50.39 Decreased

Decreased( tbl, reducibles, mat )
Decreased( tbl, reducibles, mat, choice )

tries to solve the output of OrthogonalEmbeddings OrthogonalEmbeddings or Extract Extract in order to find irreducible characters. tbl must be a character table, reducibles the list of characters used for the call of OrtgogonalEmbeddings or Extract, mat one solution, and in the case of a solution returned by Extract, choice must be the corresponding choice component.

Decreased returns a record with components

irreducibles:

the list of found irreducible characters,

remainders:

the remaining reducible characters, and

matrix:

the decomposition matrix of the characters in the remainders component, which could not be solved.

    # see example in "Extract" 'Extract'
    gap> d := Decreased( s4, y, e.solution[1], e.choice[1] );
    rec(
      irreducibles :=
       [ [ 1, 1, 1, 1, 1 ], [ 3, -1, -1, 0, 1 ], [ 1, -1, 1, 1, -1 ],
          [ 3, 1, -1, 0, -1 ], [ 2, 0, 2, -1, 0 ] ],
      remainders := [  ],
      matrix := [  ] )

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