#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-6.2
Component: algebra | Resolution:
Keywords: polynomials, power series, | Merged in:
inexact rings | Reviewers:
Authors: | Work issues:
Report Upstream: N/A | Commit:
Branch: | Stopgaps:
Dependencies: |
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Changes (by niles):
* cc: niles, wuthrich (added)
Comment:
David, could you give us a rebase for sage 6.1? I know you're doing a lot
of other work for padics, but we're trying to solve a more basic issue
with power series comparison at #9457. Power series over padics are a
confusing obstacle there, and we wanted to see if the patch here would
help.
Here's the specific bug we're trying to track down (in sage 6.1): Power
series over p-adics are changing inexact zeros to exact zeros -- this
looks similar to the problem with polynomials on this ticket, but notice
that the problem happens even for p-adics:
{{{
sage: Ct.<t> = PowerSeriesRing(Qp(11))
sage: O(11^2) # inexact zero
O(11^2)
sage: Ct(O(11^2)) # coercing to power series ring looses finite precision
0
sage: Ct(1+O(11^2)) # finite precision is retained for non-zero elements
1 + O(11^2)
}}}
There is a problem with multiplication of a p-adic by an element of the
power series ring, which might be caused by the problem above:
{{{
sage: 1+O(11^2)*t # finite precision is retained
1 + O(11^20) + O(11^2)*t
sage: O(11^2)*t # finite precision is lost
0
}}}
Note that there is a similar problem for more general power series ring
over power series ring:
{{{
sage: D.<x> = PowerSeriesRing(QQ)
sage: Ds.<s> = PowerSeriesRing(D)
sage: O(x) # inexact zero
O(x^1)
sage: Ds(O(x)) # finite precision is lost
0
sage: Ds(1+O(x)) # finite precision is retained
1 + O(x)
sage: 1+O(x)*s # !! this is different from behavior of power series over
padic ring
1
}}}
My hope is that starting with a rebase of this patch would be a step
toward solving this problem. Perhaps it will have to be extended to power
series over inexact rings too. Unfortunately I don't understand the
current status of padics well enough to do this rebase myself.
--
Ticket URL: <http://trac.sagemath.org/ticket/5075#comment:6>
Sage <http://www.sagemath.org>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica,
and MATLAB
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