<?xml version="1.0" encoding="UTF-8"?>
<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.1 plus MathML 2.0 plus SVG 1.1//EN" "http://www.w3.org/2002/04/xhtml-math-svg/xhtml-math-svg-flat.dtd">
<html xmlns="http://www.w3.org/1999/xhtml" xml:lang="en" lang="en">
<head>
  <title>Ritex Unit Test Report</title>
  <meta http-equiv="Content-Type" content="text/html; charset=utf-8" />
</head>
<body>
<table>
<tr><td align="right">Input:</td><td style='font-family: monospace'><code>""</code></td></tr>
<tr><td align="right">Output:</td><td ><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"></math></td></tr>
<tr><td colspan="2"><hr/></td></tr>
<tr><td align="right">Input:</td><td style='font-family: monospace'><code>"  a"</code></td></tr>
<tr><td align="right">Output:</td><td ><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><mi>a</mi></math></td></tr>
<tr><td colspan="2"><hr/></td></tr>
<tr><td align="right">Input:</td><td style='font-family: monospace'><code>" a"</code></td></tr>
<tr><td align="right">Output:</td><td ><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><mi>a</mi></math></td></tr>
<tr><td colspan="2"><hr/></td></tr>
<tr><td align="right">Input:</td><td style='font-family: monospace'><code>"(\hat{x}) = {(\hat{x}})"</code></td></tr>
<tr><td align="right">Output:</td><td ><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><mo stretchy='false'>(</mo><mover><mrow><mi>x</mi></mrow><mo>&Hat;</mo></mover><mo stretchy='false'>)</mo><mo>=</mo><mrow><mo stretchy='false'>(</mo><mover><mrow><mi>x</mi></mrow><mo>&Hat;</mo></mover></mrow><mo stretchy='false'>)</mo></math></td></tr>
<tr><td colspan="2"><hr/></td></tr>
<tr><td align="right">Input:</td><td style='font-family: monospace'><code>","</code></td></tr>
<tr><td align="right">Output:</td><td ><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><mo>,</mo></math></td></tr>
<tr><td colspan="2"><hr/></td></tr>
<tr><td align="right">Input:</td><td style='font-family: monospace'><code>",\,\,,,\,"</code></td></tr>
<tr><td align="right">Output:</td><td ><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><mo>,</mo><mspace width="thinmathspace"/><mspace width="thinmathspace"/><mo>,</mo><mo>,</mo><mspace width="thinmathspace"/></math></td></tr>
<tr><td colspan="2"><hr/></td></tr>
<tr><td align="right">Input:</td><td style='font-family: monospace'><code>"-1"</code></td></tr>
<tr><td align="right">Output:</td><td ><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><mo lspace="verythinmathspace" rspace="0em">&minus;</mo><mn>1</mn></math></td></tr>
<tr><td colspan="2"><hr/></td></tr>
<tr><td align="right">Input:</td><td style='font-family: monospace'><code>"-\infty"</code></td></tr>
<tr><td align="right">Output:</td><td ><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><mo lspace="verythinmathspace" rspace="0em">&minus;</mo><mn>&infin;</mn></math></td></tr>
<tr><td colspan="2"><hr/></td></tr>
<tr><td align="right">Input:</td><td style='font-family: monospace'><code>"-\log(1 - X)/\lambda"</code></td></tr>
<tr><td align="right">Output:</td><td ><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><mo lspace="verythinmathspace" rspace="0em">&minus;</mo><mi>log</mi><mo stretchy='false'>(</mo><mn>1</mn><mo>&minus;</mo><mi>X</mi><mo stretchy='false'>)</mo><mo>/</mo><mi>&lambda;</mi></math></td></tr>
<tr><td colspan="2"><hr/></td></tr>
<tr><td align="right">Input:</td><td style='font-family: monospace'><code>"-x"</code></td></tr>
<tr><td align="right">Output:</td><td ><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><mo lspace="verythinmathspace" rspace="0em">&minus;</mo><mi>x</mi></math></td></tr>
<tr><td colspan="2"><hr/></td></tr>
<tr><td align="right">Input:</td><td style='font-family: monospace'><code>"100!"</code></td></tr>
<tr><td align="right">Output:</td><td ><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><mn>100</mn><mo>!</mo></math></td></tr>
<tr><td colspan="2"><hr/></td></tr>
<tr><td align="right">Input:</td><td style='font-family: monospace'><code>"F(x) = \Pr(X \leq x)\ \text{for}\ -\infinity &lt; x &lt; \infinity"</code></td></tr>
<tr><td align="right">Output:</td><td ><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><mi>F</mi><mo stretchy='false'>(</mo><mi>x</mi><mo stretchy='false'>)</mo><mo>=</mo><mi>Pr</mi><mo stretchy='false'>(</mo><mi>X</mi><mo>&leq;</mo><mi>x</mi><mo stretchy='false'>)</mo><mspace width="mediummathspace"/><mtext>for</mtext><mspace width="mediummathspace"/><mo lspace="verythinmathspace" rspace="0em">&minus;</mo><mn>&infin;</mn><mo>&lt;</mo><mi>x</mi><mo>&lt;</mo><mn>&infin;</mn></math></td></tr>
<tr><td colspan="2"><hr/></td></tr>
<tr><td align="right">Input:</td><td style='font-family: monospace'><code>"G(y) = \left\{\array{ 1 - e^{-\lambda y} &amp; \text{ if } y \geq 0 \\
                               0                  &amp; \text{ if } y &lt; 0 }\right."</code></td></tr>
<tr><td align="right">Output:</td><td ><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><mi>G</mi><mo stretchy='false'>(</mo><mi>y</mi><mo stretchy='false'>)</mo><mo>=</mo><mrow><mo>{</mo><mrow><mtable><mtr><mtd><mn>1</mn><mo>&minus;</mo><msup><mi>e</mi><mrow><mo lspace="verythinmathspace" rspace="0em">&minus;</mo><mi>&lambda;</mi><mi>y</mi></mrow></msup></mtd><mtd><mtext> if </mtext><mi>y</mi><mo>&geq;</mo><mn>0</mn></mtd></mtr><mtr><mtd><mn>0</mn></mtd><mtd><mtext> if </mtext><mi>y</mi><mo>&lt;</mo><mn>0</mn></mtd></mtr></mtable></mrow></mrow></math></td></tr>
<tr><td colspan="2"><hr/></td></tr>
