Macro for a sequence of variables

Question

Currently, I have a macro \bigseq which takes a variable name and a last number and produces #1_{1},#1_{2},\ldots,#1_{#2}, and for example x_{1},x_{2},\ldots,x_{n}.

Now, sometimes I want to produce a full sequence when given specific numbers. I would like a macro \seq that takes a first and last index and outputs the entire sequence. For example, for 3 and 7, I want to get x_{3},x_{4},x_{5},x_{6},x_{7}. Is that possible?

Answer 1

\documentclass[a4paper]{article}
\usepackage{etoolbox}
\newcommand{\bigseqx}[3]{{#1_{#2}%
  \count255=\numexpr#2\relax
  \whileboolexpr{ test {\ifnumcomp{\count255}{<}{\numexpr#3\relax}}}
    {\advance\count255 by 1 ,#1_{\number\count255 }}%
}}

\begin{document}
$\bigseqx{x}{3}{7}$
\end{document}

Some explanations. We use the \whileboolexpr macro of etoolbox (there are other packages that offer similar functionality); it takes two arguments: the first one is a test introduced by the test keyword, followed by the actual test, so we'll execute the code in the second argument as long as the test evaluates as true. But before starting this loop, we typeset the first element of the sequence and set a temporary counter to the second argument to \bigseqx (the first one is the symbol for the variable). The code increments the counter and typesets a comma and the next subscripted variable. The test evaluates as false when the counter becomes equal to the third argument.

We set the temporary counter to a value computed by \numexpr and use again \numexpr for comparing the counter to the third argument, so input such as

\bigseqx{x}{\value{cnt}}{\value{cnt}+9}

(where cnt is a LaTeX counter) is valid; \numexpr\value{cnt}+9\relax evaluates the expression (and the \relax token is swallowed because it's simply a terminator for the numeric expression).

---

_{Note: at the moment I wrote the answer I wasn't using expl3.}

It's even shorter with expl3

\documentclass{article}
\usepackage{xparse}
\ExplSyntaxOn
\NewDocumentCommand{\bigseqx}{mmm}
 {
  #1\sb{#2}
  \int_step_inline:nnnn { #2+1 } { 1 } { #3 }
   {
    , #1\sb{##1}
   }
 }
\ExplSyntaxOff
\begin{document}

$\bigseqx{x}{3}{7}$

\end{document}

The idea is the same as above, but the working should be clearer: we print the first element, then a comma and the next element until we're finished. The key point is \int_step_inline:nnnn that takes as arguments the starting point, the step, the final point and the action to perform, in which we can refer to the current value by #1 (it's ##1 because \int_step_inline:nnnn is used in a definition). Each of the first three arguments can be an integer expression using any of the math facilities of expl3.

Answer 2

Here the adjusted form of my answer to Writing a macro to typeset a variable number of terms of a series, which now allows for a user-defined minimal index. It is fully expandable, except of the robust \ensuremath which can be removed if required.. Use it like \seq{<var>}{<min>}{<max>}, e.g. \seq{x}{3}{7}.

\documentclass{article}

\usepackage{amsmath}

\newcommand*{\seq}[3]{% #1 = variable, #2/#3 = min./max. number of terms
    \ensuremath{%
    \ifnum#2<0 \else
        #1_{#2}\expandafter\seqx\expandafter{\the\numexpr#2+1\relax}{#3}{#1}%
    \fi
    }%
}

% Internal recursive macro
\newcommand*{\seqx}[4]{% #1 = current index, #2 = max index, #3 = variable, #4 = \fi
    #4% = \fi
    \ifnum#1>#2 \else
        +#3_{#1}%
        \expandafter\seqx\expandafter{\the\numexpr#1+1\relax}{#2}{#3}%
    \fi
}

\begin{document}

\seq{x}{1}{10}

\seq{x}{3}{7}

\end{document}

Answer 3

I guess you could also do that with the \forloop package, below is a small example:

\documentclass{report}
\usepackage{forloop}
\begin{document}
\newcounter{themenumber}
\newcommand{\seq}[2]
{%
\forloop{themenumber}{#1}{\value{themenumber} < #2}{%
    $ x_{\arabic{themenumber}}, $%
}%
}

\seq{2}{6}
\end{document}