A newcommand for more than one formula

Question

I have some formula such as z_{(h_{1},h_{2},h_{3})} and z_{(h_{4},h_{5},h_{6})}. How can one introduce a \newcommand{}{} for all of such formulas?

Thanks in advance

Answer 1

They forgot xinttools.

\documentclass{article}

\usepackage{xinttools}

% Thank you very much. I will be very thankful if you write the commands for
% z_{j_{1}(h_{1},h_{2})} and z_{k(h_{3},h_{4},h_{5})}

\newcommand{\zz}[2]{z_{#1(\xintFor ##1 in {#2}\do {h_{##1}\xintifForLast{}{,}})}}
\begin{document}

\[ \zz{j_{1}}{1,2} = \zz{k}{3, 4, 5}\]

\end{document}

Answer 2

  \newcommand\zz[3]{z_{(h_{#1},h_{#2},h_{#3})} 

then you can use and \zz{1}{2}{3} and \zz{4}{5}{6} or even \zz123 and \zz456

Answer 3

It's not difficult to extend it to any number of subscripts:

\documentclass{article}
\usepackage{xparse}

\ExplSyntaxOn
\NewDocumentCommand{\zz}{m}
 {
  z
  \sp{}\sb
   {
    \clist_map_inline:nn { #1 }
     {
      \seq_put_right:Nn \l_fahim_z_subscripts_seq { h\sb{##1} }
     }
    (\seq_use:Nn \l_fahim_z_subscripts_seq { , })
   }
 }
\seq_new:N \l_fahim_z_subscripts_seq
\ExplSyntaxOff

\begin{document}

$\zz{1,2,3}+\zz{4,5,6}=\zz{1,2,3,4,5,6}$

\end{document}

This can be generalized to different base letters and different processing of the subscripts. The trailing optional argument sets how to treat each item in the comma separated list, see the examples.

\documentclass{article}
\usepackage{xparse}

\ExplSyntaxOn
\NewDocumentCommand{\zz}{O{z}mO{h\sb{##1}}}
 {
  #1
  \sp{}\sb
   {
    \cs_set_protected:Nn \__fahim_z_subscript:n { #3 }
    \clist_map_inline:nn { #2 }
     {
      \seq_put_right:Nn \l_fahim_z_subscripts_seq { \__fahim_z_subscript:n { ##1 } }
     }
    (\seq_use:Nn \l_fahim_z_subscripts_seq { , })
   }
 }
\seq_new:N \l_fahim_z_subscripts_seq
\ExplSyntaxOff

\begin{document}

$\zz{1,2,3}+\zz{4,5,6}=\zz{1,2,3,4,5,6}$

$\zz[Z]{1,2,3}[k_{#1}]$

$\zz{1,2,3}[(#1)]$

\end{document}

For more complex settings, I suggest a key-value syntax. Here the keys are var (for the name of the variable), outer to set the overall setting (default is just adding the parentheses) and inner for the sequence of actual subscripts. See the given examples. At any moment you can issue \zzset to change (in the current scope) one or more of the values.

\documentclass{article}
\usepackage{xparse}

\ExplSyntaxOn
\NewDocumentCommand{\zz}{O{}m}
 {
  \group_begin:
  \keys_set:nn { fahim/zz } { #1 }
  \fahim_zz:n { #2 }
  \group_end:
 }

\NewDocumentCommand{\zzset}{m}
 {
  \keys_set:nn { fahim/zz } { #1 }
 }

\keys_define:nn { fahim/zz }
 {
  var .tl_set:N = \l__fahim_zz_var_tl,
  outer .code:n = \cs_set_protected:Nn \__fahim_zz_outer:n { #1 },
  inner .code:n = \cs_set_protected:Nn \__fahim_zz_inner:n { #1 },
 }

\seq_new:N \l__fahim_zz_subscripts_seq

\cs_new_protected:Nn \fahim_zz:n
 {
  \tl_use:N \l__fahim_zz_var_tl
  \sp{} % a dummy superscript to lower the subscript
  \sb
   {
    \__fahim_zz_outer:n
     {
      \clist_map_inline:nn { #1 }
       {
        \seq_put_right:Nn \l__fahim_zz_subscripts_seq { \__fahim_zz_inner:n { ##1 } }
       }
      \seq_use:Nn \l__fahim_zz_subscripts_seq { , }
     }
   }
 }
\ExplSyntaxOff

