 6*a15*b73 - 2*a16*b29
- 2*a16*b31 + 4*a19*b66 + 2*a19*b67 - a20*b65 + 2*a20*b66 + 2*a20*b67 + 2*a21*
b56 + 6*a21*b59 + 6*a21*b60 + 2*a6*b70,
a9*b29 - 24*a11*b15 - 4*a11*b16 - 4*a11*b17 + 4*a11*b57 + 72*a1*b35 - 6*a19*
b29 - 2*a19*b30 - 2*a19*b31 - 6*a20*b29 - 2*a20*b30 - 2*a20*b31 - a6*b33 + 8*a6
*b72 + 4*a6*b73 + 4*a7*b72 + 8*a7*b73 + 2*a8*b29 + 2*a8*b31,
60*a12*b54 + 12*a13*b10 + a14*b52 + 9*a15*b52 + 2*a16* b9 - a16*b50 - 3*a16*b51
+ 4*a16*b8 + 2*a17*b48 + 2*a17*b49 - 3*a18*b44 - 3*a18*b46 - 18*a18*b47 + 3*
a18*b6 - 4*a2*b52 - 2*a3*b52 - 8*a4*b48 - 2*a4*b49 - 36*a5*b42 - 8*a5*b43,
6*a10*b38 - 9*a12*b68 - 6*a12*b69 + 2*a13*b62 - a14*b21 - 2*a14*b22 + 9*a16*b55
+ 3*a16*b58 + 6*a17*b55 - 2*a19*b43 - a19*b44 - 2*a19*b45 + 2*a21*b39 + 3*a21*
b40 + a2*b62 + 2*a3*b62 + a8*b44 + 2*a8*b45,
2* a9*b44 + 2* a9*b45 + 12*a10*b38 - 6*a12*b68 - 12*a12*b69 - 12*a12*b70 - a14*
b23 - 2*a14*b25 - 2*a15*b63 - a15*b65 - 2*a15*b67 + 2*a16*b58 - 2*a17*b18 + 6*
a17*b58 + 2*a20*b46 + 6*a21*b40 + 24*a21*b41 + 2*a7*b50 + 2*a8*b44,
3* a9*b3 + 40*a10*b1 + 2*a12*b22 + a14*b18 + 2*a15*b18 + a16*b13 + 4*a16*b14 +
12*a17*b14 - 2*a1*b22 - 3*a1*b23 - 6*a1*b25 - 2*a3*b18 - a3*b20 - a7*b45 - 2*a7
*b46 - 2*a7*b47 + 3*a7*b7 + 2*a8*b3 - 2*a8*b40,
3* a9*b15 + 8*a11*b4 + 4*a13*b29 + 2*a14*b29 - 12*a1*b32 - 3*a1*b33 + a19*b16 +
a20*b16 + 3*a21*b13 + 12*a21*b14 - a2*b29 + a6*b21 - 2*a6*b61 - 2*a6*b62 - 2*
a7*b61 - 2*a7*b63 - a7*b66 + 6*a8*b15 - a8*b16,
240*a11*b1 - 12*a1*b29 - 12*a1*b30 - 18*a1*b31 + 4*a19*b12 + 6*a19*b13 + 24*a19
*b14 + 10*a20*b12 + 3*a20*b13 + 18*a20*b14 + 2*a6*b18 - 2*a6*b56 - 2*a6*b58 +
a7*b18 + a7*b19 - 3*a7*b56 - 4*a7*b57 - 3*a7*b58 - 2*a7*b59,
a9*b26 - a9*b69 - a9*b70 + 2*a10*b21 - 2*a10*b66 + 4*a11*b8 + a17*b33 + 4*
a18*b29 + a19*b27 + a20*b27 + 2*a21*b24 + 2*a21*b25 - 4*a2*b34 - a4*b33 - 4*a5*
b29 + 4*a6*b28 - 2*a6*b71 - 2*a7*b71 - a8*b27,
36*a12*b52 + 10*a13* b9 + 6*a13*b8 + 2*a14*b48 + 2*a14*b49 + 2*a15*b48 + 5*a15*
b49 - a16*b44 - a16*b45 - 3*a16*b46 + 2*a16*b6 + 3*a16*b7 - 6*a18*b39 - 18*a18*
b40 - 36*a18*b41 - 3*a2*b49 - 2*a3*b48 - 4*a3*b49 - 12*a4*b42 - 8*a4*b43 - 144*
a5*b37,
2*a10*b38 - 3*a12*b68 - 2*a12*b69 + 2*a13*b64 + a13*b65 - a14*b21 + a14*b64 - 2
*a15*b61 - a15*b62 + 3*a16*b55 + a16*b58 - 2*a17*b15 + 2*a17*b55 + 2*a1*b69 - 2
*a19*b42 - a19*b44 + 4*a21*b41 + a2*b62 + a8*b44,
2* a9*b43 + 24*a10*b37 - 6*a12*b68 - 6*a12*b70 - 2*a13*b22 - 2*a13*b23 - 2*a13*
b25 - a14*b67 + a15*b63 - a16*b18 + a16*b58 + a16*b59 + 3*a16*b60 + 6*a17*b60 -
a20*b46 + 6*a21*b40 + a3*b67 + a7*b49 + 2*a8*b43,
3* a9*b3 + 4* a9*b4 + 120*a10*b1 + 2*a13*b17 + a14*b16 + 2*a14*b17 + 9*a16*b13
+ 6*a17*b13 - 6*a1*b21 - 12*a1*b22 - 9*a1*b23 - 6*a1*b24 - 2*a3*b16 - 2*a6*b43
- 2*a6*b44 - 4*a6*b45 + a6*b6 + 6*a8*b3 + 4*a8*b4,
a9*b44 - 3* a9*b5 - a9*b6 - 24*a10*b2 - 4*a10*b4 - 2*a13*b24 - 2*a14*b24 - 2*
