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<h1><strong class="pkg">numericalsgps</strong>-- a package java.lang.StringIndexOutOfBoundsException: Index 62 out of bounds for length 7
<p> Version 1.4.0</p>
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<p><b> Manuel Delgado
< class=chlinkprevnexttop>&bsp<href=chap0.">Top Book]<a>nbsp;<ahref=".#">Contents]</a> <a href="chap1.html">[Next Chapter]</a> </div>
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<br />Email: <span class="URL"><a href="mailto:mdelgado@fc.<>a" java.lang.StringIndexOutOfBoundsException: Range [34, 33) out of bounds for length 62
<br />Homepage: <<p> Version 1.4.0</p
<<divjava.lang.StringIndexOutOfBoundsException: Index 6 out of bounds for length 6
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<br />Email: <span class="URL"><a href="mailto:pedro@ugr.es">pedro<>:class"RL>ahref="/.fcuppt/>/www.fcu.cmupmdelgado</>/
<span =URL>ahref"ttp:/wwwugr.es/pedro">:/wwugr./pedro</<span>
</p><p><b> José João Morais
</b>
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<p><a id="X81488B807F2A1CF1
<3Copyright/>
<p>© 2005--2015 Centro de Matemática da Universidade<br/Email span class">a href":@ugr.es>@ugr.s<a><sjava.lang.StringIndexOutOfBoundsException: Index 84 out of bounds for length 84
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<Acknowledgements<h3>
<p>
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<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>
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<span class="ContSS"><br /><span class="nocss"> </span><a href="chap2.html#X7D74299B8083E882">2.1-1 NumericalSemigroup</a></span>
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<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>
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<span class="ContSS"><br /><span class="nocss"> </span><a href="chap3.html#X82B1868F7A780B49">3.1-29 IsOrdinary</a></span>
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<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap4.html#X795E7F5682A6C8B3">4.2 <span class="Heading">Binomial ideals associated to numerical semigroups</span></a>
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<span class="ContSS"><br /><span class="nocss"> </span><a href="chap4.html#X7E6BBAA7803DE7F3">4.2-1 BinomialIdealOfNumericalSemigroup</a></span>
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<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap4.html#X7D7EA20F818A5994">4.3 <span class="Heading">Uniquely Presented Numerical Semigroups</span></a>
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<span class="ContSS"><br /><span class="nocss"> </span><a href="chap4.html#X7C6F554486274CAE">4.3-1 IsUniquelyPresented</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap4.html#X79C010537C838154">4.3-2 IsGeneric</a></span>
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<div class="ContChap"><a href="chap5.html#X8148F05A830EE2D5">5 <span class="Heading">
Constructing numerical semigroups from others
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<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap5.html#X782F3AB97ACF84B8">5.1 <span class="Heading">
Adding and removing elements of a numerical semigroup
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<span class="ContSS"><br /><span class="nocss"> </span><a href="chap5.html#X7C94611F7DD9E742">5.1-1 RemoveMinimalGeneratorFromNumericalSemigroup</a></span>
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Constructing the set of all numerical semigroups containing a given numerical semigroup
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Constructing the set of numerical semigroups with a given set of pseudo-Frobenius numbers
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<span class="ContSS"><br /><span class="nocss"> </span><a href="chap6.html<spanclass=ContSS"><br /><span class="nocss"> </span><a href="chap7.html#X79DFDCA27D3268FD"><code>7.1-18 <span>\</span class="ContSS"><br /><span class="nocss"> </span><a href="chap7.html#X8341AE847D005E9F"><code>7.1-19 \{ \}</code
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<span class="ContSS"><br /><span class="nocss"> </span><a href="chap6.html#X78345A267ADEFBAB">6.spanclass= >span""&;&<span>a =chap7java.lang.StringIndexOutOfBoundsException: Range [86, 85) out of bounds for length 158
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap6.html#X87C2738C7AA109DC">6.1-6 IrreducibleNumericalSemigroupsWithFrobeniusNumberAndMultiplicity</<pan"> /<spanclass=">nbsp&bsp<span><href=chap7X8321A10885D2DEF8>.- Differencea<
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap6.html#X8753F78D7FD732E2">6.1-7 DecomposeIntoIrreducibles</a></span>
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<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap6.span class="ContSS"><br /><span class="nocss"> </span><a href="chap7.html#X7B34033979009F64>/spanjava.lang.StringIndexOutOfBoundsException: Index 135 out of bounds for length 135
