#8304: Remove stray factors of 2 in Coleman integration
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Reporter: kedlaya | Owner: was
Type: defect | Status: needs_review
Priority: major | Milestone: sage-4.3.3
Component: number theory | Keywords: Coleman integration, hyperelliptic
curves
Author: | Upstream: N/A
Reviewer: | Merged:
Work_issues: |
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Changes (by jen):
* status: new => needs_review
Comment:
The attached patch should fix these issues (+doctests), so that invariant
differential always behaves as dx/2y:
{{{
sage: R.<x> = QQ['x']
sage: H = HyperellipticCurve(x^3+1)
sage: K = Qp(5,8)
sage: HK = H.change_ring(K)
sage: w = HK.invariant_differential()
sage: P = HK(0,1)
sage: Q = HK.lift_x(5)
sage: x,y = HK.monsky_washnitzer_gens()
sage: (2*y*w).coleman_integral(P,Q)
5 + O(5^9)
sage: x,y,z = HK.local_analytic_interpolation(P,Q)
sage: I2 = (x.derivative()/(2*y)).integral()
sage: I2(1)-I2(0)
3*5 + 2*5^2 + 2*5^3 + 5^4 + 4*5^6 + 5^7 + O(5^9)
sage: HK.coleman_integral(w,P,Q)
3*5 + 2*5^2 + 2*5^3 + 5^4 + 4*5^6 + 5^7 + O(5^9)
}}}
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Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/8304#comment:1>
Sage <http://www.sagemath.org>
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