README-Zad1.txt

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+Program jest napisany w Python 3.
+
+Po wprowadzeniu liczby program nie czeka na kolejne dane.
+
+Co za tym idzie, okno zostanie zamknięte zaraz po wyświetleniu listy.
+
+Rozwiązaniem jest rzecz jasna wejście do folderu w emulatorze konsoli i wywołanie interpretera Pythona:
+    Na systemie Windows:
+        python modulo.py
+    Na systemach uniksopodobnych:
+        python3 modulo.py

modulo.py

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+import math
+
+def radical(n):
+    if n == 0:
+        return 0
+
+    factors = set()
+    i = 1
+
+    while n > 1:
+        if math.gcd(i, n) != 1:
+            n = n // i
+            factors.add(i)
+        else:
+            i = i + 1
+
+    rad = 1
+    for factor in factors:
+        rad = rad * factor
+
+    return rad
+
+class ModuloRing:
+
+    def __init__(self, number):
+        self.number = number
+        self.elements = [x for x in range(number)]
+        self.radical = radical(number)
+
+    def inverse_elements(self):
+        if self.number == 0:
+            return []
+
+        ring_inverses = []
+
+        for element in self.elements:
+            if math.gcd(element, self.number) == 1:
+                ring_inverses.append(element)
+
+        return ring_inverses
+
+
+    def zero_divisor_elements(self):
+        if self.number == 0:
+            return []
+
+        ring_zero_divisors = set()
+        ring_zero_divisors.add(0)
+        
+        for element in self.elements:
+            if element != 0:
+                for second_element in self.elements:
+                    if second_element != 0:
+                        if (element * second_element) % self.number == 0:
+                            ring_zero_divisors.add(element)
+
+        return list(ring_zero_divisors)
+
+
+    def nilpotent_elements(self):
+        if self.number == 0:
+            return []
+            
+        ring_nilpotents = []
+
+        for element in self.elements:
+            if math.gcd(element, self.radical) == self.radical:
+                ring_nilpotents.append(element)
+
+        return ring_nilpotents
+
+    def idempotent_elements(self):
+        if self.number == 0:
+            return []
+            
+        ring_idempotents = []
+
+        for element in self.elements:
+            if (element ** 2) % self.number == element:
+                ring_idempotents.append(element)
+
+        return ring_idempotents
+
+    def get_lists(self):
+        ring_list = []
+        ring_list.append(self.inverse_elements())
+        ring_list.append(self.zero_divisor_elements())
+        ring_list.append(self.nilpotent_elements())
+        ring_list.append(self.idempotent_elements())
+        return ring_list
+
+if __name__ == "__main__":
+    modulo_ring = ModuloRing(int(input()))
+    print(modulo_ring.get_lists())