Skip to content
New issue

Have a question about this project? Sign up for a free GitHub account to open an issue and contact its maintainers and the community.

Sign up for GitHub

By clicking “Sign up for GitHub”, you agree to our terms of service and privacy statement. We’ll occasionally send you account related emails.

Already on GitHub? Sign in to your account

Jump to bottom

search for a pair of pre- and post-isomorphism instead of just a post-isomorphism when computing dual isogeny #37175

Merged
merged 2 commits into from
Feb 2, 2024
Merged

search for a pair of pre- and post-isomorphism instead of just a post-isomorphism when computing dual isogeny #37175

Changes from all commits
Commits
Show all changes
2 commits
Select commit Hold shift + click to select a range
d409888
search for a pair of pre- and post-isomorphism instead of just a post…
yyyyx4 Jan 27, 2024
42a2547
:trac: → :issue: throughout ell_curve_isogeny.py
yyyyx4 Jan 29, 2024
File filter

Filter by extension

Filter by extension
Conversations
Failed to load comments.
Loading
Jump to
Jump to file
Failed to load files.
Loading
Diff view
Diff view
61 changes: 37 additions & 24 deletions src/sage/schemes/elliptic_curves/ell_curve_isogeny.py
View file
Open in desktop
Original file line number Diff line number Diff line change
Expand Up @@ -847,7 +847,7 @@

TESTS:

Domain and codomain tests (see :trac:`12880`)::
Domain and codomain tests (see :issue:`12880`)::

sage: E = EllipticCurve(QQ, [0,0,0,1,0])
sage: phi = EllipticCurveIsogeny(E, E(0,0))
Expand All @@ -863,7 +863,7 @@
sage: phi.codomain()
Elliptic Curve defined by y^2 + x*y = x^3 + 24*x + 6 over Finite Field of size 31

Composition tests (see :trac:`16245`, cf. :trac:`34410`)::
Composition tests (see :issue:`16245`, cf. :issue:`34410`)::

sage: E = EllipticCurve(j=GF(7)(0))
sage: phi = E.isogeny([E(0), E((0,1)), E((0,-1))]); phi
Expand All @@ -875,7 +875,7 @@
From: Elliptic Curve defined by y^2 = x^3 + 1 over Finite Field of size 7
To: Elliptic Curve defined by y^2 = x^3 + 1 over Finite Field of size 7

Examples over relative number fields used not to work (see :trac:`16779`)::
Examples over relative number fields used not to work (see :issue:`16779`)::

sage: # long time, needs sage.rings.number_field
sage: pol26 = hilbert_class_polynomial(-4*26)
Expand All @@ -891,7 +891,7 @@
sage: iso3 = EL.isogenies_prime_degree(3); len(iso3)
2

Examples over function fields used not to work (see :trac:`11327`)::
Examples over function fields used not to work (see :issue:`11327`)::

sage: F.<t> = FunctionField(QQ)
sage: E = EllipticCurve([0,0,0,-t^2,0])
Expand Down Expand Up @@ -1189,7 +1189,7 @@

TESTS:

Tests for :trac:`10888`::
Tests for :issue:`10888`::

sage: # needs sage.rings.number_field
sage: x = polygen(ZZ, 'x')
Expand All @@ -1204,7 +1204,7 @@
sage: phihat(Q)
(-1/48 : 127/576*th : 1)

Call a composed isogeny (added for :trac:`16238`)::
Call a composed isogeny (added for :issue:`16238`)::

sage: E = EllipticCurve(j=GF(7)(0))
sage: phi = E.isogeny([E(0), E((0,1)), E((0,-1))])
Expand All @@ -1214,7 +1214,7 @@
sage: phi2(E.points()[0])
(0 : 1 : 0)

Coercion works fine with :meth:`_call_` (added for :trac:`16238`)::
Coercion works fine with :meth:`_call_` (added for :issue:`16238`)::

sage: # needs sage.rings.number_field
sage: K.<th> = NumberField(x^2 + 3)
Expand Down Expand Up @@ -1243,7 +1243,7 @@
sage: phi(Q)._order
27

Test for :trac:`35983`::
Test for :issue:`35983`::

sage: E = EllipticCurve([1,0,0,-1,0])
sage: P = E([1,0])
Expand Down Expand Up @@ -2106,7 +2106,7 @@

TESTS:

Check for :trac:`33214`::
Check for :issue:`33214`::

sage: # needs sage.rings.finite_rings
sage: z2 = GF(71^2).gen()
Expand All @@ -2120,7 +2120,7 @@
(33 : 61*z2 + 10 : 1)

