#Please do not post homework
#Caroline Cote, Feb 28th, 2026, Assignment 11
HelpHW11:=proc(): print(``): end:

#problem 1
#CountNuCompsClever(a,b,A,B,N): inputs the positive integers a and b
# and a subset A of {1,..., a} and a subset B of {0,...,b-1} and outputs 
#the first N terms of the sequence enumerating compositions all whose
# parts have the property that i mod a belongs to A 
# and the number of parts mod b belongs to B

CountNuCompsClever:= proc(a,b,A,B,N) local x, f, i:

f:= GenCompsGF(a,b,A,B,x):
[seq(coeff( taylor(f,x=0,N+3),x,i),i=0..N)]:
end:


#problem 2
with(combinat):
read "C11.txt":
read "C10.txt":
#CountNuCompsStupid(a,b,A,B,N): same thing but longer

CountNuCompsStupid1:= proc(a,b,A,B,n) local co, good, L,i, x, k :

co:= 0:

for L in Comps(n) do
    if member(nops(L) mod b, B) then 
        
        good := true:
        
        for i from 1 to nops(L) do
            k := L[i]:
            x := k mod a:
            if x = 0 then
                x:= a:
            fi:
            if not member(x,A) then 
                 good:= false:
             fi:
         od:
        
          
     if good then 
         co := co + 1:
      fi:
   fi:
 od:
 co:
 end:
 
 CountNuCompsStupid:= proc(a,b,A,B,N) local n:
 [seq(CountNuCompsStupid1(a,b,A,B,n), n = 0..N)]:
 end:
 
 
a := 3;
b := 4;
A := {1, 2};
B := {0, 3};
evalb(CountNuCompsClever(a, b, A, B, 15) = CountNuCompsStupid(a, b, A, B, 15));
#                              true

a := 2;
b := 3;
A := {1};
B := {2};
evalb(CountNuCompsClever(a, b, A, B, 15) = CountNuCompsStupid(a, b, A, B, 15));
#                              true