Problem l21o35
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 |
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Unknowns
All solutions for the following 52 unknowns have to be determined:
a1, ..., a12, b1, ..., b40
Inequalities
Each of the following lists represents one inequality which states
that not all unknowns in this list may vanish. These inequalities
filter out solutions which are trivial for the application.
{a1,a4,a8},
{a5,a3,a4,a7,a6},
{a9,a10},
{b1,b7,b23},
{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}
Equations
All comma separated 162 expressions involving 1678 terms have to vanish.
All terms are products of one a- and one b-unknown.
5*a10*b23 - 3*a8*b27,
3*a1*b2 - 5*a2*b1,
3*a1*b3 - 10*a2*b1,
2*a1*b4 - a2*b2,
4*a1*b4 - a2*b3,
5*a11*b23 - 3*a8*b30,
a10*b15 - 2*a6*b29,
a6*b28 - a9*b15,
a4*b24 - a9*b7,
a7*b36 - a9*b22,
2*a10*b27 + a2*b27 - 6*a8*b29,
a10*b29 + a10*b4 - 2*a2*b29,
a1*b2 + a1*b3 - 5*a2*b1,
a10*b28 - 2*a2*b28 + 2*a9*b4,
6*a11*b27 + a6*b27 - 6*a8*b37,
a4*b28 + a6*b24 - a9*b13,
2*a5*b28 + a6*b28 - 2*a9*b14,
a6*b36 + a7*b28 - a9*b21,
a4*b36 + a7*b24 - a9*b18,
2*a5*b36 + a7*b28 - 4*a9*b20,
10*a10*b23 - 3*a8*b26 - 3*a8*b27 + 5*a9*b23,
2*a10*b26 + a2*b26 - 3*a8*b28 - 6*a8*b29,
a1*b24 - a8*b24 - a9*b1 + a9*b23,
3*a2*b24 - 3*a8*b28 + a9*b25 - a9*b3,
a10*b28 - a2*b28 - a9*b29 + a9*b4,
20*a11*b23 + 5*a12*b23 - 6*a8*b30 - 3*a8*b31,
a10*b7 - 5*a12*b23 - a4*b25 + 3*a8*b35,
3*a1*b14 - 3*a2*b8 + 3*a4*b28 - a9*b9,
a10*b15 - a2*b15 - a6*b29 + a6*b4,
a1*b7 - a4*b1 + a4*b23 - a8*b7,
6*a11*b30 + 2*a12*b30 + a7*b27 - 12*a8*b39,
a10*b22 + 2*a11*b40 - 4*a12*b39 - a7*b37,
3*a10*b30 - a11*b27 + a5*b27 - 3*a8*b37 + 2*a9*b30,
20*a11*b23 + 10*a12*b23 + a4*b27 - 3*a8*b31 - 3*a8*b33,
6*a11*b27 + 3*a12*b27 + a6*b26 - 6*a8*b37 - 3*a8*b38,
10*a11*b23 + 10*a12*b23 + a4*b26 - 3*a8*b33 - 3*a8*b35,
a10*b13 - 3*a12*b27 - 2*a4*b29 - a6*b25 + 3*a8*b38,
10*a12*b23 + 3*a3*b24 + a4*b24 - 3*a8*b34 - a9*b5,
3*a12*b27 + a3*b28 + 3*a6*b24 - 3*a8*b38 - a9*b12,
3*a1*b5 + a1*b6 - 10*a3*b1 - 5*a4*b1 - a8*b6,
3*a11*b31 + a12*b31 + a7*b26 - 12*a8*b39 - 3*a8*b40,
a10*b21 + 2*a11*b38 - 2*a12*b37 - a6*b37 - 2*a7*b29,
2*a11*b34 + 2*a12*b34 + 6*a7*b24 - 6*a8*b40 - a9*b17,
2*a11*b38 - 2*a12*b37 + a6*b38 + 2*a7*b28 - 2*a9*b21,
2*a11*b40 - 4*a12*b39 + 2*a7*b36 + a7*b38 - 4*a9*b22,
a1*b27 + 10*a10*b23 - 3*a8*b25 - 3*a8*b26 - a8*b27 + 10*a9*b23,
