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Quelle chap3_mj.html
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<div class="chlinkprevnexttop">&<panclass="ontSS< /span class=nocss>n;nbsp;/><href"chap3_mj.tml#X7F0EDFA77F929120">3.1-6 FirstElementsOfNumericalSemigroup</a></span>
<pspan class=ContSS>br>spanclass""&;nbsp</><a =chap3_mjhtmlX81A2505E8120F4D7<>318<><span> <span\/><></a><><span>
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<div class=" class="ContSS><br >span =""&bsp;nbsp;<span>< href="chap3_mj.html#X7CB24F5E84793BE1">3.1-15 AperyList</a></span>
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<>312Generators>
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<span class="ContSS"><br /><span class="nocss"> </span><a href="chap3_mj.html#span class="ContSS"><br /><span class="nocss"> </span><a href="chap3_mj.html#X835C729D7D8B1B36 /<span class=nocss" /spana href=chap3_mj.tmlX835C729D7D8B1B363.=C> />=n">;nbsp;</>a="h".- java.lang.StringIndexOutOfBoundsException: Range [132, 130) out of bounds for length 141
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<span class="ContSS"><br /><span class="nocss"> </span><a href="chap3_mj.html#X7B6C82DD86E5422F">3.1-11 ElementNumber_NumericalSemigroup</a></span>
< class=ContSS<br /<span class="nocss"> </span><a href="chap3_mj.html#X78F4A7A7797E26D4">3.1-12 NumberElement_NumericalSemigroup</a></span>
=ContSS< ><pan "";bsp/><=.XC729java.lang.StringIndexOutOfBoundsException: Range [107, 106) out of bounds for length 135
<panclassC"< /class=nocss>&bsp;nbsp;/>a href="hap3_mj#7>.- </a<span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap3_mj.span classContSS>br /> class">n&bsp<span< "hap3_mj.#865E2E12804CFCD3"3.1- /<span
class="<br />span java.lang.StringIndexOutOfBoundsException: Range [39, 38) out of bounds for length 135
<span<spanclass=ContSS>br><an=nocssbsp&bsp<span<href"chap3_mjhtml#794E615F85C2AAB0"3.1-32 LatticePathAssociatedToNumericalSemigroup</<span class=ContSS"><br /><span class="nocss"> </span><a href="<panclass=ContSS"br/>span class="nocss"> </span><a href="chap3_mj.html#X7EC438CC7BF539D0">3span class="ContSS" /<spanclass="nocss"> </span><a href="chap3_mj.html#X803D550C78717A7C">3.1-35 SpecialGaps</a></spandiv>></div
java.lang.StringIndexOutOfBoundsException: Range [6, 5) out of bounds for length 162
< classContSS>br><span class"ocss"nbspnbsp<span>ahref"hap3_mj.html#X80B398537887FD87">3.1-19 <span class="ContSS"><br /><span class="nocss"> </span><a href="chap3_mj.html#X7B45623E7D539CB6">3.2-3 ProfileOfNumeric
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap3_mj.html#X7C21E5417A3894EC">3.1-20 KunzPolytope</a></span>
<span class="ContSS"><br /><java.lang.StringIndexOutOfBoundsException: Index 32 out of bounds for length 28
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<span
<>31<span =Heading>
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<span class="ontSS"br/<span class="nocss"> </span><a href="chap3_mj.html#X82B1868F7A780B49">3span class="ContSS"><br /><span class="nocss"> </spanspan class=ContSS>< span""&bsp;&bsp;/span>< =chap3_mj.java.lang.StringIndexOutOfBoundsException: Index 93 out of bounds for length 0
<panclass="ontSS"><br /><span class="nocss"> </span><a href="chap3_mj.html#X83D4AFE882A79096">3.1-30 IsAcute</a></span>
<class>nbsp<span>ajava.lang.StringIndexOutOfBoundsException: Range [74, 73) out of bounds for length 131
<span class="ContSS"><br/<spanclass=java.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0
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></h3
<p java.lang.StringIndexOutOfBoundsException: Range [6, 5) out of bounds for length 86
<p>sclassjava.lang.StringIndexOutOfBoundsException: Range [12, 10) out of bounds for length 242
<h4
Invariants
/<h4
<< ""<pre>
<p[,3 ]
<h5> ,3 ]
<div /pre><java.lang.StringIndexOutOfBoundsException: Range [5, 4) out of bounds for length 227
<div class="func"><table class="func" width="100%"><tr><>aid"" nameX7A56569F853DADED/a<p
java.lang.StringIndexOutOfBoundsException: Range [116, 115) out of bounds for length 553
<div class="example"><pre>
<=Gjava.lang.StringIndexOutOfBoundsException: Range [24, 22) out of bounds for length 93
gt
<span p><code class="code< java.lang.StringIndexOutOfBoundsException: Index 1 out of bounds for length 0
3
<span class="GAPprompt">gap></span> <span class=panjava.lang.StringIndexOutOfBoundsException: Range [13, 11) out of bounds for length 91
<java.lang.StringIndexOutOfBoundsException: Index 34 out of bounds for length 1
java.lang.StringIndexOutOfBoundsException: Range [22, 5) out of bounds for length 105
8
</pre></div>
<p><a<java.lang.StringIndexOutOfBoundsException: Range [5, 4) out of bounds for length 242
<h5>3.java.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0
divclass"unc><table=f0 java.lang.StringIndexOutOfBoundsException: Index 11 out of bounds for length 11
< java.lang.StringIndexOutOfBoundsException: Range [11, 10) out of bounds for length 238
<java.lang.StringIndexOutOfBoundsException: Range [5, 4) out of bounds for length 225
div"03 java.lang.StringIndexOutOfBoundsException: Index 11 out of bounds for length 11
<div class="func"><table classpa"Ajava.lang.StringIndexOutOfBoundsException: Range [28, 27) out of bounds for length 62
<<classA"<varisa =java.lang.StringIndexOutOfBoundsException: Range [109, 103) out of bounds for length 535
<div class<<div>
<span class<>a =X7D2B3AA9823371AE=X7java.lang.StringIndexOutOfBoundsException: Range [53, 52) out of bounds for length 62
&h5.- <""java.lang.StringIndexOutOfBoundsException: Range [25, 24) out of bounds for length 381
<span class<
[11,12 13,,53
<span class="< class="rg>S</varjava.lang.StringIndexOutOfBoundsException: Index 1 out of bounds for length 0
<Numerical semigroup
java.lang.StringIndexOutOfBoundsException: Range [12, 11) out of bounds for length 103
[ =GAPprompt>gapgt;/>span =GAPinput>(ns
< java.lang.StringIndexOutOfBoundsException: Range [12, 11) out of bounds for length 90
[ 3, 5 ]
<span class="GAPprompt">gap&
[ 3, 5 java.lang.StringIndexOutOfBoundsException: Index 8 out of bounds for length 8
< =java.lang.StringIndexOutOfBoundsException: Range [23, 22) out of bounds for length 143
java.lang.StringIndexOutOfBoundsException: Range [9, 10) out of bounds for length 4
<>gapg<span spanclassGAPinput> :=NumericalSemigroup,,>c"java.lang.StringIndexOutOfBoundsException: Range [25, 24) out of bounds for length 163
ltN semigroup &t;
<span java.lang.StringIndexOutOfBoundsException: Index 8 out of bounds for length 0
true
<=java.lang.StringIndexOutOfBoundsException: Range [28, 22) out of bounds for length 93
false
<span classjava.lang.StringIndexOutOfBoundsException: Range [12, 11) out of bounds for length 133
[]
<java.lang.StringIndexOutOfBoundsException: Index 4 out of bounds for length 0
[,,,15
</pre></div>
d=/java.lang.StringIndexOutOfBoundsException: Range [7, 5) out of bounds for length 12
<<<Xjava.lang.StringIndexOutOfBoundsException: Range [29, 27) out of bounds for length 62
<java.lang.StringIndexOutOfBoundsException: Range [12, 11) out of bounds for length 102
<div class=< class"APprompt"gapjava.lang.StringIndexOutOfBoundsException: Range [31, 30) out of bounds for length 75
<p><code"java.lang.StringIndexOutOfBoundsException: Range [17, 16) out of bounds for length 246
<div class="example"java.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0
>/>java.lang.StringIndexOutOfBoundsException: Range [45, 44) out of bounds for length 103
&;java.lang.StringIndexOutOfBoundsException: Range [14, 13) out of bounds for length 45
<span<05 ,12,,, ,,24]
3
<span class="GAPprompt">gap></<span class="GAPprompt">gap></span=GAPinputspanclass=">ap&;<spanspan class="ElementsUpTo,);</span>
3
</pre></div>
<p><a,,10 12,14 15 ,19,20 ,,24,26 27]
<h5>3.
<divh5>java.lang.StringIndexOutOfBoundsException: Range [10, 9) out of bounds for length 59
<div class="func"><table class=
<p">NS
<p><var="Arg"Svar is a numerical< var class""><var> is .It the ="/>element < class"">/>/java.lang.StringIndexOutOfBoundsException: Index 180 out of bounds for length 180
<span class=GAPprompt">>gt;/ <="(NumericalSemigroup(,57))<java.lang.StringIndexOutOfBoundsException: Index 109 out of bounds for length 2
[0,3, 5 ]
<span class="GAPprompt">gap></span> <span class="GAPinput">SmallElementsOfNumericalSemigroup(NumericalSemigroup(3,5,7));</span>
[ 0, 3, 5 ]
</pre><
<p
<53.15 Length
<p> =Arg><var is a semigroup <var class""ls/ar <div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣>(varclass=Arg/>,varclass"rg>r/var>/>td =t"(nbspoperation;)</td<< class=ArgSvar>isanumericalsemigroup =Arg">r</var> is
<p><code class="code">span class="">gap&t;/>=span class="GAPprompt">gap></span> <span class="GAPinput<java.lang.StringIndexOutOfBoundsException: Range [52, 50) out of bounds for length 79
<p><var class="Arg">S</var" < "<> aninteger. returns thereturns the least than var class=">< belongingtovar"S</var./>
<spanclassGAPprompt>gap&t<span> <span class="GAPinput">Length(NumericalSemigroup(3,5,7));</span>
2
</pre></div>
<>a=X7F0EDFA77F929120="X7F0EDFA77F929120">/>java.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0
./java.lang.StringIndexOutOfBoundsException: Index 48 out of bounds for length 48
<div java.lang.StringIndexOutOfBoundsException: Index 2 out of bounds for length 2
<>""
<div class
<span -11 ElementNumber_NumericalSemigroup
[ <>31-3 div class="functablejava.lang.StringIndexOutOfBoundsException: Range [32, 30) out of bounds for length 265
<java.lang.StringIndexOutOfBoundsException: Range [11, 5) out of bounds for length 133
[0,3,5 6 7, 8,9, 10,12 ]
</pre/div>
<p><a id="X7D2B3AA9823371AE" name="X7D2B3AA9823371AE"></a></p>
<h5>3.1-7 ElementsUpTo</h5>
<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">&#an style='color: green'>8227; ElementsUpTo</code>( <var class="Arg">NS</varspanclass="GAPprompt">gap></span> <span class="GAPinput">iter:=Iterator(S&t;terator=GAPprompt><span>< class=GAPinput"NextIterator(iter);</span>
> <>a var="</ar positveinteger< semigroups outputisthe spanclass""textitjava.lang.StringIndexOutOfBoundsException: Index 116 out of bounds for length 0
<div class="example"><pre>
<span class="GAPprompt">gap></span> <span class="GAPinput">ns := span class="GAPprompt">gap></span> <span class="GAPinput">ns2 := NumericalSemigroup(7,11,12);;</span>
<span class="GAPprompt">gap></span> <span class="GAPinput">span class="GAPprompt">gap></span> <span class="GAPinput">Differencespan>
[19, 20, 21,22,24 ]
<span class="APprompt">gap></span> <span class="GAPinput">ElementsUpTo(ns,18);</span>
[java.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0
<span
[ 0, 5, < =""< class""width"00%>tr>td =tdleft"><ode "unc">#8227; java.lang.StringIndexOutOfBoundsException: Index 1 out of bounds for length 0
