Opened 6 years ago
Closed 5 years ago
#17425 closed enhancement (fixed)
Rational isometry test for quadratic forms over number fields
Reported by:  annahaensch  Owned by:  

Priority:  major  Milestone:  sage6.9 
Component:  quadratic forms  Keywords:  
Cc:  Merged in:  
Authors:  Anna Haensch  Reviewers:  Vincent Delecroix 
Report Upstream:  N/A  Work issues:  
Branch:  729976e (Commits)  Commit:  729976e5b068df72836f6700b71e8fdddc524949 
Dependencies:  Stopgaps: 
Description
This introduces a new function is_rationally_isometric which tests for isometry between two regular rational forms over some number field.
Change History (49)
comment:1 Changed 6 years ago by
 Branch set to u/annahaensch/ticket/17425
 Created changed from 12/01/14 13:51:11 to 12/01/14 13:51:11
 Modified changed from 12/01/14 13:51:11 to 12/01/14 13:51:11
comment:2 Changed 6 years ago by
 Commit set to 613901acd98fc0235f871336df3eaed5c6cf5a74
 Status changed from new to needs_review
comment:3 Changed 5 years ago by
 Milestone changed from sage6.5 to sage6.9
 Reviewers set to Vincent Delecroix
 Status changed from needs_review to needs_work
Hello,
I am sorry that this ticket waited that long before a review.
 There are some (minor) problems with typography:
 indentation is not correct. It should be
def my_function(a, b): """ The text here ... """
and notdef my_function(a, b): """ The text here ... """
 try to keep a space around the
==
and!=
signs. In other wordsa == b
instead ofa==b
. Similarly, add space after a comma asfunction(a, b)
and notfunction(a,b)
. This is just to clarify the reading. It is not mandatory.
 indentation is not correct. It should be
 There is a method
.diagonal()
to extract the diagonal of a matrixsage: K.<a> = NumberField(x^23) sage: V = QuadraticForm(K,4,[1,0,0,0,2*a,0,0,a,0,2]) sage: m = V.Gram_matrix_rational() sage: m.diagonal() [1, 2*a, a, 2]
would be better than using themap(lambda x: M.Gram_matrix_rational()[x][x], ...)
 Instead of
if self.base_ring()==QQ: return self.signature() == other.signature(): Rat_Isom_flag = False
you can doif self.base_ring() == QQ: return self.signature() == other.signature()
And more generally you do not need to carry over this variableRat_Isom_flag
, just write somereturn
in the conditional statements.
 You can simplify the following
for i in range(len(K.real_embeddings())): Mentries_emb = map(lambda(x):K.real_embeddings()[i](x),Mentries) Nentries_emb = map(lambda(x):K.real_embeddings()[i](x),Nentries) Mpos=0 for i in range(self.dim()): if Mentries_emb[i]>=0: Mpos += 1 ...
intofor emb in K.real_embeddings(): Mpos = 0 for x in Mentries: Mpos += emb(x) >= 0 ...
I used two simplifications here you can iterate over a list elements
 adding a boolean to an integer is equivalent to adding
0
or1
depending on the truth value
Vincent
comment:4 Changed 5 years ago by
 Commit changed from 613901acd98fc0235f871336df3eaed5c6cf5a74 to f7d2f4f2e520952a936d04eebcd9886881153f5b
Branch pushed to git repo; I updated commit sha1. New commits:
f7d2f4f  Incorporated changes 1,2, and 4 from reviewer comments.

comment:5 Changed 5 years ago by
 Status changed from needs_work to needs_review
Thank you kindly for the review, Vincent. I implemented all of your changes with the exception of item 3 (that one ended up causing more difficulty than simplicity). Things should still run as desired.
Anna
comment:6 Changed 5 years ago by
Hi Anna,
You made a small typo
if self.base_ring() == QQ: return self.signature() == other.signature(): Rat_Isom_flag = False
You need to replace the return
with if
!
comment:7 Changed 5 years ago by
 Commit changed from f7d2f4f2e520952a936d04eebcd9886881153f5b to 8972c8097f74e9bd8e393a839b7ff9e250476af7
Branch pushed to git repo; I updated commit sha1. New commits:
8972c80  fixed two small typos