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>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap6.html#X7A0DF10F85F32194">6.2-2 IsCompleteIntersection</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap6.html#X86350BCE7D047599">6.2-3 CompleteIntersectionNumericalSemigroupsWithFrobeniusNumber</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap6.html#X7CD2A77778432E7B">6.2-4 IsFree</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap6.html#X86B4BA6A79F734A8">6.2-5 FreeNumericalSemigroupsWithFrobeniusNumber</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap6.html#X830D0E0F7B8C6284">6.2-6 IsTelescopic</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap6.html#X84475353846384E8">6.2-7 TelescopicNumericalSemigroupsWithFrobeniusNumber</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap6.html#X7A1C2C737BC1C4CE">6.2-8 IsUniversallyFree</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap6.html#X847CD0EF8452F771">6.2-9 IsNumericalSemigroupAssociatedIrreduciblePlanarCurveSingularity</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap6.html#X8784D11578C912F2">6.2-10 NumericalSemigroupsPlanarSingularityWithFrobeniusNumber</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap6.html#X80CAA1FA7F6FF4FD">6.2-11 IsAperySetGammaRectangular</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap6.html#X7E6E262C7C421635">6.2-12 IsAperySetBetaRectangular</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap6.html#X86F52FB67F76D2CB">6.2-13 IsAperySetAlphaRectangular</a></span>
</div></div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap6.html#X7998FF857F70C9A2">6.3 <span class="Heading">
Almost-symmetric numerical semigroups
</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap6.html#X7A81F31479DB5DF2">6.3-1 AlmostSymmetricNumericalSemigroupsFromIrreducible</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap6.html#X8788F6597DBC6D98">6.3-2 AlmostSymmetricNumericalSemigroupsFromIrreducibleAndGivenType</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap6.html#X84C44C7A7D9270BB">6.3-3 IsAlmostSymmetric</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap6.html#X7B0DF2FE7D00A9E0">6.3-4 AlmostSymmetricNumericalSemigroupsWithFrobeniusNumber</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap6.html#X85C4DA6E82E726D2">6.3-5 AlmostSymmetricNumericalSemigroupsWithFrobeniusNumberAndType</a></span>
</div></div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap6.html#X7FDC79A285EE016B">6.4 <span class="Heading">
Several approaches generalizing the concept of symmetry
</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap6.html#X8221EC44802E5158">6.4-1 IsGeneralizedGorenstein</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap6.html#X866E48B47D66CFF2">6.4-2 IsNearlyGorenstein</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap6.html#X78049FC380A0006E">6.4-3 NearlyGorensteinVectors</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap6.html#X83F13D6482F021B2">6.4-4 IsGeneralizedAlmostSymmetric</a></span>
</div></div>
</div>
<div class="ContChap"><a href="chap7.html#X83C2F0CF825B3869">7 <span class="Heading">
Ideals of numerical semigroups
</span></a>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap7.html#X84B6453A8015B40B">7.1 <span class="Heading">
Definitions and basic operations
</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap7.html#X78E5F44E81485C17">7.1-1 IdealOfNumericalSemigroup</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap7.html#X85BD6FAD7EA3B5DD">7.1-2 IsIdealOfNumericalSemigroup</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap7.html#X85144E0F791038AE">7.1-3 MinimalGenerators</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap7.html#X7A842A4385B73C63">7.1-4 Generators</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap7.html#X81E445518529C175">7.1-5 AmbientNumericalSemigroupOfIdeal</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap7.html#X7B0343BF794AC7EA">7.1-6 IsIntegral</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap7.html#X80233A6F80CA0615">7.1-7 IsComplementOfIntegralIdeal</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap7.html#X8774724085D3371D">7.1-8 IdealByDivisorClosedSet</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap7.html#X7811E92487110941">7.1-9 SmallElements</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap7.html#X7EDDC78883A98A6E">7.1-10 Conductor</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap7.html#X7A8AF91C7D1F1B4E">7.1-11 FrobeniusNumber</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap7.html#X805149CA847F6461">7.1-12 PseudoFrobenius</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap7.html#X7D4C7C997EEAADF7">7.1-13 Type</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a spanclassContSS>br /< class=nocss&bsp <>a=".htmlX82C2329380B9882D>.3-RatliffRushClosurea<span>
<spanclass=ContSS>br /span ""&&<span>a=chap7."7-15</a><span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap7.html#X83D0996D811A35C6">7.1-16 span class="ContSS"><br /><span class="nocss"> </span><a href="chap7.html#X8344B30D7EDE3B04">7.3-10 MultiplicitySequence
