linear independence of points on an elliptic curve

[jen]

During Sage Days 21 (while porting David Roberts' and John Cremona's implementation of 2-descent for elliptic curves over function fields), we came across the Magma function IsLinearlyIndependent?, which does not appear to have an analogue in Sage.

What it does is the following: given a list of points on an elliptic curve, it returns true iff the points are linearly independent; else it returns false and a vector of coefficients specifying a linear combination of the points that results in torsion.

We would like to have a function that does this in Sage.

[cremona]

+1!

Such a function exists somewhere in eclib. I'm not suggesting that it should be wrapped, but could be used as a model. Something I would be happy to do!