3.1 More about Transformations

A transformation alpha on n points is completely defined by its list of images. It is stored as a record with the following category components.

isTransformation:

is always set to true.

domain:

is always set to Transformations.

Moreover it has the identification component

images:

containing the list of images in such a way that i^alpha = alpha.'images[i]' for all i leq n.

The multiplication of these transformations can be efficiently implemented by using the sublist operator { }. The product r * l of two transformations l and r can be computed as Transformation( r.images{ l.images } ). Note that the order has been chosen to have transformations act from the right on their domain.

  
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