Problem l1323o24
Unknowns | Inequalities |
Equations |
Relevance |
Back to overview
Unknowns
All solutions for the following 64 unknowns have to be determined:
a1, ..., a10, b1, ..., b54
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,a6},
{a4,a5},
{a7,a8,a10,a9},
{b1,b23}
{b11,b12,b13,b19,b16,b9,b14,b10,b15,b20,b17,b22,b21,b18},
{b24,b25,b26,b38,b31,b27,b28,b39,b32,b29,b40,b33,b41,b50,b46,
b35,b30,b42,b34,b43,b51,b47,b36,b44,b45,b52,b48,b53,b49,b37}
Equations
All comma separated 215 expressions involving 1462 terms have to vanish.
All terms are products of one a- and one b-unknown.
a3*b30,
a3*b34,
a3*b2,
a3*b5,
a3*b8,
a5*b30,
a6*b51,
a4*b50,
a4*b22 - 8*a4*b54,
a10*b22 - 2*a10*b54,
a10*b42 + a5*b42,
a1*b50 - a6*b50,
a6*b30 - 2*a8*b23,
3*a3*b36 - a8*b8,
a1*b2 - 2*a2*b1,
a1*b3 - 15*a2*b1,
a2*b8 - 3*a3*b7,
2*a3*b37 - a9*b8,
2*a10*b23 - a6*b42,
a4*b24 - a7*b10,
a4*b42 - 4*a6*b51,
a4*b40 - 2*a6*b52,
a4*b39 - a6*b52,
2*a10*b10 - a4*b38,
a4*b51 - 12*a6*b54,
a4*b50 - 6*a6*b54,
a4*b52 - 24*a6*b54,
3*a10*b22 - a5*b22 - a5*b54,
3*a1*b2 + 2*a1*b3 - 30*a2*b1,
4*a1*b5 - 3*a2*b2 - 56*a3*b1,
2*a1*b3 + 3*a1*b4 - 45*a2*b1,
2*a1*b6 - 9*a2*b2 - 126*a3*b1,
a1*b3 + 3*a1*b4 - 30*a2*b1,
26*a1*b8 - 7*a3*b5 - 2*a3*b6,
8*a10*b23 + 3*a4*b30 - 4*a6*b42,
6*a10*b23 - a6*b40 - a6*b42,
12*a10*b23 + a4*b29 - 2*a6*b43,
a3*b42 + 3*a5*b34 + a9*b42,
a1*b51 - 2*a6*b50 - a6*b51,
a4*b40 - 4*a6*b51 - 2*a6*b52,
a4*b43 - 4*a6*b51 - 2*a6*b52,
a4*b39 - 2*a6*b50 - a6*b52,
a4*b41 - 8*a6*b50 - 4*a6*b52,
2*a10*b9 - 3*a4*b38 + 2*a6*b52,
a4*b41 + 2*a4*b44 - 6*a6*b52,
a4*b41 + 2*a4*b45 - 4*a6*b52,
4*a10*b51 + a5*b51 - 3*a8*b22,
2*a6*b29 + 3*a6*b30 - 4*a7*b23 - 18*a8*b23,
a2*b30 - 4*a6*b34 + 2*a8*b30 + 8*a9*b23,
a6*b28 + a6*b29 - 6*a7*b23 - 12*a8*b23,
2*a2*b34 + 3*a3*b29 - 6*a6*b36 + 6*a9*b30,
6*a1*b7 - 2*a2*b5 - 42*a3*b2 - 3*a3*b3,
a1*b24 - a6*b24 - a7*b1 + a7*b23,
a1*b25 - 3*a6*b25 - 6*a6*b27 + 30*a7*b23,
a1*b42 + 6*a10*b23 - a6*b40 - a6*b42,
12*a10*b23 + a4*b29 - 2*a6*b42 - 2*a6*b43,
3*a10*b30 + 3*a4*b34 + a5*b29 - 2*a6*b47,
a1*b40 + 8*a10*b23 - 2*a6*b38 - a6*b40,
8*a10*b23 + a4*b26 - 2*a6*b45 - 3*a8*b10,
5*a3*b47 + 9*a5*b36 - 3*a8*b18 + 2*a9*b47,
a1*b38 - 2*a10*b1 + 2*a10*b23 - a6*b38,
