#5430 closed defect (fixed)
[with patch, positive review] Coleman integrals of differential forms from different rings
Reported by: | jen | Owned by: | robertwb |
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Priority: | major | Milestone: | sage-4.0.1 |
Component: | algebraic geometry | Keywords: | |
Cc: | robertwb | Merged in: | 4.0.1.alpha0 |
Authors: | Kiran Kedlaya | Reviewers: | Robert Bradshaw |
Report Upstream: | Work issues: | ||
Branch: | Commit: | ||
Dependencies: | Stopgaps: |
Description
The coercion seems to be fine, but the Coleman integral fails:
sage: R.<x> = QQ['x'] sage: H = HyperellipticCurve(x*(x-1)*(x+9)) sage: K = Qp(7,10) sage: HK = H.change_ring(K) sage: import sage.schemes.elliptic_curves.monsky_washnitzer as mw sage: M_frob, forms = mw.matrix_of_frobenius_hyperelliptic(HK) sage: w = HK.invariant_differential() sage: x,y = HK.monsky_washnitzer_gens() sage: f = forms[0] sage: S= HK(9,36) sage: Q = HK.teichmuller(S) sage: P = HK(-1,4) sage: b = x*w*w._coeff.parent()(f) #this is ok sage: HK.coleman_integral(b,P,Q) #this is not
Attachments (3)
Change History (16)
comment:1 follow-up: ↓ 3 Changed 13 years ago by
comment:2 Changed 13 years ago by
- Milestone changed from sage-3.4 to sage-3.4.1
No patch -> better luck in 3.4.1.
Cheers,
Michael
comment:3 in reply to: ↑ 1 Changed 13 years ago by
The question is, should this be an error, or just work?
sage: K = Qp(5, 10) sage: a = K(1/250037); a 3 + 4*5 + 3*5^2 + 3*5^3 + 5^4 + 5^5 + 5^6 + 5^7 + 4*5^8 + 4*5^9 + O(5^10) sage: ZZ(a) 9472973 sage: QQ(a) Traceback (most recent call last): ... ValueError: Rational reconstruction of 9472973 (mod 9765625) does not exist.
It seems like a valid error: 250037 is too large compared to 5^{10. }
comment:4 Changed 13 years ago by
THe question is, should QQ(a) be the same as QQ(ZZ(a)) if rational reconstruction isn't possible? (I'm not convinced either way yet.)
comment:5 Changed 13 years ago by
I'd say (and I think Robert agrees) that the correct way to fix the original problem is to do all the arithmetic for Coleman integration in the p-adics, eliminating the casting to/from the rationals altogether. That was a hack from back when p-adic arithmetic was unusably slow.
If there is an issue with rational reconstruction, I'd say make that a separate ticket.
Changed 13 years ago by
Changed 13 years ago by
comment:6 Changed 13 years ago by
See attached patches. The first one eliminates all casting to/from QQ (I think). The second one adds a doctest to confirm that the above example now works:
sage: R.<x> = QQ['x'] sage: H = HyperellipticCurve(x*(x-1)*(x+9)) sage: K = Qp(7,10) sage: HK = H.change_ring(K) sage: import sage.schemes.elliptic_curves.monsky_washnitzer as mw sage: M_frob, forms = mw.matrix_of_frobenius_hyperelliptic(HK) sage: w = HK.invariant_differential() sage: x,y = HK.monsky_washnitzer_gens() sage: f = forms[0] sage: S= HK(9,36) sage: Q = HK.teichmuller(S) sage: P = HK(-1,4) sage: b = x*w*w._coeff.parent()(f) sage: HK.coleman_integral(b,P,Q) 7 + 7^2 + 4*7^3 + 5*7^4 + 3*7^5 + 7^6 + 5*7^7 + 3*7^8 + 4*7^9 + 4*7^10 + O(7^11)
comment:7 Changed 13 years ago by
- Summary changed from Coleman integrals of differential forms from different rings to [with patch, needs review] Coleman integrals of differential forms from different rings
comment:8 Changed 13 years ago by
- Cc robertwb added
Changed 13 years ago by
comment:9 Changed 13 years ago by
Rebased against the revised patch to #5948. You may ignore the previous two patches.
comment:10 Changed 13 years ago by
- Summary changed from [with patch, needs review] Coleman integrals of differential forms from different rings to [with patch, positive review] Coleman integrals of differential forms from different rings
It's nice to have decent enough p-adics to use them!
comment:11 Changed 13 years ago by
So it looks like I didn't manage to get out all of the casting; there is still some in matrix_of_frobenius_hyperelliptic. But I'd say we should wait until #6084 is resolved before looking into that; in the interim, this suffices to fix the bug in question.
comment:12 Changed 13 years ago by
- Resolution set to fixed
- Status changed from new to closed
Merged 5430-v2.patch in 4.0.1.alpha0.
comment:13 Changed 13 years ago by
- Merged in set to 4.0.1.alpha0
- Reviewers set to Robert Bradshaw
The end of the traceback is
The question is, should this be an error, or just work?