\contentsline {chapter}{\numberline {1}\leavevmode {\color {Chapter }Set-Theoretic Unions of Residue Classes}}{5}{chapter.1}
\contentsline {section}{\numberline {1.1}\leavevmode {\color {Chapter }Entering residue classes and set-theoretic unions thereof}}{5}{section.1.1}
\contentsline {subsection}{\numberline {1.1.1}\leavevmode {\color {Chapter }ResidueClass (by ring, modulus and residue)}}{5}{subsection.1.1.1}
\contentsline {subsection}{\numberline {1.1.2}\leavevmode {\color {Chapter }ResidueClassUnion (by ring, modulus and residues)}}{5}{subsection.1.1.2}
\contentsline {subsection}{\numberline {1.1.3}\leavevmode {\color {Chapter }AllResidueClassesModulo (of a given ring, modulo a given modulus)}}{6}{subsection.1.1.3}
\contentsline {section}{\numberline {1.2}\leavevmode {\color {Chapter }Methods for residue class unions}}{7}{section.1.2}
\contentsline {subsection}{\numberline {1.2.1}\leavevmode {\color {Chapter }SplittedClass (for a residue class and a number of parts)}}{7}{subsection.1.2.1}
\contentsline {subsection}{\numberline {1.2.2}\leavevmode {\color {Chapter }AsUnionOfFewClasses (for a residue class union)}}{8}{subsection.1.2.2}
\contentsline {subsection}{\numberline {1.2.3}\leavevmode {\color {Chapter }PartitionsIntoResidueClasses (of a given ring, of given length)}}{8}{subsection.1.2.3}
\contentsline {subsection}{\numberline {1.2.4}\leavevmode {\color {Chapter }RandomPartitionIntoResidueClasses (of a given ring, of given length)}}{9}{subsection.1.2.4}
\contentsline {subsection}{\numberline {1.2.5}\leavevmode {\color {Chapter }Density (of a residue class union)}}{9}{subsection.1.2.5}
\contentsline {section}{\numberline {1.3}\leavevmode {\color {Chapter }The categories and families of residue class unions}}{9}{section.1.3}
\contentsline {subsection}{\numberline {1.3.1}\leavevmode {\color {Chapter }IsResidueClassUnion}}{9}{subsection.1.3.1}
\contentsline {subsection}{\numberline {1.3.2}\leavevmode {\color {Chapter }ResidueClassUnionsFamily (of a ring)}}{10}{subsection.1.3.2}
\contentsline {chapter}{\numberline {2}\leavevmode {\color {Chapter }Unions of Residue Classes with Fixed Representatives}}{11}{chapter.2}
\contentsline {section}{\numberline {2.1}\leavevmode {\color {Chapter } Entering unions of residue classes with fixed representatives }}{11}{section.2.1}
\contentsline {subsection}{\numberline {2.1.1}\leavevmode {\color {Chapter }ResidueClassWithFixedRepresentative (by ring, modulus and residue)}}{11}{subsection.2.1.1}
\contentsline {subsection}{\numberline {2.1.2}\leavevmode {\color {Chapter }UnionOfResidueClassesWithFixedReps (by ring and list of classes)}}{11}{subsection.2.1.2}
\contentsline {subsection}{\numberline {2.1.3}\leavevmode {\color {Chapter }AllResidueClassesWithFixedRepsModulo (by ring and modulus)}}{12}{subsection.2.1.3}
\contentsline {section}{\numberline {2.2}\leavevmode {\color {Chapter } Methods for unions of residue classes with fixed representatives }}{12}{section.2.2}
\contentsline {subsection}{\numberline {2.2.1}\leavevmode {\color {Chapter }Multiplicity (of an element in a union of residue classes with fixed rep's)}}{12}{subsection.2.2.1}
\contentsline {subsection}{\numberline {2.2.2}\leavevmode {\color {Chapter }Union (for unions of residue classes with fixed representatives)}}{14}{subsection.2.2.2}
\contentsline {subsection}{\numberline {2.2.3}\leavevmode {\color {Chapter }Intersection (for unions of residue classes with fixed representatives)}}{14}{subsection.2.2.3}
\contentsline {subsection}{\numberline {2.2.4}\leavevmode {\color {Chapter }Difference (for unions of residue classes with fixed representatives)}}{14}{subsection.2.2.4}
\contentsline {section}{\numberline {2.3}\leavevmode {\color {Chapter } The invariant Delta }}{15}{section.2.3}
\contentsline {subsection}{\numberline {2.3.1}\leavevmode {\color {Chapter }Delta (for a union of residue classes with fixed representatives)}}{15}{subsection.2.3.1}
\contentsline {subsection}{\numberline {2.3.2}\leavevmode {\color {Chapter }RepresentativeStabilizingRefinement (of a union of res.-classes with fixed rep's)}}{15}{subsection.2.3.2}
\contentsline {section}{\numberline {2.4}\leavevmode {\color {Chapter } The categories of unions of residue classes with fixed rep's }}{15}{section.2.4}
\contentsline {chapter}{\numberline {3}\leavevmode {\color {Chapter }Semilocalizations of the Integers}}{16}{chapter.3}
\contentsline {section}{\numberline {3.1}\leavevmode {\color {Chapter }Entering semilocalizations of the integers}}{16}{section.3.1}
\contentsline {subsection}{\numberline {3.1.1}\leavevmode {\color {Chapter }Z{\textunderscore }pi (by set of noninvertible primes)}}{16}{subsection.3.1.1}
\contentsline {section}{\numberline {3.2}\leavevmode {\color {Chapter }Methods for semilocalizations of the integers}}{16}{section.3.2}
\contentsline {chapter}{\numberline {4}\leavevmode {\color {Chapter }Installation and auxiliary functions}}{18}{chapter.4}
\contentsline {section}{\numberline {4.1}\leavevmode {\color {Chapter }Requirements}}{18}{section.4.1}
\contentsline {section}{\numberline {4.2}\leavevmode {\color {Chapter }Installation}}{18}{section.4.2}
\contentsline {section}{\numberline {4.3}\leavevmode {\color {Chapter }The testing routine}}{18}{section.4.3}
\contentsline {subsection}{\numberline {4.3.1}\leavevmode {\color {Chapter }ResClassesTest}}{18}{subsection.4.3.1}
\contentsline {section}{\numberline {4.4}\leavevmode {\color {Chapter }Building the manual}}{18}{section.4.4}
\contentsline {subsection}{\numberline {4.4.1}\leavevmode {\color {Chapter }ResClassesBuildManual}}{18}{subsection.4.4.1}
\contentsline {section}{\numberline {4.5}\leavevmode {\color {Chapter }SendEmail and EmailLogFile}}{19}{section.4.5}
\contentsline {subsection}{\numberline {4.5.1}\leavevmode {\color {Chapter }SendEmail}}{19}{subsection.4.5.1}
\contentsline {subsection}{\numberline {4.5.2}\leavevmode {\color {Chapter }EmailLogFile}}{19}{subsection.4.5.2}