Opened 10 years ago
Closed 10 years ago
#12404 closed defect (fixed)
is_squarefree() incorrect over imperfect fields
Reported by: | saraedum | Owned by: | malb |
---|---|---|---|
Priority: | minor | Milestone: | sage-5.1 |
Component: | commutative algebra | Keywords: | sd40.5 |
Cc: | sydahmad | Merged in: | sage-5.1.beta3 |
Authors: | Julian Rueth | Reviewers: | Paul Zimmermann, Jeroen Demeyer |
Report Upstream: | N/A | Work issues: | |
Branch: | Commit: | ||
Dependencies: | #9054,#13043, #12988, #10902 | Stopgaps: |
Description (last modified by )
The method is_squarefree()
is incorrect for polynomials over function fields over finite fields:
sage: K.<x> = FunctionField(GF(3)) sage: R.<T> = K[] sage: f=T^3-x sage: f.factor(proof=False) T^3 + 2*x sage: f.is_squarefree() False
Apply:
to the sage library.
Attachments (3)
Change History (27)
comment:1 follow-up: ↓ 2 Changed 10 years ago by
comment:2 in reply to: ↑ 1 Changed 10 years ago by
Replying to saraedum:
True in [d>=2 for (f,d) in f.factor(proof=False)]
This would be "is_not_squarefree()" of course.
comment:3 Changed 10 years ago by
see also #12198.
Paul
comment:4 Changed 10 years ago by
see also #12129.
Paul
comment:5 Changed 10 years ago by
Thanks for pointing these out. Since both are in the multivariate case, I don't think they're related.
comment:6 Changed 10 years ago by
- Dependencies changed from #9054 to #9054, #12404
- Status changed from new to needs_review
The attached patch should fix the problem.
comment:7 Changed 10 years ago by
- Dependencies changed from #9054, #12404 to #9054, #12988
comment:8 Changed 10 years ago by
- Keywords sd40.5 added
comment:9 follow-up: ↓ 10 Changed 10 years ago by
- Reviewers set to Paul Zimmermann
- Status changed from needs_review to needs_work
- Work issues set to coherence with squarefree_decomposition, fix error
the documentation of is_squarefree
says that f
is not square-free if g^2
divides f
where g
is a non-unit. In particular 4*x
is not considered
square free by is_squarefree
, but it is by squarefree_decomposition
:
sage: R.<x> = ZZ[] sage: f = 4*x sage: f.is_squarefree() False sage: f.squarefree_decomposition() (4) * x
Sage should be coherent in that matter. Personally I prefer not to decompose the coefficient content.
Moreover the following produces an error:
sage: R.<x> = ZZ[] sage: f = 2*x^2 sage: f.is_squarefree() ... AttributeError: 'int' object has no attribute 'is_zero'
Paul
comment:10 in reply to: ↑ 9 Changed 10 years ago by
Replying to zimmerma:
the documentation of
is_squarefree
says thatf
is not square-free ifg^2
dividesf
whereg
is a non-unit. In particular4*x
is not considered square free byis_squarefree
, but it is bysquarefree_decomposition
:sage: R.<x> = ZZ[] sage: f = 4*x sage: f.is_squarefree() False sage: f.squarefree_decomposition() (4) * xSage should be coherent in that matter. Personally I prefer not to decompose the coefficient content.
That is true. I also noted this inconsistency. To not break existing code, I'd rather add a warning section in the docstring. Generally I agree that having squarefree_decomposition()
factor the content is not what one wants for most purposes.
Would you be ok with just adding a warning and an example showing this problem?
Moreover the following produces an error:
sage: R.<x> = ZZ[] sage: f = 2*x^2 sage: f.is_squarefree() ... AttributeError: 'int' object has no attribute 'is_zero'
This should not happen when applying the dependency #12988.
comment:11 Changed 10 years ago by
- Status changed from needs_work to needs_info
comment:12 Changed 10 years ago by
I added a patch with such a warning. I still have to check how it renders in the docs.
comment:13 Changed 10 years ago by
- Description modified (diff)
- Status changed from needs_info to needs_review
I made a few docstring changes in the latest patch.
comment:14 Changed 10 years ago by
Btw. I will add the respective warning for squarefree_decomposition()
in #13008.
comment:15 follow-up: ↓ 17 Changed 10 years ago by
Julian, there is a typo in trac_12404_warning.patch
: not to consider to content
should read not to consider the content
.
Would it break a lot of code if is_squarefree
returns False for 4*x
?
Did you try?
Paul
comment:16 Changed 10 years ago by
Thanks, the typo should be fixed now.
No I haven't tried. I was actually thinking about external code using that method. If you insist we can change it. I don't have a very strong opinion about this. I just believe that inconsistency isn't bad as long as it's documented. IMHO breaking the interface is worse than documented inconsistency.
comment:17 in reply to: ↑ 15 Changed 10 years ago by
Replying to zimmerma:
Would it break a lot of code if
is_squarefree
returns False for4*x
?
Did you mean "if is_squarefree
returns True for 4*x
"?
comment:18 Changed 10 years ago by
- Dependencies changed from #9054, #12988 to #9054, #12988, #10902
Changed 10 years ago by
comment:19 Changed 10 years ago by
- Description modified (diff)
- Reviewers changed from Paul Zimmermann to Paul Zimmermann, Jeroen Demeyer
Positive review to the first two patches. Anybody else can review my patch?
comment:20 Changed 10 years ago by
- Status changed from needs_review to positive_review
jdmeyer -- I positively review your patch.
comment:21 Changed 10 years ago by
- Report Upstream changed from Not yet reported upstream; Will do shortly. to N/A
- Work issues coherence with squarefree_decomposition, fix error deleted
comment:22 Changed 10 years ago by
- Milestone set to sage-5.1
comment:23 Changed 10 years ago by
- Dependencies changed from #9054, #12988, #10902 to #9054,#13043, #12988, #10902
comment:24 Changed 10 years ago by
- Merged in set to sage-5.1.beta3
- Resolution set to fixed
- Status changed from positive_review to closed
The method
is_squarefree()
returnsself.derivative().gcd(self).degree() <= 0
. In the example the derivative vanishes which leads to the incorrect behaviour.As a quick workaround one can do: