#13619: Enable polynomial content over padic fields
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Reporter: saraedum | Owner: roed
Type: enhancement | Status: new
Priority: trivial | Milestone: sage-5.5
Component: padics | Keywords:
Work issues: | Report Upstream: N/A
Reviewers: | Authors:
Merged in: | Dependencies:
Stopgaps: |
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Currently, one cannot call {{{content()}}} for a polynomial defined over
{{{Qp}}}:
{{{
sage: K = Qp(3)
sage: R.<t> = K[]
sage: t.content()
TypeError: ground ring is a field. Answer is only defined up to units.
}}}
The intention is apparently to protect the user from calling
{{{content()}}} if he mistakenly got from {{{Zp}}} into {{{Qp}}}, since
the content there would be always zero or one. However, this can be
annoying when writing algorithms which work over {{{Zp}}} and {{{Qp}}} but
which have to take the content into account over {{{Zp}}}.
Additionally, the content shows a somewhat strange behaviour for zero
polynomials::
{{{
sage: R = Zp(3)
sage: S.<t> = R[]
sage: f = S(R(0,3)); f
(O(3^3))
sage: f.is_zero()
True
sage: f.content()
3 + O(3^23)
sage: _.is_zero()
False
}}}
I don't think that the current behaviour is mathematically incorrect, but
I believe it's not very intuitive.
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/13619>
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