#8304: Remove stray factors of 2 in Coleman integration
-----------------------------+----------------------------------------------
Reporter: kedlaya | Owner: was
Type: defect | Status: new
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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Jen discovered some stray factors of 2 buried in the Coleman integration
code. (Apply patches at #7927 before trying these examples.)
On one hand, the invariant differential sometimes thinks it's dx/2y (as it
should):
{{{
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)
}}}
but on the other hand, it sometimes behaves as if it were dx/y (as it
shouldn't):
{{{
sage: x,y,z = HK.local_analytic_interpolation(P,Q)
sage: I1 = (x.derivative()/y).integral()
sage: I2 = (x.derivative()/(2*y)).integral()
sage: I1(1)-I1(0)
5 + 3*5^4 + 3*5^6 + 3*5^7 + O(5^9)
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)
5 + 3*5^4 + 3*5^6 + 3*5^7 + O(5^9)
}}}
The apparent fix is to insert an extra division by two in tiny_integrals
(which then needs a corrected docstring and some doctests, and similarly
for tiny_integrals_on_basis) and then remove the multiplication by 2 in
coleman_integrals_on_basis. Then correct all the doctests which currently
give answers which are off by a factor of 2.
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/8304>
Sage <http://www.sagemath.org>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica,
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