a16*b19 - a17*b16 - 2*a17*b19 - 9*a18*b13 + 6*a1*b26 + 9*a1*b27 + 2*a2*b21 + 2*
a2*b23 + a2*b24 + a4*b16 + 2*a6*b48 + 2*a6*b50 - 3*a6*b8 - 6*a8*b5,
a9*b26 - a9*b69 - a9*b70 + 2*a10*b21 - 2*a10*b64 - 2*a10*b67 - 4*a11*b51 + 4
*a11*b8 + 4*a15*b34 + a17*b33 + 4*a18*b30 + a19*b27 + a20*b27 + 4*a21*b25 - 4*
a2*b34 - a4*b33 - 4*a5*b30 + 4*a7*b28 - 4*a7*b71 - a8*b27,
27*a12*b52 + 36*a12*b53 + 2*a14* b9 + 3*a14*b8 + 4*a15*b48 + 4*a15*b49 + 6*a15*
b50 - 2*a16*b46 - 9*a16*b47 - a17*b44 + 2*a17*b45 - 2*a17*b46 - 6*a17*b47 + 2*
a17*b6 - 6*a18*b39 - 9*a18*b40 - 72*a18*b41 - 3*a2*b50 - 2*a3*b50 - 7*a4*b44 -
2*a4*b45 - 36*a5*b38,
3* a9*b50 + 8*a10*b44 + 4*a10*b45 - 36*a12*b71 - 2*a14*b26 - 3*a14*b27 - 4*a15*
b68 - 8*a15*b69 - 4*a15*b70 + 2*a16*b65 - 2*a17*b23 + 3*a17*b65 + 6*a18*b56 + 6
*a18*b57 + 6*a18*b58 + 4*a21*b46 + 12*a21*b47 + a4*b65 + 2*a8*b50,
4* a9*b52 + 8*a10*b48 + 4*a10*b49 - 16*a13*b28 - 12*a15*b71 - 2*a16*b26 - 4*a16
*b27 + 2*a16*b70 - 3*a18*b23 + 2*a18*b63 + 3*a18*b65 + 6*a18*b66 + 6*a18*b67 -
2*a20*b52 - 4*a20*b53 + 4*a21*b51 + 2*a4*b70 + 4*a5*b63 + 2*a8*b52,
2* a9*b42 + a9*b44 - 2* a9*b5 - 16*a10*b2 + 2*a10*b38 - 2*a10*b3 - 2*a13*b24 -
2*a13*b25 - a14*b25 - a16*b19 - 3*a16*b20 - 2*a17*b15 - 2*a17*b20 - 3*a18*b13
- 12*a18*b14 + 6*a1*b26 + 4*a2*b21 + 2*a4*b15 + 2*a6*b48 + 2*a7*b48 + a7*b50 -
6*a8*b5,
12* a9*b2 + 3* a9*b3 + 60*a10*b1 + a14*b19 + a15*b18 + a15*b19 + 2*a16*b12 + 8*
a17*b12 - 3*a1*b23 - 12*a1*b24 - 6*a1*b25 - 2*a2*b17 - a2*b18 - 2*a2*b19 - 2*a3
*b19 - 2*a4*b12 + 2*a6*b6 - a7*b46 + a7*b6 + 6*a8*b2,
a9*b16 - 2* a9*b55 - a9*b56 - a9*b58 - 2* a9*b60 + 32*a11*b2 + 2*a12*b33 + 2
*a15*b31 - 8*a1*b33 + 8*a19*b20 + a20*b19 + 5*a20*b20 + 4*a21*b13 + 16*a21*b14
- 4*a2*b30 - 2*a2*b31 - 2*a6*b67 + a7*b23 - 4*a7*b64 - 2*a7*b65 - 2*a7*b67,
3*a10*b44 - 9*a12*b71 + 2*a13*b69 - a14*b26 + a14*b69 - 2*a15*b68 - 2*a15*b69 +
2*a16*b64 + a16*b65 - 2*a17*b21 - a17*b62 + 2*a17*b64 + 9*a18*b55 + 3*a18*b58
- 2*a19*b48 - a19*b50 + 3*a21*b47 + 2*a2*b69 + a4*b62 + a8*b50,
2* a9*b44 + 2* a9*b45 + 12*a10*b38 - 6*a12*b68 - 12*a12*b69 - 12*a12*b70 - a14*
b23 - 2*a14*b24 - 2*a15*b62 - 2*a15*b63 - 2*a15*b65 - 2*a15*b66 + 2*a16*b57 - 2
*a17*b17 + 6*a17*b57 + 2*a19*b46 + 2*a20*b46 + 6*a21*b40 + 24*a21*b41 + 2*a6*
b50 + 2*a8*b44,
a9*b45 - 2* a9*b6 - 3* a9*b7 - 24*a10*b2 - 12*a10*b3 - a14*b23 - 2*a16*b17 - 2
*a16*b19 - 4*a17*b17 - 2*a17*b19 - 18*a18*b13 + 12*a1*b26 + 18*a1*b27 + 2*a2*
b22 + 2*a2*b23 + 2*a2*b24 + 2*a3*b23 + 2*a3*b24 - 2*a6* b9 + 2*a6*b49 + 4*a6*
b50 - 2*a8*b6,
3* a9*b15 - 4*a11*b39 + 8*a11*b4 + 4*a13*b30 + 2*a14*b30 + a15*b30 - 12*a1*b32
- 3*a1*b33 + a19*b16 + a20*b16 + 2*a21*b12 + 18*a21*b14 - a2*b30 + a7*b21 - 4*
a7*b61 - 2*a7*b62 - 2*a7*b63 - a7*b64 - a7*b67 + 6*a8*b15 - a8*b16,
a9*b13 - 160*a11*b1 - 2*a12*b31 + 12*a1*b29 + 12*a1*b30 + 8*a1*b31 - 8*a19*b13
- 8*a19*b14 - 6*a20*b13 - 16*a20*b14 - 2*a6*b16 + 4*a6*b55 + 2*a6*b56 + 2*a6*
