[Tex/LaTex] Book: Chapter/Section/Subsection Numbering

Question

I'm new to LaTeX but want to try to tex my Linear Algebra lecture. My lecturer is using the following structure:

Chapter 0: Basics

• § 1 Sets
  • Def. 1.1: Some definition
  • Def. 1.2: Some definition
  • Pro. 1.3: Some proposition
  • Exm. 1.4: Some example
• § 2 Other section
• § 3 Other section
  • Def. 3.1: Some definition
  • Def. 3.2: Some definition
  • Pro. 3.3: Some proposition
  • Exm. 3.4: Some example
• § 4 Other section

Chapter 1: Groups, Rings and Fields

• § 5 Groups
  • Def. 5.1: Some definition
  • …
• § 6 Rings

The structure in words:

• Chapters
  • Numbered (starting from 0)
• Section (in Chapters)
  • Numbered
  • not affected by chapter numbered
  • don't reset when a new chapter is started
  • Start with a §-symbol
• Subsections (Definitions, Examples, Propositions)
  • Numbered with current Section-Number as prefix
  • Reset each new section

It would be great to be able to write something like this:

\documentclass{book}
...


\begin{document}

\chapter{Basics}

\section{Sets}
\subsection{Def. :}
Some definition.

\subsection{Example :}
Some example.


\section{NewSection}
....


\chapter{Groupds, Rings, Fields}

\section{Groups}

\subsection{Def. :}
Some definition

...

\end{document}

The behaviour differs from the desired behaviour in the following ways: Chapter-Numbering starts at 1, Section-Numbering reset each chapter. Sections don't start with a §-symbol automatically. Subsections contain chapter/section and subsection numbers.

How can I get my desired layout?

Answer 1

In case of numbering sections independent from chapters, the question will be raised how to number definitions/propositions/examples that are placed in a chapter but are not be placed in a section?

E.g.:

Chapter 0 Basics
  1 Elements
  2 Combinations
    Def. 2.1: Some definition
    Def. 2.2: Some definition    
    Pro. 2.3  Some proposition
    Exm. 2.4: Some Example
    2.1 Permutations
    2.2 Sets
      Def. 2.2.1: Some definition
      Def. 2.2.2: Some definition
      Pro. 2.2.3  Some proposition
      Exm. 2.2.4: Some Example
Chapter 1 Groups
  Def. <???>1: Some definition
  Pro. <???>2  Some proposition
  Exm. <???>3: Some Example
  3 Groups
    Def. 3.1: Some definition
    Pro. 3.2  Some proposition
    Exm. 3.3: Some Example
Chapter 2 Rings and Fields  
  Def. <???>1: Some definition
  Pro. <???>2  Some proposition
  Exm. <???>3: Some Example
  4 Rings 
  5 Fields    

How should definitions/propositions/examples in Chapter 1 be named?
They don't belong to section 2. And they don't belong to section 3.

How should definitions/propositions/examples in Chapter 2 be named? They don't belong to section 3. And they don't belong to section 4.

I suggest <???>=<chapter>/<definition/proposition/example number> in these cases:

Chapter 0 Basics
  1 Elements
  2 Combinations
    Def. 2.1: Some definition
    Def. 2.2: Some definition
    Pro. 2.3  Some proposition
    Exm. 2.4: Some Example
    2.1 Permutations
    2.2 Sets
      Def. 2.2.1: Some definition
      Def. 2.2.2: Some definition
      Pro. 2.2.3  Some proposition
      Exm. 2.2.4: Some Example
Chapter 1 Groups
  Def. 1/1: Some definition
  Pro. 1/2  Some proposition
  Exm. 1/3: Some Example
  3 Groups
    Def. 3.1: Some definition
    Def. 3.2: Some definition        
    Pro. 3.3  Some proposition
    Exm. 3.4: Some Example
Chapter 2 Rings and Fields
  Def. 2/1: Some definition
  Pro. 2/2  Some proposition
  Pro. 2/3  Some proposition      
  Exm. 2/4: Some Example
  4 Rings
  5 Fields

Another question is about the numbering of footnotes, tables, figures and equations.

