Common Divisors of Solvable Polynomials in JAS
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.
KeywordsGeneric multivariate solvable polynomials Common divisors
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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