import sys import ast class Polynomial: n = 0 def __init__(self, coef_list): self.degree = len(coef_list) - 1 self.coefficients = coef_list @staticmethod def multiply(p1, p2): result = [0] * (p1.degree + p2.degree + 1) f = p1.coefficients g = p2.coefficients for i in range(0, len(f)): for j in range(0, len(g)): result[i+j] += f[i] * g[j] result = [x % int(n) for x in result] return Polynomial(result) @staticmethod def divide(p1, p2): def inverse(x): for i in range(1, int(n)): r = (i * x) % int(n) if r == 1: break else: raise ZeroDivisionError return i if p1.degree < p2.degree: return p1 f = p1.coefficients g = p2.coefficients g_lead_coef = g[-1] g_deg = p2.degree while len(f) >= len(g): f_lead_coef = f[-1] tmp_coef = f_lead_coef * inverse(g_lead_coef) tmp_exp = len(f) - 1 - g_deg tmp = [] for i in range(tmp_exp): tmp.append(0) tmp.append(tmp_coef) tmp_poly = Polynomial(tmp) sub = Polynomial.multiply(p2, tmp_poly) f = [x - y for x, y in zip(f, sub.coefficients)] f = [x % int(n) for x in f] while f and f[-1] == 0: f.pop() return Polynomial(f) @staticmethod def gcd(p1, p2): if len(p2.coefficients) == 0: return p1 return Polynomial.gcd(p2, Polynomial.divide(p1, p2)) def main(): c1 = ast.literal_eval(sys.argv[2]) c2 = ast.literal_eval(sys.argv[3]) f = Polynomial(c1) g = Polynomial(c2) ans = [] mul = Polynomial.multiply(f, g) ans.append(mul.coefficients) try: div = Polynomial.divide(f, g) ans.append(div.coefficients) except ZeroDivisionError as e: ans.append(e) try: gcd = Polynomial.gcd(f, g) ans.append(gcd.coefficients) except ZeroDivisionError as e: ans.append(e) print(ans) if __name__ == "__main__": n = int(sys.argv[1]) main()