I am trying to solve the so called Bethe ansatz equations in Mathematical Physics.
I have four multivariate polynomials equations with four unknown p_i(x[1],x[2],x[3],x[4]) i=1,2,3,4; which have integer coefficients. The equations are mixed; P_i is linear in x[j] for x[j]\ne x[i]; and x[i] is of order 10. Due to this structure, I first eliminate x[4] from these equations. Then use resultant to eliminate x[3], I got error messages (invalid series, in gcd...