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 lefthand 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.