/><div
<p><a id="X81A2505E8120F4D7" name="X81A2505E8120F4D7"></a></spanclass=">><span =GAPinput"java.lang.StringIndexOutOfBoundsException: Index 92 out of bounds for length 85
<h5><code> 0,13, 26 39,52 53,54,43,32,33,22 11 ]
<div [,13 ,39 52,53, 54 43 32,33,22<varA"Svar numerical semigroup.It <varclass"">/ar><pjava.lang.StringIndexOutOfBoundsException: Index 111 out of bounds for length 111
<p><var class=<>aid="X80431F487C71D67B" name="X80431F487C71D67B"></a></p>
<div class="example"><pre>
>< "java.lang.StringIndexOutOfBoundsException: Range [61, 60) out of bounds for length 102
<classGAPprompt">&t;/span> <span class="APinput>[53;<span;&java.lang.StringIndexOutOfBoundsException: Index 16 out of bounds for length 16
68
</pre></div>
<<><class"g"<java.lang.StringIndexOutOfBoundsException: Range [27, 26) out of bounds for length 174
<h5><code>3.1-9 \{ \}</<div class="example"><pre
<div span class="GAPprompt">gap></span> <span
ar"</> numerical semigroupand<var class=>java.lang.StringIndexOutOfBoundsException: Range [77, 76) out of bounds for length 170
<div class="xample"><pre>
<span class="GAPprompt">gap></span> <span class="GAPinput">S := NumericalSemigroup
<span class="GAPprompt">gap<java.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0
[0,7 ,14, 15 java.lang.StringIndexOutOfBoundsException: Index 19 out of bounds for length 19
</<div>
<p><a id="X84345D5E7CAA9B77" name="X84345D5E7CAA9B77"></a></p>
<h5>3.1-10 NextElementOfNumericalSemigroup</h5>
<div class="func"><table class="func" width="100%"
></ anumerical varclass=Arg>/>isinteger span=GAPprompt>gap&;/spanjava.lang.StringIndexOutOfBoundsException: Range [45, 44) out of bounds for length 105
<div class="example"><pre>
<span class="GAPprompt">gap></span> <span class="GAPinput">S := NumericalSemigroup(7,8,[0 10,13,1920,23 26,2729 32,33 36,39 42 <panclassGAPprompt"gap&tspan>< =GAPinput> =5,);span>
<span class="[,,23]
14
<span class="GAPpromptB"name"X7CB24F5E84793BE1>/p>
17
<span class="GAPprompt">java.lang.StringIndexOutOfBoundsException: Index 27 out of bounds for length 0
</pre></div[0,13,19 26,27 32,38,51 54 ]
<p><a id="X7B6C82DD86E5422F" name="[ 0, 51, 32, 13, 54, 45, 26, 27, 38, 19
<h5>3.1-11 ElementNumber_NumericalSemigroup</h5>
<div class="func"><table class="func" width="100%"><tr>< class=GAPprompt">< ="S/var isa numerical semigroup and <var ""<>isapositive <java.lang.StringIndexOutOfBoundsException: Index 111 out of bounds for length 2
<="100%"><trtd ="tdleft"><code class="func">‣ java.lang.StringIndexOutOfBoundsException: Range [1, 107) out of bounds for length 85
pvar ""S/>isa<=Argr/>isinteger (java.lang.StringIndexOutOfBoundsException: Range [119, 118) out of bounds for length 217
<class=<span"">gapgt;<span> span ="<span "&;/>class="(,10;/>
<span class=APinputS:NumericalSemigroup17;/>
<span class="GAPprompt">gap></span> <classContSS>br ><spanjava.lang.StringIndexOutOfBoundsException: Range [40, 38) out of bounds for length 135
68
java.lang.StringIndexOutOfBoundsException: Index 8 out of bounds for length 0
68
<div class="func"><table="func"width"100%><tr>tdclass"dleft>codeclass"func"‣MinimalGeneratingSystemOfNumericalSemigroup</ode> < class="rg"Svar>)/td><td class="">&java.lang.StringIndexOutOfBoundsException: Index 1 out of bounds for length 1
<p><a id="X78F4A7A7797E26D4" name="X78F4A7A7797E26D4"></a></p>
<[ 021,12 3,14table class=func"idth=100<><td class="tdleft"><code class="func">‣ Conductor</code>( <var class="Arg">NS</var> )</td><td class="tdright">( attribute )</<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ ConductorOfNumericalSemigroup</code>( <var class="Arg">NS</var> )</td><td class="tdright">( div>
<div class="func"><table
<p><var div classexample"<>
<div class="example"><pre>
pan ""apgt<span spanclass""S=NumericalSemigroup7,,;;<span>
<span class="GAPprompt">gap></span
53
</pre></div>
<p><a id="X867ABF7C7991ED7C" name="X867ABF7C7991ED7C"/re
<>31-3 </>
<div class="func"><table classh53.- </h5
<p><var class="Arg">S</div =func>table class="func"="%>trjava.lang.StringIndexOutOfBoundsException: Range [59, 58) out of bounds for length 251
<div class="example"><pre>
spanGjava.lang.StringIndexOutOfBoundsException: Range [24, 22) out of bounds for length 102
& Apé var"> < class">/>thejava.lang.StringIndexOutOfBoundsException: Range [91, 90) out of bounds for length 286
l;gt
<panclass=GAPprompt"gap></span><span class="GAPinput">NextIterator(iter);</span>
0
< class"GAPprompt">gap></span> <span class="GAPinput
7
<span class="GAPprompt">gap></span> <span class=<pre</>
8
</pre></div>
<>aid"span "APpromptgap>< java.lang.StringIndexOutOfBoundsException: Range [45, 44) out of bounds for length 88
<h5>3.1< ="h53. <5
<div class="func"><table class<pan="GAPprompt"gap&t<span <class"APinput>(s,5);<span<iv =unc> class="func"width=100%>><tdclass=tdleft"<code=fjava.lang.StringIndexOutOfBoundsException: Range [92, 91) out of bounds for length 233
<div class="funcspan class="GAPprompt">gap></span> <span class="GAPinput">S := NumericalSemigroup("modular",&t;odular numerical semigroup satisfying 5x mod 53 <= x >
< is the set"impleMath"(\java.lang.StringIndexOutOfBoundsException: Range [114, 113) out of bounds for length 150
<div
<span class="GAPprompt/pre>/div ,1,0, ]
<span =GAPprompt">gap></span> <span class=java.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0
