rings alternatives and similar packages
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vector
An efficient implementation of Intindexed arrays (both mutable and immutable), with a powerful loop optimisation framework . 
hgeometry
HGeometry is a library for computing with geometric objects in Haskell. It defines basic geometric types and primitives, and it implements some geometric data structures and algorithms. The main two focusses are: (1) Strong type safety, and (2) implementations of geometric algorithms and data structures that have good asymptotic running time guarantees. 
dimensional
Dimensional library variant built on Data Kinds, Closed Type Families, TypeNats (GHC 7.8+). 
numhask
A haskell numeric prelude, providing a clean structure for numbers and operations that combine them. 
poly
Fast polynomial arithmetic in Haskell (dense and sparse, univariate and multivariate, usual and Laurent) 
eigen
Haskel binding for Eigen library. Eigen is a C++ template library for linear algebra: matrices, vectors, numerical solvers, and related algorithms.
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README
Semirings
This library provides constraint kinds for (right) presemirings, semirings, and rings, as well as some useful instances.
The Semiring
kind imposes fairly minimal requirements—the various 'addon' properties (e.g. multiplicative commutativity) are catalogued in Data.Semiring.Property
.