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{éron--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, returns the
local height λPl(P) at Pl of P.
Returns the height pairing of the points P and Q,
defined as <P, Q> = (hat(h)(P + Q) - hat(h)(P) - hat(h)(Q))/2
(where as usual hat(h) denotes the N{éron--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 Néron--Tate pairing.
Given a sequence S of points on an elliptic curve, returns a
sequence of independent points in the free part of the subgroup
generated by S such that these points
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.
V2.28, 13 July 2023