Opened 14 years ago
Closed 11 years ago
#2329 closed enhancement (fixed)
Add interface to PARI's rnfisnorm()
Reported by: | craigcitro | Owned by: | craigcitro |
---|---|---|---|
Priority: | blocker | Milestone: | sage-4.7 |
Component: | number fields | Keywords: | editor_craigcitro pari |
Cc: | ncalexan, mstreng, jdemeyer | Merged in: | sage-4.7.alpha2 |
Authors: | Craig Citro, Marco Streng, Francis Clarke, Jeroen Demeyer | Reviewers: | Nick Alexander, David Loeffler, Jeroen Demeyer, David Kirkby |
Report Upstream: | N/A | Work issues: | |
Branch: | Commit: | ||
Dependencies: | Stopgaps: |
Description (last modified by )
This patch adds support to solve norm equations via PARI.
Quick summary: given an element x
of any number field (even QQ
), x.is_norm(L)
will return True
if and only if x
is a norm from L
. It is also able to return an element of L
whose norm is x
.
The data used by PARI to compute whether or not an element is a norm can be computed once for each extension L/K
. The function pari_rnfnorm_data
computes exactly this, and hopefully in a later version its result can be passed to is_norm
to avoid recomputing it each time in the case that K != QQ
. If K
is QQ
, there is no need to save any such data -- the only data needed is that of K.pari_bnf()
, which is used instead, and is already cached by K
.
Dependencies: #10677
Apply:
- trac_2329_rnfisnorm5.patch (positive_review)
- 2329_reviewer.patch (positive_review)
- 2329_selmer.patch (needs_review)
Attachments (11)
Change History (71)
Changed 14 years ago by
comment:1 Changed 14 years ago by
- Cc ncalexan added
comment:2 Changed 14 years ago by
- Owner changed from was to craigcitro
- Status changed from new to assigned
comment:3 Changed 14 years ago by
- Milestone changed from sage-2.11 to sage-2.10.4
comment:4 Changed 14 years ago by
Craig, what's the status on this patch? I need it as we speak :) Are you interested in completing this or should I implement the changes I think are necessary and kick it back to you for refereeing?
comment:5 Changed 14 years ago by
Nick, I'd be more than happy to have you finish this guy off. I think all the code is there, it just needs to be cleaned up and unified here and there. I just haven't had time to get back to it since you posted the referee report -- but if you want to clean this up, I'll review it for you lickety-split.
comment:6 Changed 14 years ago by
Added a second patch that addresses all of the above issues.
Changed 14 years ago by
comment:7 Changed 14 years ago by
- Summary changed from [with patch, needs review] add interface to Pari's rnfisnorm to [with patch, pending another patch] add interface to Pari's rnfisnorm
Changed 14 years ago by
comment:8 Changed 14 years ago by
The last patch separates out very useful fixes to the pari/gen.pyx that should be applied now.
The remainder of the functionality requires some more substantial changes and is a work in progress.
comment:9 Changed 13 years ago by
- Keywords editor_craigcitro added
comment:10 Changed 13 years ago by
This has been sitting around forever. Any movement here?
Cheers,
Michael
comment:11 Changed 12 years ago by
- Component changed from number theory to number fields
comment:12 Changed 11 years ago by
- Cc mstreng added
- Report Upstream set to N/A
Same question as mabshoff 22 months ago...
comment:13 Changed 11 years ago by
- Description modified (diff)
- Priority changed from minor to major
- Reviewers set to Nick Alexander
As nobody replied here any more, I attacked the ticket myself by changing Craig's patch.
I've addressed Nick's concerns and replaced the documentation to reflect better what is in the Pari documentation (which weakens some claims considerably unfortunately).
x.is_norm() now decides whether an element x is a norm (proven output), while x.rnfisnorm() gives exactly the output that Pari's rnfisnorm would give.
