Re: [Maxima-discuss] A Hyper-Catalan Series Solution to Polynomial Equations, and the Geode

[Richard F. <fa...@gm...>]

I haven't studied that paper thoroughly but base on Stavros' comment,
consider this ..
https://dl.acm.org/doi/pdf/10.1145/74540.74543
where one can see how to find a series solution to not just polynomial
equations, but
algebraic or differential equations.

One of the features of mathematics is that there are many ways of
making "more" of it, some with applications, some that are amusing,
entertaining (etc),
some that are overly esoteric and pointless.  Some studies were historically
significant but have faded. Some are revived.
Hyper-catalan numbers may be in one of these categories.
For an example of a topic in analysis that, so far as I can tell, has
a few fans, but hasn't caught on, consider fractional differentiation.
Could it be put in maxima? Has it been programmed for maxima?
Is it of any use?
  Just asking.
RJF



On Mon, May 5, 2025 at 10:16 AM Stavros Macrakis <mac...@gm...> wrote:

> I took a quick look at the paper. If I understand correctly, it produces a
> power series for one real root of a univariate polynomial.
> It appears like an interesting result, but I seriously doubt it's more
> practical than *realroots *and *allroots *in actually finding roots.
> On the other hand, Maxima may well be a helpful tool for those studying
> the authors' hyper-Catalan numbers and their Geode array.
>
>              -s
>
> On Mon, May 5, 2025 at 1:32 AM Matti Nykänen <
> mat...@gm...> wrote:
>
>> Hello Maximisericordia,
>>
>> Would A Hyper-Catalan Series Solution to Polynomial Equations, and the
>> Geode
>> <https://www.tandfonline.com/doi/full/10.1080/00029890.2025.2460966> be
>> relevant to Maxima? Or is it already something that Maxima can do (almost)
>> straight out of the box?
>>
>> According to my feeble understanding, it replaces radicals&co. with sums
>> of (generalised) Catalan numbers as the concept necessary for solving
>> polynomials.
>>
>> --
>> Matti Nykänen
>>
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