#20086: rational powers in ZZ[X] and QQ[X]
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Reporter: cheuberg | Owner:
Type: defect | Status: needs_info
Priority: major | Milestone: sage-7.2
Component: basic arithmetic | Resolution:
Keywords: | Merged in:
Authors: Clemens | Reviewers: Benjamin Hackl,
Heuberger, Vincent Delecroix, | Vincent Delecroix
Benjamin Hackl | Work issues:
Report Upstream: N/A | Commit:
Branch: public/20086 | 6f91df97a81fa094c04583314ad38cd5fd199cdb
Dependencies: | Stopgaps:
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Changes (by nbruin):
* status: positive_review => needs_info
Comment:
Taking an n-th root of an element in a ring R by computing a factorization
is an insane way to go about it. A much better generic strategy is to hope
that the univariate polynomial ring over R has a root finding algorithm
and see if the polynomial `x^n-a` has a root. You will see that:
- it actually has a decent performance over QQ (although there the
algorithm should really be special-cases)
- it will work over most fields, including the ones that are not
constructed as fraction fields of rings with a factorization algorithm.
- you don't have to mess around with the unit part that a factorization
algorithm probably won't recognize.
--
Ticket URL: <http://trac.sagemath.org/ticket/20086#comment:58>
Sage <http://www.sagemath.org>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica,
and MATLAB
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