products/Sources/formale Sprachen/GAP/pkg/numericalsgps/doc/chap0_mj.html
<?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) - Contents</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="chap0" 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="chap1_mj.html" >[Next Chapter]</a> </div >"mathjaxlink" class="pcenter" ><a href="chap0.html" >[MathJax off]</a></p>"X7D2C85EC87DD46E5" name="X7D2C85EC87DD46E5" ></a></p>div class="pcenter" >h1 ><strong class="pkg" >numericalsgps</strong >-- a package for numerical semigroups</h1 >div >br />Email: <span class="URL" ><a href="mailto:mdelgado@fc.up.pt" >mdelgado@fc.up.pt</a></span >br />Homepage: <span class="URL" ><a href="http://www.fc.up.pt/cmup/mdelgado " >http://www.fc.up.pt/cmup/mdelgado</a></span >br />Email: <span class="URL" ><a href="mailto:pedro@ugr.es" >pedro@ugr.es</a></span >br />Homepage: <span class="URL" ><a href="http://www.ugr.es/~pedro " >http://www.ugr.es/~pedro</a></span >"X81488B807F2A1CF1" name="X81488B807F2A1CF1" ></a></p>a, Spain</p>em >Numericalsgps</em > is free software; you can redistribute it and/or modify it under the terms of the <span class="URL" ><a href="http://www.fsf.org/licenses/gpl.html " >GNU General Public License</a></span > as published by the Free Software Foundation; either version 2 of the License, or (at your option ) any later version. For details , see the file 'GPL' included in the package or see the FSF's own site. "X82A988D47DFAFCFA" name="X82A988D47DFAFCFA" ></a></p>available in Appendix <a href="chapC_mj.html#X7F1146137C92FF0E" ><span class="RefLink" >C</span ></a>. We are also in debt with H. Schönemann, C. Söeger and M. Barakat for their fruitful advices concerning SingularInterface, Singular, Normaliz, NormalizInterface and GradedModules.</p>code class="code" >GAPDays</code > in their several editions.</p>), Universidad de Granada, for providing the computing time , specially Rafael Arco Arredondo for installing this package and the extra software needed in alhambra.ugr.es, and Santiago Melchor Ferrer for helping in job submission to the cluster.</p>strong class="button" >Funding</strong ></p>'s work was (partially) supported by the Centro de Matemática da Universidade do Porto (CMUP), financed by FCT (Portugal) through the programs POCTI (Programa Operacional "Ciência, Tecnologia, Inovação") and POSI (Programa Operacional Sociedade da Informação), with national and European Community structural funds and a sabbatical grant of FCT. e Andalucía group FQM-343, and FEDER founds.</p>rship given by <em >Centro de Matemática da Universidade do Porto</em >.</p>y the <em >Centro de Matemática da Universidade do Porto</em > (CMUP), funded by the European Regional Development Fund through the programme COMPETE and by the Portuguese Government through the FCT - Fundação para a Ciência e a Tecnologia under the project PEst-C/MAT/UI0144/2011.</p>67-P, which were funded by Ministerio de Economía y Competitividad and the Fondo Europeo de Desarrollo Regional FEDER.</p>AT/00144/2019), which is funded by FCT (Portugal) with national (MEC) and European structural funds through the programs FEDER, under the partnership agreement PT2020.</p>ded by Ministerio de Economía y Competitividad and Fondo Europeo de Desarrollo Regional FEDER.</p>.13039/501100011033 and by "ERDF A way of making Europe" .</p>guese national funds through FCT – Fundação para a Ciência e a Tecnologia, I.P., under the project with reference UIDB/00144/2020 and UIDP/00144/2020.</p>"Proyecto de Excelencia de la Junta de Andalucía" (ProyExcel 00868).</p>"X7982162280BC7A61" name="X7982162280BC7A61" ></a></p>sabbatical year. Since Version 0.96 (released in 2008), the package is maintained by the first two authors. Bug reports, suggestions and comments are, of course, welcome. Please use our email addresses to this effect.</p>cite it in addition to GAP itself, following the scheme proposed in <span class="URL" ><a href="https://www.gap-system.org/Contacts/cite.html " >https://www.gap-system.org/Contacts/cite .html </a></span >.</p>lease cite in addition these authors, referring "software implementations available in the GAP package NumericalSgps" .</p>"X8537FEB07AF2BEC8" name="X8537FEB07AF2BEC8" ></a></p>div class="contents" >"contents" name="contents" ></a></h3>div class="ContChap" ><a href="chap1_mj.html#X7DFB63A97E67C0A1" >1 <span class="Heading" >span ></a>div >div class="ContChap" ><a href="chap2_mj.html#X8324E5D97DC2A801" >2 <span class="Heading" >span ></a>div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chap2_mj.html#X7E89D7EB7FCC2197" >2.1 <span class="Heading" >span ></a>span >div class="ContSSBlock" >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap2_mj.html#X7D74299B8083E882" >2.1-1 NumericalSemigroup</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap2_mj.html#X86D9D2EE7E1C16C2" >2.1-2 NumericalSemigroupBySubAdditiveFunction</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap2_mj.html#X799AC8727DB61A99" >2.1-3 NumericalSemigroupByAperyList</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap2_mj.html#X81A7E3527998A74A" >2.1-4 NumericalSemigroupBySmallElements</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap2_mj.html#X7BB0343D86EC5FEC" >2.1-5 NumericalSemigroupByGaps</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap2_mj.html#X86AC8B0E7C11147F" >2.1-6 NumericalSemigroupByFundamentalGaps</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap2_mj.html#X7ACD94F478992185" >2.1-7 NumericalSemigroupByAffineMap</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap2_mj.html#X87206D597873EAFF" >2.1-8 ModularNumericalSemigroup</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap2_mj.html#X879171CD7AC80BB5" >2.1-9 ProportionallyModularNumericalSemigroup</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap2_mj.html#X7D8F9D2A8173EF32" >2.1-10 NumericalSemigroupByInterval</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap2_mj.html#X7C800FB37D76612F" >2.1-11 NumericalSemigroupByOpenInterval</a></span >div ></div >div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chap2_mj.html#X7EF4254C81ED6665" >2.2 <span class="Heading" >Some