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| 1 | +semigroups: An optional GAP package |
| 2 | +=================================== |
| 3 | + |
| 4 | +Description |
| 5 | +----------- |
| 6 | + |
| 7 | +Installing this SPKG will install the corresponding GAP package, but |
| 8 | +before you can use them in Sage, they still have to be loaded into |
| 9 | +either the GAP interface or libgap:: |
| 10 | + |
| 11 | + sage: gap.eval('LoadPackage("semigroups")') # optional - semigroups |
| 12 | + 'true' |
| 13 | + sage: libgap.LoadPackage("semigroups") # optional - semigroups |
| 14 | + true |
| 15 | + |
| 16 | +Those correspond to:: |
| 17 | + |
| 18 | + gap> LoadPackage("semigroups"); |
| 19 | + |
| 20 | +within the GAP interface and libgap, respectively. |
| 21 | + |
| 22 | +Upstream Contact |
| 23 | +---------------- |
| 24 | + |
| 25 | +See https://semigroups.github.io/Semigroups/ |
| 26 | + |
| 27 | +Dependencies |
| 28 | +------------ |
| 29 | + |
| 30 | +- GAP (a standard spkg), gap_packages and libsemigroups (optional packages) |
| 31 | + |
| 32 | +Notes |
| 33 | +----------- |
| 34 | +This is a GAP package for semigroups, and monoids. There are |
| 35 | +particularly efficient methods for finitely presented semigroups and monoids, |
| 36 | +and for semigroups and monoids consisting of transformations, partial |
| 37 | +permutations, bipartitions, partitioned binary relations, subsemigroups of |
| 38 | +regular Rees 0-matrix semigroups, and matrices of various semirings including |
| 39 | +boolean matrices, matrices over finite fields, and certain tropical matrices. |
| 40 | +Semigroups contains efficient methods for creating semigroups, monoids, and |
| 41 | +inverse semigroups and monoids, calculating their Green's structure, ideals, |
| 42 | +size, elements, group of units, small generating sets, testing membership, |
| 43 | +finding the inverses of a regular element, factorizing elements over the |
| 44 | +generators, and so on. It is possible to test if a semigroup satisfies a |
| 45 | +particular property, such as if it is regular, simple, inverse, completely |
| 46 | +regular, and a large number of further properties. There are methods for |
| 47 | +finding presentations for a semigroup, the congruences of a semigroup, the |
| 48 | +maximal subsemigroups of a finite semigroup, smaller degree partial |
| 49 | +permutation representations, and the character tables of inverse semigroups. |
| 50 | +There are functions for producing pictures of the Green's structure of a |
| 51 | +semigroup, and for drawing graphical representations of certain types of |
| 52 | +elements. |
| 53 | +(Authors: James Mitchell, Marina Anagnostopoulou-Merkouri, |
| 54 | +Thomas Breuer, Stuart Burrell, Reinis Cirpons, Tom Conti-Leslie, |
| 55 | +Joseph Edwards, Attila Egri-Nagy, Luke Elliott, Fernando Flores Brito, |
| 56 | +Tillman Froehlich, Nick Ham, Robert Hancock, Max Horn, Christopher Jefferson, |
| 57 | +Julius Jonusas, Chinmaya Nagpal, Olexandr Konovalov, Artemis Konstantinidi, |
| 58 | +Hyeokjun Kwon, Dima V. Pasechnik, Markus Pfeiffer, Christopher Russell, |
| 59 | +Jack Schmidt, Sergio Siccha, Finn Smith, Ben Spiers, Nicolas Thiéry, |
| 60 | +Maria Tsalakou, Chris Wensley, Murray Whyte, Wilf A. Wilson, Tianrun Yang, |
| 61 | +Michael Young and Fabian Zickgraf) |
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