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Parametric Solvable Polynomial Rings and Applications

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Computer Algebra in Scientific Computing (CASC 2015)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 9301))

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Abstract

We recall definitions and properties of parametric solvable polynomial rings and variants. For recursive solvable polynomial rings, i.e. solvable polynomial rings with coefficients from a solvable polynomial ring, also commutator relations between main and coefficient variables are introduced. From these rings solvable quotient and residue class rings can be constructed and used as coefficients of solvable polynomials. The resulting skew extension fields of the ground field can be applied for skew root finding or primary ideal decomposition. We present the design and implementation of these rings in the strongly typed, generic, object oriented computer algebra system JAS.

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Authors and Affiliations

  1. IT-Center, 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. Laboratory of Information Technologies, Joint Institute of Nuclear Research, Dubna, Russia

    Vladimir P. Gerdt

  2. Institute for Mathematics, Universität Kassel, Kassel, Germany

    Wolfram Koepf

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

    Werner M. Seiler

  4. Novosibirsk, Russia

    Evgenii V. Vorozhtsov

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Kredel, H. (2015). Parametric Solvable Polynomial Rings and Applications. In: Gerdt, V., Koepf, W., Seiler, W., Vorozhtsov, E. (eds) Computer Algebra in Scientific Computing. CASC 2015. Lecture Notes in Computer Science(), vol 9301. Springer, Cham. https://doi.org/10.1007/978-3-319-24021-3_21

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  • DOI: https://doi.org/10.1007/978-3-319-24021-3_21

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-24020-6

  • Online ISBN: 978-3-319-24021-3

  • eBook Packages: Computer ScienceComputer Science (R0)

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