From 55226d91b2bb1c2ee17dd857b0bb6c7d785ebad5 Mon Sep 17 00:00:00 2001
From: QuantumNovice <43876848+QuantumNovice@users.noreply.github.com>
Date: Sat, 20 Jul 2019 19:47:14 +0500
Subject: [PATCH 01/11] Add files via upload

---
 maths/is_square_free.py  | 42 ++++++++++++++++++++++++++++++++++++++++
 maths/mobius_function.py | 42 ++++++++++++++++++++++++++++++++++++++++
 2 files changed, 84 insertions(+)
 create mode 100644 maths/is_square_free.py
 create mode 100644 maths/mobius_function.py

diff --git a/maths/is_square_free.py b/maths/is_square_free.py
new file mode 100644
index 000000000000..4dbf1b235689
--- /dev/null
+++ b/maths/is_square_free.py
@@ -0,0 +1,42 @@
+'''
+References: wikipedia:square free number
+'''
+from typing import List
+
+def is_square_free(factors:List[int]) -> bool:
+    '''
+    This functions takes a list of prime factors as input.
+    returns True if the factors are square free.
+
+    >>> is_square_free([1,1,2,3,4])
+    False
+
+    These are wrong but should return some value
+    it simply checks for repition in the numb
+    >>> is_square_free([1,3,4,'sd', 0.0])
+    True
+    
+    >>> is_square_free([1,0.5, 2, 0.0])
+    True
+    
+    >>> is_square_free([1,2, 2, 5])
+    False
+    
+    >>> is_square_free('asd')
+    True
+    
+    >>> is_square_free(24)
+    Traceback (most recent call last):
+        ...
+    TypeError: 'int' object is not iterable
+    '''
+    i: int
+    if len(set(factors)) != len(factors):
+            return False
+    return True
+
+
+if __name__ == "__main__":
+    import doctest
+
+    doctest.testmod()
diff --git a/maths/mobius_function.py b/maths/mobius_function.py
new file mode 100644
index 000000000000..2217b9b05f25
--- /dev/null
+++ b/maths/mobius_function.py
@@ -0,0 +1,42 @@
+'''
+Refrences: https://en.wikipedia.org/wiki/M%C3%B6bius_function
+'''
+
+from prime_factors import prime_factors
+from is_square_free import is_square_free
+
+
+def mobius(n:int) -> int:
+    '''
+    Mobius function
+    >>> mobius(24)
+    0
+    >>> mobius(-1)
+    1
+    >>> mobius('asd')
+    Traceback (most recent call last):
+        ...
+    TypeError: '<=' not supported between instances of 'int' and 'str'
+    >>> mobius(10**400)
+    0
+    >>> mobius(10**-400)
+    1
+    >>> mobius(-1424)
+    1
+    >>> mobius([1, '2', 2.0])
+    Traceback (most recent call last):
+        ...
+    TypeError: '<=' not supported between instances of 'int' and 'list'
+    '''
+    factors = prime_factors(n)
+    if is_square_free(factors):
+        if len(factors)%2 == 0:
+            return 1
+        elif len(factors)%2 != 0:
+            return -1
+    else:
+        return 0
+
+if __name__ == '__main__':
+    import doctest
+    doctest.testmod()

From 2f069f540b6b2ed916c8462134a3881ef85ee7fe Mon Sep 17 00:00:00 2001
From: QuantumNovice <43876848+QuantumNovice@users.noreply.github.com>
Date: Sat, 20 Jul 2019 19:56:59 +0500
Subject: [PATCH 02/11] Update mobius_function.py

---
 maths/mobius_function.py | 118 ++++++++++++++++++++++++++++++++++++++-
 1 file changed, 117 insertions(+), 1 deletion(-)

diff --git a/maths/mobius_function.py b/maths/mobius_function.py
index 2217b9b05f25..7c9345f2e6aa 100644
--- a/maths/mobius_function.py
+++ b/maths/mobius_function.py
@@ -2,7 +2,123 @@
 Refrences: https://en.wikipedia.org/wiki/M%C3%B6bius_function
 '''
 
