  
  
                                  [1X Smallsemi [101X
  
  
                        [1X A library of small semigroups [101X
  
  
                                 Version 0.6.13
  
  
                                28 February 2022
  
  
                                Andreas Distler
  
                                 James Mitchell
  
  
  
  Andreas Distler
      Email:    [7Xmailto:a.distler@tu-bs.de[107X
  James Mitchell
      Email:    [7Xmailto:jdm3@st-and.ac.uk[107X
      Homepage: [7Xhttp://tinyurl.com/jdmitchell[107X
      Address:  [33X[0;14YMathematical Institute[133X
                [33X[0;14YNorth Haugh[133X
                [33X[0;14YSt Andrews[133X
                [33X[0;14YFife[133X
                [33X[0;14YKY16 9SS[133X
                [33X[0;14YScotland[133X
  
  
  
  -------------------------------------------------------
  [1XCopyright[101X
  [33X[0;0Y© 2008-19 A. Distler & J. D. Mitchell.[133X
  
  [33X[0;0Y[5XSmallsemi[105X  is  free software: you can redistribute it and/or modify it under
  the  terms  of  the  GNU  General  Public  License  as published by the Free
  Software  Foundation,  either  version 3 of the license, or (at your option)
  any later version.[133X
  
  [33X[0;0Y[5XSmallsemi[105X is distributed in the hope that it will be useful, but WITHOUT ANY
  WARRANTY;  without  even  the implied warranty of MERCHANTABILITY or FITNESS
  FOR  A  PARTICULAR  PURPOSE.  See  the  GNU  General Public License for more
  details.[133X
  
  [33X[0;0YA copy of the GNU General Public License is available in the file 'LICENSE';
  for the latest version see [7Xhttps://www.gnu.org/licenses/#GPL[107X.[133X
  
  [33X[0;0YThis file is part of [5XSmallsemi[105X, though as documentation it is released under
  the GNU Free Documentation License (see [7Xhttps://www.gnu.org/licenses/#FDL[107X).[133X
  
  
  -------------------------------------------------------
  [1XAcknowledgements[101X
  [33X[0;0YWe  would  like  to  thank  Tom  Kelsey  for making this library possible by
  running all the initial computations in Minion [GJM06].[133X
  [33X[0;0YThe  first  author  acknowledges  financial  support of the University of St
  Andrews.  The  second  author  acknowledges  support  of  EPSRC grant number
  GR/S/56085/01.[133X
  
  
  -------------------------------------------------------
  [1XColophon[101X
  [33X[0;0YIf you find any bugs or have any suggestions or comments, we would very much
  appreciate  it  if  you  would  let  us  know  via  our  issue  tracker (see
  [7Xhttps://github.com/gap-packages/smallsemi/issues[107X).[133X
  
