Opened 10 years ago
Last modified 7 years ago
#8327 closed enhancement
Implement the universal cyclotomic field, using Zumbroich basis — at Version 105
Reported by: | nthiery | Owned by: | |
---|---|---|---|
Priority: | major | Milestone: | sage-5.7 |
Component: | number fields | Keywords: | Cyclotomic field, Zumbroich basis |
Cc: | sage-combinat, cwitty | Merged in: | |
Authors: | Christian Stump, Simon King | Reviewers: | |
Report Upstream: | N/A | Work issues: | |
Branch: | Commit: | ||
Dependencies: | #4539, #10771, #7980, #9651, #13727, #13728 | Stopgaps: |
Description (last modified by )
This patch provides the universal cyclotomic field
sage: UCF Universal Cyclotomic Field endowed with the Zumbroich basis
in sage. This field is the smallest field extension of QQ which contains all roots of unity.
sage: E(3); E(3)^3 E(3) 1 sage: E(6); E(6)^2; E(6)^3; E(6)^6 -E(3)^2 E(3) -1 1
It comes equipped with a distinguished basis, called the Zumbroich basis, which gives, for any n, A basis of QQ( E(n) ) over QQ, where (n,k) stands for E(n)^{k. }
sage: UCF.zumbroich_basis(6) [(6, 2), (6, 4)]
As seen for E(6), every element in UCF is expressed in terms of the smallest cyclotomic field in which it is contained.
sage: E(6)*E(4) -E(12)^11
It provides arithmetics on UCF as addition, multiplication, and inverses:
sage: E(3)+E(4) E(12)^4 - E(12)^7 - E(12)^11 sage: E(3)*E(4) E(12)^7 sage: (E(3)+E(4)).inverse() E(12)^4 + E(12)^8 + E(12)^11 sage: (E(3)+E(4))*(E(3)+E(4)).inverse() 1
And also things like Galois conjugates.
sage: (E(3)+E(4)).galois_conjugates() [E(12)^4 - E(12)^7 - E(12)^11, -E(12)^7 + E(12)^8 - E(12)^11, E(12)^4 + E(12)^7 + E(12)^11, E(12)^7 + E(12)^8 + E(12)^11]
The ticket does not use the gap interface.
Change History (105)
comment:1 Changed 10 years ago by
- Cc sage-combinat added
comment:2 follow-up: ↓ 3 Changed 10 years ago by
comment:3 in reply to: ↑ 2 ; follow-up: ↓ 4 Changed 10 years ago by
Replying to craigcitro:
So this seems interesting (I'd never heard of the Zumbrioch basis before). I don't have anything useful to say about the utility of this, or implementing it.
However, I'd like to suggest we might want to use a different convention for the constructor -- I don't like the idea of
CyclotomicField()
working. That seems like something that's too easy for a user to accidentally do (leave out then
they intended to use), and I'd much rather they see an error than have it quietly succeed, only to discover that their cyclotomic field isn't quite what they expected (and likely slower to boot). Maybe something likeF = CyclotomicField(n=Infinity)
?
I indeed take any better suggestion! In Gap that would be Cyclotomics, but it does sound good in Field in the name. n=infinity might be misleading, since it's not about infinite roots of unity.
comment:4 in reply to: ↑ 3 ; follow-up: ↓ 5 Changed 10 years ago by
Replying to nthiery:
I indeed take any better suggestion! In Gap that would be Cyclotomics, but it does sound good in Field in the name. n=infinity might be misleading, since it's not about infinite roots of unity.
True. Maybe it's a bit too "cutesy," but using n=0
might be nice -- after all, the n
th cyclotomic field has roots of unity for all divisors of n
, so this would still hold for the universal cyclotomic field and n=0
.
comment:5 in reply to: ↑ 4 Changed 10 years ago by
Replying to craigcitro:
True. Maybe it's a bit too "cutesy," but using
n=0
might be nice -- after all, then
th cyclotomic field has roots of unity for all divisors ofn
, so this would still hold for the universal cyclotomic field andn=0
.
Mmm, any complex number is a 0-th root of unity, isn't it?
comment:6 Changed 10 years ago by
- Status changed from new to needs_work
Does anyone have a pdf copy of Zumbroich's thesis where the algorithms are described?
There is a nice version of a modified Zumbroich basis in the article I used (both are implemented in the attached file) but I don't see how the author expresses any root of unity in terms of the basis (probably just due to my lack of knowledge). But Zumbroich should describe it in more detail in his thesis.
comment:7 Changed 10 years ago by
The attached class NewCyclotomicField? uses the modified Zumbroich basis and behaves already somehow as it should (beside pretty printing).
If people think the Zumbroich basis itself is nicer, it's easy to change. I personally think the modified version as defined in Breuer - "Integral bases for subfields of cyclotomic fields" AAECC8, 279--289 (1997) has nicer properties (see the definition of the set S_n and Remark 1).
Here are some implementation problems I have:
- how can I replace CombinatorialAlgebra? by a new field constructor (I haven't found a description how to define a field)?
- how can I embed a CombinatorialAlgebra? into another one (here: NewCyclotomicField?(m) into NewCyclotomicField?(n) for m | n)?
- how can I define a new class UniversalCyclotomicField? containing all cyclotomic fields?
- how can I define the attribute self._one in the constructor of NewCyclotomicField? properly?
comment:8 Changed 10 years ago by
- Cc cwitty added
comment:9 Changed 10 years ago by
- Status changed from needs_work to needs_review
comment:10 Changed 10 years ago by
comment:11 Changed 9 years ago by
- Description modified (diff)
comment:12 Changed 9 years ago by
- Milestone set to sage-feature
- Status changed from needs_review to needs_work
Apply trac_8327_universal_cyclotomic_field-cs.2.patch
(for patchbot -- I hope that's right!).
This doesn't quite look ready to me. I haven't tried applying the patch, but just on a visual check, I can see that lots of methods aren't documented or have no tests (*every* function added to Sage must be doctested, even those whose entire body is "raise NotImplementedError"
). Also, the new module should be added to the reference manual, and the formatting should be valid ReST markup.
