Abstract
Implementation of modern algorithms in computer algebra requires the use of generic and high-performance instruments. Rings is an open-source library, written in Java and Scala programming languages, which implements basic concepts and algorithms from computational commutative algebra while demonstrating quite a high performance among existing software. It rigorously uses generic programming approach, providing a well-designed generic API with a fully typed hierarchy of algebraic structures and algorithms for commutative algebra. Polynomial arithmetic, GCDs, factorization, and Gröbner bases are implemented with the use of modern asymptotically fast algorithms. The use of the Scala language brings a quite novel powerful, strongly typed functional programming model allowing to write short, expressive, and fast code for applications in high-energy physics and other research areas.
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