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| author | mistic100 <mistic@strangeplanet.fr> | 2015-07-24 22:44:39 +0200 |
|---|---|---|
| committer | mistic100 <mistic@strangeplanet.fr> | 2015-07-26 19:11:36 +0200 |
| commit | 4e71ba9d3ea40cd2d817965e5eed4a2fe1b876b3 (patch) | |
| tree | af7f5291540806e5fde21db1d98d590579549055 /plugins/LocalFilesEditor/codemirror/mode/stex/index.html | |
| parent | 32138f1fbd7637dffaaad0c8ca677e43a0d13831 (diff) | |
Remove core plugins from core repository
Diffstat (limited to 'plugins/LocalFilesEditor/codemirror/mode/stex/index.html')
| -rw-r--r-- | plugins/LocalFilesEditor/codemirror/mode/stex/index.html | 96 |
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 deleted file mode 100644 index 73b07ac13..000000000 --- a/plugins/LocalFilesEditor/codemirror/mode/stex/index.html +++ /dev/null @@ -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> |