相关论文: Software for the Algorithmic Work with Orthogonal …
In this article we present a method to implement orthogonal polynomials and many other special functions in Computer Algebra systems enabling the user to work with those functions appropriately, and in particular to verify different types…
We provide algorithms for symbolic integration of hyperlogarithms multiplied by rational functions, which also include multiple polylogarithms when their arguments are rational functions. These algorithms are implemented in Maple and we…
In this paper we present a Maple library (MOPs) for computing Jack, Hermite, Laguerre, and Jacobi multivariate polynomials, as well as eigenvalue statistics for the Hermite, Laguerre, and Jacobi ensembles of Random Matrix theory. We also…
In many applications (hupergeometric-type) special functions like orthogonal polynomials are needed. For example in more than 50% of the published solutions for the (application-oriented) questions in the "Problems Section" of SIAM Review…
Symmetry plays a central role in accelerating symbolic computation involving polynomials. This chapter surveys recent developments and foundational methods that leverage the inherent symmetries of polynomial systems to reduce complexity,…
In this paper, we propose a new and simple approach to the approximation algorithms that are modified and improved from our published results. The computational and graphical examples are presented with the aid of Maple procedures.
A computation scheme for solving elliptic boundary value problems with axially symmetric confining potentials using different sets of one-parameter basis functions is presented. The efficiency of the proposed symbolic-numerical algorithms…
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…
Our Chapter in the upcoming Volume I: Computer Science and Software Engineering of Computing Handbook (Third edition), Allen Tucker, Teo Gonzales and Jorge L. Diaz-Herrera, editors, covers Algebraic Algorithms, both symbolic and numerical,…
This article presents some aspects and experience in the use of algebraic manipulation software applied to general relativity. Some years ago certain results were reported using computer algebra platforms, but the growing popularity of…
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…
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…
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…
Symbolic summation as an active research topic of symbolic computation provides efficient algorithmic tools for evaluating and simplifying different types of sums arising from mathematics, computer science, physics and other areas. Most of…
Orthogonal systems in $\mathrm{L}_2(\mathbb{R})$, once implemented in spectral methods, enjoy a number of important advantages if their differentiation matrix is skew-symmetric and highly structured. Such systems, where the differentiation…
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…
DifferentialGeometry is a Maple software package which symbolically performs fundamental operations of calculus on manifolds, differential geometry, tensor calculus, Lie algebras, Lie groups, transformation groups, jet spaces, and the…
We are interested in the fast computation of the exact value of integrals of polynomial functions over convex polyhedra. We present speed ups and extensions of the algorithms presented in previous work. We present the new software…
Quadratically optimized polynomials are described which are useful in multi-bosonic algorithms for Monte Carlo simulations of quantum field theories with fermions. Algorithms for the computation of the coefficients and roots of these…
The technique of guessing can be very fruitful when dealing with sequences which arise in practice. This holds true especially when guessing is performed algorithmically and efficiently. One highly useful tool for this purpose is the…