Related papers: Symbolic Computing with Grassman Variables
We present the Mathematica package QMeS-Derivation. It derives symbolic functional equations from a given master equation. The latter include functional renormalisation group equations, Dyson-Schwinger equations, Slavnov-Taylor and Ward…
The Python colorspace package provides a toolbox for mapping between different color spaces which can then be used to generate a wide range of perceptually-based color palettes for qualitative or quantitative (sequential or diverging)…
Author presents a study of certain category of the integrals, which might look quite difficult to compute, but in fact are easily computable, because they do not depend on the parameter in the integrand. As simple and elementary the…
The paper deals with the process of mathematical modeling representations of exponential and logarithmic functions hypercomplex number system of generalized quaternions via determining a linear differential equation with hypercomplex…
We provide a survey of results from symbolic dynamics and algebraic topology relating to Grout, a new user-friendly program developed to calculate combinatorial properties and topological invariants of a large class of symbolic…
In this short article I introduce the mvp package, which provides some functionality for handling multivariate polynomials. The package uses the C++ Standard Template Library's map class to store and retrieve elements; it conforms to…
The construction of soft noncommutative schemes via toric geometry in arXiv:2108.05328 [math.AG] (D(15.1), NCS(1)) can be generalized and applied to a commutative scheme with a distinguished atlas of reasonably good affine local coordinate…
We present a method for symbolic calculation of Feynman amplitudes for processes involving both massless and massive fermions. With this approach fermion strings in a specific amplitude can be easily evaluated and expressed as basic Lorentz…
A method of computing a basis for the second Yang-Baxter cohomology of a finite biquandle with coefficients in Q and Z_p from a matrix presentation of the finite biquandle is described. We also describe a method for computing the…
In this paper the main results in arXiv:0901.3179v3, related to the matrix representation of polynomial maps, are restated in traditional way of linear algebra assuming that variable vectors are presented as column vectors. Some new results…
We describe a package realized in the Julia programming language which performs symbolic manipulations applied to nonlinear evolution equations, their flows, and commutators of such objects. This tool was employed to perform contrived…
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 give asymptotic expressions for the number of commuting matrices over finite fields. For this, we use product expansions for the corresponding generating functions.
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…
A numerical procedure and its MAPLE implementation capable of rigorously, albeit in a brute-force manner, proving specific strict one-variable inequalities in specific finite intervals is described. The procedure is useful, for instance, to…
We propose a new static program analysis called program behavior analysis. The analysis aims to calculate possible symbolic expressions for every variable at each program point. We design a new lattice, transfer function, and widening…
A software for simplification of Dirac matrix polynomials that arise in particle physics problems is implemented.
This paper describes the RationalMaps package for Macaulay2. This package provides functionality for computing several aspects of rational maps such as whether a map is birational, or a closed embedding.
Cylindrical Algebraic Decomposition (CAD) is an important tool within computational real algebraic geometry, capable of solving many problems for polynomial systems over the reals. It has long been studied by the Symbolic Computation…
We present the Mathematica package MultivariateResidues, which allows for the efficient evaluation of multivariate residues based on methods from computational algebraic geometry. Multivariate residues appear in several contexts of…