On Wed, Mar 26, 2008 at 11:42 AM, Craig Citro <[EMAIL PROTECTED]> wrote:
>
> Hey all,
>
> (I'm cc'ing this to sage-devel, because I think there are people there
> who care about modular forms who might not read sage-support.)
>
> So I've also posted a patch on #2674, which actually fixes both of
> these issues, as well as the fact that it currently is the case that
> adding an element of CuspForms(22) to an element of ModularForms(22)
> breaks.
>
> Now, I agree with William's point here:
>
>
> > Note that
> >
> > b[0] + 0
> >
> > and
> >
> > 0 + b[0]
> >
> > should *not* work, since in each case that's a canonical coercion,
> > and there is no natural map from ZZ (the parent of 0) into CuspForms(...)
> > for any weight except 0. In Sage coercions should not happen
> automatically
> > unless they are in some way natural and well defined on the whole domain
> > of the coercion (in this case ZZ).
> >
>
> However, the modular forms code isn't the culprit -- it just tries to
> coerce in by calling the coercion code for the underlying free module.
> Here's why this actually works:
>
> sage: M = ZZ**3
> sage: M(0)
> (0, 0, 0)
> sage: M(1) # goes boom
Wait -- it's perfectly fine that M(0) works! It's only bad if this
were to work:
sage: M._coerce_impl(0)
(0, 0, 0)
In fact, the above does work. That's because this code is wrong:
def _coerce_impl(self, x):
"""
Canonical coercion of x into this free module.
(0, 4/3, 8/3, 4, 16/3)
"""
if isinstance(x, (int, long, sage.rings.integer.Integer)) and x==0:
return self.zero_vector()
...
>
>
>
> > There are some canonical coercions that one *should* have in the context
> > of modular forms that aren't there, probably partly because this whole
> > "canonical
> > coercions" business was after I wrote the modular forms code. Here's
> > an example bug (=lack of a coercion that should be there):
> >
> >
> > sage: b=CuspForms(22).basis()
> > sage: sum(b, b[0].parent()(0))
>
> This now works fine with the patch I posted to #2674.
>
> Currently, there are no coercions between different levels; which such
> coercions would people like to see?
The map f(q) |--> f(q) is a canonical coercion from level Gamma to level Gamma'
for any subgroup Gamma' of Gamma. It's the 1-th degeneracy map, but is the
most canonical since it is the identity map on q-expansions.
> Coercing from Gamma0(M) to
> Gamma0(Md) seems plausible, though one argue that it's a choice of one
> specific degeneracy map. That is, it seems "standard" but not
> canonical. I think it's the same as asking for a natural map from
> ZZ['x'] to ZZ['y'].
I disagree. A modular form -- viewed as a function on the upper half
plane -- for
Gamma0(M) is automatically also one for Gamma0(Md) in a canonical way.
It's invariant under the smaller group.
> Of course, this works in Sage, so maybe the above
> map should, too. Maybe also maps from Gamma0 to Gamma1 and GammaH? And
> GammaH to Gamma1?
Whenever one group is contained in another, coerce.
> Which maps seem reasonable to people? Jay, are there any of these that
> you would expect to work that don't?
>
> -cc
>
>
>
> >
>
--
William Stein
Associate Professor of Mathematics
University of Washington
http://wstein.org
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