In addition to the usual components of an H class record, the record
representing the H class hClass of s in a transformation monoid can
have the following components. They are created by the function
SchutzenbergerGroup (see SchutzenbergerGroup) which is called
whenever the size, the list of elements of hClass, or a membership test
in hClass is asked for.
hClass.representative.The following functions have a special implementation in terms of these components.
Size( hClass )
returns the size of the H class hClass. This function calls
SchutzenbergerGroup and determines the size of hClass as the size of
the resulting group.
Elements( hClass )
returns the set of elements of the H class hClass. This function calls
SchutzenbergerGroup and determines the set of elements of hClass as
the set of elements of the resulting group multiplied by the
representative of hClass.
x in hClass
true if x is an element of the H class hClass and
otherwise. This function calls
SchutzenbergerGroup and tests whether
the quotient of the representative of hClass and x (see
PermLeftQuoTrans) is in the resulting group.