\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} \seccontents {1.5}{Acknowledgement} {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} \seccontents {2.4}{Extensions} {7} \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}{Creating quasigroups and loops}{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}{Creating quasigroups and loops by sections} {13} \seccontents {4.7}{Creating quasigroups and loops by extensions} {14} \seccontents {4.8}{Conversions} {14} \seccontents {4.9}{Products of loops} {15} \seccontents {4.10}{Opposite quasigroups and loops} {15} \chapcontents {5}{Basic methods and attributes}{16} \seccontents {5.1}{Basic attributes} {16} \seccontents {5.2}{Basic arithmetic operations} {16} \seccontents {5.3}{Powers and inverses} {17} \seccontents {5.4}{Associators and commutators} {17} \seccontents {5.5}{Generators} {17} \chapcontents {6}{Methods based on permutation groups}{18} \seccontents {6.1}{Parent of a quasigroup} {18} \seccontents {6.2}{Comparing quasigroups with common parent} {18} \seccontents {6.3}{Subquasigroups and subloops} {19} \seccontents {6.4}{Translations and sections} {19} \seccontents {6.5}{Multiplication groups} {20} \seccontents {6.6}{Inner mapping groups} {20} \seccontents {6.7}{Nuclei, commutant, center, and associator subloop} {21} \seccontents {6.8}{Normal subloops} {21} \seccontents {6.9}{Factor loops} {22} \seccontents {6.10}{Nilpotency and central series} {22} \seccontents {6.11}{Solvability} {22} \seccontents {6.12}{Isomorphisms and automorphisms} {23} \seccontents {6.13}{How are isomorphisms computed} {23} \seccontents {6.14}{Isotopisms} {24} \chapcontents {7}{Testing properties of quasigroups and loops}{25} \seccontents {7.1}{Associativity, commutativity and generalizations} {25} \seccontents {7.2}{Inverse properties} {25} \seccontents {7.3}{Some properties of quasigroups} {26} \seccontents {7.4}{Loops of Bol-Moufang type} {26} \seccontents {7.5}{Power alternative loops} {27} \seccontents {7.6}{Conjugacy closed loops and related properties} {28} \seccontents {7.7}{Additional varieties of loops} {28} \chapcontents {8}{Specific methods}{29} \seccontents {8.1}{Core methods for Bol loops} {29} \seccontents {8.2}{Moufang modifications} {29} \seccontents {8.3}{Triality for Moufang loops} {30} \chapcontents {9}{Libraries of small loops}{31} \seccontents {9.1}{A typical library} {31} \seccontents {9.2}{Left Bol loops} {31} \seccontents {9.3}{Moufang loops} {32} \seccontents {9.4}{Code loops} {32} \seccontents {9.5}{Steiner loops} {32} \seccontents {9.6}{CC-loops} {33} \seccontents {9.7}{Small loops} {33} \seccontents {9.8}{Paige loops} {33} \seccontents {9.9}{Interesting loops} {33} \seccontents {9.10}{Libraries of loops up to isotopism} {34} \chapcontents {A}{Files}{35} \chapcontents {B}{Filters built into the package}{36} \chapcontents {}{Bibliography}{39} \chapcontents {}{Index}{40}