Compound representation of numbers. Possible?

Question

I’ve got a Glagolitic font (Epistula Croatica) with letters mapped to numbers and some ligatures programmed. I don’t want to describe the nature of the Glagolitic numeral system here but to present what I’d like to achieve (the font’s licence doesn’t allow me to modify it). I’m trying to find a solution that will allow me to use custom numerical system in page numbers, the enumerate environment and in text.

What I need is just a different representation of arabic numerals, as in the examples below:

• 1 through 9 — no change
• 11 — 10 1
• 19 — 10 9
• 25 — 20 5
• 347 — 300 40 7
• 901 — 900 1
• 50681 — 50000 600 80 1 etc.

Between the numbers I’d like to have a \textcompwordmark.

I’d really appreciate any answers for the following questions:

• Is it possible to define such a numerical system with way of using as roman, arabic, alph, fnsymbol? I use LuaLaTeX so the solution can be a Lua code.
• If yes, how to use it in page numbers or the enumerate environment?
• Is it possible to have a text-mode command similar to \mynumerals{123}?

Thank you in advance.

Answer 1

Here's an implementation using expl3

\documentclass{article}
\usepackage[T1]{fontenc}
\usepackage{xparse}
\ExplSyntaxOn
\NewDocumentCommand{\glagonumeral}{m}{\glago_numeral:n { \int_eval:n { #1 } } }

\seq_new:N \l_glago_digits_seq
\int_new:N \l_glago_position_int

\cs_new_protected:Npn \glago_numeral:n #1
 {
  \cs_set:Npn \glago_reverse_ten: { }
  \seq_set_split:Nnx \l_glago_digits_seq { } { #1 }
  \int_set:Nn \l_glago_position_int {\seq_length:N \l_glago_digits_seq - 1 }
  \seq_map_inline:Nn \l_glago_digits_seq
   {
    \glago_symbol:x { \glago_make_digit:nn { ##1 } { \l_glago_position_int } }
    \int_decr:N \l_glago_position_int
   }
   \glago_reverse_ten:
 }
\cs_generate_variant:Nn \seq_set_split:Nnn {Nnx}
\cs_new:Npn \glago_make_digit:nn #1 #2
  {
   #1 \prg_replicate:nn { \l_glago_position_int } { 0 }
  }
\cs_new:Npn \glago_symbol:n #1
 {
  \int_compare:nTF { #1 == 10 }
   {
    \cs_set:Npx \glago_reverse_ten: { \prop_get:Nn \g_glago_numerals_prop { #1 } }
   }
   {
    \prop_get:Nn \g_glago_numerals_prop { #1 }
   }
 }
\cs_generate_variant:Nn \glago_symbol:n {x} 

\prop_new:N \g_glago_numerals_prop
\prop_put:Nnn \g_glago_numerals_prop {0}{\textcompwordmark}
\prop_put:Nnn \g_glago_numerals_prop {1}{A}
\prop_put:Nnn \g_glago_numerals_prop {2}{B}
\prop_put:Nnn \g_glago_numerals_prop {3}{C}
\prop_put:Nnn \g_glago_numerals_prop {4}{D}
\prop_put:Nnn \g_glago_numerals_prop {5}{E}
\prop_put:Nnn \g_glago_numerals_prop {6}{F}
\prop_put:Nnn \g_glago_numerals_prop {7}{G}
\prop_put:Nnn \g_glago_numerals_prop {8}{H}
\prop_put:Nnn \g_glago_numerals_prop {9}{I}
\prop_put:Nnn \g_glago_numerals_prop {00}{\textcompwordmark}
\prop_put:Nnn \g_glago_numerals_prop {10}{J}
\prop_put:Nnn \g_glago_numerals_prop {20}{K}
\prop_put:Nnn \g_glago_numerals_prop {30}{L}
\prop_put:Nnn \g_glago_numerals_prop {40}{M}
\prop_put:Nnn \g_glago_numerals_prop {50}{N}
\prop_put:Nnn \g_glago_numerals_prop {60}{O}
\prop_put:Nnn \g_glago_numerals_prop {70}{P}
\prop_put:Nnn \g_glago_numerals_prop {80}{Q}
\prop_put:Nnn \g_glago_numerals_prop {90}{R}
\prop_put:Nnn \g_glago_numerals_prop {000}{\textcompwordmark}
\prop_put:Nnn \g_glago_numerals_prop {100}{S}
\prop_put:Nnn \g_glago_numerals_prop {200}{T}
\prop_put:Nnn \g_glago_numerals_prop {300}{U}
\prop_put:Nnn \g_glago_numerals_prop {400}{V}
\prop_put:Nnn \g_glago_numerals_prop {500}{W}
\prop_put:Nnn \g_glago_numerals_prop {600}{X}
\prop_put:Nnn \g_glago_numerals_prop {700}{Y}
\prop_put:Nnn \g_glago_numerals_prop {800}{Z}
\prop_put:Nnn \g_glago_numerals_prop {900}{@}

