62.11 Operations for transformations

t1 * t2

The product operator * returns the transformation which is obtained from the transformations t1 and t2, by composition of t1 and t2 (i.e. performing t2 after t1). This function works for both set transformations as well as group transformations.

 
  gap> t1:=Transformation( [1..3], [1,1,2] );
  Transformation( [ 1, 2, 3 ], [ 1, 1, 2 ] )
  gap> t2:=Transformation( [1..3], [2,3,3] );
  Transformation( [ 1, 2, 3 ], [ 2, 3, 3 ] )
  gap> t1*t2;
  Transformation( [ 1, 2, 3 ], [ 2, 2, 3 ] )
  gap> t2*t1;
  Transformation( [ 1, 2, 3 ], [ 1, 2, 2 ] )

t1 + t2

The add operator + returns the group transformation which is obtained from the group transformations t1 and t2 by pointwise addition of t1 and t2. (Note that in this context addition means performing the GAP operation p * q for the corresponding permutations p and q).

t1 - t2

The subtract operator - returns the group transformation which is obtained from the group transformations t1 and t2 by pointwise subtraction of t1 and t2. (Note that in this context subtraction means performing the GAP operation p * q^-1 for the corresponding permutations p and q).

Of course, those two functions + and - work only for group transformations.

  gap> g:=Group( (1,2,3) );
  Group( (1,2,3) )
  gap> gt1:=Transformation( g, [2,3,3] );
  Transformation( Group( (1,2,3) ), [ 2, 3, 3 ] )
  gap> gt2:=Transformation( g, [1,3,2] );
  Transformation( Group( (1,2,3) ), [ 1, 3, 2 ] )
  gap> gt1+gt2;
  Transformation( Group( (1,2,3) ), [ 2, 2, 1 ] )
  gap> gt1-gt2;
  Transformation( Group( (1,2,3) ), [ 2, 1, 2 ] )

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