%!latex-faq
\documenttype{article}
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\newcommand{\gellmu}{\abbr{GELLMU}}
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\newcommand{\mathml}{\abbr{MathML}}
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  #3 }
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  #3 }
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  \section[][\label[:series="frame"]{#1}][\evalref{#1}]{#2}%
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\item[A.]\ #2 %
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\surtitle{Slides for TUG 2007}
\title{Dual Presentation with Math\\ Using \gellmu}
\subtitle{\tex Users Group (\abbr{TUG}) in San Diego}
\author{William F. Hammond}
\address{
  Dept. of Mathematics \& Statistics\\
  University at Albany\\
  Albany, New York\ \ 12222\ \ (USA) \\
  \urlanch{http://www.albany.edu/\tld;hammond/}  % that ; is somewhat like {}
}
\date{July, 2007}

\begin{document}

\sframe{theidea}{The Idea}{

\begin{display}
\begin{tabular}{p{.14}p{.06}p{.14}}
~ &  & \tbox{\pdf}          \\
~ & \ari{.06}{ne}           \\
\tbox{\latex-like source}               \\
~ & \ari{.06}{se}           \\
~ &  & \tbox{\mxhtml}
\end{tabular}
\end{display}
}

\sframe{gammaid}{Example}{

\begin{Menu}
\item
\cbox{0.85}{
The following identity may be regarded as a formulation of the
Weierstrass product for the Gamma function.
\[ \int_{0}^{\infty} t^x e^{-t} \frac{dt}{t} \int:
   = \frac{1}{x}
     \prod_{k=1}^{\infty}
       \frac{\bal{1 + \frac{1}{k}}^x}{\bal{1 + \frac{x}{k}}}
     \prod: \]
Understanding the derivation of this identity is reasonable for
a bright student of first year undergraduate calculus in the
United States.
}
\end{Menu}

\subhdrc{These are \mxhtml slides!}
}

\sframe{confrac}{Computation of a Continued Fraction}{

\begin{eqnarray}[:nonum="true"]
\ \sqrt{10} & = & 3 + \frac{1}{\frac{1}{\sqrt{10}-3}} \\
\      & = & 3 + \frac{1}{\sqrt{10}+3} \\
\      & = & 3 + \frac{1}{6 + \frac{1}{\frac{1}{\sqrt{10}-3}}} \\
\      & = & 3 + \frac{1}{6 + \frac{1}{\sqrt{10}+3}} \\
\      & = & 3 + \frac{1}{6 + \frac{1}{6 + \frac{1}{\ldots}}}
\end{eqnarray}
}

\sframe{classroom}{Finding the tangent at a point}{

\begin{Menu}
\item
\bold{Curve:}\ \ $y^2 = x^3 - 7 x + 10$\\
\bold{Point:}\ \ $B = (1, -2)$

Use implicit differentiation to find the slope:
\[ 2 y y' = 3 x^2 - 7 \]
Evaluate when $(x, y) = (1, -2)$: \ $y' = 1$
The tangent line at $(1, -2)$ is parallel to any vector with slope $1$,
e.g., $V = (1, 1)$.

Parametric equation:
\[ p(t) = B + t V = (1, -2) + t(1, 1) = (1 + t, -2 + t) \]
\end{Menu}
}



\sframe{torture13}{Mozilla \mathml Torture Test 13}{

\[ \sqrt{1+\sqrt{1+\sqrt{1+\sqrt{1+\sqrt{1+\sqrt{1+\sqrt{1+x}}}}}}} \]
}

\sframe{torture24}{Mozilla \mathml Torture Test 24}{

\[ \mbox{det}\balvbr{\begin{array}{ccccc}
  c_0   &  c_1    &  c_2    & \ldots &  c_n     \\
  c_1   &  c_2    &  c_3    & \ldots &  c_{n+1} \\
  c_2   &  c_3    &  c_4    & \ldots &  c_{n+2} \\
 \vdots & \vdots  & \vdots  &        & \vdots   \\
  c_n   & c_{n+1} & c_{n+2} & \ldots &  c_{2n}
\end{array}} > 0 \]
}

