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2020 | OriginalPaper | Chapter

Curtains in CAD: Why Are They a Problem and How Do We Fix Them?

Authors : Akshar Nair, James Davenport, Gregory Sankaran

Published in: Mathematical Software – ICMS 2020

Publisher: Springer International Publishing

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Abstract

This paper is part of our ongoing research on the adaptation of Lazard’s CAD to benefit from equational constraints in formulae. In earlier work we combined the CAD methods of McCallum and Lazard so as to produce an efficient algorithm for decomposing a hypersurface rather than the whole of \(\mathbb {R}^n\) (exploiting an equational constraint \(f=0\)). That method, however, fails if f is nullified (in McCallum’s terminology): we call the set where this happens a curtain. Here we provide a further modification which, at the cost of a trade off in terms of complexity, is valid for any hypersurface, including one containing curtains.

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Including \(\theta _0=-\infty \) and \(\theta _{k+1}=+\infty \).

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Title: Curtains in CAD: Why Are They a Problem and How Do We Fix Them?
Authors: Akshar Nair
James Davenport
Gregory Sankaran
Publisher: Springer International Publishing
Book: Mathematical Software – ICMS 2020
Print ISBN: 978-3-030-52199-8

Electronic ISBN: 978-3-030-52200-1

Copyright Year: 2020
DOI: https://doi.org/10.1007/978-3-030-52200-1_2

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