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<?xml version="1.0" encoding="UTF-8" ?>DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Strict//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-strict.dtd " >html xmlns="http://www.w3.org/1999/xhtml " xml:lang="en" >head >script type="text/javascript" "https://cdn.jsdelivr.net/npm/mathjax@2/MathJax.js?config=TeX-AMS-MML_HTMLorMML " >script >title >GAP (NumericalSgps) - Index</title >meta http-equiv="content-type" content="text/html; charset=UTF-8" />meta name="generator" content="GAPDoc2HTML" />link rel="stylesheet" type="text/css" href="manual.css" />script src="manual.js" type="text/javascript" ></script >script type="text/javascript" >overwriteStyle();</script >head >body class="chapInd" onload="jscontent()" >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 >div class="chlinkprevnexttop" > <a href="chap0_mj.html" >[Top of Book]</a> <a href="chap0_mj.html#contents" >[Contents]</a> <a href="chapBib_mj.html" >[Previous Chapter]</a> </div >"mathjaxlink" class="pcenter" ><a href="chapInd.html" >[MathJax off]</a></p>"X83A0356F839C696F" name="X83A0356F839C696F" ></a></p>div class="index" >code class="func" >*</code >, for multiple of ideal of affine semigroup <a href="chap11_mj.html#X7D056A0C7F868209" >11.5-9</a> <br />"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 />"chap7_mj.html#X78E5F44E81485C17" >7.1-1</a> <br />"chap11_mj.html#X83A4392281981911" >11.5-8</a> <br />"chap7_mj.html#X7B39610D7AD5A654" >7.1-21</a> <br />"chap11_mj.html#X788264A27ACD6AB5" >11.5-10</a> <br />"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" br />"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 />"chap12_mj.html#X79EBBF6D7A2C9A12" >12.2-1</a> <br />"chap2_mj.html#X864C2D8E80DD6D16" >2.2-7</a> <br />"chap11_mj.html#X851788D781A13C50" >11.1-17</a> <br "chap11_mj.html#X7F00912C853AA83D" >11.5-7</a> <br />"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 />"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 />"chap11_mj.html#X83F6DDB787E07771" >11.1-5</a> <br />"chap11_mj.html#X7D7B03E17C8DBEA2" >11.1-1</a> <br />"chap11_mj.html#X7846AD1081C14EF1" >11.1-3</a> <br />"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" 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 />"chap7_mj.html#X82D2784B813C67D8" >7.3-13</a> <br />"chap3_mj.html#X7CB24F5E84793BE1" >3.1-15</a> <br />"chap3_mj.html#X7D06B00D7C305C64" >3.1-17</a> <br />"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 />"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 />"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 />"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 />"chap11_mj.html#X80742F2F7DECDB4C" >11.4-6</a> <br />"chap9_mj.html#X797147AA796D1AFE" >9.3-5</a> <br />"chap9_mj.html#X785B83F17BEEA894" >9.3-7</a> <br />"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 />"chap7_mj.html#X7EDDC78883A98A6E" >7.1-10</a> <br />"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 />"chap9_mj.html#X79C953B5846F7057" >9.2-5</a> <br />"chap11_mj.html#X839549448300AD26" >11.4-5</a> <br />"chap9_mj.html#X7DB8BA5B7D6F81CB" >9.2-6</a> <br />"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 />"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 />"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 />"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 />"chap9_mj.html#X7A2B01BB87086283" >9.2-4</a> <br />"chap9_mj.html#X860E461182B0C6F5" >9.2-3</a> <br />"chap11_mj.html#X7F394FA67BE5151B" >11.4-3</a> <br />"chap9_mj.html#X860E461182B0C6F5" >9.2-3</a> <br />"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 />"chap9_mj.html#X80EF105B82447F30" >9.1-2</a> <br />"chap9_mj.html#X80EF105B82447F30" >9.1-2</a> <br />"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 />"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 />"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 />"chap11_mj.html#X8086C1EE7EAAB33D" >11.5-4</a> <br />"chap7_mj.html#X7A842A4385B73C63" >7.1-4</a> <br />"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 />"chap12_mj.html#X7D70CD958333D49B" >12.2-13</a> <br />"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 />"chap7_mj.html#X7B34033979009F64" >7.1-27</a> <br />"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 />"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 />"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 "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 />"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 />"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 />"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 />"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 />"chap9_mj.html#X790308B07AB1A5C8" >9.2-14</a> <br />"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 />"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 />"chap7_mj.html#X85144E0F791038AE" >7.1-3</a> <br />"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 />"chap11_mj.html#X7F16A5A27CBB7B93" >11.5-3</a> <br />"chap7_mj.html#X85144E0F791038AE" >7.1-3</a> <br />"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 />"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 />"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 />map <a href="chap2_mj.html#X7ACD94F478992185" >2.1-7</a> <br />"chap2_mj.html#X799AC8727DB61A99" >2.1-3</a> <br />"chap2_mj.html#X86AC8B0E7C11147F" >2.1-6</a> <br />"chap2_mj.html#X7BB0343D86EC5FEC" >2.1-5</a> <br />"chap2_mj.html#X7D74299B8083E882" >2.1-1</a> <br />"chap2_mj.html#X87206D597873EAFF" >2.1-8</a> <br />"chap2_mj.html#X7C800FB37D76612F" >2.1-11</a> <br />"chap2_mj.html#X879171CD7AC80BB5" >2.1-9</a> <br />small elements <a href="chap2_mj.html#X81A7E3527998A74A" >2.1-4</a> <br />"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" 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 />"chap9_mj.html#X83075D7F837ACCB8" >9.4-1</a> <br />"chap11_mj.html#X7A3571E187D0FCDE" >11.4-12</a> <br />"chap11_mj.html#X850790EE8442FD7D" >11.4-11</a> <br />"chap9_mj.html#X83075D7F837ACCB8" >9.4-1</a> <br />"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 />"chap11_mj.html#X80C3CD2082CE02F7" >11.1-9</a> <br />"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 />quality 100%
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