% initialize
\zzset{
  var=z,
  outer=(#1),
  inner=h_{#1},
}

\begin{document}

$\zz{1,2,3}+\zz{4,5,6}=\zz{1,2,3,4,5,6}$

$\zz[var=Z,inner=k_{#1}]{1,2,3}$

$\zz[outer=i(#1)]{1,2,3}$

$\zz[outer=i(#1),inner=k_{#1}]{1,2,3}$

\end{document}

Answer 4

It's not difficult to extend it to any number of subscripts and without using ExplSyntaxOn:

\def\zz#1{\zzA#1,,}
\def\zzA#1,{z_\bgroup(h_{#1}\zzB}
\def\zzB#1,{\ifx\end#1\end)\egroup \else ,h_{#1}\expandafter\zzB\fi}

$\zz{1,2,3}+\zz{4,5,6}=\zz{1,2,3,4,5,6}$

\bye

EDIT If you need to add an ``index letter'' (i, j like in your comment), then it is possible to do using this code:

\def\zz#1#{z_\bgroup#1\zzI}
\def\zzI#1{\zzA#1,,}
\def\zzA#1,{(h_{#1}\zzB}
\def\zzB#1,{\ifx\end#1\end)\egroup \else ,h_{#1}\expandafter\zzB\fi}

$\zz i{1,2,3}+\zz j{4,5,6}=\zz{1,2,3,4,5,6}$

\bye

Answer 5

Very easy with the listofitems package:

\documentclass{article}
\usepackage{listofitems}
\newcommand\zz[1]{
  z_{(
    \setsepchar{,}
    \readlist*\zlist{#1}
    \foreachitem\i\in\zlist{\ifnum\icnt=1\relax\else,\fi h_{\i}}
  )}
}
\begin{document}
$\zz{1,2,3}+\zz{4,5,6}=\zz{1,2,3,4,5,6}$
\end{document}

By the way, listofitems works in plain TeX, as well:

\input listofitems.tex
\def\zz#1{
  z_{(
    \setsepchar{,}
    \readlist*\zlist{#1}
    \foreachitem\i\in\zlist{\ifnum\icnt=1\relax\else,\fi h_{\i}}
  )}
}
$\zz{1,2,3}+\zz{4,5,6}=\zz{1,2,3,4,5,6}$
\end

Answer 6

You could also use e-TeX. (It seems rather simple to me.) Assuming that you have three subsequent indices every time you would say

\newcommand*\zz[1]{%
  \@tempcnta\numexpr#1+1\relax
  \@tempcntb\numexpr#1+2\relax
  z_{(%
    h_{#1}+h_{\the\@tempcnta}+h_{\the\@tempcntb}%
  )}
}

and then call \zz{1} resp. \zz{4}.

To add in a few generalisations, i.e. arbitrary number of indices and specified indices is not a big deal:

\newcommand*\zzz[2][h]{%
  \def\forplus{\def\forplus{+}}
  z_{(%
    \@for\i:=#2\do{\forplus#1_{\i}}%
  )}
}

Note the optional parameter for the subscripts of first order:

\begin{gather*}
  \zzz{1,2,3}\\
  \zzz{4,5,6}\\
  \zzz[p]{7,11,13,17}
\end{gather*}

If you want to you can get really sophisticated by declaring something that acts like

\indexloop[<delimiter>][<format>]{<indices>}

where <format>:='<superscript>_<opt. delimiter><subscript><opt. delimiter>'

