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<div class="chlinktop"><span class="chlink1">Goto Chapter: </span><a href="chap0_mj.html">Top</a>  <a href="chap1_mj.html">1</a>  <a href="chap2_mj.html">2</a>  <a href="chap3_mj.html">3</a>  <a href="chap4_mj.html">4</a>  <a href="chap5_mj.html">5</a>  <a href="chap6_mj.html">6</a>  <a href="chap7_mj.html">7</a>  <a href="chap8_mj.html">8</a>  <a href="chap9_mj.html">9</a>  <a href="chap10_mj.html">10</a>  <a href="chap11_mj.html">11</a>  <a href="chap12_mj.html">12</a>  <a href="chap13_mj.html">13</a>  <a href="chap14_mj.html">14</a>  <a href="chapA_mj.html">A</a>  <a href="chapB_mj.html">B</a>  <a href="chapC_mj.html">C</a>  <a href="chapBib_mj.html">Bib</a>  <a href="chapInd_mj.html">Ind</a>  </div>

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<h3>Index</h3>

<code class="func">*</code>, for multiple of ideal of affine semigroup  <a href="chap11_mj.html#X7D056A0C7F868209">11.5-9</a>  <br />
    for multiple of ideal of numerical semigroup  <a href="chap7_mj.html#X857FE5C57EE98F5E">7.1-22</a>  <br />
<code class="func">+</code>, for defining ideal of affine semigroup  <a href="chap11_mj.html#X85775D4E7B9C7DAB">11.5-1</a>  <br />
    for defining ideal of numerical semigroup  <a href="chap7_mj.html#X78E5F44E81485C17">7.1-1</a>  <br />
    for ideals of affine semigroup  <a href="chap11_mj.html#X83A4392281981911">11.5-8</a>  <br />
    for ideals of numerical semigroup  <a href="chap7_mj.html#X7B39610D7AD5A654">7.1-21</a>  <br />
    translation of ideal of affine semigroup  <a href="chap11_mj.html#X788264A27ACD6AB5">11.5-10</a>  <br />
    translation of ideal of numerical semigroup  <a href="chap7_mj.html#X803921F97BEDCA88">7.1-25</a>  <br />
<code class="func">-</code>, for ideals of numerical semigroup  <a href="chap7_mj.html#X78743CE2845B5860">7.1-23</a>  <br />
<code class="func">\+</code>, for numerical semigroups  <a href="chap5_mj.html#X7F308BCE7A0E9D91">5.2-2</a>  <br />
<code class="func">\/</code>, quotient of numerical semigroup  <a href="chap5_mj.html#X83CCE63C82F34C25">5.2-3</a>  <br />
<code class="func"><span>\</span>[ <span>\</span>]</code>, for ideals of numerical semigroups  <a href="chap7_mj.html#X79DFDCA27D3268FD">7.1-18</a>  <br />
    for numerical semigroups  <a href="chap3_mj.html#X81A2505E8120F4D7">3.1-8</a>  <br />
<code class="func">\in</code>, membership for good ideal  <a href="chap12_mj.html#X797999937E4E1E2B">12.5-5</a>  <br />
    membership for good semigroup  <a href="chap12_mj.html#X79EBBF6D7A2C9A12">12.2-1</a>  <br />
    membership test for numerical semigroup  <a href="chap2_mj.html#X864C2D8E80DD6D16">2.2-7</a>  <br />
    membership test in affine semigroup  <a href="chap11_mj.html#X851788D781A13C50">11.1-17</a>  <br />
    membership test in ideal of affine semigroup  <a href="chap11_mj.html#X7F00912C853AA83D">11.5-7</a>  <br />
    membership test in ideal of numerical semigroup  <a href="chap7_mj.html#X87508E7A7CFB0B20">7.1-15</a>  <br />
<code class="func">\{ \}</code>, for ideals of numerical semigroups  <a href="chap7_mj.html#X8341AE847D005E9F">7.1-19</a>  <br />
    for numerical semigroups  <a href="chap3_mj.html#X7A34F16F8112C2B5">3.1-9</a>  <br />
<code class="func">AbsoluteIrreduciblesOfGoodSemigroup</code>  <a href="chap12_mj.html#X7DC7A4B57BC2E55C">12.5-8</a>  <br />
<code class="func">AddSpecialGapOfAffineSemigroup</code>  <a href="chap11_mj.html#X7B78E02F7C50583F">11.1-14</a>  <br />
<code class="func">AddSpecialGapOfNumericalSemigroup</code>  <a href="chap5_mj.html#X865EA8377D632F53">5.1-2</a>  <br />
<code class="func">AdjacentCatenaryDegreeOfSetOfFactorizations</code>  <a href="chap9_mj.html#X7DDB40BB84FF0042">9.3-2</a>  <br />
<code class="func">Adjustment</code>  <a href="chap9_mj.html#X87F633D98003DE52">9.2-17</a>  <br />
<code class="func">AdjustmentOfNumericalSemigroup</code>  <a href="chap9_mj.html#X87F633D98003DE52">9.2-17</a>  <br />
<code class="func">AffineSemigroup</code>, by equations  <a href="chap11_mj.html#X855C8667830AEDDC">11.1-2</a>  <br />
    by gaps  <a href="chap11_mj.html#X83F6DDB787E07771">11.1-5</a>  <br />
    by generators  <a href="chap11_mj.html#X7D7B03E17C8DBEA2">11.1-1</a>  <br />
    by inequalities  <a href="chap11_mj.html#X7846AD1081C14EF1">11.1-3</a>  <br />
    by pminequality  <a href="chap11_mj.html#X7CC110D4798AAD99">11.1-4</a>  <br />
<code class="func">AffineSemigroupByEquations</code>  <a href="chap11_mj.html#X855C8667830AEDDC">11.1-2</a>  <br />
<code class="func">AffineSemigroupByGaps</code>  <a href="chap11_mj.html#X83F6DDB787E07771">11.1-5</a>  <br />
<code class="func">AffineSemigroupByGenerators</code>  <a href="chap11_mj.html#X7D7B03E17C8DBEA2">11.1-1</a>  <br />
<code class="func">AffineSemigroupByInequalities</code>  <a href="chap11_mj.html#X7846AD1081C14EF1">11.1-3</a>  <br />
<code class="func">AffineSemigroupByPMInequality</code>  <a href="chap11_mj.html#X7CC110D4798AAD99">11.1-4</a>  <br />
<code class="func">AllMinimalRelationsOfNumericalSemigroup</code>  <a href="chap4_mj.html#X8750A6837EF75CA2">4.1-5</a>  <br />
<code class="func">AlmostSymmetricNumericalSemigroupsFromIrreducible</code>  <a href="chap6_mj.html#X7A81F31479DB5DF2">6.3-1</a>  <br />
<code class="func">AlmostSymmetricNumericalSemigroupsFromIrreducibleAndGivenType</code>  <a href="chap6_mj.html#X8788F6597DBC6D98">6.3-2</a>  <br />
<code class="func">AlmostSymmetricNumericalSemigroupsWithFrobeniusNumber</code>  <a href="chap6_mj.html#X7B0DF2FE7D00A9E0">6.3-4</a>  <br />
<code class="func">AlmostSymmetricNumericalSemigroupsWithFrobeniusNumberAndType</code>  <a href="chap6_mj.html#X85C4DA6E82E726D2">6.3-5</a>  <br />
<code class="func">AmalgamationOfNumericalSemigroups</code>  <a href="chap12_mj.html#X873FE7B37A747247">12.1-3</a>  <br />
<code class="func">AmbientAffineSemigroupOfIdeal</code>  <a href="chap11_mj.html#X82D18D7B877582B0">11.5-5</a>  <br />
<code class="func">AmbientGoodSemigroupOfGoodIdeal</code>  <a href="chap12_mj.html#X82D384397EE5CAC4">12.5-3</a>  <br />
<code class="func">AmbientNumericalSemigroupOfIdeal</code>  <a href="chap7_mj.html#X81E445518529C175">7.1-5</a>  <br />
<code class="func">AnIrreducibleNumericalSemigroupWithFrobeniusNumber</code>  <a href="chap6_mj.html#X7C8AB03F7E0B71F0">6.1-4</a>  <br />
<code class="func">ANumericalSemigroupWithPseudoFrobeniusNumbers</code>  <a href="chap5_mj.html#X862DBFA379D52E2C">5.7-4</a>  <br />
<code class="func">AperyList</code>, for ideals of numerical semigroups with respect to element  <a href="chap7_mj.html#X805C984685EBC65C">7.3-12</a>  <br />
    for ideals of numerical semigroups with respect to multiplicity  <a href="chap7_mj.html#X82D2784B813C67D8">7.3-13</a>  <br />
    for numerical semigroup with respect to element  <a href="chap3_mj.html#X7CB24F5E84793BE1">3.1-15</a>  <br />
    for numerical semigroup with respect to integer  <a href="chap3_mj.html#X7D06B00D7C305C64">3.1-17</a>  <br />
    for numerical semigroup with respect to multiplicity  <a href="chap3_mj.html#X80431F487C71D67B">3.1-16</a>  <br />
<code class="func">AperyListOfIdealOfNumericalSemigroupWRTElement</code>  <a href="chap7_mj.html#X805C984685EBC65C">7.3-12</a>  <br />
<code class="func">AperyListOfNumericalSemigroup</code>  <a href="chap3_mj.html#X80431F487C71D67B">3.1-16</a>  <br />
<code class="func">AperyListOfNumericalSemigroupAsGraph</code>  <a href="chap3_mj.html#X8022CC477E9BF678">3.1-18</a>  <br />
<code class="func">AperyListOfNumericalSemigroupWRTElement</code>  <a href="chap3_mj.html#X7CB24F5E84793BE1">3.1-15</a>  <br />
<code class="func">AperyListOfNumericalSemigroupWRTInteger</code>  <a href="chap3_mj.html#X7D06B00D7C305C64">3.1-17</a>  <br />
<code class="func">AperySetOfGoodSemigroup</code>  <a href="chap12_mj.html#X809E0C077A613806">12.2-15</a>  <br />
