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

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 [Formula...

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Detalles Bibliográficos
Autores principales: Nair, Akshar, Davenport, James, Sankaran, Gregory
Formato: Online Artículo Texto
Lenguaje:English
Publicado: 2020
Materias:
Article
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7340948/
http://dx.doi.org/10.1007/978-3-030-52200-1_2
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author Nair, Akshar
Davenport, James
Sankaran, Gregory
author_facet Nair, Akshar
Davenport, James
Sankaran, Gregory
author_sort Nair, Akshar
collection PubMed
description 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 [Formula: see text] (exploiting an equational constraint [Formula: see text]). 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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spelling pubmed-73409482020-07-08 Curtains in CAD: Why Are They a Problem and How Do We Fix Them? Nair, Akshar Davenport, James Sankaran, Gregory Mathematical Software – ICMS 2020 Article 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 [Formula: see text] (exploiting an equational constraint [Formula: see text]). 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. 2020-06-06 /pmc/articles/PMC7340948/ http://dx.doi.org/10.1007/978-3-030-52200-1_2 Text en © Springer Nature Switzerland AG 2020 This article is made available via the PMC Open Access Subset for unrestricted research re-use and secondary analysis in any form or by any means with acknowledgement of the original source. These permissions are granted for the duration of the World Health Organization (WHO) declaration of COVID-19 as a global pandemic.
spellingShingle Article
Nair, Akshar
Davenport, James
Sankaran, Gregory
Curtains in CAD: Why Are They a Problem and How Do We Fix Them?
title Curtains in CAD: Why Are They a Problem and How Do We Fix Them?
title_full Curtains in CAD: Why Are They a Problem and How Do We Fix Them?
title_fullStr Curtains in CAD: Why Are They a Problem and How Do We Fix Them?
title_full_unstemmed Curtains in CAD: Why Are They a Problem and How Do We Fix Them?
title_short Curtains in CAD: Why Are They a Problem and How Do We Fix Them?
title_sort curtains in cad: why are they a problem and how do we fix them?
topic Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7340948/
http://dx.doi.org/10.1007/978-3-030-52200-1_2
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AT davenportjames curtainsincadwhyaretheyaproblemandhowdowefixthem
AT sankarangregory curtainsincadwhyaretheyaproblemandhowdowefixthem

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