#20086: rational powers in ZZ[X] and QQ[X]
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Reporter: cheuberg | Owner:
Type: defect | Status: needs_work
Priority: major | Milestone: sage-7.1
Component: basic arithmetic | Resolution:
Keywords: | Merged in:
Authors: Clemens | Reviewers: Benjamin Hackl
Heuberger, Vincent Delecroix | Work issues:
Report Upstream: N/A | Commit:
Branch: | c8350c631287dd71a9b79fb422d769a1e480cdc8
u/behackl/polynomial/rational- | Stopgaps:
powers |
Dependencies: |
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Comment (by behackl):
Well, wouldn't it be more natural to let the unit be an element of the
base ring? (As far as I see the parent of the unit of polynomials over QQ
always is from QQ, for example.)
Of course, we can also add checks like if `u` is one etc., but with this
ticket only polynomial rings over the rationals and the integers use this
method---and both of them have implemented a `nth_root` method; this is
why I still think that this would be good to go and why special treatment
isn't needed. And the inconsistency mentioned in #20214 only introduces a
recursion of depth 2, which would be resolved if the `unit` method would
behave for integers like for rationals.
It isn't even necessary to separately implement `nth_root` for polynomials
such that the case of constant polynomials is handled by the base ring:
over `ZZ`, the overall coefficient is decomposed w.r.t. PFD and handled
like a non-constant polynomial (which is what I would have implemented in
the base ring as well). For QQ, the overall factor is in the unit and
handled separately in the `nth_root` method.
Letting other polynomial rings profit from this procedure should be
realized in a follow-up ticket, IMHO.
However, what should be added before this ships is a special treatment of
the zero polynomial. I'll push this in a minute.
--
Ticket URL: <http://trac.sagemath.org/ticket/20086#comment:40>
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