Module scirust::algebra::structure::semigroup

Defines the semigroup algebraic structure.

A semigroup is an algebraic structure consisting of a set together with an associative binary operation.

Semigroup builds on top of magma and provides associativity.

We define four kinds of semigroups.

• Semigroup with an addition operation with partial equivalence
• Semigroup with an addition operation with full equivalence
• Semigroup with a multiplication operation with partial equivalence
• Semigroup with a multiplication operation with full equivalence

It is not possible to check the associativity of the group operation at the compile time. We do provide a function (with each semigroup trait) to validate the associativity of the operation.

References:

• http://en.wikipedia.org/wiki/Algebraic_structure
• http://en.wikipedia.org/wiki/Semigroup

Traits

SemiGroupAdd	Semigroup with an addition operation with full equivalence
SemiGroupAddPartial	Semigroup with an addition operation with partial equivalence
SemiGroupMul	Semigroup with a multiplication operation with full equivalence
SemiGroupMulPartial	Semigroup with a multiplication operation with partial equivalence