File modules/editor/codemirror/mode/stex/index.html

Last commit: Sun Dec 17 01:14:09 2017 +0100	Jan Dankert	Integration eines weiteren Code-Editors: Codemirror. Demnächst müssen wir hier mal aufräumen und andere Editoren rauswerfen.


     1 <!doctype html>
     2 
     3 <title>CodeMirror: sTeX mode</title>
     4 <meta charset="utf-8"/>
     5 <link rel=stylesheet href="../../doc/docs.css">
     6 
     7 <link rel="stylesheet" href="../../lib/codemirror.css">
     8 <script src="../../lib/codemirror.js"></script>
     9 <script src="stex.js"></script>
    10 <style>.CodeMirror {background: #f8f8f8;}</style>
    11 <div id=nav>
    12   <a href="http://codemirror.net"><h1>CodeMirror</h1><img id=logo src="../../doc/logo.png"></a>
    13 
    14   <ul>
    15     <li><a href="../../index.html">Home</a>
    16     <li><a href="../../doc/manual.html">Manual</a>
    17     <li><a href="https://github.com/codemirror/codemirror">Code</a>
    18   </ul>
    19   <ul>
    20     <li><a href="../index.html">Language modes</a>
    21     <li><a class=active href="#">sTeX</a>
    22   </ul>
    23 </div>
    24 
    25 <article>
    26 <h2>sTeX mode</h2>
    27 <form><textarea id="code" name="code">
    28 \begin{module}[id=bbt-size]
    29 \importmodule[balanced-binary-trees]{balanced-binary-trees}
    30 \importmodule[\KWARCslides{dmath/en/cardinality}]{cardinality}
    31 
    32 \begin{frame}
    33   \frametitle{Size Lemma for Balanced Trees}
    34   \begin{itemize}
    35   \item
    36     \begin{assertion}[id=size-lemma,type=lemma] 
    37     Let $G=\tup{V,E}$ be a \termref[cd=binary-trees]{balanced binary tree} 
    38     of \termref[cd=graph-depth,name=vertex-depth]{depth}$n>i$, then the set
    39      $\defeq{\livar{V}i}{\setst{\inset{v}{V}}{\gdepth{v} = i}}$ of
    40     \termref[cd=graphs-intro,name=node]{nodes} at 
    41     \termref[cd=graph-depth,name=vertex-depth]{depth} $i$ has
    42     \termref[cd=cardinality,name=cardinality]{cardinality} $\power2i$.
    43    \end{assertion}
    44   \item
    45     \begin{sproof}[id=size-lemma-pf,proofend=,for=size-lemma]{via induction over the depth $i$.}
    46       \begin{spfcases}{We have to consider two cases}
    47         \begin{spfcase}{$i=0$}
    48           \begin{spfstep}[display=flow]
    49             then $\livar{V}i=\set{\livar{v}r}$, where $\livar{v}r$ is the root, so
    50             $\eq{\card{\livar{V}0},\card{\set{\livar{v}r}},1,\power20}$.
    51           \end{spfstep}
    52         \end{spfcase}
    53         \begin{spfcase}{$i>0$}
    54           \begin{spfstep}[display=flow]
    55            then $\livar{V}{i-1}$ contains $\power2{i-1}$ vertexes 
    56            \begin{justification}[method=byIH](IH)\end{justification}
    57           \end{spfstep}
    58           \begin{spfstep}
    59            By the \begin{justification}[method=byDef]definition of a binary
    60               tree\end{justification}, each $\inset{v}{\livar{V}{i-1}}$ is a leaf or has
    61             two children that are at depth $i$.
    62           \end{spfstep}
    63           \begin{spfstep}
    64            As $G$ is \termref[cd=balanced-binary-trees,name=balanced-binary-tree]{balanced} and $\gdepth{G}=n>i$, $\livar{V}{i-1}$ cannot contain
    65             leaves.
    66           \end{spfstep}
    67           \begin{spfstep}[type=conclusion]
    68            Thus $\eq{\card{\livar{V}i},{\atimes[cdot]{2,\card{\livar{V}{i-1}}}},{\atimes[cdot]{2,\power2{i-1}}},\power2i}$.
    69           \end{spfstep}
    70         \end{spfcase}
    71       \end{spfcases}
    72     \end{sproof}
    73   \item 
    74     \begin{assertion}[id=fbbt,type=corollary]	
    75       A fully balanced tree of depth $d$ has $\power2{d+1}-1$ nodes.
    76     \end{assertion}
    77   \item
    78       \begin{sproof}[for=fbbt,id=fbbt-pf]{}
    79         \begin{spfstep}
    80           Let $\defeq{G}{\tup{V,E}}$ be a fully balanced tree
    81         \end{spfstep}
    82         \begin{spfstep}
    83           Then $\card{V}=\Sumfromto{i}1d{\power2i}= \power2{d+1}-1$.
    84         \end{spfstep}
    85       \end{sproof}
    86     \end{itemize}
    87   \end{frame}
    88 \begin{note}
    89   \begin{omtext}[type=conclusion,for=binary-tree]
    90     This shows that balanced binary trees grow in breadth very quickly, a consequence of
    91     this is that they are very shallow (and this compute very fast), which is the essence of
    92     the next result.
    93   \end{omtext}
    94 \end{note}
    95 \end{module}
    96 
    97 %%% Local Variables: 
    98 %%% mode: LaTeX
    99 %%% TeX-master: "all"
   100 %%% End: \end{document}
   101 </textarea></form>
   102     <script>
   103       var editor = CodeMirror.fromTextArea(document.getElementById("code"), {});
   104     </script>
   105 
   106     <p><strong>MIME types defined:</strong> <code>text/x-stex</code>.</p>
   107 
   108     <p><strong>Parsing/Highlighting Tests:</strong> <a href="../../test/index.html#stex_*">normal</a>,  <a href="../../test/index.html#verbose,stex_*">verbose</a>.</p>
   109 
   110   </article>



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Sun, 17 Dec 2017 01:14:09 +0100	Jan Dankert	Integration eines weiteren Code-Editors: Codemirror. Demnächst müssen wir hier mal aufräumen und andere Editoren rauswerfen.