#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 jsrn):
Replying to [comment:10 arpitdm]:
> Replying to [comment:4 jsrn]:
> Based on the discussions before, the plan was to add these in the finite
fields ticket.
Yes, at that point I hadn't realised that all the functions apply to
general skew polynomial rings.
> 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.
I don't know what to reply to that. If you don't *know*, then 1) try to
figure it out, using math; and if you fail at that 2) ask (and we will try
to do step 1 ourselves). By now you should be well-enough versed in the
basics of skew polynomials that you at least shouldn't try to put q-powers
everywhere. I would have expected you just to put the functions it in the
finite field-class since that is the only case that you studied. If you
thought it might apply generally, you should prove it and/or discuss with
us.
Your "mistake" of course lead me to reflect upon it, which turned out for
the better, but still.
> Just to confirm again, should I create a new ticket and place them
there?
Yes please, as they do not pertain specifically to finite fields.
> > - 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?
0 is not a valid input. 0 does not span a vector space (well, it spans a
vector space of dimension 0), and *any* skew polynomial evaluates to 0 on
0.
> > - `x = self([0,1])` should be `x = self._parent.gen()`.
> um.. you mean self.gen(), right? Because self._parent.gen() would give
an error.
Yes I meant `self.gen()`.
> Done. And I'll report back with some timing results once I test that
these are working properly.
OK.
--
Ticket URL: <https://trac.sagemath.org/ticket/21088#comment:12>
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