Opened 9 years ago
Last modified 8 years ago
#9944 closed defect
categories for polynomial rings — at Version 59
Reported by: | robertwb | Owned by: | nthiery |
---|---|---|---|
Priority: | major | Milestone: | sage-4.7.1 |
Component: | categories | Keywords: | |
Cc: | sage-combinat | Merged in: | |
Authors: | Robert Bradshaw, Simon King | Reviewers: | Nicolas M. Thiéry, Mike Hansen, Martin Raum |
Report Upstream: | N/A | Work issues: | |
Branch: | Commit: | ||
Dependencies: | sage-4.7 | Stopgaps: |
Description (last modified by )
Currently, they're always just commutative rings.
Apply:
Change History (67)
Changed 9 years ago by
comment:1 Changed 9 years ago by
- Status changed from new to needs_review
comment:2 Changed 9 years ago by
Changed 9 years ago by
comment:3 Changed 9 years ago by
- Reviewers set to Nicolas M. Thiéry, Mike Hansen
I went ahead and moved the functionality to it's own category since we want the mathematical information at the category level. Could someone look over these changes?
comment:4 follow-up: ↓ 8 Changed 9 years ago by
The first patch only concerned univarite polynomial rings, the logic is not all correct for multivariate polynomial rings (though on an orthogonal note, that could use some fixing up as well). It seems odd to have a category of univariate polynomial rings over a fixed basering, which is why I put the logic into the concrete object. I suppose the category should a be declared as a graded R-algebra as well (do we have join categories yet?).
I don't know if PolynomialRing? asserts its basering is commutative, but IIRC it's been assumed for a long time.
comment:5 Changed 9 years ago by
Apply only 9944-poly-cat.patch
Changed 9 years ago by
comment:6 Changed 9 years ago by
Apply 9944-poly-cat.patch and 9944-poly-cat-doctests.patch .
Changed 9 years ago by
comment:7 Changed 9 years ago by
- Description modified (diff)
I would give this a positive review for Robert's idea and I would open a new ticket for the multivariate rings. I'll just send a mail to Mike whether he is ok with that or no.
comment:8 in reply to: ↑ 4 ; follow-up: ↓ 9 Changed 9 years ago by
Replying to robertwb:
The first patch only concerned univarite polynomial rings, the logic is not all correct for multivariate polynomial rings (though on an orthogonal note, that could use some fixing up as well). It seems odd to have a category of univariate polynomial rings over a fixed basering, which is why I put the logic into the concrete object. I suppose the category should a be declared as a graded R-algebra as well (do we have join categories yet?).
Sorry for the very late answer. In MuPAD, we had a category for univariate polynomial rings: there are several possible implementations of such, and it's natural to factor out the generic code, together with the category inheritance logic, in a category.
And yes, we have join categories. See Category.join.
I let you see whether to create the UnivariatePolynomialRing? category in this ticket or in a later ticket.
comment:9 in reply to: ↑ 8 ; follow-up: ↓ 12 Changed 9 years ago by
Replying to nthiery:
Sorry for the very late answer. In MuPAD, we had a category for univariate polynomial rings: there are several possible implementations of such, and it's natural to factor out the generic code, together with the category inheritance logic, in a category.
Aparently there is a doctest failure. I fixed it, but unfortunately it went into my patch submitted for #9138. Therefore, "needs work".
Question: Do we really want a category of polynomial rings? Or do we want that (1) polynomial rings use the category framework (that's the purpose of my patch for #9138) and (2) the category to which a given polynomial ring belongs is a bit narrower than simply "category of rings"? I hope it is the latter.
My suggestion is that I submit a small patch fixing the doctests. Please tell whether my patch for #9138 improves the multivariate case. Then, perhaps it would be possible to give Roberts patches (+ doctest fix) a positive review, so that we can focus on #9138.
comment:10 Changed 9 years ago by
- Status changed from needs_review to needs_work
- Work issues set to Fix one test
comment:11 Changed 9 years ago by
At #9138, Jason Bandlow reported a slow-down, that is at least partially caused by the patches here. Do you have any idea what could be the reason?
comment:12 in reply to: ↑ 9 Changed 9 years ago by
- Description modified (diff)
Replying to SimonKing:
Aparently there is a doctest failure. I fixed it, but unfortunately it went into my patch submitted for #9138. Therefore, "needs work".
Strange: Although the patch bot did see that error in one run, I can not reproduce it (but I had to change that test in my patch for #9138, because it turns QQ['x'].category()
into the join of the category of euclidean domains and commutative algebras over QQ
.
The other issue, namely the performance loss, was studied on sage-devel.
Florent Hivert found that a long mro does not matter for Python, but it does matter if the classes inherit from a cdef class. That is the case for most classes in Sage (inheriting from SageObject
), so, we should address the problem of a long mro.
Eventually, that should be fixed in Cython (and I think Florent reported it upstream). But for now, it seems to me we should think of a work-around.