<tr><td align="right">Input:</td><td style='font-family: monospace'><code>"G^{-1}(x) = -\log(1 - x)/\lambda\text{ if } 0 &lt; x &lt; 1."</code></td></tr>
<tr><td align="right">Output:</td><td ><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><msup><mi>G</mi><mrow><mo lspace="verythinmathspace" rspace="0em">&minus;</mo><mn>1</mn></mrow></msup><mo stretchy='false'>(</mo><mi>x</mi><mo stretchy='false'>)</mo><mo>=</mo><mo lspace="verythinmathspace" rspace="0em">&minus;</mo><mi>log</mi><mo stretchy='false'>(</mo><mn>1</mn><mo>&minus;</mo><mi>x</mi><mo stretchy='false'>)</mo><mo>/</mo><mi>&lambda;</mi><mtext> if </mtext><mn>0</mn><mo>&lt;</mo><mi>x</mi><mo>&lt;</mo><mn>1</mn><mo>.</mo></math></td></tr>
<tr><td colspan="2"><hr/></td></tr>
<tr><td align="right">Input:</td><td style='font-family: monospace'><code>"P(x) = P^*(x)/Z"</code></td></tr>
<tr><td align="right">Output:</td><td ><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><mi>P</mi><mo stretchy='false'>(</mo><mi>x</mi><mo stretchy='false'>)</mo><mo>=</mo><msup><mi>P</mi><mo>*</mo></msup><mo stretchy='false'>(</mo><mi>x</mi><mo stretchy='false'>)</mo><mo>/</mo><mi>Z</mi></math></td></tr>
<tr><td colspan="2"><hr/></td></tr>
<tr><td align="right">Input:</td><td style='font-family: monospace'><code>"\ -\infty"</code></td></tr>
<tr><td align="right">Output:</td><td ><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><mspace width="mediummathspace"/><mo lspace="verythinmathspace" rspace="0em">&minus;</mo><mn>&infin;</mn></math></td></tr>
<tr><td colspan="2"><hr/></td></tr>
<tr><td align="right">Input:</td><td style='font-family: monospace'><code>"\,"</code></td></tr>
<tr><td align="right">Output:</td><td ><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><mspace width="thinmathspace"/></math></td></tr>
<tr><td colspan="2"><hr/></td></tr>
<tr><td align="right">Input:</td><td style='font-family: monospace'><code>"\Pr(a &lt; X \leq b) = \int_a^b f(x)\ dx"</code></td></tr>
<tr><td align="right">Output:</td><td ><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><mi>Pr</mi><mo stretchy='false'>(</mo><mi>a</mi><mo>&lt;</mo><mi>X</mi><mo>&leq;</mo><mi>b</mi><mo stretchy='false'>)</mo><mo>=</mo><msubsup><mo>&Integral;</mo><mi>a</mi><mi>b</mi></msubsup><mi>f</mi><mo stretchy='false'>(</mo><mi>x</mi><mo stretchy='false'>)</mo><mspace width="mediummathspace"/><mi>d</mi><mi>x</mi></math></td></tr>
<tr><td colspan="2"><hr/></td></tr>
<tr><td align="right">Input:</td><td style='font-family: monospace'><code>"\alpha"</code></td></tr>
<tr><td align="right">Output:</td><td ><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><mi>&alpha;</mi></math></td></tr>
<tr><td colspan="2"><hr/></td></tr>
<tr><td align="right">Input:</td><td style='font-family: monospace'><code>"\alpha + b + c"</code></td></tr>
<tr><td align="right">Output:</td><td ><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><mi>&alpha;</mi><mo>+</mo><mi>b</mi><mo>+</mo><mi>c</mi></math></td></tr>
<tr><td colspan="2"><hr/></td></tr>
<tr><td align="right">Input:</td><td style='font-family: monospace'><code>"\alpha - x"</code></td></tr>
<tr><td align="right">Output:</td><td ><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><mi>&alpha;</mi><mo>&minus;</mo><mi>x</mi></math></td></tr>
<tr><td colspan="2"><hr/></td></tr>
<tr><td align="right">Input:</td><td style='font-family: monospace'><code>"\array{  \colspan{3} (1,1) \text{ to } (1,3) &amp; (1,4) \\
                     (2,1)  &amp;   (2,2)   &amp;   (2,3)    &amp; (2,4)  }"</code></td></tr>
<tr><td align="right">Output:</td><td ><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><mrow><mtable><mtr><mtd columnspan='3'><mo stretchy='false'>(</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo stretchy='false'>)</mo><mtext> to </mtext><mo stretchy='false'>(</mo><mn>1</mn><mo>,</mo><mn>3</mn><mo stretchy='false'>)</mo></mtd><mtd><mo stretchy='false'>(</mo><mn>1</mn><mo>,</mo><mn>4</mn><mo stretchy='false'>)</mo></mtd></mtr><mtr><mtd><mo stretchy='false'>(</mo><mn>2</mn><mo>,</mo><mn>1</mn><mo stretchy='false'>)</mo></mtd><mtd><mo stretchy='false'>(</mo><mn>2</mn><mo>,</mo><mn>2</mn><mo stretchy='false'>)</mo></mtd><mtd><mo stretchy='false'>(</mo><mn>2</mn><mo>,</mo><mn>3</mn><mo stretchy='false'>)</mo></mtd><mtd><mo stretchy='false'>(</mo><mn>2</mn><mo>,</mo><mn>4</mn><mo stretchy='false'>)</mo></mtd></mtr></mtable></mrow></math></td></tr>
<tr><td colspan="2"><hr/></td></tr>
<tr><td align="right">Input:</td><td style='font-family: monospace'><code>"\array{ (1,1) &amp; \rowspan{2} \int dx &amp; (1,3) \\
                 (2,1) &amp;                       (2,3) \\
                 (3,1) &amp; (3,2)               &amp; (3,3) }"</code></td></tr>
<tr><td align="right">Output:</td><td ><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><mrow><mtable><mtr><mtd><mo stretchy='false'>(</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo stretchy='false'>)</mo></mtd><mtd rowspan='2'><mo>&Integral;</mo><mi>d</mi><mi>x</mi></mtd><mtd><mo stretchy='false'>(</mo><mn>1</mn><mo>,</mo><mn>3</mn><mo stretchy='false'>)</mo></mtd></mtr><mtr><mtd><mo stretchy='false'>(</mo><mn>2</mn><mo>,</mo><mn>1</mn><mo stretchy='false'>)</mo></mtd><mtd><mo stretchy='false'>(</mo><mn>2</mn><mo>,</mo><mn>3</mn><mo stretchy='false'>)</mo></mtd></mtr><mtr><mtd><mo stretchy='false'>(</mo><mn>3</mn><mo>,</mo><mn>1</mn><mo stretchy='false'>)</mo></mtd><mtd><mo stretchy='false'>(</mo><mn>3</mn><mo>,</mo><mn>2</mn><mo stretchy='false'>)</mo></mtd><mtd><mo stretchy='false'>(</mo><mn>3</mn><mo>,</mo><mn>3</mn><mo stretchy='false'>)</mo></mtd></mtr></mtable></mrow></math></td></tr>
