From 19fe8162b8801b7ec2ede8d4ff03c4d69dc14edd Mon Sep 17 00:00:00 2001 From: mikeshulman Date: Thu, 16 Jan 2014 09:16:04 -0800 Subject: [PATCH 1/2] macros for fractional theorem numbers, see #601 --- macros.tex | 86 +++++++++++++++++++++++++++++++++++++++++++++++++----- 1 file changed, 78 insertions(+), 8 deletions(-) diff --git a/macros.tex b/macros.tex index ba442c37b..c27dd5bd2 100644 --- a/macros.tex +++ b/macros.tex @@ -676,18 +676,77 @@ % Corollary 1.2 rather than Corollary 1.1. This makes it much easier % for the reader to find a particular theorem when flipping through % the document. +% +% We also allow for fractional theorem numbers, for theorems added +% after publication in between existing theorems without changing +% their numbers. To create a fractional theorem number, use the +% environment "newthm" (or "newcor", "newlem", etc.) which takes two +% arguments, the numerator and denominator of the fraction. Such +% fractions must be strictly between zero and one, and must strictly +% increase in between each pair of ordinary (integer-numbered) +% theorems. \makeatletter +% We start by defining the primary theorem environment. The counter +% "thm" is the one we will use for all theorem environments. +\newtheorem{thm}{Theorem}[section] +% Auxiliary counters which store the most recently used fraction. +\newcounter{@newthmnum} +\setcounter{@newthmnum}{0} +\newcounter{@newthmdenom} +\setcounter{@newthmdenom}{1} +% This macro will be called to create and munge all theorem +% environments, *including* the base one "thm" that we have already +% created. \def\defthm#1#2#3{% - %% Ensure all theorem types are numbered with the same counter - \newaliascnt{#1}{thm} - \newtheorem{#1}[#1]{#2} - \aliascntresetthe{#1} - %% This command tells cleveref's \cref what to call things - \crefname{#1}{#2}{#3}} + % The actual "theorem environment" we use internally is not "thm" or + % "cor", but rather "my@thm" or "my@cor". The aliascnt commands + % ensure that all such environments use the same counter "thm". + \newaliascnt{my@#1}{thm} + \newtheorem{my@#1}[my@#1]{#2} + \aliascntresetthe{my@#1} + % This command tells cleveref's \cref what to call things + \crefname{#1}{#2}{#3} + % Now we define "thm"/"cor"/etc. to be a wrapper around its my@ + % version, which resets the "most recently seen fraction" counters + % afterwards. + \expandafter\def\csname #1\endcsname{\begin{my@#1}} + \expandafter\def\csname end#1\endcsname{\end{my@#1}\setcounter{@newthmnum}{0}\setcounter{@newthmdenom}{1}} + % Next we define the "newthm" environment for fractions. Again, there + % is an internal "my@newthm" version. Note that this does *not* use + % the "thm" counter, since we don't want that counter to get + % incremented when we pass through a newthm. Instead it creates its + % own my@newthm counter, which we never actually use. + \newtheorem{my@new#1}{#2} + \crefname{my@new#1}{#2}{#3} + % Instead of using the "my@newthm" counter, when we need to number a + % newthm, we call the special macro \newthm defined below. + \expandafter\renewcommand\csname themy@new#1\endcsname{\thenewthm} + % Finally, we define the "newthm" environment to first check + % validity of the fraction passed and then create the theorem. + \newenvironment{new#1}[2]{\checknewthmfrac{##1}{##2}\setcounter{@newthmnum}{##1}\setcounter{@newthmdenom}{##2}\begin{my@new#1}}{\end{my@new#1}} +} +% How to display fractional theorem numbers. +% (In particular, we leave off the zero if it is there) +\def\thenewthm{\ifnum0<\value{my@thm}\themy@thm\else\thesection.\fi$\frac{\arabic{@newthmnum}}{\arabic{@newthmdenom}}$} +% Reset the fraction at section boundaries too. This is a bit of a +% hack; \@seccntformat is not intended for this. +\let\my@seccntformat\@seccntformat +\renewcommand*{\@seccntformat}[1]{\setcounter{@newthmnum}{0}\setcounter{@newthmdenom}{1}\my@seccntformat{#1}} +% Test to make sure newthm fractions increase and are all in between zero and one +\newcount\@xone +\newcount\@xtwo +\def\checknewthmfrac#1#2{ + \ifnum0<#1\else\errmessage{Fractional theorem numbers must be greater than zero}\fi + \ifnum#1<#2\else\errmessage{Fractional theorem numbers must be less than one}\fi + \@xone=#1 + \@xtwo=#2 + \multiply\@xtwo by \value{@newthmnum} + \multiply\@xone by \value{@newthmdenom} + \ifnum\@xone>\@xtwo\else\errmessage{Theorem numbers out of order}\fi +} % Now define a bunch of theorem-type environments. -\newtheorem{thm}{Theorem}[section] -\crefname{thm}{Theorem}{Theorems} +\defthm{thm}{Theorem}{Theorems} %\defthm{prop}{Proposition} % Probably we shouldn't use "Proposition" in this way \defthm{cor}{Corollary}{Corollaries} \defthm{lem}{Lemma}{Lemmas} @@ -745,6 +804,17 @@ \let\c@equation\c@thm \numberwithin{equation}{section} +% Fractional equation numbering. Use a numbered equation environment +% like "equation", and inside it, call "newtag" with two arguments: +% the numerator and denominator, as for "newthm". The same +% restrictions apply (fractions must be strictly between 0 and 1, and +% strictly increase in between ordinary integer-numbered theorems or +% equations). +\def\newtag#1#2{\checknewthmfrac{#1}{#2}% + \setcounter{@newthmnum}{#1}% + \setcounter{@newthmdenom}{#2}% + \tag{\thenewthm}} + %%%% ENUMERATE NUMBERING %%%% From fc089b3dab1212ee3ce9c0e87142bafdb5e0a85a Mon Sep 17 00:00:00 2001 From: mikeshulman Date: Thu, 16 Jan 2014 09:53:13 -0800 Subject: [PATCH 2/2] remark on errata and numbering in intro --- introduction.tex | 8 ++++++-- 1 file changed, 6 insertions(+), 2 deletions(-) diff --git a/introduction.tex b/introduction.tex index 7be56c2e5..ebb325d4e 100644 --- a/introduction.tex +++ b/introduction.tex @@ -494,8 +494,12 @@ \subsection*{How to read this book} Finally, recall that this book was written as a massively collaborative effort by a large number of people. We have done our best to achieve consistency in terminology and notation, and to put the mathematics in a linear sequence that flows logically, but it is very likely that some imperfections remain. -We ask the reader's forgiveness for any such infelicities, and welcome suggestions for improvement of the next edition. - +We ask the reader's forgiveness for any such infelicities, and welcome suggestions for improvement. +% +Errata and updated copies are available at \url{http://homotopytypetheory.org/book}; +the copy you are now reading is version \texttt{\OPTversion}and incorporates all errata with prior versions. +While page numbering may differ between copies, the numbering of sections, theorems, exercises, and equations will remain constant throughout the first edition. +New theorems and equations may be added at the end of a section, or be given fractional numbers (thus Theorem 1.2.3$\frac12$ may be added between Theorems 1.2.3 and 1.2.4). % Local Variables: % TeX-master: "hott-online"