-from prime_factors import prime_factors
+from prime_factors import prime_factors'''
+Refrences: https://en.wikipedia.org/wiki/M%C3%B6bius_function
+References: wikipedia:square free number
+'''
+
+from typing import List
+
+
+
+def prime_factors(n: int) -> List[int]:
+    """
+    Returns prime factors of n as a list.
+    
+    >>> prime_factors(0)
+    []
+    >>> prime_factors(100)
+    [2, 2, 5, 5]
+    >>> prime_factors(2560)
+    [2, 2, 2, 2, 2, 2, 2, 2, 2, 5]
+    >>> prime_factors(10**-2)
+    []
+    >>> prime_factors(0.02)
+    []
+    >>> x = prime_factors(10**241) # doctest: +NORMALIZE_WHITESPACE
+    >>> x == [2]*241 + [5]*241
+    True
+    >>> prime_factors(10**-354)
+    []
+    >>> prime_factors('hello')
+    Traceback (most recent call last):
+        ...
+    TypeError: '<=' not supported between instances of 'int' and 'str'
+    >>> prime_factors([1,2,'hello'])
+    Traceback (most recent call last):
+        ...
+    TypeError: '<=' not supported between instances of 'int' and 'list'
+
+    """
+    i = 2
+    factors = []
+    while i * i <= n:
+        if n % i:
+            i += 1
+        else:
+            n //= i
+            factors.append(i)
+    if n > 1:
+        factors.append(n)
+    return factors
+
+def is_square_free(factors:List[int]) -> bool:
+    '''
+    This functions takes a list of prime factors as input.
+    returns True if the factors are square free.
+
+    >>> is_square_free([1,1,2,3,4])
+    False
+
+    These are wrong but should return some value
+    it simply checks for repition in the numb
+    >>> is_square_free([1,3,4,'sd', 0.0])
+    True
+    
+    >>> is_square_free([1,0.5, 2, 0.0])
+    True
+    
+    >>> is_square_free([1,2, 2, 5])
+    False
+    
+    >>> is_square_free('asd')
+    True
+    
+    >>> is_square_free(24)
+    Traceback (most recent call last):
+        ...
+    TypeError: 'int' object is not iterable
+    '''
+    i: int
+    if len(set(factors)) != len(factors):
+            return False
+    return True
+
+def mobius(n:int) -> int:
+    '''
+    Mobius function
+    >>> mobius(24)
+    0
+    >>> mobius(-1)
+    1
+    >>> mobius('asd')
+    Traceback (most recent call last):
+        ...
+    TypeError: '<=' not supported between instances of 'int' and 'str'
+    >>> mobius(10**400)
+    0
+    >>> mobius(10**-400)
+    1
+    >>> mobius(-1424)
+    1
+    >>> mobius([1, '2', 2.0])
+    Traceback (most recent call last):
+        ...
+    TypeError: '<=' not supported between instances of 'int' and 'list'
+    '''
+    factors = prime_factors(n)
+    if is_square_free(factors):
+        if len(factors)%2 == 0:
+            return 1
+        elif len(factors)%2 != 0:
+            return -1
+    else:
+        return 0
+
+if __name__ == '__main__':
+    import doctest
+    doctest.testmod()
+
 from is_square_free import is_square_free
 
 

From 7df62b75c1e2b74682e965175a831b5a53223a49 Mon Sep 17 00:00:00 2001
From: QuantumNovice <43876848+QuantumNovice@users.noreply.github.com>
Date: Sat, 20 Jul 2019 20:06:01 +0500
Subject: [PATCH 03/11] Add files via upload

---
 maths/mobius_function.py | 42 ----------------------------------------
 1 file changed, 42 deletions(-)

diff --git a/maths/mobius_function.py b/maths/mobius_function.py
index 7c9345f2e6aa..3e98af97d678 100644
--- a/maths/mobius_function.py
+++ b/maths/mobius_function.py
@@ -1,9 +1,5 @@
 '''
 Refrences: https://en.wikipedia.org/wiki/M%C3%B6bius_function
-'''
-
-from prime_factors import prime_factors'''
-Refrences: https://en.wikipedia.org/wiki/M%C3%B6bius_function
 References: wikipedia:square free number
 '''
 
