\chapcontents {1}{Introduction}{5}
\seccontents {1.1}{Installation} {5}
\seccontents {1.2}{Documentation} {5}
\seccontents {1.3}{Test files} {5}
\seccontents {1.4}{Feedback} {5}
\chapcontents {2}{Mathematical background}{6}
\seccontents {2.1}{Quasigroups and loops} {6}
\seccontents {2.2}{Translations} {6}
\seccontents {2.3}{Homomorphisms and homotopisms} {6}
\chapcontents {3}{How the package works}{8}
\seccontents {3.1}{Representing quasigroups} {8}
\seccontents {3.2}{Conversions between magmas, quasigroups, loops and groups} {8}
\seccontents {3.3}{Calculating with quasigroups} {9}
\seccontents {3.4}{Naming, viewing and printing quasigroups and their elements} {9}
\chapcontents {4}{Basic methods and attributes}{11}
\seccontents {4.1}{About Cayley tables} {11}
\seccontents {4.2}{Testing Cayley tables} {11}
\seccontents {4.3}{Canonical and normalized Cayley tables} {11}
\seccontents {4.4}{Creating quasigroups and loops manually} {12}
\seccontents {4.5}{Creating quasigroups and loops from a file} {12}
\seccontents {4.6}{Conversions} {13}
\seccontents {4.7}{Products of loops} {13}
\seccontents {4.8}{Opposite quasigroups and loops} {13}
\seccontents {4.9}{Basic attributes} {14}
\seccontents {4.10}{Basic arithmetic operations} {14}
\seccontents {4.11}{Powers and inverses} {15}
\seccontents {4.12}{Associators and commutators} {15}
\seccontents {4.13}{Generators} {16}
\chapcontents {5}{Some methods based on permutation groups}{17}
\seccontents {5.1}{Parent of a quasigroup} {17}
\seccontents {5.2}{Comparing quasigroups with common parent} {17}
\seccontents {5.3}{Subquasigroups and subloops} {18}
\seccontents {5.4}{Translations and sections} {18}
\seccontents {5.5}{Multiplication groups} {19}
\seccontents {5.6}{Inner mapping groups} {19}
\seccontents {5.7}{Nuclei, commutant, center, and associator subloop} {20}
\seccontents {5.8}{Normal subloops} {20}
\seccontents {5.9}{Factor loops} {20}
\seccontents {5.10}{Nilpotency and central series} {21}
\seccontents {5.11}{Solvability} {21}
\seccontents {5.12}{Isomorphisms and automorphisms} {21}
\seccontents {5.13}{How are isomorphisms computed} {22}
\chapcontents {6}{Testing properties of quasigroups and loops}{23}
\seccontents {6.1}{Associativity, commutativity and generalizations} {23}
\seccontents {6.2}{Inverse properties} {23}
\seccontents {6.3}{Some properties of quasigroups} {24}
\seccontents {6.4}{Loops of Bol-Moufang type} {24}
\seccontents {6.5}{Power alternative loops} {25}
\seccontents {6.6}{Conjugacy closed loops and related properties} {26}
\seccontents {6.7}{Additional varieties of loops} {26}
\chapcontents {7}{Specific methods}{27}
\seccontents {7.1}{Moufang modifications} {27}
\seccontents {7.2}{Triality for Moufang loops} {28}
\chapcontents {8}{Libraries of small loops}{29}
\seccontents {8.1}{A typical library} {29}
\seccontents {8.2}{Left Bol loops} {29}
\seccontents {8.3}{Small Moufang loops} {30}
\seccontents {8.4}{Steiner loops} {30}
\seccontents {8.5}{CC-loops} {31}
\seccontents {8.6}{Paige loops} {31}
\seccontents {8.7}{Interesting loops} {31}
\chapcontents {A}{Files}{32}
\chapcontents {B}{Filters built into the package}{33}
\chapcontents {}{Bibliography}{35}
\chapcontents {}{Index}{36}