The output of is_norm is True or False. With element=True, it also gives an element of norm x (or None if it doesn't exist). The function element_of_norm is removed, to avoid confusion with elements_of_norm.
comment:14 Changed 11 years ago by
- Status changed from needs_work to needs_review
- Summary changed from [with patch, pending another patch] add interface to Pari's rnfisnorm to add interface to Pari's rnfisnorm
Ready for review, volunteer needed!
The only doctest that failed fails without the patch as well:
K.<a> = QuadraticField(-5) K.selmer_group([K.ideal(2, -a+1), K.ideal(3, a+1), K.ideal(a)], 3) [2, a + 1, a]
The documentation says it should be [2, a+1, -a]
comment:15 follow-up: ↓ 17 Changed 11 years ago by
- Status changed from needs_review to needs_work
- Work issues set to compilation problems
Patch applies fine under 4.6.alpha1 but fails to compile:
Error converting Pyrex file to C: ------------------------------------------------------------ ... return self.new_gen(thueinit(self.g, flag, prec)) def rnfisnorminit(self, polrel, flag=2): _sig_on return self.new_gen(rnfisnorminit(self.g, (<gen>polrel).g, flag)) ^ ------------------------------------------------------------ /storage/masiao/sage-4.6.alpha1/devel/sage-hacking/sage/libs/pari/gen.pyx:7160:41: undeclared name not builtin: rnfisnorminit
Adding
GEN rnfisnorminit(GEN T, GEN relpol, int galois)
to sage/libs/pari/decl.pxi
fixes that issue, but this reveals another failure:
sage/libs/pari/gen.c: In function ‘__pyx_pf_4sage_4libs_4pari_3gen_3gen_bnfisnorm’: sage/libs/pari/gen.c:24097: error: too many arguments to function ‘bnfisnorm’
This seems to be because the "prec" argument to "bnfisnorm" has been removed, but taking out the extra argument, it *still* doesn't work:
sage -t number_field_element.pyx ********************************************************************** File "/storage/masiao/sage-4.6.alpha1/devel/sage-hacking/sage/rings/number_field/number_field_element.pyx", line 971: sage: (beta/2).is_norm(L) Exception raised: Traceback (most recent call last): File "/storage/masiao/sage-4.6.alpha1/local/bin/ncadoctest.py", line 1231, in run_one_test self.run_one_example(test, example, filename, compileflags) File "/storage/masiao/sage-4.6.alpha1/local/bin/sagedoctest.py", line 38, in run_one_example OrigDocTestRunner.run_one_example(self, test, example, filename, compileflags) File "/storage/masiao/sage-4.6.alpha1/local/bin/ncadoctest.py", line 1172, in run_one_example compileflags, 1) in test.globs File "<doctest __main__.example_28[5]>", line 1, in <module> (beta/Integer(2)).is_norm(L)###line 971: sage: (beta/2).is_norm(L) File "number_field_element.pyx", line 999, in sage.rings.number_field.number_field_element.NumberFieldElement.is_norm (sage/rings/number_field/number_field_element.cpp:8726) return self.is_norm(L, element = True, proof = proof)[0] File "number_field_element.pyx", line 1017, in sage.rings.number_field.number_field_element.NumberFieldElement.is_norm (sage/rings/number_field/number_field_element.cpp:9083) a, b = self.rnfisnorm(L, certify = proof) File "number_field_element.pyx", line 1108, in sage.rings.number_field.number_field_element.NumberFieldElement.rnfisnorm (sage/rings/number_field/number_field_element.cpp:9820) x, q = self._pari_('y').rnfisnorm(rnf_data) File "gen.pyx", line 9470, in sage.libs.pari.gen._pari_trap (sage/libs/pari/gen.c:45353) PariError: (5) **********************************************************************
At that point I gave up. Sorry. That's "needs work".
