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

I would check for the consistency of the data each time you set a parameter.

import math
tol = 1e-9
class Ellipse(object):
    def __init__(self, a=None, b=None, A=None, a_b=None):
        self.a = self.b = self.A = self.a_b = None 
        self.set_short_axis(a)
        self.set_long_axis(b)
        self.set_area(A)
        self.set_maj_min_axis(a_b)

    def set_short_axis(self, a):
        self.a = a
        self.check()

    def set_long_axis(self, b):
        self.b = b
        self.check()

    def set_maj_min_axis(self, a_b):
        self.a_b = a_b
        self.check()

    def set_area(self, A):
        self.A = A
        self.check()

    def check(self):
        if self.a and self.b and self.A:
            if not math.fabs(self.A - self.a * self.b * math.pi) <= tol:
                raise Exception('A=a*b*pi does not check!')
        if self.a and self.b and self.a_b:
            if not math.fabs(self.a / float(self.b) - self.a_b) <= tol:
                raise Exception('a_b=a/b does not check!')

The main:

e1 = Ellipse(a=3, b=3, a_b=1)
e2 = Ellipse(a=3, b=3, A=27)

The first ellipse object is consistent; set_maj_min_axis(1) passes fine.

The second is not; set_area(27) fails, at least within the 1e-9 tolerance specified, and raises an error.

Edit 1

Some additional lines are needed for the cases when the uses supply a, a_b and A, in the check() method:

    if self.a and self.A and self.a_b:
        if not math.fabs(self.A - self.a **2 / self.a_b * math.pi) <= tol:
            raise Exception('A=a*a/a_b*pi does not check!')
    if self.b and self.A and self.a_b:
        if not math.fabs(self.A - self.b **2 * self.a_b * math.pi) <= tol:
            raise Exception('A=b*b*a_b*pi does not check!')

Main:

e3 = Ellipse(b=3.0, a_b=1.0, A=27) 

An arguably wiser way would be to calculate self.b = self.a / float(self.a_b) directly into the set method of a_b. Since you decide yourself of the order of the set methods in the constructor, that might be more manageable than to write dozens of checks.