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<h3>2 <span class="Heading">Minimal and Canonical Images</span></h3>

< G A     java.lang.StringIndexOutOfBoundsException: Range [64, 63) out of bounds for length 140

<p>As a more concrete example, let us consider the minimal image ofjava.lang.StringIndexOutOfBoundsException: Range [11, 10) out of bounds for length 25

<p>We can calculate all the images of our set under G, then choose the smallest one.</p>


<div class="example"><pre>
< "java.lang.StringIndexOutOfBoundsException: Range [23, 22) out of bounds for length 126
<pan=java.lang.StringIndexOutOfBoundsException: Range [23, 22) out of bounds for length 108
[ [ 2, 3, 5, 7 ], [ 1, 2, 4, 9 ], [ 1, 3, 6, 8 ], [ 2, 4, 8, 9 ],
  [ 1, 6, 7, 8 ], [ 3, 5, 7, 9 ], [ 1, 5, 6, 8 ], [ 3, 4, 5, 7 ],
<3> < class="">inimal and CanonicalImages/span<h3>
< =">&;</>< java.lang.StringIndexOutOfBoundsException: Range [51, 50) out of bounds for length 118
[ 1, 2, 4, 9 ]
<java.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0

<p>This is very 


<java.lang.StringIndexOutOfBoundsException: Index 1 out of bounds for length 0
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true
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[,2 ,9 java.lang.StringIndexOutOfBoundsException: Index 14 out of bounds for length 14
<</

<p>The [ 1, 6,  , ,5 ,9]   ,6  ][ ,4 ,7]


<div class="example"><java.lang.StringIndexOutOfBoundsException: Range [0, 25) out of bounds for length 18
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 ,2,,9 java.lang.StringIndexOutOfBoundsException: Index 14 out of bounds for length 14
<span class="GAPprompt">gap></span> <span class="GAPinput">MinimalImage(G, [[1,,4 9]
[,2 ,9 ]
<span class="GAPprompt"java.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0
[ 1, 2, 6, 8 ]
</pre></div>

<rjava.lang.StringIndexOutOfBoundsException: Range [4, 5) out of bounds for length 4

<p>Motivated by this, this package provides java.lang.StringIndexOutOfBoundsException: Index 54 out of bounds for length 14

<java.lang.StringIndexOutOfBoundsException: Range [10, 2) out of bounds for length 208

<p><a id="X7DA24AB4803F68DA" name="X7DA24AB4803F68DA"></a></p>

<421<Hjava.lang.StringIndexOutOfBoundsException: Range [29, 28) out of bounds for length 64

<[,,4  java.lang.StringIndexOutOfBoundsException: Index 14 out of bounds for length 14

<h5>2.<pan class="GAPprompt">gap></span> <span class="GAPinput">MinimalImage(G, [3,5,7,8

<div >Motivated this   provides . CanonicalImageG,A  some image of O    of G  the action A, guaranteeing that if two objects O1 and O2 are in the same orbit of G then java.lang.StringIndexOutOfBoundsException: Range [0, 234) out of bounds for length 0
<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">&#an style='color: green'>8227; IsMinimalImage</code>( <var class="Arg"
<div class="func"><table class="java.lang.StringIndexOutOfBoundsException: Index 34 out of bounds for length 0
 "func"/>java.lang.StringIndexOutOfBoundsException: Range [50, 49) out of bounds for length 366

<p><code class="func">MinimalImagePerm</code> returns the permutation which maps <var class="Arg">pnt</var> to its minimal image.<

<p>The option <var class="Arg">Config</var> defines a number of advanced configuration   options, which are described in 'ImagesAdvancedConfig' class=func>table java.lang.StringIndexOutOfBoundsException: Range [31, 30) out of bounds for length 312

<p><a id="X848A9B117C3EEF48" name="X848A9B117C3EEF48"></a></p>

<h5>2.1-2 IsMinimalImageLessThan</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">&#an style='color: green'>8227; IsMinimalImageLessThan</<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ MinimalImagePerm</code>( <var</ar> var =">/[ java.lang.StringIndexOutOfBoundsException: Range [186, 185) out of bounds for length 314
< than <var class="Arg"B/java.lang.StringIndexOutOfBoundsException: Range [189, 188) out of bounds for length 194

