What is the correct way to generate notation for a finite set using for loop in Latex?

Question

I am trying to create a command that will take an index n as a parameter, and generate the the expanded form of this {a_1, a_2, a_3,...,a_n}.

For my first attempt, I tried to use the syntax suggested in pgffor: Special treatment for last item in \foreach-list and https://stackoverflow.com/questions/2561791/iteration-in-latex to create code that would output a_1 if the index was 1, and output a "," followed by a_n, if the index was not 1.

\usepackage{pgffor}
\newcommand{\sigi}[1]{\foreach \n [count=\ni] in {1,...#1}{%
    \ifnum\ni=1%
        \sigma_#1%
    \else%
        ,\sigma_#1%
}}

Unfortunately, I have worked with neither LaTeX for loops nor the pgffor package before, so I am unclear about how to interpret the compile error that occurs when I try to use this command as follows:

$\sigi{1}$

Error message:

! Undefined control sequence.
\pgffor@count@@parse ...mathresult }\pgfmathparse
                                                  {int(#3-1)}\let #1=\pgfmat...
l.363 \sigi{1}

Answer 1

Here's a rather customizable version using LaTeX3.

\documentclass{article}
\usepackage{xparse}
\ExplSyntaxOn
% the user level macro
\NewDocumentCommand{\sigi}{ s O{a} D<>{2} m }
 {
  \{ % initial delimiter
  \IfBooleanTF{#1}
   {
    \merlin_sigi_nodots:nn { #2 } { #3 }, \dots, #2\sb{#4}
   }
   {
    \merlin_sigi:nnn { #2 } { #3 } { #4 }
   }
  \} % final delimiter
 }
% the inner main function that decides if dots are necessary or not
\cs_new_protected:Npn \merlin_sigi:nnn #1 #2 #3
 {
  \int_compare:nTF { #3 < #2 }
   {\merlin_sigi_nodots:nn { #1 } { #3 } }
   {
    \int_compare:nTF { #3 <= #2 + 2 }
     { \merlin_sigi_nodots:nn { #1 } { #3 } }
     { \merlin_sigi_dots:nnn   { #1 } { #2 } { #3 } }
   }
 }
% the loop for printing the sequence when no dots are required
\cs_new_protected:Npn \merlin_sigi_nodots:nn #1 #2
 {
  \int_step_inline:nnnn { 1 } { 1 } { #2 - 1 } { #1\sb{##1}, }
  #1\sb{#2}
 }
% the loop for printing the sequence when dots are required
\cs_new_protected:Npn \merlin_sigi_dots:nnn #1 #2 #3
 {
  \int_step_inline:nnnn { 1 } { 1 } { #2 } { #1\sb{##1}, }
  \dots,
  #1\sb{#3}
 }
\ExplSyntaxOff

\begin{document}
$\sigi{3}$

$\sigi{4}$

$\sigi[b]{5}$

$\sigi<3>{10}$

$\sigi[c]<4>{20}$

$\sigi<5>{4}$

$\sigi{1}$

$\sigi{2}$

\bigskip

$\sigi*{n}$

$\sigi*[b]{m}$

$\sigi*[c]<3>{k}$
\end{document}

You can specify both the variable name (default a) and the number of initial indexed elements (default 2). If the number given as argument is less than the default number or one or two bigger, the full list is printed, as a list

{a₁,a₂,…,a₄}

would be rather awkward.

Specification

The \sigi macro has

• One optional argument (in brackets) representing the variable name (default a)
• One optional argument (between < and >) representing the number of elements spelled out at the beginning
• A mandatory argument (in braces, as usual) representing the final number

Non positive integer input in the second optional argument or in the mandatory argument will cause errors.

However the macro admits also a *-variant for a "generic" last argument, as shown in the last three lines of input. The syntax is the same for the optional arguments; the mandatory argument can be anything.

Answer 2

The idea was ok, but there were several mistakes in your code. Here's a fixed version:

\documentclass{article}
\usepackage{pgffor,pgfmath}

\begin{document}

\newcommand{\sigi}[1]{\foreach \ni in {1,...,#1}{%
    \ifnum\ni=1
        \sigma_{\ni}%
    \else%
        ,\sigma_{\ni}%
    \fi
}}

$\sigi{12}$

\end{document}

The problems were:

• missing pgfmath package
• missing comma after ...
• superfluous % after \ifnum\ni=1
• the subscript of \sigma should be \ni, not #1, and it should be enclosed in braces (important when #1>9)
• missing \fi
• \foreach \n [count=\ni] was ok, but \foreach \ni is simpler