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概括（位置数字系统）

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概括（位置数字系统）

我需要使用 fractur 字体定义计数器和希伯来语字母表。对于希腊字母表，我使用包恩格莱克。有什么建议吗？谢谢

答案1

约翰·科米洛 (John Kormylo) 可能意味着是，如果列举所有可能发生的情况是合理的，那么您可以解释\alphLaTeX 中的定义，它依赖于 TeX 的\ifcase条件，如下所示：

\def\alph#1{\expandafter\@alph\csname c@#1\endcsname}

\def\@alph#1{%
  \ifcase#1\or a\or b\or c\or d\or e\or f\or g\or h\or i\or j\or
   k\or l\or m\or n\or o\or p\or q\or r\or s\or t\or u\or v\or w\or x\or
    y\or z\else\@ctrerr\fi}

例如，以下是使用著名的（？）格式化 LaTeX 计数器的一种愚蠢方法沙多克数字系统。这是一个以 4 为基数的数字系统，其中每个数字的可用符号为 Ga = 0、Bu = 1、Zo = 2 和 Meu = 3。

\documentclass{article}
\usepackage{pgffor}     % only for the demo code
\usepackage{multicol}   % only for the demo code

\makeatletter
\newcommand*{\@shadokNumber}[1]{%
  \ifcase #1% #1 is supposed to be a <number>
        Ga\or      Bu\or      Zo\or      Meu\or
      BuGa\or    BuBu\or    BuZo\or    BuMeu\or
      ZoGa\or    ZoBu\or    ZoZo\or    ZoMeu\or
     MeuGa\or   MeuBu\or   MeuZo\or   MeuMeu\or
    BuGaGa\or  BuGaBu\or  BuGaZo\or  BuGaMeu\or
    BuBuGa\or  BuBuBu\or  BuBuZo\or  BuBuMeu\or
    BuZoGa\or  BuZoBu\or  BuZoZo\or  BuZoMeu\or
   BuMeuGa\or BuMeuBu\or BuMeuZo\or BuMeuMeu\or
    ZoGaGa\or  ZoGaBu\or  ZoGaZo\or  ZoGaMeu\or
    ZoBuGa\or  ZoBuBu\or  ZoBuZo\or  ZoBuMeu\or
    ZoZoGa\or  ZoZoBu\or  ZoZoZo\or  ZoZoMeu\or
   ZoMeuGa\or ZoMeuBu\or ZoMeuZo\or ZoMeuMeu\or
   MeuGaGa\or  MeuGaBu\or  MeuGaZo\or  MeuGaMeu\or
   MeuBuGa\or  MeuBuBu\or  MeuBuZo\or  MeuBuMeu\or
   MeuZoGa\or  MeuZoBu\or  MeuZoZo\or  MeuZoMeu\or
  MeuMeuGa\or MeuMeuBu\or MeuMeuZo\or MeuMeuMeu\or BuGaGaGa% = 64 in decimal
  % etc.
  \else \@ctrerr \fi
}

\newcommand*{\shadokNumber}[1]{%
  \expandafter\@shadokNumber\csname c@#1\endcsname
}
\makeatother

\newcounter{myctr}

\begin{document}

\begin{multicols}{3}
  \noindent
  \foreach \i in {0,...,64} {%
    \shadokNumber{myctr}\\
    \stepcounter{myctr}%
  }%
  etc.
\end{multicols}

\end{document}

在此处输入图片描述

概括（位置数字系统）

常规位置数字系统可以用通用代码处理。以下内容借鉴了 的实现expl3并对其进行了改编，\int_to_base:nn以便提供 Shadok 数字系统中任意整数的格式。这里可用的数字符号仍然是Ga、Bu和（每个都有几个标记），但您可以用您选择的任何 LaTeX 代码替换它们。只是不要忘记更新 中的可用符号数量（此处：4）。ZoMeu\g_guidone_nb_symbols_int

\documentclass{article}
\usepackage{expl3}
\usepackage{multicol}   % only for the demo code

\ExplSyntaxOn
% Ga, Bu, Zo, Meu: 4 symbols. Replace with the number of digit symbols you have.
\int_const:Nn \c_guidone_nb_shadok_digit_symbols_int { 4 }

