########################################################
##
##  Very simple commands to compute orbital integrals
##  and basis class functions for a finite group G.
##
##8-2000,wdj, 
#########################################################

orbital_integral:=function(g,f,G)
 local x,y;
  y:=List(Elements(G),x->f(x^(-1)*g*x)/Size(G));
 return Sum(y);
end;

class_fcn:=function(x,y,G)
 if x in ConjugacyClass(G,y) then return 1; fi;
 return 0;
end;

########### Examples
A5:=AlternatingGroup(5);
f:=function(x)
 return(class_fcn(x,(1,2,3),A5));
end;
f:=function(x)
 return(class_fcn(x,(1,2)(3,5),A5)+3*class_fcn(x,(1,2,3),A5)-class_fcn(x,(),A5));
end;
G:=SymmetricGroup(4);
f1:=function(x)
if x=(1,2,3) then return 1; fi;
 if x<>(1,2,3) then return 0; fi;
end;
orbital_integral((1,2,3),f1,G);
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