Related papers: A SageTeX Hypermatrix Algebra Package
This paper presents the XAMG library for solving large sparse systems of linear algebraic equations with multiple right-hand side vectors. The library specializes but is not limited to the solution of linear systems obtained from the…
We discuss a selection of recent developments in arithmetic combinatorics having to do with ``approximate algebraic structure'' together with some of their applications.
Nowadays sparse systems of equations occur frequently in science and engineering. In this contribution we deal with sparse systems common in cryptanalysis. Given a cipher system, one converts it into a system of sparse equations, and then…
We present OGRe, a modern Mathematica package for tensor calculus, designed to be both powerful and user-friendly. The package can be used in a variety of contexts where tensor calculations are needed, in both mathematics and physics, but…
In this paper we introduce Redberry --- an open source computer algebra system with native support of tensorial expressions. It provides basic computer algebra tools (algebraic manipulations, substitutions, basic simplifications etc.) which…
We introduce new classes of integrable models that exhibit a structure similar to that of flag vector spaces. We present their Hamiltonians, R-matrices and Bethe-ansatz solutions. These models have a new type of generalized graded algebra…
In our article we consider some algebraical methods which may be useful in some inverse spectral problems. The reconstraction of the matrix from its minors is considered.
In this article, we will show the existence of lattice packings in a sparse family of dimensions. This construction will be a generalisation of Venkatesh's lattice packing result. In our construction, we replace the appearance of the…
A simple iteration methodology for the solution of a set of a linear algebraic equations is presented. The explanation of this method is based on a pure geometrical interpretation and pictorial representation. Convergence using this method…
Computer Algebra Systems (e.g. Maple) are used in research, education, and industrial settings. One of their key functionalities is symbolic integration, where there are many sub-algorithms to choose from that can affect the form of the…
We offer a Maple package SL\_2\_Inv\_Ker for calculating of minimal generating sets for the algebras of joint invariants/semi-invariants of binary forms and for calculations of the kernels of Weitzenb\"ock derivations.
In this paper an exponential multiplicative formula for the R-matrix is provided for the twisted affine quantum algebras.
We present a distributed-memory library for computations with dense structured matrices. A matrix is considered structured if its off-diagonal blocks can be approximated by a rank-deficient matrix with low numerical rank. Here, we use…
Given a basic compact semi-algebraic set $\K\subset\R^n$, we introduce a methodology that generates a sequence converging to the volume of $\K$. This sequence is obtained from optimal values of a hierarchy of either semidefinite or linear…
A prototype for an extensible interactive graphical term manipulation system is presented that combines pattern matching and nondeterministic evaluation to provide a convenient framework for doing tedious algebraic manipulations that so far…
We describe the computer algebra software package SpectralSequences for the computer algebra system Macaulay2. This package implements many data types, objects and algorithms which pertain to, among other things, filtered complexes,…
Matrix-matrix multiplication is a fundamental operation of great importance to scientific computing and, increasingly, machine learning. It is a simple enough concept to be introduced in a typical high school algebra course yet in practice…
We present a MATLAB/Octave toolbox to decompose finite dimensionial representations of compact groups. Surprisingly, little information about the group and the representation is needed to perform that task. We discuss applications to…
An algorithm is presented that generates sets of size equal to the degree of a given variety defined by a homogeneous ideal. This algorithm suggests a versatile framework to study various problems in combinatorial algebraic geometry and…
The purpose of this note is to survey a methodology to solve systems of polynomial equations and inequalities. The techniques we discuss use the algebra of multivariate polynomials with coefficients over a field to create large-scale linear…