# Canonical way of turning implicit equations into a subspace and vice versa

Many times I want to go back and forth between the parametric equations of a subspace and its representation as an implicit equation.

For example, I may have a hyperplane in QQ^3 defined by the equation $ax+by+cz=0$, and I may want to turn it into a subspace object in sage. Or I may start with a subspace generated by span([v2,v3]) and I may want to compute its associated subspace in the dual and thus its implicit equations. What is the canonical way of doing so in Sage?

I thought that the method annihilator was what I was looking for, but so far I have not managed to make it work. Any other suggestions?