How to pythonically have partially-mutually exclusive optional arguments?

Question

As a simple example, take a class Ellipse that can return its properties such as area A, circumference C, major/minor axis a/b

Answer 1

My proposal is focused on data encapsulation and code readability.

a) Pick pair on unambigous measurements to represent ellipse internally

class Ellipse(object):
    def __init__(a, b):
        self.a = a
        self.b = b

b) Create family of properties to get desired metrics about ellipse

class Ellipse(object):
    @property
    def area(self):
        return math.pi * self._x * self._b

c) Create factory class / factory methods with unambigous names:

class Ellipse(object):
    @classmethod
    def fromAreaAndCircumference(cls, area, circumference):
        # convert area and circumference to common format
        return cls(a, b)

Sample usage:

ellipse = Ellipse.fromLongAxisAndEccentricity(axis, eccentricity)
assert ellipse.a == axis
assert ellipse.eccentricity == eccentricity