a1*b39 + 4*a10*b23 - a6*b38 - a6*b39,
a1*b38 + 6*a10*b23 - a6*b38 - 2*a6*b39,
24*a10*b23 + 3*a4*b27 - 2*a6*b41 - 2*a6*b45,
16*a10*b23 + a4*b25 - 4*a6*b45 - 2*a7*b10,
6*a10*b23 + 3*a4*b24 - 2*a6*b44 - a7*b9,
a4*b31 + 2*a5*b24 - a7*b15 - 6*a9*b10,
2*a1*b12 + a4*b25 - 18*a5*b1 - 6*a7*b10,
a1*b10 - a4*b1 + a4*b23 - a6*b10,
a3*b18 - a5*b37 + 5*a5*b8 + a9*b18,
a4*b40 - 8*a6*b50 - 8*a6*b51 - 2*a6*b52,
a1*b52 + a4*b38 - 8*a6*b50 - a6*b52,
2*a1*b19 - 6*a10*b10 + a4*b38 + 2*a4*b39,
6*a1*b22 - a4*b19 + a4*b51 + a4*b52,
12*a1*b22 - a4*b20 + 2*a4*b51 + 2*a4*b52,
3*a1*b30 - 2*a6*b29 - 3*a6*b30 + 4*a7*b23 + 18*a8*b23,
a1*b29 - 2*a6*b26 - a6*b29 + 6*a7*b23 + 12*a8*b23,
30*a1*b5 + 20*a1*b6 - 36*a2*b2 - 9*a2*b3 - 1260*a3*b1,
10*a1*b6 - 3*a2*b2 - 3*a2*b3 - 3*a2*b4 - 420*a3*b1,
a1*b25 - 4*a6*b24 - a6*b25 - 2*a7*b1 + 10*a7*b23,
2*a1*b24 + a1*b25 - 2*a6*b24 - 3*a6*b25 + 20*a7*b23,
3*a1*b27 - 2*a6*b24 - 2*a6*b25 - 3*a6*b27 + 20*a7*b23,
24*a10*b23 + a4*b29 - 2*a6*b40 - 4*a6*b42 - 2*a6*b43,
a1*b40 + 24*a10*b23 - 2*a6*b38 - 4*a6*b39 - 3*a6*b40,
24*a10*b23 + a4*b28 - a6*b41 - 2*a6*b43 - 2*a6*b45,
6*a10*b30 + a4*b33 + 2*a5*b26 - 2*a6*b48 - 3*a8*b15,
a1*b41 + 16*a10*b23 + 2*a4*b24 - 4*a6*b38 - a6*b41,
2*a1*b45 + 24*a10*b23 + a4*b25 - 2*a6*b41 - 2*a6*b45,
24*a10*b23 + 3*a4*b27 - 2*a6*b39 - 2*a6*b41 - 2*a6*b44,
8*a10*b23 + 4*a4*b24 - 2*a6*b45 - a7*b10 - a7*b9,
4*a1*b11 + 2*a4*b24 + a4*b25 - 24*a5*b1 - 8*a7*b10,
a4*b31 - 3*a5*b2 + 2*a5*b24 - a7*b15 - 6*a9*b10,
a1*b10 + 3*a1*b9 - 10*a4*b1 - a6*b10 - a6*b9,
2*a1*b10 + a1*b9 - 5*a4*b1 + a4*b23 - a6*b9,
2*a10*b47 + a3*b51 + 5*a5*b47 - 3*a8*b21 + 4*a9*b51,
a10*b18 - 2*a3*b53 - 4*a5*b49 + 3*a9*b21 - 2*a9*b53,
a10*b18 - a3*b21 + 3*a5*b18 - a5*b49 + 2*a9*b21,
a10*b21 - a10*b53 - 2*a5*b53 + 3*a9*b22 - 3*a9*b54,
12*a1*b22 - a4*b19 + 6*a4*b50 + a4*b51 + a4*b52,
6*a1*b22 - a4*b19 + a4*b51 + a4*b52 - 6*a6*b22,
2*a10*b21 - 3*a3*b22 + a5*b21 - a5*b53 + 3*a9*b22,
a1*b29 - 2*a6*b26 - 2*a6*b28 - 3*a6*b29 + 18*a7*b23 + 36*a8*b23,
a1*b26 - 2*a6*b24 - a6*b26 + 4*a7*b23 - 3*a8*b1 + 3*a8*b23,
a1*b26 - a6*b25 - a6*b26 - a6*b28 + 12*a7*b23 + 9*a8*b23,
3*a2*b36 + 4*a3*b33 - 8*a6*b37 - 2*a8*b36 - a8*b7 + 4*a9*b34,
