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<!DOCTYPE html>
<html lang="en">
<head>
<meta charset="utf-8"/>
<title>IF# Notebook
</title>
<meta name="viewport" content="width=device-width, initial-scale=1.0"/>
<meta name="description" content="Math.NET Numerics, providing methods and algorithms for numerical computations in science, engineering and every day use. .Net 4, .Net 3.5, SL5, Win8, WP8, PCL 47 and 136, Mono, Xamarin Android/iOS."/>
<meta name="author" content="Christoph Ruegg, Marcus Cuda, Jurgen Van Gael"/>
<script src="https://code.jquery.com/jquery-1.8.0.js"></script>
<script src="https://code.jquery.com/ui/1.8.23/jquery-ui.js"></script>
<script src="https://netdna.bootstrapcdn.com/twitter-bootstrap/2.2.1/js/bootstrap.min.js"></script>
<link href="https://netdna.bootstrapcdn.com/twitter-bootstrap/2.2.1/css/bootstrap-combined.min.css" rel="stylesheet"/>
<link type="text/css" rel="stylesheet" href="https://numerics.mathdotnet.com/content/style.css" />
<style>
#main table:not(.pre) {
border: 1px solid #dddddd;
max-width: 100%;
border-style: solid;
border-width: 1px;
border-color: gray;
border-collapse: collapse;
border-right-width: 1px;
border-bottom-width: 1px;
margin-top: 15px;
margin-bottom: 25px;
}
#main table:not(.pre) th, #main table:not(.pre) td {
border: 1px solid #dddddd;
padding: 6px;
}
#main table:not(.pre) th p, #main table:not(.pre) td p {
margin-bottom: 5px;
}
</style>
<script type="text/javascript" src="https://numerics.mathdotnet.com/content/tips.js"></script>
<!-- HTML5 shim, for IE6-8 support of HTML5 elements -->
<!--[if lt IE 9]>
<script src="https://oss.maxcdn.com/html5shiv/3.7.2/html5shiv.min.js"></script>
<![endif]-->
<script type="text/javascript" src="https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.1/MathJax.js?config=TeX-AMS-MML_HTMLorMML"></script>
</head>
<body>
<div class="container">
<div class="masthead">
<ul class="nav nav-pills pull-right">
<li><a href="https://www.mathdotnet.com">Math.NET Project</a></li>
<li><a href="https://numerics.mathdotnet.com">Math.NET Numerics</a></li>
<li><a href="https://github.com/mathnet/mathnet-numerics">GitHub</a></li>
</ul>
<h3 class="muted">Math.NET Numerics</h3>
</div>
<hr />
<div class="row">
<div class="span9" id="main">
<h1><a name="IF-Notebook" class="anchor" href="#IF-Notebook">IF# Notebook</a></h1>
<p><a href="https://ipython.org/">iPython</a> provides a rich browser-based interactive notebook with support for code, text, mathematical expressions,
inline plots and other rich media. <a href="https://github.com/BayardRock/IfSharp">IfSharp</a>, developed by Bayard Rock, is an F# profile
for iPython with IntelliSense and embedded FSharp.Charting. Thanks to its NuGet support it can load other packages like Math.NET Numerics on demand.</p>
<p><img src="img/IfSharp-GenerateIS.png" alt="Screenshot" /></p>
<h2><a name="Installing-IF-Notebook" class="anchor" href="#Installing-IF-Notebook">Installing IF# Notebook</a></h2>
<p>Follow the instructions at <a href="https://bayardrock.github.io/IfSharp/installation.html">IfSharp/Installation</a>.</p>
<p>Essentially:</p>
<ol>
<li><p>Install <a href="https://continuum.io/downloads">Anaconda</a></p></li>
<li>
<p>In a shell, run</p>
<p>conda update conda
conda update ipython</p>
</li>
<li><p>Install <a href="https://github.com/BayardRock/IfSharp/releases">IfSharp</a>.</p></li>
</ol>
<h2><a name="Display-Printers-for-Matrices-and-Vectors" class="anchor" href="#Display-Printers-for-Matrices-and-Vectors">Display Printers for Matrices and Vectors</a></h2>
<p>By itself IfSharp does not know how to display matrices and vectors in a nice way, but we can tell it how to do so by providing our own display printers for them.