comment:8 Changed 5 years ago by
Thanks, Vincent. I fixed that, and added some blank space around another instance of '!='
comment:9 Changed 5 years ago by
 Status changed from needs_review to needs_work
With the current code there is something wrong going on. If the dimensions are different then Rat_Isom_flag
is set to False
. This is fine. But then it will try to multiply the Gram determinant (for nothing since we already knew that they were not equivalent).
Similarly, in this loop
for p in L: if self.hasse_invariant(p) != other.hasse_invariant(p): Rat_Isom_flag = False
if you found out that something is wrong during the first pass you will have to wait!
This is why I suggested to modify the code to
if bad behavior 1: return False if bad behavior 2: return False for i in some test case: if bad behavior 3: return False return True
comment:10 Changed 5 years ago by
 Commit changed from 8972c8097f74e9bd8e393a839b7ff9e250476af7 to 91c47046f8c18487b8e76469ece0618b868df1ef
Branch pushed to git repo; I updated commit sha1. New commits:
91c4704  Removed isom_flag from code

comment:11 Changed 5 years ago by
 Status changed from needs_work to needs_review
Ah, I understand. I changed that throughout, and also caught one error with the signature test over QQ.
comment:12 followups: ↓ 15 ↓ 46 Changed 5 years ago by
Instead of doing L=L1+L2
you can do L=set().union(L1,L2)
. That way you will remove duplicates as in
sage: V = DiagonalQuadraticForm(K,[1,a,2*a]) sage: W = DiagonalQuadraticForm(K,[1,a,2*a]) sage: L1 = V.Gram_det().support() sage: L1 [Fractional ideal (a + 1), Fractional ideal (a)] sage: L 2 =W.Gram_det().support() sage: L2 [Fractional ideal (a + 1), Fractional ideal (a)] sage: L1+L2 [Fractional ideal (a + 1), Fractional ideal (a), Fractional ideal (a + 1), Fractional ideal (a)] sage: set().union(L1,L2) {Fractional ideal (a + 1), Fractional ideal (a)}
And there is no need to declare L
(but you might find it simpler) by doing
for p in set().union(L1,L2): ...
M
and N
are computed early but not used early. It would make sense to move there declarations since if the dimension differ (the first test) then there is no need to compute them. You can move them after the else
in the case that the base ring is not QQ
. You can also move the declaration of L1
and L2
.
Could you add some tests for all the cases (starting from the Gram determinant being 0)?
More interesting: is there a way to return the transformation in case they are equivalent?
comment:13 Changed 5 years ago by
 Commit changed from 91c47046f8c18487b8e76469ece0618b868df1ef to 8b2f1aa042fae06af40366d50d86b02e17d6e66e
Branch pushed to git repo; I updated commit sha1. New commits:
8b2f1aa  Minor changes in syntax