David
comment:16 Changed 11 years ago by
If anyone wants to fix this, go ahead. It worked just fine on my 4.5.something, so I guess a solution can be found by looking at the differences between the pari interfaces of 4.5 and 4.6.
comment:17 in reply to: ↑ 15 Changed 11 years ago by
- Work issues changed from compilation problems to bug in Pari 2.3.5
Replying to davidloeffler:
..., it *still* doesn't work:
sage -t number_field_element.pyx ********************************************************************** File "/storage/masiao/sage-4.6.alpha1/devel/sage-hacking/sage/rings/number_field/number_field_element.pyx", line 971: sage: (beta/2).is_norm(L) Exception raised: Traceback (most recent call last): ... File "gen.pyx", line 9470, in sage.libs.pari.gen._pari_trap (sage/libs/pari/gen.c:45353) PariError: (5) **********************************************************************
At that point I gave up. Sorry. That's "needs work".
Looks like a Pari bug. This is what the doctest asks Pari to do (with the equivalent of beta.is_norm(L) first):
trousseau-bash% sage-4.6/sage -gp GP/PARI CALCULATOR Version 2.4.3 (development svn-12577:12605) i386 running darwin (x86-64/GMP-4.2.1 kernel) 64-bit version ... parisize = 8000000, primelimit = 500509 ? bnf = bnfinit(y^3 + 5); ? p = x^2 + x + Mod(y, y^3 + 5); ? T = rnfisnorminit(bnf, p); ? rnfisnorm(T, Mod(y, y^3 + 5)) %4 = [Mod(x, x^2 + x + Mod(y, y^3 + 5)), 1] ? rnfisnorm(T, Mod(y/2, y^3 + 5)) *** at top-level: rnfisnorm(T,Mod(y/2, *** ^-------------------- *** rnfisnorm: zero argument in factorint. *** Break loop: type 'break' to go back to GP break> break
But previously, it worked alright:
trousseau-bash% sage-4.5.3/sage -gp GP/PARI CALCULATOR Version 2.3.5 (released) i386 running darwin (x86-64/GMP-4.2.1 kernel) 64-bit version ... parisize = 8000000, primelimit = 500000 ? bnf = bnfinit(y^3 + 5); ? p = x^2 + x + Mod(y, y^3 + 5); ? T = rnfisnorminit(bnf, p); ? rnfisnorm(T, Mod(y, y^3 + 5)) %4 = [Mod(-x, x^2 + x + Mod(y, y^3 + 5)), 1] ? rnfisnorm(T, Mod(y/2, y^3 + 5)) %5 = [Mod(Mod(-1/2, y^3 + 5)*x, x^2 + x + Mod(y, y^3 + 5)), 2] ?
Note also that the two versions give a different result at %4.
comment:18 follow-up: ↓ 19 Changed 11 years ago by
Hi Francis, Did you report this bug to pari? Marco
comment:19 in reply to: ↑ 18 Changed 11 years ago by
comment:20 Changed 11 years ago by
- Work issues changed from bug in Pari 2.3.5 to bug in Pari 2.4.3
The bug with non-integral elements in rnfisnorm was reported to pari by fwclarke, and I wrote a simple workaround for the time it takes a pari-fix to reach sage.
Turns out there is another problem:
sage: K.<a> = NumberField(x^2 + x + 1) sage: Q.<X> = K[] sage: L.<b> = NumberField(X^3 + a) sage: K.pari_rnfnorm_data(L) PariError: incorrect type (11)
Again caused by something that works fine in pari 2.3.4 and is broken in pari 2.4.3 (alpha)
gp > bnf = bnfinit(y^2+y+1); gp > polrel = Mod(1, y^2 + y + 1)*x^3 + Mod(y, y^2 + y + 1); gp > rnfisnorminit(bnf, polrel) *** at top-level: rnfisnorminit(bnf,po *** ^-------------------- *** rnfisnorminit: incorrect type in RgX_RgXQ_eval. *** Break loop: type 'break' to go back to GP
Ideas anyone?
comment:21 Changed 11 years ago by
- Work issues changed from bug in Pari 2.4.3 to testing
I've added a new file that seems to work after the pari upgrade, including workarounds for 2 new pari bugs. I'll do some additional testing before I make it "needs review" again.