@@ -84,44 +80,6 @@ def is_square_free(factors:List[int]) -> bool:
             return False
     return True
 
-def mobius(n:int) -> int:
-    '''
-    Mobius function
-    >>> mobius(24)
-    0
-    >>> mobius(-1)
-    1
-    >>> mobius('asd')
-    Traceback (most recent call last):
-        ...
-    TypeError: '<=' not supported between instances of 'int' and 'str'
-    >>> mobius(10**400)
-    0
-    >>> mobius(10**-400)
-    1
-    >>> mobius(-1424)
-    1
-    >>> mobius([1, '2', 2.0])
-    Traceback (most recent call last):
-        ...
-    TypeError: '<=' not supported between instances of 'int' and 'list'
-    '''
-    factors = prime_factors(n)
-    if is_square_free(factors):
-        if len(factors)%2 == 0:
-            return 1
-        elif len(factors)%2 != 0:
-            return -1
-    else:
-        return 0
-
-if __name__ == '__main__':
-    import doctest
-    doctest.testmod()
-
-from is_square_free import is_square_free
-
-
 def mobius(n:int) -> int:
     '''
     Mobius function

From b79bddb2335cf208ef8e02893331f699256e6731 Mon Sep 17 00:00:00 2001
From: QuantumNovice <43876848+QuantumNovice@users.noreply.github.com>
Date: Sat, 20 Jul 2019 20:11:14 +0500
Subject: [PATCH 04/11] Add files via upload

---
 maths/mobius_function.py | 3 +--
 1 file changed, 1 insertion(+), 2 deletions(-)

diff --git a/maths/mobius_function.py b/maths/mobius_function.py
index 3e98af97d678..065189528b73 100644
--- a/maths/mobius_function.py
+++ b/maths/mobius_function.py
@@ -108,8 +108,7 @@ def mobius(n:int) -> int:
             return 1
         elif len(factors)%2 != 0:
             return -1
-    else:
-        return 0
+    return 0
 
 if __name__ == '__main__':
     import doctest

From 6393f220f3fbb3a82b888eee9b5f5970158fbd35 Mon Sep 17 00:00:00 2001
From: QuantumNovice <43876848+QuantumNovice@users.noreply.github.com>
Date: Sat, 20 Jul 2019 21:24:45 +0500
Subject: [PATCH 05/11] Add files via upload

---
 maths/is_square_free.py  | 35 +++++++++++++++-----------------
 maths/mobius_function.py | 43 ++++++++++++++++++++--------------------
 2 files changed, 38 insertions(+), 40 deletions(-)

diff --git a/maths/is_square_free.py b/maths/is_square_free.py
index 4dbf1b235689..acc13fa5f833 100644
--- a/maths/is_square_free.py
+++ b/maths/is_square_free.py
@@ -1,39 +1,36 @@
-'''
+"""
 References: wikipedia:square free number
-'''
+python/black : True
+flake8 : True
+"""
 from typing import List
 
-def is_square_free(factors:List[int]) -> bool:
-    '''
+
+def is_square_free(factors: List[int]) -> bool:
+    """
+    # doctest: +NORMALIZE_WHITESPACE
     This functions takes a list of prime factors as input.
     returns True if the factors are square free.
-
-    >>> is_square_free([1,1,2,3,4])
+    >>> is_square_free([1, 1, 2, 3, 4])
     False
-
+    
     These are wrong but should return some value
-    it simply checks for repition in the numb
-    >>> is_square_free([1,3,4,'sd', 0.0])
+    it simply checks for repition in the numbers.
+    >>> is_square_free([1, 3, 4, 'sd', 0.0])
     True
     