basic tests</span ></a>span >div class="ContSSBlock" >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap2_mj.html#X7B1B6B8C82BD7084" >2.2-1 IsNumericalSemigroup</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap2_mj.html#X87B02A9F7AF90CB9" >2.2-2 RepresentsSmallElementsOfNumericalSemigroup</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap2_mj.html#X78906CCD7BEE0E58" >2.2-3 RepresentsGapsOfNumericalSemigroup</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap2_mj.html#X84A611557B5ACF42" >2.2-4 IsAperyListOfNumericalSemigroup</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap2_mj.html#X86D5B3517AF376D4" >2.2-5 IsSubsemigroupOfNumericalSemigroup</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap2_mj.html#X79CA175481F8105F" >2.2-6 IsSubset</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap2_mj.html#X864C2D8E80DD6D16" >2.2-7 BelongsToNumericalSemigroup</a></span >div ></div >div >div class="ContChap" ><a href="chap3_mj.html#X7A9D13C778697F6C" >3 <span class="Heading" >span ></a>div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chap3_mj.html#X87AF9D4F7FD9E820" >3.1 <span class="Heading" >span ></a>span >div class="ContSSBlock" >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap3_mj.html#X80D23F08850A8ABD" >3.1-1 Multiplicity</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap3_mj.html#X850F430A8284DF9A" >3.1-2 Generators</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap3_mj.html#X7884AE27790E687F" >3.1-3 EmbeddingDimension</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap3_mj.html#X84A6B16E8113167B" >3.1-4 SmallElements</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap3_mj.html#X7A56569F853DADED" >3.1-5 Length</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap3_mj.html#X7F0EDFA77F929120" >3.1-6 FirstElementsOfNumericalSemigroup</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap3_mj.html#X7D2B3AA9823371AE" >3.1-7 ElementsUpTo</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap3_mj.html#X81A2505E8120F4D7" ><code >3.1-8 <span >\</span >[ <span >\</span >]</code ></a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap3_mj.html#X7A34F16F8112C2B5" ><code >3.1-9 \{ \}</code ></a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap3_mj.html#X84345D5E7CAA9B77" >3.1-10 NextElementOfNumericalSemigroup</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap3_mj.html#X7B6C82DD86E5422F" >3.1-11 ElementNumber_NumericalSemigroup</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap3_mj.html#X78F4A7A7797E26D4" >3.1-12 NumberElement_NumericalSemigroup</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap3_mj.html#X867ABF7C7991ED7C" >3.1-13 Iterator</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap3_mj.html#X7E6F5D6F7B0C9635" >3.1-14 Difference</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap3_mj.html#X7CB24F5E84793BE1" >3.1-15 AperyList</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap3_mj.html#X80431F487C71D67B" >3.1-16 AperyList</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap3_mj.html#X7D06B00D7C305C64" >3.1-17 AperyList</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap3_mj.html#X8022CC477E9BF678" >3.1-18 AperyListOfNumericalSemigroupAsGraph</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap3_mj.html#X80B398537887FD87" >3.1-19 KunzCoordinates</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap3_mj.html#X7C21E5417A3894EC" >3.1-20 KunzPolytope</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap3_mj.html#X7802096584D32795" >3.1-21 CocycleOfNumericalSemigroupWRTElement</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap3_mj.html#X847BAD9480D186C0" >3.1-22 FrobeniusNumber</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap3_mj.html#X835C729D7D8B1B36" >3.1-23 Conductor</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap3_mj.html#X861DED207A2B5419" >3.1-24 PseudoFrobenius</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap3_mj.html#X865E2E12804CFCD3" >3.1-25 Type</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap3_mj.html#X8688B1837E4BC079" >3.1-26 Gaps</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap3_mj.html#X7F71983880DF4B9D" >3.1-27 Weight</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap3_mj.html#X7EB81BF886DDA29A" >3.1-28 Deserts</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap3_mj.html#X82B1868F7A780B49" >3.1-29 IsOrdinary</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap3_mj.html#X83D4AFE882A79096" >3.1-30 IsAcute</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap3_mj.html#X7CCFC5267FD27DDE" >3.1-31 Holes</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap3_mj.html#X794E615F85C2AAB0" >3.1-32 LatticePathAssociatedToNumericalSemigroup</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap3_mj.html#X7E9C8E157C4EAAB0" >3.1-33 Genus</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap3_mj.html#X7EC438CC7BF539D0" >3.1-34 FundamentalGaps</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap3_mj.html#X803D550C78717A7C" >3.1-35 SpecialGaps</a></span >div ></div >div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chap3_mj.html#X7EE22CA979CCAAB9" >3.2 <span class="Heading" >Wilf's conjecture
</
span >
<
div class=
"ContSSBlock" >
<
span class=
"ContSS" ><
br /><
span class=
"nocss" > </
span ><a href=
"chap3_mj.html#X78C2F4C77FB096F0" >3.2-1 WilfNumber</a></
span >
<
span class=
"ContSS" ><
br /><
span class=
"nocss" > </
span ><a href=
"chap3_mj.html#X80F9EC9A7BF4E606" >3.2-2 EliahouNumber</a></
span >
<
span class=
"ContSS" ><
br /><
span class=
"nocss" > </
span ><a href=
"chap3_mj.html#X7B45623E7D539CB6" >3.2-3 ProfileOfNumericalSemigroup</a></
span >
<
span class=
"ContSS" ><
br /><
span class=
"nocss" > </
span ><a href=
"chap3_mj.html#X7846F90E7EA43C47" >3.2-4 EliahouSlicesOfNumericalSemigroup</a></
span >
</
div ></
div >
</
div >
<
div class=
"ContChap" ><a href=
"chap4_mj.html#X7969F7F27AAF0BF1" >4 <
span class=
"Heading" >
Presentations of Numerical Semigroups
</
span ></a>
<
div class=
"ContSect" ><
span class=
"tocline" ><
span class=
"nocss" > </
span ><a href=
"chap4_mj.html#X7969F7F27AAF0BF1" >4.1 <
span class=
