% (find-LATEX "2022dep-vars.tex")
% (defun c () (interactive) (find-LATEXsh "lualatex -record 2022dep-vars.tex" :end))
% (defun C () (interactive) (find-LATEXSH "lualatex 2022dep-vars.tex" "Success!!!"))
% (defun D () (interactive) (find-pdf-page      "~/LATEX/2022dep-vars.pdf"))
% (defun d () (interactive) (find-pdftools-page "~/LATEX/2022dep-vars.pdf"))
% (defun e () (interactive) (find-LATEX "2022dep-vars.tex"))
% (defun u () (interactive) (find-latex-upload-links "2022dep-vars"))
% (defun v () (interactive) (find-2a '(e) '(d)))
% (defun cv () (interactive) (C) (ee-kill-this-buffer) (v) (g))
% (defun d0 () (interactive) (find-ebuffer "2022dep-vars.pdf"))
%          (code-eec-LATEX "2022dep-vars")
% (find-pdf-page   "~/LATEX/2022dep-vars.pdf")
% (find-sh0 "cp -v  ~/LATEX/2022dep-vars.pdf /tmp/")
% (find-sh0 "cp -v  ~/LATEX/2022dep-vars.pdf /tmp/pen/")
%   file:///home/edrx/LATEX/2022dep-vars.pdf
%               file:///tmp/2022dep-vars.pdf
%           file:///tmp/pen/2022dep-vars.pdf
% http://angg.twu.net/LATEX/2022dep-vars.pdf
% (find-LATEX "2019.mk")
% (find-lualatex-links "2022dep-vars")

\documentclass[oneside,a5paper,12pt]{article}
\usepackage[colorlinks,citecolor=DarkRed,urlcolor=DarkRed]{hyperref} % (find-es "tex" "hyperref")
\usepackage{amsmath}
\usepackage{amsfonts}
\usepackage{amssymb}
\usepackage{pict2e}
\usepackage[x11names,svgnames]{xcolor} % (find-es "tex" "xcolor")
%\usepackage{colorweb}                 % (find-es "tex" "colorweb")
%\usepackage{tikz}
%
% (find-dn6 "preamble6.lua" "preamble0")
%\usepackage{proof}   % For derivation trees ("%:" lines)
%\input diagxy        % For 2D diagrams ("%D" lines)
%\xyoption{curve}     % For the ".curve=" feature in 2D diagrams
%
\usepackage{edrx21}               % (find-LATEX "edrx21.sty")
\input edrxaccents.tex            % (find-LATEX "edrxaccents.tex")
\input edrx21chars.tex            % (find-LATEX "edrx21chars.tex")
\input edrxheadfoot.tex           % (find-LATEX "edrxheadfoot.tex")
\input edrxgac2.tex               % (find-LATEX "edrxgac2.tex")
%\input 2017planar-has-defs.tex    % (find-LATEX "2017planar-has-defs.tex")
%
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%
% (find-es "tex" "geometry")
\begin{document}

\catcode`\^^J=10
\directlua{dofile "dednat6load.lua"}  % (find-LATEX "dednat6load.lua")

\title{Dependent variables for \\
       people who hate them --- \\
       using Maxima in part \\
       of the translation}

\author{
{\large  Eduardo Ochs}\thanks{\url{http://angg.twu.net/eev-maxima.html}}\\
{\small UFF, Rio das Ostras, RJ, Brazil} \\
}

\maketitle

\section{``Physicists' notation'' (``PN'')}

When I was an undergrad the Physics courses used some conventions on
variables in which things like this were perfectly valid,
%
$$z = z(x,y)$$
%
and {\sl most} of the courses on Maths used other conventions, in
which arguments could never be omitted, and variables and functions
could never share names; there were some exceptions, though --- the
courses on PDEs and on Calculus of Variations used ``physicist's
notation'', that allowed tricks like the one above.

I will use the term ``physicist's notation'' (``PN'') to refer to the
conventions in which dependent variables and omitted arguments are
valid, and ``mathematician's notation'' (``MN'') to refer to the
conventions in which these things are forbidden. {\sl These terms are
  informal} --- I don't know where I can find the exact rules of PN,
and over the years I've tried to ask several of my colleagues who work
in areas that use PN for references on its rules or on how to
translate PN to MN, and they didn't know anything to recommend. One of
my intents with these notes is to ask those questions to more people.

\section{People who hate PN}

One of the courses that I usually teach in the campus in which I work
is Calculus 3, that is mainly about functions from $\R^m$ to $\R^n$,
where $(m,n)≠(1,1)$. Our basic textbook is \cite{Bortolossi}, and its
author is one of the ``people who hate PN''; this is a bit of an
exaggeration, but in its pages 171--173 and 278--279 he shows how PN
can be a source of ambiguities and confusion and says that it is
better to avoid it, and the expression ``hates PN'' is colorful and
short --- so, from here on, Humberto Bortolossi ``hates PN''.

Before the pandemic I always reserved some days of the course for
activities in which the students would gather in groups and try to
decypher together some pages of \cite{Bortolossi} in which the
notation is especially heavy. With the pandemic the classes became
online, and in each new semester the students participated less in the
online discussion and had shorter attention spans, so I decided to try
a new strategy --- and I started to use two main textbooks:
\cite{Bortolossi}, that ``hates PN'', and \cite{Thompson}, that uses
PN heavily. I explained that in PN several of the main formulas and
calculations of the course would much shorter, but that PN would only
makes sense if 1) they studied it for hundreds of hours, or 2) if we
treated PN as a secondary language and as a way to {\sl abbreviate}
MN. We took the approach (2), and I showed them the rules for PN that
I had discovered --- {\sl or invented} --- and I stressed that that
set of rules was incomplete and a work in progress, and that they
should tell me every time that they had doubts or got stuck; every bit
of feedback would help me to find a clearer way to present the
translation between PN and MN.

\section{The rules}


% (c3m212nfp 9 "regras-de-traducao")
% (c3m212nfa   "regras-de-traducao")

% subst, gradef, pdiff


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% %L dofile "edrxpict.lua"  -- (find-LATEX "edrxpict.lua")
% \pu

%\printbibliography

\GenericWarning{Success:}{Success!!!}  % Used by `M-x cv'

\end{document}

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% <make>

 (eepitch-shell)
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# (find-LATEXfile "2019planar-has-1.mk")
make -f 2019.mk STEM=2022dep-vars veryclean
make -f 2019.mk STEM=2022dep-vars pdf

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% coding: utf-8-unix
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