#5075: Polynomials over inexact rings should not truncate inexact leading zeroes
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Reporter: kedlaya | Owner: roed
Type: defect | Status: new
Priority: major | Milestone: sage-3.4.1
Component: algebra | Keywords: polynomials, power series, inexact rings
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The generic polynomial class truncates leading zeroes, and this can cause
problems when working over an inexact ring in which is_zero can return
True even for an inexact zero (e.g., see #2943). Here is a simple example:
{{{
sage: C.<t> = PowerSeriesRing(Integers())
sage: D.<s> = PolynomialRing(C)
sage: y = O(t)
sage: y
O(t^1)
sage: z = y*s
sage: z
0
sage: z.list()
[]
}}}
This was recognized earlier for p-adics and fixed (I'm not sure which
ticket this was):
{{{
sage: C = pAdicField(11)
sage: D.<s> = PolynomialRing(C)
sage: y = O(11)
sage: y
O(11)
sage: z = y*s
sage: z
(O(11))*s
}}}
The other main class of inexact rings are interval fields, but I believe
for those is_zero returns False for an inexact zero, so this doesn't come
up.
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/5075>
Sage <http://sagemath.org/>
Sage - Open Source Mathematical Software: Building the Car Instead of
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