"Heading" >Presentations of Numerical Semigroups</
span ></
a>span >div class="ContSSBlock" >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap4_mj.html#X81A2C4317A0BA48D" >4.1-1 MinimalPresentation</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap4_mj.html#X81CC5A6C870377E1" >4.1-2 GraphAssociatedToElementInNumericalSemigroup</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap4_mj.html#X815C0AF17A371E3E" >4.1-3 BettiElements</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap4_mj.html#X7FC66A1B82E86FAF" >4.1-4 IsMinimalRelationOfNumericalSemigroup</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap4_mj.html#X8750A6837EF75CA2" >4.1-5 AllMinimalRelationsOfNumericalSemigroup</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap4_mj.html#X7A9B5AE782CAEA2F" >4.1-6 DegreesOfPrimitiveElementsOfNumericalSemigroup</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap4_mj.html#X7C42DEB68285F2B8" >4.1-7 ShadedSetOfElementInNumericalSemigroup</a></span >div ></div >div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chap4_mj.html#X795E7F5682A6C8B3" >4.2 <span class="Heading" >Binomial ideals associated to numerical semigroups</span ></a>span >div class="ContSSBlock" >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap4_mj.html#X7E6BBAA7803DE7F3" >4.2-1 BinomialIdealOfNumericalSemigroup</a></span >div ></div >div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chap4_mj.html#X7D7EA20F818A5994" >4.3 <span class="Heading" >Uniquely Presented Numerical Semigroups</span ></a>span >div class="ContSSBlock" >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap4_mj.html#X7C6F554486274CAE" >4.3-1 IsUniquelyPresented</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap4_mj.html#X79C010537C838154" >4.3-2 IsGeneric</a></span >div ></div >div >div class="ContChap" ><a href="chap5_mj.html#X8148F05A830EE2D5" >5 <span class="Heading" >span ></a>div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chap5_mj.html#X782F3AB97ACF84B8" >5.1 <span class="Heading" >span ></a>span >div class="ContSSBlock" >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap5_mj.html#X7C94611F7DD9E742" >5.1-1 RemoveMinimalGeneratorFromNumericalSemigroup</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap5_mj.html#X865EA8377D632F53" >5.1-2 AddSpecialGapOfNumericalSemigroup</a></span >div ></div >div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chap5_mj.html#X7DC65D547FB274D8" >5.2 <span class="Heading" >Intersections, sums, quotients, dilatations, numerical duplications and multiples by integers</span ></a>span >div class="ContSSBlock" >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap5_mj.html#X875A8D2679153D4B" >5.2-1 Intersection</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap5_mj.html#X7F308BCE7A0E9D91" ><code >5.2-2 \+</code ></a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap5_mj.html#X83CCE63C82F34C25" >5.2-3 QuotientOfNumericalSemigroup</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap5_mj.html#X7BE8DD6884DE693F" >5.2-4 MultipleOfNumericalSemigroup</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap5_mj.html#X7F395079839BBE9D" >5.2-5 NumericalDuplication</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap5_mj.html#X8176CEB4829084B4" >5.2-6 AsNumericalDuplication</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap5_mj.html#X7DCEC67A82130CD8" >5.2-7 InductiveNumericalSemigroup</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap5_mj.html#X81632C597E3E3DFE" >5.2-8 DilatationOfNumericalSemigroup</a></span >div ></div >div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chap5_mj.html#X867D9A9A87CEB869" >5.3 <span class="Heading" >span ></a>span >div class="ContSSBlock" >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap5_mj.html#X7FBA34637ADAFEDA" >5.3-1 OverSemigroups</a></span >div ></div >div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chap5_mj.html#X8634CFB1848430DC" >5.4 <span class="Heading" > Constructing the set of numerical semigroups with given Frobenius number</span ></a>span >div class="ContSSBlock" >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap5_mj.html#X81759C3482B104D6" >5.4-1 NumericalSemigroupsWithFrobeniusNumberFG</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap5_mj.html#X7DB3994B872C4940" >5.4-2 NumericalSemigroupsWithFrobeniusNumberAndMultiplicity</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap5_mj.html#X87369D567AA6DBA0" >5.4-3 NumericalSemigroupsWithFrobeniusNumber</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap5_mj.html#X80CACB287B4609E1" >5.4-4 NumericalSemigroupsWithFrobeniusNumberPC</a></span >div ></div >div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chap5_mj.html#X8021419483185FE3" >5.5 <span class="Heading" > Constructing the set of numerical semigroups with given maximum primitive</span ></a>span >div class="ContSSBlock" >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap5_mj.html#X7C17AB04877559B6" >5.5-1 NumericalSemigroupsWithMaxPrimitiveAndMultiplicity</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap5_mj.html#X875A8B337DFA01F0" >5.5-2 NumericalSemigroupsWithMaxPrimitive</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap5_mj.html#X7DA1FA7780684019" >5.5-3 NumericalSemigroupsWithMaxPrimitivePC</a></span >div ></div >div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chap5_mj.html#X7D6635CB7D041A54" >5.6 <span class="Heading" >span ></a>span >div class="ContSSBlock" >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap5_mj.html#X86970F6A868DEA95" >5.6-1 NumericalSemigroupsWithGenus</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap5_mj.html#X7B4F3B5E841E3853" >5.6-2 NumericalSemigroupsWithGenusPC</a></span >div ></div >div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chap5_mj.html#X8265233586477CC7" >5.7 <span class="Heading" >span ></a>span >div class="ContSSBlock" >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap5_mj.html#X874B252180BD7EB4" >5.7-1 ForcedIntegersForPseudoFrobenius</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap5_mj.html#X87AAFFF9814E9BD2" >5.7-2 SimpleForcedIntegersForPseudoFrobenius</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap5_mj.html#X7D6775A57B800892" >5.7-3 