<code class="func">AperyTable</code>  <a href="chap7_mj.html#X8244CCAE7D957F46">7.3-14</a>  <br />
<code class="func">AperyTableOfNumericalSemigroup</code>  <a href="chap7_mj.html#X8244CCAE7D957F46">7.3-14</a>  <br />
<code class="func">ApplyPatternToIdeal</code>  <a href="chap7_mj.html#X7F4E597278AF31C8">7.4-5</a>  <br />
<code class="func">ApplyPatternToNumericalSemigroup</code>  <a href="chap7_mj.html#X7CFDFF6D7B9B595B">7.4-6</a>  <br />
<code class="func">ArfCharactersOfArfNumericalSemigroup</code>  <a href="chap8_mj.html#X83C242468796950D">8.2-3</a>  <br />
<code class="func">ArfClosure</code>, of good semigroup  <a href="chap12_mj.html#X87248BD481228F36">12.4-1</a>  <br />
    of numerical semigroup  <a href="chap8_mj.html#X7E34F28585A2922B">8.2-2</a>  <br />
<code class="func">ArfGoodSemigroupClosure</code>  <a href="chap12_mj.html#X87248BD481228F36">12.4-1</a>  <br />
<code class="func">ArfNumericalSemigroupClosure</code>  <a href="chap8_mj.html#X7E34F28585A2922B">8.2-2</a>  <br />
<code class="func">ArfNumericalSemigroupsWithFrobeniusNumber</code>  <a href="chap8_mj.html#X85CD144384FD55F3">8.2-4</a>  <br />
<code class="func">ArfNumericalSemigroupsWithFrobeniusNumberUpTo</code>  <a href="chap8_mj.html#X7E308CCF87448182">8.2-5</a>  <br />
<code class="func">ArfNumericalSemigroupsWithGenus</code>  <a href="chap8_mj.html#X80A13F7C81463AE5">8.2-6</a>  <br />
<code class="func">ArfNumericalSemigroupsWithGenusAndFrobeniusNumber</code>  <a href="chap8_mj.html#X7EE73B2F813F7E85">8.2-8</a>  <br />
<code class="func">ArfNumericalSemigroupsWithGenusUpTo</code>  <a href="chap8_mj.html#X80EB35C17C83694D">8.2-7</a>  <br />
<code class="func">ArfOverSemigroups</code>  <a href="chap8_mj.html#X7DD2831683F870C5">8.2-10</a>  <br />
<code class="func">ArfSpecialGaps</code>  <a href="chap8_mj.html#X7CC73F15831B06CE">8.2-9</a>  <br />
<code class="func">AsAffineSemigroup</code>  <a href="chap11_mj.html#X844806D97B4781B5">11.1-15</a>  <br />
<code class="func">AsGluingOfNumericalSemigroups</code>  <a href="chap6_mj.html#X848FCB49851D19B8">6.2-1</a>  <br />
<code class="func">AsIdealOfNumericalSemigroup</code>  <a href="chap7_mj.html#X799542C57E4E0D5E">7.4-3</a>  <br />
<code class="func">AsNumericalDuplication</code>  <a href="chap5_mj.html#X8176CEB4829084B4">5.2-6</a>  <br />
<code class="func">AsymptoticRatliffRushNumber</code>  <a href="chap7_mj.html#X79494A587A549E15">7.3-9</a>  <br />
<code class="func">AsymptoticRatliffRushNumberOfIdealOfNumericalSemigroup</code>  <a href="chap7_mj.html#X79494A587A549E15">7.3-9</a>  <br />
<code class="func">BasisOfGroupGivenByEquations</code>  <a href="chap11_mj.html#X7A1CE5A98425CEA1">11.1-22</a>  <br />
<code class="func">BelongsToAffineSemigroup</code>  <a href="chap11_mj.html#X851788D781A13C50">11.1-17</a>  <br />
<code class="func">BelongsToGoodIdeal</code>  <a href="chap12_mj.html#X797999937E4E1E2B">12.5-5</a>  <br />
<code class="func">BelongsToGoodSemigroup</code>  <a href="chap12_mj.html#X79EBBF6D7A2C9A12">12.2-1</a>  <br />
<code class="func">BelongsToHomogenizationOfNumericalSemigroup</code>  <a href="chap9_mj.html#X856B689185C1F5D9">9.5-1</a>  <br />
<code class="func">BelongsToIdealOfAffineSemigroup</code>  <a href="chap11_mj.html#X7F00912C853AA83D">11.5-7</a>  <br />
<code class="func">BelongsToIdealOfNumericalSemigroup</code>  <a href="chap7_mj.html#X87508E7A7CFB0B20">7.1-15</a>  <br />
<code class="func">BelongsToNumericalSemigroup</code>  <a href="chap2_mj.html#X864C2D8E80DD6D16">2.2-7</a>  <br />
<code class="func">BettiElements</code>, of affine semigroup  <a href="chap11_mj.html#X86BCBD32781EBC2D">11.3-7</a>  <br />
    of numerical semigroup  <a href="chap4_mj.html#X815C0AF17A371E3E">4.1-3</a>  <br />
<code class="func">BettiElementsOfAffineSemigroup</code>  <a href="chap11_mj.html#X86BCBD32781EBC2D">11.3-7</a>  <br />
<code class="func">BettiElementsOfNumericalSemigroup</code>  <a href="chap4_mj.html#X815C0AF17A371E3E">4.1-3</a>  <br />
<code class="func">BezoutSequence</code>  <a href="chapA_mj.html#X86859C84858ECAF1">A.1-1</a>  <br />
<code class="func">BinomialIdealOfNumericalSemigroup</code>  <a href="chap4_mj.html#X7E6BBAA7803DE7F3">4.2-1</a>  <br />
<code class="func">BlowUp</code>, for ideals of numerical semigroups  <a href="chap7_mj.html#X79A1A22D8615BF78">7.3-3</a>  <br />
    for numerical semigroups  <a href="chap7_mj.html#X7BFC52B7804542F5">7.3-5</a>  <br />
<code class="func">BlowUpIdealOfNumericalSemigroup</code>  <a href="chap7_mj.html#X79A1A22D8615BF78">7.3-3</a>  <br />
<code class="func">BlowUpOfNumericalSemigroup</code>  <a href="chap7_mj.html#X7BFC52B7804542F5">7.3-5</a>  <br />
<code class="func">BoundForConductorOfImageOfPattern</code>  <a href="chap7_mj.html#X7F13F7CB7FBCF006">7.4-4</a>  <br />
<code class="func">BuchsbaumNumberOfAssociatedGradedRingNumericalSemigroup</code>  <a href="chap7_mj.html#X7E16B6947BE375B2">7.5-4</a>  <br />
<code class="func">CanonicalBasisOfKernelCongruence</code>  <a href="chap11_mj.html#X7AD2271E84F705D3">11.3-4</a>  <br />
<code class="func">CanonicalIdeal</code>, for numerical semigroups  <a href="chap7_mj.html#X85975C3C86C2BC53">7.1-29</a>  <br />
<code class="func">CanonicalIdealOfGoodSemigroup</code>  <a href="chap12_mj.html#X7DA7AE32837CC1C7">12.5-7</a>  <br />
<code class="func">CanonicalIdealOfNumericalSemigroup</code>  <a href="chap7_mj.html#X85975C3C86C2BC53">7.1-29</a>  <br />
<code class="func">CartesianProductOfNumericalSemigroups</code>  <a href="chap12_mj.html#X855341C57F43DB72">12.1-4</a>  <br />
<code class="func">CatenaryDegree</code>, for a numerical semigroup and one of its elements  <a href="chap9_mj.html#X797147AA796D1AFE">9.3-5</a>  <br />
    for affine semigroups  <a href="chap11_mj.html#X80742F2F7DECDB4C">11.4-6</a>  <br />
    for element in a numerical semigroup  <a href="chap9_mj.html#X797147AA796D1AFE">9.3-5</a>  <br />
    for numerical semigroups  <a href="chap9_mj.html#X785B83F17BEEA894">9.3-7</a>  <br />
    for sets of factorizations  <a href="chap9_mj.html#X86F9D7868100F6F9">9.3-1</a>  <br />
<code class="func">CatenaryDegreeOfAffineSemigroup</code>  <a href="chap11_mj.html#X80742F2F7DECDB4C">11.4-6</a>  <br />
<code class="func">CatenaryDegreeOfElementInNumericalSemigroup</code>  <a href="chap9_mj.html#X797147AA796D1AFE">9.3-5</a>  <br />
<code class="func">CatenaryDegreeOfNumericalSemigroup</code>  <a href="chap9_mj.html#X785B83F17BEEA894">9.3-7</a>  <br />
<code class="func">CatenaryDegreeOfSetOfFactorizations</code>  <a href="chap9_mj.html#X86F9D7868100F6F9">9.3-1</a>  <br />
<code class="func">CeilingOfRational</code>  <a href="chapA_mj.html#X7C9DCBAF825CF7B2">A.1-3</a>  <br />
<code class="func">CircuitsOfKernelCongruence</code>  <a href="chap11_mj.html#X795EEE4481E0497C">11.3-1</a>  <br />
<code class="func">CocycleOfNumericalSemigroupWRTElement</code>  <a href="chap3_mj.html#X7802096584D32795">3.1-21</a>  <br />
<code class="func">CompleteIntersectionNumericalSemigroupsWithFrobeniusNumber</code>  <a href="chap6_mj.html#X86350BCE7D047599">6.2-3</a>  <br />
<code class="func">Conductor</code>, for good semigroups  <a href="chap12_mj.html#X78A2A60481EE02E7">12.2-2</a>  <br />
    for ideal of numerical semigroup  <a href="chap7_mj.html#X7EDDC78883A98A6E">7.1-10</a>  <br />
    for numerical Semigroup  <a href="chap3_mj.html#X835C729D7D8B1B36">3.1-23</a>  <br />
<code class="func">ConductorOfGoodSemigroup</code>  <a href="chap12_mj.html#X78A2A60481EE02E7">12.2-2</a>  <br />
<code class="func">ConductorOfIdealOfNumericalSemigroup</code>  <a href="chap7_mj.html#X7EDDC78883A98A6E">7.1-10</a>  <br />
<code class="func">ConductorOfNumericalSemigroup</code>  <a href="chap3_mj.html#X835C729D7D8B1B36">3.1-23</a>  <br />
<code class="func">CurveAssociatedToDeltaSequence</code>  <a href="chap10_mj.html#X87B819B886CA5A5C">10.2-4</a>  <br />
<code class="func">CyclotomicExponentSequence</code>  <a href="chap10_mj.html#X7B428FA2877EC733">10.1-9</a>  <br />