The bugs have been reported to pari http://pari.math.u-bordeaux.fr/cgi-bin/bugreport.cgi?bug=1143 and http://pari.math.u-bordeaux.fr/cgi-bin/bugreport.cgi?bug=1144
comment:22 Changed 11 years ago by
- Reviewers changed from Nick Alexander to Nick Alexander, David Loeffler
- Status changed from needs_work to needs_review
- Work issues testing deleted
All tests pass again.
comment:23 Changed 11 years ago by
- Description modified (diff)
comment:24 Changed 11 years ago by
- Description modified (diff)
comment:25 Changed 11 years ago by
For the Buildbot's sake:
Apply trac_2329_rnfisnorm3.patch
comment:26 follow-up: ↓ 27 Changed 11 years ago by
Can you justify why you use <gen>
instead of the t0GEN()
mechanism in gen.pyx
? Even if <gen>
happens to work, using t0GEN()
is safer because it will prevent the GEN
from being garbage collected.
comment:27 in reply to: ↑ 26 Changed 11 years ago by
Replying to jdemeyer
No I can't, I didn't write that part.
comment:28 follow-up: ↓ 37 Changed 11 years ago by
There remain several problems for relative extensions. In particular, the function sage.rings.number_field.number_field_rel.NumberField_relative.is_galois_relative
cannot be relied on at present (4.6.1.alpha3):
sage: K.<w> = NumberField(x^2 + x + 1) sage: L.<a> = K.extension(x^3 - 2) sage: L.is_galois_relative() False
But
sage: L.is_galois_absolute() True
and indeed
sage: len([g for g in End(L) if g(w) == w]) == L.relative_degree() True
I will post a patch for this in the next couple of days, and suggest other changes to improve the behaviour of is_norm
with relative extensions.
comment:29 follow-up: ↓ 34 Changed 11 years ago by
Here's a new file that addresses Jeroen's "<gen>" issue.
I don't think #9390, which Francis mentions, should stop anyone from reviewing the patch here at #2329. There must be more functionality of sage that assumes is_galois_relative to be correct, this is just one more of them, and Francis says #9390 will be fixed soon anyway. No fix of #9390 will conflict with #2329.
As for "changes to improve behaviour of is_norm". I'm not sure what you're aiming at, but if you want, you can make these changes yourself, in this ticket or a future ticket. That would be a lot more efficient.
So it is still "needs review" at the moment.
comment:30 Changed 11 years ago by
- Reviewers changed from Nick Alexander, David Loeffler to Nick Alexander, David Loeffler, Jeroen Demeyer
- Status changed from needs_review to needs_work
Planning to make a reviewer patch, focusing on the PARI interface.
comment:31 Changed 11 years ago by
- Milestone changed from sage-4.6.1 to sage-4.6.2
Also: it might be better to wait make this ticket depend on #10430 (so we don't need the workaround).
comment:32 Changed 11 years ago by
Macro, I recommend you to take a look at my new PARI spkg at #10430, you can download it from http://sage.math.washington.edu/home/jdemeyer/spkg/pari-2.4.3.alpha.p1.spkg. Could you please check whether this fixes the issues you had? If this works, you should remove the workarounds for these bugs.
comment:33 Changed 11 years ago by
- Description modified (diff)
- Summary changed from add interface to Pari's rnfisnorm to Add interface to PARI's rnfisnorm()
comment:34 in reply to: ↑ 29 Changed 11 years ago by
Replying to mstreng:
... I don't think #9390, which Francis mentions, should stop anyone from reviewing the patch here at #2329. There must be more functionality of sage that assumes is_galois_relative to be correct, this is just one more of them, and Francis says #9390 will be fixed soon anyway.