a1*b26 + 5*a10*b23 - 3*a8*b24 - 3*a8*b25 - a8*b26 + 10*a9*b23,
a10*b26 - 3*a10*b27 - a2*b26 + 3*a8*b28 + 6*a8*b29 - 3*a9*b27,
a1*b25 - a10*b1 + a10*b23 - 3*a8*b24 - a8*b25 + 5*a9*b23,
a1*b28 - a10*b24 + a2*b24 - a8*b28 - a9*b2 + a9*b27,
a1*b28 + 4*a2*b24 - 4*a8*b28 - a9*b2 + a9*b26 - a9*b3,
a10*b14 + 2*a11*b28 + 2*a11*b29 - a2*b37 - 2*a5*b29 - 2*a9*b37,
a11*b28 + a12*b28 - a2*b36 - a5*b28 + a9*b14 - 2*a9*b36,
5*a12*b23 + a3*b24 + 3*a4*b24 - 3*a8*b35 - a9*b6 - a9*b7,
3*a1*b14 - 3*a2*b8 + 4*a4*b28 + 2*a5*b24 - a9*b11 - 2*a9*b8,
3*a1*b15 - a10*b12 + a2*b12 + a3*b29 - a3*b4 - 3*a6*b2,
a1*b6 + 3*a1*b7 - a3*b1 + a3*b23 - 5*a4*b1 - a8*b6,
6*a11*b30 + 3*a12*b30 + a12*b31 + a7*b26 - 12*a8*b39 - 3*a8*b40,
a10*b20 - a10*b39 + 2*a11*b36 + a11*b37 - a5*b37 - 4*a9*b39,
a11*b36 + a12*b36 - a5*b36 + a9*b20 - a9*b39 - a9*b40,
a11*b22 + a12*b22 - a5*b22 + a7*b20 - a7*b39 - a7*b40,
a10*b25 + a10*b26 - a10*b3 + 3*a2*b25 - 9*a8*b28 - 6*a8*b29 + 2*a9*b26,
60*a11*b23 + 30*a12*b23 + a3*b27 - 6*a8*b30 - 9*a8*b31 - 6*a8*b32 - 3*a8*b33,
3*a10*b30 - a11*b26 + a5*b26 - 3*a8*b36 - 3*a8*b37 + 3*a9*b30 + a9*b31,
30*a11*b23 + 30*a12*b23 + a3*b26 - 3*a8*b31 - 6*a8*b32 - 3*a8*b33 - 3*a8*b34,
a10*b12 - 6*a11*b27 - 9*a12*b27 - 2*a3*b29 - 3*a6*b25 + 6*a8*b37 + 9*a8*b38,
15*a12*b23 + 4*a3*b24 + 3*a4*b24 - 3*a8*b34 - 3*a8*b35 - a9*b5 - a9*b6,
3*a12*b27 + a3*b28 + a4*b28 + 4*a6*b24 - 3*a8*b38 - a9*b12 - a9*b13,
a1*b5 + 3*a1*b6 + 3*a1*b7 - 6*a3*b1 + a3*b23 - 10*a4*b1 - a8*b5,
a10*b18 + 2*a11*b35 - 3*a12*b30 - a12*b33 - a4*b37 - a7*b25 + 3*a8*b40,
3*a12*b30 - a12*b34 + 3*a12*b35 + a3*b36 + 3*a7*b24 - 3*a8*b40 - a9*b16,
6*a11*b35 - a12*b31 + a12*b34 + 3*a12*b35 + 6*a7*b24 - 6*a8*b40 - a9*b19,
2*a1*b29 - a10*b2 - a10*b25 + a10*b27 + a2*b25 - 3*a8*b28 - 2*a8*b29 + 3*a9*b27
,
3*a10*b31 + 4*a11*b26 + 2*a5*b26 + a6*b26 - 6*a8*b36 - 12*a8*b37 - 3*a8*b38 + 2
*a9*b31,
a10*b6 - 10*a11*b23 - 25*a12*b23 - a3*b25 - 2*a4*b25 + 3*a8*b33 + 3*a8*b34 + 6*
a8*b35,
a1*b36 - a11*b24 - a12*b24 + a5*b24 - a8*b36 + a9*b30 + a9*b35 - a9*b8,
a10*b36 + a11*b28 + a12*b28 - a2*b36 - a5*b28 + a9*b14 - a9*b37 - a9*b38,
2*a12*b28 + 2*a12*b29 - a2*b38 - 2*a5*b28 - 2*a6*b28 + 2*a9*b14 + 2*a9*b15 - 2*
a9*b38,
6*a1*b8 - a10*b7 + a3*b24 + 3*a4*b24 + a4*b25 - 10*a5*b1 - a9*b6 - 5*a9*b7,
6*a1*b8 + 3*a1*b9 - a10*b6 + 2*a3*b24 + a3*b25 - 20*a5*b1 - 5*a6*b1 - 4*a9*b6,
3*a1*b14 + 3*a1*b15 - a10*b10 + a3*b28 + a3*b29 - a5*b3 - a6*b3 - a9*b10,
