6 papers · 1 filter
LinApart2: efficient parallel partial fraction decomposition algorithm for denominators with polynomials of general degree
Levente Fekésházy, Oliver Schnetz
We present LinApart2, a major update to the LinApart algorithm for univariate partial fraction decomposition. Unlike its predecessor, LinApart2 can handle denominators of arbitrary…
HyperFORM -- a FORM package for parametric integration with hyperlogarithms
Adam Kardos, Sven-Olaf Moch, Oliver Schnetz
We present an implementation of algorithms for the symbolic integration of hyperlogarithms multiplied by rational functions in the computer algebra system FORM. This implementation…
theory at six loops
Oliver Schnetz
We present the renormalization functions of dimensionally regularized theory in six dimensions up to loop order six in the minimal subtraction scheme.
Graphical functions with spin
Oliver Schnetz
The theory of graphical functions is generalized from scalar theories to theories with spin, leading to a numerator structure in Feynman integrals. The main part of this article tr…
The five-twist identity for Feynman periods
Oliver Schnetz
We prove a new identity for Feynman periods that acts on five-vertex cuts of completed primitive Feynman graphs. It is shown that in theory this identity is independent from…
Notes on color reductions and traces
Oliver Schnetz
We present efficient algorithms to calculate the color factors for the gauge group and to evaluate traces. The aim of these notes is to give a self-contained, proved ac…