Force macro expansion

Question

I am writing a macro that will read a system of linear equations in a custom format and call \begin{array} with the appropriate format. For that I need to loop through each row and compute what is going to be displayed.

This is what I have so far.

\documentclass[10pt,a4paper]{article}
\usepackage{xstring}

\newcommand{\lineareqsys}[3]{
\noexpandarg
\StrCount{#3}{\\}[\rows] %check \rows = arg > 0
\newcounter{i} \setcounter{i}{0}
\def\str{#3}
\def\strout{}
\expandafter\StrSubstitute\expandafter{\str}{+}{+&}[\str]
\expandafter\StrSubstitute\expandafter{\str}{-}{-&}[\str]
\loop
\stepcounter{i}
\expandafter\def\csname strout\roman{i}\endcsname{}
\expandafter\StrCut\expandafter{\str}{\\}{\str}{\rest}
\expandafter\StrPosition\expandafter{\str}{x}[\xpos]
\expandafter\StrLeft\expandafter{\str}{\xpos}[\strappx]
\expandafter\def\expandafter\strout\expandafter{\strout \strappx &}
\expandafter\StrGobbleLeft\expandafter{\str}{\xpos}[\str]
\expandafter\StrPosition\expandafter{\str}{y}[\ypos]
\expandafter\StrLeft\expandafter{\str}{\ypos}[\strappy]
\expandafter\def\expandafter\strout\expandafter{\strout \strappy &}
\expandafter\StrGobbleLeft\expandafter{\str}{\ypos}[\str]
\expandafter\StrPosition\expandafter{\str}{=}[\eqpos]
\expandafter\StrLeft\expandafter{\str}{\eqpos}[\strappeq]
\expandafter\def\expandafter\strout\expandafter{\strout \strappeq &}
\expandafter\StrGobbleLeft\expandafter{\str}{\eqpos}[\str]
\expandafter\StrRight\expandafter{\str}{\eqpos}[\strapplb]
\expandafter\def\expandafter\strout\expandafter{\strout \strapplb \\}
\expandafter\def\expandafter\str\expandafter{\rest}
\expandafter\def\csname strout\roman{i}\endcsname{\strout}
\ifnum \thei < #1 \relax
\repeat
\newcounter{j} \setcounter{j}{0}
\def\alig{r}
\loop
\stepcounter{j}
\expandafter\def\expandafter\alig\expandafter{\alig cr}
\ifnum \thej < #2 \relax
\repeat
\left\lbrace
\begin{array}{\alig}
\strout
\end{array}
\right.
}


\begin{document}
$\lineareqsys{2}{2}{
x + y = 5 \\
x - y = 3 \\
}$
\end{document}

There is a problem with line

\expandafter\def\csname strout\roman{i}\endcsname{\strout}

because \strout is not fully expanded, so after the second time of the loop data is replaced and I get the last row repeated twice.

I've been checking other threads but I haven't managed to get it right. How can I solve this problem?

Note1: The code isn't finished so it doesn't handle the cases where there is no x or y or a line starts with a - sign.

Note2: The format I was referring to is straightforward.

ax + by + cz = d \\

for as many rows as necessary.

Edit: Simpler version of previous code.

\documentclass{article}
\newcommand{\lineareqsys}{
\newcounter{i} \setcounter{i}{0}
\def\strout{}
\loop
\stepcounter{i}
\expandafter\def\expandafter\strout\expandafter{\strout \arabic{i} row \\}
\ifnum \thei < 2 \relax
\repeat
\begin{array}{l}
\strout
\end{array}
}
\begin{document}
$\lineareqsys$
\end{document}

This ilustrates the same problem. \arabic{i} is expanded at the end when it's value is 2. Not dinamic.

Answer 1

The core problem is that you are not expanding things. As you can see, here is meaning of \strout after a while

> \strout=macro:
->\strappx &\strappy &\strappeq &\strapplb \\\strappx &\strappy &\strappeq &\st
rapplb \\.
\iterate ... {\strout \strapplb \\} \show \strout 
                                                  \expandafter \def \expanda...
l.57 }
      $

You have to find a way to add to \strout the expanded contents of the \strappx, \strappy etc... whatever they are.

Besides, you do \newcounter inside your command call, which is very wrong. But this is other issue.

To debug, I added \show\strout at various places of your command.

Also you are lucky to call this macro only in math mode because you have tons of space tokens in it.

---

For example, this can give an idea of what needs to be done:

%\expandafter\def\expandafter\strout\expandafter{\strout \strapplb \\}
\expandafter\g@addto@macro\expandafter\strout\expandafter{\strapplb\\}

The RHS of first equation is fixed.

Answer 2

There are big expansion problems, as you saw.

Here's a completely different solution, which uses expl3, but has, like yours, the defect that missing unknowns spoil the result.

I also offer a comparison with systeme, that doesn't suffer from the defect.

\documentclass[10pt,a4paper]{article}
\usepackage{xparse}
%\usepackage{array} % also works with this uncommented
\usepackage{systeme} % for comparison

\ExplSyntaxOn
\NewDocumentCommand{\lineareqsys}{mm}
 {
  \seq_set_split:Nnn \l__mendus_system_in_seq { \\ } { #2 }
  \seq_clear:N \l__mendus_system_out_seq
  \seq_map_inline:Nn \l__mendus_system_in_seq
   {
    \__mendus_system_make_row:nn { #1 } { ##1 }
   }
  \left\lbrace
  \setlength{\arraycolsep}{0pt}
  \renewcommand{\arraystretch}{1.2}
  \exp_args:Nnx \begin{array}{r \prg_replicate:nn { \clist_count:n { #1 } } { c r } }
  \seq_use:Nn \l__mendus_system_out_seq { \\ }
  \end{array}
  \right.
 }

\cs_new_protected:Nn \__mendus_system_make_row:nn
 {
  \tl_set:Nn \l__mendus_system_row_tl { #2 }
  \regex_replace_all:nnN { (.+?)(\+|\-|\=) } { \1\cB\{\cE\}\2\cB\{\cE\}\cT& } \l__mendus_system_row_tl
  \clist_map_inline:nn { #1 }
   {
    \regex_replace_all:nnN { ##1 } { \cL##1 \cT& } \l__mendus_system_row_tl
   }
  \seq_put_right:NV \l__mendus_system_out_seq \l__mendus_system_row_tl
 }
\cs_generate_variant:Nn \regex_count:nnN { nV }
\ExplSyntaxOff

\begin{document}

\[
\lineareqsys{x,y}{
x + y = 5 \\
x - y = 3 \\
}
\qquad
\lineareqsys{x,y,z}{
  2x-3y+4z=0 \\
  x+12y-z=0 \\
  -x+8y+z=3
}
\]

\[
\systeme{
  x + y = 5,
  x - y = 3
}
\qquad
\systeme{
  2x-3y+4z=0,
  x+12y-z=0,
  -x+8y+z=3
}
\]

\end{document}