java.lang.StringIndexOutOfBoundsException: Range [12, 11) out of bounds for length 89
[ 5, 10, 15, 17, 20, 27 ]
<span="GAPprompt"gap;/java.lang.StringIndexOutOfBoundsException: Index 37 out of bounds for length 0
[, 18
<panclass="APprompt"gap;span span class="GAPinput">DifferenceOfNumericalSemigroups(ns2,ns1);</span>
11,18, 23 ]
</pre></div>
<p><ap> Kunz java.lang.StringIndexOutOfBoundsException: Index 1 out of bounds for length 0
<h5>3.div class="example"><pre>
<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code , 2 3 4,6,8,9, 13java.lang.StringIndexOutOfBoundsException: Index 27 out of bounds for length 27
<div ="">table =f "%">< class=tdleft>codeclass"[1,2 ]
<p><var java.lang.StringIndexOutOfBoundsException: Index 1 out of bounds for length 0
<div class="example"><pre>
nclass"GAPprompt">gapgt<span <spanclass>S=NumericalSemigroupmodular", 5,53;<span
<span class="GAPprompt">gap></span> <span class="GAPinput">AperyList(S,12);</span>
[0,13 ,, ,43 32 , 11
<span class="GAPprompt">span "&t;java.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0
[ 0, 13, 26,<prejava.lang.StringIndexOutOfBoundsException: Range [12, 11) out of bounds for length 12
<span class="GAPpromptp><a id=X7EB81BF886DDA29A" name="X7EB81BF886DDA29A
13
</>div
<java.lang.StringIndexOutOfBoundsException: Range [27, 2) out of bounds for length 62
<h5>3.1-16 java.lang.StringIndexOutOfBoundsException: Index 14 out of bounds for length 0
<"func">table class="unc class"func" class="func" width[0 ,0],[,4 ] 0 4, ]
<func<"w=100>td class=dleft"<class""&;AperyListOfNumericalSemigroup<class""S/>)/=""
<> ""</aris numerical. theApé java.lang.StringIndexOutOfBoundsException: Range [0, 80) out of bounds for length 45
<div class= class=GAPprompt>>span =GAPprompt>gapgt<span><class"GAPinput"Desertss;span
<span class="GAPprompt">gap> 3, 5 ]
<< ="< =func"=100"<r><td ""<ode class">#java.lang.StringIndexOutOfBoundsException: Index 99 out of bounds for length 12
java.lang.StringIndexOutOfBoundsException: Range [6, 5) out of bounds for length 102
[ 0, 12, 13, 25java.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0
</pre></div>f> java.lang.StringIndexOutOfBoundsException: Range [31, 30) out of bounds for length 221
<p><a id="X7D06B00D7C305C64" java.lang.StringIndexOutOfBoundsException: Index 33 out of bounds for length 26
<h5>3.1-17 AperyList4
<div class="func"><table class="func" widthjava.lang.StringIndexOutOfBoundsException: Range [0, 10) out of bounds for length 1
< class=func>tableclass="java.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0
<p
divclass=""<java.lang.StringIndexOutOfBoundsException: Range [26, 5) out of bounds for length 136
<span class=< java.lang.StringIndexOutOfBoundsException: Range [12, 11) out of bounds for length 86
<span class="GAPprompt">div class="func"><table class="func" width="100%"><tr><td class=-java.lang.StringIndexOutOfBoundsException: Index 2 out of bounds for length 2
[ 0, 10, 13, 19, 20, 23, 26, 27, 29, 32, 33, 36, 39, 42, 45, 46, 52, 55 ]
<span class="GAPprompt">gap></span> <span class="GAPinput">java.lang.StringIndexOutOfBoundsException: Index 67 out of bounds for length 42
[ 0, 10, 13, 19, 20, 23, 26, 27, 29,div ""<java.lang.StringIndexOutOfBoundsException: Range [25, 24) out of bounds for length 235
<span class="GAPprompt">gap></span> <span class="GAPinput">Length(last);</span>
<span class="GAPprompt">gap>java.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0
[ 0
<span class="GAPprompt">gap&java.lang.StringIndexOutOfBoundsException: Index 30 out of bounds for length 26
[ 45,26<classjava.lang.StringIndexOutOfBoundsException: Range [22, 19) out of bounds for length 26
<panclass=GAPprompt>gt<span spanclass="GAPinput">AperyList(s,10);</span>
[ 0, 51, 32, 13, 54, 45, 26, 27, 38, 19 ]
<spanjava.lang.StringIndexOutOfBoundsException: Range [12, 11) out of bounds for length 82
10
</pre></div>
<p><a id="X8022CC477E9BF678" name="X8022CC477E9BF678"></a></p>
<h5>3.1-18 AperyListOfNumericalSemigroupAsGraph</h5>
<div class="func"><table class="func" width="100%"><tr><td java.lang.StringIndexOutOfBoundsException: Index 62 out of bounds for length 12
<p><var class="Arg
<div class="example"><pre>
<span class="GAPprompt">gap></span> <span class="GAPinput">s:=p<code =code"</code> a semigroup.Let< ="impleMath(\)/> and<java.lang.StringIndexOutOfBoundsException: Range [109, 108) out of bounds for length 844
<span class="GAPprompt">gap></span> <span class="GAPinput">AperyListOfNumericalSemigroupWRTElement(s,10);</span>
[ 0, 21, 12, 3, 14, 15, 6, 7, 18, 9 ]
<span class="GAPprompt">gap></span> <span class="GAPinput">AperyListOfNumericalSemigroupAsGraph(last);</span>
[ ,, [ 3, 6, 9, 12, 15, 18, 21 ],,, [ 6, 9, 12, 15, 18, 21 ],
[ 7, 14, 21 ],, [ 9, 12, 15, 18, 21 ],,, [ 12, 15, 18, 21 ],,
[ 14, 21 ], [ 15, 18, 21 ],,, [ 18, 21 ],,, [ 21 ] ]
</pre></div>
<p><a id="X80B398537887FD87" name="X80B398537887FD87"></a></p>
<h5>3.1-19 KunzCoordinates</h5>
<div class="func"><table java.lang.StringIndexOutOfBoundsException: Range [0, 30) out of bounds for length 12
<java.lang.StringIndexOutOfBoundsException: Range [5, 4) out of bounds for length 270
<="Arg">S</var>. java.lang.StringIndexOutOfBoundsException: Range [144, 143) out of bounds for length 250
<p>Then the Apéry set of <var class="Arg"0 ,7 ,10,12,14 java.lang.StringIndexOutOfBoundsException: Index 26 out of bounds for length 26
<div class="example"><pre>
