62.13 Transformation records

As almost all objects in GAP, transformations, too, are representend by records. Such a transformation record has the following components:

isGeneralMapping:

this is always true, since in particular, any transformation is a general mapping.

domain:

the entry of this record field is Mappings.

isMapping:

this is always true since a transformation is in particular a single valued mapping.

isTransformation:

always true for a transformation.

isSetTransformation:

this exists and is set to true for set transformations exclusively.

isGroupTransformation, isGroupElement:

these two exist and are set to true for group transformations exclusively.

elements:

this record field holds a list of the elements of the source.

source, range:

both entries contain the same set in case of a set transformation, resp. the same group in case of a group transformation.

tfl:

this contains the transformation list which uniquely determines the transformation.

operations:

the operations record of the transformation. E.g. * or =, etc. can be found here.

image, rank, ker:

these are bound and contain image, rank, kernel in case they have already been computed for the transformation.

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