Advances on the simplification of sine-cosine equations
type: Item
instance of: scholarly article
title: Advances on the simplification of sine-cosine equations
zbMATH Open document ID: 0912.65041
author: Jaime Gutierrez
author: Tomas Recio
published in: Journal of Symbolic Computation
publication date: 1999-05-03T00:00:00Z
review text: The paper is concerned with the solution or simplification of systems \(f(s,c)= 0\), \(s^2+ c^2- 1=0\). Applications are taken from the field of kinematics. The authors present fast algorithms for the functional decomposition and factorization problems, reducing the solution of the above equations (for sine-cosine polynomials) to a sequence of lower degree ones. Moreover, they show that triangularization of a given sine-cosine equation provides a conceptional understanding of the conditions that yield extraneous roots in the half-angle tangent substitution.
Mathematics Subject Classification ID: 65H10
Mathematics Subject Classification ID: 70B15
Mathematics Subject Classification ID: 65T40
Mathematics Subject Classification ID: 13P10
Mathematics Subject Classification ID: 70B10
Mathematics Subject Classification ID: 70E15
zbMATH DE Number: 1204267
zbMATH Keywords: sine-cosine equations
zbMATH Keywords: Gröbner bases
zbMATH Keywords: kinematics
zbMATH Keywords: fast algorithms
zbMATH Keywords: factorization
zbMATH Keywords: triangularization
reviewed by: Gabriele Steidl
MaRDI profile type: Publication
full work available at URL: jsco.1998.0200
OpenAlex ID: W2013940215
DOI: 10.1006/JSCO.1998.0200
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description: scientific article; zbMATH DE number 1204267