Sparse Rational Univariate Representation

Angelos Mantzaflaris (1) , Éric Schost (2) , Elias Tsigaridas (3)

1 RICAM - Johann Radon Institute for Computational and Applied Mathematics
2 CS - Cheriton School of Computer Science [Waterloo]
3 PolSys - Polynomial Systems

We present explicit worst case degree and height bounds for the rational univariate representation of the isolated roots of polynomial systems based on mixed volume. We base our estimations on height bounds of resultants and we consider the case of 0-dimensional, positive dimensional, and parametric polynomial systems.

Mots clés: separation bound; sparse resultant; DMM; polynomial system; rational univariate representation; Keywords; •Computing methodologies → Symbolic calculus algorithms; CCS Concepts

Domaines: Calcul formel [cs.SC]

Angelos Mantzaflaris, Éric Schost, Elias Tsigaridas. Sparse Rational Univariate Representation. ISSAC 2017 - International Symposium on Symbolic and Algebraic Computation, Jul 2017, Kaiserslautern, Germany. pp.8, ⟨10.1145/3087604.3087653⟩. ⟨hal-01528377⟩