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4 changes: 2 additions & 2 deletions PackageInfo.g
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Expand Up @@ -34,8 +34,8 @@ _STANDREWSCS := Concatenation(["Jack Cole Building, North Haugh, ",
SetPackageInfo(rec(
PackageName := "Semigroups",
Subtitle := "A package for semigroups and monoids",
Version := "5.3.0",
Date := "18/09/2023", # dd/mm/yyyy format
Version := "5.3.1",
Date := "19/09/2023", # dd/mm/yyyy format
License := "GPL-3.0-or-later",

ArchiveFormats := ".tar.gz",
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6 changes: 3 additions & 3 deletions _data/package.yml
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@@ -1,6 +1,6 @@
name: Semigroups
version: 5.3.0
date: 2023-09-18
version: 5.3.1
date: 2023-09-19
description: |
A package for semigroups and monoids
Expand Down Expand Up @@ -105,7 +105,7 @@ packageinfo: https://semigroups.github.io/Semigroups/PackageInfo.g

downloads:
- name: .tar.gz
url: https://github.com/semigroups/Semigroups/releases/download/v5.3.0/semigroups-5.3.0.tar.gz
url: https://github.com/semigroups/Semigroups/releases/download/v5.3.1/semigroups-5.3.1.tar.gz

abstract: |
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4 changes: 2 additions & 2 deletions doc/chap0.html
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Expand Up @@ -29,10 +29,10 @@ <h1>Semigroups</h1>
<h2>A package for semigroups and monoids</h2>

<p>
5.3.0</p>
5.3.1</p>

<p>
18 September 2023
19 September 2023
</p>

</div>
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4 changes: 2 additions & 2 deletions doc/chap0.txt
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Expand Up @@ -6,10 +6,10 @@
 A package for semigroups and monoids 


5.3.0
5.3.1


18 September 2023
19 September 2023


James Mitchell
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4 changes: 2 additions & 2 deletions doc/chap0_mj.html
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Expand Up @@ -32,10 +32,10 @@ <h1>Semigroups</h1>
<h2>A package for semigroups and monoids</h2>

<p>
5.3.0</p>
5.3.1</p>

<p>
18 September 2023
19 September 2023
</p>

</div>
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2 changes: 1 addition & 1 deletion doc/chap1.html
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Expand Up @@ -48,7 +48,7 @@ <h4>1.1 <span class="Heading">
Introduction
</span></h4>

<p>This is the manual for the <strong class="pkg">Semigroups</strong> package for <strong class="pkg">GAP</strong> version 5.3.0. <strong class="pkg">Semigroups</strong> 5.3.0 is a distant descendant of the <span class="URL"><a href=" http://schmidt.nuigalway.ie/monoid/index.html">Monoid package for GAP 3</a></span> by Goetz Pfeiffer, Steve A. Linton, Edmund F. Robertson, and Nik Ruskuc.</p>
<p>This is the manual for the <strong class="pkg">Semigroups</strong> package for <strong class="pkg">GAP</strong> version 5.3.1. <strong class="pkg">Semigroups</strong> 5.3.1 is a distant descendant of the <span class="URL"><a href=" http://schmidt.nuigalway.ie/monoid/index.html">Monoid package for GAP 3</a></span> by Goetz Pfeiffer, Steve A. Linton, Edmund F. Robertson, and Nik Ruskuc.</p>

<p>From Version 3.0.0, <strong class="pkg">Semigroups</strong> includes a copy of the <span class="URL"><a href="https://libsemigroups.readthedocs.io/en/latest/">libsemigroups</a></span> C++ library which contains implementations of the Froidure-Pin, Todd-Coxeter, and Knuth-Bendix algorithms (among others) that <strong class="pkg">Semigroups</strong> utilises.</p>

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4 changes: 2 additions & 2 deletions doc/chap1.txt
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Expand Up @@ -4,8 +4,8 @@

1.1 Introduction

This is the manual for the Semigroups package for GAP version 5.3.0.
Semigroups 5.3.0 is a distant descendant of the Monoid package for GAP 3
This is the manual for the Semigroups package for GAP version 5.3.1.
Semigroups 5.3.1 is a distant descendant of the Monoid package for GAP 3
(http://schmidt.nuigalway.ie/monoid/index.html) by Goetz Pfeiffer, Steve A.
Linton, Edmund F. Robertson, and Nik Ruskuc.

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112 changes: 56 additions & 56 deletions doc/chap10.html
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Expand Up @@ -310,61 +310,61 @@ <h5>10.1-4 <span class="Heading">GreensXClasses</span></h5>
<span class="GAPprompt">gap&gt;</span> <span class="GAPinput">S := Semigroup(Transformation([3, 4, 4, 4]),</span>
<span class="GAPprompt">&gt;</span> <span class="GAPinput"> Transformation([4, 3, 1, 2]));;</span>
<span class="GAPprompt">gap&gt;</span> <span class="GAPinput">GreensDClasses(S);</span>
[ &lt;Green's D-class: Transformation( [ 3, 4, 4, 4 ] )&gt;,
&lt;Green's D-class: Transformation( [ 4, 3, 1, 2 ] )&gt;,
[ &lt;Green's D-class: Transformation( [ 3, 4, 4, 4 ] )&gt;,
&lt;Green's D-class: Transformation( [ 4, 3, 1, 2 ] )&gt;,
&lt;Green's D-class: Transformation( [ 4, 4, 4, 4 ] )&gt; ]
<span class="GAPprompt">gap&gt;</span> <span class="GAPinput">GreensRClasses(S);</span>
[ &lt;Green's R-class: Transformation( [ 3, 4, 4, 4 ] )&gt;,
&lt;Green's R-class: Transformation( [ 4, 3, 1, 2 ] )&gt;,
&lt;Green's R-class: Transformation( [ 4, 4, 4, 4 ] )&gt;,
&lt;Green's R-class: Transformation( [ 4, 4, 3, 4 ] )&gt;,
&lt;Green's R-class: Transformation( [ 4, 3, 4, 4 ] )&gt;,
[ &lt;Green's R-class: Transformation( [ 3, 4, 4, 4 ] )&gt;,
&lt;Green's R-class: Transformation( [ 4, 3, 1, 2 ] )&gt;,
&lt;Green's R-class: Transformation( [ 4, 4, 4, 4 ] )&gt;,
&lt;Green's R-class: Transformation( [ 4, 4, 3, 4 ] )&gt;,
&lt;Green's R-class: Transformation( [ 4, 3, 4, 4 ] )&gt;,
&lt;Green's R-class: Transformation( [ 4, 4, 4, 3 ] )&gt; ]
<span class="GAPprompt">gap&gt;</span> <span class="GAPinput">D := GreensDClasses(S)[1];</span>
&lt;Green's D-class: Transformation( [ 3, 4, 4, 4 ] )&gt;
<span class="GAPprompt">gap&gt;</span> <span class="GAPinput">GreensLClasses(D);</span>
[ &lt;Green's L-class: Transformation( [ 3, 4, 4, 4 ] )&gt;,
[ &lt;Green's L-class: Transformation( [ 3, 4, 4, 4 ] )&gt;,
&lt;Green's L-class: Transformation( [ 1, 2, 2, 2 ] )&gt; ]
<span class="GAPprompt">gap&gt;</span> <span class="GAPinput">GreensRClasses(D);</span>
[ &lt;Green's R-class: Transformation( [ 3, 4, 4, 4 ] )&gt;,
&lt;Green's R-class: Transformation( [ 4, 4, 3, 4 ] )&gt;,
&lt;Green's R-class: Transformation( [ 4, 3, 4, 4 ] )&gt;,
[ &lt;Green's R-class: Transformation( [ 3, 4, 4, 4 ] )&gt;,
&lt;Green's R-class: Transformation( [ 4, 4, 3, 4 ] )&gt;,
&lt;Green's R-class: Transformation( [ 4, 3, 4, 4 ] )&gt;,
&lt;Green's R-class: Transformation( [ 4, 4, 4, 3 ] )&gt; ]
<span class="GAPprompt">gap&gt;</span> <span class="GAPinput">R := GreensRClasses(D)[1];</span>
&lt;Green's R-class: Transformation( [ 3, 4, 4, 4 ] )&gt;
<span class="GAPprompt">gap&gt;</span> <span class="GAPinput">GreensHClasses(R);</span>
[ &lt;Green's H-class: Transformation( [ 3, 4, 4, 4 ] )&gt;,
[ &lt;Green's H-class: Transformation( [ 3, 4, 4, 4 ] )&gt;,
&lt;Green's H-class: Transformation( [ 1, 2, 2, 2 ] )&gt; ]
<span class="GAPprompt">gap&gt;</span> <span class="GAPinput">S := InverseSemigroup([</span>
<span class="GAPprompt">&gt;</span> <span class="GAPinput">PartialPerm([2, 4, 1]), PartialPerm([3, 0, 4, 1])]);;</span>
