first commit

chain_fraction.py

@@ -0,0 +1,53 @@
+import re, sys
+
+def gcd(a, b):
+    while b != 0:
+        b, a = a % b, b
+    return a
+
+def get_q_list(m, a):
+    l = []
+    while a:
+        r, q = m % a, m // a
+        m, a = a, r
+        l.append(q)
+    return l
+
+def get_p_n(n, q_list):
+    if n == 0:
+        return q_list[0]
+    if n == 1:
+        return q_list[0] * q_list[1] + 1
+    return q_list[n] * get_p_n(n - 1, q_list) + get_p_n(n - 2, q_list)
+
+def get_x0(a, b, m):
+    q_list = get_q_list(m, a)
+    n = len(q_list) - 1
+    p = get_p_n(n-1, q_list)
+    x = ((-1)**n*p*b)%m
+    return x, f'x={x}mod{m}'
+
+def solve(task):
+    f = re.fullmatch(r'(\d+)x=(\d+)mod(\d+)', task)
+    if f == None:
+        return "Usage Example: py chain_fraction.py '7x=8mod13'"
+    a, b, m = int(f.groups()[0]), int(f.groups()[1]), int(f.groups()[2]) 
+    d = gcd(a, m) # Находим НОД
+    if d == 1: # нод = 1 => 1 решение
+        return get_x0(a, b, m)[1]
+    if d > 1 and b % d != 0:
+        return 'No solutions'
+    else:
+        d = gcd(gcd(a, b), m)
+        a1, b1, m1 = a // d, b // d, m // d
+        x0 = get_x0(a1, b1, m1)[0]
+        s = ""
+        for k in range(d):
+            s += f'x={(x0+m1*k)%m}mod{m}\n'
+        return s[:-1]
+
+if __name__ == "__main__":
+    if len(sys.argv) != 2:
+        print("Usage Example: py chain_fraction.py '7x=8mod13'")
+        sys.exit(1)
+    print(solve(sys.argv[1]))

euclid.py

@@ -0,0 +1,31 @@
+import sys, re 
+
+def gcd(a, b):
+    if b == 0:
+        return 1, 0, a
+    x, y, d = gcd(b, a % b)
+    x = y
+    y = (d - x*a) // b
+    return x, y, d
+
+def solve(task):
+    f = re.fullmatch(r'(\d+)x=(\d+)mod(\d+)', task)
+    if f == None:
+        return "Usage Example: py euclid.py '7x=8mod13'"
+    a, b, m = int(f.groups()[0]), int(f.groups()[1]), int(f.groups()[2]) 
+    d = gcd(a, m)[2]
+    if d > 1 and b % d != 0:
+        return 'No solutions'
+    a1, b1, m1 = a // d, b // d, m // d
+    u, _, _ = gcd(a1, m1)
+    x0 = b1*u
+    s = ""
+    for i in range(0, d):
+        s += f'x={(x0+m//d*i)%m}mod{m}\n'
+    return s[:-1]
+
+if __name__ == "__main__":
+    if len(sys.argv) != 2:
+        print("Usage Example: py euclid.py '7x=8mod13'")
+        sys.exit(1)
+    print(solve(sys.argv[1]))

euler.py

@@ -0,0 +1,40 @@
+import sys, re
+
+def gcd(a, b):
+    while b != 0:
+        b, a = a % b, b
+    return a
+
+def euler(n):
+    result = n
+    p = 2
+    while p * p <= n:
+        if n % p == 0:
+            while n % p == 0:
+                n //= p
+            result -= result // p
+        p += 1
+    if n > 1:
+        result -= result // n
+    return result
+
+def solve(task):
+    f = re.fullmatch(r'(\d+)x=(\d+)mod(\d+)', task)
+    if f == None:
+        return "Usage Example: py euler.py '7x=8mod13'"
+    a, b, m = int(f.groups()[0]), int(f.groups()[1]), int(f.groups()[2]) 
+    d = gcd(a, m)
+    if d > 1 and b % d != 0:
+        return 'No solutions'
+    a1, b1, m1 = a // d, b // d, m // d
+    x0 = (b1 * pow(a1, euler(m1) - 1, m1)) % m1
+    s=''
+    for i in range(d):
+        s += f"x={(x0 + i * m//d) % m}mod{m}\n"
+    return s[:-1]
+
+if __name__ == "__main__":
+    if len(sys.argv) != 2:
+        print("Usage Example: py euler.py '7x=8mod13'")
+        sys.exit(1)
+    print(solve(sys.argv[1]))