78 citations · 172 across the 17 of their papers we have counts for
20 papers
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…
New efficient algorithms for computing Gröbner bases of saturation ideals (F4SAT) and colon ideals (Sparse-FGLM-colon)
Jérémy Berthomieu, Christian Eder, Mohab Safey El Din
This paper is concerned with linear algebra based methods for solving exactly polynomial systems through so-called Gröbner bases, which allow one to compute modulo the polynomial i…
msolve: A Library for Solving Polynomial Systems
Jérémy Berthomieu, Christian Eder, Mohab Safey El Din
We present a new open source C library \texttt{msolve} dedicated to solving multivariate polynomial systems of dimension zero through computer algebra methods. The core algorithmic…
Breaking the Hidden Irreducible Polynomials Scheme
Christian Eder
In 2019 Gómez described a new public key cryptography scheme based on ideas from multivariate public key cryptography using hidden irreducible polynomials. We show that the scheme'…
Existence of quantum symmetries for graphs on up to seven vertices: a computer based approach
Christian Eder, Viktor Levandovskyy, Julien Schanz +3
The symmetries of a finite graph are described by its automorphism group; in the setting of Woronowicz's quantum groups, a notion of a quantum automorphism group has been defined b…