Interpreting formulas with ΣΣ (two sigma) in Python

Consider the function f(x,y) that equals to two sigma (ΣΣ) where i ranges from 1 to 10 and (first sigma) and j ranges from 1 to 10 (second sigma) of the quantity {ix^2 + jy^3)

I believe the first sigma would be an inner loop and the second sigma an outer loop but I am having trouble rewriting this into Python.

Can someone please help me convert this into python?

Please Click to see the mathematical expression, cannot embed

Submitted October 11th 2021 by Admin


I'm no mathematician, but as far as I could tell, that would translate to

def f(x, y): return sum( sum( i * x ** 2 + j * y ** 3 for j in range(1, 11) ) for i in range(1, 11) )

or written out as for loops,

def f(x, y): value = 0 for i in range(1, 11): for j in range(1, 11): value += i * x ** 2 + j * y ** 3 return value

Admin | 1 week ago


The first answer's approaches all work. Often the "pythonic" approach is to define a list comprehension before using sum so another approach would be:

def f(x, y): return sum([(i * x ** 2 + j * y ** 3) for i in range(1,11) for j in range(1, 11)]);

Admin | 1 week ago

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