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python hw.py

hw.py

@@ -0,0 +1,47 @@
+from fractions import gcd
+class Modulo:
+    def __init__(self, n):
+        self.elems = list(range(n))
+        self.n = n
+        self.reversibles = self.get_reversibles()
+        self.idempotent = self.get_idempotent()
+        self.zero_divisors = self.get_zero_divisors()
+        self.nilpotent = self.get_nilpotent()
+    '''elementy odwracalne to te, ktorych nwd z n jest rowne 1'''
+    def get_reversibles(self): 
+        return list(filter(lambda x: gcd(x, self.n) == 1, self.elems))
+    
+    '''nie rozwazamy elementow odwracalnych ani liczby 0
+    #dzielnik zera nie moze byc elementem odwracalnym'''
+    def get_zero_divisors(self):
+        potential_zeros = [ elem for elem in self.elems if elem not in self.reversibles ][1:]
+        results = []
+        for elem in potential_zeros:
+            for elem2 in potential_zeros:
+                if (elem * elem2) % self.n == 0:
+                    results.append(elem)
+                    break
+        return list(results) 
+
+    def get_idempotent(self):
+        '''element idempotentny => a^2 przystaje do a'''
+        return list(filter(lambda x: x*x % self.n == x, self.elems))
+
+    def get_nilpotent(self):
+        '''jesli pierscien nie zawiera dzielnikow zera, to nie zawiera takze elementow
+        nilpotentnych; wystarczy sprawdzic wsrod dzielnikow zera '''
+        potential_nils = self.zero_divisors
+        phi = len(self.reversibles) #funkcja fi
+        results = [] 
+        for elem in potential_nils:
+            for i in range(1, phi+1):
+                if elem**i % self.n == 0:
+                    results.append(elem)
+                    break
+        return results    
+
+def main():
+    m = Modulo(int(input()))
+    print([m.reversibles, m.zero_divisors, m.nilpotent, m.idempotent])
+if __name__ == '__main__':
+    main()

hw2.py

@@ -0,0 +1,121 @@
+import sys
+import ast
+import operator
+from fractions import gcd
+
+class Polynomial():
+    def __init__(self, lst, mod):
+        super().__init__()
+        self.poly = list(map(lambda x: x % mod, lst))    
+        self.mod = mod
+        self.normalize()
+    def normalize(self):
+        while self.poly and self.poly[-1] == 0:
+            self.poly.pop() 
+
+    def arithm(self, p1, p2, op):
+        len_p1, len_p2= len(p1.poly), len(p2.poly)
+        res = [0] * max(len_p1, len_p2)
+        if len_p1 > len_p2:
+            for _ in range(len_p1-len_p2):
+                p2.poly.append(0)
+        else:
+            for _ in range(len_p2-len_p1):
+                p1.poly.append(0)
+
+        for i in range(len(res)):
+            res[i] = op(p1.poly[i], p2.poly[i]) % self.mod
+        return Polynomial(res, self.mod)
+
+    def __add__(self, p2):
+        return self.arithm(self, p2, operator.add)
+
+    def __sub__(self, p2):
+        return self.arithm(self, p2, operator.sub)
+
+    def __mul__(self, p2):
+        res = [0]*(len(self.poly)+len(p2.poly)-1)
+        for i, x1 in enumerate(self.poly):
+            for j, x2 in enumerate(p2.poly):
+                res[i+j] += x1 * x2 % self.mod
+        return Polynomial(res, self.mod)
+    
+    def __truediv__(self, p2):
+        p1 = self
+        m = self.mod
+        
+        if len(p1.poly) < len(p2.poly):
+            return p1
+        
+        if len(p2.poly) == 0:
+            raise ZeroDivisionError
+            
+        divisor_coeff = p2.poly[-1]
+        divisor_exp = len(p2.poly) - 1 
+        while len(p1.poly) >= len(p2.poly):   
+            max_coeff_p1 = p1.poly[-1] #wspolczynnik przy najwyzszej potedze
+            try:
+              tmp_coeff = modDiv(max_coeff_p1, divisor_coeff, m)
+            except ZeroDivisionError as e:
+                raise e
+            
+            tmp_exp = len(p1.poly)-1 - divisor_exp
+            '''tmp to pomocniczy wielomian o reprezentacji [0, 0, .., c^n], gdzie c^n to
+            mnożnik w danym kroku algorytmu dzielenia w słupku. 
+            Następnie mnożymy go z wielomianem-dzielnikiem (p2) i
+            odejmujemy (sub) od wielomianu-dzielnej (p1)'''
+            tmp = []
+            for i in range(tmp_exp):
+                tmp.append(0)
+            tmp.append(tmp_coeff)
+            sub = Polynomial(tmp, m) * p2
+            p1 = p1 - sub
+            p1.normalize() #obcinamy zbędne zera dopisane do wielomianu podczas odejmowania
+        return Polynomial(p1.poly, m)
+
+    def poly_gcd(self, p2):
+        p1 = self
+        try:
+            divisible = p2
+        except ZeroDivisionError as e:
+            raise e
+        if p2.poly == []:
+            return p1
+        return p2.poly_gcd(p1 / p2)
+
+def modDiv(a, b, m): # a*b^-1 (mod m)
+    if gcd(b, m) != 1:
+        raise ZeroDivisionError
+    else:
+        return (a * modinv(b, m)) % m
+
+#rozszerzony algorytm euklidesa
+def egcd(a, b):
+    if a == 0:
+        return (b, 0, 1)
+    else:
+        g, y, x = egcd(b % a, a)
+        return (g, x - (b // a) * y, y)
+
+def modinv(a, m):
+    g, x, y = egcd(a, m)
+    return x % m
+
+def main():
+    n, p1, p2 = int(sys.argv[1]), ast.literal_eval(sys.argv[2]), ast.literal_eval(sys.argv[3])
+    P1 = Polynomial(p1, n)
+    P2 = Polynomial(p2, n)
+    mul = (P1 * P2).poly
+    try:
+        div = (P1 / P2).poly
+    except ZeroDivisionError as e:
+        div = e
+    try:    
+        gcd = P1.poly_gcd(P2).poly
+    except ZeroDivisionError as e:
+        gcd = e
+    print([mul, div, gcd])
+    
+    
+if __name__ == '__main__':
+    main()