I very much hope you can get this code into shape -- it'd be a great thing to have in Sage -- but for now I'm afraid it's a thumbs down.
comment:13 follow-up: ↓ 14 Changed 9 years ago by
- Work issues set to Won't build, needs more doctests and Sphinxified docstrings
I've looked at the patchbot logs, and it gets worse -- the Cython code isn't valid apparently.
comment:14 in reply to: ↑ 13 Changed 9 years ago by
Replying to davidloeffler:
I've looked at the patchbot logs, and it gets worse -- the Cython code isn't valid apparently.
This was only as cython booleans changed in the meantime. Beside that, the code was always working properly. I changed this minor problem, and it should be working now again.
I improved the documentation but there are still some things to be done...
comment:15 Changed 9 years ago by
- Status changed from needs_work to needs_review
For the buildbot:
Apply trac_8327_universal_cyclotomic_field-cs.patch
All other files are obsolete, but I cannot delete them. Some documentation is still missing, but only for methods which are helper functions for others.
Would be nice to get some feedback!
comment:16 Changed 9 years ago by
Can some delete all but the youngest attached patch, the buildbot gets confused.
Thanks, Christian
comment:17 Changed 9 years ago by
- Description modified (diff)
comment:18 Changed 9 years ago by
Apply trac_8327_universal_cyclotomic_field-cs.patch
comment:19 Changed 9 years ago by
Apply only trac_8327_universal_cyclotomic_field-cs.patch
comment:20 Changed 9 years ago by
- Work issues changed from Won't build, needs more doctests and Sphinxified docstrings to needs more doctests and Sphinxified docstrings
Apply only trac_8327_universal_cyclotomic_field-cs.patch
comment:21 Changed 9 years ago by
Apply only trac_8327_universal_cyclotomic_field-cs.patch
comment:22 Changed 9 years ago by
Apply trac_8327_universal_cyclotomic_field-cs.patch
comment:23 Changed 9 years ago by
- Dependencies set to #10963
- Owner changed from davidloeffler to (none)
comment:24 Changed 9 years ago by
- Milestone changed from sage-feature to sage-4.7.2
comment:25 Changed 8 years ago by
- Dependencies #10963 deleted
comment:26 follow-up: ↓ 27 Changed 8 years ago by
- Status changed from needs_review to needs_work
When applying the sage-combinat queue on sage 4.8.alpha0, we got a compilation error on universal_cyclotomic_field_c.pyx, most likely due to the updated cython (#11761)
comment:27 in reply to: ↑ 26 Changed 8 years ago by
- Status changed from needs_work to needs_review
Replying to nthiery:
When applying the sage-combinat queue on sage 4.8.alpha0, we got a compilation error on universal_cyclotomic_field_c.pyx, most likely due to the updated cython (#11761)
My patch seems to fix the problem. At least, when one uses the new Cython spkg and applies the combinat queue up to and including Christian's patch and adds my patch as well (which is also in the combinat queue, I think), then sage builds and starts.
Note that the my patch does not add the new Cython as a dependency - it should run with the old Cython as well.
However, I already get a doctest error in devel/sage-combinat/doc/en/thematic_tutorials/sandpile.rst
. Now it is needed to test whether this error is due to the patches from here, or due to some other patch in the combinat queue.
Since it is not sure whether THIS ticket is the culprit, and since it builds with the new cython, I am promiting it to "needs review".
Apply trac_8327_universal_cyclotomic_field-cs.patch trac_8327_universal_cyclotomic_field_new_cython-sk.patch
comment:28 Changed 8 years ago by
- Description modified (diff)
Sorry, I forgot to change the ticket description.
comment:29 Changed 8 years ago by
- Status changed from needs_review to needs_work
- Work issues changed from needs more doctests and Sphinxified docstrings to needs more doctests and Sphinxified docstrings, rebase first patch
Note that the first patch does not apply on a clean sage-4.8.alpha0: The hunk that adds from sage.misc.lazy_import import lazy_import
to sage/categories/all.py does not match.
But is importing lazy_import really needed? If I see that correctly, it is not used in sage/categories/all.py
comment:30 follow-up: ↓ 31 Changed 8 years ago by
- Work issues changed from needs more doctests and Sphinxified docstrings, rebase first patch to Find dependency. Needs more doctests and Sphinxified docstrings.
Gosh. And my patch fails to apply as well, in both hunks.
So, apparently there is a dependency in the combinat queue. It should be named as a dependency for this ticket.
comment:31 in reply to: ↑ 30 Changed 8 years ago by
- Work issues changed from Find dependency. Needs more doctests and Sphinxified docstrings. to Find dependency or rebase first patch. Needs more doctests and Sphinxified docstrings.
Replying to SimonKing:
Gosh. And my patch fails to apply as well, in both hunks.
O dear, where is my mind? I had accidentally reverted the order of the patches when I tried to apply my patch.
So, for the record: The first patch does need to be rebased (or a dependency must be given). The second patch applies cleanly.
comment:32 Changed 8 years ago by
- Work issues changed from Find dependency or rebase first patch. Needs more doctests and Sphinxified docstrings. to Find dependency or rebase first patch. Fix doctests. Needs more doctests and Sphinxified docstrings.
There are several doctest errors, even when one just has
11761-cython-0.15-rebased.patch trac12029_clonable_int_array_2_list.patch trac_8327_universal_cyclotomic_field-cs.patch trac_8327_universal_cyclotomic_field_new_cython-sk.patch
with the obvious modification on trac_8327_universal_cyclotomic_field-cs.patch
.
Namely:
sage -t devel/sage-main/sage/matrix/matrix2.pyx # 25 doctests failed sage -t devel/sage-main/sage/modules/free_module.py # 2 doctests failed sage -t devel/sage-main/sage/modular/modsym/p1list_nf.py # 5 doctests failed sage -t devel/sage-main/sage/tests/startup.py # 1 doctests failed sage -t devel/sage-main/sage/rings/universal_cyclotomic_field/universal_cyclotomic_field_c.pyx # 1 doctests failed
This one here
File "/mnt/local/king/SAGE/rebase/sage-4.8.alpha0/devel/sage-main/sage/rings/universal_cyclotomic_field/universal_cyclotomic_field_c.pyx", line 239: sage: ZumbroichDecomposition_list( 6, 1 ) Expected: array([1, 1]) Got: [1, 1]
could be caused by my patch, which touches ZumbroichDecomposition
. However, I have no idea about the other errors.
comment:33 follow-up: ↓ 34 Changed 8 years ago by
Thanks for working in this patch -- I will have a look at it this morning and see what the issues are...
