Trouble Defining a LaTeX Command

Question

I am trying to define a table of direct sums of {\chi_i}in LaTeX, meaning that the entries will be things of the form: 5 \chi_2 \bigoplus \chi_4 \bigoplus 2 \chi_7 for given data like {{1,0},{2,5},{3,0},{4,1},{5,0},{6,0},{7,2}} that tells you how many copies of each \chi_i we want for a given entry. How I wrote the data is just an example. I can format the data in whatever the most convenient form happens to be.

In order to avoid hardcoding in each entry of the table, I'm trying to define a new command in LaTeX, either via \newcommand or \def, that will take in such data and return it in the form of a direct sum as written above, but I'm a bit new to it and don't know how I should go about creating a command with what will be a variable number of arguments, since not each direct sum can be written with just three terms. The fact that \newcommand and \def take in a fixed number of arguments make me think that I should not be using them for this task. Any suggestions would be appreciated.

EDIT:

More accurately, the data concerning the coefficients of the sum is going to look like {5,2,7,8,2,0,0,1,3} where this is meant to be read as 5 \chi_1 \bigoplus 2 \chi_2 \bigoplus \ldot \bigoplus 3 \chi_9 where the sequence is always going to be a fixed size. It should also be the case that the terms with zeros should not show up in the sum.

Answer 1

Updated for new format:

\documentclass{article}

\makeatletter
\def\zz#1{{\@for\tmp:=#1\do{\expandafter\zzz\tmp\relax}}}
\def\zzz#1,#2\relax{\zzsep#1\chi_{#2}}
\def\zzsep{\def\zzsep{\bigoplus}}

\def\yy#1{{\count@\z@
\@for\tmp:=#1\do{\advance\count@\@ne
\ifnum\tmp=\z@\else\zzsep\tmp\chi_{\the\count@}\fi}}}
\makeatother
\begin{document}


\[
 \zz{{1,0},{2,5},{3,0},{4,1},{5,0},{6,0},{7,2}}
\]

\[
\yy{5,2,7,8,2,0,0,1,3} 
\]
\end{document}

Answer 2

This code is longer than David's, but way more modern and fashionable, as it uses LaTeX3 functions.

\documentclass{article}
\usepackage{xparse}
\ExplSyntaxOn
\NewDocumentCommand{\chisum}{m} % a homage to John Wayne
 {
  \aentropy_chisum:n { #1 }
 }
\cs_new_protected:Npn \aentropy_chisum:n #1
 {
  \seq_clear:N \l_aentropy_chisum_seq
  \clist_map_inline:nn { #1 }
   {
    \aentropy_add_summand:n { ##1 }
   }
  \seq_use:Nn \l_aentropy_chisum_seq { \oplus }
 }
\cs_new:Npn \aentropy_add_summand:n #1
 {
  \__aentropy_add_summand:w #1 \q_stop
 }
\cs_new:Npn \__aentropy_add_summand:w #1 , #2 \q_stop
 {
  \int_compare:nTF { #1 = 1 }
   {% if the number of summands is 1, we don't show it
    \seq_put_right:Nn \l_aentropy_chisum_seq { \chi\c_math_subscript_token{#2} }
   }
   {
    \seq_put_right:Nn \l_aentropy_chisum_seq { #1\chi\c_math_subscript_token{#2} }
   }
 }
\ExplSyntaxOff

\begin{document}
$\chisum{{1,0},{2,5},{3,0},{4,1},{5,0},{6,0},{7,2}}$
\end{document}

The idea is just the same: we process the comma separated list and split each item into two components (coefficient and index); we store the built summand in a sequence and then deliver it separating its items with \oplus.

---

In order to comply with the second specification, some adaptations must be made.

\documentclass{article}
\usepackage{xparse}
\ExplSyntaxOn
\NewDocumentCommand{\chisum}{m} % a homage to John Wayne
 {
  \aentropy_chisum:n { #1 }
 }
\seq_new:N \l_aentropy_chisum_seq
\int_new:N \l_aentropy_chisum_index_int
\cs_new_protected:Npn \aentropy_chisum:n #1
 {
  \seq_clear:N \l_aentropy_chisum_seq
  \int_zero:N \l_aentropy_chisum_index_int
  \clist_map_inline:nn { #1 }
   {
    \int_incr:N \l_aentropy_chisum_index_int
    \aentropy_add_summand:n { ##1 }
   }
  \seq_use:Nn \l_aentropy_chisum_seq { \oplus }
 }
\cs_new:Npn \aentropy_add_summand:n #1
 {
  \int_compare:nF { #1 = 0 }
   {
    \seq_put_right:Nx \l_aentropy_chisum_seq
     {
      \int_compare:nF { #1 = 1 } { #1 }
      \exp_not:n { \chi }
      \c_math_subscript_token
      { \int_to_arabic:n { \l_aentropy_chisum_index_int } }
     }
   }
 }
\ExplSyntaxOff

\begin{document}
$\chisum{5,2,7,8,2,0,0,1,3}$

\end{document}

Note that \exp_not:n { \chi } is not really necessary, because \chi is not expandable; but you might want to change the symbol and so it's better to be safe than sorry.

Zero terms are omitted, one terms are printed without the coefficient 1.

With a different definition of \aentropy_add_summand:n you can also use symbolic coefficients. Each item will be compared to the string 0 and, in this case, no summand will be added; otherwise, the item is compared to 1 and, in this case, no coefficient is added.

\cs_new:Npn \aentropy_add_summand:n #1
 {
  \str_if_eq:nnF { #1 } { 0 }
   {
    \seq_put_right:Nx \l_aentropy_chisum_seq
     {
      \str_if_eq:nnF { #1 } { 1 } { #1 }
      \exp_not:n { \chi }
      \c_math_subscript_token
      { \int_to_arabic:n { \l_aentropy_chisum_index_int } }
     }
   }
 }

Try with

$\chisum{5,2,7,8,2,0,0,1,3}$

$\chisum{a,b,2,0,0,0,0,1,3}$

and you'll get