GAP Manual: 9.8. Dimension

Dimension( V )

Dimension computes the dimension of the given vector space V over its field.

The dimension of a vector space V is defined to be the length of a minimal generating set of V, which is called a base of V (see Base).

The implementation of Dimension strictly follows its above definition, so that this function will always determine a base of V.

    gap> f := GF( 3^4 );
    GF(3^4)
    gap> f.base;
    [ Z(3)^0, Z(3^4), Z(3^4)^2, Z(3^4)^3 ]
    gap> V := VectorSpace( f.base, GF( 3 ) );
    VectorSpace( [ Z(3)^0, Z(3^4), Z(3^4)^2, Z(3^4)^3 ], GF(3) )
    gap> Dimension( V );
    4