< "";java.lang.StringIndexOutOfBoundsException: Range [51, 50) out of bounds for length 98
&tjava.lang.StringIndexOutOfBoundsException: Range [14, 13) out of bounds for length 45
<span class="java.lang.StringIndexOutOfBoundsException: Index 20 out of bounds for length 0
[ 2, 1 ]
< "java.lang.StringIndexOutOfBoundsException: Range [28, 22) out of bounds for length 108
[ 2, 1 ]
<span class="<>
[ 1, 1, 0, 1 ]
<span class="GAPprompt">gap></span> <span class="GAPinput">KunzCoordinatesOfNumericalSemigroup(s,5
[ 1, 1, 0, 1 ]
</pre></div>
<p><a id="X7C21E5417A3894EC" name="<iv classfunc"table=f =100"<td ">code=f>#8227;TypeOfNumericalSemigroup>(< =""NS/var)/>class"dright"(nbsp <td>tr></table/>
<h5 java.lang.StringIndexOutOfBoundsException: Range [11, 10) out of bounds for length 26
<div class="func"><table class="func" width="l;odular satisfying 5x 53&t; &;
<> "">< ajava.lang.StringIndexOutOfBoundsException: Range [42, 41) out of bounds for length 54
<p<classGjava.lang.StringIndexOutOfBoundsException: Range [24, 22) out of bounds for length 97
<div class="java.lang.StringIndexOutOfBoundsException: Index 15 out of bounds for length 12
<span><id"java.lang.StringIndexOutOfBoundsException: Range [29, 27) out of bounds for length 62
[ [ 1, 0, >.-26</>
</pre></div>
<p><a id="X7802096584D32795" name="X7802096584D32795"></a></p>
<h5>3.1-21 p> <em></> of numericalsemigroupspan ="impleMath"\S)<> java.lang.StringIndexOutOfBoundsException: Range [281, 83) out of bounds for length 281
<div class="func"><table class="func" width="100%"><tr><td class="tdleft"calSemigroup(5,7,))<span>
<emigroup, ="< java.lang.StringIndexOutOfBoundsException: Range [96, 95) out of bounds for length 564
<div class="example"><pre>
<span class="GAPprompt">
<span class="GAPprompt">gap></span> <span java.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0
[ [ 0, 0, 0 ], [ 0, 3, 4 ], [ 0, 4, 1 ] ]
</pre></div>
<p>
<>.22>
<div class="func"><table class="java.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0
<class="func" width=100"<> class=tdleft"<odeclass=func>#8227; </code(<class=></var> )</>=>&a)/>/>><>
<p>The largest <span class="GAPprompt><span><span class="APinput">Weight45,7)/java.lang.StringIndexOutOfBoundsException: Range [105, 104) out of bounds for length 105
< classc"/java.lang.StringIndexOutOfBoundsException: Range [31, 30) out of bounds for length 274
<div
<span class="java.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0
4
<span class="="< =%>< java.lang.StringIndexOutOfBoundsException: Range [65, 64) out of bounds for length 235
4
</pre></div>
<p< "CDD java.lang.StringIndexOutOfBoundsException: Range [34, 33) out of bounds for length 62
<h5>3.1-23 Conductor</h5>
<""<class"java.lang.StringIndexOutOfBoundsException: Range [37, 36) out of bounds for length 218
<java.lang.StringIndexOutOfBoundsException: Range [11, 10) out of bounds for length 238
<is java.lang.StringIndexOutOfBoundsException: Range [26, 25) out of bounds for length 165
<div class="example"><pre>
<span class="GAPprompt">gap></span> <span class="GAPinput">Conductor(NumericalSemigroup(3,5,7));</span>
5
<span class="GAPprompt">gap></span> <span class="GAPinput">ConductorOfNumericalSemigroup(NumericalSemigroup(3,5,7));</span>
5
</pre></div>
<p><a id="X861DED207A2B5419" name="X861DED207A2B5419"></a></p>
<h5>3.1-24 PseudoFrobenius</h5>
< java.lang.StringIndexOutOfBoundsException: Range [11, 10) out of bounds for length 223
<"java.lang.StringIndexOutOfBoundsException: Range [17, 16) out of bounds for length 243
<Anjava.lang.StringIndexOutOfBoundsException: Range [15, 13) out of bounds for length 203
<p><code class="code">S</code> is a numerical semigroup. It returns the set of pseudo-Frobenius numbers of <var class="Arg">S</var>.</p>
<div class="example"><pre>
<span class="GAPprompt">gap></span> <span class="GAPinput">S := NumericalSemigroup("modular", 5,53);</span>
<Modular numerical semigroup satisfying 5x mod 53 <
<gapg;>< ""java.lang.StringIndexOutOfBoundsException: Range [78, 77) out of bounds for length 88
[ 21, 40, 41, 42 ]
<span class="GAPprompt">gap></span> <span class="GAPinput">PseudoFrobeniusOfNumericalSemigroup(S);</span
[21,40,41, ]
</pre></div>
<p><a id="X865E2E12804CFCD3" name="X865E2E12804CFCD3"></a></p>
<h5>3.1-25 Type</h5>
<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="><var class="Arg">NS</var> is a numerical semigroup. Dectects if the semigroup is ordinary/>
<div class="func"><table class="func" width="100%"><java.lang.StringIndexOutOfBoundsException: Index 54 out of bounds for length 0
<p>Stands for <codeclassjava.lang.StringIndexOutOfBoundsException: Range [23, 22) out of bounds for length 99
< classexample>pre>
<span class="GAPprompt">gap></span> <span class="GAPinput">S := java.lang.StringIndexOutOfBoundsException: Index 74 out of bounds for length 5
<Modular numerical semigroup satisfying 5x mod 53 <= x >
<span class="GAPprompt">gap></span
4
<span class="GAPprompt">gap></span> <span class="GAPinput">TypeOfNumericalSemigroup(S);</span>
4
</pre></div>
<<p>varclass"></ semigroup ,,java.lang.StringIndexOutOfBoundsException: Range [106, 105) out of bounds for length 274
<h5>3.1-26 Gaps</h5>
<div class="java.lang.StringIndexOutOfBoundsException: Range [0, 16) out of bounds for length 0
<div class="func"><table class="func" width="100%"><tr><tdjava.lang.StringIndexOutOfBoundsException: Range [12, 11) out of bounds for length 99
