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Multivariate Greatest Common Divisors in the Java Computer Algebra System
"... Abstract. This paper considers the implementation of recursive algorithms for multivariate polynomial greatest common divisors (gcd) in the Java computer algebra library (JAS). The implementation of gcds and resultants is part of the essential building blocks for any computation in algebraic geometr ..."
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Abstract. This paper considers the implementation of recursive algorithms for multivariate polynomial greatest common divisors (gcd) in the Java computer algebra library (JAS). The implementation of gcds and resultants is part of the essential building blocks for any computation in algebraic geometry, in particular in automated deduction in geometry. There are various implementations of these algorithms in procedural programming languages. Our aim is an implementation in a modern object oriented programming language with generic data types, as it is provided by Java programming language. We exemplify that the type design and implementation of JAS is suitable for the implementation of several greatest common divisor algorithms for multivariate polynomials. Due to the design we can employ this package in very general settings not commonly seen in other computer algebra systems. As for example in the coefficient arithmetic for advanced Gröbner basis computations like in polynomial rings over rational function fields or (finite, commutative) regular rings. The new package provides factory methods for the selection of one of the several implementations for non experts. Further we introduce a parallel proxy for gcd implementations which runs different implementations concurrently. 1

