FIRE is a program which performs integration-by-parts (IBP) reductions of Feynman
integrals. Originally, the C++ version of FIRE relies on the computer algebra system Fermat …

A bstract We describe the formalism to compute gravitational-wave observables for compact
binaries via the effective field theory framework in combination with modern tools from …

The recently developed algorithm FIRE performs the reduction of Feynman integrals to
master integrals. It is based on a number of strategies, such as applying the Laporta …

The existence of a finite basis of algebraically independent one-loop integrals has
underpinned important developments in the computation of one-loop amplitudes in field …

Deriving a comprehensive set of reduction rules for Feynman integrals has been a long-
standing challenge. In this paper, we present a proposed solution to this problem utilizing …

In this paper we present an algorithmic approach to the generation of fully conservative
difference schemes for linear partial differential equations. The approach is based on …

Investigating the correspondence between systems of partial differential equations and their
analytic solutions using a formal approach, this monograph presents algorithms to …

We describe how Gröbner bases can be used to solve the reduction problem for Feynman
integrals, ie to construct an algorithm that provides the possibility to express a Feynman …

LNCS 8372 - Basic Module Theory over Non-commutative Rings with Computational Aspects of
Operator Algebras Page 1 Basic Module Theory over Non-commutative Rings with …

This paper is a detailed description of an algorithm based on a generalized Buchberger
algorithm for constructing Gröbner-type bases associated with polynomials of shift operators …