Hi,
  I take two vectors as follows:
 R=[(1, 3), (1, 0)]

Then I span it over integers like
R=(ZZ^2).span(R)

It is clear that vector([0,3]) is in R.
I want to find corresponding coordinates i.e,
(1,-1). How can I find this using Sage?

Instead of integers, is it possible to span over the ring
Integers(15) and find the coordinates?

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