Hi Alexandr,
> V = VectorSpace(F,n)S = V.subspace(basis)
>
>
> but basis!=S.basis()
>
> However, I need to basis has not changed.
Do you know "tab completion"? It is rather practical. If you start to
type V.subsp and then hit the tab key, Sage (and Python) will show you
all available methods of V stat start with "subsp". Here, you will
obtain "subspace", "subspaces" and "subspace_with_basis".
And according to the documentation of "subspace_with_basis", it seems to
do what you need.
Best regards,
Simon