Best, Christian
comment:34 in reply to: ↑ 33 ; follow-up: ↓ 35 Changed 8 years ago by
Replying to stumpc5:
Thanks for working in this patch -- I will have a look at it this morning and see what the issues are...
I guess, I should first compile 4.7.2; that will take a while first...
comment:35 in reply to: ↑ 34 Changed 8 years ago by
Thanks for working in this patch -- I will have a look at it this morning and see what the issues are...
Cool!
I guess, I should first compile 4.7.2; that will take a while first...
4_8 alpha0 actually
Cheers,
comment:36 follow-up: ↓ 37 Changed 8 years ago by
- Description modified (diff)
- Status changed from needs_work to needs_review
I found the bug and fixed it, all the above doctests now work (but only on 4.7.1, the other version is still building and will take more time).
What about "needs more doctests and Sphinxified docstrings"? I agree that the cython part is still not well documented. Could you be specific where I should explain better what's going on? Part of the problem is that computing the Zumbroich basis is something that is not simple to understand without really looking at the paper. And even after understanding that, everything becomes unreadable after implementing it in a (hopefully fairly) fast way in cython...
comment:37 in reply to: ↑ 36 ; follow-up: ↓ 38 Changed 8 years ago by
Replying to stumpc5:
I found the bug and fixed it, all the above doctests now work (but only on 4.7.1, the other version is still building and will take more time).
Good! I'll test it a bit later.
What about "needs more doctests and Sphinxified docstrings"? I agree that the cython part is still not well documented. Could you be specific where I should explain better what's going on?
If by "you" you mean me, then I can't: The statement "needs more doctests ..." has been there before and is due to David Loeffler. I didn't come that far in reading the patch, I was first testing whether it applies, builds and passes tests.
comment:38 in reply to: ↑ 37 ; follow-up: ↓ 39 Changed 8 years ago by
- Work issues changed from Find dependency or rebase first patch. Fix doctests. Needs more doctests and Sphinxified docstrings. to Find dependency or rebase first patch. Fix doctests.
Replying to SimonKing:
If by "you" you mean me, then I can't: The statement "needs more doctests ..." has been there before and is due to David Loeffler. I didn't come that far in reading the patch, I was first testing whether it applies, builds and passes tests.
(That was 10 months ago and applied to a much earlier version of the patch.)
comment:39 in reply to: ↑ 38 Changed 8 years ago by
(That was 10 months ago and applied to a much earlier version of the patch.)
I now remember seeing it back then, the patch indeed changed substantially since then. So I guess it simply needs a new review.
comment:40 Changed 8 years ago by
It's perfectly permissible, and indeed a good idea, to clear the "work issues" field when uploading a new patch.
comment:41 follow-ups: ↓ 42 ↓ 44 Changed 8 years ago by
- Dependencies set to #10771
- Status changed from needs_review to needs_work
- Work issues changed from Find dependency or rebase first patch. Fix doctests. to Rebase wrt #10771. Fix doctests.
When starting with sage-4.8.alpha0 plus the stuff from #11761 (new cython), one quite big hunk of your new patch fails to apply. It concerns sage/categories/fields.py.
I found at least one reason for the mismatch: By trac ticket #10771 (sorry, it's one of mine...), Fields()
has some ElementMethods
(your patch assumes that there are none). Since #10771 has been merged in sage-4.7.2, I make this a dependency.
Well, I understand that you are building 4.7.2 anyway, aren't you?
comment:42 in reply to: ↑ 41 ; follow-up: ↓ 43 Changed 8 years ago by
Replying to SimonKing:
When starting with sage-4.8.alpha0 plus the stuff from #11761 (new cython), one quite big hunk of your new patch fails to apply. It concerns sage/categories/fields.py.
I found at least one reason for the mismatch: By trac ticket #10771 (sorry, it's one of mine...),
Fields()
has someElementMethods
(your patch assumes that there are none). Since #10771 has been merged in sage-4.7.2, I make this a dependency.Well, I understand that you are building 4.7.2 anyway, aren't you
I am building 4.7.2 and 4.8, but te later just failed to build... l will do the rebase after 4.7.2 has finished (or you do it, if you want to, it will basically take the whole day until the building is done)
comment:43 in reply to: ↑ 42 Changed 8 years ago by
Replying to stumpc5:
I am building 4.7.2 and 4.8, but te later just failed to build...
What, 4.8.alpha0 (or alpha1) failed to build?? That should not happen. Perhaps you can report on sage-release?
comment:44 in reply to: ↑ 41 ; follow-up: ↓ 45 Changed 8 years ago by
Replying to SimonKing:
When starting with sage-4.8.alpha0 plus the stuff from #11761 (new cython), one quite big hunk of your new patch fails to apply. It concerns sage/categories/fields.py.
I found at least one reason for the mismatch: By trac ticket #10771 (sorry, it's one of mine...),
Fields()
has someElementMethods
(your patch assumes that there are none). Since #10771 has been merged in sage-4.7.2, I make this a dependency.
IIRC, this patch already applies on 4.7.2: I already rebased it last week upon 10771. Ah ah, I was in a hurry, and probably forgot to upload it on trac, sorry. Please take the latest version from the sage-combinat patch server.
comment:45 in reply to: ↑ 44 Changed 8 years ago by
Replying to nthiery:
Replying to SimonKing:
When starting with sage-4.8.alpha0 plus the stuff from #11761 (new cython), one quite big hunk of your new patch fails to apply. It concerns sage/categories/fields.py.
I found at least one reason for the mismatch: By trac ticket #10771 (sorry, it's one of mine...),
Fields()
has someElementMethods
(your patch assumes that there are none). Since #10771 has been merged in sage-4.7.2, I make this a dependency.IIRC, this patch already applies on 4.7.2: I already rebased it last week upon 10771. Ah ah, I was in a hurry, and probably forgot to upload it on trac, sorry. Please take the latest version from the sage-combinat patch server.