Would it be acceptable coding practice to explicitly state in a derived class (say, MPolynomialRing_generic
), that frequently used methods such as base or base_ring are the same as Parent.base
or Parent.base_ring
? David Roe stated that it might be dangerous to do so, at least if cpdef
methods are involved.
comment:13 Changed 9 years ago by
Concerning performance loss:
It seems to me that part of the reason is the fact that with the patchse, __init_extra__
is not executed when it should. Sometimes, the parent methods of a category provide a useful __init_extra__
, for example the category of algebras.
I am not sure yet why that happens, but I think it would happen if Parent.__init__
is called without providing the category: Namely, doing self._init_category_(...)
alone will not trigger the execution of __init_extra__
.
comment:14 Changed 9 years ago by
It seems I was right!
Namely, the whole ring stuff is (unfortunately) inherited from ParentWithGens
, which inherits from ParentWithBase
, which inherits from parent_old.Parent
.
And parent_old.Parent
inherits from "the one and only Parent" -- but forgets to call Parent.__init__
!! Instead, it just does self._init_category_(...)
.
I'll change it and see what happens.
comment:15 Changed 9 years ago by
Very bad things happen. As soon as parent.Parent.__init__
is called in parent_old.Parent.__init__
, an infinite recursion occurs.
comment:16 Changed 9 years ago by
- Description modified (diff)
I attached a small patch to solve part of the problem of the missing parent initialisation: I call Parent.__init__
and ParentWithGens.__init__
explicitly, during initialisation of a ring. In that way, the __init_extra__
methods are correctly picked up.
However, that does not solve the performance problem.
Question one: How can one come to speed?
Question two: Is my patch really trivial enough to be called a referee patch?
For the patchbot:
Apply 9944-poly-cat.patch 9944-poly-cat-doctests.patch trac-9944-poly-cat-review.patch trac9944_second_referee.patch
comment:17 follow-up: ↓ 18 Changed 9 years ago by
- Status changed from needs_work to needs_info
- Work issues Fix one test deleted
FWIW: The doc tests pass.
Here is another idea what the slow down may come from. It was pointed out by Nicolas that the mro from the polynomial ring to Parent
does not become longer by initialising the category properly: The inheritance from category parent classes comes after Python inheritance. However, when all the parent classes of all super categories must be searched, it takes considerably longer before an AttributeError
can be raised.
A similar issue has been studied at #10467. It seems to be important that an attribute error is raised as quickly as possible. That becomes difficult, if 60 parent classes need to be searched, before one eventually finds that the requested attribute does not exist.
But probably that question is out of the scope of this ticket.
So, what shall one do? Give it a positive review and accept the deceleration, or wait until someone has a model for improved attribute access?
comment:18 in reply to: ↑ 17 Changed 9 years ago by
Replying to SimonKing:
A similar issue has been studied at #10467. It seems to be important that an attribute error is raised as quickly as possible. That becomes difficult, if 60 parent classes need to be searched, before one eventually finds that the requested attribute does not exist.
No, that is not the problem here! I was inserting print statements into getattr_from_other_class
in order to find out what attributes are actually requested from the category when doing arithmetic. It turned out that, during the first computation of (2*x-1)^2+5
, some attributes are requested. But when one repeats that computation, getattr_from_other_class
is not involved.
But what else could be the reason?
comment:19 Changed 9 years ago by
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 Âµs per loop sage: timeit('f(100)',number=10^5) 100000 loops, best of 3: 1.75 Âµs 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?
comment:20 Changed 9 years ago by
And aparently the univariate polynomial rings are special in their choice of a conversion from the base ring. Again with #9138
sage: R.<m> = ZZ[] sage: R.convert_map_from(R.base_ring()) Polynomial base injection morphism: From: Integer Ring To: Univariate Polynomial Ring in m over Integer Ring sage: R.<x,y> = QQ['t'][] sage: R.convert_map_from(R.base_ring()) Generic morphism: From: Univariate Polynomial Ring in t over Rational Field To: Multivariate Polynomial Ring in x, y over Univariate Polynomial Ring in t over Rational Field
comment:21 Changed 9 years ago by
- Status changed from needs_info to needs_work
- Work issues set to Speedup
I suggest to speed things up by modifying "Polynomial base injection morphism". Internally, it uses rather slow ways of creating a polynomial of degree zero. It is likely to be faster to do what R.from_base
does: Take the One of the ring (if it exists!) and use its _lmul_
method (if it has _lmul_
).
I also understand why Algebras(...).parent_class.__init_extra__(R)
has no effect on the choice of a conversion map from R.base()
to R
: It calls R.one()
in order to create a better coercion map; but R.one()
will, internally, construct a conversion from the base to R
. At that point, the "better" coercion is not defined, and thus the usual conversion is created and cached.
In other words, R.from_base
will only be used for conversion if R
does not obey the rules of the new coercion framework (e.g., if it has a custom __call__
).
Since the polynomial base injection morphism is a specialised method, it should be possible to internally construct the One of R without invoking coercion. My plan is to combine it with trac9944_second_referee.patch and submit a patch that then certainly needs a reviewer.
comment:22 follow-up: ↓ 25 Changed 9 years ago by
- Description modified (diff)
- Status changed from needs_work to needs_review
Good news! Things are now faster than without the patches!
