System of equations comming from the Jacobi formula

Using the Jacobi formula we obtain a system of 5 polynomial equations on 4 unknowns: a, b, x, y. We prove that in this ideal there exist:

• A quadratic equation on b with coefficients polynomials in t_k, d_k,

• A linear equation on a, b with coefficients polynomials in t_k, d_k,

• Two independen linear equations on x, y with coefficients polynomials in a, b, t_k, d_k.