Related papers: PolyLogTools - Polylogs for the masses
The Python package pylimer-tools is a comprehensive toolkit for computational studies of polymer networks, particularly bead-spring networks. The package provides functionality to generate polymer networks using Monte Carlo (MC) procedures…
Multiple polylogarithms appear in analytic calculations of higher order corrections in quantum field theory. In this article we study the numerical evaluation of multiple polylogarithms. We provide algorithms, which allow the evaluation for…
Loop invariants are properties of a program loop that hold before and after each iteration of the loop. They are often employed to verify programs and ensure that algorithms consistently produce correct results during execution.…
In this paper we present a Maple library (MOPs) for computing Jack, Hermite, Laguerre, and Jacobi multivariate polynomials, as well as eigenvalue statistics for the Hermite, Laguerre, and Jacobi ensembles of Random Matrix theory. We also…
The Hopf fibration is an important object in mathematics and physics. A landmark discovery in topology and a fundamental object in the theory of Lie groups, the Hopf fibration has a wide variety of physical applications including magnetic…
This is the first one in a series of two papers on the continuation of our study in cup products in Hopf cyclic cohomology. In this note we construct cyclic cocycles of algebras out of Hopf cyclic cocycles of algebras and coalgebras. In the…
Recent advances in stochastic PDEs, Hopf algebras of typed trees and integral equations have inspired the study of algebraic structures with replicating operations. To understand their algebraic and combinatorial nature, we first use rooted…
This article introduces a method, which starting from simple and quite general mathematical data, allows to construct linear algebras of operators which are, each of them, endowed with a bialgebra structure (coproduct and counity). Moreover…
Using integration by parts relations, Feynman integrals can be represented in terms of coupled systems of differential equations. In the following we suppose that the unknown Feynman integrals can be given in power series representations,…
This is a study on pattern Hopf algebras in combinatorial structures. We introduce the notion of combinatorial presheaf, by adapting the algebraic framework of species to the study of substructures in combinatorics. Afterwards, we consider…
It's well known that multiple polylogarithms give rise to good unipotent variations of mixed Hodge-Tate structures. In this paper we shall {\em explicitly} determine these structures related to multiple logarithms and some other multiple…
An explicit construction is presented of homotopy-invariant iterated integrals on a Riemann surface of arbitrary genus in terms of a flat connection valued in a freely generated Lie algebra. The integration kernels consist of modular…
In this paper, we extend the iterated integrals from smooth manifolds to digraphs and develop the associated algebraic and geometric structures. Iterated integrals on a digraph naturally give rise to the iterated path algebra and the…
The most popular method for computing the matrix logarithm is a combination of the inverse scaling and squaring method in conjunction with a Pad\'e approximation, sometimes accompanied by the Schur decomposition. The main computational…
Our goal is to study the feasibility of porting termination analysis techniques developed for one programming paradigm to another paradigm. In this paper, we show how to adapt termination analysis techniques based on polynomial…
This work presents the Polynomiogram framework, an integrated computational platform for exploring, visualizing, and generating art from polynomial root systems. The main innovation is a flexible sampling scheme in which two independent…
We describe a version of the FGLM algorithm that can be used to compute generic fibers of positive-dimensional polynomial ideals. It combines the FGLM algorithm with a Hensel lifting strategy. In analogy with Hensel lifting, we show that…
We present recent computer algebra methods that support the calculations of (multivariate) series solutions for (certain coupled systems of partial) linear differential equations. The summand of the series solutions may be built by…
We study the computational model of polygraphs. For that, we consider polygraphic programs, a subclass of these objects, as a formal description of first-order functional programs. We explain their semantics and prove that they form a…
We present explicit expressions for multi-fold logarithmic integrals that are equivalent to sums over polygamma functions at integer argument. Such relations find application in perturbative quantum field theory, quantum chemistry, analytic…