I found that one can considerably improve the conversion of an element of the base ring into a polynomial ring. Some polynomial rings used a generic conversion map, some used a polynomial base injection map -- and both were slow.
My inspiration came from Algebras.ParentMethods.__init_extra__
: If R is a polynomial ring, then multiplication of a scalar with R.one()
often is a very fast method to convert the scalar into R.
Problems:
- We should not assume that any ring has a unit (ok, polynomial rings over a unital ring have...).
- Calling
R.one()
will usually trigger the creation of a generic conversion - hence, it would be difficult to register it as conversion. - Not all flavours of polynomial elements have a
_rmul_
(polynomial_element_generic has not). - Sometimes, other conversion maps are registered when one wants to register the polynomial base injection map.
So, I implemented _rmul_
and _lmul_
for polynomial_element_generic, try various ways (old and new coercion model) of creating a One bypassing conversion maps, and in one init method of polynomial rings I decided to re-initialise the conversion maps.
Timings
I tried to test as many cases (multi- versus univariate, libSingular
and others, different base rings,...). Without all the patches, we have the following:
sage: R.<x> = ZZ[] sage: timeit('(2*x-1)^2+5', number=10^4) 10000 loops, best of 3: 23.4 µs per loop sage: R.<x> = QQ[] sage: timeit('(2*x-1)^2+5', number=10^4) 10000 loops, best of 3: 24.6 µs per loop sage: R.<x> = GF(3)[] sage: timeit('(2*x-1)^2+5', number=10^4) 10000 loops, best of 3: 87.9 µs per loop sage: R.<x> = QQ['t'][] sage: timeit('(2*x-1)^2+5', number=10^4) 10000 loops, best of 3: 113 µs per loop sage: R.<x,y> = ZZ[] sage: timeit('(2*x-1)^2+5', number=10^4) 10000 loops, best of 3: 13 µs per loop sage: R.<x,y> = QQ[] sage: timeit('(2*x-1)^2+5', number=10^4) 10000 loops, best of 3: 16.6 µs per loop sage: R.<x,y> = GF(3)[] sage: timeit('(2*x-1)^2+5', number=10^4) 10000 loops, best of 3: 10.8 µs per loop sage: R.<x,y> = QQ['t'][] sage: timeit('(2*x-1)^2+5', number=10^4) 10000 loops, best of 3: 238 µs per loop sage: R.<x,y> = Qp(3)[] sage: timeit('(2*x-1)^2+5', number=10^4) 10000 loops, best of 3: 511 µs per loop sage: R.<x> = Qp(3)[] sage: timeit('(2*x-1)^2+5', number=10^4) 10000 loops, best of 3: 1.06 ms per loop
With the patches, I get
sage: R.<x> = ZZ[] sage: timeit('(2*x-1)^2+5', number=10^4) 10000 loops, best of 3: 8.97 µs per loop sage: R.<x> = QQ[] sage: timeit('(2*x-1)^2+5', number=10^4) 10000 loops, best of 3: 8.3 µs per loop sage: R.<x> = GF(3)[] sage: timeit('(2*x-1)^2+5', number=10^4) 10000 loops, best of 3: 70.3 µs per loop sage: R.<x> = QQ['t'][] sage: timeit('(2*x-1)^2+5', number=10^4) 10000 loops, best of 3: 82.6 µs per loop sage: R.<x,y> = ZZ[] sage: timeit('(2*x-1)^2+5', number=10^4) 10000 loops, best of 3: 12.6 µs per loop sage: R.<x,y> = QQ[] sage: timeit('(2*x-1)^2+5', number=10^4) 10000 loops, best of 3: 16.4 µs per loop sage: R.<x,y> = GF(3)[] sage: timeit('(2*x-1)^2+5', number=10^4) 10000 loops, best of 3: 10.5 µs per loop sage: R.<x,y> = QQ['t'][] sage: timeit('(2*x-1)^2+5', number=10^4) 10000 loops, best of 3: 187 µs per loop sage: R.<x,y> = Qp(3)[] sage: timeit('(2*x-1)^2+5', number=10^4) 10000 loops, best of 3: 503 µs per loop sage: R.<x> = Qp(3)[] sage: timeit('(2*x-1)^2+5', number=10^4) 10000 loops, best of 3: 1.08 ms per loop
So, there is no significant slow down at all, but a considerable speed up in most cases.
I suppose it can now be reviewed. I understood that the Robert's patches essentially have a positive review, except for the slow-down. So, would it suffice if some of you test my patch?
Apply 9944-poly-cat.patch 9944-poly-cat-doctests.patch trac-9944-poly-cat-review.patch trac9944_polynomial_speedup.patch
comment:23 Changed 9 years ago by
Wow, that is an amazingly good result! I will take my time to review this by next week. But if anybody is faster than me, feel free to go for it!
comment:24 Changed 9 years ago by
- Cc sage-combinat added
- Work issues Speedup deleted
That's excellent indeed! Thanks!
Simon: I guess I'll focus on the reviewing of the other patches.
Nicolas
comment:25 in reply to: ↑ 22 Changed 9 years ago by
Replying to SimonKing:
Problems:
- We should not assume that any ring has a unit (ok, polynomial rings over a unital ring have...).
