## ST4test.txt    check of P-Q pairs
#  if following X** =0, then the relation EPQE holds
with(DEtools):
read "equations.txt":
read "ST4PQ.txt":   

#list of shifts:
#      1n2n,1p2p,1n3n,1p3p,1n5n,1p5p,3n4n,3p4p,3n5n,3p5p,5n6n,5p6p
#      1n2p,1p2n,1n3p,1p3n,1n5p,1p5n,1nn,1pp,3n4p,3p4n,3n5p,3p5n
#      3nn,3pp,5n6p,5p6n,5nn,5pp

st4pq:=proc(A,B,EE)  
          return(factor(mult(EE,A,[dx,x])-mult(B,ST4,[dx,x]))):
       end proc:

X1n2n:=st4pq(P1n2n,Q1n2n,subs({e1=e1-1,e2=e2-1},ST4));
X1p2p:=st4pq(P1p2p,Q1p2p,subs({e1=e1+1,e2=e2+1},ST4));
X1n3n:=st4pq(P1n3n,Q1n3n,subs({e1=e1-1,e3=e3-1},ST4));
X1p3p:=st4pq(P1p3p,Q1p3p,subs({e1=e1+1,e3=e3+1},ST4));
X1n5n:=st4pq(P1n5n,Q1n5n,subs({e1=e1-1,e5=e5-1},ST4));
X1p5p:=st4pq(P1p5p,Q1p5p,subs({e1=e1+1,e5=e5+1},ST4));
X3n4n:=st4pq(P3n4n,Q3n4n,subs({e3=e3-1,e4=e4-1},ST4));
X3p4p:=st4pq(P3p4p,Q3p4p,subs({e3=e3+1,e4=e4+1},ST4));
X3n5n:=st4pq(P3n5n,Q3n5n,subs({e3=e3-1,e5=e5-1},ST4));
X3p5p:=st4pq(P3p5p,Q3p5p,subs({e3=e3+1,e5=e5+1},ST4));
X5n6n:=st4pq(P5n6n,Q5n6n,subs({e5=e5-1,e6=e6-1},ST4));
X5p6p:=st4pq(P5p6p,Q5p6p,subs({e5=e5+1,e6=e6+1},ST4));

X1n2p:=st4pq(P1n2p,Q1n2p,subs({e1=e1-1,e2=e2+1},ST4));
X1p2n:=st4pq(P1p2n,Q1p2n,subs({e1=e1+1,e2=e2-1},ST4));
X1n3p:=st4pq(P1n3p,Q1n3p,subs({e1=e1-1,e3=e3+1},ST4));
X1p3n:=st4pq(P1p3n,Q1p3n,subs({e1=e1+1,e3=e3-1},ST4));
X1n5p:=st4pq(P1n5p,Q1n5p,subs({e1=e1-1,e5=e5+1},ST4));
X1p5n:=st4pq(P1p5n,Q1p5n,subs({e1=e1+1,e5=e5-1},ST4));

X1nn:=st4pq(P1nn,Q1nn,subs({e1=e1-2},ST4));
X1pp:=st4pq(P1pp,Q1pp,subs({e1=e1+2},ST4));
X3nn:=st4pq(P3nn,Q3nn,subs({e3=e3-2},ST4));
X3pp:=st4pq(P3pp,Q3pp,subs({e3=e3+2},ST4));
X5nn:=st4pq(P5nn,Q5nn,subs({e5=e5-2},ST4));
X5pp:=st4pq(P5pp,Q5pp,subs({e5=e5+2},ST4));

X3n4p:=st4pq(P3n4p,Q3n4p,subs({e3=e3-1,e4=e4+1},ST4));
X3p4n:=st4pq(P3p4n,Q3p4n,subs({e3=e3+1,e4=e4-1},ST4));
X3n5p:=st4pq(P3n5p,Q3n5p,subs({e3=e3-1,e5=e5+1},ST4));
X3p5n:=st4pq(P3p5n,Q3p5n,subs({e3=e3+1,e5=e5-1},ST4));
X5n6p:=st4pq(P5n6p,Q5n6p,subs({e5=e5-1,e6=e6+1},ST4));
X5p6n:=st4pq(P5p6n,Q5p6n,subs({e5=e5+1,e6=e6-1},ST4));