#HomeWork#11
#Please do not post homework
#Abrar Almahmeed, March 1

#Question 1:

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

##Check##
CountNuCompsClever(3,4,{1,2},{0,3},15);
[1, 0, 0, 1, 4, 7, 10, 18, 34, 62, 114, 211, 390, 717, 1316, 2420]

CountNuCompsClever(2,3,{1},{2},15);
   [0, 0, 1, 0, 2, 1, 3, 5, 5, 15, 13, 36, 42, 81, 128, 192]

#Question 2:

CountNuCompsStupid1:= proc(a,b,A,B,n)
local C,L,i,check,S:
if n=0 then
    if member(0 mod b,B) then
         return 1:
    else
        return 0:
    fi:
fi:
C:= Comps(n):
S:= {}:
for L in C do
    if member(nops(L) mod b, B) then
        check:= true:
        for i from 1 to nops(L) do
            if not member(((L[i]-1) mod a)+1, A) then
                check:= false:
                break:
            fi:
       od:
       if check then
           S := S union {L}:
       fi:
    fi:
od:
nops(S):
end:
CountNuCompsStupid:= proc(a,b,A,B,N)
local n:
[seq(CountNuCompsStupid1(a,b,A,B,n),n=0..N)]:
end:

##Check##
CountNuCompsStupid(3,4,{1,2},{0,3},15);
[1, 0, 0, 1, 4, 7, 10, 18, 34, 62, 114, 211, 390, 717, 1316, 2420]


CountNuCompsStupid(2,3,{1},{2},15);
   [0, 0, 1, 0, 2, 1, 3, 5, 5, 15, 13, 36, 42, 81, 128, 192]