Actually is_galois_relative
doesn't seem to be used anywhere else.
But anyway I have now added a (very short) patch to #9390.
comment:35 Changed 11 years ago by
- Cc jdemeyer added
comment:36 Changed 11 years ago by
comment:37 in reply to: ↑ 28 ; follow-up: ↓ 38 Changed 11 years ago by
- Status changed from needs_work to needs_review
The patch trac_2329_rnfisnorm4.patch
is a modified version of trac_2329_rnfisnorm3.patch
, designed to be applied after
- #10430's http://sage.math.washington.edu/home/jdemeyer/spkg/pari-2.4.3.alpha.p2.spkg;
- #9390's
trac_9390-3rd_replacement.patch
.
The following changes have been made:
- The workarounds to deal with the pari bugs have been removed.
- The doctests to
sage.rings.number_field.number_field_element.is_norm
involving non-Galois extensions have been changed. The first such example was in fact a Galois extension (isomorphic toCyclotomicField(9)
), which without the patch to #9390 was asserted to be Galois byis_galois_relative
. - A minor change to
pari_rnfnorm_data
innumber_field.py
(replacingdefining_polynomial
byabsolute_polynomial
) and more significant changes tornfisnorm
innumber_field_element.pyx
to allow this function to work with extensions L/K where K itself is a relative extension. These are the changes I was referring to above. Doctests have been added to illustrate this functionality. - Several spaces have been removed in order to comply more closely with the style conventions given in the Developer's Guide, in particular: "Don't use spaces around the '=' sign when used to indicate a keyword argument or a default parameter value".
This all seems to work with 4.6.1.alpha3.
comment:38 in reply to: ↑ 37 Changed 11 years ago by
comment:39 Changed 11 years ago by
- Description modified (diff)
- Keywords pari added
- Reviewers changed from Nick Alexander, David Loeffler, Jeroen Demeyer to Nick Alexander, David Loeffler
- Status changed from needs_review to needs_work
Making some changes...
comment:40 Changed 11 years ago by
- Description modified (diff)
comment:41 Changed 11 years ago by
comment:42 Changed 11 years ago by
- Status changed from needs_work to needs_review
comment:43 Changed 11 years ago by
- Description modified (diff)
comment:44 Changed 11 years ago by
- Milestone changed from sage-4.6.2 to sage-4.7
- Reviewers changed from Nick Alexander, David Loeffler to Nick Alexander, David Loeffler, Jeroen Demeyer
For me, this ticket gets positive review. However, somebody needs to review my reviewer patch.
comment:45 follow-up: ↓ 46 Changed 11 years ago by
This line worries me slightly:
2613 Kbnf = self.pari_bnf(certify=certify).nf_subst("'y")
Is that supposed to be ("y")
or ("'y'")
perhaps?
comment:46 in reply to: ↑ 45 Changed 11 years ago by
Replying to davidloeffler:
Is that supposed to be
("y")
or("'y'")
perhaps?
No, 'y
is correct. I have added some comments to that code in the patch.
Basically, the 'y
syntax is PARI's way of refering to a variable (as opposed to the value of a variable). See the following gp
session:
gp> y = 42 %1 = 42 gp> y %2 = 42 gp> 'y %3 = y gp> subst(x^3, x, y) %4 = 74088 gp> subst(x^3, x, 'y) %5 = y^3
comment:47 Changed 11 years ago by
Let me also clarify that, even though I uploaded trac_2329_rnfisnorm5.patch, I only rebased the existing patch and moved parts of it to #10677. So I believe that I am allowed to review that patch. Only 2329_reviewer.patch still needs review.
comment:48 Changed 11 years ago by
- Status changed from needs_review to positive_review
Thanks for the very clear explanation. The two patches apply and compile fine, and all doctests pass.