Since v3.3 the Math.NET Numerics F# package includes a script <code>MathNet.Numerics.IfSharp.fsx</code> to do so.
Unfortunately loading this script requires the exact version in the path - if you know a way to avoid this please let us know.</p>
<p><img src="img/IfSharp-MatrixVector.png" alt="Screenshot" /></p>
<p>Alternatively you can also use the code below and adapt it to your needs, e.g. if you want it to show more rows.</p>
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</pre></td>
<td class="snippet"><pre class="fssnip highlighted"><code lang="fsharp"><span class="k">open</span> <span class="i">MathNet</span><span class="o">.</span><span class="i">Numerics</span><span class="o">.</span><span class="i">LinearAlgebra</span>
<span class="k">let</span> <span class="k">inline</span> (|<span class="p">Float</span>|_|) (<span onmouseout="hideTip(event, 'fs1', 1)" onmouseover="showTip(event, 'fs1', 1)" class="i">v</span><span class="o">:</span><span onmouseout="hideTip(event, 'fs2', 2)" onmouseover="showTip(event, 'fs2', 2)" class="t">obj</span>) <span class="o">=</span>
<span class="k">if</span> <span onmouseout="hideTip(event, 'fs1', 3)" onmouseover="showTip(event, 'fs1', 3)" class="i">v</span> <span class="o">:?</span> <span onmouseout="hideTip(event, 'fs3', 4)" onmouseover="showTip(event, 'fs3', 4)" class="t">float</span> <span class="k">then</span> <span onmouseout="hideTip(event, 'fs4', 5)" onmouseover="showTip(event, 'fs4', 5)" class="p">Some</span>(<span onmouseout="hideTip(event, 'fs1', 6)" onmouseover="showTip(event, 'fs1', 6)" class="i">v</span> <span class="o">:?&gt;</span> <span onmouseout="hideTip(event, 'fs3', 7)" onmouseover="showTip(event, 'fs3', 7)" class="t">float</span>) <span class="k">else</span> <span onmouseout="hideTip(event, 'fs5', 8)" onmouseover="showTip(event, 'fs5', 8)" class="p">None</span>
<span class="k">let</span> <span class="k">inline</span> (|<span class="p">Float32</span>|_|) (<span onmouseout="hideTip(event, 'fs1', 9)" onmouseover="showTip(event, 'fs1', 9)" class="i">v</span><span class="o">:</span><span onmouseout="hideTip(event, 'fs2', 10)" onmouseover="showTip(event, 'fs2', 10)" class="t">obj</span>) <span class="o">=</span>
<span class="k">if</span> <span onmouseout="hideTip(event, 'fs1', 11)" onmouseover="showTip(event, 'fs1', 11)" class="i">v</span> <span class="o">:?</span> <span onmouseout="hideTip(event, 'fs6', 12)" onmouseover="showTip(event, 'fs6', 12)" class="t">float32</span> <span class="k">then</span> <span onmouseout="hideTip(event, 'fs4', 13)" onmouseover="showTip(event, 'fs4', 13)" class="p">Some</span>(<span onmouseout="hideTip(event, 'fs1', 14)" onmouseover="showTip(event, 'fs1', 14)" class="i">v</span> <span class="o">:?&gt;</span> <span onmouseout="hideTip(event, 'fs6', 15)" onmouseover="showTip(event, 'fs6', 15)" class="t">float32</span>) <span class="k">else</span> <span onmouseout="hideTip(event, 'fs5', 16)" onmouseover="showTip(event, 'fs5', 16)" class="p">None</span>
<span class="k">let</span> <span class="k">inline</span> (|<span class="p">PositiveInfinity</span>|_|) (<span onmouseout="hideTip(event, 'fs7', 17)" onmouseover="showTip(event, 'fs7', 17)" class="i">v</span><span class="o">:</span> <span class="o">^</span><span class="i">T</span>) <span class="o">=</span>
