<?xml version="1.0" encoding="utf-8"?>

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<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.1 plus MathML 2.0//EN"
"http://www.w3.org/TR/MathML2/dtd/xhtml-math11-f.dtd" [
      <!ENTITY mathml "http://www.w3.org/1998/Math/MathML">
   ]>

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<head>
	<title>MathToWeb (MathML example)</title>
	<link rel="stylesheet" href="./../../css/mathtoweb_web.css" type="text/css" />
	<link rel="shortcut icon" href="./images/mathtoweb16x16.ico" />
</head>

<body>

<p class="small">
MathML generated by <a href="http://www.mathtoweb.com">MathToWeb</a>
</p>
<p class="small">
A MathML example displaying the <a href="http://www.ams.org/tex/amslatex.html">AMS-Latex</a> math environment
<span class="code">align</span> being used to annotate an equation line-by-line with cross-references to other
equations being made from within.
MathToWeb treats references (which are, in fact, just links) that are inside MathML differently that those that are outside.
Looking at the MathML code below (we have set the pertinent code in bold),
we see that the hyperlinks that represent the cross-references are actually XML <code>xlink</code> calls made from <code>&lt;mrow&gt;</code> tags, for example, <br/>
<code>&lt;mrow&nbsp;xmlns:xlink="http://www.w3.org/1999/xlink" xlink:type="simple"&nbsp;xlink:href="#align-eq1"&gt;1.6&lt;/mrow&gt;</code>, rather
than normal HTML hyperlinks <code>&lt;a&nbsp;href="#align-eq1"&gt;1.6&lt;/a&gt;</code>.  The former is necessary for
links inside MathML because it is, after all, an XML application.
</p>


<p>
	<table width="100%" border="0"><tr>

	<td width="50%">
<table><tr><td>
<code>
<pre class="latex">\begin{align}
y&amp; = x_0+x_1-x_2+x_3-\dotsb  &amp;&amp; \text{by \ref{align-eq1}}    <span class="mtw_specific">\tag{1.9}</span>\label{align-eq4}\\
 &amp; = y_0+y_1                 &amp;&amp; \text{by \eqref{align-eq2}}  \notag \\
 &amp; = q_0-q_1+q_2             &amp;&amp; \text {by Axiom 4.}          <span class="mtw_specific">\tag{2.0}</span>\label{align-eq5}
\end{align}</pre>
</code>
</td></tr></table>
	</td>
	
	<td align="center">
		<!-- (your Latex) $\xrightarrow{\; \text{              } \;}$ -->
		<math xmlns="http://www.w3.org/1998/Math/MathML">
		<mrow>
			<mstyle displaystyle="true">
				<mover>
					<mo stretchy="true">&xrarr;</mo>
					<mrow>
						<mo>&nbsp;</mo>
						<mspace width="0.278em" />
						<mtext>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;</mtext>
						<mspace width="0.278em" />
						<mo>&nbsp;</mo>
					</mrow>
				</mover>
			</mstyle>
		</mrow>
		</math>
	</td>

	</tr>
	<tr>
	

	<td colspan="2">
		
		<!-- begin MathToWeb -->
		<!-- (your Latex) \begin{align}
		y& = x_0+x_1-x_2+x_3-\dotsb  && \text{by \ref{align-eq1}}    \tag{1.9}\label{align-eq4}\\
		 & = y_0+y_1                 && \text{by \eqref{align-eq2}}  \notag \\
		 & = q_0-q_1+q_2             && \text {by Axiom 4.}          \tag{2.0}\label{align-eq5}
		\end{align} -->

		<table class="align" style="width: 100%; margin-top: 1.0%; margin-right: 0.0%; margin-bottom: 1.0%; margin-left: 0.0%;">
		<tr>
		<td style="width: 50%"></td> <!-- Adjusted from 5% to 50% in order to shift eq right -->
		<td rowspan="136">

