From 24087c2bb4a7023d4bbf3770c638faab82b6e287 Mon Sep 17 00:00:00 2001
From: Szymon Wojciechowski <szywoj3@st.amu.edu.pl>
Date: Wed, 30 May 2018 18:35:47 +0000
Subject: [PATCH 01/17] =?UTF-8?q?Prze=C5=9Blij=20pliki=20do=20''?=
MIME-Version: 1.0
Content-Type: text/plain; charset=UTF-8
Content-Transfer-Encoding: 8bit

---
 Ring.py | 48 ++++++++++++++++++++++++++++++++++++++++++++++++
 1 file changed, 48 insertions(+)
 create mode 100644 Ring.py

diff --git a/Ring.py b/Ring.py
new file mode 100644
index 0000000..88345d4
--- /dev/null
+++ b/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())
-- 
2.20.1


From 448979c654b0966b86ebaf8a8d4d94c1013aa6e5 Mon Sep 17 00:00:00 2001
From: Szymon Wojciechowski <szywoj3@st.amu.edu.pl>
Date: Wed, 6 Jun 2018 23:25:32 +0000
Subject: [PATCH 02/17] Dodaj 'wielomiany.py'

---
 wielomiany.py | 87 +++++++++++++++++++++++++++++++++++++++++++++++++++
 1 file changed, 87 insertions(+)
 create mode 100644 wielomiany.py

diff --git a/wielomiany.py b/wielomiany.py
new file mode 100644
index 0000000..c00ab5f
--- /dev/null
+++ b/wielomiany.py
@@ -0,0 +1,87 @@
+class Polynomial:
+    
+    n = 0
+
+    def __init__(self, *args):
+        self.degree = len(args) - 1
+        self.coefficients = list(args)
+
+    @staticmethod
+    def multiply(p1, p2):
+        result = [0] * (p1.degree + p2.degree + 1)
+        f = p1.coefficients
+        g = p2.coefficients
+        for i in range(0, len(f)):
+            for j in range(0, len(g)):
+                result[i+j] += f[i] * g[j]
+        result = [x % int(n) for x in result]
+        return Polynomial(*result)
+
+    @staticmethod
+    def divide(p1, p2):          
+        def inverse(x):
+            for i in range(1, int(n)):
+                r = (i * x) % int(n)
+                if r == 1:
+                    break
+            else:
+                raise ZeroDivisionError
+            return i       
+        if p1.degree < p2.degree:
+            return p1
+        f = p1.coefficients
+        g = p2.coefficients
+        g_lead_coef = g[-1]
+        g_deg = p2.degree
+        while len(f) >= len(g):
+            f_lead_coef = f[-1]
+            tmp_coef = f_lead_coef * inverse(g_lead_coef)
+            tmp_exp = len(f) - 1 - g_deg
+            tmp = []
+            for i in range(tmp_exp):
+                tmp.append(0)
+            tmp.append(tmp_coef)
+            tmp_poly = Polynomial(*tmp)
+            sub = Polynomial.multiply(p2, tmp_poly)
+            f = [x - y for x, y in zip(f, sub.coefficients)]
+            f = [x % int(n) for x in f]
+            while f and f[-1] == 0:
+                f.pop()
+        return Polynomial(*f)
+
+    @staticmethod
+    def gcd(p1, p2):
+        if len(p2.coefficients) == 0:
+            return p1
+        return Polynomial.gcd(p2, Polynomial.divide(p1, p2))
+
+
+n = input("Enter n: ")
+Polynomial.n = int(n)
+
+c1 = [int(x) for x in input("Enter 1st polynomial (coefficients divided by space): ").split()]
+c1 = [x % Polynomial.n for x in c1]
+c2 = [int(x) for x in input("Enter 2nd polynomial: ").split()]
+c2 = [x % Polynomial.n for x in c2]
+
+f = Polynomial(*c1)
+g = Polynomial(*c2)
+
+ans = []
+
+mul = Polynomial.multiply(f, g)
+ans.append(mul.coefficients)
+
+try:
+    div = Polynomial.divide(f, g)
+    ans.append(div.coefficients)
+except ZeroDivisionError as e:
+    ans.append(e)
+
+try:
+    gcd = Polynomial.gcd(f, g)
+    ans.append(gcd.coefficients)
+except ZeroDivisionError as e:
+    ans.append(e)
+
+print(ans)
\ No newline at end of file
-- 
2.20.1


From 78f79da83cc4fc43b6840de833447a1b0c5dc974 Mon Sep 17 00:00:00 2001
From: Szymon Wojciechowski <szywoj3@st.amu.edu.pl>
Date: Thu, 7 Jun 2018 08:06:57 +0000
Subject: [PATCH 03/17] Zaktualizuj 'wielomiany.py'

---
 wielomiany.py | 59 +++++++++++++++++++++++++++------------------------
 1 file changed, 31 insertions(+), 28 deletions(-)

diff --git a/wielomiany.py b/wielomiany.py
index c00ab5f..833e9d6 100644
--- a/wielomiany.py
+++ b/wielomiany.py
@@ -1,10 +1,13 @@
+import sys
+import ast
+
 class Polynomial:
     
     n = 0
 
-    def __init__(self, *args):
-        self.degree = len(args) - 1
-        self.coefficients = list(args)
+    def __init__(self, coef_list):
+        self.degree = len(coef_list) - 1
+        self.coefficients = coef_list
 
     @staticmethod
     def multiply(p1, p2):
@@ -15,7 +18,7 @@ class Polynomial:
             for j in range(0, len(g)):
                 result[i+j] += f[i] * g[j]
         result = [x % int(n) for x in result]
-        return Polynomial(*result)
+        return Polynomial(result)
 