<span class="k">if</span> (<span class="o">^</span><span class="i">T</span> <span class="o">:</span> (<span class="k">static</span> <span class="k">member</span> <span class="i">IsPositiveInfinity</span><span class="o">:</span> <span class="o">&#39;</span><span class="i">T</span> <span class="k">-&gt;</span> <span onmouseout="hideTip(event, 'fs8', 18)" onmouseover="showTip(event, 'fs8', 18)" class="t">bool</span>) (<span onmouseout="hideTip(event, 'fs7', 19)" onmouseover="showTip(event, 'fs7', 19)" class="i">v</span>))
<span class="k">then</span> <span onmouseout="hideTip(event, 'fs4', 20)" onmouseover="showTip(event, 'fs4', 20)" class="p">Some</span> <span class="p">PositiveInfinity</span> <span class="k">else</span> <span onmouseout="hideTip(event, 'fs5', 21)" onmouseover="showTip(event, 'fs5', 21)" class="p">None</span>
<span class="k">let</span> <span class="k">inline</span> (|<span class="p">NegativeInfinity</span>|_|) (<span onmouseout="hideTip(event, 'fs9', 22)" onmouseover="showTip(event, 'fs9', 22)" class="i">v</span><span class="o">:</span> <span class="o">^</span><span class="i">T</span>) <span class="o">=</span>
<span class="k">if</span> (<span class="o">^</span><span class="i">T</span> <span class="o">:</span> (<span class="k">static</span> <span class="k">member</span> <span class="i">IsNegativeInfinity</span><span class="o">:</span> <span class="o">&#39;</span><span class="i">T</span> <span class="k">-&gt;</span> <span onmouseout="hideTip(event, 'fs8', 23)" onmouseover="showTip(event, 'fs8', 23)" class="t">bool</span>) (<span onmouseout="hideTip(event, 'fs9', 24)" onmouseover="showTip(event, 'fs9', 24)" class="i">v</span>))
<span class="k">then</span> <span onmouseout="hideTip(event, 'fs4', 25)" onmouseover="showTip(event, 'fs4', 25)" class="p">Some</span> <span class="p">NegativeInfinity</span> <span class="k">else</span> <span onmouseout="hideTip(event, 'fs5', 26)" onmouseover="showTip(event, 'fs5', 26)" class="p">None</span>
<span class="k">let</span> <span class="k">inline</span> (|<span class="p">NaN</span>|_|) (<span onmouseout="hideTip(event, 'fs10', 27)" onmouseover="showTip(event, 'fs10', 27)" class="i">v</span><span class="o">:</span> <span class="o">^</span><span class="i">T</span>) <span class="o">=</span>
<span class="k">if</span> (<span class="o">^</span><span class="i">T</span> <span class="o">:</span> (<span class="k">static</span> <span class="k">member</span> <span class="i">IsNaN</span><span class="o">:</span> <span class="o">&#39;</span><span class="i">T</span> <span class="k">-&gt;</span> <span onmouseout="hideTip(event, 'fs8', 28)" onmouseover="showTip(event, 'fs8', 28)" class="t">bool</span>) (<span onmouseout="hideTip(event, 'fs10', 29)" onmouseover="showTip(event, 'fs10', 29)" class="i">v</span>))
<span class="k">then</span> <span onmouseout="hideTip(event, 'fs4', 30)" onmouseover="showTip(event, 'fs4', 30)" class="p">Some</span> <span class="p">NaN</span> <span class="k">else</span> <span onmouseout="hideTip(event, 'fs5', 31)" onmouseover="showTip(event, 'fs5', 31)" class="p">None</span>
<span class="k">let</span> <span class="k">inline</span> <span onmouseout="hideTip(event, 'fs11', 32)" onmouseover="showTip(event, 'fs11', 32)" class="f">formatMathValue</span> (<span onmouseout="hideTip(event, 'fs12', 33)" onmouseover="showTip(event, 'fs12', 33)" class="i">floatFormat</span><span class="o">:</span><span onmouseout="hideTip(event, 'fs13', 34)" onmouseover="showTip(event, 'fs13', 34)" class="t">string</span>) <span class="o">=</span> <span class="k">function</span>