<p>A <em>gap</em> of a numerical semigroup
<div class="java.lang.StringIndexOutOfBoundsException: Index 14 out of bounds for length 0
<span class="gap<><java.lang.StringIndexOutOfBoundsException: Range [45, 44) out of bounds for length 102
[ 1, 2, 3, 4, 6, 8, 9, 13 ]
<pan="">&; java.lang.StringIndexOutOfBoundsException: Range [45, 44) out of bounds for length 121
[ 1, 2, 4 ]
<>/>
<>a"7 java.lang.StringIndexOutOfBoundsException: Range [34, 33) out of bounds for length 62
<3.- /java.lang.StringIndexOutOfBoundsException: Range [22, 21) out of bounds for length 22
<div class="func"><table class=java.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0
<p>If <span class="SimpleMath">\(l_1<\cdots <l_g\)</span> are ">< java.lang.StringIndexOutOfBoundsException: Range [51, 50) out of bounds for length 97
<div class="example"><pre>
<span class="GAPprompt">gap></span> <span class="GAPinput">Weight(NumericalSemigroup(4java.lang.StringIndexOutOfBoundsException: Range [6, 5) out of bounds for length 98
0
<java.lang.StringIndexOutOfBoundsException: Index 2 out of bounds for length 0
9
</pre></div>
<p><a id="X7EB81BF886DDA29A" name="X7EB81BF886DDA29A"></a></p>
<h5>3.1-28 Deserts</h5>
<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">&#an style='color: green'>8227; Deserts</code>( <var java.lang.StringIndexOutOfBoundsException: Index 127 out of bounds for length 0
<div class="unc><able ="unc"="100%>><""> java.lang.StringIndexOutOfBoundsException: Range [86, 85) out of bounds for length 235
<p><var class="Arg">NS</var> is a numerical semigroup. The output is the list with the runs of gaps of <var class="Arg">NS</var>.</p>
<div class="example"><pre>
<span class="java.lang.StringIndexOutOfBoundsException: Index 1 out of bounds for length 0
<div=example>pre>
[ [ 1 class=GAPprompt>&;span spanclassGAPinput>=(16,,,);/pan
<span class="GAPprompt">gap></span> <span class="GAPinput">DesertsOfNumericalSemigroup(s);</span>
[ [ 1, 2 ], [ 4 ] ]
</pre></div>
<p><a id="X82B1868F7A780B49" name="X82B1868F7A780B49"></a></p>
<h5>3.1-29 IsOrdinary</h5>
<div ="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">&#yle='color: green'>8227; IsOrdinary</code>( <var class="Arg">NS</var> )</td><td class="tdright">( property [ 14,0
< class="unc"<able class=""width=100>tr<td =">code class=func>#8227;IsOrdinaryNumericalSemigroupcode(<class""NS<var>)/>td ="tdright>&pnbsp<<<java.lang.StringIndexOutOfBoundsException: Range [230, 229) out of bounds for length 236
< A"NS<> java.lang.StringIndexOutOfBoundsException: Range [44, 43) out of bounds for length 134
<p>This filter implies <code class="func">IsAcuteNumericalSemigroup</code> (<a href="chap3_mj.html#X83D4AFE882A79096"><spanp<java.lang.StringIndexOutOfBoundsException: Range [9, 8) out of bounds for length 124
<div class="example"><pre>
<java.lang.StringIndexOutOfBoundsException: Range [12, 11) out of bounds for length 99
<span class="GAPprompt">gap></span> <span class="GAPinput">IsOrdinary(s);</span>
alse
</pre></div>
<>< =X83D4AFE882A79096namegt<>< =GAPinput> :=NumericalSemigroupm" ,)<span
<h5>3.1-30 IsAcute</h5>
<div class="func"><table class="span ="APpromptgap&/>< =""Genus
<java.lang.StringIndexOutOfBoundsException: Range [11, 10) out of bounds for length 233
<p< class="Arg"NS/java.lang.StringIndexOutOfBoundsException: Range [28, 27) out of bounds for length 274
<div class="example"><pre>
<span class="GAPprompt">gap&java.lang.StringIndexOutOfBoundsException: Range [0, 30) out of bounds for length 0
<span class="GAPprompt">gap></span> <span class="GAPinput">IsAcute>.-4 FundamentalGaps</h5
true
</pre></div>
<p><a id="X7CCFC5267FD27DDE" name="X7CCFC5267FD27DDE =f> ="unc"width="100%>tr>td"dleft">class""&8227 </code> var =ArgS<var>)/>td tdright>&;&)/>/tr>/>>
<h5>3.1-31 Holes</h5>
<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">&#an style='color: green'>8227; Holes</code>( <var class="Arg">NS</var> )</td><td class="tdright">( attribute )</td></tr></table></div>
<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">&#an style='color: green'>8227; HolesOfNumericalSemigrouplt; numerical satisfying5&; gt;
<p><code class="code">S</code> is a numerical semigroup. Returns the set of gaps <span class="SimpleMath">\(x\)</span> of <java.lang.StringIndexOutOfBoundsException: Index 127 out of bounds for length 97
<div class="example"><pre>
<span class="GAPprompt">gap></span> <span class="GAPinput"java.lang.StringIndexOutOfBoundsException: Range [23, 22) out of bounds for length 102
<span class="GAPprompt">gap></span> <span class="GAPinput">Holes(s);</span>
[ ]
<span class="GAPprompt">gap></span> <span class="GAPinput">s:=
<h5>1- />
[ 2 ]
</pre></div>
<p><a id="X794E615F85C2AAB0" name="X794E615F85C2AAB0"></a></p>
<h5>3.1-32 LatticePathAssociatedToNumericalSemigroup</h5>
<div class="func"><table "java.lang.StringIndexOutOfBoundsException: Range [37, 36) out of bounds for length 301
<p><code class="code">S</code> is a numerical semigroup and <code class="code">p,q</code> are two coprime elements in <code class="code">S</code>.</p>
<p>In this setting <code class=dclass>>
<p>The output is a path in <span class="SimpleMath">\(\mathbb{N}^2\)</span> such thatlt;numericaljava.lang.StringIndexOutOfBoundsException: Range [32, 31) out of bounds for length 65
<java.lang.StringIndexOutOfBoundsException: Range [11, 10) out of bounds for length 26
