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Computing Gröbner bases in monoid and group rings

Authors:

Klaus Madlener,

Birgit ReinertAuthors Info & Claims

ISSAC '93: Proceedings of the 1993 international symposium on Symbolic and algebraic computation

Pages 254 - 263

https://doi.org/10.1145/164081.164139

Published: 01 August 1993 Publication History

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Cited By

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Barkee BCeria MMoriarty TVisconti A(2020)Why you cannot even hope to use Gröbner bases in cryptography: an eternal golden braid of failuresApplicable Algebra in Engineering, Communication and Computing10.1007/s00200-020-00428-wOnline publication date: 17-Apr-2020
https://doi.org/10.1007/s00200-020-00428-w
Mora FRobertz DLinton SYokoyama K(2015)De Nugis Groebnerialium 4Proceedings of the 2015 ACM International Symposium on Symbolic and Algebraic Computation10.1145/2755996.2756640(283-290)Online publication date: 24-Jun-2015
https://dl.acm.org/doi/10.1145/2755996.2756640
Hall B(2013)Computing homology using generalized Gröbner basesJournal of Symbolic Computation10.1016/j.jsc.2013.01.00454(59-71)Online publication date: 1-Jul-2013
https://dl.acm.org/doi/10.1016/j.jsc.2013.01.004
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Computing Gröbner bases in monoid and group rings

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Comprehensive Gröbner bases for parametric polynomial ideals were introduced, constructed, and studied by the author in 1992. Since then the construction has been implemented in the computer algebra systems ALDES/SAC-2, MAS, REDUCE and MAPLE. A ...
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In this paper we propose a 1-to-1 correspondence between graded two-sided ideals of the free associative algebra and some class of ideals of the algebra of polynomials, whose variables are double-indexed commuting ones. We call these ideals the ''...

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ISSAC '93: Proceedings of the 1993 international symposium on Symbolic and algebraic computation

August 1993

321 pages

ISBN:0897916042

DOI:10.1145/164081

Editor:
Manuel Bronstein

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Published: 01 August 1993

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SIGSAM

ISSAC93: International Symposium on Symbolic and Algebraic

July 6 - 8, 1993

Kiev, Ukraine

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Overall Acceptance Rate 395 of 838 submissions, 47%

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Cited By

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Barkee BCeria MMoriarty TVisconti A(2020)Why you cannot even hope to use Gröbner bases in cryptography: an eternal golden braid of failuresApplicable Algebra in Engineering, Communication and Computing10.1007/s00200-020-00428-wOnline publication date: 17-Apr-2020
https://doi.org/10.1007/s00200-020-00428-w
Mora FRobertz DLinton SYokoyama K(2015)De Nugis Groebnerialium 4Proceedings of the 2015 ACM International Symposium on Symbolic and Algebraic Computation10.1145/2755996.2756640(283-290)Online publication date: 24-Jun-2015
https://dl.acm.org/doi/10.1145/2755996.2756640
Hall B(2013)Computing homology using generalized Gröbner basesJournal of Symbolic Computation10.1016/j.jsc.2013.01.00454(59-71)Online publication date: 1-Jul-2013
https://dl.acm.org/doi/10.1016/j.jsc.2013.01.004
Reinert BZeckzer D(2010)Coset Enumeration Using Prefix Gröbner Bases: An Experimental ApproachLMS Journal of Computation and Mathematics10.1112/S14611570000008264(74-134)Online publication date: 1-Feb-2010
https://doi.org/10.1112/S1461157000000826
Sattler-Klein A(2007)Some complexity results for prefix Gröbner bases in free monoid ringsProceedings of the 16th international conference on Fundamentals of Computation Theory10.5555/2391495.2391538(470-481)Online publication date: 27-Aug-2007
https://dl.acm.org/doi/10.5555/2391495.2391538
Sattler-Klein A(2007)An exponential lower bound for prefix Gröbner bases in free monoid ringsProceedings of the 24th annual conference on Theoretical aspects of computer science10.5555/1763424.1763462(308-319)Online publication date: 22-Feb-2007
https://dl.acm.org/doi/10.5555/1763424.1763462
Ackermann PKreuzer M(2006)Gröbner Basis CryptosystemsApplicable Algebra in Engineering, Communication and Computing10.1007/s00200-006-0002-017:3-4(173-194)Online publication date: 1-Aug-2006
https://dl.acm.org/doi/10.1007/s00200-006-0002-0
Bachmair LTiwari A(2005)D-bases for polynomial ideals over commutative noetherian ringsRewriting Techniques and Applications10.1007/3-540-62950-5_65(113-127)Online publication date: 2-Jun-2005
https://doi.org/10.1007/3-540-62950-5_65
Grabmeier JKaltofen EWeispfenning V(2003)Cited ReferencesComputer algebra handbook10.5555/940131.940137(493-622)Online publication date: 1-Jan-2003
https://dl.acm.org/doi/10.5555/940131.940137
Mansfield ESzanto AHong H(2003)Elimination theory for differential difference polynomialsProceedings of the 2003 international symposium on Symbolic and algebraic computation10.1145/860854.860897(191-198)Online publication date: 3-Aug-2003
https://dl.acm.org/doi/10.1145/860854.860897
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