I did the same mistake the other way round: I did changes about 5 weeks ago, and only putted it on trac but not on the combinat queue...
I just merged both versions, and the doctest should pass now, and it should be rebased (both only if I didn't do any mistakes...).
comment:46 Changed 8 years ago by
The new patch does not apply, because of the hunk
--- all.py +++ all.py @@ -1,3 +1,5 @@ +from sage.misc.lazy_import import lazy_import + from category import is_Category, Category, HomCategory
The point is that this hunk shold be totally removed, because lazy import is not needed in sage/categories/all.py.
For testing, I'm doing this change myself. But please post a patch without that hunk
comment:47 follow-up: ↓ 48 Changed 8 years ago by
- Status changed from needs_work to needs_review
Sorry, lazy_import is used. So, don't delete the patch. However, it does not apply. Reason: The first line of sage/categories/all.py currently is
from category import is_Category, Category, HomCategory, AbstractCategory
My guess is that you worked on top of Nicolas's "multiple realizations" patch.
So, either submit a patch on trac that differs from the one in the combinat queue, or name #7980 as a dependency.
Suggestion: I can manually rebase your patch, so that I can test (and review) it now. The merge conflict is trivial and can be sorted out later.
comment:48 in reply to: ↑ 47 ; follow-up: ↓ 49 Changed 8 years ago by
Replying to SimonKing:
Suggestion: I can manually rebase your patch, so that I can test (and review) it now. The merge conflict is trivial and can be sorted out later.
I am a little lost now: you don't want the current patch but the one I had before without Nicolas' rebase?
comment:49 in reply to: ↑ 48 Changed 8 years ago by
Replying to stumpc5:
I am a little lost now: you don't want the current patch but the one I had before without Nicolas' rebase?
The patch that is attached here does not apply on pure sage-4.7.2 or sage-4.8.alpha0. The reason is that this patch depends on Nicolas's patch from #7980.
So, at some point, the merge conflict has to be sorted out. However, for my review I don't need that you rebase it now.
comment:50 Changed 8 years ago by
I get one error in startup.py:
File "/mnt/local/king/SAGE/rebase/sage-4.8.alpha0/devel/sage-main/sage/tests/startup.py", line 13: sage: sage0("'numpy' in sys.modules") Expected: False Got: True
Do you import numpy at startup? Nicolas has just found that ticket #11714 explicitly avoids numpy being loaded at startup.
comment:51 Changed 8 years ago by
You import and cimport numpy. Nicolas suggest to try and lazy_import numpy instead of import (cimport should be fine).
comment:52 Changed 8 years ago by
... or lazy-import the stuff from sage/rings/universal_cyclotomic_field/all.py? I'm preparing a patch that does this.
comment:53 Changed 8 years ago by
- Description modified (diff)
OK, done.
When applying both patches, one gets
sage: 'numpy' in sys.modules False sage: sage0("'numpy' in sys.modules") False sage: UCF Universal Cyclotomic Field endowed with the Zumbroich basis sage: 'numpy' in sys.modules True sage: sage0("'numpy' in sys.modules") False
So, numpy is only imported when needed, and this is what #11714 was about.
Apply trac_8327_universal_cyclotomic_field-cs.patch trac8327_lazy_import_UCF.patch
comment:54 follow-up: ↓ 55 Changed 8 years ago by
- Status changed from needs_review to needs_work
- Work issues changed from Rebase wrt #10771. Fix doctests. to Rebase wrt #10771. Fix one doctest.
Starting with sage-4.8.alpha0 plus the new Cython plus your patch (rebased in the obvious way) plus the lazy_import patch, we are down to one error:
sage -t "devel/sage-main/sage/rings/universal_cyclotomic_field/universal_cyclotomic_field.py" ********************************************************************** File "/mnt/local/king/SAGE/rebase/sage-4.8.alpha0/devel/sage-main/sage/rings/universal_cyclotomic_field/universal_cyclotomic_field.py", line 274: sage: UCF.is_subring(UCF) Expected: True Got: False ********************************************************************** 1 items had failures: 1 of 4 in __main__.example_5 ***Test Failed*** 1 failures. For whitespace errors, see the file /mnt/local/king/.sage/tmp/universal_cyclotomic_field_4421.py [3.3 s]
Any idea why that occurs?
comment:55 in reply to: ↑ 54 ; follow-up: ↓ 56 Changed 8 years ago by
Replying to SimonKing:
sage: UCF.is_subring(UCF)
Expected:
True
Got:
False
UCF.is_subring(UCF) just returns
sage: UCF is UCF
and as UniversalCyclotomicField
inherits from UniqueRepresentation
, this should return True
. I don't know if this error might come from some lazy import which makes UCF not unique, or if something changed in UniqueRepresentation
? Nicolas might know...
comment:56 in reply to: ↑ 55 ; follow-up: ↓ 57 Changed 8 years ago by
Replying to stumpc5:
UCF.is_subring(UCF) just returns
sage: UCF is UCFand as
UniversalCyclotomicField
inherits fromUniqueRepresentation
, this should returnTrue
.
That's independent of UniqueRepresentation?: X is X
is true for any
Python object X.
So the test above breaks, my best bet is that the is_ring method that gets called is the wrong one.
Good chase!
Nicolas
comment:57 in reply to: ↑ 56 Changed 8 years ago by
Replying to nthiery:
Replying to stumpc5: So the test above breaks, my best bet is that the is_ring method that gets called is the wrong one.
I found the problem with building sage (see #11970).
4.7.2 has finished, and I now build 4.8.alpha1. I will investigate the above problem as soon as it is finished...
comment:58 follow-up: ↓ 59 Changed 8 years ago by
- Description modified (diff)
- Status changed from needs_work to needs_review
It is rebased and applies now on a new 4.8.alpha1 (NOT alpha0, but alpha1!)
There was a syntax error on the plain 4.8.alpha1, which I first had to get rid off.
