#8281: bug in hecke_operator_on_basis over finite fields
-----------------------------+----------------------------------------------
Reporter: AlexGhitza | Owner: craigcitro
Type: defect | Status: needs_review
Priority: major | Milestone: sage-4.3.3
Component: modular forms | Keywords:
Author: Alex Ghitza | Upstream: N/A
Reviewer: | Merged:
Work_issues: |
-----------------------------+----------------------------------------------
Changes (by newvalueoldvalue):
* status: new => needs_review
* author: => Alex Ghitza
Old description:
> This happens in 4.3.3.alpha0:
>
> {{{
> sage: bas_mod5 = [f.change_ring(GF(5)) for f in victor_miller_basis(12,
> 20)]
> sage: hecke_operator_on_basis(bas_mod5, 2, 12)
> ---------------------------------------------------------------------------
> TypeError Traceback (most recent call
> last)
>
> /home/ghitza/shared/articles/eigensystems/code/<ipython console> in
> <module>()
>
> /home/ghitza/sage-devel/local/lib/python2.6/site-
> packages/sage/modular/modform/hecke_operator_on_qexp.pyc in
> hecke_operator_on_basis(B, n, k, eps, already_echelonized)
> 186 V = A.span_of_basis([g.padded_list(prec) for g in B],
> 187 already_echelonized =
> already_echelonized)
> --> 188 return _hecke_operator_on_basis(B, V, n, k, eps)
> 189
> 190
>
> /home/ghitza/sage-devel/local/lib/python2.6/site-
> packages/sage/modular/modform/hecke_operator_on_qexp.pyc in
> _hecke_operator_on_basis(B, V, n, k, eps)
> 119 prec = V.degree()
> 120 TB = [hecke_operator_on_qexp(f, n, k, eps, prec, check=False,
> _return_list=True)
> --> 121 for f in B]
> 122 TB = [V.coordinate_vector(w) for w in TB]
> 123 return matrix(V.base_ring(), len(B), len(B), TB,
> sparse=False)
>
> /home/ghitza/sage-devel/local/lib/python2.6/site-
> packages/sage/modular/modform/hecke_operator_on_qexp.pyc in
> hecke_operator_on_qexp(f, n, k, eps, prec, check, _return_list)
> 87 for m in range(prec):
> 88 am = sum([eps(d) * d**l * f[m*n//(d*d)] for \
> ---> 89 d in divisors(gcd(n, m)) if (m*n) % (d*d) ==
> 0])
> 90 v.append(am)
> 91 if _return_list:
>
> /home/ghitza/sage-devel/local/lib/python2.6/site-
> packages/sage/structure/element.so in
> sage.structure.element.RingElement.__mul__
> (sage/structure/element.c:11336)()
>
> /home/ghitza/sage-devel/local/lib/python2.6/site-
> packages/sage/structure/coerce.so in
> sage.structure.coerce.CoercionModel_cache_maps.bin_op
> (sage/structure/coerce.c:6990)()
>
> TypeError: unsupported operand parent(s) for '*': 'Cyclotomic Field of
> order 1 and degree 1' and 'Finite Field of size 5'
> }}}
>
> I'm putting this in modular forms, but the underlying issue is likely a
> more general coercion problem.
>
> I'm ccing Craig because I seem to remember that he fixed something like
> this before :).
New description:
This happens in 4.3.3.alpha0:
{{{
sage: bas_mod5 = [f.change_ring(GF(5)) for f in victor_miller_basis(12,
20)]
sage: hecke_operator_on_basis(bas_mod5, 2, 12)
---------------------------------------------------------------------------
TypeError Traceback (most recent call
last)
/home/ghitza/shared/articles/eigensystems/code/<ipython console> in
<module>()
/home/ghitza/sage-devel/local/lib/python2.6/site-
packages/sage/modular/modform/hecke_operator_on_qexp.pyc in
hecke_operator_on_basis(B, n, k, eps, already_echelonized)
186 V = A.span_of_basis([g.padded_list(prec) for g in B],
187 already_echelonized = already_echelonized)
--> 188 return _hecke_operator_on_basis(B, V, n, k, eps)
189
190
/home/ghitza/sage-devel/local/lib/python2.6/site-
packages/sage/modular/modform/hecke_operator_on_qexp.pyc in
_hecke_operator_on_basis(B, V, n, k, eps)
119 prec = V.degree()
120 TB = [hecke_operator_on_qexp(f, n, k, eps, prec, check=False,
_return_list=True)
--> 121 for f in B]
122 TB = [V.coordinate_vector(w) for w in TB]
123 return matrix(V.base_ring(), len(B), len(B), TB, sparse=False)
/home/ghitza/sage-devel/local/lib/python2.6/site-
packages/sage/modular/modform/hecke_operator_on_qexp.pyc in
hecke_operator_on_qexp(f, n, k, eps, prec, check, _return_list)
87 for m in range(prec):
88 am = sum([eps(d) * d**l * f[m*n//(d*d)] for \
---> 89 d in divisors(gcd(n, m)) if (m*n) % (d*d) == 0])
90 v.append(am)
91 if _return_list:
/home/ghitza/sage-devel/local/lib/python2.6/site-
packages/sage/structure/element.so in
sage.structure.element.RingElement.__mul__
(sage/structure/element.c:11336)()
/home/ghitza/sage-devel/local/lib/python2.6/site-
packages/sage/structure/coerce.so in
sage.structure.coerce.CoercionModel_cache_maps.bin_op
(sage/structure/coerce.c:6990)()
TypeError: unsupported operand parent(s) for '*': 'Cyclotomic Field of
order 1 and degree 1' and 'Finite Field of size 5'
}}}
--
Comment:
This is not, as I first thought, a coercion problem (there is no coercion
between the cyclotomic field of degree 1 aka QQ and a finite field).
The problem is this: when the character eps is not given, it defaults to
the trivial character *over QQ*. It should really be over the base ring
of the elements of the given basis instead. The attached patch fixes
this.
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/8281#comment:1>
Sage <http://www.sagemath.org>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica,
and MATLAB
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