Here is the code that I want to run. I am using notebook(), since I am still
working on learning how to create sage scripts
J=JonesDatabase()
P=Primes()
for E in cremona_optimal_curves([0..50]):
T=E.torsion_subgroup()
i=E.conductor()
if i.is_prime():
for K in J.unramified_outside([i],3):
F=E.base_extend(K)
T_1=F.torsion_subgroup()
if T != T_1:
E.label();
K.is_galois();
T;
T_1;
else:
j=2
while j < i :
if j.is_prime():
n=i/j
if n.is_integral():
for K in J.unramified_outside([j],3):
F=E.base_extend(K)
T_1=F.torsion_subgroup()
if T != T_1:
E.label();
K.is_galois();
T;
T_1;
j=P.next(j)
And I get the following error.
Traceback (most recent call last): for K in
J.unramified_outside([i],3):
File "", line 1, in <module>
File
"/private/var/folders/6r/6rhDNnQhH9aXA0rGlw4Jbk++8Bk/-Tmp-/tmpfYvGji/___code___.py",
line 5, in <module>
for E in cremona_optimal_curves((ellipsis_range(_sage_const_3000
,Ellipsis,_sage_const_4000 ))):\u000a T=E.torsion_subgroup()\u000a
i=E.conductor()\u000a if i.is_prime():\u000a for K in
J.unramified_outside([i],_sage_const_3 ):\u000a
F=E.base_extend(K)\u000a T_1=F.torsion_subgroup()
\u000a if T != T_1:\u000a
E.label();\u000a K.is_galois();\u000a
T;\u000a T_1;\u000a else:\u000a
j=_sage_const_2 \u000a while j < i :\u000a if
j.is_prime():\u000a n=i/j\u000a if
n.is_integral():\u000a for K in
J.unramified_outside([j],_sage_const_3 ):\u000a
F=E.base_extend(K)\u000a
T_1=F.torsion_subgroup() \u000a if T !=
T_1:\u000a E.label();\u000a
K.is_galois();\u000a T;\u000a
T_1;\u000a j=P.next(j)
File "", line 20, in <module>
File
"/Applications/sage/local/lib/python2.6/site-packages/sage/schemes/elliptic_curves/ell_generic.py",
line 1258, in base_extend
return constructor.EllipticCurve([R(a) for a in self.a_invariants()])
File
"/Applications/sage/local/lib/python2.6/site-packages/sage/schemes/elliptic_curves/constructor.py",
line 296, in EllipticCurve
return ell_number_field.EllipticCurve_number_field(x, y)
File
"/Applications/sage/local/lib/python2.6/site-packages/sage/schemes/elliptic_curves/ell_number_field.py",
line 101, in __init__
EllipticCurve_field.__init__(self, [field(x) for x in ainvs])
File
"/Applications/sage/local/lib/python2.6/site-packages/sage/schemes/elliptic_curves/ell_generic.py",
line 166, in __init__
x, y, z = PP.coordinate_ring().gens()
File
"/Applications/sage/local/lib/python2.6/site-packages/sage/schemes/generic/projective_space.py",
line 289, in coordinate_ring
self.variable_names(), self.dimension_relative()+1)
File
"/Applications/sage/local/lib/python2.6/site-packages/sage/rings/polynomial/polynomial_ring_constructor.py",
line 335, in PolynomialRing
R = _multi_variate(base_ring, names, n, sparse, order)
File
"/Applications/sage/local/lib/python2.6/site-packages/sage/rings/polynomial/polynomial_ring_constructor.py",
line 459, in _multi_variate
R = MPolynomialRing_libsingular(base_ring, n, names, order)
File "multi_polynomial_libsingular.pyx", line 303, in
sage.rings.polynomial.multi_polynomial_libsingular.MPolynomialRing_libsingular.__init__
(sage/rings/polynomial/multi_polynomial_libsingular.cpp:3610)
File "ring.pyx", line 171, in
sage.libs.singular.ring.singular_ring_new
(sage/libs/singular/ring.cpp:2965)
File
"/Applications/sage/local/lib/python2.6/site-packages/sage/rings/rational_field.py",
line 208, in __init__
self._assign_names(('x',),normalize=False) # ???
File "parent_gens.pyx", line 327, in
sage.structure.parent_gens.ParentWithGens._assign_names
(sage/structure/parent_gens.c:2854)
File "category_object.pyx", line 336, in
sage.structure.category_object.CategoryObject._assign_names
(sage/structure/category_object.c:3286)
ValueError: variable names cannot be changed after object creation.
Above is what I get when I run it on the desktop in my office which
has sage 4.3.2.
But it seems to run fine on my laptop which has sage 4.3.
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On Fri, Feb 12, 2010 at 9:33 AM, gagan <[email protected]> wrote:
> The following commands worked find in sage 4.3.
> E=EllipticCurve('11a1')
> E.torsion_subgroup();
>
> However in sage 4.3.2 they give m the following error
>
> Traceback (most recent call last):
> File "<stdin>", line 1, in <module>
> File "_sage_input_28.py", line 9, in <module>
> open("___code___.py","w").write("# -*- coding: utf-8 -*-\n" +
>
> _support_.preparse_worksheet_cell(base64.b64decode("RT1FbGxpcHRpY0N1cnZlKCcxMWExJykKRS50b3JzaW9uX3N1Ymdyb3VwKCk7"),globals())
> +"\n"); execfile(os.path.abspath("___code___.py"))
> File "", line 1, in <module>
>
> File "/private/var/folders/6r/6rhDNnQhH9aXA0rGlw4Jbk++8Bk/-Tmp-/
> tmpSaWNtz/___code___.py", line 3, in <module>
> E.torsion_subgroup();
> File "", line 1, in <module>
>
> File "/Applications/sage/local/lib/python2.6/site-packages/sage/
> schemes/elliptic_curves/ell_rational_field.py", line 3515, in
> torsion_subgroup
> self.__torsion_subgroup =
> ell_torsion.EllipticCurveTorsionSubgroup(self, algorithm)
> File "/Applications/sage/local/lib/python2.6/site-packages/sage/
> schemes/elliptic_curves/ell_torsion.py", line 159, in __init__
> if self.__K is RationalField() and algorithm in
> pari_torsion_algorithms:
> File "/Applications/sage/local/lib/python2.6/site-packages/sage/
> rings/rational_field.py", line 208, in __init__
> self._assign_names(('x',),normalize=False) # ???
> File "parent_gens.pyx", line 327, in
> sage.structure.parent_gens.ParentWithGens._assign_names (sage/
> structure/parent_gens.c:2854)
> File "category_object.pyx", line 336, in
> sage.structure.category_object.CategoryObject._assign_names (sage/
> structure/category_object.c:3286)
> ValueError: variable names cannot be changed after object creation.
>
> Please help. My actually program is much longer, but I went through
> each function I was using and found that torsion_subgroup() was the
> one that was giving me error.
>
> --
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