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Gröbner Basis Construction Algorithms Based on Theorem Proving Saturation Loops

Authors: Grant Olney Passmore, Leonardo de Moura, and Paul B. Jackson

Published in: Dagstuhl Seminar Proceedings, Volume 10161, Decision Procedures in Software, Hardware and Bioware (2010)


Abstract
We present novel Gr"obner basis algorithms based on saturation loops used by modern superposition theorem provers. We illustrate the practical value of the algorithms through an experimental implementation within the Z3 SMT solver.

Cite as

Grant Olney Passmore, Leonardo de Moura, and Paul B. Jackson. Gröbner Basis Construction Algorithms Based on Theorem Proving Saturation Loops. In Decision Procedures in Software, Hardware and Bioware. Dagstuhl Seminar Proceedings, Volume 10161, pp. 1-17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2010)


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@InProceedings{passmore_et_al:DagSemProc.10161.3,
  author =	{Passmore, Grant Olney and de Moura, Leonardo and Jackson, Paul B.},
  title =	{{Gr\"{o}bner Basis Construction Algorithms Based on Theorem Proving Saturation Loops}},
  booktitle =	{Decision Procedures in Software, Hardware and Bioware},
  pages =	{1--17},
  series =	{Dagstuhl Seminar Proceedings (DagSemProc)},
  ISSN =	{1862-4405},
  year =	{2010},
  volume =	{10161},
  editor =	{Nikolaj Bjorner and Robert Nieuwenhuis and Helmut Veith and Andrei Voronkov},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/DagSemProc.10161.3},
  URN =		{urn:nbn:de:0030-drops-27345},
  doi =		{10.4230/DagSemProc.10161.3},
  annote =	{Keywords: Groebner bases, ideal theory, automated theorem proving, SMT solvers}
}
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