#2943: [with patch, not ready for review] bug with power series and/or p-adics
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Reporter: jen | Owner: was
Type: defect | Status: new
Priority: critical | Milestone: sage-3.4.1
Component: number theory | Resolution:
Keywords: power series, p-adic extensions |
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Comment (by kedlaya):
I traced through the computation of 1/y in my previous example by hand,
and this turned up the following perhaps more telling example.
{{{
sage: C.<t> = PowerSeriesRing(Integers())
sage: D.<s> = PolynomialRing(C)
sage: z = 1 + (t + O(t^2))*s + (t^2 + O(t^3))*s^2
sage: z*z
(t^4 + O(t^5))*s^4 + (2*t + O(t^2))*s + 1
}}}
By contrast, this is correct:
{{{
sage: z = 1 + (t + O(t^3))*s + (t^2 + O(t^3))*s^2
sage: z*z
(t^4 + O(t^5))*s^4 + (2*t^3 + O(t^4))*s^3 + (3*t^2 + O(t^3))*s^2 + (2*t +
O(t^3))*s + 1
}}}
I think multiplication here uses z._mul_karatsuba, so maybe dmharvey needs
to look at this again. Karatsuba may cause problems when working over an
inexact coefficient ring.
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/2943#comment:17>
Sage <http://sagemath.org/>
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