comment:49 Changed 11 years ago by
- Status changed from positive_review to needs_work
comment:50 Changed 11 years ago by
- Description modified (diff)
- Status changed from needs_work to needs_review
I have a new patch to change the Selmer group test, since the signs can change randomly. Needs review.
comment:51 Changed 11 years ago by
- Priority changed from major to blocker
comment:52 follow-up: ↓ 53 Changed 11 years ago by
Probably related, I got this on x86 with 4.7.alpha2
sage -t -long -force_lib devel/sage-main/sage/rings/rational.pyx ********************************************************************** File "/storage/strogdon/gentoo/usr/share/sage/devel/sage-main/sage/rings/rational.pyx", line 1222: sage: (1/5).is_norm(QuadraticField(5/4, 'a'), element=True) Expected: (True, -1/5*a + 1/2) Got: (True, 1/5*a - 1/2)
The log is from a friend of mine who has it as well on x86 but it doesn't show up on his amd64 hardware. I cannot test on amd64 or OSX at the present time.
comment:53 in reply to: ↑ 52 Changed 11 years ago by
- Status changed from needs_review to needs_work
- Work issues set to fix on 32-bit
Replying to fbissey:
Probably related, I got this on x86 with 4.7.alpha2
Good to know this. But keep in mind that sage-4.7.alpha2 has not been released (not even sage-4.7.alpha0). In the future it would be better to test released versions with patches applied instead of unreleased versions.
I will test this patch on a 32-bit system and see what needs to be fixed.
comment:54 Changed 11 years ago by
- Description modified (diff)
- Status changed from needs_work to needs_review
comment:55 Changed 11 years ago by
- Work issues fix on 32-bit deleted
comment:56 Changed 11 years ago by
- Reviewers changed from Nick Alexander, David Loeffler, Jeroen Demeyer to Nick Alexander, David Loeffler, Jeroen Demeyer, David Kirkby
I can confirm that the doctest now passes on a 32-bit build of sage-4.7.alpha1 on OpenSolaris 06/2009 (Intel Xeon chip)
sage -t -long -force_lib "devel/sage/sage/rings/number_field/number_field.py" [48.8 s] ---------------------------------------------------------------------- All tests passed! Total time for all tests: 48.8 seconds
Prior to adding the 3 patches to sage-4.7.alpha1, I got.
File "/export/home/drkirkby/sage-4.7.alpha1/devel/sage-main/sage/rings/number_field/number_field.py", line 3035: sage: K.selmer_group([K.ideal(2, -a+1), K.ideal(3, a+1), K.ideal(a)], 3) Expected: [2, a + 1, a] Got: [2, a + 1, -a]
I don't know enough about the maths to understand what the patch does, so whilst it appears to fix the problems I see in sage-4.7.alpha1, I don't feel I should give this a positive review - it needs a mathematician to check it too.
Dave
comment:57 follow-up: ↓ 58 Changed 11 years ago by
David, could you please test both with and without -long
.
comment:58 in reply to: ↑ 57 Changed 11 years ago by
Replying to jdemeyer:
David, could you please test both with and without
-long
.
With the patch applied, it is taking about 22 seconds without -long, and 46 seconds with -long.
If the patch is not applied, it fails with or without -long.
comment:59 Changed 11 years ago by
- Status changed from needs_review to positive_review
it needs a mathematician to check it too.
Looks OK to me.
comment:60 Changed 11 years ago by
- Merged in set to sage-4.7.alpha2
- Resolution set to fixed
- Status changed from positive_review to closed
I have some questions.
There seems to be two things in this patch: changes to pari/gen, and access to stuff to do with norms. Is the latter independent of the former? I'd be a lot happier with the latter if that's true, because I'm not expert in the Pari interface.
Also, what relation does this have to "elements_of_norm"? There needs to be some unification, I think. Also, having is_norm() not always return a boolean is not good, IMO. I say is_norm -> Boolean and element_of_norm raises an exception if is_norm is not True.
I will gladly referee and have cc'ed myself.