Concerning the is_subring method, I get the following behaviour:
sage: UCF is UCF True sage: UCF.is_subring?? def is_subring(self,other): r""" Returns currently True if ``self`` and ``other`` coincide. EXAMPLES:: sage: UCF.is_subring(UCF) True """ return other is self sage: UCF.is_subring(UCF) False
This behaviour seems to be wired! But when replacing the lazy import of the UCF by a proper import in sage.rings.all, the wired behaviour disappears, so the problem must be something with the lazy import!
comment:59 in reply to: ↑ 58 ; follow-up: ↓ 60 Changed 8 years ago by
Replying to stumpc5:
sage: UCF.is_subring(UCF) FalseThis behaviour seems to be wired! But when replacing the lazy import of the UCF by a proper import in sage.rings.all, the wired behaviour disappears, so the problem must be something with the lazy import!
Ach ja! Sorry, I should have thought about this: it is an instance of #10906: "lazy import can break unique representation". So UCF should not be lazy imported. One probably can't lazy cimport numpy in universal_cyclotomic_field_c.pyx. Hopefully one could replace, in universal_cyclotomic_field.py:
from sage.rings.universal_cyclotomic_field.universal_cyclotomic_field_c import *
by explicit lazy imports of the various functions:
lazy_import('sage.rings.universal_cyclotomic_field.universal_cyclotomic_field_c', 'ZumbroichBasis...')
or maybe just lazy import that module as, say, ucfc, and qualify all its functions with it.
I don't have a working Sage in which I could insert the UCF patch right now. But let me know if you need help!
Cheers,
Nicolas
comment:60 in reply to: ↑ 59 ; follow-up: ↓ 61 Changed 8 years ago by
comment:61 in reply to: ↑ 60 ; follow-up: ↓ 62 Changed 8 years ago by
Replying to stumpc5:
I now do that, and all tests pass -- but I somehow missed why we want to lazy import anything; is it about importing numpy?
Apparently, there was a patch recently merged that explicitly had the purpose of "do not import numpy at startup". SO, I guess it would be better to not re-introduce the numpy import, unless we really need it.
comment:62 in reply to: ↑ 61 ; follow-up: ↓ 63 Changed 8 years ago by
Replying to SimonKing:
Replying to stumpc5: Apparently, there was a patch recently merged that explicitly had the purpose of "do not import numpy at startup". SO, I guess it would be better to not re-introduce the numpy import, unless we really need it.
I see -- I made some mistake last night, but now, the cython part is lazy imported, and all tests pass...
comment:63 in reply to: ↑ 62 Changed 8 years ago by
Replying to stumpc5:
I see -- I made some mistake last night, but now, the cython part is lazy imported, and all tests pass...
Cool. Thanks! This is as much saved for Sage's startup.
Cheers,
Nicolas
comment:64 follow-up: ↓ 65 Changed 8 years ago by
Ping. I think we should try to get this in shortly.
comment:65 in reply to: ↑ 64 Changed 8 years ago by
Replying to mhansen:
Ping. I think we should try to get this in shortly.
+1.
Simon, are you planning to review it? Or anyone else volunteering?
Christian
comment:66 follow-up: ↓ 67 Changed 8 years ago by
I'm a bit lost. I am listed as an author, and some comments mention a patch of mine. But where is that patch? I'm talking about trac_8327_universal_cyclotomic_field_new_cython-sk.patch
Similarly, where is trac8327_lazy_import_UCF.patch ?
I thought it is impossible (unless for administrators) to remove an attachment from trac?
Also, there are two work issues mentioned. Are these fixed? I.e., is it really "needs review", or is it "needs work"?
comment:67 in reply to: ↑ 66 ; follow-ups: ↓ 68 ↓ 69 Changed 8 years ago by
- Work issues Rebase wrt #10771. Fix one doctest. deleted
Replying to SimonKing:
I'm a bit lost. I am listed as an author, and some comments mention a patch of mine. But where is that patch? I'm talking about trac_8327_universal_cyclotomic_field_new_cython-sk.patch
Similarly, where is trac8327_lazy_import_UCF.patch ?
As your patches were only a few lines, I folded them into mine so the whole ticket is easier to handle (and then deleted your patches to not confuse the patchbot).
I thought it is impossible (unless for administrators) to remove an attachment from trac?
I guess, I have admin rights then.
Also, there are two work issues mentioned. Are these fixed? I.e., is it really "needs review", or is it "needs work"?
sorry for not deleting them, I fixed both 4 weeks ago (though I don't know if there is another rebase needed for sage-4.8.alpha4).
Best, Christian
comment:68 in reply to: ↑ 67 Changed 8 years ago by
Replying to stumpc5:
(though I don't know if there is another rebase needed for sage-4.8.alpha4).
No need -- patch applies fine to 4.8.alpha4. The new files pass their doctests (I haven't run a full doctest cycle).
comment:69 in reply to: ↑ 67 ; follow-up: ↓ 70 Changed 8 years ago by
Replying to stumpc5:
I thought it is impossible (unless for administrators) to remove an attachment from trac?
I guess, I have admin rights then.
If you just didn't want to confuse the patchbot, you should insert a line in some comment, stating what patches have to be applied in what order:
Apply trac_8327_universal_cyclotomic_field-cs.patch
But then, what is the status of your "syntax error" patch?
comment:70 in reply to: ↑ 69 Changed 8 years ago by
Replying to SimonKing:
But then, what is the status of your "syntax error" patch?
I wasn't able to run 4.8.alpha1 due to a non-ascii character in /rings/arith.py. The patch only deletes this character -- I don't know if it is still present in 4.8.alpha4, but I will check after it has finished building.
comment:71 Changed 8 years ago by
- Dependencies changed from #10771 to #4539 #10771
- Description modified (diff)
Apply trac_8327-rebased_for_v5.patch
(for the patchbot).