4*a1*b5 + 3*a1*b6 + a1*b7 - 15*a3*b1 - 11*a4*b1 + a4*b23 - a8*b5 - a8*b7,
a1*b13 - a10*b7 + a2*b7 - a4*b2 + a4*b27 - a6*b1 + a6*b23 - a8*b13,
a1*b15 - a10*b13 + a2*b13 + a4*b29 - a4*b4 - a6*b2 + a6*b27 - a8*b15,
a10*b19 - 6*a11*b33 - 2*a12*b31 - 2*a12*b32 - 4*a12*b33 - 6*a7*b25 + 24*a8*b39
+ 18*a8*b40,
6*a11*b22 + 6*a12*b22 - 4*a5*b22 - a6*b22 + 2*a7*b20 + a7*b21 - 6*a7*b39 - 6*a7
*b40,
40*a11*b23 + 40*a12*b23 + a3*b26 + a4*b26 - 3*a8*b31 - 6*a8*b32 - 6*a8*b33 - 3*
a8*b34 - 3*a8*b35,
a10*b11 - 3*a10*b33 - 2*a12*b26 - 2*a5*b25 - 2*a6*b25 + 6*a8*b36 + 6*a8*b37 + 6
*a8*b38 - 2*a9*b33,
a10*b5 - 20*a11*b23 - 50*a12*b23 - 3*a3*b25 - a4*b25 + 6*a8*b32 + 3*a8*b33 + 9*
a8*b34 + 3*a8*b35,
a10*b34 + 6*a5*b24 + 3*a6*b24 - 6*a8*b36 - 3*a8*b38 - a9*b10 + a9*b32 + 2*a9*
b34 - a9*b9,
3*a10*b35 - a12*b27 + a4*b28 + 2*a5*b24 + 3*a6*b24 - 3*a8*b38 - a9*b11 - a9*b13
+ 2*a9*b35,
3*a1*b12 + a1*b13 - a10*b5 + a2*b5 - 3*a3*b2 - a4*b2 + a4*b27 - 10*a6*b1 - a8*
b13,
a10*b16 - 6*a11*b30 + 2*a11*b34 - 9*a12*b30 - 3*a12*b33 - a3*b37 - 3*a7*b25 +
12*a8*b39 + 9*a8*b40,
3*a12*b30 - a12*b34 + 3*a12*b35 + a3*b36 + a4*b36 + 4*a7*b24 - 3*a8*b40 - a9*
b16 - a9*b18,
2*a11*b34 + 6*a11*b35 - a12*b31 + 3*a12*b34 + 3*a12*b35 + 12*a7*b24 - 12*a8*b40
- a9*b17 - a9*b19,
2*a10*b21 + 2*a11*b15 + 2*a12*b15 - 2*a2*b21 + a6*b15 - 2*a6*b37 - 2*a6*b38 - 2
*a7*b29 + 2*a7*b4,
3*a1*b22 - a11*b16 - 3*a12*b18 - a3*b20 + a3*b39 + 3*a4*b40 + a5*b16 + a7*b34 -
3*a7*b8,
a1*b37 + a10*b30 - a10*b8 - 2*a11*b24 - a11*b25 + a5*b25 - 3*a8*b36 - a8*b37 +
3*a9*b30 + a9*b33,
a10*b10 - 3*a10*b32 - 2*a11*b26 - 2*a12*b26 - 2*a5*b25 - 2*a6*b25 + 6*a8*b36 +
6*a8*b37 + 6*a8*b38 - 2*a9*b32,
6*a1*b14 + 6*a1*b15 - 2*a10*b11 + a3*b28 + 3*a4*b28 + 6*a4*b29 + 2*a5*b26 - 2*
a5*b3 - 2*a6*b3 - 2*a9*b11,
2*a10*b14 + a10*b15 - 2*a2*b14 - a2*b15 - 2*a5*b29 + 2*a5*b4 - 2*a6*b28 - 2*a6*
b29 + 2*a6*b4 + 2*a9*b15,
a10*b17 - 2*a11*b31 - 4*a11*b32 - 2*a11*b33 - 2*a12*b31 - 4*a12*b32 - 2*a12*b33
- 6*a7*b25 + 24*a8*b39 + 18*a8*b40,
8*a11*b35 - 2*a12*b30 - a12*b33 + a12*b34 + 3*a12*b35 + a4*b38 + 8*a7*b24 - 6*
a8*b40 - 2*a9*b18 - a9*b19,
6*a1*b21 - a10*b17 - 2*a11*b12 - 2*a12*b12 + a2*b17 + 2*a3*b37 + 2*a3*b38 - a6*
b10 + a6*b32 - 6*a7*b2,
a10*b21 + a11*b15 + a12*b15 - a2*b21 - a5*b15 + a6*b14 - a6*b37 - a6*b38 - a7*
b29 + a7*b4,
a1*b18 - a11*b7 - a12*b7 + a4*b30 + a4*b35 - a4*b8 + a5*b7 - a7*b1 + a7*b23 -
