division of elliptic-curve morphisms #38902
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GiacomoPope
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Jul 15, 2025
| Denominator: 2 | ||
| """ | ||
| from sage.rings.integer import Integer | ||
| if not isinstance(other, (int, Integer)): |
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Is it worth trying to cast the value here to an Integer and return NotImplemented when we cant?
I'm thinking of the case where somehow 2 is an element of the rationals or finite field and then this fails somewhat silently
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| - Lorenz Panny (2024) |
| return self._phi.inseparable_degree() / self._domain.scalar_multiplication(self._d).inseparable_degree() | ||
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| def _torsion_gens(E, EE, l, e, psi=None): |
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is there not something appropriate we can use from the curve object itself here?
GiacomoPope
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Jul 16, 2025
vbraun
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Jul 18, 2025
sagemathgh-38902: division of elliptic-curve morphisms This patch adds a class for representing symbolic fractions $\phi/d$ of elliptic-curve morphisms. As a corollary, we get left- and right- division of isogenies, which are emulated by composing with the dual and dividing out the degree. Fractional isogenies often appear in computations with endomorphism rings (e.g., $(1+\pi_q)/2$ is an endomorphism of any elliptic curve over $\mathbb F_q$ with rational $2$-torsion). The new class is designed to fully support the `EllipticCurveHom` interface, albeit with *extremely* basic algorithms in some cases. Indeed, the goal of this patch is to establish the interface and basic functionality — any optimizations are left for future work. URL: sagemath#38902 Reported by: Lorenz Panny Reviewer(s): Giacomo Pope
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This patch adds a class for representing symbolic fractions$\phi/d$ of elliptic-curve morphisms. As a corollary, we get left- and right-division of isogenies, which are emulated by composing with the dual and dividing out the degree. Fractional isogenies often appear in computations with endomorphism rings (e.g., $(1+\pi_q)/2$ is an endomorphism of any elliptic curve over $\mathbb F_q$ with rational $2$ -torsion).
The new class is designed to fully support the
EllipticCurveHominterface, albeit with extremely basic algorithms in some cases. Indeed, the goal of this patch is to establish the interface and basic functionality — any optimizations are left for future work.