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
GAP 3.4.4