linear independence of points on an elliptic curve
|Reported by:||jen||Owned by:||cremona|
|Report Upstream:||N/A||Work issues:|
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.