-    >>> is_square_free([1,0.5, 2, 0.0])
+    >>> is_square_free([1, 0.5, 2, 0.0])
     True
-    
-    >>> is_square_free([1,2, 2, 5])
+    >>> is_square_free([1, 2, 2, 5])
     False
-    
     >>> is_square_free('asd')
     True
-    
     >>> is_square_free(24)
     Traceback (most recent call last):
         ...
     TypeError: 'int' object is not iterable
-    '''
-    i: int
-    if len(set(factors)) != len(factors):
-            return False
-    return True
+    """
+    return len(set(factors)) == len(factors)
 
 
 if __name__ == "__main__":
diff --git a/maths/mobius_function.py b/maths/mobius_function.py
index 065189528b73..ecda70078b94 100644
--- a/maths/mobius_function.py
+++ b/maths/mobius_function.py
@@ -1,12 +1,13 @@
-'''
+"""
 Refrences: https://en.wikipedia.org/wiki/M%C3%B6bius_function
 References: wikipedia:square free number
-'''
+python/black : True
+flake8 : True
+"""
 
 from typing import List
 
 
-
 def prime_factors(n: int) -> List[int]:
     """
     Returns prime factors of n as a list.
@@ -30,7 +31,7 @@ def prime_factors(n: int) -> List[int]:
     Traceback (most recent call last):
         ...
     TypeError: '<=' not supported between instances of 'int' and 'str'
-    >>> prime_factors([1,2,'hello'])
+    >>> prime_factors([1, 2, 'hello'])
     Traceback (most recent call last):
         ...
     TypeError: '<=' not supported between instances of 'int' and 'list'
@@ -48,23 +49,24 @@ def prime_factors(n: int) -> List[int]:
         factors.append(n)
     return factors
 
-def is_square_free(factors:List[int]) -> bool:
-    '''
+
+def is_square_free(factors: List[int]) -> bool:
+    """
     This functions takes a list of prime factors as input.
     returns True if the factors are square free.
 
-    >>> is_square_free([1,1,2,3,4])
+    >>> is_square_free([1, 1, 2, 3, 4])
     False
 
     These are wrong but should return some value
     it simply checks for repition in the numb
-    >>> is_square_free([1,3,4,'sd', 0.0])
+    >>> is_square_free([1, 3, 4, 'sd', 0.0])
     True
     
-    >>> is_square_free([1,0.5, 2, 0.0])
+    >>> is_square_free([1, 0.5, 2, 0.0])
     True
     
-    >>> is_square_free([1,2, 2, 5])
+    >>> is_square_free([1, 2, 2, 5])
     False
     
     >>> is_square_free('asd')
@@ -74,14 +76,14 @@ def is_square_free(factors:List[int]) -> bool:
     Traceback (most recent call last):
         ...
     TypeError: 'int' object is not iterable
-    '''
-    i: int
+    """
     if len(set(factors)) != len(factors):
-            return False
+        return False
     return True
 
-def mobius(n:int) -> int:
-    '''
+
+def mobius(n: int) -> int:
+    """
     Mobius function
     >>> mobius(24)
     0
@@ -101,15 +103,14 @@ def mobius(n:int) -> int:
     Traceback (most recent call last):
         ...
     TypeError: '<=' not supported between instances of 'int' and 'list'
-    '''
+    """
     factors = prime_factors(n)
     if is_square_free(factors):
-        if len(factors)%2 == 0:
-            return 1
-        elif len(factors)%2 != 0:
-            return -1
+        return -1 if len(factors) % 2 else 1
     return 0
 
-if __name__ == '__main__':
+
+if __name__ == "__main__":
     import doctest
+
     doctest.testmod()

From e00ff91099ec3140da9f35861375b7fc5fca5c7a Mon Sep 17 00:00:00 2001
From: QuantumNovice <43876848+QuantumNovice@users.noreply.github.com>
Date: Sat, 20 Jul 2019 21:48:38 +0500
Subject: [PATCH 06/11] Add files via upload

---
 mobius_function.py | 43 +++++++++++++++++++++++++++++++++++++++++++
 1 file changed, 43 insertions(+)
 create mode 100644 mobius_function.py