<span class="GAPprompt">gap></span> <span class="GAPinput">s:=java.lang.StringIndexOutOfBoundsException: Index 75 out of bounds for length 12
<classGAPprompt>g;/>< =GAPinput"LatticePathAssociatedToNumericalSemigroup;<span>
[ [ 0, 14 ], [ 1, 13 ], [ 2, 12 ], [ 3, 11 ], [ 4, 10 ], [ 5, 9 ], [ 6, 8 ],
[ 7, 7 ], [ 8, 6 ], [ 9, 5 ], [ 10, 4 ], [ 11, 3 ], [ 12, 2 ], [ 13, 1 ],
[ 14, 0 ] ]
/>
<p><a id="X7E9C8E157C4EAAB0" name="X7E9C8E157C4EAAB0"></a></div=><table class="func" width="100%"< java.lang.StringIndexOutOfBoundsException: Range [65, 64) out of bounds for length 218
java.lang.StringIndexOutOfBoundsException: Index 43 out of bounds for length 21
<class=f"< class=func"width"00%>tr>< class="<code class=func>#8227;Genus/code(<""NS/> )/>tdclass"dright>&bsp;ttributen;)/>/>java.lang.StringIndexOutOfBoundsException: Range [208, 207) out of bounds for length 214
<div class="java.lang.StringIndexOutOfBoundsException: Index 16 out of bounds for length 0
<p><code class="code">NS</code> is a numerical semigroupdiv ">>
<div <span class"APprompt">gap></span> <span class="GAPinput">WilfNumber(s);</span>
<span class="GAPprompt">gap></span> <span class="GAPinput">s:=NumericalSemigroup(span ="APprompt>></pan><span class=""l:=NumericalSemigroupsWithGenus(0);<>
<span class="GAPprompt">gap></span> <span class="GAPinput">java.lang.StringIndexOutOfBoundsException: Range [0, 67) out of bounds for length 4
80
<spanjava.lang.StringIndexOutOfBoundsException: Index 2 out of bounds for length 2
80
<span class="GAPprompt">gap></span> <span class="GAPinput">S :p< =java.lang.StringIndexOutOfBoundsException: Range [28, 27) out of bounds for length 62
<Modular numerical semigroup satisfying 5x mod 53 <=java.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0
<span class="GAPprompt">gap></span> <span class="GAPinput">Genus(S);</span>
26
</pre></div>
<p><a id="X7EC438CC7BF539D0" name="X7EC438CC7BF539D0"></a></p>
<h5>3.1-34 FundamentalGaps</h5>
<div p><"<> ajava.lang.StringIndexOutOfBoundsException: Range [46, 45) out of bounds for length 972
< java.lang.StringIndexOutOfBoundsException: Range [11, 10) out of bounds for length 243
<><ode"</>The em>java.lang.StringIndexOutOfBoundsException: Range [51, 50) out of bounds for length 311
<div class="example"><pre>
<span class="GAPprompt">gap></span> <span class="GAPinput">FundamentalGaps(NumericalSemigroup(5,7,11));</span>
[ 6, 8, 9, 13 ]
<span class="GAPprompt">gap></span> <span class="GAPinput">S := NumericalSemigroup("modular", 5,53);</span>
<Modular numerical semigroup satisfying 5x mod 53 <= x >
<span class="GAPprompt">gap></span> <span1
[ ]
<span class="GAPprompt">gap></span> <span class="GAPinput">GapsOfNumericalSemigroup(S);</span>
[ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 14, 15, 16, 17, 18, 19, 20, 21, 27, 28, 29,
30, 31, 40, 41, 42 ]
<span class="GAPprompt">gap></span> <span class="GAPinput">Gaps(NumericalSemigroup(5,7,11));</span>
[ 1, 2, 3, 4, 6, 8, 9, 13 ]
</pre></div>
<p><a id="X803D550C78717A7C" name100">tr><td class="tdleft"><code class="func">‣ ProfileOfNumericalSemigroup</code>( <var class="Arg">S</var> )</td><td class="tdright">( attribute )</td></tr></table></div>
<h5>3.1-35 SpecialGaps</h5>
<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">&#an style='color: green'>8227; SpecialGaps</code>( <var class="Arg">S</var> )</td><td class="tdright">( java.lang.StringIndexOutOfBoundsException: Index 0 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; SpecialGapsOfNumericalSemigroupspan =GAPprompt">gapgt;<span <span class="GAPinput">ProfileOfNumericalSemigroup(s);</span>
<p>The emspecial gaps/em>of a numerical semigroup <span class="SimpleMath">\(S\)</span> are those fundamental gaps such that if they are added to the given numerical semigroup, then the resulting set is again a numerical semigroup. <code class="code">S</code> is a numerical semigroup. It returns the special gaps of <var class="Arg">S</span class="GAPprompt">gap></span> <span class="GAPinput">ProfileOfNumericalSemigroup(s);</span>
<div class="example"><pre>
<span class="GAPprompt">gap></span> <span class="GAPinput">S := NumericalSemigroup("modular", 5,53);</span>
<Modular numerical semigroup satisfying 5xcode"ode"><code> anumerical semigroup.Letspan=S"()/> and span =S>(<span the conductor and multiplicity of <var class="Arg">S</var>, respectively. Let <span class="SimpleMath">\(q\)</span> and <span class="SimpleMath">\(r\)</span> be the quotient and nonpositive
<span class"APprompt">gap></span> <span class="GAPinput">SpecialGaps(S);</span>
[<span class="GAPprompt">gap></span> <span class="GAPinput">EliahouSlicesOfNumericalSemigroup(s);</span>
<span class="GAPprompt">gap></span> <span class="GAPinput">SpecialGapsOfNumericalSemigroup(S);</span>
[ 40,41, 42
</pre></div>
<p>aid="7EE22CA979CCAAB9"name="X7EE22CA979CCAAB9"></a></p>
<h4>3.2 <span class="Heading">Wilf's conjecture</span></h4>
<p>Let <span class="SimpleMath">\(S\)</span> be a numerical semigroup, with conductor <span class
<p><a id="X78C2F4C77FB096F0" name="X78C2F4C77FB096F0"></a></p>
<h5>3.2-1 WilfNumber</h5
<class="func">table class="unc"width="100%"><tr><td class="tdleft"><code class="func">&#tyle='color: green'>8227; WilfNumber</code>( <var class="Arg">S</var> )</td><td class="tdright">( attribute )</td></tr></table></div>
