PreImagesRange( map ) A
is the set of preimages of the range of the general mapping map.
PreImagesRange delegates to PreImagesSet,
it is introduced only to store the preimage of map as attribute value.
PreImagesElm( map, elm ) O
If elm is an element of the range of the general mapping map then
PreImagesElm returns the set of all preimages of elm under map.
Anything may happen if elm is not an element of the range of map.
PreImageElm( map, elm ) O
If elm is an element of the range of the injective and surjective
general mapping map then
PreImageElm returns the unique preimage of elm under map.
Anything may happen if elm is not an element of the range of map.
PreImagesRepresentative( map, elm ) O
If elm is an element of the range of the general mapping map then
PreImagesRepresentative returns either a representative of the set of
preimages of elm under map or fail, the latter if and only if elm
has no preimages under map.
Anything may happen if elm is not an element of the range of map.
PreImagesSet( map, elms ) O
If elms is a subset of the range of the general mapping map then
PreImagesSet returns the set of all preimages of elms under map.
Anything may happen if elms is not a subset of the range of map.
PreImage( map ) F
PreImage( map, elm ) F
PreImage( map, coll ) F
PreImage( map ) is the preimage of the general mapping map, i.e.,
the subset of elements of the source of map that actually have values
under map.
Note that in this case the argument may also be non-injective or
non-surjective.
PreImage( map, elm ) is the preimage of the element elm of the
range of the injective and surjective mapping map under map, i.e.,
the unique element of the source which is mapped under map to elm.
Note that map must be injective and surjective (see PreImages).
PreImage( map, coll ) is the preimage of the subset coll of the
range of the general mapping map under map, i.e., the subset of the
source which is mapped under map to 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 non-injective or
non-surjective.
PreImage delegates to PreImagesRange when called with one argument,
and to PreImageElm resp. PreImagesSet when called with two arguments.
If the second argument is not an element or a subset of the range of the first argument, an error is signalled.
PreImages( map ) F
PreImages( map, elm ) F
PreImages( map, coll ) F
PreImages( map ) is the preimage of the general mapping map, i.e.,
the subset of elements of the source of map that have actually values
under map.
PreImages( map, elm ) is the set of preimages of the element elm
of the range of the general mapping map under map, i.e., the set of
elements of the source which map maps to elm.
PreImages( map, coll ) is the set of images of the subset coll of
the range of the general mapping map under map, i.e., the subset
of the source which map maps to elements of coll.
coll may be a proper set or a domain.
The result will be either a proper set or a domain.
PreImages delegates to PreImagesRange when called with one argument,
and to PreImagesElm resp. PreImagesSet when called with two
arguments.
If the second argument is not an element or a subset of the range of the first argument, an error is signalled.
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GAP 4 manual