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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())