9.1 VectorSpace

VectorSpace( generators, field )

Let generators be a list of objects generating a vector space over the field field. Then VectorSpace returns this vector space represented as a GAP record.

    gap> f := GF( 3^2 );
    GF(3^2)
    gap> m := [ [ f.one, f.one ], [ f.zero, f.zero ] ];
    [ [ Z(3)^0, Z(3)^0 ], [ 0*Z(3), 0*Z(3) ] ]
    gap> n := [ [ f.one, f.zero ], [ f.zero, f.one ] ];
    [ [ Z(3)^0, 0*Z(3) ], [ 0*Z(3), Z(3)^0 ] ]
    gap> VectorSpace( [ m, n ], f );
    VectorSpace( [ [ [ Z(3)^0, Z(3)^0 ], [ 0*Z(3), 0*Z(3) ] ], 
      [ [ Z(3)^0, 0*Z(3) ], [ 0*Z(3), Z(3)^0 ] ] ], GF(3^2) ) 

VectorSpace( generators, field, zero )

VectorSpace returns the vector space generated by generators over the field field having zero as the uniquely determined neutral element. This call of VectorSpace always is requested if generators is the empty list.

    gap> VectorSpace( [], f, [ [ f.zero, f.zero ], [ f.zero, f.zero ] ] );
    VectorSpace( [  ], GF(3^2), [ [ 0*Z(3), 0*Z(3) ], [ 0*Z(3), 0*Z(3) ]
     ] ) 

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