I suggest numbering footnotes per chapter.
I suggest numbering tables, figures and equations per section as deeper sectioning-levels might have equally numbered definition/proposition/example-pendants.

I suggest handling the case of tables/figures/equations in a chapter but not in a section in the same way as definition/proposition/example in a chapter but not in a section, i.e. by prepending "/" to the corresponding number.

Yet another question:

Do you want definitions/propositions/examples to occur within the table of contents as well?

Do you wish something like a separate List of definitions / List of propositions / List of examples.

I suggest not having definitions/propositions/examples occur within the table of contents.
I suggest not having a a separate List of definitions / List of propositions / List of examples.
These things require more crude hacking of the documentclass / of the book class.

\documentclass{book}
\usepackage{hyperref}
\makeatletter
\newcounter{TheoremElement}
\newcounter{sectionfake}
\begingroup
\def\tempa#1{\global\csname c@#1\endcsname\z@}%
\expandafter\endgroup\ifx\tempa\@stpelt
  \expandafter\@firstoftwo\else\expandafter\@secondoftwo\fi
{%
  \def\c@sectionfakehack\z@
}{%
  \def\c@sectionfakehack\m@ne\stepcounter#1%
}%
{%
  \let\c@sectionfake\c@sectionfake\stepcounter{sectionfake}%
}%
\renewcommand\cl@chapter{%
  \@elt{sectionfake}%
  \@elt{footnote}%
  \@elt{equation}\@elt{figure}\@elt{table}%
  \@elt{subsection}\@elt{subsubsection}%
  \@elt{paragraph}\@elt{subparagraph}%
  \@elt{TheoremElement}%
}%
\renewcommand\cl@section{%
  \@elt{sectionfakehack}%<-the hack increments sectionfake instead of resetting
                        %  to zero whenever section is incremented via \stepcounter
  \@elt{equation}\@elt{figure}\@elt{table}%
  \@elt{subsection}\@elt{subsubsection}%
  \@elt{paragraph}\@elt{subparagraph}%
  \@elt{TheoremElement}%
}%
\renewcommand\cl@subsection{%
  \@elt{subsubsection}%
  \@elt{paragraph}\@elt{subparagraph}%
  \@elt{TheoremElement}%
}%
\renewcommand\cl@subsubsection{%
  \@elt{paragraph}\@elt{subparagraph}%
  \@elt{TheoremElement}%
}%
\renewcommand\cl@paragraph{%
  \@elt{subparagraph}%
  \@elt{TheoremElement}%
}%
\renewcommand\cl@subparagraph{%
  \@elt{TheoremElement}%
}%
\renewcommand*\cl@TheoremElement{}%
%
\newcommand\sectionfakefork{%
  \ifnum\number\value{sectionfake}>0 %
  \expandafter\@firstoftwo\else\expandafter\@secondoftwo\fi
}%
\newcommand\AllSectionLevelsArabic{%
  \sectionfakefork
  {%
    \AllSectionLevelsArabicLoop{\AllSectionLevelsArabicLoop{%
      \AllSectionLevelsArabicLoop{\AllSectionLevelsArabicLoop{%
        \@firstoftwo{\arabic{section}.}%
      }{subsection}.}{subsubsection}.%
    }{paragraph}.}{subparagraph}.%
    \@firstoftwo
  }{%
    \arabic{chapter}/%
  }%
  \arabic{TheoremElement}%
}%
\newcommand\AllSectionLevelsArabicLoop[4]{%
  #4{\ifnum\number\value{#2}>0 %
     \expandafter\@firstoftwo\else\expandafter\@secondoftwo\fi
     {#1\@secondoftwo\arabic{#2}#3}{#1#4}%
    }{#1\@secondoftwo\arabic{#2}#3}%
}%
\newcommand\insertbehindnumber[2]{%
  #1\@insertbehimdnumber{#2}%
}%
\newcommand\@insertbehimdnumber{}%
\long\def\@insertbehimdnumber#1#2\endcsname{#2\endcsname#1}%
\renewcommand\theTheoremElement{\AllSectionLevelsArabic}
\newtheorem{definition}[TheoremElement]{\insertbehindnumber{Def.}{:}}%
\newtheorem{proposition}[TheoremElement]{\insertbehindnumber{Pro.}{:}}%
\newtheorem{example}[TheoremElement]{\insertbehindnumber{Exm.}{:}}%
\renewcommand\theequation{\sectionfakefork{\arabic{section}.}{\arabic{chapter}/}\arabic{equation}}%
\renewcommand\thetable{\sectionfakefork{\arabic{section}.}{\arabic{chapter}/}\arabic{table}}%
\renewcommand\thefigure{\sectionfakefork{\arabic{section}.}{\arabic{chapter}/}\arabic{figure}}%
\renewcommand\thesection{\protect\S\texorpdfstring{\protect\,}{ }\arabic{section}}%
\AtBeginDocument{%
  % Remove the dot after chapter-numbers in headers of verso pages:
  %\renewcommand*\chaptermark[1]{%
  %  \markboth{%
  %    \MakeUppercase{%
  %      \ifnum\c@secnumdepth>\m@ne\if@mainmatter\@chapapp\ \thechapter\quad\fi\fi#1%
  %    }%
  %  }{}%
  %}%
  % Remove the dot after sectioning-paragraph-numbers in headers of recto pages:
  \renewcommand*\sectionmark[1]{%
     \markright{%
       \MakeUppercase{\ifnum\c@secnumdepth>\z@\thesection\quad\fi#1}%
     }%
  }%
  \@ifpackageloaded{hyperref}{%
    % Ensure uniqueness of hyperref' anchor names:
    \renewcommand\theHsection{\arabic{section}}%
    \renewcommand\theHTheoremElement{\AllSectionLevelsArabic}%
    \renewcommand\theHequation{\sectionfakefork{\arabic{section}.}{\arabic{chapter}/}\arabic{equation}}%
    \renewcommand\theHtable{\sectionfakefork{\arabic{section}.}{\arabic{chapter}/}\arabic{table}}%
    \renewcommand\theHfigure{\sectionfakefork{\arabic{section}.}{\arabic{chapter}/}\arabic{figure}}%
    \renewcommand\theHfootnote{\arabic{chapter}.\arabic{footnote}}%
  }{%
    \providecommand\texorpdfstring[2]{#1}%
  }%
}%
\makeatother

