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\title{Topical tip: Numbering theorems and corollaries in \LaTeX}
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\author[R.~A.~Bailey]{R.~A.~Bailey\\Goldsmiths' College, University of London}
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\newcommand{\lamport}{{\itshape \LaTeX: A Document Preparation System\/} by Leslie 
Lamport}
\newcommand{\shortlamp}{{\itshape The Manual}}

\begin{Article}

\begin{question}
We Mathematicians can't use \LaTeX. We need to be able to choose how to label 
our theorems. For example, I like to have my important theorems numbered in a 
sequence Theorem~A, Theorem~B and so on, 
and the less important theorems numbered
Theorem~1, Theorem~2 and so on. You can't do that in \LaTeX.
\label{sieb}
\end{question}

\begin{answer}
Oh yes you can, and using nothing more than you can find in
\lamport, hereafter called \shortlamp.

Pages 58--59 of \shortlamp\ show how to set up a simple theorem environment.
The command
\begin{verbatim}
   \newtheorem{thm}{Theorem}
\end{verbatim}
creates an environment called \latexword{thm}. Then each use of this 
environment produces something whose heading is \theoremheadfont{Theorem}. It 
is true that these theorems are numbered 1, 2,~3, etc. To obtain something 
numbered A, B,~C, etc., use the numbering commands given on page~92 of 
\shortlamp. Thus
\begin{verbatim}
   \newtheorem{main}{Theorem}
   \renewcommand{\themain}{\Alph{main}}
\end{verbatim}
creates an environment called \latexword{main} whose heading is also
\theoremheadfont{Theorem} but whose instances are numbered A, B, \ldots.
Cross-references work correctly too: if you label the third 
\latexword{main}  with
\verb+\label{mmm}+
and refer to it with \verb+Theorem~\ref{mmm}+ then it will be called 
Theorem~C.
\end{answer}

\begin{question}
Journal editors are so fussy. They all want me to number my corollaries in
different ways. The first wants corollaries numbered in the same sequence as 
theorems; the second wants them numbered in a separate sequence of their own; 
the third wants the corollaries after Theorem~7 to be numbered Corollary~7.1, 
Corollary~7.2, etc.; while the fourth also wants the corollaries to start 
renumbering after each theorem, but wants the corollaries after Theorem~7 to be
numbered Corollary~1, Corollary~2 etc. How do I do all of this?
\end{question}

\begin{answer}
It is not hard to do these things, because \LaTeX\ is provided with the 
\latexword{newtheorem} command. I shall assume that you have defined an 
environment \latexword{thm} as in the answer to Question~\ref{sieb}. The 
instructions on pages~58--59 of \shortlamp\ show us how to satisfy the first 
three editors. For the first, put
\begin{verbatim}
   \newtheorem{cor}[thm]{Corollary}
\end{verbatim}
and you will get an environment called \latexword{cor} whose instances are 
called \theoremheadfont{Corollary} numbered in the same sequence as the 
theorems. For the second, put
\begin{verbatim}
   \newtheorem{cor}{Corollary}
\end{verbatim}
and for the third put
\begin{verbatim}
   \newtheorem{cor}{Corollary}[thm]
\end{verbatim}

For the fourth editor, we need the extra information from page~92. The third 
command above makes the \latexword{cor} counter start again after each 
\latexword{thm}, but it causes the Corollary number to be printed as, say, 7.1 
rather than~1. We can cure this by putting
\begin{verbatim}
   \newtheorem{cor}{Corollary}[thm]
   \renewcommand{\thecor}{\arabic{cor}}
\end{verbatim}

In each of the four cases you get an environment called \latexword{cor} 
whose instances are 
called \theoremheadfont{Corollary}.
Only the system of numbering is different.

You should now be able to work out how to make the corollaries after Theorem~5 
come out as Corollary~5a, Corollary~5b, and so on.
\end{answer}
\end{Article}
