55 citations · 152 across the 16 of their papers we have counts for
17 papers
Commutative Algebra and Algebraic Geometry using OSCAR
Janko Boehm, Wolfram Decker, Frank-Olaf Schreyer
We give illustrative examples of how the computer algebra system OSCAR can support research in commutative algebra and algebraic geometry. We start with a thorough introduction to…
Module Intersection for the Integration-by-Parts Reduction of Multi-Loop Feynman Integrals
Dominik Bendle, Janko Boehm, Wolfram Decker +4
In this manuscript, which is to appear in the proceedings of the conference "MathemAmplitude 2019" in Padova, Italy, we provide an overview of the module intersection method for th…
Integration-by-parts reductions of Feynman integrals using Singular and GPI-Space
Dominik Bendle, Janko Boehm, Wolfram Decker +5
We introduce an algebro-geometrically motived integration-by-parts (IBP) reduction method for multi-loop and multi-scale Feynman integrals, using a framework for massively parallel…
Towards Massively Parallel Computations in Algebraic Geometry
Janko Boehm, Wolfram Decker, Anne Frühbis-Krüger +3
Introducing parallelism and exploring its use is still a fundamental challenge for the computer algebra community. In high performance numerical simulation, on the other hand, tran…
Modular Techniques For Noncommutative Gröbner Bases
Wolfram Decker, Christian Eder, Viktor Levandovskyy +1
In this note, we extend modular techniques for computing Gröbner bases from the commutative setting to the vast class of noncommutative -algebras. As in the commutative case, an…
Bad Primes in Computational Algebraic Geometry
Janko Boehm, Wolfram Decker, Claus Fieker +2
Computations over the rational numbers often suffer from intermediate coefficient swell. One solution to this problem is to apply the given algorithm modulo a number of primes and…