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<h1><strong class="pkg">numericalsgps</strong>-- a package for numerical semigroups</h1>
>
/>
<p><b> Manuel Delgado
</b>
<br />Email: <span class="URL"><a java.lang.StringIndexOutOfBoundsException: Index 35 out of bounds for length 4
br /Homepage <span =U"<a ="ttp:/wwwfc.up./cmupmdelgado"http:/wwwfc.ppt//<a<span>
</p><p><b> <br />Homepage: class"">< =h/www.es/"http://..s~pedro<>/java.lang.StringIndexOutOfBoundsException: Range [104, 103) out of bounds for length 104
h><h3java.lang.StringIndexOutOfBoundsException: Index 18 out of bounds for length 18
br >:<spanclass="URL"<href=mailtopedroes"pedro@ugre<>/pan>
<br />Homepage: <span class="URL"><a href="http://www.ugr.es/~pedro">http://www.ugr.es/~java.lang.StringIndexOutOfBoundsException: Index 90 out of bounds for length 0
<p>pb JoséJoã Morais
java.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0
<p><a id="X82A988D47DFAFCFA" name="X82A988D47DFAFCFA"></a></p>
<h3>Acknowledgements</h3>
Centro Servicios de Informá yRedesde Comunicaciones (),Universidadde for providing computingtime Rafael Arredondo installingthis theextrasoftware inalhambraugres Santiago Ferrer in to cluster./java.lang.StringIndexOutOfBoundsException: Index 345 out of bounds for length 345
java.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0
<p>java.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0
<p>The first and second authors warmly thank María Burgos java.lang.StringIndexOutOfBoundsException: Index 59 out of bounds for length 0
<p><strong class="button">Funding</strong></p>
<p>The first author
p> byprojectsMTM2004- MTM2007-,the deAndalucí 343 FEDER ounds<pjava.lang.StringIndexOutOfBoundsException: Index 143 out of bounds for length 143
<p>The third author acknowledges financial support of java.lang.StringIndexOutOfBoundsException: Index 1 out of bounds for length 0
<p>The first author was (partiallyjava.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0
<p>Both maintainers java.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0
<p>java.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0
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<p>The asabbatical ://2018.>
<p>The second author was supported in part by Grant java.lang.StringIndexOutOfBoundsException: Index 55 out of bounds for length 0
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<p><a id="X7982162280BC7A61" name="X7982162280BC7A61"></pThisworkstartedwhen( )theauthor visitedthe of Granada inpartofa year Version . releasedin ) the maintained authors reportssuggestions are coursewelcome useouremail addresses effect<pjava.lang.StringIndexOutOfBoundsException: Index 321 out of bounds for length 321
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<p>If you have predominantly used the functions in the Appendix
<ph3Contentsaid="" ="">/>/>
<div class="contents">
<h3>java.lang.StringIndexOutOfBoundsException: Index 11 out of bounds for length 0
<div class="ContChap"><a href="chap1.html#X7DFB63A97E67C0A1">1 <span class="Heading"> Introduction
Introduction
</span></a>
</div>
<div class="ContChap"><a href="chap2.html#X8324E5D97DC2A801">2 <span class="Heading">
Numerical Semigroups
</span></a>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap2.html#X7E89D7EB7FCC2197">2.1 <span class="Heading">
Generating Numerical Semigroups
</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap2.html#X7D74299B8083E882">2.1-1 NumericalSemigroup</a></span>
spanclass"> >spannocss>nbsp&;</span><a href=chap2html#X86D9D2EE7E1C16C2">2.1-2 NumericalSemigroupBySubAdditiveFunction</a></span>
<span""<r/<class=nocss"&;nbsp<spanahref=".#X799AC8727DB61A99">2.1-3 NumericalSemigroupByAperyList</a></span>
span =ContSS>< /< class=>nbsp&;span< hrefchap2html#X81A7E3527998A74A">2.1-4 NumericalSemigroupBySmallElements</a></span>
<panclass;<span< "html
