#21088: Base Class for Skew Polynomials over Finite Fields
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Reporter: arpitdm | Owner:
Type: enhancement | Status: new
Priority: major | Milestone: sage-7.3
Component: coding theory | Resolution:
Keywords: | Merged in:
Authors: Xavier Caruso, | Reviewers:
Arpit Merchant |
Report Upstream: N/A | Work issues:
Branch: | Commit:
u/arpitdm/finite_fields_skew_polynomial|
a6e93e12c1fefffde3615c8eab75a45b3c277ab2
Dependencies: #13215 | Stopgaps:
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Comment (by arpitdm):
Replying to [comment:4 jsrn]:
> I've been thinking about whether the functions
minimum_subspace_polynomial, multi_point_evaluation and
interpolation_polynomial make any sense for general skew polynomial rings.
I politely doubt that you were really considering this when you put the
functions in SkewPolynomial_general (since the current implementation not
at all works for general skew polynomial rings). But it turns out they
*do* make sense and the algorithms more-or-less immediately works. So I
suggest those three functions should be in their own tickets.
Based on the discussions before, the plan was to add these in the finite
fields ticket. That meant these had to either go in the general or finite
field ring classes. I looked up some papers and found that the theory for
polynomial interpolation of skew polynomial rings exists, although I
didn't really try and study any of that. I just went kinda assumed that
the algorithms by Wachter-Zeh would be valid and placed it there.
Just to confirm again, should I create a new ticket and place them there?
> - Given a singleton point a, return x - sigma(a)/a. (use pen-
and-paper to see that I am right)
If the singleton point is 0, I simply return x and otherwise x -
sigma(a)/a as you pointed out, right?
> - `x = self([0,1])` should be `x = self._parent.gen()`.
um.. you mean self.gen(), right? Because self._parent.gen() would give an
error.
> - minimum_subspace_polynomial and multi_point_evaluation are mutually
recursive and will generate the same minimum subspace polynomials an
exponential number of times right now. We need to add caching: add
`@cached_method` to minimum_subspace_polynomial.
Done. And I'll report back with some timing results once I test that these
are working properly.
--
Ticket URL: <https://trac.sagemath.org/ticket/21088#comment:10>
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