\contentsline {chapter}{\numberline {1}\textcolor {Chapter }{Set-Theoretic Unions of Residue Classes}}{4}{chapter.1}%
\contentsline {section}{\numberline {1.1}\textcolor {Chapter }{Entering residue classes and set-theoretic unions thereof}}{4}{section.1.1}%
\contentsline {subsection}{\numberline {1.1.1}\textcolor {Chapter }{ResidueClass (by ring, modulus and residue)}}{4}{subsection.1.1.1}%
\contentsline {subsection}{\numberline {1.1.2}\textcolor {Chapter }{ResidueClassUnion (by ring, modulus and residues)}}{4}{subsection.1.1.2}%
\contentsline {subsection}{\numberline {1.1.3}\textcolor {Chapter }{AllResidueClassesModulo (of a given ring, modulo a given modulus)}}{5}{subsection.1.1.3}%
\contentsline {section}{\numberline {1.2}\textcolor {Chapter }{Methods for residue class unions}}{6}{section.1.2}%
\contentsline {subsection}{\numberline {1.2.1}\textcolor {Chapter }{SplittedClass (for a residue class and a number of parts)}}{7}{subsection.1.2.1}%
\contentsline {subsection}{\numberline {1.2.2}\textcolor {Chapter }{AsUnionOfFewClasses (for a residue class union)}}{7}{subsection.1.2.2}%
\contentsline {subsection}{\numberline {1.2.3}\textcolor {Chapter }{PartitionsIntoResidueClasses (of a given ring, of given length)}}{8}{subsection.1.2.3}%
\contentsline {subsection}{\numberline {1.2.4}\textcolor {Chapter }{RandomPartitionIntoResidueClasses (of a given ring, of given length)}}{8}{subsection.1.2.4}%
\contentsline {subsection}{\numberline {1.2.5}\textcolor {Chapter }{CoverByResidueClasses (of the integers, by residue classes with given moduli)}}{8}{subsection.1.2.5}%
\contentsline {subsection}{\numberline {1.2.6}\textcolor {Chapter }{Density (of a residue class union)}}{9}{subsection.1.2.6}%
\contentsline {section}{\numberline {1.3}\textcolor {Chapter }{On residue class unions of ${\ensuremath {\mathbb Z}}^2$}}{9}{section.1.3}%
\contentsline {section}{\numberline {1.4}\textcolor {Chapter }{The categories and families of residue class unions}}{11}{section.1.4}%
\contentsline {subsection}{\numberline {1.4.1}\textcolor {Chapter }{IsResidueClassUnion}}{11}{subsection.1.4.1}%
\contentsline {subsection}{\numberline {1.4.2}\textcolor {Chapter }{ResidueClassUnionsFamily (of a ring)}}{11}{subsection.1.4.2}%
\contentsline {chapter}{\numberline {2}\textcolor {Chapter }{Unions of Residue Classes with Fixed Representatives}}{12}{chapter.2}%
\contentsline {section}{\numberline {2.1}\textcolor {Chapter }{ Entering unions of residue classes with fixed representatives }}{12}{section.2.1}%
\contentsline {subsection}{\numberline {2.1.1}\textcolor {Chapter }{ResidueClassWithFixedRepresentative (by ring, modulus and residue)}}{12}{subsection.2.1.1}%
\contentsline {subsection}{\numberline {2.1.2}\textcolor {Chapter }{UnionOfResidueClassesWithFixedReps (by ring and list of classes)}}{12}{subsection.2.1.2}%
\contentsline {subsection}{\numberline {2.1.3}\textcolor {Chapter }{AllResidueClassesWithFixedRepsModulo (by ring and modulus)}}{13}{subsection.2.1.3}%
\contentsline {section}{\numberline {2.2}\textcolor {Chapter }{ Methods for unions of residue classes with fixed representatives }}{13}{section.2.2}%
\contentsline {subsection}{\numberline {2.2.1}\textcolor {Chapter }{Multiplicity (of an element in a union of residue classes with fixed rep's)}}{13}{subsection.2.2.1}%
\contentsline {subsection}{\numberline {2.2.2}\textcolor {Chapter }{Union (for unions of residue classes with fixed representatives)}}{15}{subsection.2.2.2}%