diff --git a/mobius_function.py b/mobius_function.py
new file mode 100644
index 000000000000..3e49ae62de95
--- /dev/null
+++ b/mobius_function.py
@@ -0,0 +1,43 @@
+"""
+Refrences: https://en.wikipedia.org/wiki/M%C3%B6bius_function
+References: wikipedia:square free number
+python/black : True
+flake8 : True
+"""
+
+from typing import List
+from .prime_factors import prime_factors
+from .is_square_free import is_square_free
+
+def mobius(n: int) -> int:
+    """
+    Mobius function
+    >>> mobius(24)
+    0
+    >>> mobius(-1)
+    1
+    >>> mobius('asd')
+    Traceback (most recent call last):
+        ...
+    TypeError: '<=' not supported between instances of 'int' and 'str'
+    >>> mobius(10**400)
+    0
+    >>> mobius(10**-400)
+    1
+    >>> mobius(-1424)
+    1
+    >>> mobius([1, '2', 2.0])
+    Traceback (most recent call last):
+        ...
+    TypeError: '<=' not supported between instances of 'int' and 'list'
+    """
+    factors = prime_factors(n)
+    if is_square_free(factors):
+        return -1 if len(factors) % 2 else 1
+    return 0
+
+
+if __name__ == "__main__":
+    import doctest
+
+    doctest.testmod()

From b577a5209bfb9430c2bf81ddd1430a9554bc72c5 Mon Sep 17 00:00:00 2001
From: QuantumNovice <43876848+QuantumNovice@users.noreply.github.com>
Date: Sat, 20 Jul 2019 21:57:04 +0500
Subject: [PATCH 07/11] Add files via upload

---
 maths/mobius_function.py | 77 ++--------------------------------------
 1 file changed, 2 insertions(+), 75 deletions(-)

diff --git a/maths/mobius_function.py b/maths/mobius_function.py
index ecda70078b94..f8987e9075ed 100644
--- a/maths/mobius_function.py
+++ b/maths/mobius_function.py
@@ -6,81 +6,8 @@
 """
 
 from typing import List
-
-
-def prime_factors(n: int) -> List[int]:
-    """
-    Returns prime factors of n as a list.
-    
-    >>> prime_factors(0)
-    []
-    >>> prime_factors(100)
-    [2, 2, 5, 5]
-    >>> prime_factors(2560)
-    [2, 2, 2, 2, 2, 2, 2, 2, 2, 5]
-    >>> prime_factors(10**-2)
-    []
-    >>> prime_factors(0.02)
-    []
-    >>> x = prime_factors(10**241) # doctest: +NORMALIZE_WHITESPACE
-    >>> x == [2]*241 + [5]*241
-    True
-    >>> prime_factors(10**-354)
-    []
-    >>> prime_factors('hello')
-    Traceback (most recent call last):
-        ...
-    TypeError: '<=' not supported between instances of 'int' and 'str'
-    >>> prime_factors([1, 2, 'hello'])
-    Traceback (most recent call last):
-        ...
-    TypeError: '<=' not supported between instances of 'int' and 'list'
-
-    """
-    i = 2
-    factors = []
-    while i * i <= n:
-        if n % i:
-            i += 1
-        else:
-            n //= i
-            factors.append(i)
-    if n > 1:
-        factors.append(n)
-    return factors
-
-
-def is_square_free(factors: List[int]) -> bool:
-    """
-    This functions takes a list of prime factors as input.
-    returns True if the factors are square free.
-
-    >>> is_square_free([1, 1, 2, 3, 4])
-    False
-
-    These are wrong but should return some value
-    it simply checks for repition in the numb
-    >>> is_square_free([1, 3, 4, 'sd', 0.0])
-    True
-    
-    >>> is_square_free([1, 0.5, 2, 0.0])
-    True
-    
-    >>> is_square_free([1, 2, 2, 5])
-    False
-    
-    >>> is_square_free('asd')
-    True
-    
-    >>> is_square_free(24)
-    Traceback (most recent call last):
-        ...
-    TypeError: 'int' object is not iterable
-    """
-    if len(set(factors)) != len(factors):
-        return False
-    return True
-
+from math.prime_factors import prime_factors
+from math.is_square_free import is_square_free
 
 def mobius(n: int) -> int:
     """

From aba05dfe7972731cd1768a3d05b8a0fff22cd211 Mon Sep 17 00:00:00 2001
From: QuantumNovice <43876848+QuantumNovice@users.noreply.github.com>
Date: Sat, 20 Jul 2019 22:01:07 +0500
Subject: [PATCH 08/11] Add files via upload

