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For some time now I have been wondering how well the existing polynomial factorization algorithms perform on some of the more difficult multivariate polynomials. Below are ten (of the over 300) multivariate polynomials that the heuristic program (POLYFACT) with learning factored while I was...
This is a brief summary and exposition of the paper "Quantifier Elimination for Real Closed Fields by Cylindrical Algebraic Decomposition," which was presented at the Second GI Conference on Automata Theory and Formal Languages, University of Kaiserslautern, May 1975, and which appears in the...
ALDES is a formalization of the method to describe algorithms used in Knuth's books. The largest documentation of algebraic algorithms, Collins' SAC system for Computer Algebra, is written in this language. In contrast to PASCAL it provides automatic storage deallocation. Compared to LISP equal...
Generate a set of equations for an explicit k-th order, m stage, Runge-Kutta method for integrating an autonomous system of ordinary differential equations, k and m as large as possible. The number of conditions and variables for various k and m are given in Table 1. Tabulate the costs C(m,k).
Many problems in numerical mathematics can be described by formulas and sentences of elementary real algebra, i.e. by real variables, +, ., -, >, =, by logical operations EQUATION and by existential and universal quantifiers. In 1933 A. Tarski found a method which enables one to decide in a...
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