\setcounter{secnumdepth}{4}
\setcounter{tocdepth}{\value{secnumdepth}}
\usepackage[open,openlevel=\value{secnumdepth},atend,numbered]{bookmark}    

\begin{document}
\tableofcontents

\setcounter{chapter}{-1}%

\chapter{Basics}

\begin{definition}
Some definition.
\end{definition}

\section{Sets}

\begin{definition}
\label{deflabel}Some definition.
\end{definition}

\begin{definition}
Some definition.
\end{definition}

\begin{proposition}
\label{proplabel}Some proposition.
\end{proposition}

\begin{example}
\label{exlabel}Some example.
\end{example}

\section{Other section}

\section{Other section}

\begin{definition}
Some definition.
\end{definition}

\begin{definition}
Some definition.
\end{definition}

\begin{proposition}
Some proposition.
\end{proposition}

\begin{example}
Some example.
\end{example}

\section{Other section}

\chapter{Groups, Rings and Fields}

\begin{definition}
\label{otherdeflabel}Some definition.
\end{definition}

\section{Groups}

\begin{definition}
Some definition.
\end{definition}

\subsection{SubGroups}

\begin{definition}
Some definition.
\end{definition}

\subsubsection{SubSubGroups}

\begin{definition}
\label{yetanotherdeflabel}Some definition.
\end{definition}

\section{Rings}

\cleardoublepage
\section{Testing referencing}

referencing a definition: \ref{deflabel}\\
referencing a proposition: \ref{proplabel}\\
referencing an example: \ref{exlabel}\\
referencing another definition: \ref{otherdeflabel}\\
referencing yet another definition: \ref{yetanotherdeflabel}
\end{document}