\contentsline {chapter}{\numberline {1}\leavevmode {\color {Chapter }Unions of Residue Classes}}{5}{chapter.1}
\contentsline {section}{\numberline {1.1}\leavevmode {\color {Chapter }Entering residue classes and unions thereof}}{5}{section.1.1}
\contentsline {subsection}{\numberline {1.1.1}\leavevmode {\color {Chapter }ResidueClass (R, m, r)}}{5}{subsection.1.1.1}
\contentsline {subsection}{\numberline {1.1.2}\leavevmode {\color {Chapter }ResidueClassUnion (R, m, r)}}{5}{subsection.1.1.2}
\contentsline {subsection}{\numberline {1.1.3}\leavevmode {\color {Chapter }AllResidueClassesModulo (R, m)}}{6}{subsection.1.1.3}
\contentsline {section}{\numberline {1.2}\leavevmode {\color {Chapter }Methods for unions of residue classes}}{7}{section.1.2}
\contentsline {subsection}{\numberline {1.2.1}\leavevmode {\color {Chapter }SplittedClass (cl, t)}}{7}{subsection.1.2.1}
\contentsline {subsection}{\numberline {1.2.2}\leavevmode {\color {Chapter }AsUnionOfFewClasses (U)}}{8}{subsection.1.2.2}
\contentsline {subsection}{\numberline {1.2.3}\leavevmode {\color {Chapter }Density (U)}}{8}{subsection.1.2.3}
\contentsline {subsection}{\numberline {1.2.4}\leavevmode {\color {Chapter }RandomPartitionIntoResidueClasses (R, length, primes)}}{9}{subsection.1.2.4}
\contentsline {section}{\numberline {1.3}\leavevmode {\color {Chapter }The categories and families of unions of residue classes}}{9}{section.1.3}
\contentsline {subsection}{\numberline {1.3.1}\leavevmode {\color {Chapter }IsUnionOfResidueClasses (U)}}{9}{subsection.1.3.1}
\contentsline {subsection}{\numberline {1.3.2}\leavevmode {\color {Chapter }ResidueClassUnionsFamily (R)}}{9}{subsection.1.3.2}
\contentsline {chapter}{\numberline {2}\leavevmode {\color {Chapter }Unions of Residue Classes with Fixed Representatives}}{10}{chapter.2}
\contentsline {section}{\numberline {2.1}\leavevmode {\color {Chapter } Entering unions of residue classes with fixed representatives }}{10}{section.2.1}
\contentsline {subsection}{\numberline {2.1.1}\leavevmode {\color {Chapter }ResidueClassWithFixedRep (R, m, r)}}{10}{subsection.2.1.1}
\contentsline {subsection}{\numberline {2.1.2}\leavevmode {\color {Chapter }ResidueClassUnionWithFixedReps (R, classes)}}{10}{subsection.2.1.2}
\contentsline {subsection}{\numberline {2.1.3}\leavevmode {\color {Chapter }AllResidueClassesWithFixedRepsModulo (R, m)}}{11}{subsection.2.1.3}
\contentsline {section}{\numberline {2.2}\leavevmode {\color {Chapter } Methods for unions of residue classes with fixed representatives }}{11}{section.2.2}
\contentsline {subsection}{\numberline {2.2.1}\leavevmode {\color {Chapter }Multiplicity (x, U)}}{11}{subsection.2.2.1}
\contentsline {subsection}{\numberline {2.2.2}\leavevmode {\color {Chapter }Union (U1, U2)}}{13}{subsection.2.2.2}
\contentsline {subsection}{\numberline {2.2.3}\leavevmode {\color {Chapter }Intersection (U1, U2)}}{13}{subsection.2.2.3}
\contentsline {subsection}{\numberline {2.2.4}\leavevmode {\color {Chapter }Difference (U1, U2)}}{13}{subsection.2.2.4}
\contentsline {section}{\numberline {2.3}\leavevmode {\color {Chapter } The invariant Delta }}{14}{section.2.3}
\contentsline {subsection}{\numberline {2.3.1}\leavevmode {\color {Chapter }Delta (U)}}{14}{subsection.2.3.1}
\contentsline {subsection}{\numberline {2.3.2}\leavevmode {\color {Chapter }RepresentativeStabilizingRefinement (U, k)}}{14}{subsection.2.3.2}
\contentsline {section}{\numberline {2.4}\leavevmode {\color {Chapter } The categories of unions of residue classes with fixed rep's }}{14}{section.2.4}
\contentsline {chapter}{\numberline {3}\leavevmode {\color {Chapter }Semilocalizations of the Integers}}{15}{chapter.3}
\contentsline {section}{\numberline {3.1}\leavevmode {\color {Chapter }Entering semilocalizations of the integers}}{15}{section.3.1}
\contentsline {subsection}{\numberline {3.1.1}\leavevmode {\color {Chapter }Z\_pi (pi)}}{15}{subsection.3.1.1}
\contentsline {section}{\numberline {3.2}\leavevmode {\color {Chapter }Methods for semilocalizations of the integers}}{15}{section.3.2}
\contentsline {chapter}{\numberline {4}\leavevmode {\color {Chapter }Installation and auxiliary functions}}{17}{chapter.4}
\contentsline {section}{\numberline {4.1}\leavevmode {\color {Chapter }Requirements}}{17}{section.4.1}
\contentsline {section}{\numberline {4.2}\leavevmode {\color {Chapter }Installation}}{17}{section.4.2}
\contentsline {section}{\numberline {4.3}\leavevmode {\color {Chapter }The testing routine}}{17}{section.4.3}
\contentsline {subsection}{\numberline {4.3.1}\leavevmode {\color {Chapter }ResClassesTest}}{17}{subsection.4.3.1}
\contentsline {section}{\numberline {4.4}\leavevmode {\color {Chapter }Building the manual}}{17}{section.4.4}
\contentsline {subsection}{\numberline {4.4.1}\leavevmode {\color {Chapter }ResClassesBuildManual}}{17}{subsection.4.4.1}
