#11327: isogeny code uses deprecated(?) multi-variate gcd
-------------------------------------+-------------------------------------
Reporter: cjh | Owner: cremona
Type: defect | Status: needs_review
Priority: major | Milestone: sage-6.3
Component: elliptic curves | Resolution:
Keywords: isogeny | Merged in:
multivariate dual | Reviewers:
Authors: John Cremona | Work issues:
Report Upstream: N/A | Commit:
Branch: | e043ae8eeb0ed3b12f748131904d5e0e0476a83e
u/cremona/ticket/11327 | Stopgaps:
Dependencies: |
-------------------------------------+-------------------------------------
Changes (by cremona):
* dependencies: #16779 =>
Old description:
> In sage.schemes.elliptic_curves.ell_curve_isogeny (of sage 4.6.2) the
> routine two_torsion_part() invokes a gcd on two polynomials. When the
> polynomials belong to a multivariate ring, an error occurs. Perhaps this
> is because the gcd routine in
> sage.rings.polynomial.multi_polynomial_element has been commented out
> (because it uses Singular?!).
>
> Converting psi (and perhaps psi2) to univariate polynomials within
> two_torsion_part() before taking the gcd seems to work, but there seems
> to be other code in the module which uses a multivariate ring when a
> univariate ring would suffice (e.g. in __init_from_kernel_polynomial).
>
> I discovered this error when trying to create a dual isogeny (for an
> elliptic curve over Q(t)). The original isogeny was a cyclic 2-isogeny
> and thus the dual should also be a cyclic 2-isogeny. Without giving more
> details on how I created the curve, let me simply report the error
> message which results when I call isogeny.dual():
>
> Traceback (most recent call last):
> File "<stdin>", line 1, in <module>
> File "_sage_input_5.py", line 10, in <module>
> exec compile(u'open("___code___.py","w").write("# -*- coding: utf-8
> -*-\\n" +
> _support_.preparse_worksheet_cell(base64.b64decode("cHNpID0gcGhpLmR1YWwoKQ=="),globals())+"\\n");
> execfile(os.path.abspath("___code___.py"))
> File "", line 1, in <module>
>
> File
> "/private/var/folders/4V/4VAOdForFpanThca5kJ5xE+++TI/-Tmp-/tmp8DXIBC/___code___.py",
> line 2, in <module>
> exec compile(u'psi = phi.dual()
> File "", line 1, in <module>
>
> File "/Applications/sage/local/lib/python2.6/site-
> packages/sage/schemes/elliptic_curves/ell_curve_isogeny.py", line 3248,
> in dual
> phi_hat = EllipticCurveIsogeny(E1, None, E2, d)
> File "/Applications/sage/local/lib/python2.6/site-
> packages/sage/schemes/elliptic_curves/ell_curve_isogeny.py", line 914, in
> __init__
> self.__init_from_kernel_polynomial(kernel, degree)
> File "/Applications/sage/local/lib/python2.6/site-
> packages/sage/schemes/elliptic_curves/ell_curve_isogeny.py", line 2038,
> in __init_from_kernel_polynomial
> psi_G = two_torsion_part(E, poly_ring, psi, degree);
> File "/Applications/sage/local/lib/python2.6/site-
> packages/sage/schemes/elliptic_curves/ell_curve_isogeny.py", line 453, in
> two_torsion_part
> psi_G = poly_ring(psi.gcd(psi_2))
> File "element.pyx", line 327, in
> sage.structure.element.Element.__getattr__
> (sage/structure/element.c:2715)
> File "parent.pyx", line 277, in
> sage.structure.parent.getattr_from_other_class
> (sage/structure/parent.c:2841)
> File "parent.pyx", line 177, in
> sage.structure.parent.raise_attribute_error
> (sage/structure/parent.c:2663)
> AttributeError: 'MPolynomial_polydict' object has no attribute 'gcd'
New description:
New branch sorts out the use of uni- versus multi-variate polynomials
systematically, and makes a lot of minor improvements and simplifications
and improves many docstrings. The specific errors originally reported
here (see below) and at #16779 are fixed.
In sage.schemes.elliptic_curves.ell_curve_isogeny (of sage 4.6.2) the
routine two_torsion_part() invokes a gcd on two polynomials. When the
polynomials belong to a multivariate ring, an error occurs. Perhaps this
is because the gcd routine in
sage.rings.polynomial.multi_polynomial_element has been commented out
(because it uses Singular?!).
Converting psi (and perhaps psi2) to univariate polynomials within
two_torsion_part() before taking the gcd seems to work, but there seems to
be other code in the module which uses a multivariate ring when a
univariate ring would suffice (e.g. in __init_from_kernel_polynomial).
I discovered this error when trying to create a dual isogeny (for an
elliptic curve over Q(t)). The original isogeny was a cyclic 2-isogeny
and thus the dual should also be a cyclic 2-isogeny. Without giving more
details on how I created the curve, let me simply report the error message
which results when I call isogeny.dual():
Traceback (most recent call last):
File "<stdin>", line 1, in <module>
File "_sage_input_5.py", line 10, in <module>
exec compile(u'open("___code___.py","w").write("# -*- coding: utf-8
-*-\\n" +
_support_.preparse_worksheet_cell(base64.b64decode("cHNpID0gcGhpLmR1YWwoKQ=="),globals())+"\\n");
execfile(os.path.abspath("___code___.py"))
File "", line 1, in <module>
File
"/private/var/folders/4V/4VAOdForFpanThca5kJ5xE+++TI/-Tmp-/tmp8DXIBC/___code___.py",
line 2, in <module>
exec compile(u'psi = phi.dual()
File "", line 1, in <module>
File "/Applications/sage/local/lib/python2.6/site-
packages/sage/schemes/elliptic_curves/ell_curve_isogeny.py", line 3248, in
dual
phi_hat = EllipticCurveIsogeny(E1, None, E2, d)
File "/Applications/sage/local/lib/python2.6/site-
packages/sage/schemes/elliptic_curves/ell_curve_isogeny.py", line 914, in
__init__
self.__init_from_kernel_polynomial(kernel, degree)
File "/Applications/sage/local/lib/python2.6/site-
packages/sage/schemes/elliptic_curves/ell_curve_isogeny.py", line 2038, in
__init_from_kernel_polynomial
psi_G = two_torsion_part(E, poly_ring, psi, degree);
File "/Applications/sage/local/lib/python2.6/site-
packages/sage/schemes/elliptic_curves/ell_curve_isogeny.py", line 453, in
two_torsion_part
psi_G = poly_ring(psi.gcd(psi_2))
File "element.pyx", line 327, in
sage.structure.element.Element.__getattr__ (sage/structure/element.c:2715)
File "parent.pyx", line 277, in
sage.structure.parent.getattr_from_other_class
(sage/structure/parent.c:2841)
File "parent.pyx", line 177, in
sage.structure.parent.raise_attribute_error (sage/structure/parent.c:2663)
AttributeError: 'MPolynomial_polydict' object has no attribute 'gcd'
--
--
Ticket URL: <http://trac.sagemath.org/ticket/11327#comment:8>
Sage <http://www.sagemath.org>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica,
and MATLAB
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