LazyPowerSeriesRing Replacement

[Travis Scrimshaw]

Hi everyone,

   Now that https://trac.sagemath.org/ticket/32324 is positively reviewed, I was wondering if there would be any opposition to replacing the current LazyPowerSeriesRing with the next LazyTaylorSeriesRing. This is already happening as the backend for species in https://trac.sagemath.org/ticket/32367. Are there any features missing that people want from LazyPowerSeries?

I should also point out that the framework on https://trac.sagemath.org/ticket/32324 also easily allows us to work with formal infinite series over any graded algebra (at least where each graded piece is a finite sum of elements). I plan on doing the slight refactoring and adding a noncommutative Cauchy product stream to the code to support this somewhat soon for some computations I need.

Best,

Travis

PS - Side question: Do we have q-commuting polynomials as a graded algebra in Sage? I don't think so, but perhaps there is an easy way to construct it. I know in 2 variables, I can build it as a SkewPolynomialRing in y over R['x'], but this it doesn't have the right grading.

[Kwankyu Lee]

If LazyTaylorSeriesRing could be a complete replacement of LazyPowerSeriesRing, then I think we should remove the old LazyPowerSeriesRing

and rename LazyTaylorSeriesRing to LazyPowerSeriesRing. Do you mean this?

Mathematically, Taylor series means power series derived from a function. So aTaylor series is always attached to a function. The name LazyTaylorSeriesRing seems a misnomer.

[John Cremona]

I agree with all these points!

John

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[Vincent Delecroix]

On Mon, 15 Aug 2022 at 09:50, John Cremona <john.c...@gmail.com> wrote:
>
> On Mon, 15 Aug 2022 at 08:21, Kwankyu Lee <ekwa...@gmail.com> wrote:
> >
> > If LazyTaylorSeriesRing could be a complete replacement of LazyPowerSeriesRing, then I think we should remove the old LazyPowerSeriesRing
> > and rename LazyTaylorSeriesRing to LazyPowerSeriesRing. Do you mean this?
> >
> > Mathematically, Taylor series means power series derived from a function. So aTaylor series is always attached to a function. The name LazyTaylorSeriesRing seems a misnomer.
>
> I agree with all these points!

Me too.

[Travis Scrimshaw]

I will let Martin discuss the naming as I think the is attached to the name LazyTaylorSeries(Ring). A quick counterpoint to Kwankyu's claim, the power series "is" a function (well, formally), we just usually think of it as being equal to an "easier" function.

However, it is meant to be a complete replacement with removing the old LazyPowerSeriesRing code. This new version should be faster, more robust, and have more functionality.

Best,

Travis

[Kwankyu Lee]

On Tuesday, August 16, 2022 at 9:04:00 AM UTC+9 Travis Scrimshaw wrote:

 the power series "is" a function (well, formally), we just usually think of it as being equal to an "easier" function.

No. You know that a power series is an expression. It has variables, but not domain and codomain. 

[Martin R]

That's a misunderstanding: I am NOT attached to the name LazyTaylorSeries(Ring).

I would prefer that the ticket goes in with the name we agree on, rather than going in with a name that we deprecate in the same release.

Moreover, I do not know whether there will be a conflict with the LazyPowerSeries(Ring) in the species directory, and I am somewhat unwilling to find out, because that code seems to have a few bugs and will be replaced anyway.

[Martin R]

PS: there are probably some things that have to be replaced.  For example, LazyPowerSeriesRing has methods `sum_generator` and `product_generator`, which are undocumented but seem to compute the sum/product of a sequence of series where the n-th series (-1 in the product case) has valuation at least n.

Martin