<code class="func">DecomposeIntegralIdealIntoIrreducibles</code>  <a href="chap7_mj.html#X83E064C684FA534C">7.2-2</a>  <br />
<code class="func">DecomposeIntoArfIrreducibles</code>  <a href="chap8_mj.html#X848E5559867D2D81">8.2-12</a>  <br />
<code class="func">DecomposeIntoIrreducibles</code>, for numerical semigroup  <a href="chap6_mj.html#X8753F78D7FD732E2">6.1-7</a>  <br />
<code class="func">DegreesOffEqualPrimitiveElementsOfNumericalSemigroup</code>  <a href="chap9_mj.html#X863E3EF986764267">9.3-8</a>  <br />
<code class="func">DegreesOfMonotonePrimitiveElementsOfNumericalSemigroup</code>  <a href="chap9_mj.html#X7E19683D7ADDE890">9.3-10</a>  <br />
<code class="func">DegreesOfPrimitiveElementsOfAffineSemigroup</code>  <a href="chap11_mj.html#X7DCAFC5F7F74F3CB">11.3-11</a>  <br />
<code class="func">DegreesOfPrimitiveElementsOfNumericalSemigroup</code>  <a href="chap4_mj.html#X7A9B5AE782CAEA2F">4.1-6</a>  <br />
<code class="func">DeltaSequencesWithFrobeniusNumber</code>  <a href="chap10_mj.html#X824ABFD680A34495">10.2-3</a>  <br />
<code class="func">DeltaSet</code>, for a numerical semigroup  <a href="chap9_mj.html#X83B06062784E0FD9">9.2-11</a>  <br />
    for a set of integers  <a href="chap9_mj.html#X79C953B5846F7057">9.2-5</a>  <br />
    for an affine semigroup  <a href="chap11_mj.html#X839549448300AD26">11.4-5</a>  <br />
    for the factorizations in a numerical semigroup of one of its elements  <a href="chap9_mj.html#X7DB8BA5B7D6F81CB">9.2-6</a>  <br />
    for the factorizations of an element in a numerical semigroup  <a href="chap9_mj.html#X7DB8BA5B7D6F81CB">9.2-6</a>  <br />
<code class="func">DeltaSetListUpToElementWRTNumericalSemigroup</code>  <a href="chap9_mj.html#X80B5DF908246BEB1">9.2-9</a>  <br />
<code class="func">DeltaSetOfAffineSemigroup</code>  <a href="chap11_mj.html#X839549448300AD26">11.4-5</a>  <br />
<code class="func">DeltaSetOfFactorizationsElementWRTNumericalSemigroup</code>  <a href="chap9_mj.html#X7DB8BA5B7D6F81CB">9.2-6</a>  <br />
<code class="func">DeltaSetOfNumericalSemigroup</code>  <a href="chap9_mj.html#X83B06062784E0FD9">9.2-11</a>  <br />
<code class="func">DeltaSetOfSetOfIntegers</code>  <a href="chap9_mj.html#X79C953B5846F7057">9.2-5</a>  <br />
<code class="func">DeltaSetPeriodicityBoundForNumericalSemigroup</code>  <a href="chap9_mj.html#X7A08CF05821DD2FC">9.2-7</a>  <br />
<code class="func">DeltaSetPeriodicityStartForNumericalSemigroup</code>  <a href="chap9_mj.html#X8123FC0E83ADEE45">9.2-8</a>  <br />
<code class="func">DeltaSetUnionUpToElementWRTNumericalSemigroup</code>  <a href="chap9_mj.html#X85C6973E81583E8B">9.2-10</a>  <br />
<code class="func">DenumerantFunction</code>  <a href="chap9_mj.html#X801DA4247A0BEBDA">9.1-8</a>  <br />
<code class="func">DenumerantIdeal</code>, denumerant ideal of a given number of factorizations in a numerical semigroup  <a href="chap9_mj.html#X7D91A9377DAFAE35">9.1-9</a>  <br />
    denumerant ideal of semigroup with respect to a number of factorizations  <a href="chap9_mj.html#X7D91A9377DAFAE35">9.1-9</a>  <br />
<code class="func">DenumerantOfElementInNumericalSemigroup</code>  <a href="chap9_mj.html#X86D58E0084CFD425">9.1-7</a>  <br />
<code class="func">Deserts</code>  <a href="chap3_mj.html#X7EB81BF886DDA29A">3.1-28</a>  <br />
<code class="func">DesertsOfNumericalSemigroup</code>  <a href="chap3_mj.html#X7EB81BF886DDA29A">3.1-28</a>  <br />
<code class="func">Difference</code>, for ideals of numerical semigroups  <a href="chap7_mj.html#X8321A10885D2DEF8">7.1-24</a>  <br />
    for numerical semigroups  <a href="chap3_mj.html#X7E6F5D6F7B0C9635">3.1-14</a>  <br />
<code class="func">DifferenceOfIdealsOfNumericalSemigroup</code>  <a href="chap7_mj.html#X8321A10885D2DEF8">7.1-24</a>  <br />
<code class="func">DifferenceOfNumericalSemigroups</code>  <a href="chap3_mj.html#X7E6F5D6F7B0C9635">3.1-14</a>  <br />
<code class="func">DilatationOfNumericalSemigroup</code>  <a href="chap5_mj.html#X81632C597E3E3DFE">5.2-8</a>  <br />
<code class="func">DivisorsOfElementInNumericalSemigroup</code>  <a href="chap9_mj.html#X8771F39A7C7E031E">9.6-3</a>  <br />
<code class="func">DotBinaryRelation</code>  <a href="chap14_mj.html#X7FEF6EC77E489886">14.1-1</a>  <br />
<code class="func">DotEliahouGraph</code>  <a href="chap14_mj.html#X83F1423980D2AEA4">14.1-9</a>  <br />
<code class="func">DotFactorizationGraph</code>  <a href="chap14_mj.html#X7EC75F477D4F8CC3">14.1-8</a>  <br />
<code class="func">DotOverSemigroupsNumericalSemigroup</code>  <a href="chap14_mj.html#X7F43955582F472B6">14.1-6</a>  <br />
<code class="func">DotRosalesGraph</code>, for affine semigroup  <a href="chap14_mj.html#X8195A2027B726448">14.1-7</a>  <br />
    for numerical semigroup  <a href="chap14_mj.html#X8195A2027B726448">14.1-7</a>  <br />
<code class="func">DotSplash</code>  <a href="chap14_mj.html#X7D1999A88268979F">14.1-11</a>  <br />
<code class="func">DotTreeOfGluingsOfNumericalSemigroup</code>  <a href="chap14_mj.html#X7F62870F8652EDE6">14.1-5</a>  <br />
<code class="func">Elasticity</code>, for affine semigroups  <a href="chap11_mj.html#X819CDBAA84DB7E83">11.4-4</a>  <br />
    for numerical semigroups  <a href="chap9_mj.html#X7A2B01BB87086283">9.2-4</a>  <br />
    for the factorizations in a numerical semigroup of one of its elements  <a href="chap9_mj.html#X860E461182B0C6F5">9.2-3</a>  <br />
    for the factorizations in an affine semigroup of one of its elements  <a href="chap11_mj.html#X7F394FA67BE5151B">11.4-3</a>  <br />
    for the factorizations of an element in a numerical semigroup  <a href="chap9_mj.html#X860E461182B0C6F5">9.2-3</a>  <br />
    for the factorizations of an element in an affine semigroup  <a href="chap11_mj.html#X7F394FA67BE5151B">11.4-3</a>  <br />
<code class="func">ElasticityOfAffineSemigroup</code>  <a href="chap11_mj.html#X819CDBAA84DB7E83">11.4-4</a>  <br />
<code class="func">ElasticityOfFactorizationsElementWRTAffineSemigroup</code>  <a href="chap11_mj.html#X7F394FA67BE5151B">11.4-3</a>  <br />
<code class="func">ElasticityOfFactorizationsElementWRTNumericalSemigroup</code>  <a href="chap9_mj.html#X860E461182B0C6F5">9.2-3</a>  <br />
<code class="func">ElasticityOfNumericalSemigroup</code>  <a href="chap9_mj.html#X7A2B01BB87086283">9.2-4</a>  <br />
<code class="func">ElementNumber_IdealOfNumericalSemigroup</code>  <a href="chap7_mj.html#X83D0996D811A35C6">7.1-16</a>  <br />
<code class="func">ElementNumber_NumericalSemigroup</code>  <a href="chap3_mj.html#X7B6C82DD86E5422F">3.1-11</a>  <br />
<code class="func">ElementsUpTo</code>  <a href="chap3_mj.html#X7D2B3AA9823371AE">3.1-7</a>  <br />
<code class="func">EliahouNumber</code>, for numerical semigroup  <a href="chap3_mj.html#X80F9EC9A7BF4E606">3.2-2</a>  <br />
<code class="func">EliahouSlicesOfNumericalSemigroup</code>  <a href="chap3_mj.html#X7846F90E7EA43C47">3.2-4</a>  <br />
<code class="func">EmbeddingDimension</code>, for numerical semigroup  <a href="chap3_mj.html#X7884AE27790E687F">3.1-3</a>  <br />
<code class="func">EmbeddingDimensionOfNumericalSemigroup</code>  <a href="chap3_mj.html#X7884AE27790E687F">3.1-3</a>  <br />
<code class="func">EqualCatenaryDegreeOfAffineSemigroup</code>  <a href="chap11_mj.html#X7EADD306875FCBE6">11.4-7</a>  <br />
<code class="func">EqualCatenaryDegreeOfNumericalSemigroup</code>  <a href="chap9_mj.html#X780E2C737FA8B2A9">9.3-9</a>  <br />
<code class="func">EqualCatenaryDegreeOfSetOfFactorizations</code>  <a href="chap9_mj.html#X86E0CAD28655839C">9.3-3</a>  <br />
<code class="func">EquationsOfGroupGeneratedBy</code>  <a href="chap11_mj.html#X8307A0597864B098">11.1-21</a>  <br />
<code class="func">Factorizations</code>  <a href="chap11_mj.html#X820A0D06857C4EF5">11.4-2</a>  <br />
    for a numerical semigroup and one of its elements  <a href="chap9_mj.html#X80EF105B82447F30">9.1-2</a>  <br />
