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Rational Solutions of Underdetermined Polynomial Equations
Thomas Wolf, Chimaobi Amadi
In this paper we report on an application of computer algebra in which mathematical puzzles are generated of a type that had been widely used in mathematics contests by a large num…
Solving large linear algebraic systems in the context of integrable non-abelian Laurent ODEs
Thomas Wolf, Eberhard Schruefer, Kenneth Webster
The paper reports on a computer algebra program LSSS (Linear Selective Systems Solver) for solving linear algebraic systems with rational coefficients. The program is especially ef…
The Parametric Solution of Underdetermined linear ODEs
Thomas Wolf
The purpose of this paper is twofold. An immediate practical use of the presented algorithm is its applicability to the parametric solution of underdetermined linear ordinary diffe…
A comparison of four approaches to the calculation of conservation laws
Thomas Wolf
The paper compares computational aspects of four approaches to compute conservation laws of single differential equations (DEs) or systems of them, ODEs and PDEs. The only restrict…
Size reduction and partial decoupling of systems of equations
Thomas Wolf
A method is presented that reduces the number of terms of systems of linear equations (algebraic, ordinary and partial differential equations). As a byproduct these systems have a…
The integration of systems of linear PDEs using conservation laws of syzygies
Thomas Wolf
A new integration technique is presented for systems of linear partial differential equations (PDEs) for which syzygies can be formulated that obey conservation laws. These syzygie…