| <span onmouseout="hideTip(event, 'fs14', 35)" onmouseover="showTip(event, 'fs14', 35)" class="p">PositiveInfinity</span> <span class="k">-&gt;</span> <span class="s">&quot;</span><span class="e">\\</span><span class="s">infty&quot;</span>
| <span onmouseout="hideTip(event, 'fs15', 36)" onmouseover="showTip(event, 'fs15', 36)" class="p">NegativeInfinity</span> <span class="k">-&gt;</span> <span class="s">&quot;-</span><span class="e">\\</span><span class="s">infty&quot;</span>
| <span onmouseout="hideTip(event, 'fs16', 37)" onmouseover="showTip(event, 'fs16', 37)" class="p">NaN</span> <span class="k">-&gt;</span> <span class="s">&quot;</span><span class="e">\\</span><span class="s">times&quot;</span>
| <span onmouseout="hideTip(event, 'fs17', 38)" onmouseover="showTip(event, 'fs17', 38)" class="p">Float</span> <span onmouseout="hideTip(event, 'fs18', 39)" onmouseover="showTip(event, 'fs18', 39)" class="i">v</span> <span class="k">-&gt;</span> <span onmouseout="hideTip(event, 'fs18', 40)" onmouseover="showTip(event, 'fs18', 40)" class="i">v</span><span class="o">.</span><span onmouseout="hideTip(event, 'fs19', 41)" onmouseover="showTip(event, 'fs19', 41)" class="f">ToString</span>(<span onmouseout="hideTip(event, 'fs12', 42)" onmouseover="showTip(event, 'fs12', 42)" class="i">floatFormat</span>)
| <span onmouseout="hideTip(event, 'fs20', 43)" onmouseover="showTip(event, 'fs20', 43)" class="p">Float32</span> <span onmouseout="hideTip(event, 'fs21', 44)" onmouseover="showTip(event, 'fs21', 44)" class="i">v</span> <span class="k">-&gt;</span> <span onmouseout="hideTip(event, 'fs21', 45)" onmouseover="showTip(event, 'fs21', 45)" class="i">v</span><span class="o">.</span><span onmouseout="hideTip(event, 'fs22', 46)" onmouseover="showTip(event, 'fs22', 46)" class="f">ToString</span>(<span onmouseout="hideTip(event, 'fs12', 47)" onmouseover="showTip(event, 'fs12', 47)" class="i">floatFormat</span>)
| <span onmouseout="hideTip(event, 'fs23', 48)" onmouseover="showTip(event, 'fs23', 48)" class="i">v</span> <span class="k">-&gt;</span> <span onmouseout="hideTip(event, 'fs23', 49)" onmouseover="showTip(event, 'fs23', 49)" class="i">v</span><span class="o">.</span><span onmouseout="hideTip(event, 'fs24', 50)" onmouseover="showTip(event, 'fs24', 50)" class="f">ToString</span>()
<span class="k">let</span> <span class="k">inline</span> <span onmouseout="hideTip(event, 'fs25', 51)" onmouseover="showTip(event, 'fs25', 51)" class="f">formatMatrix</span> (<span onmouseout="hideTip(event, 'fs26', 52)" onmouseover="showTip(event, 'fs26', 52)" class="i">matrix</span><span class="o">:</span> <span class="i">Matrix</span><span class="o">&lt;</span><span class="o">&#39;</span><span class="i">T</span><span class="o">&gt;</span>) <span class="o">=</span>
<span onmouseout="hideTip(event, 'fs27', 53)" onmouseover="showTip(event, 'fs27', 53)" class="t">String</span><span class="o">.</span><span onmouseout="hideTip(event, 'fs28', 54)" onmouseover="showTip(event, 'fs28', 54)" class="f">concat</span> <span class="i">Environment</span><span class="o">.</span><span class="i">NewLine</span>
[ <span class="s">&quot;</span><span class="e">\\</span><span class="s">begin{bmatrix}&quot;</span>
<span onmouseout="hideTip(event, 'fs26', 55)" onmouseover="showTip(event, 'fs26', 55)" class="i">matrix</span><span class="o">.</span><span class="i">ToMatrixString</span>(<span class="n">10</span>,<span class="n">4</span>,<span class="n">7</span>,<span class="n">2</span>,<span class="s">&quot;</span><span class="e">\\</span><span class="s">cdots&quot;</span>,<span class="s">&quot;</span><span class="e">\\</span><span class="s">vdots&quot;</span>,<span class="s">&quot;</span><span class="e">\\</span><span class="s">ddots&quot;</span>,
