AdditiveGroup concept

Description

This is the concept for numerical data types used as values in vectors and matrices. It provides addition, and substraction as well as a zero element.

Refinement of

DefaultConstructible, EqualityComparable.

Associated types

Notation

`X`	A type that is a model of AdditiveGroup
`Y`	A type that is a model of AdditiveGroup
`x`	Object of type `X`
`y`	Object of type `Y`

Definitions

Valid expressions

In addition to those of DefaultConstructible, EqualityComparable:

Name	Expression	Type requirements	Return type
Addition	`x + y`		`X`
Addition	`x += y`	`y` is convertible to `X`	`X`
Negation	`- x`		`X`
Subtraction	`x - y`		`X`
Subtraction	`x -= y`	`y` is convertible to `X`	`X`

Expression semantics

In addition to those of HasZero DefaultConstructible, EqualityComparable:

Name	Expression	Precondition	Semantics	Postcondition
Addition	`x + y`
Addition	`x += y`		Is equivalent to `x = x + y`
Negation	`- x`
Subtraction	`x - y`
Subtraction	`x -= y`		Is equivalent to `x = x - y`

Complexity guarantees

Invariants

x+y==y+x
x-y == x+(-y)

Models

int
float
double
std::complex< float >
std::complex< double >

Notes