Merge branch 'refs/heads/master' into components

author: Valerio Virgillito 2012-02-15 17:04:39 -0800
committer: Valerio Virgillito 2012-02-15 17:04:39 -0800
commit: fe71cb9aa1700199c0089166ad54fc56eb760644 (patch)
tree: b0c7c24b1f45a079e1c09312ca716e3d35aecad4 /js/codemirror/mode/stex/index.html
parent: 747616980cad14f0b65fbcc7f497ed9680a39d29 (diff)
parent: d366c0bd1af6471511217ed574083e15059519b5 (diff)
download: ninja-fe71cb9aa1700199c0089166ad54fc56eb760644.tar.gz
1 files changed, 0 insertions, 96 deletions
diff --git a/js/codemirror/mode/stex/index.html b/js/codemirror/mode/stex/index.html
deleted file mode 100644
index 7a27d11e..00000000
--- a/js/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="../../theme/default.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>
author	Valerio Virgillito	2012-02-15 17:04:39 -0800
committer	Valerio Virgillito	2012-02-15 17:04:39 -0800
commit	fe71cb9aa1700199c0089166ad54fc56eb760644 (patch)
tree	b0c7c24b1f45a079e1c09312ca716e3d35aecad4 /js/codemirror/mode/stex/index.html
parent	747616980cad14f0b65fbcc7f497ed9680a39d29 (diff)
parent	d366c0bd1af6471511217ed574083e15059519b5 (diff)
download	ninja-fe71cb9aa1700199c0089166ad54fc56eb760644.tar.gz

diff --git a/js/codemirror/mode/stex/index.html b/js/codemirror/mode/stex/index.html deleted file mode 100644 index 7a27d11e..00000000 --- a/js/codemirror/mode/stex/index.html +++ /dev/null
@@ -1,96 +0,0 @@
1	<!doctype html>
2	<html>
3	<head>
4	<title>CodeMirror 2: sTeX mode</title>
5	<link rel="stylesheet" href="../../lib/codemirror.css">
6	<script src="../../lib/codemirror.js"></script>
7	<script src="stex.js"></script>
8	<link rel="stylesheet" href="../../theme/default.css">
9	<style>.CodeMirror {background: #f8f8f8;}</style>
10	<link rel="stylesheet" href="../../css/docs.css">
11	</head>
12	<body>
13	<h1>CodeMirror 2: sTeX mode</h1>
14	<form><textarea id="code" name="code">
15	\begin{module}[id=bbt-size]
16	\importmodule[balanced-binary-trees]{balanced-binary-trees}
17	\importmodule[\KWARCslides{dmath/en/cardinality}]{cardinality}
18
19	\begin{frame}
20	\frametitle{Size Lemma for Balanced Trees}
21	\begin{itemize}
22	\item
23	\begin{assertion}[id=size-lemma,type=lemma]
24	Let $G=\tup{V,E}$ be a \termref[cd=binary-trees]{balanced binary tree}
25	of \termref[cd=graph-depth,name=vertex-depth]{depth}$n>i$, then the set
26	$\defeq{\livar{V}i}{\setst{\inset{v}{V}}{\gdepth{v} = i}}$ of
27	\termref[cd=graphs-intro,name=node]{nodes} at
28	\termref[cd=graph-depth,name=vertex-depth]{depth} $i$ has
29	\termref[cd=cardinality,name=cardinality]{cardinality} $\power2i$.
30	\end{assertion}
31	\item
32	\begin{sproof}[id=size-lemma-pf,proofend=,for=size-lemma]{via induction over the depth $i$.}
33	\begin{spfcases}{We have to consider two cases}
34	\begin{spfcase}{$i=0$}
35	\begin{spfstep}[display=flow]
36	then $\livar{V}i=\set{\livar{v}r}$, where $\livar{v}r$ is the root, so
37	$\eq{\card{\livar{V}0},\card{\set{\livar{v}r}},1,\power20}$.
38	\end{spfstep}
39	\end{spfcase}
40	\begin{spfcase}{$i>0$}
41	\begin{spfstep}[display=flow]
42	then $\livar{V}{i-1}$ contains $\power2{i-1}$ vertexes
43	\begin{justification}[method=byIH](IH)\end{justification}
44	\end{spfstep}
45	\begin{spfstep}
46	By the \begin{justification}[method=byDef]definition of a binary
47	tree\end{justification}, each $\inset{v}{\livar{V}{i-1}}$ is a leaf or has
48	two children that are at depth $i$.
49	\end{spfstep}
50	\begin{spfstep}
51	As $G$ is \termref[cd=balanced-binary-trees,name=balanced-binary-tree]{balanced} and $\gdepth{G}=n>i$, $\livar{V}{i-1}$ cannot contain
52	leaves.
53	\end{spfstep}
54	\begin{spfstep}[type=conclusion]
55	Thus $\eq{\card{\livar{V}i},{\atimes[cdot]{2,\card{\livar{V}{i-1}}}},{\atimes[cdot]{2,\power2{i-1}}},\power2i}$.
56	\end{spfstep}
57	\end{spfcase}
58	\end{spfcases}
59	\end{sproof}
60	\item
61	\begin{assertion}[id=fbbt,type=corollary]
62	A fully balanced tree of depth $d$ has $\power2{d+1}-1$ nodes.
63	\end{assertion}
64	\item
65	\begin{sproof}[for=fbbt,id=fbbt-pf]{}
66	\begin{spfstep}
67	Let $\defeq{G}{\tup{V,E}}$ be a fully balanced tree
68	\end{spfstep}
69	\begin{spfstep}
70	Then $\card{V}=\Sumfromto{i}1d{\power2i}= \power2{d+1}-1$.
71	\end{spfstep}
72	\end{sproof}
73	\end{itemize}
74	\end{frame}
75	\begin{note}
76	\begin{omtext}[type=conclusion,for=binary-tree]
77	This shows that balanced binary trees grow in breadth very quickly, a consequence of
78	this is that they are very shallow (and this compute very fast), which is the essence of
79	the next result.
80	\end{omtext}
81	\end{note}
82	\end{module}
83
84	%%% Local Variables:
85	%%% mode: LaTeX
86	%%% TeX-master: "all"
87	%%% End: \end{document}
88	</textarea></form>
89	<script>
90	var editor = CodeMirror.fromTextArea(document.getElementById("code"), {});
91	</script>
92
93	<p><strong>MIME types defined:</strong> <code>text/stex</code>.</p>
94
95	</body>
96	</html>