25.79 LinearOperation

LinearOperation( U, V, varphi )

Let U be an ag group with an induced generating system u_1, ..., u_m and V a vector space with base (o_1, ..., o_n). U must act linearly on V. Let v be an element of V, u be an element of U. The action of U on V should be given as follows. If v^u = a_1*o_1+ ... +a_n*o_n, then the function <varphi>( v, u ) must return (a_1, ..., a_n) as list of finite field elements. If these condition are fulfilled, LinearOperation returns a matrix group M describing this action.

Note that M.images is bound to a list of matrices m_i, such that m_i describes the action of u_i.

    gap> v4 := AgSubgroup( s4, [ c, d ], true );
    Subgroup( s4, [ c, d ] )
    gap> v4.field := GF( 2 );
    GF(2)
    gap> V := rec( base := [ c, d ], isDomain := true );
    rec(
      base := [ c, d ],
      isDomain := true )
    gap> phi := function( v, g )
    >      return Exponents( v4, v^g, v4.field );
    >    end;
    function ( v, g ) ... end
    gap> LinearOperation( s4, V, phi );
    Group( [ [ Z(2)^0, Z(2)^0 ], [ 0*Z(2), Z(2)^0 ] ],
    [ [ 0*Z(2), Z(2)^0 ], [ Z(2)^0, Z(2)^0 ] ] ) 

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