NewRepresentation( name, super, slots )
NewRepresentation returns a new representation rep that has the name
name and is a subrepresentation of the representation super.
This means that every object in rep lies automatically also in super.
We say also that super is an implied filter of rep.
Each representation in GAP is a subrepresentation of exactly one
of the four representations IsInternalRep, IsDataObjectRep,
IsComponentObjectRep, IsPositionalObjectRep.
The data describing objects in the former two can be accessed only via
GAP kernel functions, the data describing objects in the latter two
is accessible also in library functions, see Component Objects
and Positional Objects for the details.
The third argument slots is a list either of integers or of strings.
In the former case, rep must be IsPositionalObjectRep or a
subrepresentation of it, and slots tells what positions of the objects
in the representation rep may be bound.
In the latter case, rep must be IsComponentObjectRep or a
subrepresentation of, and slots lists the admissible names of
components that objects in the representation rep may have.
The admissible positions resp. component names of super need not be
be listed in slots.
The incremental rank (see Filters in the Reference Manual) of rep is 1.
Note that for objects in the representation rep, of course some of the component names and positions reserved via slots may be unbound.
Examples for the use of NewRepresentation can be found
in Component Objects, Positional Objects, and also
in A Second Attempt to Implement Elements of Residue Class Rings.
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GAP 4 manual