The previous patch conflicts with #4539, so I have done a new rebased patch. There was one change in free_module.py
which was rejected, and whose purpose was not at all clear to me, so I didn't include it in the rebased patch -- all doctests seem to pass without it.
comment:72 Changed 8 years ago by
- Status changed from needs_review to needs_work
And now it's failing to apply again with the latest beta (5.0.beta11), due to a conflict in sage/categories/all.py coming from with #7980.
comment:73 Changed 8 years ago by
- Status changed from needs_work to needs_review
I've re-rebased the patch.
comment:74 Changed 8 years ago by
Apply trac_8327-rebased_for_v5.patch, trac_8327-docfix.patch
(I got some error messages building the documentation -- the above patch fixes them.)
comment:75 follow-up: ↓ 78 Changed 8 years ago by
- Description modified (diff)
comment:76 Changed 8 years ago by
- Dependencies changed from #4539 #10771 to #4539 #10771 #7980
comment:77 Changed 8 years ago by
Apply trac_8327-rebased_for_v5.patch, trac_8327-docfix.patch
(patchbot's confused again)
comment:78 in reply to: ↑ 75 Changed 8 years ago by
Hi guys,
Just my 2 cents, but Christian did an awfull amount of work on this patch; I really appreciate your efforts to help him get this in (I should participate to that too!), and I know you added yourself to share the blame in case of trouble later; still I feel he deserves to be single author. What do you think?
Cheers,
Nicolas
comment:79 Changed 8 years ago by
- Reviewers set to David Loeffler
Sure -- my contribution was just rebasing + reformatting some docstrings. I've removed myself as author (but added myself as reviewer).
comment:80 Changed 8 years ago by
Hi,
Thanks for pushing the patch forward - I actually don't care whose name appears in the authors field, but I would appreciate if we can get the patch ready soon (maybe even for 5.0)!
I have a slightly newer version of the patch locally containing some missing docstrings and stuff. Do you mind if I delete all 4 attached patches and push one patch containing
+ all my new docstrings
+ rebased for 5.0.beta6 (is that recent enough? I haven't build anything newer, so I cannot rebase the patch for beta11; I could do that tomorrow after building.)
+ David's improvements in the docstrings
?
Best, Christian
comment:81 follow-up: ↓ 82 Changed 8 years ago by
I think it would be rather counterproductive to erase a patch that applies to the current beta, and replace it with one that almost certainly wouldn't. The most recent bout of conflicts was caused by #7980, which was only merged in beta11. So please build a copy of beta11 before you do any further work on this.
comment:82 in reply to: ↑ 81 ; follow-up: ↓ 83 Changed 8 years ago by
Replying to davidloeffler:
I think it would be rather counterproductive to erase a patch that applies to the current beta, and replace it with one that almost certainly wouldn't. The most recent bout of conflicts was caused by #7980, which was only merged in beta11. So please build a copy of beta11 before you do any further work on this.
Alright, I will then first build and do attach another version tomorrow then.
comment:83 in reply to: ↑ 82 Changed 8 years ago by
Replying to stumpc5:
Replying to davidloeffler:
I think it would be rather counterproductive to erase a patch that applies to the current beta, and replace it with one that almost certainly wouldn't. The most recent bout of conflicts was caused by #7980, which was only merged in beta11. So please build a copy of beta11 before you do any further work on this.
Alright, I will then first build and do attach another version tomorrow then.
For the record: if Christian's latest version is that on the sage-combinat patch server, then it should be already based on #7980 and likely to apply smoothly.
comment:84 Changed 8 years ago by
- Description modified (diff)
comment:85 Changed 8 years ago by
I attached a new version that contains everything I have, which is rebased for 5.0.beta11, and also contains David's docfixes.
comment:86 Changed 8 years ago by
Apply trac_8327_universal_cyclotomic_field-cs.patch
(for patchbot)
comment:87 follow-up: ↓ 88 Changed 8 years ago by
- Reviewers David Loeffler deleted
- Status changed from needs_review to needs_work
sage -t -force_lib devel/sage-8327/sage/rings/universal_cyclotomic_field/universal_cyclotomic_field_c.pyx ********************************************************************** File "/storage/masiao/sage-5.0.beta11-patchbot/devel/sage-8327/sage/rings/universal_cyclotomic_field/universal_cyclotomic_field_c.pyx", line 239: sage: ZumbroichDecomposition_list( 6, 1 ) Expected: array([1, 1]) Got: [1, 1] ********************************************************************** 1 items had failures: 1 of 7 in __main__.example_7 ***Test Failed*** 1 failures. For whitespace errors, see the file /home/masiao/.sage/tmp/fermat-21656/universal_cyclotomic_field_c_22797.py [1.7 s] sage -t -force_lib devel/sage-8327/sage/rings/polynomial/polynomial_quotient_ring.py ********************************************************************** File "/storage/masiao/sage-5.0.beta11-patchbot/devel/sage-8327/sage/rings/polynomial/polynomial_quotient_ring.py", line 262: sage: [s for s in dir(Q.category().element_class) if not s.startswith('_')] Expected: ['cartesian_product', 'gcd', 'is_idempotent', 'is_one', 'lcm', 'lift'] Got: ['cartesian_product', 'gcd', 'is_idempotent', 'is_one', 'is_unit', 'lcm', 'lift'] ********************************************************************** 1 items had failures: 1 of 30 in __main__.example_2 ***Test Failed*** 1 failures. For whitespace errors, see the file /home/masiao/.sage/tmp/fermat-21656/polynomial_quotient_ring_22987.py [42.5 s] sage -t -force_lib devel/sage-8327/sage/tests/startup.py ********************************************************************** File "/storage/masiao/sage-5.0.beta11-patchbot/devel/sage-8327/sage/tests/startup.py", line 13: sage: sage0("'numpy' in sys.modules") Expected: False Got: True **********************************************************************
(All three of these failures had already been reported, and fixed, before this latest patch re-broke them.)
comment:88 in reply to: ↑ 87 ; follow-up: ↓ 89 Changed 8 years ago by
Replying to davidloeffler:
(All three of these failures had already been reported, and fixed, before this latest patch re-broke them.)
These were not fixed in the docfix patch but in the rebase patch, so I didn't see them. (I actually fixed the first, but forgot to refresh the patch afterwards.)
I now attached the new version that should have the issues fixed. including the last which seems to me like not related to this patch, is it?
comment:89 in reply to: ↑ 88 ; follow-up: ↓ 90 Changed 8 years ago by
- Work issues set to don't import numpy
Replying to stumpc5:
I now attached the new version that should have the issues fixed. including the last which seems to me like not related to this patch, is it?
