MultiplicativeGroup concept
Description
An AdditiveGroup (denoted as (G,*)) is a Group with the multiplication (*)
as operator.
For an MultiplicativeGroup
- the identity element is denoted as '1',
- the inverse element of a is denoted as '1/a'.
Refinement of
Group.
Notation
X |
type that is a model of Group |
a, b |
Object of type X |
1 |
identity element |
Definitions
Valid expressions
In addition to those defined by Group
Name |
Expression |
Return type |
Identity element |
one(a) |
void |
Multiplication |
a * b |
X |
Division |
a / b |
X |
Multiplication assignment |
a *= b |
X |
Division assignment |
a /= b |
X |
Expression semantics
Name |
Expression |
Precondition |
Semantics |
Postcondition |
One element |
one(a) |
|
Set a to the identity element (1) |
|
Multiplication |
a * b |
|
|
|
Division |
a / b |
|
equivalent to a * (1/b) |
|
Multiplication assignment |
a *= b |
|
equivalent to a = a * b |
|
Division assignment |
a /= b |
|
equivalent to a = a / b |
|
Complexity guarantees
Invariants
Inherited from Group.
Models
- double without 0.0
- std::complex<double> without 0.0
- non-zero rational numbers
Notes