\contentsline {chapter}{\numberline {1}\leavevmode {\color {Chapter }Preface}}{5}{chapter.1}
\contentsline {chapter}{\numberline {2}\leavevmode {\color {Chapter }Semilocalizations of the Integers}}{6}{chapter.2}
\contentsline {section}{\numberline {2.1}\leavevmode {\color {Chapter }Entering semilocalizations of the integers}}{6}{section.2.1}
\contentsline {subsection}{\numberline {2.1.1}\leavevmode {\color {Chapter }Z{\_}pi (pi)}}{6}{subsection.2.1.1}
\contentsline {subsection}{\numberline {2.1.2}\leavevmode {\color {Chapter }IsZ{\_}pi (R)}}{6}{subsection.2.1.2}
\contentsline {subsection}{\numberline {2.1.3}\leavevmode {\color {Chapter }NoninvertiblePrimes (R)}}{6}{subsection.2.1.3}
\contentsline {section}{\numberline {2.2}\leavevmode {\color {Chapter }Methods for semilocalizations of the integers}}{7}{section.2.2}
\contentsline {chapter}{\numberline {3}\leavevmode {\color {Chapter }Unions of Residue Classes}}{8}{chapter.3}
\contentsline {section}{\numberline {3.1}\leavevmode {\color {Chapter }Entering residue classes and unions thereof}}{8}{section.3.1}
\contentsline {subsection}{\numberline {3.1.1}\leavevmode {\color {Chapter }ResidueClass (R, m, r)}}{8}{subsection.3.1.1}
\contentsline {subsection}{\numberline {3.1.2}\leavevmode {\color {Chapter }IsResidueClass (obj)}}{8}{subsection.3.1.2}
\contentsline {subsection}{\numberline {3.1.3}\leavevmode {\color {Chapter }ResidueClassUnion (R, m, r)}}{9}{subsection.3.1.3}
\contentsline {subsection}{\numberline {3.1.4}\leavevmode {\color {Chapter }AllResidueClassesModulo (R, m)}}{9}{subsection.3.1.4}
\contentsline {subsection}{\numberline {3.1.5}\leavevmode {\color {Chapter }AllResidues (R, m)}}{10}{subsection.3.1.5}
\contentsline {section}{\numberline {3.2}\leavevmode {\color {Chapter }Methods for unions of residue classes}}{10}{section.3.2}
\contentsline {subsection}{\numberline {3.2.1}\leavevmode {\color {Chapter }Union (U1, U2)}}{11}{subsection.3.2.1}
\contentsline {subsection}{\numberline {3.2.2}\leavevmode {\color {Chapter }Intersection (U1, U2)}}{11}{subsection.3.2.2}
\contentsline {subsection}{\numberline {3.2.3}\leavevmode {\color {Chapter }Difference (U1, U2)}}{12}{subsection.3.2.3}
\contentsline {subsection}{\numberline {3.2.4}\leavevmode {\color {Chapter }SplittedClass (cl, t)}}{12}{subsection.3.2.4}
\contentsline {subsection}{\numberline {3.2.5}\leavevmode {\color {Chapter }AsUnionOfFewClasses (U)}}{13}{subsection.3.2.5}
\contentsline {subsection}{\numberline {3.2.6}\leavevmode {\color {Chapter }\texttt {\char 92\relax }+ (U, x)}}{13}{subsection.3.2.6}
\contentsline {subsection}{\numberline {3.2.7}\leavevmode {\color {Chapter }\texttt {\char 92\relax }- (U, x)}}{13}{subsection.3.2.7}
\contentsline {subsection}{\numberline {3.2.8}\leavevmode {\color {Chapter }\texttt {\char 92\relax }* (U, x)}}{14}{subsection.3.2.8}
\contentsline {subsection}{\numberline {3.2.9}\leavevmode {\color {Chapter }\texttt {\char 92\relax }/ (U, x)}}{14}{subsection.3.2.9}
\contentsline {subsection}{\numberline {3.2.10}\leavevmode {\color {Chapter }Density (U)}}{14}{subsection.3.2.10}
\contentsline {section}{\numberline {3.3}\leavevmode {\color {Chapter }The categories and families of unions of residue classes}}{15}{section.3.3}
\contentsline {subsection}{\numberline {3.3.1}\leavevmode {\color {Chapter }IsUnionOfResidueClasses (U)}}{15}{subsection.3.3.1}
\contentsline {subsection}{\numberline {3.3.2}\leavevmode {\color {Chapter }ResidueClassUnionsFamily (R)}}{15}{subsection.3.3.2}
\contentsline {chapter}{\numberline {4}\leavevmode {\color {Chapter }Unions of Residue Classes with Fixed Representatives}}{16}{chapter.4}
\contentsline {section}{\numberline {4.1}\leavevmode {\color {Chapter } About unions of residue classes with fixed representatives }}{16}{section.4.1}
\contentsline {section}{\numberline {4.2}\leavevmode {\color {Chapter } Entering unions of residue classes with fixed representatives }}{16}{section.4.2}
