main.cpp

@@ -0,0 +1,106 @@
+#include <iostream>
+#include <math.h>
+
+using namespace std;
+
+bool odwracalny(int i, int n){
+    for(int x=0; x<n; x++){
+            if((x * i) % n == 1){
+               return true ;
+            }
+    return false;
+    }
+}
+
+void el_odwracalne(int n){
+    int lista[n];
+    int index=0;
+    for(int i=0; i<n; i++){
+         if(odwracalny(i,n)){
+            lista[index]=i;
+            index++;
+         }
+    }
+    for (int i=0; i<index; i++){
+        cout << lista[i] << endl;
+    }
+}
+
+bool dzieli_zero(int i, int n){
+    for(int x=0; x<n; x++){
+            if((x * i) % n == 0){
+               return true ;
+            }
+    return false;
+    }
+}
+
+
+void dzielniki_zera(int n){
+    int lista[n];
+    int index=0;
+    for(int i=0; i<n; i++){
+         if(dzieli_zero(i,n)){
+            lista[index]=i;
+            index++;
+         }
+    }
+    for (int i=0; i<index; i++){
+        cout << lista[i] << endl;
+    }
+}
+
+
+bool nilpotent(int i, int n){
+    int power=0;
+    for(int x=0; x<n; x++){
+            power = pow(x, i);
+            if(power % n == 0){
+               return true;
+            }
+    return false;
+    }
+}
+
+void el_nilpotentne(int n){
+    int lista[n];
+    int index=0;
+    for(int i=0; i<n; i++){
+         if(nilpotent(i,n)){
+            lista[index]=i;
+            index++;
+         }
+    }
+    for (int i=0; i<index; i++){
+        cout << lista[i] << endl;
+    }
+}
+
+
+void el_idempotentne(int n){
+    int lista[n];
+    int index=0;
+    for(int i=0; i<n; i++){
+         if(i*i % n == i){
+            lista[index]=i;
+            index++;
+         }
+    }
+    for (int i=0; i<index; i++){
+        cout << lista[i] << endl;
+    }
+}
+
+
+int main()
+{
+    int n = 5;
+    cout << "(";
+    el_odwracalne(n);
+    cout << ")";
+    dzielniki_zera(n);
+
+    el_nilpotentne(n);
+
+    el_idempotentne(n);
+}

zad2.py

@@ -0,0 +1,99 @@
+import math
+
+class Polynomial:
+	n = 0
+
+	def __init__(self, n):
+		self.n = n
+
+	def normalize(self, w):
+		while 0 in w: 
+			w.remove(0)
+		return w
+
+	def multiply(self, f, g):
+		result = []
+		tmp=0
+		for i in range(0, len(f)):
+			for j in range(0, len(g)):
+				tmp=f[i]*g[j]
+				if i+j < len(result):
+					tmp = tmp + result[i+j]
+					result[i+j] = tmp % self.n
+				else:
+					while i+j >= len(result):
+						result.append(0)
+					result[i+j] = tmp % self.n
+		return self.normalize(result)
+
+	def multiplyConst(self, f, a):
+		result = []
+		for i in f:
+			result.append((i*a)%self.n)
+		return result
+
+	def substract(self, f, g):
+		result = []
+		for i in range(0, len(f)):
+			if i < len(g):
+				result.append(math.fmod(f[i]-g[i], self.n))
+			else:
+				result.append(f[i])
+		return result
+
+	def zero(self, a, b):
+		i = 0
+		while True:
+			if (a + (-(b*i))) == 0:
+				return i
+			i = i + 1 
+			
+
+	def divide(self, f, g):
+		quotient = []
+		reminder = f
+		tmpList = []
+		a = (len(f) - 1)
+		b = (len(g) - 1)
+
+		for i in range(0, a-b+1):
+			quotient.append(0)
+
+		q = len(quotient)-1
+		tmp = 0
+
+		while a>=b:
+			tmp = self.zero(reminder[a], g[b])
+			quotient[q] = tmp
+			q = q - 1
+			tmpList = self.multiplyConst(g, tmp)
+			while len(tmpList) <= a:
+				tmpList.append(0)
+			reminder = self.substract(reminder, tmpList)
+			a = a - 1
+		return self.normalize(reminder)
+
+	def nwd(self, f, g):
+		if len(g)==0:
+			return f
+		return self.nwd(g, self.divide(f, g))
+
+
+
+
+polynomial = Polynomial(2)
+f = [1, 1, 1, 0, 1]
+g = [0, 1, 1]
+print(polynomial.multiply(f, g))
+print(polynomial.divide(f, g))
+print(polynomial.nwd(f, g))
+
+polynomial1 = Polynomial(6)
+ff = [2, 1, 0, 2, 1, 3]
+gg = [1, 0, 0, 5]
+print(polynomial1.multiply(ff, gg))
+print(polynomial1.divide(ff, gg))
+print(polynomial1.nwd(ff, gg))
+
+
+