     @staticmethod
     def divide(p1, p2):          
@@ -41,13 +44,13 @@ class Polynomial:
             for i in range(tmp_exp):
                 tmp.append(0)
             tmp.append(tmp_coef)
-            tmp_poly = Polynomial(*tmp)
+            tmp_poly = Polynomial(tmp)
             sub = Polynomial.multiply(p2, tmp_poly)
             f = [x - y for x, y in zip(f, sub.coefficients)]
             f = [x % int(n) for x in f]
             while f and f[-1] == 0:
                 f.pop()
-        return Polynomial(*f)
+        return Polynomial(f)
 
     @staticmethod
     def gcd(p1, p2):
@@ -56,32 +59,32 @@ class Polynomial:
         return Polynomial.gcd(p2, Polynomial.divide(p1, p2))
 
 
-n = input("Enter n: ")
-Polynomial.n = int(n)
+def main():
+    c1 = ast.literal_eval(sys.argv[2])
+    c2 = ast.literal_eval(sys.argv[3])
 
-c1 = [int(x) for x in input("Enter 1st polynomial (coefficients divided by space): ").split()]
-c1 = [x % Polynomial.n for x in c1]
-c2 = [int(x) for x in input("Enter 2nd polynomial: ").split()]
-c2 = [x % Polynomial.n for x in c2]
+    f = Polynomial(c1)
+    g = Polynomial(c2)
 
-f = Polynomial(*c1)
-g = Polynomial(*c2)
+    ans = []
 
-ans = []
+    mul = Polynomial.multiply(f, g)
+    ans.append(mul.coefficients)
 
-mul = Polynomial.multiply(f, g)
-ans.append(mul.coefficients)
+    try:
+        div = Polynomial.divide(f, g)
+        ans.append(div.coefficients)
+    except ZeroDivisionError as e:
+        ans.append(e)
 
-try:
-    div = Polynomial.divide(f, g)
-    ans.append(div.coefficients)
-except ZeroDivisionError as e:
-    ans.append(e)
+    try:
+        gcd = Polynomial.gcd(f, g)
+        ans.append(gcd.coefficients)
+    except ZeroDivisionError as e:
+        ans.append(e)
 
-try:
-    gcd = Polynomial.gcd(f, g)
-    ans.append(gcd.coefficients)
-except ZeroDivisionError as e:
-    ans.append(e)
+    print(ans)
 
-print(ans)
\ No newline at end of file
+if __name__ == "__main__":
+    n =  int(sys.argv[1])
+    main()
\ No newline at end of file
-- 
2.20.1


From 0cee287283b3e867d6db404035ca1a0c055ecf5f Mon Sep 17 00:00:00 2001
From: Szymon Wojciechowski <szywoj3@st.amu.edu.pl>
Date: Wed, 20 Jun 2018 15:28:24 +0000
Subject: [PATCH 04/17] Dodaj 'crc16.py'

---
 crc16.py | 139 +++++++++++++++++++++++++++++++++++++++++++++++++++++++
 1 file changed, 139 insertions(+)
 create mode 100644 crc16.py

diff --git a/crc16.py b/crc16.py
new file mode 100644
index 0000000..bd75c00
--- /dev/null
+++ b/crc16.py
@@ -0,0 +1,139 @@
+import sys
+import ast
+import time
+from itertools import zip_longest
+
+class Polynomial:
+
+    def __init__(self, coef_list):
+        self.degree = len(coef_list) - 1
+        self.coefficients = coef_list
+
+    @staticmethod
+    def add(p1, p2):
+        result = []
+        f = p1.coefficients
+        g = p2.coefficients
+        if len(f) >= len(g):
+            result = f
+            for i in range(0, len(g)):
+                result[i] = f[i] + g[i]
+        else:
+            result = g
+            for i in range(0, len(f)):
+                result[i] = f[i] + g[i]
+        result = [x % int(n) for x in result]        
+        return Polynomial(result)             
+
+    @staticmethod
+    def multiply(p1, p2):
+        result = [0] * (p1.degree + p2.degree + 1)
+        f = p1.coefficients
+        g = p2.coefficients
+        for i in range(0, len(f)):
+            for j in range(0, len(g)):
+                result[i+j] += f[i] * g[j]
+        result = [x % int(n) for x in result]
+        return Polynomial(result)
+
+    @staticmethod
+    def divide(p1, p2):          
+        def inverse(x):
+            for i in range(1, int(n)):
+                r = (i * x) % int(n)
+                if r == 1:
+                    break
+            else:
+                raise ZeroDivisionError
+            return i       
+        if p1.degree < p2.degree:
+            return p1
+        f = p1.coefficients
+        g = p2.coefficients
+        g_lead_coef = g[-1]
+        g_deg = p2.degree
+        while len(f) >= len(g):
+            f_lead_coef = f[-1]
+            tmp_coef = f_lead_coef * inverse(g_lead_coef)
+            tmp_exp = len(f) - 1 - g_deg
+            tmp = []
+            for _ in range(tmp_exp):
+                tmp.append(0)
+            tmp.append(tmp_coef)
+            tmp_poly = Polynomial(tmp)
+            sub = Polynomial.multiply(p2, tmp_poly)
+            f = [x - y for x, y in zip(f, sub.coefficients)]
+            f = [x % int(n) for x in f]
+            while f and f[-1] == 0:
+                f.pop()
+        return Polynomial(f)
+
+
+n = 2
+
+
+def normalize_byte(data):
+    while len(data) != 8:
+        if len(data) < 8:
+            data = str(0) + data
+        else:
+            data.replace(data[0], '')
+    return data
+
+
+def encode(in_data):
+    data = in_data
+    data = list(data)
+    data_binary = [bin(ord(char)).replace('b', '') for char in data]
+    data_binary = [normalize_byte(byte) for byte in data_binary]
+    data_binary = [int(bit) for bit in list(''.join(data_binary))]
+    data_binary.reverse()
+
+    M = [0] * 16 + data_binary
+    L = [0] * (len(data_binary)) + [1] * 16
+    G = [1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1]
+    FCS_poly = Polynomial.divide(Polynomial.add(Polynomial(M), Polynomial(L)), Polynomial(G))
+    FCS = FCS_poly.coefficients + [0] * (16 - len(FCS_poly.coefficients))
+
+    FCS.reverse()
+    data_binary.reverse()
+    data_binary = data_binary + FCS
+    data_binary = [data_binary[i:i+8] for i in range(0, len(data_binary), 8)]
+    data = [chr(int(''.join(map(str, byte)), 2)) for byte in data_binary]
+
+    return ''.join(data)
+
+
+def check_fcs(in_data):
+    data = in_data
+    data = list(data)
+    data_binary = [bin(ord(char)).replace('b', '') for char in data]
+    data_binary = [normalize_byte(byte) for byte in data_binary]
+    data_binary = [int(bit) for bit in list(''.join(data_binary))]
+    data_binary.reverse()
+
+    C = [0] * 16 + data_binary
+    L = [0] * len(data_binary) + [1] * 16
+    G = [1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1]
+    S = Polynomial.divide(Polynomial.add(Polynomial(C), Polynomial(L)), Polynomial(G))
+
+    if S.coefficients == []:
+        return True
+
+    return False
+
+
+def main():
+    try:
+        if sys.argv[1] == '-e' or sys.argv[1] == '-encode':
+            print(encode(sys.argv[2]))
+        elif sys.argv[1] == '-c' or sys.argv[1] == '-check':
+            print(check_fcs(sys.argv[2]))
+        else:
+            raise IndexError
+    except IndexError:
+        print("To encode: python3 CRC16.py -e [argument]\nTo check FCS: python3 CRC16.py -c [argument]")
+
+
+if __name__ == "__main__":
+    main()
-- 
2.20.1


