  
  [1X1 [33X[0;0YThe [5XSemigroups[105X[101X[1X package[133X[101X
  
  
  [1X1.1 [33X[0;0YIntroduction[133X[101X
  
  [33X[0;0YThis  is  the  manual  for  the  [5XSemigroups[105X  package  for [5XGAP[105X version 5.2.0.
  [5XSemigroups[105X  5.2.0  is  a  distant descendant of the Monoid package for GAP 3
  ([7Xhttp://schmidt.nuigalway.ie/monoid/index.html[107X)  by Goetz Pfeiffer, Steve A.
  Linton, Edmund F. Robertson, and Nik Ruskuc.[133X
  
  [33X[0;0YFrom  Version  3.0.0,  [5XSemigroups[105X  includes  a copy of the [5Xlibsemigroups[105X C++
  library  which  contains  implementations of the Froidure-Pin, Todd-Coxeter,
  and Knuth-Bendix algorithms (among others) that [5XSemigroups[105X utilises.[133X
  
  [33X[0;0YIf  you  find  a  bug  or  an issue with the package, please visit the issue
  tracker ([7Xhttps://github.com/semigroups/Semigroups/issues[107X).[133X
  
  
  [1X1.2 [33X[0;0YOverview[133X[101X
  
  [33X[0;0YThis manual is organised as follows:[133X
  
  [8XPart I: elements[108X
        [33X[0;6Ythe  different types of elements that are introduced in [5XSemigroups[105X are
        described  in Chapters [14X3[114X, [14X4[114X, and [14X5[114X. These include [2XBipartition[102X ([14X3.2-1[114X),
        [2XPBR[102X  ([14X4.2-1[114X),  and  [2XMatrix[102X  ([14X5.1-5[114X),  which  supplement  those already
        defined  in  the  [5XGAP[105X  library,  such  as  [2XTransformation[102X  ([14XReference:
        Transformation   for   an   image  list[114X)  or  [2XPartialPerm[102X  ([14XReference:
        PartialPerm for a domain and image[114X).[133X
  
  [8XPart II: semigroups and monoids defined by generating sets[108X
        [33X[0;6Yfunctions  and  operations for creating semigroups and monoids defined
        by  generating  sets (of the type descibed in Part I) are described in
        Chapter [14X6[114X.[133X
  
  [8XPart III: standard examples and constructions[108X
        [33X[0;6Ystandard  examples of semigroups, such as [2XFullBooleanMatMonoid[102X ([14X7.6-1[114X)
        or  [2XUniformBlockBijectionMonoid[102X  ([14X7.3-8[114X),  are described in Chapter [14X7[114X,
        and standard constructions, such as [2XDirectProduct[102X ([14X8.1-1[114X) are given in
        Chapter [14X8[114X.[133X
  
  [8XPart IV: the structure of a semigroup or monoid[108X
        [33X[0;6Ythe  functionality  for determining various structural properties of a
        given semigroup or monoid are described in Chapters [14X9[114X, [14X10[114X, [14X11[114X, and [14X12[114X.[133X
  
  [8XPart V: congruences, quotients, and homomorphisms[108X
        [33X[0;6Ymethods  for  creating  and manipulating congruences and homomorphisms
        are described by Chapters [14X13[114X and [14X14[114X.[133X
  
  [8XPart VI: finitely presented semigroups and monoids[108X
        [33X[0;6Ymethods  for finitely presented semigroups and monoids, in particular,
        for Tietze transformations can be found in Chapters [14X15[114X.[133X
  
  [8XPart VII: utilities and helper functions[108X
        [33X[0;6Yfunctions  for  reading and writing semigroups and their elements, and
        for  visualising  semigroups, and some of their elements, can be found
        in Chapters [14X16[114X and [14X17[114X.[133X
  