    for an element in a numerical semigroup  <a href="chap9_mj.html#X80EF105B82447F30">9.1-2</a>  <br />
    for an element in an affine semigroup  <a href="chap11_mj.html#X820A0D06857C4EF5">11.4-2</a>  <br />
<code class="func">FactorizationsElementListWRTNumericalSemigroup</code>  <a href="chap9_mj.html#X87C9E03C818AE1AA">9.1-3</a>  <br />
<code class="func">FactorizationsElementWRTNumericalSemigroup</code>  <a href="chap9_mj.html#X80EF105B82447F30">9.1-2</a>  <br />
<code class="func">FactorizationsInHomogenizationOfNumericalSemigroup</code>  <a href="chap9_mj.html#X85D03DBB7BA3B1FB">9.5-2</a>  <br />
<code class="func">FactorizationsIntegerWRTList</code>  <a href="chap9_mj.html#X8429AECF78EE7EAB">9.1-1</a>  <br />
<code class="func">FactorizationsVectorWRTList</code>  <a href="chap11_mj.html#X8780C7E5830B9AE2">11.4-1</a>  <br />
<code class="func">FengRaoDistance</code>  <a href="chap9_mj.html#X7939BCE08655B62D">9.7-1</a>  <br />
<code class="func">FengRaoNumber</code>  <a href="chap9_mj.html#X83F9F4C67D4535EF">9.7-2</a>  <br />
<code class="func">FiniteComplementIdealExtension</code>  <a href="chap11_mj.html#X7A3648D67CF81370">11.1-6</a>  <br />
<code class="func">FirstElementsOfNumericalSemigroup</code>  <a href="chap3_mj.html#X7F0EDFA77F929120">3.1-6</a>  <br />
<code class="func">ForcedIntegersForPseudoFrobenius</code>  <a href="chap5_mj.html#X874B252180BD7EB4">5.7-1</a>  <br />
<code class="func">FreeNumericalSemigroupsWithFrobeniusNumber</code>  <a href="chap6_mj.html#X86B4BA6A79F734A8">6.2-5</a>  <br />
<code class="func">FrobeniusNumber</code>, for ideal of numerical semigroup  <a href="chap7_mj.html#X7A8AF91C7D1F1B4E">7.1-11</a>  <br />
    for numerical semigroup  <a href="chap3_mj.html#X847BAD9480D186C0">3.1-22</a>  <br />
<code class="func">FrobeniusNumberOfIdealOfNumericalSemigroup</code>  <a href="chap7_mj.html#X7A8AF91C7D1F1B4E">7.1-11</a>  <br />
<code class="func">FrobeniusNumberOfNumericalSemigroup</code>  <a href="chap3_mj.html#X847BAD9480D186C0">3.1-22</a>  <br />
<code class="func">FundamentalGaps</code>, for numerical semigroup  <a href="chap3_mj.html#X7EC438CC7BF539D0">3.1-34</a>  <br />
<code class="func">FundamentalGapsOfNumericalSemigroup</code>  <a href="chap3_mj.html#X7EC438CC7BF539D0">3.1-34</a>  <br />
<code class="func">Gaps</code>, for affine semigroup  <a href="chap11_mj.html#X8361194C86AE807B">11.1-7</a>  <br />
    for numerical semigroup  <a href="chap3_mj.html#X8688B1837E4BC079">3.1-26</a>  <br />
<code class="func">GapsOfNumericalSemigroup</code>  <a href="chap3_mj.html#X8688B1837E4BC079">3.1-26</a>  <br />
<code class="func">Generators</code>, for affine semigroup  <a href="chap11_mj.html#X84FDF85D7CDEDF3E">11.1-11</a>  <br />
    for ideal of an affine semigroup  <a href="chap11_mj.html#X8086C1EE7EAAB33D">11.5-4</a>  <br />
    for ideal of numerical semigroup  <a href="chap7_mj.html#X7A842A4385B73C63">7.1-4</a>  <br />
    for numerical semigroup  <a href="chap3_mj.html#X850F430A8284DF9A">3.1-2</a>  <br />
<code class="func">GeneratorsKahlerDifferentials</code>  <a href="chap10_mj.html#X836D31F787641C22">10.2-9</a>  <br />
<code class="func">GeneratorsModule_Global</code>  <a href="chap10_mj.html#X7EE8528484642CEE">10.2-8</a>  <br />
<code class="func">GeneratorsOfAffineSemigroup</code>  <a href="chap11_mj.html#X84FDF85D7CDEDF3E">11.1-11</a>  <br />
<code class="func">GeneratorsOfIdealOfNumericalSemigroup</code>  <a href="chap7_mj.html#X7A842A4385B73C63">7.1-4</a>  <br />
<code class="func">GeneratorsOfKernelCongruence</code>  <a href="chap11_mj.html#X7EE005267DEBC1DE">11.3-3</a>  <br />
<code class="func">GeneratorsOfNumericalSemigroup</code>  <a href="chap3_mj.html#X850F430A8284DF9A">3.1-2</a>  <br />
<code class="func">Genus</code>, for affine semigroup  <a href="chap11_mj.html#X867B27BD81104BEE">11.1-8</a>  <br />
    for good semigroup  <a href="chap12_mj.html#X7D70CD958333D49B">12.2-13</a>  <br />
    for numerical semigroup  <a href="chap3_mj.html#X7E9C8E157C4EAAB0">3.1-33</a>  <br />
<code class="func">GenusOfGoodSemigroup</code>  <a href="chap12_mj.html#X7D70CD958333D49B">12.2-13</a>  <br />
<code class="func">GenusOfNumericalSemigroup</code>  <a href="chap3_mj.html#X7E9C8E157C4EAAB0">3.1-33</a>  <br />
<code class="func">GluingOfAffineSemigroups</code>  <a href="chap11_mj.html#X7FE3B3C380641DDC">11.2-1</a>  <br />
<code class="func">GoodGeneratingSystemOfGoodIdeal</code>  <a href="chap12_mj.html#X7E4FC6DB794992E0">12.5-2</a>  <br />
<code class="func">GoodIdeal</code>  <a href="chap12_mj.html#X843CA9D5874A33F2">12.5-1</a>  <br />
<code class="func">GoodSemigroup</code>  <a href="chap12_mj.html#X7856241678224958">12.1-5</a>  <br />
<code class="func">GoodSemigroupByMaximalElements</code>  <a href="chap12_mj.html#X78B456D27856761F">12.2-10</a>  <br />
<code class="func">GoodSemigroupBySmallElements</code>  <a href="chap12_mj.html#X7E538585815C94D0">12.2-7</a>  <br />
<code class="func">GraeffePolynomial</code>  <a href="chap10_mj.html#X87C88E5C7B56931F">10.1-5</a>  <br />
<code class="func">GraphAssociatedToElementInNumericalSemigroup</code>  <a href="chap4_mj.html#X81CC5A6C870377E1">4.1-2</a>  <br />
<code class="func">GraverBasis</code>  <a href="chap11_mj.html#X7C3546477E07A1EA">11.3-5</a>  <br />
<code class="func">HasseDiagramOfAperyListOfNumericalSemigroup</code>  <a href="chap14_mj.html#X8050862F79EA9620">14.1-4</a>  <br />
<code class="func">HasseDiagramOfBettiElementsOfNumericalSemigroup</code>  <a href="chap14_mj.html#X832901FF85EB8F1C">14.1-3</a>  <br />
<code class="func">HasseDiagramOfNumericalSemigroup</code>  <a href="chap14_mj.html#X868991B084E42CE9">14.1-2</a>  <br />
<code class="func">HilbertBasisOfSystemOfHomogeneousEquations</code>  <a href="chap11_mj.html#X7D4D017A79AD98E2">11.1-19</a>  <br />
<code class="func">HilbertBasisOfSystemOfHomogeneousInequalities</code>  <a href="chap11_mj.html#X825B1CD37B0407A6">11.1-20</a>  <br />
<code class="func">HilbertFunction</code>  <a href="chap7_mj.html#X81F1F3EB868D2117">7.3-2</a>  <br />
<code class="func">HilbertFunctionOfIdealOfNumericalSemigroup</code>  <a href="chap7_mj.html#X82156F18807B00BF">7.3-1</a>  <br />
<code class="func">HilbertSeriesOfNumericalSemigroup</code>  <a href="chap10_mj.html#X780479F978D166B0">10.1-4</a>  <br />
<code class="func">Holes</code>, for numerical semigroup  <a href="chap3_mj.html#X7CCFC5267FD27DDE">3.1-31</a>  <br />
<code class="func">HolesOfNumericalSemigroup</code>  <a href="chap3_mj.html#X7CCFC5267FD27DDE">3.1-31</a>  <br />
<code class="func">HomogeneousBettiElementsOfNumericalSemigroup</code>  <a href="chap9_mj.html#X857CC7FF85C05318">9.5-3</a>  <br />
<code class="func">HomogeneousCatenaryDegreeOfAffineSemigroup</code>  <a href="chap11_mj.html#X84FE571A7E9E1AE9">11.4-8</a>  <br />
<code class="func">HomogeneousCatenaryDegreeOfNumericalSemigroup</code>  <a href="chap9_mj.html#X7DFFCAC87B3B632B">9.5-4</a>  <br />
<code class="func">IdealByDivisorClosedSet</code>  <a href="chap7_mj.html#X8774724085D3371D">7.1-8</a>  <br />
<code class="func">IdealOfAffineSemigroup</code>  <a href="chap11_mj.html#X85775D4E7B9C7DAB">11.5-1</a>  <br />
<code class="func">IdealOfNumericalSemigroup</code>  <a href="chap7_mj.html#X78E5F44E81485C17">7.1-1</a>  <br />
<code class="func">InductiveNumericalSemigroup</code>  <a href="chap5_mj.html#X7DCEC67A82130CD8">5.2-7</a>  <br />
<code class="func">Intersection</code>, for ideals of affine semigroups  <a href="chap11_mj.html#X7ED03363783D8FCD">11.5-12</a>  <br />
    for ideals of numerical semigroups  <a href="chap7_mj.html#X7B34033979009F64">7.1-27</a>  <br />
    for numerical semigroups  <a href="chap5_mj.html#X875A8D2679153D4B">5.2-1</a>  <br />
<code class="func">IntersectionIdealsOfAffineSemigroup</code>  <a href="chap11_mj.html#X7ED03363783D8FCD">11.5-12</a>  <br />
