#9944: categories for polynomial rings
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Reporter: robertwb | Owner: nthiery
Type: defect | Status: needs_info
Priority: major | Milestone: sage-4.7
Component: categories | Keywords:
Author: Robert Bradshaw | Upstream: N/A
Reviewer: Nicolas M. Thiéry, Mike Hansen | Merged:
Work_issues: |
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Comment(by SimonKing):
Perhaps it is a conversion map that is slower than necessary?
If you look at
`sage.categories.algebras.Algebras.ParentMethods.__init_extra__`, you see
that it tries to register a certain set morphism as a coercion from the
base ring into the algebra (that obviously works only if the algebra is
unital).
But aparently a different coercion is used -- a slower coercion!
Namely, together with my patch from #9138:
{{{
sage: R.<x> = ZZ[]
sage: R.category() # the __init_extra__ was supposed to be used.
Join of Category of unique factorization domains and Category of
commutative algebras over Integer Ring
sage: c = R.convert_map_from(R.base_ring())
sage: c
Polynomial base injection morphism:
From: Integer Ring
To: Univariate Polynomial Ring in x over Integer Ring
}}}
That is not what `__init_extra__` attempted to register!
Let us compare:
{{{
sage: from sage.categories.morphism import SetMorphism
sage: H = R.base().Hom(R)
sage: f = SetMorphism(H,R.from_base_ring)
sage: timeit('c(100)',number=10^5)
100000 loops, best of 3: 8.13 µs per loop
sage: timeit('f(100)',number=10^5)
100000 loops, best of 3: 1.75 µs per loop
}}}
So, things could be considerably improved. Obvious questions: Will
`from_base` always yield a faster approach than the base injection
morphism? And can we enforce to use the faster coercion?
Aparently it is not so easy:
{{{
sage: AC = Algebras(ZZ).parent_class
sage: R._unset_coercions_used()
sage: AC.__init_extra__(R)
sage: R.convert_map_from(R.base_ring())
Polynomial base injection morphism:
From: Integer Ring
To: Univariate Polynomial Ring in x over Integer Ring
sage: R._unset_coercions_used()
sage: f.register_as_coercion()
sage: R.convert_map_from(R.base_ring())
Polynomial base injection morphism:
From: Integer Ring
To: Univariate Polynomial Ring in x over Integer Ring
}}}
Can you explain how to force the use of a particular map for coercion of
the base ring?
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/9944#comment:19>
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