<span class="GAPprompt">gap&gt;</span> <span class="GAPinput">GreensDClasses(S);</span>
[ &lt;Green's D-class: &lt;identity partial perm on [ 1, 2, 4 ]&gt;&gt;,
&lt;Green's D-class: &lt;identity partial perm on [ 1, 3, 4 ]&gt;&gt;,
&lt;Green's D-class: &lt;identity partial perm on [ 1, 3 ]&gt;&gt;,
&lt;Green's D-class: &lt;identity partial perm on [ 4 ]&gt;&gt;,
[ &lt;Green's D-class: &lt;identity partial perm on [ 1, 2, 4 ]&gt;&gt;,
&lt;Green's D-class: &lt;identity partial perm on [ 1, 3, 4 ]&gt;&gt;,
&lt;Green's D-class: &lt;identity partial perm on [ 1, 3 ]&gt;&gt;,
&lt;Green's D-class: &lt;identity partial perm on [ 4 ]&gt;&gt;,
&lt;Green's D-class: &lt;empty partial perm&gt;&gt; ]
<span class="GAPprompt">gap&gt;</span> <span class="GAPinput">GreensLClasses(S);</span>
[ &lt;Green's L-class: &lt;identity partial perm on [ 1, 2, 4 ]&gt;&gt;,
&lt;Green's L-class: [4,2,1,3]&gt;,
&lt;Green's L-class: &lt;identity partial perm on [ 1, 3, 4 ]&gt;&gt;,
&lt;Green's L-class: &lt;identity partial perm on [ 1, 3 ]&gt;&gt;,
&lt;Green's L-class: [3,1,2]&gt;, &lt;Green's L-class: [1,4][3,2]&gt;,
&lt;Green's L-class: [1,3,4]&gt;, &lt;Green's L-class: [3,1,4]&gt;,
&lt;Green's L-class: [1,2](3)&gt;,
&lt;Green's L-class: &lt;identity partial perm on [ 4 ]&gt;&gt;,
&lt;Green's L-class: [4,1]&gt;, &lt;Green's L-class: [4,3]&gt;,
[ &lt;Green's L-class: &lt;identity partial perm on [ 1, 2, 4 ]&gt;&gt;,
&lt;Green's L-class: [4,2,1,3]&gt;,
&lt;Green's L-class: &lt;identity partial perm on [ 1, 3, 4 ]&gt;&gt;,
&lt;Green's L-class: &lt;identity partial perm on [ 1, 3 ]&gt;&gt;,
&lt;Green's L-class: [3,1,2]&gt;, &lt;Green's L-class: [1,4][3,2]&gt;,
&lt;Green's L-class: [1,3,4]&gt;, &lt;Green's L-class: [3,1,4]&gt;,
&lt;Green's L-class: [1,2](3)&gt;,
&lt;Green's L-class: &lt;identity partial perm on [ 4 ]&gt;&gt;,
&lt;Green's L-class: [4,1]&gt;, &lt;Green's L-class: [4,3]&gt;,
&lt;Green's L-class: [4,2]&gt;, &lt;Green's L-class: &lt;empty partial perm&gt;&gt; ]
<span class="GAPprompt">gap&gt;</span> <span class="GAPinput">D := GreensDClasses(S)[3];</span>
&lt;Green's D-class: &lt;identity partial perm on [ 1, 3 ]&gt;&gt;
<span class="GAPprompt">gap&gt;</span> <span class="GAPinput">GreensLClasses(D);</span>
[ &lt;Green's L-class: &lt;identity partial perm on [ 1, 3 ]&gt;&gt;,
&lt;Green's L-class: [3,1,2]&gt;, &lt;Green's L-class: [1,4][3,2]&gt;,
&lt;Green's L-class: [1,3,4]&gt;, &lt;Green's L-class: [3,1,4]&gt;,
[ &lt;Green's L-class: &lt;identity partial perm on [ 1, 3 ]&gt;&gt;,
&lt;Green's L-class: [3,1,2]&gt;, &lt;Green's L-class: [1,4][3,2]&gt;,
&lt;Green's L-class: [1,3,4]&gt;, &lt;Green's L-class: [3,1,4]&gt;,
&lt;Green's L-class: [1,2](3)&gt; ]
<span class="GAPprompt">gap&gt;</span> <span class="GAPinput">GreensRClasses(D);</span>
[ &lt;Green's R-class: &lt;identity partial perm on [ 1, 3 ]&gt;&gt;,
&lt;Green's R-class: [2,1,3]&gt;, &lt;Green's R-class: [2,3][4,1]&gt;,
&lt;Green's R-class: [4,3,1]&gt;, &lt;Green's R-class: [4,1,3]&gt;,
[ &lt;Green's R-class: &lt;identity partial perm on [ 1, 3 ]&gt;&gt;,
&lt;Green's R-class: [2,1,3]&gt;, &lt;Green's R-class: [2,3][4,1]&gt;,
&lt;Green's R-class: [4,3,1]&gt;, &lt;Green's R-class: [4,1,3]&gt;,
&lt;Green's R-class: [2,1](3)&gt; ]</pre></div>

