You are right!  (U.0).lift() gives what I want. Thank you very much.

By the way, do you know how to get the image in the modulo space? 


On Monday, April 10, 2017 at 3:47:44 PM UTC+8, Nils Bruin wrote:
>
> 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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