Opened 8 years ago
Closed 6 years ago
#12095 closed defect (duplicate)
integral_points missing solutions
Reported by: | dsm | Owned by: | cremona |
---|---|---|---|
Priority: | major | Milestone: | sage-duplicate/invalid/wontfix |
Component: | elliptic curves | Keywords: | |
Cc: | Merged in: | ||
Authors: | Reviewers: | Travis Scrimshaw | |
Report Upstream: | N/A | Work issues: | |
Branch: | Commit: | ||
Dependencies: | Stopgaps: |
Description (last modified by )
As reported on sage-support, integral_points can miss solutions:
sage: E=EllipticCurve([0,-82569375]) sage: E.integral_points(verbose=True) Using mw_basis [(450 : 2925 : 1), (900 : 25425 : 1), (1800 : 75825 : 1), (4600/9 : 192725/27 : 1)] e1,e2,e3: -217.725687258292 - 377.111952444214*I -217.725687258292 + 377.111952444214*I 435.451374516585 Minimal eigenvalue of height pairing matrix: 2.03352484556965 x-coords of points on non-compact component with 436 <=x<= 870 [436, 450, 666] starting search of remaining points using coefficient bound 4 x-coords of extra integral points: [436, 450, 666, 900, 1150, 1800, 2619, 26154, 27675] Total number of integral points: 9 [(436 : 559 : 1), (450 : 2925 : 1), (666 : 14589 : 1), (900 : 25425 : 1), (1150 : 37925 : 1), (1800 : 75825 : 1), (2619 : 133722 : 1), (26154 : 4229667 : 1), (27675 : 4603950 : 1)]
but
sage: 20477027135825**2==748476100**3-82569375 True
The (only?) missing solution can be found by increasing the precision in integral_points_with_bounded_mw_coeffs from 100 to 120:
[(436 : 559 : 1), (450 : 2925 : 1), (666 : 14589 : 1), (900 : 25425 : 1), (1150 : 37925 : 1), (1800 : 75825 : 1), (2619 : 133722 : 1), (26154 : 4229667 : 1), (27675 : 4603950 : 1), (748476100 : 20477027135825 : 1)]
but obviously this isn't robust. With a bit of tweaking (and maybe some RealIntervalFieldElements?) we could ensure that we use sufficient precision without hardcoding an arbitrary parameter.
Change History (9)
comment:1 Changed 8 years ago by
- Description modified (diff)
comment:2 Changed 8 years ago by
- Type changed from PLEASE CHANGE to defect
comment:3 Changed 8 years ago by
comment:4 Changed 8 years ago by
Not sure how I missed that-- it shows up in the first page of searches! Maybe I assumed it was only about generalization to other number fields?
Anyway, we can close this as a duplicate. The latest patch there fixes this case, though I still think hardcoding the precision is asking for trouble.
comment:5 Changed 8 years ago by
- Milestone changed from sage-4.8 to sage-duplicate/invalid/wontfix
comment:6 Changed 8 years ago by
I marked this as a duplicate and put in a cross-reference at #10973.
I agree strongly with your comment about hard-coding precision in that function, for which I take 100% of the blame.
comment:7 Changed 6 years ago by
- Status changed from new to needs_review
comment:8 Changed 6 years ago by
- Reviewers set to Travis Scrimshaw
- Status changed from needs_review to positive_review
comment:9 Changed 6 years ago by
- Resolution set to duplicate
- Status changed from positive_review to closed
Please see #10973: I don't think this needs a separate ticket. But it is a very useful observation to make. There are still issues at #10973.