Related papers: Symbolic Computing with Grassman Variables
Let $G$ be a commutative algebraic group embedded in projective space and $\Gamma$ a finitely generated subgroup of $G$. From these data we construct a chain of algebraic subgroups of $G$ which is intimately related to obstructions to…
Getting good performance out of numerical equation solvers requires that the user has provided stable and efficient functions representing their model. However, users should not be trusted to write good code. In this manuscript we describe…
We introduce the MathGR package, written in Mathematica. The package can manipulate tensor and GR calculations with either abstract or explicit indices, simplify tensors with permutational symmetries, decompose tensors from abstract indices…
Nonclassical symmetries and reductions of polynomial equations and systems of polynomial equations are considered. It is shown that specific polynomial equations having "hidden" symmetries can be reduced to classical symmetric systems of…
In the spirit of "multi-culturalism", we use four kinds of computations: simulation, numeric, symbolic, and "conceptual" to explore some "games of pure chance" inspired by children board games like "Snakes and Ladders" (aka as "Chutes and…
When exoplanets pass in front of their stars, they imprint a transit signature on the stellar light curve which to date has been assumed to be symmetric in time, owing to the planet being modelled as a circular area occulting the stellar…
In this paper we provide novel closed-form expressions enabling differentiation of any scalar function of the Kalman filter's outputs with respect to all its tuning parameters and to the measurements. The approach differs from the previous…
The computation of triangular decompositions are based on two fundamental operations: polynomial GCDs modulo regular chains and regularity test modulo saturated ideals. We propose new algorithms for these core operations relying on modular…
In this paper, a variable-coefficient symbolic computation approach is proposed to solve the multiple rogue wave solutions of nonlinear equation with variable coefficients. As an application, a (2+1)-dimensional variable-coefficient…
\pkg{multiplex} is a computer program that provides algebraic tools for the analysis of multiple network structures within the \proglang{R} environment. Apart from the possibility to create and manipulate multivariate data representing…
FCMpy is an open source package in Python for building and analyzing Fuzzy Cognitive Maps. More specifically, the package allows 1) deriving fuzzy causal weights from qualitative data, 2) simulating the system behavior, 3) applying machine…
Interpretability and uncertainty quantification in machine learning can provide justification for decisions, promote scientific discovery and lead to a better understanding of model behavior. Symbolic regression provides inherently…
We consider the problem of minimizing the makespan on batch processing identical machines, subject to compatibility constraints, where two jobs are compatible if they can be processed simultaneously in a same batch. These constraints are…
In this paper we present a Hamiltonian formulation of multisymplectic type of an invariant variational problem on smooth submanifold of dimension $p$ in a smooth manifold of dimension $n$ with $p<n$.
In this paper we present methods for the synthesis of polynomial invariants for probabilistic transition systems. Our approach is based on martingale theory. We construct invariants in the form of polynomials over program variables, which…
Two effective methods for writing the dynamical equations for non-holonomic systems are illustrated. They are based on the two types of representation of the constraints: by parametric equations or by implicit equations. They can be applied…
We devise a new formulation for the vertex coloring problem. Different from other formulations, decision variables are associated with the pairs of vertices. Consequently, colors will be distinguishable. Although the objective function is…
In present paper we propose seemingly new method for finding solutions of some types of nonlinear PDEs in closed form. The method is based on decomposition of nonlinear operators on sequence of operators of lower orders. It is shown that…
This preprint contains a description of a package for Mathematica called EinS. This package allows one to perform various calculations with indexed objects.
In this paper we present an open source framework developed in Python and consisting of three distinct classes designed to manipulate in a simple and intuitive way both symbolic representations of neutrosophic sets over universes of various…