\expandafter, \expandbefor : what else?

Question

I have a macro that prints exactly what I want, but I can't use it nested in another one. As far as I understand it is because the fist one is not completely executed and commands from first macro mixt together with those from the second one.

How to proceed ?

\documentclass{article}
\usepackage{tikz,pgfplots}
\usetikzlibrary{calc}
\pgfplotsset{compat=1.9}

\makeatletter
\def\L@ste#1#2{
    \count255 = 1
    \loop   
    \def\n{\the\count255}%
    #1%
    \advance\count255 by 1
    \ifnum\count255>#2
    \else
    ,%
    \repeat
    }
\def\Liste#1#2{\L@ste{#1}{#2}}
\makeatother

\begin{document}

\verb+\Liste{\n-\n/(6-\n)*x}{5}+

Prints exactly what I need :

\Liste{\n-\n/(6-\n)*x}{5}

\bigskip    

But I can't use it directly :

\verb+max(\Liste{\n-\n/(6-\n)*x}{5})+

produces errors ...

\bigskip    

\begin{tikzpicture}

\begin{axis}[xmin=0,xmax=5,ymax=7]
  \addplot[color=black,smooth,samples=400] 
  {
% can't use it here, Why ?
    %max(\Liste{\n-\n/(6-\n)*x}{5})
max(1-1/(6-1)*x,2-2/(6-2)*x,3-3/(6-3)*x,4-4/(6-4)*x,5-5/(6-5)*x)
  };
\end{axis}
\end{tikzpicture}
\end{document}

Answer 1

The loop via \loop is not expandable, because it contains assignments. For the same reason \def\n{\the\count255 } (BTW, note the space) is not expandable as advancing the counter via \advance.

\Liste could be implemented in an expandable way:

• Package intcalc helps in incrementing in an expandable way,
• \n needs to be exchanged by the number in an expandable way.

But it is much easier to construct a macro (also token register) that contains the expanded list. In the following example \Liste generates the list and stores the result in macro \ListeResult. The latter can be used in max:

\documentclass{article}
\usepackage{tikz,pgfplots}
\usetikzlibrary{calc}
\pgfplotsset{compat=1.9}

\makeatletter
\newcommand*{\Liste}[2]{%
  \count@ = 1 %
  \let\ListeResult\@empty
  \loop
    \def\n{\the\count@}%
    \edef\ListeResult{\ListeResult#1}%
    \advance\count@ by 1 %
  \ifnum#2<\count@
  \else
    \edef\ListeResult{\ListeResult,}%
  \repeat
}
\makeatother

\begin{document}

Prints exactly what I need :

\Liste{\n-\n/(6-\n)*x}{5}
\ListeResult

\bigskip

\begin{tikzpicture}

\begin{axis}[xmin=0,xmax=5,ymax=7]
  \Liste{\n-\n/(6-\n)*x}{5}
  \addplot[color=black,smooth,samples=400] {max(\ListeResult)};
\end{axis}
\end{tikzpicture}
\end{document}

Answer 2

You can't feed \Liste to max, because it wants a syntactically correct list of functions, not the instructions for printing them.

Here's a working implementation; you must first compute the substitutions and define a macro to contain the list. Then you can use this macro in the argument of \max.

\documentclass{article}
\usepackage{tikz,pgfplots}
\usetikzlibrary{calc}
\pgfplotsset{compat=newest}

\makeatletter
\newcommand\Liste[3][]{%
  \def\Liste@temp{\@gobble}%
  \count@=\z@
  \loop\ifnum\count@<#3\relax
  \advance\count@ by \@ne
  \begingroup\edef\n{\the\count@}%
  \edef\x{\endgroup\def\noexpand\Liste@temp{\Liste@temp,#2}}\x%
  \repeat
  \if\relax\detokenize{#1}\relax
    \Liste@temp
  \else
    \let#1=\Liste@temp
  \fi
}
\makeatother

\begin{document}

\Liste{\n-\n/(6-\n)*x}{5}

\bigskip    

\begin{tikzpicture}

\begin{axis}[xmin=0,xmax=5,ymax=7]
   \Liste[\foo]{\n-\n/(6-\n)*x}{5}
  \addplot[color=black,smooth,samples=400] 
  {
    max(\foo)
  };
\end{axis}
\end{tikzpicture}
\end{document}

A new implementation with expl3.

\documentclass{article}
\usepackage{geometry}
\usepackage{xparse}
\usepackage{tikz,pgfplots}
\usetikzlibrary{calc}
\pgfplotsset{compat=newest}

\ExplSyntaxOn
\NewDocumentCommand{\addplotlist}{smO{1}mmO{}}
 {% #1 = * if printing
  % #2 = function to apply to the list
  % #3 = starting point, default 1
  % #4 = end point
  % #5 = list building function
  % #6 = options for addplot
  \cs_set:Nn \__tarass_process:n { ,#5 }
  \clist_set:Nx \l__tarass_process_clist
   {
    \int_step_function:nnnN { #3 } { 1 } { #4 } \__tarass_process:n
   }
  \IfBooleanTF{#1}
   {
    $\use:c{#2}(\clist_use:Nn \l__tarass_process_clist { ,~ })$
   }
   {
    \addplot[#6]{ #2(\l__tarass_process_clist) }
   }
 }
\clist_new:N \l__tarass_process_clist
\ExplSyntaxOff

\begin{document}

\addplotlist*{max}{5}{#1-#1/(6-#1)*x}

\addplotlist*{min}{5}{#1+#1/(6-#1)*x}

\bigskip

\begin{tikzpicture}
\begin{axis}[xmin=0,xmax=5,ymax=7]
  \addplotlist{max}{5}{#1-#1/(6-#1)*x}[color=black,smooth,samples=400];
  \addplotlist{min}{5}{#1+#1/(6-#1)*x}[color=red,smooth,samples=400];
\end{axis}
\end{tikzpicture}
\end{document}

The variable parameter is denoted by #1. The * version prints the obtained list.