<tr><td colspan="2"><hr/></td></tr>
<tr><td align="right">Input:</td><td style='font-family: monospace'><code>"\array{ \arrayopts{\colalign{left center right}} a &amp; b &amp; c \\ 100000 &amp; 100000 &amp; 10000}"</code></td></tr>
<tr><td align="right">Output:</td><td ><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><mrow><mtable columnalign='left center right'><mtr><mtd><mi>a</mi></mtd><mtd><mi>b</mi></mtd><mtd><mi>c</mi></mtd></mtr><mtr><mtd><mn>100000</mn></mtd><mtd><mn>100000</mn></mtd><mtd><mn>10000</mn></mtd></mtr></mtable></mrow></math></td></tr>
<tr><td colspan="2"><hr/></td></tr>
<tr><td align="right">Input:</td><td style='font-family: monospace'><code>"\array{ \arrayopts{\colalign{left}} a &amp; b &amp; c \\ 100000 &amp; 100000 &amp; 10000}"</code></td></tr>
<tr><td align="right">Output:</td><td ><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><mrow><mtable columnalign='left'><mtr><mtd><mi>a</mi></mtd><mtd><mi>b</mi></mtd><mtd><mi>c</mi></mtd></mtr><mtr><mtd><mn>100000</mn></mtd><mtd><mn>100000</mn></mtd><mtd><mn>10000</mn></mtd></mtr></mtable></mrow></math></td></tr>
<tr><td colspan="2"><hr/></td></tr>
<tr><td align="right">Input:</td><td style='font-family: monospace'><code>"\array{ \arrayopts{\rowalign{top center bottom}} \binom{\alpha}{\omega} &amp; a &amp; b \\ \frac{3}{4} &amp; c &amp; d \\ \int_0^1 &amp; e &amp; f}"</code></td></tr>
<tr><td align="right">Output:</td><td ><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><mrow><mtable rowalign='top center bottom'><mtr><mtd><mfrac linethickness="0"><mrow><mi>&alpha;</mi></mrow><mrow><mi>&omega;</mi></mrow></mfrac></mtd><mtd><mi>a</mi></mtd><mtd><mi>b</mi></mtd></mtr><mtr><mtd><mfrac><mrow><mn>3</mn></mrow><mrow><mn>4</mn></mrow></mfrac></mtd><mtd><mi>c</mi></mtd><mtd><mi>d</mi></mtd></mtr><mtr><mtd><msubsup><mo>&Integral;</mo><mn>0</mn><mn>1</mn></msubsup></mtd><mtd><mi>e</mi></mtd><mtd><mi>f</mi></mtd></mtr></mtable></mrow></math></td></tr>
<tr><td colspan="2"><hr/></td></tr>
<tr><td align="right">Input:</td><td style='font-family: monospace'><code>"\array{ \arrayopts{\rowalign{top}} \binom{\alpha}{\omega} &amp; a &amp; b \\ \frac{3}{4} &amp; c &amp; d \\ \int_0^1 &amp; e &amp; f}"</code></td></tr>
<tr><td align="right">Output:</td><td ><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><mrow><mtable rowalign='top'><mtr><mtd><mfrac linethickness="0"><mrow><mi>&alpha;</mi></mrow><mrow><mi>&omega;</mi></mrow></mfrac></mtd><mtd><mi>a</mi></mtd><mtd><mi>b</mi></mtd></mtr><mtr><mtd><mfrac><mrow><mn>3</mn></mrow><mrow><mn>4</mn></mrow></mfrac></mtd><mtd><mi>c</mi></mtd><mtd><mi>d</mi></mtd></mtr><mtr><mtd><msubsup><mo>&Integral;</mo><mn>0</mn><mn>1</mn></msubsup></mtd><mtd><mi>e</mi></mtd><mtd><mi>f</mi></mtd></mtr></mtable></mrow></math></td></tr>
<tr><td colspan="2"><hr/></td></tr>
<tr><td align="right">Input:</td><td style='font-family: monospace'><code>"\array{1 &amp; 0 \\
                0 &amp; 1}"</code></td></tr>
<tr><td align="right">Output:</td><td ><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><mrow><mtable><mtr><mtd><mn>1</mn></mtd><mtd><mn>0</mn></mtd></mtr><mtr><mtd><mn>0</mn></mtd><mtd><mn>1</mn></mtd></mtr></mtable></mrow></math></td></tr>
<tr><td colspan="2"><hr/></td></tr>
<tr><td align="right">Input:</td><td style='font-family: monospace'><code>"\array{1 &amp; 0 \\ 0 &amp; 1}"</code></td></tr>
<tr><td align="right">Output:</td><td ><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><mrow><mtable><mtr><mtd><mn>1</mn></mtd><mtd><mn>0</mn></mtd></mtr><mtr><mtd><mn>0</mn></mtd><mtd><mn>1</mn></mtd></mtr></mtable></mrow></math></td></tr>
<tr><td colspan="2"><hr/></td></tr>
<tr><td align="right">Input:</td><td style='font-family: monospace'><code>"\array{1 &amp; 0}"</code></td></tr>
<tr><td align="right">Output:</td><td ><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><mrow><mtable><mtr><mtd><mn>1</mn></mtd><mtd><mn>0</mn></mtd></mtr></mtable></mrow></math></td></tr>
<tr><td colspan="2"><hr/></td></tr>
<tr><td align="right">Input:</td><td style='font-family: monospace'><code>"\array{1}"</code></td></tr>
<tr><td align="right">Output:</td><td ><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><mrow><mtable><mtr><mtd><mn>1</mn></mtd></mtr></mtable></mrow></math></td></tr>
<tr><td colspan="2"><hr/></td></tr>
<tr><td align="right">Input:</td><td style='font-family: monospace'><code>"\array{\arrayopts{\collines{solid}} a}"</code></td></tr>
<tr><td align="right">Output:</td><td ><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><mrow><mtable columnlines='solid'><mtr><mtd><mi>a</mi></mtd></mtr></mtable></mrow></math></td></tr>
<tr><td colspan="2"><hr/></td></tr>
<tr><td align="right">Input:</td><td style='font-family: monospace'><code>"\array{\arrayopts{\equalcols{true}} a}"</code></td></tr>
<tr><td align="right">Output:</td><td ><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><mrow><mtable equalcolumns='true'><mtr><mtd><mi>a</mi></mtd></mtr></mtable></mrow></math></td></tr>
<tr><td colspan="2"><hr/></td></tr>
<tr><td align="right">Input:</td><td style='font-family: monospace'><code>"\array{\arrayopts{\equalrows{true}} a}"</code></td></tr>
<tr><td align="right">Output:</td><td ><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><mrow><mtable equalrows='true'><mtr><mtd><mi>a</mi></mtd></mtr></mtable></mrow></math></td></tr>
<tr><td colspan="2"><hr/></td></tr>
<tr><td align="right">Input:</td><td style='font-family: monospace'><code>"\array{\arrayopts{\frame{solid}} a}"</code></td></tr>
<tr><td align="right">Output:</td><td ><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><mrow><mtable frame='solid'><mtr><mtd><mi>a</mi></mtd></mtr></mtable></mrow></math></td></tr>
<tr><td colspan="2"><hr/></td></tr>
<tr><td align="right">Input:</td><td style='font-family: monospace'><code>"\array{\arrayopts{\padding{20}} a &amp; b &amp; c \\ d &amp; e &amp; f \\ \alpha &amp; \beta &amp; \gamma}"</code></td></tr>
<tr><td align="right">Output:</td><td ><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><mrow><mtable rowspacing='20' columnspacing='20'><mtr><mtd><mi>a</mi></mtd><mtd><mi>b</mi></mtd><mtd><mi>c</mi></mtd></mtr><mtr><mtd><mi>d</mi></mtd><mtd><mi>e</mi></mtd><mtd><mi>f</mi></mtd></mtr><mtr><mtd><mi>&alpha;</mi></mtd><mtd><mi>&beta;</mi></mtd><mtd><mi>&gamma;</mi></mtd></mtr></mtable></mrow></math></td></tr>
<tr><td colspan="2"><hr/></td></tr>
<tr><td align="right">Input:</td><td style='font-family: monospace'><code>"\array{\arrayopts{\rowlines{solid}} a}"</code></td></tr>
<tr><td align="right">Output:</td><td ><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><mrow><mtable rowlines='solid'><mtr><mtd><mi>a</mi></mtd></mtr></mtable></mrow></math></td></tr>
<tr><td colspan="2"><hr/></td></tr>
<tr><td align="right">Input:</td><td style='font-family: monospace'><code>"\array{\cellopts{\colspan{2}} a \\ b &amp; c}"</code></td></tr>
<tr><td align="right">Output:</td><td ><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><mrow><mtable><mtr><mtd columnspan='2'><mi>a</mi></mtd></mtr><mtr><mtd><mi>b</mi></mtd><mtd><mi>c</mi></mtd></mtr></mtable></mrow></math></td></tr>
<tr><td colspan="2"><hr/></td></tr>
<tr><td align="right">Input:</td><td style='font-family: monospace'><code>"\array{\cellopts{\rowspan{2}} a &amp; b \\ c}"</code></td></tr>
<tr><td align="right">Output:</td><td ><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><mrow><mtable><mtr><mtd rowspan='2'><mi>a</mi></mtd><mtd><mi>b</mi></mtd></mtr><mtr><mtd><mi>c</mi></mtd></mtr></mtable></mrow></math></td></tr>
<tr><td colspan="2"><hr/></td></tr>
<tr><td align="right">Input:</td><td style='font-family: monospace'><code>"\array{\colspan{2} a \\ b &amp; c}"</code></td></tr>
<tr><td align="right">Output:</td><td ><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><mrow><mtable><mtr><mtd columnspan='2'><mi>a</mi></mtd></mtr><mtr><mtd><mi>b</mi></mtd><mtd><mi>c</mi></mtd></mtr></mtable></mrow></math></td></tr>
<tr><td colspan="2"><hr/></td></tr>
<tr><td align="right">Input:</td><td style='font-family: monospace'><code>"\array{\rowspan{2} a &amp; b \\ c}"</code></td></tr>
<tr><td align="right">Output:</td><td ><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><mrow><mtable><mtr><mtd rowspan='2'><mi>a</mi></mtd><mtd><mi>b</mi></mtd></mtr><mtr><mtd><mi>c</mi></mtd></mtr></mtable></mrow></math></td></tr>
<tr><td colspan="2"><hr/></td></tr>
<tr><td align="right">Input:</td><td style='font-family: monospace'><code>"\bar{x}"</code></td></tr>
<tr><td align="right">Output:</td><td ><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><mover><mrow><mi>x</mi></mrow><mo>&OverBar;</mo></mover></math></td></tr>
<tr><td colspan="2"><hr/></td></tr>
<tr><td align="right">Input:</td><td style='font-family: monospace'><code>"\binom{x}{2}"</code></td></tr>
<tr><td align="right">Output:</td><td ><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><mfrac linethickness="0"><mrow><mi>x</mi></mrow><mrow><mn>2</mn></mrow></mfrac></math></td></tr>
<tr><td colspan="2"><hr/></td></tr>
<tr><td align="right">Input:</td><td style='font-family: monospace'><code>"\check{x}"</code></td></tr>
<tr><td align="right">Output:</td><td ><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><mover><mrow><mi>x</mi></mrow><mo>&macr;</mo></mover></math></td></tr>
<tr><td colspan="2"><hr/></td></tr>
<tr><td align="right">Input:</td><td style='font-family: monospace'><code>"\ddot{x}"</code></td></tr>
<tr><td align="right">Output:</td><td ><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><mover><mrow><mi>x</mi></mrow><mo>&Dot;</mo></mover></math></td></tr>
<tr><td colspan="2"><hr/></td></tr>
<tr><td align="right">Input:</td><td style='font-family: monospace'><code>"\dot{x}"</code></td></tr>
<tr><td align="right">Output:</td><td ><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><mover><mrow><mi>x</mi></mrow><mo>&dot;</mo></mover></math></td></tr>
<tr><td colspan="2"><hr/></td></tr>
<tr><td align="right">Input:</td><td style='font-family: monospace'><code>"\forall x\,x&lt;0"</code></td></tr>
<tr><td align="right">Output:</td><td ><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><mo>&forall;</mo><mi>x</mi><mspace width="thinmathspace"/><mi>x</mi><mo>&lt;</mo><mn>0</mn></math></td></tr>
<tr><td colspan="2"><hr/></td></tr>
<tr><td align="right">Input:</td><td style='font-family: monospace'><code>"\frac{1}{2}"</code></td></tr>
<tr><td align="right">Output:</td><td ><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><mfrac><mrow><mn>1</mn></mrow><mrow><mn>2</mn></mrow></mfrac></math></td></tr>
<tr><td colspan="2"><hr/></td></tr>
<tr><td align="right">Input:</td><td style='font-family: monospace'><code>"\frac{1}{N} \sum_r \phi({x^{(r)}})"</code></td></tr>
<tr><td align="right">Output:</td><td ><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><mfrac><mrow><mn>1</mn></mrow><mrow><mi>N</mi></mrow></mfrac><msub><mo lspace="thinmathspace" rspace="thinmathspace">&Sum;</mo><mi>r</mi></msub><mi>&phi;</mi><mo stretchy='false'>(</mo><mrow><msup><mi>x</mi><mrow><mo stretchy='false'>(</mo><mi>r</mi><mo stretchy='false'>)</mo></mrow></msup></mrow><mo stretchy='false'>)</mo></math></td></tr>
<tr><td colspan="2"><hr/></td></tr>
<tr><td align="right">Input:</td><td style='font-family: monospace'><code>"\frac{\sum_r w_r \phi({x^{(r)}})}{\sum_r w_r}"</code></td></tr>
<tr><td align="right">Output:</td><td ><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><mfrac><mrow><msub><mo lspace="thinmathspace" rspace="thinmathspace">&Sum;</mo><mi>r</mi></msub><msub><mi>w</mi><mi>r</mi></msub><mi>&phi;</mi><mo stretchy='false'>(</mo><mrow><msup><mi>x</mi><mrow><mo stretchy='false'>(</mo><mi>r</mi><mo stretchy='false'>)</mo></mrow></msup></mrow><mo stretchy='false'>)</mo></mrow><mrow><msub><mo lspace="thinmathspace" rspace="thinmathspace">&Sum;</mo><mi>r</mi></msub><msub><mi>w</mi><mi>r</mi></msub></mrow></mfrac></math></td></tr>
<tr><td colspan="2"><hr/></td></tr>
<tr><td align="right">Input:</td><td style='font-family: monospace'><code>"\frac{{N-x}}{2}"</code></td></tr>
<tr><td align="right">Output:</td><td ><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><mfrac><mrow><mrow><mi>N</mi><mo>&minus;</mo><mi>x</mi></mrow></mrow><mrow><mn>2</mn></mrow></mfrac></math></td></tr>
<tr><td colspan="2"><hr/></td></tr>
<tr><td align="right">Input:</td><td style='font-family: monospace'><code>"\hat{x}"</code></td></tr>
<tr><td align="right">Output:</td><td ><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><mover><mrow><mi>x</mi></mrow><mo>&Hat;</mo></mover></math></td></tr>
<tr><td colspan="2"><hr/></td></tr>
<tr><td align="right">Input:</td><td style='font-family: monospace'><code>"\int_x f(x)\ dx"</code></td></tr>
<tr><td align="right">Output:</td><td ><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><msub><mo>&Integral;</mo><mi>x</mi></msub><mi>f</mi><mo stretchy='false'>(</mo><mi>x</mi><mo stretchy='false'>)</mo><mspace width="mediummathspace"/><mi>d</mi><mi>x</mi></math></td></tr>
<tr><td colspan="2"><hr/></td></tr>
<tr><td align="right">Input:</td><td style='font-family: monospace'><code>"\int_{-\infinity}^\infinity f(x)\ dx = 1"</code></td></tr>
<tr><td align="right">Output:</td><td ><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><msubsup><mo>&Integral;</mo><mrow><mo lspace="verythinmathspace" rspace="0em">&minus;</mo><mn>&infin;</mn></mrow><mn>&infin;</mn></msubsup><mi>f</mi><mo stretchy='false'>(</mo><mi>x</mi><mo stretchy='false'>)</mo><mspace width="mediummathspace"/><mi>d</mi><mi>x</mi><mo>=</mo><mn>1</mn></math></td></tr>
<tr><td colspan="2"><hr/></td></tr>
<tr><td align="right">Input:</td><td style='font-family: monospace'><code>"\left ( \binom{2}{3} \right )"</code></td></tr>
<tr><td align="right">Output:</td><td ><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><mrow><mo>(</mo><mfrac linethickness="0"><mrow><mn>2</mn></mrow><mrow><mn>3</mn></mrow></mfrac><mo>)</mo></mrow></math></td></tr>
<tr><td colspan="2"><hr/></td></tr>
<tr><td align="right">Input:</td><td style='font-family: monospace'><code>"\left ( \frac{2}{4+x} \right )^3"</code></td></tr>
<tr><td align="right">Output:</td><td ><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><msup><mrow><mo>(</mo><mfrac><mrow><mn>2</mn></mrow><mrow><mn>4</mn><mo>+</mo><mi>x</mi></mrow></mfrac><mo>)</mo></mrow><mn>3</mn></msup></math></td></tr>
<tr><td colspan="2"><hr/></td></tr>
<tr><td align="right">Input:</td><td style='font-family: monospace'><code>"\left ( x \right"</code></td></tr>
<tr><td align="right">Output:</td><td ><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><mrow><mo>(</mo><mi>x</mi></mrow></math></td></tr>
<tr><td colspan="2"><hr/></td></tr>
<tr><td align="right">Input:</td><td style='font-family: monospace'><code>"\left ( x \right )"</code></td></tr>
<tr><td align="right">Output:</td><td ><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow></math></td></tr>
<tr><td colspan="2"><hr/></td></tr>
<tr><td align="right">Input:</td><td style='font-family: monospace'><code>"\left ( x \right + 3"</code></td></tr>
<tr><td align="right">Output:</td><td ><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><mrow><mo>(</mo><mi>x</mi></mrow><mo>+</mo><mn>3</mn></math></td></tr>
<tr><td colspan="2"><hr/></td></tr>
<tr><td align="right">Input:</td><td style='font-family: monospace'><code>"\left \frac{x}{y} \right|_{x=0}"</code></td></tr>
<tr><td align="right">Output:</td><td ><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><msub><mrow><mfrac><mrow><mi>x</mi></mrow><mrow><mi>y</mi></mrow></mfrac><mo>|</mo></mrow><mrow><mi>x</mi><mo>=</mo><mn>0</mn></mrow></msub></math></td></tr>
<tr><td colspan="2"><hr/></td></tr>
<tr><td align="right">Input:</td><td style='font-family: monospace'><code>"\left \{ x \right \}"</code></td></tr>
<tr><td align="right">Output:</td><td ><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><mrow><mo>{</mo><mi>x</mi><mo>}</mo></mrow></math></td></tr>
<tr><td colspan="2"><hr/></td></tr>
<tr><td align="right">Input:</td><td style='font-family: monospace'><code>"\lim_3"</code></td></tr>
<tr><td align="right">Output:</td><td ><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><msub><mi>lim</mi><mn>3</mn></msub></math></td></tr>
<tr><td colspan="2"><hr/></td></tr>
<tr><td align="right">Input:</td><td style='font-family: monospace'><code>"\lim_{x\to\infty}f(x)=0"</code></td></tr>
<tr><td align="right">Output:</td><td ><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><msub><mi>lim</mi><mrow><mi>x</mi><mo>&rightarrow;</mo><mn>&infin;</mn></mrow></msub><mi>f</mi><mo stretchy='false'>(</mo><mi>x</mi><mo stretchy='false'>)</mo><mo>=</mo><mn>0</mn></math></td></tr>
<tr><td colspan="2"><hr/></td></tr>
<tr><td align="right">Input:</td><td style='font-family: monospace'><code>"\ln x"</code></td></tr>
<tr><td align="right">Output:</td><td ><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><mi>ln</mi><mi>x</mi></math></td></tr>
<tr><td colspan="2"><hr/></td></tr>
<tr><td align="right">Input:</td><td style='font-family: monospace'><code>"\mathbb{Hello}"</code></td></tr>
<tr><td align="right">Output:</td><td ><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><mi>&Hopf;&eopf;&lopf;&lopf;&oopf;</mi></math></td></tr>
<tr><td colspan="2"><hr/></td></tr>
<tr><td align="right">Input:</td><td style='font-family: monospace'><code>"\mathcal{Hello}"</code></td></tr>
<tr><td align="right">Output:</td><td ><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><mi>&Hscr;&escr;&lscr;&lscr;&oscr;</mi></math></td></tr>
<tr><td colspan="2"><hr/></td></tr>
<tr><td align="right">Input:</td><td style='font-family: monospace'><code>"\mathop{monkey}
         &lt;
         b"</code></td></tr>
<tr><td align="right">Output:</td><td ><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><mo lspace="0em" rspace="thinmathspace">monkey</mo><mo>&lt;</mo><mi>b</mi></math></td></tr>
<tr><td colspan="2"><hr/></td></tr>
<tr><td align="right">Input:</td><td style='font-family: monospace'><code>"\overset{\text{n terms}}{\overbrace{1+2+\cdots+n}}"</code></td></tr>
<tr><td align="right">Output:</td><td ><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><mover><mrow><mover><mrow><mn>1</mn><mo>+</mo><mn>2</mn><mo>+</mo><mo>&ctdot;</mo><mo>+</mo><mi>n</mi></mrow><mo>&OverBrace;</mo></mover></mrow><mrow><mtext>n terms</mtext></mrow></mover></math></td></tr>
<tr><td colspan="2"><hr/></td></tr>
<tr><td align="right">Input:</td><td style='font-family: monospace'><code>"\root{3}{x+y}"</code></td></tr>
<tr><td align="right">Output:</td><td ><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><mroot><mrow><mi>x</mi><mo>+</mo><mi>y</mi></mrow><mrow><mn>3</mn></mrow></mroot></math></td></tr>
<tr><td colspan="2"><hr/></td></tr>
<tr><td align="right">Input:</td><td style='font-family: monospace'><code>"\sqrt{i}"</code></td></tr>
<tr><td align="right">Output:</td><td ><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><msqrt><mrow><mi>i</mi></mrow></msqrt></math></td></tr>
<tr><td colspan="2"><hr/></td></tr>
<tr><td align="right">Input:</td><td style='font-family: monospace'><code>"\sum_{n=1}^\infty \frac{(-1)^n}{n} = \ln 2"</code></td></tr>
<tr><td align="right">Output:</td><td ><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><msubsup><mo lspace="thinmathspace" rspace="thinmathspace">&Sum;</mo><mrow><mi>n</mi><mo>=</mo><mn>1</mn></mrow><mn>&infin;</mn></msubsup><mfrac><mrow><mo stretchy='false'>(</mo><mo lspace="verythinmathspace" rspace="0em">&minus;</mo><mn>1</mn><msup><mo stretchy='false'>)</mo><mi>n</mi></msup></mrow><mrow><mi>n</mi></mrow></mfrac><mo>=</mo><mi>ln</mi><mn>2</mn></math></td></tr>
<tr><td colspan="2"><hr/></td></tr>
<tr><td align="right">Input:</td><td style='font-family: monospace'><code>"\sum_{n=1}^\infty \frac{1}{n} \text{ is divergent, but } \lim_{n \to \infty} \sum_{i=1}^n \frac{1}{i} - \ln n \text{ exists.}"</code></td></tr>
<tr><td align="right">Output:</td><td ><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><msubsup><mo lspace="thinmathspace" rspace="thinmathspace">&Sum;</mo><mrow><mi>n</mi><mo>=</mo><mn>1</mn></mrow><mn>&infin;</mn></msubsup><mfrac><mrow><mn>1</mn></mrow><mrow><mi>n</mi></mrow></mfrac><mtext> is divergent, but </mtext><msub><mi>lim</mi><mrow><mi>n</mi><mo>&rightarrow;</mo><mn>&infin;</mn></mrow></msub><msubsup><mo lspace="thinmathspace" rspace="thinmathspace">&Sum;</mo><mrow><mi>i</mi><mo>=</mo><mn>1</mn></mrow><mi>n</mi></msubsup><mfrac><mrow><mn>1</mn></mrow><mrow><mi>i</mi></mrow></mfrac><mo>&minus;</mo><mi>ln</mi><mi>n</mi><mtext> exists.</mtext></math></td></tr>
<tr><td colspan="2"><hr/></td></tr>
<tr><td align="right">Input:</td><td style='font-family: monospace'><code>"\text{ if }"</code></td></tr>
<tr><td align="right">Output:</td><td ><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><mtext> if </mtext></math></td></tr>
<tr><td colspan="2"><hr/></td></tr>
<tr><td align="right">Input:</td><td style='font-family: monospace'><code>"\text{for}\ -\infty"</code></td></tr>
<tr><td align="right">Output:</td><td ><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><mtext>for</mtext><mspace width="mediummathspace"/><mo lspace="verythinmathspace" rspace="0em">&minus;</mo><mn>&infin;</mn></math></td></tr>
<tr><td colspan="2"><hr/></td></tr>
<tr><td align="right">Input:</td><td style='font-family: monospace'><code>"\text{if \alpha}"</code></td></tr>
<tr><td align="right">Output:</td><td ><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><mtext>if \alpha</mtext></math></td></tr>
<tr><td colspan="2"><hr/></td></tr>
<tr><td align="right">Input:</td><td style='font-family: monospace'><code>"\text{if}"</code></td></tr>
<tr><td align="right">Output:</td><td ><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><mtext>if</mtext></math></td></tr>
<tr><td colspan="2"><hr/></td></tr>
<tr><td align="right">Input:</td><td style='font-family: monospace'><code>"\underoverset{S}{\alpha}{x=\infty}"</code></td></tr>
<tr><td align="right">Output:</td><td ><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><munderover><mrow><mi>x</mi><mo>=</mo><mn>&infin;</mn></mrow><mrow><mi>S</mi></mrow><mrow><mi>&alpha;</mi></mrow></munderover></math></td></tr>
<tr><td colspan="2"><hr/></td></tr>
<tr><td align="right">Input:</td><td style='font-family: monospace'><code>"\vec{x}"</code></td></tr>
