Opened 10 years ago

Last modified 7 years ago

#8327 closed enhancement

Implement the universal cyclotomic field, using Zumbroich basis — at Version 53

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: Rebase wrt #10771. Fix doctests.
Branch: Commit:
Dependencies: #10771 Stopgaps:

Description (last modified by SimonKing)

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; it depends on #9651 (Addition of combinatorial free module).

Apply

Change History (53)

comment:1 Changed 10 years ago by nthiery

  • Cc sage-combinat added

comment:2 follow-up: Changed 10 years ago by 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 the n 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 like F = CyclotomicField(n=Infinity)?

comment:3 in reply to: ↑ 2 ; follow-up: Changed 10 years ago by nthiery

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 the n 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 like F = 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: Changed 10 years ago by craigcitro

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 nth 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 nthiery

Replying to craigcitro:

True. Maybe it's a bit too "cutesy," but using n=0 might be nice -- after all, the nth cyclotomic field has roots of unity for all divisors of n, so this would still hold for the universal cyclotomic field and n=0.

Mmm, any complex number is a 0-th root of unity, isn't it?

comment:6 Changed 10 years ago by stumpc5

  • 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 stumpc5

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)?

comment:8 Changed 10 years ago by cwitty

  • Cc cwitty added

comment:9 Changed 10 years ago by stumpc5

  • Status changed from needs_work to needs_review

comment:10 Changed 10 years ago by stumpc5

  • Authors set to Christian Stump

comment:11 Changed 10 years ago by stumpc5

  • Description modified (diff)

comment:12 Changed 10 years ago by davidloeffler

  • 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: Changed 10 years ago by davidloeffler

  • 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 10 years ago by stumpc5

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 stumpc5

  • 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 stumpc5

Can some delete all but the youngest attached patch, the buildbot gets confused.

Thanks, Christian

comment:17 Changed 9 years ago by stumpc5

  • Description modified (diff)

comment:18 Changed 9 years ago by davidloeffler

Apply trac_8327_universal_cyclotomic_field-cs.patch

comment:19 Changed 9 years ago by stumpc5

Apply only trac_8327_universal_cyclotomic_field-cs.patch

comment:20 Changed 9 years ago by stumpc5

  • 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 stumpc5

Apply only trac_8327_universal_cyclotomic_field-cs.patch

comment:22 Changed 9 years ago by chapoton

Apply trac_8327_universal_cyclotomic_field-cs.patch

comment:23 Changed 9 years ago by stumpc5

  • Dependencies set to #10963
  • Owner changed from davidloeffler to (none)

comment:24 Changed 9 years ago by stumpc5

  • Milestone changed from sage-feature to sage-4.7.2

comment:25 Changed 9 years ago by stumpc5

  • Dependencies #10963 deleted

comment:26 follow-up: Changed 9 years ago by nthiery

  • 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 9 years ago by SimonKing

  • Authors changed from Christian Stump to Christian Stump, Simon King
  • 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 9 years ago by SimonKing

  • Description modified (diff)

Sorry, I forgot to change the ticket description.

comment:29 Changed 9 years ago by SimonKing

  • 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: Changed 9 years ago by SimonKing

  • 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 9 years ago by SimonKing

  • 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 9 years ago by SimonKing

  • 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: Changed 9 years ago by stumpc5

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: Changed 9 years ago by stumpc5

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 9 years ago by nthiery

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: Changed 9 years ago by stumpc5

  • 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: Changed 9 years ago by SimonKing

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: Changed 9 years ago by davidloeffler

  • 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 9 years ago by stumpc5

(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 9 years ago by davidloeffler

It's perfectly permissible, and indeed a good idea, to clear the "work issues" field when uploading a new patch.

comment:41 follow-ups: Changed 9 years ago by SimonKing

  • 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: Changed 9 years ago by stumpc5

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 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

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 9 years ago by SimonKing

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: Changed 9 years ago by 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 some ElementMethods (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 9 years ago by stumpc5

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 some ElementMethods (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 9 years ago by SimonKing

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: Changed 9 years ago by SimonKing

  • 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: Changed 9 years ago by stumpc5

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 9 years ago by SimonKing

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 9 years ago by SimonKing

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 9 years ago by SimonKing

You import and cimport numpy. Nicolas suggest to try and lazy_import numpy instead of import (cimport should be fine).

comment:52 Changed 9 years ago by SimonKing

... or lazy-import the stuff from sage/rings/universal_cyclotomic_field/all.py? I'm preparing a patch that does this.

comment:53 Changed 9 years ago by SimonKing

  • 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

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