A mapping map is represented by a record with the following components
true, indicating that this is a general mapping.
The following entries are optional. The functions with the corresponding names will generally test if they are present. If they are then their value is simply returned. Otherwise the functions will perform the computation and add those fields to those record for the next time.
trueif map is a single valued mapping and
trueif map has the corresponding property and
map.sourceof elements pre that are actually mapped to at least one element, i.e., for which
Images( map, pre )is nonempty.
map.rangeof the elements img that are actually values of the mapping, i.e., for which
PreImages( map, img )is nonempty.
map.sourcethat maps each element img to the set
PreImages( map, img ).
The following entry is optional. It must be bound only if the inverse of map is indeed a single valued mapping.
The following entry is optional. It must be bound only if map is a homomorphism.
map.sourcethat are mapped to the identity element of
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