<span class="s">&quot; &amp; &quot;</span>, <span class="s">&quot;</span><span class="e">\\</span><span class="s"></span><span class="e">\\</span><span class="s"> &quot;</span> <span class="o">+</span> <span class="i">Environment</span><span class="o">.</span><span class="i">NewLine</span>, (<span class="k">fun</span> <span class="i">x</span> <span class="k">-&gt;</span> <span onmouseout="hideTip(event, 'fs11', 56)" onmouseover="showTip(event, 'fs11', 56)" class="i">formatMathValue</span> <span class="s">&quot;G4&quot;</span> <span class="i">x</span>))
<span class="s">&quot;</span><span class="e">\\</span><span class="s">end{bmatrix}&quot;</span> ]
<span class="k">let</span> <span class="k">inline</span> <span onmouseout="hideTip(event, 'fs29', 57)" onmouseover="showTip(event, 'fs29', 57)" class="f">formatVector</span> (<span onmouseout="hideTip(event, 'fs30', 58)" onmouseover="showTip(event, 'fs30', 58)" class="i">vector</span><span class="o">:</span> <span class="i">Vector</span><span class="o">&lt;</span><span class="o">&#39;</span><span class="i">T</span><span class="o">&gt;</span>) <span class="o">=</span>
<span onmouseout="hideTip(event, 'fs27', 59)" onmouseover="showTip(event, 'fs27', 59)" class="t">String</span><span class="o">.</span><span onmouseout="hideTip(event, 'fs28', 60)" onmouseover="showTip(event, 'fs28', 60)" class="f">concat</span> <span class="i">Environment</span><span class="o">.</span><span class="i">NewLine</span>
[ <span class="s">&quot;</span><span class="e">\\</span><span class="s">begin{bmatrix}&quot;</span>
<span onmouseout="hideTip(event, 'fs30', 61)" onmouseover="showTip(event, 'fs30', 61)" class="i">vector</span><span class="o">.</span><span class="i">ToVectorString</span>(<span class="n">12</span>, <span class="n">80</span>, <span class="s">&quot;</span><span class="e">\\</span><span class="s">vdots&quot;</span>, <span class="s">&quot; &amp; &quot;</span>, <span class="s">&quot;</span><span class="e">\\</span><span class="s"></span><span class="e">\\</span><span class="s"> &quot;</span> <span class="o">+</span> <span class="i">Environment</span><span class="o">.</span><span class="i">NewLine</span>,
(<span class="k">fun</span> <span class="i">x</span> <span class="k">-&gt;</span> <span onmouseout="hideTip(event, 'fs11', 62)" onmouseover="showTip(event, 'fs11', 62)" class="i">formatMathValue</span> <span class="s">&quot;G4&quot;</span> <span class="i">x</span>))
<span class="s">&quot;</span><span class="e">\\</span><span class="s">end{bmatrix}&quot;</span> ]
<span class="i">App</span><span class="o">.</span><span class="i">AddDisplayPrinter</span> (<span class="k">fun</span> (<span class="i">x</span><span class="o">:</span><span class="i">Matrix</span><span class="o">&lt;</span><span onmouseout="hideTip(event, 'fs3', 63)" onmouseover="showTip(event, 'fs3', 63)" class="i">float</span><span class="o">&gt;</span>) <span class="k">-&gt;</span>
{ <span class="i">ContentType</span> <span class="o">=</span> <span class="s">&quot;text/latex&quot;</span>; <span onmouseout="hideTip(event, 'fs31', 64)" onmouseover="showTip(event, 'fs31', 64)" class="i">Data</span> <span class="o">=</span> <span onmouseout="hideTip(event, 'fs25', 65)" onmouseover="showTip(event, 'fs25', 65)" class="i">formatMatrix</span> <span class="i">x</span> })
