Solving parametric polynomial systems using Generic Rational Univariate Representation

In this paper, we present a generic parametrization of generically zero-dimensional parametric polynomial systems. More specifically, we study the specialization properties of the Rational Univariate Representation and derive bounds on the degrees and heights of its elements. In addition to that, we propose two algorithms to effectively compute this parametrization.

💡 Research Summary

The paper addresses the problem of solving parametric polynomial systems that are generically zero‑dimensional, i.e., for almost all values of the parameters the associated ideal has a finite number of solutions. The authors introduce the notion of a Generic Rational Univariate Representation (GRUR), which extends the classical Rational Univariate Representation (RUR) to the parametric setting.

Starting from a system f₁,…,f_n ∈ ℂ