Problem v2l1o23
Unknowns | Inequalities |
Equations |
Solution 1 |
Solution 2 |
Computing time
Unknowns
All solutions for the following 24 unknowns have to be determined:
a1,a3,a4,a5,a6,a13,a14,a15,a16,
b1,b3,b4,b6,b7,b9,b12,b13,b21,
b24,b26,b27,b30,b31,b32
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,a5,a6},{a13,a14,a15},{b1}
Equations
All comma separated 78 expressions involving 242 terms have to vanish.
All terms are products of one a- and one b-unknown.
b13,
b21,
a6,
a13,
a16*b12,
a3*b4,
a16*b32,
a3*b24,
a3*b3,
a16*b31,
a4*b21 - a4*b3,
a4*b13 - a4*b31,
a15*b21 - a15*b3,
a15*b13 - a15*b31,
a15*b7 + a4*b7,
a15*b26 + a4*b26,
3*a3*b6 - a4*b4,
a15*b32 - 3*a16*b30,
2*a1*b3 - 3*a3*b1,
2*a1*b31 + 3*a16*b1,
a1*b12 - 3*a6*b1,
a1*b24 + 3*a13*b1,
2*a1*b7 - 3*a5*b1,
2*a1*b26 + 3*a14*b1,
2*a1*b24 + 3*a13*b1,
2*a1*b27 + 3*a14*b1,
a1*b30 + 3*a15*b1,
a1*b32 + 3*a16*b1,
a1*b4 - 3*a3*b1,
a1*b6 - 3*a4*b1,
2*a1*b12 - 3*a6*b1,
2*a1*b9 - 3*a5*b1,
a5*b32 + a6*b30 - a6*b9,
a4*b30 - a4*b9 + a5*b30,
a4*b12 - a4*b32 - a6*b30,
a4*b6 - a4*b9 + a5*b6,
a3*b9 - a4*b4 - a5*b4,
a5*b13 - a5*b31 + a6*b9,
a13*b27 + a14*b21 - a14*b3,
a14*b32 + a15*b32 - a16*b27,
a14*b30 - a15*b27 + a15*b30,
a14*b6 - a15*b27 + a15*b6,
a13*b6 - a15*b24 + a15*b4,
a13*b27 - a13*b6 - a14*b4,
a1*b7 + a1*b9 - 3*a5*b1,
a1*b26 + a1*b27 + 3*a14*b1,
a1*b3 + a1*b4 - 3*a3*b1,
a1*b31 + a1*b32 + 3*a16*b1,
a15*b12 + a16*b9 - a5*b12 + a6*b9,
2*a14*b12 - 2*a4*b12 + a5*b12 + 2*a6*b6,
a15*b6 + a15*b9 + 2*a4*b9 - a5*b6,
a15*b12 + a16*b6 + 2*a4*b12 - a6*b6,
a13*b12 + a14*b6 + 2*a3*b12 + a5*b6,
a14*b30 + 2*a16*b24 + a5*b30 + a6*b24,
a14*b30 - 2*a15*b27 - a4*b27 - a4*b30,
a13*b30 - 2*a15*b24 - a3*b30 - a4*b24,
2*a13*b30 + a14*b24 - 2*a15*b24 + 2*a5*b24,
a13*b27 - a14*b24 + a3*b27 + a4*b24,
a4*b26 - a4*b7 + a6*b21 - a6*b3,
a13*b13 - a13*b31 - a15*b26 + a15*b7,
a13*b7 + a3*b7 + 2*a4*b3 + 2*a5*b3,
2*a13*b13 + a14*b7 + a5*b7 + 2*a6*b3,
2*a14*b13 + 2*a15*b13 + a16*b7 + a6*b7,
a13*b26 + a3*b26 + 2*a4*b21 + 2*a5*b21,
2*a13*b31 + a14*b26 + a5*b26 + 2*a6*b21,
2*a14*b31 + 2*a15*b31 + a16*b26 + a6*b26,
a13*b12 + a14*b9 - 2*a3*b12 + a5*b9 + 2*a6*b4,
a5*b12 - a6*b26 - 2*a6*b27 + 2*a6*b6 + a6*b7,
a13*b26 + 2*a13*b30 - a13*b7 - 2*a13*b9 + a14*b24,
2*a13*b32 + a14*b27 - 2*a16*b24 + a5*b27 + a6*b24,
a5*b26 + a5*b27 - a5*b7 - a5*b9 + a6*b24 - 2*a6*b4,
a4*b27 - a4*b6 - a5*b6 + a6*b21 + a6*b24 - a6*b3,
a4*b24 - a4*b4 + a5*b21 + a5*b24 - a5*b3 - a5*b4,
a13*b6 + a13*b9 - 2*a3*b6 + 2*a3*b9 + 2*a4*b4 + a5*b4,
a14*b32 + 2*a15*b32 + 2*a16*b27 - 2*a16*b30 + a6*b27 + a6*b30,
a14*b12 + a14*b13 - a14*b31 - a14*b32 + a15*b12 - a15*b32,
a13*b12 + a13*b13 - a13*b31 - a14*b30 - a15*b30 + a15*b9,
a13*b12 - 2*a13*b32 - a14*b26 - a14*b27 + a14*b7 + a14*b9
Computing time
On a Pentium 4 PC with 1.7GHz running REDUCE 3.7 with 120MB RAM
under Linux the problem was solved in 3 sec.