b59 + 2*a6*b60 - 2*a7*b16 + 2*a7*b57 + 2*a7*b58 + 2*a7*b59 + 2*a7*b60,
a9*b21 - a9*b64 - a9*b67 + 2*a10*b15 - a10*b20 - 2*a10*b55 - 2*a10*b60 - 4*
a11*b47 + 4*a11*b5 + 4*a12*b34 + a15*b33 + a17*b30 - 4*a1*b34 + a19*b25 + a20*
b25 + 4*a21*b20 - a2*b33 - a4*b30 + a7*b26 - a7*b69 - a7*b70 - a8*b25,
2* a9*b43 + 48*a10*b37 - 18*a12*b68 - 6*a12*b70 - 4*a13*b21 - 8*a13*b22 - 3*a13
*b23 + 2*a13*b63 - a16*b16 + 3*a16*b56 + 3*a16*b59 + 9*a16*b60 + 6*a17*b60 - 2*
a20*b43 - a20*b44 - 2*a20*b45 + 4*a21*b39 + 6*a21*b40 + a2*b63 + 2*a3*b63 + 6*
a8*b43,
4*a10*b48 - 4*a13*b28 + 2*a13*b71 - 3*a15*b71 - a16*b26 + a16*b69 + a16*b70 -
a17*b68 - 3*a18*b21 + 2*a18*b61 + 3*a18*b64 + 3*a18*b67 - a19*b52 - a20*b52 - 2
*a21*b48 + a21*b51 - a21*b8 + 3*a2*b71 + a4*b68 + 4*a5*b61 + a8*b52,
9* a9*b42 + 3* a9*b43 + 48*a10*b37 - 6*a12*b68 - 18*a12*b70 - 3*a13*b23 - 8*a13
*b24 - 4*a13*b25 - 2*a15*b63 - 2*a15*b66 - 2*a15*b67 - 2*a16*b17 - a16*b18 - 2*
a16*b19 + 2*a16*b59 + 6*a17*b59 + 2*a20*b46 + 6*a21*b40 + 24*a21*b41 + 4*a6*b49
+ 2*a7*b49 + 6*a8*b42,
a9*b3 + 80*a10*b1 + 2*a13*b17 + 2*a13*b18 + 2*a14*b15 + a14*b18 + 4*a16*b13 +
16*a16*b14 + 8*a17*b14 - 12*a1*b21 - 12*a1*b22 - 3*a1*b23 + 2*a2*b16 - 4*a3*b15
- 2*a6*b42 - 2*a6*b43 - 2*a7*b42 - 2*a7*b43 - 2*a7*b44 - 2*a7*b45 - 2*a8*b38 +
8*a8*b3,
2* a9*b48 + a9*b50 - 3* a9*b8 + 2*a10*b44 - 12*a10*b5 - 2*a10*b6 - 2*a13*b27 -
a14*b27 - 2*a16*b24 - 2*a16*b25 - 2*a17*b21 - 2*a17*b25 - 2*a18*b16 - 3*a18*
b19 - 9*a18*b20 + 24*a1*b28 + 4*a2*b26 + a2*b27 + 2*a4*b21 + 2*a6*b52 + 2*a7*
b52 + 4*a7*b53 - 4*a8*b8,
2* a9* b9 - a9*b50 + 2* a9*b8 + 12*a10*b5 + 2*a10*b6 + a14*b27 + 2*a16*b24 +
a17*b23 + 4*a17*b24 + 2*a18*b17 + 6*a18*b19 - 24*a1*b28 - 2*a2*b26 - 6*a2*b27 -
2*a3*b27 - a4*b23 - 2*a4*b24 + 4*a6*b10 - 2*a6*b52 - 8*a6*b53 + 2*a8*b8,
4* a9*b2 + a9*b3 - a9*b40 - a9*b41 + 20*a10*b1 + a12*b23 + a14*b20 + a15*b18
+ 3*a15*b20 + 2*a16*b14 + 8*a17*b14 - a1*b23 - 6*a1*b25 - a2*b18 - 2*a2*b20 -
2*a3*b20 - 2*a4*b14 - a7*b46 - 4*a7*b47 + a7*b6 + 2*a8*b2 - 2*a8*b41,
3* a9*b15 + 4*a11*b3 - 4*a11*b40 + 4*a12*b32 + a14*b30 + 2*a15*b30 - 4*a1*b32 -
3*a1*b33 + a19*b18 + a20*b18 + a21*b13 + 12*a21*b14 - 2*a3*b30 + 2*a7*b22 - a7
*b62 - a7*b63 - 2*a7*b64 - 2*a7*b67 + 2*a8*b15 - a8*b18 - 2*a8*b55 - 2*a8*b60,
2*a10*b44 + 4*a10*b45 - 18*a12*b71 - 2*a14*b26 - 2*a14*b69 - 2*a15*b68 - 2*a15*
b69 + 2*a16*b62 + 2*a16*b64 + a16*b65 - 2*a17*b22 + 2*a17*b62 + 2*a17*b64 + 18*
a18*b55 + 6*a18*b58 - 2*a19*b49 - 2*a19*b50 + 2*a21*b46 + 2*a3*b69 + 2*a4*b62 +
2*a8*b50,
8*a10*b37 - 4*a12*b68 - 2*a13*b21 - 2*a13*b22 + a13*b62 + a13*b63 - a14*b61 -
a16*b15 + 4*a16*b55 + 4*a16*b60 + a1*b68 - a19*b42 - a19*b43 - a20*b42 - a20*
b43 + a21*b38 - a21*b3 + a21*b40 + 2*a2*b61 + 2*a3*b61 + a8*b42 + a8*b43,
3*a10*b42 - 3*a12*b71 - a13*b26 + a13*b69 + a13*b70 - a15*b68 - a16*b21 + a16*
b64 + a16*b67 - a17*b61 - 3*a18*b15 + 3*a18*b55 + 3*a18*b60 + 3*a1*b71 - a19*
b48 - a20*b48 - 2*a21*b42 + a21*b47 - a21*b5 + a2*b68 + a4*b61 + a8*b48,
2* a9*b48 + 2* a9*b49 + 12*a10*b42 + 2*a10*b43 - 18*a12*b71 - 2*a13*b26 - 6*a13
*b27 - 2*a15*b68 - 4*a15*b70 - a16*b23 - 3*a16*b24 + 2*a16*b66 + 3*a17*b66 - 3*
a18*b17 + 3*a18*b57 + 6*a18*b59 + 2*a21*b46 + 6*a21*b47 + a4*b66 + 3*a6*b52 + 2
*a8*b48,
2* a9*b48 + 2* a9*b49 + 12*a10*b42 + 2*a10*b43 - 18*a12*b71 - 2*a13*b26 - 6*a13
*b27 - 3*a15*b70 - a16*b23 - 3*a16*b25 + 2*a16*b67 + 3*a17*b67 - 3*a18*b18 + 3*
a18*b58 + 3*a18*b59 + 9*a18*b60 - 3*a20*b51 + 6*a21*b47 + a4*b67 + 3*a7*b52 + 2
*a8*b48,
9* a9*b3 + 120*a10*b1 + 2*a14*b17 + a14*b18 + 2*a15*b17 + 4*a16*b12 + 3*a16*b13
+ 4*a17*b12 + 6*a17*b13 - 6*a1*b22 - 9*a1*b23 - 12*a1*b24 - 6*a1*b25 - 4*a3*
b17 - 2*a3*b18 - a3*b19 - 2*a6*b45 - 2*a6*b46 + 6*a6*b7 - a7*b45 + 3*a7*b7 + 6*
a8*b3,
4* a9*b10 - 2* a9*b52 - 4* a9*b53 + 4*a10* b9 - 2*a10*b50 + 8*a10*b8 + 2*a14*
b28 + 2*a16*b27 + 2*a17*b26 + 2*a17*b27 + 2*a18*b23 + 6*a18*b24 + 6*a18*b25 -
16*a2*b28 - 4*a3*b28 - 2*a4*b26 - 2*a4*b27 + a5*b23 - 10*a6*b54 - 10*a7*b54 + 2
*a8*b10 - 2*a8*b53,
4* a9*b15 - a9*b55 - a9*b59 - a9*b60 - 2*a10*b13 + 16*a11*b2 + a12*b33 + 2*
a15*b29 - 4*a1*b33 + a19*b19 + a19*b20 + 4*a20*b20 + 2*a21*b13 + 8*a21*b14 - 2*
a2*b29 - 2*a2*b30 + 2*a6*b21 - 2*a6*b64 + 2*a7*b21 - 2*a7*b66 - 2*a7*b67 - a8*
b19 - a8*b20,
12*a12*b48 + 6*a12*b49 + 8*a12*b50 - 2*a13*b46 + a14*b44 - a14*b46 + 2*a14*b5 +
a14*b6 + 2*a15*b42 + 2*a15*b43 + 2*a15*b44 + 2*a15*b45 - 3*a16*b40 - 16*a16*
b41 - 2*a17*b38 + 2*a17*b3 - 2*a17*b40 - 8*a17*b41 - 120*a18*b36 - 2*a1*b50 - 2
*a2*b44 - 2*a2*b45 - 2*a3*b44 - 8*a4*b38,
12*a12*b52 + 2*a13* b9 - a13*b50 + 6*a13*b8 + a14*b48 + 4*a15*b48 + 2*a15*b49 -
a16*b46 - 4*a16*b47 + 3*a16*b5 + a16*b6 + a17*b42 + a17*b43 - 3*a18*b38 + 3*
a18*b3 - 3*a18*b40 - 24*a18*b41 - 3*a1*b52 - 2*a2*b48 - 2*a2*b49 - 2*a3*b48 - 9
*a4*b42 - a4*b43 - 48*a5*b37,
3* a9*b42 + a9*b43 + 24*a10*b37 - 6*a12*b68 - 6*a12*b70 - 2*a13*b21 - 2*a13*
b23 - 2*a13*b25 + 2*a13*b67 + 2*a14*b67 - 2*a15*b63 - a16*b16 - a16*b18 + a16*
b58 + a16*b59 + 3*a16*b60 + 6*a17*b60 - a20*b46 + 12*a21*b41 + a2*b67 + 2*a7*
b48 + 6*a8*b42,
4* a9*b2 - a9*b38 + a9*b3 - a9*b39 + 40*a10*b1 + a13*b19 + 3*a13*b20 + 3*a14
*b20 + 2*a15*b15 + a15*b20 + 2*a16*b12 + 6*a16*b14 + 8*a17*b14 - 6*a1*b21 - 3*
a1*b23 - 2*a2*b15 - 2*a2*b16 - 2*a7*b42 - 2*a7*b44 - a7*b46 + 2*a7*b5 + 12*a8*
b2,
2* a9*b68 + 8*a10*b61 + 2*a10*b63 + 8*a11*b49 - 16*a13*b34 - 8*a15*b74 - 4*a16*
b32 - 2*a16*b33 + 4*a16*b73 + 2*a17*b73 - 2*a19*b70 - 2*a20*b68 - 2*a20*b69 - 2
*a20*b70 - a21*b23 + 2*a21*b63 + 4*a21*b64 + a21*b65 + 2*a21*b66 + 6*a21*b67 +
2*a8*b68 + 2*a8*b70,
2* a9*b44 + 12*a10*b38 - 12*a12*b68 - 12*a12*b69 - 6*a12*b70 + 2*a13*b65 - 2*
a14*b21 - a14*b23 + 2*a14*b65 - 4*a15*b61 - 4*a15*b62 - 2*a15*b63 - a15*b65 + 2
*a16*b56 + 2*a16*b57 + 2*a16*b58 - 2*a17*b16 + 2*a17*b56 + 2*a17*b58 + 4*a21*
b39 + 24*a21*b41 + a2*b65 + 4*a8*b44,
3* a9*b42 + a9*b43 + 24*a10*b37 - 6*a12*b68 - 6*a12*b70 - 2*a13*b21 - 2*a13*
b23 - 2*a13*b24 + 2*a13*b66 + 2*a14*b66 - 2*a15*b61 - 2*a15*b63 - a15*b66 - a16
*b16 - a16*b17 + a16*b57 + 2*a16*b59 + 2*a17*b59 + 2*a21*b39 + 12*a21*b41 + a2*
b66 + 2*a6*b48 + 6*a8*b42,
6* a9*b2 - a9*b39 - a9*b40 + 2* a9*b4 + 40*a10*b1 + 2*a12*b21 + 2*a13*b20 + 3
*a14*b20 + a15*b16 + 3*a15*b20 + a16*b13 + 4*a16*b14 + 12*a17*b14 - 2*a1*b21 -
3*a1*b23 - 6*a1*b25 - a2*b16 - 2*a2*b18 - a2*b20 - a7*b44 - 2*a7*b46 - 2*a7*b47
+ a7*b6 + 8*a8*b2,
2* a9*b42 + 16*a10*b37 - 6*a12*b68 - 2*a12*b70 - 4*a13*b21 - a13*b23 + a13*b65
+ 2*a13*b66 + 2*a13*b67 + a14*b67 - 4*a15*b61 - a15*b63 - 2*a16*b15 - a16*b16 +
a16*b56 + a16*b59 + 3*a16*b60 + 2*a17*b60 + 2*a1*b70 - 2*a20*b42 - a20*b44 + 8
*a21*b41 + a2*b63 + 6*a8*b42,
2*a10*b48 + 5*a10*b49 - 12*a13*b28 - 3*a14*b71 - 6*a15*b71 - 3*a16*b26 + 2*a16*
b68 + a16*b69 + a16*b70 - a17*b68 - 3*a18*b22 + 3*a18*b62 + 3*a18*b63 + 6*a18*
b64 + 6*a18*b67 - 3*a19*b52 - 3*a20*b52 - a21* b9 - 2*a21*b49 + a21*b50 + 3*a3*
b71 + 3*a4*b68 + 12*a5*b61 + 3*a8*b52,
3* a9*b3 + 4* a9*b4 + 120*a10*b1 + 2*a13*b18 + a14*b16 + 2*a14*b18 + a15*b16 +
a15*b18 + 6*a16*b12 + 18*a16*b14 + 24*a17*b14 - 6*a1*b21 - 12*a1*b22 - 9*a1*b23
- 6*a1*b25 - 2*a3*b16 - 2*a7*b43 - 2*a7*b44 - 4*a7*b45 - 3*a7*b46 + a7*b6 + 6*
a8*b3 - 2*a8*b39 + 4*a8*b4,
a9*b22 + 12*a10*b15 + 2*a10*b16 - 4*a11*b45 + 12*a11*b7 + 4*a14*b32 + 2*a16*
b29 + 2*a16*b30 + 2*a16*b31 + 2*a17*b30 - 24*a1*b34 + 2*a19*b22 + 2*a20*b22 + 2
*a21*b17 + 6*a21*b18 - 8*a3*b32 - a3*b33 - 2*a6*b68 - 6*a7*b68 - 2*a7*b69 - 2*
a7*b70 + 2*a8*b22 - 2*a8*b62 - 2*a8*b63,
a9*b17 + a9*b18 - a9*b56 - a9*b57 - a9*b58 + 48*a11*b2 + 2*a15*b29 - 12*a1
*b33 + 2*a19*b19 + 6*a19*b20 + 3*a20*b19 + 3*a20*b20 + 4*a21*b12 + 6*a21*b13 +
12*a21*b14 - 2*a2*b29 - 2*a2*b30 - 4*a2*b31 + 2*a6*b25 - 2*a6*b65 - 2*a6*b67 +
2*a7*b24 - 2*a7*b64 - 2*a7*b65 - 2*a7*b66,
16* a9*b2 + 4* a9*b3 - a9*b40 + 80*a10*b1 + a12*b23 + a14*b19 + a14*b20 + 2*
a15*b17 + 2*a15*b19 + 2*a16*b13 + 8*a17*b13 - 4*a1*b23 - 12*a1*b24 - 12*a1*b25
- 2*a2*b17 - 2*a2*b18 - 2*a2*b19 - 2*a2*b20 - 2*a3*b19 - 2*a3*b20 - 2*a4*b13 -
2*a6*b46 - 4*a6*b47 + 2*a6*b6 + 2*a7*b6 + 8*a8*b2,
2* a9*b16 + 24*a11*b3 + 2*a14*b29 + 2*a14*b31 - 24*a1*b32 - 18*a1*b33 + 4*a19*
b17 + 2*a19*b18 + 4*a20*b17 + 2*a20*b18 + 18*a21*b13 + 24*a21*b14 - 4*a3*b29 -
4*a3*b31 + a6*b23 - 4*a6*b62 - 4*a6*b63 - 2*a6*b65 - 2*a6*b66 - 2*a7*b62 - 2*a7
*b63 - 2*a7*b65 - 2*a7*b66 + 2*a8*b16 + 2*a8*b17 - 2*a8*b57,
3* a9*b16 - a9*b56 - 2* a9*b57 - a9*b58 - 2* a9*b59 + 96*a11*b2 + 2*a15*b31 -
24*a1*b33 + 6*a19*b19 + 6*a19*b20 + 5*a20*b19 + 9*a20*b20 + 8*a21*b12 + 12*a21
*b13 + 24*a21*b14 - 8*a2*b29 - 4*a2*b30 - 6*a2*b31 + 2*a6*b23 - 4*a6*b64 - 2*a6
*b65 - 4*a6*b66 - 2*a6*b67 + a7*b23 - 4*a7*b65 - 4*a7*b66 - 2*a7*b67,
a9*b23 + a9*b24 - 2* a9*b65 - 2* a9*b66 + 2*a10*b16 + 2*a10*b17 - 2*a10*b57 +
24*a11*b5 + 2*a17*b29 + 2*a17*b31 - 24*a1*b34 + 4*a19*b24 + 2*a19*b25 + 4*a20*
b24 + 2*a20*b25 + 6*a21*b19 + 6*a21*b20 - 6*a2*b33 - 2*a4*b29 - 2*a4*b31 + 3*a6
*b27 - 4*a6*b69 - 4*a6*b70 - 2*a7*b69 - 2*a7*b70,
18* a9*b2 - a9*b39 + 6* a9*b4 + 120*a10*b1 + 2*a13*b19 + 3*a14*b19 + a15*b16 +
a15*b19 + 4*a16*b12 + 3*a16*b13 + 4*a17*b12 + 6*a17*b13 - 6*a1*b21 - 9*a1*b23
- 12*a1*b24 - 6*a1*b25 - 3*a2*b16 - 4*a2*b17 - 2*a2*b18 - a2*b19 - 2*a6*b44 - 2
*a6*b46 + 2*a6*b6 - a7*b44 + a7*b6 + 24*a8*b2,
a9*b44 + a9*b46 - 3* a9*b5 - a9*b6 - 24*a10*b2 + 2*a10*b39 - 4*a10*b4 - 2*
a13*b25 - 2*a14*b25 - 2*a15*b21 - a15*b25 - a16*b19 - 3*a16*b20 - a17*b16 - 6*
a17*b20 - 6*a18*b12 - 18*a18*b14 + 6*a1*b26 + 9*a1*b27 + 2*a2*b21 + 2*a2*b23 +
a2*b25 + a4*b16 + 2*a7*b48 + 2*a7*b50 + 3*a7*b51 - 3*a7*b8 - 6*a8*b5,
a9*b23 - 2* a9*b62 - 2* a9*b63 - a9*b65 + 8*a10*b16 + 8*a11*b6 + 2*a14*b33 +
4*a16*b31 + 4*a17*b31 - 48*a1*b34 + 2*a19*b23 + 2*a20*b23 + 4*a21*b17 + 4*a21*
b18 + 4*a21*b19 + 12*a21*b20 - 8*a2*b32 - 4*a2*b33 - 4*a3*b33 - 2*a4*b31 - 4*a6
*b68 - 4*a6*b70 - 4*a7*b68 - 8*a7*b69 - 4*a7*b70 + 2*a8*b23 - 2*a8*b65,
3* a9*b21 - a9*b64 - 2* a9*b66 - a9*b67 + 6*a10*b15 - a10*b19 - 2*a10*b59 +
12*a11*b5 + a15*b33 + 2*a17*b29 + a17*b30 - 12*a1*b34 + 2*a19*b24 + a19*b25 + 3
*a20*b25 + 2*a21*b19 + 6*a21*b20 - 3*a2*b33 - 2*a4*b29 - a4*b30 + 2*a6*b26 - 2*
a6*b69 + a7*b26 - a7*b69 - 3*a7*b70 - 2*a8*b24 - a8*b25,
a9*b23 + a9*b25 - 2* a9*b64 - 2* a9*b65 - 2* a9*b67 + 2*a10*b16 + 2*a10*b18 -
2*a10*b56 - 2*a10*b58 + 24*a11*b5 + 2*a15*b33 + 2*a17*b30 + 2*a17*b31 - 24*a1*
b34 + 6*a19*b25 + 2*a20*b24 + 4*a20*b25 + 4*a21*b19 + 12*a21*b20 - 6*a2*b33 - 2
*a4*b30 - 2*a4*b31 - 2*a6*b70 + 3*a7*b27 - 6*a7*b69 - 4*a7*b70,
a9*b46 + 2* a9*b47 - 3* a9*b5 - a9*b6 - 16*a10*b2 - 2*a10*b3 + 2*a10*b40 - 2*
a12*b26 - a14*b25 - a15*b23 - 2*a15*b25 - 2*a16*b20 - a17*b18 - 6*a17*b20 - 3*
a18*b13 - 12*a18*b14 + 2*a1*b26 + 9*a1*b27 + a2*b23 + 4*a2*b25 + 2*a3*b25 + a4*
b18 + 2*a4*b20 - 2*a7* b9 + a7*b50 + 6*a7*b51 + 2*a8*b47 - 2*a8*b5,
a9*b21 - 4* a9*b61 - a9*b62 - a9*b63 + 12*a10*b15 - 4*a11*b44 + 4*a11*b6 + 4
*a13*b33 + a14*b33 + 2*a16*b29 + 2*a16*b30 + 2*a16*b31 + 2*a17*b30 - 24*a1*b34
+ 2*a19*b21 + 2*a20*b21 + 4*a21*b16 + a21*b19 + 9*a21*b20 - 8*a2*b32 - a2*b33 -
2*a6*b68 - 6*a7*b68 - 2*a7*b69 - 2*a7*b70 + 2*a8*b21,
9* a9*b15 + 12*a11*b3 + 2*a14*b29 + a14*b30 + 2*a15*b29 - 12*a1*b32 - 9*a1*b33
+ 2*a19*b17 + a19*b18 + 3*a20*b18 + 4*a21*b12 + 3*a21*b13 + 24*a21*b14 - 4*a3*
b29 - 2*a3*b30 + 4*a6*b22 - 2*a6*b62 - 2*a6*b64 + 2*a7*b22 - a7*b62 - 3*a7*b63
- 4*a7*b66 - 2*a7*b67 + 6*a8*b15 - 2*a8*b17 - a8*b18 - 2*a8*b59,
2* a9*b16 + 24*a11*b3 + 2*a14*b30 + 2*a14*b31 + 2*a15*b31 - 24*a1*b32 - 18*a1*
b33 + 6*a19*b18 + 2*a20*b17 + 4*a20*b18 + 8*a21*b12 + 6*a21*b13 + 48*a21*b14 -
4*a3*b30 - 4*a3*b31 - 2*a6*b63 - 2*a6*b67 + a7*b23 - 6*a7*b62 - 4*a7*b63 - 4*a7