defined by

\makeatletter
\def\defaultsup{z}
\def\defaultsub{h}
\def\defaultdll{(}
\def\defaultdlr{)}
\def\defaultsep{+}
\def\indexloop{%
  \kernel@ifnextchar[
    {\indexl@op}
    {\indexl@op[\defaultsup_\defaultdll\defaultsub\defaultdlr]}
}
\def\indexl@op[#1]{%
  \kernel@ifnextchar[
    {\indexl@@p[{#1}]}
    {\indexl@@p[\defaultsep][{#1}]}
}
\def\indexl@@p[#1][#2]#3{%
  \def\forsep{\def\forsep{#1}}
  \def\customsup{}
  \def\customsub{}
  \def\customdll{}
  \def\customdlr{}
  \process@format#2\@end
  \customsup_{%
    \customdll
    \@for\i:=#3\do{\forsep\customsub_{\i}}%
    \customdlr
  }%
}
\def\process@format#1_#2\@end{%
\def\customsup{#1}
\process@sub#2\@@end
}
\def\process@sub#1{
\ifx#1\@@end\else
  \ifcat#1x
    \edef\customsub{\customsub#1}
  \else
    \ifx\customdll\@empty
      \def\customdll{#1}
    \else
      \ifx\customdlr\@empty
        \def\customdlr{#1}
      \fi
    \fi
  \fi
  \expandafter\process@sub
\fi
}
\makeatother

Here is a short test of the last solution.

\begin{gather*}
  \indexloop{1,2,3}\\
  \indexloop{4,5,6}\\
  \indexloop[z_(p)]{7,11,13,17}\\
  \indexloop[-][z_\langle x\rangle]{8,9,10,12,14,15,16}\\
  \indexloop[,][{a_[i]}]{1,2}
\end{gather*}

Complete Code

% arara: pdflatex
\documentclass{article}
\usepackage{amsmath}

\makeatletter
\newcommand*\zz[1]{%
  \@tempcnta\numexpr#1+1\relax
  \@tempcntb\numexpr#1+2\relax
  z_{(%
    h_{#1}+h_{\the\@tempcnta}+h_{\the\@tempcntb}%
  )}
}
\newcommand*\zzz[2][h]{%
  \def\forplus{\def\forplus{+}}
  z_{(%
    \@for\i:=#2\do{\forplus#1_{\i}}%
  )}
}
\def\defaultsup{z}
\def\defaultsub{h}
\def\defaultdll{(}
\def\defaultdlr{)}
\def\defaultsep{+}
\def\indexloop{%
  \kernel@ifnextchar[
    {\indexl@op}
    {\indexl@op[\defaultsup_\defaultdll\defaultsub\defaultdlr]}
}
\def\indexl@op[#1]{%
  \kernel@ifnextchar[
    {\indexl@@p[{#1}]}
    {\indexl@@p[\defaultsep][{#1}]}
}
\def\indexl@@p[#1][#2]#3{%
  \def\forsep{\def\forsep{#1}}
  \def\customsup{}
  \def\customsub{}
  \def\customdll{}
  \def\customdlr{}
  \process@format#2\@end
  \customsup_{%
    \customdll
    \@for\i:=#3\do{\forsep\customsub_{\i}}%
    \customdlr
  }%
}
\def\process@format#1_#2\@end{%
\def\customsup{#1}
\process@sub#2\@@end
}
\def\process@sub#1{
\ifx#1\@@end\else
  \ifcat#1x
    \edef\customsub{\customsub#1}
  \else
    \ifx\customdll\@empty
      \def\customdll{#1}
    \else
      \ifx\customdlr\@empty
        \def\customdlr{#1}
      \fi
    \fi
  \fi
  \expandafter\process@sub
\fi
}
\makeatother

\begin{document}
\begin{gather*}
  \zz{1}\\
  \zz{4}
\end{gather*}

\begin{gather*}
  \zzz{1,2,3}\\
  \zzz{4,5,6}\\
  \zzz[p]{7,11,13,17}
\end{gather*}

\begin{gather*}
  \indexloop{1,2,3}\\
  \indexloop{4,5,6}\\
  \indexloop[z_(p)]{7,11,13,17}\\
  \indexloop[-][z_\langle x\rangle]{8,9,10,12,14,15,16}\\
  \indexloop[,][{a_[i]}]{1,2}
\end{gather*}
\end{document}

Edit

Even the first solution can be more sophisticated by implementing the step length:

\newcommand*\zz[2][1]{%
  \@tempcnta\numexpr#2+1*#1\relax
  \@tempcntb\numexpr#2+2*#1\relax
  z_{(%
    h_{#2}+h_{\the\@tempcnta}+h_{\the\@tempcntb}%
  )}
}

\[\zz[2]{0}\] would then compile to z_{h_0+h_2+h_4} as expected.