<span class="ContSS"><br /><span class="nocss"> </span>< href="chap8.html#X7CC73F15831B06CE">8.2-9 ArfSpecialGaps</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap7.html#X79DFDCA27D3268FD"><code>7.1-18 <span>\</span>[ <span>\</span>]</code></a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap7.html#X8341AE847D005E9F"><code>7.1-19 \{ \}</code></a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap7.html#X7A55BD4D82580537">7.1-20 Iterator</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap7.html#X7B39610D7AD5A654">7.1-21 SumIdealsOfNumericalSemigroup</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap7.html#X857FE5C57EE98F5E">7.1-22 MultipleOfIdealOfNumericalSemigroup</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap7.html#X78743CE2845B5860">7.1-23 SubtractIdealsOfNumericalSemigroup</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap7.html#X8321A10885D2DEF8">7.1-24 Difference</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap7.html#X803921F97BEDCA88">7.1-25 TranslationOfIdealOfNumericalSemigroup</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap7.html#X7CD66453842CD0AD">7.1-26 Union</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap7.html#X7B34033979009F64">7.1-27 Intersection</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap7.html#X7D77F1BA7F22DA70">7.1-28 MaximalIdeal</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap7.html#X85975C3C86C2BC53">7.1-29 CanonicalIdeal</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap7.html#X7D15FA4C843A13B7">7.1-30 IsCanonicalIdeal</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap7.html#X829C9685798BB553">7.1-31 IsAlmostCanonicalIdeal</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap7.html#X811B096B87636B8E">7.1-32 TraceIdeal</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap7.html#X7BB2A1B28139AA7E">7.1-33 TypeSequence</a></span>
</div></div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap7.html#X7F09B9A085E226EF">7.2 <span class="Heading">
Decomposition into irreducibles
</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap7.html#X7B83DEAC866B65E8">7.2-1 IrreducibleZComponents</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap7.html#X83E064C684FA534C">7.2-2 DecomposeIntegralIdealIntoIrreducibles</a></span>
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<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap7.html#X81CD9B12807EEA85">7.3 <span class="Heading">
Blow ups and closures
</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap7.html#X82156F18807B00BF">7.3-1 HilbertFunctionOfIdealOfNumericalSemigroup</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap7.html#X81F1F3EB868D2117">7.3-2 HilbertFunction</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap7.html#X79A1A22D8615BF78">7.3-3 BlowUp</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap7.html#X7FAABCBF8299B12F">7.3-4 ReductionNumber</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap7.html#X7BFC52B7804542F5">7.3-5 BlowUp</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap7.html#X8799F0347FF0D510">7.3-6 LipmanSemigroup</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap7.html#X7D6F643687DF8724">7.3-7 RatliffRushNumber</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap7.html#X82C2329380B9882D">7.3-8 RatliffRushClosure</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap7.html#X79494A587A549E15">7.3-9 AsymptoticRatliffRushNumber</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap7.html#X8344B30D7EDE3B04">7.3-10 MultiplicitySequence</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap7.html#X87AC917578976B1E">7.3-11 MicroInvariants</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap7.html#X805C984685EBC65C">7.3-12 AperyList</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap7.html#X82D2784B813C67D8">7.3-13 AperyList</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap7.html#X8244CCAE7D957F46">7.3-14 AperyTable</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap7.html#X7A16238D7EDB2AB3">7.3-15 StarClosureOfIdealOfNumericalSemigroup</a></span>
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<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap7.html#X78F124CC82E7B585">7.4 <span class="Heading">
Patterns for ideals
</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap7.html#X865042FD7EBD15EE">7.4-1 IsAdmissiblePattern</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap7.html#X7ED8306681407D0F">7.4-2 IsStronglyAdmissiblePattern</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap7.html#X799542C57E4E0D5E">7.4-3 AsIdealOfNumericalSemigroup</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap7.html#X7F13F7CB7FBCF006">7.4-4 BoundForConductorOfImageOfPattern</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap7.html#X7F4E597278AF31C8">7.4-5 ApplyPatternToIdeal</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap7.html#X7CFDFF6D7B9B595B">7.4-6 ApplyPatternToNumericalSemigroup</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap7.html#X7F9232047F85C4D8">7.4-7 IsAdmittedPatternByIdeal</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap7.html#X827BB22083390CB9">7.4-8 IsAdmittedPatternByNumericalSemigroup</a></span>