<span class="i">App</span><span class="o">.</span><span class="i">AddDisplayPrinter</span> (<span class="k">fun</span> (<span class="i">x</span><span class="o">:</span><span class="i">Matrix</span><span class="o">&lt;</span><span onmouseout="hideTip(event, 'fs6', 66)" onmouseover="showTip(event, 'fs6', 66)" class="i">float32</span><span class="o">&gt;</span>) <span class="k">-&gt;</span>
{ <span class="i">ContentType</span> <span class="o">=</span> <span class="s">&quot;text/latex&quot;</span>; <span onmouseout="hideTip(event, 'fs31', 67)" onmouseover="showTip(event, 'fs31', 67)" class="i">Data</span> <span class="o">=</span> <span onmouseout="hideTip(event, 'fs25', 68)" onmouseover="showTip(event, 'fs25', 68)" class="i">formatMatrix</span> <span class="i">x</span> })
<span class="i">App</span><span class="o">.</span><span class="i">AddDisplayPrinter</span> (<span class="k">fun</span> (<span class="i">x</span><span class="o">:</span><span class="i">Vector</span><span class="o">&lt;</span><span onmouseout="hideTip(event, 'fs3', 69)" onmouseover="showTip(event, 'fs3', 69)" class="i">float</span><span class="o">&gt;</span>) <span class="k">-&gt;</span>
{ <span class="i">ContentType</span> <span class="o">=</span> <span class="s">&quot;text/latex&quot;</span>; <span onmouseout="hideTip(event, 'fs31', 70)" onmouseover="showTip(event, 'fs31', 70)" class="i">Data</span> <span class="o">=</span> <span onmouseout="hideTip(event, 'fs29', 71)" onmouseover="showTip(event, 'fs29', 71)" class="i">formatVector</span> <span class="i">x</span> })
<span class="i">App</span><span class="o">.</span><span class="i">AddDisplayPrinter</span> (<span class="k">fun</span> (<span class="i">x</span><span class="o">:</span><span class="i">Vector</span><span class="o">&lt;</span><span onmouseout="hideTip(event, 'fs6', 72)" onmouseover="showTip(event, 'fs6', 72)" class="i">float32</span><span class="o">&gt;</span>) <span class="k">-&gt;</span>
{ <span class="i">ContentType</span> <span class="o">=</span> <span class="s">&quot;text/latex&quot;</span>; <span onmouseout="hideTip(event, 'fs31', 73)" onmouseover="showTip(event, 'fs31', 73)" class="i">Data</span> <span class="o">=</span> <span onmouseout="hideTip(event, 'fs29', 74)" onmouseover="showTip(event, 'fs29', 74)" class="i">formatVector</span> <span class="i">x</span> })
</code></pre></td>
</tr>
</table>
<div class="tip" id="fs1">val v : obj</div>
<div class="tip" id="fs2">type obj = System.Object<br /><br />Full name: Microsoft.FSharp.Core.obj</div>
<div class="tip" id="fs3">Multiple items<br />val float : value:&#39;T -&gt; float (requires member op_Explicit)<br /><br />Full name: Microsoft.FSharp.Core.Operators.float<br /><br />--------------------<br />type float = System.Double<br /><br />Full name: Microsoft.FSharp.Core.float<br /><br />--------------------<br />type float&lt;&#39;Measure&gt; = float<br /><br />Full name: Microsoft.FSharp.Core.float&lt;_&gt;</div>
<div class="tip" id="fs4">union case Option.Some: Value: &#39;T -&gt; Option&lt;&#39;T&gt;</div>
<div class="tip" id="fs5">union case Option.None: Option&lt;&#39;T&gt;</div>
