wielomiany.py

@@ -0,0 +1,87 @@
+class Polynomial:
+    
+    n = 0
+
+    def __init__(self, *args):
+        self.degree = len(args) - 1
+        self.coefficients = list(args)
+
+    @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))
+
+
+n = input("Enter n: ")
+Polynomial.n = int(n)
+
+c1 = [int(x) for x in input("Enter 1st polynomial (coefficients divided by space): ").split()]
+c1 = [x % Polynomial.n for x in c1]
+c2 = [int(x) for x in input("Enter 2nd polynomial: ").split()]
+c2 = [x % Polynomial.n for x in c2]
+
+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)