From 772736120b54377dc291118984ca775689d6ac10 Mon Sep 17 00:00:00 2001
From: Szymon Wojciechowski <szywoj3@st.amu.edu.pl>
Date: Mon, 25 Jun 2018 15:21:17 +0000
Subject: [PATCH 05/17] bugfix

---
 crc16.py | 10 +++++-----
 1 file changed, 5 insertions(+), 5 deletions(-)

diff --git a/crc16.py b/crc16.py
index bd75c00..f3d1777 100644
--- a/crc16.py
+++ b/crc16.py
@@ -1,7 +1,5 @@
 import sys
 import ast
-import time
-from itertools import zip_longest
 
 class Polynomial:
 
@@ -77,7 +75,7 @@ def normalize_byte(data):
         if len(data) < 8:
             data = str(0) + data
         else:
-            data.replace(data[0], '')
+            data = data[1:]
     return data
 
 
@@ -126,7 +124,9 @@ def check_fcs(in_data):
 def main():
     try:
         if sys.argv[1] == '-e' or sys.argv[1] == '-encode':
-            print(encode(sys.argv[2]))
+            arg = encode(sys.argv[2])
+            print(arg)
+            print(check_fcs(arg)) # powinno zawsze zwracać true
         elif sys.argv[1] == '-c' or sys.argv[1] == '-check':
             print(check_fcs(sys.argv[2]))
         else:
@@ -136,4 +136,4 @@ def main():
 
 
 if __name__ == "__main__":
-    main()
+    main()
\ No newline at end of file
-- 
2.20.1


From 09dcfac9ab436cf8ae72d5fac712bd8710f21553 Mon Sep 17 00:00:00 2001
From: Szymon Wojciechowski <szywoj3@st.amu.edu.pl>
Date: Mon, 25 Jun 2018 17:54:51 +0000
Subject: [PATCH 06/17] changed input

---
 crc16.py | 36 ++++++++++++++++++++++++------------
 1 file changed, 24 insertions(+), 12 deletions(-)

diff --git a/crc16.py b/crc16.py
index f3d1777..ade6f26 100644
--- a/crc16.py
+++ b/crc16.py
@@ -90,24 +90,34 @@ def encode(in_data):
     M = [0] * 16 + data_binary
     L = [0] * (len(data_binary)) + [1] * 16
     G = [1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1]
-    FCS_poly = Polynomial.divide(Polynomial.add(Polynomial(M), Polynomial(L)), Polynomial(G))
-    FCS = FCS_poly.coefficients + [0] * (16 - len(FCS_poly.coefficients))
+    result_poly = Polynomial.divide(Polynomial.add(Polynomial(M), Polynomial(L)), Polynomial(G))
+    result = result_poly.coefficients + [0] * (16 - len(result_poly.coefficients))
 
-    FCS.reverse()
+    result.reverse()
     data_binary.reverse()
-    data_binary = data_binary + FCS
+    data_binary = data_binary + result
     data_binary = [data_binary[i:i+8] for i in range(0, len(data_binary), 8)]
-    data = [chr(int(''.join(map(str, byte)), 2)) for byte in data_binary]
+    data_binary = [int(''.join(map(str, byte)), 2) for byte in data_binary]
 
-    return ''.join(data)
+    fcs = [hex(byte) for byte in data_binary]
+    fcs = fcs[-2:]
+
+    data = [chr(byte) for byte in data_binary]
+    data = ''.join(data[0:-2])
+
+    return data, fcs
 
 
-def check_fcs(in_data):
+def check_fcs(in_data, fcs):
     data = in_data
     data = list(data)
     data_binary = [bin(ord(char)).replace('b', '') for char in data]
     data_binary = [normalize_byte(byte) for byte in data_binary]
     data_binary = [int(bit) for bit in list(''.join(data_binary))]
+    fcs_binary = [bin(int(in_hex, 16)).replace('b', '') for in_hex in fcs]
+    fcs_binary = [normalize_byte(byte) for byte in fcs_binary]
+    fcs_binary = [int(bit) for bit in list(''.join(fcs_binary))]
+    data_binary += fcs_binary
     data_binary.reverse()
 