*b64 - 4*a7*b65 - 2*a7*b67 + 2*a8*b16 + 2*a8*b18 - 2*a8*b56 - 2*a8*b58,
3* a9*b49 + 12*a10*b42 + 8*a10*b43 - 36*a12*b71 - 8*a13*b26 - 6*a13*b27 - 2*a14
*b70 - 4*a15*b68 - 2*a15*b70 - 2*a16*b22 - 2*a16*b23 + 2*a16*b63 + a16*b65 + 2*
a16*b66 + 2*a16*b67 + 2*a17*b63 + 2*a17*b67 + 6*a18*b56 + 6*a18*b59 + 18*a18*
b60 - 2*a20*b49 - 2*a20*b50 + 4*a21*b46 + 2*a3*b70 + 2*a4*b63 + 4*a8*b49,
a9*b45 + a9*b46 - 2* a9*b6 - 3* a9*b7 - 24*a10*b2 - 12*a10*b3 - a14*b23 - 2*
a15*b22 - a15*b23 - 2*a16*b18 - a16*b19 - 3*a16*b20 - 4*a17*b18 - 6*a17*b20 -
12*a18*b12 - 36*a18*b14 + 12*a1*b26 + 18*a1*b27 + 2*a2*b22 + 2*a2*b23 + 2*a2*
b25 + 2*a3*b23 + 2*a3*b25 - 2*a7* b9 + 2*a7*b49 + 4*a7*b50 + 6*a7*b51 + 2*a8*
b46 - 2*a8*b6,
2* a9* b9 - a9*b50 - 3* a9*b51 + 2* a9*b8 - 2*a10*b46 + 12*a10*b5 + 2*a10*b6 +
a14*b27 + 2*a15*b26 + a15*b27 + 2*a16*b25 + a17*b23 + 4*a17*b25 + 2*a18*b18 +
3*a18*b19 + 9*a18*b20 - 24*a1*b28 - 2*a2*b26 - 6*a2*b27 - 2*a3*b27 - a4*b23 - 2
*a4*b25 + 4*a7*b10 - 2*a7*b52 - 8*a7*b53 - 2*a8*b51 + 2*a8*b8,
3* a9*b48 + 12*a10*b42 + 2*a10*b43 - 18*a12*b71 - 4*a13*b26 - 3*a13*b27 + 2*a13
*b70 + a14*b70 - 4*a15*b68 - 2*a15*b70 - 2*a16*b21 - a16*b23 + a16*b65 + 2*a16*
b66 + 2*a16*b67 - a17*b63 + 2*a17*b67 - 3*a18*b16 + 3*a18*b56 + 3*a18*b59 + 9*
a18*b60 - 2*a20*b48 - a20*b50 + 6*a21*b47 + 2*a2*b70 + a4*b63 + 4*a8*b48,
2* a9*b21 + 2* a9*b22 - a9*b62 - a9*b63 - a9*b66 + 12*a10*b15 + 4*a11*b6 +
a14*b33 + 4*a16*b29 + 4*a17*b29 - 24*a1*b34 + a19*b23 + a20*b23 + 2*a21*b17 + 2
*a21*b18 + 2*a21*b19 + 6*a21*b20 - 4*a2*b32 - 2*a2*b33 - 2*a3*b33 - 2*a4*b29 +
2*a6*b26 - 2*a6*b68 - 4*a6*b69 - 2*a7*b68 - 4*a7*b70 + 2*a8*b21 - a8*b23 - 2*a8
*b66,
a9*b46 - 9* a9*b5 - 3* a9*b6 - 48*a10*b2 - 6*a10*b3 - 2*a14*b24 - a14*b25 -
a15*b23 - 2*a15*b24 - 2*a16*b19 - 2*a17*b17 - a17*b18 - 6*a17*b19 - 12*a18*b12
- 9*a18*b13 + 6*a1*b26 + 27*a1*b27 + 3*a2*b23 + 8*a2*b24 + 4*a2*b25 + 4*a3*b24
+ 2*a3*b25 + 2*a4*b17 + a4*b18 + 2*a4*b19 - 4*a6* b9 + 2*a6*b50 + 6*a6*b51 - 2*
a7* b9 + a7*b50 - 6*a8*b5,
6*a10*b42 + 4*a10*b43 - 18*a12*b71 - 6*a13*b26 + 2*a13*b68 - a14*b68 - 3*a15*
b68 - 2*a16*b21 - 2*a16*b22 + 2*a16*b61 + a16*b62 + a16*b63 + 3*a16*b64 + 3*a16
*b67 + 18*a18*b55 + 18*a18*b60 - 2*a19*b48 - 2*a19*b49 - 2*a20*b48 - 2*a20*b49
- 2*a21*b43 + a21*b44 + a21*b46 - a21*b6 + 2*a2*b68 + 2*a3*b68 + 6*a4*b61 + 2*
a8*b48 + 2*a8*b49,
3* a9* b9 - 2* a9*b49 - 2* a9*b50 - 2*a10*b45 + 12*a10*b5 + 8*a10*b6 + 6*a10*b7
+ 2*a14*b26 + 2*a16*b23 + 2*a16*b24 + 2*a16*b25 + 2*a17*b22 + 2*a17*b23 + 2*
a17*b25 + 6*a18*b17 + 6*a18*b18 + 6*a18*b19 + 18*a18*b20 - 72*a1*b28 - 8*a2*b26
- 6*a2*b27 - 4*a3*b26 - 3*a3*b27 - 2*a4*b22 + 12*a5*b16 - 6*a6*b52 - 6*a7*b52
- 12*a7*b53 + 4*a8* b9 - 2*a8*b50,
2* a9*b21 + 2* a9*b22 - a9*b62 - a9*b63 - a9*b64 - a9*b67 + 12*a10*b15 - 4*
a11*b46 + 4*a11*b6 + a14*b33 + 4*a15*b32 + a15*b33 + 4*a16*b30 + 4*a17*b30 - 24
