Solving parametric polynomial systems using Generic Rational Univariate Representation
Florent Corniquel (SU, UPCit\'e, IMJ-PRG, OURAGAN)
TL;DR
This paper introduces a generic rational univariate representation for solving zero-dimensional parametric polynomial systems, providing bounds and algorithms for effective computation.
Contribution
It presents a new generic parametrization method for zero-dimensional parametric polynomial systems, along with bounds and algorithms for computation.
Findings
Derived bounds on degrees and heights of the representation
Proposed two algorithms for effective computation
Analyzed specialization properties of the Rational Univariate Representation
Abstract
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.
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Taxonomy
TopicsPolynomial and algebraic computation · Advanced Differential Equations and Dynamical Systems · Advanced Optimization Algorithms Research