\contentsline {chapter}{\numberline {1}\leavevmode {\color {Chapter }Introduction}}{4}{chapter.1}
\contentsline {section}{\numberline {1.1}\leavevmode {\color {Chapter }Introduction to the \textsf {HAPprime} package}}{4}{section.1.1}
\contentsline {section}{\numberline {1.2}\leavevmode {\color {Chapter }Required software}}{4}{section.1.2}
\contentsline {section}{\numberline {1.3}\leavevmode {\color {Chapter }Installing \textsf {HAPprime}}}{4}{section.1.3}
\contentsline {section}{\numberline {1.4}\leavevmode {\color {Chapter }Loading and testing \textsf {HAPprime}}}{5}{section.1.4}
\contentsline {section}{\numberline {1.5}\leavevmode {\color {Chapter }Documentation}}{5}{section.1.5}
\contentsline {subsection}{\numberline {1.5.1}\leavevmode {\color {Chapter }MakeHAPprimeDoc}}{5}{subsection.1.5.1}
\contentsline {section}{\numberline {1.6}\leavevmode {\color {Chapter }Displaying progress and calculation information}}{6}{section.1.6}
\contentsline {subsection}{\numberline {1.6.1}\leavevmode {\color {Chapter }InfoHAPprime}}{6}{subsection.1.6.1}
\contentsline {chapter}{\numberline {2}\leavevmode {\color {Chapter }Examples}}{7}{chapter.2}
\contentsline {section}{\numberline {2.1}\leavevmode {\color {Chapter }Computing the mod $p$ group cohomology}}{7}{section.2.1}
\contentsline {section}{\numberline {2.2}\leavevmode {\color {Chapter }Computing mod-$p$ cohomology rings and their Poincar{\'e} series}}{8}{section.2.2}
\contentsline {subsection}{\numberline {2.2.1}\leavevmode {\color {Chapter }A ring presentation for the mod $p$ cohomology (up to degree $n$)}}{8}{subsection.2.2.1}
\contentsline {subsection}{\numberline {2.2.2}\leavevmode {\color {Chapter }Calculating a provably-correct mod-$p$ cohomology}}{9}{subsection.2.2.2}
\contentsline {subsection}{\numberline {2.2.3}\leavevmode {\color {Chapter }Computing Poincar{\'e} series}}{11}{subsection.2.2.3}
\contentsline {section}{\numberline {2.3}\leavevmode {\color {Chapter }Comparing the memory usage and speed of \textsf {HAPprime} and \textsf {HAP}'s \texttt {ResolutionPrimePowerGroup} functions}}{12}{section.2.3}
\contentsline {subsection}{\numberline {2.3.1}\leavevmode {\color {Chapter }\textsf {HAPprime} takes less memory to store resolutions}}{12}{subsection.2.3.1}
\contentsline {subsection}{\numberline {2.3.2}\leavevmode {\color {Chapter }\textsf {HAPprime} takes less memory to compute resolutions}}{13}{subsection.2.3.2}
\contentsline {subsection}{\numberline {2.3.3}\leavevmode {\color {Chapter }Automatic selection of the best method}}{14}{subsection.2.3.3}
\contentsline {chapter}{\numberline {3}\leavevmode {\color {Chapter }Functions for Homological Algebra}}{16}{chapter.3}
\contentsline {section}{\numberline {3.1}\leavevmode {\color {Chapter }Resolutions}}{16}{section.3.1}
\contentsline {subsection}{\numberline {3.1.1}\leavevmode {\color {Chapter }ResolutionPrimePowerGroup}}{16}{subsection.3.1.1}
\contentsline {subsection}{\numberline {3.1.2}\leavevmode {\color {Chapter }ExtendResolutionPrimePowerGroup}}{17}{subsection.3.1.2}
\contentsline {section}{\numberline {3.2}\leavevmode {\color {Chapter }Poincar{\'e} Series}}{17}{section.3.2}
\contentsline {subsection}{\numberline {3.2.1}\leavevmode {\color {Chapter }PoincareSeriesLHS}}{17}{subsection.3.2.1}
\contentsline {section}{\numberline {3.3}\leavevmode {\color {Chapter }Cohomology Ring structure}}{17}{section.3.3}
\contentsline {subsection}{\numberline {3.3.1}\leavevmode {\color {Chapter }Mod2CohomologyRingPresentation (for group)}}{17}{subsection.3.3.1}