<p><a id="X865387A87FAAC395" name="X865387A87FAAC395"></a></p>
Expand Down Expand Up @@ -393,19 +393,19 @@ <h5>10.1-5 <span class="Heading">XClassReps</span></h5>
<span class="GAPprompt">gap&gt;</span> <span class="GAPinput">S := Semigroup(Transformation([3, 4, 4, 4]),</span>
<span class="GAPprompt">&gt;</span> <span class="GAPinput"> Transformation([4, 3, 1, 2]));;</span>
<span class="GAPprompt">gap&gt;</span> <span class="GAPinput">DClassReps(S);</span>
[ Transformation( [ 3, 4, 4, 4 ] ), Transformation( [ 4, 3, 1, 2 ] ),
[ Transformation( [ 3, 4, 4, 4 ] ), Transformation( [ 4, 3, 1, 2 ] ),
Transformation( [ 4, 4, 4, 4 ] ) ]
<span class="GAPprompt">gap&gt;</span> <span class="GAPinput">LClassReps(S);</span>
[ Transformation( [ 3, 4, 4, 4 ] ), Transformation( [ 1, 2, 2, 2 ] ),
Transformation( [ 4, 3, 1, 2 ] ), Transformation( [ 4, 4, 4, 4 ] ),
Transformation( [ 2, 2, 2, 2 ] ), Transformation( [ 3, 3, 3, 3 ] ),
[ Transformation( [ 3, 4, 4, 4 ] ), Transformation( [ 1, 2, 2, 2 ] ),
Transformation( [ 4, 3, 1, 2 ] ), Transformation( [ 4, 4, 4, 4 ] ),
Transformation( [ 2, 2, 2, 2 ] ), Transformation( [ 3, 3, 3, 3 ] ),
Transformation( [ 1, 1, 1, 1 ] ) ]
<span class="GAPprompt">gap&gt;</span> <span class="GAPinput">D := GreensDClasses(S)[1];</span>
&lt;Green's D-class: Transformation( [ 3, 4, 4, 4 ] )&gt;
<span class="GAPprompt">gap&gt;</span> <span class="GAPinput">LClassReps(D);</span>
[ Transformation( [ 3, 4, 4, 4 ] ), Transformation( [ 1, 2, 2, 2 ] ) ]
<span class="GAPprompt">gap&gt;</span> <span class="GAPinput">RClassReps(D);</span>
[ Transformation( [ 3, 4, 4, 4 ] ), Transformation( [ 4, 4, 3, 4 ] ),
[ Transformation( [ 3, 4, 4, 4 ] ), Transformation( [ 4, 4, 3, 4 ] ),
Transformation( [ 4, 3, 4, 4 ] ), Transformation( [ 4, 4, 4, 3 ] ) ]
<span class="GAPprompt">gap&gt;</span> <span class="GAPinput">R := GreensRClasses(D)[1];;</span>
<span class="GAPprompt">gap&gt;</span> <span class="GAPinput">HClassReps(R);</span>
Expand All @@ -415,7 +415,7 @@ <h5>10.1-5 <span class="Heading">XClassReps</span></h5>
<span class="GAPprompt">gap&gt;</span> <span class="GAPinput">M := MunnSemigroup(e);;</span>
<span class="GAPprompt">gap&gt;</span> <span class="GAPinput">L := LClassNC(M, PartialPerm([51, 63], [51, 47]));;</span>
<span class="GAPprompt">gap&gt;</span> <span class="GAPinput">HClassReps(L);</span>
[ &lt;identity partial perm on [ 47, 51 ]&gt;, [27,47](51), [50,47](51),
[ &lt;identity partial perm on [ 47, 51 ]&gt;, [27,47](51), [50,47](51),
[64,47](51), [63,47](51), [59,47](51) ]</pre></div>

