13.16 RationalizedMat

RationalizedMat( mat )

returns the set of rationalized rows of mat, i.e. the set of sums over orbits under the action of the Galois group of the elements of mat (see GaloisMat).

This may be viewed as a kind of trace operation for the rows.

Note that mat should be a set, i.e. no two rows should be equal.

    gap> mat:= CharTable( "A5" ).irreducibles;
    [ [ 1, 1, 1, 1, 1 ], [ 3, -1, 0, -E(5)-E(5)^4, -E(5)^2-E(5)^3 ], 
      [ 3, -1, 0, -E(5)^2-E(5)^3, -E(5)-E(5)^4 ], [ 4, 0, 1, -1, -1 ], 
      [ 5, 1, -1, 0, 0 ] ]
    gap> RationalizedMat( mat );
    [ [ 1, 1, 1, 1, 1 ], [ 6, -2, 0, 1, 1 ], [ 4, 0, 1, -1, -1 ], 
      [ 5, 1, -1, 0, 0 ] ]

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