## SE6test.txt       check of P-Q pairs
#  if following X** =0, then the relation EPQE holds
with(DEtools):
read "equations.txt":
read "SE6PQ.txt":

se6pq:=proc(A,B,EE)  
   return(factor(mult(EE,A,[dx,x])-mult(B,SE6,[dx,x]))):
end proc:
se6pq2:=proc(EE,A,B,EE2) 
   return(factor(mult(EE,A,[dx,x])-mult(B,EE2,[dx,x]))):
   end proc:

Xan:=se6pq(Pan,Qan,subs({a=a-1},SE6)); 
Xap:=se6pq2(SE6,Pap,Qap,subs({a=a-1},SE6)); 
Xbn:=se6pq(Pbn,Qbn,subs({b=b-1},SE6)); 
Xbp:=se6pq2(SE6,Pbp,Qbp,subs({b=b-1},SE6)); 
Xcn:=se6pq(Pcn,Qcn,subs({c=c-1},SE6)); 
Xcp:=se6pq(Pcp,Qcp,subs({c=c+1},SE6)); 
Xgn:=se6pq(Pgn,Qgn,subs({g=g-2},SE6)); 
Xgp:=se6pq(Pgp,Qgp,subs({g=g+2},SE6)); 
Xpn:=se6pq(Ppn,Qpn,subs({p=p-1},SE6)); 
Xpp:=se6pq(Ppp,Qpp,subs({p=p+1},SE6)); 
Xqn:=se6pq(Pqn,Qqn,subs({q=q-1},SE6)); 
Xqp:=se6pq(Pqp,Qqp,subs({q=q+1},SE6)); 
Xrn:=se6pq(Prn,Qrn,subs({r=r-1},SE6)); 
Xrp:=se6pq(Prp,Qrp,subs({r=r+1},SE6)); 
Xbcp:=se6pq(Pbcp,Qbcp,subs({b=b+1,c=c-1,p=p+1},SE6)); 
XRbcp:=se6pq2(SE6,PRbcp,QRbcp,subs({b=b+1,c=c-1,p=p+1},SE6));  
Xcpq:=se6pq(Pcpq,Qcpq,subs({c=c+1,p=p-1,q=q-1},SE6)); 
XRcpq:=se6pq2(SE6,PRcpq,QRcpq,subs({c=c+1,p=p-1,q=q-1},SE6));  
Xaandp:=se6pq(Paandp,Qaandp,subs({a=a+1,p=p-1},SE6)); 
XRaandp:=se6pq2(SE6,PRaandp,QRaandp,subs({a=a+1,p=p-1},SE6));  
Xabpq:=se6pq(Pabpq,Qabpq,subs({a=a-1,b=b+1,p=p+1,q=q-1},SE6)); 
Xcg:=se6pq(Pcg,Qcg,subs({c=c+1,g=g-2},SE6)); 
XRcg:=se6pq2(SE6,PRcg,QRcg,subs({c=c+1,g=g-2},SE6));  

# remark: PRabpq, QRabpq are not computed