\ExplSyntaxOff

\newcommand{\glagovalue}[1]{\glagonumeral{\number\value{#1}}}

\renewcommand{\thesection}{\glagovalue{section}}

\begin{document}

\tableofcontents

\section{A section}

\setcounter{section}{100}

\section{Another}

\glagonumeral{909}

\glagonumeral{1} --
\glagonumeral{2} --
\glagonumeral{3} --
\glagonumeral{4} --
\glagonumeral{5} --
\glagonumeral{6} --
\glagonumeral{7} --
\glagonumeral{8} --
\glagonumeral{9} --
\glagonumeral{10} --
\glagonumeral{11} --
\glagonumeral{12} --
\glagonumeral{13} --
\glagonumeral{14} --
\glagonumeral{15} --
\glagonumeral{16} --
\glagonumeral{17} --
\glagonumeral{18} --
\glagonumeral{19} --
\glagonumeral{20} --
\glagonumeral{21} --
\glagonumeral{22} --
\glagonumeral{312} --
\glagonumeral{321} --
\glagonumeral{322}

\end{document}

What you have to do now is to change the letters I've used for the digits into suitable commands giving the appropriate glagolitic letters.

You can use \glagovalue{<counter>} just like \arabic{<counter>}.

Note: this version correctly sets 12 to "AJ", while 21 becomes "KA".

---

Important change

Due to the changes made to expl3 in Summer 2012, \seq_length:N should be replaced by \seq_count:N

\cs_new_protected:Npn \glago_numeral:n #1
 {
  \cs_set:Npn \glago_reverse_ten: { }
  \seq_set_split:Nnx \l_glago_digits_seq { } { #1 }
  \int_set:Nn \l_glago_position_int {\seq_count:N \l_glago_digits_seq - 1}
  \seq_map_inline:Nn \l_glago_digits_seq
   {
    \glago_symbol:x { \glago_make_digit:nn { ##1 } { \l_glago_position_int } }
    \int_decr:N \l_glago_position_int
   }
   \glago_reverse_ten:
 }

Answer 2

A half baked LuaTeX solution. I don't know the LaTeX stuff that is needed to define the page counter, but this Lua function prints a string as you need. Perhaps someone can edit this code to make it work with LaTeX counters.

Edit: take the reverse numbering between 10 and 20 into account.

\documentclass{article}
\usepackage{luacode}
\begin{luacode*}
glagolitic = function(cnt)
  local glag_reverse = {}
  local i = 0
  local m
  while cnt > 0 do
    m = cnt % 10
    cnt = cnt - m
    glag_reverse[#glag_reverse + 1] = string.rep("0",i) .. m
    cnt = cnt / 10
    i = i + 1
  end
  if glag_reverse[2] == "01" then
    glag_reverse[1], glag_reverse[2] = glag_reverse[2], glag_reverse[1]
  end
  -- insert \textcompwordmark between elements and reverse the string
  tex.sprint(string.reverse(table.concat(glag_reverse,"kramdrowpmoctxet\\")))
end
\end{luacode*}

% (here we need to define some macros that use the function glagolitic)
\begin{document}

%  prints: 310 203 100203 400506 500710 ...
\directlua{glagolitic(13)} 
\directlua{glagolitic(23)}
\directlua{glagolitic(123)}
\directlua{glagolitic(456)}
\directlua{glagolitic(517)}
...
\end{document}