Related papers: A SageTeX Hypermatrix Algebra Package
We present a novel algebraic combinatorial view on low-rank matrix completion based on studying relations between a few entries with tools from algebraic geometry and matroid theory. The intrinsic locality of the approach allows for the…
SARAH is a Mathematica package for building and studying supersymmetric models. It calculates for a given superpotential and gauge sector the full Lagrangian of a model. With the new version of SARAH it is possible to calculate…
A method for converting the geometrical problem of rectangle packing to an algebraic problem of solving a system of polynomial equations is described.
We consider the extension of the Heisenberg vertex operator algebra by all its irreducible modules. We give an elementary construction for the intertwining vertex operators and show that they satisfy a complex parametrized generalized…
In this paper, we review the problem of matrix completion and expose its intimate relations with algebraic geometry, combinatorics and graph theory. We present the first necessary and sufficient combinatorial conditions for matrices of…
We present a Sage implementation of Ore algebras. The main features for the most common instances include basic arithmetic and actions; gcrd and lclm; D-finite closure properties; natural transformations between related algebras; guessing;…
We present a SageMath package for calculating elliptic genera of homogeneous spaces and their complete intersections. This includes the calculation of the basis of weak Jacobi forms, Chern numbers of homogeneous spaces and their complete…
In this paper, we describe general characteristics of the MathPartner computer algebra system (CAS) and Mathpar programming language thereof. MathPartner can be used for scientific and engineering calculations, as well as in high schools…
A tutorial of the Mathematica package CGAlgebra, for conformal geometric algebra calculations is presented. Using rule-based programming, the 5-dimensional conformal geometric algebra is implemented and defined functions simplify the…
We propose a sparse algebra for samplet compressed kernel matrices, to enable efficient scattered data analysis. We show the compression of kernel matrices by means of samplets produces optimally sparse matrices in a certain S-format. It…
Presentation of set matrices and demonstration of their efficiency as a tool using the path/cycle problem.
The Invar package is introduced, a fast manipulator of generic scalar polynomial expressions formed from the Riemann tensor of a four-dimensional metric-compatible connection. The package can maximally simplify any polynomial containing…
We use Bernstein's presentation of the Iwahori-Matsumoto Hecke algebra to obtain a simple proof of the Satake isomorphism and, in the same stroke, compute the center of the Iwahori-Matsumoto Hecke algebra.
In this paper, we examine the structure of systems that are weighted homogeneous for several systems of weights, and how it impacts the computation of Gr\"obner bases. We present several linear algebra algorithms for computing Gr\"obner…
The article mainly presents some results in using MAPLE platform for computer algebra and GrTensorII package in doing calculations for theoretical and numerical cosmology
This paper summarizes the essential functionality of the computer algebra package HarmonicSums. On the one hand HarmonicSums can work with nested sums such as harmonic sums and their generalizations and on the other hand it can treat…
The boundary of the multi-scale differential compactification of strata of abelian differentials admits an explicit combinatorial description. However, even for low-dimensional strata, the complexity of the boundary requires use of a…
We report on a package of routines for the computer algebra system Maple which supports the explicit determination of the geometric quantities, field equations, equations of motion, and conserved quantities of General Relativity in the…
We present IntU package for Mathematica computer algebra system. The presented package performs a symbolic integration of polynomial functions over the unitary group with respect to unique normalized Haar measure. We describe a number of…
We study the properties of ultrametric matrices aiming to design methods for fast ultrametric matrix-vector multiplication. We show how to encode such a matrix as a tree structure in quadratic time and demonstrate how to use the resulting…