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Export weierstrass_chart_on_minimal_model and patch transform_to_weierstrass #3458

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merged 2 commits into from
Feb 29, 2024
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Export weierstrass_chart_on_minimal_model and patch transform_to_weierstrass #3458

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e66e58d
Export weierstrass_chart_on_minimal_model.
HechtiDerLachs Feb 28, 2024
6f46bd2
Repair transform_to_weierstrass.
HechtiDerLachs Feb 15, 2024
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23 changes: 18 additions & 5 deletions experimental/Schemes/elliptic_surface.jl
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Original file line number Diff line number Diff line change
@@ -1,4 +1,4 @@
export elliptic_surface, trivial_lattice, weierstrass_model, weierstrass_chart, algebraic_lattice, zero_section, section, weierstrass_contraction, fiber_components, generic_fiber, reducible_fibers, fibration_type, mordell_weil_lattice, elliptic_parameter, set_mordell_weil_basis!, EllipticSurface, weierstrass_chart, transform_to_weierstrass
export elliptic_surface, trivial_lattice, weierstrass_model, weierstrass_chart, algebraic_lattice, zero_section, section, weierstrass_contraction, fiber_components, generic_fiber, reducible_fibers, fibration_type, mordell_weil_lattice, elliptic_parameter, set_mordell_weil_basis!, EllipticSurface, weierstrass_chart_on_minimal_model, transform_to_weierstrass

@doc raw"""
EllipticSurface{BaseField<:Field, BaseCurveFieldType} <: AbsCoveredScheme{BaseField}
Expand Down Expand Up @@ -1494,6 +1494,23 @@ on the curve defined by `g`, i.e. `g(P) == 0`.
"""
function transform_to_weierstrass(g::MPolyRingElem, x::MPolyRingElem, y::MPolyRingElem, P::Vector{<:RingElem})
R = parent(g)
F = fraction_field(R)

# In case of variables in the wrong order, switch and transform the result.
if x == R[2] && y == R[1]
switch = hom(R, R, reverse(gens(R)))
g_trans, trans = transform_to_weierstrass(switch(g), y, x, reverse(P))
new_trans = MapFromFunc(F, F, f->begin
switch_num = switch(numerator(f))
switch_den = switch(denominator(f))
interm_res = trans(F(switch_num))//trans(F(switch(den)))
num = numerator(interm_res)
den = denominator(interm_res)
switch(num)//switch(den)
end
)
return switch(g_trans), new_trans
end
@assert ngens(R) == 2 "input polynomial must be bivariate"
@assert x in gens(R) "second argument must be a variable of the parent of the first"
@assert y in gens(R) "third argument must be a variable of the parent of the first"
Expand All @@ -1503,9 +1520,6 @@ function transform_to_weierstrass(g::MPolyRingElem, x::MPolyRingElem, y::MPolyRi
kkxy, Y = polynomial_ring(kkx, :y, cached=false)

imgs = [kkxy(X), Y]
if x == R[2] && y == R[1]
imgs = reverse(imgs)
end
split_map = hom(R, kkxy, imgs)

G = split_map(g)
Expand Down Expand Up @@ -1558,7 +1572,6 @@ function transform_to_weierstrass(g::MPolyRingElem, x::MPolyRingElem, y::MPolyRi
#@assert x == evaluate(x1, [x2, y2])
#@assert y == evaluate(y1, [x2, y2])
end
F = fraction_field(R)
@assert F === parent(x1) "something is wrong with caching of fraction fields"
# TODO: eventually add the inverse.
trans = MapFromFunc(F, F, f->evaluate(numerator(f), [x1, y1])//evaluate(denominator(f), [x1, y1]))
Expand Down
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