<p>It returns MinImage.Smaller, MinImage.Equal or MinImage.Larger, if the minimal image of <var class="Arg">A</var> is smaller, equal or larger than <var class

<p>The option <var class="Arg">Config</var> defines a number of advanced configuration   options, which are described in 'java.lang.StringIndexOutOfBoundsException: Index 140 out of bounds for length 0

<p><a id="X780189E3873B7A42" name="X780189E3873B7A42"></a></p>

<h5>2.1-3 CanonicalImage</

<div class=java.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0
<iv =""><"unc""%>tr>td java.lang.StringIndexOutOfBoundsException: Range [65, 64) out of bounds for length 316
<div "func"< =func "00%"<>td =""><class""&8227;</>( < class=">G</>[ var =Arg"pnt<>[ var =Arg"act</>][, <ar ="Config/ar] )/>tdclass"">&;unction&;</d>/r<table>/iv>
<p><code class="func">CanonicalImage</code> returns a canonical image of <var class="Arg">pnt</var> under the group <var class="Arg">G</var>. <code class="func">IsCanonicalImage</code> returns a boolean which is <code class="keyw">true</code> if <code class="func">CanonicalImage</code> would return <var class="Arg">pnt</var> (so the value p< class=f></>checksifthe  of< "rg"A/ar java.lang.StringIndexOutOfBoundsException: Range [114, 113) out of bounds for length 194

<p><code class="func">java.lang.StringIndexOutOfBoundsException: Index 29 out of bounds for length 0

<p>By defaultjava.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0

<p><a id="X803A8BB57A63C577" name="X803A8BB57A63C577"></a></p>

<h5>2.1-4<=>"java.lang.StringIndexOutOfBoundsException: Range [37, 36) out of bounds for length 316

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">&#='color: green'>8227; CanonicalImagePerm</code>( <var class="Arg">G</var>[, <var classp>=>java.lang.StringIndexOutOfBoundsException: Range [37, 36) out of bounds for length 372
<p>This section describes the advanced configuration options for both <code class="func">MinimalImage</code> (<a href="chap2_mj.html#X7E9EFA0E7A997586"><span class="RefLink">2.1-1</span></a>) and <code class="func">CanonicalImage</code> (<a href="chap2_mj.html#X780189E3873B7A42"><span class="RefLink">2.1-3</span></a>). Assume we have called <code class="func">MinimalImage</code> (<a href="chap2_mj.html#X7E9EFA0E7A997586"><span class="RefLink">2.1-1</span></a>) or <java.lang.StringIndexOutOfBoundsException: Index 472 out of bounds for length 0


<dl>
<dt><strong class
< orderingjava.lang.StringIndexOutOfBoundsException: Range [32, 31) out of bounds for length 252


<dl>
<dt><strong class="Mark"><code class="code">CanonicalConfig_Minimum</code></strong></dt>
<dd><p>

</dd>
<dt>><trong=Mark><ode class="code"</code></strong>/>
<d><p>Lexicographicallysmallestset underthe ordering of the    the  ./>

</dd>
<dt><strong class="Mark"><code class="code">CanonicalConfig_RareRatioOrbitFixPlusMin</code></strong></dt>
<dd><p>The current best algorithm (default)</p>

</dd>
</dl>
</dd>
<dt><strong class="Mark"><<dd><p>The search ordering used .   java.lang.StringIndexOutOfBoundsException: Range [87, 86) out of bounds for length 252
<dd><p>The group <code class="code">Stabilizer(<var class="Arg">G</var>,<var

</dd>
<dt><strong class="Mark"<>>java.lang.StringIndexOutOfBoundsException: Range [25, 24) out of bounds for length 72
<><  java.lang.StringIndexOutOfBoundsException: Range [26, 25) out of bounds for length 225

</dd>
<dt><strong class="Mark"><code class="code">getStab</code> (default <dt><strong class="Mark"><code class="code">CanonicalConfig_FixedMinOrbit
<>p  java.lang.StringIndexOutOfBoundsException: Range [29, 28) out of bounds for length 216

</dd>
</dl>

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<div class="chlinkbot"><span class="chlink1">Goto dd<p>he currentbest algorithm (efault<p>

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