It is related to your patch, as discussed in the comment thread above. It is important that Sage must not import numpy at startup, because it takes a very long time to load (cf. tickets #11714, #6494, and several others I think). Your patch causes numpy to be imported at startup; Nicolas and Simon put in a fair bit of work using lazy_import
to stop this happening (see comments 50-53). You will see that trac_8327-rebased_for_v5.patch does not need to disable this test in startup.py as you have done.
comment:90 in reply to: ↑ 89 Changed 8 years ago by
Replying to davidloeffler:
Replying to stumpc5:
It is related to your patch, as discussed in the comment thread above. It is important that Sage must not import numpy at startup, because it takes a very long time to load (cf. tickets #11714, #6494, and several others I think). Your patch causes numpy to be imported at startup; Nicolas and Simon put in a fair bit of work using
lazy_import
to stop this happening (see comments 50-53). You will see that trac_8327-rebased_for_v5.patch does not need to disable this test in startup.py as you have done.
Were is my mind, thanks for telling me again! -- The patch attached here and the one I had on the combinat queue were both changed, I now made numpy got lazy imported again. I will post the patch as soon as there are no further test failures.
comment:91 Changed 8 years ago by
- Status changed from needs_work to needs_review
- Work issues don't import numpy deleted
numpy is now lazy imported:
sage: 'numpy' in sys.modules False sage: sage0("'numpy' in sys.modules") False sage: UCF Universal Cyclotomic Field endowed with the Zumbroich basis sage: 'numpy' in sys.modules False sage: E(5) E(5) sage: 'numpy' in sys.modules True sage: sage0("'numpy' in sys.modules") False
I hope I haven't forgotten any further things!
comment:92 Changed 8 years ago by
Apply trac_8327_universal_cyclotomic_field-cs.patch
(for patchbot)
comment:93 follow-up: ↓ 94 Changed 8 years ago by
- Status changed from needs_review to needs_work
Right, so now we have a patch which actually works, we can start testing it. And we find the following bug:
---------------------------------------------------------------------- | Sage Version 5.0.beta11, Release Date: 2012-03-28 | | Type notebook() for the GUI, and license() for information. | ---------------------------------------------------------------------- ********************************************************************** * * * Warning: this is a prerelease version, and it may be unstable. * * * ********************************************************************** sage: z1 = E(3) sage: z2 = UCF(CyclotomicField(3).gen()) sage: z1 == z2 False sage: z1 + z2 --------------------------------------------------------------------------- AttributeError Traceback (most recent call last) /home/masiao/<ipython console> in <module>() /storage/masiao/sage-5.0.beta11/local/lib/python2.7/site-packages/sage/structure/element.so in sage.structure.element.RingElement.__add__ (sage/structure/element.c:11990)() /storage/masiao/sage-5.0.beta11/local/lib/python2.7/site-packages/sage/structure/element.so in sage.structure.element.ModuleElement._add_ (sage/structure/element.c:8612)() /storage/masiao/sage-5.0.beta11/local/lib/python2.7/site-packages/sage/rings/universal_cyclotomic_field/universal_cyclotomic_field.pyc in _add_(self, other) 890 E(12)^4 - E(12)^7 - E(12)^11 891 """ --> 892 n,m = self.field_order(),other.field_order() 893 l = cached_lcm( [ n, m ] ) 894 /storage/masiao/sage-5.0.beta11/local/lib/python2.7/site-packages/sage/rings/universal_cyclotomic_field/universal_cyclotomic_field.pyc in field_order(self) 1020 3 1021 """ -> 1022 if bool(self.value._monomial_coefficients): 1023 return iter(self.value._monomial_coefficients).next()[0] 1024 else: /storage/masiao/sage-5.0.beta11/local/lib/python2.7/site-packages/sage/structure/element.so in sage.structure.element.Element.__getattr__ (sage/structure/element.c:2919)() /storage/masiao/sage-5.0.beta11/local/lib/python2.7/site-packages/sage/structure/parent.so in sage.structure.parent.getattr_from_other_class (sage/structure/parent.c:3329)() AttributeError: 'sage.rings.number_field.number_field_element_quadratic.NumberFieldElement_quadratic' object has no attribute '_monomial_coefficients'
This is even worse, since the element involved isn't cyclotomic in the first place:
sage: K.<a> = NumberField(x^3 - 7) sage: UCF(a) a sage: UCF(a) in UCF True
In fact UCF will attempt to construct an element from anything whatsoever:
sage: UCF(None) None sage: UCF(QQ) Rational Field sage: UCF('hello') 'hello'
The following are not great either:
sage: UCF.has_coerce_map_from(CyclotomicField(3)) False sage: QQbar.has_coerce_map_from(UCF) False
comment:94 in reply to: ↑ 93 ; follow-up: ↓ 95 Changed 8 years ago by
Replying to davidloeffler:
In fact UCF will attempt to construct an element from anything whatsoever:
sage: UCF(None) None sage: UCF(QQ) Rational Field sage: UCF('hello') 'hello'
I didn't implement the __call__
method - what is the behaviour you would expect here?
The following are not great either:
sage: UCF.has_coerce_map_from(CyclotomicField(3)) False
how can I get a coerce from CyclotomicField(n)
for all n
?
sage: QQbar.has_coerce_map_from(UCF) False
I fixed this.
comment:95 in reply to: ↑ 94 ; follow-up: ↓ 96 Changed 8 years ago by
Replying to stumpc5:
I didn't implement the
__call__
method - what is the behaviour you would expect here?
Oh, I don't know, maybe the same behaviour as every other parent object in the Sage library? The default __call__
calls _element_constructor_
, which you should override, in order to create an element of self from the given arguments. This includes checking whether the given arguments are reasonable, and raising a TypeError otherwise.
You should also set the attribute wrapped_class for your element class to something other than the default (which is "object"), so the __init__
it inherits from ElementWrapper knows what it's supposed to be wrapping and doesn't wrap obviously bogus objects as in the examples above.
how can I get a coerce from
CyclotomicField(n)
for alln
?
