Re: Adding a generic mathematical library

[Christopher Dimech <dimech@gmx.com>]

> Sent: Sunday, July 28, 2024 at 7:07 AM
> From: "Shouran Ma" <shouran.ma@gmail.com>
> To: "Emanuel Berg" <incal@dataswamp.org>
> Cc: emacs-devel@gnu.org, "Sergey Kostyaev" <sskostyaev@gmail.com>, "Philip Kaludercic" <philipk@posteo.net>
> Subject: Re: Adding a generic mathematical library
>
>
> > Sent: Saturday, July 27, 2024 at 16:57 +0200
> > From: "Shouran Ma" <shouran.ma@gmail.com>
> >
> > However, WE DON'T EVEN HAVE A UNIFIED WAY TO REPRESENTING A VECTOR.
>
> I need to elaborate this statement, otherwise it cause confusion to
> others.
>
> Elisp provides "List" and "Vector" as an array of numbers:
> https://www.gnu.org/software/emacs/manual/html_node/elisp/Sequences-Arrays-Vectors.html
>
> To express an array of numbers, a developer would either use two of them
> - (setq x '(1 2 3 4))  ; (type-of x) => cons
> - (setq x [1 2 3 4])   ; (type-of x) => vector
>
> "cons" (or "list") is the first thing that everybody would choose, for
> example, in Sergey's elisa:
> https://github.com/s-kostyaev/elisa/blob/main/elisa.el
> In the function "elisa--distances", Sergey puts "head" and "(car tail)"
> as arguments to "elisa-cosine-distance", this means Sergey uses
> cons/list to organize array of numbers.
>
> However, Elisp also has "array" types:
> https://www.gnu.org/software/emacs/manual/html_node/elisp/Arrays.html
> > An array object has slots that hold a number of other Lisp objects,
> > called the elements of the array. Any element of an array MAY BE
> > ACCESSED IN CONSTANT TIME. In contrast, the time to access an element
> > of a list is proportional to the position of that element in the list.
>
> cons/list is something like "linked list" which is not accessed in const
> time, but vector support this, e.g. it takes more time to access the
> last element if we use cons/list, but less time if use vector.
>
> However, Elisp provides too few functions on operating the vector type,
> for example, to slice a vector like the way in python: array[2:4].
>
> So my saying "don't even have a unified way to representing a vector", I
> mean, to organize/represent a MATHEMATICAL vector
> - I would prefer to choose the object that support const time access,
> i.e. the BUILTIN vector type, over the cons/list.
> - However, the BUILTIN vector type supports quite a few functions, which
> forces me to change my mind to organize/represent the MATHEMATICAL
> vectors by cons/list.
>
> This is the dilemma during developing my own math libraries.
>
> Besides, in the Calc subroutine, the MATHEMATICAL vectors are
> represented by cons/list in this way
> (vec 3 5 2 1 0)  ; not (3 5 2 1 0) or [3 5 2 1 0]
> i.e. a symbol "vec" is placed at the beginning of the list, in order to
> simplify the predication. But this leads to the indexing problem, that
> elements are indexed since 1, not 0. Such an indexing scheme would cause
> a nightmare to the developer who want to use our math subroutine to do
> further development.

An indexing task should never be a problem to the seasoned developer.
If they find it a nightmare, there is something missing with the developer.

Indexing in an everyday task in scientific programming.  One just has to focus
and think about what one is doing a little bit.

> In summary, if the builtin vector type is preferred way to represent the
> MATHEMATICAL vector, we should first of all complete the fundamental
> vector operations, like vector slicing etc. And of course, we should
> take a look at how sbcl
> https://git.code.sf.net/p/sbcl/sbcl
> organize their vector and their vector functions.
>
> From my side, I don't want to touch the vector things so far, but instead
> the rational number (the bullet 2 & 3 in my previous mail).
>
> Finally,
> > Sent: Saturday, July 27, 2024 at 17:49 +0200
> > From: "Emanuel Berg" <incal@dataswamp.org>
> >
> > However it used to be even worse, when we didn't even have clocks!
>
> If the "clock" you said is the clock to measure how long a function
> runs, we have, it is "benchmark-run".
>
>
> --
> Best Regards,
> Shouran Ma
>
>