a8*b18,
a10*b31 + a10*b33 - a10*b9 + 4*a5*b25 + a6*b25 - 12*a8*b36 - 6*a8*b37 - 3*a8*
b38 + 2*a9*b31 + 2*a9*b32 + 2*a9*b33,
3*a10*b35 - a12*b26 + 6*a5*b24 + 3*a6*b24 - 6*a8*b36 - 3*a8*b38 - a9*b11 + a9*
b33 + a9*b34 + 3*a9*b35 - a9*b9,
3*a10*b34 + 2*a12*b26 + a3*b28 + 6*a5*b24 + 9*a6*b24 - 6*a8*b36 - 9*a8*b38 - 2*
a9*b10 - a9*b11 - a9*b12 + 2*a9*b34,
6*a1*b8 + 3*a1*b9 - 5*a10*b7 + a3*b24 + 3*a4*b24 + 3*a4*b25 + a4*b26 - 20*a5*b1
- 5*a6*b1 - a9*b5 - 10*a9*b7,
6*a1*b10 + 3*a1*b11 + 3*a1*b12 + 3*a1*b9 - 3*a10*b5 + a3*b25 + a3*b26 - a3*b3 -
30*a5*b1 - 30*a6*b1 - 3*a9*b5,
4*a1*b12 + 3*a1*b13 - a10*b5 - a10*b6 + a2*b5 + a2*b6 - 4*a3*b2 + a3*b27 - 3*a4
*b2 - 15*a6*b1 - a8*b12,
a10*b22 + a11*b21 + a12*b21 - a2*b22 - a5*b21 + a6*b20 - a6*b39 - a6*b40 + a7*
b14 - a7*b37 - a7*b38,
a1*b22 - a11*b18 - a12*b18 - a4*b20 + a4*b39 + a4*b40 + a5*b18 + a7*b30 + a7*
b35 - a7*b8 - a8*b22,
2*a10*b22 + 2*a11*b21 + 2*a12*b21 - 2*a2*b22 - a5*b21 - 2*a6*b39 - 2*a6*b40 +
a7*b14 + a7*b15 - 2*a7*b37 - 2*a7*b38,
6*a1*b14 + 6*a1*b15 - a10*b12 - a10*b9 + a2*b9 + 2*a3*b28 + 2*a3*b29 - 6*a5*b2
- 3*a6*b2 + a6*b25 - a6*b3 - 2*a9*b12,
a1*b11 + 3*a1*b13 - 5*a10*b7 + a2*b7 + a4*b26 + 3*a4*b27 - a4*b3 - 2*a5*b1 + 2*
a5*b23 - 5*a6*b1 - a8*b11 - 2*a9*b7,
a1*b12 + 3*a1*b13 - a10*b6 - a10*b7 + a2*b6 + a2*b7 - a3*b2 + a3*b27 - 3*a4*b2
- 6*a6*b1 + a6*b23 - a8*b12,
4*a1*b15 - a10*b12 - a10*b13 + a2*b12 + a2*b13 + a3*b29 - a3*b4 + a4*b29 - a4*
b4 - 4*a6*b2 + a6*b27 - a8*b15,
a10*b40 - a11*b38 - 2*a12*b36 - a12*b37 - a12*b38 + 2*a5*b36 + a5*b38 + a6*b36
+ a7*b28 - 4*a9*b20 - a9*b21 + 4*a9*b40,
3*a1*b16 + a1*b18 - a11*b5 - 10*a12*b7 - 3*a3*b8 + a4*b30 + 3*a4*b34 + a4*b35 -
a4*b8 + a5*b5 - 10*a7*b1 - a8*b18,
3*a1*b21 - a10*b16 - a11*b12 - 3*a12*b13 + a2*b16 - a3*b14 + a3*b37 + 3*a4*b38
+ a5*b12 + a6*b34 - 3*a6*b8 - 3*a7*b2,
2*a1*b18 + 3*a1*b19 - 20*a11*b7 - a12*b5 - 10*a12*b7 - a4*b13 + 2*a4*b30 + 3*a4
*b31 + 3*a4*b33 + 2*a4*b35 - 20*a7*b1 - 2*a8*b18,
a10*b22 + 4*a11*b20 + 4*a12*b20 - a2*b22 - 2*a5*b20 - 2*a5*b39 - 2*a5*b40 + a7*
b14 - 6*a7*b36 - a7*b37 - a7*b38 + 6*a9*b22,
12*a1*b22 - 2*a11*b16 - a11*b17 - 2*a12*b16 - a12*b17 + 4*a3*b39 + 2*a3*b40 + 6
*a4*b40 + a5*b17 - a7*b10 + a7*b32 - 6*a7*b8,
48*a1*b22 - 8*a11*b19 - 2*a12*b17 - 6*a12*b19 + 8*a3*b40 + 48*a4*b39 + 24*a4*
b40 + a6*b19 - 2*a7*b11 + 2*a7*b31 + 2*a7*b33 - 6*a7*b9,
