Related papers: Symbolic Computing with Grassman Variables
Polylab is a MATLAB toolbox for multivariate polynomial scalars and polynomial matrices with a unified symbolic-numeric interface across CPU and GPU-oriented backends. The software exposes three aligned classes: MPOLY for CPU execution,…
In this paper we introduce MATMPC, an open source software built in MATLAB for nonlinear model predictive control (NMPC). It is designed to facilitate modelling, controller design and simulation for a wide class of NMPC applications. MATMPC…
A set of Maplev R.3 software routines, for plotting 2D/3D projections of Poincar\'e surfaces-of-section of Hamiltonian dynamical systems, is presented. The package consists of a plotting-command plus a set of facility-commands for a quick…
Algorithms are presented for the tanh- and sech-methods, which lead to closed-form solutions of nonlinear ordinary and partial differential equations (ODEs and PDEs). New algorithms are given to find exact polynomial solutions of ODEs and…
A program package, which facilitates computations in the framework of Analytic approach to QCD, is developed and described in details. The package includes the explicit expressions for relevant spectral functions calculated up to the…
We present a novel approach for explaining Gaussian processes (GPs) that can utilize the full analytical covariance structure present in GPs. Our method is based on the popular solution concept of Shapley values extended to stochastic…
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…
Malware analysis techniques are divided into static and dynamic analysis. Both techniques can be bypassed by circumvention techniques such as obfuscation. In a series of works, the authors have promoted the use of symbolic executions…
In this paper, we investigate the implementation of a Python code for a Kalman Filter using the Numpy package. A Kalman Filtering is carried out in two steps: Prediction and Update. Each step is investigated and coded as a function with…
While there has been some discussion on how Symbolic Computation could be used for AI there is little literature on applications in the other direction. However, recent results for quantifier elimination suggest that, given enough example…
We introduce the Probability package for Macaulay2, which provides an interface for users to compute probabilities and generate random variates from a wide variety of univariate probability distributions.
We present a review of the symbol map, a mathematical tool that can be useful in simplifying expressions among multiple polylogarithms, and recall its main properties. A recipe is given for how to obtain the symbol of a multiple…
Many interesting and useful symbolic computation algorithms manipulate mathematical expressions in mathematically meaningful ways. Although these algorithms are commonplace in computer algebra systems, they can be surprisingly difficult to…
Pattern matching is a powerful tool for symbolic computations. Applications include term rewriting systems, as well as the manipulation of symbolic expressions, abstract syntax trees, and XML and JSON data. It also allows for an intuitive…
Gradient Symbolic Computation is proposed as a means of solving discrete global optimization problems using a neurally plausible continuous stochastic dynamical system. Gradient symbolic dynamics involves two free parameters that must be…
We present the Refinement Calculus of Reactive Systems Toolset, an environment for compositional modeling and reasoning about reactive systems, built on top of Isabelle, Simulink, and Python.
This article presents an introduction to MMPDElab, a package written in MATLAB for adaptive mesh movement and adaptive moving mesh P1 finite element solution of second-order partial different equations having continuous solutions in one,…
Lattice Boltzmann methods are a popular mesoscopic alternative to macroscopic computational fluid dynamics solvers. Many variants have been developed that vary in complexity, accuracy, and computational cost. Extensions are available to…
In this article we consider a method for proving a class of analytical inequalities via minimax rational approximations. All numerical calculations in this paper are given by Maple computer program.
The Chisholm rational approximant is a natural generalization to two variables of the well-known single variable Pad\'e approximant, and has the advantage of reducing to the latter when one of the variables is set equals to 0. We present,…