Opened 10 years ago
Closed 7 years ago
#11554 closed defect (fixed)
Fix for denominator_ideal function
Reported by: | bleveque | Owned by: | davidloeffler |
---|---|---|---|
Priority: | minor | Milestone: | sage-duplicate/invalid/wontfix |
Component: | number fields | Keywords: | denominator, ideal, number field |
Cc: | wstein | Merged in: | |
Authors: | Reviewers: | Ben LeVeque, William Stein, Jeroen Demeyer | |
Report Upstream: | N/A | Work issues: | |
Branch: | Commit: | ||
Dependencies: | Stopgaps: |
Description (last modified by )
The denominator_ideal
of 0 should return the ideal (1), but it currently returns a ValueError
.
Attachments (1)
Change History (20)
Changed 10 years ago by
comment:1 Changed 10 years ago by
- Status changed from new to needs_review
comment:2 Changed 10 years ago by
- Description modified (diff)
comment:3 Changed 10 years ago by
- Milestone changed from sage-4.7.2 to sage-duplicate/invalid/wontfix
The problem really is that Sage only supports the zero ideal and fractional ideals of number fields. Sage simply does not know about the ideal (1)
in a number field.
So proposing to close this as "wontfix".
comment:4 Changed 10 years ago by
- Status changed from needs_review to positive_review
I'm with Jeroen on this. I think ValueError? is the right behaviour here. Positive review to the proposal to close as wontfix.
comment:5 Changed 10 years ago by
- Resolution set to wontfix
- Reviewers set to David Loeffler
- Status changed from positive_review to closed
comment:6 follow-up: ↓ 11 Changed 10 years ago by
- Resolution wontfix deleted
- Status changed from closed to new
Huh? Obviously, the denominator ideal of 0 should be the unit ideal, just at the denominator if 0 is 1:
sage: K.<a> = NumberField(x^2 + 1) sage: K(0).denominator() 1
The statement "Sage only supports the zero ideal and fractional ideals of number fields. Sage simply does not know about the ideal (1) in a number field." sounds like nonsense to me. The ideal generated by 1 is a perfectly good fractional ideal. That's why people say "the *group* of fractional ideals" -- groups have an identity element.
sage: K.maximal_order().ideal(1) Fractional ideal (1)
comment:7 Changed 10 years ago by
- Status changed from new to needs_review
Also, I give this patch a positive review.
comment:8 Changed 10 years ago by
- Milestone changed from sage-duplicate/invalid/wontfix to sage-4.8
- Status changed from needs_review to positive_review
comment:9 follow-up: ↓ 12 Changed 10 years ago by
- Priority changed from major to minor
Sage simply does not know about the ideal (1) in a number field." sounds like nonsense to me. The ideal generated by 1 is a perfectly good fractional ideal.
What I believe Jeroen meant here is not the OK-submodule OK of K, but the K-submodule K of K -- the unit ideal of K in the purely ring-theoretic sense. This is indeed an object Sage genuinely doesn't know about -- we special-case the zero ideal, but not the whole-of-K ideal.
This is just FYI; I'm not trying to dispute your decision to give the patch a positive review. Frankly I'm not convinced that the denominator of 0 is worth losing much sleep over.
comment:10 Changed 10 years ago by
- Reviewers changed from David Loeffler to William Stein
comment:11 in reply to: ↑ 6 Changed 10 years ago by
Please DO NOT reopen tickets!
If you disagree with me closing the ticket, that's fine, just state it in the comments.
But DO NOT reopen tickets!
You can totally disagree with me about closing a ticket. I am a reasonable person and will very likely listen. But it's very annoying if my idea of which tickets are open/closed does not correspond to reality.
So, DO NOT reopen tickets!
comment:12 in reply to: ↑ 9 Changed 10 years ago by
- Reviewers changed from William Stein to William Stein, Jeroen Demeyer
- Status changed from positive_review to needs_work
Replying to davidloeffler:
What I believe Jeroen meant here is not the OK-submodule OK of K, but the K-submodule K of K -- the unit ideal of K in the purely ring-theoretic sense. This is indeed an object Sage genuinely doesn't know about -- we special-case the zero ideal, but not the whole-of-K ideal.
This is what I meant, yes. But it is indeed mostly matter of definition.
I don't understand why the patch changes the documentation of the function. I think the old documentation is more clear and I think it also justifies better the choice that the numerator of (0) is the fractional ideal (1).
However, if you want to define the denominator_ideal
of zero to be the fractional ideal (1), then certainly the numerator_ideal
of zero should be (0). So this still needs work.
comment:13 Changed 10 years ago by
Hello,
In response to Jeroen's comment, I opened a new ticket -- http://trac.sagemath.org/sage_trac/ticket/12046 -- with a proposed change to the numerator_ideal function. Sorry if it's confusing having two tickets dealing with a similar issue.
-Ben
comment:14 Changed 8 years ago by
- Milestone changed from sage-5.11 to sage-5.12
comment:15 Changed 7 years ago by
- Milestone changed from sage-6.1 to sage-6.2
comment:16 Changed 7 years ago by
- Milestone changed from sage-6.2 to sage-6.3
comment:17 Changed 7 years ago by
- Milestone changed from sage-6.3 to sage-6.4
comment:18 Changed 7 years ago by
- Milestone changed from sage-6.4 to sage-duplicate/invalid/wontfix
- Reviewers changed from William Stein, Jeroen Demeyer to Ben LeVeque, William Stein, Jeroen Demeyer
- Status changed from needs_work to positive_review
Fixed by #12046.
comment:19 Changed 7 years ago by
- Resolution set to fixed
- Status changed from positive_review to closed
fixes denominator_ideal for input 0