A Stabilized Normal Form Algorithm for Generic Systems of Polynomial Equations

We propose a numerical linear algebra based method to find the multiplication operators of the quotient ring C[x]/I associated to a zero-dimensional ideal I generated by n C-polynomials in n variables. We assume that the polynomials are generic in the sense that the number of solutions in Cn equals the Bézout number. The main contribution of this paper is an automated choice of basis for C[x]/I , which is crucial for the feasibility of normal form methods in finite precision arithmetic. This choice is based on numerical linear algebra techniques and it depends on the given generators of I .