24*a1*b7 - 2*a2*b5 - a2*b6 - 70*a3*b2 - 14*a3*b3 - 5*a3*b4,
4*a2*b37 + 5*a3*b35 - 5*a7*b8 - 4*a8*b37 + 2*a9*b36 - 2*a9*b7,
6*a10*b30 + 2*a2*b42 + 5*a5*b29 - 10*a6*b47 + 2*a7*b42 + 4*a8*b42,
48*a10*b23 + a4*b28 - 4*a6*b39 - 4*a6*b40 - 2*a6*b41 - 2*a6*b43,
24*a10*b23 + a4*b28 - a6*b40 - a6*b41 - 2*a6*b43 - 2*a6*b44,
24*a10*b23 + 3*a4*b26 - 2*a6*b43 - 4*a6*b44 - 2*a6*b45 - 3*a8*b9,
6*a10*b30 + a4*b33 + 2*a5*b26 - 2*a6*b47 - 2*a6*b48 - 3*a8*b14,
a1*b41 + 48*a10*b23 + a4*b25 - 4*a6*b38 - 8*a6*b39 - 3*a6*b41,
2*a1*b44 + 24*a10*b23 + a4*b25 - 2*a6*b38 - 2*a6*b41 - 2*a6*b44,
48*a10*b23 + 3*a4*b25 - 2*a6*b41 - 8*a6*b44 - 4*a6*b45 - 2*a7*b9,
2*a3*b45 + a4*b35 + 2*a5*b31 - a7*b17 - 6*a9*b15 + 2*a9*b45,
5*a3*b48 + 12*a4*b37 + 2*a5*b35 - 2*a7*b18 - 6*a9*b17 + 2*a9*b48,
a10*b37 + a10*b8 - 4*a3*b49 - 6*a5*b37 + 3*a9*b18 - a9*b49,
2*a1*b11 + 4*a1*b12 + a4*b25 + 3*a4*b27 - 36*a5*b1 - 12*a7*b10,
2*a10*b15 - 2*a10*b45 - a4*b46 - 2*a5*b38 - 2*a5*b45 + a7*b20,
4*a10*b44 + 4*a10*b45 + 5*a4*b48 + 2*a5*b41 - 8*a6*b53 - 2*a7*b20,
2*a10*b11 + 2*a10*b15 - a4*b46 + 2*a5*b11 - 2*a5*b38 + a7*b20,
2*a10*b20 - 4*a10*b52 - 4*a4*b53 - 2*a5*b50 - a5*b52 + 6*a7*b22,
5*a2*b29 - 10*a6*b33 - 30*a6*b34 + 6*a7*b30 + 4*a8*b29 + 18*a8*b30 + 180*a9*b23
,
a1*b28 - 2*a6*b24 - a6*b25 - 2*a6*b26 - a6*b28 + 16*a7*b23 + 12*a8*b23,
a1*b28 - 2*a6*b25 - 2*a6*b26 - 6*a6*b27 - 5*a6*b28 + 48*a7*b23 + 36*a8*b23,
a1*b43 + 24*a10*b23 + a4*b26 - 2*a6*b38 - 2*a6*b40 - a6*b41 - a6*b43,
4*a10*b34 + 2*a3*b43 + 9*a4*b36 + 2*a5*b33 - 4*a6*b49 - 3*a8*b17 + 2*a9*b43,
6*a10*b30 + 3*a4*b31 + 6*a5*b24 - 2*a6*b48 - 2*a7*b14 - a7*b15 - 6*a9*b9,
2*a1*b11 + 2*a1*b13 + a4*b26 - a4*b3 - 36*a5*b1 - 2*a7*b9 - 3*a8*b9,
2*a3*b11 - a4*b35 - 2*a5*b31 + 6*a5*b5 + a7*b17 + 2*a9*b11 + 6*a9*b15,
2*a1*b14 + a1*b15 + a2*b9 - 3*a4*b2 - 6*a5*b1 - a6*b15 - a8*b9,
4*a10*b42 + 4*a10*b43 + 5*a4*b47 + 2*a5*b40 + 2*a5*b43 - 8*a6*b53 - 3*a8*b20,
8*a1*b19 - 18*a10*b10 - 2*a10*b9 - 2*a4*b11 + 4*a4*b38 + a4*b40 + a4*b41,
6*a1*b20 - 6*a10*b10 - 6*a10*b9 - a4*b13 - 3*a4*b14 + 2*a4*b43 + 2*a4*b44,
a1*b20 - 4*a10*b10 - a4*b11 + a4*b42 + a4*b45 + 3*a5*b10 - a6*b20,
2*a10*b19 - 2*a10*b50 - 2*a10*b51 - 2*a10*b52 - 3*a5*b50 + 3*a7*b22 - 6*a7*b54,