<p><a id="X81E5A04F7DA3A1E1" name="X81E5A04F7DA3A1E1"></a></p>
Expand All @@ -434,7 +434,7 @@ <h5>10.1-6 MinimalDClass</h5>

<div class="example"><pre>
<span class="GAPprompt">gap&gt;</span> <span class="GAPinput">D := MinimalDClass(JonesMonoid(8));</span>
&lt;Green's D-class: &lt;bipartition: [ 1, 2 ], [ 3, 4 ], [ 5, 6 ],
&lt;Green's D-class: &lt;bipartition: [ 1, 2 ], [ 3, 4 ], [ 5, 6 ],
[ 7, 8 ], [ -1, -2 ], [ -3, -4 ], [ -5, -6 ], [ -7, -8 ]&gt;&gt;
<span class="GAPprompt">gap&gt;</span> <span class="GAPinput">S := InverseSemigroup(</span>
<span class="GAPprompt">&gt;</span> <span class="GAPinput">PartialPerm([1, 2, 3, 5, 7, 8, 9], [2, 6, 9, 1, 5, 3, 8]),</span>
Expand All @@ -458,8 +458,8 @@ <h5>10.1-7 <span class="Heading">MaximalXClasses</span></h5>

<div class="example"><pre>
<span class="GAPprompt">gap&gt;</span> <span class="GAPinput">MaximalDClasses(BrauerMonoid(8));</span>
[ &lt;Green's D-class: &lt;block bijection: [ 1, -1 ], [ 2, -2 ],
[ 3, -3 ], [ 4, -4 ], [ 5, -5 ], [ 6, -6 ], [ 7, -7 ],
[ &lt;Green's D-class: &lt;block bijection: [ 1, -1 ], [ 2, -2 ],
[ 3, -3 ], [ 4, -4 ], [ 5, -5 ], [ 6, -6 ], [ 7, -7 ],
[ 8, -8 ]&gt;&gt; ]
<span class="GAPprompt">gap&gt;</span> <span class="GAPinput">MaximalDClasses(FullTransformationMonoid(5));</span>
[ &lt;Green's D-class: IdentityTransformation&gt; ]
Expand All @@ -469,7 +469,7 @@ <h5>10.1-7 <span class="Heading">MaximalXClasses</span></h5>
<span class="GAPprompt">&gt;</span> <span class="GAPinput">PartialPerm([1, 2, 3, 4, 6, 8], [4, 3, 2, 7, 6, 5]),</span>
<span class="GAPprompt">&gt;</span> <span class="GAPinput">PartialPerm([1, 2, 4, 5, 6, 7, 8], [7, 1, 4, 2, 5, 6, 3]));;</span>
<span class="GAPprompt">gap&gt;</span> <span class="GAPinput">MaximalDClasses(S);</span>
[ &lt;Green's D-class: [2,8](1,3)(4)(5)(6)(7)&gt;,
[ &lt;Green's D-class: [2,8](1,3)(4)(5)(6)(7)&gt;,
&lt;Green's D-class: [8,3](1,7,6,5,2)(4)&gt; ]</pre></div>

<p><a id="X7AA3F0A77D0043FB" name="X7AA3F0A77D0043FB"></a></p>
Expand All @@ -495,8 +495,8 @@ <h5>10.1-8 NrRegularDClasses</h5>
<span class="GAPprompt">gap&gt;</span> <span class="GAPinput">NrDClasses(S);</span>
7
<span class="GAPprompt">gap&gt;</span> <span class="GAPinput">AsSet(RegularDClasses(S));</span>
[ &lt;Green's D-class: Transformation( [ 1, 4, 1, 1, 4, 3 ] )&gt;,
&lt;Green's D-class: Transformation( [ 1, 1, 1, 1, 1 ] )&gt;,
[ &lt;Green's D-class: Transformation( [ 1, 4, 1, 1, 4, 3 ] )&gt;,
