We present the new version 2.0 of the Feynman integral reduction program Kira and
describe the new features. The primary new feature is the reconstruction of the final …

We present the main improvements and new features in version 2.0 of the open-source C++
library FireFly for the interpolation of rational functions. This includes algorithmic …

We present new baby steps/giant steps algorithms of asymptotically fast running time for
dense matrix problems. Our algorithms compute the determinant, characteristic polynomial …

A bstract We introduce an algebro-geometrically motived integration-by-parts (IBP) re-
duction method for multi-loop and multi-scale Feynman integrals, using a framework for …

We address the problem of unambiguous reconstruction of rational functions of many
variables. This is particularly relevant for recovery of exact expansion coefficients in …

A probabilistic strategy, early termination, enables different interpolation algorithms to adapt
to the degree or the number of terms in the target polynomial when neither is supplied in the …

We recall that the calculation of homology with integer coefficients of a simplicial complex
reduces to the calculation of the Smith Normal Form of the boundary matrices which in …

We present a new algorithm to compute the Integer Smith normal form of large sparse
matrices. We reduce the computation of the Smith form to independent, and therefore …

Black box techniques¹2 are enabling exact linear algebra computations of a scale well
beyond anything previously possible. The development of new and interesting algorithms …

Consider the black box interpolation of a τ-sparse, n-variate rational function f, where τ is the
maximum number of terms in either numerator or denominator. When numerator and …