a1*b38 + a10*b35 - 2*a12*b24 - a12*b25 + 6*a5*b24 + a6*b24 - 6*a8*b36 - a8*b38
+ a9*b31 + a9*b34 + 3*a9*b35 - 2*a9*b8 - a9*b9,
6*a1*b14 - a10*b13 - 2*a10*b8 + 2*a2*b8 + a3*b28 + 3*a4*b28 + 2*a4*b29 - 6*a5*
b2 - a6*b2 + 2*a6*b24 + a6*b25 - a9*b12 - 3*a9*b13,
3*a1*b11 + 3*a1*b13 + a1*b9 - 10*a10*b7 + a4*b25 + 3*a4*b26 + 3*a4*b27 - a4*b3
- 10*a5*b1 - 10*a6*b1 - a8*b9 - a9*b6 - 5*a9*b7,
6*a11*b34 + 6*a11*b35 + 2*a12*b31 - 2*a12*b32 - a12*b33 + 3*a12*b34 + 9*a12*b35
+ a3*b38 + 24*a7*b24 - 24*a8*b40 - 2*a9*b16 - 2*a9*b17 - a9*b19,
6*a1*b16 + 9*a1*b17 + 3*a1*b19 - 6*a11*b5 - 6*a11*b6 - 3*a12*b5 - 12*a12*b6 -
a3*b10 + a3*b31 + 3*a3*b32 + a3*b33 + 2*a3*b34 - 90*a7*b1,
6*a1*b16 + 18*a1*b17 + 9*a1*b19 - 6*a11*b5 - 24*a11*b6 - 9*a12*b5 - 18*a12*b6 -
a3*b12 + 3*a3*b31 + 6*a3*b32 + 3*a3*b33 + 2*a3*b34 - 180*a7*b1,
6*a1*b21 - a10*b19 - 6*a11*b13 - a12*b12 - 3*a12*b13 + a2*b19 + a3*b38 + 6*a4*
b37 + 3*a4*b38 - a6*b11 + a6*b31 + a6*b33 - 6*a7*b2,
48*a1*b22 - 6*a11*b17 - 2*a11*b19 - 6*a12*b17 - 2*a12*b19 + 8*a3*b39 + 10*a3*
b40 + 24*a4*b39 + 18*a4*b40 + a6*b17 - 2*a7*b10 + 2*a7*b32 - 6*a7*b9,
6*a1*b10 + 3*a1*b11 + 6*a1*b8 + 9*a1*b9 - a10*b5 - 4*a10*b6 - a3*b2 + 2*a3*b24
+ 3*a3*b25 + a3*b26 - 60*a5*b1 - 30*a6*b1 - 3*a9*b5 - 6*a9*b6,
3*a1*b11 + 2*a1*b8 + 3*a1*b9 - 10*a10*b7 - a4*b2 + 2*a4*b24 + 3*a4*b25 + 3*a4*
b26 + a4*b27 - 20*a5*b1 - 10*a6*b1 - 2*a8*b8 - a9*b5 - 10*a9*b7,
18*a1*b14 + 6*a1*b15 - a10*b11 - a10*b9 - 2*a2*b9 + 3*a3*b28 + 9*a4*b28 + 6*a4*
b29 + 2*a5*b25 - 6*a5*b3 - a6*b3 - 2*a9*b10 - 2*a9*b11 - 2*a9*b9,
2*a1*b10 + 3*a1*b11 + 3*a1*b12 + 6*a1*b13 - 5*a10*b6 + a2*b6 + a3*b26 + 2*a3*
b27 - a3*b3 - 2*a4*b3 - 10*a5*b1 - 25*a6*b1 - 2*a8*b10 - 2*a9*b6,
4*a1*b16 + 3*a1*b18 - a11*b5 - a11*b6 - 15*a12*b7 + a3*b30 - 4*a3*b8 + 4*a4*b34
+ 3*a4*b35 - 3*a4*b8 + a5*b5 + a5*b6 - 15*a7*b1 - a8*b16,
6*a1*b18 + 4*a1*b19 - 30*a11*b7 - a12*b5 - a12*b6 - 15*a12*b7 + a3*b35 - a4*b11
+ 6*a4*b30 + 4*a4*b31 + 4*a4*b33 + 3*a4*b35 - 30*a7*b1 - a8*b19,
12*a1*b22 - 6*a11*b18 - a11*b19 - a12*b16 - 3*a12*b18 - a12*b19 + a3*b40 + 12*
a4*b39 + 9*a4*b40 + a5*b19 - a7*b11 + a7*b31 + a7*b33 - 6*a7*b8,
6*a1*b14 + 6*a1*b15 - 3*a10*b13 - a10*b9 + a2*b9 + a3*b28 + 3*a4*b28 + 6*a4*b29
- 6*a5*b2 - 3*a6*b2 + a6*b25 + a6*b26 - a6*b3 - a9*b12 - 3*a9*b13,
6*a1*b10 + 4*a1*b11 + 9*a1*b12 + 3*a1*b13 - 5*a10*b5 + a2*b5 + a3*b26 + a3*b27
- 3*a3*b3 + a4*b26 - a4*b3 - 20*a5*b1 - 50*a6*b1 - a8*b11 - 2*a9*b5,