Rings() assumes its objects to be unital. If we want to support polynomials over non unital rings, then this should go through the use of Rngs(). If we make sure the coercion morphism from the base ring is always declared by Algebras(), all we will have to do is to use some new category NonUnitalAlgebras?() when the base ring is just in Rngs(). Bwt: having a PolynomialRings?() (PolynomialRngs??) category would be a good way to factor out this logic.
But one thing at a time :-)
Cheers,
Nicolas
Changed 9 years ago by
comment:26 Changed 9 years ago by
- Description modified (diff)
I applied the second patch and exported the commit, so that Jeroen will have an easier life (http://groups.google.com/group/sage-devel/browse_thread/thread/f5a9c012f6299a9e).
The patchs are very good. I am waiting for the tests to finish, but I guess this will be through very soon.
comment:27 Changed 9 years ago by
- Reviewers changed from Nicolas M. Thiéry, Mike Hansen to Nicolas M. Thiéry, Mike Hansen, Martin Raum
- Status changed from needs_review to positive_review
The speed up is significant and all tests pass. This gets a positive review.
Let me point out the following (that won't show up in many use case, but still might deserve some consideration later):
unpatched:
sage: R = PolynomialRing(ZZ, ['a' + str(n) for n in range(10000)]) sage: x = R.gen(0) sage: timeit('(2*x - 1)^2 + 5', number = 10^4) 10000 loops, best of 3: 94.5 µs per loop
patched:
sage: R = PolynomialRing(ZZ, ['a' + str(n) for n in range(10000)]) sage: x = R.gen(0) sage: timeit('(2*x - 1)^2 + 5', number = 10^4) 10000 loops, best of 3: 131 µs per loop
comment:28 Changed 9 years ago by
- Status changed from positive_review to needs_work
The PDF documentation doesn't build:
! Missing { inserted. <to be read again> $ l.358009 ...ment with the One by means of $_rmul_$ . ? ! Emergency stop. <to be read again> $ l.358009 ...ment with the One by means of $_rmul_$ . ! ==> Fatal error occurred, no output PDF file produced! Transcript written on reference.log. make[1]: *** [reference.pdf] Error 1
comment:29 Changed 9 years ago by
- Status changed from needs_work to positive_review
It should now be fine. The problem was single back tick (Latex math mode) versus double back tick (verbose code).
comment:30 Changed 9 years ago by
- Status changed from positive_review to needs_work
Sorry, I changed but one instance of single back tick versus double back tick. But there are more left. So, needs work, for now.
comment:31 Changed 9 years ago by
- Status changed from needs_work to positive_review
Now it seems solved. sage -docbuild all html
did not complain!
Apply 9944-poly-cat.patch 9944-poly-cat-doctests.patch trac-9944-poly-cat-review.patch trac9944_polynomial_speedup.patch
comment:32 Changed 9 years ago by
- Milestone changed from sage-4.7 to sage-4.7.1
comment:33 Changed 9 years ago by
- Merged in set to sage-4.7.1.alpha0
- Resolution set to fixed
- Status changed from positive_review to closed
comment:34 follow-up: ↓ 35 Changed 9 years ago by
- Merged in sage-4.7.1.alpha0 deleted
- Resolution fixed deleted
- Status changed from closed to new
- Work issues set to fix on 32-bit
For some obscure reason, this breaks the following test on 32-bit systems:
sage -t "devel/sage-main/sage/modular/abvar/morphism.py"
The problem is that the following command hangs forever:
sage: J = J1(12345) sage: J.hecke_operator(997)
Interestingly, interrupting at this point makes the command return the correct output without raising a KeyboardInterrupt
which is a bug within the bug.
comment:35 in reply to: ↑ 34 Changed 9 years ago by
Replying to jdemeyer:
For some obscure reason, this breaks the following test on 32-bit systems: The problem is that the following command hangs forever:
sage: J = J1(12345) sage: J.hecke_operator(997)
Interesting. If I remember correctly, I had problems with that exact doctest on my machine and was able to solve it. But my machine is 64 bit.
So, I'll try with a 32 bit installation on bsd.math.
comment:36 follow-up: ↓ 38 Changed 9 years ago by
I get a different error on bsd.math in 32bit mode:
sage: J = J1(12345) sage: J.hecke_operator(997) python(6506) malloc: *** mmap(size=1870024854642688) failed (error code=12) *** error: can't allocate region *** set a breakpoint in malloc_error_break to debug python(6506) malloc: *** mmap(size=1870024854642688) failed (error code=12) *** error: can't allocate region *** set a breakpoint in malloc_error_break to debug Hecke operator T_997 on Abelian variety J1(12345) of dimension 5405473
So, it reports problem with memory allocation, but in almost no time it still returns the correct answer!
comment:37 Changed 9 years ago by
I think I remember what turned out to be the problem: In J.hecke_operator(...)
, some matrix space is created - a very big one (kind of 5405473x5405473). And if I am not mistaken, the changes in the patch make the matrix space create a zero and a unit matrix - perhaps too much for 32 bit.
