# basis of subspace of complex field

Hi -

Given a set of elements of `CC`

, or perhaps `QQbar`

, I want to compute a basis for a subspace over `QQ`

that contains those elements.

For example, given $3$, $1+\sqrt{5}$, $i$, and $i-1$, I'd expect my output to be $\{1, \sqrt{5}, i\}$, since my original four elements can be written as $(3,0,0)$, $(1,1,0)$, $(0,0,1)$, and $(-1,0,1)$ with respect to that basis.

Obviously, the basis won't be unique.

Can anybody suggest what tools in Sage might be useful for this calculation?