12*a1*b20 - a10*b18 - 2*a11*b8 - 2*a12*b8 + a3*b36 + 9*a4*b36 + a4*b37 + a4*b38
- 4*a5*b8 - a7*b2 + 4*a7*b24 + a7*b25 - a9*b16 - 3*a9*b18 - a9*b19,
24*a1*b20 + 6*a1*b21 - a10*b19 - 2*a11*b9 - 2*a12*b9 + 4*a3*b36 + a3*b38 + 12*
a4*b36 + 6*a4*b37 + 3*a4*b38 - 4*a5*b9 + 2*a7*b25 - 2*a7*b3 - 2*a9*b17 - 2*a9*
b19,
a1*b16 + 3*a1*b18 - a11*b6 - a11*b7 - 6*a12*b7 + a3*b30 - a3*b8 + a4*b34 + 3*a4
*b35 - 3*a4*b8 + a5*b6 + a5*b7 - 6*a7*b1 + a7*b23 - a8*b16,
a1*b17 + 6*a1*b18 + 3*a1*b19 - 2*a11*b6 - 20*a11*b7 - 5*a12*b6 - 5*a12*b7 + a3*
b33 + 2*a3*b35 - a4*b10 + 6*a4*b30 + 3*a4*b31 + a4*b32 - 30*a7*b1 - a8*b17,
6*a1*b18 + a1*b19 - 12*a11*b7 - a12*b6 - 7*a12*b7 + a3*b35 + 6*a4*b30 + a4*b31
+ a4*b33 + 3*a4*b35 - a4*b9 + a6*b7 - 12*a7*b1 + 2*a7*b23 - a8*b19,
a1*b21 - a10*b18 - a11*b13 - a12*b13 + a2*b18 - a4*b14 + a4*b37 + a4*b38 + a5*
b13 + a6*b30 + a6*b35 - a6*b8 - a7*b2 + a7*b27 - a8*b21,
6*a1*b14 + 18*a1*b15 - 2*a10*b10 - a10*b11 - 3*a10*b12 + 2*a2*b10 + a2*b11 + a2
*b12 + 2*a3*b28 + 6*a3*b29 - 2*a3*b4 - 6*a5*b2 - 9*a6*b2 + a6*b26 - 3*a6*b3 - 2
*a9*b12,
12*a1*b20 + 3*a1*b21 - a10*b16 - a11*b9 - a12*b9 + 2*a3*b36 + a3*b37 + 6*a4*b36
+ 3*a4*b38 - 6*a5*b8 + a5*b9 - 3*a6*b8 + a7*b25 - a7*b3 - 2*a9*b16 - a9*b17,
4*a10*b20 + a10*b21 + 2*a11*b14 + 2*a12*b14 - 4*a2*b20 - a2*b21 - 2*a5*b37 - 2*
a5*b38 + a6*b14 - 4*a6*b36 - a6*b37 - a6*b38 - 4*a7*b28 - 2*a7*b29 + 2*a7*b4 +
4*a9*b21,
6*a1*b16 + 6*a1*b17 + 6*a1*b19 - 6*a11*b5 - 30*a11*b7 - 6*a12*b5 - 30*a12*b7 -
a3*b11 + a3*b31 + a3*b33 + a3*b34 + 3*a4*b31 + 6*a4*b32 + 3*a4*b33 + 3*a4*b34 -
90*a7*b1,
4*a1*b22 - a11*b16 - a11*b18 - 4*a12*b18 - a3*b20 + a3*b39 - a4*b20 + a4*b39 +
4*a4*b40 + a5*b16 + a5*b18 + a7*b30 + a7*b34 + a7*b35 - 4*a7*b8 - a8*b22,
2*a1*b14 + 6*a1*b15 - a10*b11 - 3*a10*b13 + a2*b11 + a2*b13 + 2*a4*b28 + 6*a4*
b29 - 2*a4*b4 - 2*a5*b2 + 2*a5*b27 - 3*a6*b2 + a6*b26 + a6*b27 - a6*b3 - 2*a8*
b14 - 2*a9*b13,
6*a1*b10 + 6*a1*b11 + 3*a1*b12 + 3*a1*b13 + 4*a1*b9 - a10*b5 - 6*a10*b6 + a3*
b25 + 2*a3*b26 + a3*b27 - a3*b3 + a4*b25 - a4*b3 - 40*a5*b1 - 40*a6*b1 - a8*b9
- 2*a9*b5 - 4*a9*b6,
12*a1*b20 + 3*a1*b21 - 3*a10*b18 - a11*b9 - a12*b9 + a3*b36 + 9*a4*b36 + 3*a4*
b37 + 3*a4*b38 - 6*a5*b8 + a5*b9 - 3*a6*b8 + a7*b25 + a7*b26 - a7*b3 - a9*b16 -
3*a9*b18 - a9*b19,
6*a1*b16 + 10*a1*b17 + 6*a1*b18 + 6*a1*b19 - 2*a11*b5 - 20*a11*b6 - 2*a12*b5 -
20*a12*b6 - a3*b10 + 2*a3*b30 + 2*a3*b31 + 3*a3*b32 + 2*a3*b33 + 2*a3*b34 + 2*