</div></div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap7.html#X79C6CE8D7EF1632D">7.5 <span class="Heading">Graded associated ring of numerical semigroup</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap7.html#X7876199778D6B320">7.5-1 IsGradedAssociatedRingNumericalSemigroupCM</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap7.html#X782D557583CEDD04">7.5-2 IsGradedAssociatedRingNumericalSemigroupBuchsbaum</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap7.html#X78E57B9982F6E1DC">7.5-3 TorsionOfAssociatedGradedRingNumericalSemigroup</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap7.html#X7E16B6947BE375B2">7.5-4 BuchsbaumNumberOfAssociatedGradedRingNumericalSemigroup</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap7.html#X7A5752C0836370FA">7.5-5 IsGradedAssociatedRingNumericalSemigroupGorenstein</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap7.html#X7800C5D68641E2B7">7.5-6 IsGradedAssociatedRingNumericalSemigroupCI</a></span>
</div></div>
</div>
<div class="ContChap"><a href="chap8.html#X7D2E70FC82D979D3">8 <span class="Heading">
Numerical semigroups with maximal embedding dimension
</span></a>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap8.html#X7D2E70FC82D979D3">8.1 <span class="Heading">
Numerical semigroups with maximal embedding dimension
</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap8.html#X783A0BE786C6BBBE">8.1-1 IsMED</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap8.html#X7A6379A382D1FC20<pan classContSS> /><span class="nocss"> </span><a href="chap9.html#X7F4CBFF17BBB37DE">9.6-5 NumericalSemigroupByTauSequence</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap8.html#java.lang.StringIndexOutOfBoundsException: Index 99 out of bounds for length 70
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<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap8.html#X82E40EFD83A4A186">8.2 <span class="Heading">
semigroups with the Arf property and Arf losures
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</div>
<div class="ContChap"><a href="chap9.html#X7B6F914879CD505F">9 <span class="Heading">
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<div class="span class="ContSS"><br /><span class="nocss"> </span><a href="chap8.html#X848FD3FA7DB2DD4C">8.1-3 MinimalMEDGeneratingSystemOfMEDNumericalSemigroup</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap9.html#X8429AECF78EE7EAB">9.1-1 FactorizationsIntegerWRTList</a></span>
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<span class="ContSS"><br /><span class="nocss"> </span><a href="chap9.html#X801DA4247A0BEBDA">9.1-8 DenumerantFunction</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap9.html#X7D91A9377DAFAE35">9.1-9 DenumerantIdeal</a></span>
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<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap9.html#X846FEE457D4EC03D">9.2 <span class="Heading">
basedonlengths
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<span class="ContSSspan "ontSS></<class="ocss>nbsp; </span><a href="chap10.html#X7FFF949A7BEEA912">10.2-1 SemigroupOfValuesOfPlaneCurveWithSinglePlaceAtInfinity</a></span>
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<span class="ContSS"><br /><span class="nocss"> </span><a href="chap9.html#X79C953B5846F7057">9.2-5 DeltaSet</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap9.html#X7DB8BA5B7D6F81CB">9.2-6 DeltaSet</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap9.html#X7A08CF05821DD2FC">9.2-7 DeltaSetPeriodicityBoundForNumericalSemigroup</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap9.html#X8123FC0E83ADEE45">9.2-8 DeltaSetPeriodicityStartForNumericalSemigroup</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap9.html#X80B5DF908246BEB1">9.2-9 DeltaSetListUpToElementWRTNumericalSemigroup</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap9.html#X85C6973E81583E8B">9.2-10 DeltaSetUnionUpToElementWRTNumericalSemigroup</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap9.html#X83B06062784E0FD9">9.2-11 DeltaSet</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap9.html#X7AEFE27E87F51114">9.2-12 MaximumDegree</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap9.">9.2-13 sAdditiveNumericalSemigroup</>/span>
<span class=ContSS"><br /><span class="nocss"> </span><a href="chap9.html#X790308B07AB1A5C8">9.2-14 MaximalDenumerant</a></span>
span class"><br ><span class="nocss"> </span><a href="chap9.html#X7DFC4ED0827761C1">9.2-15 MaximalDenumerantOfSetOfFactorizations</a></span>
< class="ContSS">br/><spanclass=nocss" &bsp;/<href".tmlX811E5FFB83CCA4CE>9216 MaximalDenumerant</a</
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Invariants based on distances
