Algebra

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Algebra is a subfield of mathematics, concerned with structured sets, and the structure-preserving maps between such sets. From the viewpoint of generic programming, algebra provides a set of concepts which we can map directly to concept requirements.

Of particular interest to us is the formalization of different kinds of numbers; the integers, the rational numbers, and the real numbers. However, many algorithms which are familiar for integers generalize far further. It is here where algebra clarifies the minimal set of requirements for a given algorithm to work.

Files

An aggregate file for algebraic concepts.

Element concept

Field concept

Group concept

Linearly-ordered element concept

Monoid concept

Native types as a group concept

Native types as a monoid concept

Native types as a semi-group concept

Native types as an ordered monoid concept

Ordered additive group concept

Ordered additive monoid concept

Ordered element concept

Ordered field concept

Ordered group concept

Ordered ring concept

Ring concept

Semi-group concept