  
  -------------------------------------------------------
  
  
  [1XContents (Smallsemi)[101X
  
  1 [33X[0;0YIntroduction[133X
    1.1 [33X[0;0YRequirements[133X
      1.1-1 [33X[0;0YOperating System[133X
      1.1-2 [33X[0;0YRAM[133X
      1.1-3 [33X[0;0YDisk Space[133X
    1.2 [33X[0;0YInstallation and Setup[133X
      1.2-1 [33X[0;0YDownload and Extract [5XSmallsemi[105X[133X
      1.2-2 [33X[0;0YContents[133X
      1.2-3 [33X[0;0YLoading[133X
      1.2-4 [33X[0;0YMemory Issues[133X
      1.2-5 [33X[0;0YTesting[133X
      1.2-6 [33X[0;0YCustomizing[133X
  2 [33X[0;0YThe Data in the Library[133X
    2.1 [33X[0;0YCreation of the Semigroups[133X
    2.2 [33X[0;0YStoring the Semigroups[133X
  3 [33X[0;0YExtended Examples[133X
    3.1 [33X[0;0YLists, Enumerators and Iterators of Semigroups[133X
      3.1-1 [33X[0;0YPrecomputed properties[133X
      3.1-2 [33X[0;0YUser functions[133X
      3.1-3 [33X[0;0YSemigroups of order 8[133X
    3.2 [33X[0;0YIdentifying Semigroups[133X
  4 [33X[0;0YFunctionality[133X
    4.1 [33X[0;0YIndividual Semigroups[133X
      4.1-1 SmallSemigroup
      4.1-2 IsSmallSemigroup
      4.1-3 IsSmallSemigroupElt
      4.1-4 RecoverMultiplicationTable
      4.1-5 SemigroupByMultiplicationTableNC
      4.1-6 IdSmallSemigroup
      4.1-7 EquivalenceSmallSemigroup
      4.1-8 InfoSmallsemi
      4.1-9 UnloadSmallsemiData
    4.2 [33X[0;0YProperties of Semigroups[133X
      4.2-1 Annihilators
      4.2-2 DiagonalOfMultiplicationTable
      4.2-3 DisplaySmallSemigroup
      4.2-4 IndexPeriod
      4.2-5 IsBand
      4.2-6 IsBrandtSemigroup
      4.2-7 IsCliffordSemigroup
      4.2-8 IsCommutativeSemigroup
      4.2-9 IsCompletelyRegularSemigroup
      4.2-10 IsFullTransformationSemigroupCopy
      4.2-11 IsGroupAsSemigroup
      4.2-12 [33X[0;0YIsIdempotentGenerated[133X
      4.2-13 IsInverseSemigroup
      4.2-14 IsLeftZeroSemigroup
      4.2-15 IsMonogenicSemigroup
      4.2-16 IsMonoidAsSemigroup
      4.2-17 IsMultSemigroupOfNearRing
      4.2-18 IsNGeneratedSemigroup
      4.2-19 IsNIdempotentSemigroup
      4.2-20 [33X[0;0YIsNilpotentSemigroup[133X
      4.2-21 IsOrthodoxSemigroup
      4.2-22 IsRectangularBand
      4.2-23 IsRegularSemigroup
      4.2-24 IsRightZeroSemigroup
      4.2-25 IsSelfDualSemigroup
      4.2-26 IsSemigroupWithClosedIdempotents
      4.2-27 IsSemigroupWithZero
      4.2-28 [33X[0;0YIsSimpleSemigroup[133X
      4.2-29 IsSingularSemigroupCopy
      4.2-30 IsZeroGroup
      4.2-31 IsZeroSemigroup
      4.2-32 IsZeroSimpleSemigroup
      4.2-33 MinimalGeneratingSet
      4.2-34 NilpotencyDegree
    4.3 [33X[0;0YNilpotent semigroups by coclass[133X
      4.3-1 NilpotentSemigroupsByCoclass
    4.4 [33X[0;0YStarred Green's relations[133X
      4.4-1 IsStarRelation
      4.4-2 RStarRelation
      4.4-3 RStarClass
      4.4-4 RStarClass
      4.4-5 IsStarClass
      4.4-6 RStarClasses
    4.5 [33X[0;0YFamilies of Semigroups[133X
      4.5-1 AllSmallSemigroups
      4.5-2 EnumeratorOfSmallSemigroups
      4.5-3 EnumeratorOfSmallSemigroupsByIds
      4.5-4 EnumeratorSortedOfSmallSemigroups
      4.5-5 FuncsOfSmallSemisInEnum
      4.5-6 FuncsOfSmallSemisInIter
      4.5-7 IdsOfSmallSemigroups
      4.5-8 IsEnumeratorOfSmallSemigroups
      4.5-9 IsIdSmallSemigroup
      4.5-10 IsIteratorOfSmallSemigroups
      4.5-11 IteratorOfSmallSemigroups
      4.5-12 NamesFuncsSmallSemisInEnum
      4.5-13 NamesFuncsSmallSemisInIter
      4.5-14 Nr3NilpotentSemigroups
      4.5-15 NrSmallSemigroups
      4.5-16 OneSmallSemigroup
      4.5-17 PositionsOfSmallSemigroups
      4.5-18 PositionsOfSmallSemisInEnum
      4.5-19 PrecomputedSmallSemisInfo
      4.5-20 RandomSmallSemigroup
      4.5-21 SizesOfSmallSemisInEnum
      4.5-22 SizesOfSmallSemisInIter
      4.5-23 UpToIsomorphism
  
  
  [32X
