The goal of this paper is to present a new major release of the program FIESTA (Feynman Integral Evaluation by a Sector decomposiTion Approach). This version presents features likeâ€¦ (More)

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 algorithm, the s-basesâ€¦ (More)

We describe how GrÃ¶bner bases can be used to solve the reduction problem for Feynman integrals, i.e. to construct an algorithm that provides the possibility to express a Feynman integral of a givenâ€¦ (More)

New features of the Mathematica code FIRE are presented. In particular, it can be applied together with the recently developed code LiteRed by Lee in order to provide an integration by partsâ€¦ (More)

This paper is a detailed description of an algorithm based on a generalized Buchberger algorithm for constructing GrÃ¶bner-type bases associated with polynomials of shift operators. The algorithm isâ€¦ (More)

We evaluate multiple polylogarithm values at sixth roots of unity up to weight six, i.e. of the form G(a1, . . . , aw; 1) where the indices ai are equal to zero or a sixth root of unity, with a1 6=â€¦ (More)

One of the two existing strategies of resolving singularities of multifold Mellinâ€“Barnes integrals in the dimensional regularization parameter, or a parameter of the analytic regularization, isâ€¦ (More)

Up to the moment there are two known algorithms of sector decomposition: an original private algorithm of Binoth and Heinrich and an algorithm made public last year by Bogner and Weinzierl. Weâ€¦ (More)