The rational maps are also computed via this code path; check
that they are plausible (this failed prior to :trac:`33214`)::
that they are plausible (this failed prior to :issue:`33214`)::

sage: # needs sage.rings.finite_rings
sage: fx,fy = phi.rational_maps() # indirect doctest
Expand Down Expand Up @@ -2601,7 +2601,7 @@
sage: phi._EllipticCurveIsogeny__compute_omega_general(E, psi, psi_pr, fi, fi_pr)
(x^3 + (alpha^2 + 1)*x^2 + (alpha^2 + 1)*x + alpha)*y + (alpha^2 + alpha + 1)*x^2 + (alpha^2 + alpha)*x + alpha

A bug fixed in :trac:`7907`::
A bug fixed in :issue:`7907`::

sage: # needs sage.rings.finite_rings
sage: F = GF(128,'a')
Expand Down Expand Up @@ -3151,7 +3151,7 @@

TESTS:

Test for :trac:`23928`::
Test for :issue:`23928`::

sage: E = EllipticCurve(j=GF(431**2)(4)) # needs sage.rings.finite_rings
sage: phi = E.isogeny(E.lift_x(0)) # needs sage.rings.finite_rings
Expand All @@ -3160,7 +3160,7 @@
from Elliptic Curve defined by y^2 = x^3 + 427*x over Finite Field in z2 of size 431^2
to Elliptic Curve defined by y^2 = x^3 + x over Finite Field in z2 of size 431^2

Test (for :trac:`7096`)::
Test (for :issue:`7096`)::

sage: E = EllipticCurve('11a1')
sage: phi = E.isogeny(E(5,5))
Expand All @@ -3186,7 +3186,7 @@
from Elliptic Curve defined by y^2 + x*y = x^3 + 84*x + 34 over Finite Field of size 103
to Elliptic Curve defined by y^2 + x*y = x^3 + x + 102 over Finite Field of size 103

Check that :trac:`17293` is fixed::
Check that :issue:`17293` is fixed::

sage: # needs sage.rings.number_field
sage: k.<s> = QuadraticField(2)
Expand All @@ -3197,6 +3197,18 @@
sage: phi._EllipticCurveIsogeny__clear_cached_values() # forget the dual
sage: -phi.dual() == (-phi).dual()
True

Check that :issue:`37168` is fixed::

sage: R.<x> = GF(23)[]
sage: F.<a> = FiniteField(23^2, modulus=x^2-x+1)
sage: E0 = EllipticCurve(F, (0, 1))
sage: E1 = EllipticCurve(F, (8, 1))
sage: phi = E0.isogeny(kernel=E0((a, 0)), codomain=E1)
sage: phi.dual()
Isogeny of degree 2
from Elliptic Curve defined by y^2 = x^3 + 8*x + 1 over Finite Field in a of size 23^2
to Elliptic Curve defined by y^2 = x^3 + 1 over Finite Field in a of size 23^2
"""
if self.__base_field.characteristic() in (2, 3):
raise NotImplementedError("computation of dual isogenies not yet implemented in characteristics 2 and 3")
Expand Down Expand Up @@ -3260,17 +3272,18 @@
E2 = E2pr.change_weierstrass_model(u/F(d), 0, 0, 0)

phi_hat = EllipticCurveIsogeny(E1, None, E2, d)

pre_iso = self._codomain.isomorphism_to(E1)
post_iso = E2.isomorphism_to(self._domain)

# assert phi_hat.scaling_factor() == 1
sc = u * pre_iso.scaling_factor() * post_iso.scaling_factor() / F(d)
if not sc.is_one():
auts = self._codomain.automorphisms()
aut = [a for a in auts if a.u == sc]
assert len(aut) == 1, "bug in dual()"
pre_iso *= aut[0]

for pre_iso in self._codomain.isomorphisms(E1):
for post_iso in E2.isomorphisms(self._domain):
sc = u * pre_iso.scaling_factor() * post_iso.scaling_factor()
if sc == d:
break
else:
continue

Check warning on line 3283 in src/sage/schemes/elliptic_curves/ell_curve_isogeny.py

View check run for this annotation

Codecov / codecov/patch

src/sage/schemes/elliptic_curves/ell_curve_isogeny.py#L3283 

Added line #L3283 was not covered by tests
break
else:
assert "bug in dual()"

Check warning on line 3286 in src/sage/schemes/elliptic_curves/ell_curve_isogeny.py

View check run for this annotation

Codecov / codecov/patch

src/sage/schemes/elliptic_curves/ell_curve_isogeny.py#L3286 

Added line #L3286 was not covered by tests

phi_hat._set_pre_isomorphism(pre_iso)
phi_hat._set_post_isomorphism(post_iso)
Expand Down
Loading