<div class="tip" id="fs6">Multiple items<br />val float32 : value:&#39;T -&gt; float32 (requires member op_Explicit)<br /><br />Full name: Microsoft.FSharp.Core.Operators.float32<br /><br />--------------------<br />type float32 = System.Single<br /><br />Full name: Microsoft.FSharp.Core.float32<br /><br />--------------------<br />type float32&lt;&#39;Measure&gt; = float32<br /><br />Full name: Microsoft.FSharp.Core.float32&lt;_&gt;</div>
<div class="tip" id="fs7">val v : &#39;T (requires member IsPositiveInfinity)</div>
<div class="tip" id="fs8">type bool = System.Boolean<br /><br />Full name: Microsoft.FSharp.Core.bool</div>
<div class="tip" id="fs9">val v : &#39;T (requires member IsNegativeInfinity)</div>
<div class="tip" id="fs10">val v : &#39;T (requires member IsNaN)</div>
<div class="tip" id="fs11">val formatMathValue : floatFormat:string -&gt; _arg1:&#39;a -&gt; string (requires member IsNaN and member IsPositiveInfinity and member IsNegativeInfinity)<br /><br />Full name: IFsharpNotebook.formatMathValue</div>
<div class="tip" id="fs12">val floatFormat : string</div>
<div class="tip" id="fs13">Multiple items<br />val string : value:&#39;T -&gt; string<br /><br />Full name: Microsoft.FSharp.Core.Operators.string<br /><br />--------------------<br />type string = System.String<br /><br />Full name: Microsoft.FSharp.Core.string</div>
<div class="tip" id="fs14">active recognizer PositiveInfinity: &#39;T -&gt; unit option<br /><br />Full name: IFsharpNotebook.( |PositiveInfinity|_| )</div>
<div class="tip" id="fs15">active recognizer NegativeInfinity: &#39;T -&gt; unit option<br /><br />Full name: IFsharpNotebook.( |NegativeInfinity|_| )</div>
<div class="tip" id="fs16">active recognizer NaN: &#39;T -&gt; unit option<br /><br />Full name: IFsharpNotebook.( |NaN|_| )</div>
<div class="tip" id="fs17">active recognizer Float: obj -&gt; float option<br /><br />Full name: IFsharpNotebook.( |Float|_| )</div>
<div class="tip" id="fs18">val v : float</div>
<div class="tip" id="fs19">System.Double.ToString() : string<br />System.Double.ToString(provider: System.IFormatProvider) : string<br />System.Double.ToString(format: string) : string<br />System.Double.ToString(format: string, provider: System.IFormatProvider) : string</div>
<div class="tip" id="fs20">active recognizer Float32: obj -&gt; float32 option<br /><br />Full name: IFsharpNotebook.( |Float32|_| )</div>
<div class="tip" id="fs21">val v : float32</div>
<div class="tip" id="fs22">System.Single.ToString() : string<br />System.Single.ToString(format: string) : string<br />System.Single.ToString(provider: System.IFormatProvider) : string<br />System.Single.ToString(format: string, provider: System.IFormatProvider) : string</div>
<div class="tip" id="fs23">val v : &#39;a (requires member IsNaN and member IsPositiveInfinity and member IsNegativeInfinity)</div>
<div class="tip" id="fs24">System.Object.ToString() : string</div>
<div class="tip" id="fs25">val formatMatrix : matrix:&#39;a -&gt; string<br /><br />Full name: IFsharpNotebook.formatMatrix</div>
<div class="tip" id="fs26">val matrix : &#39;a</div>
<div class="tip" id="fs27">module String<br /><br />from Microsoft.FSharp.Core</div>
<div class="tip" id="fs28">val concat : sep:string -&gt; strings:seq&lt;string&gt; -&gt; string<br /><br />Full name: Microsoft.FSharp.Core.String.concat</div>
<div class="tip" id="fs29">val formatVector : vector:&#39;a -&gt; string<br /><br />Full name: IFsharpNotebook.formatVector</div>
<div class="tip" id="fs30">val vector : &#39;a</div>
<div class="tip" id="fs31">namespace Microsoft.FSharp.Data</div>
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