hw4.py

@@ -1,84 +1,84 @@
-from poly import Polynomial
+from poly import Polynomial
-from sys import argv
+from sys import argv
-from ast import literal_eval
+from ast import literal_eval
-from fractions import gcd
+from fractions import gcd
-
+
-class QuotientRing():
+class QuotientRing():
-    def __init__(self, f, m):
+    def __init__(self, f, m):
-        self.f = Polynomial(f, m)
+        self.f = Polynomial(f, m)
-        self.m = m
+        self.m = m
-        self.remainders = self.remainders()
+        self.remainders = self.remainders()
-        self.reversibles = self.reversibles() 
+        self.reversibles = self.reversibles() 
-        self.zero_divisors = self.zero_divisors()
+        self.zero_divisors = self.zero_divisors()
-        self.idempotent = self.idempotent()
+        self.idempotent = self.idempotent()
-        self.nilpotent = self.nilpotent()
+        self.nilpotent = self.nilpotent()
-   
+   
-    def remainders(self): #n - exponent
+    def remainders(self): #n - exponent
-        rems = [] #lista reszt
+        rems = [] #lista reszt
-        m = self.m
+        m = self.m
-        t = [0] 
+        t = [0] 
-        i = 0
+        i = 0
-        while len(t) < len(self.f.poly):
+        while len(t) < len(self.f.poly):
-            rems.append(Polynomial(t, m))
+            rems.append(Polynomial(t, m))
-            i = (i + 1) % m
+            i = (i + 1) % m
-            t[0] = i 
+            t[0] = i 
-            if i == 0:
+            if i == 0:
-                if len(t) == 1:
+                if len(t) == 1:
-                    t.append(1)
+                    t.append(1)
-                else: 
+                else: 
-                    t[1] += 1
+                    t[1] += 1
-                    for j in range(1, len(t)):
+                    for j in range(1, len(t)):
-                        if t[j] == 0 or t[j] % m != 0:
+                        if t[j] == 0 or t[j] % m != 0:
-                            break
+                            break
-                        temp = t[j] % m
+                        temp = t[j] % m
-                        t[j] = 0
+                        t[j] = 0
-                        if temp == 0:
+                        if temp == 0:
-                            if (j + 1) < len(t):
+                            if (j + 1) < len(t):
-                                t[j+1] += 1
+                                t[j+1] += 1
-                            else:
+                            else:
-                                t.append(1)
+                                t.append(1)
-        return rems
+        return rems
-    
+    
-    def reversibles(self):
+    def reversibles(self):
-        return [ rem for rem in self.remainders if len(rem.poly_gcd(self.f).poly) == 1 ]
+        return [ rem for rem in self.remainders if len(rem.poly_gcd(self.f).poly) == 1 ]
-
+
-    #dopelnienie elementow odwracalnych
+    #dopelnienie elementow odwracalnych
-    def zero_divisors(self):
+    def zero_divisors(self):
-        return [ rem for rem in self.remainders if rem not in self.reversibles ]
+        return [ rem for rem in self.remainders if rem not in self.reversibles ]
-    
+    
-    def idempotent(self):
+    def idempotent(self):
-        idems = []
+        idems = []
-        for rem in self.remainders:
+        for rem in self.remainders:
-            if (rem * rem / self.f) == (rem / self.f):
+            if (rem * rem % self.f) == (rem % self.f):
-                idems.append(rem)
+                idems.append(rem)
-        try:
+        try:
-            if idems[0].poly == []:     #implementacja wielomianow ucina zera
+            if idems[0].poly == []:     #implementacja wielomianow ucina zera
-                idems[0].poly = [0]
+                idems[0].poly = [0]
-        except IndexError:
+        except IndexError:
-            return idems
+            return idems
-        return idems
+        return idems
-
+
-    def nilpotent(self):
+    def nilpotent(self):
-        nils = []
+        nils = []
-        phi = len([ i for i in range(1, self.m) if gcd(i, self.m) == 1 ])
+        phi = len([ i for i in range(1, self.m) if gcd(i, self.m) == 1 ])
-        for zero_div in self.zero_divisors:
+        for zero_div in self.zero_divisors:
-            for i in range(self.m):
+            for i in range(self.m):
-               if len((zero_div ** i / self.f).poly) == 0:
+               if len((zero_div ** i % self.f).poly) == 0:
-                   nils.append(zero_div)
+                   nils.append(zero_div)
-                   break
+                   break
-        return nils
+        return nils
-
+
-def main():
+def main():
-    m = int(argv[1])
+    m = int(argv[1])
-    f = literal_eval(argv[2])
+    f = literal_eval(argv[2])
-    qr = QuotientRing(f, m)
+    qr = QuotientRing(f, m)
-    out = [
+    out = [
-            [ rev.poly for rev in qr.reversibles ],
+            [ rev.poly for rev in qr.reversibles ],
-            [ zero_div.poly for zero_div in qr.zero_divisors ],
+            [ zero_div.poly for zero_div in qr.zero_divisors ],
-            [ nil.poly for nil in qr.nilpotent ],
+            [ nil.poly for nil in qr.nilpotent ],
-            [ idem.poly for idem in qr.idempotent ] 
+            [ idem.poly for idem in qr.idempotent ] 
-           ]
+           ]
-    print(*out, sep='\n')
+    print(*out, sep='\n')
-
+
-if __name__ == '__main__':
+if __name__ == '__main__':
     main()