Basic use of derivative with cool package fails with “Missing \endcsname inserted”

Question

In exploring options for typesetting derivatives I came across the cool package. But a basic example from Page 22 of the Content Oriented LaTeX documentation (October 7, 2006) seems to result in the error:

 Missing \endcsname inserted.
  <to be read again> 
                \toks@ 

Uncommenting the line in the MWE below yields the above error. As is, the MWE produces:

References:

• Can I have a flexible partial derivative macro? I would prefer to use one of the solutions mentioned here as they do not require another package, but the syntax proposed here is different that the cool package. This is problematic in that if I later need the flexibility provided by the the cool package will not be as easy to switch.

Code

\documentclass{article}
\usepackage{amsmath}
\usepackage{cool}
\begin{document}
\begin{align*}
    \D[1]{f}{x,y,z} &= \cdots\\
    %\D[2,n,3]{f}{x,y,z} &= x
\end{align*}
\end{document}

Answer 1

This is a bug in the cool package v1.35 (2006/12/29). Lines 2056 to 2063 read

\whiledo{ \boolean{COOL@isint} \AND
\NOT \value{COOL@multideriv}>\value{COOL@ct}  }%
{%
\def\COOL@tempd%
{\csname COOL@deriv@powers@\roman{COOL@multideriv}\endcsname}%
\isint{\COOL@tempd}{COOL@isint}%
\stepcounter{COOL@multideriv}%
}

The \def (line 2059) must be an \edef. After changing it (in a local copy, of course) the MWE ran without errors.

BTW: the style of the “d” can be changed through:

\Style{DSymb={\mathrm d}}

Answer 2

I use the following macro to set multiple partial derivatives:

\newcommand*\mdiff[3]{\frac{\partial^{#2}{#1}}{\pABLN{#3}}}
\newcounter{pABLCounter}
\def\pABLN#1{\setcounter{pABLCounter}{1}\xpABLN#1;pABLEnde;}
\def\pABLEnde{pABLEnde}
\def\xpABLN#1;{\def\temp{#1}%
  \ifx\temp\pABLEnde
  \else 
    \stepcounter{pABLCounter}
    \ifodd \value{pABLCounter} 
      \if1#1\,\else {{}^{#1}\,}\fi%
      \else{\partial{#1}}% 
    \fi %
    \expandafter\xpABLN
  \fi  
}

to set in your case:

\mdiff{f}{3}{x;1;y;1;z;1}

other possibilities are:

\mdiff{f}{5}{x;1;z;4}

giving \frac{\partial^5f}{\partial x\partial z^4}.

If you really want d instead of \partial just replace it in the code.