MyWikiBiz

Changes

User:Jon Awbrey/WORDPRESS (view source)

Revision as of 03:28, 5 June 2013

19,785 bytes added ,  03:28, 5 June 2013
→‎Fourier Transforms of Boolean Functions
Line 1: Line 1:  +
'''WordPress versions of HTML and LaTeX markup'''
 +
 +
<div class="nonumtoc">__TOC__</div>
 +
 +
==Tables==
 +
 +
* Examples of LaTeX tabular markup from [http://inquiryintoinquiry.com/tables/ Inquiry Into Inquiry : Tables]
 +
 +
===Boolean Functions and Propositional Calculus===
 +
 +
====Table A1. Propositional Forms on Two Variables====
 +
 +
<pre>
 +
$latex
 +
\begin{tabular}{|*{7}{c|}}
 +
\multicolumn{7}{c}{Table A1. Propositional Forms on Two Variables} \\
 +
\hline
 +
\(L_1\)&amp;\(L_2\)&amp;&amp;\(L_3\)&amp;\(L_4\)&amp;\(L_5\)&amp;\(L_6\) \\
 +
\hline
 +
&amp;&amp;\(x=\)&amp;1 1 0 0&amp;&amp;&amp; \\
 +
&amp;&amp;\(y=\)&amp;1 0 1 0&amp;&amp;&amp; \\
 +
\hline
 +
\(f_{0}\)&amp;
 +
\(f_{0000}\)&amp;&amp;
 +
0 0 0 0&amp;
 +
\((~)\)&amp;
 +
false&amp;
 +
\(0\)
 +
\\
 +
\(f_{1}\)&amp;
 +
\(f_{0001}\)&amp;&amp;
 +
0 0 0 1&amp;
 +
\((x)(y)\)&amp;
 +
neither \(x\) nor \(y\)&amp;
 +
\(\lnot x \land \lnot y\)
 +
\\
 +
\(f_{2}\)&amp;
 +
\(f_{0010}\)&amp;&amp;
 +
0 0 1 0&amp;
 +
\((x)~y~\)&amp;
 +
\(y\) without \(x\)&amp;
 +
\(\lnot x \land y\)
 +
\\
 +
\(f_{3}\)&amp;
 +
\(f_{0011}\)&amp;&amp;
 +
0 0 1 1&amp;
 +
\((x)\)&amp;
 +
not \(x\)&amp;
 +
\(\lnot x\)
 +
\\
 +
\(f_{4}\)&amp;
 +
\(f_{0100}\)&amp;&amp;
 +
0 1 0 0&amp;
 +
\(~x~(y)\)&amp;
 +
\(x\) without \(y\)&amp;
 +
\(x \land \lnot y\)
 +
\\
 +
\(f_{5}\)&amp;
 +
\(f_{0101}\)&amp;&amp;
 +
0 1 0 1&amp;
 +
\((y)\)&amp;
 +
not \(y\)&amp;
 +
\(\lnot y\)
 +
\\
 +
\(f_{6}\)&amp;
 +
\(f_{0110}\)&amp;&amp;
 +
0 1 1 0&amp;
 +
\((x,~y)\)&amp;
 +
\(x\) not equal to \(y\)&amp;
 +
\(x \ne y\)
 +
\\
 +
\(f_{7}\)&amp;
 +
\(f_{0111}\)&amp;&amp;
 +
0 1 1 1&amp;
 +
\((x~~y)\)&amp;
 +
not both \(x\) and \(y\)&amp;
 +
\(\lnot x \lor \lnot y\)
 +
\\
 +
\hline
 +
\(f_{8}\)&amp;
 +
\(f_{1000}\)&amp;&amp;
 +
1 0 0 0&amp;
 +
\(~x~~y~\)&amp;
 +
\(x\) and \(y\)&amp;
 +
\(x \land y\)
 +
\\
 +
\(f_{9}\)&amp;
 +
\(f_{1001}\)&amp;&amp;
 +
1 0 0 1&amp;
 +
\(((x,~y))\)&amp;
 +
\(x\) equal to \(y\)&amp;
 +
\(x = y\)
 +
\\
 +
\(f_{10}\)&amp;
 +
\(f_{1010}\)&amp;&amp;
 +
1 0 1 0&amp;
 +
\(y\)&amp;
 +
\(y\)&amp;
 +
\(y\)
 +
\\
 +
\(f_{11}\)&amp;
 +
\(f_{1011}\)&amp;&amp;
 +
1 0 1 1&amp;
 +
\((~x~(y))\)&amp;
 +
not \(x\) without \(y\)&amp;
 +
\(x \Rightarrow y\)
 +
\\
 +
\(f_{12}\)&amp;
 +
\(f_{1100}\)&amp;&amp;
 +
1 1 0 0&amp;
 +
\(x\)&amp;
 +
\(x\)&amp;
 +
\(x\)
 +
\\
 +
\(f_{13}\)&amp;
 +
\(f_{1101}\)&amp;&amp;
 +
1 1 0 1&amp;
 +
\(((x)~y~)\)&amp;
 +
not \(y\) without \(x\)&amp;
 +
\(x \Leftarrow y\)
 +
\\
 +
\(f_{14}\)&amp;
 +
\(f_{1110}\)&amp;&amp;
 +
1 1 1 0&amp;
 +
\(((x)(y))\)&amp;
 +
\(x\) or \(y\)&amp;
 +
\(x \lor y\)
 +
\\
 +
\(f_{15}\)&amp;
 +
\(f_{1111}\)&amp;&amp;
 +
1 1 1 1&amp;
 +
\(((~))\)&amp;
 +
true&amp;
 +
\(1\)
 +
\\
 +
\hline
 +
\end{tabular}
 +
&amp;fg=000000$
 +
</pre>
 +
 +
====Table A2. Propositional Forms on Two Variables====
 +
 +
<pre>
 +
$latex
 +
\begin{tabular}{|*{7}{c|}}
 +
\multicolumn{7}{c}{Table A2. Propositional Forms on Two Variables} \\
 +
\hline
 +
\(L_1\)&amp;\(L_2\)&amp;&amp;\(L_3\)&amp;\(L_4\)&amp;\(L_5\)&amp;\(L_6\) \\
 +
\hline
 +
&amp;&amp;\(x =\)&amp;1 1 0 0&amp;&amp;&amp; \\
 +
&amp;&amp;\(y =\)&amp;1 0 1 0&amp;&amp;&amp; \\
 +
\hline