comment:14 Changed 5 years ago by
There is a way to return the transformation, in fact I have a student writing that as a separate function right now. I think it's best to keep it separate from this function, since in principle, his functions work for integral lattices as well, whereas this one is only applicable to fields. Nevertheless, I suppose I should open a trac ticket for that...
comment:15 in reply to: ↑ 12 Changed 5 years ago by
Replying to vdelecroix:
Could you add some tests for all the cases (starting from the Gram determinant being 0)?
You forgot this one. I would be happy with more specifications and degenerate tests. For example, you can copy paste the following
TESTS: The diagonal form must have the same base ring otherwise a `TypeError` is raised:: sage: K1.<a> = QuadraticField(5) sage: K2.<b> = QuadraticField(7) sage: V = DiagonalQuadraticForm(K1,[1,a]) sage: W = DiagonalQuadraticForm(K2,[1,b]) sage: V.is_rationally_isometric(W) Traceback (most recent call last): ... TypeError: forms must have the same base ring.
Beyond that the code looks good to me. I am compiling the documentation right now to see how it looks.
Replying to annahaensch:
There is a way to return the transformation, in fact I have a student writing that as a separate function right now. I think it's best to keep it separate from this function, since in principle, his functions work for integral lattices as well, whereas this one is only applicable to fields. Nevertheless, I suppose I should open a trac ticket for that...
Nice! He or she might open the ticket. That is part of the learning curve ;)
comment:16 followup: ↓ 17 Changed 5 years ago by
Too true, I'll have him start a ticket. I'm actually having difficult getting my local copy of sage to recognize the function is_rationally_isometric. I am on the branch 17425 and ran ./sage b but it still says " 'Quadratic Form' has no attribute 'is_rationally_isometric', what step am I missing?
comment:17 in reply to: ↑ 16 Changed 5 years ago by
Replying to annahaensch:
Too true, I'll have him start a ticket. I'm actually having difficult getting my local copy of sage to recognize the function is_rationally_isometric. I am on the branch 17425 and ran ./sage b but it still says " 'Quadratic Form' has no attribute 'is_rationally_isometric', what step am I missing?
What do you see if you do on the command line inside the sage repository
$ git status sb $ git log oneline 10
(it is to get the name of the branch your on and the last 10 commits)
comment:18 Changed 5 years ago by
This:
haenschach:sage annahaensch$ git status sb ## ticket/17425...trac/u/annahaensch/ticket/17425 M src/sage/quadratic_forms/quadratic_form__equivalence_testing.py ?? build/make/ ?? src/sage/libs/pari/auto_gen.pxi ?? src/sage/libs/pari/auto_instance.pxi
And this:
haenschach:sage annahaensch$ git log oneline 10 8b2f1aa Minor changes in syntax 91c4704 Removed isom_flag from code 8972c80 fixed two small typos f7d2f4f Incorporated changes 1,2, and 4 from reviewer comments. 613901a Removed trailing whitespace fa4812b Updated imports in quadratic_form.py 6e5a563 Adjusted preamble in quadratic_forms__equivalence_testing.py 57f6b6a Added is_rationally_isometric to library 76b4ac4 Updated Sage version to 6.4.1 f045b63 Trac #15316: Make gf2x respect SAGE_FAT_BINARY and use libdir
comment:19 Changed 5 years ago by
It looks strange that you do not have access to the method! Note that you have pending modifications on the file quadratic_form__equivalence_testing.py
as shown by git status
(the M
on the left). There might be something wrong with them. You can temporarily disable these with $ git stash
. And then retry sage b
. You will be able to recover them later on by doing $ git stash pop
.
sided note: your sage version is very old (but this is of no importance for this ticket since your modifications apply cleanly on the last version).
comment:20 Changed 5 years ago by
The pending modification is the TEST that I pasted from your message above. I'm definitely running Sage 6.8, and that sage path that I reference above is actually the clone that I build from git, so it should be very new.
It's not technically the correct way to do things, but if you just give me the text from the test that you want (like you did above), I can just paste them into my patch and then commit and push that. Otherwise, well, I'm not really sure how to do it.
comment:21 followup: ↓ 23 Changed 5 years ago by
Your ticket is based over sage6.4.1! What tells you sage version
? You have only one version of sage installed?
comment:22 Changed 5 years ago by
I guess that what is wrong is that the source code that you currently seeing and editing has nothing to do with your binary that you are executing. sage b
is not enough to rebuild sage from different version (here 6.8 agains 6.4.1).
The safest way to proceed would be to merge your changes with the last version of sage. First discard your changes with $ git stash
