Re: Adding a generic mathematical library

[Immanuel Litzroth <immanuel.litzroth@gmail.com>]

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> Indexing in an everyday task ...
Like writing?
Immanuel

On Sat, Jul 27, 2024 at 9:40 PM Christopher Dimech <dimech@gmx.com> wrote:

>
> > 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
> >
> >
>
>

-- 
-- A man must either resolve to point out nothing new or to become a slave
to defend it. -- Sir Isaac Newton

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