*a1*b34 + a19*b23 + a20*b23 + 4*a21*b18 + a21*b19 + 9*a21*b20 - 4*a2*b32 - 2*a2
*b33 - 2*a3*b33 - 2*a4*b30 + 2*a7*b26 - 4*a7*b68 - 4*a7*b69 - 4*a7*b70 + 2*a8*
b21 - a8*b23 - 2*a8*b64 - 2*a8*b67,
2* a9*b26 - 4* a9*b68 - 2* a9*b69 - 2* a9*b70 + 8*a10*b21 + 4*a10*b22 + a10*b23
- 2*a10*b62 - 2*a10*b63 + 8*a11* b9 - 4*a11*b50 + 4*a14*b34 + 4*a16*b33 + 4*
a17*b32 + 2*a17*b33 + 6*a18*b29 + 6*a18*b30 + 6*a18*b31 + 2*a19*b26 + 2*a20*b26
+ 4*a21*b23 + 2*a21*b24 + 6*a21*b25 - 16*a2*b34 - 8*a3*b34 - 4*a4*b32 - 2*a4*
b33 - 6*a6*b71 - 18*a7*b71 - 2*a8*b69 - 2*a8*b70,
2* a9*b43 + a9*b44 + 2* a9*b45 - 2* a9*b6 - 48*a10*b2 - 12*a10*b3 - 16*a10*b4
- 2*a13*b23 - 2*a14*b21 - a14*b23 - 2*a16*b16 - 2*a16*b17 - 2*a16*b18 - 3*a16*
b19 - 9*a16*b20 - 2*a17*b16 - 2*a17*b18 - 6*a17*b20 - 18*a18*b13 - 72*a18*b14 +
36*a1*b26 + 18*a1*b27 + 4*a2*b21 + 8*a2*b22 + 2*a2*b23 + 4*a3*b21 - 4*a4*b16 +
4*a6*b48 + 4*a6*b49 + 4*a7*b48 + 4*a7*b49 + 6*a7*b50 + 2*a8*b44 - 6*a8*b6
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 *a2*u + u *a3 + u *f(v,v)*a8 + u *a4*u + f(v ,v )*a6
t 3x 2x x x x x x
2 2 4
+ f(v,v )*a7 + f(v,v )* a9*u + f(v,v) *a11 + f(v,v)*a10*u + a5*u
2x x
v = u *a13*v + u *v *a14 + u *a16*u*v + v *a12 + v *a15*u + v *f(v,v)*a19
t 2x x x x 3x 2x x
2 3
+ v *a17*u + f(v,v )*a20*v + f(v,v)*a21*u*v + a18*u *v
x x
For any solution of the above algebraic conditions for the
a's and b's this system has the following symmetry:
2 2
u = u *b1 + u *b2*u + u *u *b3 + u *f(v,v)*b15 + u *b5*u + u *b4
t 5x 4x 3x x 3x 3x 2x
3 3
+ u *u *b6*u + u *f(v,v )*b16 + u *f(v,v)*b21*u + u *b8*u + u *b7
2x x 2x x 2x 2x x
2 2 2
+ u *f(v,v)*b22 + u * b9*u + u *f(v ,v )*b17 + u *f(v,v )*b18
x x x x x x 2x
2 2 4
+ u *f(v,v )*b23*u + u *f(v,v) *b32 + u *f(v,v)*b26*u + u *b10*u
x x x x x
+ f(v ,v )*b12 + f(v ,v )*b13 + f(v ,v )*b19*u
2x 2x x 3x x 2x
2
+ f(v ,v )*f(v,v)*b29 + f(v ,v )*b24*u + f(v,v )*b14 + f(v,v )*b20*u
x x x x 4x 3x
2 2
+ f(v,v )*f(v,v)*b30 + f(v,v )*b25*u + f(v,v ) *b31
2x 2x x
3 3 2 2
+ f(v,v )*f(v,v)*b33*u + f(v,v )*b27*u + f(v,v) *b35 + f(v,v) *b34*u
x x
4 6
+ f(v,v)*b28*u + b11*u
v = u *b37*v + u *v *b38 + u *b42*u*v + u *u *b43*v + u *v *b39
t 4x 3x x 3x 2x x 2x 2x
2 2
+ u *v *b44*u + u *f(v,v)*b61*v + u *b48*u *v + u *v *b45
2x x 2x 2x x x
2
+ u *b49*u*v + u *v *b40 + u *v *b46*u + u *v *f(v,v)*b62
x x 3x x 2x x x
2 3
+ u *v *b50*u + u *f(v,v )*b63*v + u *f(v,v)*b68*u*v + u *b52*u *v
x x x x x x
2
+ v *b36 + v *b41*u + v *f(v,v)*b55 + v *b47*u + v *f(v,v )*b56
5x 4x 3x 3x 2x x
3
+ v *f(v,v)*b64*u + v *b51*u + v *f(v ,v )*b57 + v *f(v,v )*b58
2x 2x x x x x 2x
2 2 4
+ v *f(v,v )*b65*u + v *f(v,v) *b72 + v *f(v,v)*b69*u + v *b53*u
x x x x x
+ f(v ,v )*b59*v + f(v ,v )*b66*u*v + f(v,v )*b60*v
x 2x x x 3x
2
+ f(v,v )*b67*u*v + f(v,v )*f(v,v)*b73*v + f(v,v )*b70*u *v
2x x x
2 3 5
+ f(v,v) *b74*u*v + f(v,v)*b71*u *v + b54*u *v