     C = [0] * 16 + data_binary
@@ -124,15 +134,17 @@ def check_fcs(in_data):
 def main():
     try:
         if sys.argv[1] == '-e' or sys.argv[1] == '-encode':
-            arg = encode(sys.argv[2])
-            print(arg)
-            print(check_fcs(arg)) # powinno zawsze zwracać true
+            arg, fcs = encode(sys.argv[2])
+            print(arg, fcs)
+            print(check_fcs(arg, fcs)) # powinno zawsze zwracać true
         elif sys.argv[1] == '-c' or sys.argv[1] == '-check':
-            print(check_fcs(sys.argv[2]))
+            arg = sys.argv[2]
+            fcs = ast.literal_eval(sys.argv[3])
+            print(check_fcs(arg, fcs))
         else:
             raise IndexError
     except IndexError:
-        print("To encode: python3 CRC16.py -e [argument]\nTo check FCS: python3 CRC16.py -c [argument]")
+        print("To encode: python3 CRC16.py -e [argument]\nTo check result: python3 CRC16.py -c [argument] [fcs]")
 
 
 if __name__ == "__main__":
-- 
2.20.1


From bc3dcdaabe2971fc0328316e7a898e8a7bf64c55 Mon Sep 17 00:00:00 2001
From: Szymon Wojciechowski <szywoj3@st.amu.edu.pl>
Date: Wed, 27 Jun 2018 17:29:48 +0000
Subject: [PATCH 07/17] added polynomial addition

---
 wielomiany.py => poly.py | 30 +++++++++++++++++++++++-------
 1 file changed, 23 insertions(+), 7 deletions(-)
 rename wielomiany.py => poly.py (73%)

diff --git a/wielomiany.py b/poly.py
similarity index 73%
rename from wielomiany.py
rename to poly.py
index 833e9d6..2f335ff 100644
--- a/wielomiany.py
+++ b/poly.py
@@ -9,6 +9,22 @@ class Polynomial:
         self.degree = len(coef_list) - 1
         self.coefficients = coef_list
 
+    @staticmethod
+    def add(p1, p2):
+        result = []
+        f = p1.coefficients
+        g = p2.coefficients
+        if len(f) >= len(g):
+            result = f
+            for i in range(0, len(g)):
+                result[i] = f[i] + g[i]
+        else:
+            result = g
+            for i in range(0, len(f)):
+                result[i] = f[i] + g[i]
+        result = [x % int(Polynomial.n) for x in result]        
+        return Polynomial(result)
+
     @staticmethod
     def multiply(p1, p2):
         result = [0] * (p1.degree + p2.degree + 1)
@@ -17,14 +33,14 @@ class Polynomial:
         for i in range(0, len(f)):
             for j in range(0, len(g)):
                 result[i+j] += f[i] * g[j]
-        result = [x % int(n) for x in result]
+        result = [x % int(Polynomial.n) for x in result]
         return Polynomial(result)
 
     @staticmethod
     def divide(p1, p2):          
         def inverse(x):
-            for i in range(1, int(n)):
-                r = (i * x) % int(n)
+            for i in range(1, int(Polynomial.n)):
+                r = (i * x) % int(Polynomial.n)
                 if r == 1:
                     break
             else:
@@ -41,13 +57,13 @@ class Polynomial:
             tmp_coef = f_lead_coef * inverse(g_lead_coef)
             tmp_exp = len(f) - 1 - g_deg
             tmp = []
-            for i in range(tmp_exp):
+            for _ in range(tmp_exp):
                 tmp.append(0)
             tmp.append(tmp_coef)
             tmp_poly = Polynomial(tmp)
             sub = Polynomial.multiply(p2, tmp_poly)
             f = [x - y for x, y in zip(f, sub.coefficients)]
-            f = [x % int(n) for x in f]
+            f = [x % int(Polynomial.n) for x in f]
             while f and f[-1] == 0:
                 f.pop()
         return Polynomial(f)
@@ -60,6 +76,7 @@ class Polynomial:
 
 
 def main():
+    Polynomial.n =  int(sys.argv[1])
     c1 = ast.literal_eval(sys.argv[2])
     c2 = ast.literal_eval(sys.argv[3])
 
@@ -86,5 +103,4 @@ def main():
     print(ans)
 
 if __name__ == "__main__":
-    n =  int(sys.argv[1])
-    main()
\ No newline at end of file
+    main()
-- 
2.20.1


From f76cc9e06d4f0a1b509b8f9d565849cefcb81865 Mon Sep 17 00:00:00 2001
From: Szymon Wojciechowski <szywoj3@st.amu.edu.pl>
Date: Wed, 27 Jun 2018 17:38:32 +0000
Subject: [PATCH 08/17] import poly

---
 crc16.py | 70 ++------------------------------------------------------
 1 file changed, 2 insertions(+), 68 deletions(-)

diff --git a/crc16.py b/crc16.py
index ade6f26..0a44f74 100644
--- a/crc16.py
+++ b/crc16.py
@@ -1,74 +1,8 @@
+from poly import Polynomial
 import sys
 import ast
 
