Opened 7 years ago
Closed 3 years ago
#16613 closed defect (fixed)
fix content of polynomials
Reported by:  vdelecroix  Owned by:  

Priority:  major  Milestone:  sage8.1 
Component:  commutative algebra  Keywords:  polynomial, content 
Cc:  mkosters, davidloeffler  Merged in:  
Authors:  Bruno Grenet  Reviewers:  Julian Rüth 
Report Upstream:  N/A  Work issues:  followup ticket mentioned in source code, update ticket summary 
Branch:  017adb6 (Commits)  Commit:  017adb67f3a274526c94b79d3d8683723dc14e80 
Dependencies:  Stopgaps: 
Description (last modified by )
There is an inconsistency between several implementations of methods content
for polynomials which either return the gcd of the coefficients or the ideal generated by the coefficients.
To remove the inconsistency, we implement two distinct methods:
content
returns the gcd of the coefficients;content_ideal
returns the ideal generated by the coefficients.
In a period of deprecation, for (most) univariate polynomial rings, content
is a deprecated alias for content_ideal
. In the future, content
will be defined everywhere as described above.
Change History (37)
comment:1 Changed 6 years ago by
 Milestone changed from sage6.3 to sage6.4
comment:2 Changed 5 years ago by
 Cc mkosters davidloeffler added
 Status changed from new to needs_info
comment:3 Changed 5 years ago by
Addendum: One could also let the possibility of having the ideal, with one of the following two propositions. I am not sure this is useful.
 Add a keyword
ideal
so that an ideal is returned ifideal
is set toTrue
(defautFalse
).  Create a new method
content_ideal
orideal_content
for today's behavior of the generic implementation.
comment:4 followup: ↓ 5 Changed 5 years ago by
I'm okay with having a method content_ideal
for the generic behavior. But what is supposed to be returned by content
when the content ideal is not principal? This is certainly likely to happen if the base ring is the ring of integers in a number field. Perhaps it is best if content
is only implemented in those cases where it has a sensible definition at the level of elements.
comment:5 in reply to: ↑ 4 Changed 5 years ago by
Replying to kedlaya:
I'm okay with having a method
content_ideal
for the generic behavior. But what is supposed to be returned bycontent
when the content ideal is not principal? This is certainly likely to happen if the base ring is the ring of integers in a number field. Perhaps it is best ifcontent
is only implemented in those cases where it has a sensible definition at the level of elements.
Of course, this is a difficulty... Well, I propose then to implement content
for polynomials over principal ideal domains (so that it returns a element of the domain, not an ideal), and content_ideal
more generally. And of course to add a deprecation warning for content
over non principal ideal domains. We may also add a warning (no deprecation) for the new behavior of content
in the generic implementation.
I'll work on a proposal and let you tell me what you think about it.
comment:6 followup: ↓ 7 Changed 5 years ago by
I am trying to provide some code for this. I'd like opinions on two points:
 To avoid future inconsistencies, I plan to implement not only
content
andcontent_ideal
, but also the relatedprimitive_part
andis_primitive
for all polynomial rings with consistent semantics. Do you think it is appropriate to do so in this ticket, or do you think that it's better to stick withcontent
andcontent_ideal
only?
 What should it be the semantic for fields?
Remarks for the semantics for fields:
Currently, there is a method is_primitive
which uses three distinct (and documented!) semantics:
 An irreducible polynomial of degree m over F_{p} is primitive if its roots generate F_{pm}^{; }
 A polynomial over a ring is primitive if its coefficients generate the unit ideal;
 Primitivity is undefined for polynomials over an infinite field, that is an exception is raised.
I guess that there should not be any opposition for content_ideal
to return the unit ideal. For content
, I see three possibilities (there may be more):
 Raise an exception;
 Return
1
(or more preciselyself._parent.one()
);  Return
gcd(self.coefficients())
(knowing thatgcd(2/3,4/5)=2/15
with the current semantics forgcd
.
And I would say that in all three cases, primitive_part
should return self
divided by its content, using for content the same semantic as above. Finally, the case of is_primitive
is complicated because of the semantic for finite fields. One possibility could be to find another name for this semantic for finite fields but 1. I guess that "primitive" is really the word used in mathematics for this property, and 2. this may break some existing code (and given the current discussions on sagedevel, I doubt the community would favor this!).
P.S.: I really would like that we reach some consensus on the semantics before including any code in order to limit as much as possible future backward incompatible changes!
comment:7 in reply to: ↑ 6 Changed 5 years ago by
It generally is best for the development workflow if individual tickets are as limited as possible. So I would vote in favor of creating a second ticket to deal with is_primitive
and primitive_part
after the status of content
is resolved.
Regarding primitive
, both uses seem to be quite entrenched in the mathematical literature, and so I think we are obliged to maintain the dichotomy.
comment:8 Changed 5 years ago by
 Branch set to u/bruno/content
 Commit set to 78d45b9b13fcf242d0f7de248a9891f6a64298a6
 Description modified (diff)
 Keywords polynomial content added
 Status changed from needs_info to needs_review
Based on answers on this ticket and on sagedevel, I've implemented the solution with two methods content
and content_ideal
. Right now, there is now warning nor deprecation. If necessary, I can add a warning for the generic method content
as follows:
from sage.warnings import warn warn("This method now returns the gcd of the coefficients of the input polynomial. Use content_ideal()` to get the ideal generated by the coefficients.")
comment:9 followup: ↓ 11 Changed 4 years ago by
The changes look fine to me.
It is my understanding that we should deprecate, i.e., content()
should say content() is not going to return an ideal but an element in the future. Use content_ideal() instead.
What do you think?
comment:10 Changed 4 years ago by
 Reviewers set to Julian Rüth
 Status changed from needs_review to needs_info
comment:11 in reply to: ↑ 9 ; followup: ↓ 12 Changed 4 years ago by
Replying to saraedum:
The changes look fine to me. It is my understanding that we should deprecate, i.e.,
content()
should saycontent() is not going to return an ideal but an element in the future. Use content_ideal() instead.
Do you mean that right now, content()
should still return an ideal but be deprecated, and that it should only later (in one year from now) return the gcd of the coefficients? What about changing the behavior right now, but with a warning? Another idea (to combine both in some sense) is the following:
 Make
content()
still return an ideal, with deprecation;  Add right now a flag
ideal=True
to the method, so that people can already use the "new behavior" in their codes, usingcontent(ideal=False)
;  In one year: remove deprecation and make the default value of
ideal
toFalse
, or even remove completely theideal=...
parameter, or make it useless.
What do you think?
comment:12 in reply to: ↑ 11 Changed 4 years ago by
Replying to bruno:
Replying to saraedum:
The changes look fine to me. It is my understanding that we should deprecate, i.e.,
content()
should saycontent() is not going to return an ideal but an element in the future. Use content_ideal() instead.
Do you mean that right now,
content()
should still return an ideal but be deprecated, and that it should only later (in one year from now) return the gcd of the coefficients?
Yes.
What about changing the behavior right now, but with a warning?
That would certainly break existing code. It points you to the place where you have to fix it so it would be fine with me. I am not sure what our policy is here.
Another idea (to combine both in some sense) is the following:
 Make
content()
still return an ideal, with deprecation; Add right now a flag
ideal=True
to the method, so that people can already use the "new behavior" in their codes, usingcontent(ideal=False)
; In one year: remove deprecation and make the default value of
ideal
toFalse
, or even remove completely theideal=...
parameter, or make it useless.
If we go for this we should remove that parameter completely after some time. I am also fine with this approach but I find it a bit weird to do deprecation by introducing something deprecated (the ideal
parameter).
What do you think?
I think the first option (do not change content()
at first but print a warning) is the cleanest option.
comment:13 Changed 4 years ago by
 Commit changed from 78d45b9b13fcf242d0f7de248a9891f6a64298a6 to 57077e53525ae33a8b10c77df307b89709f42c43
Branch pushed to git repo; I updated commit sha1. New commits:
57077e5  16613: Deprecate content

