An algorithm to construct Gröbner bases for solving integration by parts relations

2006/02/09 by A. V. Smirnov, Alexander V Smirnov · 1 citation
Computer Science · Mathematics · Physics and Astronomy · #Algebra over a field #Construct (python library) #Cryptography and Residue Arithmetic #Feynman diagram #Feynman integral #Integration by parts #Numerical methods for differential equations #Polynomial and algebraic computation #hep-ph #hep-th

paper · pdf · doi:10.1088/1126-6708/2006/04/026

published as JHEP 0604 (2006) 026 · LaTeX, 9 pages

arxiv created 2006/02/09 · openalex publication_date 2006/04/13 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05

Abstract

This paper is a detailed description of an algorithm based on a generalized Buchberger algorithm for constructing Groebner-type bases associated with polynomials of shift operators. The algorithm is used for calculating Feynman integrals and has proven itself efficient in several complicated cases.

Citations

• Explicit solutions of the multi-loop integral recurrence relations and its application
• Integration by parts: The algorithm to calculate β-functions in 4 loops
• Explicit solutions of the 3-loop vacuum integral recurrence relations

Cited by

• Reinforcement Learning and Metaheuristics for Feynman Integral Reduction