Zaktualizuj 'wielomiany.py'

Ring.py

@@ -0,0 +1,48 @@
+from fractions import gcd
+
+class Modulo:
+
+    def __init__(self, n):
+        self.n = int(n)
+        self.modulo_set = list(range(self.n))
+        self.answer = []
+
+    def get_inverse_elements(self):
+        self.inverse_elements = []
+        for i in self.modulo_set:
+            if gcd(i, self.n) == 1:
+                self.inverse_elements.append(i)
+        self.answer.append(self.inverse_elements)
+
+    def get_zero_divisors(self):
+        self.zero_divisors = []
+        for i in self.modulo_set:
+            for j in self.modulo_set:
+                if (i * j) % self.n == 0 and i != 0 and j != 0:
+                    self.zero_divisors.append(i)
+        self.answer.append(list(set(self.zero_divisors)))
+
+    def get_nilpotent_elements(self):
+        self.nilpotent_elements = []
+        for i in self.modulo_set:
+            for j in range(1, len(self.inverse_elements) + 1):
+                if (i**j) % self.n == 0 and i != 0:
+                    self.nilpotent_elements.append(i) 
+        self.answer.append(list(set(self.nilpotent_elements)))
+
+    def get_idempotent_elements(self):
+        self.idempotent_elements = []
+        for i in self.modulo_set:
+            if (i*i) % self.n == i:
+                self.idempotent_elements.append(i)
+        self.answer.append(self.idempotent_elements)
+
+    def get_all(self):
+        self.get_inverse_elements()
+        self.get_zero_divisors()
+        self.get_nilpotent_elements()
+        self.get_idempotent_elements()
+        return self.answer
+
+s = Modulo(input("Enter n: "))
+print(s.get_all())

wielomiany.py

@@ -0,0 +1,90 @@
+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()