4*a10*b19 + 2*a10*b20 - 3*a2*b22 - 4*a4*b53 + a5*b19 - 2*a5*b50 + 6*a7*b22,
6*a1*b34 + a2*b29 - 2*a6*b33 - 6*a6*b34 + 3*a7*b30 - a8*b29 + 9*a8*b30 + 36*a9*
b23,
a1*b31 + a2*b24 - a6*b31 - a7*b2 + a7*b30 - a8*b24 - 6*a9*b1 + 6*a9*b23,
6*a2*b24 + 6*a2*b25 + 9*a2*b27 - 12*a6*b32 + 2*a7*b28 + 2*a7*b29 - 3*a7*b4 +
360*a9*b23,
2*a10*b34 + 2*a3*b44 + a4*b35 + 2*a5*b31 - 2*a6*b49 - a7*b17 - 6*a9*b14 + 2*a9*
b44,
4*a1*b11 - 3*a4*b2 + 2*a4*b24 + a4*b26 - 24*a5*b1 - 3*a7*b10 - a7*b9 - 3*a8*b10
,
2*a1*b12 + 4*a1*b13 + 6*a1*b14 + a4*b28 - 3*a4*b4 - 72*a5*b1 - 4*a7*b9 - 6*a8*
b9,
3*a2*b18 - 5*a3*b16 + 12*a4*b37 + 2*a5*b35 - 9*a5*b7 - 2*a7*b18 - 2*a9*b16 - 6*
a9*b17,
2*a1*b18 + a2*b17 + 4*a3*b14 + a4*b36 - a4*b7 - 2*a5*b5 - a8*b17 - 2*a9*b14,
a1*b15 + a2*b10 - a4*b2 + a4*b30 - 2*a5*b1 + 2*a5*b23 - a6*b15 - a8*b10,
2*a2*b18 + a3*b17 + 2*a4*b37 - 13*a4*b8 + 2*a5*b36 - 2*a5*b7 - 2*a8*b18 - 2*a9*
b17,
2*a10*b14 - 2*a10*b42 - 2*a10*b45 - a4*b46 - 2*a5*b38 - 2*a5*b44 + 4*a6*b53 +
a7*b20,
8*a1*b19 + 2*a1*b20 - 18*a10*b10 - 2*a10*b9 - a4*b12 + 4*a4*b39 + a4*b40 + a4*
b41,
4*a1*b19 + 4*a1*b20 - 12*a10*b10 - 4*a10*b9 - 2*a4*b12 + a4*b40 + a4*b41 + 2*a4
*b44,
4*a1*b19 + 4*a1*b20 - 12*a10*b10 - 4*a10*b9 - a4*b13 + a4*b40 + a4*b41 + a4*b43
,
a1*b33 + a2*b26 - 2*a6*b31 - a6*b33 + 3*a7*b30 - 3*a8*b2 - a8*b26 + 3*a8*b30 +
24*a9*b23,
a1*b35 + a2*b31 + 9*a3*b24 - a6*b35 + a7*b34 - a7*b5 - a8*b31 - 6*a9*b2 + 6*a9*
b30,
12*a1*b37 + a2*b35 + 12*a3*b31 - 12*a6*b37 + a7*b36 - a7*b7 - a8*b35 + 6*a9*b34
- 6*a9*b5,
4*a1*b12 + 2*a1*b13 + 2*a4*b27 + a4*b28 - a4*b4 - 48*a5*b1 - 6*a7*b10 - 2*a7*b9
- 6*a8*b10,
2*a10*b40 + 4*a10*b42 + 2*a10*b43 + a2*b51 + 4*a5*b40 - 8*a6*b53 + 4*a7*b51 - 3
*a8*b19 + 2*a8*b51,
2*a10*b17 - 2*a10*b48 - a3*b52 - 8*a4*b49 - 2*a5*b46 - 5*a5*b48 + 4*a7*b21 + 6*
a9*b20 - 4*a9*b52,
3*a1*b20 - 6*a10*b10 - 2*a10*b9 - 3*a4*b11 + a4*b42 + 2*a4*b44 + a4*b45 + 3*a5*
b9 - a6*b20,
6*a1*b20 - 12*a10*b10 - 4*a10*b9 - a4*b13 - 3*a4*b15 + 2*a4*b42 + 2*a4*b43 + 2*
a4*b45 - 2*a6*b20,
6*a10*b20 - 6*a2*b22 + 5*a4*b21 - 6*a4*b53 + 2*a5*b19 - a5*b20 - 2*a5*b51 - 2*
a5*b52 + 6*a8*b22,
9*a1*b36 + a2*b33 + 9*a3*b26 - 2*a6*b35 - 9*a6*b36 + 2*a7*b34 - a8*b33 + 3*a8*
b34 - 3*a8*b5 + 18*a9*b30,
