Module scirust::algebra::structure::group

Defines the group algebraic structure.

A group is an algebraic structure consisting of a set of elements together with an operation that combines any two elements to form a third element. The operation satisfies four conditions called the group axioms, namely closure, associativity, identity and invertibility.

Essentially a group is a monoid and a loop both.

A commutative or Abelian group is a group whose group operation is also commutative.

We define four kinds of groups.

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

We define four kinds of commutative groups.

• Commutative group with an addition operation with partial equivalence
• Commutative group with an addition operation with full equivalence
• Commutative group with a multiplication operation with partial equivalence
• Commutative group with a multiplication operation with full equivalence

References:

• http://en.wikipedia.org/wiki/Algebraic_structure
• http://en.wikipedia.org/wiki/Group_(mathematics)
• http://en.wikipedia.org/wiki/Abelian_group

Traits

CommutativeGroupAdd	Commutative group with an addition operation with full equivalence
CommutativeGroupAddPartial	Commutative group with an addition operation with partial equivalence
CommutativeGroupMul	Commutative group with a multiplication operation with full equivalence
CommutativeGroupMulPartial	Commutative group with a multiplication operation with partial equivalence
GroupAdd	Group with an addition operation with full equivalence
GroupAddPartial	Group with an addition operation with partial equivalence
GroupMul	Group with a multiplication operation with full equivalence
GroupMulPartial	Group with a multiplication operation with partial equivalence