% Replace Ga, Bu, Zo, Meu with LaTeX code producing each possible digit symbol.
\cs_new:Npn \__guidone_to_shadok_digit:n #1
  {
    \exp_after:wN \__guidone_remove_fi:nw
    \if_case:w #1 \c_space_token  % this finishes the <number>
      { Ga }
    \or:
      { Bu }
    \or:
      { Zo }
    \or:
      { Meu }
    \else:
      { \msg_expandable_error:nnn { guidone } { too-large-for-a-digit } {#1} }
    \fi:
  }

\msg_new:nnn { guidone } { too-large-for-a-digit }
  { Too~large~for~a~digit:~\exp_not:n {#1}. }

% Define aliases that can be used outside \ExplSyntaxOn ... \ExplSyntaxOff.
\cs_new_eq:NN \nbShadokDigitSymbols \c_guidone_nb_shadok_digit_symbols_int
\cs_new_eq:NN \toShadokDigit \__guidone_to_shadok_digit:n

% The \exp_stop_f: stops f-expansion from the \__guidone_deliver:nfw call.
% \__guidone_to_digit:n should normally be used within f-expansion,
% otherwise the \exp_stop_f: (implicit space token) will precede the wanted
% result (digit).
\cs_new:Npn \__guidone_remove_fi:nw #1#2\fi:
  { \fi: \exp_stop_f: #1 }

% #1: base (= number of available digit symbols)
% #2: function such as \__guidone_to_shadok_digit:n (input: a number between 0
%     and #1 - 1, both inclusive; output: a single digit)
% #3: number to format
\cs_new:Npn \guidone_format_number:nNn #1#2#3
  {
    \exp:w
    \__guidone_to_base:nnN {#3} {#1} #2
    \q_stop
  }

% The \*_to_base:* functions are based on code from l3int.dtx, with
% modifications so that \guidone_format_number:nNn can deliver potentially
% sensitive material with \exp_not:n in exactly two expansion steps.
\cs_new:Npn \__guidone_to_base:nnN #1
  { \exp_args:Nf \__guidone_to_base_aux:nnN { \int_eval:n {#1} } }

\cs_new:Npn \__guidone_to_base_aux:nnN #1#2#3
  {
    \int_compare:nNnTF {#1} < { 0 }
      { \exp_args:No \__guidone_to_base:nnnN { \use_none:n #1 } {#2} { - } #3 }
      { \__guidone_to_base:nnnN {#1} {#2} { } #3 }
  }

% #1: empty or minus sign
% #2: leftmost digit of the number (i.e., the last digit produced by
%     \guidone_format_number:nNn)
% #3: the remaining digits
%
% The \exp_end: terminates the expansion started by \exp:w in
% \guidone_format_number:nNn.
\cs_new:Npn \__guidone_deliver:nnw #1#2#3\q_stop
  { \exp_end: \exp_not:n { #1#2#3 } }

\cs_generate_variant:Nn \__guidone_deliver:nnw { nf }

\cs_new:Npn \__guidone_to_base:nnnN #1#2#3#4
  {
    \int_compare:nNnTF {#1} < {#2}
      { \__guidone_deliver:nfw {#3} { #4 {#1} } }
      {
        \exp_args:Nf \__guidone_to_base:nnnnN
          { #4 { \int_mod:nn {#1} {#2} } }
          {#1}
          {#2}
          {#3}
          #4
      }
  }

\cs_new:Npn \__guidone_to_base:nnnnN #1#2#3#4#5
  {
    \exp_args:Nf \__guidone_to_base:nnnN
      { \int_div_truncate:nn {#2} {#3} }
      {#3}
      {#4}
      #5
    #1
  }

% Define aliases that can be used outside \ExplSyntaxOn ... \ExplSyntaxOff.
% Note that \guideoneFormatNumber is fully expandable and delivers the result
% in two expansion steps.
\cs_new_eq:NN \guideoneFormatNumber \guidone_format_number:nNn
\cs_new_eq:NN \intstepinline \int_step_inline:nnnn
\ExplSyntaxOff

% What follows \shadokNumber in the input stream will be the third argument of
% \guideoneFormatNumber, i.e.: the number to convert.
\newcommand*{\shadokNumber}{%
  \guideoneFormatNumber{\nbShadokDigitSymbols}{\toShadokDigit}%
}