But perhaps I am mistaken. After all, the memory consumption is not big at all when I do the computation on my computer.
comment:38 in reply to: ↑ 36 Changed 9 years ago by
Replying to SimonKing:
So, it reports problem with memory allocation, but in almost no time it still returns the correct answer!
The fact that errors (including interrupts) are ignored in this code is very bad in itself, I think there must be some except:
catching all this.
comment:39 Changed 9 years ago by
Using trace
, it seems to me that the error occurs in line 245 of sage/matrix/matrix_space.py
:
if nrows >= 2**63 or ncols >= 2**63:
Is computing 2**63
(with Python ints) a problem on 32 bit?? Apparently not:
sage: int(2)**int(63) 9223372036854775808L
So, the problem isn't solved, yet.
comment:40 Changed 9 years ago by
Sorry, I had misinterpreted something.
comment:41 Changed 9 years ago by
But there is something else:
sage: sage.misc.misc.is_64_bit True sage: os.environ['SAGE64'] 'no'
Could that be the problem?
comment:42 Changed 9 years ago by
It seems that trace does not show the whole story. I see that some memory errors are raise (when it is attempted to create huge zero or unit matrices), but I don't see where they are caught. So, there seems Cython code involved that is invisible to trace.
comment:43 Changed 9 years ago by
I think I found it!
The problem occurs during initialisation of sage.modular.abvar.homspace.EndomorphismSubring
. It is first initialised as a homset with a specific category cat
that does not belong to the category of rings, and then as a ring. The second initialisation tries to put it into the category of rings, which seems to be a bad idea after the first initialisation.
Solution:
Form the join of cat
with the category of rings. Initialise it as a ring with that join category (which became possible with #9944!). Eventually, initialise it as a homspace, with the same category.
With that little magic, the error seems to disappear. But now I need to do tests.
Cheers,
Simon
Changed 9 years ago by
Fix a problem with initialisation of endomorphism rings of abelian varieties on 32 bit
comment:44 Changed 9 years ago by
- Description modified (diff)
- Status changed from new to needs_review
- Work issues fix on 32-bit deleted
The problem seems solved.
What I did: Initialise the endomorphism ring first as a ring, and provide it with the intended category. Then initialise it as a homset as well. That solves the problem in the sense that it disappears.
Admittedly I can not explain how exactly the problem has originally emerged. But I guess it makes sense that it is a problem if a homset gives itself a certain category and then sage.rings.ring.Ring tries to work with another category.
With the new patch, we have (also as an additional doc test)
sage: J = J1(12345) sage: J.endomorphism_ring() Endomorphism ring of Abelian variety J1(12345) of dimension 5405473
both on my machine (x86_64 Linux) and on bsd.math in a 32 bit installation. Moreover, on both machines, the tests in sage.modular pass.
Needs review, I guess.
Apply 9944-poly-cat.patch 9944-poly-cat-doctests.patch trac-9944-poly-cat-review.patch trac9944_polynomial_speedup.patch trac9944_abvar_endomorphism.patch
comment:45 Changed 9 years ago by
FWIW: The long doctests pass on bsd.math in 32bit installation.
comment:46 Changed 9 years ago by
The patch at #11310 solves the "exceptions are ignored" problem.
comment:47 follow-up: ↓ 48 Changed 9 years ago by
- Status changed from needs_review to needs_work
There is a huge performance regression in creating iterated polynomial rings:
BEFORE:
sage: S = GF(9,'a') sage: %time for n in range(11): S = PolynomialRing(S,'w') CPU times: user 0.00 s, sys: 0.00 s, total: 0.00 s Wall time: 0.00 s
AFTER:
sage: S = GF(9,'a') sage: %time for n in range(11): S = PolynomialRing(S,'w') CPU times: user 53.38 s, sys: 0.19 s, total: 53.57 s Wall time: 53.58 s
comment:48 in reply to: ↑ 47 Changed 9 years ago by
Replying to jdemeyer:
There is a huge performance regression in creating iterated polynomial rings: ... sage: %time for n in range(11): S = PolynomialRing?(S,'w')
Note that the whole point of this ticket is to do more things during initialisation of polynomial rings. So, no surprise that initialisation becomes a lot slower. However, I agree that it should not be that slow.
comment:49 Changed 9 years ago by
Strange. With the patches, I get
sage: S = GF(9,'a') sage: %time for n in range(5): S = PolynomialRing(S,'w') CPU times: user 0.00 s, sys: 0.00 s, total: 0.00 s Wall time: 0.00 s
So, that's quick. Continuing:
sage: %time S = PolynomialRing(S,'w') CPU times: user 0.00 s, sys: 0.00 s, total: 0.00 s Wall time: 0.00 s sage: %time S = PolynomialRing(S,'w') CPU times: user 0.00 s, sys: 0.00 s, total: 0.00 s Wall time: 0.00 s sage: %time S = PolynomialRing(S,'w') CPU times: user 0.00 s, sys: 0.00 s, total: 0.00 s Wall time: 0.00 s sage: %time S = PolynomialRing(S,'w') CPU times: user 0.00 s, sys: 0.00 s, total: 0.00 s Wall time: 0.00 s sage: %time S = PolynomialRing(S,'w') CPU times: user 8.38 s, sys: 0.00 s, total: 8.38 s Wall time: 8.38 s
So, suddenly there is a jump in the initialisation time.
comment:50 Changed 9 years ago by
Sorry, my fault. I did not restart before doing the test above, so, rings were found in the cache.