\sframe{madramhardy}{Madore's Challenge}{

\begin{Menu}
\item
\cbox{0.85}{
In a letter to Godfrey Harold Hardy, S\b{r}\={\i}\b{n}iv\={a}sa
R\={a}m\={a}\b{n}uja\b{n} Aiya\.{n}k\={a}r asserts that
\[
\frac{1
}{1+\frac{e^{-2\pi\sqrt{5}}
}{1+\frac{e^{-4\pi\sqrt{5}}
}{1+\frac{e^{-6\pi\sqrt{5}}
}{\ldots}}}}
=
\bal{\frac{\sqrt{5}
}{
1+\sqrt[5]{5^{3/4}\bal{\frac{\sqrt{5}-1}{2}}^{5/2}-1}}
-\frac{\sqrt{5}+1}{2}}
e^{{2\pi}/{\sqrt{5}}}
\]
}
\end{Menu}
}



\sframe{zeta}{Zeta function calculation}{

\begin{Menu}
\item
\cbox{0.85}{
With the condition $Z_X(0) = 1$ the function $Z_X(t)$ is
determined by its logarithmic derivative:
}
\end{Menu}

\begin{eqnarray}[: nonum="true"]
 \frac{d}{dt} \func{log} Z_X(t) & = &
      \sum_{x \text{ closed}} d(x) \frac{t^{d(x)-1}}{1 - t^{d(x)}} \sum:    \\
~ & = & \frac{1}{t} \sum_{r \geq 1}
  \sum_{\setOf{x \text{ closed}}{d(x) = r}} r \frac{t^r}{1 - t^r} \sum:\sum:\\
~ & = & \frac{1}{t} \sum_{r \geq 1} r c_r \frac{t^r}{1 - t^r} \sum:
\ \ = \ \ \frac{1}{t}\sum_{r \geq 1} r c_r\sum_{m \geq 1} t^{rm} \sum:\sum: \\
~ & = & \sum_{\nu \geq 1} N_{\nu} t^{\nu-1} \sum:
\end{eqnarray}
}

\sframe{dualpres}{Dual Presentation}{

\begin{Menu}
\item\parb
\begin{itemize}
\item One source
\item Print and \html outputs
\item Print and \mxhtml if math is involved
\end{itemize}
\end{Menu}
}



\sframe{stdans}{How to write for dual presentation\ \ (I)}{

\subhdrc{Standard Answers}

\begin{Menu}
\item\parb
\begin{enumerate}
\item Write \latex, then translate to \html
\item Write \sgml or \xml, then
  \begin{enumerate}
  \item Translate to \latex
  \item Translate to \mxhtml
  \end{enumerate}
\end{enumerate}
\end{Menu}
}

\sframe{translating}{How to write for dual presentation\ \ (II)}{

\subhdrc{Translating}

\begin{Menu}
\item\parb
Translating from \latex involves
\begin{itemize}
\item Carefully written \latex source
\item Customized tuning
\item Hidden learning curve
\end{itemize}

\begin{menu}
\item \bold{Tough}
\end{menu}
\end{Menu}
}

\sframe{gapproach}{How to write for dual presentation\ \ (III)}{

\subhdrc{The \gellmu Approach}

\begin{Menu}
\item\parb
\begin{itemize}
\item  Must first learn how
\item  Write with \latex-like syntax
\item  Use the vocabulary of an \sgml document type
\end{itemize}

\begin{menu}
\item \bold{Easier!}
\end{menu}
\end{Menu}
}



\sframe{conceptdiffs}{Conceptual Differences}{

\begin{Menu}
\item\parb
\begin{itemize}
\item No pages
\item No vertical lengths
\item Relative horizontal lengths
\item Content, yes.
\item Style, no.
\item Fonts, no.
\end{itemize}
\end{Menu}
}


\sframe{markupdiffs}{Markup Differences in \gellmu}{

\begin{Menu}
\item\parb
\begin{itemize}
\item No declaration style markup (like |{\centering ...}|) 
\item Braced zones provide logical grouping but not scope.
\item |\begin{display} ... \end{display}| is the same as |\display{ ... }|
\item No space allowed between a command and its arguments or between
      its successive arguments.
\item The 33 non-alphanumeric but printable \ascii characters may all be
      referenced by names, e.g., |\tld;| for ``\tld;'' is useful
      in \abbr{URL}s.
\item Counters ride with labels.
\end{itemize}
\end{Menu}
}