<span class="ContSS"><br /><span class="<span class="ContSS"><br /><span class="nocss;&;/>< =chap2htmlX86AC8B0E7C11147F">2.1-6 NumericalSemigroupByFundamentalGaps</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap2.html#X7ACD94F478992185">2.1-7 NumericalSemigroupByAffineMap</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap2.html#X87206D597873EAFF">2.1-8 ModularNumericalSemigroup</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap2.html#X879171CD7AC80BB5">2.1-9 ProportionallyModularNumericalSemigroup</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap2.html#X7D8F9D2A8173EF32">2.1-10 NumericalSemigroupByInterval</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap2.html#X7C800FB37D76612F">2.1-11 NumericalSemigroupByOpenInterval</a></span>
</div></div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap2.html#X7EF4254C81ED6665">2.2 <span class="Heading">Some basic tests</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap2.html#X7B1B6B8C82BD7084">2.2-1 IsNumericalSemigroup</a></span>
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<span=ContSS>br/< =nocss>nbsp;;/<href.#java.lang.StringIndexOutOfBoundsException: Range [155, 103) out of bounds for length 155
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class=nocss>nbsp&</< =chap2html
<span class="ContSS"><br /><span class="nocss"<class""<r/<spanclass"">nbsp;nbsp<span<href=chap2#X87B02A9F7AF90CB9">2.2-2 RepresentsSmallElementsOfNumericalSemigroup</a></span>
/></java.lang.StringIndexOutOfBoundsException: Index 12 out of bounds for length 12
/>
<div class="ContChap"><a href="chap3.html#X7A9D13C778697F6C">3 <span class="Heading">
Basic operations withspanclass="ContSS>br/<pan=nocss"&;nbsp<spanahref=".
/<ajava.lang.StringIndexOutOfBoundsException: Index 23 out of bounds for length 23
< class=ContSect"< class"ocline>spanclass"">nbsp<span>a ="hap3htmlX87AF9D4F7FD9E820">3.1 <span class="Heading">
Invariants
</span></a>
</</div>
<div class="ContSSBlock">
<spanclass=ContChap"ahref=chap3html#X7A9D13C778697F6C">3 <span class="Heading">
<span =""< >span class=nocss>nbsp;<span< "htmlX850F430A8284DF9A>.1- <a<span>
<span class="ContSS"><br /><span class="nocss"> /span>/>
span "ContSS>br/<class=nocss"&;nbsp<span< =chap3html#X84A6B16E8113167B">3.1-4 SmallElements</a></span>
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class=nocss"&;nbsp/< "html
<span class="ContSS"><<">br/< class""&;&;/< =chap3htmlX7D2B3AA9823371AE">3.1-7 ElementsUpTo</a></span>
<span class="ContSS"><< class"ContSS"<r/< =nocss&; </>ahrefchap3html#X81A2505E8120F4D7"><code>3.1-8 <span>\</span>[ <span>\</span>]</code></a></span>
spanclassContSS"<r/span ">nbsp;nbsp<span<ahref=chap3html#X80431F487C71D67B">3.1-16 AperyList</a></span>
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<span class="ContSS"><br /><span class="nocss"> </span><a href="chap3.html#X7C21E5417A3894EC">3.1-20 KunzPolytope</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap3.html#X7802096584D32795">3.1-21 CocycleOfNumericalSemigroupWRTElement</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap3.html#X847BAD9480D186C0">3.1-22 FrobeniusNumber</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap3.html#X835C729D7D8B1B36">3.1-23 Conductor</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap3.html#X861DED207A2B5419">3.1-24 PseudoFrobenius</a></span>
<spanclass=ContSS"</>span class=">nbsp;/>a=chap3#X865E2E12804CFCD33125</>/>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap3.html#X8688B1837E4BC079<span="ContSS"< >span class="nocss"> </span><a href="chap3.html#X7E6F5D6F7B0C9635">3.1-14 Difference</a></span>
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<span class="ContSS"><br /><span class="nocss"> <class="ContSS>/<spanclass="nocss> nbsp;/< "chap3.tml#80431F487C71D67B>.- AperyList/>span>
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=""< /< "">n;nbsp;</>< =.XEC438CC7BF539D0>.- FundamentalGaps/><>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap3.html#X803D550C78717A7C">3.1-35 SpecialGaps</a></span>
java.lang.StringIndexOutOfBoundsException: Index 48 out of bounds for length 12
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<div class="ContSSBlock">
