Problem v1l1o35
Unknowns | Inequalities |
Equations |
Solution 1 |
Solution 2 |
Computing time
Unknowns
All solutions for the following 12 unknowns have to be determined:
a1,a2,a3,b1, ..., b9
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}, {a2,a3}, {b1}
Equations
All comma separated 26 expressions involving 121 terms have to vanish.
All terms are products of one a- and one b-unknown.
3*a1*b2 - 5*a2*b1,
3*a1*b6 - 10*a3*b1,
3*a1*b7 - 5*a3*b1,
a2*b9 - 2*a3*b8,
a1*b6 + a1*b7 - 5*a3*b1,
6*a1*b8 - 3*a2*b2 - a3*b2,
3*a1*b9 - a2*b6 - a3*b6,
6*a1*b2 + 3*a1*b3 - 20*a2*b1 - 5*a3*b1,
3*a1*b3 + 3*a1*b5 - 20*a2*b1 - 10*a3*b1,
3*a1*b5 + 3*a1*b7 - 10*a2*b1 - 10*a3*b1,
12*a1*b8 + 3*a1*b9 - 3*a2*b3 - a3*b3,
3*a1*b9 + 2*a2*b7 - 3*a3*b2 - a3*b5,
3*a1*b9 - 3*a3*b2 + a3*b6 - 3*a3*b7,
3*a1*b5 + 3*a1*b6 + 6*a1*b7 - 10*a2*b1 - 25*a3*b1,
12*a1*b8 + 3*a1*b9 - 6*a2*b2 - 3*a3*b2 - a3*b3,
6*a1*b9 - 6*a2*b7 + a3*b3 - a3*b6 - 3*a3*b7,
2*a1*b2 + 3*a1*b3 + 2*a1*b4 + a1*b5 - 20*a2*b1 - 10*a3*b1,
a1*b3 + 2*a1*b4 + a1*b5 + a1*b6 - 10*a2*b1 - 10*a3*b1,
6*a1*b4 + 3*a1*b5 + 9*a1*b6 + 3*a1*b7 - 20*a2*b1 - 50*a3*b1,
12*a1*b8 + 9*a1*b9 - 6*a2*b2 + 2*a2*b6 - 9*a3*b2 - 3*a3*b5,
12*a1*b8 + 9*a1*b9 - 3*a2*b5 - a3*b3 - a3*b4 - 2*a3*b5,
12*a1*b9 - 2*a2*b6 - 6*a2*b7 + a3*b3 - 3*a3*b6 - 3*a3*b7,
6*a1*b9 - 8*a2*b7 + 2*a3*b2 + a3*b5 - a3*b6 - 3*a3*b7,
3*a1*b3 + 6*a1*b4 + 6*a1*b5 + 3*a1*b6 + 3*a1*b7 - 40*a2*b1 - 40*a3*b1,
12*a1*b8 + 9*a1*b9 - a2*b3 - 2*a2*b4 - a2*b5 - a3*b3 - 2*a3*b4 - a3*b5,
24*a1*b9 - 6*a2*b6 - 6*a2*b7 - 2*a3*b3 + 2*a3*b4 + a3*b5 - 3*a3*b6 - 9*a3*b7
Computing time
On a Pentium 4 PC with 1.7GHz running REDUCE 3.7 with 120MB RAM
under Linux the problem was solved in 0.5 sec.