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Common Divisors of Solvable Polynomials in JAS

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Mathematical Software – ICMS 2016 (ICMS 2016)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 9725))

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Abstract

We present generic, type safe (non-unique) common divisors of solvable polynomials software. The solvable polynomial rings are defined with non-commuting variables, moreover, in case of parametric (solvable) coefficients the main variables may not commute with the coefficients. The interface, class organization is described in the object-oriented programming environment of the Java Algebra System (JAS). The implemented algorithms can be applied, for example, in solvable extension field and root construction. We show the design and feasibility of the implementation in the mentioned applications.

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Acknowledgments

We thank Thomas Becker for discussions on the implementation of a generic polynomial library and Raphael Jolly for the fruitful cooperation. We thank moreover our colleagues Wolfgang K. Seiler, Thomas Sturm, Axel Kramer, Victor Levandovskyy, Joachim Apel, Markus Aleksy and others for various discussions on the design and the requirements for JAS and its mathematical foundations. Thanks also for helpful suggestions from the reviewers.

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Authors and Affiliations

  1. University of Mannheim, Mannheim, Germany

    Heinz Kredel

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  1. Heinz Kredel
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Correspondence to Heinz Kredel .

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Editors and Affiliations

  1. Universität Kaiserslautern , Kaiserslautern, Germany

    Gert-Martin Greuel

  2. Zuse Institute Berlin , Berlin, Germany

    Thorsten Koch

  3. Johannes Kepler University Linz , Hagenberg, Austria

    Peter Paule

  4. University of Notre Dame , Notre Dame, Indiana, USA

    Andrew Sommese

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Kredel, H. (2016). Common Divisors of Solvable Polynomials in JAS. In: Greuel, GM., Koch, T., Paule, P., Sommese, A. (eds) Mathematical Software – ICMS 2016. ICMS 2016. Lecture Notes in Computer Science(), vol 9725. Springer, Cham. https://doi.org/10.1007/978-3-319-42432-3_22

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  • DOI: https://doi.org/10.1007/978-3-319-42432-3_22

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-42431-6

  • Online ISBN: 978-3-319-42432-3

  • eBook Packages: Computer ScienceComputer Science (R0)

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