// IsSplit.mgm originally developed by J.M. Belk - RHIT REU 1997
// the script determines whether a tiling splits at a reflection R
// the full tiling group Gs and its generators p,q, and r must be supplied
// R is the reflection we are testing for separability, it is uusally one of p,q, or r.

IsSplit := function(Gs,p,q,r,R)
   Xold := {};
   X := {Id(Gs)};
   repeat
        bX  := X diff Xold;
        Xold := X;
        Xnew := {{x*p,x*q,x*r} diff {R*x} : x in bX}; // in triples and doubles 
        Xnew := {xn : xn in yn,yn in Xnew};           // as single elements 
        X := Xold join Xnew;
        until #Xold eq #X;
   if #X eq #Gs
      then return false;
      else return true;
      end if;
   end function;