NumericalSemigroupsWithPseudoFrobeniusNumbers</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap5_mj.html#X862DBFA379D52E2C" >5.7-4 ANumericalSemigroupWithPseudoFrobeniusNumbers</a></span >div ></div >div >div class="ContChap" ><a href="chap6_mj.html#X83C597EC7FAA1C0F" >6 <span class="Heading" >span ></a>div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chap6_mj.html#X83C597EC7FAA1C0F" >6.1 <span class="Heading" >span ></a>span >div class="ContSSBlock" >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap6_mj.html#X83E8CC8F862D1FC0" >6.1-1 IsIrreducible</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap6_mj.html#X7C381E277917B0ED" >6.1-2 IsSymmetric</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap6_mj.html#X7EA0D85085C4B607" >6.1-3 IsPseudoSymmetric</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap6_mj.html#X7C8AB03F7E0B71F0" >6.1-4 AnIrreducibleNumericalSemigroupWithFrobeniusNumber</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap6_mj.html#X78345A267ADEFBAB" >6.1-5 IrreducibleNumericalSemigroupsWithFrobeniusNumber</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap6_mj.html#X87C2738C7AA109DC" >6.1-6 IrreducibleNumericalSemigroupsWithFrobeniusNumberAndMultiplicity</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap6_mj.html#X8753F78D7FD732E2" >6.1-7 DecomposeIntoIrreducibles</a></span >div ></div >div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chap6_mj.html#X7D3FD9C8786B5D72" >6.2 <span class="Heading" >span ></a>span >div class="ContSSBlock" >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap6_mj.html#X848FCB49851D19B8" >6.2-1 AsGluingOfNumericalSemigroups</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap6_mj.html#X7A0DF10F85F32194" >6.2-2 IsCompleteIntersection</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap6_mj.html#X86350BCE7D047599" >6.2-3 CompleteIntersectionNumericalSemigroupsWithFrobeniusNumber</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap6_mj.html#X7CD2A77778432E7B" >6.2-4 IsFree</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap6_mj.html#X86B4BA6A79F734A8" >6.2-5 FreeNumericalSemigroupsWithFrobeniusNumber</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap6_mj.html#X830D0E0F7B8C6284" >6.2-6 IsTelescopic</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap6_mj.html#X84475353846384E8" >6.2-7 TelescopicNumericalSemigroupsWithFrobeniusNumber</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap6_mj.html#X7A1C2C737BC1C4CE" >6.2-8 IsUniversallyFree</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap6_mj.html#X847CD0EF8452F771" >6.2-9 IsNumericalSemigroupAssociatedIrreduciblePlanarCurveSingularity</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap6_mj.html#X8784D11578C912F2" >6.2-10 NumericalSemigroupsPlanarSingularityWithFrobeniusNumber</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap6_mj.html#X80CAA1FA7F6FF4FD" >6.2-11 IsAperySetGammaRectangular</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap6_mj.html#X7E6E262C7C421635" >6.2-12 IsAperySetBetaRectangular</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap6_mj.html#X86F52FB67F76D2CB" >6.2-13 IsAperySetAlphaRectangular</a></span >div ></div >div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chap6_mj.html#X7998FF857F70C9A2" >6.3 <span class="Heading" >span ></a>span >div class="ContSSBlock" >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap6_mj.html#X7A81F31479DB5DF2" >6.3-1 AlmostSymmetricNumericalSemigroupsFromIrreducible</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap6_mj.html#X8788F6597DBC6D98" >6.3-2 AlmostSymmetricNumericalSemigroupsFromIrreducibleAndGivenType</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap6_mj.html#X84C44C7A7D9270BB" >6.3-3 IsAlmostSymmetric</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap6_mj.html#X7B0DF2FE7D00A9E0" >6.3-4 AlmostSymmetricNumericalSemigroupsWithFrobeniusNumber</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap6_mj.html#X85C4DA6E82E726D2" >6.3-5 AlmostSymmetricNumericalSemigroupsWithFrobeniusNumberAndType</a></span >div ></div >div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chap6_mj.html#X7FDC79A285EE016B" >6.4 <span class="Heading" >span ></a>span >div class="ContSSBlock" >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap6_mj.html#X8221EC44802E5158" >6.4-1 IsGeneralizedGorenstein</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap6_mj.html#X866E48B47D66CFF2" >6.4-2 IsNearlyGorenstein</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap6_mj.html#X78049FC380A0006E" >6.4-3 NearlyGorensteinVectors</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap6_mj.html#X83F13D6482F021B2" >6.4-4 IsGeneralizedAlmostSymmetric</a></span >div ></div >div >div class="ContChap" ><a href="chap7_mj.html#X83C2F0CF825B3869" >7 <span class="Heading" >span ></a>div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chap7_mj.html#X84B6453A8015B40B" >7.1 <span class="Heading" >span ></a>span >div class="ContSSBlock" >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap7_mj.html#X78E5F44E81485C17" >7.1-1 IdealOfNumericalSemigroup</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap7_mj.html#X85BD6FAD7EA3B5DD" >7.1-2 IsIdealOfNumericalSemigroup</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap7_mj.html#X85144E0F791038AE" >7.1-3 MinimalGenerators</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap7_mj.html#X7A842A4385B73C63" >7.1-4 Generators</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap7_mj.html#X81E445518529C175" >7.1-5 AmbientNumericalSemigroupOfIdeal</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap7_mj.html#X7B0343BF794AC7EA" >7.1-6 IsIntegral</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap7_mj.html#X80233A6F80CA0615" >7.1-7 IsComplementOfIntegralIdeal</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap7_mj.html#X8774724085D3371D" >7.1-8 IdealByDivisorClosedSet</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap7_mj.html#X7811E92487110941" >7.1-9 SmallElements</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap7_mj.html#X7EDDC78883A98A6E" >7.1-10 