read `DyckClever.txt`:

with(combinat):



print(` Given sets A and B of affine linear expressions in the variable r, we interested in counting the number of Dyck paths `):
print(`whose peak-heights are never in the range of A and valley-heights are never in  the range of B`):
print(``):
for N from 2 to 6 do
print(`Below we give the quadratic equations satisfied by the generating function for all sets A and B that are subsets of`):
print(``):
print({seq(N*r+i,i=0..N-1)}):

S:=powerset({seq(N*r+i,i=0..N-1)}):

for A in S do
for B in S do
print(``):
print(`----------------------------`):
print(``):
 print(`(A,B)= `, (A,B)):
print(``):
 print(fABr(A,B,r,x,P)=0  ):
print(``):
od:
od:
od:


print(``):
print(`-------------------------`):
print(``):
print(`This took`, time(), `second. `):
print(``):
quit: