# Rings: efficient Java/Scala library for polynomial rings¶

Rings is an efficient lightweight library for commutative algebra. Polynomial arithmetic, GCDs, polynomial factorization and Groebner bases are implemented with the use of modern asymptotically fast algorithms. Rings can be easily interacted or embedded in applications via simple API with fully typed hierarchy of algebraic structures and algorithms for commutative algebra. As well, an interactive REPL is also provided. The use of 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 or even unmatched in some cases performance among existing software for algebraic calculations.

The key features of Rings include:

- Rings →

integers, fractions, finite and algebraic fields, multiple field extensions, polynomial rings and more- Polynomials →

Efficient univariate and multivariate polynomials over arbitrary coefficient rings- Polynomial GCD →

Highly performant polynomial GCD over arbitrary coefficient domains- Univariate and multivariate polynomial factorization →

Highly performant polynomial factorization over almost arbitrary rings- Ideals and Gröbner bases →

Polynomial ideals and efficient algorithms for Gröbner bases- Scala DSL →

Powerful domain specific language in Scala- Fast →

Really fast library suitable for real-world computational challenges

For a quick overview of what Rings can do proceed to Quick Tour and try out Rings*.repl*.

Rings sources are hosted at GitHub: https://github.com/PoslavskySV/rings.

## License¶

Apache License, Version 2.0 http://www.apache.org/licenses/LICENSE-2.0.txt