Rings: an efficient Java/Scala library for polynomial rings

TL;DR

Rings is a high-performance, lightweight Java/Scala library that efficiently implements polynomial algebra operations using modern algorithms, with a user-friendly API suitable for research applications.

Contribution

It introduces a novel, fast, and easy-to-use algebraic library in Scala that combines modern algorithms with a strongly typed functional programming approach.

Findings

Shows competitive performance in algebraic calculations

Provides a simple API for integration in research applications

Implements advanced algorithms like polynomial GCDs and Gr"obner bases

Abstract

In this paper we briefly discuss \Rings --- an efficient lightweight library for commutative algebra. Polynomial arithmetic, GCDs, polynomial factorization and Gr\"obner bases are implemented with the use of modern asymptotically fast algorithms. \Rings can be easily interacted or embedded in applications in high-energy physics and other research areas via a simple API with fully typed hierarchy of algebraic structures and algorithms for commutative algebra. 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. At the same time Rings shows one of the best performances among existing software for algebraic calculations. \Rings is available from http://github.com/PoslavskySV/rings