ImagesSource( map ) A
is the set of images of the source of the general mapping map.
ImagesSource delegates to ImagesSet,
it is introduced only to store the image of map as attribute value.
ImagesRepresentative( map, elm ) O
If elm is an element of the source of the general mapping map then
ImagesRepresentative returns either a representative of the set of
images of elm under map or fail, the latter if and only if elm
has no images under map.
Anything may happen if elm is not an element of the source of map.
ImagesElm( map, elm ) O
If elm is an element of the source of the general mapping map then
ImagesElm returns the set of all images of elm under map.
Anything may happen if elm is not an element of the source of map.
ImagesSet( map, elms ) O
If elms is a subset of the source of the general mapping map then
ImagesSet returns the set of all images of elms under map.
Anything may happen if elms is not a subset of the source of map.
ImageElm( map, elm ) O
If elm is an element of the source of the total and single-valued
mapping map then
ImageElm returns the unique image of elm under map.
Anything may happen if elm is not an element of the source of map.
Image( map ) F
Image( map, elm ) F
Image( map, coll ) F
Image( map ) is the image of the general mapping map, i.e.,
the subset of elements of the range of map that are actually values of
map.
Note that in this case the argument may also be multi-valued.
Image( map, elm ) is the image of the element elm of the source
of the mapping map under map, i.e., the unique element of the range
to which map maps elm.
This can also be expressed as elm ^ map.
Note that map must be total and single valued, a multi valued general
mapping is not allowed (see Images).
Image( map, coll ) is the image of the subset coll of the source
of the mapping map under map, i.e., the subset of the range
to which map maps elements of coll.
coll may be a proper set or a domain.
The result will be either a proper set or a domain.
Note that in this case map may also be multi-valued.
Image delegates to ImagesSource when called with one argument,
and to ImageElm resp. ImagesSet when called with two arguments.
If the second argument is not an element or a subset of the source of the first argument, an error is signalled.
Images( map ) F
Images( map, elm ) F
Images( map, coll ) F
Images( map ) is the image of the general mapping map, i.e.,
the subset of elements of the range of map that are actually values of
map.
Images( map, elm ) is the set of images of the element elm of
the source of the general mapping map under map, i.e., the set of
elements of the range to which map maps elm.
Images( map, coll ) is the set of images of the subset coll of
the source of the general mapping map under map, i.e., the subset
of the range to which map maps elements of coll.
coll may be a proper set or a domain.
The result will be either a proper set or a domain.
Images delegates to ImagesSource when called with one argument,
and to ImagesElm resp. ImagesSet when called with two arguments.
If the second argument is not an element or a subset of the source of the first argument, an error is signalled.
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GAP 4 manual