Conductor</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap7_mj.html#X7A8AF91C7D1F1B4E" >7.1-11 FrobeniusNumber</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap7_mj.html#X805149CA847F6461" >7.1-12 PseudoFrobenius</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap7_mj.html#X7D4C7C997EEAADF7" >7.1-13 Type</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap7_mj.html#X821919B47D3D191A" >7.1-14 Minimum</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap7_mj.html#X87508E7A7CFB0B20" >7.1-15 BelongsToIdealOfNumericalSemigroup</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap7_mj.html#X83D0996D811A35C6" >7.1-16 ElementNumber_IdealOfNumericalSemigroup</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap7_mj.html#X7B8B46CF7E81513D" >7.1-17 NumberElement_IdealOfNumericalSemigroup</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap7_mj.html#X79DFDCA27D3268FD" ><code >7.1-18 <span >\</span >[ <span >\</span >]</code ></a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap7_mj.html#X8341AE847D005E9F" ><code >7.1-19 \{ \}</code ></a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap7_mj.html#X7A55BD4D82580537" >7.1-20 Iterator</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap7_mj.html#X7B39610D7AD5A654" >7.1-21 SumIdealsOfNumericalSemigroup</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap7_mj.html#X857FE5C57EE98F5E" >7.1-22 MultipleOfIdealOfNumericalSemigroup</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap7_mj.html#X78743CE2845B5860" >7.1-23 SubtractIdealsOfNumericalSemigroup</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap7_mj.html#X8321A10885D2DEF8" >7.1-24 Difference</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap7_mj.html#X803921F97BEDCA88" >7.1-25 TranslationOfIdealOfNumericalSemigroup</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap7_mj.html#X7CD66453842CD0AD" >7.1-26 Union</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap7_mj.html#X7B34033979009F64" >7.1-27 Intersection</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap7_mj.html#X7D77F1BA7F22DA70" >7.1-28 MaximalIdeal</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap7_mj.html#X85975C3C86C2BC53" >7.1-29 CanonicalIdeal</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap7_mj.html#X7D15FA4C843A13B7" >7.1-30 IsCanonicalIdeal</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap7_mj.html#X829C9685798BB553" >7.1-31 IsAlmostCanonicalIdeal</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap7_mj.html#X811B096B87636B8E" >7.1-32 TraceIdeal</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap7_mj.html#X7BB2A1B28139AA7E" >7.1-33 TypeSequence</a></span >div ></div >div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chap7_mj.html#X7F09B9A085E226EF" >7.2 <span class="Heading" >span ></a>span >div class="ContSSBlock" >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap7_mj.html#X7B83DEAC866B65E8" >7.2-1 IrreducibleZComponents</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap7_mj.html#X83E064C684FA534C" >7.2-2 DecomposeIntegralIdealIntoIrreducibles</a></span >div ></div >div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chap7_mj.html#X81CD9B12807EEA85" >7.3 <span class="Heading" >span ></a>span >div class="ContSSBlock" >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap7_mj.html#X82156F18807B00BF" >7.3-1 HilbertFunctionOfIdealOfNumericalSemigroup</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap7_mj.html#X81F1F3EB868D2117" >7.3-2 HilbertFunction</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap7_mj.html#X79A1A22D8615BF78" >7.3-3 BlowUp</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap7_mj.html#X7FAABCBF8299B12F" >7.3-4 ReductionNumber</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap7_mj.html#X7BFC52B7804542F5" >7.3-5 BlowUp</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap7_mj.html#X8799F0347FF0D510" >7.3-6 LipmanSemigroup</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap7_mj.html#X7D6F643687DF8724" >7.3-7 RatliffRushNumber</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap7_mj.html#X82C2329380B9882D" >7.3-8 RatliffRushClosure</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap7_mj.html#X79494A587A549E15" >7.3-9 AsymptoticRatliffRushNumber</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap7_mj.html#X8344B30D7EDE3B04" >7.3-10 MultiplicitySequence</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap7_mj.html#X87AC917578976B1E" >7.3-11 MicroInvariants</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap7_mj.html#X805C984685EBC65C" >7.3-12 AperyList</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap7_mj.html#X82D2784B813C67D8" >7.3-13 AperyList</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap7_mj.html#X8244CCAE7D957F46" >7.3-14 AperyTable</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap7_mj.html#X7A16238D7EDB2AB3" >7.3-15 StarClosureOfIdealOfNumericalSemigroup</a></span >div ></div >div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chap7_mj.html#X78F124CC82E7B585" >7.4 <span class="Heading" >span ></a>span >div class="ContSSBlock" >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap7_mj.html#X865042FD7EBD15EE" >7.4-1 IsAdmissiblePattern</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap7_mj.html#X7ED8306681407D0F" >7.4-2 IsStronglyAdmissiblePattern</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap7_mj.html#X799542C57E4E0D5E" >7.4-3 AsIdealOfNumericalSemigroup</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap7_mj.html#X7F13F7CB7FBCF006" >7.4-4 BoundForConductorOfImageOfPattern</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap7_mj.html#X7F4E597278AF31C8" >7.4-5 ApplyPatternToIdeal</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap7_mj.html#X7CFDFF6D7B9B595B" >7.4-6 ApplyPatternToNumericalSemigroup</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap7_mj.html#X7F9232047F85C4D8" >7.4-7 IsAdmittedPatternByIdeal</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap7_mj.html#X827BB22083390CB9" >7.4-8 IsAdmittedPatternByNumericalSemigroup</a></span >div ></div >div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chap7_mj.html#X79C6CE8D7EF1632D" >7.5 <span class="Heading" >Graded associated ring of numerical semigroup</span ></a>span >div class="ContSSBlock" >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap7_mj.html#X7876199778D6B320" >7.5-1 IsGradedAssociatedRingNumericalSemigroupCM</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap7_mj.html#X782D557583CEDD04" >7.5-2 IsGradedAssociatedRingNumericalSemigroupBuchsbaum</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap7_mj.html#X78E57B9982F6E1DC" >7.5-3 TorsionOfAssociatedGradedRingNumericalSemigroup</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap7_mj.html#X7E16B6947BE375B2" >7.5-4 BuchsbaumNumberOfAssociatedGradedRingNumericalSemigroup</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap7_mj.html#X7A5752C0836370FA" >7.5-5 IsGradedAssociatedRingNumericalSemigroupGorenstein</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap7_mj.html#X7800C5D68641E2B7" >7.5-6 IsGradedAssociatedRingNumericalSemigroupCI</a></span >div ></div >div >div class="ContChap" ><a href="chap8_mj.html#X7D2E70FC82D979D3" >8 <span class="Heading" >span ></a>div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chap8_mj.html#X7D2E70FC82D979D3" >8.1 <span class="Heading" >span ></a>span >div class="ContSSBlock" >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap8_mj.html#X783A0BE786C6BBBE" >8.1-1 IsMED</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap8_mj.html#X7A6379A382D1FC20" >8.1-2 MEDClosure</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap8_mj.html#X848FD3FA7DB2DD4C" >8.1-3 MinimalMEDGeneratingSystemOfMEDNumericalSemigroup</a></span >div ></div >div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chap8_mj.html#X82E40EFD83A4A186" >8.2 <span class="Heading" >span ></a>span >div class="ContSSBlock" >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap8_mj.html#X86137A2A7D27F7EC" >8.2-1 IsArf</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap8_mj.html#X7E34F28585A2922B" >8.2-2 ArfClosure</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap8_mj.html#X83C242468796950D" >8.2-3 ArfCharactersOfArfNumericalSemigroup</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap8_mj.html#X85CD144384FD55F3" >8.2-4 ArfNumericalSemigroupsWithFrobeniusNumber</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap8_mj.html#X7E308CCF87448182" >8.2-5 ArfNumericalSemigroupsWithFrobeniusNumberUpTo</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap8_mj.html#X80A13F7C81463AE5" >8.2-6 ArfNumericalSemigroupsWithGenus</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap8_mj.html#X80EB35C17C83694D" >8.2-7 ArfNumericalSemigroupsWithGenusUpTo</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap8_mj.html#X7EE73B2F813F7E85" >8.2-8 ArfNumericalSemigroupsWithGenusAndFrobeniusNumber</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap8_mj.html#X7CC73F15831B06CE" >8.2-9 ArfSpecialGaps</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap8_mj.html#X7DD2831683F870C5" >8.2-10 ArfOverSemigroups</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap8_mj.html#X8052BCE67CC2472F" >8.2-11 IsArfIrreducible</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap8_mj.html#X848E5559867D2D81" >8.2-12 DecomposeIntoArfIrreducibles</a></span >div ></div >div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chap8_mj.html#X7E6D857179E5BF1B" >8.3 <span class="Heading" >span ></a>span >div class="ContSSBlock" >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap8_mj.html#X81CCD9A88127E549" >8.3-1 IsSaturated</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap8_mj.html#X78E6F00287A23FC1" >8.3-2 SaturatedClosure</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap8_mj.html#X7CC07D997880E298" >8.3-3 SaturatedNumericalSemigroupsWithFrobeniusNumber</a></span >div ></div >div >div class="ContChap" ><a href="chap9_mj.html#X7B6F914879CD505F" >9 <span class="Heading" >span ></a>div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chap9_mj.html#X7FDB54217B15148F" >9.1 <span class="Heading" >span ></a>span >div class="ContSSBlock" >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap9_mj.html#X8429AECF78EE7EAB" >9.1-1 FactorizationsIntegerWRTList</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap9_mj.html#X80EF105B82447F30" >9.1-2 Factorizations</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap9_mj.html#X87C9E03C818AE1AA" >9.1-3 FactorizationsElementListWRTNumericalSemigroup</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap9_mj.html#X813D2A3A83916A36" >9.1-4 RClassesOfSetOfFactorizations</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap9_mj.html#X7C5EED6D852C24DD" >9.1-5 LShapes</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap9_mj.html#X86062FCA85A51870" >9.1-6 RFMatrices</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap9_mj.html#X86D58E0084CFD425" >9.1-7 DenumerantOfElementInNumericalSemigroup</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap9_mj.html#X801DA4247A0BEBDA" >9.1-8 DenumerantFunction</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap9_mj.html#X7D91A9377DAFAE35" >9.1-9 DenumerantIdeal</a></span >div ></div >div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chap9_mj.html#X846FEE457D4EC03D" >9.2 <span class="Heading" >span ></a>span >div class="ContSSBlock" >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap9_mj.html#X7D4CC092859AF81F" >9.2-1 LengthsOfFactorizationsIntegerWRTList</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap9_mj.html#X7FDE4F94870951B1" >9.2-2 LengthsOfFactorizationsElementWRTNumericalSemigroup</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap9_mj.html#X860E461182B0C6F5" >9.2-3 Elasticity</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap9_mj.html#X7A2B01BB87086283" >9.2-4 Elasticity</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap9_mj.html#X79C953B5846F7057" >9.2-5 DeltaSet</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap9_mj.html#X7DB8BA5B7D6F81CB" >9.2-6 DeltaSet</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap9_mj.html#X7A08CF05821DD2FC" >9.2-7 DeltaSetPeriodicityBoundForNumericalSemigroup</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap9_mj.html#X8123FC0E83ADEE45" >9.2-8 