Re: [Maxima-discuss] "f:x^2" versus "g(x):=x^2", and a question on dependent variables

[Eduardo O. <edu...@gm...>]

Ta-da:

(%i1) display2d:false$
(%i2) f : x^2$
(%i3) g(x) := x^3$
(%i4) h(x) ::= x^4$
(%i5) values;
(%o5) [f]
(%i6) functions;
(%o6) [g(x)]
(%i7) macros;
(%o7) [h(x)]
(%i8) fundef(g);
(%o8) g(x):=x^3
(%i9) fundef(h);
(%o9) h(x)::=x^4
(%i10)

So f is in "values". Thanks! =)
  E.


On Tue, 11 Jan 2022 at 00:46, David Billinghurst <dbm...@gm...> wrote:

> I can help with some simple stuff.   See if chapter 36. Function
> Definition in the manual makes more sense after you have tried a few
> examples.
>
> (%i1) display2d:false$
> (%i2) f:x^2$
> (%i3) g(x):=x^2;
> (%o3) g(x):=x^2
> (%i4) functions;
> (%o4) [g(x)]
> (%i5) fundef(g);
> (%o5) g(x):=x^2
>
> f is an expression, not a function.  That is why it is not on the list
> functions.
>
> g is a function.  You can find the function definition using the
> fundef() and dispfun() functions.
>
> ::= is the macro function definition.  We can come back to macros later.
>
> On 11/01/2022 13:58, Eduardo Ochs wrote:
> > Hi list,
> >
> > I am trying - first - to understand the difference between these ways
> > of defining functions,
> >
> >   f    :   x^2;
> >   g(x) :=  x^3;
> >   h(x) ::= x^4;
> >
> > both from a user's points of view and from a common lisper's point of
> > view, and - second - I'm looking for some references on how people
> > decided to implement things in this way... let me explain.
> >
> > First: what are your favorite ways to show how the innards of Maxima
> > see the "f", the "g(x)", and the "h(x)" above? I executed this,
> >
> >   f    :   x^2;
> >   g(x) :=  x^3;
> >   h(x) ::= x^4;
> >   f;
> >   g;
> >   g(x);
> >   g(y);
> >   dispfun(g);
> >   dispfun(h);
> >
> >   :lisp #$[f]$
> >   :lisp #$[F]$
> >   :lisp #$[g]$
> >   :lisp #$[g(x)]$
> >   :lisp         #$[g(y+z)]$
> >   :lisp (displa #$[g(y+z)]$)
> >   :lisp         '((MLIST SIMP) ((MEXPT SIMP) ((MPLUS SIMP) $Y $Z) 3))
> >   :lisp (displa '((MLIST SIMP) ((MEXPT SIMP) ((MPLUS SIMP) $Y $Z) 3)))
> >
> >   :lisp                $functions
> >   :lisp           (cdr $functions)
> >   :lisp (dispfun1 (cdr $functions) t nil)
> >   :lisp                $macros
> >   :lisp           (cdr $macros)
> >   :lisp (dispfun1 (cdr $macros) t nil)
> >
> > I haven't progressed much beyond this point yet... for example, I
> > still don't know where f is stored, and I am trying to understand the
> > "(defmspec $dispfun ...)" and the "(defun dispfun1 ...)" in
> > src/mlisp.lisp, but my attempts to run parts of their code in "(let
> > (...) ...)" inside the Lisp REPL, i.e., inside a "to_lisp();" /
> > "(to-maxima)" block in the Maxima REPL, are not working - and I don't
> > even know why first line below works but the second one doesn't:
> >
> >   dispfun(g);
> >   :lisp #$[dispfun(g)]#
> >
> > So I'm a beginner asking questions that may look too advanced...
> > sorry! By the way, my favorite style for explaining these inner
> > details _in Emacs Lisp_ is with tutorials like this one,
> >
> > http://angg.twu.net/eev-intros/find-elisp-intro.html#6
> >
> > in which I expect people to execute lots of sexps in different orders,
> > and understand their results.
> >
> >
> >
> > Now the second question. This one is more open-ended, and any pointer
> > to references and/or to keywords to search for are more than welcome.
> >
> > I teach Calculus 2 and 3 in a small university in Brazil - or, more
> > precisely, in a small countryside campus that is part of a big
> > university whose main campus is 300 Km away - and I started an
> > experiment a few semesters ago. Instead of teaching the students only
> > the modern notational conventions, in which in
> >
> >   g(x) := x^3;
> >
> > the name "x" is always totally irrelevant and can be replaced by any
> > other name, I am trying to teach them both the "old" convention and
> > the "new" one, and I trying to show how to translate between the two,
> > even though I don't know all the rules of the translation...
> >
> > The "old" convention can be seen for example here,
> >
> >   Silvanus P. Thompson - "Calculus Made Easy" (1914) - p.14:
> > https://www.gutenberg.org/files/33283/33283-pdf.pdf#page=25
> >
> > and the "new" convention is the one that says that variables and
> > functions must have different names, all arguments should be explicit,
> > there is no such thing as a "dependent variable", and so on.
> >
> > I call the "old" convention "physicists' notation" and the "new" one
> > the "mathematicians' notation", always between quotes, and I always
> > explain to the students that my attempts to formalize the translation
> > are totally improvised, and that I've asked my friends who work in
> > EDPs or in Mathematical Physics where I can find formalizations of the
> > translation and they simply don't know...
> >
> > So: Maxima has some support for dependent variables - see "? depends"
> > - and I _guess_ that as Maxima is quite old some of its old papers may
> > contain discussions on how people were trying to implement both the
> > "mathematicians' notation" and the "physicists' notation" on Computer
> > Algebra Systems, and how they reached the implementation that Maxima
> > still uses today... I took a look here,
> >
> > http://ftp.math.utah.edu/pub/tex/bib/macsyma.html
> >
> > but that list is huge, it has very few links to online versions, and
> > most of them are broken, and none of the titles mention dependent
> > variables explicitly...
> >
> >   Thanks in advance!!!
> >     Eduardo Ochs
> > http://angg.twu.net/eev-maxima.html
> >
> >
> > P.S.: for the sake of completeness, my material on the "physicists'
> > notation" is here -
> > http://angg.twu.net/LATEX/2021-2-C3-notacao-de-fisicos.pdf - but it is
> > messy and in Portuguese...
> >
> >
> >
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