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Decoupled computation of height so it can be called for ambient spaces #1187

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Aug 11, 2023
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Decoupled computation of height so it can be called for ambient spaces #1187

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36 changes: 22 additions & 14 deletions src/EllCrv/Heights.jl
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Original file line number Diff line number Diff line change
Expand Up @@ -35,23 +35,17 @@
################################################################################

export local_height, canonical_height, naive_height, height_pairing,
regulator, neron_tate_height, CPS_dvev_real, CPS_dvev_complex, CPS_non_archimedean, CPS_height_bounds, derivative, refine_alpha_bound
regulator, neron_tate_height, CPS_dvev_real, CPS_dvev_complex, CPS_non_archimedean,
CPS_height_bounds, derivative, refine_alpha_bound

################################################################################
#
# Naive Height
#
################################################################################

@doc raw"""
naive_height(P::EllCrvPt{QQFieldElem}, prec) -> arb

Return the naive height of a point $P$ on an elliptic curve defined over
$\mathbb{Q}$.
"""
function naive_height(P::EllCrvPt{QQFieldElem}, prec::Int = 100)
function naive_height_coordinate(x::QQFieldElem, prec::Int = 100)
attempt = 1
x = P[1]
p = numerator(x)
q = denominator(x)
r = max(abs(p), abs(q))
Expand All @@ -69,18 +63,21 @@ function naive_height(P::EllCrvPt{QQFieldElem}, prec::Int = 100)
end

@doc raw"""
naive_height(P::EllCrvPt{nf_elem}, prec) -> arb
naive_height(P::EllCrvPt{QQFieldElem}, prec) -> arb

Return the naive height of a point $P$ on an elliptic curve defined over
a number field.
$\mathbb{Q}$.
"""
function naive_height(P::EllCrvPt{nf_elem}, prec::Int = 100)
function naive_height(P::EllCrvPt{QQFieldElem}, prec::Int = 100)
return naive_height_coordinate(P[1], prec)
end

function naive_height_coordinate(x::nf_elem, prec::Int = 100)
attempt = 1

K = base_field(parent(P))
K = parent(x)
OK = ring_of_integers(K)

x = P[1]
q = K(denominator(x))

N = norm(ideal(OK, x) + 1*OK)
Expand Down Expand Up @@ -115,6 +112,17 @@ function naive_height(P::EllCrvPt{nf_elem}, prec::Int = 100)
end
end

@doc raw"""
naive_height(P::EllCrvPt{nf_elem}, prec) -> arb

Return the naive height of a point $P$ on an elliptic curve defined over
a number field.
"""
function naive_height(P::EllCrvPt{nf_elem}, prec::Int = 100)
return naive_height_coordinate(P[1], prec)
end


################################################################################
#
# Local Height at finite prime
Expand Down
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