Related papers: A SageTeX Hypermatrix Algebra Package
The article presents and documents the Mathematica package SymBuild. This package implements the computation and manipulation of integrable symbols appearing in various calculations in high-energy scattering amplitudes. By using Gr\"obner…
Since its introduction by Gauss, Matrix Algebra has facilitated understanding of scientific problems, hiding distracting details and finding more elegant and efficient ways of computational solving. Today's largest problems, which often…
We present new algorithms that efficiently approximate the hypergeometric function of a matrix argument through its expansion as a series of Jack functions. Our algorithms exploit the combinatorial properties of the Jack function, and have…
We present here algorithms for efficient computation of linear algebra problems over finite fields.
This article introduces the Mathematica package \emph{HEPMath} which provides a number of utilities and algorithms for High Energy Physics computations in Mathematica. Its functionality is similar to packages like FormCalc or FeynCalc, but…
For some research questions that involve Spin(p, q) representation theory, using symbolic algebra based techniques might be an attractive option for simplifying and manipulating expressions. Yet, for some such problems, especially as they…
We are developing a Maple package of functions related to Rota's Umbral Calculus. A Mathematica version of this package is being developed in parallel.
In many-particle problems involving interacting fermions or bosons, the most natural language for expressing the Hamiltonian, the observables, and the basis states is the language of the second-quantization operators. It thus appears…
It is our intention here only to discuss the nature, complexity and tools concerning the design of Smart Help, an expert help facility for aiding users of Computer Algebra Systems. Although the expert help system presented here has been…
This article summarizes new features and enhancements of the first major update of Package-X. Package-X 2.0 can now generate analytic expressions for arbitrarily high rank dimensionally regulated tensor integrals with up to four distinct…
Efficiently processing basic linear algebra subroutines is of great importance for a wide range of computational problems. In this paper, we consider techniques to implement matrix functions on a quantum computer, which are composed of…
In this paper, we present a new approach to the semantic enrichment of mathematical expression problem. Our approach is a combination of statistical machine translation and disambiguation which makes use of surrounding text of the…
We describe here the package {\tt subdivision\\_solver} for the mathematical software {\tt SageMath}. It provides a solver on real numbers for square systems of large dense polynomials. By large polynomials we mean multivariate polynomials…
Huang's geometric interpretation of vertex operator algebras is extended to a supergeometric interpretation of vertex operator superalgebras. In particular, the geometry of spheres with punctures and local analytic coordinates in terms of…
We define alternating cyclotomic Hecke algebras in higher levels as subalgebras of cyclotomic Hecke algebras under an analogue of Goldman's hash involution. We compute the rank of these algebras and construct a full set of irreducible…
We introduce a class of regular unit Hadamard matrices whose entries consist of two complex numbers and their conjugates for a total of four complex numbers. We then show that these matrices are contained in the Bose-Mesner algebra of an…
These lecture notes present a method for symbolic tensor calculus that (i) runs on fully specified smooth manifolds (described by an atlas), (ii) is not limited to a single coordinate chart or vector frame, (iii) runs even on…
simpcomp is an extension (a so called package) to GAP, the well known system for computational discrete algebra. The package enables the user to compute numerous properties of (abstract) simplicial complexes, provides functions to construct…
This article describes the REDUCE package ZEILBERG implemented by Gregor St\"olting and the author. The REDUCE package ZEILBERG is a careful implementation of the Gosper and Zeilberger algorithms for indefinite, and definite summation of…
We present in this paper some fundamental tools for developing matrix analysis over the complex quaternion algebra. As applications, we consider generalized inverses, eigenvalues and eigenvectors, similarity, determinants of complex…