a3*b35 - a4*b10 + a4*b32 - 120*a7*b1 - a8*b17,
12*a1*b21 - a10*b17 - a10*b19 - 2*a11*b12 - 6*a11*b13 - 3*a12*b12 - 3*a12*b13 +
a2*b17 + a2*b19 + 2*a3*b37 + 3*a3*b38 + 6*a4*b37 + 3*a4*b38 - a6*b10 - a6*b11
+ a6*b31 + a6*b32 + a6*b33 - 12*a7*b2,
12*a1*b20 + 9*a1*b21 - 3*a10*b16 - 2*a11*b10 - a11*b11 - 3*a12*b11 + a2*b16 -
a3*b14 + 2*a3*b36 + 3*a3*b37 + 6*a4*b36 + 9*a4*b38 + 2*a5*b10 + a5*b11 + 2*a5*
b34 - 6*a5*b8 - 9*a6*b8 + a7*b26 - 3*a7*b3 - 4*a9*b16,
24*a1*b20 + 18*a1*b21 - 3*a10*b17 - 4*a11*b10 - 2*a11*b11 - 4*a12*b10 - 2*a12*
b11 + a2*b17 + 6*a3*b36 + 4*a3*b37 + 4*a3*b38 + 6*a4*b36 + 6*a4*b37 + 6*a4*b38
- 2*a5*b10 + 2*a5*b32 - 2*a5*b9 - 2*a6*b9 - 6*a7*b3 - 4*a9*b17,
4*a1*b20 + 3*a1*b21 - 3*a10*b18 - a11*b11 - a12*b11 + a2*b18 - a4*b14 + 4*a4*
b36 + 3*a4*b37 + 3*a4*b38 + a5*b11 + 2*a5*b30 + 2*a5*b35 - 2*a5*b8 - 3*a6*b8 +
a7*b26 + a7*b27 - a7*b3 - 4*a8*b20 - 4*a9*b18,
24*a1*b20 + 18*a1*b21 - 3*a10*b19 - 6*a11*b11 - 2*a12*b10 - 4*a12*b11 + a2*b19
+ 4*a3*b36 + 3*a3*b38 + 12*a4*b36 + 18*a4*b37 + 9*a4*b38 - 2*a5*b11 + 2*a5*b31
+ 2*a5*b33 - 2*a5*b9 - 2*a6*b9 + 2*a7*b26 - 6*a7*b3 - 4*a9*b19,
8*a1*b21 - 2*a10*b18 - a10*b19 - 8*a11*b13 - a12*b12 - 5*a12*b13 + 2*a2*b18 +
a2*b19 + a3*b38 - 2*a4*b15 + 8*a4*b37 + 5*a4*b38 + 2*a6*b30 + a6*b31 + a6*b33 +
2*a6*b35 - a6*b9 - 8*a7*b2 + 2*a7*b27 - 2*a8*b21,
6*a1*b16 + 2*a1*b17 + 12*a1*b18 + 3*a1*b19 - 10*a11*b6 - 10*a11*b7 - 7*a12*b6 -
25*a12*b7 + 4*a3*b30 + a3*b31 + a3*b34 + 2*a3*b35 - a3*b9 + 2*a4*b32 + 3*a4*
b33 + 3*a4*b34 + 6*a4*b35 - 2*a4*b9 + a6*b6 - 60*a7*b1 - 2*a8*b17,
24*a1*b22 - 2*a11*b16 - a11*b17 - 6*a11*b18 - a11*b19 - 3*a12*b16 - a12*b17 - 3
*a12*b18 - a12*b19 + 4*a3*b39 + 3*a3*b40 + 12*a4*b39 + 15*a4*b40 + a5*b17 + a5*
b19 - a7*b10 - a7*b11 + a7*b31 + a7*b32 + a7*b33 - 12*a7*b8,
16*a1*b22 - 10*a11*b18 - a11*b19 - a12*b16 - 7*a12*b18 - a12*b19 + a3*b40 - a4*
b21 + 16*a4*b39 + 13*a4*b40 + 2*a5*b18 + a5*b19 + a6*b18 - a7*b13 + 4*a7*b30 +
a7*b31 + a7*b33 + 4*a7*b35 - 8*a7*b8 - a7*b9 - 4*a8*b22,
4*a1*b21 - a10*b16 - a10*b18 - a11*b12 - a11*b13 - 4*a12*b13 + a2*b16 + a2*b18
- a3*b14 + a3*b37 - a4*b14 + a4*b37 + 4*a4*b38 + a5*b12 + a5*b13 + a6*b30 + a6*
b34 + a6*b35 - 4*a6*b8 - 4*a7*b2 + a7*b27 - a8*b21,
2*a1*b16 + 6*a1*b17 + 6*a1*b18 + 12*a1*b19 - 2*a11*b5 - 8*a11*b6 - 60*a11*b7 -
6*a12*b5 - 6*a12*b6 - 30*a12*b7 - a3*b13 + a3*b31 + 3*a3*b33 + 2*a3*b35 - a4*