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</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap9.html#X86F9D7868100F6F9">9.3-1 CatenaryDegree</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap9.html#X7DDB40BB84FF0042">9.3-2 AdjacentCatenaryDegreeOfSetOfFactorizations</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap9.html#X86E0CAD28655839C">9.3-3 EqualCatenaryDegreeOfSetOfFactorizations</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap9.html#X845D850F7812E176">9.3-4 MonotoneCatenaryDegreeOfSetOfFactorizations</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap9.html#X797147AA796D1AFE">9.3-5 CatenaryDegree</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap9.html#X80D478418403E7CB">9.3-6 TameDegree</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap9.html#X785B83F17BEEA894">9.3-7 CatenaryDegree</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap9.html#X863E3EF986764267">9.3-8 DegreesOffEqualPrimitiveElementsOfNumericalSemigroup</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap9.html#X780E2C737FA8B2A9">9.3-9 EqualCatenaryDegreeOfNumericalSemigroup</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap9.html#X7E19683D7ADDE890">9.3-10 DegreesOfMonotonePrimitiveElementsOfNumericalSemigroup</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap9.html#X7E0458187956C395">9.3-11 MonotoneCatenaryDegreeOfNumericalSemigroup</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap9.html#X809D97A179765EE6">9.3-12 TameDegree</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap9.html#X7F7619BD79009B64">9.3-13 TameDegree</a></span>
</div></div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap9.html#X78EBC6A57B8167E6">9.4 <span class="Heading">
Primality
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<div class="ContSect"><span class="tocline"><span classspan class="ContSS"><br /><span class="nocss"> </span><a href="chap11.html#X7A1CE5A98425CEA1">11.1-22 BasisOfGroupGivenByEquations</a></span>
NumericalSemigroups
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</span>
<div class="ContSSBlock">
<span class="ContSS"><div class="ContSSBlock
java.lang.StringIndexOutOfBoundsException: Range [6, 5) out of bounds for length 172
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap9.html#X857CC7FF85C05318">9.5-3 HomogeneousBettiElementsOfNumericalSemigroup</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap9.html#X7DFFCAC87B3B632B">9.5-4 HomogeneousCatenaryDegreeOfNumericalSemigroup</a></span>
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<div class="ContSect"><span class="tocline"><span />
Divisors, posets
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<span class="ContSS"><br /><span class="nocss"> </span><a href="chap9.html#X853930E97F7F8A43">9.6-1 span class="ContSS"><br /><span class="nocss"> </span><a href="chap11.html#X7EE005267DEBC1DE">11.3-3 GeneratorsOfKernelCongruence</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap9.html#X7DF6825185C619AC">.62 MoebiusFunction<a<span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap9.html#span class="ContSS"><br /><span class="nocss"> </span><a href="chap11.html#X7C3546477E07A1EA<>/span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap9.pan =ContSS"></span="">nbsp&;/span>ah=chap11html#X80A7BD7478D8A94A">11.3-6 MinimalPresentation</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap9.html#X7F4CBFF17BBB37DE">9.6-5 NumericalSemigroupByTauSequence</a></span>
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<div class="ContSect"><span class="tocline"><span class="nocss"> </span><spanclass=""> >span =nocss"&&;</pan>a href=chap11.#X81CA53DA8216DC82">.- /a>/
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<span class="ContSS"><br /><span class="nocss"> </span><a href="chap9.html#X8400FB5D81EFB5FE">9.8-2 IsMpure</a></span>
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<span class="ContSS"><br /><span class="nocss"> </span><a href="chap9.html#X8630DEF77A350D76">9.8-4 IsSuperSymmetricNumericalSemigroup</a></span>
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<div class="ContSect"><span/span><a href="chap9.html#X856B689185C1F5D9">9.5-1 BelongsToHomogenizationOfNumericalSemigroup</a></span>
Generating functions or Hilbert series
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<span class="ContSS<span class="ContSS"><br /><span class="nocss"> </span><a href="chap11.html#X80742F2F7DECDB4C">11.4-6 CatenaryDegree</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap10.html#X7F59E1167C1EE578">10.1-2 IsNumericalSemigroupPolynomial</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap10.html#X855497F77D13436F">10.1-3 NumericalSemigroupFromNumericalSemigroupPolynomial</a></span>
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Semigroup of values of algebraic curves
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<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap10.html#X7FFF949A7BEEA912">10.2-1 SemigroupOfValuesOfPlaneCurveWithSinglePlaceAtInfinity</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap10.html#X834D6B1A7C421B9F">10.2-2 IsDeltaSequence</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap10.html#X824ABFD680A34495">10.2-3 DeltaSequencesWithFrobeniusNumber</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap10.html#X87B819B886CA5A5C">10.2-4 CurveAssociatedToDeltaSequence</a></span>