After restart with all patches, I get
sage: S = GF(9,'a') sage: %time S = PolynomialRing(S,'w') CPU times: user 0.00 s, sys: 0.00 s, total: 0.00 s Wall time: 0.01 s sage: %time S = PolynomialRing(S,'w') CPU times: user 0.00 s, sys: 0.00 s, total: 0.00 s Wall time: 0.01 s sage: %time S = PolynomialRing(S,'w') CPU times: user 0.00 s, sys: 0.00 s, total: 0.00 s Wall time: 0.01 s sage: %time S = PolynomialRing(S,'w') CPU times: user 0.01 s, sys: 0.00 s, total: 0.01 s Wall time: 0.01 s sage: %time S = PolynomialRing(S,'w') CPU times: user 0.02 s, sys: 0.00 s, total: 0.02 s Wall time: 0.03 s sage: %time S = PolynomialRing(S,'w') CPU times: user 0.09 s, sys: 0.00 s, total: 0.09 s Wall time: 0.10 s sage: %time S = PolynomialRing(S,'w') CPU times: user 0.22 s, sys: 0.00 s, total: 0.22 s Wall time: 0.22 s sage: %time S = PolynomialRing(S,'w') CPU times: user 0.70 s, sys: 0.00 s, total: 0.70 s Wall time: 0.70 s sage: %time S = PolynomialRing(S,'w') CPU times: user 2.58 s, sys: 0.00 s, total: 2.58 s Wall time: 2.58 s
I found that the problem comes up with trac9944-polynomial_speedup.patch. So, let's work on it.
comment:51 Changed 9 years ago by
Using prun, I found for one case:
Ordered by: internal time ncalls tottime percall cumtime percall filename:lineno(function) 1 0.141 0.141 0.238 0.238 polynomial_ring.py:178(__init__) 1414 0.055 0.000 0.071 0.000 polynomial_ring.py:234(_element_constructor_) 11104 0.020 0.000 0.020 0.000 polynomial_ring.py:1821(modulus) 1420 0.005 0.000 0.005 0.000 finite_field_givaro.py:153(degree) ...
In other words: In order to construct just one polynomial ring over an iterated polynomial ring, the element constructor is called 1414 times and the modulus method 11104 times. At a different ticket, I suggested to turn the modulus method into a cached method. Perhaps that should already be done here. However, there should be no need to construct 1414 elements, just to initialise one ring!
comment:52 Changed 9 years ago by
Interesting. Now it seems to me that the element constructor is in fact called from the _repr_
method of sage.rings.polynomial.polynomial_element.Polynomial_generic_dense
. That sound like using the string representation of elements in order to convert something.
comment:53 Changed 9 years ago by
I think I somehow located the problem. I created recursively a univariate polynomial ring, as in your example, with a total of 8 variables:
sage: S Univariate Polynomial Ring in w over Univariate Polynomial Ring in w over Univariate Polynomial Ring in w over Univariate Polynomial Ring in w over Univariate Polynomial Ring in w over Univariate Polynomial Ring in w over Univariate Polynomial Ring in w over Univariate Polynomial Ring in w over Finite Field in a of size 3^2
Then, with the patches
sage: timeit("S(0)") 5 loops, best of 3: 83 ms per loop
but without the patches
sage: timeit("S(0)") 625 loops, best of 3: 121 µs per loop
Since the above relies on coercion maps, which are compositions of polynomial base injection maps, and since my patch touched the polynomial base injection maps, it is conceivable that we'll find the problem there.
Note, however, that it might be a better solution to let the composition of two polynomial base injection maps be another polynomial base injection map -- that ought to be a lot faster than a composite map.
comment:54 Changed 9 years ago by
The original implementation of a polynomial basering injection relies on a method _new_constant_poly
, which turns out to be rather slow in most cases except the case of dense univariate polynomials -- they have a custom version of _new_constant_poly
, while the others rely on a generic implementation.
So, instead of my former suggestion ("use one._rmul_(x)
to coerce x into P with one = P.one_element()
), it may be better to provide the other polynomial classes with a faster implementation of _new_constant_poly
. That's what I am trying now.
comment:55 Changed 9 years ago by
Or, even better: Implement _new_constant_poly
not (only) for the elements of a polynomial ring, but for the ring itself - that should be more natural, provided that there is only one possible polynomial class.
comment:56 follow-ups: ↓ 57 ↓ 58 Changed 9 years ago by
I am totally frustrated.
I made some improvements to _new_constant_poly
, whose purpose is to provide the quickest way in the given implementation to construct a constant polynomial, and made some other changes that should improve the coercions. There were improvements in all examples above.
However, I am now getting tons of failures and even segfaults in sage/schemes.
I tracked one type of error down, I thought. But apparently I only covered one special case of that one type of error.