		<math xmlns="http://www.w3.org/1998/Math/MathML">
		<mrow>
			<mtable class="m-align">
				<mtr>
					<mtd columnalign="right">
						<mi>y</mi>
					</mtd>
					<mtd columnalign="left">
						<mo>=</mo>
						<msub>
							<mi>x</mi>
							<mn>0</mn>
						</msub>
						<mo>+</mo>
						<msub>
							<mi>x</mi>
							<mn>1</mn>
						</msub>
						<mo>-</mo>
						<msub>
							<mi>x</mi>
							<mn>2</mn>
						</msub>
						<mo>+</mo>
						<msub>
							<mi>x</mi>
							<mn>3</mn>
						</msub>
						<mo>-</mo>
						<mo>&ctdot;</mo>
					</mtd>
					<mtd>
						<mspace width="1em" />
					</mtd>
					<mtd columnalign="right">
					</mtd>
					<mtd columnalign="left">
						<mtext>by&nbsp;<mrow xmlns:xlink="http://www.w3.org/1999/xlink" xlink:type="simple" xlink:href="#align-eq1">1.6</mrow>
						</mtext>
					</mtd>
				</mtr>
				<mtr>
					<mtd columnalign="right">
					</mtd>
					<mtd columnalign="left">
						<mo>=</mo>
						<msub>
							<mi>y</mi>
							<mn>0</mn>
						</msub>
						<mo>+</mo>
						<msub>
							<mi>y</mi>
							<mn>1</mn>
						</msub>
					</mtd>
					<mtd>
						<mspace width="1em" />
					</mtd>
					<mtd columnalign="right">
					</mtd>
					<mtd columnalign="left">
						<mtext>by&nbsp;(<mrow xmlns:xlink="http://www.w3.org/1999/xlink" xlink:type="simple" xlink:href="#align-eq2">1.7</mrow>)
						</mtext>
					</mtd>
				</mtr>
				<mtr>
					<mtd columnalign="right">
					</mtd>
					<mtd columnalign="left">
						<mo>=</mo>
						<msub>
							<mi>q</mi>
							<mn>0</mn>
						</msub>
						<mo>-</mo>
						<msub>
							<mi>q</mi>
							<mn>1</mn>
						</msub>
						<mo>+</mo>
						<msub>
							<mi>q</mi>
							<mn>2</mn>
						</msub>
					</mtd>
					<mtd>
						<mspace width="1em" />
					</mtd>
					<mtd columnalign="right">
					</mtd>
					<mtd columnalign="left">
						<mtext>by Axiom 4.</mtext>
					</mtd>
				</mtr>
			</mtable>
		</mrow>
		</math>

		</td>
		<td style="text-align: right"><a id="align-eq4">(1.9)</a></td>
		</tr>
		<tr>
		<td style="width: 5%"></td>
		<td style="text-align: right"><a id=""><span style="color: #FFFFFF">()</span></a></td>
		</tr>
		<tr>
		<td style="width: 5%"></td>
		<td style="text-align: right"><a id="align-eq5">(2.0)</a></td>
		</tr>
		</table>
		<!-- end MathToWeb -->
	
	</td>

	</tr></table>

</p>

<p class="small">
Note:&nbsp;&nbsp;The two equations to which the above example makes reference (i.e. 1.6 and 1.7) are below.<br/>
They have equation numbers that resemble the following:&nbsp;&nbsp;
<code>&lt;a&nbsp;id="align-eq1"&gt;(1.6)&lt;/a&gt;</code>.<!-- A normal HTML link to this 'id', providing it
is on the same page, is written simply as: <code>&lt;a href="#align-eq1"&gt;...&lt;/a&gt;</code>.-->
</p>

<p class="small">
<!-- begin MathToWeb -->
<!-- (your Latex) \begin{align}
a&=b     & A&=B     & x&=y+z  \tag{1.6}\label{align-eq1}\\
cd&=ef   & CD&=EF   & k&=m    \tag{1.7}\label{align-eq2}\\
g+h&=i+j & G+H&=I+J & nq&=rs  \tag{1.8}\label{align-eq3}
\end{align} -->

<table class="align" style="width: 100%; margin-top: 1.0%; margin-right: 0.0%; margin-bottom: 1.0%; margin-left: 0.0%;">
<tr>
<td style="width: 5%"></td>
<td rowspan="134">

