FIRE4, LiteRed and accompanying tools to solve integration by parts relations

This program has been imported from the CPC Program Library held at Queen's University Belfast (1969-2018) Abstract We present the new version of the Mathematica code FIRE and ideas behind it. It can be applied together with the recently developed code LiteRed by Lee in order to provide an integration by parts reduction to master integrals for quite complicated families of Feynman integrals. As an example, we consider four-loop massless propagator integrals for which LiteRed provides reduction rules and FIRE assists to apply these rules. So, as a by-product one obtains a four-loop variant of the well-known... Title of program: FIRE4 Catalogue Id: AEPW_v1_0 Nature of problem Reducing Feynman integrals to master integrals can be treated as a task to solve a huge system of sparse linear equations with polynomial coefficients. Versions of this program held in the CPC repository in Mendeley Data AEPW_v1_0; FIRE4; 10.1016/j.cpc.2013.06.016 AEPW_v2_0; FIRE5; 10.1016/j.cpc.2014.11.024