<tr><td align="right">Output:</td><td ><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><mover><mrow><mi>x</mi></mrow><mo>&RightVector;</mo></mover></math></td></tr>
<tr><td colspan="2"><hr/></td></tr>
<tr><td align="right">Input:</td><td style='font-family: monospace'><code>"a &lt; b"</code></td></tr>
<tr><td align="right">Output:</td><td ><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><mi>a</mi><mo>&lt;</mo><mi>b</mi></math></td></tr>
<tr><td colspan="2"><hr/></td></tr>
<tr><td align="right">Input:</td><td style='font-family: monospace'><code>"a = -3"</code></td></tr>
<tr><td align="right">Output:</td><td ><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><mi>a</mi><mo>=</mo><mo lspace="verythinmathspace" rspace="0em">&minus;</mo><mn>3</mn></math></td></tr>
<tr><td colspan="2"><hr/></td></tr>
<tr><td align="right">Input:</td><td style='font-family: monospace'><code>"a ^ b"</code></td></tr>
<tr><td align="right">Output:</td><td ><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><msup><mi>a</mi><mi>b</mi></msup></math></td></tr>
<tr><td colspan="2"><hr/></td></tr>
<tr><td align="right">Input:</td><td style='font-family: monospace'><code>"a+3"</code></td></tr>
<tr><td align="right">Output:</td><td ><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><mi>a</mi><mo>+</mo><mn>3</mn></math></td></tr>
<tr><td colspan="2"><hr/></td></tr>
<tr><td align="right">Input:</td><td style='font-family: monospace'><code>"a-b"</code></td></tr>
<tr><td align="right">Output:</td><td ><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><mi>a</mi><mo>&minus;</mo><mi>b</mi></math></td></tr>
<tr><td colspan="2"><hr/></td></tr>
<tr><td align="right">Input:</td><td style='font-family: monospace'><code>"a=-b"</code></td></tr>
<tr><td align="right">Output:</td><td ><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><mi>a</mi><mo>=</mo><mo lspace="verythinmathspace" rspace="0em">&minus;</mo><mi>b</mi></math></td></tr>
<tr><td colspan="2"><hr/></td></tr>
<tr><td align="right">Input:</td><td style='font-family: monospace'><code>"a\in S"</code></td></tr>
<tr><td align="right">Output:</td><td ><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><mi>a</mi><mo>&Element;</mo><mi>S</mi></math></td></tr>
<tr><td colspan="2"><hr/></td></tr>
<tr><td align="right">Input:</td><td style='font-family: monospace'><code>"a\mathbb{GOAT}"</code></td></tr>
<tr><td align="right">Output:</td><td ><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><mi>a</mi><mi>&Gopf;&Oopf;&Aopf;&Topf;</mi></math></td></tr>
<tr><td colspan="2"><hr/></td></tr>
<tr><td align="right">Input:</td><td style='font-family: monospace'><code>"a\text{ if a fd ew s }b"</code></td></tr>
<tr><td align="right">Output:</td><td ><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><mi>a</mi><mtext> if a fd ew s </mtext><mi>b</mi></math></td></tr>
<tr><td colspan="2"><hr/></td></tr>
<tr><td align="right">Input:</td><td style='font-family: monospace'><code>"a\text{ if }b"</code></td></tr>
<tr><td align="right">Output:</td><td ><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><mi>a</mi><mtext> if </mtext><mi>b</mi></math></td></tr>
<tr><td colspan="2"><hr/></td></tr>
<tr><td align="right">Input:</td><td style='font-family: monospace'><code>"a\text{ if}b"</code></td></tr>
<tr><td align="right">Output:</td><td ><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><mi>a</mi><mtext> if</mtext><mi>b</mi></math></td></tr>
<tr><td colspan="2"><hr/></td></tr>
<tr><td align="right">Input:</td><td style='font-family: monospace'><code>"a\text{if }b"</code></td></tr>
<tr><td align="right">Output:</td><td ><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><mi>a</mi><mtext>if </mtext><mi>b</mi></math></td></tr>
<tr><td colspan="2"><hr/></td></tr>
<tr><td align="right">Input:</td><td style='font-family: monospace'><code>"a\text{if}b"</code></td></tr>
<tr><td align="right">Output:</td><td ><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><mi>a</mi><mtext>if</mtext><mi>b</mi></math></td></tr>
<tr><td colspan="2"><hr/></td></tr>
<tr><td align="right">Input:</td><td style='font-family: monospace'><code>"a^b"</code></td></tr>
<tr><td align="right">Output:</td><td ><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><msup><mi>a</mi><mi>b</mi></msup></math></td></tr>
<tr><td colspan="2"><hr/></td></tr>
<tr><td align="right">Input:</td><td style='font-family: monospace'><code>"a^b_c"</code></td></tr>
<tr><td align="right">Output:</td><td ><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><msubsup><mi>a</mi><mi>c</mi><mi>b</mi></msubsup></math></td></tr>
<tr><td colspan="2"><hr/></td></tr>
<tr><td align="right">Input:</td><td style='font-family: monospace'><code>"a^{b_c} &lt; a^b_c"</code></td></tr>
<tr><td align="right">Output:</td><td ><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><msup><mi>a</mi><mrow><msub><mi>b</mi><mi>c</mi></msub></mrow></msup><mo>&lt;</mo><msubsup><mi>a</mi><mi>c</mi><mi>b</mi></msubsup></math></td></tr>
<tr><td colspan="2"><hr/></td></tr>
<tr><td align="right">Input:</td><td style='font-family: monospace'><code>"a_b"</code></td></tr>
<tr><td align="right">Output:</td><td ><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><msub><mi>a</mi><mi>b</mi></msub></math></td></tr>
<tr><td colspan="2"><hr/></td></tr>
<tr><td align="right">Input:</td><td style='font-family: monospace'><code>"if"</code></td></tr>
<tr><td align="right">Output:</td><td ><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><mi>i</mi><mi>f</mi></math></td></tr>
<tr><td colspan="2"><hr/></td></tr>