b12 + 6*a4*b30 + 9*a4*b31 + 6*a4*b32 + 3*a4*b33 + 2*a4*b34 - 120*a7*b1 - 2*a8*
b16,
24*a1*b21 - 2*a10*b16 - 2*a10*b17 - a10*b19 - 6*a11*b12 - 6*a11*b13 - 5*a12*b12
- 9*a12*b13 + 2*a2*b16 + 2*a2*b17 + a2*b19 - 2*a3*b15 + 6*a3*b37 + 5*a3*b38 +
6*a4*b37 + 9*a4*b38 + a6*b31 + 2*a6*b32 + a6*b33 + 2*a6*b34 - 3*a6*b9 - 24*a7*
b2,
18*a1*b16 + 6*a1*b17 + 6*a1*b18 + 4*a1*b19 - 10*a11*b5 - 20*a11*b7 - 2*a12*b5 -
10*a12*b6 - 50*a12*b7 + 2*a3*b30 + a3*b31 + 3*a3*b34 + a3*b35 - 3*a3*b9 + a4*
b31 + 6*a4*b32 + 4*a4*b33 + 9*a4*b34 + 3*a4*b35 - a4*b9 + a6*b5 - 120*a7*b1 -
a8*b19,
6*a1*b16 + 6*a1*b17 + 6*a1*b18 + 10*a1*b19 - 2*a11*b5 - 12*a11*b6 - 40*a11*b7 -
6*a12*b5 - 4*a12*b6 - 40*a12*b7 - a3*b11 + 2*a3*b30 + 2*a3*b31 + a3*b33 + a3*
b34 + a3*b35 - a4*b11 + 4*a4*b31 + 6*a4*b32 + 7*a4*b33 + 3*a4*b34 + 3*a4*b35 -
120*a7*b1 - a8*b19,
48*a1*b22 - 8*a11*b16 - 2*a11*b17 - 6*a11*b18 - a11*b19 - 7*a12*b16 - 9*a12*b18
- 3*a12*b19 - a3*b21 + 12*a3*b39 + 5*a3*b40 + 12*a4*b39 + 33*a4*b40 + 2*a5*b16
+ 2*a5*b17 + a5*b19 + a6*b16 - a7*b12 + a7*b31 + 2*a7*b32 + a7*b33 + 4*a7*b34
- 24*a7*b8 - 3*a7*b9
Relevance
In the following evolutionary system u=u(t,x) is a scalar function,
v=v(t,x) is a vector function and f(..,..) stands for the scalar
product of both vector arguments of f.
u = u *a1 + u *f(v,v)*a5 + u *a2*u + f(v ,v )*a3 + f(v,v )*a4
t 3x x x x 2x 3x
+ f(v,v )*f(v,v)*a7 + f(v,v )*a6*u,
x x
v = u *a9*v + v *a8 + v *f(v,v)*a11 + v *a10*u + f(v,v )*a12*v
t x 3x x x x
For any solution of the above algebraic conditions for the
a's and b's this system has the following symmetry:
u = u *b1 + u *f(v,v)*b8 + u *b2*u + u *u *b3 + u *f(v,v )*b9
t 5x 3x 3x 2x x 2x x
2
+ u *f(v ,v )*b10 + u *f(v,v )*b11 + u *f(v,v) *b20 + u *f(v,v)*b14*u
x x x x 2x x x
2
+ u *b4*u + f(v ,v )*b5 + f(v ,v )*b6 + f(v ,v )*f(v,v)*b16
x 2x 3x x 4x x 2x
+ f(v ,v )*b12*u + f(v ,v )*f(v,v )*b17 + f(v,v )*b7
x 2x x x x 5x
+ f(v,v )*f(v,v)*b18 + f(v,v )*b13*u + f(v,v )*f(v,v )*b19
3x 3x 2x x
2 2
+ f(v,v )*f(v,v) *b22 + f(v,v )*f(v,v)*b21*u + f(v,v )*b15*u ,
x x x
v = u *b24*v + u *v *b25 + u *v *b26 + u *f(v,v)*b36*v + u *b28*u*v
t 3x 2x x x 2x x x
+ v *b23 + v *f(v,v)*b30 + v *b27*u + v *f(v,v )*b31
5x 3x 3x 2x x
2
+ v *f(v ,v )*b32 + v *f(v,v )*b33 + v *f(v,v) *b39 + v *f(v,v)*b37*u
x x x x 2x x x
2
+ v *b29*u + f(v ,v )*b34*v + f(v,v )*b35*v + f(v,v )*f(v,v)*b40*v
x x 2x 3x x
+ f(v,v )*b38*u*v
x