International Workshop on Computer Algebra in Scientific Computing

Computer Algebra in Scientific Computing pp 275-291

Parametric Solvable Polynomial Rings and Applications

Conference paper

DOI: 10.1007/978-3-319-24021-3_21

Volume 9301 of the book series Lecture Notes in Computer Science (LNCS)
Cite this paper as:
Kredel H. (2015) Parametric Solvable Polynomial Rings and Applications. In: Gerdt V., Koepf W., Seiler W., Vorozhtsov E. (eds) Computer Algebra in Scientific Computing. Lecture Notes in Computer Science, vol 9301. Springer, Cham

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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Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  1. 1.IT-CenterUniversity of MannheimMannheimGermany