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EllipticCurve_generic.lift_x() is not always deterministic #36189

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yyyyx4 opened this issue Sep 4, 2023 · 0 comments
Open

EllipticCurve_generic.lift_x() is not always deterministic #36189

yyyyx4 opened this issue Sep 4, 2023 · 0 comments

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@yyyyx4
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yyyyx4 commented Sep 4, 2023

After #35644, the .lift_x() method is supposed to return deterministic results. However, the following code produces different outputs on 64-bit and 32-bit machines, per this comment:

sage: from sage.schemes.elliptic_curves.ell_field import point_of_order
sage: E = EllipticCurve(QQ, [7,7])
sage: point_of_order(E, 3)

The root cause is the incomparability of number-field elements, as pointed out in this comment:

sage: K.<Y> = NumberField(x^3 - x^2 + 7*x + 7)
sage: Y <= -Y
False
sage: -Y <= Y
False

It is not quite clear how to resolve this in general; see also this comment.

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