\contentsline {subsection}{\numberline {4.2.1}\leavevmode {\color {Chapter }ResidueClassWithFixedRepresentative (R, m, r)}}{16}{subsection.4.2.1}
\contentsline {subsection}{\numberline {4.2.2}\leavevmode {\color {Chapter }ResidueClassUnionWithFixedRepresentatives (R, classes)}}{17}{subsection.4.2.2}
\contentsline {subsection}{\numberline {4.2.3}\leavevmode {\color {Chapter }AllResidueClassesWithFixedRepresentativesModulo (R, m)}}{17}{subsection.4.2.3}
\contentsline {section}{\numberline {4.3}\leavevmode {\color {Chapter } Methods for unions of residue classes with fixed representatives }}{17}{section.4.3}
\contentsline {subsection}{\numberline {4.3.1}\leavevmode {\color {Chapter }Multiplicity (x, U)}}{17}{subsection.4.3.1}
\contentsline {subsection}{\numberline {4.3.2}\leavevmode {\color {Chapter }IsOverlappingFree (U)}}{18}{subsection.4.3.2}
\contentsline {subsection}{\numberline {4.3.3}\leavevmode {\color {Chapter }AsOrdinaryUnionOfResidueClasses (U)}}{18}{subsection.4.3.3}
\contentsline {subsection}{\numberline {4.3.4}\leavevmode {\color {Chapter }\texttt {\char 92\relax }in (cl, U)}}{18}{subsection.4.3.4}
\contentsline {subsection}{\numberline {4.3.5}\leavevmode {\color {Chapter }AsListOfClasses (U)}}{19}{subsection.4.3.5}
\contentsline {subsection}{\numberline {4.3.6}\leavevmode {\color {Chapter }IsSubset (U1, U2)}}{19}{subsection.4.3.6}
\contentsline {subsection}{\numberline {4.3.7}\leavevmode {\color {Chapter }Density (U)}}{19}{subsection.4.3.7}
\contentsline {subsection}{\numberline {4.3.8}\leavevmode {\color {Chapter }Union (U1, U2)}}{19}{subsection.4.3.8}
\contentsline {subsection}{\numberline {4.3.9}\leavevmode {\color {Chapter }Intersection (U1, U2)}}{20}{subsection.4.3.9}
\contentsline {subsection}{\numberline {4.3.10}\leavevmode {\color {Chapter }Difference (U1, U2)}}{20}{subsection.4.3.10}
\contentsline {subsection}{\numberline {4.3.11}\leavevmode {\color {Chapter }\texttt {\char 92\relax }+ (U, x)}}{20}{subsection.4.3.11}
\contentsline {subsection}{\numberline {4.3.12}\leavevmode {\color {Chapter }\texttt {\char 92\relax }- (U, x)}}{21}{subsection.4.3.12}
\contentsline {subsection}{\numberline {4.3.13}\leavevmode {\color {Chapter }\texttt {\char 92\relax }* (U, x)}}{21}{subsection.4.3.13}
\contentsline {subsection}{\numberline {4.3.14}\leavevmode {\color {Chapter }\texttt {\char 92\relax }/ (U, x)}}{21}{subsection.4.3.14}
\contentsline {section}{\numberline {4.4}\leavevmode {\color {Chapter } The invariant Delta }}{22}{section.4.4}
\contentsline {subsection}{\numberline {4.4.1}\leavevmode {\color {Chapter }RepresentativeStabilizingRefinement (U, k)}}{22}{subsection.4.4.1}
\contentsline {subsection}{\numberline {4.4.2}\leavevmode {\color {Chapter }Delta (U)}}{22}{subsection.4.4.2}
\contentsline {subsection}{\numberline {4.4.3}\leavevmode {\color {Chapter }Rho (U)}}{22}{subsection.4.4.3}
\contentsline {section}{\numberline {4.5}\leavevmode {\color {Chapter } The categories of unions of residue classes with fixed rep's }}{23}{section.4.5}
\contentsline {chapter}{\numberline {5}\leavevmode {\color {Chapter }Installation and auxiliary functions}}{24}{chapter.5}
\contentsline {section}{\numberline {5.1}\leavevmode {\color {Chapter }Installation}}{24}{section.5.1}
\contentsline {section}{\numberline {5.2}\leavevmode {\color {Chapter }Building the manual}}{24}{section.5.2}
\contentsline {subsection}{\numberline {5.2.1}\leavevmode {\color {Chapter }ResClassesBuildManual}}{24}{subsection.5.2.1}
\contentsline {section}{\numberline {5.3}\leavevmode {\color {Chapter }The testing routine}}{24}{section.5.3}
\contentsline {subsection}{\numberline {5.3.1}\leavevmode {\color {Chapter }ResClassesTest}}{24}{subsection.5.3.1}
\contentsline {section}{\numberline {5.4}\leavevmode {\color {Chapter }Changing the viewing format for residue class unions}}{25}{section.5.4}
\contentsline {subsection}{\numberline {5.4.1}\leavevmode {\color {Chapter }ResidueClassUnionViewingFormat (format)}}{25}{subsection.5.4.1}
