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Comments on latest draft
\documentclass{article}
\def\arccot{\mathop{\rm arccot}\nolimits}
\begin{document}
\title{Comments on MathML 2\\
Version 2U306 --- Stephen Watt's copy\\
edition of 9 March 2000}
\author{James Davenport
\tt jhd@maths.bath.ac.uk\\
jhd@csd.uwo.ca}
\maketitle
Stephen very kindly lent me his copy: here are my observations.
\begin{description}
\item[p. 113; Line 10 of 4.1.2.] ``BA-level or Baccealaureate''. Would
it be sensible to add ``etc.'', or name, say ``Abitur''?
\item[p. 116; line 5]This says that the default is that a {\tt ci}
comes from a commutative field. Apart from the pedantic point that all
fields are commutative, is this really necessary? After all, variables
often stand for integers. Maybe all you ned is a commutative ring. I
also note that page 125, at line 2 after {\tt ci} says ``no default is
specified''.
\item[p. 120]Ath the bottom, it is stated that the definition of
inverse trigs can differ sligtly. A stronger statement is true: the definition of
$\arccot(-1)$.
\begin{tabular}{llrl}
\cite{AS}&1st printing&$\frac{3\pi}4$&inconsistent\\
\cite{AS}&9th printing&$\frac{-\pi}4$\\
\cite{CRC}&30th edition&$\frac{3\pi}4$&inconsistent\\
Maple&V release 5&$\frac{3\pi}4$\\
Axiom&2.1&$\frac{3\pi}4$\\
Mathematica&\cite{Mma}&$\frac{-\pi}4$\\
Reduce&3.4.1&$\frac{-\pi}4$&in floating point\\
Matlab&5.3.0&$\frac{-\pi}4$&in floating point\\
\end{tabular}
\item[p. 121; top]No doubt the definition of {\tt inverse} has already
been fought over, but mightn't it be better to say ``for some $x$ in
$D$''. Otherwise, since $\arcsin(\sin(3\pi))\ne3\pi$ (normally), one
might have problems saying what $\arcsin(-1)$ is.
\item[p. 121; 13 lines up]What is ``the scope of the declare''? See
similar unspecified phrases on p. 128.
\item[p. 126]It is not stated that {\tt type=normal} is the default
for {\tt set}: I assume that it is.
\item[p. 126; {\tt set and list} +9]``the order defaults to a numeric
or lexicographic ordering''. Does this mean that $(z,y,x)$ renders as
$(x,y,z)$?, or does this only apply to lists generated via constructors?
\item[p. 271]This described {\tt and} as $n$-ary, but {\tt or} and
{\tt xor} as binary. This is certainly inconsistent, and is
inconsistent with p. 129, which declares all three to be $n$-ary ---
DPC says that p. 129 is consistent with the DTD
\begin{verbatim}
<!ENTITY % clogicopnary '%MathML.and.qname; |
%MathML.or.qname; |
%MathML.xor.qname;' >
\end{verbatim}
OpenMath defines all three as $n$-ary, which seems like the correct answer.
\item [p. 338; third point in chapter 4]. ``Classifical''.
\end{description}
More comments to follow,
\begin{thebibliography}{9}
\bibitem{AS}
Abramowitz,M. \& Stegun,I.,
Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical
Tables.
US Government Printing Office, 1964.
10th Printing December 1972.
\bibitem{Mma}
Wolfram,S.,
The Mathematica Book.
Wolfram Media/C.U.P., 1999.
\bibitem{CRC}
Zwillinger,D. (ed.),
CRC Standard Mathematical Tables and Formulae.
30th. ed., CRC Press, Boca Raton, 1996.
\end{thebibliography}
\end{document}