5*a1*b31 + 9*a2*b24 + a2*b25 - 5*a6*b31 - 2*a6*b32 + a7*b26 - a7*b3 + 6*a7*b30
- a8*b25 + 90*a9*b23,
11*a2*b35 + 42*a3*b31 + 18*a3*b32 - 132*a6*b37 + 2*a7*b36 - 11*a7*b7 - 8*a8*b35
+ 6*a9*b33 + 30*a9*b34 - 6*a9*b6,
12*a10*b30 + 2*a2*b45 + 2*a4*b32 + 18*a5*b24 + 2*a5*b25 - 10*a6*b48 - a7*b13 -
5*a7*b15 + 2*a7*b45 + 4*a8*b45,
2*a1*b11 + 2*a1*b13 + a4*b26 + a4*b29 - a4*b3 - 36*a5*b1 - 2*a6*b11 - 3*a7*b10
- a7*b9 - 9*a8*b10,
3*a1*b13 + 12*a1*b14 + 6*a1*b15 + 3*a2*b9 + a4*b29 - 3*a4*b3 - 72*a5*b1 - a6*
b13 - 2*a7*b9 - 9*a8*b9,
a1*b13 + 6*a1*b15 + 3*a2*b10 + a4*b29 - a4*b3 + 3*a4*b30 - 24*a5*b1 - a6*b13 -
2*a7*b10 - 9*a8*b10,
2*a1*b14 + 2*a1*b15 + a2*b10 + a2*b9 - 4*a4*b2 + a4*b30 - 8*a5*b1 - 2*a6*b14 -
a8*b10 - a8*b9,
a1*b17 + a2*b15 + 7*a3*b10 + a4*b34 - a4*b5 - 2*a5*b2 + 2*a5*b30 - a6*b17 - a8*
b15 - 2*a9*b10,
2*a1*b18 + a2*b17 + 4*a3*b15 + a4*b36 - a4*b7 + 2*a5*b34 - 2*a5*b5 - 2*a6*b18 -
a8*b17 - 2*a9*b15,
10*a1*b21 - a10*b12 - a10*b13 - a10*b15 + 2*a4*b46 - 3*a5*b11 - 2*a5*b12 + a5*
b39 - 2*a7*b19 - a7*b20,
4*a1*b19 + 4*a1*b20 - 18*a10*b10 - 2*a10*b9 - 2*a4*b12 + a4*b40 + a4*b41 + 2*a4
*b42 + 2*a4*b45 - 4*a6*b19,
2*a10*b16 + 2*a10*b17 - 3*a2*b21 + a3*b19 - 8*a4*b49 + 5*a5*b16 - 2*a5*b46 + 4*
a7*b21 + 4*a9*b19 + 6*a9*b20,
4*a1*b21 - 2*a10*b14 - 2*a10*b15 + a2*b20 - a4*b16 + a4*b47 + a4*b48 - 2*a5*b11
+ 2*a5*b44 - a8*b20,
4*a1*b21 - 2*a10*b14 - 2*a10*b15 + a2*b20 - 3*a4*b17 + a4*b47 + a4*b48 - a5*b13
+ a5*b43 - a8*b20,
6*a2*b26 + 7*a2*b28 - 8*a6*b32 - 20*a6*b33 + 4*a7*b29 + 6*a7*b30 + 2*a8*b28 + 6
*a8*b29 + 6*a8*b30 - 3*a8*b4 + 480*a9*b23,
8*a2*b33 + 42*a3*b26 + 15*a3*b28 - 16*a6*b35 - 72*a6*b36 + 4*a7*b34 - 2*a8*b33
+ 6*a8*b34 - 3*a8*b6 + 12*a9*b29 + 90*a9*b30,
5*a1*b47 + 6*a10*b30 + a2*b40 + 5*a5*b26 - 2*a6*b46 - 5*a6*b47 + 2*a7*b42 + a7*
b43 - 3*a8*b11 - a8*b40 + 3*a8*b42,
4*a10*b34 + 5*a2*b47 + 8*a3*b40 + 8*a5*b33 - 16*a6*b49 + 2*a7*b47 - 3*a8*b16 -
2*a8*b47 + 2*a9*b40 + 12*a9*b42 + 6*a9*b43,
a1*b46 - 2*a10*b2 - 2*a10*b24 + 2*a10*b30 + a2*b38 + 5*a5*b24 - a6*b46 - a7*b11
+ a7*b42 + a7*b45 - a8*b38,
4*a1*b11 + 4*a1*b12 + 2*a1*b13 + a4*b25 + a4*b26 + a4*b28 - a4*b3 - 72*a5*b1 -
9*a7*b10 - 3*a7*b9 - 9*a8*b10,