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</div></div>
<div>
<div class="ContChap"><a href="chap4.html#X7969F7F27AAF0BF1">4 <span class="Heading">
of
</span></a>
<div class="div class="ContSSBlock
n>
<div class="<span class="ontSS> /<spanclass">nbsp;nbsp<span><a =chap5html#X7F308BCE7A0E9D91"<>52- /<a/pan
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<span class="ContSS"><br /><span class="nocss"> </span><a href="chap4.html#X815C0AF17A371E3E">4.1-3 BettiElements</a></span>
<pan =C"< /<span class="nocss"> </span><a href="chap4.html#X7FC66A1B82E86FAF">4.1-4 IsMinimalRelationOfNumericalSemigroup</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap4.html#X8750A6837EF75CA2">4.1- AsNumericalDuplication</a></span>
<spanclass="</<span="nocss>nbsp;nbsp/a=chap4html>4.1-6 DegreesOfPrimitiveElementsOfNumericalSemigroup</java.lang.StringIndexOutOfBoundsException: Index 168 out of bounds for length 168
<span <div classdiv class=ContSSBlock"
</iv>/iv
<div classclass=""<br /<class"&; </< href=chap3#>322<a<span>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss"> <class"ontSS" /< class="ocss>&;;<span< href=".XF90E7EA43C47.24EliahouSlicesOfNumericalSemigroupa<span>
</</div
<< ""><ahref=chap4.X7969F7F27AAF0BF1">4 <span class="Heading">
</span>
<div class="ContSSBlock Presentations of Numerical Semigroups
<span class="ContSS"><br /><span class="java.lang.StringIndexOutOfBoundsException: Index 43 out of bounds for length 23
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap4.html#X79C010537C838154">4.3-2 IsGeneric</a></span>
<java.lang.StringIndexOutOfBoundsException: Index 12 out of bounds for length 12
</div>
<div class="ContChap"><a href="chap5.html#X8148F05A830EE2D5">5 <span class="Heading">
Constructing semigroups
</span></a>
<ivclass=ContSect>span"tocline"< nocss"&;/< href".#">51<java.lang.StringIndexOutOfBoundsException: Range [126, 125) out of bounds for length 142
<span class="ContSS"><br>span =">nbsp; <span>ahref=chap4.htmlX8750A6837EF75CA2"415<a<java.lang.StringIndexOutOfBoundsException: Range [161, 160) out of bounds for length 161
</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap5.html#X7C94611F7DD9E742">5.1-1 RemoveMinimalGeneratorFromNumericalSemigroup</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap5.html#X865EA8377D632F53">5.1-2 AddSpecialGapOfNumericalSemigroup</a></span>
</div></div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap5.html#X7DC65D547FB274D8">5.2 <span class="Heading">Intersections, sums, quotients, dilatations, numerical duplications and multiples by integers</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap5.html#X875A8D2679153D4B">5.2-1 Intersection</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap5.html#X7F308BCE7A0E9D91"><code>5.2-2 \+</code></a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap5.html#X83CCE63C82F34C25">5.2-3 QuotientOfNumericalSemigroup</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap5.html#X7BE8DD6884DE693F">5.2-4 MultipleOfNumericalSemigroup</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap5.html#X7F395079839BBE9D">5.2-5 NumericalDuplication</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap5.html#X8176CEB4829084B4">5.2-6 AsNumericalDuplication</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap5.html#X7DCEC67A82130CD8">5.2-7 InductiveNumericalSemigroup</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap5.html#X81632C597E3E3DFE">5.2-8 DilatationOfNumericalSemigroup</a></span>
</div></div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap5.html#X867D9A9A87CEB869">5.3 <span class="Heading">
Constructing the set of all numerical semigroups containing a given numerical semigroup
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><div"ContSect>span ="ocline"< ">n;/>ahref".#">.< classH>,java.lang.StringIndexOutOfBoundsException: Range [162, 161) out of bounds for length 246
<div<div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap5.html#X8634CFB1848430DCspan class""< >span class="nocss"> </span><a href="chap5.html#X7F308BCE7A0E9D91"><code>5.2-2 \+</code></a></span>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss"> </span>spanclass=""><br /span="ocss"nbsp; <>< =".html#X7BE8DD6884DE693F">.- MultipleOfNumericalSemigroup/><span>
<class">br/<span=n"&; </span<ahref"html#"54-2NumericalSemigroupsWithFrobeniusNumberAndMultiplicityspan>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap5.html#X87369D567AA6DBA0">5.4-3 NumericalSemigroupsWithFrobeniusNumber</a></span> 4-4</a<java.lang.StringIndexOutOfBoundsException: Index 162 out of bounds for length 162
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</panjava.lang.StringIndexOutOfBoundsException: Index 7 out of bounds for length 7
<div class="ContSSBlock">
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<span class="ContSS"><br /><span class="nocss"> </span><a href="chap5.html#X7DA1FA7780684019">5.5-3 NumericalSemigroupsWithMaxPrimitivePCspan>
/<div>
<div class="ContSect"><span class="tocline"><span class="<span class="Heading">
Constructing the set of numerical semigroups with genus g
</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap5.html#X86970F6A868DEA95">5.6-1 NumericalSemigroupsWithGenus</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap5.html#X7B4F3B5E841E3853">5.6-2 NumericalSemigroupsWithGenusPC</a></span>
</div></div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap5.html#X8265233586477CC7">5.7 <span class="Heading">
Constructing the set of numerical semigroups with a given set of pseudo-Frobenius numbers
</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap5.html#X874B252180BD7EB4">5.7-1 ForcedIntegersForPseudoFrobenius</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap5.html#X87AAFFF9814E9BD2">5.7-2 SimpleForcedIntegersForPseudoFrobenius</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap5.html#X7D6775A57B800892">5.7-3 NumericalSemigroupsWithPseudoFrobeniusNumbers</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap5.html#X862DBFA379D52E2C">5.7-4 ANumericalSemigroupWithPseudoFrobeniusNumbers</a></span>
</div></div>
</div>
<div class="ContChap"><a href="chap6.html#X83C597EC7FAA1C0F">6 <span class="Heading">
Irreducible numerical semigroups
</span></a>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap6.html#X83C597EC7FAA1C0F">6.1 <span class="Heading">
Irreducible numerical semigroups
</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap6.html#X83E8CC8F862D1FC0">6.1-1 IsIrreducible</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap6.html#X7C381E277917B0ED">6.1-2 IsSymmetric</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap6.html#X7EA0D85085C4B607">6.1-3 IsPseudoSymmetric</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap6.html#X7C8AB03F7E0B71F0">6.1-4 AnIrreducibleNumericalSemigroupWithFrobeniusNumber</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap6.html#X78345A267ADEFBAB">6.1-5 IrreducibleNumericalSemigroupsWithFrobeniusNumber</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap6.html#X87C2738C7AA109DC">6.1-6 IrreducibleNumericalSemigroupsWithFrobeniusNumberAndMultiplicity</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap6.html#X8753F78D7FD732E2">6.1-7 DecomposeIntoIrreducibles</a></span>
</div></div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap6.html#X7D3FD9C8786B5D72">6.2 <span class="Heading">
Complete intersection numerical semigroups
</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap6.html#X848FCB49851D19B8">6.2-1 AsGluingOfNumericalSemigroups</a></span>
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Decomposition into irreducibles
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Patterns for ideals
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Saturated numerical semigroups
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Factorizations in Numerical Semigroups
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Generating functions or Hilbert series
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Affine semigroups
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