\sframe{components}{Flow Chart}{

\begin{display}
\begin{tabular}{p{.19}p{.06}p{.14}p{.06}p{.14}p{.06}p{.14}}
\tbox{\gellmu source} & \ari{.06}{right} & \tbox{\sgml} & & & & \tbox{\pdf}\\
~  &  & \ari{.009}{down} &  &  & \ari{.06}{ne}                              \\
\tbox{Outside \sgml/\xml source} & \ari{.06}{right} & \tbox{Author-level \xml}
~& \ari{.06}{right}& \tbox{Elaborated \xml}& \ari{.06}{right}& \tbox{\mxhtml}\\
~  &  &  &  &  & \ari{.06}{se}                                             \\
~  &  &  &  &  &  & \tbox{Classic \html}
\end{tabular}
\end{display}
}

\sframe{pointersb}{Style}{

\display{\bold{Style choices are made in formatters}\\
               (arrows at the right end of the chart)}
}



\sframe{stylevcontent}{Style vs. Content}{

\begin{display}
\begin{tabular}{ll}
\bold{Style}                      &  \bold{Content}    \\
|\begin{center} ... \end{center}| &  |\display{ ... }|  \\
|\it| or |\textit|                &  |\emph|           \\
|\bf| or |\textbf|                &  |\bold|           \\
  |\textsc|                       &  |\abbr|           \\
|\tt| or |\texttt|                &  |\quostr| or |\path|
\end{tabular}
\end{display}
}

\sframe{elements}{Commands Correspond to \xml Elements}{

\begin{display}
%\begin{tabular}{p{.22}p{.24}p{.49}}
\begin{tabular}{lll}
\bold{LaTeX} & \bold{\gellmu source} & \bold{\gellmu \xml} \\
|\\|         &  |\\|                 & |<brk/>| or |<fcell>...</fcell>|  \\
|&|          &  |&|                  & |<acell>...</acell>|              \\
|\'e|        & |\acute{e}|           & |<acute>e</acute>|                \\
\acute{e}    & |&#xE9;| or \acute{e} & \acute{e}                         \\
|\frac23| & |\frac{2}{3}| & |<frac><nm>2</nm><dn>3</dn></frac>|   \\
|\left\{...\right\}| & |\balbr{ ... }|  & |<balbr> ... </balbr>|    \\
|\sum_j ...| &  |\sum_j ... \sum:| & |<sum><sub>j</sub>...</sum>|
\end{tabular}
\end{display}
}



\sframe{smalldoc}{Write a Document}{

\begin{Menu}

\item\parb

\begin{menu}
\item
Source for a document:
\end{menu}

\begin{verbatim}
\documenttype{article}
\title{A Simple Sum}
\begin{document}

This is a simple summation formula:
\[ \sum_{k=1}^n k \sum: = \frac{n(n+1)}{2} \ \eos \]
It may be proved easily using mathematical induction.

Mathematical induction is part of deductive, not
inductive, logic.

\end{document}
\end{verbatim}
\end{Menu}
}

\sframe{build}{Build a Document}{

\begin{Menu}
\item\parb
\begin{enumerate}
\item
Save it as \qquostr{smalldoc.glm}.

\item
At a command line enter
\display{|mmkg  smalldoc| \ \eos}

\item
Read the \Href{smalldoc.out}{scroll}.

\item
Inspect the yield:
\begin{display}
\begin{tabular}{p{.20}p{.14}p{.14}p{.14}p{.14}}
   \smd{xhtml}{\xhtml}
 & \smd{pdf}{\pdf}
 & \smd{xml}{\xml}
 & \smd{ltx}{\latex}
 & \smd{html}{\html}
\end{tabular}
\end{display}
\end{enumerate}
\end{Menu}
}

\sframe{examples}{Example Documents}{

\begin{itemize}
\item \tref{../Doc/userdoc}{The \emph{User Guide}}
\item \tref{../Doc/glman}{The \emph{Manual}}
\item \tref{../Examples/gamma}{A calculus handout}
\item \tref{../Examples/gsample2e}{A port to \gellmu of Lamport's
           \qquostr{sample2e.tex}}
\item \Href{../Examples/9-8.xhtml}{Port of an article} from
           \emph{The New Journal of Mathematics}
\end{itemize}
}

\sframe{ack}{Acknowedgement}{

The \mxhtml version of these slides uses \Href{http://www.w3.org}{W3C}'s
\Href{http://www.w3.org/Talks/Tools/Slidy/}{\softw{Slidy}} by
Dave Raggett, a JavaScript/\css package for sizing and flow control of
an \html or \xhtml slide show.

(The slides were generated in a non-standard fashion from \gellmu source.)
}

\hdrc{\label{end}}

\end{document}