Re: [Maxima-discuss] use of subscripts, was: Yamwi (was: Construct sequence of identifiers)

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

Often there is a conflict between the needs or expectations of a
mathematician / engineer /textbook/ reference ...
and the design of a computer algebra system.  In fact, the conventions of
one
application area may be in conflict with another, and so it is difficult to
have a CAS
treat "all" users' domains naturally (and potentially simultaneously!)

How far do we push the notation?

Mathematica has a syntax for functions as f[x]. not f(x).  You can write
f(x)., but it means f*x.
f'[x] means the same as Derivative[1][f][x].  and to define a function you
write something like
f[x_]:= x+1   and there are more "non-mathematical" constructions that will
have to be learned.

Maxima is closer to ordinarily high-school level algebra and conventional
programming language
syntax, but requires some adaptation as well. For instance,

Maxima insists on a*x  for multiplication,  with ax being a single symbol
and  a x  being illegal syntax.

Some notational context issues can be dealt with by extending syntax,
or by defining special displays, but in reality,
there is a trade-off between humans learning to adapt to the existing
formal CAS
versus trying to make some kinds of notational hacks to make a superficial
match to
some application context.
Is it worth doing?   Frankly, why should a calculus student have to learn
the syntax of a
CAS like Mathematica, in order to do homework, when even the conventional
version of
 the course is simply a requirement whose content is irrelevant: just a
barrier to graduation?

Anyway, to emphasize Robert's point:  The f[i] notation in Maxima is quite
powerful, and
includes array referencing as a special case.  But this is possible too:

f[x]:=x+1   /*   in general ...   f[3] will return 4 */
f[1/2]: 34  /* except  f[1/2] will return 34 */

note the use of :=,  :,   which may not correspond to what your textbook
uses.

Should we redefine these and other usages like ::=,  =,  etc?  Should we
also allow
notations from programming languages like Python, C, etc?   How about x++1 ?

These are matters of taste and convenience so people will have different
approaches
depending on their needs and background.

In discussion forums like this, I can only point out the breadth of
notations and conventions ranging
across a context of fields of "computational" mathematics as well as
programming formalisms.

RJF







On Sat, Jul 22, 2023 at 9:04 AM Robert Dodier <rob...@gm...>
wrote:

> On Sat, Jul 22, 2023 at 12:38 AM Wolfgang Hugemann <Au...@hu...>
> wrote:
>
> > Thanks for that hint. But in engineering subscripts are not always meant
> > as a variable index, but often serve as a means to distinguish
> quantities.
> >
> > If you denote the drag coefficient as c_d
> > (https://en.wikipedia.org/wiki/Drag_(physics)), you surely don't mean
> > c[d].
>
> Well, Maxima doesn't require subscripts to correspond to indices; instead
> a more general correspondence is allowed. In fact, subscripts can be any
> expressions, and there is no requirement that they form a complete set of
> anything. (Internally values assigned to subscripted variables are stored
> in a hash table.) In that sense, the subscript does indeed just serve as an
> indicator to distinguish conceptually-related quantities.
>
> Also of interest in this context, a recently-added feature (present in
> Maxima 5.44 and later) is that one can declare subscripts to be displayed
> above or below, before or after the base symbol. See
> declare_index_properties. E.g.:
>
> (%i11) declare_index_properties (FOO, [presubscript, presuperscript,
> postsuperscript, postsubscript]);
> (%o11)                        done
> (%i12) FOO[a, b, c, d];
>                               b   c
> (%o12)                         FOO
>                               a   d
>
>
> All the best,
>
> Robert
>
> PS. I see now that the function is misnamed; it should be called
> declare_subscript_properties. See, I got myself mixed up ... oh well!
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