. Then, do you know the name of the branch with the last version? Otherwise you should be able to guess it from $ git branch
(should be either develop
or master
and you can check with git log MAIN_BRANCH
that the last commit says something like update to version 6.8
). Then just do
$ git merge MAIN_BRANCH
That will fusion your modifications with sage6.8. Then you should be able to run sage b
and get it work.
comment:23 in reply to: ↑ 21 Changed 5 years ago by
Replying to vdelecroix:
Your ticket is based over sage6.4.1! What tells you
sage version
? You have only one version of sage installed?
I have 6.8 and 6.4 installed, but I am doing everything through the clone that I building off of git (that is sage 6.8). I am working on a different computer now than I was 8 months ago when I first wrote the patch, so I wasn't even working with my original code.
I currently have two branches here: master and ticket/17425
comment:24 Changed 5 years ago by
You should be on ticket/17425
(as was said before by $ git status sb
). Check the version in master with $ git log master 1
(the 1
is to get the last commit only) and do
git merge master
comment:25 Changed 5 years ago by
I am on ticket/17425. When I run git log master 1
it returns (as expected) "Updated Sage version 6.8"
Now I tried to run git merge master
and it says
fatal: You have no concluded your merge (MERGE_HEAD exists). Please commit your changes before you can merge.
I think this is because I tried to merge earlier and got stuck in a vi window and couldn't get out...oops. What do I do?
Thanks for your help!
comment:26 Changed 5 years ago by
Do
git merge continue
In the vim window there should be an automatic message already written. Then just enter :wq
(w
for write and q
for quit). For later on you can configure the editor you wish, see this page.
comment:27 Changed 5 years ago by
You might need to commit your changes (sorry). Do $ git stash
to discard them. That would be simpler. And then do $ git merge continue
.
comment:28 Changed 5 years ago by
The other option is to cancel the merge that you interrupted with $ git merge abort
. And then you can start again a fresh merge.
comment:29 followup: ↓ 30 Changed 5 years ago by
Ok, now I've added the tests, merged with the main, staged the commits. But I'm getting an error when I try to push to trac. I've uploaded by ssh key (did it again just now, to be sure), but I'm getting an error
Push to remote branch? [Yes/no] Yes GitError: git exited with a nonzero exit code (128). This happened while executing "git push ssh://git@trac.sagemath.org:2222/sage.git ticket/17425:u/annahaensch/ticket/17425". git printed nothing to STDOUT. git printed the following to STDERR: ssh: connect to host trac.sagemath.org port 2222: Connection refused fatal: Could not read from remote repository. Please make sure you have the correct access rights and the repository exists.
Any ideas?
comment:30 in reply to: ↑ 29 Changed 5 years ago by
Hi,
Replying to annahaensch:
Ok, now I've added the tests, merged with the main, staged the commits.
Cool.
But I'm getting an error when I try to push to trac. I've uploaded by ssh key (did it again just now, to be sure), but I'm getting an error ...
Why did you upload again the ssh key? Did you have some trouble before that?
In order to test your access to the git server you can run $ ssh git@trac.sagemath.org info
. If it tells you who you are this is fine. Otherwise, there is an identification problem.
comment:31 Changed 5 years ago by
 Commit changed from 8b2f1aa042fae06af40366d50d86b02e17d6e66e to 17c277600a085dcc04437ec614cfe60aaa4e5fff
comment:32 Changed 5 years ago by
Nevermind, I sorted it out, I guess I just needed to reinstall the git trac command. But the most recent commits should have everything. I added several tests, but let me know if this is what you had in mind! Anna
comment:33 Changed 5 years ago by
Argh! You reintroduced a lot of trailing whitespaces.
Perhaps in the TESTS
section, you can add
sage: K.<a> = NumberField(x^5  x + 2, 'a') sage: Q = QuadraticForm(K,3,[a,1,0,a**2,a**3,1]) sage: m = Q.matrix() sage: for _ in range(5): ....: t = random_matrix(ZZ,3,algorithm='unimodular') ....: m2 = t*m*t.transpose() ....: Q2 = QuadraticForm(K, 3, [m2[i,j] / (2 if i==j else 1) ....: for i in range(3) for j in range(i,3)]) ....: print Q.is_rationally_isometric(Q2) True True True True True
I had some trouble going from the matrix to the quadratic form. There might be a simpler way.
EDIT: there was a type m[i,j]
had to be replaced with m2[i,j]
... otherwise the equivalence tested would have been between a quadratic form and itself!
comment:34 Changed 5 years ago by
 Commit changed from 17c277600a085dcc04437ec614cfe60aaa4e5fff to 31a3d9331afff8d167d3e084060b53af6e9f67be
comment:35 Changed 5 years ago by
 Commit changed from 31a3d9331afff8d167d3e084060b53af6e9f67be to 324f92d2fdb841ff239181e453a6896a646590a5
Branch pushed to git repo; I updated commit sha1. New commits:
324f92d  Added test with matrix

