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| author | Wu Cheng-Han | 2015-05-04 15:53:29 +0800 |
|---|---|---|
| committer | Wu Cheng-Han | 2015-05-04 15:53:29 +0800 |
| commit | 4b0ca55eb79e963523eb6c8197825e9e8ae904e2 (patch) | |
| tree | 574f3923af77b37b41dbf1b00bcd7827ef724a28 /public/vendor/codemirror/mode/stex/index.html | |
| parent | 61eb11d23c65c9e5c493c67d055f785cbec139e2 (diff) | |
First commit, version 0.2.7
Diffstat (limited to 'public/vendor/codemirror/mode/stex/index.html')
| -rwxr-xr-x | public/vendor/codemirror/mode/stex/index.html | 110 |
1 files changed, 110 insertions, 0 deletions
diff --git a/public/vendor/codemirror/mode/stex/index.html b/public/vendor/codemirror/mode/stex/index.html new file mode 100755 index 00000000..14679da4 --- /dev/null +++ b/public/vendor/codemirror/mode/stex/index.html @@ -0,0 +1,110 @@ +<!doctype html> + +<title>CodeMirror: sTeX mode</title> +<meta charset="utf-8"/> +<link rel=stylesheet href="../../doc/docs.css"> + +<link rel="stylesheet" href="../../lib/codemirror.css"> +<script src="../../lib/codemirror.js"></script> +<script src="stex.js"></script> +<style>.CodeMirror {background: #f8f8f8;}</style> +<div id=nav> + <a href="http://codemirror.net"><h1>CodeMirror</h1><img id=logo src="../../doc/logo.png"></a> + + <ul> + <li><a href="../../index.html">Home</a> + <li><a href="../../doc/manual.html">Manual</a> + <li><a href="https://github.com/codemirror/codemirror">Code</a> + </ul> + <ul> + <li><a href="../index.html">Language modes</a> + <li><a class=active href="#">sTeX</a> + </ul> +</div> + +<article> +<h2>sTeX mode</h2> +<form><textarea id="code" name="code"> +\begin{module}[id=bbt-size] +\importmodule[balanced-binary-trees]{balanced-binary-trees} +\importmodule[\KWARCslides{dmath/en/cardinality}]{cardinality} + +\begin{frame} + \frametitle{Size Lemma for Balanced Trees} + \begin{itemize} + \item + \begin{assertion}[id=size-lemma,type=lemma] + Let $G=\tup{V,E}$ be a \termref[cd=binary-trees]{balanced binary tree} + of \termref[cd=graph-depth,name=vertex-depth]{depth}$n>i$, then the set + $\defeq{\livar{V}i}{\setst{\inset{v}{V}}{\gdepth{v} = i}}$ of + \termref[cd=graphs-intro,name=node]{nodes} at + \termref[cd=graph-depth,name=vertex-depth]{depth} $i$ has + \termref[cd=cardinality,name=cardinality]{cardinality} $\power2i$. + \end{assertion} + \item + \begin{sproof}[id=size-lemma-pf,proofend=,for=size-lemma]{via induction over the depth $i$.} + \begin{spfcases}{We have to consider two cases} + \begin{spfcase}{$i=0$} + \begin{spfstep}[display=flow] + then $\livar{V}i=\set{\livar{v}r}$, where $\livar{v}r$ is the root, so + $\eq{\card{\livar{V}0},\card{\set{\livar{v}r}},1,\power20}$. + \end{spfstep} + \end{spfcase} + \begin{spfcase}{$i>0$} + \begin{spfstep}[display=flow] + then $\livar{V}{i-1}$ contains $\power2{i-1}$ vertexes + \begin{justification}[method=byIH](IH)\end{justification} + \end{spfstep} + \begin{spfstep} + By the \begin{justification}[method=byDef]definition of a binary + tree\end{justification}, each $\inset{v}{\livar{V}{i-1}}$ is a leaf or has + two children that are at depth $i$. + \end{spfstep} + \begin{spfstep} + As $G$ is \termref[cd=balanced-binary-trees,name=balanced-binary-tree]{balanced} and $\gdepth{G}=n>i$, $\livar{V}{i-1}$ cannot contain + leaves. + \end{spfstep} + \begin{spfstep}[type=conclusion] + Thus $\eq{\card{\livar{V}i},{\atimes[cdot]{2,\card{\livar{V}{i-1}}}},{\atimes[cdot]{2,\power2{i-1}}},\power2i}$. + \end{spfstep} + \end{spfcase} + \end{spfcases} + \end{sproof} + \item + \begin{assertion}[id=fbbt,type=corollary] + A fully balanced tree of depth $d$ has $\power2{d+1}-1$ nodes. + \end{assertion} + \item + \begin{sproof}[for=fbbt,id=fbbt-pf]{} + \begin{spfstep} + Let $\defeq{G}{\tup{V,E}}$ be a fully balanced tree + \end{spfstep} + \begin{spfstep} + Then $\card{V}=\Sumfromto{i}1d{\power2i}= \power2{d+1}-1$. + \end{spfstep} + \end{sproof} + \end{itemize} + \end{frame} +\begin{note} + \begin{omtext}[type=conclusion,for=binary-tree] + This shows that balanced binary trees grow in breadth very quickly, a consequence of + this is that they are very shallow (and this compute very fast), which is the essence of + the next result. + \end{omtext} +\end{note} +\end{module} + +%%% Local Variables: +%%% mode: LaTeX +%%% TeX-master: "all" +%%% End: \end{document} +</textarea></form> + <script> + var editor = CodeMirror.fromTextArea(document.getElementById("code"), {}); + </script> + + <p><strong>MIME types defined:</strong> <code>text/x-stex</code>.</p> + + <p><strong>Parsing/Highlighting Tests:</strong> <a href="../../test/index.html#stex_*">normal</a>, <a href="../../test/index.html#verbose,stex_*">verbose</a>.</p> + + </article> |