1: Commutative Rings with Unity. 2: Polynomial Rings. 3: Vector Spaces and Modules. 4: Orders and Abstract Reduction Relations. 5: Gr bner Bases. 6: First Applications of Gr bner Bases. 7: Field… Expand

Some notes on the computation of Groebner Bases using Buchberger's algorithm over different coefficient domains and the solution of systems of algebraic equations.Expand

We present an algorithm that computes the dimension and maximal independent sets for a polynomial ideal I from a Grobner basis for I with respect to a lexicographical term order, and extends Buchberger's test for zero-dimensionality.Expand

This paper describes the implementation of recursive algorithms in unique factorization domains, namely multivariate polynomial greatest common divisors (gcd) and factorization into irreducible parts in the Java computer algebra library (JAS).Expand

We present a set of algorithms which are already implemented in the SAC-2 Computer Algebra System and a complete example of a primary decomposition using these programs.Expand

In this paper we explore novel areas of solvable polynomial rings which have partly been addressed in theory, but lack implementations in computer algebra systems.Expand