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 (exploiting an equational constraint). 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.

Original languageEnglish
Title of host publicationMathematical Software – ICMS 2020 - 7th International Conference, Proceedings
EditorsAnna Maria Bigatti, Jacques Carette, James H. Davenport, Michael Joswig, Timo de Wolff
Place of PublicationSingapore
PublisherSpringer, Singapore
Pages17-26
Number of pages10
ISBN (Print)9783030521998
DOIs
Publication statusPublished - 8 Jul 2020
Event7th International Congress on Mathematical Software, ICMS 2020 - Braunschweig, Germany
Duration: 13 Jul 202016 Jul 2020

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume12097 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Conference

Conference7th International Congress on Mathematical Software, ICMS 2020
CountryGermany
CityBraunschweig
Period13/07/2016/07/20

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science(all)

Cite this

Nair, A., Davenport, J., & Sankaran, G. (2020). Curtains in CAD: Why Are They a Problem and How Do We Fix Them? In A. M. Bigatti, J. Carette, J. H. Davenport, M. Joswig, & T. de Wolff (Eds.), Mathematical Software – ICMS 2020 - 7th International Conference, Proceedings (pp. 17-26). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 12097 LNCS). Springer, Singapore. https://doi.org/10.1007/978-3-030-52200-1_2