I compute a freemodule U=V/M, where V and M are vector space,  as follows.

I'm wondering that how I can get the image in U of v /in V, that is v 
modulo W.
On the other hand, how can I get the lift in V of u /in U? For this, I 
tried the command lift(), but it seems not to work, since I 
input lift(U.0), but it gives (1), which is not in V.

Any one has an idea please?


sage: k.<i> = QuadraticField(-1)sage: A = k^3; V = A.span([[1,0,i], 
[2,i,0]])sage: W = A.span([[3,i,i]])sage: U = V/W; U

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