4.15 Transformation Monoid Records

Monoid Records and Semigroup Records) the record representing a transformation monoid M has a component

isTransMonoid:

which is always set to true. Moreover, such a record will (after a while) acquire the following components.

orbitClasses:

a list of R classes of M such that every orbit of image sets is represented exactly once.

images:

the list of lists where images[ k ] is the list of all different image sets of size k of the elements of M. imagePos:
stores the relation between orbitClasses and images. The image set images[k][l] occurs in the orbit of the R class with index imagePos[k][l] in the list orbitClasses. rClassReps:
a list of lists, where rClassReps[l] contains the complete list of representatives of the R classes with the same image orbit as the R class orbitClasses[l]. lTrans:
a list of lists, where lTrans[l][k] is a transformation alpha such that lTrans[l][k] * rClassReps[l][k] is an element of the R class orbitClasses[l]. kernels:
a list of lists, where kernels[l][k] is the common kernel of the elements in the R class of rClassReps[l][k].

  
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