&lt;Green's D-class: Transformation( [ 1, 1, 1, 1, 1 ] )&gt;,
&lt;Green's D-class: Transformation( [ 1, 1, 1, 1, 1, 1 ] )&gt; ]</pre></div>

<p><a id="X7E45FD9F7BADDFBD" name="X7E45FD9F7BADDFBD"></a></p>
Expand Down Expand Up @@ -683,15 +683,15 @@ <h5>10.1-12 IsGreensDGreaterThanFunc</h5>
<span class="GAPprompt">&gt;</span> <span class="GAPinput"> Transformation([2, 5, 3, 5, 3]),</span>
<span class="GAPprompt">&gt;</span> <span class="GAPinput"> Transformation([5, 5, 1, 1, 3]));;</span>
<span class="GAPprompt">gap&gt;</span> <span class="GAPinput">reps := ShallowCopy(AsSet(DClassReps(S)));</span>
[ Transformation( [ 1, 1, 1, 1, 1 ] ),
Transformation( [ 1, 3, 1, 3, 3 ] ),
Transformation( [ 1, 3, 4, 1, 3 ] ),
[ Transformation( [ 1, 1, 1, 1, 1 ] ),
Transformation( [ 1, 3, 1, 3, 3 ] ),
Transformation( [ 1, 3, 4, 1, 3 ] ),
Transformation( [ 2, 4, 1, 5, 5 ] ) ]
<span class="GAPprompt">gap&gt;</span> <span class="GAPinput">Sort(reps, IsGreensDGreaterThanFunc(S));</span>
<span class="GAPprompt">gap&gt;</span> <span class="GAPinput">reps;</span>
[ Transformation( [ 2, 4, 1, 5, 5 ] ),
Transformation( [ 1, 3, 4, 1, 3 ] ),
Transformation( [ 1, 3, 1, 3, 3 ] ),
[ Transformation( [ 2, 4, 1, 5, 5 ] ),
Transformation( [ 1, 3, 4, 1, 3 ] ),
Transformation( [ 1, 3, 1, 3, 3 ] ),
Transformation( [ 1, 1, 1, 1, 1 ] ) ]
<span class="GAPprompt">gap&gt;</span> <span class="GAPinput">IsGreensLessThanOrEqual(DClass(S, reps[2]),</span>
<span class="GAPprompt">&gt;</span> <span class="GAPinput"> DClass(S, reps[1]));</span>
Expand Down Expand Up @@ -1016,10 +1016,10 @@ <h5>10.4-2 SchutzenbergerGroup</h5>
<span class="GAPprompt">&gt;</span> <span class="GAPinput">PartialPerm([1, 2, 3, 5, 6, 7, 8, 9],</span>
<span class="GAPprompt">&gt;</span> <span class="GAPinput"> [7, 4, 1, 6, 9, 5, 2, 3]));;</span>
<span class="GAPprompt">gap&gt;</span> <span class="GAPinput">List(DClasses(S), SchutzenbergerGroup);</span>
[ Group(()), Group(()), Group(()), Group(()), Group([ (4,9) ]),
Group(()), Group(()), Group([ (5,8,6), (5,8) ]), Group(()),
Group(()), Group(()), Group(()), Group(()), Group(()),
Group([ (1,7,5,6,9,3) ]), Group([ (1,6)(3,5) ]), Group(()),
[ Group(()), Group(()), Group(()), Group(()), Group([ (4,9) ]),
Group(()), Group(()), Group([ (5,8,6), (5,8) ]), Group(()),
Group(()), Group(()), Group(()), Group(()), Group(()),
Group([ (1,7,5,6,9,3) ]), Group([ (1,6)(3,5) ]), Group(()),
Group(()), Group(()), Group(()), Group(()), Group(()), Group(()) ]</pre></div>

