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/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 >1 .4 .0 </p>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>2005 --2015 Centro de Matemática da Universidade do Porto, Portugal and Universidad de Granada, 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.</p> "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 <em>Centro de Matemática da Universidade do Porto</em> (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.</p> 01446 and MTM2007-62346 , the Junta de Andalucía group FQM-343 , and FEDER founds.</p>rship given by <em >Centro de Matemática da Universidade do Porto</em >.</p>65481 /2006 and also by 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>15595 and MTM2014-55367 -P, which were funded by Ministerio de Economía y Competitividad and the Fondo Europeo de Desarrollo Regional FEDER.</p>00144 /2013 and UID/MAT/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>84890 -P, which is funded by Ministerio de Economía y Competitividad and Fondo Europeo de Desarrollo Regional FEDER.</p>142918 /2018 .</p>096446 -B-C21 funded by MCIN/AEI/10 .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>2004 ) the first author visited the University of Granada in part of a 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></a> 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" >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 >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap11_mj.html#X8307A0597864B098" >11 .1 -21 EquationsOfGroupGeneratedBy</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap11_mj.html#X7A1CE5A98425CEA1" >11 .1 -22 BasisOfGroupGivenByEquations</a></span >div ></div >div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chap11_mj.html#X7F13DF9D7A4FB547" >11 .2 <span class="Heading" >span ></a>span >div class="ContSSBlock" >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap11_mj.html#X7FE3B3C380641DDC" >11 .2 -1 GluingOfAffineSemigroups</a></span >div ></div >div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chap11_mj.html#X86A1018D7CB7BA81" >11 .3 <span class="Heading" >span ></a>span >div class="ContSSBlock" >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap11_mj.html#X795EEE4481E0497C" >11 .3 -1 CircuitsOfKernelCongruence</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap11_mj.html#X78B04C198258D3F8" >11 .3 -2 PrimitiveRelationsOfKernelCongruence</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap11_mj.html#X7EE005267DEBC1DE" >11 .3 -3 GeneratorsOfKernelCongruence</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap11_mj.html#X7AD2271E84F705D3" >11 .3 -4 CanonicalBasisOfKernelCongruence</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap11_mj.html#X7C3546477E07A1EA" >11 .3 -5 GraverBasis</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap11_mj.html#X80A7BD7478D8A94A" >11 .3 -6 MinimalPresentation</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap11_mj.html#X86BCBD32781EBC2D" >11 .3 -7 BettiElements</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap11_mj.html#X7C1B355F83A55285" >11 .3 -8 ShadedSetOfElementInAffineSemigroup</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap11_mj.html#X81CA53DA8216DC82" >11 .3 -9 IsGeneric</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap11_mj.html#X79EC6F7583B0CBDD" >11 .3 -10 IsUniquelyPresented</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap11_mj.html#X7DCAFC5F7F74F3CB" >11 .3 -11 DegreesOfPrimitiveElementsOfAffineSemigroup</a></span >div ></div >div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chap11_mj.html#X80A934B0826E21A6" >11 .4 <span class="Heading" >span ></a>span >div class="ContSSBlock" >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap11_mj.html#X8780C7E5830B9AE2" >11 .4 -1 FactorizationsVectorWRTList</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap11_mj.html#X820A0D06857C4EF5" >11 .4 -2 Factorizations</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap11_mj.html#X7F394FA67BE5151B" >11 .4 -3 Elasticity</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap11_mj.html#X819CDBAA84DB7E83" >11 .4 -4 Elasticity</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap11_mj.html#X839549448300AD26" >11 .4 -5 DeltaSet</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap11_mj.html#X80742F2F7DECDB4C" >11 .4 -6 CatenaryDegree</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap11_mj.html#X7EADD306875FCBE6" >11 .4 -7 EqualCatenaryDegreeOfAffineSemigroup</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap11_mj.html#X84FE571A7E9E1AE9" >11 .4 -8 HomogeneousCatenaryDegreeOfAffineSemigroup</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap11_mj.html#X8510C1527F2FE18E" >11 .4 -9 MonotoneCatenaryDegreeOfAffineSemigroup</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap11_mj.html#X8457595E7AA542E6" >11 .4 -10 TameDegree</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap11_mj.html#X850790EE8442FD7D" >11 .4 -11 OmegaPrimality</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap11_mj.html#X7A3571E187D0FCDE" >11 .4 -12 OmegaPrimality</a></span >div ></div >div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chap11_mj.html#X849D1ECC808F2BBA" >11 .5 <span class="Heading" >span ></a>span >div class="ContSSBlock" >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap11_mj.html#X85775D4E7B9C7DAB" >11 .5 -1 IdealOfAffineSemigroup</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap11_mj.html#X82A647B27FDFE49B" >11 .5 -2 IsIdealOfAffineSemigroup</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap11_mj.html#X7F16A5A27CBB7B93" >11 .5 -3 MinimalGenerators</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap11_mj.html#X8086C1EE7EAAB33D" >11 .5 -4 Generators</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap11_mj.html#X82D18D7B877582B0" >11 .5 -5 AmbientAffineSemigroupOfIdeal</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap11_mj.html#X7B0FBEC285F54B8D" >11 .5 -6 IsIntegral</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap11_mj.html#X7F00912C853AA83D" >11 .5 -7 BelongsToIdealOfAffineSemigroup</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap11_mj.html#X83A4392281981911" >11 .5 -8 SumIdealsOfAffinSemigroup</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap11_mj.html#X7D056A0C7F868209" >11 .5 -9 MultipleOfIdealOfAffineSemigroup</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap11_mj.html#X788264A27ACD6AB5" >11 .5 -10 TranslationOfIdealOfAffineSemigroup</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap11_mj.html#X7880F29982B559F2" >11 .5 -11 UnionIdealsOfAffineSemigroup</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap11_mj.html#X7ED03363783D8FCD" >11 .5 -12 Intersection</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap11_mj.html#X79ECACE4793A6B00" >11 .5 -13 MaximalIdeal</a></span >div ></div >div >div class="ContChap" ><a href="chap12_mj.html#X7A9271AC84C7277F" >12 <span class="Heading" >span ></a>div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chap12_mj.html#X82B9F71084D2358E" >12 .1 <span class="Heading" >span ></a>span >div class="ContSSBlock" >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap12_mj.html#X79E86DEE79281BF2" >12 .1 -1 IsGoodSemigroup</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap12_mj.html#X82A8863E78650FC4" >12 .1 -2 NumericalSemigroupDuplication</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap12_mj.html#X873FE7B37A747247" >12 .1 -3 AmalgamationOfNumericalSemigroups</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap12_mj.html#X855341C57F43DB72" >12 .1 -4 CartesianProductOfNumericalSemigroups</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap12_mj.html#X7856241678224958" >12 .1 -5 GoodSemigroup</a></span >div ></div >div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chap12_mj.html#X8431465B82643392" >12 .2 <span class="Heading" >span ></a>span >div class="ContSSBlock" >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap12_mj.html#X79EBBF6D7A2C9A12" >12 .2 -1 BelongsToGoodSemigroup</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap12_mj.html#X78A2A60481EE02E7" >12 .2 -2 Conductor</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap12_mj.html#X7B2F716B7985872B" >12 .2 -3 Multiplicity</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap12_mj.html#X792BCCF87CF63122" >12 .2 -4 IsLocal</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap12_mj.html#X836AB83682858A11" >12 .2 -5 SmallElements</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap12_mj.html#X82D40159783F0D48" >12 .2 -6 RepresentsSmallElementsOfGoodSemigroup</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap12_mj.html#X7E538585815C94D0" >12 .2 -7 GoodSemigroupBySmallElements</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap12_mj.html#X83F444E586D96723" >12 .2 -8 MaximalElementsOfGoodSemigroup</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap12_mj.html#X8503AC767A90C2BD" >12 .2 -9 IrreducibleMaximalElementsOfGoodSemigroup</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap12_mj.html#X78B456D27856761F" >12 .2 -10 GoodSemigroupByMaximalElements</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap12_mj.html#X8742875C836C9488" >12 .2 -11 MinimalGoodGenerators</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap12_mj.html#X806865CB794CAC5D" >12 .2 -12 ProjectionOfAGoodSemigroup</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap12_mj.html#X7D70CD958333D49B" >12 .2 -13 Genus</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap12_mj.html#X81BD57ED80145EB0" >12 .2 -14 Length</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap12_mj.html#X809E0C077A613806" >12 .2 -15 AperySetOfGoodSemigroup</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap12_mj.html#X7B234A537F0C0AEF" >12 .2 -16 StratifiedAperySetOfGoodSemigroup</a></span >div ></div >div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chap12_mj.html#X87FE42227F47666F" >12 .3 <span class="Heading" >span ></a>span >div class="ContSSBlock" >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap12_mj.html#X85A0D9C485431828" >12 .3 -1 IsSymmetric</a></span >div ></div >div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chap12_mj.html#X80A3D64386A152EB" >12 .4 <span class="Heading" >span ></a>span >div class="ContSSBlock" >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap12_mj.html#X87248BD481228F36" >12 .4 -1 ArfClosure</a></span >div ></div >div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chap12_mj.html#X7FA8DCAC7951F7FB" >12 .5 <span class="Heading" >span ></a>span >div class="ContSSBlock" >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap12_mj.html#X843CA9D5874A33F2" >12 .5 -1 GoodIdeal</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap12_mj.html#X7E4FC6DB794992E0" >12 .5 -2 GoodGeneratingSystemOfGoodIdeal</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap12_mj.html#X82D384397EE5CAC4" >12 .5 -3 AmbientGoodSemigroupOfGoodIdeal</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap12_mj.html#X84636A127ECEDA24" >12 .5 -4 MinimalGoodGeneratingSystemOfGoodIdeal</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap12_mj.html#X797999937E4E1E2B" >12 .5 -5 BelongsToGoodIdeal</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap12_mj.html#X842F3CE07E893949" >12 .5 -6 SmallElements</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap12_mj.html#X7DA7AE32837CC1C7" >12 .5 -7 CanonicalIdealOfGoodSemigroup</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap12_mj.html#X7DC7A4B57BC2E55C" >12 .5 -8 AbsoluteIrreduciblesOfGoodSemigroup</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap12_mj.html#X87AB3B09857B383A" >12 .5 -9 TracksOfGoodSemigroup</a></span >div ></div >div >div class="ContChap" ><a href="chap13_mj.html#X84A2793F7A9F3E6A" >13 <span class="Heading" >span ></a>div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chap13_mj.html#X7BD18FC581F0C4D3" >13 .1 <span class="Heading" >span ></a>span >div class="ContSSBlock" >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap13_mj.html#X8736665E7CBEAB20" >13 .1 -1 NumSgpsUse4ti2</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap13_mj.html#X875001717A8CF032" >13 .1 -2 NumSgpsUse4ti2gap</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap13_mj.html#X875040237A692C3C" >13 .1 -3 NumSgpsUseNormalize</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap13_mj.html#X7CD12ADD78089CBE" >13 .1 -4 NumSgpsUseSingular</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap13_mj.html#X7F7699A9829940C2" >13 .1 -5 NumSgpsUseSingularInterface</a></span >div ></div >div >div class="ContChap" ><a href="chap14_mj.html#X7B8D661F79E957A6" >14 <span class="Heading" >span ></a>div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chap14_mj.html#X7B8D661F79E957A6" >14 .1 <span class="Heading" >span ></a>span >div class="ContSSBlock" >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap14_mj.html#X7FEF6EC77E489886" >14 .1 -1 DotBinaryRelation</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap14_mj.html#X868991B084E42CE9" >14 .1 -2 HasseDiagramOfNumericalSemigroup</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap14_mj.html#X832901FF85EB8F1C" >14 .1 -3 HasseDiagramOfBettiElementsOfNumericalSemigroup</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap14_mj.html#X8050862F79EA9620" >14 .1 -4 HasseDiagramOfAperyListOfNumericalSemigroup</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap14_mj.html#X7F62870F8652EDE6" >14 .1 -5 DotTreeOfGluingsOfNumericalSemigroup</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap14_mj.html#X7F43955582F472B6" >14 .1 -6 DotOverSemigroupsNumericalSemigroup</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap14_mj.html#X8195A2027B726448" >14 .1 -7 DotRosalesGraph</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap14_mj.html#X7EC75F477D4F8CC3" >14 .1 -8 DotFactorizationGraph</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap14_mj.html#X83F1423980D2AEA4" >14 .1 -9 DotEliahouGraph</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap14_mj.html#X81F579B783CF4363" >14 .1 -10 SetDotNSEngine</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap14_mj.html#X7D1999A88268979F" >14 .1 -11 DotSplash</a></span >div ></div >div >div class="ContChap" ><a href="chapA_mj.html#X7AF8D94A7E56C049" >A <span class="Heading" >Generalities</span ></a>div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chapA_mj.html#X7A5D608487A8C98F" >A.1 <span class="Heading" >Bézout sequences</span ></a>span >div class="ContSSBlock" >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chapA_mj.html#X86859C84858ECAF1" >A.1 -1 BezoutSequence</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chapA_mj.html#X86C990AC7F40E8D0" >A.1 -2 IsBezoutSequence</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chapA_mj.html#X7C9DCBAF825CF7B2" >A.1 -3 CeilingOfRational</a></span >div ></div >div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chapA_mj.html#X7D3D347987953F44" >A.2 <span class="Heading" >Periodic subadditive functions</span ></a>span >div class="ContSSBlock" >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chapA_mj.html#X8466A4DC82F07579" >A.2 -1 RepresentsPeriodicSubAdditiveFunction</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chapA_mj.html#X7DFEDA6B87BB2E1F" >A.2 -2 IsListOfIntegersNS</a></span >div ></div >div >div class="ContChap" ><a href="chapB_mj.html#X86746B487B54A2D6" >B <span class="Heading" >"Random" functions</span ></a>div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chapB_mj.html#X7F3FF11486C5CA4B" >B.1 <span class="Heading" >Random functions for numerical semigroups</span ></a>span >div class="ContSSBlock" >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chapB_mj.html#X7CC477867B00AD13" >B.1 -1 RandomNumericalSemigroup</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chapB_mj.html#X79E73F8787741190" >B.1 -2 RandomListForNS</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chapB_mj.html#X82E22E9B843DF70F" >B.1 -3 RandomModularNumericalSemigroup</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chapB_mj.html#X8598F10A7CD4A135" >B.1 -4 RandomProportionallyModularNumericalSemigroup</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chapB_mj.html#X8665F6B08036AFFB" >B.1 -5 RandomListRepresentingSubAdditiveFunction</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chapB_mj.html#X7B459C8C825194E4" >B.1 -6 NumericalSemigroupWithRandomElementsAndFrobenius</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chapB_mj.html#X78A2A0107CCBBB79" >B.1 -7 RandomNumericalSemigroupWithGenus</a></span >div ></div >div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chapB_mj.html#X7D86D133840F6860" >B.2 <span class="Heading" >Random functions for affine semigroups</span ></a>span >div class="ContSSBlock" >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chapB_mj.html#X7FBFEE457E823E15" >B.2 -1 