-class Polynomial:
-
-    def __init__(self, coef_list):
-        self.degree = len(coef_list) - 1
-        self.coefficients = coef_list
-
-    @staticmethod
-    def add(p1, p2):
-        result = []
-        f = p1.coefficients
-        g = p2.coefficients
-        if len(f) >= len(g):
-            result = f
-            for i in range(0, len(g)):
-                result[i] = f[i] + g[i]
-        else:
-            result = g
-            for i in range(0, len(f)):
-                result[i] = f[i] + g[i]
-        result = [x % int(n) for x in result]        
-        return Polynomial(result)             
-
-    @staticmethod
-    def multiply(p1, p2):
-        result = [0] * (p1.degree + p2.degree + 1)
-        f = p1.coefficients
-        g = p2.coefficients
-        for i in range(0, len(f)):
-            for j in range(0, len(g)):
-                result[i+j] += f[i] * g[j]
-        result = [x % int(n) for x in result]
-        return Polynomial(result)
-
-    @staticmethod
-    def divide(p1, p2):          
-        def inverse(x):
-            for i in range(1, int(n)):
-                r = (i * x) % int(n)
-                if r == 1:
-                    break
-            else:
-                raise ZeroDivisionError
-            return i       
-        if p1.degree < p2.degree:
-            return p1
-        f = p1.coefficients
-        g = p2.coefficients
-        g_lead_coef = g[-1]
-        g_deg = p2.degree
-        while len(f) >= len(g):
-            f_lead_coef = f[-1]
-            tmp_coef = f_lead_coef * inverse(g_lead_coef)
-            tmp_exp = len(f) - 1 - g_deg
-            tmp = []
-            for _ in range(tmp_exp):
-                tmp.append(0)
-            tmp.append(tmp_coef)
-            tmp_poly = Polynomial(tmp)
-            sub = Polynomial.multiply(p2, tmp_poly)
-            f = [x - y for x, y in zip(f, sub.coefficients)]
-            f = [x % int(n) for x in f]
-            while f and f[-1] == 0:
-                f.pop()
-        return Polynomial(f)
-
-
-n = 2
-
+Polynomial.n = 2
 
 def normalize_byte(data):
     while len(data) != 8:
-- 
2.20.1


From 965b5a039490ff49cb6257956f8eae147a7b1e5a Mon Sep 17 00:00:00 2001
From: Szymon Wojciechowski <szywoj3@st.amu.edu.pl>
Date: Wed, 27 Jun 2018 17:43:04 +0000
Subject: [PATCH 09/17] Update 'poly.py'

---
 poly.py | 33 +--------------------------------
 1 file changed, 1 insertion(+), 32 deletions(-)

diff --git a/poly.py b/poly.py
index 2f335ff..9ace2ef 100644
--- a/poly.py
+++ b/poly.py
@@ -72,35 +72,4 @@ class Polynomial:
     def gcd(p1, p2):
         if len(p2.coefficients) == 0:
             return p1
-        return Polynomial.gcd(p2, Polynomial.divide(p1, p2))
-
-
-def main():
-    Polynomial.n =  int(sys.argv[1])
-    c1 = ast.literal_eval(sys.argv[2])
-    c2 = ast.literal_eval(sys.argv[3])
-
-    f = Polynomial(c1)
-    g = Polynomial(c2)
-
-    ans = []
-
-    mul = Polynomial.multiply(f, g)
-    ans.append(mul.coefficients)
-
-    try:
-        div = Polynomial.divide(f, g)
-        ans.append(div.coefficients)
-    except ZeroDivisionError as e:
-        ans.append(e)
-
-    try:
-        gcd = Polynomial.gcd(f, g)
-        ans.append(gcd.coefficients)
-    except ZeroDivisionError as e:
-        ans.append(e)
-
-    print(ans)
-
-if __name__ == "__main__":
-    main()
+        return Polynomial.gcd(p2, Polynomial.divide(p1, p2))
\ No newline at end of file
-- 
2.20.1


From 074d255dabf29fb5320ca087fefa2d3082e5daf8 Mon Sep 17 00:00:00 2001
From: Szymon Wojciechowski <szywoj3@st.amu.edu.pl>
Date: Wed, 27 Jun 2018 19:59:00 +0000
Subject: [PATCH 10/17] Update 'poly.py'

---
 poly.py | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/poly.py b/poly.py
index 9ace2ef..d9ddd32 100644
--- a/poly.py
+++ b/poly.py
@@ -7,7 +7,7 @@ class Polynomial:
 
     def __init__(self, coef_list):
         self.degree = len(coef_list) - 1
-        self.coefficients = coef_list
+        self.coefficients = [x % Polynomial.n for x in coef_list]
 
     @staticmethod
     def add(p1, p2):
@@ -72,4 +72,4 @@ class Polynomial:
     def gcd(p1, p2):
         if len(p2.coefficients) == 0:
             return p1
-        return Polynomial.gcd(p2, Polynomial.divide(p1, p2))
\ No newline at end of file
+        return Polynomial.gcd(p2, Polynomial.divide(p1, p2))
-- 
2.20.1


From 39addf92dafb4ed1f22f340e7b90cdbd5c421fa3 Mon Sep 17 00:00:00 2001
From: Szymon Wojciechowski <szywoj3@st.amu.edu.pl>
Date: Thu, 28 Jun 2018 08:57:27 +0000
Subject: [PATCH 11/17] Upload files to 'Zadanie-4'

