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authormistic100 <mistic@strangeplanet.fr>2015-07-24 22:44:39 +0200
committermistic100 <mistic@strangeplanet.fr>2015-07-26 19:11:36 +0200
commit4e71ba9d3ea40cd2d817965e5eed4a2fe1b876b3 (patch)
treeaf7f5291540806e5fde21db1d98d590579549055 /plugins/LocalFilesEditor/codemirror/mode/stex/index.html
parent32138f1fbd7637dffaaad0c8ca677e43a0d13831 (diff)
Remove core plugins from core repository
Diffstat (limited to 'plugins/LocalFilesEditor/codemirror/mode/stex/index.html')
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1 files changed, 0 insertions, 96 deletions
diff --git a/plugins/LocalFilesEditor/codemirror/mode/stex/index.html b/plugins/LocalFilesEditor/codemirror/mode/stex/index.html
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--- a/plugins/LocalFilesEditor/codemirror/mode/stex/index.html
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@@ -1,96 +0,0 @@
-<!doctype html>
-<html>
- <head>
- <title>CodeMirror 2: sTeX mode</title>
- <link rel="stylesheet" href="../../lib/codemirror.css">
- <script src="../../lib/codemirror.js"></script>
- <script src="stex.js"></script>
- <link rel="stylesheet" href="stex.css">
- <style>.CodeMirror {background: #f8f8f8;}</style>
- <link rel="stylesheet" href="../../css/docs.css">
- </head>
- <body>
- <h1>CodeMirror 2: sTeX mode</h1>
- <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/stex</code>.</p>
-
- </body>
-</html>