Does U.lift(U.0) do the trick? 

It looks like (U.0).lift() (and hence lift(U.0) ) attempts to do a 
coordinate-wise lift, which is not what you want. It's perhaps a bug that 
does that.

On Monday, April 10, 2017 at 12:28:12 AM UTC-7, Peng wrote:
>
> 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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