<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">&#an style='color: green'>8227; WilfNumberOfNumericalSemigroup</code>( <var class="Arg">S</var> )</<html>
<p><code class="code">S</code> is a numerical semigroup. Let <span class="SimpleMath">\(c\)</span>, <span class="SimpleMath">\(e\)</span> and <span class="SimpleMath">\(l\)</span> be the conductor, embedding dimension and number of elements smaller than <span class="SimpleMath">\(c\)</span> in <var class="Arg">S</var>. Returns <span class="SimpleMath">\(e l-c\)</span>, which was conjetured by Wilf to be nonnegative.</p>
<div class="example"><pre>
<span class="GAPprompt">gap></span> <span class="GAPinput">s := NumericalSemigroup(13,25,37);;</span>
<span class="GAPprompt">gap></span> <span class="GAPinput">WilfNumber(s);</span>
96
<span class="GAPprompt">gap></span> <span class="GAPinput">l:=NumericalSemigroupsWithGenus(10);;</span>
<span class="GAPprompt">gap></span> <span class="GAPinput">Filtered(l, s->WilfNumber(s)<0);</span>
[ ]
<span class="GAPprompt">gap></span> <span class="GAPinput">Maximum(Set(l, s->WilfNumberOfNumericalSemigroup(s)));</span>
70
</pre></div>
<p><a id="X80F9EC9A7BF4E606" name="X80F9EC9A7BF4E606"></a></p>
<h5>3.2-2 EliahouNumber</h5>
<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">&#an style='color: green'>8227; EliahouNumber</code>( <var class="Arg">S</var> )</td><td class="tdright">( attribute )</td></tr></table></div>
<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">&#an style='color: green'>8227; TruncatedWilfNumberOfNumericalSemigroup</code>( <var class="Arg">S</var> )</td><td class="tdright">( attribute )</td></tr></table></div>
<p><code class="code">S</code> is a numerical semigroup. Let <span class="SimpleMath">\(c\)</span>, <span class="SimpleMath">\(m\)</span>, <span class="SimpleMath">\(s\)</span> and <span class="SimpleMath">\(l\)</span> be the conductor, multiplicity, number of generators smaller than <span class="SimpleMath">\(c\)</span>, and number of elements smaller than <span class="SimpleMath">\(c\)</span> in <var class="Arg">S</var>, respectively. Let <span class="SimpleMath">\(q\)</span> and <span class="SimpleMath">\(r\)</span> be the quotient and nonpositive remainder of the division of <span class="SimpleMath">\(c\)</span> by <span class="SimpleMath">\(m\)</span>, that is, <span class="SimpleMath">\(c=qm-r\)</span>. Returns <span class="SimpleMath">\(s l-qd_q+r\)</span>, where <span class="SimpleMath">\(d_q\)</span> corresponds with the number of integers in <span class="SimpleMath">\([c,c+m[\)</span> that are not minimal generators of <var class="Arg">S</var>.</p>
<div class="example"><pre>
<span class="GAPprompt">gap></span> <span class="GAPinput">s:=NumericalSemigroupWithGivenElementsAndFrobenius([14,22,23],55);;</span>
<span class="GAPprompt">gap></span> <span class="GAPinput">EliahouNumber(s);</span>
-1
<span class="GAPprompt">gap></span> <span class="GAPinput">s:=NumericalSemigroup(5,7,9);;</span>
<span class="GAPprompt">gap></span> <span class="GAPinput">TruncatedWilfNumberOfNumericalSemigroup(s);</span>
4
</pre></div>
<p><a id="X7B45623E7D539CB6" name="X7B45623E7D539CB6"></a></p>
<h5>3.2-3 ProfileOfNumericalSemigroup</h5>
<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">&#an style='color: green'>8227; ProfileOfNumericalSemigroup</code>( <var class="Arg">S</var> )</td><td class="tdright">( attribute )</td></tr></table></div>
<p><code class="code">S</code> is a numerical semigroup. Let <span class="SimpleMath">\(c\)</span> and <span class="SimpleMath">\(m\)</span> be the conductor and multiplicity of <var class="Arg">S</var>, respectively. Let <span class="SimpleMath">\(q\)</span> and <span class="SimpleMath">\(r\)</span> be the quotient and nonpositive remainder of the division of <span class="SimpleMath">\(c\)</span> by <span class="SimpleMath">\(m\)</span>, that is, <span class="SimpleMath">\(c=qm-r\)</span>. Returns a list of lists of integers, each list is the cardinality of <span class="SimpleMath">\( S \cap [jm-r, (j+1)m-r[\)</span> with <span class="SimpleMath">\( j\)</span> in [1..q-1].</p>
<div class="example"><pre>
<span class="GAPprompt">gap></span> <span class="GAPinput">s:=NumericalSemigroup(5,7,9);;</span>
<span class="GAPprompt">gap></span> <span class="GAPinput">ProfileOfNumericalSemigroup(s);</span>
[ 2, 1 ]
<span class="GAPprompt">gap></span> <span class="GAPinput">s:=NumericalSemigroupWithGivenElementsAndFrobenius([14,22,23],55);;</span>
<span class="GAPprompt">gap></span> <span class="GAPinput">ProfileOfNumericalSemigroup(s);</span>
[ 3, 0, 0 ]
</pre></div>
<p><a id="X7846F90E7EA43C47" name="X7846F90E7EA43C47"></a></p>
<h5>3.2-4 EliahouSlicesOfNumericalSemigroup</h5>
<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">&#an style='color: green'>8227; EliahouSlicesOfNumericalSemigroup</code>( <var class="Arg">S</var> )</td><td class="tdright">( attribute )</td></tr></table></div>
<p><code class="code">S</code> is a numerical semigroup. Let <span class="SimpleMath">\(c\)</span> and <span class="SimpleMath">\(m\)</span> be the conductor and multiplicity of <var class="Arg">S</var>, respectively. Let <span class="SimpleMath">\(q\)</span> and <span class="SimpleMath">\(r\)</span> be the quotient and nonpositive remainder of the division of <span class="SimpleMath">\(c\)</span> by <span class="SimpleMath">\(m\)</span>, that is, <span class="SimpleMath">\(c=qm-r\)</ | | |