---
 maths/mobius_function.py | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/maths/mobius_function.py b/maths/mobius_function.py
index f8987e9075ed..79ed432ab5da 100644
--- a/maths/mobius_function.py
+++ b/maths/mobius_function.py
@@ -6,8 +6,8 @@
 """
 
 from typing import List
-from math.prime_factors import prime_factors
-from math.is_square_free import is_square_free
+from maths.prime_factors import prime_factors
+from maths.is_square_free import is_square_free
 
 def mobius(n: int) -> int:
     """

From e18d9b2dd3773e0055ef8234da5ef267d61c19ec Mon Sep 17 00:00:00 2001
From: QuantumNovice <43876848+QuantumNovice@users.noreply.github.com>
Date: Sat, 20 Jul 2019 22:08:02 +0500
Subject: [PATCH 09/11] Update mobius_function.py

---
 maths/mobius_function.py | 1 -
 1 file changed, 1 deletion(-)

diff --git a/maths/mobius_function.py b/maths/mobius_function.py
index 79ed432ab5da..fb7a7b60fe7f 100644
--- a/maths/mobius_function.py
+++ b/maths/mobius_function.py
@@ -36,7 +36,6 @@ def mobius(n: int) -> int:
         return -1 if len(factors) % 2 else 1
     return 0
 
-
 if __name__ == "__main__":
     import doctest
 

From cbb584b210940294266d54971c8133e4c262182a Mon Sep 17 00:00:00 2001
From: QuantumNovice <43876848+QuantumNovice@users.noreply.github.com>
Date: Sun, 21 Jul 2019 13:25:53 +0500
Subject: [PATCH 10/11] Delete mobius_function.py

---
 mobius_function.py | 43 -------------------------------------------
 1 file changed, 43 deletions(-)
 delete mode 100644 mobius_function.py

diff --git a/mobius_function.py b/mobius_function.py
deleted file mode 100644
index 3e49ae62de95..000000000000
--- a/mobius_function.py
+++ /dev/null
@@ -1,43 +0,0 @@
-"""
-Refrences: https://en.wikipedia.org/wiki/M%C3%B6bius_function
-References: wikipedia:square free number
-python/black : True
-flake8 : True
-"""
-
-from typing import List
-from .prime_factors import prime_factors
-from .is_square_free import is_square_free
-
-def mobius(n: int) -> int:
-    """
-    Mobius function
-    >>> mobius(24)
-    0
-    >>> mobius(-1)
-    1
-    >>> mobius('asd')
-    Traceback (most recent call last):
-        ...
-    TypeError: '<=' not supported between instances of 'int' and 'str'
-    >>> mobius(10**400)
-    0
-    >>> mobius(10**-400)
-    1
-    >>> mobius(-1424)
-    1
-    >>> mobius([1, '2', 2.0])
-    Traceback (most recent call last):
-        ...
-    TypeError: '<=' not supported between instances of 'int' and 'list'
-    """
-    factors = prime_factors(n)
-    if is_square_free(factors):
-        return -1 if len(factors) % 2 else 1
-    return 0
-
-
-if __name__ == "__main__":
-    import doctest
-
-    doctest.testmod()

From 77b29ceaf0e7665769847fa2f7267e40730027b6 Mon Sep 17 00:00:00 2001
From: QuantumNovice <43876848+QuantumNovice@users.noreply.github.com>
Date: Sun, 21 Jul 2019 13:31:16 +0500
Subject: [PATCH 11/11] Add files via upload

---
 maths/mobius_function.py | 3 ++-
 1 file changed, 2 insertions(+), 1 deletion(-)

diff --git a/maths/mobius_function.py b/maths/mobius_function.py
index fb7a7b60fe7f..15fb3d4380f4 100644
--- a/maths/mobius_function.py
+++ b/maths/mobius_function.py
@@ -5,10 +5,10 @@
 flake8 : True
 """
 
-from typing import List
 from maths.prime_factors import prime_factors
 from maths.is_square_free import is_square_free
 
+
 def mobius(n: int) -> int:
     """
     Mobius function
@@ -36,6 +36,7 @@ def mobius(n: int) -> int:
         return -1 if len(factors) % 2 else 1
     return 0
 
+
 if __name__ == "__main__":
     import doctest