While I was at it, I fixed the documentation for hyperelliptic_padic_field
, which is not yet included into the manual, and which had syntax errors in all doc strings.
comment:57 in reply to: ↑ 56 Changed 9 years ago by
Replying to SimonKing:
While I was at it, I fixed the documentation for
hyperelliptic_padic_field
, which is not yet included into the manual, and which had syntax errors in all doc strings.
Or perhaps the inclusion of sage/schemes into the manual should be on a different ticket, since most files are missing.
comment:58 in reply to: ↑ 56 Changed 9 years ago by
Replying to SimonKing:
I am totally frustrated.
Still the case, although I am already down to 251 doctest failures and one timeout. That's the disadvantage of doing changes in coercion.
comment:59 Changed 9 years ago by
- Dependencies set to sage-4.7
- Description modified (diff)
- Status changed from needs_work to needs_review
Finally I got my new patch to work. Here are the new features and, in particular, the new timings. I think it was worth the effort!
Polynomial Construction Functors
sage: R.<x> = PolynomialRing(GF(5), sparse=True) sage: F,B = R.construction() sage: F(B) is R True # was False
zero_element
In various places, constructions such as self.parent()(0) are used. It should be more efficient to have self.parent().zero_element() instead, in particular if this is cached using the improved cached methods from #11115.
That means I had to introduce zero_element() for various classes, mostly in sage/modular.
Fix zero element of free module homomorphisms
The following used to fail with an error:
sage: V = span([[1/2,1,1],[3/2,2,1],[0,0,1]],ZZ) sage: V.Hom(V).zero() Free module morphism defined by the matrix [0 0 0] [0 0 0] [0 0 0] Domain: Free module of degree 3 and rank 3 over Integer Ring Echelon ... Codomain: Free module of degree 3 and rank 3 over Integer Ring Echelon ...
Calling any parent with None should return zero
This used to be true for finite prime fields, but failed with an error for finite non-prime fields:
sage: GF(5)(None) 0 sage: GF(5^2,'a')(None) 0
Implement/improve _new_constant_poly
for various polynomial classes
This is the main reason why the timings stated below have improved. I thought that _new_constant_poly
should be a method of a polynomial ring, but I think it should better stay as a method of polynomials: Polynomials are often implemented in Cython, but polynomial rings in Python.
In order to get a little bit of more speed, I introduce another parameter to _new_constant_poly
, namely the parent in which the new polynomial is supposed to be created. This is because often the parent P
of a polynomial self
is already known when calling self._new_constant_poly(a, P)
, so that it would be a waste of time to call self.parent()
internally to determine the parent.
Improve Polynomial Base Injection Morphisms and use it for coercion
Conversion into a polynomial ring P from its base ring occurs frequently and should be as quick as possible.
I had already improved the performance in the old patch version. However, it turned out to be better to use _new_constant_poly
, rather than always using multiplication with P.one()
.
The rule is now: If P.an_element()
has a _new_constant_poly
method then it is used. Otherwise, if one can construct a one element in P
without calling coercion, and if it has _rmul_
and if _rmul_
does not return None
then it is used. Otherwise, P._element_constructor_
is used.
Polynomial base injection morphisms are now always registered as coercion.
Call method for compiled polynomials
The documentation for compiled polynomials states that it can be called, although the cdef method .eval(...)
has less overhead. That was not true, there has been no __call__
method. I added one.
Constant polynomial section
It was stated that it uses the constant_coefficient
method, which can be optimized for a particulare polynomial type. However, in fact a generic constant_coefficient
method was explicitly called, even if a polynomial type did provide a more efficient method. That has now changed.
Sparse versus dense versus differently implemented polynomial rings
A univariate polynomial ring can be sparse or dense, and if it is dense and over ZZ
(or also QQ
) they can be implemented with FLINT
or NTL
. Dense and sparse rings used to be equal, but they were not identical - a violation to the unique parent assumption.
Moreover, in the multivariate case, the implementation
and sparse
arguments had no effect on the resulting ring, but were used in the cache key, yielding another violation of the unique parent assumption.
I resolved these violations. I was not sure whether one should silently ignore arguments that are not used, or should raise an error if they are provided. I decided to ignore sparse
if it is not supported, and raise an error for dense or multivariate rings if an implementation is not supported.
We have, e.g.:
sage: S.<x,y> = PolynomialRing(ZZ,sparse=True) sage: S is ZZ['x','y'] True # used to be False sage: R.<x> = PolynomialRing(ZZ,sparse=True,implementation='FLINT') sage: S.<x> = PolynomialRing(ZZ,sparse=True,implementation='NTL') sage: R is S True # used to be False sage: R == ZZ['x'] False # used to be True sage: S.<x,y> = PolynomialRing(ZZ, implementation='NTL') Traceback (most recent call last): ... ValueError: The NTL implementation is not known for multivariate polynomial rings
The last example used to return a ring that was equal but not identic to ZZ['x','y']
!