RandomAffineSemigroupWithGenusAndDimension</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chapB_mj.html#X82569F0079599515" >B.2 -2 RandomAffineSemigroup</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chapB_mj.html#X7F7BB53A7DF77ED5" >B.2 -3 RandomFullAffineSemigroup</a></span >div ></div >div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chapB_mj.html#X7DB89F2078A6095F" >B.3 <span class="Heading" >Random functions for good semigroups</span ></a>span >div class="ContSSBlock" >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chapB_mj.html#X7F582A997B4B05EE" >B.3 -1 RandomGoodSemigroupWithFixedMultiplicity</a></span >div ></div >div >div class="ContChap" ><a href="chapC_mj.html#X7F1146137C92FF0E" >C <span class="Heading" >Contributions</span ></a>div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chapC_mj.html#X8516272A7ACC7C02" >C.1 <span class="Heading" >Functions implemented by A. Sammartano</span ></a>span >div >div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chapC_mj.html#X821A695C7C0BDF59" >C.2 <span class="Heading" >Functions implemented by C. O'Neill</span></a> span >div >div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chapC_mj.html#X7F4C9F8A7F7CDBC8" >C.3 <span class="Heading" >Functions implemented by K. Stokes</span ></a>span >div >div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chapC_mj.html#X81478D2D862B6213" >C.4 <span class="Heading" >Functions implemented by I. Ojeda and C. J. Moreno Ávila</span ></a>span >div >div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chapC_mj.html#X7C7DCFA37C8B5260" >C.5 <span class="Heading" >Functions implemented by I. Ojeda</span ></a>span >div >div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chapC_mj.html#X8549AE427919FFDC" >C.6 <span class="Heading" >Functions implemented by A. Sánchez-R. Navarro</span ></a>span >div >div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chapC_mj.html#X7FAE71B27B0E3889" >C.7 <span class="Heading" >Functions implemented by G. Zito</span ></a>span >div >div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chapC_mj.html#X85067C3383705D0B" >C.8 <span class="Heading" >Functions implemented by A. Herrera-Poyatos</span span >div >div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chapC_mj.html#X81EA8996840BD031" >C.9 <span class="Heading" >Functions implemented by Benjamin Heredia</span ></a>span >div >div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chapC_mj.html#X7ED672F578B6FDC3" >C.10 <span class="Heading" >Functions implemented by Juan Ignacio García-García</span ></a>span >div >div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chapC_mj.html#X8348844883A78B05" >C.11 <span class="Heading" >Functions implemented by C. Cisto</span ></a>span >div >div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chapC_mj.html#X8130D17C7D6B5096" >C.12 <span class="Heading" >Functions implemented by N. Matsuoka</span ></a>span >div >div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chapC_mj.html#X78ED0D447B74A9FF" >C.13 <span class="Heading" >Functions implemented by N. Maugeri</span ></a>span >div >div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chapC_mj.html#X8283CFD584D2E3EE" >C.14 <span class="Heading" >Functions implemented by H. Martín Cruz</span ></a>span >div >div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chapC_mj.html#X82919F927DC72A52" >C.15 <span class="Heading" >Functions implemented by J. Angulo Rodríguez</span span >div >div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chapC_mj.html#X7C4C93CD8200C606" >C.16 <span class="Heading" >Functions implemented by F. Strazzanti</span ></a>span >div >div >div class="ContChap" ><a href="chapBib_mj.html" ><span class="Heading" >References</span ></a></div >div class="ContChap" ><a href="chapInd_mj.html" ><span class="Heading" >Index</span ></a></div >br />div >div class="chlinkprevnextbot" > <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 >div class="chlinkbot" ><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 >hr />"foot" >generated by <a href="https://www.math.rwth-aachen.de/~Frank.Luebeck/GAPDoc " >GAPDoc2HTML</a></p>body >html > Messung V0.5 in Prozent C=96 H=99 G=97
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