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Topic: variable elimination from polynomial system
Replies: 12   Last Post: Apr 12, 2014 7:11 PM

 Messages: [ Previous | Next ]
 Martin Posts: 5 Registered: 7/27/10
variable elimination from polynomial system
Posted: Apr 5, 2014 2:49 PM

Maybe you can do this faster than Derive 6.10. I want to eliminate the
two variables x1, x2 from the three polynomial equations

2*x1^3*x2*(4*x2^2 - 3*(4*x4^2 + 1)) - x1^2*(12*x2^4 + 3*x2^2*(24*x3*x4 -
24*x4^2 - 1) - 6*x3*x4*(4*x4^2 + 3) + 12*x4^4 + 3*x4^2 - 2) +
6*x1*x2*(x2^4 - 2*x2^2*(2*x3^2 - 8*x3*x4 + 5*x4^2) + 3*x3^2*(4*x4^2 + 1)
- 2*x3*x4*(8*x4^2 + 1) + 5*x4^4) - x2^6 + 3*x2^4*(4*x3^2 - 10*x3*x4 +
5*x4^2) + 3*x2^2*(8*x3^3*x4 - x3^2*(24*x4^2 + 1) + 20*x3*x4^3 - 5*x4^4)
- 2*x3^3*x4*(4*x4^2 + 3) + x3^2*(12*x4^4 + 3*x4^2 - 2) - 6*x3*x4^5 +
x4^6 = 0

- 2*(x1^3*x4*(12*x2^2 - 4*x4^2 - 3) + 3*x1^2*x2*(4*x2^2*(x3 - 2*x4) -
3*x3*(4*x4^2 + 1) + x4*(8*x4^2 + 1)) - x1*(3*x2^4*(4*x3 - 5*x4) +
3*x2^2*(12*x3^2*x4 - x3*(24*x4^2 + 1) + 10*x4^3) - 3*x3^2*x4*(4*x4^2 +
3) + x3*(12*x4^4 + 3*x4^2 - 2) - 3*x4^5) + x2*(x3 - x4)*(3*x2^4 -
2*x2^2*(2*x3^2 - 10*x3*x4 + 5*x4^2) + 3*(x3^2*(4*x4^2 + 1) - 4*x3*x4^3 +
x4^4))) = 0

x2^2 + x4^2 - 2 = 0

Thus I started GROEBNER_BASIS([lhs1, lhs2, lhs3], [x1, x2, x3, x4]) on
Derive, where lhs1, lhs2, lhs3 are the left-hand sides of the three
equations; the computation is still running. However, I am interested
only in the basis elements not involving x1 and x2.

Thanks,

Martin.