\contentsline {subsection}{\numberline {2.2.3}\textcolor {Chapter }{Intersection (for unions of residue classes with fixed representatives)}}{15}{subsection.2.2.3}%
\contentsline {subsection}{\numberline {2.2.4}\textcolor {Chapter }{Difference (for unions of residue classes with fixed representatives)}}{15}{subsection.2.2.4}%
\contentsline {section}{\numberline {2.3}\textcolor {Chapter }{ The invariant Delta }}{16}{section.2.3}%
\contentsline {subsection}{\numberline {2.3.1}\textcolor {Chapter }{Delta (for a union of residue classes with fixed representatives)}}{16}{subsection.2.3.1}%
\contentsline {subsection}{\numberline {2.3.2}\textcolor {Chapter }{RepresentativeStabilizingRefinement (of a union of res.-classes with fixed rep's)}}{16}{subsection.2.3.2}%
\contentsline {section}{\numberline {2.4}\textcolor {Chapter }{ The categories of unions of residue classes with fixed rep's }}{16}{section.2.4}%
\contentsline {chapter}{\numberline {3}\textcolor {Chapter }{Semilocalizations of the Integers}}{17}{chapter.3}%
\contentsline {section}{\numberline {3.1}\textcolor {Chapter }{Entering semilocalizations of the integers}}{17}{section.3.1}%
\contentsline {subsection}{\numberline {3.1.1}\textcolor {Chapter }{Z{\textunderscore }pi (by set of non-invertible primes)}}{17}{subsection.3.1.1}%
\contentsline {section}{\numberline {3.2}\textcolor {Chapter }{Methods for semilocalizations of the integers}}{17}{section.3.2}%
\contentsline {chapter}{\numberline {4}\textcolor {Chapter }{Installation and Auxiliary Functions}}{19}{chapter.4}%
\contentsline {section}{\numberline {4.1}\textcolor {Chapter }{Requirements}}{19}{section.4.1}%
\contentsline {section}{\numberline {4.2}\textcolor {Chapter }{Installation}}{19}{section.4.2}%
\contentsline {section}{\numberline {4.3}\textcolor {Chapter }{The testing routines}}{19}{section.4.3}%
\contentsline {subsection}{\numberline {4.3.1}\textcolor {Chapter }{ResClassesTest}}{19}{subsection.4.3.1}%
\contentsline {subsection}{\numberline {4.3.2}\textcolor {Chapter }{ResClassesTestExamples}}{19}{subsection.4.3.2}%
\contentsline {section}{\numberline {4.4}\textcolor {Chapter }{Creating timestamped logfiles}}{19}{section.4.4}%
\contentsline {subsection}{\numberline {4.4.1}\textcolor {Chapter }{LogToDatedFile}}{20}{subsection.4.4.1}%
\contentsline {section}{\numberline {4.5}\textcolor {Chapter }{DownloadFile, SendEmail and EmailLogFile}}{20}{section.4.5}%
\contentsline {subsection}{\numberline {4.5.1}\textcolor {Chapter }{DownloadFile}}{20}{subsection.4.5.1}%
\contentsline {subsection}{\numberline {4.5.2}\textcolor {Chapter }{SendEmail}}{20}{subsection.4.5.2}%
\contentsline {subsection}{\numberline {4.5.3}\textcolor {Chapter }{EmailLogFile}}{20}{subsection.4.5.3}%
\contentsline {section}{\numberline {4.6}\textcolor {Chapter }{Creating bitmap pictures}}{20}{section.4.6}%
\contentsline {subsection}{\numberline {4.6.1}\textcolor {Chapter }{SaveAsBitmapPicture (picture, filename)}}{21}{subsection.4.6.1}%
\contentsline {subsection}{\numberline {4.6.2}\textcolor {Chapter }{DrawLineNC (pic, x1, y1, x2, y2, color, width)}}{21}{subsection.4.6.2}%
\contentsline {section}{\numberline {4.7}\textcolor {Chapter }{Some general utility functions}}{21}{section.4.7}%
\contentsline {chapter}{References}{23}{chapter*.4}%
\contentsline {chapter}{Index}{24}{section*.5}%
