Group concept
Description
A group is an algebraic structure on a finite or infinite set
equipped with an operator (in the following we use the notation '@'
for the operator).
Let a and b be arbitrary elements of the group.
The following properties hold:
- closure: a @ b is an element of the group.
- associativity: ( a @ b ) @ c = a @ ( b @ c )
- identity: there is an element, denoted by e, so that a @ e = a
- inverse: for each a, there is an element u so that
a @ u = e.
Refinement of
Assignable,
DefaultConstructible
and
EqualityComparable.
Notation
X |
type that is a model of Group |
a, b |
Object of type X |
e |
identity element |
Definitions
Valid expressions
In addition to those defined by Assignable,
DefaultConstructible
and
EqualityComparable:
Name |
Expression |
Return type |
Expression semantics
Name |
Expression |
Precondition |
Semantics |
Postcondition |
Complexity guarantees
Invariants
Models
Notes