how to calculate complement of vector space in gap

Question

I have a finite dimensional (but large dimension) vector space over GF(2), $V$. I also have a subspace $ A \subset V$. I have basis for $V$ and for $A$. I'd like to find a basis for the complement of $A$ in $V$, $B : V = A \oplus B; A \cap B = 0$. (Note this is not the orthogonal complement). What would be a good way to do this in gap? If there are no built-in functions, what would be a good approach/algorithm?

Answer 1

If you have the bases given as list of vectors, BaseSteinitzVectors(basV,basA).factorspace gives a basis of a complement. This should be reasonably effective. Make sure that your vectors are in compressed form, as this will be faster.