Related papers: HPL, a Mathematica implementation of the harmonic …
We consider the problem of symbolic-numeric integration of symbolic functions, focusing on rational functions. Using a hybrid method allows the stable yet efficient computation of symbolic antiderivatives while avoiding issues of…
The purpose of this manuscript is to derive two distinct integral representations of the generalized polylogarithm using two different techniques. The first approach involves the Dirichlet series and its Laplace representation, which leads…
In this paper, we explore the merits of various algorithms for polynomial optimization problems, focusing on alternatives to sum of squares programming. While we refer to advantages and disadvantages of Quantifier Elimination, Reformulation…
We review a method for the algebraic treatment of a family of functions which contains the multiple polylogarithms, with applications to the symbolic calculation of Feynman integrals.
We present an implementation of algorithms for the symbolic integration of hyperlogarithms multiplied by rational functions in the computer algebra system FORM. This implementation encompasses cases where hyperlogarithms have rational…
This paper describes algorithms to deal with nested symbolic sums over combinations of harmonic series, binomial coefficients and denominators. In addition it treats Mellin transforms and the inverse Mellin transformation for functions that…
In this talk, we discuss recent progress in the application of generalizations of polylogarithms in the symbolic computation of multi-loop integrals. We briefly review the Maple program MPL which supports a certain approach for the…
Multiple elliptic polylogarithms can be written as (multiple) integrals of products of basic hypergeometric functions. The latter are computable, to arbitrary precision, using a q-difference equation and q-contiguous relations.
We introduce and study properties of certain new harmonic function spaces on products of upper half-spaces.Norm estimates for the so-called expanded Bergman projections are obtained.Sharp theorems on multipliers acting on certain Sobolev…
In this paper, we study linearly constrained optimization problems (LCP). After applying Hadamard parametrization, the feasible set of the parametrized problem (LCPH) becomes an algebraic variety, with conducive geometric properties which…
This study presents the derivation of a recursive formula for integrals of products of $N$ Hermite polynomials, establishing a numerically stable scheme for their accurate evaluation in computer codes. The derivation is notably simple and…
We consider the harmonic balance method for finding approximate periodic solutions of the Lorenz system. When developing software that implements the described method, the math package Maxima was chosen. The drawbacks of symbolic…
We present a new package ZpL for the mathematical software system SM. It implements a sharp tracking of precision on p-adic numbers, following the theory of ultrametric precision introduced in [4]. The underlying algorithms are mostly based…
The two-dimensional harmonic polylogarithms $\G(\vec{a}(z);y)$, a generalization of the harmonic polylogarithms, themselves a generalization of Nielsen's polylogarithms, appear in analytic calculations of multi-loop radiative corrections in…
We present the $\textit{NumericalImplicitization}$ package for $\textit{Macaulay2}$, which allows for user-friendly computation of the invariants of the image of a polynomial map, such as dimension, degree, and Hilbert function values. This…
We determine the explicit formulas for the sum of products of homogeneous multiple harmonic sums $\sum_{k=1}^n \prod_{j=1}^r H_k(\{1\}^{\lambda_j})$ when $\sum_{j=1}^r \lambda_j\leq 5$. We apply these identities to the study of two…
We discuss in detail a recently proposed hybrid particle-continuum scheme for complex fluids and evaluate it at the example of a confined homopolymer solution in slit geometry. The hybrid scheme treats polymer chains near the impenetrable…
We present a simple representation for analytically continued nested harmonic sums for the arbitrary complex argument. This representation can be obtained for a wide range of nested harmonic sums from a precomputed database for the pole…
We introduce different classical characteristics used to regularize a subharmonic function and compare them. As an application we give a complete proof of a useful characterization of the modulus of continuity of such functions in terms of…
Algebraic effects and handlers support composable and structured control-flow abstraction. However, existing designs of algebraic effects often require effects to be executed sequentially. This paper studies parallel algebraic effect…