Polynomial rings are now equal if and only if they are identical. Coercions exist from the non-default to the default version of a ring (hence, from sparse to dense, from NTL to FLINT.
sage: R.<x> = PolynomialRing(ZZ) sage: S.<x> = PolynomialRing(ZZ, implementation='NTL') sage: R == S False sage: R.has_coerce_map_from(S) True sage: S.has_coerce_map_from(R) False sage: S.<x> = PolynomialRing(ZZ, sparse=True) sage: R == S False sage: R.has_coerce_map_from(S) True sage: S.has_coerce_map_from(R) False
By consequence, the parent of a sum of polynomials is now unique - it used to depend on the summation order if dense and sparse summands were involved.
Documentation and examples
I think all changes are covered by doctests. Occasionally I fixed wrongly formatted docstrings.
Performance
Here are the new timings for the examples that we had discussed above. I use sage-4.7.alpha5 with the patches from this ticket applied, and I compare with timings that I had obtained with an unpatched version of sage-4.7.alpha5
There is no significant change in the startup time: I got 1.253
for sage.all in unpatched sage, but the margin of error seems rather wide.
$ sage -startuptime ... == Slowest (including children) == 1.100 sage.all (None) 0.279 sage.schemes.all (sage.all) 0.178 twisted.persisted.styles (sage.all) 0.164 elliptic_curves.all (sage.schemes.all) 0.162 ell_rational_field (elliptic_curves.all) 0.150 ell_number_field (ell_rational_field) ...
Here is the example brought up by Jeroen. There is now a drastic speedup were previously was a drastic slow down:
sage: S = GF(9,'a') sage: %time for n in range(8): S = PolynomialRing(S,'w') CPU times: user 0.03 s, sys: 0.00 s, total: 0.03 s Wall time: 0.03 s # unpatched: 0.04 s sage: len(S.variable_names_recursive()) 8 sage: timeit("S(0)") 625 loops, best of 3: 27.9 µs per loop # with only the other patches: 83 ms # unpatched: 121 µs
Here is the example brought up by Martin Raum:
sage: R = PolynomialRing(ZZ, ['a' + str(n) for n in range(10000)]) sage: x = R.gen(0) sage: timeit('(2*x - 1)^2 + 5', number = 10^4) 10000 loops, best of 3: 58.2 µs per loop # unpatched: 66.9 µs
Here are the arithmetic examples that I had provided earlier:
sage: R.<x> = ZZ[] sage: timeit('(2*x-1)^2+5', number=10^4) 10000 loops, best of 3: 8.58 µs per loop # unpatched: 23.6 µs sage: R.<x> = QQ[] sage: timeit('(2*x-1)^2+5', number=10^4) 10000 loops, best of 3: 8.4 µs per loop # unpatched: 25.8 µs sage: R.<x> = GF(3)[] # sage.rings.polynomial.polynomial_zmod_flint.Polynomial_zmod_flint sage: timeit('(2*x-1)^2+5', number=10^4) 10000 loops, best of 3: 66.4 µs per loop # unpatched: 90.1 µs sage: R.<x> = QQ['t'][] sage: timeit('(2*x-1)^2+5', number=10^4) 10000 loops, best of 3: 75.4 µs per loop # unpatched: 117 µs sage: R.<x,y> = ZZ[] # sage.rings.polynomial.multi_polynomial_libsingular.MPolynomial_libsingular sage: timeit('(2*x-1)^2+5', number=10^4) 10000 loops, best of 3: 7.85 µs per loop # unpatched: 13.6 µs sage: R.<x,y> = QQ[] sage: timeit('(2*x-1)^2+5', number=10^4) 10000 loops, best of 3: 7.33 µs per loop # unpatched: 16.9 µs sage: R.<x,y> = GF(3)[] sage: timeit('(2*x-1)^2+5', number=10^4) 10000 loops, best of 3: 6.59 µs per loop # unpatched: 11.2 µs sage: R.<x,y> = QQ['t'][] sage: timeit('(2*x-1)^2+5', number=10^4) 10000 loops, best of 3: 158 µs per loop # unpatched: 251 µs sage: R.<x,y> = Qp(3)[] sage: timeit('(2*x-1)^2+5', number=10^4) 10000 loops, best of 3: 488 µs per loop # unpatched: 521 µs sage: R.<x> = Qp(3)[] sage: timeit('(2*x-1)^2+5', number=10^4) 10000 loops, best of 3: 894 µs per loop # unpatched: 1.06 ms sage: R.<x> = PolynomialRing(GF(9,'a'), sparse=True) sage: timeit('(2*x-1)^2+5', number=10^4) 10000 loops, best of 3: 236 µs per loop # unpatched: 265 µs
So, in all examples there is a noticeable speedup.
Conclusion
The new patch cleans coercion of polynomial rings, by enforcing uniqueness of parents.
It considerably improves the performance, even when comparing with the improvements that were introduced in the previous patches.
sage -testall -long
passed. So, it is finally ready for review again.
Depends on sage-4.7
Apply Apply 9944-poly-cat.patch 9944-poly-cat-doctests.patch trac-9944-poly-cat-review.patch trac9944_polynomial_speedup.patch trac9944_abvar_endomorphism.patch trac9944_faster_and_cleaner_coercion.patch
I have been through the patch, and it sounds good! I won't have the time to actually test it before some time, so please anyone beat me to it!
Just one micro question: does PolynomialRing? actually check that the ring is commutative?
Cheers