__HEADER__(Declaring of math symbols with automatic indexing)

\RequirePackage{imakeidx}
\RequirePackage{xparse}

% Keys used for declaring symbols
\keys_define:nn { symbol }
  {
    operator      .tl_set:N   = \l_symbol_operator_tl,
    operator      .default:n  = \use:n,
    formula       .tl_set:N   = \l_symbol_formula_tl,
    formula       .default:n  = \c_novalue_tl,
    ordered       .tl_set:N   = \l_symbol_ordered_tl,
    ordered       .default:n  = \c_novalue_tl,
    description   .tl_set:N   = \l_symbol_description_tl,
    description   .default:n  = \c_novalue_tl,
    group         .tl_set:N   = \l_symbol_group_tl,
    group         .default:n  = \c_novalue_tl,
    defaultargs   .tl_set:N   = \l_symbol_defaultargs_tl,
    defaultargs   .default:n  = \c_novalue_tl
  }

% Core macro not to be used publicly directly. Usage:
  % #1 = indexname / group
  % #2 = symbolname,
  % #3 = description
  % #4 = operator to apply (one argument) - can be \use:n for identity
  % #5 = substitution when called
  % #6 = default appendices to macro in index (e.g. _R)
  % #7 = ordering in index
\cs_new_protected:Nn\symbol_define:nnnnnnn
  {
    \bool_new:c { used_#2 }
    \cs_new_protected:cn { symbol_#2: }
      {
        \bool_if:cF { used_#2 }
        {
          \index[#1]
            {
              #7
              @
              $#4{#5}#6$
              #3
            }
          \bool_gset_true:c { used_#2 }
        }
        #4{#5}
      }
    \expandafter\protected\expandafter\gdef\csname#2\endcsname
      {
        \use:c { symbol_#2: }
      }
  }
\cs_generate_variant:Nn\symbol_define:nnnnnnn { V n V V V V V}


% Main package interface
\NewDocumentCommand{\DeclareSymbol}{ O{} m}
  {
    \keys_set:nn{ symbol }
      {
        operator,
        formula,
        ordered,
        description,
        group,
        defaultargs
      }
    \keys_set:nn{ symbol }{#1}
    \tl_if_eq:NnTF\l_symbol_description_tl{\c_novalue_tl}
      {
        \tl_set:Nn\l_symbol_description_tl { \c_empty_tl }
      }
      {
        \tl_put_left:Nn\l_symbol_description_tl { ,\c_space_tl }
      }
    \tl_if_eq:NnT\l_symbol_formula_tl{\c_novalue_tl}
      {
        \tl_set:Nn\l_symbol_formula_tl {#2}
      }
    \tl_if_eq:NnT\l_symbol_ordered_tl{\c_novalue_tl}
      {
        \tl_set:Nn\l_symbol_ordered_tl {#2}
      }
    \tl_if_eq:NnT\l_symbol_defaultargs_tl{\c_novalue_tl}
      {
        \tl_clear:N\l_symbol_defaultargs_tl
      }
    \symbol_define:VnVVVVV
        \l_symbol_group_tl
        {
          #2
        }
        \l_symbol_description_tl
        \l_symbol_operator_tl
        \l_symbol_formula_tl
        \l_symbol_defaultargs_tl
        \l_symbol_ordered_tl
  }