p = 23
a_L = [0, 1, 0, 1]
a_R = [-1, 0, -1, 0]
n_2 = [1, 2, 4, 8]
n_1 = [1, 1, 1, 1]

y = 15
z = 13

def expo(a, n_1, p) :
    tmp = [1]
    for i in range(0, len(n_1)) :
        tmp.append((a * tmp[i]) % p)
    return tmp

def inner_product(a, b, p) :
    tmp = 0
    for i in range(0, len(a)) :
        tmp += ( a[i] * b[i] ) % p
        tmp = tmp % p
    return tmp

def vector_minus(a, b, p) :
    tmp = []
    for i in range(0, len(a)) :
        tmp.append( (a[i] - b[i]) % p)
    return tmp

def vector_add(a, b, p) :
    tmp = 0
    for i in range(0, len(a)) :
        tmp.append( (a[i] + b[i]) % p)
    return tmp

def hadamard(a, b, p) :
    tmp = []
    for i in range(0, len(a)) :
        #print(str(i))
        tmp.append( (a[i] * b[i]) % p )
    return tmp

print(str(inner_product(a_L, a_R, p)))
print(str(inner_product(a_L, n_2, p)))
print(str(hadamard(a_L, a_R, p)))

v = inner_product(a_L, n_2, p)

print(expo(y, n_1, p))
n_y = expo(y, n_1, p)
print("n_y : ")
print(n_y)
print("and the value is : " + str(v))
left_side = (pow(z, 2, p) * v) % p

R_1 = (pow(z, 2, p) * inner_product(a_L, n_2, p))  % p
R_2 = (z * inner_product(vector_minus(vector_minus(a_L, n_1, p), a_R, p), n_y, p)) % p
R_3 = inner_product(a_L, hadamard(a_R, n_y, p), p)

print(R_2)
print(R_3)

right_side = (R_1 + R_2 + R_3)%p

print("left_side : " + str(left_side))
print("right_side : " + str(right_side))