4 papers
A data structure for monomial ideals with applications to signature Gröbner bases
Pierre Lairez, Rafael Mohr, Théo Ternier
We introduce monomial divisibility diagrams (MDDs), a data structure for monomial ideals that supports insertion of new generators and fast membership tests. MDDs stem from a canon…
Computing Generic Fibers of Polynomial Ideals with FGLM and Hensel Lifting
Jérémy Berthomieu, Rafael Mohr
We describe a version of the FGLM algorithm that can be used to compute generic fibers of positive-dimensional polynomial ideals. It combines the FGLM algorithm with a Hensel lifti…
A Direttissimo Algorithm for Equidimensional Decomposition
Christian Eder, Pierre Lairez, Rafael Mohr +1
We describe a recursive algorithm that decomposes an algebraic set into locally closed equidimensional sets, i.e. sets which each have irreducible components of the same dimension.…
A Signature-based Algorithm for Computing the Nondegenerate Locus of a Polynomial System
Christian Eder, Pierre Lairez, Rafael Mohr +1
Polynomial system solving arises in many application areas to model non-linear geometric properties. In such settings, polynomial systems may come with degeneration which the end-u…