I don't quite understand the question, but if you're going to implement a class and call it "universal cyclotomic field", surely it had better satisfy a universal property with respect to cyclotomic fields? If your question is "how do I recognise a cyclotomic field", you might find isinstance(K, sage.rings.number_field.number_field.NumberField_cyclotomic)
or perhaps sage.rings.number_field.number_field.is_CyclotomicField(K)
helpful. You should also check K.coerce_embedding
, since it's possible to create cyclotomic fields with complex embeddings other than the standard one.
comment:96 in reply to: ↑ 95 Changed 8 years ago by
Replying to davidloeffler:
Replying to stumpc5: Oh, I don't know, maybe the same behaviour as every other parent object in the Sage library? The default
__call__
calls_element_constructor_
, which you should override, in order to create an element of self from the given arguments. This includes checking whether the given arguments are reasonable, and raising a TypeError otherwise.
The idea is that one should *not* construct elements of the universal cyclotomic field using UCF(arg)
but only through the function E
, e.g., E(5)
. So UCF(arg)
should only be called for coercion.
I could overwrite _element_constructor_
by
def _element_constructor_(self,arg): raise TypeError, "No coercion found for %s"%str(arg)
This would prevent UCF
from ever constructing any element, and only using the coercion model to coerce objects if possible.
You should also set the attribute wrapped_class for your element class to something other than the default (which is "object"), so the
__init__
it inherits from ElementWrapper knows what it's supposed to be wrapping and doesn't wrap obviously bogus objects as in the examples above.
Do I see it right that this would then also be obsolete?
how can I get a coerce from
CyclotomicField(n)
for alln
?I don't quite understand the question, but if you're going to implement a class and call it "universal cyclotomic field", surely it had better satisfy a universal property with respect to cyclotomic fields?
Let me define one coercion:
sage: from sage.rings.number_field.number_field_morphisms import NumberFieldEmbedding sage: n = 5 sage: X = CyclotomicField(n) sage: f = NumberFieldEmbedding(X,UCF,E(n)) sage: UCF.register_coercion(f) sage: x = X.gen() sage: UCF(x) E(5)
First, how can I register this coercion for all n
? Second, are there further number fields I should have a coercion from?
comment:97 follow-up: ↓ 98 Changed 8 years ago by
Aargh! This is so disastrously wrong I don't even know where to start. For heavens' sake, go and read the Sage reference manual -- there's a whole huge tutorial on how to implement coercions properly.
I think I've had enough of this ticket; perhaps someone else can take over "reviewing" it from here onwards.
comment:98 in reply to: ↑ 97 Changed 8 years ago by
Replying to davidloeffler:
Aargh! This is so disastrously wrong I don't even know where to start. For heavens' sake, go and read the Sage reference manual -- there's a whole huge tutorial on how to implement coercions properly.
I think I've had enough of this ticket; perhaps someone else can take over "reviewing" it from here onwards.
First, I consider this strongly unfriendly.
Second, after looking again at the coercion section of the reference manual, I still don't see what is so disastrously wrong (which obviously doesn't mean that it is not wrong), and how to tell a parent to register coercion from an infinite family of other parents.
comment:99 follow-up: ↓ 100 Changed 8 years ago by
I'm sorry, please pardon my earlier outburst -- it was uncalled for, your message just caught me at a bad time.
See http://www.sagemath.org/doc/reference/coercion.html#methods-to-implement. The magic routines here are _element_constructor_
and _coerce_map_from_
. In this case, you can make UCF._coerce_map_from_(K)
return the natural morphism from K to self whenever K is a cyclotomic field (but you need to watch out for cyclotomic fields with non-standard embeddings).
comment:100 in reply to: ↑ 99 Changed 8 years ago by
Replying to davidloeffler:
See http://www.sagemath.org/doc/reference/coercion.html#methods-to-implement. The magic routines here are
_coerce_map_from_
Thanks, I now see how I can do the coercion here - except that I do not know how to handle non-standard embeddings. I do not know how to test if a non-standard embedding is used, and if so, I also do not know how to coerce then into the UCF
.
_element_constructor_
I want that an element of UCF
is never constructed using the __call__
method but only using the function E
. In the 4 steps in http://www.sagemath.org/doc/reference/coercion.html#provided-methods __call__
, I want the first 3 to proceed, and if no coercion is found, that an error is raised. The idea here is that UCF
has an infinite number of generators, and the easiest to play with them seems to be the same way this is done in GAP
; simply doing things like
sage: E(3) E(3) sage: E(3)+E(4) E(12)^4 - E(12)^7 - E(12)^11
Also, I want to see
sage: UCF(5) 5 sage: UCF(5).parent() Universal Cyclotomic Field endowed with the Zumbroich basis sage: X = CyclotomicField(6) sage: UCF(X.gen()) -E(3)^2
Is this generally wrong, or is the way I proposed to define _element_constructor_
in my last comment just not the way to do that?
comment:101 follow-up: ↓ 102 Changed 7 years ago by
Ok, I am willing to try a review. I am not sure to be competent enough. We will see.
Let us first try to get a full green light from the bot. Could you please upload the latest version, rebased on a recent copy of sage ?
comment:102 in reply to: ↑ 101 Changed 7 years ago by
Replying to chapoton:
Ok, I am willing to try a review. I am not sure to be competent enough. We will see.
Let us first try to get a full green light from the bot. Could you please upload the latest version, rebased on a recent copy of sage ?
That would be really great! I will do that now (and also get the documentation into a good state-of-the-art shape), and let you know once the patch is ready for you to look at.
comment:103 follow-up: ↓ 104 Changed 7 years ago by
- Dependencies changed from #4539 #10771 #7980 to #4539, #10771, #7980, #13727, #13728
comment:104 in reply to: ↑ 103 Changed 7 years ago by
comment:105 Changed 7 years ago by
- Dependencies changed from #4539, #10771, #7980, #13727, #13728 to #4539, #10771, #7980, #9651, #13727, #13728
- Description modified (diff)
- Status changed from needs_work to needs_review
So this seems interesting (I'd never heard of the Zumbrioch basis before). I don't have anything useful to say about the utility of this, or implementing it.
However, I'd like to suggest we might want to use a different convention for the constructor -- I don't like the idea of
CyclotomicField()
working. That seems like something that's too easy for a user to accidentally do (leave out then
they intended to use), and I'd much rather they see an error than have it quietly succeed, only to discover that their cyclotomic field isn't quite what they expected (and likely slower to boot). Maybe something likeF = CyclotomicField(n=Infinity)
?