(******************************************************************************) (******************************************************************************) (** **) (** **) (** REGGE CALCULUS **) (** **) (** Z. PERJES, KFKI RMKI, HUNGARY **) (** perjes@rmk530.rmki.kfki.hu **) (** Spring, 1995. **) (** **) (**--------------------------------------------------------------------------**) (** **) (** Fill out the question form in the frames below to compute **) (** the action and various features of your triangulated space-time. **) (** An example of how to fill out is given for a 10-vertex **) (** triangulation of CP^2. Replace the answers **) (** to questions 1-4 by yours. The example given here runs **) (** under Mathematica 2.2 for 5 mins on the DecStation COSMIC. **) (** **) (******************************************************************************) (******************************************************************************) (** **) (** **) (** Q U E S T I O N N A I R E **) (** **) (**--------------------------------------------------------------------------**) (** 1. The name of your triangulation? **) (** **) (**) name = CP10; (**) (**) (**) (**--------------------------------------------------------------------------**) (** 2. Specify below the parameters of your triangulation: **) (**) (**) (**) p=2; (**) (**) n=p^2+p+1; (**) (**) (**) (**--------------------------------------------------------------------------**) (** 3. List the vertices of the 4-simplices in the form **) (** t4 = {{0,3,7,1,4},{2,0,3,5,4},...}; . **) (** Or generate the list by an algorithm as in the example below: **) (** **) (** **) (**) s1=Flatten[Table[{j-1, j , k+j ,j+k+1 ,x},{j,n},{k,p-1}],1]; (**) (**) s2=Flatten[Table[{j-1,p+j ,(k+1)(p+1)+j-1, (**) (**) (k+2)(p+1)+j-1,x},{j,n},{k,p-1}],1]; (**) (**) s3=Flatten[Table[{j-1,p+j-1,(k+1) p+j-1, (**) (**) (k+2) p+j-1,x},{j,n},{k,p-1}],1]; (**) (**) (**) (**) t4 = Join[Mod[s1,n]/.Mod[x,n]->n, Mod[s1,n]/.Mod[x,n]->n+1, (**) (**) Mod[s2,n]/.Mod[x,n]->n, Mod[s2,n]/.Mod[x,n]->n+2, (**) (**) Mod[s3,n]/.Mod[x,n]->n+1, Mod[s3,n]/.Mod[x,n]->n+2]; (**) (**) (**) (**--------------------------------------------------------------------------**) (** 4. Define all the edge length squares between vertices e1 and e2, **) (** m={{0,c,b,...},{c,0,...},...}; s[e1_,e2_]:=m[[e1,e2]]^2; or cf.: **) (**) (**) (**) s[e1_,e2_]:= If[e1==e2,0, (**) (**) If[e1>n-1 || e2>n-1,bb^2,Module[{k},k=Min[Abs[e1-e2],n-Abs[e1-e2]];(**) (**) If[k==1||k==p||k==p+1,aa^2, If[k