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<span class="ContSS"><br /><span class=span class=""br/<class="nocss"> </span><a href="chap12.html#X79E86DEE79281BF2">12.1-1 IsGoodSemigroup</a></span>
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Semigroups and Legendrian curves
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Affine semigroups
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Defining affine semigroups
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< class">br ><class=">nbsp&bsp;/>< href=".X7846AD1081C14EF1">111-3AffineSemigroupByInequalities/>/span>
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<span class="ContSS"><br /><span class="nocss"> </span><a href="chap11.html#X83F6DDB787E07771">11.1-5 AffineSemigroupByGaps</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap11.html#X7A3648D67CF81370">11.1-6 FiniteComplementIdealExtension</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap11.html#X8361194C86AE807B">11.1-7 Gaps</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap11.html#X867B27BD81104BEE">11.1-8 Genus</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap11.html#X80C3CD2082CE02F7">11.1-9 PseudoFrobenius</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap11.html#X82D42FCE81F20277">11.1-10 SpecialGaps</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap11.html#X84FDF85D7CDEDF3E">11.1-11 Generators</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap11.html#X7ED1549486C251CA">11.1-12 MinimalGenerators</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap11.html#X80516BCC78FDD45D">11java.lang.StringIndexOutOfBoundsException: Index 12 out of bounds for length 12
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap11.html#X7B78E02F7C50583F">11.1-14 AddSpecialGapOfAffineSemigroup</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap11.html#X844806D97B4781B5">11.1-15 AsAffineSemigroup</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap11.html#X7A2902207BAA3936">11.1-16 IsAffineSemigroup</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap11.html#X851788D781A13C50">11.1-17 BelongsToAffineSemigroup</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap11.html#X8607B621833FAECB">11.1-18 IsFull</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap11.html#X7D4D017A79AD98E2">11.1-19 java.lang.StringIndexOutOfBoundsException: Index 135 out of bounds for length 12
<span class="ContSS"><br /><span class="nocss"> </span><a href goodsemigroups
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Gluings of affine semigroups
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<span class="ContSS"><br /><span class="nocss"> </span><a href="chap11.html#X78B04C198258D3F8">11.3-2 PrimitiveRelationsOfKernelCongruence</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap11.html#X7EE005267DEBC1DE">11.3-3 GeneratorsOfKernelCongruencespan "ontSS">>class"ocss nbsp;/span>ahref=".htmlX842F3CE07E893949"125-6 SmallElements>/span
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap11.html#X7AD2271E84F705D3">11.3-4 CanonicalBasisOfKernelCongruence</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap11.html#X7C3546477E07A1EA">11.3-5 GraverBasis</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap11.html#X80A7BD7478D8A94A">11.3-6 MinimalPresentation</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap11.html#X86BCBD32781EBC2D">11.3-7 BettiElements</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap11.html#X7C1B355F83A55285">11.3-8 ShadedSetOfElementInAffineSemigroup</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap11.html#X81CA53DA8216DC82">11.3-9 IsGeneric</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap11.html#X79EC6F7583B0CBDD">11.3-10 IsUniquelyPresented</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap11.html#X7DCAFC5F7F74F3CB">11.3-11 DegreesOfPrimitiveElementsOfAffineSemigroup</a></span>
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<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap11.html#X80A934B0826E21A6">11.4 <span class="Heading">
Factorizations in affine semigroups
</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap11.html#X8780C7E5830B9AE2">11.4-1 FactorizationsVectorWRTList</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap11.html#X820A0D06857C4EF5">11.4-2 Factorizations</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap11.html#X7F394FA67BE5151B">11.4-3 Elasticity</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap11.html#X819CDBAA84DB7E83">11.4-4 Elasticity</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap11.html#X839549448300AD26">11.4-5 DeltaSet</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap11.html#X80742F2F7DECDB4C">11.4-6 CatenaryDegree</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap11.html#X7EADD306875FCBE6">11.4-7 EqualCatenaryDegreeOfAffineSemigroup</a></span
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap11.html#X84FE571A7E9E1AE9">11.4-8 HomogeneousCatenaryDegreeOfAffineSemigroupUsingexternal packages
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