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fix for elliptic_parameter in case of torsion #2692

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Aug 21, 2023
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fix for elliptic_parameter in case of torsion #2692

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24 changes: 13 additions & 11 deletions experimental/Schemes/elliptic_surface.jl
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Original file line number Diff line number Diff line change
Expand Up @@ -1021,26 +1021,28 @@ function elliptic_parameter(X::EllipticSurface, F::Vector{QQFieldElem})
P0_div = section(X, P0)
@vprint :EllipticSurface 2 "Computing basis representation of $(P0)\n"
p0 = basis_representation(X, P0_div) # this could be done from theory alone
F1 = F - p0 # should be contained in the trivial lattice
F1 = F - p0 # should be contained in the QQ-trivial-lattice
F2 = F1
tmp = F1
if all(denominator(i)==1 for i in F1)
if all(isone(denominator(i)) for i in F1)
# no torsion
P = P0
P_div = P0_div
else
for (T, tor) in tors
if all(denominator(i)==1 for i in F1-tor)
found = false
for (i,(T, tor)) in enumerate(tors)
d = F2-vec(tor)
if all(isone(denominator(i)) for i in d)
found = true
T0 = mordell_weil_torsion(X)[i]
P = P0 + T0
break
flag = true
P = P0 - T
F2 = F1 - tor
tmp = tor
end
end
@assert flag
@assert found
P_div = section(X, P)
@assert basis_representation(X, P_div) == tmp
p = basis_representation(X, P_div)
F2 = F1 - p
@assert all( isone(denominator(i)) for i in F2)
end
D = P_div
D = D + ZZ(F2[2])*zero_section(X)
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