MultiplicativeMagma concept

Description

A multiplicative magma is a magma equipped with the multiplication operator.

Refinement of

Associated types

Corresponding functor glas::mult_functor

Notation

S	Type of a set
A	type of a set convertible to S
B	type of a set convertible to S
a	Object of type `A`
b	Object of type `B`
s	Object of type `S`

Definitions

Valid expressions

In addition to those defined by Assignable:

Name	Expression	Return type
Multiplication	a*b	`mult_functor<A,B>::result_type`, convertible to S
MultiplicatonAssignment	a*=b	S

Expression semantics

Name	Expression	Precondition	Semantics	Postcondition
Multiplication	a*b		can actually be anything as long as it fulfills the requirements of the multiplication
MultiplicatonAssignment	a*=b		equivalent to a=a*b

Complexity guarantees

Invariants

Closure a*b returns an element of the set S

Models

Notes

If the type S models MultiplicativeMagma then the module {S, glas::mult_functor<S,S>} models Magma.
From the mathematical prospective MultiplicativeMagma could be defined without the binary operator a*=b, which does not add new semantic. In order to ease the programming with concepts we require that all models of MultiplicativeMagma provide this operator and encourage everybody who introduces new types to add this operator consistently.