 +
\(f_{0}\)&amp;
 +
\(f_{0000}\)&amp;&amp;
 +
0 0 0 0&amp;
 +
\((~)\)&amp;
 +
false&amp;
 +
\(0\)
 +
\\
 +
\hline
 +
\(f_{1}\)&amp;
 +
\(f_{0001}\)&amp;&amp;
 +
0 0 0 1&amp;
 +
\((x)(y)\)&amp;
 +
neither \(x\) nor \(y\)&amp;
 +
\(\lnot x \land \lnot y\)
 +
\\
 +
\(f_{2}\)&amp;
 +
\(f_{0010}\)&amp;&amp;
 +
0 0 1 0&amp;
 +
\((x)~y~\)&amp;
 +
\(y\) without \(x\)&amp;
 +
\(\lnot x \land y\)
 +
\\
 +
\(f_{4}\)&amp;
 +
\(f_{0100}\)&amp;&amp;
 +
0 1 0 0&amp;
 +
\(~x~(y)\)&amp;
 +
\(x\) without \(y\)&amp;
 +
\(x \land \lnot y\)
 +
\\
 +
\(f_{8}\)&amp;
 +
\(f_{1000}\)&amp;&amp;
 +
1 0 0 0&amp;
 +
\(~x~~y~\)&amp;
 +
\(x\) and \(y\)&amp;
 +
\(x \land y\)
 +
\\
 +
\hline
 +
\(f_{3}\)&amp;
 +
\(f_{0011}\)&amp;&amp;
 +
0 0 1 1&amp;
 +
\((x)\)&amp;
 +
not \(x\)&amp;
 +
\(\lnot x\)
 +
\\
 +
\(f_{12}\)&amp;
 +
\(f_{1100}\)&amp;&amp;
 +
1 1 0 0&amp;
 +
\(x\)&amp;
 +
\(x\)&amp;
 +
\(x\)
 +
\\
 +
\hline
 +
\(f_{6}\)&amp;
 +
\(f_{0110}\)&amp;&amp;
 +
0 1 1 0&amp;
 +
\((x,~y)\)&amp;
 +
\(x\) not equal to \(y\)&amp;
 +
\(x \ne y\)
 +
\\
 +
\(f_{9}\)&amp;
 +
\(f_{1001}\)&amp;&amp;
 +
1 0 0 1&amp;
 +
\(((x,~y))\)&amp;
 +
\(x\) equal to \(y\)&amp;
 +
\(x = y\)
 +
\\
 +
\hline
 +
\(f_{5}\)&amp;
 +
\(f_{0101}\)&amp;&amp;
 +
0 1 0 1&amp;
 +
\((y)\)&amp;
 +
not \(y\)&amp;
 +
\(\lnot y\)
 +
\\
 +
\(f_{10}\)&amp;
 +
\(f_{1010}\)&amp;&amp;
 +
1 0 1 0&amp;
 +
\(y\)&amp;
 +
\(y\)&amp;
 +
\(y\)
 +
\\
 +
\hline
 +
\(f_{7}\)&amp;
 +
\(f_{0111}\)&amp;&amp;
 +
0 1 1 1&amp;
 +
\((~x~~y~)\)&amp;
 +
not both \(x\) and \(y\)&amp;
 +
\(\lnot x \lor \lnot y\)
 +
\\
 +
\(f_{11}\)&amp;
 +
\(f_{1011}\)&amp;&amp;
 +
1 0 1 1&amp;
 +
\((~x~(y))\)&amp;
 +
not \(x\) without \(y\)&amp;
 +
\(x \Rightarrow y\)
 +
\\
 +
\(f_{13}\)&amp;
 +
\(f_{1101}\)&amp;&amp;
 +
1 1 0 1&amp;
 +
\(((x)~y~)\)&amp;
 +
not \(y\) without \(x\)&amp;
 +
\(x \Leftarrow y\)
 +
\\
 +
\(f_{14}\)&amp;
 +
\(f_{1110}\)&amp;&amp;
 +
1 1 1 0&amp;
 +
\(((x)(y))\)&amp;
 +
\(x\) or \(y\)&amp;
 +
\(x \lor y\)
 +
\\
 +
\hline
 +
\(f_{15}\)&amp;
 +
\(f_{1111}\)&amp;&amp;
 +
1 1 1 1&amp;
 +
\(((~))\)&amp;
 +
true&amp;
 +
\(1\)
 +
\\
 +
\hline
 +
\end{tabular}
 +
&amp;fg=000000$
 +
</pre>
 +
 +
====Table A3. Ef Expanded Over Differential Features {dx, dy}====
 +
 +
<pre>
 +
$latex
 +
\begin{tabular}{|c|c||c|c|c|c|}
 +
\multicolumn{6}{c}{Table A3. \(\mathrm{E}f\) Expanded Over Differential Features \(\{\mathrm{d}x, \mathrm{d}y\}\)} \\
 +
\hline
 +
&amp;
 +
\(~~~~~~~~ f ~~~~~~~~\)&amp;
 +
\(~~~~\mathrm{T}_{11}f~~~~\)&amp;
 +
\(~~~~\mathrm{T}_{10}f~~~~\)&amp;
 +
\(~~~~\mathrm{T}_{01}f~~~~\)&amp;
 +
\(~~~~\mathrm{T}_{00}f~~~~\)
 +
\\
 +
&amp;&amp;
 +
\(\mathrm{E}f|_{~\mathrm{d}x ~\mathrm{d}y~}~\)&amp;
 +
\(\mathrm{E}f|_{~\mathrm{d}x~(\mathrm{d}y)}~\)&amp;
 +
\(\mathrm{E}f|_{(\mathrm{d}x)~\mathrm{d}y~}~\)&amp;
 +
\(\mathrm{E}f|_{(\mathrm{d}x)(\mathrm{d}y)}~\)
 +
\\
 +
\hline\hline
 +
\(f_{0}\)&amp;
 +
\(0\)&amp;
 +
\(0\)&amp;
 +
\(0\)&amp;
 +
\(0\)&amp;
 +
\(0\)
 +
\\
 +
\hline
 +
\(f_{1}\)&amp;
 +
\((x)(y)\)&amp;
 +
\(~x~~y~\)&amp;
 +
\(~x~(y)\)&amp;
 +
\((x)~y~\)&amp;
 +
\((x)(y)\)
 +
\\
 +
\(f_{2}\)&amp;
 +
\((x)~y~\)&amp;
 +
\(~x~(y)\)&amp;
 +
\(~x~~y~\)&amp;
 +
\((x)(y)\)&amp;
 +
\((x)~y~\)
 +
\\
 +
\(f_{4}\)&amp;
 +
\(~x~(y)\)&amp;
 +
\((x)~y~\)&amp;
 +
\((x)(y)\)&amp;
 +
\(~x~~y~\)&amp;
 +
\(~x~(y)\)
 +
\\
 +
\(f_{8}\)&amp;
 +
\(~x~~y~\)&amp;
 +
\((x)(y)\)&amp;
 +
\((x)~y~\)&amp;
 +