comment:14 Changed 4 years ago by
 Commit changed from 57077e53525ae33a8b10c77df307b89709f42c43 to 618a016fdda4530d9cada1c1b3b340851d78a99a
Branch pushed to git repo; I updated commit sha1. New commits:
618a016  16613: doctest fix

comment:15 Changed 4 years ago by
 Status changed from needs_info to needs_review
Ok, I've deprecated content
when it existed and returned an ideal, and we'll perform the complete switch later on.
comment:16 Changed 4 years ago by
 Status changed from needs_review to needs_info
Does SEEALSO: :meth:content
still make sense?
comment:17 Changed 4 years ago by
 Commit changed from 618a016fdda4530d9cada1c1b3b340851d78a99a to 78415d78151d2b7632c98cd41b681c4501275faa
comment:18 Changed 4 years ago by
 Status changed from needs_info to needs_review
Removed irrelevant SEEALSO.
comment:19 Changed 4 years ago by
 Milestone changed from sage6.4 to sage7.6
My 2 cents: I don't like the deprecation of content
then only to replace it by something that has different functionality. I am close to considering this a bug, and as such, we do not need to deprecate. So the idea of using a temporary flag, which we then deprecate after we remove the ability to return an ideal from content
, is the best way forward IMO. It's two steps, but it is the most consistent with Sage's policies.
comment:20 Changed 4 years ago by
 Commit changed from 78415d78151d2b7632c98cd41b681c4501275faa to 00127fdfb079b324f140cf01c354914acf98b865
comment:21 Changed 4 years ago by
I've merged develop
(8.0.beta11) into this ticket's branch since it did not apply.
Now I agree with Travis that the deprecation is a bit a pity. It will force users to make two changes instead of one when they need the content (as a value rather than an ideal): Now they write p.content().gen()
, they need to change to p.content_ideal().gen()
due to the current deprecation warning, and in some months (years?) they'll finally be able to write p.content()
to avoid the useless construction of the ideal. I'm strongly in favor of having a way for users to directly use the new semantic.
As such, I would go for making content
return a value without any deprecation. If the there's enough time left, this backward incompatible change may occur with the new release 8.0.
comment:23 Changed 3 years ago by
 Commit changed from 00127fdfb079b324f140cf01c354914acf98b865 to 61d122a792a764472bbbc52b8562b4a616a51d8a
Branch pushed to git repo; I updated commit sha1. New commits:
61d122a  Merge branch 'develop' into 16613_content