<tr><td align="right">Input:</td><td style='font-family: monospace'><code>"w_r \equiv \frac{P^*({x^{(r)}})}{Q^*({x^{(r)}})}."</code></td></tr>
<tr><td align="right">Output:</td><td ><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><msub><mi>w</mi><mi>r</mi></msub><mo>&equiv;</mo><mfrac><mrow><msup><mi>P</mi><mo>*</mo></msup><mo stretchy='false'>(</mo><mrow><msup><mi>x</mi><mrow><mo stretchy='false'>(</mo><mi>r</mi><mo stretchy='false'>)</mo></mrow></msup></mrow><mo stretchy='false'>)</mo></mrow><mrow><msup><mi>Q</mi><mo>*</mo></msup><mo stretchy='false'>(</mo><mrow><msup><mi>x</mi><mrow><mo stretchy='false'>(</mo><mi>r</mi><mo stretchy='false'>)</mo></mrow></msup></mrow><mo stretchy='false'>)</mo></mrow></mfrac><mo>.</mo></math></td></tr>
<tr><td colspan="2"><hr/></td></tr>
<tr><td align="right">Input:</td><td style='font-family: monospace'><code>"x"</code></td></tr>
<tr><td align="right">Output:</td><td ><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><mi>x</mi></math></td></tr>
<tr><td colspan="2"><hr/></td></tr>
<tr><td align="right">Input:</td><td style='font-family: monospace'><code>"x + - x"</code></td></tr>
<tr><td align="right">Output:</td><td ><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><mi>x</mi><mo>+</mo><mo lspace="verythinmathspace" rspace="0em">&minus;</mo><mi>x</mi></math></td></tr>
<tr><td colspan="2"><hr/></td></tr>
<tr><td align="right">Input:</td><td style='font-family: monospace'><code>"x - x"</code></td></tr>
<tr><td align="right">Output:</td><td ><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><mi>x</mi><mo>&minus;</mo><mi>x</mi></math></td></tr>
<tr><td colspan="2"><hr/></td></tr>
<tr><td align="right">Input:</td><td style='font-family: monospace'><code>"x--x"</code></td></tr>
<tr><td align="right">Output:</td><td ><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><mi>x</mi><mo>&minus;</mo><mo lspace="verythinmathspace" rspace="0em">&minus;</mo><mi>x</mi></math></td></tr>
<tr><td colspan="2"><hr/></td></tr>
<tr><td align="right">Input:</td><td style='font-family: monospace'><code>"x\textstyle{\int_0^1}\displaystyle{\int_0^1}y"</code></td></tr>
<tr><td align="right">Output:</td><td ><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><mi>x</mi><mstyle displaystyle="false"><mrow><msubsup><mo>&Integral;</mo><mn>0</mn><mn>1</mn></msubsup></mrow></mstyle><mstyle displaystyle="true"><mrow><msubsup><mo>&Integral;</mo><mn>0</mn><mn>1</mn></msubsup></mrow></mstyle><mi>y</mi></math></td></tr>
<tr><td colspan="2"><hr/></td></tr>
<tr><td align="right">Input:</td><td style='font-family: monospace'><code>"{E_\theta\left[\hat{\theta}\right]}"</code></td></tr>
<tr><td align="right">Output:</td><td ><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><mrow><msub><mi>E</mi><mi>&theta;</mi></msub><mrow><mo>[</mo><mover><mrow><mi>&theta;</mi></mrow><mo>&Hat;</mo></mover><mo>]</mo></mrow></mrow></math></td></tr>
<tr><td colspan="2"><hr/></td></tr>
<tr><td align="right">Input:</td><td style='font-family: monospace'><code>"{\frac{\alpha-\delta}{\beta-\gamma}}"</code></td></tr>
<tr><td align="right">Output:</td><td ><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><mrow><mfrac><mrow><mi>&alpha;</mi><mo>&minus;</mo><mi>&delta;</mi></mrow><mrow><mi>&beta;</mi><mo>&minus;</mo><mi>&gamma;</mi></mrow></mfrac></mrow></math></td></tr>
<tr><td colspan="2"><hr/></td></tr>
<tr><td align="right">Input:</td><td style='font-family: monospace'><code>"{\frac{\alpha-{\mathbb{GOAT}}}{\beta-{{\mathbb{GOAT}}-x}}}"</code></td></tr>
<tr><td align="right">Output:</td><td ><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><mrow><mfrac><mrow><mi>&alpha;</mi><mo>&minus;</mo><mrow><mi>&Gopf;&Oopf;&Aopf;&Topf;</mi></mrow></mrow><mrow><mi>&beta;</mi><mo>&minus;</mo><mrow><mrow><mi>&Gopf;&Oopf;&Aopf;&Topf;</mi></mrow><mo>&minus;</mo><mi>x</mi></mrow></mrow></mfrac></mrow></math></td></tr>
<tr><td colspan="2"><hr/></td></tr>
<tr><td align="right">Input:</td><td style='font-family: monospace'><code>"{\mathbb{GOAT}}_3"</code></td></tr>
<tr><td align="right">Output:</td><td ><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><msub><mrow><mi>&Gopf;&Oopf;&Aopf;&Topf;</mi></mrow><mn>3</mn></msub></math></td></tr>
<tr><td colspan="2"><hr/></td></tr>
<tr><td align="right">Input:</td><td style='font-family: monospace'><code>"{x}"</code></td></tr>
<tr><td align="right">Output:</td><td ><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><mrow><mi>x</mi></mrow></math></td></tr>
<tr><td colspan="2"><hr/></td></tr>
<tr><td align="right">Input:</td><td style='font-family: monospace'><code>"{y-x}"</code></td></tr>
<tr><td align="right">Output:</td><td ><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><mrow><mi>y</mi><mo>&minus;</mo><mi>x</mi></mrow></math></td></tr>
<tr><td colspan="2"><hr/></td></tr>
<tr><td align="right">Input:</td><td style='font-family: monospace'><code>"{{N-x}-x}"</code></td></tr>
<tr><td align="right">Output:</td><td ><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><mrow><mrow><mi>N</mi><mo>&minus;</mo><mi>x</mi></mrow><mo>&minus;</mo><mi>x</mi></mrow></math></td></tr>
<tr><td colspan="2"><hr/></td></tr>
<tr><td align="right">Input:</td><td style='font-family: monospace'><code>"{{{N-x}-x}-x}"</code></td></tr>
<tr><td align="right">Output:</td><td ><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><mrow><mrow><mrow><mi>N</mi><mo>&minus;</mo><mi>x</mi></mrow><mo>&minus;</mo><mi>x</mi></mrow><mo>&minus;</mo><mi>x</mi></mrow></math></td></tr>
<tr><td colspan="2"><hr/></td></tr>
</table></body></html>