comment:36 Changed 5 years ago by
 Commit changed from 324f92d2fdb841ff239181e453a6896a646590a5 to 862b8a0a6cd95938361ee2941f1833394df63de3
Branch pushed to git repo; I updated commit sha1. New commits:
862b8a0  Fix typo in TEST

comment:37 Changed 5 years ago by
Ack! That trailing white space, I always forget. I should be gone. I added your test and then fixed the typo in a second commit.
comment:38 Changed 5 years ago by
There should be no need to import hasse_invariant
. Could you remove the line
from quadratic_form__local_field_invariants import hasse_invariant
that you added?
comment:39 Changed 5 years ago by
 Commit changed from 862b8a0a6cd95938361ee2941f1833394df63de3 to 26d73c90698392a8be39971b85b25b62c8866749
Branch pushed to git repo; I updated commit sha1. New commits:
26d73c9  Remove unnecessary hasse_invariant import

comment:40 Changed 5 years ago by
 Status changed from needs_review to needs_work
I got a doctest failure
sage: K.<a>=QuadraticField(3) sage: V=DiagonalQuadraticForm(K,[1,2]) sage: W=DiagonalQuadraticForm(K,[1,0]) sage: V.is_rationally_isometric(W) ... NotImplementedError: This only tests regular forms
The output should be
Traceback (most recent call last): ... NotImplementedError: This only tests regular forms
You can check that the tests pass with sage t NAME_OF_THE_FILE
.
comment:41 Changed 5 years ago by
 Commit changed from 26d73c90698392a8be39971b85b25b62c8866749 to 0e0d462674ff9153cae6beaeca689232e11c8560
Branch pushed to git repo; I updated commit sha1. New commits:
0e0d462  Edited doctest

comment:42 Changed 5 years ago by
Did you run the test on the file with sage t
? I am pretty sure that the colon is needed at the end of the first line.
comment:43 Changed 5 years ago by
 Commit changed from 0e0d462674ff9153cae6beaeca689232e11c8560 to 729976e5b068df72836f6700b71e8fdddc524949
Branch pushed to git repo; I updated commit sha1. New commits:
729976e  Added colon in test

comment:44 Changed 5 years ago by
So right, that should do it.
comment:45 followup: ↓ 47 Changed 5 years ago by
 Status changed from needs_work to positive_review
All right. The test pass for me! Let this ticket go.
comment:46 in reply to: ↑ 12 ; followup: ↓ 48 Changed 5 years ago by
Replying to vdelecroix:
More interesting: is there a way to return the transformation in case they are equivalent?
I'm also (weakly) interested in that. It's certainly something which is on my Sage TODO list (even though I don't yet have a ticket for it). I currently have several quadratic_form tickets in "needs_review" right now, and the conflicts would be annoying.
comment:47 in reply to: ↑ 45 Changed 5 years ago by
Replying to vdelecroix:
All right. The test pass for me! Let this ticket go.
Vincent, thanks so much for your review and assistance with this! Anna
comment:48 in reply to: ↑ 46 Changed 5 years ago by
Replying to jdemeyer:
Replying to vdelecroix:
More interesting: is there a way to return the transformation in case they are equivalent?
I'm also (weakly) interested in that. It's certainly something which is on my Sage TODO list (even though I don't yet have a ticket for it). I currently have several quadratic_form tickets in "needs_review" right now, and the conflicts would be annoying.
Good news, you can take it off your TODO list, because I actually have a student working on exactly that right now. His ticket should be up soon.
comment:49 Changed 5 years ago by
 Branch changed from u/annahaensch/ticket/17425 to 729976e5b068df72836f6700b71e8fdddc524949
 Resolution set to fixed
 Status changed from positive_review to closed
New commits:
Added is_rationally_isometric to library
Adjusted preamble in quadratic_forms__equivalence_testing.py
Updated imports in quadratic_form.py
Removed trailing whitespace