#12612: Fix is_unit() in padics so that it is mathematically correct
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Reporter: mmasdeu | Owner: roed
Type: defect | Status: new
Priority: minor | Milestone: sage-5.0
Component: padics | Keywords: padics is_unit
Work_issues: | Upstream: N/A
Reviewer: | Author:
Merged: | Dependencies:
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Consider the following code:
{{{
sage: R = Qp(5,5)
sage: S.<x> = PowerSeriesRing(R,3)
sage: f=5+x
sage: f**(-1)
5^-1 + O(5^4) + (4*5^-2 + 4*5^-1 + 4 + 4*5 + 4*5^2 + O(5^3))*x + (5^-3 +
O(5^2))*x^2 + O(x^3)
sage: f.is_unit()
False
}}}
This does not make mathematical sense, and the reason for this behavior is
that is_unit() in `p`-adics does not return whether a given element can be
inverted in its parent ring. Instead, it returns whether the element has
valuation zero. Since the function is_unit() is used in generic algorithms
(for instance when trying to invert a power series) it should return what
its name promises.
I attach a patch with corrected output and doctests.
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/12612>
Sage <http://www.sagemath.org>
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