\BOOKMARK [0][-]{chapter.1}{ Introduction }{}% 1
\BOOKMARK [0][-]{chapter.2}{ Numerical Semigroups }{}% 2
\BOOKMARK [1][-]{section.2.1}{ Generating Numerical Semigroups }{chapter.2}% 3
\BOOKMARK [1][-]{section.2.2}{Some basic tests}{chapter.2}% 4
\BOOKMARK [0][-]{chapter.3}{ Basic operations with numerical semigroups }{}% 5
\BOOKMARK [1][-]{section.3.1}{ The definitions }{chapter.3}% 6
\BOOKMARK [1][-]{section.3.2}{Frobenius Number}{chapter.3}% 7
\BOOKMARK [1][-]{section.3.3}{Gaps}{chapter.3}% 8
\BOOKMARK [0][-]{chapter.4}{ Presentations of Numerical Semigroups }{}% 9
\BOOKMARK [1][-]{section.4.1}{Presentations of Numerical Semigroups}{chapter.4}% 10
\BOOKMARK [1][-]{section.4.2}{Uniquely Presented Numerical Semigroups}{chapter.4}% 11
\BOOKMARK [0][-]{chapter.5}{ Constructing numerical semigroups from others }{}% 12
\BOOKMARK [1][-]{section.5.1}{ Adding and removing elements of a numerical semigroup }{chapter.5}% 13
\BOOKMARK [1][-]{section.5.2}{Intersections and quotients by integers}{chapter.5}% 14
\BOOKMARK [1][-]{section.5.3}{ Constructing the set of all numerical semigroups containing a given numerical semigroup }{chapter.5}% 15
\BOOKMARK [1][-]{section.5.4}{ Constructing the set of numerical semigroup with given Frobenius number}{chapter.5}% 16
\BOOKMARK [1][-]{section.5.5}{ Constructing the set of numerical semigroups with genus g, that is, numerical semigroups with exactly g gaps }{chapter.5}% 17
\BOOKMARK [1][-]{section.5.6}{ Constructing the set of numerical semigroups with a given set of pseudo-Frobenius numbers }{chapter.5}% 18
\BOOKMARK [0][-]{chapter.6}{ Irreducible numerical semigroups }{}% 19
\BOOKMARK [1][-]{section.6.1}{ Irreducible numerical semigroups }{chapter.6}% 20
\BOOKMARK [1][-]{section.6.2}{ Complete intersection numerical semigroups }{chapter.6}% 21
\BOOKMARK [1][-]{section.6.3}{ Almost-symmetric numerical semigroups }{chapter.6}% 22
\BOOKMARK [0][-]{chapter.7}{ Ideals of numerical semigroups }{}% 23
\BOOKMARK [1][-]{section.7.1}{ Definitions and basic operations }{chapter.7}% 24
\BOOKMARK [1][-]{section.7.2}{ Other functions for ideals }{chapter.7}% 25
\BOOKMARK [0][-]{chapter.8}{ Numerical semigroups with maximal embedding dimension }{}% 26
\BOOKMARK [1][-]{section.8.1}{ Numerical semigroups with maximal embedding dimension }{chapter.8}% 27
\BOOKMARK [1][-]{section.8.2}{ Numerical semigroups with the Arf property and Arf closures }{chapter.8}% 28
\BOOKMARK [1][-]{section.8.3}{ Saturated numerical semigroups }{chapter.8}% 29
\BOOKMARK [0][-]{chapter.9}{ Nonunique invariants for factorizations in numerical semigroups }{}% 30
\BOOKMARK [1][-]{section.9.1}{ Factorizations in Numerical Semigroups }{chapter.9}% 31
\BOOKMARK [1][-]{section.9.2}{ Invariants based on lengths }{chapter.9}% 32
\BOOKMARK [1][-]{section.9.3}{ Invariants based on distances }{chapter.9}% 33
\BOOKMARK [1][-]{section.9.4}{ Primality }{chapter.9}% 34
\BOOKMARK [1][-]{section.9.5}{ Homogenization of Numerical Semigroups }{chapter.9}% 35
\BOOKMARK [1][-]{section.9.6}{ Divisors, posets }{chapter.9}% 36
\BOOKMARK [0][-]{chapter.10}{ Polynomials and numerical semigroups }{}% 37
\BOOKMARK [1][-]{section.10.1}{ Generating functions or Hilbert series }{chapter.10}% 38
\BOOKMARK [1][-]{section.10.2}{ Semigroup of values of algebraic curves }{chapter.10}% 39
\BOOKMARK [0][-]{chapter.11}{ Affine semigroups }{}% 40
\BOOKMARK [1][-]{section.11.1}{ Using external packages }{chapter.11}% 41
\BOOKMARK [1][-]{section.11.2}{ Defining affine semigroups }{chapter.11}% 42
\BOOKMARK [1][-]{section.11.3}{ Gluings of affine semigroups }{chapter.11}% 43
\BOOKMARK [1][-]{section.11.4}{ Presentations of affine semigroups }{chapter.11}% 44
\BOOKMARK [1][-]{section.11.5}{ Factorizations in affine semigroups }{chapter.11}% 45
\BOOKMARK [0][-]{appendix.A}{Generalities}{}% 46
\BOOKMARK [1][-]{section.A.1}{B\351zout sequences}{appendix.A}% 47
\BOOKMARK [1][-]{section.A.2}{Periodic subadditive functions}{appendix.A}% 48
\BOOKMARK [0][-]{appendix.B}{Random functions}{}% 49
\BOOKMARK [1][-]{section.B.1}{Random functions}{appendix.B}% 50
\BOOKMARK [0][-]{appendix.C}{Contributions}{}% 51
\BOOKMARK [1][-]{section.C.1}{Functions implemented by A. Sammartano}{appendix.C}% 52
\BOOKMARK [1][-]{section.C.2}{Functions implemented by C. O'Neill}{appendix.C}% 53
\BOOKMARK [0][-]{appendix*.5}{References}{}% 54
\BOOKMARK [0][-]{section*.6}{Index}{}% 55