10*a1*b16 - 6*a2*b11 + 5*a4*b31 + 2*a4*b32 - 18*a5*b2 + 2*a5*b25 - 5*a5*b3 - 2*
a7*b11 - a7*b13 - 6*a7*b15 - 90*a9*b10,
2*a1*b12 + 4*a1*b13 + 6*a1*b15 + a4*b28 + 2*a4*b29 - 3*a4*b4 - 72*a5*b1 - 2*a6*
b12 - 6*a7*b10 - 2*a7*b9 - 18*a8*b10,
3*a1*b17 + 2*a2*b14 + a2*b15 + 7*a3*b9 + a4*b34 - 3*a4*b5 - 6*a5*b2 - a6*b17 -
2*a8*b14 - a8*b15 - 2*a9*b9,
4*a1*b53 - 2*a10*b11 + 2*a10*b42 + 2*a10*b45 + a2*b50 + 4*a5*b38 - 4*a6*b53 -
a7*b19 + a7*b51 + a7*b52 - a8*b50,
4*a1*b21 - 4*a10*b15 + a2*b20 - a4*b16 + a4*b47 + a4*b48 - 2*a5*b11 + 2*a5*b42
+ 2*a5*b45 - 4*a6*b21 - a8*b20,
4*a10*b17 - 4*a2*b21 - 5*a3*b20 + 9*a4*b18 - 4*a4*b49 + 2*a5*b16 + 3*a5*b17 - 2
*a5*b47 - 2*a5*b48 + 4*a8*b21 + 4*a9*b20,
2*a1*b32 + 14*a2*b24 + a2*b25 - 10*a6*b31 - 2*a6*b32 - 5*a7*b2 + a7*b29 - a7*b3
+ 8*a7*b30 - 2*a8*b24 - a8*b25 + 120*a9*b23,
4*a10*b29 + 24*a10*b30 + 2*a2*b43 + 5*a4*b33 + 12*a5*b26 + 4*a5*b28 - 4*a6*b46
- 20*a6*b47 - 10*a6*b48 + 2*a7*b43 - 3*a8*b13 + 4*a8*b43,
2*a10*b29 + 12*a10*b30 + 2*a2*b44 + 2*a4*b32 + 18*a5*b24 + 2*a5*b25 - 2*a6*b46
- 10*a6*b48 - a7*b13 - 5*a7*b14 + 2*a7*b44 + 4*a8*b44,
20*a1*b16 - 6*a2*b11 - 3*a2*b12 + 4*a4*b32 - 6*a5*b2 + 2*a5*b27 - 6*a5*b3 - 7*
a5*b4 - 2*a7*b12 - 2*a7*b13 - 2*a7*b15 - 120*a9*b10,
36*a1*b18 - 21*a3*b11 - 4*a3*b12 + 4*a4*b35 + a5*b32 - 3*a5*b5 - 4*a5*b6 - a7*
b16 - a7*b17 - a9*b12 - 3*a9*b13 - 15*a9*b15,
2*a1*b16 + 12*a1*b17 + a2*b13 + 3*a2*b14 + a4*b33 - 2*a4*b6 - 18*a5*b2 - 2*a5*
b3 - 2*a7*b14 - a8*b13 - 6*a8*b14 - 12*a9*b9,
4*a10*b29 + 6*a10*b30 + 4*a2*b40 + 6*a5*b26 + 7*a5*b28 - 8*a6*b46 - 20*a6*b47 +
2*a7*b40 + 4*a7*b42 + 2*a7*b43 - 3*a8*b12 + 2*a8*b40 + 6*a8*b42,
2*a10*b35 - 2*a10*b36 + 2*a10*b7 - 8*a2*b49 - 11*a3*b46 - 11*a5*b35 + 11*a7*b18
- 2*a7*b49 + 8*a8*b49 + 6*a9*b16 - 2*a9*b46 - 6*a9*b47 - 6*a9*b48,
2*a10*b12 - 2*a10*b40 - 2*a10*b41 - 2*a10*b42 - 2*a10*b45 - 3*a2*b50 - 6*a5*b38
- 6*a5*b39 + 12*a6*b53 + 3*a7*b19 - 4*a7*b50 - 2*a7*b51 - 2*a7*b52,
2*a10*b16 - 2*a10*b47 - 2*a10*b48 - 4*a2*b53 - 7*a3*b50 - 7*a5*b46 + 7*a7*b21 -
4*a7*b53 + 4*a8*b53 + 6*a9*b19 - 4*a9*b50 - 6*a9*b51 - 6*a9*b52,
5*a1*b33 + 11*a2*b26 + 2*a2*b28 - 10*a6*b31 - 4*a6*b32 - 15*a6*b33 + 2*a7*b29 +
18*a7*b30 + a8*b26 - 2*a8*b28 + 3*a8*b29 - 3*a8*b3 + 18*a8*b30 + 360*a9*b23,