---
 Zadanie-4/poly.py          | 83 +++++++++++++++++++++++++++++++++++
 Zadanie-4/quotient_ring.py | 88 ++++++++++++++++++++++++++++++++++++++
 2 files changed, 171 insertions(+)
 create mode 100644 Zadanie-4/poly.py
 create mode 100644 Zadanie-4/quotient_ring.py

diff --git a/Zadanie-4/poly.py b/Zadanie-4/poly.py
new file mode 100644
index 0000000..ab3ac44
--- /dev/null
+++ b/Zadanie-4/poly.py
@@ -0,0 +1,83 @@
+import sys
+import ast
+
+class Polynomial:
+    
+    n = 0
+
+    def __init__(self, coeff_list):
+        self.degree = len(coeff_list) - 1
+        self.coefficients = [x % Polynomial.n for x in coeff_list]
+
+    def __pow__(self, n):
+        result = self
+        for i in range(n):
+            result = Polynomial.multiply(result, result)
+        return result
+
+    @staticmethod
+    def add(p1, p2):
+        result = []
+        f = p1.coefficients
+        g = p2.coefficients
+        if len(f) >= len(g):
+            result = f
+            for i in range(len(g)):
+                result[i] = f[i] + g[i]
+        else:
+            result = g
+            for i in range(len(f)):
+                result[i] = f[i] + g[i]
+        result = [x % int(Polynomial.n) for x in result]        
+        return Polynomial(result)
+
+    @staticmethod
+    def multiply(p1, p2):
+        result = [0] * (p1.degree + p2.degree + 1)
+        f = p1.coefficients
+        g = p2.coefficients
+        for i in range(len(f)):
+            for j in range(len(g)):
+                result[i+j] += f[i] * g[j]
+        result = [x % int(Polynomial.n) for x in result]
+        return Polynomial(result)
+
+    @staticmethod
+    def divide(p1, p2):          
+        
+        def inverse(x):
+            for i in range(1, int(Polynomial.n)):
+                r = (i * x) % int(Polynomial.n)
+                if r == 1:
+                    break
+            else:
+                raise ZeroDivisionError
+            return i    
+           
+        if p1.degree < p2.degree:
+            return p1
+        f = p1.coefficients
+        g = p2.coefficients
+        g_lead_coef = g[-1]
+        g_deg = p2.degree
+        while len(f) >= len(g):
+            f_lead_coef = f[-1]
+            tmp_coef = f_lead_coef * inverse(g_lead_coef)
+            tmp_exp = len(f) - 1 - g_deg
+            tmp = []
+            for _ in range(tmp_exp):
+                tmp.append(0)
+            tmp.append(tmp_coef)
+            tmp_poly = Polynomial(tmp)
+            sub = Polynomial.multiply(p2, tmp_poly)
+            f = [x - y for x, y in zip(f, sub.coefficients)]
+            f = [x % int(Polynomial.n) for x in f]
+            while f and f[-1] == 0:
+                f.pop()
+        return Polynomial(f)
+
+    @staticmethod
+    def gcd(p1, p2):
+        if len(p2.coefficients) == 0:
+            return p1
+        return Polynomial.gcd(p2, Polynomial.divide(p1, p2))
diff --git a/Zadanie-4/quotient_ring.py b/Zadanie-4/quotient_ring.py
new file mode 100644
index 0000000..f9e963b
--- /dev/null
+++ b/Zadanie-4/quotient_ring.py
@@ -0,0 +1,88 @@
+from poly import Polynomial as P
+import sys
+import ast
+
+class QuotientRing:
+
+    def __init__(self, coeffs):
+        self.fx = P(coeffs)
+        self.remainder_set = self.create_remainder_set()
+        self.invertible_elements = self.get_invertible_elements()
+        self.zero_divisors = self.get_zero_divisors()
+        self.nilpotent_elements = self.get_nilpotent_elements()
+        self.idempotent_elements = self.get_idempotent_elements()
+
+    def create_remainder_set(self):
+        remainders = []
+        rem = [0]
+        i = 0
+        while len(rem) < len(self.fx.coefficients):
+            remainders.append(P(rem))
+            i = (i + 1) % P.n
+            rem[0] = i
+            if i == 0:
+                if len(rem) == 1:
+                    rem.append(1)
+                else:
+                    rem[1] += 1
+                    for j in range(1, len(rem)):
+                        if rem[j] == 0 or rem[j] % P.n != 0:
+                            break
+                        tmp = rem[j] % P.n
+                        rem[j] = 0
+                        if tmp == 0:
+                            if (j + 1) < len(rem):
+                                rem[j+1] += 1
+                            else:
+                                rem.append(1)
+        return remainders
+
+    def get_invertible_elements(self):
+        invertible_elements = []
+        for i in self.remainder_set:
+            if i.coefficients != [0] and len(P.gcd(self.fx, i).coefficients) == 1:
+                invertible_elements.append(i)
+        return invertible_elements
+
+    def get_zero_divisors(self):
+        zero_diviors = []
+        for i in self.remainder_set:
+            if i not in self.invertible_elements:
+                zero_diviors.append(i)
+        return zero_diviors
+
+    def get_nilpotent_elements(self):
+        nilpotent_elements = []
+        for i in self.zero_divisors:
+            for j in range(1, len(self.invertible_elements) + 1):
+                if i.coefficients == [0] or len(P.divide(i**j, self.fx).coefficients) == 0:
+                    nilpotent_elements.append(i)
+                break
+        return nilpotent_elements
+
+    def get_idempotent_elements(self):
+        idempotent_elements = []
+        for i in self.remainder_set:
+            if P.divide(i**2, self.fx).coefficients == P.divide(i, self.fx).coefficients:
+                idempotent_elements.append(i)
+        return idempotent_elements
+
+
+def main():
+    P.n = int(sys.argv[1])
+    coeffs = ast.literal_eval(sys.argv[2])
+    Q = QuotientRing(coeffs)
+    
+    ans = [
+            [x.coefficients for x in Q.invertible_elements],
+            [x.coefficients for x in Q.zero_divisors],
+            [x.coefficients for x in Q.nilpotent_elements],
+            [x.coefficients for x in Q.idempotent_elements]
+          ] 
+    
+    for i in range(len(ans)):
+        print(ans[i])
+
+
+if __name__ == '__main__':
+    main()
\ No newline at end of file
-- 
2.20.1


From e3e55f9e0d07840af027604109f81fe8916dee67 Mon Sep 17 00:00:00 2001
From: Szymon Wojciechowski <szywoj3@st.amu.edu.pl>
Date: Thu, 28 Jun 2018 09:01:41 +0000
Subject: [PATCH 12/17] Delete '02-Wielomiany.md'

