#14793: Unique representation for homsets
-------------------------------+--------------------------------------------
Reporter: nthiery | Owner: nthiery
Type: enhancement | Status: new
Priority: major | Milestone: sage-5.12
Component: categories | Resolution:
Keywords: | Work issues:
Report Upstream: N/A | Reviewers:
Authors: Simon King | Merged in:
Dependencies: | Stopgaps:
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Comment (by SimonKing):
This works:
{{{
sage: M = ModularSymbols(6)
sage: f = M.hecke_operator(7).matrix_form()
sage: loads(dumps(M)) == M
True
}}}
Continuing the example, this makes it fail:
{{{
sage: phi = f.hecke_module_morphism()
sage: loads(dumps(M)) == M
Traceback (most recent call last):
...
<type 'str'>: (<type 'exceptions.AttributeError'>,
AttributeError('ModularSymbolsAmbient_wt2_g0_with_category' object has no
attribute '_HeckeModule_generic__level',))
}}}
Continuing the example, this makes it work again:
{{{
sage: del M._HeckeModule_generic__hecke_algebra
sage: loads(dumps(M)) == M
True
}}}
Hence, I think the following happens.
- `s = dumps(M)` pickles the content of `M.__dict__`. `loads(s)` then
starts with unpickling the stored content of `M.__dict__`, after creating
a would-be-copy N of M, which is not initialised at this point (this is
what Python does in those cases). The unpickled content of M.__dict__
would later be assigned to N.__dict__
- The Hecke algebra of M is stored as an attribute of M. `Hom(M,M)`
somehow becomes stored as an attribute of `M.hecke_algebra()` when calling
`.hecke_module_morphism()`. Hence, when deleting the attribute containing
`M.hecke_algebra()`, all is good.
- When unpickling the content of `M.__dict__`, Python eventually tries to
unpickle `Hom(M,M)`, but replaces M with its would-be-copy N. But since N
is not initialised, `Hom(N,N)` fails.
This suggests a way out: We could implement "proper" unpickling of
`M.hecke_algebra()`, so that `Hom(M,M)` will not be called prematurely.
It might also be a good idea to use @cached_method when a method is
cached. Namely, I often see stuff like
{{{
#!python
def free_module(self):
"""
Return the free module underlying this ambient Hecke module (the
forgetful functor from Hecke modules to modules over the base
ring)
EXAMPLE::
sage: ModularForms(59, 2).free_module()
Vector space of dimension 6 over Rational Field
"""
try:
return self.__free_module
except AttributeError:
M = sage.modules.all.FreeModule(self.base_ring(), self.rank())
self.__free_module = M
return M
}}}
which uses `__dict__` and hence will result in errors during unpickling.
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/14793#comment:19>
Sage <http://www.sagemath.org>
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