<math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow>
	<mtable class="m-align">
		<mtr>
			<mtd columnalign="right">
				<mi>a</mi>
			</mtd>
			<mtd columnalign="left">
				<mo>=</mo>
				<mi>b</mi>
			</mtd>
			<mtd>
				<mspace width="1em" />
			</mtd>
			<mtd columnalign="right">
				<mi>A</mi>
			</mtd>
			<mtd columnalign="left">
				<mo>=</mo>
				<mi>B</mi>
			</mtd>
			<mtd>
				<mspace width="1em" />
			</mtd>
			<mtd columnalign="right">
				<mi>x</mi>
			</mtd>
			<mtd columnalign="left">
				<mo>=</mo>
				<mi>y</mi>
				<mo>+</mo>
				<mi>z</mi>
			</mtd>
		</mtr>
		<mtr>
			<mtd columnalign="right">
				<mi>c</mi>
				<mi>d</mi>
			</mtd>
			<mtd columnalign="left">
				<mo>=</mo>
				<mi>e</mi>
				<mi>f</mi>
			</mtd>
			<mtd>
				<mspace width="1em" />
			</mtd>
			<mtd columnalign="right">
				<mi>C</mi>
				<mi>D</mi>
			</mtd>
			<mtd columnalign="left">
				<mo>=</mo>
				<mi>E</mi>
				<mi>F</mi>
			</mtd>
			<mtd>
				<mspace width="1em" />
			</mtd>
			<mtd columnalign="right">
				<mi>k</mi>
			</mtd>
			<mtd columnalign="left">
				<mo>=</mo>
				<mi>m</mi>
			</mtd>
		</mtr>
		<mtr>
			<mtd columnalign="right">
				<mi>g</mi>
				<mo>+</mo>
				<mi>h</mi>
			</mtd>
			<mtd columnalign="left">
				<mo>=</mo>
				<mi>i</mi>
				<mo>+</mo>
				<mi>j</mi>
			</mtd>
			<mtd>
				<mspace width="1em" />
			</mtd>
			<mtd columnalign="right">
				<mi>G</mi>
				<mo>+</mo>
				<mi>H</mi>
			</mtd>
			<mtd columnalign="left">
				<mo>=</mo>
				<mi>I</mi>
				<mo>+</mo>
				<mi>J</mi>
			</mtd>
			<mtd>
				<mspace width="1em" />
			</mtd>
			<mtd columnalign="right">
				<mi>n</mi>
				<mi>q</mi>
			</mtd>
			<mtd columnalign="left">
				<mo>=</mo>
				<mi>r</mi>
				<mi>s</mi>
			</mtd>
		</mtr>
	</mtable>
</mrow>
</math>

</td>
<td style="text-align: right"><a id="align-eq1">(1.6)</a></td>
</tr>
<tr>
<td style="width: 5%"></td>
<td style="text-align: right"><a id="align-eq2">(1.7)</a></td>
</tr>
<tr>
<td style="width: 5%"></td>
<td style="text-align: right"><a id="align-eq3">(1.8)</a></td>
</tr>
</table>
<!-- end MathToWeb -->
</p>