6*a2*b31 + 10*a2*b32 + 210*a3*b24 + 42*a3*b25 + 21*a3*b27 - 56*a6*b35 + 2*a7*
b33 + 2*a7*b34 - 7*a7*b6 - 4*a8*b32 + 6*a9*b28 + 30*a9*b29 + 120*a9*b30 - 6*a9*
b4,
4*a1*b16 + 2*a2*b11 + 2*a4*b31 + a4*b33 - 6*a4*b5 - 18*a5*b2 + 2*a5*b26 - 2*a5*
b3 - 2*a7*b14 - 2*a7*b15 - 2*a8*b11 - 3*a8*b15 - 18*a9*b10 - 6*a9*b9,
4*a1*b32 + 36*a2*b24 + 13*a2*b25 + 3*a2*b27 - 20*a6*b31 - 20*a6*b32 + 2*a7*b26
+ a7*b28 + 6*a7*b29 - 4*a7*b3 + 12*a7*b30 - 3*a7*b4 - a8*b25 - 3*a8*b27 + 720*
a9*b23,
5*a1*b48 + 12*a10*b30 + a2*b41 + 5*a4*b31 + 18*a5*b24 + 2*a5*b25 - 4*a6*b46 - 5
*a6*b48 - 2*a7*b11 - a7*b13 + a7*b43 + 2*a7*b44 + 2*a7*b45 - a8*b41 + 3*a8*b45,
8*a1*b35 + 14*a2*b31 + 2*a2*b32 + 126*a3*b24 + 15*a3*b25 - 24*a6*b35 + a7*b33 +
6*a7*b34 - 8*a7*b5 - 2*a7*b6 - 5*a8*b31 - 2*a8*b32 + 6*a9*b26 + 6*a9*b29 - 6*
a9*b3 + 90*a9*b30,
8*a1*b49 - 2*a10*b31 + 2*a10*b34 - 2*a10*b5 + a2*b46 + 8*a3*b38 + 8*a5*b31 - 8*
a6*b49 - a7*b16 + a7*b47 + a7*b48 - a8*b46 - 6*a9*b11 + 2*a9*b38 + 6*a9*b42 + 6
*a9*b45,
2*a10*b27 - 2*a10*b28 - 2*a10*b29 + 2*a10*b4 - 6*a2*b38 - 6*a2*b39 - 6*a5*b24 -
6*a5*b25 - 9*a5*b27 + 12*a6*b46 + 3*a7*b12 - 2*a7*b39 - 2*a7*b40 - 2*a7*b41 -
2*a7*b42 - 2*a7*b45,
8*a10*b34 + 5*a2*b48 + 8*a3*b41 + 8*a4*b35 + 12*a5*b31 + 4*a5*b32 - 32*a6*b49 -
2*a7*b16 - 8*a7*b17 + 2*a7*b48 - 2*a8*b48 - 6*a9*b13 + 2*a9*b41 + 6*a9*b43 +
12*a9*b44 + 12*a9*b45,
2*a1*b16 + 12*a1*b17 + a2*b13 + 3*a2*b15 + a4*b33 + 6*a4*b34 - 2*a4*b6 - 18*a5*
b2 + 2*a5*b29 - 2*a5*b3 - 2*a6*b16 - 2*a7*b15 - a8*b13 - 6*a8*b15 - 18*a9*b10 -
6*a9*b9,
36*a1*b18 + 2*a2*b16 + 3*a2*b17 - 2*a3*b13 + 2*a4*b35 + 9*a4*b36 - 9*a4*b7 + 2*
a5*b33 - 12*a5*b5 - 4*a5*b6 - 2*a7*b17 - 2*a8*b16 - 3*a8*b17 - 2*a9*b13 - 12*a9
*b14 - 12*a9*b15,
2*a10*b13 - 2*a10*b41 - 8*a10*b42 - 2*a10*b43 - 4*a10*b44 - 12*a10*b45 - a2*b52
- 4*a4*b46 - 12*a5*b38 - 4*a5*b39 - 4*a5*b41 + 32*a6*b53 + 4*a7*b19 + 4*a7*b20
- 4*a7*b52 - 2*a8*b52,
4*a10*b29 + 6*a10*b30 + 2*a2*b41 + 2*a4*b32 + 18*a5*b24 + 6*a5*b25 + 3*a5*b27 -
8*a6*b46 - 10*a6*b48 - a7*b12 - 2*a7*b13 + a7*b41 + a7*b43 + 2*a7*b44 + 2*a7*
b45 + a8*b41 + 3*a8*b45,
20*a1*b16 + 30*a1*b17 + 2*a2*b12 + 2*a4*b32 + 5*a4*b33 - 5*a4*b6 - 36*a5*b2 + 2
