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Solving systems of linear one-sided equations in integer monoid and group rings

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Birgit ReinertAuthors Info & Claims

ISSAC '00: Proceedings of the 2000 international symposium on Symbolic and algebraic computation

Pages 281 - 287

https://doi.org/10.1145/345542.345653

Published: 01 July 2000 Publication History

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Abstract

One of the applications of Gröbner bases in commutative polynomial rings is to solve linear equations. Here we show how similar results can be obtained for systems of one-sided linear equations in the more general setting of monoid and group rings.

References

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F. Baader. Unij~cation in commutative theories~ Hilbert~s basis theorem and CrSbner bases. In Proc. UNIFY39, 1989.

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T. Becket and V. Weispfenning. CrSbner Bases - A Computational Approach to Commutative Algebra. Springer, 1992.

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K. Madlener and B. Reinert. On CrSbner bases in monoid and group rings. $EKI Report $R-93-08, UniversitSt Kaiserslautern, 1993. http://www-madlener, informat ik. uni-kl, de / agmadlener/st aff/reinert/publications_en, ht ml

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K. Madlener and B. Reinert. CrSbner bases in non-commutative reduction rings. In B. Buchberger and F. Winkler, editors, CrSbner Bases and Applications (Proc. of the Conference 33 Years of CrSbner Bases), volume 251 of London Mathematical Society Lecture Notes Series, pages 408-420. Cambridge University Press, 1998.

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K. Madlener and B. Reinert. String rewriting and CrSbner bases - a general approach to monoid and group rings. In M. Bronstein, J. Grabmeier, and V. Weispfenning, editors, Proceedings of the Workshop on Symbolic Rewriting Techniques~ Monte Verita~ 1995, volume 15 of Progress in Computer Science and Applied Logic, pages 127-180. BirkhSuser, 1998.

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B. Reinert. On CrSbner Bases in Monoid and Croup Rings. PhD thesis, UniversitSt Kaiserslautern, 1995. http://www-madlener, informat ik. uni-kl, de / agmadlener/st aff/reinert/publications_en, ht ml

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Solving systems of linear one-sided equations in integer monoid and group rings

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ISSAC '00: Proceedings of the 2000 international symposium on Symbolic and algebraic computation

July 2000

309 pages

ISBN:1581132182

DOI:10.1145/345542

Editor:
Carlo Traverso
Univ. di Pisa

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Association for Computing Machinery

New York, NY, United States

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Published: 01 July 2000

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ISSAC '00 Paper Acceptance Rate 40 of 98 submissions, 41%;

Overall Acceptance Rate 395 of 838 submissions, 47%

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Globally Solving Nonconvex Quadratic Programs via Linear Integer Programming Techniques

An interior point method for solving systems of linear equations and inequalities

Analyzing Infeasible Mixed-Integer and Integer Linear Programs

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