Rings: An efficient Java/Scala library for polynomial rings

Abstract

In this paper we briefly discuss Rings -an efficient lightweight library for commutative algebra. Polynomial arithmetic, GCDs, polynomial factorization and Gröbner 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.

Integrating linear ordinary fourth-order differential equations in the MAPLE programming environment

“…Subsequent studies [15][16][17][18][19][20] developed the above heuristic methods for exploring differential equations by using computer algebra. Algebraic substitutions are employed to solve a differential equation in [15].…”

“…Subsequent studies [15][16][17][18][19][20] developed the above heuristic methods for exploring differential equations by using computer algebra. Algebraic substitutions are employed to solve a differential equation in [15]. Functional substitutions are used to solve a differential equation and the original differential equations of a special kind are considered in [16].…”

MultivariateResidues: A Mathematica package for computing multivariate residues

“…In this paper we provide the Mathematica package Multi-variateResidues for efficient evaluation of multivariate residues based on methods from computational algebraic geometry. Related work has recently appeared in the package Rings [20] which provides a library for computing factorization, GCDs etc. of multivariate polynomials over arbitrary coefficient rings.…”