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Parametric solvable polynomial rings and applications. (English) Zbl 1434.16021
Gerdt, Vladimir P. (ed.) et al., Computer algebra in scientific computing. 17th international workshop, CASC 2015, Aachen, Germany, September 14–18, 2015. Proceedings. Cham: Springer. Lect. Notes Comput. Sci. 9301, 275-291 (2015).
Summary: 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.
For the entire collection see [Zbl 1321.68010].

MSC:
16Z05 Computational aspects of associative rings (general theory)
68W30 Symbolic computation and algebraic computation
Software:
SINGULAR; REDLOG; Plural; JAS; PGB
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