78 citations · 147 across the 7 of their papers we have counts for
6 papers · 1 filter
Reducing the size and number of linear programs in a dynamic Gröbner basis algorithm
Massimo Caboara, John Perry
The dynamic algorithm to compute a Gröbner basis is nearly twenty years old, yet it seems to have arrived stillborn; aside from two initial publications, there have been no publish…
Signature-based algorithms to compute Groebner bases
Christian Eder, John Perry
This paper describes a Buchberger-style algorithm to compute a Groebner basis of a polynomial ideal, allowing for a selection strategy based on "signatures". We explain how three r…
The F5 Criterion revised
Alberto Arri, John Perry
The purpose of this work is to generalize part of the theory behind Faugere's "F5" algorithm. This is one of the fastest known algorithms to compute a Groebner basis of a polynomia…
Modifying Faugère's F5 Algorithm to ensure termination
Christian Eder, Justin Gash, John Perry
The structure of the F5 algorithm to compute Gröbner bases makes it very efficient. However, while it is believed to terminate for so-called regular sequences, it is not clear whet…
An extension of Buchberger's criteria for Groebner basis decision
John Perry
Two fundamental questions in the theory of Groebner bases are decision ("Is a basis G of a polynomial ideal a Groebner basis?") and transformation ("If it is not, how do we transfo…
F5C: a variant of Faugere's F5 algorithm with reduced Groebner bases
Christian Eder, John Perry
Faugere's F5 algorithm computes a Groebner basis incrementally, by computing a sequence of (non-reduced) Groebner bases. The authors describe a variant of F5, called F5C, that repl…