#13215: Skew polynomials
-------------------------------------+-------------------------------------
Reporter: caruso | Owner: tbd
Type: enhancement | Status: needs_work
Priority: major | Milestone: sage-7.3
Component: algebra | Resolution:
Keywords: skew polynomials | Merged in:
Authors: Xavier Caruso | Reviewers: Burcin Erocal
Report Upstream: N/A | Work issues:
Branch: | Commit:
u/arpitdm/skew_polynomials | e189fec13d005a7fba39a429876c501fe95c05da
Dependencies: #13214, #13303, | Stopgaps:
#13640, #13641, #13642 |
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Comment (by tscrim):
Replying to [comment:76 jsrn]:
> Replying to [comment:75 tscrim]:
> > - You seem to be using the exact same format of polynomials, which
contains a lot of old code. For example, don't implement a `_repr_()` that
just calls (a ''Python'' function) `_repr()`. This is useless (even in the
usual polynomial ring code it seems); instead just implement `_repr_()`.
Similarly, there are a number of methods you could simply `cpdef`.
>
> That would be great. Can you give us the full list of the methods for
which we can do this, or point us to how we can figure it out?
Anything python method (a `def`) which only calls a `cdef` method. Another
example is `list` calling `_list_c`. IIRC, you can't do this for
`__hash__` because this is a Python special method. I think `_list_c` is
the only other one (and you can replace this by just calling the attribute
`__coeffs`).
> > - You can use
> > {{{
> > self._no_generic_basering_coercion = True
> > }}}
> > to avoid constructing the coercion from the base ring when
initializing the skew polynomial ring.
>
> To be precise, do you mean that can insert the above line in
`SkewPolynomialRing_general.__init__` just before the call to
`Algebra.__init__`, and then remove the call to
`self._unset_coercions_used()`? Or is there more to it?
Yes, exactly.
> > - `_cmp_` is planned to be removed. Use `_richcmp_` instead.
>
> Are you talking about `SkewPolynomial._cmp_`? We spent many hours
debugging the comparison code because it threw strange errors and
segfaults. To avoid me spending many more hours, could I ask you to tell
us exactly how to write the correct comparison code then?
You can look at `src/sage/rings/real_arb.pyx` or
`src/sage/rings/real_double.pyx` for example. We can include the `_cmp_`
as it is now, but it means some more hardship when we finally start
converting.
> Simon King's tutorial on implementing algebraic structures should be
updated to be more informative on this, I think.
Yes, it should be. It was written before we really had to worry about
going to Python3.
> > - You should lazy import the ring constructor.
>
> Do you mean `sage.rings.ring` in `skew_polynomial_ring.py`? Why is
exactly that one important to lazily import?
It is the thing which imports the rest of the code (once the `is_*`
functions are gone). So all of the other files are not imported on
startup, which helps keep that down because this is not a "common" object
that the average user will use (IMO).
> Thanks for the help!
Thank you for the good discussions and work.
--
Ticket URL: <https://trac.sagemath.org/ticket/13215#comment:79>
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