\contentsline {chapter}{\numberline {1}\leavevmode {\color {Chapter }Preface}}{5}{chapter.1}
\contentsline {chapter}{\numberline {2}\leavevmode {\color {Chapter }Unions of Residue Classes}}{6}{chapter.2}
\contentsline {section}{\numberline {2.1}\leavevmode {\color {Chapter }Entering residue classes and unions thereof}}{6}{section.2.1}
\contentsline {subsection}{\numberline {2.1.1}\leavevmode {\color {Chapter }ResidueClass (R, m, r)}}{6}{subsection.2.1.1}
\contentsline {subsection}{\numberline {2.1.2}\leavevmode {\color {Chapter }ResidueClassUnion (R, m, r)}}{6}{subsection.2.1.2}
\contentsline {subsection}{\numberline {2.1.3}\leavevmode {\color {Chapter }AllResidueClassesModulo (R, m)}}{7}{subsection.2.1.3}
\contentsline {section}{\numberline {2.2}\leavevmode {\color {Chapter }Methods for unions of residue classes}}{8}{section.2.2}
\contentsline {subsection}{\numberline {2.2.1}\leavevmode {\color {Chapter }SplittedClass (cl, t)}}{8}{subsection.2.2.1}
\contentsline {subsection}{\numberline {2.2.2}\leavevmode {\color {Chapter }AsUnionOfFewClasses (U)}}{9}{subsection.2.2.2}
\contentsline {subsection}{\numberline {2.2.3}\leavevmode {\color {Chapter }Density (U)}}{9}{subsection.2.2.3}
\contentsline {section}{\numberline {2.3}\leavevmode {\color {Chapter }The categories and families of unions of residue classes}}{10}{section.2.3}
\contentsline {subsection}{\numberline {2.3.1}\leavevmode {\color {Chapter }IsUnionOfResidueClasses (U)}}{10}{subsection.2.3.1}
\contentsline {subsection}{\numberline {2.3.2}\leavevmode {\color {Chapter }ResidueClassUnionsFamily (R)}}{10}{subsection.2.3.2}
\contentsline {chapter}{\numberline {3}\leavevmode {\color {Chapter }Unions of Residue Classes with Fixed Representatives}}{11}{chapter.3}
\contentsline {section}{\numberline {3.1}\leavevmode {\color {Chapter } Entering unions of residue classes with fixed representatives }}{11}{section.3.1}
\contentsline {subsection}{\numberline {3.1.1}\leavevmode {\color {Chapter }ResidueClassWithFixedRep (R, m, r)}}{11}{subsection.3.1.1}
\contentsline {subsection}{\numberline {3.1.2}\leavevmode {\color {Chapter }ResidueClassUnionWithFixedReps (R, classes)}}{11}{subsection.3.1.2}
\contentsline {subsection}{\numberline {3.1.3}\leavevmode {\color {Chapter }AllResidueClassesWithFixedRepsModulo (R, m)}}{12}{subsection.3.1.3}
\contentsline {section}{\numberline {3.2}\leavevmode {\color {Chapter } Methods for unions of residue classes with fixed representatives }}{12}{section.3.2}
\contentsline {subsection}{\numberline {3.2.1}\leavevmode {\color {Chapter }Multiplicity (x, U)}}{12}{subsection.3.2.1}
\contentsline {subsection}{\numberline {3.2.2}\leavevmode {\color {Chapter }Union (U1, U2)}}{14}{subsection.3.2.2}
\contentsline {subsection}{\numberline {3.2.3}\leavevmode {\color {Chapter }Intersection (U1, U2)}}{14}{subsection.3.2.3}
\contentsline {subsection}{\numberline {3.2.4}\leavevmode {\color {Chapter }Difference (U1, U2)}}{14}{subsection.3.2.4}
\contentsline {section}{\numberline {3.3}\leavevmode {\color {Chapter } The invariant Delta }}{15}{section.3.3}
\contentsline {subsection}{\numberline {3.3.1}\leavevmode {\color {Chapter }Delta (U)}}{15}{subsection.3.3.1}
\contentsline {subsection}{\numberline {3.3.2}\leavevmode {\color {Chapter }RepresentativeStabilizingRefinement (U, k)}}{15}{subsection.3.3.2}
\contentsline {section}{\numberline {3.4}\leavevmode {\color {Chapter } The categories of unions of residue classes with fixed rep's }}{15}{section.3.4}
\contentsline {chapter}{\numberline {4}\leavevmode {\color {Chapter }Semilocalizations of the Integers}}{16}{chapter.4}
\contentsline {section}{\numberline {4.1}\leavevmode {\color {Chapter }Entering semilocalizations of the integers}}{16}{section.4.1}
\contentsline {subsection}{\numberline {4.1.1}\leavevmode {\color {Chapter }Z{\_}pi (pi)}}{16}{subsection.4.1.1}
\contentsline {section}{\numberline {4.2}\leavevmode {\color {Chapter }Methods for semilocalizations of the integers}}{16}{section.4.2}
\contentsline {chapter}{\numberline {5}\leavevmode {\color {Chapter }Installation and auxiliary functions}}{18}{chapter.5}
\contentsline {section}{\numberline {5.1}\leavevmode {\color {Chapter }Requirements}}{18}{section.5.1}
\contentsline {section}{\numberline {5.2}\leavevmode {\color {Chapter }Installation}}{18}{section.5.2}
\contentsline {section}{\numberline {5.3}\leavevmode {\color {Chapter }The testing routine}}{18}{section.5.3}
\contentsline {subsection}{\numberline {5.3.1}\leavevmode {\color {Chapter }ResClassesTest}}{18}{subsection.5.3.1}
\contentsline {section}{\numberline {5.4}\leavevmode {\color {Chapter }Building the manual}}{18}{section.5.4}
\contentsline {subsection}{\numberline {5.4.1}\leavevmode {\color {Chapter }ResClassesBuildManual}}{18}{subsection.5.4.1}