---
 02-Wielomiany.md | 19 -------------------
 1 file changed, 19 deletions(-)
 delete mode 100644 02-Wielomiany.md

diff --git a/02-Wielomiany.md b/02-Wielomiany.md
deleted file mode 100644
index 4e9830d..0000000
--- a/02-Wielomiany.md
+++ /dev/null
@@ -1,19 +0,0 @@
-## Zadanie
-
-Napisać program, który dla danego pierścienia współczynników `R = ℤ/nℤ, n ∈ ℕ` oraz wielomianów `f,g ∈ R[x] ` zmiennej `x `  znajdzie:
-
-1. iloczyn `f⋅g ∈ R[x]`
-2. klasę reszty `f ∈ R[x]/(g)`
-3. największy wspólny dzielnik `nwd(f,g)` korzystając z algorytmu Euklidesa.
-
-**Uwaga**: wielomiany są podawane jako ciąg współczynników **od wyrazu wolnego, do współczynnika wiodącego**.
-
-Termin: 07.06
-
-### Przykłady:
-
-> Input: `2, [1,1,1,0,1], [0,1,1]` (i.e. `f = 1 + x + x² + x⁴, g = x² + x`)  
-> Output: `[[0,1,0,0,1,1,1], [1,1], [1,1]]`
-
-> Input: `6, [2,1,0,2,1,3], [1,0,0,5]`  
-> Output: `[[3,1,0,5,0,1,4,5,5], [5,2,1], DivisionError]`
-- 
2.20.1


From 12abe0d15680a48b30342d1bb70ab215a9294acc Mon Sep 17 00:00:00 2001
From: Szymon Wojciechowski <szywoj3@st.amu.edu.pl>
Date: Thu, 28 Jun 2018 09:01:54 +0000
Subject: [PATCH 13/17] =?UTF-8?q?Delete=20'01-Pier=C5=9Bcie=C5=84-Zn.md'?=
MIME-Version: 1.0
Content-Type: text/plain; charset=UTF-8
Content-Transfer-Encoding: 8bit

---
 01-Pierścień-Zn.md | 21 ---------------------
 1 file changed, 21 deletions(-)
 delete mode 100644 01-Pierścień-Zn.md

diff --git a/01-Pierścień-Zn.md b/01-Pierścień-Zn.md
deleted file mode 100644
index 93c5417..0000000
--- a/01-Pierścień-Zn.md
+++ /dev/null
@@ -1,21 +0,0 @@
-## Zadanie
-
-Napisać algorytm, który dla danego `n ∈ ℕ` znajdzie wszystkie:
-
-  1. elementy odwracalne
-  2. dzielniki zera
-  3. elementy nilpotentne
-  4. elementy idempotentne
-
-w pierścieniu `{ℤ/nℤ, +, ⋅}`.
-
-Termin: 31.05
-
-### Przykłady:
-
-> Input: `4`  
-> Output: `[[1,3], [0,2], [0,2], [0,1]]`
-
-> Input: `6`  
-> Output: `[[1,5], [0,2,3,4], [0], [0,1,3,4]]`
-
-- 
2.20.1


From db0b78d7715f350394c5427811d671bd5c25b334 Mon Sep 17 00:00:00 2001
From: Szymon Wojciechowski <szywoj3@st.amu.edu.pl>
Date: Thu, 28 Jun 2018 09:02:32 +0000
Subject: [PATCH 14/17] Delete 'poly.py'

---
 poly.py | 75 ---------------------------------------------------------
 1 file changed, 75 deletions(-)
 delete mode 100644 poly.py

diff --git a/poly.py b/poly.py
deleted file mode 100644
index d9ddd32..0000000
--- a/poly.py
+++ /dev/null
@@ -1,75 +0,0 @@
-import sys
-import ast
-
-class Polynomial:
-    
-    n = 0
-
-    def __init__(self, coef_list):
-        self.degree = len(coef_list) - 1
-        self.coefficients = [x % Polynomial.n for x in coef_list]
-
-    @staticmethod
-    def add(p1, p2):
-        result = []
-        f = p1.coefficients
-        g = p2.coefficients
-        if len(f) >= len(g):
-            result = f
-            for i in range(0, len(g)):
-                result[i] = f[i] + g[i]
-        else:
-            result = g
-            for i in range(0, len(f)):
-                result[i] = f[i] + g[i]
-        result = [x % int(Polynomial.n) for x in result]        
-        return Polynomial(result)
-
-    @staticmethod
-    def multiply(p1, p2):
-        result = [0] * (p1.degree + p2.degree + 1)
-        f = p1.coefficients
-        g = p2.coefficients
-        for i in range(0, len(f)):
-            for j in range(0, len(g)):
-                result[i+j] += f[i] * g[j]
-        result = [x % int(Polynomial.n) for x in result]
-        return Polynomial(result)
-
-    @staticmethod
-    def divide(p1, p2):          
-        def inverse(x):
-            for i in range(1, int(Polynomial.n)):
-                r = (i * x) % int(Polynomial.n)
-                if r == 1:
-                    break
-            else:
-                raise ZeroDivisionError
-            return i       
-        if p1.degree < p2.degree:
-            return p1
-        f = p1.coefficients
-        g = p2.coefficients
-        g_lead_coef = g[-1]
-        g_deg = p2.degree
-        while len(f) >= len(g):
-            f_lead_coef = f[-1]
-            tmp_coef = f_lead_coef * inverse(g_lead_coef)
-            tmp_exp = len(f) - 1 - g_deg
-            tmp = []
-            for _ in range(tmp_exp):
-                tmp.append(0)
-            tmp.append(tmp_coef)
-            tmp_poly = Polynomial(tmp)
-            sub = Polynomial.multiply(p2, tmp_poly)
-            f = [x - y for x, y in zip(f, sub.coefficients)]
-            f = [x % int(Polynomial.n) for x in f]
-            while f and f[-1] == 0:
-                f.pop()
-        return Polynomial(f)
-
-    @staticmethod
-    def gcd(p1, p2):
-        if len(p2.coefficients) == 0:
-            return p1
-        return Polynomial.gcd(p2, Polynomial.divide(p1, p2))
-- 
2.20.1


