Opened 10 years ago
Closed 10 years ago
#7930 closed defect (fixed)
strange bug for elliptic curves over number fields
Reported by: | wuthrich | Owned by: | cremona |
---|---|---|---|
Priority: | major | Milestone: | sage-4.5.2 |
Component: | elliptic curves | Keywords: | |
Cc: | cremona, was, robertwb | Merged in: | sage-4.5.2.alpha0 |
Authors: | Chris Wuthrich | Reviewers: | John Cremona |
Report Upstream: | N/A | Work issues: | |
Branch: | Commit: | ||
Dependencies: | Stopgaps: |
Description
The following code
E = EllipticCurve('99d1') R.<X> = QQ[] K.<t> = NumberField(X^3 + X^2 - 2*X - 1) L.<s> = NumberField(X^3 + X^2 - 36*X - 4) EK = E.base_extend(K) toK = EK.torsion_order() da = EK.local_data() EL = E.base_extend(L) da = EL.local_data()
produces a TypeError
. Having played around with this for hours, I believe that all lines in the above code are necessary to produce the bug. Especially both the torsion and local data computations over another field. I have no idea whatsoever of where to look for the error.
Attachments (1)
Change History (12)
comment:1 Changed 10 years ago by
comment:2 Changed 10 years ago by
- Cc robertwb added
In the middle of Tate's algorithm it needs to know how many roots a cubic mod P has, where P is the prime, and in doing this it constructs the polynomial ring over the residue field on the fly. These poly rings are constructed in such a way that for each field the rings is only constructed once (I think). the errors a re something which goes wrong in that construction.
I am CC'ing robertwb who I hope will be able to help!
comment:3 Changed 10 years ago by
No time to look t it now, but I've added this to my bug hit list for this upcoming week.
comment:4 Changed 10 years ago by
Note that in #7935 we have added a #random to line 1026 in ell_number_field.py, because the output of the minimal_global_model produced two differnt answers. Maybe this is linked to this bug and the #random can be removed once the issue here is fixed.
This is very strange. For that curve E2, I sometimes get
Elliptic Curve defined by y^2 + a*x*y + (a+1)*y = x^3 + (a+1)*x^2 + (12289755603565800754*a-75759141535687466985)*x + (51556320144761417221790307379*a-317814501841918807353201512829) over Number Field in a with defining polynomial x^2 - 38but sometimes I get
Elliptic Curve defined by y^2 + a*x*y + (a+1)*y = x^3 + (a+1)*x^2 + (368258520200522046806318444*a-2270097978636731786720859345)*x + (8456608930173478039472018047583706316424*a-52130038506793883217874390501829588391299) over Number Field in a with defining polynomial x^2 - 38
comment:5 Changed 10 years ago by
Note that E has bad reductions at 3 and 11, which are both inert in both those cubic fields. That means that when we are finding the local data for each field, we construct the residue fields which are of order 3^3
and 11^3
in each case, but the generating polynomial (called the "modulus" in the finite field constructors) will be different, namely X^3 + X^2 - 2*X - 1
and then X^3 + X^2 - 36*X - 4
.
This might help debugging the session will have more than one field of the same order, with different defining polynomials.
comment:6 Changed 10 years ago by
Any news on this ?
comment:7 Changed 10 years ago by
This problem seems to have gone away now -- in 4.4.4 the above script works fine. Can we close the ticket?
comment:8 Changed 10 years ago by
Almost. Here is a patch that adds the example as a doctest (in a _function so as not to appear in the documentation) to make sure that the bug does not appear again in the future. Because we are not certain what caused the bug in the first place.
comment:9 Changed 10 years ago by
- Status changed from new to needs_review
comment:10 Changed 10 years ago by
- Reviewers set to John Cremona
- Status changed from needs_review to positive_review
Looks good & tests fine on 4.4.4.alpha0.
comment:11 Changed 10 years ago by
- Merged in set to sage-4.5.2.alpha0
- Resolution set to fixed
- Status changed from positive_review to closed
More precisely it produces