#14214: Cythoned homsets
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Reporter: SimonKing | Owner: tbd
Type: enhancement | Status: new
Priority: major | Milestone: sage-5.8
Component: performance | Resolution:
Keywords: Hom, cython, cached method | Work issues:
Report Upstream: N/A | Reviewers:
Authors: Simon King | Merged in:
Dependencies: #14159, #12951 | Stopgaps:
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Comment (by SimonKing):
Ideally, sage.categories.homset.Homset should be a cdef class, with cdef
attributes _domain, _codomain, `__category`.
__Problem and potential long term solutions__
`sage.modular.abvar.homspace.EndomorphimSubring` inherits from
sage.categories.homset.Homset and from sage.rings.ring.Ring. Making Homset
cdef with cdef attributes results in incompatible base classes.
- One could think of creating a new cdef class
`sage.categories.homset.EndomorphismRing` inheriting from
sage.rings.ring.Ring and copying the methods implemented in
sage.categories.homset.Homset, and use it in sage.modular.abvar.homspace.
- However, that's code duplication, and I doubt that we want that.
- One could think of dropping `sage.rings.ring.Ring` and let
`EndomorphismSubring` entirely rely on the ring functionality that is
provided by the category framework.
- I tried, but this means opening a can of worms. One would then also
need to implement the new coercion model in sage.modular. But replacing
`EndomorphismSubring.__call__` by an _element_constructor_ does not work,
because Homset has a `__call__` method, too. Hence, we would then also
need to use the new coercion model for sage.categories.homset. Yes, that's
desirable. But it is not available in short time.
- One could try to make some important basic methods of Homset fast, by
inheritance from `WithEqualityById` that I introduced in #14054. It would
be desirable that two homsets are equal if and only if they are identical
if and only if both domain, codomain and category are identical.
- Unfortunately, the old parts of sage (about elliptic curves and stuff)
rely on the assumption that we do ''not'' have unique parents and do
''not'' have unique homsets. This would be another can of worms.
__Short term improvements suggested in my patch__
- Changing sage.categories.homset into a Cython module means: We can cdef
the homset cache, and can thus use fast get/set methods for `TripleDict`.
That's a speed-up.
- One can make Homset cdef, but keep the _domain and _codomain attributes
Python attributes. Then, there are no layout conflicts.
- I suggest to change `__category` into a single underscore attribute, to
avoid name mangling.
- Accessing a Python attribute _domain defined for a Homset can be
surprisingly slow. It is fast, if one has an instance of Homset itself.
But it is slow if one considers an instance of a sub-class, such as
`EndomorphismSubring`. It turns out that calling a cached method is
''faster'' than accessing the attribute! Hence, I suggest using cached
method decorators on the domain() and codomain() methods (these methods
are internally used in `EndomorphismSubring` anyway).
- As a step towards uniqueness, I suggest that `Homset.__cmp__` tests by
identity rather than equality, and uses `cmp` only on non-identical
domain/codomain/category.
Making Homset cdef requires to put `Set_generic` into
sage.structure.parent.pxd.
Timings will be in the next post.
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/14214#comment:1>
Sage <http://www.sagemath.org>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica,
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