<p><a id="X81202126806443F9" name="X81202126806443F9"></a></p>
Expand Down Expand Up @@ -1180,8 +1180,8 @@ <h5>10.4-7 InjectionPrincipalFactor</h5>
&lt;Green's D-class: &lt;bipartition: [ 1, 5, -2, -4 ], [ 2, 3, 4, -1, -5 ]
, [ -3 ]&gt;&gt;
<span class="GAPprompt">gap&gt;</span> <span class="GAPinput">InjectionNormalizedPrincipalFactor(D);</span>
MappingByFunction( &lt;Green's D-class: &lt;bipartition: [ 1, 5, -2, -4 ],
[ 2, 3, 4, -1, -5 ], [ -3 ]&gt;&gt;, &lt;Rees matrix semigroup 1x1 over
MappingByFunction( &lt;Green's D-class: &lt;bipartition: [ 1, 5, -2, -4 ],
[ 2, 3, 4, -1, -5 ], [ -3 ]&gt;&gt;, &lt;Rees matrix semigroup 1x1 over
Group([ (1,2) ])&gt;, function( x ) ... end, function( x ) ... end )</pre></div>

<p><a id="X86C6D777847AAEC7" name="X86C6D777847AAEC7"></a></p>
Expand Down Expand Up @@ -1211,7 +1211,7 @@ <h5>10.4-8 PrincipalFactor</h5>
<span class="GAPprompt">&gt;</span> <span class="GAPinput">Bipartition([[1, -5], [2, 3, 4, 5, -1, -3], [-2, -4]]),</span>
<span class="GAPprompt">&gt;</span> <span class="GAPinput">Bipartition([[1, 5, -4], [2, 4, -1, -5], [3, -2, -3]]));;</span>
<span class="GAPprompt">gap&gt;</span> <span class="GAPinput">D := MinimalDClass(S);</span>
&lt;Green's D-class: &lt;bipartition: [ 1, 2, 3, 4, 5, -1, -3 ],
&lt;Green's D-class: &lt;bipartition: [ 1, 2, 3, 4, 5, -1, -3 ],
[ -2, -5 ], [ -4 ]&gt;&gt;
<span class="GAPprompt">gap&gt;</span> <span class="GAPinput">NormalizedPrincipalFactor(D);</span>
&lt;Rees matrix semigroup 1x5 over Group(())&gt;</pre></div>
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