  
  
                                    [1X[5XLieRing[105X[101X
  
  
                                   [1XLie Rings[101X
  
  
                                  Version 2.3
  
  
                                 November 2016
  
  
                                 Serena Cicalò
  
                                Willem de Graaf
  
  
  
  Serena Cicalò
      Email:    [7Xmailto:cicalo@science.unitn.it[107X
      Address:  [33X[0;14YDipartimento di Matematica e Informatica[133X
                [33X[0;14YVia Ospedale, 72[133X
                [33X[0;14Y09124 Cagliari[133X
                [33X[0;14YItaly[133X
  
  
  Willem de Graaf
      Email:    [7Xmailto:degraaf@science.unitn.it[107X
      Homepage: [7Xhttp://www.science.unitn.it/~degraaf/[107X
      Address:  [33X[0;14YDipartimento di Matematica[133X
                [33X[0;14YVia Sommarive 14[133X
                [33X[0;14YI-38050 Povo (Trento)[133X
                [33X[0;14YItaly[133X
  
  
  
  -------------------------------------------------------
  [1XAbstract[101X
  [33X[0;0YThis package provides functions for constructing and working with Lie rings.
  There  are  functions for dealing with finitely-presented Lie rings, and for
  performing  the  Lazard  correspondence.  The  package also contains a small
  database of finitely-generated Lie rings satisfying an Engel condition.[133X
  
  
  -------------------------------------------------------
  [1XCopyright[101X
  [33X[0;0Y© 2016 Serena Cicalò and Willem de Graaf[133X
  
  
  -------------------------------------------------------
  
  
  [1XContents (LieRing)[101X
  
  1 [33X[0;0YIntroduction[133X
    1.1 [33X[0;0YPreliminaries[133X
    1.2 [33X[0;0YThe free Lie ring[133X
    1.3 [33X[0;0YThe Lazard correspondence[133X
  2 [33X[0;0YThe functions[133X
    2.1 [33X[0;0YThe free Lie ring[133X
      2.1-1 FreeLieRing
      2.1-2 Degree
    2.2 [33X[0;0YCreating Lie rings[133X
      2.2-1 IsLieRing
      2.2-2 LieRingByStructureConstants
      2.2-3 FpLieRing
      2.2-4 FpLieAlgebra
    2.3 [33X[0;0YWorking with Lie rings[133X
      2.3-1 Basis
      2.3-2 StructureConstantsTable
      2.3-3 Torsion
      2.3-4 Coefficients
      2.3-5 SubLieRing
      2.3-6 LieRingIdeal
      2.3-7 NaturalHomomorphismByIdeal
      2.3-8 LieLowerCentralSeries
      2.3-9 LieLowerPCentralSeries
      2.3-10 LieCentre
      2.3-11 TensorWithField
    2.4 [33X[0;0YThe Lazard correspondence[133X
      2.4-1 PGroupToLieRing
      2.4-2 LieRingToPGroup
    2.5 [33X[0;0YThe database of [22Xn[122X-Engel Lie rings[133X
      2.5-1 SmallNEngelLieRing
  
  
  [32X