\newcounter{myctr}

% Make it so that \themyctr uses our custom numeration style.
\renewcommand{\themyctr}{%
  \shadokNumber{\value{myctr}}%
}


\begin{document}

\begin{multicols}{3}
  \noindent
  % Initial value, step, final value
  \intstepinline{0}{1}{64}{%
    \themyctr\\
    \stepcounter{myctr}%
  }%
  etc.
\end{multicols}

Most importantly:
\[ 65536 = \shadokNumber{65536} \]
and  % We can handle any 〈integer expression〉, including negative ones.
\[ -(3\times 64 + 2\times 16 + 1\times 4 + 0\times 1) =
   \shadokNumber{-1*(3*64 + 2*16 + 1*4 + 0*1)} \]

% Verify that the desired result is obtained in exactly two expansion steps.
% If you uncomment the following seven lines, TeX will print on the terminal:
%   > \exp_not:n {-MeuZoBuGa}.
%
% \def\zzz#1{\expandafter\showtokens\expandafter{#1}}
% \expandafter\zzz\expandafter{%
%   \guideoneFormatNumber
%     {\nbShadokDigitSymbols}
%     {\toShadokDigit}
%     {-1*(3*64 + 2*16 + 1*4 + 0*1)}%
% }

\end{document}

在此处输入图片描述

从以下定义可以看出：

\newcommand*{\shadokNumber}{%
  \guideoneFormatNumber{\nbShadokDigitSymbols}{\toShadokDigit}%
}

为了在同一文档中定义其他数字系统的转换函数，您唯一需要做的就是传递\guideoneFormatNumber：

  • 可用数字符号的数量，即根据（\nbShadokDigitSymbols在我们的例子中为 4）；

  • 一个函数，例如\toShadokDigit（即\__guidone_to_shadok_digit:n），将数字在 0 和根据- 1 为目标数字系统中的 1 位表示形式。

要转换的数字必须位于输入流的下一个位置，并且不需要作为参数来抓取\shadokNumber（这是一个小的优化）。

希伯来数字

希伯来数字似乎没有上述代码设计的那样规则。如果只需要少量值，则可以使用第一种方法。否则，恐怕您需要另一种转换算法。该polyglossia包提供了诸如 和 之类的命令\hebrewnumeral，\Hebrewnumeral这些\Hebrewnumeralfinal命令可能会引起您的兴趣。您可能对以下内容感兴趣这个问题例如。唉，我不懂希伯来语，所以在这方面不能给你更多帮助。

答案2

刚刚发布的 3.41 版本基于babelCSS，为一些语言提供了一组预定义的加法和字母数字现成的柜台风格（数字样式自 3.20 开始可用babel）。更重要的是，它们是在文件中的一组键/值对的帮助下定义的ini，这意味着您也可以使用 定义自己的样式\babelprovide。注意，此工具适用于xetex和luatex，但它可能工作pdftex。下面是带有一些解释的示例。

\documentclass{article}

\usepackage[italian]{babel}

\babelprovide[
     % To define a purely alphabetic numeral, just provide a space-
     % separated list of ordered symbols, characters, etc. Let's name
     % it 'lower' (you can choose another name):
  counters/lower=Aa Bb Cc Dd Ee Ff Gg Hh Ii Jj Kk Ll,
     % For additive numerals, a set of four keys are required, numbered
     % with a digit from 1 (for 1-9) to 4 (for 1000-9000) preceded by a
     % dot. Let's name it 'letters':
  counters/letters.1= a b c d e f g h i,
  counters/letters.2= k l m n o p q r s, 
  counters/letters.3= A B C D E F G H I,
  counters/letters.4= K L M N O P Q R S,
     % Fixed representations for specific values of additive numerals
     % are allowed, too. Just end the key with dot, uppercase F, dot,
     % number:
  counters/letters.F.55 = Oohh
     % Redefining \alph to print these numerals is simple:
  alph = letters    
  ]{italian}

\begin{document}

\localenumeral{lower}{4}     % Prints Dd

\localenumeral{lower}{2}     % Prints Bb

\localenumeral{letters}{956} % Prints Iof

\localenumeral{letters}{55}  % Prints Oohh

\alph{page}  % Prints a, because it's the first page and \alph uses the
             % 'letters' numerals

\end{document}

有关详细信息，请参阅babel 3.41 中的新功能。

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