# comb will return all combinations of three element in the input.
# this algorithm deals with all different cases: a=b=c or two of them equal and they aren't equal to each other.
comb:=proc(a,b,c)
   local i,j,k, A; A:={};
   if nops({a,b,c})=1 then return {[a,b,c]} fi;
   if nops({a,b,c})=2 then 
      if a=b then return {[a,b,c],[a,c,b],[c,a,b]}
         elif a=c then return {[a,b,c],[a,c,b],[b,a,c]}
              else return {[a,b,c],[b,a,c],[b,c,a]}
      fi
   fi;
   for i in {a,b,c} do
       for j in {a,b,c} minus {i} do
           for k in {a,b,c} minus {i,j} do
           A:=A union {[i,j,k]};
           od; od; od; A;
end:


# ei are generalized exponents of the given operator L
# fi are generalized exponents of the operator Lc~F1(a,b1,b2,c,u,v)
MatchExp1:=proc(e1,e2,e3,f1,f2,f3)
    #options trace;
    local d,A,d1,d2,C,i,s,j,k,n,ind,neweq; A:={};
    d1:=e2-e1; d2:=e3-e2; #d3:=e3-e1;                # take differences
    C:=comb(f1,f2,f3);                              # include 6 cases
    for i in C do
        s:={i[2]-i[1]=d1,i[3]-i[2]=d2}; 
        A:=A union {s};
    od;  
    for i in A do
        if solve(i)=NULL then A:=A minus {i}; fi;
    od; A;
end: