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The naive x-coordinate height of a point P on an elliptic curve
over a function field K,
in other words, the degree of the point (x(P):1) on the projective line.
The N{'e}ron-Tate height of the given point P on an elliptic curve defined over a function field.
Given a point P on an elliptic curve defined over a function field
F and a place Pl of the function field F, the function returns the
local height λPl(P) at Pl of P.
Given points P and Q, the function computes the height pairing,
defined as <P, Q> = (h(P + Q) - h(P) - h(Q))/2 where h denotes
the N{'e}ron-Tate height.
Given a sequence S of points Pi on an elliptic curve defined over a
function field, this function returns the matrix (< Pi, Pj >),
where < , > is the height pairing.
The height pairing lattice of a sequence of independent points on
an elliptic curve defined over a function field.
Given a sequence s of points on an elliptic curve, returns a
sequence of points that form a basis for the free part of the subgroup
generated by the points in s. The second returned value is a Gram matrix for this basis
with respect to the N'eron-Tate pairing.
Given a sequence seq of points on an elliptic curve, returns a
sequence of independent points in the free part of the subgroup
generated by the given points, which
generate a lattice of rank r and discriminant disc.
The answer is returned as soon as such a lattice has been found,
ignoring any additional points in the given sequence.
IsLinearlyIndependent(points) : [PtEll] -> BoolElt, ModTupRngElt
IndependentGenerators(points) : [PtEll] -> [PtEll]
These functions are available for elliptic curves over function fields,
and behave the same way as for elliptic curves over the rationals.
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