<code class="func">IntersectionIdealsOfNumericalSemigroup</code>  <a href="chap7_mj.html#X7B34033979009F64">7.1-27</a>  <br />
<code class="func">IntersectionOfNumericalSemigroups</code>  <a href="chap5_mj.html#X875A8D2679153D4B">5.2-1</a>  <br />
<code class="func">IrreducibleMaximalElementsOfGoodSemigroup</code>  <a href="chap12_mj.html#X8503AC767A90C2BD">12.2-9</a>  <br />
<code class="func">IrreducibleNumericalSemigroupsWithFrobeniusNumber</code>  <a href="chap6_mj.html#X78345A267ADEFBAB">6.1-5</a>  <br />
<code class="func">IrreducibleNumericalSemigroupsWithFrobeniusNumberAndMultiplicity</code>  <a href="chap6_mj.html#X87C2738C7AA109DC">6.1-6</a>  <br />
<code class="func">IrreducibleZComponents</code>  <a href="chap7_mj.html#X7B83DEAC866B65E8">7.2-1</a>  <br />
<code class="func">IsACompleteIntersectionNumericalSemigroup</code>  <a href="chap6_mj.html#X7A0DF10F85F32194">6.2-2</a>  <br />
<code class="func">IsAcute</code>, for numerical semigroups  <a href="chap3_mj.html#X83D4AFE882A79096">3.1-30</a>  <br />
<code class="func">IsAcuteNumericalSemigroup</code>  <a href="chap3_mj.html#X83D4AFE882A79096">3.1-30</a>  <br />
<code class="func">IsAdditiveNumericalSemigroup</code>  <a href="chap9_mj.html#X7F8B10C2870932B8">9.2-13</a>  <br />
<code class="func">IsAdmissiblePattern</code>  <a href="chap7_mj.html#X865042FD7EBD15EE">7.4-1</a>  <br />
<code class="func">IsAdmittedPatternByIdeal</code>  <a href="chap7_mj.html#X7F9232047F85C4D8">7.4-7</a>  <br />
<code class="func">IsAdmittedPatternByNumericalSemigroup</code>  <a href="chap7_mj.html#X827BB22083390CB9">7.4-8</a>  <br />
<code class="func">IsAffineSemigroup</code>  <a href="chap11_mj.html#X7A2902207BAA3936">11.1-16</a>  <br />
<code class="func">IsAffineSemigroupByEquations</code>  <a href="chap11_mj.html#X7A2902207BAA3936">11.1-16</a>  <br />
<code class="func">IsAffineSemigroupByGenerators</code>  <a href="chap11_mj.html#X7A2902207BAA3936">11.1-16</a>  <br />
<code class="func">IsAffineSemigroupByInequalities</code>  <a href="chap11_mj.html#X7A2902207BAA3936">11.1-16</a>  <br />
<code class="func">IsAlmostCanonicalIdeal</code>  <a href="chap7_mj.html#X829C9685798BB553">7.1-31</a>  <br />
<code class="func">IsAlmostSymmetric</code>  <a href="chap6_mj.html#X84C44C7A7D9270BB">6.3-3</a>  <br />
<code class="func">IsAlmostSymmetricNumericalSemigroup</code>  <a href="chap6_mj.html#X84C44C7A7D9270BB">6.3-3</a>  <br />
<code class="func">IsAperyListOfNumericalSemigroup</code>  <a href="chap2_mj.html#X84A611557B5ACF42">2.2-4</a>  <br />
<code class="func">IsAperySetAlphaRectangular</code>  <a href="chap6_mj.html#X86F52FB67F76D2CB">6.2-13</a>  <br />
<code class="func">IsAperySetBetaRectangular</code>  <a href="chap6_mj.html#X7E6E262C7C421635">6.2-12</a>  <br />
<code class="func">IsAperySetGammaRectangular</code>  <a href="chap6_mj.html#X80CAA1FA7F6FF4FD">6.2-11</a>  <br />
<code class="func">IsArf</code>  <a href="chap8_mj.html#X86137A2A7D27F7EC">8.2-1</a>  <br />
<code class="func">IsArfIrreducible</code>  <a href="chap8_mj.html#X8052BCE67CC2472F">8.2-11</a>  <br />
<code class="func">IsArfNumericalSemigroup</code>  <a href="chap8_mj.html#X86137A2A7D27F7EC">8.2-1</a>  <br />
<code class="func">IsBezoutSequence</code>  <a href="chapA_mj.html#X86C990AC7F40E8D0">A.1-2</a>  <br />
<code class="func">IsCanonicalIdeal</code>  <a href="chap7_mj.html#X7D15FA4C843A13B7">7.1-30</a>  <br />
<code class="func">IsCanonicalIdealOfNumericalSemigroup</code>  <a href="chap7_mj.html#X7D15FA4C843A13B7">7.1-30</a>  <br />
<code class="func">IsComplementOfIntegralIdeal</code>  <a href="chap7_mj.html#X80233A6F80CA0615">7.1-7</a>  <br />
<code class="func">IsCompleteIntersection</code>  <a href="chap6_mj.html#X7A0DF10F85F32194">6.2-2</a>  <br />
<code class="func">IsCyclotomicNumericalSemigroup</code>  <a href="chap10_mj.html#X8366BB727C496D31">10.1-8</a>  <br />
<code class="func">IsCyclotomicPolynomial</code>  <a href="chap10_mj.html#X87A46B53815B158F">10.1-6</a>  <br />
<code class="func">IsDeltaSequence</code>  <a href="chap10_mj.html#X834D6B1A7C421B9F">10.2-2</a>  <br />
<code class="func">IsFree</code>  <a href="chap6_mj.html#X7CD2A77778432E7B">6.2-4</a>  <br />
<code class="func">IsFreeNumericalSemigroup</code>  <a href="chap6_mj.html#X7CD2A77778432E7B">6.2-4</a>  <br />
<code class="func">IsFull</code>  <a href="chap11_mj.html#X8607B621833FAECB">11.1-18</a>  <br />
<code class="func">IsFullAffineSemigroup</code>  <a href="chap11_mj.html#X8607B621833FAECB">11.1-18</a>  <br />
<code class="func">IsGeneralizedAlmostSymmetric</code>  <a href="chap6_mj.html#X83F13D6482F021B2">6.4-4</a>  <br />
<code class="func">IsGeneralizedGorenstein</code>  <a href="chap6_mj.html#X8221EC44802E5158">6.4-1</a>  <br />
<code class="func">IsGeneric</code>, for affine semigroups  <a href="chap11_mj.html#X81CA53DA8216DC82">11.3-9</a>  <br />
    for numerical semigroups  <a href="chap4_mj.html#X79C010537C838154">4.3-2</a>  <br />
<code class="func">IsGenericAffineSemigroup</code>  <a href="chap11_mj.html#X81CA53DA8216DC82">11.3-9</a>  <br />
<code class="func">IsGenericNumericalSemigroup</code>  <a href="chap4_mj.html#X79C010537C838154">4.3-2</a>  <br />
<code class="func">IsGoodSemigroup</code>  <a href="chap12_mj.html#X79E86DEE79281BF2">12.1-1</a>  <br />
<code class="func">IsGradedAssociatedRingNumericalSemigroupBuchsbaum</code>  <a href="chap7_mj.html#X782D557583CEDD04">7.5-2</a>  <br />
<code class="func">IsGradedAssociatedRingNumericalSemigroupCI</code>  <a href="chap7_mj.html#X7800C5D68641E2B7">7.5-6</a>  <br />
<code class="func">IsGradedAssociatedRingNumericalSemigroupCM</code>  <a href="chap7_mj.html#X7876199778D6B320">7.5-1</a>  <br />
<code class="func">IsGradedAssociatedRingNumericalSemigroupGorenstein</code>  <a href="chap7_mj.html#X7A5752C0836370FA">7.5-5</a>  <br />
<code class="func">IsHomogeneousNumericalSemigroup</code>  <a href="chap9_mj.html#X80B707EE79990E1E">9.8-3</a>  <br />
<code class="func">IsIdealOfAffineSemigroup</code>  <a href="chap11_mj.html#X82A647B27FDFE49B">11.5-2</a>  <br />
<code class="func">IsIdealOfNumericalSemigroup</code>  <a href="chap7_mj.html#X85BD6FAD7EA3B5DD">7.1-2</a>  <br />
<code class="func">IsIntegral</code>, for ideal of numerical semigroup  <a href="chap7_mj.html#X7B0343BF794AC7EA">7.1-6</a>  <br />
    for ideals of affine semigroups  <a href="chap11_mj.html#X7B0FBEC285F54B8D">11.5-6</a>  <br />
<code class="func">IsIntegralIdealOfAffineSemigroup</code>  <a href="chap11_mj.html#X7B0FBEC285F54B8D">11.5-6</a>  <br />
<code class="func">IsIntegralIdealOfNumericalSemigroup</code>  <a href="chap7_mj.html#X7B0343BF794AC7EA">7.1-6</a>  <br />
<code class="func">IsIrreducible</code>, for numerical semigroups  <a href="chap6_mj.html#X83E8CC8F862D1FC0">6.1-1</a>  <br />
<code class="func">IsIrreducibleNumericalSemigroup</code>  <a href="chap6_mj.html#X83E8CC8F862D1FC0">6.1-1</a>  <br />
<code class="func">IsKroneckerPolynomial</code>  <a href="chap10_mj.html#X7D9618ED83776B0B">10.1-7</a>  <br />
<code class="func">IsListOfIntegersNS</code>  <a href="chapA_mj.html#X7DFEDA6B87BB2E1F">A.2-2</a>  <br />
<code class="func">IsLocal</code>, for good semigroups  <a href="chap12_mj.html#X792BCCF87CF63122">12.2-4</a>  <br />
<code class="func">IsMED</code>  <a href="chap8_mj.html#X783A0BE786C6BBBE">8.1-1</a>  <br />
<code class="func">IsMEDNumericalSemigroup</code>  <a href="chap8_mj.html#X783A0BE786C6BBBE">8.1-1</a>  <br />
<code class="func">IsMinimalRelationOfNumericalSemigroup</code>  <a href="chap4_mj.html#X7FC66A1B82E86FAF">4.1-4</a>  <br />
<code class="func">IsModularNumericalSemigroup</code>  <a href="chap2_mj.html#X7B1B6B8C82BD7084">2.2-1</a>  <br />
<code class="func">IsMonomialNumericalSemigroup</code>  <a href="chap10_mj.html#X7A04B8887F493733">10.2-10</a>  <br />
<code class="func">IsMpure</code>  <a href="chap9_mj.html#X8400FB5D81EFB5FE">9.8-2</a>  <br />
