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### 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?