From 79d5960ebdafaa9bab50d007d9cfcc8329e793d3 Mon Sep 17 00:00:00 2001
From: Szymon Wojciechowski <szywoj3@st.amu.edu.pl>
Date: Thu, 28 Jun 2018 09:02:37 +0000
Subject: [PATCH 15/17] Delete 'crc16.py'

---
 crc16.py | 85 --------------------------------------------------------
 1 file changed, 85 deletions(-)
 delete mode 100644 crc16.py

diff --git a/crc16.py b/crc16.py
deleted file mode 100644
index 0a44f74..0000000
--- a/crc16.py
+++ /dev/null
@@ -1,85 +0,0 @@
-from poly import Polynomial
-import sys
-import ast
-
-Polynomial.n = 2
-
-def normalize_byte(data):
-    while len(data) != 8:
-        if len(data) < 8:
-            data = str(0) + data
-        else:
-            data = data[1:]
-    return data
-
-
-def encode(in_data):
-    data = in_data
-    data = list(data)
-    data_binary = [bin(ord(char)).replace('b', '') for char in data]
-    data_binary = [normalize_byte(byte) for byte in data_binary]
-    data_binary = [int(bit) for bit in list(''.join(data_binary))]
-    data_binary.reverse()
-
-    M = [0] * 16 + data_binary
-    L = [0] * (len(data_binary)) + [1] * 16
-    G = [1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1]
-    result_poly = Polynomial.divide(Polynomial.add(Polynomial(M), Polynomial(L)), Polynomial(G))
-    result = result_poly.coefficients + [0] * (16 - len(result_poly.coefficients))
-
-    result.reverse()
-    data_binary.reverse()
-    data_binary = data_binary + result
-    data_binary = [data_binary[i:i+8] for i in range(0, len(data_binary), 8)]
-    data_binary = [int(''.join(map(str, byte)), 2) for byte in data_binary]
-
-    fcs = [hex(byte) for byte in data_binary]
-    fcs = fcs[-2:]
-
-    data = [chr(byte) for byte in data_binary]
-    data = ''.join(data[0:-2])
-
-    return data, fcs
-
-
-def check_fcs(in_data, fcs):
-    data = in_data
-    data = list(data)
-    data_binary = [bin(ord(char)).replace('b', '') for char in data]
-    data_binary = [normalize_byte(byte) for byte in data_binary]
-    data_binary = [int(bit) for bit in list(''.join(data_binary))]
-    fcs_binary = [bin(int(in_hex, 16)).replace('b', '') for in_hex in fcs]
-    fcs_binary = [normalize_byte(byte) for byte in fcs_binary]
-    fcs_binary = [int(bit) for bit in list(''.join(fcs_binary))]
-    data_binary += fcs_binary
-    data_binary.reverse()
-
-    C = [0] * 16 + data_binary
-    L = [0] * len(data_binary) + [1] * 16
-    G = [1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1]
-    S = Polynomial.divide(Polynomial.add(Polynomial(C), Polynomial(L)), Polynomial(G))
-
-    if S.coefficients == []:
-        return True
-
-    return False
-
-
-def main():
-    try:
-        if sys.argv[1] == '-e' or sys.argv[1] == '-encode':
-            arg, fcs = encode(sys.argv[2])
-            print(arg, fcs)
-            print(check_fcs(arg, fcs)) # powinno zawsze zwracać true
-        elif sys.argv[1] == '-c' or sys.argv[1] == '-check':
-            arg = sys.argv[2]
-            fcs = ast.literal_eval(sys.argv[3])
-            print(check_fcs(arg, fcs))
-        else:
-            raise IndexError
-    except IndexError:
-        print("To encode: python3 CRC16.py -e [argument]\nTo check result: python3 CRC16.py -c [argument] [fcs]")
-
-
-if __name__ == "__main__":
-    main()
\ No newline at end of file
-- 
2.20.1


From 0947fadbdfb96f36862b7c123e27c402beb4cd4c Mon Sep 17 00:00:00 2001
From: Szymon Wojciechowski <szywoj3@st.amu.edu.pl>
Date: Thu, 28 Jun 2018 09:02:51 +0000
Subject: [PATCH 16/17] Delete 'Ring.py'

---
 Ring.py | 48 ------------------------------------------------
 1 file changed, 48 deletions(-)
 delete mode 100644 Ring.py

diff --git a/Ring.py b/Ring.py
deleted file mode 100644
index 88345d4..0000000
--- a/Ring.py
+++ /dev/null
@@ -1,48 +0,0 @@
-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())
-- 
2.20.1


From fc718efb6ca62a5d895a46533dd416617037039b Mon Sep 17 00:00:00 2001
From: Szymon Wojciechowski <szywoj3@st.amu.edu.pl>
Date: Thu, 28 Jun 2018 12:40:44 +0000
Subject: [PATCH 17/17] Update 'Zadanie-4/poly.py'

---
 Zadanie-4/poly.py | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/Zadanie-4/poly.py b/Zadanie-4/poly.py
index ab3ac44..8900371 100644
--- a/Zadanie-4/poly.py
+++ b/Zadanie-4/poly.py
@@ -11,7 +11,7 @@ class Polynomial:
 
     def __pow__(self, n):
         result = self
-        for i in range(n):
+        for _ in range(n):
             result = Polynomial.multiply(result, result)
         return result
 
-- 
2.20.1