  
  [1X13 [33X[0;0YGenerators and relators of groups[133X[101X
  
  [33X[0;0Y::::::::::::::::::::::::[133X
  [33X[0;0Y[10XCayleyGraphOfGroupDisplay(G,X) [110X[133X
  [33X[0;0Y[10XCayleyGraphOfGroupDisplay(G,X,"mozilla") [110X[133X
  
  [33X[0;0YInputs  a  finite  group  [22XG[122X  together  with a subset [22XX[122X of [22XG[122X. It displays the
  corresponding  Cayley  graph as a .gif file. It uses the Mozilla web browser
  as  a default to view the diagram. An alternative browser can be set using a
  second argument.[133X
  
  [33X[0;0YThe argument [22XG[122X can also be a finite set of elements in a (possibly infinite)
  group  containing  [22XX[122X. The edges of the graph are coloured according to which
  element  of  [22XX[122X  they  are labelled by. The list [22XX[122X corresponds to the list of
  colours [blue, red, green, yellow, brown, black] in that order.[133X
  
  [33X[0;0YThis function requires Graphviz software.[133X
  [33X[0;0Y::::::::::::::::::::::::[133X
  [33X[0;0Y[10XIdentityAmongRelatorsDisplay(R,n) [110X[133X
  [33X[0;0Y[10XIdentityAmongRelatorsDisplay(R,n,"mozilla") [110X[133X
  
  [33X[0;0YInputs  a  free  [22XZG[122X-resolution  [22XR[122X and an integer [22Xn[122X. It displays the boundary
  R!.boundary(3,n) as a tessellation of a sphere. It displays the tessellation
  as  a  .gif  file  and  uses  the  Mozilla  web browser as a default display
  mechanism.  An  alternative browser can be set using a second argument. (The
  resolution  [22XR[122X  should  be  reduced and, preferably, in dimension 1 it should
  correspond to a Cayley graph for [22XG[122X. )[133X
  
  [33X[0;0YThis function uses GraphViz software.[133X
  [33X[0;0Y::::::::::::::::::::::::[133X
  [33X[0;0Y[10XIsAspherical(F,R) [110X[133X
  
  [33X[0;0YInputs  a  free group [22XF[122X and a set [22XR[122X of words in [22XF[122X. It performs a test on the
  2-dimensional  CW-space  [22XK[122X  associated  to  this  presentation for the group
  [22XG=F/[122X<[22XR[122X>[22X^F[122X.[133X
  
  [33X[0;0YThe  function returns "true" if [22XK[122X has trivial second homotopy group. In this
  case it prints: Presentation is aspherical.[133X
  
  [33X[0;0YOtherwise  it  returns  "fail"  and  prints:  Presentation is NOT piece-wise
  Euclidean non-positively curved. (In this case [22XK[122X may or may not have trivial
  second  homotopy group. But it is NOT possible to impose a metric on K which
  restricts to a Euclidean metric on each 2-cell.)[133X
  
  [33X[0;0YThe function uses Polymake software.[133X
  [33X[0;0Y::::::::::::::::::::::::[133X
  [33X[0;0Y[10XPresentationOfResolution(R) [110X[133X
  
  [33X[0;0YInputs  at least two terms of a reduced [22XZG[122X-resolution [22XR[122X and returns a record
  [22XP[122X with components[133X
  [33X[0;0Y[22XP.freeGroup[122X is a free group [22XF[122X,[133X
  [33X[0;0Y[22XP.relators[122X is a list [22XS[122X of words in [22XF[122X,[133X
  [33X[0;0Y[22XP.gens[122X  is  a  list of positive integers such that the [22Xi[122X-th generator of the
  presentation corresponds to the group element R!.elts[P[i]] .[133X
  [33X[0;0Ywhere [22XG[122X is isomorphic to [22XF[122X modulo the normal closure of [22XS[122X. This presentation
  for [22XG[122X corresponds to the 2-skeleton of the classifying CW-space from which [22XR[122X
  was constructed. The resolution [22XR[122X requires no contracting homotopy.[133X
  [33X[0;0Y::::::::::::::::::::::::[133X
  [33X[0;0Y[10XTorsionGeneratorsAbelianGroup(G) [110X[133X
  
  [33X[0;0YInputs an abelian group [22XG[122X and returns a generating set [22X[x_1, ... ,x_n][122X where
  no pair of generators have coprime orders.[133X
  