DeltaSetPeriodicityStartForNumericalSemigroup</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap9_mj.html#X80B5DF908246BEB1" >9.2-9 DeltaSetListUpToElementWRTNumericalSemigroup</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap9_mj.html#X85C6973E81583E8B" >9.2-10 DeltaSetUnionUpToElementWRTNumericalSemigroup</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap9_mj.html#X83B06062784E0FD9" >9.2-11 DeltaSet</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap9_mj.html#X7AEFE27E87F51114" >9.2-12 MaximumDegree</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap9_mj.html#X7F8B10C2870932B8" >9.2-13 IsAdditiveNumericalSemigroup</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap9_mj.html#X790308B07AB1A5C8" >9.2-14 MaximalDenumerant</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap9_mj.html#X7DFC4ED0827761C1" >9.2-15 MaximalDenumerantOfSetOfFactorizations</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap9_mj.html#X811E5FFB83CCA4CE" >9.2-16 MaximalDenumerant</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap9_mj.html#X87F633D98003DE52" >9.2-17 Adjustment</a></span >div ></div >div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chap9_mj.html#X84F5CA8D7B0F6C02" >9.3 <span class="Heading" >span ></a>span >div class="ContSSBlock" >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap9_mj.html#X86F9D7868100F6F9" >9.3-1 CatenaryDegree</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap9_mj.html#X7DDB40BB84FF0042" >9.3-2 AdjacentCatenaryDegreeOfSetOfFactorizations</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap9_mj.html#X86E0CAD28655839C" >9.3-3 EqualCatenaryDegreeOfSetOfFactorizations</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap9_mj.html#X845D850F7812E176" >9.3-4 MonotoneCatenaryDegreeOfSetOfFactorizations</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap9_mj.html#X797147AA796D1AFE" >9.3-5 CatenaryDegree</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap9_mj.html#X80D478418403E7CB" >9.3-6 TameDegree</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap9_mj.html#X785B83F17BEEA894" >9.3-7 CatenaryDegree</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap9_mj.html#X863E3EF986764267" >9.3-8 DegreesOffEqualPrimitiveElementsOfNumericalSemigroup</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap9_mj.html#X780E2C737FA8B2A9" >9.3-9 EqualCatenaryDegreeOfNumericalSemigroup</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap9_mj.html#X7E19683D7ADDE890" >9.3-10 DegreesOfMonotonePrimitiveElementsOfNumericalSemigroup</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap9_mj.html#X7E0458187956C395" >9.3-11 MonotoneCatenaryDegreeOfNumericalSemigroup</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap9_mj.html#X809D97A179765EE6" >9.3-12 TameDegree</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap9_mj.html#X7F7619BD79009B64" >9.3-13 TameDegree</a></span >div ></div >div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chap9_mj.html#X78EBC6A57B8167E6" >9.4 <span class="Heading" >span ></a>span >div class="ContSSBlock" >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap9_mj.html#X83075D7F837ACCB8" >9.4-1 OmegaPrimality</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap9_mj.html#X85EB5E2581FFB8B2" >9.4-2 OmegaPrimalityOfElementListInNumericalSemigroup</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap9_mj.html#X80B48B7886A93FAC" >9.4-3 OmegaPrimality</a></span >div ></div >div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chap9_mj.html#X86735EEA780CECDA" >9.5 <span class="Heading" >span ></a>span >div class="ContSSBlock" >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap9_mj.html#X856B689185C1F5D9" >9.5-1 BelongsToHomogenizationOfNumericalSemigroup</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap9_mj.html#X85D03DBB7BA3B1FB" >9.5-2 FactorizationsInHomogenizationOfNumericalSemigroup</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap9_mj.html#X857CC7FF85C05318" >9.5-3 HomogeneousBettiElementsOfNumericalSemigroup</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap9_mj.html#X7DFFCAC87B3B632B" >9.5-4 HomogeneousCatenaryDegreeOfNumericalSemigroup</a></span >div ></div >div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chap9_mj.html#X7A54E9FD7D4CB18F" >9.6 <span class="Heading" >span ></a>span >div class="ContSSBlock" >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap9_mj.html#X853930E97F7F8A43" >9.6-1 MoebiusFunctionAssociatedToNumericalSemigroup</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap9_mj.html#X7DF6825185C619AC" >9.6-2 MoebiusFunction</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap9_mj.html#X8771F39A7C7E031E" >9.6-3 DivisorsOfElementInNumericalSemigroup</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap9_mj.html#X871CD69180783663" >9.6-4 NumericalSemigroupByNuSequence</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap9_mj.html#X7F4CBFF17BBB37DE" >9.6-5 NumericalSemigroupByTauSequence</a></span >div ></div >div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chap9_mj.html#X82D8A59083FCDF46" >9.7 <span class="Heading" >span ></a>span >div class="ContSSBlock" >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap9_mj.html#X7939BCE08655B62D" >9.7-1 FengRaoDistance</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap9_mj.html#X83F9F4C67D4535EF" >9.7-2 FengRaoNumber</a></span >div ></div >div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chap9_mj.html#X79A8A15087CEE8C1" >9.8 <span class="Heading" >span ></a>span >div class="ContSSBlock" >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap9_mj.html#X7B894ED27D38E4B5" >9.8-1 IsPure</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap9_mj.html#X8400FB5D81EFB5FE" >9.8-2 IsMpure</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap9_mj.html#X80B707EE79990E1E" >9.8-3 IsHomogeneousNumericalSemigroup</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap9_mj.html#X8630DEF77A350D76" >9.8-4 IsSuperSymmetricNumericalSemigroup</a></span >div ></div >div >div class="ContChap" ><a href="chap10_mj.html#X7D2C77607815273E" >10 <span class="Heading" >span ></a>div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chap10_mj.html#X808FAEE28572191C" >10.1 <span class="Heading" >span ></a>span >div class="ContSSBlock" >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap10_mj.html#X8391C8E782FBFA8A" >10.1-1 NumericalSemigroupPolynomial</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap10_mj.html#X7F59E1167C1EE578" >10.1-2 IsNumericalSemigroupPolynomial</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap10_mj.html#X855497F77D13436F" >10.1-3 NumericalSemigroupFromNumericalSemigroupPolynomial</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap10_mj.html#X780479F978D166B0" >10.1-4 HilbertSeriesOfNumericalSemigroup</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap10_mj.html#X87C88E5C7B56931F" >10.1-5 GraeffePolynomial</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap10_mj.html#X87A46B53815B158F" >10.1-6 IsCyclotomicPolynomial</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap10_mj.html#X7D9618ED83776B0B" >10.1-7 IsKroneckerPolynomial</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap10_mj.html#X8366BB727C496D31" >10.1-8 IsCyclotomicNumericalSemigroup</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap10_mj.html#X7B428FA2877EC733" >10.1-9 CyclotomicExponentSequence</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap10_mj.html#X7A33BA9B813A4070" >10.1-10 WittCoefficients</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap10_mj.html#X82C6355287C3BDD1" >10.1-11 IsSelfReciprocalUnivariatePolynomial</a></span >div ></div >div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chap10_mj.html#X7EEF2A1781432A2D" >10.2 <span class="Heading" >span ></a>span >div class="ContSSBlock" >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap10_mj.html#X7FFF949A7BEEA912" >10.2-1 SemigroupOfValuesOfPlaneCurveWithSinglePlaceAtInfinity</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap10_mj.html#X834D6B1A7C421B9F" >10.2-2 IsDeltaSequence</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap10_mj.html#X824ABFD680A34495" >10.2-3 DeltaSequencesWithFrobeniusNumber</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap10_mj.html#X87B819B886CA5A5C" >10.2-4 CurveAssociatedToDeltaSequence</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap10_mj.html#X7E2C3E9A7DE7A078" >10.2-5 SemigroupOfValuesOfPlaneCurve</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap10_mj.html#X7F88774F7812D30E" >10.2-6 SemigroupOfValuesOfCurve_Local</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap10_mj.html#X8597259279D1E793" >10.2-7 SemigroupOfValuesOfCurve_Global</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap10_mj.html#X7EE8528484642CEE" >10.2-8 GeneratorsModule_Global</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap10_mj.html#X836D31F787641C22" >10.2-9 GeneratorsKahlerDifferentials</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap10_mj.html#X7A04B8887F493733" >10.2-10 IsMonomialNumericalSemigroup</a></span >div ></div >div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chap10_mj.html#X84C670E1826F8B92" >10.3 <span class="Heading" >span ></a>span >div class="ContSSBlock" >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap10_mj.html#X7980A7CE79F09A89" >10.3-1 LegendrianGenericNumericalSemigroup</a></span >div ></div >div >div class="ContChap" ><a href="chap11_mj.html#X7D92A1997D098A00" >11 <span class="Heading" >span ></a>div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chap11_mj.html#X7E39DA7780D02DF5" >11.1 <span class="Heading" >span ></a>span >div class="ContSSBlock" >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap11_mj.html#X7D7B03E17C8DBEA2" >11.1-1 AffineSemigroup</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap11_mj.html#X855C8667830AEDDC" >11.1-2 AffineSemigroupByEquations</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap11_mj.html#X7846AD1081C14EF1" >11.1-3 AffineSemigroupByInequalities</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap11_mj.html#X7CC110D4798AAD99" >11.1-4 AffineSemigroupByPMInequality</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap11_mj.html#X83F6DDB787E07771" >11.1-5 AffineSemigroupByGaps</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap11_mj.html#X7A3648D67CF81370" >11.1-6 FiniteComplementIdealExtension</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap11_mj.html#X8361194C86AE807B" >11.1-7 Gaps</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap11_mj.html#X867B27BD81104BEE" >11.1-8 Genus</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap11_mj.html#X80C3CD2082CE02F7" >11.1-9 PseudoFrobenius</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap11_mj.html#X82D42FCE81F20277" >11.1-10 SpecialGaps</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap11_mj.html#X84FDF85D7CDEDF3E" >11.1-11 Generators</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap11_mj.html#X7ED1549486C251CA" >11.1-12 MinimalGenerators</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap11_mj.html#X80516BCC78FDD45D" >11.1-13 RemoveMinimalGeneratorFromAffineSemigroup</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap11_mj.html#X7B78E02F7C50583F" >11.1-14 AddSpecialGapOfAffineSemigroup</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap11_mj.html#X844806D97B4781B5" >11.1-15 AsAffineSemigroup</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap11_mj.html#X7A2902207BAA3936" >11.1-16 IsAffineSemigroup</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap11_mj.html#X851788D781A13C50" >11.1-17 BelongsToAffineSemigroup</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap11_mj.html#X8607B621833FAECB" >11.1-18 IsFull</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap11_mj.html#X7D4D017A79AD98E2" >11.1-19 HilbertBasisOfSystemOfHomogeneousEquations</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap11_mj.html#X825B1CD37B0407A6" >11.1-20 HilbertBasisOfSystemOfHomogeneousInequalities</a></span >quality 100%
¤ Die Informationen auf dieser Webseite wurden
nach bestem Wissen sorgfältig zusammengestellt. Es wird jedoch weder Vollständigkeit, noch Richtigkeit,
noch Qualität der bereit gestellten Informationen zugesichert.0.25Bemerkung:
(vorverarbeitet)
¤ *© Formatika GbR, Deutschland
