GAP Manual: 9.7. AddBase

AddBase( V, base )

AddBase attaches a user-supplied base for the vector space V to the record that represents V.

Most of the functions for vector spaces make use of a base (see LinearCombination, Coefficients). These functions get access to a base using the function Base, which normally computes a base for the vector space using an appropriate algorithm. Once a base is computed it will always be reused, no matter whether there is a more interesting base available or not.

AddBase installs a given base for V by overwriting any other base of the vector space that has been installed before. So after AddBase has successfully been used, base will be used whenever Base is called with V as argument.

Calling AddBase with a base which is not a base for V might produce unpredictable results in following computations.

    gap> f := GF(3);
    GF(3)
    gap> m1 := [[ f.one, f.one, f.zero, f.zero ]];
    [ [ Z(3)^0, Z(3)^0, 0*Z(3), 0*Z(3) ] ]
    gap> m2 := [[ f.one, f.one, f.one, f.zero ]]; 
    [ [ Z(3)^0, Z(3)^0, Z(3)^0, 0*Z(3) ] ]
    gap> V := VectorSpace( [ m1, m2, m1+m2 ], GF(3) );
    VectorSpace( [ [ [ Z(3)^0, Z(3)^0, 0*Z(3), 0*Z(3) ] ], 
      [ [ Z(3)^0, Z(3)^0, Z(3)^0, 0*Z(3) ] ], 
      [ [ Z(3), Z(3), Z(3)^0, 0*Z(3) ] ] ], GF(3) )
    gap> Base( V );
    [ [ [ Z(3)^0, Z(3)^0, 0*Z(3), 0*Z(3) ] ], 
      [ [ Z(3)^0, Z(3)^0, Z(3)^0, 0*Z(3) ] ] ]
    gap> AddBase( V, [ m1, m1+m2 ] );
    gap> Base( V );
    [ [ [ Z(3)^0, Z(3)^0, 0*Z(3), 0*Z(3) ] ], 
      [ [ Z(3), Z(3), Z(3)^0, 0*Z(3) ] ] ]