<code class="func">IsMpureNumericalSemigroup</code>  <a href="chap9_mj.html#X8400FB5D81EFB5FE">9.8-2</a>  <br />
<code class="func">IsNearlyGorenstein</code>  <a href="chap6_mj.html#X866E48B47D66CFF2">6.4-2</a>  <br />
<code class="func">IsNumericalSemigroup</code>  <a href="chap2_mj.html#X7B1B6B8C82BD7084">2.2-1</a>  <br />
<code class="func">IsNumericalSemigroupAssociatedIrreduciblePlanarCurveSingularity</code>  <a href="chap6_mj.html#X847CD0EF8452F771">6.2-9</a>  <br />
<code class="func">IsNumericalSemigroupByAperyList</code>  <a href="chap2_mj.html#X7B1B6B8C82BD7084">2.2-1</a>  <br />
<code class="func">IsNumericalSemigroupByFundamentalGaps</code>  <a href="chap2_mj.html#X7B1B6B8C82BD7084">2.2-1</a>  <br />
<code class="func">IsNumericalSemigroupByGaps</code>  <a href="chap2_mj.html#X7B1B6B8C82BD7084">2.2-1</a>  <br />
<code class="func">IsNumericalSemigroupByGenerators</code>  <a href="chap2_mj.html#X7B1B6B8C82BD7084">2.2-1</a>  <br />
<code class="func">IsNumericalSemigroupByInterval</code>  <a href="chap2_mj.html#X7B1B6B8C82BD7084">2.2-1</a>  <br />
<code class="func">IsNumericalSemigroupByOpenInterval</code>  <a href="chap2_mj.html#X7B1B6B8C82BD7084">2.2-1</a>  <br />
<code class="func">IsNumericalSemigroupBySmallElements</code>  <a href="chap2_mj.html#X7B1B6B8C82BD7084">2.2-1</a>  <br />
<code class="func">IsNumericalSemigroupBySubAdditiveFunction</code>  <a href="chap2_mj.html#X7B1B6B8C82BD7084">2.2-1</a>  <br />
<code class="func">IsNumericalSemigroupPolynomial</code>  <a href="chap10_mj.html#X7F59E1167C1EE578">10.1-2</a>  <br />
<code class="func">IsOrdinary</code>, for numerical semigroups  <a href="chap3_mj.html#X82B1868F7A780B49">3.1-29</a>  <br />
<code class="func">IsOrdinaryNumericalSemigroup</code>  <a href="chap3_mj.html#X82B1868F7A780B49">3.1-29</a>  <br />
<code class="func">IsProportionallyModularNumericalSemigroup</code>  <a href="chap2_mj.html#X7B1B6B8C82BD7084">2.2-1</a>  <br />
<code class="func">IsPseudoSymmetric</code>, for numerical semigroups  <a href="chap6_mj.html#X7EA0D85085C4B607">6.1-3</a>  <br />
<code class="func">IsPseudoSymmetricNumericalSemigroup</code>  <a href="chap6_mj.html#X7EA0D85085C4B607">6.1-3</a>  <br />
<code class="func">IsPure</code>  <a href="chap9_mj.html#X7B894ED27D38E4B5">9.8-1</a>  <br />
<code class="func">IsPureNumericalSemigroup</code>  <a href="chap9_mj.html#X7B894ED27D38E4B5">9.8-1</a>  <br />
<code class="func">IsSaturated</code>  <a href="chap8_mj.html#X81CCD9A88127E549">8.3-1</a>  <br />
<code class="func">IsSaturatedNumericalSemigroup</code>  <a href="chap8_mj.html#X81CCD9A88127E549">8.3-1</a>  <br />
<code class="func">IsSelfReciprocalUnivariatePolynomial</code>  <a href="chap10_mj.html#X82C6355287C3BDD1">10.1-11</a>  <br />
<code class="func">IsStronglyAdmissiblePattern</code>  <a href="chap7_mj.html#X7ED8306681407D0F">7.4-2</a>  <br />
<code class="func">IsSubsemigroupOfNumericalSemigroup</code>  <a href="chap2_mj.html#X86D5B3517AF376D4">2.2-5</a>  <br />
<code class="func">IsSubset</code>  <a href="chap2_mj.html#X79CA175481F8105F">2.2-6</a>  <br />
<code class="func">IsSuperSymmetricNumericalSemigroup</code>  <a href="chap9_mj.html#X8630DEF77A350D76">9.8-4</a>  <br />
<code class="func">IsSymmetric</code>, for good semigroups  <a href="chap12_mj.html#X85A0D9C485431828">12.3-1</a>  <br />
    for numerical semigroups  <a href="chap6_mj.html#X7C381E277917B0ED">6.1-2</a>  <br />
<code class="func">IsSymmetricGoodSemigroup</code>  <a href="chap12_mj.html#X85A0D9C485431828">12.3-1</a>  <br />
<code class="func">IsSymmetricNumericalSemigroup</code>  <a href="chap6_mj.html#X7C381E277917B0ED">6.1-2</a>  <br />
<code class="func">IsTelescopic</code>  <a href="chap6_mj.html#X830D0E0F7B8C6284">6.2-6</a>  <br />
<code class="func">IsTelescopicNumericalSemigroup</code>  <a href="chap6_mj.html#X830D0E0F7B8C6284">6.2-6</a>  <br />
<code class="func">IsUniquelyPresented</code>, for affine semigroups  <a href="chap11_mj.html#X79EC6F7583B0CBDD">11.3-10</a>  <br />
    for numerical semigroups  <a href="chap4_mj.html#X7C6F554486274CAE">4.3-1</a>  <br />
<code class="func">IsUniquelyPresentedAffineSemigroup</code>  <a href="chap11_mj.html#X79EC6F7583B0CBDD">11.3-10</a>  <br />
<code class="func">IsUniquelyPresentedNumericalSemigroup</code>  <a href="chap4_mj.html#X7C6F554486274CAE">4.3-1</a>  <br />
<code class="func">IsUniversallyFree</code>  <a href="chap6_mj.html#X7A1C2C737BC1C4CE">6.2-8</a>  <br />
<code class="func">IsUniversallyFreeNumericalSemigroup</code>  <a href="chap6_mj.html#X7A1C2C737BC1C4CE">6.2-8</a>  <br />
<code class="func">Iterator</code>, for ideals of numerical semigroups  <a href="chap7_mj.html#X7A55BD4D82580537">7.1-20</a>  <br />
    for numerical semigroups  <a href="chap3_mj.html#X867ABF7C7991ED7C">3.1-13</a>  <br />
<code class="func">KunzCoordinates</code>, for a numerical semigroup and (optionally) an integer  <a href="chap3_mj.html#X80B398537887FD87">3.1-19</a>  <br />
<code class="func">KunzCoordinatesOfNumericalSemigroup</code>  <a href="chap3_mj.html#X80B398537887FD87">3.1-19</a>  <br />
<code class="func">KunzPolytope</code>  <a href="chap3_mj.html#X7C21E5417A3894EC">3.1-20</a>  <br />
<code class="func">LatticePathAssociatedToNumericalSemigroup</code>  <a href="chap3_mj.html#X794E615F85C2AAB0">3.1-32</a>  <br />
<code class="func">LegendrianGenericNumericalSemigroup</code>  <a href="chap10_mj.html#X7980A7CE79F09A89">10.3-1</a>  <br />
<code class="func">Length</code>, for good semigroup  <a href="chap12_mj.html#X81BD57ED80145EB0">12.2-14</a>  <br />
    for numerical semigroup  <a href="chap3_mj.html#X7A56569F853DADED">3.1-5</a>  <br />
<code class="func">LengthOfGoodSemigroup</code>  <a href="chap12_mj.html#X81BD57ED80145EB0">12.2-14</a>  <br />
<code class="func">LengthsOfFactorizationsElementWRTNumericalSemigroup</code>  <a href="chap9_mj.html#X7FDE4F94870951B1">9.2-2</a>  <br />
<code class="func">LengthsOfFactorizationsIntegerWRTList</code>  <a href="chap9_mj.html#X7D4CC092859AF81F">9.2-1</a>  <br />
<code class="func">LipmanSemigroup</code>  <a href="chap7_mj.html#X8799F0347FF0D510">7.3-6</a>  <br />
<code class="func">LShapes</code>  <a href="chap9_mj.html#X7C5EED6D852C24DD">9.1-5</a>  <br />
<code class="func">LShapesOfNumericalSemigroup</code>  <a href="chap9_mj.html#X7C5EED6D852C24DD">9.1-5</a>  <br />
<code class="func">MaximalDenumerant</code>  <a href="chap9_mj.html#X811E5FFB83CCA4CE">9.2-16</a>  <br />
    for a numerical semigroup and one of its elements  <a href="chap9_mj.html#X790308B07AB1A5C8">9.2-14</a>  <br />
    for element in numerical semigroup  <a href="chap9_mj.html#X790308B07AB1A5C8">9.2-14</a>  <br />
<code class="func">MaximalDenumerantOfElementInNumericalSemigroup</code>  <a href="chap9_mj.html#X790308B07AB1A5C8">9.2-14</a>  <br />
<code class="func">MaximalDenumerantOfNumericalSemigroup</code>  <a href="chap9_mj.html#X811E5FFB83CCA4CE">9.2-16</a>  <br />
<code class="func">MaximalDenumerantOfSetOfFactorizations</code>  <a href="chap9_mj.html#X7DFC4ED0827761C1">9.2-15</a>  <br />
<code class="func">MaximalElementsOfGoodSemigroup</code>  <a href="chap12_mj.html#X83F444E586D96723">12.2-8</a>  <br />
<code class="func">MaximalIdeal</code>, for affine semigroups  <a href="chap11_mj.html#X79ECACE4793A6B00">11.5-13</a>  <br />
    for numerical semigroups  <a href="chap7_mj.html#X7D77F1BA7F22DA70">7.1-28</a>  <br />
<code class="func">MaximalIdealOfNumericalSemigroup</code>  <a href="chap7_mj.html#X7D77F1BA7F22DA70">7.1-28</a>  <br />
<code class="func">MaximumDegree</code>  <a href="chap9_mj.html#X7AEFE27E87F51114">9.2-12</a>  <br />
<code class="func">MaximumDegreeOfElementWRTNumericalSemigroup</code>  <a href="chap9_mj.html#X7AEFE27E87F51114">9.2-12</a>  <br />
<code class="func">MEDClosure</code>  <a href="chap8_mj.html#X7A6379A382D1FC20">8.1-2</a>  <br />
