Added to maths and strings (#1642)

* Added to maths and strings

* added changes suggest by cclauss

maths/combinations.py

@@ -0,0 +1,19 @@
+from math import factorial
+
+
+def combinations(n, k):
+    """
+    >>> combinations(10,5)
+    252
+    >>> combinations(6,3)
+    20
+    >>> combinations(20,5)
+    15504
+    """
+    return int(factorial(n) / ((factorial(k)) * (factorial(n - k))))
+
+
+if __name__ == "__main__":
+    from doctest import testmod
+
+    testmod()

maths/gamma.py

@@ -0,0 +1,60 @@
+import math
+from scipy.integrate import quad
+from numpy import inf
+
+
+def gamma(num: float) -> float:
+    """
+    https://en.wikipedia.org/wiki/Gamma_function
+    In mathematics, the gamma function is one commonly 
+    used extension of the factorial function to complex numbers. 
+    The gamma function is defined for all complex numbers except the non-positive integers
+
+
+    >>> gamma(-1)
+    Traceback (most recent call last):
+        ...
+    ValueError: math domain error
+
+    
+
+    >>> gamma(0)
+    Traceback (most recent call last):
+        ...
+    ValueError: math domain error
+
+
+    >>> gamma(9)
+    40320.0
+
+    >>> from math import gamma as math_gamma    
+    >>> all(gamma(i)/math_gamma(i) <= 1.000000001 and abs(gamma(i)/math_gamma(i)) > .99999999 for i in range(1, 50))
+    True
+
+
+    >>> from math import gamma as math_gamma    
+    >>> gamma(-1)/math_gamma(-1) <= 1.000000001
+    Traceback (most recent call last):
+        ...
+    ValueError: math domain error
+
+
+    >>> from math import gamma as math_gamma
+    >>> gamma(3.3) - math_gamma(3.3) <= 0.00000001 
+    True
+    """
+
+    if num <= 0:
+        raise ValueError("math domain error")
+
+    return quad(integrand, 0, inf, args=(num))[0]
+
+
+def integrand(x: float, z: float) -> float:
+    return math.pow(x, z - 1) * math.exp(-x)
+
+
+if __name__ == "__main__":
+    from doctest import testmod
+
+    testmod()

maths/radians.py

@@ -0,0 +1,29 @@
+from math import pi
+
+
+def radians(degree: float) -> float:
+    """
+    Coverts the given angle from degrees to radians
+    https://en.wikipedia.org/wiki/Radian
+
+    >>> radians(180)
+    3.141592653589793
+    >>> radians(92)
+    1.6057029118347832
+    >>> radians(274)
+    4.782202150464463
+    >>> radians(109.82)
+    1.9167205845401725
+    
+    >>> from math import radians as math_radians    
+    >>> all(abs(radians(i)-math_radians(i)) <= 0.00000001  for i in range(-2, 361))
+    True
+    """
+
+    return degree / (180 / pi)
+
+
+if __name__ == "__main__":
+    from doctest import testmod
+
+    testmod()