comment:24 Changed 3 years ago by
Applies again!
comment:25 Changed 3 years ago by
 Status changed from needs_work to needs_review
comment:26 Changed 3 years ago by
failing doctests, see patchbot reports
comment:27 Changed 3 years ago by
 Commit changed from 61d122a792a764472bbbc52b8562b4a616a51d8a to 953e5aea98a4a0f5f6095b192607307669dfa8b1
Branch pushed to git repo; I updated commit sha1. New commits:
953e5ae  16613: Fix doctest due to bad merge

comment:28 Changed 3 years ago by
Should be OK now (I'll watch the patchbot logs), I made a mistake during the merge.
comment:29 Changed 3 years ago by
 Commit changed from 953e5aea98a4a0f5f6095b192607307669dfa8b1 to 84fbcf39cfab762038d64105408f863e7e1efd2b
Branch pushed to git repo; I updated commit sha1. New commits:
84fbcf3  19171: Doctest fix after merge

comment:30 followup: ↓ 34 Changed 3 years ago by
 Status changed from needs_review to needs_info
 Work issues set to followup ticket mentioned in source code
The implementation looks good to me.
What is the deprecation strategy now? Do we want this to go in and have a followup ticket (to be merged in a year) to have content return an element? If so, there should be such a ticket and a comment in the code.
Or do we want to change this without deprecation? We missed the 8.0 window, so I am slightly in favor of the two step change.
comment:31 Changed 3 years ago by
 Work issues changed from followup ticket mentioned in source code to followup ticket mentioned in source code, update ticket summary
comment:32 Changed 3 years ago by
In the docstring of content_ideal
, it would be nice to include a hint such as:
When the base ring is a gcd ring, the content as a ring element is the generator of the content ideal:
f.content_ideal().gen()
with an example.
comment:33 Changed 3 years ago by
 Commit changed from 84fbcf39cfab762038d64105408f863e7e1efd2b to 017adb67f3a274526c94b79d3d8683723dc14e80
comment:34 in reply to: ↑ 30 Changed 3 years ago by
 Description modified (diff)
 Milestone changed from sage7.6 to sage8.1
 Status changed from needs_info to needs_review
Replying to saraedum:
Or do we want to change this without deprecation? We missed the 8.0 window, so I am slightly in favor of the two step change.
I was in favor of a direct change with the argument of "the sooner the better" but the result was endless discussions and the ticket waits for 3 years! So in order for this ridiculously simple issue to be fixed at some point, let's say we implement the two phase change.
Replying to slelievre:
Agree, done! Note that I put this comment only for univariate polynomial rings since in the multivariate case, a method content
exists (and is linked).
Now needs review (again!).
comment:35 Changed 3 years ago by
I think we should just change the behavior (hopefully in an early beta) and put a .. NOTE::
if you do not want to go with the suggestion in comment:19.
comment:36 Changed 3 years ago by
 Status changed from needs_review to positive_review
comment:37 Changed 3 years ago by
 Branch changed from u/bruno/content to 017adb67f3a274526c94b79d3d8683723dc14e80
 Resolution set to fixed
 Status changed from positive_review to closed
The content of a polynomial is sometimes defined as the gcd of its coefficients, and sometimes as the ideal generated by the coefficients. In SageMath, we have inconsistencies between polynomial rings:
content
returns the gcd of the coefficients.rings.polynomial.polynomial_element.Polynomial
) returns an ideal. This is means that for polynomials over weird rings, and for all sparsely represented univariate polynomials,content
returns an ideal.I propose to make all the implementations return a element of the base ring rather than an ideal.
Rationale:
P.S.: I cc the author and reviewer of #12218 in which the generic
content
was implemented.