<code class="func">MEDNumericalSemigroupClosure</code>  <a href="chap8_mj.html#X7A6379A382D1FC20">8.1-2</a>  <br />
<code class="func">MicroInvariants</code>  <a href="chap7_mj.html#X87AC917578976B1E">7.3-11</a>  <br />
<code class="func">MicroInvariantsOfNumericalSemigroup</code>  <a href="chap7_mj.html#X87AC917578976B1E">7.3-11</a>  <br />
<code class="func">MinimalArfGeneratingSystemOfArfNumericalSemigroup</code>  <a href="chap8_mj.html#X83C242468796950D">8.2-3</a>  <br />
<code class="func">MinimalGeneratingSystem</code>, for affine semigroup  <a href="chap11_mj.html#X7ED1549486C251CA">11.1-12</a>  <br />
    for ideal of numerical semigroup  <a href="chap7_mj.html#X85144E0F791038AE">7.1-3</a>  <br />
    for numerical semigroup  <a href="chap3_mj.html#X850F430A8284DF9A">3.1-2</a>  <br />
<code class="func">MinimalGeneratingSystemOfIdealOfNumericalSemigroup</code>  <a href="chap7_mj.html#X85144E0F791038AE">7.1-3</a>  <br />
<code class="func">MinimalGeneratingSystemOfNumericalSemigroup</code>  <a href="chap3_mj.html#X850F430A8284DF9A">3.1-2</a>  <br />
<code class="func">MinimalGenerators</code>, for affine semigroup  <a href="chap11_mj.html#X7ED1549486C251CA">11.1-12</a>  <br />
    for ideal of an affine semigroup  <a href="chap11_mj.html#X7F16A5A27CBB7B93">11.5-3</a>  <br />
    for ideal of numerical semigroup  <a href="chap7_mj.html#X85144E0F791038AE">7.1-3</a>  <br />
    for numerical semigroup  <a href="chap3_mj.html#X850F430A8284DF9A">3.1-2</a>  <br />
<code class="func">MinimalGoodGeneratingSystemOfGoodIdeal</code>  <a href="chap12_mj.html#X84636A127ECEDA24">12.5-4</a>  <br />
<code class="func">MinimalGoodGeneratingSystemOfGoodSemigroup</code>  <a href="chap12_mj.html#X8742875C836C9488">12.2-11</a>  <br />
<code class="func">MinimalGoodGenerators</code>  <a href="chap12_mj.html#X8742875C836C9488">12.2-11</a>  <br />
<code class="func">MinimalMEDGeneratingSystemOfMEDNumericalSemigroup</code>  <a href="chap8_mj.html#X848FD3FA7DB2DD4C">8.1-3</a>  <br />
<code class="func">MinimalPresentation</code>, for affine semigroup  <a href="chap11_mj.html#X80A7BD7478D8A94A">11.3-6</a>  <br />
    for numerical semigroups  <a href="chap4_mj.html#X81A2C4317A0BA48D">4.1-1</a>  <br />
<code class="func">MinimalPresentationOfAffineSemigroup</code>  <a href="chap11_mj.html#X80A7BD7478D8A94A">11.3-6</a>  <br />
<code class="func">MinimalPresentationOfNumericalSemigroup</code>  <a href="chap4_mj.html#X81A2C4317A0BA48D">4.1-1</a>  <br />
<code class="func">Minimum</code>, minimum of ideal of numerical semigroup  <a href="chap7_mj.html#X821919B47D3D191A">7.1-14</a>  <br />
<code class="func">ModularNumericalSemigroup</code>  <a href="chap2_mj.html#X87206D597873EAFF">2.1-8</a>  <br />
<code class="func">MoebiusFunction</code>  <a href="chap9_mj.html#X7DF6825185C619AC">9.6-2</a>  <br />
<code class="func">MoebiusFunctionAssociatedToNumericalSemigroup</code>  <a href="chap9_mj.html#X853930E97F7F8A43">9.6-1</a>  <br />
<code class="func">MonotoneCatenaryDegreeOfAffineSemigroup</code>  <a href="chap11_mj.html#X8510C1527F2FE18E">11.4-9</a>  <br />
<code class="func">MonotoneCatenaryDegreeOfNumericalSemigroup</code>  <a href="chap9_mj.html#X7E0458187956C395">9.3-11</a>  <br />
<code class="func">MonotoneCatenaryDegreeOfSetOfFactorizations</code>  <a href="chap9_mj.html#X845D850F7812E176">9.3-4</a>  <br />
<code class="func">MultipleOfIdealOfAffineSemigroup</code>  <a href="chap11_mj.html#X7D056A0C7F868209">11.5-9</a>  <br />
<code class="func">MultipleOfIdealOfNumericalSemigroup</code>  <a href="chap7_mj.html#X857FE5C57EE98F5E">7.1-22</a>  <br />
<code class="func">MultipleOfNumericalSemigroup</code>  <a href="chap5_mj.html#X7BE8DD6884DE693F">5.2-4</a>  <br />
<code class="func">Multiplicity</code>, for good semigroups  <a href="chap12_mj.html#X7B2F716B7985872B">12.2-3</a>  <br />
    for numerical semigroup  <a href="chap3_mj.html#X80D23F08850A8ABD">3.1-1</a>  <br />
<code class="func">MultiplicityOfNumericalSemigroup</code>  <a href="chap3_mj.html#X80D23F08850A8ABD">3.1-1</a>  <br />
<code class="func">MultiplicitySequence</code>  <a href="chap7_mj.html#X8344B30D7EDE3B04">7.3-10</a>  <br />
<code class="func">MultiplicitySequenceOfNumericalSemigroup</code>  <a href="chap7_mj.html#X8344B30D7EDE3B04">7.3-10</a>  <br />
<code class="func">NearlyGorensteinVectors</code>  <a href="chap6_mj.html#X78049FC380A0006E">6.4-3</a>  <br />
<code class="func">NextElementOfNumericalSemigroup</code>  <a href="chap3_mj.html#X84345D5E7CAA9B77">3.1-10</a>  <br />
<code class="func">NumberElement_IdealOfNumericalSemigroup</code>  <a href="chap7_mj.html#X7B8B46CF7E81513D">7.1-17</a>  <br />
<code class="func">NumberElement_NumericalSemigroup</code>  <a href="chap3_mj.html#X78F4A7A7797E26D4">3.1-12</a>  <br />
<code class="func">NumericalDuplication</code>  <a href="chap5_mj.html#X7F395079839BBE9D">5.2-5</a>  <br />
<code class="func">NumericalSemigroup</code>, by (closed) interval  <a href="chap2_mj.html#X7D8F9D2A8173EF32">2.1-10</a>  <br />
    by affine map  <a href="chap2_mj.html#X7ACD94F478992185">2.1-7</a>  <br />
    by Apery list  <a href="chap2_mj.html#X799AC8727DB61A99">2.1-3</a>  <br />
    by fundamental gaps  <a href="chap2_mj.html#X86AC8B0E7C11147F">2.1-6</a>  <br />
    by gaps  <a href="chap2_mj.html#X7BB0343D86EC5FEC">2.1-5</a>  <br />
    by generators  <a href="chap2_mj.html#X7D74299B8083E882">2.1-1</a>  <br />
    by modular condition  <a href="chap2_mj.html#X87206D597873EAFF">2.1-8</a>  <br />
    by open interval  <a href="chap2_mj.html#X7C800FB37D76612F">2.1-11</a>  <br />
    by proportionally modular condition  <a href="chap2_mj.html#X879171CD7AC80BB5">2.1-9</a>  <br />
    by small elements  <a href="chap2_mj.html#X81A7E3527998A74A">2.1-4</a>  <br />
    by subadditive function  <a href="chap2_mj.html#X86D9D2EE7E1C16C2">2.1-2</a>  <br />
<code class="func">NumericalSemigroupByAffineMap</code>  <a href="chap2_mj.html#X7ACD94F478992185">2.1-7</a>  <br />
<code class="func">NumericalSemigroupByAperyList</code>  <a href="chap2_mj.html#X799AC8727DB61A99">2.1-3</a>  <br />
<code class="func">NumericalSemigroupByFundamentalGaps</code>  <a href="chap2_mj.html#X86AC8B0E7C11147F">2.1-6</a>  <br />
<code class="func">NumericalSemigroupByGaps</code>  <a href="chap2_mj.html#X7BB0343D86EC5FEC">2.1-5</a>  <br />
<code class="func">NumericalSemigroupByGenerators</code>  <a href="chap2_mj.html#X7D74299B8083E882">2.1-1</a>  <br />
<code class="func">NumericalSemigroupByInterval</code>  <a href="chap2_mj.html#X7D8F9D2A8173EF32">2.1-10</a>  <br />
<code class="func">NumericalSemigroupByNuSequence</code>  <a href="chap9_mj.html#X871CD69180783663">9.6-4</a>  <br />
<code class="func">NumericalSemigroupByOpenInterval</code>  <a href="chap2_mj.html#X7C800FB37D76612F">2.1-11</a>  <br />
<code class="func">NumericalSemigroupBySmallElements</code>  <a href="chap2_mj.html#X81A7E3527998A74A">2.1-4</a>  <br />
<code class="func">NumericalSemigroupBySubAdditiveFunction</code>  <a href="chap2_mj.html#X86D9D2EE7E1C16C2">2.1-2</a>  <br />
<code class="func">NumericalSemigroupByTauSequence</code>  <a href="chap9_mj.html#X7F4CBFF17BBB37DE">9.6-5</a>  <br />
<code class="func">NumericalSemigroupDuplication</code>  <a href="chap12_mj.html#X82A8863E78650FC4">12.1-2</a>  <br />
<code class="func">NumericalSemigroupFromNumericalSemigroupPolynomial</code>  <a href="chap10_mj.html#X855497F77D13436F">10.1-3</a>  <br />
<code class="func">NumericalSemigroupPolynomial</code>  <a href="chap10_mj.html#X8391C8E782FBFA8A">10.1-1</a>  <br />
<code class="func">NumericalSemigroupsPlanarSingularityWithFrobeniusNumber</code>  <a href="chap6_mj.html#X8784D11578C912F2">6.2-10</a>  <br />
<code class="func">NumericalSemigroupsWithFrobeniusNumber</code>  <a href="chap5_mj.html#X87369D567AA6DBA0">5.4-3</a>  <br />
<code class="func">NumericalSemigroupsWithFrobeniusNumberAndMultiplicity</code>  <a href="chap5_mj.html#X7DB3994B872C4940">5.4-2</a>  <br />
<code class="func">NumericalSemigroupsWithFrobeniusNumberFG</code>  <a href="chap5_mj.html#X81759C3482B104D6">5.4-1</a>  <br />
<code class="func">NumericalSemigroupsWithFrobeniusNumberPC</code>  <a href="chap5_mj.html#X80CACB287B4609E1">5.4-4</a>  <br />
<code class="func">NumericalSemigroupsWithGenus</code>  <a href="chap5_mj.html#X86970F6A868DEA95">5.6-1</a>  <br />
<code class="func">NumericalSemigroupsWithGenusPC</code>  <a href="chap5_mj.html#X7B4F3B5E841E3853">5.6-2</a>  <br />
<code class="func">NumericalSemigroupsWithMaxPrimitive</code>  <a href="chap5_mj.html#X875A8B337DFA01F0">5.5-2</a>  <br />
<code class="func">NumericalSemigroupsWithMaxPrimitiveAndMultiplicity</code>  <a href="chap5_mj.html#X7C17AB04877559B6">5.5-1</a>  <br />
<code class="func">NumericalSemigroupsWithMaxPrimitivePC</code>  <a href="chap5_mj.html#X7DA1FA7780684019">5.5-3</a>  <br />
<code class="func">NumericalSemigroupsWithPseudoFrobeniusNumbers</code>  <a href="chap5_mj.html#X7D6775A57B800892">5.7-3</a>  <br />
<code class="func">NumericalSemigroupWithRandomElementsAndFrobenius</code>  <a href="chapB_mj.html#X7B459C8C825194E4">B.1-6</a>  <br />
<code class="func">NumSgpsUse4ti2</code>  <a href="chap13_mj.html#X8736665E7CBEAB20">13.1-1</a>  <br />
<code class="func">NumSgpsUse4ti2gap</code>  <a href="chap13_mj.html#X875001717A8CF032">13.1-2</a>  <br />
<code class="func">NumSgpsUseNormalize</code>  <a href="chap13_mj.html#X875040237A692C3C">13.1-3</a>  <br />
<code class="func">NumSgpsUseSingular</code>  <a href="chap13_mj.html#X7CD12ADD78089CBE">13.1-4</a>  <br />
<code class="func">NumSgpsUseSingularInterface</code>  <a href="chap13_mj.html#X7F7699A9829940C2">13.1-5</a>  <br />
<code class="func">OmegaPrimality</code>, for a numerical semigroup  <a href="chap9_mj.html#X80B48B7886A93FAC">9.4-3</a>  <br />
    for a numerical semigroup and one of its elements  <a href="chap9_mj.html#X83075D7F837ACCB8">9.4-1</a>  <br />
    for an affine semigroup  <a href="chap11_mj.html#X7A3571E187D0FCDE">11.4-12</a>  <br />
    for an affine semigroup and one of its elements  <a href="chap11_mj.html#X850790EE8442FD7D">11.4-11</a>  <br />
    for an element in a numerical semigroup  <a href="chap9_mj.html#X83075D7F837ACCB8">9.4-1</a>  <br />
    for an element in an affine semigroup  <a href="chap11_mj.html#X850790EE8442FD7D">11.4-11</a>  <br />
<code class="func">OmegaPrimalityOfAffineSemigroup</code>  <a href="chap11_mj.html#X7A3571E187D0FCDE">11.4-12</a>  <br />
<code class="func">OmegaPrimalityOfElementInAffineSemigroup</code>  <a href="chap11_mj.html#X850790EE8442FD7D">11.4-11</a>  <br />
<code class="func">OmegaPrimalityOfElementInNumericalSemigroup</code>  <a href="chap9_mj.html#X83075D7F837ACCB8">9.4-1</a>  <br />
<code class="func">OmegaPrimalityOfElementListInNumericalSemigroup</code>  <a href="chap9_mj.html#X85EB5E2581FFB8B2">9.4-2</a>  <br />
<code class="func">OmegaPrimalityOfNumericalSemigroup</code>  <a href="chap9_mj.html#X80B48B7886A93FAC">9.4-3</a>  <br />
<code class="func">OverSemigroups</code>, of a numerical semigroup  <a href="chap5_mj.html#X7FBA34637ADAFEDA">5.3-1</a>  <br />
<code class="func">OverSemigroupsNumericalSemigroup</code>  <a href="chap5_mj.html#X7FBA34637ADAFEDA">5.3-1</a>  <br />
<code class="func">PrimitiveRelationsOfKernelCongruence</code>  <a href="chap11_mj.html#X78B04C198258D3F8">11.3-2</a>  <br />
<code class="func">ProfileOfNumericalSemigroup</code>  <a href="chap3_mj.html#X7B45623E7D539CB6">3.2-3</a>  <br />
<code class="func">ProjectionOfAGoodSemigroup</code>  <a href="chap12_mj.html#X806865CB794CAC5D">12.2-12</a>  <br />
<code class="func">ProportionallyModularNumericalSemigroup</code>  <a href="chap2_mj.html#X879171CD7AC80BB5">2.1-9</a>  <br />
<code class="func">PseudoFrobenius</code>  <a href="chap3_mj.html#X861DED207A2B5419">3.1-24</a>  <br />
    for affine semigroup  <a href="chap11_mj.html#X80C3CD2082CE02F7">11.1-9</a>  <br />
    for ideal of numerical semigroup  <a href="chap7_mj.html#X805149CA847F6461">7.1-12</a>  <br />
<code class="func">PseudoFrobeniusOfIdealOfNumericalSemigroup</code>, for ideal of numerical semigroup  <a href="chap7_mj.html#X805149CA847F6461">7.1-12</a>  <br />
<code class="func">PseudoFrobeniusOfNumericalSemigroup</code>  <a href="chap3_mj.html#X861DED207A2B5419">3.1-24</a>  <br />
<code class="func">QuotientOfNumericalSemigroup</code>  <a href="chap5_mj.html#X83CCE63C82F34C25">5.2-3</a>  <br />
<code class="func">RandomAffineSemigroup</code>  <a href="chapB_mj.html#X82569F0079599515">B.2-2</a>  <br />
<code class="func">RandomAffineSemigroupWithGenusAndDimension</code>  <a href="chapB_mj.html#X7FBFEE457E823E15">B.2-1</a>  <br />
<code class="func">RandomFullAffineSemigroup</code>  <a href="chapB_mj.html#X7F7BB53A7DF77ED5">B.2-3</a>  <br />
<code class="func">RandomGoodSemigroupWithFixedMultiplicity</code>  <a href="chapB_mj.html#X7F582A997B4B05EE">B.3-1</a>  <br />
<code class="func">RandomListForNS</code>  <a href="chapB_mj.html#X79E73F8787741190">B.1-2</a>  <br />
<code class="func">RandomListRepresentingSubAdditiveFunction</code>  <a href="chapB_mj.html#X8665F6B08036AFFB">B.1-5</a>  <br />
<code class="func">RandomModularNumericalSemigroup</code>  <a href="chapB_mj.html#X82E22E9B843DF70F">B.1-3</a>  <br />
<code class="func">RandomNumericalSemigroup</code>  <a href="chapB_mj.html#X7CC477867B00AD13">B.1-1</a>  <br />
<code class="func">RandomNumericalSemigroupWithGenus</code>  <a href="chapB_mj.html#X78A2A0107CCBBB79">B.1-7</a>  <br />
<code class="func">RandomProportionallyModularNumericalSemigroup</code>  <a href="chapB_mj.html#X8598F10A7CD4A135">B.1-4</a>  <br />
<code class="func">RatliffRushClosure</code>  <a href="chap7_mj.html#X82C2329380B9882D">7.3-8</a>  <br />
<code class="func">RatliffRushClosureOfIdealOfNumericalSemigroup</code>  <a href="chap7_mj.html#X82C2329380B9882D">7.3-8</a>  <br />
<code class="func">RatliffRushNumber</code>  <a href="chap7_mj.html#X7D6F643687DF8724">7.3-7</a>  <br />
<code class="func">RatliffRushNumberOfIdealOfNumericalSemigroup</code>  <a href="chap7_mj.html#X7D6F643687DF8724">7.3-7</a>  <br />
<code class="func">RClassesOfSetOfFactorizations</code>  <a href="chap9_mj.html#X813D2A3A83916A36">9.1-4</a>  <br />
<code class="func">ReductionNumber</code>, for ideals of numerical semigroups  <a href="chap7_mj.html#X7FAABCBF8299B12F">7.3-4</a>  <br />
<code class="func">ReductionNumberIdealNumericalSemigroup</code>  <a href="chap7_mj.html#X7FAABCBF8299B12F">7.3-4</a>  <br />
<code class="func">RemoveMinimalGeneratorFromAffineSemigroup</code>  <a href="chap11_mj.html#X80516BCC78FDD45D">11.1-13</a>  <br />
<code class="func">RemoveMinimalGeneratorFromNumericalSemigroup</code>  <a href="chap5_mj.html#X7C94611F7DD9E742">5.1-1</a>  <br />
<code class="func">RepresentsGapsOfNumericalSemigroup</code>  <a href="chap2_mj.html#X78906CCD7BEE0E58">2.2-3</a>  <br />
<code class="func">RepresentsPeriodicSubAdditiveFunction</code>  <a href="chapA_mj.html#X8466A4DC82F07579">A.2-1</a>  <br />
<code class="func">RepresentsSmallElementsOfGoodSemigroup</code>  <a href="chap12_mj.html#X82D40159783F0D48">12.2-6</a>  <br />
<code class="func">RepresentsSmallElementsOfNumericalSemigroup</code>  <a href="chap2_mj.html#X87B02A9F7AF90CB9">2.2-2</a>  <br />
<code class="func">RFMatrices</code>  <a href="chap9_mj.html#X86062FCA85A51870">9.1-6</a>  <br />
<code class="func">RthElementOfNumericalSemigroup</code>  <a href="chap3_mj.html#X7B6C82DD86E5422F">3.1-11</a>  <br />
<code class="func">SaturatedClosure</code>, for numerical semigroups  <a href="chap8_mj.html#X78E6F00287A23FC1">8.3-2</a>  <br />
<code class="func">SaturatedNumericalSemigroupClosure</code>  <a href="chap8_mj.html#X78E6F00287A23FC1">8.3-2</a>  <br />
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