libcoq-mathcomp-algebra

Mathematical Components library for Coq (algebra)

Description

The Mathematical Components Library is an extensive and coherent repository of formalized mathematical theories. It is based on the Coq proof assistant, powered with the Coq/SSReflect language.

These formal theories cover a wide spectrum of topics, ranging from the formal theory of general-purpose data structures like lists, prime numbers or finite graphs, to advanced topics in algebra.

The formalization technique adopted in the library, called "small scale reflection", leverages the higher-order nature of Coq's underlying logic to provide effective automation for many small, clerical proof steps. This is often accomplished by restating ("reflecting") problems in a more concrete form, hence the name. For example, arithmetic comparison is not an abstract predicate, but rather a function computing a Boolean.

This package installs the algebra part of the library (ring, fields, ordered fields, real fields, modules, algebras, integers, rationals, polynomials, matrices, vector spaces...).

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Homepage

https://math-comp.github.io/math-comp/

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