\(~x~(y)\)&amp;
 +
\(~x~~y~\)
 +
\\
 +
\hline
 +
\(f_{3}\)&amp;
 +
\((x)\)&amp;
 +
\( x \)&amp;
 +
\( x \)&amp;
 +
\((x)\)&amp;
 +
\((x)\)
 +
\\
 +
\(f_{12}\)&amp;
 +
\( x \)&amp;
 +
\((x)\)&amp;
 +
\((x)\)&amp;
 +
\( x \)&amp;
 +
\( x \)
 +
\\
 +
\hline
 +
\(f_{6}\)&amp;
 +
\( (x,y) \)&amp;
 +
\( (x,y) \)&amp;
 +
\(((x,y))\)&amp;
 +
\(((x,y))\)&amp;
 +
\( (x,y) \)
 +
\\
 +
\(f_{9}\)&amp;
 +
\(((x,y))\)&amp;
 +
\(((x,y))\)&amp;
 +
\( (x,y) \)&amp;
 +
\( (x,y) \)&amp;
 +
\(((x,y))\)
 +
\\
 +
\hline
 +
\(f_{5}\)&amp;
 +
\((y)\)&amp;
 +
\( y \)&amp;
 +
\((y)\)&amp;
 +
\( y \)&amp;
 +
\((y)\)
 +
\\
 +
\(f_{10}\)&amp;
 +
\( y \)&amp;
 +
\((y)\)&amp;
 +
\( y \)&amp;
 +
\((y)\)&amp;
 +
\( y \)
 +
\\
 +
\hline
 +
\(f_{7}\)&amp;
 +
\((~x~~y~)\)&amp;
 +
\(((x)(y))\)&amp;
 +
\(((x)~y~)\)&amp;
 +
\((~x~(y))\)&amp;
 +
\((~x~~y~)\)
 +
\\
 +
\(f_{11}\)&amp;
 +
\((~x~(y))\)&amp;
 +
\(((x)~y~)\)&amp;
 +
\(((x)(y))\)&amp;
 +
\((~x~~y~)\)&amp;
 +
\((~x~(y))\)
 +
\\
 +
\(f_{13}\)&amp;
 +
\(((x)~y~)\)&amp;
 +
\((~x~(y))\)&amp;
 +
\((~x~~y~)\)&amp;
 +
\(((x)(y))\)&amp;
 +
\(((x)~y~)\)
 +
\\
 +
\(f_{14}\)&amp;
 +
\(((x)(y))\)&amp;
 +
\((~x~~y~)\)&amp;
 +
\((~x~(y))\)&amp;
 +
\(((x)~y~)\)&amp;
 +
\(((x)(y))\)
 +
\\
 +
\hline
 +
\(f_{15}\)&amp;
 +
\(1\)&amp;
 +
\(1\)&amp;
 +
\(1\)&amp;
 +
\(1\)&amp;
 +
\(1\)
 +
\\
 +
\hline\hline
 +
\multicolumn{2}{|c||}{Fixed Point Total}&amp;
 +
4&amp;
 +
4&amp;
 +
4&amp;
 +
16
 +
\\
 +
\hline
 +
\end{tabular}
 +
&amp;fg=000000$
 +
</pre>
 +
 +
====Table A4. Df Expanded Over Differential Features {dx, dy}====
 +
 +
<pre>
 +
$latex
 +
\begin{tabular}{|c|c||c|c|c|c|}
 +
\multicolumn{6}{c}{Table A4. \(\mathrm{D}f\) Expanded Over Differential Features \(\{\mathrm{d}x, \mathrm{d}y\}\)} \\
 +
\hline
 +
&amp;
 +
\(~~~~~~~~ f ~~~~~~~~\)&amp;
 +
\(\mathrm{D}f|_{~\mathrm{d}x\;\mathrm{d}y~}~\)&amp;
 +
\(\mathrm{D}f|_{~\mathrm{d}x~(\mathrm{d}y)}~\)&amp;
 +
\(\mathrm{D}f|_{(\mathrm{d}x)~\mathrm{d}y~}~\)&amp;
 +
\(\mathrm{D}f|_{(\mathrm{d}x)(\mathrm{d}y)}~\)
 +
\\
 +
\hline\hline
 +
\( f_{0} \)&amp;
 +
\( 0 \)&amp;
 +
\( 0 \)&amp;
 +
\( 0 \)&amp;
 +
\( 0 \)&amp;
 +
\( 0 \)
 +
\\
 +
\hline
 +
\( f_{1} \)&amp;
 +
\( (x)(y) \)&amp;
 +
\( ((x,y)) \)&amp;
 +
\( (y) \)&amp;
 +
\( (x) \)&amp;
 +
\( 0 \)
 +
\\
 +
\( f_{2} \)&amp;
 +
\( (x)~y~ \)&amp;
 +
\( (x,y) \)&amp;
 +
\( y \)&amp;
 +
\( (x) \)&amp;
 +
\( 0 \)
 +
\\
 +
\( f_{4} \)&amp;
 +
\( ~x~(y) \)&amp;
 +
\( (x,y) \)&amp;
 +
\( (y) \)&amp;
 +
\( x \)&amp;
 +
\( 0 \)
 +
\\
 +
\( f_{8} \)&amp;
 +
\( ~x~~y~ \)&amp;
 +
\( ((x,y)) \)&amp;
 +
\( y \)&amp;
 +
\( x \)&amp;
 +
\( 0 \)
 +
\\
 +
\hline
 +
\( f_{3} \)&amp;
 +
\( (x) \)&amp;
 +
\( 1 \)&amp;
 +
\( 1 \)&amp;
 +
\( 0 \)&amp;
 +
\( 0 \)
 +
\\
 +
\( f_{12} \)&amp;
 +
\( x \)&amp;
 +
\( 1 \)&amp;
 +
\( 1 \)&amp;
 +
\( 0 \)&amp;
 +
\( 0 \)
 +
\\
 +
\hline
 +
\( f_{6} \)&amp;
 +
\( (x,y) \)&amp;
 +
\( 0 \)&amp;
 +
\( 1 \)&amp;
 +
\( 1 \)&amp;
 +
\( 0 \)
 +
\\
 +
\( f_{9} \)&amp;
 +
\( ((x,y)) \)&amp;
 +
\( 0 \)&amp;
 +
\( 1 \)&amp;
 +
\( 1 \)&amp;
 +
\( 0 \)
 +
\\
 +
\hline
 +
\( f_{5} \)&amp;
 +
\( (y) \)&amp;
 +
\( 1 \)&amp;
 +
\( 0 \)&amp;
 +
\( 1 \)&amp;
 +
\( 0 \)
 +
\\
 +
\( f_{10} \)&amp;
 +
\( y  \)&amp;
 +
\( 1 \)&amp;
 +
\( 0 \)&amp;
 +
\( 1 \)&amp;
 +
\( 0 \)
 +
\\
 +
\hline
 +
\( f_{7} \)&amp;
 +
\( (~x~~y~) \)&amp;
 +
\( ((x,y)) \)&amp;
 +
\( y \)&amp;
 +
\( x \)&amp;
 +
\( 0 \)
 +
\\
 +
\( f_{11}\) &amp;
 +
\( (~x~(y)) \)&amp;
 +
\( (x,y) \)&amp;
 +
\( (y) \)&amp;
 +
\( x \)&amp;
 +
\( 0 \)
 +
\\
 +
\( f_{13}\) &amp;
 +
\( ((x)~y~) \)&amp;
 +
\( (x,y) \)&amp;
 +
\( y \)&amp;
 +
\( (x) \)&amp;
 +
\( 0 \)
 +
\\
 +
\( f_{14} \)&amp;
 +
\( ((x)(y)) \)&amp;
 +
\( ((x,y)) \)&amp;
 +
\( (y) \)&amp;
 +
\( (x) \)&amp;
 +
\( 0 \)
 +
\\
 +
\hline
 +
\(f_{15}\)&amp;
 +
\( 1 \)&amp;
 +
\( 0 \)&amp;
 +
\( 0 \)&amp;
 +
\( 0 \)&amp;
 +
\( 0 \)
 +
\\
 +
\hline
 +
\end{tabular}
 +
&amp;fg=000000$
 +
</pre>
 +
 +
====Table A5. Ef Expanded Over Ordinary Features {x, y}====
 +
 +
<pre>
 +
$latex
 +
\begin{tabular}{|c|c||c|c|c|c|}
 +
\multicolumn{6}{c}{Table A5. \(\mathrm{E}f\) Expanded Over Ordinary Features \(\{x, y\}\)} \\
 +
\hline
 +
&amp;
 +
\(~~~~~~~~ f ~~~~~~~~\)&amp;
 +
\(~~\mathrm{E}f|_{ x\;y }~~~\)&amp;
 +
\(~~\mathrm{E}f|_{ x~(y)}\,~~\)&amp;
 +
\(~~\mathrm{E}f|_{(x)~y }\,~~\)&amp;
 +
\(~~\mathrm{E}f|_{(x)(y)}\;~\)
 +
\\
 +
\hline\hline
 +
\(f_{0}\)&amp;
 +
0&amp;
 +
0&amp;
 +
0&amp;
 +
0&amp;
 +
0
 +
\\
 +
\hline
 +
\(f_{1}\)&amp;
 +
\((x)(y)\)&amp;
 +
~d\(x\)~~d\(y~\)&amp;
 +
~d\(x\)~(d\(y\))&amp;
 +
(d\(x\))~d\(y~\)&amp;
 +
(d\(x\))(d\(y\))
 +
\\
 +
\(f_{2}\)&amp;
 +
\((x)~y~\)&amp;
 +
~d\(x\)~(d\(y\))&amp;
 +
~d\(x\)~~d\(y~\)&amp;
 +
(d\(x\))(d\(y\))&amp;
 +
(d\(x\))~d\(y~\)
 +
\\
 +
\(f_{4}\)&amp;
 +
\(~x~(y)\)&amp;
 +
(d\(x\))~d\(y~\)&amp;
 +
(d\(x\))(d\(y\))&amp;
 +
~d\(x\)~~d\(y~\)&amp;
 +
~d\(x\)~(d\(y\))
 +
\\
 +
\(f_{8}\)&amp;
 +
\(~x~~y~\)&amp;
 +
(d\(x\))(d\(y\))&amp;
 +
(d\(x\))~d\(y~\)&amp;
 +
~d\(x\)~(d\(y\))&amp;
 +
~d\(x\)~~d\(y~\)
 +
\\
 +
\hline
 +
\(f_{3}\)&amp;
 +
\((x)\)&amp;
 +
d\(x\) &amp;
 +
d\(x\) &amp;
 +
(d\(x\))&amp;
 +
(d\(x\))
 +
\\
 +
\(f_{12}\)&amp;
 +
\( x \)&amp;
 +
(d\(x\))&amp;
 +
(d\(x\))&amp;
 +
d\(x\) &amp;
 +
d\(x\)
 +
\\
 +
\hline
 +
\(f_{6}\)&amp;
 +
\( (x,y) \)&amp;
 +
(d\(x\), d\(y\)) &amp;
 +
((d\(x\), d\(y\)))&amp;
 +
((d\(x\), d\(y\)))&amp;
 +
(d\(x\), d\(y\))
 +
\\
 +
\(f_{9}\)&amp;
 +
\(((x,y))\)&amp;
 +
((d\(x\), d\(y\)))&amp;
 +
(d\(x\), d\(y\)) &amp;
 +
(d\(x\), d\(y\)) &amp;
 +
((d\(x\), d\(y\)))
 +
\\
 +
\hline
 +
\(f_{5}\)&amp;
 +
\((y)\)&amp;
 +
d\(y\) &amp;
 +
(d\(y\))&amp;
 +
d\(y\) &amp;
 +
(d\(y\))
 +
\\
 +
\(f_{10}\)&amp;
 +
\( y \)&amp;
 +
(d\(y\))&amp;
 +
d\(y\) &amp;
 +
(d\(y\))&amp;
 +
d\(y\)
 +
\\
 +
\hline
 +
\(f_{7}\)&amp;
 +
\((~x~~y~)\)&amp;
 +
((d\(x\))(d\(y\)))&amp;
 +
((d\(x\))~d\(y\)~)&amp;
 +
(~d\(x\)~(d\(y\)))&amp;
 +
(~d\(x\)~~d\(y\)~)
 +
\\
 +
\(f_{11}\)&amp;
 +
\((~x~(y))\)&amp;
 +
((d\(x\))~d\(y\)~)&amp;
 +
((d\(x\))(d\(y\)))&amp;
 +
(~d\(x\)~~d\(y\)~)&amp;
 +
(~d\(x\)~(d\(y\)))
 +
\\
 +
\(f_{13}\)&amp;
 +
\(((x)~y~)\)&amp;
 +
(~d\(x\)~(d\(y\)))&amp;
 +
(~d\(x\)~~d\(y\)~)&amp;
 +
((d\(x\))(d\(y\)))&amp;
 +
((d\(x\))~d\(y\)~)
 +
\\
 +
\(f_{14}\)&amp;
 +
\(((x)(y))\)&amp;
 +
(~d\(x\)~~d\(y\)~)&amp;
 +
(~d\(x\)~(d\(y\)))&amp;
 +
((d\(x\))~d\(y\)~)&amp;
 +
((d\(x\))(d\(y\)))
 +
\\
 +
\hline
 +
\(f_{15}\)&amp;
 +
1&amp;
 +
1&amp;
 +
1&amp;
 +
1&amp;
 +
1
 +
\\
 +
\hline
 +
\end{tabular}
 +
&amp;fg=000000$
 +
</pre>
 +
 +
====Table A6. Df Expanded Over Ordinary Features {x, y}====
 +
 +
<pre>
 +
$latex
 +
\begin{tabular}{|c|c||c|c|c|c|}
 +
\multicolumn{6}{c}{Table A6. \(\mathrm{D}f\) Expanded Over Ordinary Features \(\{x, y\}\)} \\
 +
\hline
 +
&amp;
 +
\(~~~~~~~~ f ~~~~~~~~\)&amp;
 +
\(~~\mathrm{D}f|_{ x\;y }~~~\)&amp;
 +
\(~~\mathrm{D}f|_{ x~(y)}\,~~\)&amp;
 +
\(~~\mathrm{D}f|_{(x)~y }\,~~\)&amp;
 +
\(~~\mathrm{D}f|_{(x)(y)}\,~\)
 +
\\
 +
\hline\hline
 +
\(f_{0}\)&amp;
 +
0&amp;
 +
0&amp;
 +
0&amp;
 +
0&amp;
 +
0
 +
\\
 +
\hline
 +
\(f_{1}\)&amp;
 +
\((x)(y)\)&amp;
 +
~~d\(x\)~~d\(y~~\)&amp;
 +
\;d\(x\)~(d\(y\))~&amp;
 +
~(d\(x\))~d\(y~~\)&amp;
 +
((d\(x\))(d\(y\)))
 +
\\
 +
\(f_{2}\)&amp;
 +
\((x)~y~\)&amp;
 +
\;d\(x\)~(d\(y\))~&amp;
 +
~~d\(x\)~~d\(y~~\)&amp;
 +
((d\(x\))(d\(y\)))&amp;
 +
~(d\(x\))~d\(y~~\)
 +
\\
 +
\(f_{4}\)&amp;
 +
\(~x~(y)\)&amp;
 +
~(d\(x\))~d\(y~~\)&amp;
 +
((d\(x\))(d\(y\)))&amp;
 +
~~d\(x\)~~d\(y~~\)&amp;
 +
~~d\(x\)~(d\(y\))~
 +
\\
 +
\(f_{8}\)&amp;
 +
\(~x~~y~\)&amp;
 +
((d\(x\))(d\(y\)))&amp;
 +
~(d\(x\))~d\(y~~\)&amp;
 +
\;d\(x\)~(d\(y\))~&amp;
 +
~~d\(x\)~~d\(y~~\)
 +
\\
 +
\hline
 +
\(f_{3}\)&amp;
 +
\((x)\)&amp;
 +
d\(x\)&amp;
 +
d\(x\)&amp;
 +
d\(x\)&amp;
 +
d\(x\)
 +
\\
 +
\(f_{12}\)&amp;
 +
\( x \)&amp;
 +
d\(x\)&amp;
 +
d\(x\)&amp;
 +
d\(x\)&amp;
 +
d\(x\)
 +
\\
 +
\hline
 +
\(f_{6}\)&amp;
 +
\( (x,y) \)&amp;
 +
(d\(x\), d\(y\))&amp;
 +
(d\(x\), d\(y\))&amp;
 +
(d\(x\), d\(y\))&amp;
 +
(d\(x\), d\(y\))
 +
\\
 +
\(f_{9}\)&amp;
 +
\(((x,y))\)&amp;
 +
(d\(x\), d\(y\))&amp;
 +
(d\(x\), d\(y\))&amp;
 +
(d\(x\), d\(y\))&amp;
 +
(d\(x\), d\(y\))
 +
\\
 +
\hline
 +
\(f_{5}\)&amp;
 +
\((y)\)&amp;
 +
d\(y\)&amp;
 +
d\(y\)&amp;
 +
d\(y\)&amp;
 +
d\(y\)
 +
\\
 +
\(f_{10}\)&amp;
 +
\( y \)&amp;
 +
d\(y\)&amp;
 +
d\(y\)&amp;
 +
d\(y\)&amp;
 +
d\(y\)
 +
\\
 +
\hline
 +
\(f_{7}\)&amp;
 +
\((~x~~y~)\)&amp;
 +
((d\(x\))(d\(y\)))&amp;
 +
~(d\(x\))~d\(y~~\)&amp;
 +
\;d\(x\)~(d\(y\))~&amp;
 +
~~d\(x\)~~d\(y~~\)
 +
\\
 +
\(f_{11}\)&amp;
 +
\((~x~(y))\)&amp;
 +
~(d\(x\))~d\(y~~\)&amp;
 +
((d\(x\))(d\(y\)))&amp;
 +
~~d\(x\)~~d\(y~~\)&amp;
 +
~~d\(x\)~(d\(y\))~
 +
\\
 +
\(f_{13}\)&amp;
 +
\(((x)~y~)\)&amp;
 +
\;d\(x\)~(d\(y\))~&amp;
 +
~~d\(x\)~~d\(y~~\)&amp;
 +
((d\(x\))(d\(y\)))&amp;
 +
~(d\(x\))~d\(y~~\)
 +
\\
 +
\(f_{14}\)&amp;
 +
\(((x)(y))\)&amp;
 +
~~d\(x\)~~d\(y~~\)&amp;
 +
\;d\(x\)~(d\(y\))~&amp;
 +
~(d\(x\))~d\(y~~\)&amp;
 +
((d\(x\))(d\(y\)))
 +
\\
 +
\hline
 +
\(f_{15}\)&amp;
 +
1&amp;
 +
0&amp;
 +
0&amp;
 +
0&amp;
 +
0
 +
\\
 +
\hline
 +
\end{tabular}
 +
&amp;fg=000000$
 +
</pre>
 +
 +
===Fourier Transforms of Boolean Functions===
 +
 +
Re: [http://rjlipton.wordpress.com/2013/05/21/twin-primes-are-useful/ Another Problem]
 +
 +
<blockquote>
 +
<p>The problem is concretely about Boolean functions <math>f\!</math> of <math>k\!</math> variables, and seems not to involve prime numbers at all.  For any subset <math>S\!</math> of the coordinates, the corresponding Fourier coefficient is given by:</p>
 +
 +
<p align="center"><math>\hat{f}(S) = \frac{1}{2^k} \sum_{x \in \mathbb{Z}_2^k} f(x)\chi_S(x)\!</math></p>
 +
 +
<p>where <math>\chi_S(x)\!</math> is <math>-1\!</math> if <math>\textstyle \sum_{i \in S} x_i\!</math> is odd, and <math>+1\!</math> otherwise.</p>
 +
</blockquote>
 +
 +
<math>k = 1\!</math>
 +
 +
&hellip;
 +
 +
<math>k = 2\!</math>
 +
 +
For ease of reading formulas, let <math>x = (x_1, x_2) = (u, v).\!</math>
 +
 +
====Table 2.1. Values of &chi;<sub>S</sub>(x)====
 +
 +
<pre>
 +
$latex
 +
\begin{tabular}{|c||*{4}{c}|}
 +
\multicolumn{5}{c}{Table 2.1. Values of \( \boldsymbol{\chi}_\mathcal{S}(x) \) for \( f : \mathbb{B}^2 \to \mathbb{B} \)} \\[4pt]
 +
\hline
 +
\( \mathcal{S} \backslash (u, v) \) &amp;
 +
\( (1, 1) \) &amp;
 +
\( (1, 0) \) &amp;
 +
\( (0, 1) \) &amp;
 +
\( (0, 0) \)
 +
\\
 +
\hline\hline
 +
\( \varnothing \) &amp; \( +1 \) &amp; \( +1 \) &amp; \( +1 \) &amp; \( +1 \) \\
 +
\( \{ u \} \)    &amp; \( -1 \) &amp; \( -1 \) &amp; \( +1 \) &amp; \( +1 \) \\
 +
\( \{ v \} \)    &amp; \( -1 \) &amp; \( +1 \) &amp; \( -1 \) &amp; \( +1 \) \\
 +
\( \{ u, v \} \)  &amp; \( +1 \) &amp; \( -1 \) &amp; \( -1 \) &amp; \( +1 \) \\
 +
\hline
 +
\end{tabular}
 +
&amp;fg=000000$
 +
</pre>
 +
 +
====Table 2.2. Fourier Coefficients of Boolean Functions on Two Variables====
 +
 +
<pre>
 +
$latex
 +
\begin{tabular}{|*{5}{c|}*{4}{r|}}
 +
\multicolumn{9}{c}{Table 2.2. Fourier Coefficients of Boolean Functions on Two Variables} \\[4pt]
 +
\hline
 +
~&amp;~&amp;~&amp;~&amp;~&amp;~&amp;~&amp;~&amp;~\\
 +
\(L_1\)&amp;\(L_2\)&amp;&amp;\(L_3\)&amp;\(L_4\)&amp;
 +
\(\hat{f}(\varnothing)\)&amp;\(\hat{f}(\{u\})\)&amp;\(\hat{f}(\{v\})\)&amp;\(\hat{f}(\{u,v\})\) \\
 +
~&amp;~&amp;~&amp;~&amp;~&amp;~&amp;~&amp;~&amp;~\\
 +
\hline
 +
&amp;&amp; \(u =\)&amp; 1 1 0 0&amp;&amp;&amp;&amp;&amp; \\
 +
&amp;&amp; \(v =\)&amp; 1 0 1 0&amp;&amp;&amp;&amp;&amp; \\
 +
\hline
 +
\(f_{0}\)&amp;
 +
\(f_{0000}\)&amp;&amp;
 +
0 0 0 0&amp;
 +
\((~)\)&amp;
 +
\(0\)&amp;
 +
\(0\)&amp;
 +
\(0\)&amp;
 +
\(0\)
 +
\\
 +
\(f_{1}\)&amp;
 +
\(f_{0001}\)&amp;&amp;
 +
0 0 0 1&amp;
 +
\((u)(v)\)&amp;
 +
\(1/4\)&amp;
 +
\(1/4\)&amp;
 +
\(1/4\)&amp;
 +
\(1/4\)
 +
\\
 +
\(f_{2}\)&amp;
 +
\(f_{0010}\)&amp;&amp;
 +
0 0 1 0&amp;
 +
\((u)~v~\)&amp;
 +
\( 1/4\)&amp;
 +
\( 1/4\)&amp;
 +
\(-1/4\)&amp;
 +
\(-1/4\)
 +
\\
 +
\(f_{3}\)&amp;
 +
\(f_{0011}\)&amp;&amp;
 +
0 0 1 1&amp;
 +
\((u)\)&amp;
 +
\(1/2\)&amp;
 +
\(1/2\)&amp;
 +
\( 0 \)&amp;
 +
\( 0 \)
 +
\\
 +
\(f_{4}\)&amp;
 +
\(f_{0100}\)&amp;&amp;
 +
0 1 0 0&amp;
 +
\(~u~(v)\)&amp;
 +
\( 1/4\)&amp;
 +
\(-1/4\)&amp;
 +
\( 1/4\)&amp;
 +
\(-1/4\)
 +
\\
 +
\(f_{5}\)&amp;
 +
\(f_{0101}\)&amp;&amp;
 +
0 1 0 1&amp;
 +
\((v)\)&amp;
 +
\(1/2\)&amp;
 +
\( 0 \)&amp;
 +
\(1/2\)&amp;
 +
\( 0 \)
 +
\\
 +
\(f_{6}\)&amp;
 +
\(f_{0110}\)&amp;&amp;
 +
0 1 1 0&amp;
 +
\((u,~v)\)&amp;
 +
\( 1/2\)&amp;
 +
\( 0 \)&amp;
 +
\( 0 \)&amp;
 +
\(-1/2\)
 +
\\
 +
\(f_{7}\)&amp;
 +
\(f_{0111}\)&amp;&amp;
 +
0 1 1 1&amp;
 +
\((u~~v)\)&amp;
 +
\( 3/4\)&amp;
 +
\( 1/4\)&amp;
 +
\( 1/4\)&amp;
 +
\(-1/4\)
 +
\\
 +
\hline
 +
\(f_{8}\)&amp;
 +
\(f_{1000}\)&amp;&amp;
 +
1 0 0 0&amp;
 +
\(~u~~v~\)&amp;
 +
\( 1/4\)&amp;
 +
\(-1/4\)&amp;
 +
\(-1/4\)&amp;
 +
\( 1/4\)
 +
\\
 +
\(f_{9}\)&amp;
 +
\(f_{1001}\)&amp;&amp;
 +
1 0 0 1&amp;
 +
\(((u,~v))\)&amp;
 +
\(1/2\)&amp;
 +
\( 0 \)&amp;
 +
\( 0 \)&amp;
 +
\(1/2\)
 +
\\
 +
\(f_{10}\)&amp;
 +
\(f_{1010}\)&amp;&amp;
 +
1 0 1 0&amp;
 +
\(v\)&amp;
 +
\( 1/2\)&amp;
 +
\( 0 \)&amp;
 +
\(-1/2\)&amp;
 +
\( 0 \)
 +
\\
 +
\(f_{11}\)&amp;
 +
\(f_{1011}\)&amp;&amp;
 +
1 0 1 1&amp;
 +
\((~u~(v))\)&amp;
 +
\( 3/4\)&amp;
 +
\( 1/4\)&amp;
 +
\(-1/4\)&amp;
 +
\( 1/4\)
 +
\\
 +
\(f_{12}\)&amp;
 +
\(f_{1100}\)&amp;&amp;
 +
1 1 0 0&amp;
 +
\(u\)&amp;
 +
\( 1/2\)&amp;
 +
\(-1/2\)&amp;
 +
\( 0 \)&amp;
 +
\( 0 \)
 +
\\
 +
\(f_{13}\)&amp;
 +
\(f_{1101}\)&amp;&amp;
 +
1 1 0 1&amp;
 +
\(((u)~v~)\)&amp;
 +
\( 3/4\)&amp;
 +
\(-1/4\)&amp;
 +
\( 1/4\)&amp;
 +
\( 1/4\)
 +
\\
 +
\(f_{14}\)&amp;
 +
\(f_{1110}\)&amp;&amp;
 +
1 1 1 0&amp;
 +
\(((u)(v))\)&amp;
 +
\( 3/4\)&amp;
 +
\(-1/4\)&amp;
 +
\(-1/4\)&amp;
 +
\(-1/4\)
 +
\\
 +
\(f_{15}\)&amp;
 +
\(f_{1111}\)&amp;&amp;
 +
1 1 1 1&amp;
 +
\(((~))\)&amp;
 +
\(1\)&amp;
 +
\(0\)&amp;
 +
\(0\)&amp;
 +
\(0\)
 +
\\
 +
\hline
 +
\end{tabular}
 +
&amp;fg=000000$
 +
</pre>
 +
 +
====Table 2.3. Fourier Coefficients of Boolean Functions on Two Variables====
 +
 +
<pre>
 +
$latex
 +
\begin{tabular}{|*{5}{c|}*{4}{r|}}
 +
\multicolumn{9}{c}{Table 2.3. Fourier Coefficients of Boolean Functions on Two Variables} \\[4pt]
 +
\hline
 +
~&amp;~&amp;~&amp;~&amp;~&amp;~&amp;~&amp;~&amp;~\\
 +
\(L_1\)&amp;\(L_2\)&amp;&amp;\(L_3\)&amp;\(L_4\)&amp;
 +
\(\hat{f}(\varnothing)\)&amp;\(\hat{f}(\{u\})\)&amp;\(\hat{f}(\{v\})\)&amp;\(\hat{f}(\{u,v\})\) \\
 +
~&amp;~&amp;~&amp;~&amp;~&amp;~&amp;~&amp;~&amp;~\\
 +
\hline
 +
&amp;&amp; \(u =\)&amp; 1 1 0 0&amp;&amp;&amp;&amp;&amp; \\
 +
&amp;&amp; \(v =\)&amp; 1 0 1 0&amp;&amp;&amp;&amp;&amp; \\
 +
\hline
 +
\(f_{0}\)&amp;
 +
\(f_{0000}\)&amp;&amp;
 +
0 0 0 0&amp;
 +
\((~)\)&amp;
 +
\(0\)&amp;
 +
\(0\)&amp;
 +
\(0\)&amp;
 +
\(0\)
 +
\\
 +
\hline
 +
\(f_{1}\)&amp;
 +
\(f_{0001}\)&amp;&amp;
 +
0 0 0 1&amp;
 +
\((u)(v)\)&amp;
 +
\(1/4\)&amp;
 +
\(1/4\)&amp;
 +
\(1/4\)&amp;
 +
\(1/4\)
 +
\\
 +
\(f_{2}\)&amp;
 +
\(f_{0010}\)&amp;&amp;
 +
0 0 1 0&amp;
 +
\((u)~v~\)&amp;
 +
\( 1/4\)&amp;
 +
\( 1/4\)&amp;
 +
\(-1/4\)&amp;
 +
\(-1/4\)
 +
\\
 +
\(f_{4}\)&amp;
 +
\(f_{0100}\)&amp;&amp;
 +
0 1 0 0&amp;
 +
\(~u~(v)\)&amp;
 +
\( 1/4\)&amp;
 +
\(-1/4\)&amp;
 +
\( 1/4\)&amp;
 +
\(-1/4\)
 +
\\
 +
\(f_{8}\)&amp;
 +
\(f_{1000}\)&amp;&amp;
 +
1 0 0 0&amp;
 +
\(~u~~v~\)&amp;
 +
\( 1/4\)&amp;
 +
\(-1/4\)&amp;
 +
\(-1/4\)&amp;
 +
\( 1/4\)
 +
\\
 +
\hline
 +
\(f_{3}\)&amp;
 +
\(f_{0011}\)&amp;&amp;
 +
0 0 1 1&amp;
 +
\((u)\)&amp;
 +
\(1/2\)&amp;
 +
\(1/2\)&amp;
 +
\( 0 \)&amp;
 +
\( 0 \)
 +
\\
 +
\(f_{12}\)&amp;
 +
\(f_{1100}\)&amp;&amp;
 +
1 1 0 0&amp;
 +
\(u\)&amp;
 +
\( 1/2\)&amp;
 +
\(-1/2\)&amp;
 +
\( 0 \)&amp;
 +
\( 0 \)
 +
\\
 +
\hline
 +
\(f_{6}\)&amp;
 +
\(f_{0110}\)&amp;&amp;
 +
0 1 1 0&amp;
 +
\((u,~v)\)&amp;
 +
\( 1/2\)&amp;
 +
\( 0 \)&amp;
 +
\( 0 \)&amp;
 +
\(-1/2\)
 +
\\
 +
\(f_{9}\)&amp;
 +
\(f_{1001}\)&amp;&amp;
 +
1 0 0 1&amp;
 +
\(((u,~v))\)&amp;
 +
\(1/2\)&amp;
 +
\( 0 \)&amp;
 +
\( 0 \)&amp;
 +
\(1/2\)
 +
\\
 +
\hline
 +
\(f_{5}\)&amp;
 +
\(f_{0101}\)&amp;&amp;
 +
0 1 0 1&amp;
 +
\((v)\)&amp;
 +
\(1/2\)&amp;
 +
\( 0 \)&amp;
 +
\(1/2\)&amp;
 +
\( 0 \)
 +
\\
 +
\(f_{10}\)&amp;
 +
\(f_{1010}\)&amp;&amp;
 +
1 0 1 0&amp;
 +
\(v\)&amp;
 +
\( 1/2\)&amp;
 +
\( 0 \)&amp;
 +
\(-1/2\)&amp;
 +
\( 0 \)
 +
\\
 +
\hline
 +
\(f_{7}\)&amp;
 +
\(f_{0111}\)&amp;&amp;
 +
0 1 1 1&amp;
 +
\((u~~v)\)&amp;
 +
\( 3/4\)&amp;
 +
\( 1/4\)&amp;
 +
\( 1/4\)&amp;
 +
\(-1/4\)
 +
\\
 +
\hline
 +
\(f_{11}\)&amp;
 +
\(f_{1011}\)&amp;&amp;
 +
1 0 1 1&amp;
 +
\((~u~(v))\)&amp;
 +
\( 3/4\)&amp;
 +
\( 1/4\)&amp;
 +
\(-1/4\)&amp;
 +
\( 1/4\)
 +
\\
 +
\(f_{13}\)&amp;
 +
\(f_{1101}\)&amp;&amp;
 +
1 1 0 1&amp;
 +
\(((u)~v~)\)&amp;
 +
\( 3/4\)&amp;
 +
\(-1/4\)&amp;
 +
\( 1/4\)&amp;
 +
\( 1/4\)
 +
\\
 +
\(f_{14}\)&amp;
 +
\(f_{1110}\)&amp;&amp;
 +
1 1 1 0&amp;
 +
\(((u)(v))\)&amp;
 +
\( 3/4\)&amp;
 +
\(-1/4\)&amp;
 +
\(-1/4\)&amp;
 +
\(-1/4\)
 +
\\
 +
\hline
 +
\(f_{15}\)&amp;
 +
\(f_{1111}\)&amp;&amp;
 +
1 1 1 1&amp;
 +
\(((~))\)&amp;
 +
\(1\)&amp;
 +
\(0\)&amp;
 +
\(0\)&amp;
 +
\(0\)
 +
\\
 +
\hline
 +
\end{tabular}
 +
&amp;fg=000000$
 +
</pre>
 +
 
==Work 2==
 
==Work 2==
 +
 +
* Examples of HTML and LaTeX markup from [http://inquiryintoinquiry.com/work/work-2/ Inquiry Into Inquiry : Work 2]
 +
 +
===Array Test===
    
<pre>
 
<pre>
−
<h3>Array Test</h3>
  −
   
$latex
 
$latex
 
|x| = \left\{
 
|x| = \left\{
Line 13: Line 1,234:  
\right.
 
\right.
 
&amp;fg=000000$
 
&amp;fg=000000$
 +
</pre>
    +
<pre>
 
$latex
 
$latex
 
|x| = \left\{
 
|x| = \left\{
Line 23: Line 1,246:  
\right.
 
\right.
 
&amp;fg=000000$
 
&amp;fg=000000$
 +
</pre>
    +
<pre>
 
$latex
 
$latex
 
\begin{array}{*{9}{l}}
 
\begin{array}{*{9}{l}}
Line 32: Line 1,257:  
Sierra &amp; Tango &amp; Uniform &amp; Victor &amp; Whiskey &amp; X\text{-}ray &amp; Yankee &amp; Zulu &amp; \varnothing
 
Sierra &amp; Tango &amp; Uniform &amp; Victor &amp; Whiskey &amp; X\text{-}ray &amp; Yankee &amp; Zulu &amp; \varnothing
 
\end{array}&amp;fg=000000$
 
\end{array}&amp;fg=000000$
 +
</pre>
   −
<h3>Matrix Test</h3>
+
===Matrix Test===
    +
<pre>
 
$latex
 
$latex
 
\begin{matrix}
 
\begin{matrix}
Line 43: Line 1,270:  
Sierra &amp; Tango &amp; Uniform &amp; Victor &amp; Whiskey &amp; X\text{-}ray &amp; Yankee &amp; Zulu &amp; \varnothing
 
Sierra &amp; Tango &amp; Uniform &amp; Victor &amp; Whiskey &amp; X\text{-}ray &amp; Yankee &amp; Zulu &amp; \varnothing
 
\end{matrix}&amp;fg=000000$
 
\end{matrix}&amp;fg=000000$
 +
</pre>
   −
<h3>Tabular Test 1</h3>
+
===Tabular Test 1===
    +
<pre>
 
$latex
 
$latex
 
\begin{tabular}{lll}
 
\begin{tabular}{lll}
Line 58: Line 1,287:  
Rome &amp; Italy &amp; 1908
 
Rome &amp; Italy &amp; 1908
 
\end{tabular}&amp;fg=000000$
 
\end{tabular}&amp;fg=000000$
 +
</pre>
   −
<h3>Tabular Test 2</h3>
+
===Tabular Test 2===
    +
<pre>
 
$latex
 
$latex
 
\begin{tabular}{|r|r|}
 
\begin{tabular}{|r|r|}
Line 78: Line 1,309:  
\hline
 
\hline
 
\end{tabular}&amp;fg=000000$
 
\end{tabular}&amp;fg=000000$
 +
</pre>
   −
<h3>Tabular Test 3</h3>
+
===Tabular Test 3===
    +
<pre>
 
$latex
 
$latex
 
\begin{tabular}{|c|c|*{16}{c}|}
 
\begin{tabular}{|c|c|*{16}{c}|}
Line 101: Line 1,334:  
\hline
 
\hline
 
\end{tabular}&amp;fg=000000$
 
\end{tabular}&amp;fg=000000$
 +
</pre>
   −
<h3>Tabular Test 4</h3>
+
===Tabular Test 4===
    +
<pre>
 
$latex
 
$latex
 
\begin{tabular}{|*{7}{c|}}
 
\begin{tabular}{|*{7}{c|}}
Line 233: Line 1,468:  
\hline
 
\hline
 
\end{tabular}&amp;fg=000000$
 
\end{tabular}&amp;fg=000000$
 +
</pre>
   −
<h3>Table Test 1</h3>
+
===Table Test 1===
    +
<pre>
 
<table border="0" style="border-width:0;width:100%;">
 
<table border="0" style="border-width:0;width:100%;">
   Line 248: Line 1,485:     
</table>
 
</table>
 +
</pre>
   −
Lately I've begun to see that these ancient riddles of change, coming to know, and communication all spring from a common root.
+
===Table Test 2===
−
 
  −
<h3>Table Test 2</h3>
      +
<pre>
 
<table align="left" border="0" style="border-width:0;">
 
<table align="left" border="0" style="border-width:0;">
   Line 270: Line 1,507:     
</table>
 
</table>
 +
</pre>
   −
<h3>Table Test 3</h3>
+
===Table Test 3===
    +
<pre>
 
<table align="center" border="0">
 
<table align="center" border="0">
   Line 293: Line 1,532:     
</table>
 
</table>
 +
</pre>
   −
<h3>Table Test 4</h3>
+
===Table Test 4===
    +
<pre>
 
<table align="center" border="0" style="border-width:0;text-align:center;">
 
<table align="center" border="0" style="border-width:0;text-align:center;">
   Line 315: Line 1,556:     
</table>
 
</table>
 +
</pre>
   −
<h3>Table Test 5</h3>
+
===Table Test 5===
    +
<pre>
 
<table align="center" border="0" style="text-align:center;">
 
<table align="center" border="0" style="text-align:center;">
   Line 337: Line 1,580:     
</table>
 
</table>
 +
</pre>
   −
<h3>Table Test 6</h3>
+
===Table Test 6===
    +
<pre>
 
<table align="center" border="0" style="text-align:center;">
 
<table align="center" border="0" style="text-align:center;">
  
Jon Awbrey
12,089

edits

Retrieved from "https://mywikibiz.com/Special:MobileDiff/181244...181988"