<p>
<code>
<pre>

&lt;math xmlns="http://www.w3.org/1998/Math/MathML"&gt;
&lt;mrow&gt;
	&lt;mtable class="m-align"&gt;
		&lt;mtr&gt;
			&lt;mtd columnalign="right"&gt;
				&lt;mi&gt;y&lt;/mi&gt;
			&lt;/mtd&gt;
			&lt;mtd columnalign="left"&gt;
				&lt;mo&gt;=&lt;/mo&gt;
				&lt;msub&gt;
					&lt;mi&gt;x&lt;/mi&gt;
					&lt;mn&gt;0&lt;/mn&gt;
				&lt;/msub&gt;
				&lt;mo&gt;+&lt;/mo&gt;
				&lt;msub&gt;
					&lt;mi&gt;x&lt;/mi&gt;
					&lt;mn&gt;1&lt;/mn&gt;
				&lt;/msub&gt;
				&lt;mo&gt;-&lt;/mo&gt;
				&lt;msub&gt;
					&lt;mi&gt;x&lt;/mi&gt;
					&lt;mn&gt;2&lt;/mn&gt;
				&lt;/msub&gt;
				&lt;mo&gt;+&lt;/mo&gt;
				&lt;msub&gt;
					&lt;mi&gt;x&lt;/mi&gt;
					&lt;mn&gt;3&lt;/mn&gt;
				&lt;/msub&gt;
				&lt;mo&gt;-&lt;/mo&gt;
				&lt;mo&gt;&amp;ctdot;&lt;/mo&gt;
			&lt;/mtd&gt;
			&lt;mtd&gt;
				&lt;mspace width="1em" /&gt;
			&lt;/mtd&gt;
			&lt;mtd columnalign="right"&gt;
			&lt;/mtd&gt;
			&lt;mtd columnalign="left"&gt;
				&lt;mtext&gt;by&amp;nbsp;<b>&lt;mrow xmlns:xlink="http://www.w3.org/1999/xlink" xlink:type="simple" xlink:href="#align-eq1"&gt;1.6&lt;/mrow&gt;</b>
				&lt;/mtext&gt;
			&lt;/mtd&gt;
		&lt;/mtr&gt;
		&lt;mtr&gt;
			&lt;mtd columnalign="right"&gt;
			&lt;/mtd&gt;
			&lt;mtd columnalign="left"&gt;
				&lt;mo&gt;=&lt;/mo&gt;
				&lt;msub&gt;
					&lt;mi&gt;y&lt;/mi&gt;
					&lt;mn&gt;0&lt;/mn&gt;
				&lt;/msub&gt;
				&lt;mo&gt;+&lt;/mo&gt;
				&lt;msub&gt;
					&lt;mi&gt;y&lt;/mi&gt;
					&lt;mn&gt;1&lt;/mn&gt;
				&lt;/msub&gt;
			&lt;/mtd&gt;
			&lt;mtd&gt;
				&lt;mspace width="1em" /&gt;
			&lt;/mtd&gt;
			&lt;mtd columnalign="right"&gt;
			&lt;/mtd&gt;
			&lt;mtd columnalign="left"&gt;
				&lt;mtext&gt;by&amp;nbsp;(<b>&lt;mrow xmlns:xlink="http://www.w3.org/1999/xlink" xlink:type="simple" xlink:href="#align-eq2"&gt;1.7&lt;/mrow&gt;</b>)
				&lt;/mtext&gt;
			&lt;/mtd&gt;
		&lt;/mtr&gt;
		&lt;mtr&gt;
			&lt;mtd columnalign="right"&gt;
			&lt;/mtd&gt;
			&lt;mtd columnalign="left"&gt;
				&lt;mo&gt;=&lt;/mo&gt;
				&lt;msub&gt;
					&lt;mi&gt;q&lt;/mi&gt;
					&lt;mn&gt;0&lt;/mn&gt;
				&lt;/msub&gt;
				&lt;mo&gt;-&lt;/mo&gt;
				&lt;msub&gt;
					&lt;mi&gt;q&lt;/mi&gt;
					&lt;mn&gt;1&lt;/mn&gt;
				&lt;/msub&gt;
				&lt;mo&gt;+&lt;/mo&gt;
				&lt;msub&gt;
					&lt;mi&gt;q&lt;/mi&gt;
					&lt;mn&gt;2&lt;/mn&gt;
				&lt;/msub&gt;
			&lt;/mtd&gt;
			&lt;mtd&gt;
				&lt;mspace width="1em" /&gt;
			&lt;/mtd&gt;
			&lt;mtd columnalign="right"&gt;
			&lt;/mtd&gt;
			&lt;mtd columnalign="left"&gt;
				&lt;mtext&gt;by Axiom 4.&lt;/mtext&gt;
			&lt;/mtd&gt;
		&lt;/mtr&gt;
	&lt;/mtable&gt;
&lt;/mrow&gt;
&lt;/math&gt;

</pre>
</code>
</p>

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