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International Workshop on Computer Algebra in Scientific Computing

CASC 2014: Computer Algebra in Scientific Computing pp 44–58Cite as

Truth Table Invariant Cylindrical Algebraic Decomposition by Regular Chains

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 8660))

Abstract

A new algorithm to compute cylindrical algebraic decompositions (CADs) is presented, building on two recent advances. Firstly, the output is truth table invariant (a TTICAD) meaning given formulae have constant truth value on each cell of the decomposition. Secondly, the computation uses regular chains theory to first build a cylindrical decomposition of complex space (CCD) incrementally by polynomial. Significant modification of the regular chains technology was used to achieve the more sophisticated invariance criteria. Experimental results on an implementation in the RegularChains Library for Maple verify that combining these advances gives an algorithm superior to its individual components and competitive with the state of the art.

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Author information

Authors and Affiliations

  1. University of Bath, Bath, BA2 7AY, UK

    Russell Bradford, James H. Davenport, Matthew England & David Wilson

  2. CIGIT, Chinese Academy of Sciences, Chongqing, 400714, China

    Changbo Chen

  3. University of Western Ontario, London, Ontario, N6A 5B7, Canada

    Marc Moreno Maza

Authors
  1. Russell Bradford
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  2. Changbo Chen
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  3. James H. Davenport
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  4. Matthew England
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  5. Marc Moreno Maza
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  6. David Wilson
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Editor information

Editors and Affiliations

  1. Laboratory of Information Technologies (LIT), Joint Institute for Nuclear Research, 141980, Dubna, Russia

    Vladimir P. Gerdt

  2. Institut für Mathematik, Universität Kassel, Heinrich-Plett-Straße 40, 34132, Kassel, Germany

    Wolfram Koepf

  3. Institut für Mathematik, Universität Kassel, 34132, Kassel, Germany

    Werner M. Seiler

  4. Institute of Theoretical and Applied Mechanics, Russian Academy of Sciences, 630090, Novosibirsk, Russia

    Evgenii V. Vorozhtsov

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© 2014 Springer International Publishing Switzerland

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Bradford, R., Chen, C., Davenport, J.H., England, M., Moreno Maza, M., Wilson, D. (2014). Truth Table Invariant Cylindrical Algebraic Decomposition by Regular Chains. In: Gerdt, V.P., Koepf, W., Seiler, W.M., Vorozhtsov, E.V. (eds) Computer Algebra in Scientific Computing. CASC 2014. Lecture Notes in Computer Science, vol 8660. Springer, Cham. https://doi.org/10.1007/978-3-319-10515-4_4

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  • DOI: https://doi.org/10.1007/978-3-319-10515-4_4

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-10514-7

  • Online ISBN: 978-3-319-10515-4

  • eBook Packages: Computer ScienceComputer Science (R0)

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