*a5*b28 - 12*a5*b3 - 6*a5*b4 - 2*a7*b13 - 4*a7*b14 - 4*a7*b15 - 2*a8*b12 - 3*a8
*b13 - 6*a8*b15 - 90*a9*b10 - 30*a9*b9,
40*a1*b21 - 4*a10*b13 - 4*a10*b14 - 12*a10*b15 + 4*a2*b19 + 3*a2*b20 - 5*a4*b16
+ 4*a4*b46 + 5*a4*b47 + 5*a4*b48 - 12*a5*b11 - 4*a5*b12 - 2*a5*b13 + 2*a5*b40
+ 2*a5*b41 - 4*a7*b20 - 4*a8*b19 - 3*a8*b20,
4*a1*b46 - 2*a10*b25 + 2*a10*b26 + 2*a10*b29 - 2*a10*b3 + 6*a10*b30 + 10*a2*b38
+ 2*a2*b39 + 18*a5*b24 + 7*a5*b25 - 12*a6*b46 - 4*a7*b11 - 2*a7*b12 + 2*a7*b38
+ a7*b40 + a7*b41 + 6*a7*b42 + 6*a7*b45 - a8*b38 - 2*a8*b39,
2*a10*b32 - 2*a10*b33 - 2*a10*b34 + 2*a10*b6 - 7*a2*b46 - 42*a3*b38 - 14*a3*b39
- 6*a5*b31 - 10*a5*b32 + 56*a6*b49 + 7*a7*b16 - 2*a7*b46 - 2*a7*b47 - 2*a7*b48
+ 4*a8*b46 + 6*a9*b12 - 2*a9*b39 - 6*a9*b40 - 6*a9*b41 - 30*a9*b42 - 30*a9*b45
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.
3 3 7
u = u *a1 + u *a2*u + f(v,v )*a4 + f(v,v)*a5*u + a3*u
t 2x x x
2 3 2 6
v = u *a7*u *v + v *a6 + v *a8*u + f(v,v)*a10*u *v + a9*u *v
t x 2x x
For any solution of the above algebraic conditions for the
a's and b's this system has the following symmetry:
3 2 2 6
u = u *b1 + u *b2*u + u *u *b3*u + u *f(v,v)*b11*u + u *b5*u
t 4x 3x 2x x 2x 2x
3 2 2 5 2
+ u *b4*u + u *f(v,v)*b12*u + u *b6*u + u *f(v,v )*b13*u
x x x x x
2 5 9
+ u *f(v,v) *b19*u + u *f(v,v)*b16*u + u *b7*u + f(v ,v )*b9
x x x x 2x
3 3
+ f(v ,v )*b14*u + f(v,v )*b10 + f(v,v )*b15*u
x x 3x 2x
2 6 3
+ f(v,v )*f(v,v)*b20*u + f(v,v )*b17*u + f(v,v) *b22*u
x x
2 5 9 13
+ f(v,v) *b21*u + f(v,v)*b18*u + b8*u
2 2
v = u *b24*u *v + u *u *b25*u*v + u *v *b26*u + u *f(v,v)*b38*u*v
t 3x 2x x 2x x 2x
5 3 2 2
+ u *b31*u *v + u *b27*v + u *v *b28*u + u *f(v,v)*b39*v
2x x x x x
2 4 2 5
+ u *b32*u *v + u *v *b29*u + u *v *f(v,v)*b40*u + u *v *b33*u
x x 2x x x x x
2 4
+ u *f(v,v )*b41*u*v + u *f(v,v) *b50*v + u *f(v,v)*b46*u *v
x x x x
8 3 2 6
+ u *b35*u *v + v *b23 + v *b30*u + v *f(v,v)*b42*u + v *b34*u
x 4x 3x 2x 2x
2 2 5 9
+ v *f(v,v )*b43*u + v *f(v,v) *b51*u + v *f(v,v)*b47*u + v *b36*u
x x x x x
2 2
+ f(v ,v )*b44*u *v + f(v,v )*b45*u *v + f(v,v )*f(v,v)*b52*u*v
x x 2x x
5 3 2 4 8
+ f(v,v )*b48*u *v + f(v,v) *b54*v + f(v,v) *b53*u *v + f(v,v)*b49*u *v
x
12
+ b37*u *v