`tr1` = `tr2`

`tr1` < `tr2`

The equality operator `=`

applied to two transformations `tr1` and `tr2`
evaluates to `true`

if the two transformations are equal and to `false`

otherwise. The inequality operator `<`

applied to two transformations
`tr1` and `tr2` evaluates to `true`

if the two transformations are not
equal and to `false`

otherwise. A transformation can also be compared to
any other object that is not a transformation, of course they are never
equal.
Two transformations are considered equal if and only if their image lists
are equal as lists. In particular, equal transformations must have the
same degree.

gap> Transformation( [ 1, 2, 3, 4 ] ) = IdentityTransformation( 4 ); true gap> Transformation( [ 1, 4, 4, 2 ] ) = > Transformation( [ 1, 4, 4, 2, 5 ] ); false

`tr1` < `tr2`

`tr1` <= `tr2`

`tr1` `tr2`

`tr1` = `tr2`

The operators `<`

, `<=`

, `, and `

`=`

evaluate to `true`

if the
transformation `tr1` is less than, less than or equal to, greater than,
or greater than or equal to the transformation `tr2`, and to `false`

otherwise.

Let `tr1` and `tr2` be two transformations that are not equal. Then
`tr1` is considered smaller than `tr2` if and only if the list of images
of `tr1` is (lexicographically) smaller than the list of images of `tr2`.
Note that this way the smallest transformation of degree *n* is the
transformation that maps every point to *1*.

You can also compare transformations with objects of other types. Here any object that is not a transformation will be considered smaller than any transformation.

Version 2.4 (May 1998)