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%%
%% This is file `mathexample.tex',
%% generated with the docstrip utility.
%%
%% The original source files were:
%%
%% texpower-doc.dtx (with options: `mathexample,mathexample-src,end')
%%
%% --------------------------------------------------------------
%% TeXPower bundle - dynamic online presentations with LaTeX
%% Copyright (C) 1999-2004 Stephan Lehmke
%% Copyright (C) 2003-2005 Hans Fredrik Nordhaug
%%
%% This program is free software; you can redistribute it and/or
%% modify it under the terms of the GNU General Public License
%% as published by the Free Software Foundation; either version 2
%% of the License, or (at your option) any later version.
%%
%% This program is distributed in the hope that it will be useful,
%% but WITHOUT ANY WARRANTY; without even the implied warranty of
%% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
%% GNU General Public License for more details.
%% --------------------------------------------------------------
%%
%% The list of all files belonging to the TeXPower bundle is
%% given in the file `00readme.txt'.
%%
\ProvidesFile{mathexample.tex}%
[2005/04/07 TeXPower example file]
%-----------------------------------------------------------------------------------------------------------------
%
% Math example for the package texpower.sty.
%
%-----------------------------------------------------------------------------------------------------------------
% Enable all color emphasis and highlighting options. Use white background and slifonts.
\PassOptionsToPackage{coloremph,colormath,colorhighlight,whitebackground}{texpower}
% Input the generic preamble.
\input{__TPpreamble}
\usepackage{tpslifonts}
\hypersetup{pdftitle={texpower math example}}
%-----------------------------------------------------------------------------------------------------------------
% Packages and Preamble settings individual for this example.
% We write some aligned equations.
\usepackage{amsmath}
% Make nested braces grow.
\delimitershortfall-1sp
%-----------------------------------------------------------------------------------------------------------------
% Finally, everything is set up. Here we go...
%
\begin{document}
\begin{slide}
%-----------------------------------------------------------------------------------------------------------------
%
\makeslidetitle{\macroname{stepwise} Example: An Aligned Equation}\label{Sec:ExEq}
% In the following, an aligned system of equations is built incrementally. We use the custom command \liststepwise to
% avoid glitches in vertical spacing.
%
\liststepwise%
{%
%
% This is just for compressing the equations so they can be squeezed on one slide.
%
\fontsize{7.8pt}{9pt}\selectfont
\renewcommand{\arraystretch}{0}%
\setlength{\arraycolsep}{0pt}%
\setlength{\abovedisplayskip}{0pt}%
\setlength{\belowdisplayskip}{0pt}%
%
% \highlightboxed will be used for underlaying some formulas with color. To minimize overlap, the width of the outer
% frame is reduced.
\setlength{\highlightboxsep}{1pt}%
%
\begin{align*}
\lefteqn
{%
\min
\left(
% The nested braces are filled `from outer to inner'. This means nesting a lot of steps inside each other...
% The outermost brace is displayed from the outset.
% The first step (which follows right here) displays the next inner brace (the first argument of \min), filled
% with an almost `empty' array (apart from one comma and some dots).
% \bstep is used to get appropriate white space when the step is not yet active.
\bstep
{\max
\left(
\begin{array}{l}
% The next two steps fill in the lines of the array.
\bstep{\min\left(F'(x),\min\left(F_1(x),G_1(y)\right)\right)},\\[-2ex]
\vdots\\
\bstep{\min\left(F'(x),\min\left(F_n(x),G_n(y)\right)\right)}
\end{array}
\right)
},
% After the first brace is filled, the next step provides the second argument of \min.
\bstep{\min\left(G_i(y),H_i(z)\right)}
\right)
}
&
% The next couple of steps will create the remaining lines of the aligned equations. These need to be
% insubstantial (as is the default for \liststepwise), because & can't go in a box.
% As a consequence, the horizontal alignment cannot kick in until the last step is performed. This would make the
% alignment `flicker' sidewise.
% So we have to bite the bullet and duplicate the widest entry here (invisibly), so that the horizontal alignment
% is constant during all steps. *sigh*
\phantom
{%
{}=
\min
\left(
F'(x),
\min
\left(
\max
\left(
\begin{array}{l}
\min\left(F_1(x),\min\left(G_1(y),G_i(y)\right)\right),\\[-1.5ex]
\vdots\\[-.5ex]
\min\left(F_n(x),\min\left(G_n(y),G_i(y)\right)\right)
\end{array}
\right),
H_i(z)
\right)
\right)
}
% The next step displays two lines at a time, but incompletely, i.e. some parts are missing (which are inside
% nested calls of \bstep).
% This way, it is demonstrated how the arguments of the nested \min's are reordered.
\step
{%
\\
&=
\max
\left(
% The macro \activatestep is used by \stepwise to `wrap' the argument of a \bstep command at the _first_ time
% it appears.
% Usually, it does nothing. Now, we redefine it to highlight its background, so it is easier to spot the
% places where the additional arguments were inserted.
\let\activatestep\highlightboxed
\begin{array}{l}
\min
\left(
% The inner \bstep's display the missing arguments, which are completely identical in both lines.
% It is intended that all the missing arguments appear at the same time, so \rebstep is used for the
% remaining arguments which have been left out.
\min\left(\bstep{F'(x)},\min\left(\rebstep{F_1(x),G_1(y)}\right)\right),\min\left(G_i(y),H_i(z)\right)
\right),\\[-2ex]
\vdots\\[-1ex]
\min
\left(
\min\left(\rebstep{F'(x)},\min\left(\rebstep{F_n(x),G_n(y)}\right)\right),\min\left(G_i(y),H_i(z)\right)
\right)
\end{array}
\right)
\\
&=
\max
\left(
\let\activatestep\highlightboxed
\begin{array}{l}
\min
\left(
\min\left(
% Here are the remaining arguments of \min which are all to be displayed in one step (together with
% those from the previous line).
\rebstep{F'(x)},\min\left(\rebstep{F_1(x)},\min\left(\rebstep{G_1(y)},G_i(y)\right)\right)
\right),
H_i(z)
\right),\\[-2.5ex]
\vdots\\[-1.5ex]
\min
\left(
\min\left(
\rebstep{F'(x)},\min\left(\rebstep{F_n(x)},\min\left(\rebstep{G_n(y)},G_i(y)\right)\right)
\right),
H_i(z)
\right)
\end{array}
\right)
}
\step
{%
\\
&=
\min
\left(
F'(x),
\min
\left(
\max
\left(
\begin{array}{l}
\min\left(F_1(x),\min\left(G_1(y),G_i(y)\right)\right),\\[-1.5ex]
\vdots\\[-.5ex]
\min\left(F_n(x),\min\left(G_n(y),G_i(y)\right)\right)
\end{array}
\right),
H_i(z)
\right)
\right)
}
\end{align*}
}%
\newslide
\end{slide}
\end{document}
\endinput
%%
%% End of file `mathexample.tex'.
|
